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Specification for Load and Resistance Factor Design of Single-Angle Members December 1, 1993
AMERICAN INSTITUTE OF STEEL CONSTRUCTION, INC. One East Wacker Drive, Suite 3100, Chicago, IL 60601-2001
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LRFD SPECIFICATION FOR DESIGN OF SINGLE-ANGLE MEMBERS
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
LRFD SPECIFICATION FOR DESIGN OF SINGLE-ANGLE MEMBERS
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PREFACE
The intention of the AISC Specification is to cover the common everyday design criteria in routine design office usage. It is not feasible to also cover the many special and unique problems encountered within the full range of structural design practice. This separate Specification and Commentary addresses one such topic—single-angle members—to provide needed design guidance for this more complex structural shape under various load and support conditions. The single-angle design criteria were developed through a consensus process by the AISC Task Committee 116 on Single-Angle Members: Donald R. Sherman, Chairman Hansraj G. Ashar Wai-Fah Chen Raymond D. Ciatto Mohamed Elgaaly Theodore V. Galambos Thomas G. Longlais LeRoy A. Lutz William A. Milek Raymond H. R. Tide Nestor R. Iwankiw, Secretary The assistance of the Structural Stability Research Council Task Group on Single Angles in the preparation and review of this document is acknowledged. The full AISC Committee on Specifications has reviewed and endorsed this Specification. A non-mandatory Commentary provides background for the Specification provisions and the user is encouraged to consult it. The principal changes in this edition include: • establishing upper limit of single-angle flexural strength at 1.25 of the yield moment • increasing resistance factor for compression to 0.90 • removing flexural-torsional buckling consideration for compression members • considering the sense of flexural stresses in the combined force interaction check The reader is cautioned that professional judgment must be exercised when data or recommendations in this Specification are applied. The publication of the material contained herein is not intended as a representation or warranty on the part of the American Institute of Steel Construction, Inc.—or any other person named herein—that this information is suitable for general or particular use, or freedom from infringement of any patent or patents. Anyone making use of this information assumes all liability arising from such use. The design of structures is within the scope of expertise of a competent licensed structural engineer, architect, or other licensed professional for the application of principles to a particular structure. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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LRFD SPECIFICATION FOR DESIGN OF SINGLE-ANGLE MEMBERS
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
LRFD SPECIFICATION FOR DESIGN OF SINGLE-ANGLE MEMBERS
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Specification for Load and Resistance Factor Design of Single-Angle Members December 1, 1993
1.
SCOPE This document contains Load and Resistance Factor Design (LRFD) criteria for hot-rolled, single-angle members with equal and unequal legs in tension, shear, compression, flexure, and for combined forces. It is intended to be compatible with, and a supplement to, the 1993 AISC Specification for Structural Steel Buildings—Load and Resistance Factor Design (AISC LRFD) and repeats some common criteria for ease of reference. For design purposes, the conservative simplifications and approximations in the Specification provisions for single angles are permitted to be refined through a more precise analysis. As an alternative to this Specification, the 1989 AISC Specification for Allowable Stress Design of Single-Angle Members is permitted. The Specification for single-angle design supersedes any comparable but more general requirements of the AISC LRFD. All other design, fabrication, and erection provisions not directly covered by this document shall be in compliance with the AISC LRFD. In the absence of a governing building code, the factored load combinations in AISC LRFD Section A4 shall be used to determine the required strength. For design of slender, cold-formed steel angles, the current AISI LRFD Specification for the Design of Cold-Formed Steel Structural Members is applicable.
2.
TENSION The tensile design strength φtPn shall be the lower value obtained according to the limit states of yielding, φt = 0.9, Pn = Fy Ag, and fracture, φt = 0.75, Pn = Fu Ae. a. For members connected by bolting, the net area and effective net area shall be determined from AISC LRFD Specification Sections B1 to B3 inclusive. b. When the load is transmitted by longitudinal welds only or a combination of AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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LRFD SPECIFICATION FOR DESIGN OF SINGLE-ANGLE MEMBERS
longitudinal and transverse welds through just one leg of the angle, the effective net area Ae shall be: Ae = AgU
(2-1)
where Ag = gross area of member _ x U = 1 − ≤ 0.9 l _ x = connection eccentricity l = length of connection in the direction of loading c. When a load is transmitted by transverse weld through just one leg of the angle, Ae is the area of the connected leg and U = 1. For members whose design is based on tension, the slenderness ratio l / r preferably should not exceed 300. Members in which the design is dictated by tension loading, but which may be subject to some compression under other load conditions, need not satisfy the compression slenderness limits. 3.
SHEAR For the limit state of yielding in shear, the shear stress, fuv, due to flexure and torsion shall not exceed: fuv ≤ φv0.6Fy φv = 0.9
4.
(3-1)
COMPRESSION The design strength of compression members shall be φcPn where φc = 0.90 Pn = AgFcr a. For λc √ Q ≤ 1.5: 2
Fcr = Q (0.658Qλc) Fy
(4-1)
0.877 Fcr = 2 Fy λc
(4-2)
b. For λc √ Q ≥ 1.5:
λc =
Kl rπ
√
Fy E
Fy = specified minimum yield stress of steel Q = reduction factor for local buckling AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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The reduction factor Q shall be:
when
b ≤ 0.446 t
√
E : Fy Q = 1.0
when 0.446
√
√
E b < < 0.910 Fy t
E : Fy
Q = 1.34 − 0.761
when
b ≥ 0.910 t
√
(4-3a)
b t
√
Fy E
(4-3b)
E : Fy Q=
0.534E
b Fy t b = full width of longest angle leg t = thickness of angle
2
(4-3c)
For members whose design is based on compressive force, the largest effective slenderness ratio preferably should not exceed 200. 5.
FLEXURE The flexure design strengths of Section 5.1 shall be used as indicated in Sections 5.2 and 5.3
5.1. Flexural Design Strength The flexural design strength shall be limited to the minimum value φbMn determined from Sections 5.1.1, 5.1.2, and 5.1.3, as applicable, with φb = 0.9. 5.1.1. For the limit state of local buckling when the tip of an angle leg is in compression: when
b ≤ 0.382 t
√
E : Fy Mn = 1.25Fy Sc
when 0.382
√
E b < ≤ 0.446 Fy t
√
E : Fy
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(5-1a)
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b/t Mn = Fy Sc 1.25 − 1.49 − 1 E 0.382 Fy
√
when
b > 0.446 t
√
(5-1b)
E : Fy Mn = QFy Sc
(5-1c)
where b = full width of angle leg with tip in compression Q = reduction factor per Equations 4-3a, b, and c Sc = elastic section modulus to the tip in compression relative to axis of bending E = modulus of elasticity 5.1.2. For the limit state of yielding when the tip of an angle leg is in tension Mn = 1.25My
(5-2)
where My = yield moment about the axis of bending 5.1.3. For the limit state of lateral-torsional buckling: when Mob ≤ My : Mn = [0.92 − 0.17Mob / My]Mob
(5-3a)
when Mob > My : My / Mob ]My ≤ 1.25My Mn = [1.58 − 0.83 √
(5-3b)
where Mob = elastic lateral-torsional buckling moment, from Section 5.2 or 5.3 as applicable 5.2. Bending about Geometric Axes 5.2.1. a. Angle bending members with lateral-torsion restraint along the length shall be designed on the basis of geometric axis bending with the nominal flexural strength Mn limited to the provisions of Sections 5.1.1 and 5.1.2. b. For equal-leg angles if the lateral-torsional restraint is only at the point of maximum moment, the required moment shall be limited to φbMn per Section 5.1. My shall be computed using the geometric axis section modulus and Mob shall be substituted by using 1.25 times Mob computed from Equation 5-4. 5.2.2. Equal-leg angle members without lateral-torsional restraint subjected to flexure applied about one of the geometric axes are permitted to be designed considering only geometric axis bending provided: AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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a. The yield moment shall be based on use of 0.80 of the geometric axis section modulus. b. For the angle-leg tips in compression, the nominal flexural strength Mn shall be determined by the provisions in Section 5.1.1 and in Section 5.1.3, where Mob =
0.66Eb4tCb [√ 1 + 0.78(lt / b2)2 − 1] l2
(5-4)
l = unbraced length 12.5Mmax ≤ 1.5 Cb = 2.5Mmax + 3MA + 4MB + 3MC where Mmax = absolute value of maximum moment in the unbraced beam segment MA = absolute value of moment at quarter point of the unbraced beam segment MB = absolute value of moment at centerline of the unbraced beam segment MC = absolute value of moment at three-quarter point of the unbraced beam segment c. For the angle-leg tips in tension, the nominal flexural strength shall be determined according to Section 5.1.2. 5.2.3. Unequal-leg angle members without lateral-torsional restraint subjected to bending about one of the geometric axes shall be designed using Section 5.3. 5.3. Bending about Principal Axes Angles without lateral-torsional restraint shall be designed considering principal-axis bending, except for the alternative of Section 5.2.2, if appropriate. Bending about both of the principal axes shall be evaluated as required in Section 6. 5.3.1. Equal-leg angles: a. Major-axis bending: The nominal flexural strength Mn about the major principal axis shall be determined by the provisions in Section 5.1.1 and in Section 5.1.3, where Mob = Cb
0.46Eb2t2 l
(5-5)
b. Minor-axis bending: The nominal design strength Mn about the minor principal axis shall AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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LRFD SPECIFICATION FOR DESIGN OF SINGLE-ANGLE MEMBERS
be determined by Section 5.1.1 when the leg tips are in compression, and by Section 5.1.2 when the leg tips are in tension. 5.3.2. Unequal-leg angles: a. Major-axis bending: The nominal flexural strength Mn about the major principal axis shall be determined by the provisions in Section 5.1.1 for the compression leg and in Section 5.1.3, where Mob = 4.9E
Iz Cb [√ β2w + 0.052(lt / rz)2 + βw] l2
(5-6)
Iz = minor principal axis moment of inertia rz = radius of gyration for minor principal axis 1 βw = ∫ z(w2 + z2)dA − 2zo, special section property for Iw A unequal-leg angles, positive for short leg in compression and negative for long leg in compression (see Commentary for values for common angle sizes). If the long leg is in compression anywhere along the unbraced length of the member, the negative value of βw shall be used. zo = coordinate along z axis of the shear center with respect to centroid Iw = moment of inertia for major principal axis b. Minor-axis bending: The nominal design strength Mn about the minor principal axis shall be determined by Section 5.1.1 when leg tips are in compression and by Section 5.1.2 when the leg tips are in tension. 6.
COMBINED FORCES The interaction equation shall be evaluated for the principal bending axes either by addition of all the maximum axial and flexural terms, or by considering the sense of the associated flexural stresses at the critical points of the cross section, the flexural terms are either added to or subtracted from the axial load term.
6.1. Members in Flexure and Axial Compression 6.1.1. The interaction of flexure and axial compression applicable to specific locations on the cross section shall be limited by Equations 6-1a and 6-1b: For
Pu ≥ 0.2 φPn Muz Pu 8 Muw φP + 9 φ M + φ M ≤ 1.0 b nz b nw n AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(6-1a)
LRFD SPECIFICATION FOR DESIGN OF SINGLE-ANGLE MEMBERS
For
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Pu ≤ 0.2 φPn
Muw Muz Pu (6-1b) 2φP + φ M + φ M ≤ 1.0 b nz n b nw Pu = required compressive strength Pn = nominal compressive strength determined in accordance with Section 4 Mu = required flexural strength Mn = nominal flexural strength for tension or compression in accordance with Section 5, as appropriate. Use section modulus for specific location in the cross section and consider the type of stress. φ = φc = resistance factor for compression = 0.90 φb = resistance factor for flexure = 0.90 w = subscript relating symbol to major-axis bending z = subscript relating symbol to minor-axis bending In Equations 6-1a and 6-1b when Mn represents the flexural strength of the compression side, the corresponding Mu shall be multiplied by B1. B1 =
Cm ≥ 1.0 Pu 1− Pe1
(6-2)
Cm = bending coefficient defined in AISC LRFD Pe1 = elastic buckling load for the braced frame defined in AISC LRFD 6.1.2. For members constrained to bend about a geometric axis with nominal flexural strength determined per Section 5.2.1, the radius of gyration r for Pe1 shall be taken as the geometric axis value. The bending terms for the principal axes in Equations 6-1a and 6-1b shall be replaced by a single geometric axis term. 6.1.3. Alternatively, for equal-leg angles without lateral-torsional restraint along the length and with bending applied about one of the geometric axes, the provisions of Section 5.2.2 are permitted for the required and design bending strength. If Section 5.2.2 is used for Mn, the radius of gyration about the axis of bending r for Pe1 shall be taken as the geometric axis value of r divided by 1.35 in the absence of a more detailed analysis. The bending terms for the principal axes in Equations 6-1a and 6-1b shall be replaced by a single geometric axis term. 6.2. Members in Flexure and Axial Tension The interaction of flexure and axial tension shall be limited by Equations 6-1a and 6-1b where Pu = required tensile strength Pn = nominal tensile strength determined in accordance with Section 2 AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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LRFD SPECIFICATION FOR DESIGN OF SINGLE-ANGLE MEMBERS
Mu = required flexural strength Mn = nominal flexural strength for tension or compression in accordance with Section 5, as appropriate. Use section modulus for specific location in the cross section and consider the type of stress. φ = φt = resistance factor for tension = 0.90 φb = resistance factor for flexure = 0.90 For members subject to bending about a geometric axis, the required bending strength evaluation shall be in accordance with Sections 6.1.2 and 6.1.3. Second-order effects due to axial tension and bending interaction are permitted to be considered in the determination of Mu for use in Formulas 6-1a and 6-1b. In lieu of using Formulas 6-1a and 6-1b, a more detailed analysis of the interaction of flexure and tension is permitted.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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Commentary on the Specification for Load and Resistance Factor Design of Single-Angle Members December 1, 1993
INTRODUCTION This Specification is intended to be complete for normal design usage in conjunction with the main 1993 AISC LRFD Specification and Commentary. This Commentary furnishes background information and references for the benefit of the engineer seeking further understanding of the derivation and limits of the specification. The Specification and Commentary are intended for use by design professionals with demonstrated engineering competence. C2. TENSION The criteria for the design of tension members in AISC LRFD Specification Section D1 have been adopted for angles with bolted connections. However, recognizing the effect of shear lag when the connection is welded, the criteria in Section B3 of the AISC LRFD Specification have been applied. The advisory upper slenderness limits are not due to strength considerations but are based on professional judgment and practical considerations of economics, ease of handling, and transportability. The radius of gyration about the z axis will produce the maximum l / r and, except for very unusual support conditions, the maximum Kl / r. Since the advisory slenderness limit for compression members is less than for tension members, an accommodation has been made for members with Kl / r > 200 that are always in tension, except for unusual load conditions which produce a small compression force. C3. SHEAR Shear stress due to factored loads in a single-angle member are the result of the AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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COMMENTARY
gradient in the bending moment along the length (flexural shear) and the torsional moment. The maximum elastic stress due to flexural shear may be computed by fv =
1.5Vb bt
(C3-1)
where Vb = component of the shear force parallel to the angle leg with length b and thickness t, kips The stress, which is constant through the thickness, should be determined for both legs to determine the maximum. The 1.5 factor is the calculated elastic value for equal-leg angles loaded along one of the principal axes. For equal-leg angles loaded along one of the geometric axes (laterally braced or unbraced) the factor is 1.35. Constants between these limits may be calculated conservatively from Vb Q / It to determine the maximum stress at the neutral axis. Alternatively, if only flexural shear is considered, a uniform flexural shear stress in the leg of Vb / bt may be used due to inelastic material behavior and stress redistribution. If the angle is not laterally braced against twist, a torsional moment is produced equal to the applied transverse load times the perpendicular distance e to the shear center, which is at the heel of the angle cross section. Torsional moments are resisted by two types of shear behavior: pure torsion (St. Venant) and warping torsion (AISC, 1983). If the boundary conditions are such that the cross section is free to warp, the applied torsional moment MT is resisted by pure shear stresses as shown in Figure C3.1a. Except near the ends of the legs, these stresses are constant along the length of the leg, and the maximum value can be approximated by fv = MT t / J =
3MT At
(C3-2)
e
P MT = Pe
(a) Pure torsion
(b) In-plane warping
(c) Across-thickness warping
Fig. C.3.1. Shear stresses due to torsion. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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where J = torsional constant (approximated by ÎŁbt3 / 3 when precomputed value unavailable) A = angle cross-sectional area At section where warping is restrained, the torsional moment is resisted by warping shear stresses of two types (Gjelsvik, 1981). One type is in-plane (contour) as shown in Figure C3.1b, which varies from zero at the toe to a maximum at the heel of the angle. The other type is across the thickness and is sometimes referred to as secondary warping shear. As indicated in Figure C3.1c, it varies from zero at the heel to a maximum at the toe. In an angle with typical boundary conditions and unrestrained load point, the torsional moment produces all three types of shear stresses (pure, in-plane warping, and secondary warping) in varying proportions along its length. The total applied moment is resisted by a combination of three types of internal moments that differ in relative proportions according to the distance from the boundary condition. Using typical angle dimensions, it can be shown that the two warping shears are approximately the same order of magnitude and are less than 20 percent of the pure shear stress for the same torsional moment. Therefore, it is conservative to compute the torsional shear stress using the pure shear equation and total applied torsional moment MT as if no warping restraint were present. This stress is added directly to the flexural shear stress to produce a maximum surface shear stress near the mid-length of a leg. Since this sum is a local maximum that does not extend through the thickness, applying the limit of Ď&#x2020;v0.6Fy adds another degree of conservatism relative to the design of other structural shapes. In general, torsional moments from laterally unrestrained transverse loads also produce warping normal stresses that are superimposed on bending stresses. However, since the warping strength for a single angle is relatively small, this additional bending effect is negligible and often ignored in design practice. C4. COMPRESSION The provisions for the critical compression stress account for the three possible limit states that may occur in an angle column depending on its proportions: general column flexural buckling, local buckling of thin legs, and flexural-torsional buckling of the member. The Q-factor in the equation for critical stress accounts for the local buckling, and the expressions for Q are nondimensionalized from AISC LRFD Specification (AISC, 1993) Appendix B5. Flexural-torsional buckling is covered in Appendix E of the AISC LRFD Specification (AISC, 1993). This strength limit state is approximated by the Q-factor reduction for slender-angle legs. For non-slender sections where Q = 1, flexural-torsional buckling is relevant for relatively short columns, but it was shown by Galambos (1991) that the error of neglecting this effect is not significant. For this reason no explicit consideration of this effect is required in these single-angle specifications. The provisions of Appendix E of AISC LRFD may be conservatively used to directly consider flexural-torsional buckling for single-angle members. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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COMMENTARY
The effective length factors for angle columns may be determined by consulting the paper by Lutz (1992). The resistance factor Ď&#x2020; was increased from 0.85 in AISC LRFD for all cross sections to 0.90 for single angles only because it was shown that a Ď&#x2020; of 0.90 provides an equivalent degree of reliability (Galambos, 1992). C5. FLEXURE Flexural strength limits are established for yielding, local buckling, and lateraltorsional buckling. In addition to addressing the general case of unequal-leg single angles, the equal-leg angle is treated as a special case. Furthermore, bending of equal-leg angles about a geometric axis, an axis parallel to one of the legs, is addressed separately as it is a very common situation. The tips of an angle refer to the free edges of the two legs. In most cases of unrestrained bending, the flexural stresses at the two tips will have the same sign (tension or compression). For constrained bending about a geometric axis, the tip stresses will differ in sign. Criteria for both tension and compression at the tip should be checked as appropriate, but in most cases it will be evident which controls. Appropriate serviceability limits for single-angle beams need also to be considered. In particular, for longer members subjected to unrestrained bending, deflections are likely to control rather than lateral-torsional or local buckling strength. C5.1.1. These provisions follow the LRFD format for nominal flexural resistance. There is a region of full yielding, a linear transition to the yield moment, and a region of local buckling. The strength at full yielding is limited to a shape factor of 1.25, which is less than that corresponding to the plastic moment of an angle. The factor of 1.25 corresponds to an allowable stress of 0.75Fy, which has traditionally been used for rectangular shapes and for weak axis bending. It is used for angles due to uncertainties in developing the full plastic moment and to limit the large distortion of sections with large shape factors. The b / t limits and the criteria for local buckling follow typical AISC criteria for single angles under uniform compression. They are conservative when the leg is subjected to non-uniform compression due to flexure. C5.1.2. Since the shape factor for angles is in excess of 1.5, the nominal design strength Mn = 1.25My for compact members is justified provided that instability does not control. C5.1.3. Lateral-torsional instability may limit the flexural strength of an unbraced single-angle beam. As illustrated in Figure C5.1, Equation 5-3a represents the elastic buckling portion with the nominal flexural strength, Mn, varying from 75 percent to 92 percent of the theoretical buckling moment, Mob. Equation 5-3b represents the inelastic buckling transition expression between 0.75My and 1.25My. At Mob greater than approximately 6My, the unbraced length is adequate to develop the AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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maximum beam flexural strength of Mn = 1.25My. These formulas were based on Australian research on single angles in flexure and on an analytical model consisting of two rectangular elements of length equal to the actual angle leg width minus one-half the thickness (Leigh and Lay, 1984; Australian Institute of Steel Construction, 1975; Leigh and Lay, 1978; Madugula and Kennedy, 1985). Figure C5.1 reflects the higher nominal moment strength than was implied by the 0.66Fy allowable stress in the ASD version. A new and more general Cb moment gradient formula consistent with the 1993 AISC LRFD Specification is used to correct lateral-torsional stability equations from the assumed most severe case of uniform moment throughout the unbraced length (Cb = 1.0). The equation for Cb used in the ASD version is applicable only to moment diagrams that are straight lines between brace points. In lieu of a more detailed analysis, the reduced maximum limit of 1.5 is imposed for single-angle beams to represent conservatively the lower envelope of this cross sectionâ&#x20AC;&#x2122;s non-uniform bending response. C5.2.1. An angle beam loaded parallel to one leg will deflect and bend about that leg only if the angle is restrained laterally along the length. In this case simple bending occurs without any torsional rotation or lateral
Mn My
1.25
Eq. 5-3b
Eq. 5-3a
0.75
Inelastic Full yielding
Elastic
Unbraced length l
0
0.16
1.0
Fig. C5.1. Lateral-torsional buckling of a single-angle beam. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
My Mob
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COMMENTARY
deflection and the geometric axis section properties should be used in the evaluation of the flexural design strength and deflection. If only the point of maximum moment is laterally braced, lateral-torsional buckling of the unbraced length under simple bending must also be checked, as outlined in Section 5.2.1b. C5.2.2. When bending is applied about one leg of a laterally unrestrained single angle, it will deflect laterally as well as in the bending direction. Its behavior can be evaluated by resolving the load and/or moments into principal axis components and determining the sum of these principal axis flexural effects. Section 5.2.2 is provided to simplify and expedite the design calculations for this common situation with equal-leg angles. For such unrestrained bending of an equal-leg angle, the resulting maximum normal stress at the angle tip (in the direction of bending) will be approximately 25 percent greater than calculated using the geometric axis section modulus. The value of Mob in Equation 5-4 and the evaluation of My using 0.80 of the geometric axis section modulus reflect bending about the inclined axis shown in Figure C5.2. The deflection calculated using the geometric axis moment of inertia has to be increased 82 percent to approximate the total deflection. Deflection has two components, a vertical component (in the direction of applied load) 1.56 times the calculated value and a horizontal component of 0.94 of the calculated value. The resultant total deflection is in the general direction of the weak principal axis bending of the angle (see Figure C5.2). These unrestrained bending deflections
δv = 1.56δ
Flexural load Y
Neutral axis
δh = 0.94δ X Geometric axis δ = deflection calculated using geometric axis moment of inertia
Fig. C5.2. Geometric axis bending of laterally unrestrained equal-leg angles. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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should be considered in evaluating serviceability and will often control the design over lateral-torsional buckling. The horizontal component of deflection being approximately 60 percent of the vertical deflection means that the lateral restraining force required to achieve purely vertical deflection (Section 5.2.1) must be 60 percent of the applied load value (or produce a moment 60 percent of the applied value) which is very significant. Lateral-torsional buckling is limited by Mob (Leigh and Lay, 1984 and 1978) in Equation 5-4, which is based on Mcr =
2.33Eb4t × (1 + 3cos2θ) (Kl)2
0.156 (1 + 3cos θ) (Kl) t √ sin θ + b 2
2
4
2 2
+ sinθ
(C5-1)
(the general expression for the critical moment of an equal-leg angle) with θ = −45° which is the most severe condition with the angle heel (shear center) in tension. Flexural loading which produces angle-heel compression can be conservatively designed by Equation 5-4 or more exactly by using the above general Mcr equation with θ = 45º (see Figure C5.3). With the angle heel in compression, Equation C5-1 will slightly exceed the yield moment limit of 1.25(0.8SxFy ) only for relatively few high slenderness cases. For pure bending situations, deflections would be unreasonably large under these conditions. However, considering the interaction of flexure and compression in an angle with Fy = 50 ksi, b / t equal to 16 and the largest l / r of 200, Equation C5-1 will produce results eight percent less than the modified yield moment. This situation could arise in a compression angle where the load is transferred by end gusset plates attached to one leg only. In this case the flexure term in the interaction is about 0.5 which reduces the effect Z (minor principal axis) W (major principal axis) b +θ
Shear center t
Mcr Centroid
Fig. C5.3. Equal-leg angle with general moment loading. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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COMMENTARY
to less than four percent and the end restraints provide an unknown increase in the lateral-torsional buckling strength. Consequently only the yield limit is required to be checked in Section 5.2.2 when the leg tips are in tension. Lateral-torsional buckling will reduce the nominal bending strength only when l / b is relatively large. If the lt / b2 parameter (which is a ratio of l / b over b / t) is small (less than approximately 2.5 with Cb = 1), there is no need to check lateral-torsional stability inasmuch as local buckling provisions of Section 5.1.1 will control the nominal bending strength. Lateral-torsional buckling will produce Mn < 1.25My for equal-leg angles only if Mob by Equation 5-4 is less than about 6My, for Cb = 1.0. Limits for l / b as a function of b / t are shown graphically in Figure C5.4. Local buckling and deflections must be checked separately. Stress at the tip of the angle leg parallel to the applied bending axis is of the same sign as the maximum stress at the tip of the other leg when the single angle is unrestrained. For an equal-leg angle this stress is about one-third of the maximum stress. It is only necessary to check the nominal bending strength based on the tip of the angle leg with the maximum stress when evaluating such an angle. Since this maximum moment per Section 5.2.2 represents combined principal axis moments and Equation 5-4 represents the design limit for these combined
400
300 l
b 200
100
0 1
2
3
4
5 Fy = 36
b
6
7
8
t Fy = 50
Fig. C5.4. Equal leg single-angle lateral buckling limits for Mn = 1.25My about geometric axis. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9
10
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flexural moments, only a single flexural term needs to be considered when evaluating combined flexural and axial effects. C5.2.3. For unequal-leg angles without lateral-torsional restraint the applied load or moment must be resolved into components along the two principal axis in all cases and designed for biaxial bending using the interaction equation. C5.3.1. Under major axis bending of equal-leg angles Equation 5-5 in combination with 5-3a or 5-3b controls the nominal design moment against overall lateral-torsional buckling of the angle. This is based on Mcr, given earlier with θ = 0. Lateral-torsional buckling for this case will reduce the stress below 1.25My only for l / t ≥ 4800 / Fy or 0.160E / Fy (Mob = 6My). If the lt / b2 parameter is small (less than approximately 1.5Cb for this case), local buckling will control the nominal design moment and Mn based on lateral-torsional buckling need not be evaluated. Local buckling must be checked using Section 5.1.1. C5.3.2. Lateral-torsional buckling about the major principal W axis of an unequal-leg angle is controled by Mob in Equation 5-6. Section property βw reflects the location of the shear center relative to the principal axis of the section and the bending direction under uniform bending. Positive βw and maximum Mob occurs when the shear center is in flexural compression while negative βw and minimum Mob occurs when the shear center is in flexural tension (see Figure C5.5). This βw effect is consistent with behavior of singly symmetric I-shaped beams which are more stable when the compression flange is larger than the tension flange. For principal W-axis bending of equal-leg angles, βw is equal to zero due to symmetry and Equation 5-6 reduces to Equation 5-5 for this special case.
Shear center
Mob
W
Z
Shear center
Mob
W
(Special case: for equal legs, βw = 0) (a) + βw
(b) – βw Fig. C5.5. Unequal-leg angle in bending. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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COMMENTARY
TABLE C5.1 βw Values for Angles Angle Size (in.)
βw (in.)*
9×4
6.54
8×6 8×4
3.31 5.48
7×4
4.37
6×4 6 × 3.5
3.14 3.69
5 × 3.5 5×3
2.40 2.99
4 × 3.5 4×3
0.87 1.65
3.5 × 3 3.5 × 2.5
0.87 1.62
3 × 2.5 3×2
0.86 1.56
2.5 × 2
0.85
Equal legs
0.00
* Has positive or negative value depending on direction of bending (see Figure C5.5).
For reverse curvature bending, part of the unbraced length has positive βw, while the remainder negative βw, and conservatively, the negative value is assigned for that entire unbraced segment.
βw is essentially independent of angle thickness (less than one percent variation from mean value) and is primarily a function of the leg widths. The average values shown in Table C5.1 may be used for design. C6. COMBINED STRESSES The stability and strength interaction equations of AISC LRFD Specification Chapter H have been adopted with modifications to account for various conditions of bending that may be encountered. Bending will usually accompany axial loading in a single-angle member since the axial load and connection along the legs are eccentric to the centroid of the cross section. Unless the situation conforms to Section 5.2.1 or 5.2.2 in that Section 6.1.2 or 6.1.3 may be used, the applied moment should be resolved about the principal axes for the interaction check. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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For the non-symmetric and singly symmetric single angles, the interaction expression related to stresses at a particular location on the cross section is the most accurate due to lack of double symmetry. At a particular location, it is possible to have stresses of different sign from the various components such that a combination of tensile and compressive stress will represent a critical condition. The absolute value of the combined terms must be checked at the angle-leg tips and heel and compared with 1.0. When using the combined force expressions for single angles, Muw and Muz are positive as customary. The evaluation of Mn in Section 5.1 is dependent on the location on the cross section being examined by using the appropriate value of section modulus, S. Since the sign of the stress is important in using Equations 6-1a and 6-1b, Mn is considered either positive or negative by assigning a sign to S to reflect the stress condition as adding to, or subtracting from, the axial load effect. A designer may choose to use any consistent sign convention. It is conservative to ignore this refinement and simply use positive critical Mn values in the bending terms and add the absolute values of all terms (Elgaaly, Davids, and Dagher, 1992 and Adluri and Madugula, 1992). Alternative special interaction equations for single angles have recently been published (Adluri and Madugula, 1992). C6.1.3. When the total maximum flexural stress is evaluated for a laterally unrestrained length of angle per Section 5.2, the bending axis is the inclined axis shown in Figure C5.2. The radius of gyration modification for the moment amplification about this axis is equal to √ 1.82 = 1.35 to account for the increased unrestrained bending deflection relative to that about the geometric axis for the laterally unrestrained length. The 1.35 factor is retained for angles braced only at the point of maximum moment to maintain a conservative calculation for this case. If the brace exhibits any flexibility permitting lateral movement of the angle, use of r = rx would not be conservative.
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LRFD SPECIFICATION FOR DESIGN OF SINGLE-ANGLE MEMBERS
List of References Alduri, S. M. and Madugula, M. K. S. (1992), “Eccentrically Loaded Steel SingleAngle Struts,” AISC Engineering Journal, 2nd Quarter. American Institute of Steel Construction, Inc. (1983), Torsional Analysis of Steel Members, Chicago, IL. American Institute of Steel Construction, Inc. (1993), Load and Resistance Factor Design Specification for Structural Steel Buildings, Chicago, IL. American Institute of Steel Construction, Inc. (1989), Specification for Allowable Stress Design of Single-Angle Members, Chicago, IL. Australian Institute of Steel Construction (1975), Australian Standard AS1250, 1975. Elgaaly, M., Davids, W. and Dagher, H. (1992), “Non-Slender Single-Angle Struts,” AISC Engineering Journal, 2nd Quarter. Galambos, T. V. (1991), “Stability of Axially Loaded Compressed Angles,” Structural Stability Research Council, Annual Technical Session Proceedings, Apr. 15–17, 1991, Chicago, IL. Gjelsvik, A. (1981), The Theory of Thin-walled Bars, John Wiley and Sons, New York. Leigh, J. M. and M. G. Lay (1978), “Laterally Unsupported Angles with Equal and Unequal Legs,” Report MRL 22/2 July 1978, Melbourne Research Laboratories, Clayton. Leigh, J. M. and M. G. Lay (1984), “The Design of Laterally Unsupported Angles,” in Steel Design Current Practice, Section 2, Bending Members, American Institute of Steel Construction, Inc., January 1984. Lutz, L. A. (1992), “Critical Slenderness of Compression Members with Effective Lengths About Nonprincipal Axes,” Structural Stability Research Council, Annual Technical Session Proceedings, Apr. 6–7, 1992, Pittsburgh, PA. Madugula, M. K. S. and J. B. Kennedy (1985), Single and Compound Angle Members, Elsevier Applied Science, New York.
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Seismic Provisions for Structural Steel Buildings June 15, 1992
AMERICAN INSTITUTE OF STEEL CONSTRUCTION, INC. One East Wacker Drive, Suite 3100, Chicago, IL 60601-2001
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PREFACE
The intention of the main AISC Specification is to cover the common everyday design criteria in routine office usage. It is not feasible to also cover the many special and unique problems encountered within the full range of structural design practice. This document is a separate Specification which addresses one such topic, steel seismic provisions. It contains its own list of Symbols, a Glossary and a non-mandatory Commentary which has been included to provide background for the provisions. The AISC Specification Task Committee 113 on Seismic Provisions to supplement the current Load and Resistance Factor Design (LRFD) and Allowable Stress Design (ASD) Specification for Structural Steel Buildings acknowledges the various contributions of several groups to the completion of this document: the Structural Engineers Association of California (SEAOC), the National Science Foundation, and the Building Seismic Safety Council. The main AISC Committee on Specification enhanced these provisions by careful scrutiny, discussions, suggestions for improvements, and endorsement. The members of this Task Committee, as principal authors of the AISC Seismic Provisions, are most grateful to all of the above groups and people. Special recognition must also be given to the leadership expertise, and perseverance of Task Committee Chairman Egor Popov and Technical Secretary Clarkson Pinkham. The principal changes in this edition of the Seismic Provisions are the conversion to the loads and design format recommended by the 1991 National Earthquake Hazards Reduction Program (NEHRP) document. The reader is cautioned that professional judgment must be exercised when data or recommendations in this Specification are applied. The publication of the material contained herein is not intended as a representation or warranty on the part of the American Institute of Steel Construction, Inc.â&#x20AC;&#x201D;or any other person named hereinâ&#x20AC;&#x201D; that this information is suitable for general or particular use, or freedom from infringement of any patent or patents. Anyone making use of this information assumes all liability arising from such use. The design of structures is within the scope of expertise of a competent licensed structural engineer, architect, or other licensed professional for the application of principles to a particular structure. By the AISC Subcommittee, E. P. Popov, Chair R. Becker G. G. Deierlein M. D. Engelhardt S. J. Fang R. E. Ferch R. D. Hanson J. R. Harris K. Kasai
S. D. Lindsey H. W. Martin C. M. Saunders J. B. Shantz I. M. Viest N. F. G. Youssef C. W. Pinkham, Technical Secretary N. Iwankiw, Recording Secretary
May 22, 1992
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Symbols The section numbers in parentheses after the definition of a symbol refers to the section where the symbol is first used. Effective net area, in.2 (9) Flange area of member, in.2 (6) Gross area, in.2 (8) Area of link stiffener, in.2 (10) Seismic coefficient representing the effective peak velocity-related acceleration. (2) Effective area of weld, in.2 (6) Link web area, in.2 (10) Response factor related to the fundamental period of the building. (3) Dead load due to the self-weight of the structure and the permanent elements on the structure, kips. (3) E Earthquake load. (3) FBM Nominal strength of the base material to be welded, ksi. (6) FEXX Classification strength of weld metal, ksi. (6) Fw Nominal strength of the weld electrode material, ksi. (6) Fy Specified minimum yield strength of the type of steel being used, ksi. (8) Fyb Fy of a beam, ksi. (8) Fyc Fy of a column, ksi. (6) H Average story height above and below a beam-to-column connection., in. (8) L Live load due to occupancy and moveable equipment, kips. (3) L Unbraced length of compression or bracing member, in. (8) Lr Roof live load, kips. (3) Mn Nominal moment strength of a member or joint, kip-in. (8) Mp Plastic bending moment, kip-in. (8) Mpa Plastic bending moment modified by axial load ratio, kip-in. (10) Mu Required flexural strength on a member or joint, kip-in. (8) PD Required axial strength on a column resulting from application of dead load, D, kips. (6) PE Required axial strength on a column resulting from application of the specified earthquake load, E, kips. (6) PL Required axial strength on a column resulting from application of live load, L, kips. (6) Pu Required axial strength on a column or a link, kips. (10) Pn Nominal axial strength of a column, kips. (6) Puâ&#x2C6;&#x2014; Required axial strength on a brace, kips. (9) Puc Required axial strength on a column based on load combination with seismic loads, kips. (8) Py Nominal yield axial strength of a member = Fy Ag, kips. (10)
Ae Af Ag Ast Av Aw Aw Cs D
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R R′ Rn S V Vn Vu Vp Vpa W Wg Zb Zc b bf bcf db dc dz e h r ry tbf tcf tf tp tw tz wz α ρ k kp kr φ φb φc φt φv φw
SYMBOLS
Response modification factor. (3) Load due to initial rainwater or ice exclusive of the ponding contribution, kips. (Symbol R is used in the Specification). (3) Nominal strength of a member. (8) Snow load, kips. (3) Base shear due to earthquake load, kips. (3) Nominal shear strength of a member, kips. (8) Required shear strength on a member, kips. (8) Nominal shear strength of an active link, kips. (10) Nominal shear strength of an active link modified by the axial load magnitude, kips. (10) Wind load, kips. (3) Total weight of the building, kips. (3) Plastic section modulus of a beam, in.3 (8) Plastic section modulus of a column, in.3 (8) Width of compression element, in. (Table 8-1) Flange width, in. (8) Column flange width, in. (8) Overall beam depth, in. (8) Overall column depth, in. (8) Overall panel zone depth between continuity plates, in. (8) EBF link length, in. (10) Assumed web depth for stability, in. (Table 8-1) Governing radius of gyration, in. (9) Radius of gyration about y axis, in. (8) Thickness of beam flange, in. (8) Thickness of column flange, in. (8) Thickness of flange, in. (8) Thickness of panel zone including doubler plates, in. (8) Thickness of web, in. (8) Thickness of panel zone (doubler plates not necessarily included), in. (8) Width of panel zone between column flanges, in. (8) Fraction of member force transferred across a particular net section. (9) Ratio of required axial force Pu to required shear strength Vu of a link. (10) Slenderness parameter. (9) Limiting slenderness parameter for compact element. (8) Limiting slenderness parameter for non-compact element. (9) Resistance factor. (6,10) Resistance factor for beams. (6) Resistance factor for columns in compression. (6,10) Resistance factor for columns in tension. (6) Resistance factor for shear strength of panel zone of beam-to-column connections. (8) Resistance factor for welds. (6)
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Glossary Beam. A structural member whose primary function is to carry loads transverse to its longitudinal axis, usually a horizontal member in a seismic frame system. Braced Frame. An essentially vertical truss system of concentric or eccentric type that resists lateral forces on the structural system. Concentrically Braced Frame (CBF). A braced frame in which all members of the bracing system are subjected primarily to axial forces. The CBF shall meet the requirements of Sect. 9. Connection. Combination of joints used to transmit forces between two or more members. Categorized by the type and amount of force transferred (moment, shear, end reaction). Continuity Plates. Column stiffeners at top and bottom of the panel zone. Design strength. Resistance (force, moment, stress, as appropriate) provided by element or connection; the product of the nominal strength and the resistance factor. Diagonal Bracing. Inclined structural members carrying primarily axial load employed to enable a structural frame to act as a truss to resist horizontal loads. Dual System. A dual system is a structural system with the following features: • An essentially complete space frame which provides support for gravity loads. • Resistance to lateral load is provided by moment resisting frames (SMF) or (OMF) which is capable of resisting at least 25 percent of the base shear and concrete or steel shear walls, steel eccentrically (EBF) or concentrically (CBF) braced frames. • Each system shall be also designed to resist the total lateral load in proportion to its relative rigidity. Eccentrically Braced Frame (EBF). A diagonal braced frame in which at least one end of each bracing member connects to a beam a short distance from a beam-to-column connection or from another beam-to-brace connection. The EBF shall meet the requirements of Sect. 10. Essential Facilities. Those facilities defined as essential in the applicable code under which the structure is designed. In the absence of such a code, see ASCE 7-92. Joint. Area where two or more ends, surfaces, or edges are attached. Categorized by type of fastener or weld used and method of force transfer. K Braced Frame. A concentric braced frame (CBF) in which a pair of diagonal braces located on one side of a column is connected to a single point within the clear column height. Lateral Support Member. Member designed to inhibit lateral buckling or lateral-torsional buckling of primary frame members. Link. In EBF, the segment of a beam which extends from column to column, located between the end of a diagonal brace and a column or between the ends of two diagonal braces of the EBF. The length of the link is defined as the clear distance AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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GLOSSARY
between the diagonal brace and the column face or between the ends of two diagonal braces. Link Intermediate Web Stiffeners. Vertical web stiffeners placed within the link. Link Rotation Angle. The link rotation angle is the plastic angle between the link and the beam outside of the link when the total story drift is E′ / E times the drift derived using the specified base shear, V. Link Shear Design Strength. The lesser of φVp or 2φMp/e, where φ = 0.9, Vp = 0.55Fy dtw and e = the link length except as modified by Sect. S9.2.f. LRFD. (Load and Resistance Factor Design). A method of proportioning structural components (members, connectors, connecting elements, and assemblages) such that no applicable limit state is exceeded when the structure is subjected to all design load combinations. Moment Frame. A building frame system in which seismic shear forces are resisted by shear and flexure in members and joints of the frame. Nominal loads. The magnitudes of the loads specified by the applicable code. Nominal strength. The capacity of a structure or component to resist the effects of loads, as determined by computations using specified material strengths and dimensions and formulas derived from accepted principles of structural mechanics or by field tests or laboratory tests of scaled models, allowing for modeling effects, and differences between laboratory and field conditions. Ordinary Moment Frame (OMF). A moment frame system which meets the requirements of Sect. 7. P - Delta effect. Secondary effect of column axial loads and lateral deflection on the shears and moments in members. Panel Zone. Area of beam-to-column connection delineated by beam and column flanges. Required Strength. Load effect (force, moment, stress, as appropriate) acting on element of connection determined by structural analysis from the factored loads (using most appropriate critical load combinations). Resistance Factor. A factor that accounts for unavoidable deviations of the actual strength from the nominal value and the manner and consequences of failure. Slip-Critical Joint. A bolted joint in which slip resistance of the connection is required. Special Moment Frame (SMF). A moment frame system which meets the requirements of Sect. 8. Structural System. An assemblage of load-carrying components which are joined together to provide regular interaction or interdependence. V Braced Frame. A concentrically braced frame (CBF) in which a pair of diagonal braces located either above or below a beam is connected to a single point within the clear beam span. Where the diagonal braces are below the beam, the system is also referred to as an Inverted V Braced Frame. X Braced Frame. A concentrically braced frame (CBF) in which a pair of diagonal braces crosses near mid-length of the braces. Y Braced Frame. An eccentrically braced frame (EBF) in which the stem of the Y is the link of the EBF system.
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Seismic Provisions for Structural Steel Buildings June 15, 1992
Part Iâ&#x20AC;&#x201D;Load and Resistance Factor Design (LRFD) 1.
SCOPE These special seismic requirements are to be applied in conjunction with the AISC Load and Resistance Factor Design Specification for Structural Steel Buildings (LRFD), 1986; hereinafter referred to as the Specification. They are intended for the design and construction of structural steel members and connections in buildings for which the design forces resulting from earthquake motions have been determined on the basis of energy dissipation in the non-linear range of response. Seismic provisions and the nominal loads for each Seismic Performance Category, Seismic Hazard Exposure Group, or Seismic Zone shall be as specified by the applicable code under which the structure is designed or where no code applies, as dictated by the conditions involved. In the absence of a code, the Performance Categories, Seismic Hazard Exposure Groups, loads and load combinations shall be as given herein.
2.
SEISMIC PERFORMANCE CATEGORIES Seismic Performance Categories vary with the Seismic Hazard Exposure Group shown in Table 2-1, the Effective Peak Velocity Related Acceleration, Av, and the Seismic Hazard Exposure Group shown in Table 2-2. In addition to the general requirements assigned to the various Seismic Performance Categories in the applicable building code for all types of construction, the following requirements apply to fabricated steel construction for buildings and structures with similar structural characteristics.
2.1. Seismic Performance Categories A, B, and C Buildings assigned to Categories A, B, and C, except Category C in Seismic Hazard Exposure Group III where the value of Av â&#x2030;Ľ 0.10, shall be designed either in accordance with solely the Specification or in accordance with the Specification and these provisions. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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TABLE 2-1 Seismic Hazard Exposure Groups Group III
Buildings having essential facilities that are necessary for postearthquake recovery and requiring special requirements for access and functionality.
Group II
Buildings that constitute a substantial public hazard because of occupancy or use.
Group I
All buildings not classified in Groups II and III.
2.2. Seismic Performance Category C Buildings assigned to Category C in Seismic Hazard Exposure Group III where the value of Av â&#x2030;Ľ 0.10 shall be designed in accordance with the Specification as modified by the additional provisions of this section. 2.2.a. Steel used in seismic resisting systems shall be limited by the provisions of Sect. 5. 2.2.b. Columns in seismic resisting systems shall be designed in accordance with Sect. 6. 2.2.c. Ordinary Moment Frames (OMF) shall be designed in accordance with the provisions of Sect. 7. 2.2.d. Special Moment Frames (SMF) are required to conform only to the requirements of Sects. 8.2, 8.7, and 8.8. 2.2.e. Braced framed systems shall conform to the requirements of Sects. 9 or 10 when used alone or in combination with the moment frames of the seismic resisting system. 2.2.f. A quality assurance plan shall be submitted to the regulatory agency for the seismic force resisting system of the building. 2.3. Seismic Performance Categories D and E Buildings assigned to Categories D and E shall be designed in accordance with the Specification as modified by the additional provisions of this section. 2.3.a. Steel used in seismic resisting systems shall be limited by the provisions of Sect. 5. 2.3.b. Columns in seismic resisting systems shall be designed in accordance with Sect. 6. 2.3.c. Ordinary Moment Frames (OMF) shall be designed in accordance with the provisions of Sect. 7. 2.3.d. Special Moment Frames (SMF) shall be designed in accordance with the provisions of Sect. 8. 2.3.e. Braced framed systems shall conform to the requirements of Sects. 9. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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TABLE 2-2 Seismic Performance Categories Seismic Hazard Exposure Group Value of Av
I
II
III
0.20 ≤ Av < 0.20 0.15 ≤ Av < 0.20 0.10 ≤ Av < 0.15 0.05 ≤ Av < 0.10 0.15 ≤ Av < 0.05
D C C B A
D D C B A
E D C C A
(CBF) or 10. (EBF) when used alone or in combination with the moment frames of the seismic resisting system. The use of K-bracing systems shall not be permitted as part of the seismic resisting system except as permitted by Sect. 9.5. (Low Buildings) 2.3.f. A quality assurance plan shall be submitted to the regulatory agency for the seismic force resisting system of the building. 3.
LOADS, LOAD COMBINATIONS, AND NOMINAL STRENGTHS
3.1. Loads and Load Combinations The following specified loads and their effects on the structure shall be taken into account: D : dead load due to the weight of the structural elements and the permanent features on the structure. L : live load due to occupancy and moveable equipment. Lr : roof live load. W : wind load. S : snow load. E : earthquake load (where the horizontal component is derived from base shear Formula V = CsWg). R′ : load due to initial rainwater or ice exclusive of the ponding contribution. In the Formula V = CsWg for base shear: Cs = Seismic design coefficient Wg = Total weight of the building, see the applicable code. For the nominal loads as defined above, see the applicable code. The required strength of the structure and its elements shall be determined from the appropriate critical combination of factored loads. The following Load Combinations and corresponding load factors shall be investigated: 1.4D
(3-1)
1.2D + 1.6L + 0.5(Lr or S or R′)
(3-2)
1.2D + 1.6(Lr or S or R′) + (0.5L or 0.8W)
(3-3)
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PART I—LOAD AND RESISTANCE FACTOR DESIGN (LRFD)
1.2D + 1.3W + 0.5L + 0.5(Lr or S or R′)
(3-4)
1.2D ± 1.0E + 0.5L + 0.2S
(3-5)
0.9D ± (1.0E or 1.3W)
(3-6)
Exception: The load factor on L in Load Combinations 3-3, 3-4, and 3-5 shall equal 1.0 for garages, areas occupied as places of public assembly, and all areas where the live load is greater than 100 psf. Other special load combinations are included with specific design requirements throughout these provisions. Orthogonal earthquake effects shall be included in the analysis unless noted specifically otherwise in the governing building code. Where required by these provisions, an amplified horizontal earthquake load of 0.4R × E (where the term 0.4R is greater or equal to 1.0) shall be applied in lieu of the horizontal component of earthquake load E in the load combinations above. The term R is the earthquake response modification coefficient contained in the applicable code. The additional load combinations using the amplified horizontal earthquake load are: 1.2D + 0.5L + 0.2S ± 0.4R × E
(3-7)
0.9D ± 0.4R × E
(3-8)
Exception: The load factor on L in Load Combinations 3-7 shall equal 1.0 for garages, areas occupied as places of public assembly and all areas where the live load is greater than 100 psf. The term 0.4R in Load Combinations 3-7 and 3-8 shall be greater or equal to 1.0. Where the amplified load is required, orthogonal effects are not required to be included. 3.2. Nominal Strengths The nominal strengths shall be as provided in the Specification. 4.
STORY DRIFT Story drift shall be calculated using the appropriate load effects consistent with the structural system and the method of analysis. Limits on story drift shall be in accordance with the governing code and shall not impair the stability of the structure.
5.
MATERIAL SPECIFICATIONS Steel used in seismic force resisting systems shall be as listed in Sect. A3.1 of the Specification, except for buildings over one story in height. The steel used in seismic resisting systems described in Sections 8, 9, and 10 shall be limited to the following ASTM Specifications: A36, A500 (Grades B and C), A501, A572 (Grades 42 and 50), and A588. The steel used for base plates shall meet one of the preceding ASTM Specifications or ASTM A283 Grade D. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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COLUMN REQUIREMENTS
6.1. Column Strength When Pu / φPn > 0.5, columns in seismic resisting frames, in addition to complying with the Specification, shall be limited by the following requirements: 6.1.a. Axial compression loads: 1.2PD + 0.5PL + 0.2PS + 0.4R × PE ≤ φcPn
(6-1)
where the term 0.4R is greater or equal to 1.0. Exception: The load factor on PL in Load Combination 6-1 shall equal 1.0 for garages, areas occupied as places of public assembly, and all areas where the live load is greater than 100 psf. 6.1.b. Axial tension loads: 0.9PD − 0.4R × PE ≤ φtPn
(6-2)
where the term 0.4R is greater or equal to 1.0. 6.1.c. The axial Load Combinations 6-1 and 6-2 are not required to exceed either of the following: 1. The maximum loads transferred to the column, considering 1.25 times the design strengths of the connecting beam or brace elements of the structure. 2. The limit as determined by the foundation capacity to resist overturning uplift. 6.2. Column Splices Column splices shall have a design strength to develop the column axial loads given in Sect. 6.1.a, b, and c as well as the Load Combinations 3-1 to 3-6. 6.2.a. In column splices using either complete or partial penetration welded joints, beveled transitions are not required when changes in thickness and width of flanges and webs occur. 6.2.b. Splices using partial penetration welded joints shall not be within 3 ft of the beam-to-column connection. Column splices that are subject to net tension forces shall comply with the more critical of the following: 1. The design strength of partial penetration welded joints, the lesser of φwFw Aw or φwFBM Aw, shall be at least 150 percent of the required strength, where φw = 0.8 and Fw = 0.6FEXX. 2. The design strength of welds shall not be less than 0.5Fyc Af, where Fyc is the yield strength of the column material and Af is the flange area of the smaller column connected. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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7.
PART Iâ&#x20AC;&#x201D;LOAD AND RESISTANCE FACTOR DESIGN (LRFD)
REQUIREMENTS FOR ORDINARY MOMENT FRAMES (OMF)
7.1. Scope Ordinary Moment Frames (OMF) shall have a design strength as provided in the Specification to resist the Load Combinations 3-1 through 3-6 as modified by the following added provisions: 7.2. Joint Requirements All beam-to-column and column to beam connections in OMF which resist seismic forces shall meet one of the following requirements: 7.2.a. FR (fully restrained) connections conforming with Sect. 8.2, except that the required flexural strength, Mu, of a column-to-beam joint is not required to exceed the nominal plastic flexural strength of the connection. 7.2.b. FR connections with design strengths of the connections meeting the requirements of Sect. 7.1 using the Load Combinations 3-7 and 3-8. 7.2.c. Either FR or PR (partially restrained) connections shall meet the following: 1. The design strengths of the members and connections meet the requirements of Sect. 7.1. 2. The connections have been demonstrated by cyclic tests to have adequate rotation capacity at a story drift calculated at a horizontal load of 0.4R Ă&#x2014; E, (where the term 0.4R is equal to or greater than 1.0). 3. The additional drift due to PR connections shall be considered in design. FR and PR connections are described in detail in Sect. A2 of the Specification. 8.
REQUIREMENTS FOR SPECIAL MOMENT FRAMES (SMF)
8.1. Scope Special Moment Frames (SMF) shall have a design strength as provided in the Specification to resist the Load Combinations 3-1 through 3-6 as modified by the following added provisions: 8.2. Beam-to-Column Joints 8.2.a. The required flexural strength, Mu, of each beam-to-column joint shall be the lesser of the following quantities: 1. The plastic bending moment, Mp, of the beam. 2. The moment resulting from the panel zone nominal shear strength, Vn, as determined using Equation 8-1. The joint is not required to develop either of the strengths defined above if it is shown that under an amplified frame deformation produced by Load Combinations 3-7 and 3-8, the design strength of the members at the connection is adequate to support the vertical loads, and the required lateral force resistance is provided by other means. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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8.2.b. The required shear strength, Vu, of a beam-to-column joint shall be determined using the Load Combination 1.2D + 0.5L + 0.2S plus the shear resulting from Mu, as defined in Sect. 8.2.a., on each end of the beam. Alternatively, Vu shall be justified by a rational analysis. The required shear strength is not required to exceed the shear resulting from Load Combination 3-7. 8.2.c. The design strength, φRn, of a beam-to-column joint shall be considered adequate to develop the required flexural strength, Mu, of the beam if it conforms to the following: 1. The beam flanges are welded to the column using complete penetration welded joints. 2. The beam web joint has a design shear strength φVn greater than the required shear, Vu, and conforms to either: a. Where the nominal flexural strength of the beam, Mn, considering only the flanges is greater than 70 percent of the nominal flexural strength of the entire beam section [i.e., bf tf (d−tf)Fyf ≥ 0.7Mp]; the web joint shall be made by means of welding or slip-critical high strength bolting, or; b. Where bf tf (d−tf)Fyf < 0.7Mp, the web joint shall be made by means of welding the web to the column directly or through shear tabs. That welding shall have a design strength of at least 20 percent of the nominal flexural strength of the beam web. The required beam shear, Vu, shall be resisted by further welding or by slip-critical high-strength bolting or both. 8.2.d. Alternate Joint Configurations: For joint configurations utilizing welds or high-strength bolts, but not conforming to Sect. 8.2.c, the design strength shall be determined by test or calculations to meet the criteria of Sect. 8.2.a. Where conformance is shown by calculation, the design strength of the joint shall be 125 percent of the design strengths of the connected elements. 8.3. Panel Zone of Beam-to-Column Connections (Beam web parallel to column web) 8.3.a. Shear Strength: The required shear strength, Vu, of the panel zone shall be based on beam bending moments determined from the Load Combinations 3-5 and 3-6. However, Vu is not required to exceed the shear forces determined from 0.9ΣφbMp of the beams framing into the column flanges at the connection. The design shear strength, φvVn, of the panel zone shall be determined by the following formula: 3bcf t2cf where for this case φv = 0.75. φvVn = 0.6φvFy dc tp 1 + db dc tp where: tp = Total thickness of panel zone including doubler plates, in. dc = Overall column section depth, in. bcf = Width of the column flange, in. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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tcf = Thickness of the column flange, in. db = Overall beam depth, in. Fy = Specified yield strength of the panel zone steel, ksi. 8.3.b. Panel Zone Thickness: The panel zone thickness, tz, shall conform to the following: tz ≥ (dz + wz) / 90
(8-2)
where: dz = the panel zone depth between continuity plates, in. wz = the panel zone width between column flanges, in. For this purpose, tz shall not include any doubler plate thickness unless the doubler plate is connected to the web with plug welds adequate to prevent local buckling of the plate. Where a doubler plate is used without plug welds to the column web, the doubler plate shall conform to Eq. 8-2. 8.3.c. Panel Zone Doubler Plates: Doubler plates provided to increase the design strength of the panel zone or to reduce the web depth thickness ratio shall be placed next to the column web and welded across the plate width along the top and bottom with at least a minimum fillet weld. The doubler plates shall be fastened to the column flanges using either butt or fillet welded joints to develop the design shear strength of the doubler plate. 8.4. Beam and Column Limitations 8.4.a. Beam Flange Area: There shall be no abrupt changes in beam flange areas in plastic hinge regions. 8.4.b. Width-Thickness Ratios: Beams and columns shall comply with λp in Table 8-1 in lieu of those in Table B5.1 of the Specification. 8.5. Continuity Plates Continuity plates shall be provided if required by the provisions in the Specification for webs and flanges with concentrated forces and if the nominal column local flange bending strength Rn is less than 1.8Fyb bf tbf, where: Rn = 6.25(tcf)2Fyf, and Fyb = Specified minimum yield strength of beam, ksi. Fyf = Specified minimum yield strength of column flange, ksi. bf = Beam flange width, in. tbf = Beam flange thickness, in. tcf = Column flange thickness, in. Continuity plates shall be fastened by welds to both the column flanges and either the column webs or doubler plates. 8.6. Column-Beam Moment Ratio At any beam-to-column connection, one of the following relationships shall be satisfied: AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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TABLE 8-1 Limiting Width Thickness Ratios λp for Compression Elements Description of Element Flanges of I-shaped nonhybrid sections and channels in flexure.
WidthThickness Ratio
Limiting WidthThickness Ratios λp
b/t
52 / √ Fy
h / tw
For Pu / φbPy ≤ 0.125
Flanges of I-shaped hybrid beams in flexure. Webs in combined flexural and axial compression.
520 Fy √
1.54Pu 1 − φ P b y
For Pu / φbPy > 0.125 191 Fy √
Pu 253 2.33 − φ P ≥ √ Fy b y
ΣZc(Fyc − Puc / Ag) ≥ 1.0, ΣZbFyb
(8-3)
ΣZc(Fyc − Puc / Ag) ≥ 1.0, Vn dbH / (H − db)
(8-4)
where: Ag = Gross area of a column, in.2 Fyb = Specified minimum yield strength of a beam, ksi. Fyc = Specified minimum yield strength of a column, ksi. H = Average of the story heights above and below the joint, in. Puc = Required axial strength in the column (in compression) ≥ 0 Vn = Nominal strength of the panel zone as determined from Equation 8-1, ksi. Zb = Plastic section modulus of a beam, in.3 Zc = Plastic section modulus of a column, in.3 db = Average overall depth of beams framing into the connection, in. These requirements do not apply in any of the following cases, provided the columns conform to the requirements of Sect. 8.4: 8.6.a. Columns with Puc < 0.3Fyc Ag. 8.6.b. Columns in any story that has a ratio of design shear strength to design force 50 percent greater than the story above. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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8.6.c. Any column not included in the design to resist the required seismic shears, but included in the design to resist axial overturning forces. 8.7. Beam-to-Column Connection Restraint 8.7.a. Restrained Connection: 1. Column flanges at a beam-to-column connection require lateral support only at the level of the top flanges of the beams when a column is shown to remain elastic outside of the panel zone, using one of the following conditions: a. Ratios calculated using Eqs. 8-3 or 8-4 are greater than 1.25. b. Column remains elastic when loaded with Load Combination 3-7. 2. When a column cannot be shown to remain elastic outside of the panel zone, the following provisions apply: a. The column flanges shall be laterally supported at the levels of both top and bottom beam flanges. b. Each column flange lateral support shall be designed for a required strength equal to 2.0 percent of the nominal beam flange strength (Fy bf tf). c. Column flanges shall be laterally supported either directly, or indirectly, by means of the column web or beam flanges. 8.7.b. Unrestrained Connections: A column containing a beam-to-column connection with no lateral support transverse to the seismic frame at the connection shall be designed using the distance between adjacent lateral supports as the column height for buckling transverse to the seismic frame and conform to Sect. H of the Specification except that: 1. The required column strength shall be determined from the Load Combination 3-5 where E is the least of: a. The amplified earthquake force 0.4R Ă&#x2014; E (where the term 0.4R shall be equal to or greater than 1.0). b. 125 percent of the frame design strength based on either beam or panel zone design strengths. 2. The L / r for these columns shall not exceed 60. 3. The required column moment transverse to the seismic frame shall include that caused by the beam flange force specified in Sect. 8.7.a.2.b plus the added second order moment due to the resulting column displacement in this direction. 8.8. Lateral Support of Beams Both flanges of beams shall be laterally supported directly or indirectly. The unbraced length between lateral supports shall not exceed 2,500 ry / Fy. In addition, lateral supports shall be placed at concentrated loads where an analysis indicates a hinge will be formed during inelastic deformations of the SMF. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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REQUIREMENTS FOR CONCENTRICALLY BRACED (CBF) BUILDINGS
9.1. Scope Concentrically Braced Frames (CBF) are braced systems whose worklines essentially intersect at points. Minor eccentricities, where the worklines intersect within the width of the bracing members, are acceptable if accounted for in the design. CBF shall have a design strength as provided in the Specification to resist the Load Combinations 3-1 through 3-6 as modified by the following added provisions: 9.2. Bracing Members L 720 except as permit9.2.a. Slenderness: Bracing members shall have an ≤ r √ Fy ted in Sect. 9.5. 9.2.b. Compressive Design Strength: The design strength of a bracing member in axial compression shall not exceed 0.8φcPn. 9.2.c. Lateral Force Distribution: Along any line of bracing, braces shall be deployed in alternate directions such that, for either direction of force parallel to the bracing, at least 30 percent but no more than 70 percent of the total horizontal force shall be resisted by tension braces, unless the nominal strength, Pn, of each brace in compression is larger than the required strength, Pu, resulting from the application of the Load Combinations 3-7 or 3-8. A line of bracing, for the purpose of this provision, is defined as a single line or parallel lines whose plan offset is 10 percent or less of the building dimension perpendicular to the line of bracing. 9.2.d. Width-Thickness Ratios: Width-thickness ratios of stiffened and unstiffened compression elements in braces shall comply with Sect. B5 in the Specification. Braces shall be compact or non-compact, but not slender (i.e., λ < λr). Circular sections shall have an outside diameter to wall thickness ratio not exceeding 1,300 / Fy; rectangular tubes shall have a flat-width to wall thickness not exceeding 110 / √ Fy , unless the circular section or tube walls are stiffened. 9.2.e. Built-up Member Stitches: For all built-up braces, the first bolted or welded stitch on each side of the midlength of a built up member shall be designed to transmit a force equal to 50 percent of the nominal strength of one element to the adjacent element. Not less than two stitches shall be equally spaced about the member centerline. 9.3. Bracing Connections 9.3.a. Forces: The required strength of bracing joints (including beam-to-column joints if part of the bracing system) shall be the least of the following: 1. The design axial tension strength of the bracing member. 2. The force in the brace resulting from the Load Combinations 3-7 or 3-8. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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3. The maximum force, indicated by an analysis, that is transferred to the brace by the system. 9.3.b. Net Area: In bolted brace joints, the minimum ratio of effective net section area to gross section area shall be limited by: Ae 1.2αPu∗ ≥ Ag φtPn
(9-1)
where: Ae = Effective net area as defined in Equation B3-1 of the Specification. Pu∗ = Required strength on the brace as determined in Sect. 9.3.a. Pn = Nominal tension strength as specified in Chapter D of the Specification. φt = Special resistance factor for tension = 0.75. α = Fraction of the member force from Sect. 9.3.a that is transferred across a particular net section. 9.3.c. Gusset Plates: 1. Where analysis indicates that braces buckle in the plane of the gusset plates, the gusset and other parts of the connection shall have a design strength equal to or greater than the in-plane nominal bending strength of the brace. 2. Where the critical buckling strength is out-of-plane of the gusset plate, the brace shall terminate on the gusset a minimum of two times the gusset thickness from the theoretical line of bending which is unrestrained by the column or beam joints. The gusset plate shall have a required compressive strength to resist the compressive design strength of the brace member without local buckling of the gusset plate. For braces designed for axial load only, the bolts or welds shall be designed to transmit the brace forces along the centroids of the brace elements. 9.4. Special Bracing Configuration Requirements 9.4.a. V and Inverted V Type Bracing: 1. The design strength of the brace members shall be at least 1.5 times the required strength using Load Combinations 3-5 and 3-6. 2. The beam intersected by braces shall be continuous between columns. 3. A beam intersected by V braces shall be capable of supporting all tributary dead and live loads assuming the bracing is not present. 4. The top and bottom flanges of the beam at the point of intersection of V braces shall be designed to support a lateral force equal to 1.5 percent of the nominal beam flange strength (Fy bf tf). 9.4.b. K bracing, where permitted: 1. The design strength of K brace members shall be at least 1.5 times the required strength using Load Combinations 3-5 and 3-6. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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2. A column intersected by K braces shall be continuous between beams. 3. A column intersected by K braces shall be capable of supporting all dead and live loads assuming the bracing is not present. 4. Both flanges of the column at the point of intersection of K braces shall be designed to support a lateral force equal to 1.5 percent of the nominal column flange strength (Fy bf tf). 9.5. Low Buildings Braced frames not meeting the requirements of Sect. 9.2 through 9.4 shall only be used in buildings not over two stories and in roof structures if Load Combinations 3-7 and 3-8 are used for determining the required strength of the members and connections. 10.
REQUIREMENTS FOR ECCENTRICALLY BRACED FRAMES (EBF)
10.1. Scope Eccentrically braced frames shall be designed so that under inelastic earthquake deformations, yielding will occur in the links. The diagonal braces, the columns, and the beam segments outside of the links shall be designed to remain elastic under the maximum forces that will be generated by the fully yielded and strain hardened links, except where permitted by this section. 10.2. Links 10.2.a. Beams with links shall comply with the width-thickness ratios in Table 8-1. 10.2.b. The specified minimum yield stress of steel used for links shall not exceed Fy = 50 ksi. 10.2.c. The web of a link shall be single thickness without doubler plate reinforcement and without openings. 10.2.d. Except as limited by Sect. 10.2.f., the required shear strength of the link, Vu, shall not exceed the design shear strength of the link, φVn, where: φVn = Link design shear strength of the link = the lesser of φVp or 2φMp / e, kips. Vp = 0.6Fy (d − 2tf) tw, kips. φ = 0.9. e = link length, in. 10.2.e. If the required axial strength, Pu, in a link is equal to or less than 0.15Py, where Py = AgFy, the effect of axial force on the link design shear strength need not be considered. 10.2.f. If the required axial strength, Pu, in a link exceeds 0.15Py, the following additional limitations shall be required: 1. The link design shear strength shall be the lesser of φVpa or 2φMpa / e, where: Vpa = Vp √ 1 − (Pu / Py)2 AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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PART I—LOAD AND RESISTANCE FACTOR DESIGN (LRFD)
Mpa = 1.18Mp[1 − (Pu / Py )] φ = 0.9 2. The length of the link shall not exceed: [1.15 − 0.5ρ(Aw / Ag)]1.6Mp / Vp for ρ(Aw / Ag) ≥ 0.3 and 1.6Mp / Vp for ρ(Aw / Ag) < 0.3, where: Aw = (d − 2tf) tw ρ = Pu / Vu 10.2.g. The link rotation angle is the plastic angle between the link and the beam outside of the link when the total story drift is 0.4R times the drift determined using the specified base shear V. The term 0.4R shall be equal to or greater than 1.0. Except as noted in Sect. 10.4.d, the link rotation angle shall not exceed the following values: 1. 0.09 radians for links of length 1.6Mp / Vp or less. 2. 0.03 radians for links of length 2.6Mp / Vp or greater. 3. Linear interpolation shall be used for links of length between 1.6Mp / Vp and 2.6Mp / Vp. 10.2.h. Alternatively, the top story of an EBF building having over five stories shall be a CBF. 10.3. Link Stiffeners 10.3.a. Full depth web stiffeners shall be provided on both sides of the link web at the diagonal brace ends of the link. These stiffeners shall have a combined width not less than (bf − 2tw) and a thickness not less than 0.75tw or 3⁄8-in., whichever is larger, where bf and tw are the link flange width and link web thickness, respectively. 10.3.b. Links shall be provided with intermediate web stiffeners as follows: 1. Links of lengths 1.6Mp / Vp or less shall be provided with intermediate web stiffeners spaced at intervals not exceeding (30tw − d / 5) for a link rotation angle of 0.09 radians or (52tw − d / 5) for link rotation angles of 0.03 radians or less. Linear interpolation shall be used for values between 0.03 and 0.09 radians. 2. Links of length greater than 2.6Mp / Vp and less than 5Mp / Vp shall be provided with intermediate web stiffeners placed at a distance of 1.5bf from each end of the link. 3. Links of length between 1.6Mp / Vp and 2.6Mp / Vp shall be provided with intermediate web stiffeners meeting the requirements of 1 and 2 above. 4. No intermediate web stiffeners are required in links of lengths greater than 5Mp / Vp. 5. Intermediate link web stiffeners shall be full depth. For links less than 25 inches in depth, stiffeners are required on only one side of the link web. The thickness of one-sided stiffeners shall not be less than tw or AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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3â &#x201E; -in., whichever is larger, and the width shall be not less than 8 (bf / 2) â&#x2C6;&#x2019; tw. For links 25 inches in depth or greater, similar intermediate stiffeners are required on both sides of the web.
10.3.c. Fillet welds connecting link stiffener to the link web shall have a design strength adequate to resist a force of AstFy, in which Ast = area of the stiffener. The design strength of fillet welds fastening the stiffener to the flanges shall be adequate to resist a force of AstFy / 4. 10.4. Link-to-Column Connections Where a link is connected to a column, the following additional requirements shall be met: 10.4.a. The length of links connected to columns shall not exceed 1.6Mp / Vp unless it is demonstrated that the link-to-column connection is adequate to develop the required inelastic rotation of the link. 10.4.b. The link flanges shall have complete penetration welded joints to the column. The joint of the link web to the column shall be welded. The required strength of the welded joint shall be at least the nominal axial, shear, and flexural strengths of the link web. 10.4.c. The need for continuity plates shall be determined according to the requirements of Sect. 8.5. 10.4.d. Where the link is connected to the column web, the link flanges shall have complete penetration welded joints to plates and the web joint shall be welded. The required strength of the link web shall be at least the nominal axial, shear, and flexural strength of the link web. The link rotation angle shall not exceed 0.015 radians for any link length. 10.5. Lateral Support of Link Lateral supports shall be provided at both the top and bottom flanges of link at the ends of the link. End lateral supports of links shall have a design strength of 6 percent of the link flange nominal strength computed as Fy bf tf. 10.6. Diagonal Brace and Beam Outside of Link 10.6.a. The required combined axial and moment strength of the diagonal brace shall be the axial forces and moments generated by 1.25 times the nominal shear strength of the link as defined in Sect. 10.2. The design strengths of the diagonal brace, as determined by Sect. H (including Appendix H) of the Specification, shall exceed the required strengths as defined above. 10.6.b. The required strength of the beam outside of the link shall be the forces generated by at least 1.25 times the nominal shear strength of the link and shall be provided with lateral support to maintain the stability of the beam. Lateral supports shall be provided at both top and bottom flanges of the beam and each shall have a design strength to resist at least 1.5 percent of the beam flange nominal strength computed as Fy bf tf. 10.6.c. At the connection between the diagonal brace and the beam at the link end of the brace, the intersection of the brace and beam centerlines shall AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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be at the end of the link or in the link. The beam shall not be spliced within or adjacent to the connection between the beam and the brace. 10.6.d. The required strength of the diagonal brace-to-beam connection at the link end of the brace shall be at least the nominal strength of the brace. No part of this connection shall extend over the link length. If the brace resists a portion of the link end moment, the connection shall be designed as Type FR (Fully Restrained). 10.6.e. The width-thickness ratio of brace shall satisfy λp of Table B5.1 of the Specification. 10.7. Beam-to-Column Connections Beam-to-column connections away from links are permitted to be designed as a pin in the plane of the web. The connection shall have a design strength to resist torsion about the longitudinal axis of the beam based on two equal and opposite forces of at least 1.5 percent of the beam flange nominal strength computed as Fy bf tf acting laterally on the beam flanges. 10.8. Required Column Strength The required strength of columns shall be determined by Load Combinations 3-5 and 3-6 except that the moments and axial loads introduced into the column at the connection of a link or brace shall not be less than those generated by 1.25 times the nominal strength of the link. 11.
QUALITY ASSURANCE The general requirements and responsibilities for performance of a quality assurance plan shall be in accordance with the requirements of the regulatory agency and specifications by the design engineer. The special inspections and special tests needed to establish that the construction is in conformance with these provisions shall be included in a quality assurance plan. The minimum special inspection and testing contained in the quality assurance plan beyond that required by the Specification shall be as follows: Groove welded joints subjected to net tensile forces which are part of the seismic force resisting systems of Sects. 8, 9, and 10 shall be tested 100 percent either by ultrasonic testing or by other approved equivalent methods conforming to AWS D1.1. Exception: The nondestructive testing rate for an individual welder shall be reduced to 25 percent with the concurrence of the person responsible for structural design, provided the reject rate is demonstrated to be 5 percent or less of the welds tested for the welder.
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Part II—Allowable Stress Design (ASD) Alternative As an alternative to the LRFD seismic design procedures for structural steel design given in PART I, the design procedures in the Specification for Structural Steel Buildings—Allowable Stress Design and Plastic Design, AISC 1989 are permitted as modified by PART II of these provisions. When using ASD, the provisions of PART I of these seismic provisions shall apply except the following sections shall be substituted for, or added to, the appropriate sections as indicated: 1.
SCOPE
Revise the first paragraph of PART I, Sect. 1 to read as follows: These special requirements are to be applied in conjunction with the AISC Specification for Structural Steel Buildings—Allowable Stress Design and Plastic Design hereinafter referred to as Specification. They are intended for the design and construction of structural steel members and connections in buildings for which the design forces resulting from earthquake motions have been determined on the basis of energy dissipation in the nonlinear range of response. 3.
LOADS, LOAD COMBINATIONS AND NOMINAL STRENGTHS
Substitute the following for Section 3.2 in PART I: 3.2. Nominal Strengths The nominal strengths of members shall be determined as follows: 3.2.a. Replace Sect. A5.2 of the Specification to read: “The nominal strength of structural steel members for resisting seismic forces acting alone or in combination with dead and live loads shall be determined by multiplying 1.7 times the allowable stresses in Sect. D, E, F, G, J, and K.” 3.2.b. Amend the first paragraph of Sect. N1 of the Specification by deleting “or earthquake” and adding: “The nominal strength of members shall be determined by the requirements contained herein. Except as modified by these rules, all pertinent provisions of Chapters A through M shall govern.” 3.2.c. In Sect H1 of the Specification the definition of Fe ′ shall read as follows: Fe ′ =
π2E (Klb / rb)2
where: lb = the actual length in the plane of bending. rb = the corresponding radius of gyration. K = the effective length factor in the plane of bending. Add the following section to PART I: 3.3. Design Strengths 3.3.a. The design strengths of structural steel members and connections subjected to seismic forces in combination with other prescribed loads shall AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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be determined by converting allowable stresses into nominal strengths and multiplying such nominal strengths by the resistance factors herein. 3.3.b. Resistance factors, φ, for use in Part II shall be as follows: Flexure
φb = 0.90
Compression and axially loaded composite members
φc = 0.85
Eyebars and pin connected members: Shear of the effective area Tension on net effective area Bearing on the project area of pin
φsf = 0.75 φt = 0.75 φt = 1.0
Tension members: Yielding on gross section Fracture in the net section
φt = 0.90 φt = 0.75
Shear
φv = 0.90
Connections: Base plates that develop the strength of the members or structural systems Welded connections that do not develop the strength of the member or structural system, including connection of base plates and anchor bolts Partial Penetration welds in columns when subjected to tension stresses High strength bolts (A325 and A490) and rivets: Tensile strength Shear strength in bearing-type joints Slip-critical joints A307 bolts: Tensile strength Shear strength in bearing-type joints
φ = 0.90 φ = 0.67 φ = 0.80 φ = 0.75 φ = 0.65 φ = 1.0 φ = 0.75 φ = 0.60
Substitute the following for Section 7 in PART I in its entirety: 7.
REQUIREMENTS FOR ORDINARY MOMENT FRAMES (OMF)
7.1. Scope Ordinary Moment Frames (OMF) shall have a design strength as provided in the Specification to resist the Load Combinations 3-5 and 3-6 as modified by the following added provisions: 7.2. Joint Requirements All beam-to-column and column to beam connections in OMF which resist seismic forces shall meet one of the following requirements: 7.2.a. Type 1 connections conforming with Sect. 8.2, except that the required flexural strength, Mu, of a column-to-beam joint are not required to exceed that required to develop the nominal plastic flexural strength of the connection. 7.2.b. Type 1 connections capable of inelastic deformation and the design AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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strengths of the connections meeting the requirements of Sect. 7.1 using the Load Combinations 3-7 and 3-8. 7.2.c. Either Type 1 or Type 3 connections are permitted provided: 1. The design strengths of the members and connections meet the requirements of Sect. 7.1. 2. The connections have been demonstrated by cyclic tests to have adequate rotation capacity at a story drift calculated at a horizontal load of 0.4R × E (where the term 0.4R is equal to or greater than 1.0). 3. The additional drift due to Type 3 connections shall be considered in design. Type 1 and Type 3 connections are described in detail in Sect. A2 of the Specification. Substitute the following in Sections 10.6.a and 10.6.d in PART I: 10.6.a. Delete reference to Appendix H. 10.6.d. The last sentence shall read: “If the brace resists a portion of the link end moment as described above, the connection shall be designed as a Type 1 connection.”
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Commentary on the Seismic Provisions for Structural Steel Buildings June 15, 1992
Part Iâ&#x20AC;&#x201D;LRFD Provisions 1.
SCOPE Load and Resistance Factor Design (LRFD) is an improved approach to the design of structural steel for buildings. The method involves explicit consideration of limit states, multiple load and resistance factors, and implicit probabilistic determination of reliability. The designation LRFD reflects the concept of factoring both loads and resistance. The LRFD method was devised to offer the designer greater flexibility, more rationality and possible overall economy. The First Edition of the LRFD Specification was published and distributed in 1986.1 It did not contain the special requirements necessary in the design and construction of steel buildings which are required to respond to high earthquake input by deformations into the nonlinear range. The seismic design forces specified in the building codes have been set with consideration given to the energy dissipation generated during the non-linear response. The provisions contained in this document are to be used in conjunction with the AISC LRFD Specification in the design of buildings in the areas of moderate and high seismicity. The load provisions have been modified from those contained in the Specification to be consistent with the load provisions contained in the soon to be published BOCA and SBCCI building codes and the ASCE 7-93, Minimum Design Loads for Buildings and Other Structures.2 All these new seismic load provisions are modeled on the the 1991 NEHRP3 earthquake provisions.
2.
SEISMIC PERFORMANCE CATEGORIES Buildings are classified into three types depending on the occupancy and use of each as related to the special hazards resulting from earthquake environment. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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The Seismic Hazard Exposure Groups listed in Table 2-1 are defined in detail, with examples of buildings in each type, in ASCE 7-93. The Seismic Performance Category to be used in the design of a specific building is defined by the seismic coefficient representing the peak velocity-related acceleration of the building site, Av, and the Seismic Hazard Exposure Group related to the occupancy and use of the building. The five categories, A through E, given in Table 2-2 specify design and detail requirements that would be required for the seismic design of the building. These categories establish the level of requirements to be used in items such as detailing limitations, quality assurance, method of analyses, orthogonal effects, and change of building use. The general requirements for each of the categories are given in ASCE 7-93. The differences related specifically to structural steel design are repeated in this Specification. 3.
LOADS AND LOAD COMBINATIONS The most frequently used load factors and load combinations given in Sect. A4.1 of the Specification are repeated in this Section to reduce the amount of cross-referencing to other documents. They have been modified to be consistent with the anticipated ASCE 7-93. The most notable modification is the reduction of the load factor on E to 1.0. This results from the limit states load model used in ASCE 7-93. For design of structures subjected to impact loads, see the Specification. The earthquake load and load effects E in ASCE 7-93 are composed of two parts. E is the sum of the seismic horizontal load effects and one half of Av times the dead load effects. The second part adds an effect simulating vertical accelerations concurrent to the usual horizontal earthquake effects. The load factors and load combinations reflect the fact that when several loads act in combination with the dead load, e.g., dead plus live plus earthquake loads, only one of these takes on its maximum lifetime value, while the other load is at its “arbitrary point-in-time value,” at a value which can be expected to be on the structure at any time. The most critical effect may occur when one or more load types are not acting. The basic requirements for dual systems are given in the Glossary to clarify the use of the EBF in a dual system and to indicate that steel moment frames can also be used as part of a dual system with concrete shear walls. An amplification factor to earthquake load E of 0.4R is prescribed for limited use in this set of provisions. It is used as an amplification of the deflections determined using the earthquake forces specified in ASCE 7-93. It was derived by assuming that deflections due to large earthquake response would be the same regardless of the reductions in applied forces due to the inelastic response of the type of lateral force resisting system.56 The amount of this amplification was assumed to be two times the deflections generated by forces specified for a buildings with R = 5. This amplification factor is thus 2R / 5 or 0.4R. However, with R = 2.5 or less it is felt that the amplification factor should not be less than 1.0. The load combinations to be used with the amplification factor are given by formulas 3-7 and 3-8. Specific values of R are not needed for determination of the amplified load because R is cancelled out when substituted in the formula for the horizontal seismic base shear, V. The added complication that would be AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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required to consider orthogonal effects with the amplified force is not deemed to be necessary. The ASCE 7-93 provisions are detailed earthquake load provisions in which two methods of analysis are provided. The first is frequently referred to as the “Static Force Procedure” or “Equivalent Lateral Force Procedure.” The second method is the “Modal Analysis Procedure.” In both methods a linearly elastic model is assumed. Other “Dynamic Analysis Procedures” are permitted both with linearly elastic or non-linear models as long as the internal forces and deformations in the members are determined using a model consistent with the procedure adopted. Guidelines for use of these other methods of analyses are provided in the Commentary to ASCE 7-93. These earthquake provisions refer to the load provisions of ASCE 7-93. By changing the load combination portion of Section 3, these provisions can be made compatible with other sets of load provisions.4 For instance, the following changes can be made to the provisions in Section 3 to make them compatible with the following document: (Sn is used in this Commentary for snow loads to distinguish them from site effects that use the symbol S). 1991 UNIFORM BUILDING CODE:5 (SEAOC seismic provisions are similar)6 The required strength on the structure and its elements must be determined from the appropriate critical combination of factored loads. The most critical effect may occur when one or more loads are not acting. The following load combinations and corresponding load factors shall be investigated: 1.4D
(3-1)
1.2D + 1.6L + 0.5(Lr or S or R′)
(3-2)
1.2D + 1.6(Lr or S or R′) + (0.5L or 0.8W)
(3-3)
1.2D + 1.3W + 0.5L + 0.5(Lr or S or R′)
(3-4)
1.2D + 1.5E + 0.5L + 0.2S
(3-5)
0.9D − (1.3W or 1.5E)
(3-6)
Exception: The load factor on L in Load Combinations 3-3, 3-4, and 3-5 shall equal 1.0 for garages, areas occupied as places of public assembly, and all areas where the live load is greater than 100 psf. Other special load combinations are included with specific design requirements throughout these provisions. Where required by these provisions, an amplification factor is applied on the earthquake load E = 3⁄8Rw, where Rw is a response factor similar to the factor R except used to reduce the earthquake load to a working stress design level. Earthquake loads are similar to those found in ASCE 7-93 except for the Rw factor. Earthquake loads are defined in detail in Section 2334 of 1991 UBC. The revised load combinations are: AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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1.2D + (3Rw / 8)E + 0.5L + 0.2S
(3-7)
0.9D − (3Rw / 8)E
(3-8)
Exception: The load factor on L in Load Combination 3-7 shall equal 1.0 for garages, areas occupied as places of public assembly, and all areas where the live load is greater than 100 psf. The amplification factor was derived by using the similar assumptions that were used in deriving the factor for ASCE 7-93. The same type of building with R = 5 in ASCE 7-93 has a Structure System Coefficient Rw = 8 in 1991 UBC. The deflection determined by this Rw was used as the value to be amplified by 3. Thus (3Rw / 8)E. Where the use of the amplification factor to load E is required, orthogonal effects need not be included. The 1991 UBC outlines in detail many of the requirements for “Dynamic Lateral Force Procedure.” The following is a summary of these requirements: The ground motion may be defined in one of five ways: 1. The plot of a normalized response spectra may be used. 2. A site specific response spectra based on geologic, tectonic seismologic, and soil characteristics of the site may be used. As per SEAOC the damping ratio shall be 5 percent unless another value is shown to be consistent with the structural behavior of the building. 3. Site specific time histories are to be representative of actual earthquake motions. Spectra developed from these time histories would follow item (2) above. 4. Site specific response spectra and time histories developed for sites with a profile having more than 40 feet of soft clay per SEAOC shall be based on ground motion having a 10 percent probability of exceedance in 50 years; the effects of lengthening of the structural period on response amplification due to soil-structure resonance shall be included; and the design base shear shall be determined by dividing by a factor not greater than Rw for the structure. 5. A two-thirds factor shall be used on horizontal motions to determine the vertical component of ground motion unless specifically determined otherwise for the site. The mathematical model shall represent the actual structure adequately for the calculation of all the significant features of the dynamic response. Three dimensional models shall be used for highly irregular plan configurations if a rigid or semi-rigid diaphragm is used. A response spectrum analysis shall be an elastic dynamic analysis of all the significant peak modal responses combined in a statistical manner to obtain an approximate total structural response. When the base shear is less than that determined from the Static Lateral Force Procedure, it shall be increased to 100 percent of the static base shear for irregular structures, shall be taken as 90 percent of the static base shear for regular structures where the fundamental period is determined using the structural characteristics of the building system, AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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and shall be set at 80 percent for regular structures. Accidental torsion shall be accounted for by appropriate adjustments in the model. Where a dual system is used, the combined system shall be accounted for in the modelling; the backup Special Moment Frame (SMF) shall be capable of resisting 25 percent of the base shear used for the design of the total system. The analysis of the backup SMF may either use the Static of Dynamic Lateral Force Procedures. A time history analysis shall be an elastic or inelastic dynamic analysis of a model of a structure subjected to specified time history of ground motion. The time dependent dynamic response of the structure to these motions is obtained through numerical integration of its equations of motion. These analyses shall be based on established principles of mechanics. Scaling of base shear determined by a response spectrum analysis results in making the Load Combinations 3-1 through 3-6 as well as 3-7 and 3-8 applicable to this method of analysis in the 1991 UBC. No scaling effect is specified for the results of time history dynamic analysis (either elastic or inelastic). In this case, it is necessary to define the specified time histories which will result in the structure responding to the limit of essentially elastic response. This would be the level to determine the required resistance of the system. In order to determine the deformations corresponding to the specified drift limits, the force level shall be divided by a factor of 1.5. 4.
STORY DRIFT Deflection limits are commonly used in design to assure the serviceability of the structure. These serviceability limit states are variable, since they depend upon the structural usage and contents. The Specification does not specify these serviceability limits, since they are regarded as a matter of engineering judgment, rather than general design limits.54 Like deflection limits, drift limits for both wind and seismic design are excluded from these Seismic Provisions. Research has shown that seismic drift control provides a function beyond assuring the serviceability of the structure. The added strength and stiffness which drift limits often provide in moment frames improves the performance of structures during earthquakes. Model codes, load standards, and resource documents contain specific seismic drift limits but there are major differences among them. There is neither uniform agreement regarding appropriate code specified drift limits nor how they should be applied. Further it is difficult to estimate the actual story drift of moment frames with panel zone yielding. Nevertheless, drift control is important to serviceability and stability of the structure. It is recommended the designer review drift limits in the appropriate code and use those applicable for the serviceability and stability of the structure under consideration. The story drift limitations of ASCE 7-93 are applied to an amplified story drift that estimates the story drift that would occur during a large earthquake. The story drift is defined as the difference of deflection between the top and bottom of the story under consideration. For determining the story drift the deflection determined using the earthquake forces E is amplified by a deflection amplification factor, Cd, which is dependent on the type of building system. The story drifts when determined by an elastic analysis, including the P-â&#x2C6;&#x2020; effect when AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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TABLE C-4.1 Tentative Allowable Story Drift Seismic Hazard Exposure Group Building
I
II
III
Single story buildings without equipment attached to the structural resisting system and with interior walls, partitions, ceilings, and exterior wall system that have been designed to accommodate the story drifts.
No limit
0.020hsx
0.015hsx
Buildings with 4 stories or less with interior walls, partitions ceilings, and exterior wall system that have been designed to accommodate the story drifts.
0.025hsx
0.020hsx
0.015hsx
All other buildings.
0.020hsx
0.015hsx
0.010hsx
Where hsx is the story height of the story drift calculated.
applicable, have limits depending on the Seismic Hazard Exposure Group of the building as shown in Table C-4.1. In calculating the elastic drift, the forces may be based on the fundamental period of the building without the arbitrary limit specified for determining the seismic design forces in the framing members. ASCE 7-93 does not prescribe explicit requirements for building separations. An admonition is included, however, that all portions of the building shall be designed and constructed as an integral unit in resisting seismic forces unless separated structurally by a sufficient distance to avoid damaging contact between components under amplified deformations. The latter are determined by multiplying the elastic deflection by a deflection amplification factor, Cd, which is based on the type and materials of the seismic resisting system. If the effects of hammering between segments can be shown not to be detrimental, separations could be reduced. 1991 UBC Requirements: In order to comply with the 1991 UBC requirements, the story drift shall be calculated including the translational and torsional deflections resulting from the application of unfactored lateral forces. Story drift is defined as the displacement of one level relative to the level above or below. The calculated story drift shall not exceed 0.04 / Rw nor 0.005 times the story height for structures with fundamental periods of less than 0.7 seconds and shall not exceed 0.03 / Rw nor 0.004 times the story height for structures with fundamental periods of 0.7 seconds or greater. For the purpose of this limit the fundamental period is the same as that used for determining the base shear. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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For calculating the drift, the lateral forces may be calculated using a base shear V defined as: V=
ZIC W, in which Rw
Z = The seismic zone coefficient. I = An importance factor. Rw = A numerical coefficient related to the type of construction. C=
1.25S , in which 2 T ⁄3
S = Site coefficient. T = Fundamental period of vibration, which may be determined using the structural properties and deformational characteristics of the resisting elements of the lateral force resisting framing. Method A of determining T need not be applied for drift determination. The lower bound of 0.075 on the ratio C / Rw may also be neglected. W = Dead load used to calculate seismic loads. The story drift limits need not be applied if it is demonstrated that greater drift can be tolerated without affecting life safety by damage to either structural and non-structural elements. There are no drift limits on single story steel framed structures with low occupancies. This would generally apply to buildings such as warehouses, parking garages, aircraft hangers, factories, workshops and agricultural buildings. These buildings are not allowed to have brittle finishes and are not allowed to have equipment attached to the structural frame unless the finish or equipment attachment is detailed to accommodate the additional drift. 5.
MATERIAL SPECIFICATIONS The list of structural steels for use in designing to earthquake motion has been chosen with consideration given to the inelastic properties of the steels and their weldability. In general, the steels selected possess the following characteristics: • Ratio of tensile strength to yield strength between 1.2 to 1.8. • Pronounced stress-strain plateau at yield strength. • Large inelastic strain capability. • Tension elongation of 20 percent or greater in a 2-in. gage length. • Good weldability for inelastic behavior. Other steels including those with a specified yield point greater than 50 ksi should not be used without demonstrating that equivalent inelastic behavior can be attained.
6.
COLUMN REQUIREMENTS
6.1. Column Strength During the maximum probable earthquake expected at any site, axial forces AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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calculated using the specified design earthquake may be exceeded. This is a result of the reduction in lateral force for use in analysis of an elastic model of the structure, the underestimation of the overturning forces in this analysis, and the concurrent vertical accelerations which are not explicitly specified as a required design load. The amplifications required in this section provide an approximation of these actions by providing a limit to the required axial force. The two special Load Combinations 6-1 and 6-2 account for these effects; one as a minimum required column compressive required strength and the other on the minimum required tensile strength. They are to be applied without consideration of any concurrent flexure on the members. The exceptions provided for these limits are self limiting conditions stating that the required axial strengths need not exceed the limits based on the design strength of the overall system to transfer axial loads to the column. For instance, if pile foundations are used, the design strength of the piles in tension may be much larger than the required strength because the size of the foundation may depend on the required strength in compression. 6.2. Column Splices Column splices are required to have design strengths adequate to join column elements together not only to resist the axial, flexural, and shear forces required at the splice location by the usual load combinations 3-1 through 3-6 but also the forces specified in 6.1. Butt weld splices in columns where it is anticipated that potential dynamic loading consists only of wind or earthquake forces are not required by these specifications to provide the transition of thicknesses given in Section 9.20 of AWS D1.1.7 If other types of frequent, high cycle dynamic loadings are also present, the transition requirements should be met. Partial penetration welds in thick members, such as occur in column flange splices, are very brittle under tensile loading, showing virtually no ductility.8â&#x20AC;&#x201C;9 Recognizing this behavior in seismic design, the location of column splices is moved away from the beam-to-column connection to reduce bending and a 50 percent increase is stipulated in required strength of the splice. The possibility for developing tensile stresses in such welds during a maximum probable seismic event should be considered. If there is probability of such a condition developing, the use of splice plates welded to the lower part of the column and bolted to the upper part is suggested. If for the noted adverse condition, the suggested detail is not practical, the possibility of fracture in partial penetration welded joints should be recognized, and some restraint from uncontrolled relative movement at the splice be provided. This can be achieved, for example, by having wide splice plates on both sides of the column web to maintain alignment. Shake table experiments have shown that if some columns, unattached at the base, reseat themselves after lifting, the performance of a steel frame remains tolerable.10 These provisions apply for common frame configurations. The designer should review the conditions found in columns in tall stories, large changes in column sizes at the splice, or where the possibility of a single curvature exists on a AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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column over multiple stories to determine if special design strength or special detailing is necessary at the splice. 7.
REQUIREMENTS FOR ORDINARY MOMENT FRAMES (OMF)
7.1. Scope Ordinary moment frames of structural steel are moment frames which do not meet the requirements for special design and detailing contained in Section 8. OMF of structural steel do exist and are being built in all areas of seismic activity. Experience has shown that in most instances the buildings of this type have responded without significant structural damage. In recent years advances in analytical procedures have minimized the natural margins of safety normally found in buildings that were designed by approximate methods. Thus it is prudent to require that the design of the beam-to-column connection be adequate to develop the strength of the members framing into the connection as is specified in Sect. 8.2 unless the connection has a design strength significantly larger than the required strengths required by Load Combinations 3-5 and 3-6. Thus unless the connection can develop the full strength of members framing into it, the Load Combinations 3-7 and 3-8 should be used to provide the required strength on the connection. 7.2. Joint Requirements Although for OMF it is not required to meet most of the special detailing requirements given in Sect. 8, consideration should be given to using as many of the requirements as practical, particularly in those locations where good engineering judgment would suggest that the use of the special detailing requirements would provide improved system and member ductility and stability. The provision requiring a demonstration of rotation capacity is included to permit the use of connections not permitted under the provisions of Sect. 8, such as top and bottom angle joints, in areas where the added drift is acceptable. 8.
REQUIREMENTS FOR SPECIAL MOMENT FRAMES (SMF)
8.1. Scope The requirements in this Section are for those buildings whose lateral force resisting systems are moment frames in the higher seismic zones. The special provisions, when reasonably applied, provide SMF with reliable ductile systems. Non-ductile behavior is inhibited so that nonlinear response to large earthquake motions can occur in components of the frames having a capability of ductile behavior. The concepts are not new but the provisions are supported by tests and analyses.11â&#x20AC;&#x201C;17 SMF systems when properly designed have, in general, resulted in reliable ductile structural systems that respond well to high earthquake motions for both low and high rise buildings. Inelastic energy absorption through ductile behavior of members of SMF can occur at three places usually adjacent to the beam-to-column connection. Flexural hinges can form in the beams and columns and shear yielding can occur in the area of the panel zone. Within limits and specific restraints, inelastic yielding is permitted in each or in combinations of these three areas. The primary concern when designing the frame for inelastic behavior is to prevent brittle AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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fracture and severe buckling in and adjacent to the zone of inelasticity. The final selection of the appropriate zones of inelasticity is left to the design engineer. Different problems are presented to the design engineer depending on which of the three areas is chosen to have the lowest inelastic threshold. Yielding in columns is permitted but is considered by many design engineers to be the least desirable. Special limitations are provided for this type of yielding by the provisions in Sect. 8.6. and the bracing required in Sect. 8.7. If the first inelastic mode is chosen to be shear yielding of the panel zone, the limitations of Sect. 8.3 would be required. This usually results in the flexibility of the panel zone being a significant contributor to the total story drift and consideration of this flexibility should be included in analyses.18 If the designer chooses to avoid inelastic behavior at the above two locations, the yield hinge will form in the beam. This requires the critical design items to be the beam-to-column connection and the beam stability. 8.2. Beam-to-Column Joints The special limitations provided for these joints are intended to assure that inelastic hinging that may occur in the connection during the response to high seismic activity will not take place at the joinery but in one of the two adjoining locations, namely in the beam or in the panel zone.19–24 Some of the more common beam-to-column connections are illustrated in Fig. C-8.1. Beam-tocolumn connections are not only designed to meet the loads prescribed by the Load Combinations 3-1 through 3-6 but also designed to resist the requirements based on the nominal strengths of the members actually used in the framing system. Frequently the frame member sizes may be sized to limit drift or to meet requirements of load combinations other than those containing seismic loads. Thus to provide frames having the capability of deforming into the nonlinear range without having a connection failure, the required strength on the connection is most frequently based on the design strength of the members actually used. An exception is provided for joints that are not designed to contribute to the lateral force resisting system. In order to demonstrate that the joint will be capable of undergoing large deformation, the elastic or inelastic joint rotations that would be induced by deforming the frame into an amplified displacement of 0.4R times that under Load Combinations 3-5 and 3-6 are required. The term 0.4R should not be less than 1.0. If the “non-moment resisting” web connection were to be a shear tab joined to the column flange by welding and bolted to the beam web, the connection should be proportioned to either yield in the tab or by use of horizontally slotted holes for the bolts. Fracture should not occur in the welded joint to the column. (See Fig. C-8.2.) The required shear strength, Vu, of the beam-to-column joint is defined as the summation of the factored gravity loads and the shear resulting from the required moments on the two ends of the beam. The easy method is to assume that Mp occurs at each end of the beam. However, when Load Combination 3-7 is used in which one end only of the beam reaches Mp, or the panel zone nominal shear reaches Vn as defined in Sect. 8.2.a, the shear resulting from hinging at both ends of the beam need not be used. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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a
b
c
d
e
f
Fig. C-8.1. Beam-to-column connections.
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When the required flexural strength of the joint is Mp of the beam, the type of joint is prescribed to be one of three types: First is the joint where both flanges and web are fully welded to develop their portions of the moment and shear strength of the beam. (See Fig. C-8.3.) Second is the joint of those beams which have a ratio of the flexural nominal strength of the flanges only to the flexural nominal strength of the full section of at least 70 percent. For this connection, the flanges are joined with complete penetration welded joints whereas the web would be designed to carry the
ROTATION BY NON LINEAR BENDING OF JOINT MEMBERS
SHORT SLOTTED HOLES
ROTATION BY BOLT SLIP
Fig. C-8.2. Simple connections.
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CONTINUITY PLATE, TOP & BOTTOM ERECTION BOLTS SHEAR PLATE
TYP.
FULL PENETRATION TOP & BOTTOM FLANGE (a)
ERECTION BOLT CONTINUITY PLATE, TOP & BOTTOM
SHEAR PLATE ERECTION BOLT
TYP.
FULL PENETRATION TOP & BOTTOM FLANGE (b)
Fig. C-8.3. Beam-column joint.
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required shear by either welds or by slip-critical high strength bolts. (See Fig. C-8.4.) Third is the joint of beams not meeting the 70 percent criteria. This would be similar to the second joint except that the beam web is required to be welded directly or through shear tabs even though the web is bolted to the shear tab. The welds are required to have a nominal moment strength at least equal to 20 percent of the nominal moment strength of the full beam web. (See Fig. C-8.5.) Other joints than the ones specified are permitted to be used but the adequacy of the joint requires substantiation either by tests or by calculations. Where the adequacy is demonstrated by calculations, additional conservatism is provided by requiring the joint to develop at least 125 percent of the nominal moment and shear strength of the beam. 8.3. Panel Zone of Beam-to-Column Connection (Beam web parallel to column web) During recent years many cyclic tests have shown the ductility of shear yielding in panel zones through many cycles of inelastic distortions.17,25–28 Thus the panel zone does not need to develop beam hinging and a method of determining the nominal shear strength of the panel zone is needed. The usual assumption of Von Mises shear limit of 0.577Fy dt did not predict the actual behavior of many of the tests. Many panel zone and beam tests have shown that strain hardening and other phenomena have enabled shear strengths in excess of 1.0Fy dt to be developed. Eq. 8-1 reflects the significant strength provided by thick column flanges. In calculating the required panel zone shear strength the UBC 1991 magnifies the specified load by a factor of 1.85. For the LRFD specification, the typical Load Combinations 3-5 and 3-6 are used and the nominal web shear strength is defined as 0.6Fy dt, rather than 0.55Fy dt which had been used in plastic design and in some previous references. In order to provide the same level of safety as determined by tests and as contained in the UBC 1991, a lower resistance factor φv = 0.75 was selected. An upper limit is placed on the required shear strength of the panel zone of 0.9 times the summation of the beam design plastic moments φb Mp framing into the connection. In order to minimize the chances of shear buckling during inelastic deformations of the panel zone, the thickness of the panel zone material is limited to not less than 1⁄90 of the sum of its depth and width. The thickness of any doubler plate used is assumed ineffective in inhibiting buckling unless it is connected to the panel zone plate in such a manner, such as plug welds, to prevent local buckling of the plate. (See Fig. C-8.6.) Whenever doubler plates are used (i.e., increased strength, compliance with Eq. 8-2, or to reduce panel zone deformations), the plates are required to be close to the column web. The doubler plates are to have at least minimum fillet welds across the top and bottom and to have either butt or fillet welds to the column flanges. These details are provided to closely simulate the joints that have been found to perform satisfactorily in the cyclic tests that have been performed. Fillet AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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CONTINUITY PLATE, TOP & BOTTOM
SHEAR PLATE
TYP.
FULL PENETRATION TOP & BOTTOM FLANGE (a)
CONTINUITY PLATE, TOP & BOTTOM
SHEAR PLATE
TYP.
FULL PENETRATION TOP & BOTTOM FLANGE (b)
Fig. C-8.4. Beam-column joint, bf tf (db − tf)Fy ≥ 0.7Fy Zx. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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CONTINUITY PLATE, TOP & BOTTOM
SHEAR PLATE
TYP.
FULL PENETRATION TOP & BOTTOM FLANGE (a)
CONTINUITY PLATE, TOP & BOTTOM
SHEAR PLATE
TYP.
FULL PENETRATION TOP & BOTTOM FLANGE (b)
Fig. C-8.5. Beam-column joint, bf tf (db − tf)Fy < 0.7Fy Zx. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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welding is encouraged to assist in minimizing the built-in weld stresses and the cost of welding. Doubler plates may be designed to extend between continuity plates which are welded directly to the column web or they may extend above and below the continuity plates which are welded to the doubler plate. For the latter case, the horizontal welds at the top and bottom of the doubler plate should be sized to transfer all loads imposed by the design system. In particular, the welds to the column web should be designed to transfer load from the doubler plate to the column web for their portion of load from the continuity plate. For the fillet or butt welds of the doubler plate to the column flanges, the following items should be considered: • The vertical shear and bending loads of beams or girders framing perpendicular to the column web and supported by the doubler plate. • The compression or tension load delivered to the column web and doubler plate by the flanges of the girders framing into the column flanges. For examples of doubler plate connections, see Ref. 55 and Fig. C-8.6. The use of diagonal stiffeners for strengthening and stiffening of the panel zone has not been adequately tested for low cycle reversed loading into the inelastic range. Thus no specific recommendations are made at this time for special seismic requirements for this detail. TOP & BOTT.
1″
BEAM JOINT NOT SHOWN
EA. END
WEB DOUBLER AS REQ’D
Fig. C-8.6. Panel zone detail (with doubler).
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8.4. Beam Limitations In order to minimize the cost of connections it has occasionally been suggested that the beam cross-section be reduced immediately adjacent to the column. This type of assemblage can result in a very brittle mode of failure. Detailing that results in a concentration of stress in an area where inelastic deformations are anticipated under large seismic response is discouraged. The width thickness ratio of projecting elements should be within those which provide the cross-section with stability against local buckling. The limits given in Table 8-1 are deemed adequate by the Committee for ductilities to 6 or 7 based on the tests performed to date.29â&#x20AC;&#x201C;32 Further testing may result in some modifications of these limits. 8.5. Continuity Plates Sect. K1 of the Specification gives the design requirements for webs and flanges with concentrated forces. Sect. K1.2 gives the design strength in local buckling in a flange under the action of a tensile force. When the design strength is inadequate, column web stiffeners are required. In moment resisting frames, an interior beam-to-column connection has tension on one flange and compression on the opposite side. When stiffeners are required, it is normal to place a full depth stiffener on each side of the column web. As this stiffener provides a load path for the flanges on both sides of the column, it is commonly called a continuity plate. The stiffener not only provides resistance to local flange buckling but also provides a boundary to the very highly stressed panel zone. When it is anticipated that there could be a plastic hinge adjacent to the column, the required force to determine whether a continuity plate is required is not the design earthquake force given by the load combinations 3-1 through 3-6. It is the force exerted by the beam connection when the full plastic moment with possible strain hardening has been formed. Tests have shown that hinging occurs due to local flange buckling when a compact section is strain hardened to about 1.3Fy.20 At the joint, the flanges of the beam can be strain-hardened to a force of 1.8Fy bf tf. Using this force as the required strength on the continuity plate is conservative as there is only a small moment strength contributed by the bolted web connection. Since the flange continuity plate is needed to protect the weld at the joint of the beam flange to column flange, consideration should be given to their use in connections where the calculations indicate they may not be required. Continuity plates have been used in almost all cyclic joint tests that have performed well.17 When tests have been performed on specimens not meeting the requirements of Sect. K1.2, the joints have performed poorly. For the actual design of the continuity plates, Sect. K1.8 of the LRFD specification would apply. 8.6. Column-Beam Moment Ratio Tests have shown that moment frame subassemblages in which yielding of columns occurred did not exhibit any loss of lateral force resistance at displacements representative of maximum expected earthquake response.33 Most engineers believe, however, that the performance of seismic moment frames is more AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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predictable if columns outside of the panel zone do not yield. The tests necessary to formulate truly appropriate criteria have not been conducted. In the past, many frames have been designed with the assumption that the first hinging occurs in the columns and until recently no code provisions for this behavior have been enforced. There have not been any documented failures in past earthquakes directly attributable to column hinging. Design situations do occur where elimination of the “strong beam-weak column” connection type would be grossly impractical. The committee feels that some interim provisions are appropriate. Thus Eqs. 8-3 and 8-4 are introduced. These formulas require that the initial potential for yielding at a beam-to-column connection be in the beam or panel zone rather than in the column. The exceptions to the “strong column-weak beam” connection type require that the column be a compact section and include one of the following characteristics: a. Have a low required axial strength. b. Be a column in a story which has a significantly stronger design story shear strength than the story above. c. Be a column that is not part of the lateral force resisting system except to support the axial load from the overturning moment of the building as a whole. Wherever possible the committee recommends that the hinging conform to the requirements of Sect. 8.2. 8.7. Beam-to-Column Connection Restraint In order to function properly, particularly if inelastic behavior in or adjacent to the beam-to-column connection occurs during high seismic activity, the column needs to be braced to prevent rotation out of the plane of the moment frame. 8.7.a. Restrained Connections: Beam-to-column connections are usually restrained laterally by roof or floor framing. For these cases, lateral support of the connection is required only at the level of the top flanges of the beams as long as the column can be shown to remain elastic. The two criteria to demonstrate that the column remains elastic are arbitrary but appear to be reasonable assumptions until otherwise demonstrated by test. If the column cannot be demonstrated to remain elastic, a hinge would be potentially forming and the column should be laterally supported at the levels of both the top and bottom flanges of the beam. The lateral support provided at the beam-to-column connection is to be designed using a required strength of 2 percent of the nominal beam strength. It is recognized from the limited test data available that the lateral support provided should also be rigid enough to inhibit lateral movement of the column flanges.32 Designers should carefully design the lateral support member to be composed of reasonably rigid elements and be anchored to rigid supports. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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The lateral support provided the beam-to-column connection is not required to be a separate member at the connection in all cases. It may be shown that the lateral support force can be adequately carried by the column web or the beam flanges. 8.7.b. Unrestrained Connection: Unrestrained connections can occur in special cases as in two story frames, at mechanical floors or for architectural space layout. When this does occur, special care should be provided to minimize the potential of out-of-plane buckling at the connection. Three arbitrary provisions are given for the columns to assure that this buckling does not occur. 8.8. Lateral Support of Beams The lateral support for beams is defined in Chapter F in the LRFD design specifications. In moment resisting frames, the beams are nearly always in double curvature between columns unless one end is pinned. If the formula for plastic design were used as a guide and assuming Mp at one end and pinned at the other, formula F1-1 would yield 3,600ry / Fy. With Fy =36 ksi, Lpd = 100ry. The 1991 UBC has 96ry for this limitation. Due to the low cycle oscillating motion of the frames under earthquake loading and the uncertainty of the locations of hinging under the various loading combinations, a more conservative approach was appropriate and set the maximum limit of the spacing of lateral support for frame beams at 2,500ry / Fy for both top and bottom flanges. 9.
REQUIREMENTS FOR CONCENTRICALLY BRACED FRAMES (CBF)
9.1
Scope The provisions contained in the Section are for braced frame systems of Building Categories C, D, and E where the braces are designed to carry all the lateral force shears or are used in combination with a moment resisting frame. If used in combination with a moment frame system, the moment frames should follow the requirements of Sects. 7 or 8 as required by the local Building Code. In a Concentrically Braced Frame (CBF), the bracing members are so arranged that the brace members primarily act with axial loading. CBF usually are in one of the following five types. (See Figs. C-9.1 through C-9.5). Ductility of CBF systems producing a pattern of reasonably stable reversible distortions provides justification for basing seismic design on reduced displacements that can be expected during a strong earthquake. CBF systems, by the fact that the primary forces in the bracing system are axial tension and compression, are very limited in reversible inelastic distortions. Tests have shown that after buckling, an axially loaded member rapidly loses strength with repeated inelastic load reversals and does not return to its original straight position.34 For this reason in high seismic areas, CBF systems have not been permitted by codes for tall or special buildings without being combined with a moment resisting frame. Codes also have required significantly higher levels of design force so that the possibility of large uncontrolled inelastic deformations will not occur. For instance, ASCE 7-88 in Sect. 9.9.5 requires that CBF be designed to a force 1.25 times the normal design force given in Sect. 9.4 for the system involved. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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Fig. C-9.1. Diagonal braced frame.
Fig. C-9.2. X-braced frame.
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Fig. C-9.3. V-braced frame.
Fig. C-9.4. Inverted V-braced frame.
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In Sect. 9.4 of this specification, for Special Configurations, this higher force factor is raised to 1.5. The performance of CBF systems in earthquakes is acceptable as long as they retain stable configuration. The emphasis of these provisions is on raising the level of stable behavior and protecting against brittle failures. When an axially loaded brace buckles in compression, several developments take place: a. When buckling occurs, additional load is transferred to the tension brace increasing the force it must carry. b. The buckling of the brace may cause excessive rotation at the brace ends and local connection failure. c. The buckling can cause local or torsional buckling to occur near mid span. d. If the buckling causes the brace to bow out of plane of the braced frame, non-structural encasement of the frame system can be destroyed. e. Brace buckling can occur non-symmetrically which would induce large torsional response. f. Excessive buckling can affect non-structural systems which are attached to the frame.6
Fig. C-9.5. K-braced frame.
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9.2. Bracing Members 9.2.a. Slenderness: Except for low buildings using the required strength given in Sect. 9.5, the slenderness (L / r) of members of CBF systems is limited. In the post-buckling range, the compressive nominal axial strength deteriorates.34 Hysteresis loops of tested assemblies take on a severely pinched shape. (See Fig. C-9.6.) Braces with small L / r dissipate more energy because in the post-buckling range they undergo cyclic inelastic bending which slender braces cannot. Very slender braces have almost no stiffness in a buckled configuration. On a load reversal, the brace quickly assumes a straightened configuration and very rapidly picks up a tensile force. This rapid increase in the brace force may cause impact loading and may lead to a brittle failure of the connection. The curvatures associated with cyclic inelastic bending of braces may be large and local buckling can develop. This local buckling may be so severe as to result in localized kinking of the brace or the connection plate elements causing crack propagation and fracture. Such fractures have been obseved rather early in tests of tubular bracing members.35 This characteristic is more prevalent in rectangular and square tube braces. Consideration should be given to using composite tubes with concrete fill to inhibit buckling.36 9.2.b. Compressive Design Strength: Due to the cyclic nature of seismic response, the compressive design strength of bracing members is reduced to 80 percent of the value given in the Specification, Chapter E. P (kips) 264 200
100 –1.0
1.0
0
Finish
2.0
δ Axial (in.) –100
–200
W6x20 L = 10 ft KL / r = 80
9 in. 3.5 in. Lateral ∆ Fig. C-9.6. P−δ diagram for a strut.
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This reduction factor is a simplified value from the factor proposed by others which varies with KL / r.6 When evaluating the nominal strength of the bracing system for the purpose of determining the maximum load the bracing will impose on other systems (such as Eq. 6-1), the reduction for cyclic behavior should not be used for design as it would underestimate the nominal strength of the bracing system during the early cycles of seismic response. 9.2.c. Lateral Force Distribution: This provision attempts to balance the tensile and compressive resistances across the width and breadth of the building since at large loads the capacity of buckled compression braces may be substantially less than that of tension braces. An exception is provided for the case where the bracing members were sufficiently oversized to provide essentially elastic seismic response. 9.2.d. Width-Thickness Ratios: In Sect. B5 of the Specification, definitions are given to three types of sections. The compact section is one which has elements with width-thickness ratios, λ, less than λp. Non-compact sections are those with elements λp ≤ λ ≤ λr. Slender compression sections are those which have at least one element for which λ is greater than λr. The latter sections are prone to local buckling and are not to be used for the bracing members covered in this Section. The circular section wall thickness limitation was chosen to be the same as for Plastic Design in the Specification. Due to the repetitive nature of cyclic loading for rectangular tubular sections, a more stringent requirement on the b / t ratios is specified based on tests.35–36 Filling of tubing with lean concrete has been shown to effectively stiffen the tube walls. 9.2.e. Built-up Member Stitches: The special requirements for built-up member stitches were chosen from test data.37 They are intended for members built up from double angles and channels, and may not be appropriate for markedly different shapes. 9.3. Bracing Connections 9.3.a. In CBF systems, the bracing members normally carry most of the seismic story shear, particularly if a dual system is not used. The required strength on brace connections should be adequate so that failure by out-of-plane buckling of gussets or brittle fracture of the connection are not the critical failure mechanism. The minimum of the three criteria, (i.e., the design axial tension strength of the bracing member, the force generated by the amplified load combinations of 3-7 and 3-8, and the maximum force that could be generated by the overall system) determine the required strength on both the brace connection and the beam-to-column connection if it is part of the bracing system. The latter criterion is intended to cover the possibility that the shear could be limited by the amount of overturning that could be developed. 9.3.b. Net Area: Eq. 9-1 extends the concepts of LRFD Sect. B3 to the forces given in Section 9.2.a above. 9.3.c. Gusset Plates: Gusset plates in CBF systems are frequently the critical AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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design element in a system required to deform into the inelastic range. The increased force required for design of CBF tends to reduce the inelastic demand but may be insufficient to totally eliminate the problem. If the critical buckling mode of the braced member is in the plane of the CBF, the gussets and their joints should have a design strength capable to resist the nominal strength of the brace in that direction. If the critical buckling mode is out of the plane of the CBF, each gusset shall be detailed to permit the formation of a hinge line in the gusset. (See Fig. C-9.7.) 9.4. Special Bracing Configuration Requirements In addition to the general requirements for bracing members and their connections given above, special limitations are applied to V and K types of CBF systems due to their special configurations. 9.4.a. V and Inverted V Type Bracing: If one diagonal of a V type brace were to buckle in compression, the force in the tension brace would become larger than the force in the buckled brace. The vertical resultant of these two forces could then impose a large vertical deformation on the horizontal member of the bracing system. (See Fig. C-9.8.) If the connection at the point of the V tip were pinned, there would be no resistance to this deformation. If a continuous horizontal member survives and undergoes a deformation reversal, the previously buckled diagonal member would
BRACING MEMBER 2t
GUSSET PLATE
t = THICKNESS OF GUSSET PLATE
Fig. C-9.7. Brace-to-gusset plate requirement for buckling out-of-plane bracing system.
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not return to its original alignment and the diagonal member which was in tension could exceed its capacity in compression. In this manner both diagonal members would be in a buckled condition. This behavior would cause the post buckling strength of the braced system to deteriorate rapidly.38 (See Fig. C-9.9.) Near the tip point of the V is a zone where inelastic rotations are likely to occur, members should be braced against out-of-plane buckling. Several options were considered for CBF systems using the V type bracing. One was to prohibit its use, a second was to impose stringent limitations on the slenderness ratios of the bracing members, and a third was to provide a larger axial load capacity for the diagonal members. The latter option was adopted by providing a design axial strength 1.5 times the required axial strength in lieu of the 1.25 normally required for other CBF. It is also required that the beam be continuous throughout the bay and that this beam be designed to carry the tributary vertical gravity loads without considering the support provided by the diagonal members of the V. A review of more recent testing of V braced systems may in future editions be able to modify some of the current limitations. 9.4.b. K Bracing: In areas of high seismicity where it is envisioned that inelastic response to large motions will be required, the K type of CBF system is not a desirable method for seismic resistance. The same behavior discussed in the V type bracing occurs, but in the case of the K system a buckled brace causes the column to deform horizontally. Potentially this could cause column buckling and subsequent collapse. In buildings of Categories A, B, and a portion of C, the K system is permitted unrestricted by these provisions. For the remainder of Category C as per
Fig. C-9.8. Failure mechanism of inverted V-braced frame.
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Sect. 2.2, however, K braces shall meet the requirements Sects. 9.4.b and 9.5. This requires a 50 percent increase in design axial load for the braces and a continuous column though at the story mid-height. It is recommended that K type bracing not be used even where permitted for seismic resistance unless other configurations are impractical. 9.5. Low Buildings One of the few problem areas observed in the seismic performance of smaller steel buildings using the CBF system pertain to the size and type of member connections used. Quite frequently the critical design horizontal load is wind rather than seismic. In these cases, the sizing of bracing members is larger than would be required if seismic loads were the only design horizontal loads. Thus for smaller buildings and roof structures, the special provisions for CBF systems have been waived if the seismic resisting system has been designed using the amplified loads given in Load Combinations 3-7 and 3-8. This waiver would permit, for instance, an X braced or diagonal braced system in which the bracing members would be assumed to be in tension only. 10.
REQUIREMENTS FOR ECCENTRICALLY BRACED FRAMES (EBF)
10.1. Scope
THIRD STORY SHEAR (KIPS)
Research39–49 has shown that buildings using the EBF system possess the ability to combine high stiffness in the elastic range together with excellent ductility and energy dissipation capacity in the inelastic range. In the elastic range, the lateral stiffness of an EBF system is comparable to that of a CBF system, particularly when short link lengths are used. In the inelastic range, EBF systems
800
400
0
–400
–800 –4
–2
0
2
4
THIRD STORY DRIFT (IN.) Fig. C-9.9. Story shear–story drift diagram for frame with inverted V-bracing.
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provide stable, ductile behavior under severe cyclic loading, comparable to that of a SMF system. The EBF is composed of columns, beams, and braces in which at least one end of each bracing member connects to a beam at a short distance from a beam-to- column connection or from an adjacent beam-to-brace connection. (See Fig. C-10.1.) The short distance of the beam between the brace connection and the column or between brace connections is called the link. The design purpose of an EBF system creates a system that will yield primarily in the links. The special provisions for EBF systems are intended to satisfy this criterion and to ensure that cyclic yielding in the links can occur in a stable manner. The yielding in the links is accomplished by ensuring that the diagonal braces, the columns, and the portion of the beam outside of the links remain essentially elastic under forces that can be generated by fully yielding and strain hardened links. Arrangements of braces can be made in which links may not be fully effective. One such arrangement is the one shown on Fig. C-10.2 in which links are provided at each end of the brace. If the upper link has significantly lower design shear strength than the story below, the upper link deforms inelastically and limits the force that can be delivered to the brace to deform the lower link inelastically. When this condition occurs the upper link is termed an active link, whereas the lower link is an inactive link. Having potentially inactive links in the EBF system increases the difficulty of analysis. The plastic analyses show that in some cases the lower link yields due to the combined effect of D, L, and E loads, and the frame capacity becomes smaller than expected.50 It also increases the cost of the structure by requiring full link details on the inactive links even though the brace would be sized by the strength of the active link and the brace connection at an inactive link could be designed as a pin. Thus it is best to arrange a system that contains only active links as those shown in Fig. C-10.1. Design suggestions have been compiled in Ref. 48. In Sect. 10.1 in conformity with the strong columnâ&#x20AC;&#x201C;weak beam concept, plastic hinges should not develop in columns at floor beam levels in EBF. The occurrence of such plastic hinges, together with those forming in the links, could result in a soft story and must be prevented. There are two important code provisions intended to prevent this from happening. First, according to Sect. 6.1, the required axial column strength includes PE, based on application of the amplified earthquake load 0.4RE. Second, per Sect. 10.8, the required strength of columns due to the forces introduced at the connection of a link and/or brace is based on these forces multiplied by a factor of 1.25. Note that for a severe earthquake the formation of plastic hinges at column bases is generally unavoidable. 10.2. Links The general provisions for links to ensure that stable yielding occurs are included under this heading. 10.2.a. Beams with links are required to be compact shapes following the same criteria as SMF systems (Table 8-1). 10.2.b. In order to provide steel with proven ductile behavior the yield stress of steel is limited to 50 ksi. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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10.2.c. Doubler plates on the link web are not permitted as they do not perform as intended in inelastic deformations. Openings are not permitted as they adversely affect the yielding of the link web. 10.2.d. The link design shear strength φVn is the lesser of that determined from the yield shear or twice the plastic moment strength divided by the link length. This φVn should be greater than or equal to the required shear determined from the Load Combinations 3-5 or 3-6. 10.2.e. If the required axial load on the link is less than 0.15Py, the effects of the axial load can be ignored, In general, the axial load is negligible because the horizontal component of the brace load is transmitted to the beam outside of the link. However, due to a particular arrangement of the framing, substantial axial forces can develop in the link. For such cases, the limitations given in f. apply, and the design shear strength and link lengths are required to be reduced to ensure stable yielding.
c
d
c
a c
d
c
d
b
b
a
d
a
c b
d
b
a
c
d
c
d
c
b
c
b
d
b
a
d
c
d
d
d c
b
d
b
b
a
a c
b
d
d
d c
b
d
b
b
a
a c
b
d
d
d
b
a
b
c a
b
a = column b = brace c = link d = portion of beam outside of link
Fig. C-10.1. Common types of eccentric braced frames.
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10.2.f. See Commentary 10.2.e. 10.2.g. The link rotation angle is defined in the Specifications as the plastic angle between the link and the beam outside the link when the total story drift ∆t, calculated using amplified earthquake forces 0.4R × E. The plastic link rotation can be conservatively determined assuming that the EBF bay will deform in a rigid-plastic mechanism. Several such mechanisms are illustrated for various EBF configurations in Fig. C-10.3. The plastic angle is determined using a story drift ∆p = ∆t − ∆e, where ∆e the elastic story drift can conservatively be assumed to be zero. The plastic story drift angle θp = ∆p / h follows from geometry. The actual plastic link rotation angle can be determined by non-linear elastic-plastic analyses if a more explicit definition of the angle is desired. An inverted Y system is shown on Fig. C-10.1. In this system the precise definition given in the Glossary for the link rotation angle does not apply but the concept is the same as in the other systems, as shown on Fig. C-10.3. As usual both ends of the link are required to be laterally supported. The link length of 1.6Mp / Vp indicates the limit chosen for the link to act primarily in shear. The link length 2.6Mp / Vp is the lower limit of a flexural link. Straight line interpolation is used for the intermediate link lengths. It has been demonstrated experimentally51–52 as well as analytically48 that the first floor links usually experience the largest plastic deformation. In extreme cases this may result in a tendency to develop a soft story. The
a
b
φVn − link a (active link) < φVn − link b (inactive link)
Fig. C-10.2. EBF—active and inactive link.
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plastic link rotations tend to attenuate at higher floors, and decrease with the increasing frame periods. Therefore for severe seismic applications a conservative design for the links in the first two or three floors is recommended. This can be achieved by increasing the minimum design shear strengths of these links on the order of 10 percent over that specified in Sect. 10.2.d. An even more conservative approach would be to have vertical connecting members at the ends of the links in a few lower floors. The use of the framing shown in Fig. C-10.1 can be advantageous where ∆p
∆p
e
e θp
γp
γp h
h
e γp
θp
L
L/2
L/2
γp = L θp e
γp = L θp 2e
∆p
∆p γp e
γp
L/2
e/2 e/2
h
h
θp
θp
L/2
γp = L θp e ∆v ∆t ∆e ∆p e h L θp γp
L γp = h θp e
= Story drift determined using base shear v, inches. = Total story drift, inches = ∆v × e′ / e. = Elastic story drift, inches = ∆v times the earthquake load factor. = Plastic story drift, inches = ∆t − ∆e (conservatively, ∆e = 0). = Link length, inches. = Story height, inches. = Column to column distance, inches. = Plastic story drift angle, radians = ∆p / h. = Link rotation angle, radians.
Fig. C-10.3. Link rotation angle. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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the beam-column-brace connections can be designed as simple connections. Welds of the link flanges are avoided in this kind of framing. By changing the link lengths the stiffness of an EBF can be modified. In this manner the frame periods can be optimized. 10.2.h. The intent of this provision is to permit a CBF on the top floor of an EBF building over five stories tall with application of an earthquake response modification coefficient R appropriate for an EBF. 10.3. Link Stiffeners Properly detailed and restrained webs can provide stable, ductile, and predictable behavior under severe cyclic loading. The design of the EBF link requires close attention to the detailing of the link web thickness and stiffeners. 10.3.a. Full depth stiffeners are required at the end of all EBF links and serve to transfer the link shears to the reacting elements as well as restraining the link web against buckling. 10.3.b. In shear links, the spacing of intermediate web stiffeners is varied depending on the magnitude of the link rotation angle.45 The closer spacing is provided for the system with the greatest angle. Flexural links having lengths greater than 2.6Mp / Vp but less than 5Mp / Vp are required to have an intermediate stiffener at a distance from the link end equal to 1.5 times the beam flange width. Links between shear and flexural limits would have intermediate stiffeners meeting the requirement of both shear and flexural links. When the link length is greater than 5Mp / Vp, no intermediate stiffeners are required. Intermediate stiffeners are required to be full depth in order to effectively react against shear buckling. Intermediate stiffeners are required on both sides of the web for links 25 inches in depth or greater. For links less than 25 in. deep, the stiffener need be on one side only. 10.3.c. All link stiffeners are required to be fillet welded to the link web. These welds shall have a required strength equal to the nominal vertical tensile strength of the stiffener. The connection to the link flanges should be similar. 10.4. Link-to-Column Connections There are special connection requirements for the connections of links to columns. The intent is to provide connections which can transfer not only the shear and moment forces of the links but also torsion due to flange buckling. The Specification does not explicitly address the column panel zone design requirements at link-column connections, as little research is available on this issue. However, from research on panel zones for SMF systems, it is believed that limited yielding of panel zones in EBF systems would not be detrimental. Pending future research on this topic, a suggested design approach is as follows: Compute the required shear strength of the panel zone based on the bending moment at the column end of the link, as given by the equations in Sect. 10.6.a in the commentary of these provisions. The corresponding panel zone design shear strength should then be computed according to Eq. 8-1 of these provisions. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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10.5. Lateral Support of the Link One of the essential items to ensure stable inelastic behavior of the EBF system is to restrain the ends of the link from twisting out of plane. The 6 percent of the nominal strength of the beam flange defines the required strength on the lateral support member and its connections. 10.6. Diagonal Brace and Beam Outside of Links 10.6.a. A basic requirement of EBF design is that yielding be restricted primarily to the links. Accordingly, the diagonal brace and the beam segment outside of the link should be designed to resist the maximum forces that can be generated by the link, accounting for the sources of link overstrength. Link overstrength can be attributed primarily to strain hardening, effects of composite floor systems, and the actual yield strength of the link exceeding the specified yield strength. In EBF research literature, for design of the brace and the beam, an overstrength factor of 1.5 has generally been applied to the nominal strength of the link. Using this overstrength factor, the brace and beam segments were checked using their nominal strength, i.e., using φ =1.0. This approach considers that designing for an overstrength factor of 1.5 represents an extreme loading condition for the beam and brace, and therefore a relaxation of the φ factor was appropriate to avoid an overly conservative design.49 Sect. 10.6.a specifies that the design strength of the beam and diagonal brace exceed the forces generated by 1.25 times the nominal link shear strength, maintaining approximately the same basic design approach for the diagonal brace and beam. That is, based on a φ factor of 0.85 on axial compression in the beam or brace, the effective overstrength factor becomes 1.25 / 0.85, or about 1.5. For bending moments in the beam or diagonal brace, for which φ is 0.9, the overstrength factor becomes 1.25 / 0.9, or about 1.4, representing a slight relaxation from the test criterion. Based on a link overstrength factor of 1.25, the required strength of the diagonal brace and beam segment outside of the link can be taken as the forces generated by the following values of link shear and link end moment: For e ≤ 2Mp / Vp,
link shear link end moment
= 1.25Vp = e(1.25Vp ) / 2
For e > 2Mp / Vp,
link shear link end moment
= 2(1.25Mp) / e = 1.25Mp
The above equations are based on the assumption that link end moments will be equal when the link achieves its limit strength. For links of length e ≤ 1.3Mp / Vp attached to columns, experiments have shown that link end moments do not equalize.44 For this situation, link shear and link end moments can be taken as: For e ≤ 1.3Mp / Vp next to column, link shear
= 1.25Vp
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SEISMIC PROVISIONS FOR STRUCTURAL STEEL BUILDINGS
moment at column end of link moment at brace end of link
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= 0.8Mp = e(1.25Vp ) − 0.8Mp
The link shear force will generate axial force in the diagonal brace, and for most EBF configurations, will also generate substantial axial force in the beam segment outside of the link. The ratio of beam or brace axial force to link shear force is controlled primarily by the geometry of the EBF and is therefore not affected by inelastic activity within the EBF.47 Therefore, this ratio can be taken from an elastic frame analysis and used to scale up the beam and brace axial force to a level corresponding to the link shear force specified in the above equations. At the brace end of the link, the link end moment will be transferred to the brace and to the beam. If the diagonal brace and its connection remains elastic, based on link overstrength design considerations, some minor inelastic rotation can be tolerated in the beam outside of the link. 10.6.b. Typically in EBF design, the intersection of the brace and beam centerlines is located at the end of the link. However, as permitted by Sect. 10.6.b, the brace connection should be designed with an eccentricity so that the brace and beam centerlines intersect inside of the link. This eccentricity in the connection generates a moment that is opposite in sign to the link end moment. Consequently, the value of link end moment
STIFF PLATE EA. SIDE OF WEB. USE FILLET WELD CONT. @ WEB & FLANGE BEAM OUTSIDE OF LINK
LINK LENGTH – e
FULL PENETRATION TOP & BOTT.
W SHAPE LINE OF INTERSECTION OF BRACE AND BEAM SHALL BE AT THE EDGE OF LINK OR INSIDE THE LINK
INTERMEDIATE STIFFENER PLATES EA. SIDE OF WEB FOR LINKS ≥ 25″ CONT. FILLET WELD @ WEB AND FLANGE
Fig. C-10.4
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COMMENTARY: PART I—LRFD PROVISIONS
given above can be reduced by the moment generated by this brace connection eccentricity. This may substantially reduce the moment that will be required to be resisted by the beam and brace, and may be advantageous in design. The intersection of the brace and beam centerlines should not be located outside of the link, as this increases the bending moment generated in the beam and brace. See Figs. C-10.4 and C-10.5. 10.6.c. If the brace connection at the link is designed as a pin, the beam by itself shall be adequate to resist the entire link end moment. This condition normally would occur only on EBF with short links. If the brace is considered to resist a portion of the link end moment, then the brace connection at the link should be designed as fully restrained, as required by Sect. 10.6.c. Test results on several brace connection details subject to axial force and bending moment are reported in Ref. 47. 10.6.d. When checking the requirements of Sect. 10.6, both the beam and diagonal brace should, in general, be treated as beam-columns in strength and stability computations. Unlike CBF, the brace of an EBF may be subject to significant bending moments. For the beam segment outside of the link, adequate lateral bracing should be provided to maintain its stability under the axial force and bending moment generSTIFF. PLATE EA. SIDE OF WEB. USE FILLET WELD CONT. @ WEB & FLANGE
LINK LENGTH – e
BEAM OUTSIDE OF LINK
FULL PENETRATION TOP & BOTT.
LINE OF INTERSECTION OF BRACE AND BEAM SHALL BE AT THE EDGE OF LINK OR INSIDE THE LINK
BENT PLATE OR TWO WELDED PLATES GUSSET PLATE TS (BRACE) SPLIT END TO FIT GUSSET
Fig. C-10.5
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
INTERMEDIATE STIFFENER PLATES EA. SIDE OF WEB FOR LINKS ≥ 25″ CONT. FILLET WELD @ WEB & FLANGE
SEISMIC PROVISIONS FOR STRUCTURAL STEEL BUILDINGS
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ated by the link, as required by Sect. 10.6.d. If the stability of the beam is provided by adequate lateral support, tests have shown that limited yielding of the beam segment is not detrimental to EBF performance, and for some EBF configurations may be unavoidable.47 However, the combined flexural strength of the beam and the brace, reduced for the presence of axial force, should be adequate to resist the link end moment. For EBF geometries with very small angles between the beam and the brace and/or for EBF with long links, satisfying the requirements of Sect. 10.6.e. may require very heavy braces, and in extreme cases, may require cover plates on the beams. EBF with relatively steep braces, e.g., brace-beam angles greater than about 40 degrees, combined with short links are preferable for avoiding design problems with the brace and beam segment outside of the link. A general discussion on design issues related to the beams and braces of an EBF is provided in Ref. 49, with further details provided in Ref. 47. 10.7. Beam-to-Column Connection If the arrangement of the EBF system is such that a link is not adjacent to a column, a simple pinned connection is considered to be adequate if the connection provides some restraint against torsion in the beam. The magnitude of torsion is calculated by considering perpendicular forces equal to 1.5 percent of the nominal axial flange tensile strength applied in opposite directions on each flange. 10.8. Required Column Strength As the shear strength of the adjoining critical link is potentially greater than the nominal strength due to strain hardening, the required column strength is required to be designed for the increased moment and axial load due to the load from the adjacent link or brace. 11.
QUALITY ASSURANCE As the behavior of all steel framing during a major earthquake is dependent on the workmanship of the fabricator in providing sound joints, the design engineer is advised to provide for adequate assurance control, particularly on the tension groove welded joints of the seismic resisting system. ASCE 7-92 provides special requirements for inspection and testing based on the Seismic Performance Category of the building to be built. The special requirements for structural steel construction are in general those that would normally be required for construction in all areas of seismic activity.
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COMMENTARY: PART II—ASD PROVISIONS
Part II—ASD Provisions 1.
SCOPE As noted in PART I, the special seismic requirements are collateral provisions related to the AISC Load and Resistance Factor Design Specification. As that document was first published in 1986, the references to earthquake load were not current. The provisions in PART I use limit state load models derived from the 1991 NEHRP3 and the soon to be published ASCE 7-93.2 The provisions in PART II allow a designer to apply AISC Allowable Stress Design Specification for Structural Steel Buildings (ASD)53 in the design of the seismic lateral force resisting system based upon limit state loads. If the user wishes to use ASD in the design of the seismic lateral force resisting system where the loads are based upon service loads, the loads need to be converted to factored levels consistent with those in PART I. The PART II provisions are intended to be used in conjunction with PART I by either adding to or substituting to the provisions of Part I.
3.2
Nominal Strengths, and
3.3
Design Strengths These provisions modify PART I to convert allowable stresses into equivalent nominal strengths by multiplying allowable stresses by 1.7 as noted. Design strengths are determined by multiplying φ times the nominal strengths.
7.2, 10.6.a, and 10.6.d These modifications to PART I requirements change FR and PR connections to Type 1 and Type 3 connections consistent with ASD nomenclature.
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List of References 1. AISC, Load and Resistance Factor Design Specification, American Institute of Steel Construction, Inc., Chicago, IL, 1986. 2. ASCE 7-93, Minimum Design Loads for Buildings and Other Structures, American Society of Civil Engineers, New York, NY, 1993 (to be published). 3. BSSC, NEHRP (National Earthquake Hazards Reduction Program) Recommended Provisions for the Development of Seismic Regulations for New Buildings, Building Seismic Safety Council, Federal Emergency Management Agency, Washington, DC, 1992. 4. Luft, R. W., “Comparison Among Earthquake Codes,” Earthquake Spectra, Earthquake Engineering Research Institute, Vol. 5, No. 4, November 1989. 5. ICBO, Uniform Building Code, International Conference of Building Officials, Whittier, CA, 1991. 6. SEAOC, Recommended Lateral Force Requirements, Seismology Committee, Structural Engineers Association of California, Sacramento/San Francisco/Los Angeles, CA, 1988. 7. AWS, D1.1-92, Structural Welding Code, American Welding Society, Inc., Miami, FL, 1992. 8. Popov, E. P., Stephen, R. M., “Tensile Capacity of Partial Penetration Welds,” Journal of the Structural Division, American Society of Civil Engineers, Vol. 103, No. ST9, September 1977. 9. Bruneau, M., Mahin, S. A., and Popov, E. P., Ultimate Behavior of Butt Welded Splices in Heavy Rolled Steel Sections, Report No. UCB/EERC-87/10, Earthquake Engineering Research Center, University of California, Berkeley, CA, 1987. 10. Huckelbridge, A. A., Clough, R. W., Earthquake Simulator Tests of Nine-Story Steel Frame with Columns Allowed to Uplift, Report No. UCB/EERC-77/23, Earthquake Engineering Research Center, University of California, Berkeley, CA, 1977. 11. Carpenter, L. D., Lu, L-W., Reversed and Repeated Load Tests of Full Scale Steel Frames, Fritz Engineering Laboratory Report No. 332.7, Lehigh University, Bethlehem, PA, 1972. 12. Galambos, T. V., Deformation and Energy Absorption Capacity of Steel Structures in the Inelastic Range, Bulletin No. 8, American Iron and Steel Institute, New York, NY, 1968. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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LIST OF REFERENCES
13. Krawinkler, H., Bertero, V. V., and Popov, E. P., Inelastic Behavior of Steel Beam-to-Column Subassemblages, Report No. UCB/EERC-71/7, Earthquake Engineering Research Center, University of California, Berkeley, CA, 1971. 14. Bertero, V. V., Popov, E. P., and Krawinkler, H., Further Studies on Seismic Behavior of Steel Beam-Column Subassemblages, Report No. UCB/EERC73/27, Earthquake Engineering Research Center, University of California, Berkeley, CA, 1973. 15. Popov, E. P., “Seismic Behavior of Structural Assemblages,” Journal of the Structural Division, American Society of Civil Engineers, Vol. 106, No. ST7, July 1980. 16. Tall Building Systems and Concepts, Monograph on Planning and Design of Tall Buildings, Council on Tall Buildings and Urban Habitat, American Society of Civil Engineers, New York, NY, 1980. 17. Popov, E. P., Amin, N. R., Louie, J. J., and Stephen, R. M., “Cyclic Behavior of Large Beam Column Assemblies,” Earthquake Spectra, Professional Journal of the Earthquake Engineering Research Institute, Vol. 1, No. 2, February 1985. 18. Tsai, K. C. and Popov, E. P., “Seismic Panel Zone Design Effect on Elastic Story Drift in Steel Moment Resisting Frames,” Journal of Structural Division, in press. 19. Nicoletti, J. P., Pinkham, C. W., Saunders, C. M., Teal, E. J., A Synthesis of Steel Research for Code Development, Structural Steel Educational Council, San Francisco, CA, 1984. 20. Popov, E. P. and Pinkney, R. B., Behavior of Steel Building Connections Subjected to Inelastic Strain Reversals—Experimental Data, Bulletin No. 14, American Iron and Steel Institute, November 1968. 21. Popov, E. P. and Stephen, R. M., Cyclic Loading of Full-Size Steel Connections, Bulletin No 21, American Iron and Steel Institute, February 1972. 22. Driscoll, G. C. and Beedle, L. S., “Suggestions for Avoiding Beam-to-Column Web Connection Failure,” Engineering Journal, American Institute of Steel Construction, Chicago, IL, 1st Qtr., 1982. 23. Tsai, K. C. and Popov, E. P., Two Beam-to-Column Web Connections, Report No. UCB/EERC-86/05, Earthquake Engineering Research Center, University of California, Berkeley, CA, 1986. 24. Popov, E. P. and Tsai, K. C., Performance of Large Seismic Steel Moment Connections Under Cyclic Loads, Proceedings; Structural Engineers Association of California Convention, San Diego, CA, October 1987. 25. Slutter, R., Tests of Panel Zone Behavior in Beam Column Connections, Lehigh University, Report No. 200.81.403.1, Bethlehem, PA. 26. Becker, E. R., Panel Zone Effect on the Strength of Rigid Steel Frames, University of Southern California Structural Mechanics Laboratory, USCOE 001, June 1971. 27. Fielding, D. J., Huang, J. S., “Shear in Steel Beam-to-Column Connections,” Welding Journal, Vol. 50, No. 7, Research Supplement, 1971. 28. Krawinkler, H., “Shear in Beam-Column Joints in Seismic Design of Steel AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SEISMIC PROVISIONS FOR STRUCTURAL STEEL BUILDINGS
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Frames,” Engineering Journal, American Institute of Steel Construction, Chicago, IL, Vol. 15, 1978. 29. Sawyer, H. A., “Post-Elastic Behavior of Wide-Flange Steel Beams,” Journal of the Structural Division, Vol. 87, No. ST8, American Society of Civil Engineers, December 1961. 30. Lay, M. G., “Flange Local Buckling in Wide-Flange Shapes,” Journal of the Structural Division, Vol. 91, No. ST6, American Society of Civil Engineers, December 1965. 31. Kemp, A. R., “Factors Affecting the Rotation Capacity of Plastically Designed Members,” The Structural Engineer, Vol. 64B, No. 2, June 1986. 32. Bansal, J. P., The Lateral Instability of Continuous Steel Beams, CESRL Dissertation No. 71-1, University of Texas, Austin, TX, 1971. 33. Krawinkler, H., Bertero, V. V., Popov, E. P., Hysteresis Behavior of Steel Columns, Report No. UCB/EERC-75/11, Earthquake Engineering Research Center, University of California, Berkeley, CA, 1975. 34. Black, R. C., Wenger, W. A., Popov, E. P., Inelastic Buckling of Steel Struts Under Cyclic Load Reversals, Report No. UCB/EERC-80/40, Earthquake Engineering Research Center, University of California, Berkeley, CA, 1980. 35. Tang, X., Goel, S. C., Seismic Analysis and Design Considerations of Braced Steel Structures, UMCE Report 87-4, University of Michigan, Ann Arbor, MI, 1987. 36. Uang, C-M., and Bertero, V. V., Earthquake Simulation Tests and Associated Studies of 0.3-Scale Model of a Six-Story Concentrically Braced Steel Structure, Report No. UCB/EERC—86/10, EERC, Berkeley, CA, December 1986. 37. Liu, Z., Goel, S. C., Investigation of Concrete Filled Steel Tubes under Cyclic Bending and Buckling, UMCE Report 87-3, University of Michigan, Ann Arbor, MI, 1987. 38. Astaneh, A., Goel, S. C., Hanson, R, D., “Earthquake-Resistant Design of Double Angle Bracings,” Engineering Journal, American Institute of Steel Construction, Chicago, IL, Vol. 23, No. 4, 1986. 39. Roeder, C. W. and Popov, E. P., “Eccentrically Braced Frames for Earthquakes,” Journal of the Structural Division, Vol. 104, No. 3, American Society of Civil Engineers, March 1978. 40. Libby, J. R., “Eccentrically Braced Frame Construction—A Case History,” Engineering Journal, American Institute of Steel Construction, Chicago, IL, Vol. 18, No. 4, 1981. 41. Merovich, A. T., Nicoletti, J. P. and Hartle, E., “Eccentric Bracing in Tall Buildings,” Journal of the Structural Division, Vol. 108, No. 9, American Society of Civil Engineers, September 1982. 42. Hjelmstad, K. D. and Popov, E. P., “Cyclic Behavior and Design of Link Beams,” Journal of the Structural Division, Vol. 109, No. 10, American Society of Civil Engineers, October 1983. 43. Malley, J. O. and Popov, E. P., “Shear Links in Eccentrically Braced Frames,” AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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LIST OF REFERENCES
Journal of the Structural Division, Vol. 110, No. 9, American Society of Civil Engineers, September 1984. 44. Kasai, K. and Popov, E. P., “General Behavior of WF Steel Shear Link Beams,” Journal of the Structural Division, Vol. 112, No. 2, American Society of Civil Engineers, February 1986. 45. Kasai, K. and Popov, E. P., “Cyclic Web Buckling Control for Shear Link Beams,” Journal of the Structural Division, Vol. 112, No. 3, American Society of Civil Engineers, March 1986. 46. Ricles, J. M. and Popov, E. P., Dynamic Analysis of Seismically Resistant Eccentrically Braced Frames, Report No. UCB/EERC-87/107, Earthquake Engineering Research Center, University of California, Berkeley, CA, 1987. 47. Engelhardt, M. D. and Popov, E. P., Behavior of Long Links in Eccentrically Braced Frames, Report No. UCB/EERC-89/01, Earthquake Engineering Research Center, University of California, Berkeley, CA, 1989. 48. Popov, E. P., Engelhardt, M. D. and Ricles, J. M., “Eccentrically Brace Frames: U. S. Practice,” Engineering Journal, American Institute of Steel Construction, Chicago, IL., Vol. 26, No. 2, 1989. p. 66–80. 49. Engelhardt, M. D. and Popov, E. P., “On Design of Eccentrically Braced Frames,” Earthquake Engineering Research Institute, El Cerrito, CA, Earthquake Spectra, Vol. 5, No.3, August 1989. 50. Kasai, K. and Popov, E. P., On Seismic Design of Eccentrically Braced Steel Frames, Proceedings, 8th World Conference on Earthquake Engineering, July 1984, San Francisco, CA., Vol. 5, pp.387–394. 51. Whittaker, A. S., Uang, C-M., and Bertero, V. V., Earthquake Simulation Tests and Associated studies of a 0.3-Scale Model of a Six-Story Eccentrically Braced Steel Structure, Report No. UBC/EERC-87/02, EERC, Berkeley, CA., 1987. 52. Foutch, D. A., “Seismic Behavior of Eccentrically Braced Steel Building,” ASCE Journal of Structural Engineering, Vol. 115, No. 8, August 1989, pp 1857–1876. 53. AISC, Allowable Stress Design Specification, American Institute of Steel Construction, Inc., Chicago, IL, 1989. 54. AISC, Serviceability Design Considerations for Low-Rise Buildings, Steel Design Guide Series 3, American Institute of Steel Construction, Inc. 55. Structural Steel Education Council, Steel Connections/Details and Relative Costs, Moraga, CA., 1986. 56. Uang, C. M., “EstablishingR (or Rw) and Cd Factors for Building Seismic Provisions,” Journal of Structural Engineering, Vol. 117, No. 1, American Society of Civil Engineers, Jan. 1991.
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LOAD AND RESISTANCE FACTOR DESIGN
Specification for Structural Joints Using ASTM A325 or A490 Bolts Approved by Research Council on Structural Connections of the Engineering Foundation, June 8, 1988. Endorsed by American Institute of Steel Construction Endorsed by Industrial Fasteners Institute
AMERICAN INSTITUTE OF STEEL CONSTRUCTION, INC. One East Wacker Drive, Suite 3100, Chicago, IL 60601-2001 AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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PREFACE
The purpose of the Research Council on Structural Connections is to stimulate and support such investigation as may be deemed necessary and valuable to determine the suitability and capacity of various types of structural connections, to promote the knowledge of economical and efficient practices relating to such structural connections, and to prepare and publish related standards and such other documents as necessary to achieving its purpose. The Council membership consists of qualified structural engineers from the academic and research institutions, practicing design engineers, suppliers, and manufacturers of threaded fasteners, fabricators and erectors and code writing authorities. Each version of the Specification is based upon deliberations and letter ballot of the full Council membership. The first Specification for Assembly of Structural Joints Using High Tensile Steel Bolts approved by the Council was published in January 1951. Since that time the Council has published 12 succeeding editions each based upon past successful usage, advances in the state of knowledge and changes in engineering design practice. This version of the Councilâ&#x20AC;&#x2122;s Load and Resistance Factor Design Specification is significantly reorganized and revised from earlier versions. The intention of the Specifications is to cover the design criteria and normal usage and practices involved in the everyday use of high-strength bolts in steel-tosteel structural connections. It is not intended to cover the full range of structural connections using threaded fasteners nor the use of high-strength bolts other than those included in ASTM A325 or ASTM A490 Specifications nor the use of ASTM A325 or A490 bolts in connections with material other than steel within the grip. A Commentary has been prepared to accompany these Specifications to provide background and aid the user to better understand and apply the provisions. The user is cautioned that independent professional judgment must be exercised when data or recommendations set forth in these Specifications are applied. The design and the proper installation and inspection of bolts in structural connections is within the scope of expertise of a competent licensed architect, structural engineer or other licensed professional for the application of the principles to a particular case.
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LOAD AND RESISTANCE FACTOR DESIGN
Specification for Structural Joints Using ASTM A325 or A490 Bolts Approved by Research Council on Structural Connections of the Engineering Foundation, June 8, 1988. Endorsed by American Institute of Steel Construction Endorsed by Industrial Fasteners Institute
1. Scope This Specification relates to the load and resistance factor design of structural joints using ASTM A325 high-strength bolts, ASTM A490 high-strength bolts or equivalent fasteners, and for the installation of such bolts in connections of structural steel members. The Specification relates only to those aspects of the connected materials that bear upon the performance of the fasteners. Design and construction shall conform to an applicable load and resistance factor design code or specification for structures of carbon, high-strength low alloy steel or quenched and tempered structural steel. Load and resistance factor design is a method of proportioning structural components such that no applicable limit state is exceeded when the structure is subject to all appropriate load combinations. When a structure or component ceases to fulfill the intended purpose in some way, it is said to have exceeded a limit state. Strength limit states concern maximum load carrying capacity, and thus generally are related to safety. Serviceability limit states are usually related to performance under normal service conditions, and thus usually are not related to strength or safety. (See Commentary. ) The term “resistance” includes both strength limit states and serviceability limit states. The design strength, φRn (nominal strength multiplied by a resistance factor), of each structural component or assemblage must equal or exceed the effect of the factored loads (nominal loads multiplied by load factors, with due recognition for load combinations). Thus, both the load factor and the resistance factor must be known to determine the reliability of the design, identified in load and resistance factor design as the “safety index.” Although the load factors are not stated in this Specification, load criteria contained in American National Standard “Building Code Requirements
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RCSC SPECIFICATION FOR STRUCTURAL JOINTS (6/8/88)
for Minimum Design Loads in Buildings and Other Structures,” ANSI A58.1-1982, were used as the basis for determining the resistance factors. For construction governed by other design load criteria, appropriate adjustment of resistance factors may be required. The attached Commentary provides background information in order that the user may better understand the provisions of the Specification. 2. Bolts, Nuts, Washers and Paint (a) Bolt Specifications. Bolts shall conform to the requirements of the current edition of the American Society for Testing and Materials’ “Specification for High-Strength Bolts for Structural Steel Joints,” ASTM A325, or “Specification for Heat Treated, Steel Structural Bolts, 150 ksi Tensile Strength,” ASTM A490, except as provided in paragraph (d) of this section. The Engineer of Record shall specify the type of bolts to be used. (b) Bolt Geometry. Bolt dimensions shall conform to the current American National Standards Institute’s standard, “Heavy Hex Structural Bolts,” ANSI Standard B18.2.1, except as provided in paragraph (d) of this section. The length of bolts shall be such that the end of the bolt will be flush with or project beyond the face of the nut when properly installed. (c) Nut Specifications. Nuts shall conform to the current chemical and mechanical requirements of the American Society for Testing and Materials’ Specification for Carbon and Alloy Steel Nuts,” ASTM A563, or “Specification for Carbon and Alloy Steel Nuts for Bolts for High-Pressure and High-Temperature Service,” ASTM A194. The grade and surface finish of nuts for each type shall be as follows: A325 Bolt Type
Nut Specification, Grade and Finish
1 and 2, plain (uncoated) A563 C, C3, D, D3 and DH3 or Al94 2 and 2H; plain 1 and 2, galvanized A563 DH or A194 2H; galvanized and lubricated 3, plain A563 C3 and DH3; plain A490 Bolt Type 1 and 2, plain 3, plain
Nut Specification, Grade and Finish A563 DH and DH3 or A194 2H; plain A563 DH3; plain
Nut dimensions shall conform to the current American National Standards Institute’s standard, “Heavy Hex Nuts,” ANSI Standard B18.2.2., except as provided in paragraph (d) of this section. (d) Alternative Fastener Designs. Other fasteners or fastener assemblies which meet the materials, manufacturing and chemical composition requirements of ASTM A325 or ASTM A490, as applicable, and which meet the mechanical property requirements of the same specifications in full-size tests, and which have a body diameter and bearing areas under the head and nut not less than those provided by a bolt and nut of the same nominal dimensions prescribed by paragraphs 2(b) and 2(c), may be used subject to the approval of the Engineer of Record. Such alternative fasteners may differ in other AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ASTM A325 OR A490 BOLTS
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dimensions from those of the specified bolts and nuts. Their installation procedure and inspection may differ from procedures specified for regular high-strength bolts in Sections 8 and 9. When a different installation procedure or inspection is used, it shall be detailed in a supplemental specification applying to the alternative fastener, and that specification must be approved by the Engineer of Record. (e) Washers. Flat circular washers and square or rectangular beveled washers shall conform to the current requirements of the American Society for Testing and Materials, “Specification for Hardened Steel Washers,” ASTM F436. (f) Load Indicating Devices. Load indicating devices may be used in conjunction with bolts, nuts and washers specified in 2(a) through 2(e). Load indicating devices shall conform to the requirements of American Society for Testing and Materials’ “Specification for Compressible-Washer-Type Direct Tension Indicators for Use with Structural Fasteners,” ASTM F959. Subject to the approval of the Engineer of Record, direct tension indicating devices different from those meeting the requirements of ASTM F959 may be used provided they satisfy the requirements of 8(d)(4). If their installation procedure and inspection are not identical to that specified in 8(d)(4), they shall be detailed in supplemental specifications provided by the manufacturer and subject to the approval of the Engineer of Record. (g) Faying Surface Coatings. Paint, if used on faying surfaces of connections which are not specified to be slip critical, may be of any formulation. Paint, used on the faying surfaces of connections specified to be slip critical, shall be qualified by test in accordance with “Test Method to Determine the Slip Coefficient for Coatings Used in Bolted Joints” as published by the Research Council on Structural Connections. (See Appendix A.) Manufacturer’s certification shall include a certified copy of the test report. 3. Bolted Parts (a) Connected Material. All material within the grip of the bolt shall be steel. There shall be no compressible material such as gaskets or insulation within the grip. Bolted steel parts shall fit solidly together after the bolts are tightened, and may be coated or noncoated. The slope of the surfaces of parts in contact with the bolt head or nut shall not exceed 1:20 with respect to a plane normal to the bolt axis. (b) Surface Conditions. When assembled, all joint surfaces, including surfaces adjacent to the bolt head and nut, shall be free of scale, except tight mill scale, and shall be free of dirt or other foreign material. Burrs that would prevent solid seating of the connected parts in the snug tight condition shall be removed. Paint is permitted unconditionally on the faying surfaces in connections except in slip-critical connections as defined in Section 5(a). The faying surfaces of slip-critical connections shall meet the requirements of the following paragraphs, as applicable. (1) In noncoated joints, paint, including any inadvertent overspray, shall be excluded from areas closer than one bolt diameter but not less AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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RCSC SPECIFICATION FOR STRUCTURAL JOINTS (6/8/88)
(2)
(3)
(4) (5)
than one inch from the edge of any hole and all areas within the bolt pattern. Joints specified to have painted faying surfaces shall be blast cleaned and coated with a paint which has been qualified as Class A or B in accordance with the requirements of paragraph 2(g), except as provided in 3(b)3. Subject to the approval of the Engineer of Record, coatings providing a slip coefficient less than 0.33 may be used provided the mean slip coefficient is established by test in accordance with the requirements of paragraph 2(g), and the design slip resistance, φRs, calculated in accordance with the formula in Section 5(b) or 5(c). Coated joints shall not be assembled before the coatings have cured for the minimum time used in the qualifying test. Faying surfaces specified to be galvanized shall be hot-dip galvanized in accordance with American Society for Testing and Materials’ “Specification for Zinc (Hot-Galvanized) Coatings on Products Fabricated from Rolled, Pressed, and Forged Steel Shapes, Plates, Bars, and Strip,” ASTM A123 and shall subsequently be roughened by means of hand wire brushing. Power wire brushing is not permitted.
(c) Hole Types. Hole types recognized under this specification are standard holes, oversize holes, short slotted holes and long slotted holes. The nominal dimensions for each type hole shall be not greater than those shown in Table 1. Holes not more than 1⁄32 inch larger in diameter than the true decimal equivalent of the nominal diameter that may result from a drill or reamer of the nominal diameter are considered acceptable. The slightly conical hole that naturally results from punching operations is considered acceptable. The width of slotted holes which are produced by flame cutting or a combination of drilling or punching and flame cutting shall generally be not more than 1⁄32 inch greater than the nominal width except that gouges not more than 1⁄16 inch deep shall be permitted. For statically loaded connections, the flame cut surface need not be ground. For dynamically loaded connections, the flame cut surface shall be ground smooth. 4. Design of Bolted Connections Expressions for design strengths, φRn, of bolts subject to axial tension, shear and combined shear and tension are given in 4(a) and 4(b). They are to be compared to the effect of the factored loads. The design resistances of bolts subject to cyclic application of axial tension are given in 4(e). They are to be compared to effect of cyclically applied nominal (service) loads. (a) Tension and Shear Strength Limit States. The design strength in axial tension for A325 and A490 bolts which are tightened to the minimum fastener tension specified in Table 4 is φRn. The design strength in shear for A325 and A490 bolts, independent of the installed bolt pretension, is φRn where: Rn = Fn Ab AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(LRFD 4.1)
ASTM A325 OR A490 BOLTS
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Table 1. Nominal Hole Dimensions Bolt Dia. 1⁄
2
5⁄
8
3⁄
4
7⁄
8
1 ≥ 11⁄8
Hole DImensions Standard (Dia.)
Oversize (Dia.)
9⁄ 16 11⁄ 16 13⁄ 16 15⁄ 16 11⁄16
5⁄ 8 13⁄ 16 15⁄ 16 11⁄16 11⁄4
d + 1⁄16
d + 5⁄16
Short Slot (Width × Length)
(d
9⁄ × 11⁄ 16 16 11⁄ × 7⁄ 16 8 13⁄ × 1 16 15⁄ × 11⁄ 16 8 11⁄16 × 15⁄16 + 1⁄16) × (d + 3⁄8)
Long Slot (Width × Length) 9⁄
1 16 × 1 ⁄4 9 16 × 1 ⁄16 13⁄ × 17⁄ 16 8 15⁄ × 23⁄ 16 16 11⁄16 × 21⁄2 + 1⁄16) × (2.5 × 11⁄
(d
d)
In this expression: Rn = nominal strength of a bolt subject to axial tension or shear, kips Fn = nominal strength from Table 2 for appropriate kind of load, ksi Ab = area of bolt corresponding to nominal diameter, in.2 φ = resistance factor from Table 2. (b) Combined Tension and Shear Strength Limit State. In bearing connections in which the applied shear force is greater than 1⁄3 the design shear strength according to 4(a). the design strength in axial tension for A325 and A190 bolts is φRn where: Rn = Fnt Ab (LRFD 4.2) Where Rn = nominal tension strength of a bolt subject to concurrent shear. kips Fnt = nominal tension strength of a bolt as calculated by formulas in Table 3, ksi Ab = area of bolt corresponding to nominal diameter, in.2 φ = resistance factor equal to 0.75 In Table 3. fv, equals the shear force on the bolt in ksi. (c) Bearing Strength Limit State. The design bearing strength on the connected material for all bolts in a connection with two or more bolts in the line of force in standard, oversize, or short slotted holes when the edge distance in direction of force is not less than 11⁄2d and the distance center to center of bolts is not less than 3d is φRn, where: Rn = 2.4dtFu
(LRFD 4.3)
The design bearing strength on the connected material for all bolts in a connection with two or more bolts in the line of force in long slotted holes perpendicular to the direction of force when the edge distance, L, is not less than 11⁄2d and the distance center to center of bolts is not less than 3d is φRn where: Rn = 2.0dtFu
(LRFD 4.4)
The design bearing strength on the connected material for the bolt nearest to the free edge in the direction of force when two or more bolts are in the line of force in standard, oversize, or short slotted holes but with the AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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Table 2. Nominal Strength of Fasteners Nominal Strength (ksi)
Load Condition a,b,c
Applied Static Tension Shear on bolt with threads in shear plane. Shear on bolt without threads in shear plane. a. b. c. d.
A325
A490
Resistance Factor, φ
90 d 48 d 60
113 d 60 d 75
0.75 0.75 0.75
Bolts must be tensioned to requirements of Table 4. See 4(e) for bolts subject to tensile fatigue. Except as required by 4(b). In shear connections transmitting axial force whose length between extreme fasteners measured parallel to the line of force exceeds 50 inches, tabulated values shall be reduced 20 percent.
Table 3. Nominal Tension Strength for Bolts in Bearing Connections (Nominal Tensile Strength, Fnt, ksi.) Fastener Grade
Threads Not Excluded from Shear Plane 2
2 0.5
Threads Excluded from Shear Plane 2
2 0.5
ASTM A325
(90 − 3.52fv )
(90 − 2.25fv )
ASTM A490
(113 − 3.54fv )
(113 − 2.27fv )
2
2 0.5
2
2 0.5
edge distance less than 11⁄2d and for a single bolt in the line of force is φRn where: Rn = LtFu ≤ 3.0dtFu
(LRFD 4.5)
When two or more bolts are in the line of force in standard, oversize, or short slotted holes and if deformation around the bolt holes is not a design consideration, the design strength in bearing for the individual bolts of a connection may be taken as φRn where: Rn = LtFu ≤ 3.0dtFu
(LRFD 4.6)
In the foregoing: Rn = nominal bearing strength of connected material, kips Fu = specified minimum tensile strength of the connected part, ksi L = distance in the direction of the force from the center of a standard hole or transverse slotted hole to the edge of the connected part or the distance center to center of standard holes or transverse slots, as applicable, in. d = nominal diameter of bolt, in. t = thickness of connected material, in. φ = resistance factor = 0.75 (d) Prying Action. The force in bolts required to support loads by means of direct tension shall be calculated considering the effects of the external load and any tension resulting from prying action produced by deformation of the connected parts. (e) Tensile Fatigue. When subject to tensile fatigue loading, the tensile stress in the bolt due to the nominal (service) load plus the prying force resulting from cyclic application of nominal load shall not exceed the following design AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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resistances in kips per square inch. The nominal diameter of the bolt shall be used in calculating the bolt stress. In no case shall the calculated prying force exceed 60 percent of the externally applied load. Number of Cycles Not more than 20,000 From 20,000 to 500,000 More than 500,000
A325 44 40 31
A490 54 49 38
Bolts subject to tensile fatigue load must be tensioned to requirements of Table 4. 5. Design Check for Slip Resistance (a) Slip-Critical Joints. Joints in which, in the judgment of the Engineer of Record, slip would be detrimental to the behavior of the joint, are defined as slip-critical. As discussed in the Commentary, these include but are not necessarily limited to joints subject to fatigue or significant load reversal, joints with bolts in oversize holes or slotted holes with the applied force approximately in the direction of the long dimension of the slots and joints in which welds and bolts share in transmitting shear loads at a common faying surface. Slip-critical joints shall be checked for slip resistance. At the option of the Engineer of Record, the required check may be based upon either nominal loads or factored loads. When serviceability at the nominal (service) load is the design criterion, the design slip resistance specified in Section 5(b) shall be compared with the effects of the nominal loads. When slip of the joint at the factored load level would affect the ability of the structure to support the factored load, the design slip resistance specified in Section 5(c) shall be compared to the effects of the factored loads. Slip-critical joints shall also be checked to ensure that the ultimate strength of the joint as a bearing joint is equal to or greater than the effect of the factored loads. Slip-critical joints must be designated on the contract plans and in the specifications. Bolts used in slip-critical joints shall be installed in accordance with the provisions of Section 8(d). (b) Slip-Critical Joints Designed at the Nominal Load Level. Slip-critical joints for which nominal loads are the design criterion shall, in addition to meeting the requirements of Section 4, be proportioned so that the force due to nominal (service) loads does not exceed the design slip resistance for use at nominal loads (service) loads, φRs, where: Rs = DµTm Nb Ns
(LRFD 5.1)
Where: Rs = nominal slip resistance of a bolt for use at nominal loads, kips Tm = minimum fastener tension given in Table 4, kips Nb = number of bolts in the joint Ns = number of slip planes D = slip probability factor* = 0.81 for µ equal to 0.33 = 0.86 for µ equal to 0.40 AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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RCSC SPECIFICATION FOR STRUCTURAL JOINTS (6/8/88)
= 0.86 for µ equal to 0.50 µ = mean slip coefficient for Class A, B or C surfaces, † as applicable, or as established by tests = 0.33 for Class A surfaces (unpainted clean mill scale steel surfaces or surfaces with Class A coating on blast-cleaned steel) = 0.50 for Class B surfaces (unpainted blast-cleaned steel surfaces or surfaces with Class B coatings on blast-cleaned steel) = 0.40 for Class C surfaces (hot-dip galvanized and roughened surfaces) φ = 1.0 for standard holes = 0.85 for oversize and short slotted holes = 0.70 for long slotted holes transverse to the direction of load = 0.60 for long slotted holes parallel to the direction of load * D is a multiplier that reflects the distribution of actual slip coefficient values about the mean, the ratio of measured bolt tensile strength to the specified minimum values, and a slip probability level. Use of other values of D (see Commentary) must be approved by the Engineer of Record. † Coatings classified as Class A or Class B includes those coatings which provide a mean slip coefficient not less than 0.33 or 0.50, respectively, as determined by “Test Method to Determine the Slip Coefficient for Coatings Used in Bolted Connections.”
Table 4. Fastener Tension Required for Slip-Critical Connections and Connections Subject to Direct Tension Nominal Bolt Size, Inches
a
Minimum Tension in 1,000s of Pounds (kips) A325 Bolts
A490 Bolts
12 19 28 39
15 24 35 49
1 11⁄8 11⁄4 13⁄8
51 56 71 85
64 80 102 121
11⁄2
103
148
1⁄
5⁄ 3⁄ 7⁄
2 8 4 8
a. Equal to 70 percent of specified minimum tensile strengths of bolts (as specified in ASTM Specifications for tests of full size A325 and A490 bolts with UNC threads loaded in axial tension) rounded to the nearest kip.
When using nominal loads as the basis for design of slip-critical connections subject to applied tension, T, that reduces the net clamping force, the slip resistance (φRs) shall be multiplied by the following factor in which T is the applied tensile force at nominal loads [1 − T / (0.82TmNb)]
(LRFD 5.2)
(c) Slip-Critical Joints Designed at Factored Load Level. Slip-critical joints for which factored loads are the design criterion shall, in addition to meeting the requirements of Section 4, be proportioned so that the force due to the factored loads shall not exceed the design slip resistance for use at factored loads, φRstr, where: AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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Rstr = 1.13µTm Nb Ns
(LRFD 5.3)
Where terms in Formula (LRFD 5.3) are as defined in 5(b). When using factored loads as the basis for design of slip-critical connections subject to applied tension, T, that reduces the net clamping force, the slip resistance (φRs) shall be multiplied by the following factor in which T is the applied tensile force at nominal loads [1 − T / (1.13Tm Nb)]
(LRFD 5.4)
6. Loads in Combination When the reduced probabilities of maximum loads acting concurrently are accounted for by load combination factors, the resistances given in this Specification shall not be increased. 7. Design Details of Bolted Connections (a) Standard Holes. In the absence of approval by the Engineer of Record for use of other hole types, standard holes shall be used in high-strength bolted connections. (b) Oversize and Slotted Holes. When approved by the Engineer of Record, oversize holes, short slotted holes or long slotted holes may be used subject to the following joint detail requirements: (1) Oversize holes may be used in all plies of connections in which the design slip resistance of the connection is greater than the factored nominal load. (2) Short slotted holes may be used in any or all plies of connections in which the design strength (Section 4(a)) is greater than the factored nominal load provided the load is applied approximately normal (between 80 and 100 degrees) to the axis of the slot. Short slotted holes may be used without regard for the direction of applied load in any or all plies of connections in which the design slip resistance (Section 5(b)) is greater than the factored nominal load. (3) Long slotted holes may be used in one of the connected parts at any individual faying surface in connections in which the design strength (Section 4(a)) is greater than the factored nominal load provided the load is applied approximately normal (between 80 and 100 degrees) to the axis of the slot. Long slotted holes may be used in one of the connected parts at any individual faying surface without regard for the direction of applied load on connections in which the design slip resistance (Section 5(b)) is greater than the factored nominal load. (4) Fully inserted finger shims between the faying surfaces of load transmitting elements of connections are not to be considered a long slot element of a connection. (c) Washer Requirements. Design details shall provide for washers in highstrength bolted connections as follows: (1) Where the outer face of the bolted parts has a slope greater than 1:20 with respect to a plane normal to the bolt axis, a hardened beveled washer shall be used to compensate for the lack of parallelism. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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RCSC SPECIFICATION FOR STRUCTURAL JOINTS (6/8/88)
(2) Hardened washers are not required for connections using A325 and A490 bolts except as required in paragraphs 7(c)(3) through 7(c)(7) for slip-critical connections and connections subject to direct tension or as required by paragraph 8(c) for shear/bearing connections. (3) Hardened washers shall be used under the element turned in tightening when the tightening is to be performed by calibrated wrench method. (4) Irrespective of the tightening method, hardened washers shall be used under both the head and the nut when A490 bolts are to be installed and tightened to the tension specified in Table 4 in material having a specified yield point less than 40 ksi. (5) Where A325 bolts of any diameter or A490 bolts equal to or less than 1 inch in diameter are to be installed and tightened in an oversize or short slotted hole in an outer ply, a hardened washer conforming to ASTM F436 shall be used. (6) When A490 bolts over 1 inch in diameter are to be installed and tightened in an oversize or short slotted hole in an outer ply, hardened washers conforming to ASTM F436 except with 5⁄16 inch minimum thickness shall be used under both the head and the nut in lieu of standard thickness hardened washers. Multiple hardened washers with combined thickness equal to or greater than 5⁄16 inch do not satisfy this requirement. (7) Where A325 bolts of any diameter or A490 bolts equal to or less than 1 inch in diameter are to be installed and tightened in a long slotted hole in an outer ply, a plate washer or continuous bar of at least 5⁄16 inch thickness with standard holes shall be provided. These washers or bars shall have a size sufficient to completely cover the slot after installation and shall be of structural grade material, but need not be hardened except as follows. When A490 bolts over 1 inch in diameter are to be used in long slotted holes in external plies, a single hardened washer conforming to ASTM F436 but with 5⁄16 inch minimum thickness shall be used in lieu of washers or bars of structural grade material. Multiple hardened washers with combined thickness equal to or greater than 5⁄16 inch do not satisfy this requirement. (8) Alternative design fasteners meeting the requirements of 2(d) with a geometry which provides a bearing circle on the head or nut with a diameter equal to or greater than the diameter of hardened washers meeting the requirements ASTM F436 satisfy the requirements for washers specified in paragraphs 7(c)(4) and 7(c)(5). 8. Installation and Tightening (a) Handling and Storage of Fasteners. Fasteners shall be protected from dirt and moisture at the job site. Only as many fasteners as are anticipated to be installed and tightened during a work shift shall be taken from protected storage. Fasteners not used shall be returned to protected storage at the end of the shift. Fasteners shall not be cleaned of lubricant that is present in asdelivered condition. Fasteners which accumulate rust or dirt resulting from job site conditions shall be cleaned and relubricated prior to installation. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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(b) Tension Calibrator. A tension measuring device shall be at all job sites where bolts in slip-critical joints or connections subject to direct tension are being installed and tightened. The tension measuring device shall be used to confirm (1) the suitability of the complete fastener assembly and method of tightening, including lubrication, if required to satisfy the requirements of Table 4, (2) to calibrate the wrenches, if applicable, and (3) to confirm the understanding and proper use by the bolting crew of the method to be used. The frequency of confirmation testing, the number of tests to be performed, and the test procedure shall be as specified in 8(d), as applicable. The accuracy of the tension measuring device shall be confirmed through calibration by an approved testing agency at least annually. (c) Joint Assembly and Tightening of Shear/Bearing Connections. (1) Snug Tightened Bolts. Bolts in connections not within the slipcritical category as defined in Section 5(a) nor subject to tension loads nor required to be pretensioned bearing connections in accordance with 8(c)(2) shall be installed in properly aligned holes, but need only be tightened to the snug tight condition. The snug tight condition is defined as the tightness that exists when all plies in a joint are in firm contact. (See Commentary.) If a slotted hole occurs in an outer ply, a flat hardened washer or common plate washer shall be installed over the slot. (2) Tensioned Shear/Bearing Connections. The Engineer of Record may designate certain shear/bearing connections to be tightened to pretension in excess of snug tight. When so designated and identified on the contract drawings, the bolts in such connections shall be installed and tightened in accordance with one of the methods described in Subsections 8(d)(1) through 8(d)(4), but shall not be subject to the requirements for faying surface conditions of slipcritical connections contained in 3(b). The bolts need not be subject to inspection testing to determine the actual level of bolt pretension unless required by the Engineer of Record. (d) Joint Assembly and Tightening of Slip-Critical and Direct Tension Connections. In slip-critical connections and connections subject to direct tension, fasteners together with washers of size and quality specified, located as required by Section 7(c), shall be installed in properly aligned holes and tightened by any of the methods described in Subsections 8(d)(1) through 8(d)(4) to at least the minimum tension specified in Table 4 when all the fasteners are tight. Tightening may be done by turning the bolt while the nut is prevented from rotating when it is impractical to turn the nut. Impact wrenches, if used, shall be of adequate capacity and sufficiently supplied with air to perform the required tightening of each bolt in approximately 10 seconds. Slip-critical connections and connections subject to direct tension shall be clearly identified on the drawings. (1) Turn-of-Nut Tightening. When turn-of-nut tightening is used, hardened washers are not required except as may be specified in 7(c). A representative sample of not less than three bolt and nut assemblies of each diameter, length, grade and lot to be used in the work shall be checked at the start of work in a device capable AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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RCSC SPECIFICATION FOR STRUCTURAL JOINTS (6/8/88)
of indicating bolt tension. The test shall demonstrate that the method for estimating the snug tight condition and controlling the turns from snug tight to be used by the bolting crew develops a tension not less than 5 percent greater than the tension required by Table 4. Bolts shall be installed in all holes of the connection and brought to a â&#x20AC;&#x153;snug tightâ&#x20AC;? condition. Snug tight is defined as the tightness that exists when the plies of the joint are in firm contact. Snug tightening shall progress systematically from the most rigid part of the connection to the free edges until all bolts are simultaneously snug tight and the connection is fully compacted. In some cases, proper tensioning of the bolts may require more than a single cycle of systematic tightening to produce a uniform snug tight condition. Following this initial operation, all bolts in the connection shall be tightened further by application of the rotation specified in Table 5. During the tightening operation, there shall be no rotation of the part not turned by the wrench. Tightening shall progress systematically from the most rigid part of the joint to its free edges. (2) Calibrated Wrench Tightening: Calibrated wrench tightening may be used only when installation procedures are calibrated on a daily basis and when a hardened washer is used under the element turned in tightening. (See the Commentary to this Section.) This specification does not recognize standard torques determined from tables or from formulas which are assumed to relate torque to tension. When calibrated wrenches are used for installation, they shall be set to provide a tension not less than 5 percent in excess of the minimum tension specified in Table 4. The installation procedures shall be calibrated at least once each working day by tightening representative sample fastener assemblies in a device capable of indicating actual bolt tension. The representative fastener assemblies shall consist of three bolts from each lot diameter, length and grade with nuts from each lot, diameter and grade and with a hardened washer from the washers being used in the work under the element turned in tightening. Wrenches shall be recalibrated when significant difference is noted in the surface condition of the boltsâ&#x20AC;&#x2122; threads, nuts or washers. It shall be verified during actual installation in the assembled steelwork that the wrench adjustment selected by the calibration does not produce a nut or bolt head rotation from snug tight greater than that permitted in Table 5. If manual torque wrenches are used, nuts shall be turned in the tightening direction when torque is measured. When calibrated wrenches are used to install and tension bolts in a connection, bolts shall be installed with hardened washers under the element turned in tightening bolts in all holes of the connection and brought to a snug tight condition. Snug tightening shall progress systematically from the most rigid part of the connections to the free edges until bolts are uniformly snug tight and the plies of the joint are in firm contact. Following this initial tightening operation, the connection shall be tightened using the calibrated wrench. Tightening shall progress systematically from the most rigid part AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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Table 5. Nut Rotation from Snug Tight Condition
Disposition of Outer Face of Bolted Parts Bolt length (underside of head to end of bolt)
Both faces normal to bolt axis
One face normal to bolt axis and other sloped not more than 1:20 (beveled washer not used)
Both faces sloped not more than 1:20 from normal to the bolt axis (beveled washer not used)
Up to and including 4 diameters
1⁄ 3
turn
1⁄ 2
turn
2⁄
3
turn
Over 4 diameters but not exceeding 8 dia.
1⁄ 2
turn
2⁄ 3
turn
5⁄
6
turn
Over 8 diameters but not exceedc ing 12 dia.
2⁄ 3
turn
5⁄ 6
turn
1 turn
a. Nut rotation is relative to bolt regardless of the element (nut or bolt) being turned. For bolts installed by 1⁄2 turn and less, the tolerance should be plus or minus 30 degrees; for bolts installed by 2⁄3 turn and more, the tolerance should be plus or minus 45 degrees. b. Applicable only to connections in which all material within the grip of the bolt is steel. c. No research has been performed by the Council to establish the turn-of-nut procedure for bolt lengths exceeding 12 diameters. Therefore, the required rotation must be determined by actual test in a suitable tension measuring device which simulates conditions of solidly fitted steel.
of the joint to its free edges. During snugging and final tightening the element not turned in tightening shall be held to prevent rotation which will damage threads. In some cases, proper tensioning of the bolts may require more than a single cycle of systematic tightening to ensure all bolts are tightened to at least the prescribed amount. (3) Installation of Alternative Design Bolts. When fasteners which incorporate a design feature intended to indicate a predetermined tension or torque has been applied or to control bolt installation tension or torque, and which have been qualified under Section 2(d) are to be installed, a representative sample of not less than three bolts of each diameter, length and grade shall be checked at the job site in a device capable of indicating bolt tension. The test assembly shall include flat hardened washers, if required in the actual connection, arranged as in the actual connections to be tensioned. The calibration test shall demonstrate that each bolt develops a tension not less than 5 percent greater than the tension required by Table 4. Manufacturer’s installation procedure as required by Section 2(d) shall be followed for installation of bolts in the calibration device and in all connections. When alternative design fasteners are used in the work, bolts shall be installed in all holes of the connection and initially tightened sufficiently to bring all plies of the joint into firm contact with the bolts uniformly tight but without yielding or fracturing the control or indicator element of the fasteners. In some cases, proper AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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RCSC SPECIFICATION FOR STRUCTURAL JOINTS (6/8/88)
tensioning of the bolts may require more than a single cycle of systematic partial tightening. After all plies of the joint are in firm contact, all fasteners shall be further tightened, progressing systematically from the most rigid part of the connection to the free edges in a manner that will minimize relaxation of previously tightened fasteners. In some cases, proper tensioning of the bolts may require more than a single cycle of systematic partial tightening prior to final yielding or fracture of the control or indicator element of individual fasteners. (4) Direct Tension Indicator Tightening. When bolts are to be installed using direct tension indicator devices to indicate bolt tension, a representative sample of not less than three devices for each diameter and grade of fastener shall be tested with three typical bolts in a calibration device capable of indicating bolt tension. The test assembly shall include flat hardened washers, if required in the actual connection, arranged as those in the actual connections to be tensioned. The calibration test shall demonstrate that the device indicates a tension not less than 5 percent greater than that required by Table 4. When bolts are installed in the work using direct tension indicators meeting the requirements of ASTM F959, bolts shall be installed in all holes of the connection and tightened until all plies of the joint are in firm contact and fasteners are uniformly snug tight. Snug tight is indicated by partial compression of the direct tension indicator protrusions. All fasteners shall then be tightened, progressing systematically from the most rigid part of the connection to the free edges in a manner that will minimize relaxation of previously tightened fasteners. In some cases, proper tensioning of the bolts may require more than a single cycle of systematic partial tightening prior to final tightening to deform the protrusion to the specified gap. Special attention shall be given to proper installation of flat hardened washers when direct tension indicator devices are used with bolts installed in oversize or slotted holes and when the load indicating devices are used under the turned element. If direct tension indicators different from those meeting the requirements of ASTM F959 are used, manufacturerâ&#x20AC;&#x2122;s installation procedure as required by Section 2(f), shall be followed for installation of bolts in the calibration device and in all connections, and in addition the general requirements for use of direct tension indicators meeting the requirements of ASTM F959 shall be met. (e) Identification of Tightening Requirements. Bolts in slip-critical connections or bolts subject to axial tension which are to be installed and tightened in accordance by one of the methods in 8(d) and which require inspection to ensure that requirements of Table 4 are satisfied shall be clearly identified on the contract drawings. Shear/bearing connections which are to be installed by one of the methods in 8(d) but which need not be inspected to ensure bolt tensions specified in Table 4 are met shall be clearly identified on the contract drawings. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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(f) Reuse of Bolts. A490 bolts and galvanized A325 bolts shall not be reused. Other A325 bolts may be reused if approved by the Engineer of Record. Touching up or retightening previously snug tightened bolts which may have been loosened by the snugging of adjacent bolts shall not be considered to be a reuse. 9. Inspection (a) Inspector Responsibility. When inspection is required by the contract documents, the Inspector shall determine while the work is in progress that the requirements of Sections 2, 3 and 8, as appropriate, of this Specification are met in the work. All connections shall be inspected to ensure that the plies of the connected elements have been brought into firm contact. Bolts in connections not identified as being slip-critical nor subject to direct tension nor as tensioned bearing connections as provided in 8(c)(2) should not be inspected for bolt tension. For connections identified to be installed in accordance with 8(c)(2), the Inspector shall monitor installation and tightening of bolts to ensure that bolts are tightened in accordance with one of the methods of 8(d), but should not test the bolts for actual installed pretension. For all connections specified to be slip critical or subject to axial tension the Inspector shall observe the demonstration testing, and calibration procedures when such calibration is required, and shall monitor the installation of bolts to determine that all plies of the material have been drawn together and that the selected procedure has been used to tighten all bolts to ensure that the specified procedure was followed to achieve the pretension specified in Table 4. Bolts installed by procedures in Section 8(d) may reach tensions substantially greater than values given in Table 4, but this shall not be cause for rejection. (b) Arbitration Inspection. When high-strength bolts in slip-critical connections and connections subject to direct tension have been installed by any of the tightening methods in Section 8(d) and inspected in accordance with Section 9(a) and a disagreement exists as to the minimum tension of the installed bolts, the following arbitration procedure may be used. Other methods for arbitration inspection may be used if approved by the Engineer of Record. (1) The Inspector shall use a manual torque wrench which indicates torque by means of a dial or which may be adjusted to give an indication that the job inspecting torque has been reached. (2) This Specification does not recognize standard torques determined from tables or from formulas which are assumed to relate torque to tension. Testing using such standard torques shall not be considered valid. (3) A representative sample of five bolts from the diameter, length and grade of the bolts being inspected shall be tightened in the tension measuring device by any convenient means to an initial condition equal to approximately 15 percent of the required fastener tension and then to the minimum tension specified in Table 4. Material under the turned element in the tension measuring device shall be the same as in the actual installation, that is, structural steel or AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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RCSC SPECIFICATION FOR STRUCTURAL JOINTS (6/8/88)
hardened washer. Tightening beyond the initial condition must not produce greater nut rotation than 11â &#x201E;2 times that permitted in Table 5. The job inspecting torque shall be taken as the average of three values thus determined after rejecting the high and low values. The inspecting wrench shall then be applied to the tightened bolts in the work and the torque necessary to turn the nut or head 5 degrees (approximately 1 inch at 12 inch radius) in the tightening direction shall be determined. (4) Bolts represented by the sample in the foregoing paragraph which have been tightened in the structure shall be inspected by applying, in the tightening direction, the inspecting wrench and its job torque to 10 percent of the bolts, but not less than 2 bolts, selected at random in each connection in question. If no nut or bolt head is turned by application of the job inspecting torque, the connection shall be accepted as properly tightened. If any nut or bolt is turned by the application of the job inspecting torque, all bolts in the connection shall be tested, and all bolts whose nut or head is turned by the job inspecting torque shall be tightened and reinspected. Alternatively, the fabricator or erector, at his option, may retighten all of the bolts in the connection and then resubmit the connection for the specified inspection. (c) Delayed Verification Inspection. The procedures specified in Sections 9(a) and (b) are intended for inspection of bolted connections and verification of pretension at the time of tensioning the joint. If verification of bolt tension is required after a passage of a period of time and exposure of the completed joints, the procedure of Section 9(b) will provide indication of bolt tension which is of questionable accuracy. Procedures appropriate to the specific situation should be used for verification of bolt tension. This might involve use of the arbitration inspection procedure contained herein, or might require the development and use of alternate procedures. (See Commentary.)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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APPENDIX A
Testing Method to Determine the Slip Coefficient for Coatings Used in Bolted Joints Reprinted from Engineering Journal American Institute of Steel Construction, Third Quarter, 1985.
JOSEPH A. YURA and KARL H. FRANK
In 1975, the Steel Structures Painting Council (SSPC) contacted the Research Council on Riveted and Bolted Structural Joints (RCRBSJ), now the Research Council on Structural Connections (RCSC), regarding the difficulties and costs which steel fabricators encounter with restrictions on coatings of contact surfaces for friction-type structural joints. The SSPC also expressed the need for a “standardized test which can be conducted by any certified testing agency at the initiative and expense of any interested party, including the paint manufacturer.” And finally, the RCSC was requested to “prepare and promulgate a specification for the conduct of such a standard test for slip coefficients.” The following Testing Method is the answer of Research Council on Structural Connections to the SSPC request. The test method was developed by Professors Joseph A. Yura and Karl H. Frank of the University of Texas at Austin under a grant from the Federal Highway Administration. The Testing Method was approved by the RCSC on June 14, 1984. 1.0 GENERAL PROVISIONS 1.1 Purpose and Scope The purpose of the testing procedure is to determine the slip coefficient of a coating for use in high-strength bolted connections. The testing specification ensures that the creep deformation of the coating due to both the clamping force of the bolt and the service load joint shear are such that the coating will provide satisfactory performance under sustained loading. Joseph A. Yura, M. ASCE, is Warren S. Bellows Centennial Professor in Civil Engineering, University of Texas at Austin, Austin, Texas. Karl H. Frank, A.M. ASCE, is Associate Professor, Department of Civil Engineering, University of Texas at Austin, Austin, Texas.
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1.2 Definition of Essential Variables Essential variables mean those variables which, if changed, will require retesting of the coating to determine its slip coefficient. The essential variables are given below. The relationship of these variables to the limitation of application of the coating for structural joints is also given. The time interval between application of the coating and the time of testing is an essential variable. The time interval must be recorded in hours and any special curing procedures detailed. Curing according to published manufacturer’s recommendations would not be considered a special curing procedure. The coatings are qualified for use in structural connections which are assembled after coating for a time equal to or greater than the interval used in the test specimens. Special curing conditions used in the test specimens will also apply to the use of the coating in the structural connections. The coating thickness is an essential variable. The maximum average coating thickness allowed on the bolted structure will be the average thickness, rounded to the nearest whole mil, of the coating used on the creep test specimens minus 2 mils. The composition of the coating, including the thinners used, and its method of manufacture are essential variables. Any change will require retesting of the coating. 1.3 Retesting A coating which fails to meet the creep or the post-creep slip test requirements given in Sect. 4 may be retested in accordance with methods in Sect. 4 at a lower slip coefficient, without repeating the static short-term tests specified in Sect. 3. Essential variables must remain unchanged in the retest. 2.0 TEST PLATES AND COATING OF THE SPECIMENS 2.1 Test Plates The test specimen plates for the short-term static tests are shown in Fig. 1. The plates are 4×4 in. plates, 5⁄8-in. thick, with a 1-in. dia. hole drilled 11⁄2 in. ± 1⁄16 in. from one edge. The specimen plates for the creep specimen are shown in Fig. 2. The plates are 4×7 in., 5⁄8-in. thick, with two 1-in. holes, 11⁄2 in. ± 1⁄16 in. from each end. The edges of the plates may be milled, as rolled or saw cut. Flame cut edges 4″
Load
1″ Clamping force
1 1/2 ″
cL
5″ 11/2 ″
11/2 ″
4″ 1-in. Dia.
1″ All plates 5/8 ″thick
Fig. 1. Compression test specimen
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are not permitted. The plates should be flat enough to ensure they will be in reasonably full contact over the faying surface. Any burrs, lips or rough edges should be filed or milled flat. The arrangement of the specimen plates for the testing is shown in Figs. 2 and 3. The plates are to be fabricated from a steel with a minimum yield strength between 36 to 50 ksi. If specimens with more than one bolt are desired, the contact surface per bolt should be 4×3 in. as shown for the single bolt specimen in Fig. 1. 2.2 Specimen Coating The coatings are to be applied to the specimens in a manner consistent with the actual intended structural application. The method of applying the coating and the surface preparation should be given in the test report. The specimens are to be coated to an average thickness 2 mils (0.05 mm) greater than average thickness to be used in the structure. The thickness of the total coating and the primer, if used, shall be measured on the contact surface of the specimens. The thickness should be measured in accordance with the Steel Structures Painting Council specification SSPCPA2, Measurement of Dry Paint Thickness with Magnetic Gages.1 Two spot readings (six gage readings) should be made for each contact surface. The overall average thickness from the three plates comprising a specimen is the average thickness for the specimen. This value should be reported for each specimen. The average coating thickness of the three creep specimens will be calculated and reported. The average thickness of the creep specimen minus two mils rounded to the nearest whole mil is the maximum average thickness of the coating to be used in the faying surface of a structure. The time between painting and specimen assembly is to be the same for all specimens within ±4 hours. The average time is to be calculated and reported. The two coating applications required in Sect. 3 are to use the same equipment and procedures. 3.0 SLIP TESTS The methods and procedures described herein are used to determine experimentally the slip coefficient (sometimes called the coefficient of friction) under shortterm static loading for high-strength bolted connections. The slip coefficient will be determined by testing two sets of five specimens. The two sets are to be coated at different times at least one week apart. 3.1 Compression Test Setup The test setup shown in Fig. 3 has two major loading components, one to apply a clamping force to the specimen plates and another to apply a compressive load to the specimen so that the load is transferred across the faying surfaces by friction. Clamping Force System. The clamping force system consists of a 7⁄8-in. dia. threaded rod which passes through the specimen and a centerhole compression ram. A 2H nut is used at both ends of the rod, and a hardened washer is used at each side of the test specimen. Between the ram and the specimen is a specially fabricated 7⁄8-in. 2H nut in which the threads have been drilled out so that it will slide with little resistance along the rod. When oil is pumped into the centerhole ram, 1. Steel Structures Painting Council, Steel Structures Painting Manual, Vols. 1 and 2, Pittsburgh, Pa., 1982.
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RCSC SPECIFICATION FOR STRUCTURAL JOINTS
2″ Load indicating washer Clamping bolt
4″
1″
7″
Pin bolt
1″ 11/2 ″
Specimen
7″
17/ 8 ″
4″
Fig. 2. Creep test specimens
Drilled nut
Load
Testing machine
Nut 7/ 8
Spherical head 50 kip Center hole ram
Dia. rod
Nut 7/ 8 -2M
Hardened washer Specimen
Plate Piston
Base
Fig. 3. Test setup AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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the piston rod extends, thus forcing the special nut against one of the outside plates of the specimen. This action puts tension in the threaded rod and applies a clamping force to the specimen which simulates the effect of a tightened bolt. If the diameter of the centerhole ram is greater than 1 in., additional plate washers will be necessary at the ends of the ram. The clamping force system must have a capability to apply a load of at least 49 kips and maintain this load during the test with an accuracy of Âą1%. Compressive Load System. A compressive load is applied to the specimen until slip occurs. This compressive load can be applied by a compression test machine or compression ram. The machine, ram and the necessary supporting elements should be able to support a force of 90 kips. The compression loading system should have an accuracy of 1.0% of the slip load. 3.2 Instrumentation Clamping Force. The clamping force must be measured within 0.5 kips. This may be accomplished by measuring the pressure in the calibrated ram or placing a load cell in series with the ram. Compression Load. The compression load must be measured during the test. This may be accomplished by direct reading from a compression testing machine, a load cell in series with the specimen and the compression loading device, or pressure readings on a calibrated compression ram. Slip Deformation. The relative displacement of the center plate and the two outside plates must be measured. This displacement, called slip for simplicity, should be the average which occurs at the centerline of the specimen. This can be accomplished by using the average of two gages placed on the two exposed edges of the specimen or by monitoring the movement of the loading head relative to the base. If the latter method is used, due regard must be taken for any slack that may be present in the loading system prior to application of the load. Deflections can be measured by dial gages or any other calibrated device which has an accuracy of 0.001 in. 3.3 Test Procedure The specimen is installed in the test setup as shown in Fig. 3. Before the hydraulic clamping force is applied, the individual plates should be positioned so that they are in, or are close to, bearing contact with the 7â &#x201E;8-in. threaded rod in a direction opposite to the planned compressive loading to ensure obvious slip deformation. Care should be taken in positioning the two outside plates so that the specimen will be straight and both plates are in contact with the base. After the plates are positioned, the centerhold ram is engaged to produce a clamping force of 49 kips. The applied clamping force should be maintained within Âą0.5 kips during the test until slip occurs. The spherical head of the compression loading machine should be brought in contact with the center plate of the specimen after the clamping force is applied. The spherical head or other appropriate device ensures uniform contact along the edge of the plate, thus eliminating eccentric loading. When 1 kip or less of compressive load is applied, the slip gages should be engaged or attached. The purpose of engaging the deflection gage(s), after a slight load is applied, is to eliminate initial specimen settling deformation from the slip readings. When the slip gages are in place, the compression load is applied at a rate not AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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RCSC SPECIFICATION FOR STRUCTURAL JOINTS
exceeding 25 kips (109 kN) per minute, or 0.003 in. of slip displacement per minute until the slip load is reached. The test should be terminated when a slip of 0.05 in. or greater is recorded. The load-slip relationship should preferably be monitored continuously on an X-Y plotter throughout the test, but in lieu of continuous data, sufficient load-slip data must be recorded to evaluate the slip load defined below. 3.4 Slip Load Typical load-slip response is shown in Fig. 4. Three types of curves are usually observed and the slip load associated with each type is defined as follows: Curve (a). Slip load is the maximum load, provided this maximum occurs before a slip of 0.02 in. is recorded. Curve (b). Slip load is the load at which the slip rate increases suddenly. Curve (c). Slip load is the load corresponding to a deformation of 0.02 in. This definition applies when the load vs. slip curves show a gradual change in response.
-slip load
a
LOAD
b c
Load Slip
0
0.020
0.040 SLIP (in.)
Fig. 4. Definition of slip load
3.5 Coefficient of Slip The slip coefficient ks for an individual specimen is calculated as follows: ks =
slip load 2 Ă&#x2014; clamping force
The mean slip coefficient for both sets of five specimens must be compared. If the two means differ by more than 25%, using the smaller mean as the base, a third five-specimen set must be tested. The mean and standard deviation of the data from all specimens tested define the slip coefficient of the coating. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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3.6 Alternate Test Methods Other test methods to determine slip may be used provided the accuracy of load measurement and clamping satisfies the conditions presented in the previous sections. For example, the slip load may be determined from a tension-type test setup rather than the compression-type as long as the contact surface area per fastener of the test specimen is the same as shown in Fig. 1. The clamping force of at least 49 kips may be applied by any means provided the force can be established within ±1%. Strain-gaged bolts can usually provide the desired accuracy. However, bolts installed by turn-of-nut method, tension indicating fasteners and load indicator washers usually show too much variation to be used in the slip test. 4.0 TENSION CREEP TESTS The test method outlined is intended to ensure the coating will not undergo significant creep deformation under service loading. The test also determines the loss in clamping force in the fastener due to the compression or creep of the paint. Three replicate specimens are to be tested. 4.1 Test Setup Tension-type specimens, as shown in Fig. 2, are to be used. The replicate specimens are to be linked together in a single chain-like arrangement, using loose pin bolts, so the same load is applied to all specimens. The specimens shall be assembled so the specimen plates are bearing against the bolt in a direction opposite to the applied tension loading. Care should be taken in the assembly of the specimens to ensure the centerline of the holes used to accept the pin bolts is in line with the bolts used to assemble the joint. The load level, specified in Sect. 4.2, shall be maintained constant within ±1% by springs, load maintainers, servo controllers, dead weights or other suitable equipment. The bolts used to clamp the specimens together shall be 7⁄8-in. dia. A490 bolts. All bolts should come from the same lot. The clamping force in the bolts should be a minimum of 49 kips. The clamping force is to be determined by calibrating the bolt force with bolt elongation, if standard bolts are used. Special fasteners which control the clamping force by other means such as bolt torque or strain gages may be used. A minimum of three bolt calibrations must be performed using the technique selected for bolt force determination. The average of the three-bolt calibration is to be calculated and reported. The method of measuring bolt force must ensure the clamping force is within ±2 kips (9 kN) of the average value. The relative slip between the outside plates and the center plates shall be measured to an accuracy of 0.001 in. (0.02 mm). This is to be measured on both sides of each specimen. 4.2 Test Procedure The load to be placed on the creep specimens is the service load permitted for 7⁄8-in. A490 bolts in slip-critical connections by the latest edition of the Specification for Structural Joints Using ASTM A325 or A490 Bolts2 for the particular slip coefficient category under consideration. The load is to be placed on the specimen and held 2. Research Council of Structural Connections, Specification for Structural Joints Using ASTM A325 or A490 Bolts, American Institute of Steel Construction, Inc., Chicago, November 1985.
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RCSC SPECIFICATION FOR STRUCTURAL JOINTS
for 1,000 hours. The creep deformation of a specimen is calculated using the average reading of the two displacements on each side of the specimen. The difference between the average after 1,000 hours and the initial average reading taken within one-half hour after loading the specimens is defined as the creep deformation of the specimen. This value is to be reported for each specimen. If the creep deformation of any specimen exceeds 0.005 in. (0.12 mm), the coating has failed the test for the slip coefficient used. The coating may be retested using new specimens in accordance with this section at a load corresponding to a lower value of slip coefficient. If the value of creep deformation is less than 0.005 in. (0.12 mm) for all specimens, the specimens are to be loaded in tension to a load calculated as Pu = average clamping force × design slip coefficient × 2 since there are two slip planes. The average slip deformation which occurs at this load must be less than 0.015 in. (0.38 mm) for the three specimens. If the deformation is greater than this value, the coating is considered to have failed to meet the requirements for the particular slip coefficient used. The value of deformation for each specimen is to be reported. COMMENTARY The slip coefficient under short-term static loading has been found to be independent of clamping force, paint thickness and hole diameter.3 The slip coefficient can be easily determined using the hydraulic bolt test setup included in this specification. The slip load measured in this setup yields the slip coefficient directly since the clamping force is controlled. The slip coefficient k, is given by ks =
slip load 2 × clamping force
The resulting slip coefficient has been found to correlate with both tension and compression tests of bolted specimens. However, tests of bolted specimens revealed that the clamping force may not be constant but decreases with time due to the compressive creep of the coating on the faying surfaces and under the nut and bolt head. The reduction of the clamping force can be considerable for joints with high clamping force and thick coatings, as much as a 20% loss. This reduction in clamping force causes a corresponding reduction in the slip load. The resulting reduction in slip load must be considered in the procedure used to determine the design allowable slip loads for the coating. The loss in clamping force is a characteristic of the coating. Consequently, it cannot be accounted for by an increase in the factor of safety or a reduction in the clamping force used for design without unduly penalizing coatings which do not exhibit this behavior. The creep deformation of the bolted joint under the applied shear loading is also an important characteristic and a function of the coating applied. Thicker coatings tend to creep more than thinner coatings. Rate of creep deformation increases as the applied load approaches the slip load. Extensive testing has shown the rate of creep is not constant with time, rather it decreases with time. After 1,000 hours of loading, the additional creep deformation is negligible. 3. Frank, K. H., and J. A. Yura, An Experimental Study of Bolted Shear Connections, FHWA/RD-81-148, Federal Highway Administration, Washington, D.C., December 1981.
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The proposed test methods are designed to provide the necessary information to evaluate the suitability of a coating for slip critical bolted connections and to determine the slip coefficient to be used in the design of the connections. The initial testing of the compression specimens provides a measure of the scatter of the slip coefficient. In order to get better statistical information, a third set of specimens must be tested whenever the means of the initial two sets differ by more than 25%. The creep tests are designed to measure the paint’s creep behavior under the service loads determined by the paint’s slip coefficient based on the compression test results. The slip test conducted at the conclusion of the creep test is to ensure the loss of clamping force in the bolt does not reduce the slip load below that associated with the design slip coefficient. A490 bolts are specified, since the loss of clamping force is larger for these bolts than A325 bolts. Qualifying of the paint for use in a structure at an average thickness of 2 mils less than the test specimen is to ensure that a casual buildup of paint due to overspray, etc., does not jeopardize the coating’s performance. The use of 1-in. (25 mm) holes in the specimens is to ensure that adequate clearance is available for slip. Fabrication tolerances, coating buildup on the holes and assembly tolerances reduce the apparent clearances.
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Commentary on Specifications for Structural Joints Using ASTM A325 or A490 Bolts June 8, 1988.
Historical Notes When first approved by the Research Council on Structural Connections of the Engineering Foundation, January 1951, the “Specification for Assembly of Structural Joints Using High-Strength Bolts” merely permitted the substitution of a like number of A325 high-strength bolts for hot driven ASTM A141 (presently identified as A502, Grade 1) steel rivets of the same nominal diameter. It was required that all contact surfaces be free of paint. As revised in 1954, the omission of paint was required to apply only to “joints subject to stress reversal, impact or vibration, or to cases where stress redistribution due to joint slippage would be undesirable.” This relaxation of the earlier provision recognized the fact that, in a great many cases, movement of the connected parts that brings the bolts into bearing against the sides of their holes is in no way detrimental. In the first edition of the Specification published in 1951, a table of torque to tension relationships for bolts of various diameters was included. It was soon demonstrated in research that a variation in the torque to tension relationship of as high as plus or minus 40 percent must be anticipated unless the relationship is established individually for each bolt lot, diameter and fastener condition. Hence, by the 1954 edition of the Specification, recognition of standard torque to tension relationships in the form of tabulated values or formulas was withdrawn. Recognition of the calibrated wrench method of tightening was retained, however, until 1980, but with the requirement that the torque required for installation or inspection be determined specifically for the bolts being installed on a daily basis. Recognition of the method was withdrawn in 1980 because of continuing controversy resulting from failure of users to adhere to the detailed requirements for valid use of the method both during installation and inspection. With the 1985 version of the Specification, the calibrated wrench method was reinstated, but with more detailed requirements which should be carefully followed. The increasing use of high-strength steels created the need for bolts substantially stronger than A325 in order to resist the much greater forces they support without resort to very large connections. To meet this need, a new ASTM specification, A490, was developed. When provisions for the use of these bolts were included in this Specification in 1964, it was required that they be tightened to their specified proof load, as was required for the installation of A325 bolts. However, the ratio of proof load to specified minimum tensile strength is approximately 0.7 for A325 bolts, whereas it is 0.8 for A490 bolts. Calibration studies have shown that highstrength bolts have ultimate load capacities in torqued tension which vary from about
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COMMENTARY ON THE RCSC SPECIFICATION (6/8/88)
80 to 90 percent of the pure-tension tensile strength.1 Hence, if minimum strength A490 bolts were supplied and they experienced the maximum reduction due to torque required to induce the tension, there is a possibility that these bolts could not be tightened to proof load by any method of installation. Also, statistical studies have shown that tightening to the 0.8 times tensile strength under calibrated wrench control may result in some “twist-off” bolt failures during installation or in some cases a slight amount of under-tightening.2 Therefore, the required installed tension for A490 bolts was reduced to 70 percent of the specified minimum tensile strength. For consistency, but with only minor change, the initial tension required for A325 bolts was also set at 70 percent of their specified minimum tensile strength and, at the same time, the values for minimum required pretension were rounded off to the nearest kip. C1 Scope This Specification deals only with two types of high-strength bolts, namely, ASTM A325 and A490, and to their installation in structural steel joints. The provisions may not be relied upon for high-strength fasteners of other chemical composition or mechanical properties or size. The provisions do not apply to ASTM A325 or A490 fasteners when material other than steel is included in the grip. The provisions do not apply to high-strength anchor bolts. The Specification relates only to the performance of fasteners in structural steel connections and those few aspects of the connected material that affect the performance of the fasteners in connections. Many other aspects of connection design and fabrication are of equal importance and must not be overlooked. For information on questions of design of connected material, not covered herein, the user is directed to standard textbooks on design of structural steel and also to Kulak, G. L., J. W. Fisher, and J. H. A. Struik, Guide to Design Criteria for Bolted and Riveted Joints, 2nd ed., New York: John Wiley & Sons, 1987. (Hereinafter referred to as the Guide.) C2 Bolts, Nuts, Washers and Paint Complete familiarity with the referenced ASTM Specification requirements is necessary for the proper application of this Specification. Discussion of referenced specifications in this Commentary is limited to only a few frequently overlooked or littleunderstood items. In this Specification, a single style of fastener (heavy hex structural bolts with heavy hex nuts) available in two strength grades (A325 and A490) is specified as a principal style, but conditions for acceptance of other types of fasteners are provided. Bolt Specifications. ASTM A325 and A490 bolts are manufactured to dimensions as specified in ANSI Standard B18.2.1 for Heavy Hex Structural Bolts. The basic dimensions, as defined in Fig. C1, are shown in Table C1. The principal geometric features of heavy hex structural bolts that distinguish them from bolts for general application are the size of the head and the body length. The head of the heavy hex 1. Christopher, R. J., G. L. Kulak, and J. W. Fisher, “Calibration of Alloy Steel Bolts,” ASCE Journal of the Structural Division, Vol. 92, No. ST2, Proc. Paper 4768, April, 1966, pp. 19–40. 2. Gill, P. J., “Specifications of Minimum Preloads for Structural Bolts,” Memorandum 30, G.K.N. Group Research Laboratory, England, 1966 (Unpublished Report).
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Table C1 Nominal Bolt Size, Inches D
Bolt Dimensions, Inches Heavy Hex Structural Bolts
Nut Dimensions, Inches Heavy Hex Nuts
Width across flats, F
Height H
Thread length
Width across flats, W
Height H
7⁄ 8 11⁄16 11⁄4 17⁄16 15⁄8 113⁄16 2 23⁄16 23⁄8
5⁄ 16 25⁄ 64 15⁄ 32 35⁄ 64 39⁄ 64 11⁄ 16 25⁄ 32 27⁄ 32 15⁄ 16
1 11⁄4 13⁄8 11⁄2 13⁄4 2 2 21⁄4 21⁄4
7⁄ 8 11⁄16 11⁄4 17⁄16 15⁄8 113⁄16 2 23⁄16 23⁄8
31⁄ 64 39⁄ 64 47⁄ 64 55⁄ 64 64⁄ 64 17⁄64 17⁄32 111⁄32 115⁄32
1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8
1 11⁄8 11⁄4 13⁄8 11⁄2
Thread Length A325
F
H
Bolt Length
H
W
Nut may be chamfered on both faces Fig. C1. Heavy hex structural bolt and heavy hex nut
structural bolt is specified to be the same size as a heavy hex nut of the same nominal diameter in order that the ironworker may use a single size wrench or socket on both the bolt head and the nut. Heavy hex structural bolts have shorter thread length than bolts for general application. By making the body length of the bolt the control dimension, it has been possible to exclude the thread from all shear planes, except in the case of thin outside parts adjacent to the nut. Depending upon the amount of bolt length added to adjust for incremental stock lengths, the full thread may extend into the grip by as much as 3⁄8 inch for 1⁄2, 5⁄8, 3⁄4, 7⁄8, 11⁄4, and 11⁄2 in. diameter bolts and as much as 1⁄2 inch for 1, 11⁄8 and 13⁄8 in. diameter bolts. Inclusion of some thread run-out in the plane of shear is permissible. Of equal or even greater importance is exercise of care to provide sufficient thread for nut tightening to keep the nut threads from jamming into the thread run-out. When the thickness of an outside part is less than the amount the threads may extend into the grip tabulated above, it may be necessary to call for the next increment of bolt length together with sufficient flat washers to ensure full tightening of the nut without jamming nut threads on the thread run-out. There is an exception to the short thread length requirements for ASTM A325 bolts discussed in the foregoing. Beginning with ASTM A325-83, supplementary requirements have been added to the ASTM A325 Specification which permit the AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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purchaser, when the bolt length is equal to or shorter than four times the nominal diameter, to specify that the bolt be threaded for the full length of the shank. This exception to the requirements for thread length of heavy hex structural bolts was provided in the Specification in order to increase economy through simplified ordering and inventory control in the fabrication and erection of structures using relatively thin materials where strength of the connection is not dependent upon shear strength of the bolt, whether threads are in the shear plane or not. The Specification requires that bolts ordered to such supplementary requirements be marked with the symbol A325T. In order to determine the required bolt length, the value shown in Table C2 should be added to the grip (i.e., the total thickness of all connected material, exclusive of washers). For each hardened flat washer that is used, add 5⁄32 inch, and for each beveled washer add 5⁄16 inch. The tabulated values provide appropriate allowances for manufacturing tolerances, and also provide for full thread engagement (defined as having the end of the bolt at least flush with the face of the nut) with an installed heavy hex nut. The length determined by the use of Table C2 should be adjusted to the next longer 1⁄4 inch length. ASTM A325 and ASTM A490 currently provide for three types (according to metallurgical classification) of high-strength structural bolts, supplied in sizes 1⁄2 inch to 11⁄2 inch inclusive except for A490 Type 2 bolts which are available in diameters from 1⁄2 inch to 1 inch inclusive: Type 1. Type 2. Type 3.
Medium carbon steel for A325 bolts, alloy steel for A490 bolts. Low carbon martensitic steel for both A325 and A490 bolts. Bolts having improved atmospheric corrosion resistance and weathering characteristics for both A325 and A490 bolts.
When the bolt type is not specified, either Type 1, Type 2 or Type 3 may be supplied at the option of the manufacturer. Special attention is called to the requirement in ASTM A325 that, where elevated temperature applications are involved, Type 1 bolts shall be specified by the purchaser. This is because the chemistry of Type 2 bolts permits heat treatment at sufficiently low temperatures that subsequent heating to elevated temperatures may affect the mechanical properties. Heavy Hex Nuts. Heavy hex nuts for use with A325 bolts may be manufactured to the requirements of ASTM A194 for grades 2 or 2H or the requirements of ASTM A563 for grades DH, except that nuts to be galvanized for use with galvanized bolts must be hardened nuts meeting the requirements for ASTM A563 grade DH. The heavy hex nuts for use with A490 bolts may be manufactured to the requirements of ASTM A194 for grade 2H or the requirements of ASTM A563 for grade DH. Galvanized High-Strength Bolts. Galvanized high-strength bolts and nuts must be considered as a manufactured matched assembly; hence, comments relative to them have not been included in the foregoing paragraphs where bolts and nuts have been considered separately. Insofar as the hot-dip galvanized bolt and nut assembly, per se, is concerned, four principal factors need be discussed in order that the provisions of the Specification may be understood and properly applied. These are (1) the effect of the hot-dip galvanizing process on the mechanical properties of highstrength steels, (2) the effect of hot-dip galvanized coatings on the nut stripping strength, (3) the effect of galvanizing upon the torque involved in the tightening operation, and (4) shipping requirements. The ASTM Specifications for galvanized A325 high-strength bolts recognize AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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Table C2 Nominal Bolt Size, Inches 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8
To Determine Required Bolt Length Add to Grip, in Inches 11⁄
16 7⁄ 8
1 11⁄8
1 11⁄8 11⁄4 13⁄8
11⁄4 11⁄2 15⁄8 13⁄4
11⁄2
17⁄8
both the hot-dip galvanizing process and the mechanical galvanizing process. The effects of the two processes upon the performance characteristics and requirements for proper installation are distinctly different: therefore, distinction between the two must be noted in the comments which follow. ASTM A325 Specifications require that all components of a fastener assembly (nuts, bolts and washers) shall have been coated by the same process and that the supplier’s option is limited to one process per item with no mixed processes in a lot. Mixing a bolt galvanized by one process with a nut galvanized by the other may result in a unworkable assembly. Effect of Hot-Dip Galvanizing on the Strength of Steels. Steels in the 200 ksi and higher tensile strength range are subject to embrittlement if hydrogen is permitted to remain in the steel and the steel is subjected to high tensile stress. The minimum tensile strength of A325 bolts is 105 or 120 ksi, depending upon the size, comfortably below the critical range. The required maximum tensile strength for A490 bolts was set at 170 ksi in order to provide a little more than a 10 percent margin below 200 ksi; however, because manufacturers must target their production slightly higher than the required minimum, A490 bolts close to the critical range of tensile strength must be anticipated. For black bolts this is not a cause for concern, but, if the bolt is hot-dip galvanized, a hazard of delayed brittle fracture in service exists because of the real possibility of introduction of hydrogen into the steel during the pickling operation of the hot-dip galvanizing process and the subsequent “sealingin” of the hydrogen by the zinc coating. There also exists the possibility of cathodic hydrogen adsorption arising from corrosion process in service in aggressive environments. ASTM Specifications provide for the galvanizing of A325 bolts but not A490 bolts. Galvanizing of A490 bolts is not permitted. Because pickling and emersion in molten zinc is not involved, galvanizing by the mechanical process essentially avoids potential for hydrogen embrittlement. The heat treatment temperatures for Type 2 ASTM A325 bolts are in the range of the molten zinc temperatures for hot-dip galvanizing; therefore there is a potential for diminishing the heat treated mechanical properties of Type 2 A325 bolts by the hot-dip galvanizing process. For this reason, the current Specifications require that only mechanical galvanizing shall be used on Type 2 ASTM A325 bolts. Nut Stripping Strength. Hot-dip galvanizing affects the stripping strength of the nut-bolt assembly primarily because, to accommodate the relatively thick zinc coatAMERICAN INSTITUTE OF STEEL CONSTRUCTION
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ings of non-uniform thickness on bolt threads, it is usual practice to hot-dip galvanize the blank nut and then to tap the nut oversize after galvanizing. This overtapping results in a reduction in the amount of engagement between the steel portions of the male and female threads with a consequent approximately 25 percent reduction in the stripping strength. Only the stronger hardened nuts have adequate strength to meet specification requirements even with the reduction due to overtapping; therefore, ASTM A325 specifies that only Grades DH and 2H be used for galvanized nuts. This requirement should not be overlooked if non-galvanized nuts are purchased and then sent to a local galvanizer for hot-dip galvanizing. Because the mechanical galvanizing process results in a more uniformly distributed and smooth zinc coating, nuts may be tapped oversize before galvanizing by an amount less than required for the hot-dip process before galvanizing. This results in a better bolt-nut fit with zinc coating on the internal threads of the nut. Effect of Galvanizing Upon Torque Involved in Tightening. Research3 has shown that, in the as-galvanized condition, galvanizing both increases the friction between the bolt and nut threads and also makes the torque induced tension much more variable. Lower torque and more consistent results are provided if the nuts are lubricated; thus, ASTM A325 requires that a galvanized bolt and lubricated galvanized nut shall be assembled in a steel joint with a galvanized washer and tested in accordance with ASTM A563 by the manufacturer prior to shipment to ensure that the galvanized nut with the lubricant provided may be rotated from the snug tight condition well in excess of the rotation required for full tensioning of the bolts without stripping. The requirement applies to both hot-dip and mechanical galvanized fasteners. Shipping Requirements for Galvanized Bolts and Nuts. The above requirements clearly indicate (1) that galvanized bolts and nuts are to be treated as a matched assembly, (2) that the seller must supply nuts which have been lubricated and tested with the supplied bolts, and (3) that nuts and bolts must be shipped together in the same shipping container. Purchase of galvanized bolts and galvanized nuts from separate sources is not in accordance with the intent of the ASTM Specifications because the control of overtapping and the testing and application of lubricant would be lost. Because some of the lubricants used to meet the requirements of ASTM Specifications are water soluble, it is advisable that galvanized bolts and nuts be shipped and stored in plastic bags in wood or metal containers. Washers. The primary function of washers is to provide a hardened non-galling surface under the element turned in tightening, particularly for those installation procedures which depend upon torque for control or inspection. Circular hardened washers meeting the requirements of ASTM A436 provide an increase in bearing area of 45 to 55 percent over the area provided by a heavy hex bolt head or nut; however, tests have shown that standard thickness washers play only a minor role in distributing the pressure induced by the bolt pretension, except where oversize or short slotted holes are used. Hence, consideration is given to this function only in the case of oversize and short slotted holes. The requirement for standard thickness hardened washers, when such washers are specified as an aid in the distribu3. Birkemoe, P. C., and D. C. Herrschaft, â&#x20AC;&#x153;Bolted Galvanized Bridgesâ&#x20AC;&#x201D;Engineering Acceptance Near,â&#x20AC;? ASCE Civil Engineering, April 1970.
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TYPE
A325 BOLT
A490 NUT
(1)
1
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NUT
XYZ A490
XYZ
MFGR IDENTIFICATION (TYPICAL) XYZ
XYZ A325
BOLT
XYZ
DH
D ARCS INDICATE GRADE C
2
XYZ A325
DH OR 2H (2)
GRADE MARK (2) D, DH, 2 OR 2H
XYZ A490
SAME AS TYPE 1
NOTE MANDATORY 3 RADIAL LINES AT 60
NOTE MANDATORY 6 RADIAL LINES AT 30
(3)
3
XYZ A325 NOTE MANDATORY UNDERLINE
SAME AS TYPE 1
(3) XYZ 3
(3)
XYZ A490
XYZ DH3
DH3 NOTE MANDATORY
(1) ADDITIONAL OPTIONAL 3 RADIAL LINES AT 120 MAY BE ADDED. (2) TYPE 3 ALSO ACCEPTABLE (3) ADDITIONAL OPTIONAL MARK INDICATING WEATHERING MAY BE ADDED
Fig. C2. Required marking for acceptable bolt and nut assemblies
tion of pressure, is waived for alternative design fasteners which incorporate a bearing surface under the head of the same diameter as the hardened washer; however, the requirements for hardened washers to satisfy the principal requirement of providing a non-galling surface under the element turned in tightening is not waived. The maximum thickness is the same for all standard washers up to and including 11⁄2 inch bolt diameter in order that washers may be produced from a single stock of material. The requirement that heat-treated washers not less than 5⁄16 inch thick be used to cover oversize and slotted holes in external plies, when A490 bolts of 11⁄8 inch or larger diameter are used, was found necessary to distribute the high clamping pressure so as to prevent collapse of the hole perimeter and enable development of the desired clamping force. Preliminary investigation has shown that a similar but less severe deformation occurs when oversize or slotted holes are in the interior plies. The reduction in clamping force may be offset by “keying,” which tends to increase the resistance to slip. These effects are accentuated in joints of thin plies . Marking. Heavy hex structural bolts and heavy hex nuts are required by ASTM Specifications to be distinctively marked. Certain markings are mandatory. In addition to the mandatory markings, the manufacturer may apply additional distinguishing marking. The mandatory and optional markings are shown in Figure C2. Paint. In the previous edition of the Specification, generic names for paints applied to faying surfaces was the basis for categories of allowable working stresses in “fricAMERICAN INSTITUTE OF STEEL CONSTRUCTION
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tion” type connections. Research4 completed since the adoption of the 1980 Specification has demonstrated that the slip coefficients for paints described by a generic type are not single values but depend also upon the type of vehicle used. Small differences in formulation from manufacturer to manufacturer or from lot to lot with a single manufacturer significantly affect slip coefficients if certain essential variables within a generic type are changed. It is unrealistic to assign paints to categories with relatively small incremental differences between categories based solely upon a generic description. As a result of the research, a test method was developed and adopted by the Council titled “Test Method to Determine the Slip Coefficient for Coatings Used in Bolted Joints.” A copy of this document is appended to this Specification as Appendix A. The method, which requires requalification if an essential variable is changed, is the sole basis for qualification of any coating to be used under this Specification. Further, normally only two categories of slip coefficient for paints to be used in slip-critical joints are recognized: Class A for coatings which do not reduce the slip coefficient below that provided by clean mill scale, and Class B for paints which do not reduce the slip coefficient below that of blast-cleaned steel surfaces. The research cited in the preceding paragraph also investigated the effect of varying the time from coating the faying surfaces to assembly of the connection and tightening the bolts. The purpose was to ascertain if partially cured paint continued to cure within the assembled joint over a period of time. It was learned that all curing ceased at the time the joint was assembled and tightened and that paint coatings that were not fully cured acted much as a lubricant would; thus, the slip resistance of the joint was severely reduced from that which was provided by faying surfaces that were fully cured prior to assembly. C3 Bolted Parts Material Within the Grip. The Specification is intended to apply to structural joints in which all of the material within the grip of the bolt is steel. Surface Conditions. The Test Method to Determine the Slip Coefficient for Coatings Used in Bolted Joints includes long-term creep test requirements to ensure reliable performance for qualified paint coatings. However, it must be recognized that in the case of hot-dip galvanized coatings, especially if the joint consists of many plies of thickly coated material, relaxation of bolt tension may be significant and may require retensioning of the bolts subsequent to the initial tightening. Research5 has shown that a loss of pretension of approximately 6.5 percent occurred for galvanized plates and bolts due to relaxation as compared with 2.5 percent for uncoated joints. This loss of bolt tension occurred in five days with negligible loss recorded thereafter. This loss can be allowed for in design or pretension may be brought back to the prescribed level by retightening the bolts after an initial period of “settling-in.” Since it was first published, this Specification has permitted the use of bolt holes 6 1⁄ 16 inch larger than the bolts installed in them. Research has shown that, where 4. Frank, Karl H. and J. A. Yura, “An Experimental Study of Bolted Shear Connections.” FHWA/RD-81/148, December 1981. 5. Munse, W. H., “Structural Behavior of Hot Galvanized Bolted Connections,” 8th International Conference on Hot-dip Galvanizing, London, England, June 1967. 6. Allen. R. N. and J. W. Fisher, “Bolted Joints With Oversize or Slotted Holes,” ASCE Journal of the Structural Division, Vol. 94, No. ST9, September, 1968.
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greater latitude is needed in meeting dimensional tolerances during erection, somewhat larger holes can be permitted for bolts 5⁄8 inch diameter and larger without adversely affecting the performance of shear connections assembled with highstrength bolts. The oversize and slotted hole provisions of this Specification are based upon these findings. Because an increase in hole size generally reduces the net area of a connected part, the use of oversize holes is subject to approval by the Engineer of Record. Burrs. Based upon tests7 which demonstrated that the slip resistance of joints was unchanged or slightly improved by the presence of burrs, burrs which do not prevent solid seating of the connected parts in the snug tight condition need not be removed. On the other hand, parallel tests in the same program demonstrated that large burrs can cause a small increase in the required turns from snug tight condition to achieve specified pretension with turn-of-nut method of tightening. Unqualified Paint on Faying Surfaces. An extension to the research on the slip resistance of shear connections cited in footnote 4 investigated the effect of ordinary paint coatings on limited portions of the contact area within joints and the effect of overspray over the total contact area. The tests8 demonstrated that the effective area for transfer of shear by friction between contact surfaces was concentrated in an annular ring around and close to the bolts. Paint on the contact surfaces approximately one inch but not less than the bolt diameter away from the edge of the hole did not reduce the slip resistance. On the other hand, in recognition of the fact that, in connections of thick material involving a number of bolts on multiple gage lines, bolt pretension might not be adequate to completely flatten and pull thick material into tight contact around every bolt, the Specification requires that all areas between bolts also be free of paint. (See Figure C3.) The new requirements have a potential for increased economy because the paint-free area may easily be protected using masking tape located relative to the hole pattern, and, further, the narrow paint strip around the perimeter of the faying surface will minimize uncoated material outside the connection requiring field touch-up. This research also investigated the effect of various degrees of inadvertent overspray on slip resistance. It was found that even the smallest amount of overspray of ordinary paint (that is, not qualified as Class A) within the specified paint-free area on clean mill scale reduced the slip resistance significantly. On blast-cleaned surfaces, the presence of a small amount of overspray was not as detrimental. For simplicity, the Specification prohibits any overspray from areas required to be free of paint in slip-critical joints regardless of whether the surface is clean mill scale or blast cleaned. Galvanized Faying Surfaces. The slip factor for initial slip with clean hot-dip galvanized surfaces is of the order of 0.19 as compared with a factor of about 0.35 for clean mill scale. However, research (see note 3) has shown that the slip factor of galvanized surfaces is significantly improved by treatments such as hand wire brushing or light “brush-off” grit blasting. In either case, the treatment must be controlled in order to achieve the necessary roughening or scoring. Power wire brushing is unsatisfactory because it tends to polish rather than roughen the surface. 7. Polyzois, D. and J. A. Yura, “Effect of Burrs on Bolted Friction Connections,” AISC Engineering Journal, 22 (No. 3) Third Quarter 1985. 8. Polyzois, D. and K. Frank, “Effect of Overspray and Incomplete Masking of Faying Surfaces on the Slip Resistance of Bolted Connections,” AISC Engineering Journal, 23 (No. 2), 2nd Quarter 1986.
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Circular area around all holes
1 ″ but not less than d d 1 ″ but not less than d and All areas in between
Perimeter of contact area
Fig. C3. Areas outside the defined area need not be free of paint
Field experience and test results have indicated that galvanized members may have a tendency to continue to slip under sustained loading.9 Tests of hot-dip galvanized joints subject to sustained loading show a creep-type behavior. Treatments to the galvanized faying surfaces prior to assembly of the joint which caused an increase in the slip resistance under short duration loads did not significantly improve the slip behavior under sustained loading. C4 Design for Strength Of Bolted Connections Background for Design Stresses. With the 1985 edition of the Specification, the arbitrary designations “friction type” and “bearing type” connections used in former editions, and which were frequently misinterpreted as implying an actual difference in the manner of performance or strength of the two types of connection, were discontinued in order to focus attention more upon the real manner of performance of bolted connections. In bolted connections subject to shear-type loading, the load is transferred between the connected parts by friction up to a certain level of force which is dependent upon the total clamping force on the faying surfaces and the coefficient of friction of the faying surfaces. The connectors are not subject to shear, nor is the connected material subject to bearing stress. As loading is increased to a level in excess of the frictional resistance between the faying surfaces, slip occurs, but failure in the sense of rupture does not occur. As even higher levels of load are applied, the load is resisted by shear in the fastener and bearing upon the connected material plus some uncertain amount of friction between the faying surfaces. The final failure will be by shear failure of the connectors, or by tear out of the connected 9. Kulak, G. L., J. W. Fisher, and J. H. A. Struik, “Guide to Design Criteria for Bolted and Riveted Joints,” 2nd ed., New York: John Wiley & Sons, 1987, p. 208. (Hereinafter referred to as the Guide.)
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material, or by unacceptable ovalization of the holes. Final failure load is independent of the clamping force provided by the bolts.10 The design of high-strength bolted connections under this Specification begins with consideration of strength required to prevent premature failure by shear of the connectors or bearing failure of the connected material. Next, for connections which are defined as “slip-critical,” the resistance to slip load is checked. Because the combined effect of frictional resistance with shear or bearing has not been systematically studied and is uncertain, any potential greater resistance due to combined effect is ignored. Connection Slip. There are practical cases in the design of structures where slip of the connection is desirable in order to permit rotation in a joint or to minimize the transfer of moment. Additionally there are cases where, because of the number of fasteners in a joint, the probability of slip is extremely small or where, if slip did occur, it would not be detrimental to the serviceability of the structure. In order to provide for such cases while at the same time making use of the higher shear strength of high-strength bolts, as contrasted to ASTM A307 bolts, the Specification now permits joints tightened only to the snug tight condition. The maximum amount of slip that can occur in connections that are not classified as slip-critical is, theoretically, an amount equal to two hole clearances. In practical terms, it is observed to be much less than this. In laboratory tests it is usually about one-half a hole clearance. This is because the acceptable inaccuracies in the location of holes within a pattern of bolts would usually cause one or more bolts to be in bearing in the initial unloaded condition. Further, in statically loaded structures, even with perfectly positioned holes, the usual method of erection would cause the weight of the connected elements to put the bolts into direct bearing at the time the member is supported on loose bolts and the lifting crane is unhooked. Subsequent additional gravity loading could not cause additional connection slip. Connections classified as slip-critical include those cases where slip could theoretically exceed an amount deemed by the Engineer of Record to affect the suitability for service of the structure by excessive distortion or reduction in strength or stability, even though the resistance to fracture of the connection, per se, may be adequate. Also included are those cases where slip of any magnitude must be prevented, for example, joints subject to load reversal. Shear and Bearing on Fasteners. Several interrelated parameters influence the shear and bearing strength of connections. These include such geometric parameters as the net-to-gross-area ratio of the connected parts, the ratio of the net area of the connected parts to the total shear-resisting area of the fasteners, and the ratio of transverse fastener spacing to fastener diameter and to the connected part thickness. In addition, the ratio of yield strength to tensile strength of the steel comprising the connected parts, as well as the total distance between extreme fasteners, measured parallel to the line of direct tensile force, play a part. In the past, a balanced design concept had been sought in developing criteria for mechanically fastened joints to resist shear between connected parts by means of bearing of the fasteners against the sides of the holes. This philosophy resulted in wide variations in the factor of safety for the fasteners, because the ratio of yield to tensile strength increases significantly with increasingly stronger grades of steel. It had no application at all in the case of very long joints used to transfer direct 10. Ibid., pp. 49–52.
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COMMENTARY ON THE RCSC SPECIFICATION (6/8/88)
tension, because the end fasteners “unbutton” before the plate can attain its full strength or before the interior fasteners can be loaded to their rated shear capacity. By means of a mathematical model it was possible to study the interrelationship of the previously mentioned parameters.11,12 It has been shown that the factor of safety against shear failure ranged from 3.3 for compact (short) joints to approximately 2.0 for joints with an overall length in excess of 50 inches. It is of interest to note that the longest (and often the most important) joints had the lowest factor, indicating that a factor of safety of 2.0 has proven satisfactory in service. The absence of design strength provisions specifically for the case where a bolt in double shear has a non-threaded shank in one shear plane and a threaded section in the other shear plane is because of the uncertainty of manner of sharing the load between the two different shear areas. It also recognizes that knowledge as to the bolt placement (which might leave both shear planes in the threaded section) is not ordinarily available to the detailer. If threads occur in one shear plane, the conservative assumption is made that threads are in all shear planes. The nominal strength and resistance factors for fasteners subject to applied tension or shear are given in Table 2. The values are based upon the research and recommendations reported in the Guide. With the wealth of data available, it was possible through statistical analyses to adjust resistances to provide more uniform reliability for all loading and joint types. The design resistances provide designs approximately equivalent to the designs provided by the allowable stresses in the 1980 edition of the Specification. The design of connections is more conservative than that of the connected members of buildings and bridges by a substantial margin, in the sense that the failure load of the fasteners is substantially in excess of the maximum serviceability limit (yield) of the connected material. Design for Tension. The nominal strengths specified for applied tension13 are intended to apply to the external bolt load plus any tension resulting from prying action produced by deformation of the connected parts. The recommended design strength is approximately equal to the initial tightening force; thus, when loaded to the nominal (service) load, high-strength bolts will experience little if any actual change in stress. For this reason, bolts in connections in which the applied loads subject the bolts to axial tension are required to be fully tensioned, even though the connection may not be subject to fatigue loading nor classified as slip-critical. Properly tightened A325 and A490 bolts are not adversely affected by repeated application of the recommended service load tensile stress, provided the fitting material is sufficiently stiff, so that the prying force is a relatively small part of the applied tension.14 The provisions covering bolt tensile fatigue are based upon study of test reports of bolts that were subjected to repeated tensile load to failure. Design for Shear. The nominal strength in shear is based upon the observation that the shear strength of a single high-strength bolt is about 0.62 times the tensile strength of that bolt.15 However, in shear connections with more than two bolts in the line of force, deformation of the connected material causes nonuniform bolt shear force distribution so that the strength of the connection in terms of the average bolt strength 11. Fisher, J. W. and L. S. Beedle, “Analysis of Bolted Butt Joints,” ASCE Journal of the Structural Division, 91 (No. ST5), October 1965. 12. Guide, pp. 89–116; 126–132. 13. Ibid., pp. 263–286. 14. Ibid., pp. 272. 15. Ibid., pp. 44–50.
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goes down as the joint length increases.16 Rather than provide a function that reflects this decrease in average fastener strength with joint length, a single reduction factor of 0.80 was applied to the 0.62 multiplier. The result will accommodate bolts in all joints up to about 50 inches in length without seriously affecting the economy of very short joints. As noted in the footnotes to Table 2, bolts in joints longer than 50 inches in length must be further discounted by an additional 20 percent. The average value of the nominal strength for bolts with threads in the shear plane has been determined by a series of tests17 to be 0.833 Fu with a standard deviation of 0.03. A value of 0.80 was taken as a factor to account for the shear strength of a bolt with threads in the shear plane based upon the area corresponding to the nominal body area of the bolt. The shear strength of bolts is not affected by pretension in the fasteners provided the connected material is in contact at the faying surfaces. The design shear strength equals the nominal shear strength multiplied by a resistance factor of 0.75. Combined Tension and Shear. The nominal strength of fasteners subject to combined tension and shear is provided by elliptical interaction curves in Table 3 which account for the connection length effect on bolts loaded in shear, the ratio of shear strength to tension strength of threaded fasteners, and the ratios of root area to nominal body area and tensile stress area to nominal body area.18 No reduction in the design shear strength is required when applied tensile stress is equal to or less than the design tensile strength. Although the elliptical interaction curve provides the best estimate of the strength of bolts subject to combined shear and tension and thus is used in this Specification, it would be within the intent of the Specification for invoking specifications to use a three straight line approximation of the ellipse. Design for Bearing. Bearing stress produced by a high-strength bolt pressing against the side of the hole in a connected part is important only as an index to behavior of the connected part. It is of no significance to the bolt. The critical value can be derived from the case of a single bolt at the end of a tension member. It has been shown,19 using finger-tight bolts, that a connected plate will not fail by tearing through the free edge of the material if the distance L, measured parallel to the line of applied force from a single bolt to the free edge of the member toward which the force is directed, is not less than the diameter of the bolt multiplied by the ratio of the bearing stress to the tensile strength of the connected part. The criterion for nominal bearing strength is L / d ≥ Rn / Fu where Rn = nominal bearing pressure Fu = specified minimum tensile strength of the connected part. As a practical consideration, a lower limit of 1.5 is placed on the ratio L/d and an upper limit of 1.5 on the ratio Fp / Fu and an upper limit of 3.0 on the ratio Rn / Fu. The foregoing leads to the rules governing bearing strength in the specification. 16. Ibid., pp. 99–104. 17. Yura. J. A., K. H. Frank, and D. Polyois, “High Strength Bolts for Bridges.” PMFSEL Report No. 87-3, May 1987, Phil M. Ferguson Structural Engineering Laboratory, University of Texas at Austin. 18. Guide, pp. 50–51. 19. Ibid., pp. 141–143.
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The bearing pressure permitted in the 1980 Specification and the current provisions are fully justifiable from the standpoint of strength of the connected material. However, even though rupture does not occur, recent tests have demonstrated that ovalization of the hole will begin to develop as the bearing stress is increased beyond the previously permitted stress, especially if it is combined with high tensile stress on the net section. Furthermore, when high bearing stress is combined with high tensile stress on the net section and the effect of exterior versus interior plies, lower ultimate strengths than previously reported result in addition to the hole ovalization. Recognizing that initiation of hole ovalization occurs well below the ultimate strength, and to facilitate standardization in detailing and fabrication, sufficiently conservative simplified criteria have been provided in a formula format for usual applications. The more accurate formula in which the strength is related to the distance L may be used for special cases such as those with very large bolts or very thin material. For connections with more than a single bolt in the direction of force, the resistance may be taken as the sum of the resistances of the individual bolts. C5 Design Check for Slip Resistance The Specification recognizes that, for a number of cases, slip of a joint would be undesirable or must be precluded. Such joints are termed “slip-critical” joints. This is somewhat different from the previous term “friction type” connection. The new terminology was adopted in order to focus attention on the fact that all tightened high-strength bolted joints resist load by friction between the faying surfaces up to the slip load and subsequently are able to resist even greater loads by shear and bearing. The strength of the joint is not related to the slip load. The Specification requires that the two different resistances be considered separately. The consequences of slip into bearing varies from application to application; hence the determination of which connections shall be designed and installed as slipcritical is best left to judgment and a conscious decision on the part of the Engineer of Record. Also, the determination of whether the potential slippage of a joint is critical at nominal load level as a serviceability consideration or whether slippage could result in distortions of the frame such that the ability of the frame to resist factored loads would be reduced can be determined only by the Engineer of Record. The following comments reflect the collective thinking of the Council as developed during numerous meetings and reviews of drafts of the Specification and Commentary. They are provided as guidance and an indication of the intent of the Specification. In the case of bolts in holes with only small clearance, such as standard holes and slotted holes loaded transverse to the axis of the slot in practical connections, the freedom to slip generally does not exist because one or more bolts are in bearing even before load is applied due to normal fabrication tolerances and erection procedures. Further, the consequences of slip, if it can occur at all, are trivial except for a few situations. If for some reason it is deemed critical, design should probably be on the basis of nominal loads (Section 5(b)). In connections containing long slots that are parallel to the direction of the applied load, slip of the connection prior to attainment of the factored load might be large enough to alter the usual assumption of analysis that the undeformed structure can be used to obtain the internal forces. The Specification allows the designer two alternatives in this case. If the connection is designed so that it will not slip under the AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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effect of the nominal loads, then the effect of the factored loads acting on the deformed structure (deformed by the maximum amount of slip in the long slots at all locations) must be included in the structural analysis. Alternatively the connection can be designed so that it will not slip at loads up to the factored load level. These requirements are noted in Clause 7(b)(3). Joints subject to full reverse cyclic loading are clearly slip-critical joints since slip would permit back-and-forth movement of the joint and early fatigue failure. However, for joints subject to pulsating load that does not involve reversal of load direction, proper fatigue design could be provided either as a slip-critical joint on the basis of stress on the gross section or as a non-slip-critical joint on the basis of stress on the net section. Because fatigue results from repeated application, the service load rather than the overload load design should be based upon nominal load criteria (Section 5(b)). For high-strength bolts in combination with welds in statically loaded conditions and considering new work only, the nominal strength may be taken as the sum of two contributions.20 One results from the slip resistance of the bolted parts and may be determined in accordance with Section 5(c). The second results from the resistance of the welds as provided by applicable welding specifications. If one type of connector is already loaded when the second type of connector is introduced, the nominal strength cannot be obtained by adding the two resistances. The Guide should be consulted in these cases. From the definition of the term “coefficient of slip” (friction), the expression for nominal slip resistances for bolts in standard holes is apparent and needs no explanation. The mean value of slip coefficients from many tests on clean mill scale, blast-cleaned steel surfaces and galvanized and roughened surfaces were taken as the basis for the three classes of surfaces. In the 1978 edition of the Specification, nine classes of faying surface conditions were introduced, and significant increases were made in the recommended allowable stresses for proportioning connections which function by transfer of shear between connected parts by friction. These classes and stresses were adopted on the basis of statistical evaluation of the information then available. Extensive data developed through research sponsored by the Council and others during the past ten years has been statistically analyzed to provide improved information on slip probability of connections in which the bolts have been preloaded to the requirements of Table 4. Two principal variables—coefficient of friction of the faying surfaces and bolt pretension—were found to dominate the slip resistance of connections. An examination of the slip (friction) coefficient data for a wide range of surface conditions indicates that the data are distributed normally, and the standard deviation is essentially the same for each surface condition class. This means that different reduction factors should be applied to classes of surfaces with different mean values of coefficients of friction—the smaller the mean value of the coefficient of friction, the smaller (more severe) the appropriate reduction factor—in order to provide equivalent reliability of slip resistance. The bolt clamping force data indicate that bolt tensions are distributed normally for each method of tightening. However, the data also indicate that the mean values of the bolt tensions are different for each method. If the calibrated wrench method is used to tighten ASTM A325 bolts, the mean value of bolt tension is about 1.13 20. Ibid., pp. 238–40.
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times the minimum specified tension in Table 4. If the turn-of-nut method is used, the mean value of tension is about 1.35 times the minimum specified preload for A325 bolts and about 1.27 for A490 bolts. The combined effects of the variability of coefficient of friction and bolt tension have been accounted for in the slip probability factor, D, of the formula for nominal slip resistance in Section 5(b). The values of the slip probability factor, D, given by 5(b) imply a 90 percent reliability that slip will not occur if the calibrated wrench method of installation is used. If the turn-of-nut method is used, a reliability of about 95 percent will be provided. Reference is made to Guide to Design Criteria for Bolted and Riveted Joints (2nd ed., New York: John Wiley and Sons. 1987 p. 135) for tables of values of D appropriate for other mean slip coefficients and slip probabilities and suitable for direct substitution into the formula for slip resistance in Section 5(b). The frequency distribution and mean value of clamping force for bolts tightened by turn-of-nut method are higher than calibrated wrench installation because of the elimination of variables which affect torque-tension ratios and due to higherthan-specified minimum strength of production bolts. Because properly applied turnof-nut installation induces yield point strain in the bolt, the higher-thanspecified yield strength of production bolts will be mobilized and result in higher clamping force by the method. On the other hand, the calibrated wrench method, which is dependent upon the calibration of wrenches to slightly more than Table 4 tensions, independent of the actual bolt properties, will not mobilize any additional strength of production bolts. High clamping force might be achieved by the calibrated wrench method if the wrench was set to a higher torque value. However, this would require more attention to the degrees of rotation to prevent excessive deformation of the bolt or torsional bolt failure. Because of the effects of oversize and slotted holes on the induced tension in bolts using any of the specified installation methods, lower values are provided for bolts in these hole types. In the case of bolts in long slotted holes, even though the slip load is the same for bolts loaded transverse or parallel to the axis of the slot, the values for bolts loaded parallel to the axis has been further reduced based upon judgment in recognition of the greater consequences of slip. Attention is called to the fact that the criteria for slip resistance are for the case of connections subject to a coaxial load. For cases in which the load tends to rotate the connection in the plane of the faying surface, a modified formula accounting for the placement of bolts relative to the center of rotation should be used.21 Connections of the type shown in Figure C4(a), in which some of the bolts (A) lose a part of their clamping force due to applied tension, suffer no overall loss of frictional resistance. The bolt tension produced by the moment is coupled with a compensating compressive force (C) on the other side of the axis of bending. In a connection of the type shown in Fig. C4(b), however, all fasteners (B) receive applied tension which reduces the initial compression force at the contact surface. If slip under load cannot be tolerated, the design slip-load value of the bolts in shear should be reduced in proportion to the ratio of residual axial force to initial tension. If slip of the joint can be tolerated, the bolt shear stress should be reduced according to the tension-shear interaction as outlined in the Guide. page 71. Because the bolts are subject to applied axial tension, they are required to be pretensioned in either case. 21. Ibid., pp. 217â&#x20AC;&#x201C;30.
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B A
M
C V (a)
T
(b)
Fig. C4
While connections with bolts pretensioned to the levels specified in Table 4 do not ordinarily slip into bearing when subject to anticipated loads, it is required that they meet the requirements of Section 5 in order to maintain the factor of safety of 2 against fracture in the event that the bolts do slip into bearing as a result of large unforeseen loads. To cover those cases where a coefficient of friction less than 0.33 might be adequate for a given situation, the Specification provides that, subject to the approval of the Engineer of Record, and provided the mean slip coefficient is determined by the specified test procedure and the appropriate slip probability factor, D, is selected from the literature, faying surface coatings providing lower slip resistance than Class A coating may be used. It should be noted that both Class A and Class B coatings are required to be applied to blast-cleaned steel. High-Strength Bolts in Combination with Welds or Rivets. For high-strength bolts in combination with welds in statically loaded conditions and considering new work only, the nominal strength may be taken as the sum of the two contributions. If one type of connector is already loaded when the second type of connector is introduced, the nominal strength cannot be obtained by sum of the two resistances. The Guide should be consulted in these cases. For high-strength bolts in combination with welds in fatigue loaded applications, available data are not sufficient to develop general design recommendations at this time. High-strength bolts in combination with rivets are rarely encountered in modern practice. If need arises, guidance may be found in the Guide. C7 Design Details of Bolted Connections A new section has been added with this edition of the Specification in order to bring together a number of requirements for proper design and detailing of high-strength bolted connections. The material covered in the Specification, and in Section 7 in particular, is not intended to provide comprehensive coverage of the design of highstrength bolted connections. For example, other design considerations of importance AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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to the satisfactory performance of the connected material such as block shear, shear lag, prying action, connection stiffness, effect on the performance of the structure and others are beyond the scope of this Specification and Commentary. Proper location of hardened washers is as important as other elements of a detail to the performance of the fasteners. Drawings and details should clearly reflect the number and disposition of washers, especially the thick hardened washers that are required for several slotted hole applications. Location of washers is a design consideration that should not be left to the experience of the iron worker. While hardened washers are not required with some methods of installation, their use will overcome the effects of galling under the element turned in tightening. Finger shims are a necessary device or tool of the trade to permit adjusting alignment and plumbing of structures. When these devices are fully and properly inserted, they do not have the same effect on bolt tension relaxation or the connection performance as do long slotted holes in an outer ply. When fully inserted, the shim provides support around approximately 75 percent of the perimeter of the bolt in contrast to the greatly reduced area that exists with a bolt centered in a long slot. Further, finger shims would always be enclosed on both sides by the connected material which would be fully effective in bridging the space between the fingers. C8 Installation and Tightening Several methods for installation and tensioning of high-strength bolts, when tensioning is required, are provided without preference in the Specification. Each method recognized in Section 8, when properly used as specified, may be relied upon to provide satisfactory results. All methods may be misused or abused. At the expense of redundancy, the provisions stipulating the manner in which each method is intended to be used are set forth in complete detail in order that the rules for each method may stand alone without need for footnotes or reference to other sections. If the methods are conscientiously implemented, good results should be routinely achieved. Connections Not Requiring Full Tensioning. In the Commentary, Section C6 of the previous edition of the Specification, it was pointed out that “bearing” type connections need not be tested to ensure that the specified pretension in the bolts had been provided, but specific provision permitting relaxation of the tensioning requirement was not contained in the body of the Specification. In the present edition of the Specification, separate installation procedures are provided for bolts that are not within the slip-critical or direct tension category. The intent in making this change is to improve the quality of bolted steel construction and reduce the frequency of costly controversies by focusing attention, both during the installation and tensioning phase and during inspection, on the true slip-critical connections, rather than diluting the effort through the requirement for costly tensioning and tension testing of the great many connections where such effort serves no useful purpose. The requirement for identification of connections on the drawings may be satisfied either by identifying the slip-critical and direct tension connections which must be fully tightened and inspected or by identifying the connections which need be tightened only to the snug tight condition. Under the provisions of some other specifications, certain shear/bearing connections are required to be tightened well beyond the snug tight conditions;22 how22. For example, American Institute of Steel Construction, “Specification for Design Fabrication and
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ever, because the joints are in bearing, prevention of slip of the joint is not a concern in these connections. Because they are not slip-critical joints, they should not be subject to the same requirements as slip-critical joints, especially the requirements for faying surface coatings and conditions. To ensure proper tightness of the connections, they should be tightened by one of the four methods in 8(d); however, inspection should be limited to monitoring the work to confirm that the bolt tightening procedure is properly applied. Inspection should not include testing to ensure that any specific level of tension has been achieved. In the Specification, snug tight is defined as the tightness that exists when all plies are in firm contact. This may usually be attained by a few impacts of an impact wrench or the full effort of a man using an ordinary spud wrench. In actuality, snug tight is a degree of tightness which will vary from joint to joint depending upon the thickness, flatness and degree of parallelism of the connected material. In most joints, the plies will pull together at snug tight; however, in some joints in thick material, it may not be possible to have continuous contact throughout the faying surface area. In such joints, the slip resistance of the completed joints will not be reduced because compressive forces between the faying surfaces, however distributed, must be in equilibrium with the total of the tensile forces in all bolts. Tension Calibrating Devices. At the present time, there is no known economical means for determining the tension in a bolt that has previously been installed in a connection. The actual tension in a bolt installed in a tension calibrator (hydraulic tension indicating device) is directly indicated by the dial of the device, provided the device is properly calibrated. Such a device is an economical and valuable tool that should be readily available whenever high-strength bolts are to be installed in either slip-critical or shear/bearing connections. The testing of as-received bolts and nuts at the job site is a requirement of the Specification because instances of counterfeit under strength fasteners not meeting the requirements of the ASTM Specification have not infrequently occurred. Job site testing provides a practical means for ensuring that nonconforming fasteners are not incorporated in the work. Further, although the several elements of a fastener assembly may conform to the minimum requirements of their separate ASTM Specifications, their compatibility in an assembly or the need for lubrication can only be ensured by testing of the assembly. Hence, such devices are important for testing the complete fastener assembly as it will be used with the method of tightening to be used to ensure the suitability of bolts and nuts (probably produced by different manufacturers), other elements, and the adequacy of impact wrenches and/or air pressure to provide the specified tension using the selected method. Testing before start of installation of fasteners in the work will also identify potential sources of problems, such as the need for lubrication to prevent failure of bolts by combined high torque with tension, under-strength assemblies due to excessive overtapping of hot-dip galvanized nuts, and to clarify for the bolting crews and inspectors the proper implementation of the selected installation method to be used. Such devices are essential to the confirmation testing of alternative design fasteners, direct tension indicators, and to verify the proper use of the turn-of-nut procedure. They are also essential to the specified procedure for the calibrated wrench method of installation, and for the specified procedure for determining a valid testing torque when such inspection by a torque method is required. Erection of Structural Steel for Buildings,â&#x20AC;? Section 1.15.12, stipulates several cases where high-strength bolts in bearing connections are to be fully tensioned independent of whether potential slip is a concern or not.
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They are the only known economically available tool for field use for determining realistic torque to tension relationships for given fastener assemblies. Experience on many projects has shown that bolts and/or nuts not meeting the requirements of the applicable ASTM specification would have been identified prior to installation if they had been tested as an assembly in a tension calibrator. The controversy and great expense of replacing bolts installed in the structure when the nonconforming bolts were discovered at a later date would have been avoided. Hydraulic tension calibrating devices capable of indicating bolt tension undergo a slight deformation under load. Hence, the nut rotation corresponding to a given tension reading may be somewhat larger than it would be if the same bolt were tightened against a solid steel abutment. Stated differently, the reading of the calibrating device tends to underestimate the tension which a given rotation of the turned element would induce in a bolt in an actual joint. This should be borne in mind when using such devices to establish a tension-rotation relationship. Slip-critical Connections and Connections Subject to Direct Tension. Four methods for joint assembly and tightening are provided for slip-critical and direct tension connections. It has repeatedly been demonstrated in the laboratory that each of the four installation methods provides the specified pretension when used properly with specified fasteners in good condition, but improperly applied methods or understrength fasteners or fasteners in poor condition provide uncertain pretensions. Therefore, regardless of the method used and prior to the commencement of work, it is required to be demonstrated by installation of a representative sample of the fastener assemblies in the tension calibrator that the specified pretension can be achieved using the procedure to be used with the fasteners to be used by the crews who will be doing the work. With any of the four described tensioning methods, it is important to install bolts in all holes of the connection and bring them to an intermediate level of tension generally corresponding to snug tight in order to compact the joint. Even after being fully tightened, some thick parts with uneven surfaces may not be in contact over the entire faying surface. In itself, this is not detrimental to the performance of the joint. As long as the specified bolt tension is present in all bolts of the completed connection, the clamping force equal to the total of the tensions in all bolts will be transferred at the locations that are in contact and be fully effective in resisting slip through friction. If however, individual bolts are installed and tightened in a single continuous operation, bolts which are tightened first will be subsequently relaxed by the tightening of the adjacent bolts. The total of the forces in all bolts will be reduced, which will reduce the slip load whether there is uninterrupted contact between the surfaces or not. With all methods, tightening should begin at the most rigidly fixed or stiffest point and progress toward the free edges, both in the initial snugging up and in the final tightening. Turn-of-Nut-Tightening. When properly implemented, turn-of-nut method provides more uniform tension in the bolts than does torque controlled tensioning methods because it is primarily dependent upon bolt elongation into the inelastic range. Consistency and reliability method is dependent upon ensuring that the joint is well compacted and all bolts are uniformly tight at a snug tight condition prior to application of the final required partial turn. Under-tightened bolts will result if this starting condition is not achieved because subsequent turning of the nut will first close the gap before meaningful elongation of the bolt occurs as would be the AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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case with solid steel in the grip. Reliability is also dependent upon ensuring that the turn that is applied is relative between the bolt and nut; thus the element not turned in tightening should be prevented from rotating while the required degree of turn is applied to the turned element. Reliability and inspectability of the method may be improved by having the outer face of the nut match-marked to the protruding end of the bolt after the joint has been snug tightened but prior to final tightening. Such marks may be applied by the wrench operator using a crayon or dab of paint. Such marks in their relatively displaced position after tightening will afford the inspector a means for noting the rotation that was applied. Problems with turn-of-nut tightening have been encountered with hot-dip galvanized bolts. In some cases, the problems have been attributed to especially effective lubricant applied by the manufacturer to ensure that bolts from stock will meet the ASTM Specification requirements without the need for relubricating and retesting. Job site tests in the tension indicating device demonstrated the lubricant reduced the coefficient of friction between the bolt and nut to the degree that â&#x20AC;&#x153;the full effort of a man using an ordinary spud wrenchâ&#x20AC;? to snug tighten the joint actually induced the full required tension. Also, because the nuts could be removed by an ordinary spud wrench they were erroneously judged improperly tightened by the inspector. Research (see note 3) confirms that lubricated high-strength bolts may require only one-half as much torque to induce the specified tension. In other cases of problems with hot-dip galvanized bolts, the absence of lubrication or lack of proper overtapping caused seizing of the nut and bolt threads which resulted in twist failure of the bolt at less than specified tension. For such situations, use of a tension indicating device and the fasteners being installed may be helpful in establishing either the need for lubrication or alternate criteria for snug tight at about one-half the tension required by Table 4. Because reliability of the method is independent of the presence or absence of washers, washers are not required except for oversize and slotted holes in an outer ply. In the absence of washers, testing after the fact using a torque wrench method is highly unreliable. That is, the turn-of-nut method of installation, properly applied, is more reliable and consistent than the testing method. The best method for inspection of the method is for the Inspector to observe the required job site confirmation testing of the fasteners and the method to be used, followed by monitoring of the work in progress to ensure that the method is routinely properly applied. Calibrated Wrench Method. Research has demonstrated that scatter in induced tension is to be expected when torque is used as an indirect indicator of tension. Numerous variables, which are not related to tension, affect torque. For example, the finish and tolerance on bolt threads, the finish and tolerance on the nut threads, the fact that the bolt and nut may not be produced by the same manufacturer, the degree of lubrication, the job site conditions contributing to dust and dirt or corrosion on the threads, the friction that exists to varying degree between the turned element and the supporting surface, the variability of the air pressure on the torque wrenches due to length of air lines or number of wrenches operating from the same source, the condition and lubrication of the wrench which may change within a work shift, and other factors all bear upon the effectiveness of the calibrated torque wrench to induce tension. Recognition of the calibrated wrench method of tightening was removed from the Specification with the 1980 edition. This action was taken because it is the least AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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reliable of all methods of installation and many costly controversies had occured. It is suspected that shortcut procedures in the use of the calibrated wrench method of installation, not in accordance with the Specification provisions, were probably being used. Further, torque controlled inspection procedures based upon “standard” or calculated inspection torques rather than torques determined as required by the Specification were being routinely used. These incorrect procedures plus others had a compounding effect upon the uncertainty of the installed bolt tension, and were responsible for many of the controversies. It is recognized, however, that if the calibrated wrench method is implemented without shortcuts as intended by the Specification, that there will be a 90 percent assurance that the tensions specified in Table 4 will be equaled or exceeded. Because the Specification should not prohibit any method which will give acceptable results when used as specified, the calibrated wrench method of installation was reinstated in the 1985 edition of the Council Specification. However, to improve upon the previous situation, the 1985 version of the Specification was modified to require better control. Wrenches must be calibrated daily for each diameter and grade of bolt. Hardened washers must be used. Fasteners must be protected from dirt and moisture at the job site. Additionally, to achieve reliable results attention should be given to the control, insofar as it is practical, of those controllable factors which contribute to variability. For example, bolts and nuts should be purchased from reliable manufacturers with a record of good quality control to minimize the variability of the fit. Bolts and nuts should be adequately and uniformly lubricated. Water soluble lubricants should be avoided. Installation of Alternative Design Fasteners. It is the policy of the Council to recognize only fasteners covered by ASTM Specifications; however, it cannot be denied that a general type of alternative design fastener produced by several manufacturers, is used on a significant number of projects as permitted by Section 2(d). The bolts referred to involve a splined end extending beyond the threaded portion of the bolt which is gripped by a specially designed wrench chuck which provides a means for turning the nut relative to the bolt. While such bolts are subject to many of the variables affecting torque mentioned in the preceding section, they are produced and shipped by the manufacturers as a nut-bolt assembly under good quality control, which apparently minimizes some of the negative aspects of the torque controlled process. While these alternative design fasteners have been demonstrated to consistently provide tension in the fastener meeting the requirements of Table 5 in controlled tests in tension indicating devices, it must be recognized that the fastener may be misused and provide results as unreliable as those with other methods. They must be used in the as-delivered clean lubricated condition. The requirements of this Specification and the installation requirements of the manufacturer’s specification required by Section 2(d) must be adhered to. As with other methods, a representative sample of the bolts to be used should be tested to ensure that, when used in accordance with the manufacturer’s instructions, they do, in fact, provide tension, as specified in Table 5. In the actual joints, bolts must be installed in all holes of a connection and all fasteners tightened to an intermediate level of tension adequate to pull all material into contact. Only after this has been accomplished should the fasteners be fully tensioned in a systematic manner and the splined end sheared off. The sheared off splined end merely signifies that at some time the bolt has been subjected to a torque adequate to cause the AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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shearing. If the fasteners are installed and tensioned in a single continuous operation, they will give a misleading indication to the Inspector that the bolts are properly tightened. Therefore, the only way to inspect these fasteners with assurance is to observe the job site testing of the fasteners and installation procedure and then monitor the work while in progress to ensure that the specified procedure is routinely followed. Direct Tension Indicator Tightening. This Specification recognizes load indicating devices covered by the American Society for Testing and Materials’ “Specification for Compressible-Washer Type Direct Tension Indicators For Use With Structural Fasteners,” ASTM F959, in Section 2(f). The referenced device is a hardened washer incorporating several small formed arches which are designed to deform in a controlled manner when subjected to load. These load indicator washers are the sole type of device known which is directly dependent upon the tension load in the bolt, rather than upon some indirect parameter, to indicate the tension in a bolt. As with the alternative design load indicating bolts, load indicating washers are dependent upon the quality control of the producer and proper use in accordance with the manufacturer’s installation procedures and these Specifications. If the load indicator washers delivered for use in a specific application are tested at the job site to demonstrate that all components of the assembly do provide a proper indication of bolt tension, they are reliable if they are properly used by the bolting crews. Direct tension indicators meeting the requirements of ASTM F959 depend upon tension in the fastener to cause inelastic deformation of the formed arches. Bolts together with the load indicator washer plus any other washers required by Specification should be installed in all holes of the connection and the bolts tightened to approximately one-half the specified tension (deformation of the formed arches by about one-half the amount required to compress them to the specified gap) to ensure that plies of the joint have been brought into firm contact. Only after this initial tightening operation should the bolts be fully tensioned in a systematic manner. If the bolts are installed and tensioned in a single continuous operation, the load indicator washers will give the inspector a misleading indication that bolts are uniformly tensioned to the specified tension. Therefore, the only way to inspect fasteners with which load indicator washers are used with assurance is to observe the job site testing of the devices and installation procedure and then routinely monitor the work while in progress to ensure that the specified procedure is followed. Use of direct tension indicators provides a reliable means for tensioning galvanized fasteners because it avoids the factors which affect other methods. During installation, care must be taken to ensure that the indicator nubs are oriented to bear against the hardened bearing surface of the bolt head or against a hardened flat washer if used under the nut. C9 Inspection It is apparent from the commentary on installation procedures that the inspection procedures giving the best assurance that bolts are properly installed and tensioned is provided by Inspector observation of the calibration testing of the fasteners using the selected installation procedure followed by monitoring of the work in progress to ensure that the procedure that was demonstrated to provide the specified tension is routinely adhered to. When such a program is followed, no further evidence of proper bolt tension is required. If testing for bolt tension using torque wrenches is conducted subsequent to the time the work of installation and tightening of bolts performed, the test procedure AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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is subject to all of the uncertainties of torque controlled calibrated wrench installation. Additionally, the absence of many of the controls necessary to minimize variability of the torque to tension relationship, which are unnecessary for the other methods of bolt installation, such as use of hardened washers, careful attention to lubrication and the uncertainty of the effect of passage of time and exposure in the installed condition all reduce the reliability of the arbitration inspection results. The fact that in many cases it may have to be based upon a job test torque determined by using bolts only assumed to be representative of the bolts in the actual job, or using bolts removed from completed joints, makes the test procedure less reliable than a properly implemented installation procedure it is used to verify. Verification inspection using ultrasonic extensometers is accurate but costly and time-consuming, and requires that each tested bolt must be loosened to zero tension for calibration. Therefore, extensometers should be used for inspection only in the most critical cases. The arbitration inspection procedure contained in the Specification is provided, in spite of its limitations, as the most feasible available at this time.
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Code of Standard Practice for Steel Buildings and Bridges
Adopted Effective June 10, 1992 American Institute of Steel Construction, Inc.
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Copyright 1992 by The American Institute of Steel Construction All rights reserved. This book or any part thereof must not be reproduced in any form without the written permission of the publisher
PREFACE
When contractual documents do not contain specific provisions to the contrary, existing trade practices are considered to be incorporated into the relationships between the parties to a contract. As in any industry, trade practices have developed among those involved in the purchase, design, fabrication and erection of structural steel. The American Institute of Steel Construction has continuously surveyed the structural steel fabrication industry to determine standard practices and, commencing in 1924, published its Code of Standard Practice. Since that date, the Code has been periodically updated to reflect new and changing technology and practices of the industry. It is the Instituteâ&#x20AC;&#x2122;s intention to provide to owners, architects, engineers, contractors and others associated with construction, a useful framework for a common understanding of acceptable standards when contracting for structural steel construction. This edition is the fourth complete revision of the Code since it was first published. It includes a number of new sections covering new subjects not included in the previous Code, but which are an integral part of the relationship of the parties to a contract. The Institute acknowledges the valuable information and suggestions provided by trade associations and other organizations associated with construction and the fabricating industry in developing this current Code of Standard Practice. While every precaution has been taken to insure that all data and information presented is as accurate as possible, the Institute cannot assume responsibility for errors or oversights in the information published herein, or the use of the information published or incorporation of such information in the preparation of detailed engineering plans. The Code should not replace the judgment of an experienced architect or engineer who has the responsibility of design for a specific structure.
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Code of Standard Practice for Steel Buildings and Bridges Adopted Effective June 10, 1992 American Institute of Steel Construction, Inc.
SECTION 1. GENERAL PROVISIONS 1.1. Scope The practices defined herein have been adopted by the AISC as the commonly accepted standards of the structural steel fabricating industry. In the absence of other instructions in the contract documents, the trade practices defined in this Code of Standard Practice, as revised to date, govern the fabrication and erection of structural steel. 1.2. Definitions AISC Specification—The Specification for the Design, Fabrication and Erection of Structural Steel for Buildings as adopted by the American Institute of Steel Construction. ANSI—American National Standards Institute. Architect/Engineer—The owner’s designated representative with full responsibility for the design and integrity of the structure. (The EOR) ASTM—The material standard of the American Society for Testing and Materials. AWS Code—The Structural Welding Code of the American Welding Society. Code—The Code of Standard Practice as adopted by the American Institute of Steel Construction. Contract Documents—The documents which define the responsibilities of the parties involved in bidding, purchasing, supplying and erecting structural steel. Such documents normally consist of a contract, plans and specifications. Drawings—Shop and field erection drawings prepared by the fabricator and erector for the performance of the work. Erector—The party responsible for the erection of the structural steel. Fabricator—The party responsible for furnishing fabricated structural steel. General Contractor—The owner’s designated representative with full responsibility for the construction of the structure. MBMA—Metal Building Manufacturers Association.
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AISC CODE OF STANDARD PRACTICE
Mill Material—Steel mill products ordered expressly for the requirements of a specific project. Owner—The owner of the proposed structure or his designated representatives, who may be the architect, engineer, general contractor, construction manager, public authority or others. Owner’s Authorized Representative—That person designated by the owner to have the responsibility for the approval of shop drawings. This is usually the structural engineer of record for the project. Plans—Design drawings furnished by the party responsible for the design of the structure. Release for Construction—The release by the owner permitting the fabricator to commence work under the contract, including ordering material and preparing shop drawings. SSPC—The Steel Structures Painting Council, publishers of the Steel Structures Painting Manual, Vol. 2, “Systems and Specifications.” Tier—The word Tier used in Section 7.11 is defined as a column shipping piece. 1.3. Design Criteria for Buildings and Similar Type Structures In the absence of other instructions, the provisions of the AISC Specification govern the design of the structural steel. 1.4. Design for Bridges In the absence of other instructions, the following provisions govern, as applicable: Standard Specifications for Highway Bridges of the American Association of State Highway and Transportation Officials Specifications for Steel Railway Bridges of the American Railway Engineering Association Structural Welding Code of the American Welding Society 1.5. Responsibility for Design 1.5.1. When the owner provides the design, plans and specifications, the fabricator and erector are not responsible for the suitability, adequacy or legality of the design. The fabricator is not responsible for the safety of erection if the structure is erected by others. 1.5.2. When the owner enters into a direct contract with the fabricator to both design and fabricate an entire, completed steel structure, the fabricator is responsible for the structural adequacy of the design. The fabricator is not responsible for the safety of erection if the structure is erected by others.
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1.6. Patented Devices Except when the contract documents call for the design to be furnished by the fabricator or erector, the fabricator and erector assume that all necessary patent rights have been obtained by the owner and that the fabricator or erector will be fully protected in the use of patented designs, devices or parts required by the contract documents.
SECTION 2.0. CLASSIFICATION OF MATERIALS 2.1. Definition of Structural Steel â&#x20AC;&#x153;Structural Steel,â&#x20AC;? as used to define the scope of work in the contract documents, consists of the steel elements of the structural steel frame essential to support the design loads. Unless otherwise specified in the contract documents, these elements consist of material as shown on the structural steel plans and described as: Anchor bolts for structural steel Base or bearing plates Beams, girders, purlins and girts Bearings of steel for girders, trusses or bridges Bracing Columns, posts Connecting materials for framing structural steel to structural steel Crane rails, splices, stops, bolts and clamps Door frames constituting part of the structural steel frame Expansion joints connected to the structural steel frame Fasteners for connecting structural steel items: Shop rivets Permanent shop bolts Shop bolts for shipment Field rivets for permanent connections Field bolts for permanent connections Permanent pins Floor plates (checkered or plain) attached to the structural steel frame Grillage beams and girders Hangers essential to the structural steel frame Leveling plates, wedges, shims & leveling screws Lintels, if attached to the structural steel frame Marquee or canopy framing Machinery foundations of rolled steel sections and/or plate attached to the structural frame AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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Monorail elements of standard structural shapes when attached to the structural frame Roof frames of standard structural shapes Shear connectors—if specified to be shop attached Struts, tie rods and sag rods forming part of the structural steel frame Trusses. 2.2. Other Steel or Metal Items The classification “Structural Steel,” does not include steel, iron or other metal items not generally described in Section 2.1, even when such items are shown on the structural steel plans or are attached to the structural frame. These items include but are not limited to: Cables for permanent bracing or suspension systems Chutes and hoppers Cold-formed steel products Concrete or masonry reinforcing steel Door and corner guards Embedded steel parts in precast or poured concrete Flagpole support steel Floor plates (checkered or plain) not attached to the structural steel frame Grating and metal deck Items required for the assembly or erection of materials supplied by trades other than structural steel fabricators or erectors Ladders and safety cages Lintels over wall recesses Miscellaneous metal Non-steel bearings Open-web, long-span joists and joist girders Ornamental metal framing Shear connectors — if specified to be field installed Stacks, tanks and pressure vessels Stairs, catwalks, handrail and toeplates Trench or pit covers.
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SECTION 3. PLANS AND SPECIFICATIONS 3.1. Structural Steel In order to insure adequate and complete bids, and to enable the timely preparation of shop drawings and timely fabrication, the fabricator must be able to rely upon the completeness of the contract documents. The contract documents can be assumed to provide complete structural steel design plans clearly showing the work to be performed and giving the size, section, material grade and the location of all members, floor levels, column centers and offsets, and camber of members, with sufficient dimensions to convey accurately the quantity and nature of the structural steel to be furnished. Structural steel specifications include any special requirements controlling the fabrication and erection of the structural steel. Contract drawings, specifications and addenda must be numbered and dated for purposes of identification. 3.1.1. Wind bracing, connections, column stiffeners, column web doubler plates, bearing stiffeners on beams and girders, web reinforcement, openings for other trades, and other special details where required are shown in sufficient detail so that they may be readily understood. 3.1.2. Plans include sufficient data concerning assumed loads, shears, moments and axial forces to be resisted by the individual members and their connections, as may be required for the development of connection details on the shop drawings. Unless otherwise indicated in the contract documents, the plans are based upon consideration of the loads and forces to be resisted by the steel frame in the completed and fully connected condition. See Section 7.9. 3.1.3. Where connections are not shown, the connections are to be in accordance with the requirements of the AISC Specification. 3.1.4. When loose lintels and leveling plates are required to be furnished as part of the contract requirements, the plans and specifications show the size, section and location of all pieces. 3.1.5. Whenever steel frames, in the completely erected and fully connected state, require interaction with other elements not classified as structural steel (see Section 2) to provide stability and strength to resist loads for which the frame is designed, the non-self-supporting frame and the major elements not classified as structural steel, such as diaphragms, masonry and/or concrete shear walls, shall be identified in the contract documents. See Section 7.9.3. 3.1.6. When camber is required for cantilevered members, the magnitude and direction of camber are shown.
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3.1.7. The contract documents specify all the painting requirements, including the identification of members to be painted, surface preparation, paint specifications, manufacturerâ&#x20AC;&#x2122;s product identification and the required minimum and maximum dry film thickness, in mils, of the shop coat. Contract documents must clearly indicate all individual members which are to be left unpainted so as to receive concrete, sprayed on fireproofing or for other reasons. 3.2. Architectural, Electrical and Mechanical Architectural, electrical and mechanical plans may be used as a supplement to the structural steel plans to define detail configurations and construction information, provided all requirements for the quantities and locations of structural steel are noted on the structural steel plans. 3.3. Discrepancies In case of discrepancies between plans and specifications for buildings, the specifications govern. In case of discrepancies between plans and specifications for bridges, the plans govern. In case of discrepancies between scale dimensions on the plans and figures written on them, the figures govern. In case of discrepancies between the structural steel plans and the architectural plans or plans for other trades, the structural steel plans govern. 3.4. Legibility of Plans Plans are clearly legible and made to a scale not less than 1â &#x201E;8 in. to the foot. More complex information is furnished to an adequate scale to convey the information clearly. 3.5. Special Conditions When it is required that a project be advertised for bidding before the requirements of Section 3.1 can be met, the owner must provide sufficient information in the form of scope, drawings, weights, outline specifications, and other descriptive data to enable the fabricator and erector to prepare a knowledgeable bid.
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SECTION 4. SHOP AND ERECTION DRAWINGS 4.1. Owner Responsibility To enable the fabricator and erector to properly and expeditiously proceed with the work, the owner must furnish, in a timely manner and in accordance with the contract documents, complete structural steel plans and specifications released for construction. “Released for construction” plans and specifications are required by the fabricator for ordering mill material and the preparation and completion of shop and erection drawings. Plans provided as part of a contract bid package are considered to be “released for construction” unless otherwise noted. 4.2. Approval When shop drawings are made by the fabricator, prints thereof are submitted to the owner for his examination and approval. The fabricator includes a maximum allowance of fourteen (14) calendar days in his schedule for the return of shop drawings. Return of shop drawings is noted with the owner’s approval, or approval subject to corrections as noted. The fabricator makes the corrections and furnishes corrected prints to the owner. Approval of shop drawings, approval “subject to corrections noted,” or similar approvals, constitute the owner’s release for the fabricator to begin fabrication. The fabricator retains flexibility to determine the fabrication schedule necessary to meet the project’s requirements. 4.2.1. Approval by the owner’s authorized representative of shop drawings prepared by the fabricator indicates that the fabricator has correctly interpreted the contract requirements, and may rely upon these drawings in the fabrication process. Where the fabricator must select or complete connection details, this approval constitutes acceptance by the owner’s authorized representative of design responsibility for the structural adequacy of such connections. If a fabricator wishes to change a connection that is fully detailed in the contract documents, the fabricator shall submit the change for review by the owner’s authorized representative in a manner that clearly indicates that a change is being requested. Approval of this submittal constitutes acceptance by the owner’s authorized representative of design responsibility for the structural adequacy of the changed detail. Approval under any of the circumstances described in this Section does not relieve the fabricator of the responsibility for accuracy of detailed dimensions on shop drawings, nor the general fit-up of parts to be assembled in the field. 4.2.2. Unless specifically stated to the contrary, any additions, deletions or changes indicated on the approval of shop and erection drawings are authorizations by the owner to release the additions, deletions or revisions for construction.
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4.3. Drawings Furnished by Owner When the shop drawings are furnished by the owner, he must deliver them to the fabricator in time to permit material procurement and fabrication to proceed in an orderly manner in accordance with the prescribed time schedule. The owner prepares these shop drawings, insofar as practicable, in accordance with the shop and drafting room standards of the fabricator. The owner is responsible for the completeness and accuracy of shop drawings so furnished.
SECTION 5. MATERIALS 5.1. Mill Materials When the fabricator receives “released for construction” plans and specifications, the fabricator may immediately place orders for the materials necessary for fabrication. The contract documents must note any material or areas which should not be ordered due to a design which is incomplete or subject to revision. 5.1.1. Mill tests are performed to demonstrate material conformance to ASTM specifications in accordance with the contract requirements. Unless special requirements are included in the contract documents, mill testing is limited to those tests required by the applicable ASTM material specifications. Mill test reports are furnished by the fabricator only if requested by the owner, either in the contract documents or in separate written instructions prior to the time the fabricator places his material orders with the mill. 5.1.2. When material received from the mill does not satisfy ASTM A6 tolerances for camber, profile, flatness or sweep, the fabricator is permitted to perform corrective work by the use of controlled heating and mechanical straightening, subject to the limitations of the AISC Specification. 5.1.3. Corrective procedures described in ASTM A6 for reconditioning the surface of structural steel plates and shapes before shipment from the producing mill may also be performed by the fabricator, at the fabricator’s option, when variations described in ASTM A6 are discovered or occur after receipt of the steel from the producing mill. 5.1.4. When special requirements demand tolerances more restrictive than allowed by ASTM A6, such requirements are defined in the contract documents and the fabricator has the option of corrective measures as described above.
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5.2. Stock Materials 5.2.1. Many fabricators maintain stocks of steel products for use in their fabricating operations. Materials taken from stock by the fabricator to be used for structural purposes must be of a quality at least equal to that required by the ASTM specifications applicable to the classification covering the intended use. 5.2.2. Mill test reports are accepted as sufficient record of the quality of materials carried in stock by the fabricator. The fabricator reviews and retains the mill test reports covering the materials he purchases for stock, but the fabricator does not maintain records that identify individual pieces of stock material against individual mill test reports. Such records are not required if the fabricator purchases for stock under established specifications as to grade and quality. 5.2.3. Stock materials purchased under no particular specifications or under specifications less rigid than those mentioned above, or stock materials which have not been subject to mill or other recognized test reports, are not used without the express approval of the owner, except where the quality of the material could not affect the integrity of the structure.
SECTION 6. FABRICATION AND DELIVERY 6.1. Identification of Material 6.1.1. High strength steel and steel ordered to special requirements is marked by the supplier, in accordance with ASTM A6 requirements, prior to delivery to the fabricator’s shop or other point of use. 6.1.2. High strength steel and steel ordered to special requirements that has not been marked by the supplier in accordance with Section 6.1.1 is not used until its identification is established by means of tests as specified in Section A3.1 of the AISC Specification, and until a fabricator’s identification mark, as described in Section 6.1.3, has been applied. 6.1.3. During fabrication, up to the point of assembling members, each piece of high strength steel and steel ordered to special requirements carries a fabricator’s identification mark or an original supplier’s identification mark. The fabricator’s identification mark is in accordance with the fabricator’s established identification system, which is on record and available for the information of the owner or his representative, the building commissioner and the inspector, prior to the start of fabrication.
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6.1.4. Members made of high strength steel and steel ordered to special requirements are not given the same assembling or erecting mark as members made of other steel, even though they are of identical dimensions and detail. 6.2. Preparation of Material 6.2.1. Thermal cutting of structural steel may be performed by hand or mechanically guided means. 6.2.2. Surfaces noted as “finished” on the drawings are defined as having a maximum ANSI roughness height value of 500. Any fabricating technique, such as friction sawing, cold sawing, milling, etc., that produces such a finish may be used. 6.3. Fitting and Fastening 6.3.1. Projecting elements of connection attachments need not be straightened in the connecting plane if it can be demonstrated that installation of the connectors or fitting aids will provide reasonable contact between faying surfaces. 6.3.2. Runoff tabs are often required to produce sound welds. The fabricator or erector does not remove them unless specified in the contract documents. When their removal is required, they may be hand flame-cut close to the edge of the finished member with no further finishing required, unless other finishing is specifically called for in the contract documents. 6.3.3. All high-strength bolts for shop attached connection material are to be installed in the shop in accordance with the Specification for Structural Joints Using A325 or A490 Bolts, unless otherwise noted on the shop drawings. 6.4. Dimensional Tolerances 6.4.1. A variation of 1⁄32 in. is permissible in the overall length of members with both ends finished for contact bearing as defined in Section 6.2.2. 6.4.2. Members without ends finished for contact bearing, which are to be framed to other steel parts of the structure, may have a variation from the detailed length not greater than 1⁄16 in. for members 30 ft or less in length, and not greater than 1⁄8 in. for members over 30 ft in length. 6.4.3. Unless otherwise specified, structural members, whether of a single-rolled shape or built-up, may vary from straightness within the tolerances allowed for wideflange shapes by ASTM Specification A6, except that the tolerance on deviation from
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straightness of compression members is 1⁄1000 of the axial length between points which are to be laterally supported. Completed members should be free from twists, bends and open joints. Sharp kinks or bends are cause for rejection of material. 6.4.4. Beams and trusses detailed without specified camber are fabricated so that after erection any camber due to rolling or shop fabrication is upward. 6.4.5. When members are specified on the contract documents as requiring camber, the shop fabrication tolerance shall be minus zero / plus 1⁄2 in. for members 50 ft and less in length, or minus zero / plus (1⁄2 in. plus 1⁄8 in. for each 10 ft or fraction thereof in excess of 50 ft in length) for members over 50 ft. Members received from the rolling mill with 75% of the specified camber require no further cambering. For purposes of inspection, camber must be measured in the fabricator’s shop in the unstressed condition. 6.4.6. Any permissible deviation in depths of girders may result in abrupt changes in depth at splices. Any such difference in depth at a bolted joint, within the prescribed tolerances, is taken up by fill plates. At welded joints the weld profile may be adjusted to conform to the variation in depth, provided that the minimum cross section of required weld is furnished and that the slope of the weld surface meets AWS Code requirements. 6.5. Shop Painting (See also Section 3.1.7.) 6.5.1. The shop coat of paint is the prime coat of the protective system. It protects the steel for only a short period of exposure in ordinary atmospheric conditions, and is considered a temporary and provisional coating. The fabricator does not assume responsibility for deterioration of the prime coat that may result from exposure to ordinary atmospheric conditions, nor from exposure to corrosive conditions more severe than ordinary atmospheric conditions. 6.5.2. In the absence of other requirements in the contract documents, the fabricator hand cleans the steel of loose rust, loose mill scale, dirt and other foreign matter, prior to painting, by means of wire brushing or by other methods elected by the fabricator, to meet the requirements of SSPC-SP2. The fabricator’s workmanship on surface preparation is considered accepted by the owner unless specifically disapproved prior to paint application. 6.5.3. Unless specifically excluded, paint is applied by brush, spray, roller coating, flow coating or dipping, at the election of the fabricator. When the term “shop coat” or “shop paint” is used with no paint system specified, the fabricator’s standard paint shall be applied to a minimum dry film thickness of one mil.
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6.5.4. Steel not requiring shop paint is cleaned of oil or grease by solvent cleaners and cleaned of dirt and other foreign material by sweeping with a fiber brush or other suitable means. 6.5.5. Abrasions caused by handling after painting are to be expected. Touch-up of these blemished areas is the responsibility of the contractor performing field touchup or field painting. 6.6. Marking and Shipping of Materials 6.6.1. Erection marks are applied to the structural steel members by painting or other suitable means, unless otherwise specified in the contract documents. 6.6.2. Rivets and bolts are commonly shipped in separate containers according to length and diameter; loose nuts and washers are shipped in separate containers according to sizes. Pins and other small parts, and packages of rivets, bolts, nuts and washers are usually shipped in boxes, crates, kegs or barrels. A list and description of the material usually appears on the outside of each closed container. 6.7. Delivery of Materials 6.7.1. Fabricated structural steel is delivered in such sequence as will permit the most efficient and economical performance of both shop fabrication and erection. If the owner wishes to prescribe or control the sequence of delivery of materials, the owner reserves such right and defines the requirements in the contract documents. If the owner contracts separately for delivery and erection, the owner must coordinate planning between contractors. 6.7.2. Anchor bolts, washers and other anchorage or grillage materials to be built into masonry should be shipped so that they will be on hand when needed. The owner must allow the fabricator sufficient time to fabricate and ship such materials before they are needed. 6.7.3. The quantities of material shown by the shipping statement are customarily accepted by the owner, fabricator and erector as correct. If any shortage is claimed, the owner or erector should immediately notify the carrier and the fabricator in order that the claim may be investigated. 6.7.4. The size and weight of structural steel assemblies may be limited by shop capabilities, the permissible weight and clearance dimensions of available transportation and the job site conditions. The fabricator limits the number of field splices to those consistent with minimum project cost.
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6.7.5. If material arrives at its destination in damaged condition, it is the responsibility of the receiving party to promptly notify the fabricator and carrier prior to unloading the material, or immediately upon discovery.
SECTION 7. ERECTION 7.1. Method of Erection When the owner wishes to control the method and sequence of erection, or when certain members cannot be erected in their normal sequence, the owner so specifies in the contract documents. In the absence of such restrictions, the erector will proceed using the most efficient and economical method and sequence available to the erector consistent with the contract documents. When the owner contracts separately for fabrication and erection services, the owner is responsible for coordinating planning between contractors. 7.2. Site Conditions The owner provides and maintains adequate access roads into and through the site for the safe delivery and movement of derricks, cranes, trucks, other necessary equipment, and the material to be erected. The owner affords the erector a firm, properly graded, drained, convenient and adequate space at the site for the operation of the erectorâ&#x20AC;&#x2122;s equipment, and removes all overhead obstructions such as power lines, telephone lines, etc., in order to provide a safe working area for erection of the steelwork. The erector provides and installs the safety protection required for his own work. Any protection for other trades not essential to the steel erection activity is the responsibility of the owner. When safety protection provided by the erector is left remaining in an area to be used by other trades after the steel erection activity is completed, the owner shall be responsible for accepting and maintaining this protection, assuring that it is adequate for the protection of all other affected trades, assuring that it complies with all applicable safety regulations when being used by other trades, indemnifying the erector from any damages incurred as a result of the safety protectionâ&#x20AC;&#x2122;s use by other trades, removing the safety equipment when no longer required, and returning it to the erector in the same condition as it was received. When the structure does not occupy the full available site, the owner provides adequate storage space to enable the fabricator and erector to operate at maximum practicable speed. 7.3. Foundations, Piers and Abutments The accurate location, strength, suitability and access to all foundations, piers and abutments is the sole responsibility of the owner.
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7.4. Building Lines and Bench Marks The owner is responsible for accurate location of building lines and bench marks at the site of the structure, and for furnishing the erector with a plan containing all such information. At each level the owner establishes offset building lines and reference elevations for the use of the erector in the positioning of adjustable construction elements. 7.5. Installation of Anchor Bolts and Embedded Items 7.5.1. Anchor bolts and foundation bolts are set by the owner in accordance with an approved drawing. They must not vary from the dimensions shown on the erection drawings by more than the following: (a)
(b) (c) (d)
(e) (f)
1⁄ 8
in. center to center of any two bolts within an anchor bolt group, where an anchor bolt group is defined as the set of anchor bolts which receive a single fabricated steel shipping piece. 1⁄ in. center to center of adjacent anchor bolt groups. 4 Elevation of the top of anchor bolts ± 1⁄2 in. Maximum accumulation of 1⁄4 in. per hundred ft along the established column line of multiple anchor bolt groups, but not to exceed a total of 1 in., where the established column line is the actual field line most representative of the centers of the as-built anchor bolt groups along a line of columns. 1⁄ in. from the center of any anchor bolt group to the established column 4 line through that group. The tolerances of paragraphs b, c and d apply to offset dimensions shown on the plans, measured parallel and perpendicular to the nearest established column line for individual columns shown on the plans to be offset from established column lines.
7.5.2. Unless shown otherwise, anchor bolts are set perpendicular to the theoretical bearing surface. 7.5.3. Other embedded items or connection materials between the structural steel and the work of other trades are located and set by the owner in accordance with approved location or erection drawings. Accuracy of these items must satisfy the erection tolerance requirements of Section 7.11.3. 7.5.4. All work performed by the owner is completed so as not to delay or interfere with the erection of the structural steel.
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7.6. Bearing Devices The owner sets to line and grade all leveling plates, leveling nuts and loose bearing plates which can be handled without a derrick or crane. All other bearing devices supporting structural steel are set and wedged, shimmed or adjusted with leveling screws by the erector to lines and grades established by the owner. The fabricator provides the wedges, shims or leveling screws that are required, and clearly scribes the bearing devices with working lines to facilitate proper alignment. Promptly after the setting of any bearing devices, the owner checks lines and grades, and grouts as required. The final location and proper grouting of bearing devices are the responsibility of the owner. Tolerance on elevation relative to established grades of bearing devices, whether set by the owner or by the erector, is ± 1⁄8 in. 7.7. Field Connection Material 7.7.1. The fabricator provides field connection details consistent with the requirements of the contract documents which will, in the fabricator’s opinion, result in the most economical fabrication and erection cost. 7.7.2. When the fabricator erects the structural steel, the fabricator supplies all materials required for temporary and permanent connection of the component parts of the structural steel. 7.7.3. When the erection of the structural steel is performed by someone other than the fabricator, the fabricator furnishes the following field connection material: (a)
(b)
(c) (d)
Bolts of required size and in sufficient quantity for all field connections of steel to steel which are to be permanently bolted. Unless high-strength bolts or other special types of bolts and washers are specified, common bolts are furnished. An extra 2 percent of each bolt size (diameter and length) is furnished. Rivets of required size and in sufficient quantity for all field connections of steel to steel which are to be riveted field connections. An extra 10 percent of each rivet size is furnished. Shims shown as necessary for make-up of permanent connections of steel to steel. Back-up bars or run-off tabs that may be required for field welding.
7.7.4. When the erection of the structural steel is performed by someone other than the fabricator, the erector furnishes all welding electrodes, fit-up bolts and drift pins used for erection of the structural steel.
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7.7.5. Field-installed shear connectors are supplied by the shear connector applicator. 7.7.6. Metal deck support angles are the responsibility of the metal deck supplier. 7.8. Loose Material Loose items of structural steel not connected to the structural frame are set by the owner without assistance from the erector, unless otherwise specified in the contract documents. 7.9. Temporary Support of Structural Steel Frames 7.9.1. General Temporary supports, such as temporary guys, braces, falsework, cribbing or other elements required for the erection operation will be determined and furnished and installed by the erector. These temporary supports will secure the steel framing, or any partly assembled steel framing, against loads comparable in intensity to those for which the structure was designed, resulting from wind, seismic forces and erection operations, but not the loads resulting from the performance of work by or the acts of others, nor such unpredictable loads as those due to tornado, explosion or collision. 7.9.2. Self-supporting Steel Frames A self-supporting steel frame is one that provides the required stability and resistance to gravity loads and design wind and seismic forces without interaction with other elements of the structure. The erector furnishes and installs only those temporary supports that are necessary to secure any element or elements of the steel framing until they are made stable without external support. Special erection sequences or other considerations which are required to provide stability during the erection process must be set out in the contract documents in detail. 7.9.3. Non-Self-supporting Steel Frames A non-self-supporting steel frame is one that, when fully assembled and connected, requires interaction with other elements not classified as Structural Steel to provide stability and strength to resist loads for which the frame is designed. Such frames shall be clearly designated as â&#x20AC;&#x153;non-self-supporting.â&#x20AC;? The major elements not classified as structural steel, such as steel deck diaphragms, masonry and/or concrete shear walls, shall be identified in the contract documents.
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When elements not classified as structural steel interact with the structural steel elements to provide stability and/or strength to resist loads, the owner is responsible for the installation, structural adequacy during installation, and timely completion of all such elements. The contract documents must specify the sequence and schedule of placement of such elements and the effects of the loads imposed on the structural steel frame by partially or completely installed interacting elements. The erector furnishes and installs temporary support as necessary in accordance with this information but does not thereby assume responsibility for the appropriateness of the sequence specified. 7.9.4. Special Erection Conditions When the design concept of a structure is dependent upon the use of shores, jacks or loads which must be adjusted as erection progresses to set or maintain camber or prestress, such requirement is specifically stated in the contract documents. 7.9.5. Removal of Temporary Supports The temporary guys, braces, falsework, cribbing and other elements required for the erection operation, which are furnished and installed by the erector, are not the property of the owner. In self-supporting structures, temporary supports are not required after the structural steel for a self-supporting element is located and finally fastened within the required tolerances. After such final fastening, the erector is no longer responsible for temporary support of the self-supporting element and may remove the temporary supports. In non-self-supporting structures, the erector may remove temporary supports when the necessary non-structural steel elements are complete. Temporary supports are not to be removed without the consent of the erector. At completion of steel erection, any temporary supports that are required to be left in place are removed by the owner and returned to the erector in good condition. 7.9.6. Temporary Supports for Other Work Should temporary supports beyond those defined as the responsibility of the erector in Sections 7.9.1, 7.9.2 and 7.9.3 be required, either during or after the erection of the structural steel, responsibility for the supply and installation of such supports rests with the owner. 7.10. Temporary Floors and Handrails for Buildings The erector provides floor coverings, handrails and walkways as required by law and applicable safety regulations for protection of his own personnel. As work progresses, the erector removes such facilities from units where the erection
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operations are completed, unless other arrangements are included in the contract documents. The owner is responsible for all protection necessary for the work of other trades. When permanent steel decking is used for protective flooring and is installed by the owner, all such work is performed so as not to delay or interfere with erection progress and is scheduled by the owner and installed in a sequence adequate to meet all safety regulations. (See Section 7.2) 7.11. Frame Tolerances 7.11 7.11.1. Overall Dimensions Some variation is to be expected in the finished overall dimensions of structural steel frames. Such variations are deemed to be within the limits of good practice when they do not exceed the cumulative effect of rolling tolerances, fabricating tolerances and erection tolerances. 7.11.2. Working Points and Working Lines Erection tolerances are defined relative to member working points and working lines as follows: (a) (b) (c) (d)
For members other than horizontal members, the member work point is the actual center of the member at each end of the shipping piece. For horizontal members, the working point is the actual center line of the top flange or top surface at each end. Other working points may be substituted for ease of reference, providing they are based upon these definitions. The member working line is a straight line connecting the member working points.
7.11.3. Position and Alignment The tolerances on position and alignment of member working points and working lines are as follows: 7.11.3.1. Columns Individual column shipping pieces are considered plumb if the deviation of the working line from a plumb line does not exceed 1:500, subject to the following limitations:
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The member working points of column shipping pieces adjacent to elevator shafts may be displaced no more than 1 in. from the established column line in the first 20 stories; above this level, the displacement may be increased 1⁄32 in. for each additional story up to a maximum of 2 in. The member working points of exterior column shipping pieces may be displaced from the established column line no more than 1 in. toward nor 2 in. away from the building line in the first 20 stories; above the 20th story, the displacement may be increased 1⁄16 in. for each additional story, but may not exceed a total displacement of 2 in. toward nor 3 in. away from the building line. The member working points of exterior column shipping pieces at any splice level for multi-tier buildings and at the tops of columns for single tier buildings may not fall outside a horizontal envelope, parallel to the building line, 11⁄2 in. wide for buildings up to 300 ft in length. The width of the envelope may be increased by 1⁄2 in. for each additional 100 ft in length, but may not exceed 3 in. The member working points of exterior column shipping pieces may be displaced from the established column line, in a direction parallel to the building line, no more than 2 in. in the first 20 stories; above the 20th story, the displacement may be increased 1⁄16 in. for each additional story, but may not exceed a total displacement of 3 in. parallel to the building line.
7.11.3.2. Members Other Than Columns (a)
(b)
(c)
(d)
Alignment of members which consist of a single straight shipping piece containing no field splices, except cantilevered members, is considered acceptable if the variation in alignment is caused solely by the variation of column alignment and/or primary supporting member alignment within the permissible limits for fabrication and erection of such members. The elevation of members connecting to columns is considered acceptable if the distance from the member working point to the upper milled splice line of the column does not deviate more than plus 3⁄16 in. or minus 5⁄16 in. from the distance specified on the drawings. The elevation of members which consist of a single shipping piece, other than members connected to columns, is considered acceptable if the variation in actual elevation is caused solely by the variation in elevation of the supporting members which are within permissible limits for fabrication and erection of such members. Individual shipping pieces which are segments of field assembled units containing field splices between points of support are considered plumb, level and aligned if the angular variation of the working line of each shipping piece relative to the plan alignment does not exceed 1:500.
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(e)
(f)
AISC CODE OF STANDARD PRACTICE
The elevation and alignment of cantilevered members shall be considered plumb, level and aligned if the angular variation of the working line from a straight line extended in the plan direction from the working point at its supported end does not exceed 1:500. The elevation and alignment of members which are of irregular shape shall be considered plumb, level and aligned if the fabricated member is within its tolerance and its supporting member or members are within the tolerances specified in this Code.
7.11.3.3. Adjustable Items The alignment of lintels, wall supports, curb angles, mullions and similar supporting members for the use of other trades, requiring limits closer than the foregoing tolerances, cannot be assured unless the owner’s plans call for adjustable connections of these members to the supporting structural frame. The fabricator may provide nonadjustable connections unless the contract documents specifically show or specify them as adjustable. When adjustable connections are specified, the owner’s plans must provide for the total adjustment required to accommodate the tolerances on the steel frame for the proper alignment of these supports for other trades. The tolerances on position and alignment of such adjustable items are as follows: (a)
(b)
(c)
Adjustable items are considered to be properly located in their vertical position when their location is within 3⁄8 in. of the location established from the upper milled splice line of the nearest column to the support location as specified on the drawings. Adjustable items are considered to be properly located in their horizontal position when their location is within 3⁄8 in. of the proper location relative to the established finish line at any particular floor. The ends of adjustable items which abut are considered to be properly located when aligned to within 3⁄16 in. of each other both vertically and horizontally.
7.11.4. Responsibility for Clearances In the design of steel structures, the owner is responsible for providing clearances and adjustments of material furnished by other trades to accommodate all of the foregoing tolerances of the structural steel frame. 7.11.5. Acceptance of Position and Alignment Prior to placing or applying any other materials, the owner is responsible for determining that the location of the structural steel is acceptable for plumbness, level and alignment within tolerances. The erector is given timely notice of acceptance by the owner or a listing of specific items to be corrected in order to obtain acceptance.
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Such notice is rendered immediately upon completion of any part of the work and prior to the start of work by other trades that may be supported, attached or applied to the structural steelwork. 7.12. Correction of Errors Normal erection operations include the correction of minor misfits by moderate amounts of reaming, chipping, welding or cutting, and the drawing of elements into line through the use of drift pins. Errors which cannot be corrected by the foregoing means, or which require major changes in member configuration, are reported immediately to the owner and fabricator by the erector, to enable whoever is responsible either to correct the error or to approve the most efficient and economic method of correction to be used by others. 7.13. Cuts, Alterations and Holes for Other Trades Neither the fabricator nor the erector will cut, drill or otherwise alter his work, or the work of other trades, to accommodate other trades, unless such work is clearly specified in the contract documents. Whenever such work is specified, the owner is responsible for furnishing complete information as to materials, size, location and number of alterations in a timely manner so that the preparation of shop drawings will not be delayed. 7.14. Handling and Storage The erector takes reasonable care in the proper handling and storage of steel during erection operations to avoid accumulation of excess dirt and foreign matter. The erector is not responsible for removal from the steel of dust, dirt or other foreign matter which accumulates during the erection period as the result of site conditions or exposure to the elements. 7.15.
Field Painting
The erector does not paint field bolt heads and nuts, field rivet heads and field welds, nor touch up abrasions of the shop coat, nor perform any other field painting. 7.16. Final Cleaning Up Upon completion of erection and before final acceptance, the erector removes all of his falsework, rubbish and temporary buildings.
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SECTION 8. QUALITY CONTROL 8.1. General 8.1.1. The fabricator maintains a quality control program to the extent deemed necessary so that the work is performed in accordance with this Code, the AISC Specification, and contract documents. The fabricator has the option to use the AISC Quality Certification Program in establishing and administering the quality control program. 8.1.2. The erector maintains a quality control program to the extent the erector deems necessary so that all of the work is performed in accordance with this Code, the AISC Specification and the contract documents. The erector shall be capable of performing the erection of the structural steel, and shall provide the equipment, personnel and management for the scope, magnitude and required quality of each project. 8.1.3. When the owner requires more extensive quality control or independent inspection by qualified personnel, or requires the fabricator to be certified by the AISC Quality Certification Program, this shall be clearly stated in the contract documents, including a definition of the scope of such inspection. 8.2. Mill Material Inspection The fabricator customarily makes a visual inspection, but does not perform any material tests, depending upon mill reports to signify that the mill product satisfies material order requirements. The owner relies on mill tests required by contract and on such additional tests as he orders the fabricator to have made at the ownerâ&#x20AC;&#x2122;s expense. If mill inspection operations are to be monitored, or if tests other than mill tests are desired, the owner so specifies in the contract documents and should arrange for such testing through the fabricator to assure coordination. 8.3. Non-Destructive Testing When non-destructive testing is required, the process, extent, technique and standards of acceptance are clearly defined in the contract documents. 8.4. Surface Preparation and Shop Painting Inspection Surface preparation and shop painting inspection must be planned for acceptance of each operation as completed by the fabricator. Inspection of the paint system, including material and thickness, is made promptly upon completion of the paint
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application. When wet film thickness is inspected, it must be measured during the application. 8.5. Independent Inspection When contract documents specify inspection by other than the fabricator’s and erector’s own personnel, both parties to the contract incur obligations relative to the performance of the inspection. 8.5.1. The fabricator and erector provide the inspector with access to all places where work is being done. A minimum of 24 hours notification is given prior to commencement of work. 8.5.2. Inspection of shop work by the owner or his representative is performed in the fabricator’s shop to the fullest extent possible. Such inspections should be in sequence, timely, and performed in such a manner as will not disrupt fabrication operations and will permit repair of non-conforming work prior to any required painting while the material is still in process in the fabrication shop. 8.5.3. Inspection of field work must be completed promptly so that corrections can be made without delaying the progress of the work. 8.5.4. Rejection of material or workmanship not in conformance with the contract documents may be made at any time during the progress of the work. However, this provision does not relieve the owner of his obligation for timely, in-sequence inspections. 8.5.5. Copies of all reports prepared by the owner’s inspection representative must be given to the fabricator and erector immediately after the inspection to allow any necessary corrective work to be performed in a timely manner. 8.5.6. The owner’s inspection representative may not suggest, direct, or approve the fabricator or erector to deviate from the contract documents or approved shop drawings, or approve such deviation, without the express written approval of the engineer of record or the person designated as the owner’s authorized representative.
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SECTION 9. CONTRACTS 9.1. Types of Contracts 9.1.1. For contracts stipulating a lump sum price, the work required to be performed by the fabricator and erector is completely defined by the contract documents. 9.1.2. For contracts stipulating a price per pound, the scope of work, type of materials, character of fabrication, and conditions of erection are based upon the contract documents which must be representative of the work to be performed. 9.1.3. For contracts stipulating a price per item, the work required to be performed by the fabricator and erector is based upon the quantity and the character of items described in the contract documents. 9.1.4. For contracts stipulating unit prices for various categories of structural steel, the scope of the work required to be performed by the fabricator and erector is based upon the quantity, character and complexity of the items in each category as described in the contract documents. The contract documents must be representative of the work to be done in each category. 9.2. Calculation of Weights Unless otherwise set forth in the contract, on contracts stipulating a price per pound for fabricated structural steel delivered and/or erected, the quantities of materials for payment are determined by the calculation of gross weight of materials as shown on the shop drawings. 9.2.1. The unit weight of steel is assumed to be 490 pounds per cubic ft. The unit weight of other materials is in accordance with the manufacturerâ&#x20AC;&#x2122;s published data for the specific product. 9.2.2. The weights of shapes, plates, bars, steel pipe and structural tubing are calculated on the basis of shop drawings showing actual quantities and dimensions of material furnished, as follows: (a) (b)
The weight of all structural shapes, steel pipe and structural tubing is calculated using the nominal weight per ft and the detailed overall length. The weight of plates and bars is calculated using the detailed overall rectangular dimensions.
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(d)
(e)
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When parts can be economically cut in multiples from material of larger dimensions, the weight is calculated on the basis of the theoretical rectangular dimensions of the material from which the parts are cut. When parts are cut from structural shapes, leaving a non-standard section not useable on the same contract, the weight is calculated on the basis of the nominal unit weight of the section from which the parts are cut. No deductions are to be made for material removed by cuts, copes, clips, blocks, drilling, punching, boring, slot milling, planing or weld joint preparation.
9.2.3. The calculated weights of castings are determined from the shop drawings of the pieces. An allowance of 10 percent is added for fillets and overrun. Scale weights of rough castings may be used if available. 9.2.4. The items for which weights are shown in tables in the AISC Manual of Steel Construction are calculated on the basis of tabulated unit weights. 9.2.5. The weight of items not included in the tables in the AISC Manual of Steel Construction shall be taken from the manufacturersâ&#x20AC;&#x2122; catalog and the manufacturersâ&#x20AC;&#x2122; shipping weight shall be used. 9.2.6. The weight of shop or field weld metal and protective coatings is not included in the calculated weight for pay purposes. 9.3. Revisions to Contract Documents 9.3.1. Revisions to the contract are made by issuance of new documents or reissuance of existing documents. In either case, all revisions, including revisions communicated by annotation of shop or erection drawings, must be clearly and individually indicated and the documents dated and identified by revision number. All contract drawings shall be identified by the same drawing number throughout the duration of the job regardless of the revision. The engineer of record is responsible for reviewing the overall structural design to identify all components which will be affected by a change to any individual component. 9.3.2. A revision to the requirements of the contract documents is made by change order, extra work order, or notations on the shop and erection drawings when returned upon approval. 9.3.3. Unless specifically stated to the contrary, the issuance of a revision is authorization by the owner to release these documents for construction.
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9.4. Contract Price Adjustment 9.4.1. When the scope of work and responsibilities of the fabricator and erector are changed from those previously established by the contract documents, an appropriate modification of the contract price is made. In computing the contract price adjustment, the fabricator and erector consider the quantity of work added or deleted, modifications in the character of the work, and the timeliness of the change with respect to the status of material ordering, detailing, fabrication and erection operations. 9.4.2. Requests for contract price adjustments are presented by the fabricator and erector in a timely manner and are accompanied by a description of the change in sufficient detail to permit evaluation and timely approval by the owner. 9.4.3. Price per pound and price per item contracts generally provide for additions or deletions to the quantity of work prior to the time work is released for construction. Changes to the character of the work, at any time, or additions and/or deletions to the quantity of the work after it is released for detailing, fabrication, or erection, may require a contract price adjustment. 9.5. Scheduling 9.5.1. The contract documents specify the schedule for the performance of the work. This schedule states when the “released for construction” plans will be issued and when the job site, foundations, piers and abutments will be ready, free from obstructions and accessible to the erector, so that erection can start at the designated time and continue without interference or delay caused by the owner or other trades. 9.5.2. The fabricator and erector have the responsibility to advise the owner, in a timely manner, of the effect any revision has on the contract schedule. 9.5.3. If the fabrication or erection is significantly delayed due to design revisions, or for other reasons which are the owner’s responsibility, the fabricator and erector are compensated for additional costs incurred. 9.6. Terms of Payment The terms of payment for the contract shall be outlined in the contract documents.
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SECTION 10. ARCHITECTURALLY EXPOSED STRUCTURAL STEEL 10.1. Scope This section of the Code defines additional requirements which apply only to members specifically designated by the contract documents as â&#x20AC;&#x153;Architecturally Exposed Structural Steelâ&#x20AC;? (AESS). All provisions of Sections 1 through 9 of the Code apply unless specifically modified in this section. AESS members or components are fabricated and erected with the care and dimensional tolerances indicated in this section. 10.2. Additional Information Required in Contract Documents (a) (b) (c)
Specific identification of members or components which are to be AESS. Fabrication and erection tolerances which are more restrictive than provided for in this section. Requirements, if any, of a test panel or components for inspection and acceptance standards prior to the start of fabrication.
10.3. Fabrication 10.3.1. Rolled Shapes Permissible tolerances for out-of-square or out-of-parallel, depth, width and symmetry of rolled shapes are as specified in ASTM Specification A6. No attempt to match abutting cross-sectional configurations is made unless specifically required by the contract documents. The as-fabricated straightness tolerances of members are one-half of the standard camber and sweep tolerances in ASTM A6. 10.3.2. Built-up Members The tolerances on overall profile dimensions of members made up from a series of plates, bars and shapes by welding are limited to the accumulation of permissible tolerances of the component parts as provided by ASTM Specification A6. The asfabricated straightness tolerances for the member as a whole are one-half the standard camber and sweep tolerances for rolled shapes in ASTM A6. 10.3.3. Weld Show-through It is recognized that the degree of weld show-through, which is any visual indication of the presence of a weld or welds on the side away from the viewer, is a function of weld size and material thickness. The members or components will be
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acceptable as produced unless specific acceptance criteria for weld show-through are included in the contract documents. 10.3.4. Joints All copes, miters and butt cuts in surfaces exposed to view are made with uniform gaps of 1â &#x201E;8 in. if shown to be open joints, or in reasonable contact if shown without gap. 10.3.5. Welding Reasonably smooth and uniform as-welded surfaces are acceptable on all welds exposed to view. Butt and plug welds do not project more than 1â &#x201E;16 in. above the exposed surface. No finishing or grinding is required except where clearances or fit of other components may necessitate, or when specifically required by the contract documents. 10.3.6. Weathering Steel Members fabricated of weathering steel which are to be AESS shall not have erection marks or other painted marks on surfaces that are to be exposed in the completed structure. If cleaning other than SSPC-SP6 is required, these requirements shall be defined in the contract documents. 10.4. Delivery of Materials The fabricator uses special care to avoid bending, twisting or otherwise distorting individual members. 10.5. Erection 10.5.1. General The erector uses special care in unloading, handling and erecting the steel to avoid marking or distorting the steel members. Care is also taken to minimize damage to any shop paint. If temporary braces or erection clips are used, care is taken to avoid unsightly surfaces upon removal. Tack welds are ground smooth and holes are filled with weld metal or body solder and smoothed by grinding or filing. The erector plans and executes all operations in such a manner that the close fit and neat appearance of the structure will not be impaired.
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10.5.2. Erection Tolerances Unless otherwise specifically designated in the contract documents, members and components are plumbed, leveled and aligned to a tolerance not to exceed one-half the amount permitted for structural steel. These erection tolerances for AESS require that the ownerâ&#x20AC;&#x2122;s plans specify adjustable connections between AESS and the structural steel frame or the masonry or concrete supports, in order to provide the erector with means for adjustment. 10.5.3. Components with Concrete Backing When AESS is backed with concrete, it is the general contractorâ&#x20AC;&#x2122;s responsibility to provide sufficient shores, ties and strongbacks to assure against sagging, bulging, etc., of the AESS resulting from the weight and pressure of the wet concrete.
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Commentary on the Code of Standard Practice for Steel Buildings and Bridges
Adopted Effective June 10, 1992 American Institute of Steel Construction, Inc.
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PREFACE
This Commentary has been prepared to assist those who use the Code of Standard Practice in understanding the background, basis and intent of its provisions. Each section in the Commentary is referenced by corresponding sections in the Code. Not all sections of the Code are discussed; sections are covered only if it is believed that additional explanation may be helpful. While every precaution has been taken to insure that all data and information presented is as accurate as possible, the Institute cannot assume responsibility for errors or oversights in the information published herein or the use of the information published or incorporating such information in the preparation of detailed engineering plans. The figures are for illustrative purposes only and are not intended to be applicable to any actual design. The information should not replace the judgment of an experienced architect or engineer who has the responsibility of design for a specific structure.
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Commentary on the Code of Standard Practice for Steel Buildings and Bridges Adopted Effective June 10, 1992 American Institute of Steel Construction, Inc.
SECTION 1. GENERAL PROVISIONS 1.1. Scope This Code is not applicable to metal building systems, which are the subject of standards published by the Metal Building Manufacturers Association in their Metal Building Systems Manual. AISC has not participated in the development of the MBMA code and, therefore, takes no position and is not responsible for any of its provisions. This Code is not applicable to standard steel joists, which are the subject of Recommended Code of Standard Practice for Steel Joists, published by the Steel Joist Institute. AISC has not participated in the development of the SJI code and, therefore, takes no position and is not responsible for any of its provisions.
SECTION 2. CLASSIFICATION OF MATERIALS 2.2. Other Steel or Metal Items These items include materials which may be supplied by the steel fabricator which require coordination between other material suppliers and trades. If they are to be supplied by the fabricator, they must be specifically called for and detailed in contract documents.
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SECTION 3. PLANS AND SPECIFICATIONS 3.1. Structural Steel Project specifications vary greatly in complexity and completeness. There is a benefit to the owner if the specifications leave the contractor reasonable latitude in performing his work. However, critical requirements affecting the integrity of the structure, or necessary to protect the ownerâ&#x20AC;&#x2122;s interest, must be covered in the contract documents. The following checklist is included for reference: Standard codes and specifications governing structural steelwork Material specifications Mill test reports Welded joint configuration Weld procedure qualification Bolting specifications Special requirements for work of other trades Runoff tabs Wind bracing Connections or data for connection development Column stiffeners Column web doubler plates Bearing stiffeners on beams and girders Web reinforcement Openings for other trades Surface preparation and shop painting Shop inspection Field inspection Non-destructive testing, including acceptance criteria Special requirements on delivery Special erection limitations Temporary bracing for non-self-supporting structures Special fabrication and erection tolerances for AESS Special pay weight provisions The structural steel plans must provide the elevations of all members as well as the dimensions to the centerline of all members (or the backs of angles or channels) relative to the grid lines, column centerline or other nearby members unless the locations of those members must be coordinated by the general contractor with the requirements of another trade. When the necessary dimensions are not given, the fabricator is not in a position to order material or start shop drawings in a timely manner and may be delayed while attempting to get the information.
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SECTION 4. SHOP AND ERECTION DRAWINGS 4.1. Owner’s Responsibility The owner’s responsibility for the proper planning of the work and the communication of all facts of his particular project is a requirement of the Code, not only at the time of bidding, but also throughout the term of any project. The contract documents, including the plans and specification, are for the purpose of communication. It is the owner’s responsibility to properly define the scope of work, and to define information or items required and outlined in the plans and specifications. When the owner releases plans and specifications for construction, the fabricator and erector rely on the fact that these are the owner’s requirements for his project. The Code defines the owner as including a designated representative such as the architect, engineer or project manager, and when these representatives direct specific action to be taken, they are acting as and for the owner. On phased construction projects, to insure the orderly flow of material procurement, detailing, fabrication and erection activities, it is essential that designs are not continuously revised after progressive releases for construction are made. In essence, once a portion of a design is released for construction, the essential elements of that design should be “frozen” to assure adherence to the construction schedule or all parties should reach an understanding on the effects of future changes as they affect scheduled deliveries and added costs, if any. 4.2. Approval 4.2.1. From the inception of the Code of Standard Practice, AISC and the industry in general have recognized that the engineer of record is the only individual who has all the information necessary to evaluate the total impact of connection details on the overall structural design of the project. This authority has traditionally been exercised during the approval process for shop and erection drawings. The EOR has retained the final and total responsibility for the adequacy and safety of the entire structure since at least the 1927 edition of the Code of Standard Practice. In those instances where a fabricator develops the detailed configuration of connections during the preparation of shop drawings, the fabricator does not thereby become responsible for the structural integrity of that part of the overall structure. In the first issue of the Code, as printed in the first AISC Manual in 1927, this was stated as “Shop Drawings prepared by the Seller and approved by a representative of the Buyer shall be deemed the correct interpretation of the work to be done, but does not relieve the Seller of responsibility for the accuracy of details.” This statement was modified in the 1952 revision of the Code to read “...the owner must return one set of prints to the fabricator with a notation of the owner’s outright approval or approval subject to corrections as noted.” In 1972 the Code stated “Approval by the
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owner of shop drawings prepared by the fabricator indicates that the fabricator has correctly interpreted the contract requirements, and that any connections designed by the fabricator are of adequate capacity for the design requirements.” The Code was again modified in 1976 saying “Approval by the owner of shop drawings prepared by the fabricator indicates that the fabricator has correctly interpreted the contract requirements. This approval constitutes the owner’s acceptance of all responsibility for the design adequacy of any connection designed by the fabricator as a part of his preparation of these shop drawings.” This statement was not changed in the 1986 revision of the Code. The current revision of Paragraph 4.2.1 of the Code is intended to clarify the use of the word “Owner.” Consequently, the term “owner” has been replaced by “owner’s authorized representative,” usually meaning the engineer of record. The continuing concept that the structural engineer of record is the sole individual who can best assure the safety of the completed structure has not been modified. This system has worked well for at least the past 65 years, and has achieved a commendable safety record where its principles have been steadfastly applied. In the preparation of contract drawings, the engineer of record (EOR) has two basic choices in the showing of connection details. The EOR may fully design and detail connections for all conditions. However, in order to allow the owner to benefit from the economies inherent in allowing the fabricator to choose the most efficient connections for the fabricator’s shop and erection processes, the EOR may allow the fabricator to select the types of connection and show them in complete detail on the shop drawings for the EOR’s approval. In either case, the approval of the shop drawings by the owner’s authorized representative constitutes acceptance by the owner’s authorized representative of design responsibility for the structural adequacy of the connections shown on the shop drawings. Contracts attempting to share or allocate design responsibility are strongly discouraged. Individual state codes and licensing requirements may vary widely in allowing such allocation of responsibility. Should the engineer of record elect to fully design and detail connections on the contract documents, the EOR has the obligation to show all fastener sizes, arrangement, quantities and grades, as well as all connection material and weld types, sizes and lengths for each individual member or part to be joined. All requirements for bracing details, stiffeners, doublers, web or cope reinforcement or similar items necessary for the completeness of the design must be sized and shown in complete detail. The fabricator is responsible for correctly reflecting this information in the preparation of shop drawings. Should the fabricator wish to deviate from these specific details or call a problem to the attention of the engineer of record, the fabricator must either do so in writing prior to the preparation of shop drawings, or clearly note the deviation on the drawings submitted for approval. This requirement is not intended in any way to negate the responsibility of the owner’s authorized representative to review completely each shop drawing for structural adequacy during the approval process. If the engineer of record does not show fully designed and detailed connections on the contract documents and allows the fabricator to select connection types when
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detailing shop drawings, the contract documents must give all reactions, moments, or other forces required for each individual member of parts to be joined so that when preparing shop drawings, the fabricatorâ&#x20AC;&#x2122;s detailers and checkers may determine the appropriate connection either by selection from tables shown in AISC publications or by simple calculation. The fabricator can assume that the reactions, moments or other forces given by the engineer are appropriate for the loads to be applied to the structure. All requirements for bracing details, stiffeners, doublers, web or cope reinforcement or similar items necessary for the completeness of the design must be shown in sufficient detail so as to allow the fabricator to submit an accurate estimate of cost at the time of bid. It is suggested that highly complex connections be fully designed on the contract documents or developed in a timely manner by the EOR after consulting with the fabricator regarding accepted, current and standard practices for fabrication and erection so that the detailing and fabricating processes will not be delayed. In the latter case, a pre-detailing meeting between the EOR and the fabricator may be appropriate to facilitate this exchange of information. In the event that design loads or other information necessary for development of connections is not shown on the contract documents, this information must be furnished to the fabricator in a timely manner. If the engineer of record elects to utilize typical details which must be interpreted or modified by the fabricator to meet conditions occurring in a structure, such interpretation is forwarded to the engineer of record for review and approval by way of detail or shop drawing submittals. Where state codes and licensing requirements allow fabricators to design and fabricate complete steel structures, and a fabricator has contracted to provide such services, submittals to the owner or applicable public reviewing authority will normally include only those documents customarily submitted by licensed design professionals on comparable projects within the same licensing jurisdiction.
SECTION 5. MATERIALS 5.1. Mill Materials The fabricator may purchase materials in stock lengths, exact lengths or multiples of exact lengths to suit the dimensions shown on the contract drawings. Such purchases will normally be job-specific in nature and may not be capable of being utilized on other projects or returned for full credit if subsequent design changes make these materials unsuitable for their originally intended use. The fabricator should be paid for these materials upon delivery from the mill, subject to appropriate additional payment or credit if subsequent unanticipated modification or reorder is required. Purchasing materials to exact lengths is not considered fabrication.
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5.1.2. Mill dimensional tolerances are completely set forth as part of ASTM A6. Variation in cross sectional geometry of rolled members must be recognized by the designer, the fabricator and erector (see Fig. 1). Such tolerances are mandatory because roll wear, thermal distortions of the hot cross section immediately after leaving the forming rolls, and differential cooling distortions that take place on the cooling beds are economically beyond precise control. Absolute perfection of cross sectional geometry is not of structural significance and, if the tolerances are recognized and provided for, also not of architectural significance. ASTM A6 also stipulates straightness and camber tolerances which are adequate for most conventional construction. However, these characteristics may be controlled or corrected to closer tolerances during the fabrication process when the unique demands of a particular project justify the added cost.
+ 1/ 4 – 3/16
Actual section
½B ± 3/16 ½ 3 B /16
T
C = d+ ¼ max. A = d ± 1/ 8 d
C = d + ¼ max.
T1
T1
Theoretical section T1
bf
T
f
C = d + ¼ max.
B=b
±
Typical
Typical Typical
Typical ½B± 3/16 ½B 3/16 ±
T + T ′ — For sections 12 ″ and under - ¼ ″ max.
B — Actual flange width A — Actual depth at cL web C — Actual depth overall
For sections over 12 ″ — 5/15 ″ max. bf — Theoretical flange width d — Theoretical depth T & T ′ — Tilt of flange
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SECTION 6. FABRICATION AND DELIVERY 6.4. Dimensional Tolerances Fabrication tolerances are stipulated in several specification documents, each applicable to a special area of construction. Basic fabrication tolerances are stipulated in Sections 6.4 and 10 of the Code and Section M2.7 of the AISC Specification. Other specifications and codes frequently incorporated by reference in the contract documents are the AWS Structural Welding Code and AASHTO Standard Specifications for Highway Bridges. 6.4.5. Due to the release of stresses, there is no known way to verify camber once members are received in the field. Camber may only be measured in the fabrication shop in the unstressed condition and does not take into account the dead weight of the member, the restraint caused by the end connections in the erected state or any dead load which may be intended to be applied. 6.5. Shop Painting 6.5.2., 6.5.3. The selection of a paint system is a design decision involving many factors including ownerâ&#x20AC;&#x2122;s preference, service life of the structure, severity of environmental exposure, cost of both initial application and future renewals, and compatibility of the various components comprising the paint system, i.e., surface preparation, prime coat and subsequent coats. Because inspection of shop painting needs to be concerned with workmanship at each stage of the operation, the fabricator provides notice of the schedule of operations and affords access to the work site to inspectors. Inspection must be coordinated with that schedule in such a way as to avoid delay of the scheduled operations. Acceptance of the prepared surface must be made prior to application of the prime coat because the degree of surface preparation cannot be readily verified after painting. Time delay between surface preparation and application of the prime coat can result in unacceptable deterioration of a properly prepared surface, necessitating a repetition of surface preparation. This is especially true with blast-cleaned surfaces. Therefore, to avoid potential deterioration of the surface it is assumed that surface preparation is accepted unless it is inspected and rejected prior to the scheduled application of the prime coat. The prime coat in any paint system is designed to maximize the wetting and adherence characteristics of the paint, usually at the expense of its weathering capabilities. Deterioration of the shop paint normally begins immediately after exposure to the elements and worsens as the duration of exposure is extended. Consequently, extended exposure of the prime coat to weather or to a corrosive atmosphere will lead to its deterioration and may necessitate repair, possibly including
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repetition of surface preparation and primer application in limited areas. With the introduction of high performance paint systems, delay in the application of the prime coat has become more critical. High performance paint systems generally require a greater degree of surface preparation, as well as early application of weathering protection for the prime coat. Since the fabricator does not control the selection of the paint system, the compatibility of the various components of the total paint system, nor the length of exposure of the prime coat, he cannot guarantee the performance of the prime coat or any other part of the system. Rather, the fabricator is responsible only for accomplishing the specified surface preparation and for applying the shop coat or coats in accordance with the contract documents. Section 6.5.2 stipulates cleaning the steel to the requirements of SSPC-SP2. This section is not meant as an exclusive cleaning level, but rather that level of surface preparation which will be furnished if the steel is to be painted and if the job specifications are silent or do not require more stringent surface preparation requirements. Further information regarding shop painting is available in A Guide to Shop Painting of Structural Steel, published jointly by the Steel Structures Painting Council and the American Institute of Steel Construction. 6.5.4. Extended exposure of unpainted steel which has been cleaned for subsequent fire protection material application can be detrimental to the fabricated product. Most levels of cleaning require the removal of all loose mill scale, but permit some amount of “tightly adhering mill scale.” When a piece of structural steel which has been cleaned to an acceptable level is left exposed to a normal environment, moisture can penetrate behind the scale, and some “lifting” of the scale by the oxidation products is to be expected. Cleanup of “lifted” mill scale is not the responsibility of the fabricator, but is assigned by contract requirement to an appropriate contractor. Section 6.5.4 of the Code is not applicable to weathering steel, for which special cleaning specifications are always required in the contract documents.
SECTION 7. ERECTION 7.5. Installation of Anchor Bolts and Embedded Items 7.5.1. While the general contractor must make every effort to set anchor bolts accurately to theoretical drawing dimensions, minor deviations may occur. The tolerances set forth in this section were compiled from data collected from general contractors and erectors. They can be attained by using reasonable care and will ordinarily allow the steel to be erected and plumbed to required tolerances. If special conditions require closer tolerances, the contractor responsible for setting the anchor
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bolts should be so informed by the contract documents. When anchor bolts are set in sleeves, the adjustment provided may be used to satisfy the required anchor bolt setting tolerances. The tolerances established in this section of the Code have been selected to be compatible with oversize holes in base plates, as recommended in the AISC textbook Detailing for Steel Construction. An anchor bolt group is the set of anchor bolts which receive a single fabricated steel shipping piece. The established column line is the actual field line most representative of the centers of the as-built anchor bolt groups along a line of columns. It must be straight or curved as shown on the plans. 7.6. Bearing Devices The 1â &#x201E;8 in. tolerance on elevation of bearing devices relative to established grades is provided to permit some variation in setting bearing devices and to account for attainable accuracy with standard surveying instruments. The use of leveling plates larger than 22 in. Ă&#x2014; 22 in. is discouraged and grouting is recommended with larger sizes. For purposes of erection stability, the use of leveling nuts is discouraged when base plates have less than four (4) anchor bolts. 7.9.3. Non Self-Supporting Steel Frames To rationally provide temporary supports and/or bracing, the erector must be informed by the owner of the sequence of installation and the effect of loads imposed by such elements at various stages during the sequence until they become effective. The overall strength and stability of a non self-supporting steel frame may be dependent upon the installation of non-structural steel elements such as concrete floor diaphragms, concrete or masonry shear walls, precast concrete facade pieces, etc. The requirement for these elements to be in place to provide overall strength and stability for the structural steel frame should be made clear in the contract documents in order that the need for temporary support may be clearly understood. For example, precast tilt-up slabs or channel slab facia elements which depend upon attachment to the steel frame for stability against overturning due to eccentricity of their gravity load may induce significant unbalanced lateral forces on the bare steel frame when partially installed. 7.11. Framing Tolerances The erection tolerances defined in this section of the Code have been developed through long-standing usage as practical criteria for the erection of structural steel. Erection tolerances were first defined by AISC in its Code of Standard Practice of
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October, 1924 in Section 7 (f), “Plumbing Up.” With the changes that took place in the types and use of materials in building construction after World War II, and the increasing demand by architects and owners for more specific tolerances, AISC adopted new standards for erection tolerances in Section 7 (h) of the March 15, 1959 edition of the Code. Experience has proven that those tolerances can be economically obtained. The current requirements were first published in the October 1,1972 edition of the Code. They provide an expanded set of criteria over earlier Code editions. The basic premise that the final accuracy of location of any specific point in a structural steel frame results from the combined mill, fabrication and erection tolerances, rather than from the erection tolerances alone, remains unchanged in this edition of the Code. However, to improve clarity, pertinent standard fabrication tolerances are now stipulated in Section 7.11, rather than by reference to the AISC Specification as in previous editions. Additionally, expanded coverage has been given to the definition of working points and working lines governing measurements of the actual steel location. Illustrations for defining and applying the applicable Code tolerances are provided in this Commentary. The recent trend in building work is away from built-in-place construction wherein compatibility of the frame and the facade or other collateral materials is automatically provided for by the routine procedures of the crafts. Building construction today frequently incorporates prefabricated components wherein large units are developed with machine-like precision to dimensions that are theoretically correct for a perfectly aligned steel frame with ideal member cross sections. This type of construction has made the magnitude of the tolerances allowed for structural steel building frames increasingly of concern to owners, architects and engineers. This has led to the inclusion in job specifications of unrealistically small tolerances, which indicate a general lack of recognition of the effects of the accumulation of dead load, temperature effects and mill, fabrication and erection tolerances. Such tolerances are not economically feasible and do not measurably increase the structure’s functional value. This edition of the Code incorporates tolerances previously found to be practical and presents them in a precise and clear manner. Actual application methods have been considered and the application of the tolerance limitations to the actual structure have been defined. 7.11.3. Position and Alignment The limitations described in Section 7.11.3.1 and illustrated in Figs. 2 and 3 make it possible to maintain built-in-place or prefabricated facades in a true vertical plane up to the 20th story, if connections which provide for 3 in. adjustment are used. Above the 20th story, the facade may be maintained within 1⁄16 in. per story with a maximum total deviation of 1 in. from a true vertical plane, if the 3 in. adjustment is provided. Section 7.11.3.1(c) limits the position of exterior column working points at any given splice elevation to a narrow horizontal envelope parallel to the building line
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(see Fig. 4). This envelope is limited to a width of 11⁄2 in., normal to the building line, in up to 300 ft of building length. The horizontal location of this envelope is not necessarily directly above or below the corresponding envelope at the adjacent splice elevations, but should be within the limitation of the 1:500 allowable tolerance in plumbness of the controlling columns (see Fig. 3). Connections permitting adjustments of plus 2 in. to minus 3 in. (5 in. total) will be necessary in cases where the architect or owner insists upon attempting to construct the facade to a true vertical plane above the 20th story. Usually there is a differential shortening of the internal versus the external columns during construction, due to non-uniform rate of accumulation of dead load stresses (see Fig. 5). The amount of such differential shortening is indeterminate because it varies dependent upon construction sequence from day to day as the construction progresses, and does not reach its maximum shortening until the building is in service. When floor concrete is placed while columns are supporting different percentages of their full design loads, the floor must be finished to slopes established by measurements from the tops of beams at column connections. The effects of
B
/2 + h/1000 +Tp
W.P.
E.C.L.
L
C
/ 2 + h/1000 + Ta
Tp Tp
E.C.L.
C
L
/2 + h/1000 +Tp
Envelope of actual location of working points to established column line. See Fig. 3
Ta Tt
C
/ 2 + h/1000
C
L
L
/ 2 + h/1000
/2 + h/1000 B/2 + h/1000
/ 2 + h/1000 + Tt
Minimum clearance envelope
B
B
L
L
For enclosures or attachments which may follow column alignment
L
For enclosures or attachments which must be held to precise plan location
L = Actual c to c columns = Plan dimension ± column cross section tolerance ± beam length tolerance. Ta = Plumbness tolerance away from building line (varies, see Fig. 3) Tt = Plumbness tolerance toward building line (varies, see Fig. 3) Tp = Plumbness tolerance parallel to building line (= Ta )
Fig. 2. Clearance required to accommodate accumulated column tolerances AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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3″
2″
Slope 1/16 ″ per story
20th Fl 2″ Plumb Elev. varies
Slope 1/ 500
1″
Established column line
Building line
36th Fl.
Splice Braced point
W.P.
Maximum out-of-plumb of individual shipping piece as defined by straight line between working points ≤ 1/500 Maximum out-of-straightness between braced points L/1000 where L is distance between braced points.
Braced point Splice
W.P.
Braced point
Individual column sections within envelope defined at left Established column line
Elev. varies
Slope 1/500
Slope 1/ 500 ¼
¼
Tolerance on location of W.P. at base
Envelope within which all working points must fall Note: The plumb line thru the base working point for an individual column is not necessarily the precise plan location because Section 7.11.3.1 deals only with plumbness tolerance and does not include inaccuracies in location of established column line, foundations and anchor bolts beyond the erector’s control.
Fig. 3. Exterior column plumbness tolerances normal to building line Building line
Ta Tt E
Established Column lines
Maximum envelope for working points of all columns at any given elevation E = 1½ ″ for up to 300 ′of length, over 300 ′ add ½ ″ for each 100 ′ of length with 3 ″max total Column plumbness tolerance — See figs. 2 and 3 — Indicates column working points At any splice elevation, envelope “E” is located within the limits Ta and T t At any splice elevation, envelope “E” may be located offset from the corresponding envelope of the adjacent splice elevations, above and below, by an amount not greater than 1/ 500 of the column length.
Fig. 4. Tolerances in plan at any splice elevation of exterior columns
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Splice elevation shown on plan
Column base
Differential shortening
Interior column Finish line
Interior column shortening due to partial dead load
Beam elevations from finish line See section 7.11.3.3 Floor elevations set by measurement from top of beams
Finish line
Floor elevations set by measurement from top of beams Beam elevations from finish line See section 7.11.3.3 Exterior column shortening due to partial dead load
Finish line
Exterior column
Finish line
On a particular date during the erection of structural steel and placement of other material, (floor concrete, facade, etc.) the interior columns will be carrying a higher percentage of their final loads than the exterior columns. Therefore, for equal design unit stresses, the actual stress on that date for interior columns will be greater than the actual stresses on exterior columns. When all dead loads have been applied, stresses and shortening in all columns will be approximately equal.
Fig. 5. Effect of differential column shortening differential shortening, plus mill camber and deflections, become very important when there is little cover over the steel, when there are electrical fittings mounted on the steel flooring whose tops are supposed to be flush with the finished floor, when there is small clearance between bottom of beams and top of door frames, etc., and when there is little clearance around ductwork. To finish floors to a precisely level plane, for example by the use of laser leveling techniques, can result in significant differential floor thicknesses, different increases above design dead loads for individual columns and, thus, permanent differential column shortening and out-oflevel completed floors. Similar considerations make it unfeasible to attempt to set the elevation of a given floor in a multistory building by reference to a bench mark at the base of the structure. Columns are fabricated to a length tolerance of Âą 1â &#x201E;32 in. while under a zero state of stress. As dead loads accumulate, the column shortening which takes place is negligible within individual stories and in low buildings, but will accumulate to significant magnitude in tall buildings. Thus, the upper floors of tall buildings will be excessively thick and the lower floors will be below the initial finish elevation if floor elevations are established relative to a ground level bench mark. If foundations and base plates are accurately set to grade and the lengths of individual column sections are checked for accuracy prior to erection, and if floor
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elevations are established by reference to the elevation of the top of beams, the effect of column shortening due to dead load will be minimized. Since a long unencased steel frame will expand or contract 1⁄8 in. per 100 ft for each change of 15°F in temperature, and since the change in length can be assumed to act about the center of rigidity, the end columns anchored to foundations will be plumb only when the steel is at normal temperature (see Fig. 6). It is therefore necessary to correct field measurements of offsets to the structure from established baselines for the expansion or contraction of the exposed steel frame. For example, a building 200-ft long that is plumbed up at 100°F should have working points at the tops of end columns positioned 1⁄2 in. out from the working point at the base in order for the column to be plumb at 60°F. Differential temperature effects on column length should also be taken into account in plumbing surveys when tall steel frames are subject to strong sun exposure on one side. The alignment of lintels, spandrels, wall supports and similar members used to connect other building construction units to the steel frame should have an adjustment of sufficient magnitude to allow for the accumulative effect of mill, fabrication and erection tolerances on the erected steel frame (see Fig. 7).
When plumbing end columns, apply temperature adjustment at rate 1/ 8 ″ per 100 ′of length from center of rigidity per each 15°F of difference between erection and working temperatures.
Length
Length
Center of rigidity Ta Tt
Tt Ta
Tt Ta
Tt Ta
C to C adjacent columns subject to mill and fabrication tolerance Tp Tp Tt Ta
Established column lines Building line
Fig. 6. Tolerances in plan location of columns AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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Column dimension + tolerances
D = Tolerances required by manufacturer of wall units plus survey tolerance D
D E.C.L.
Clearance line to accommodate column. See Figure 2
Provide connections with slotted holes and/or shims to accommodate tolerances
Column dimension + tolerances
If fascia joints are set from nearest column finish line, allow Âą 5/ 8 â&#x20AC;łfor vertical adjustment. Owners plans for fascia details must allow for progressive shortening of steel columns.
Fig. 7. Clearance required to accommodate fascia
500 1
500
500
1
1
500 1
Support points
Field splices
Fig. 8. Alignment tolerances for members with field splices AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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AISC CODE OF STANDARD PRACTICE
7.11.3.2. Alignment Tolerance for Members with Field Splices The angular misalignment of the working line of all fabricated shipping pieces relative to the line between support points of the member as a whole in erected position must not exceed 1 in 500. Note that the tolerance is not stated in terms of a linear displacement at any point and is not to be taken as the overall length between supports divided by 500. Typical examples are shown in Fig. 8. Numerous conditions within tolerance for these and other cases are possible. This condition applies to both plan and elevation tolerances. 7.11.4. Responsibility for Clearances In spite of all efforts to minimize inaccuracies, deviations will still exist; therefore, in addition, the designs of prefabricated wall panels, partition panels, fenestrations, floor-to-ceiling door frames and similar elements must provide for clearance and details for adjustment as described in Section 7.11.4. Designs must provide for adjustment in the vertical dimension of prefabricated facade panels supported by the steel frame because the accumulation of shortening of stressed steel columns will result in the unstressed facade supported at each floor level being higher than the steel frame connections to which it must be attached. Observations in the field have shown that where a heavy facade is erected to a greater height on one side of a multistory building than on the other, the steel framing will be pulled out of alignment. Facades should be erected at a relatively uniform rate around the perimeter of the structure. 7.14. Handling and Storage Handling Painted Steel During storage, loading, transport, unloading and erection, blemish marks caused by slings, chains, blocking, tie-downs, etc., occur in varying degrees. Abrasions caused by handling or cartage after painting are to be expected. The owner/engineer must recognize that any shop applied coating, no matter how carefully protected, will require touch-up in the field. Touch-up of these blemished areas is the responsibility of the contractor performing the field touch-up of field painting. Cleaning After Erection The responsibility for proper storage and handling of fabricated steel at the construction site during erection is properly the erectorâ&#x20AC;&#x2122;s. Shop-painted steel stored in the field pending erection should be kept free of the ground and so positioned as to minimize water-holding pockets. The owner or general contractor is responsible for providing suitable site conditions and proper access so that the fabricator/erector may perform its work.
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Site conditions are frequently muddy, sandy or dusty, or a combination of all three, during the erection period. Under such conditions it may be impossible to store and handle the steel in such a way as to completely avoid accumulation of mud, dirt or sand on the surface of the steel, even though the fabricator/erector manages to proceed with the work. Repairs of damage to painted surfaces and/or removal of foreign materials due to adverse site conditions are outside the scope of responsibility of the fabricator/erector when reasonable attempts at proper handling and storage have been made.
SECTION 8. QUALITY CONTROL 8.1.1. The AISC Quality Certification Program confirms to the construction industry that a certified structural steel fabricating plant has the capability by reason of commitment, personnel, organization, experience, procedures, knowledge and equipment to produce fabricated structural steel of the required quality for a given category of structural steelwork. The AISC Quality Certification Program is not intended to involve inspection and/or judgment of product quality on individual projects. Neither is it intended to guarantee the quality of specific fabricated steel products.
SECTION 9. CONTRACTS 9.2. Calculation of Weights The standard procedure for calculation of weights that is described in the Code meets the need for a universally acceptable system for defining â&#x20AC;&#x153;pay weightsâ&#x20AC;? in contracts based on the weight of delivered and/or erected materials. This procedure permits owners to easily and accurately evaluate price per pound proposals from potential suppliers and enables both parties to a contract to have a clear understanding of the basis for payment. The Code procedure affords a simple, readily understood method of calculation which will produce pay weights which are consistent throughout the industry and which may be easily verified by the owner. While this procedure does not produce actual weights, it can be used by purchasers and suppliers to define a widely accepted basis for bidding and contracting for structural steel. However, any other system can be used as the basis for a contractual agreement. When other systems are used, both supplier and purchaser should clearly understand how the alternate procedure is handled.
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9.3. Revisions to Contract Documents 9.3.1. Revisions to the Contract are implemented by issuance of new documents or re-issuance of existing documents. Individual revisions must be noted where they occur and documents must be dated with latest issue date and the reasons for issuance must be identified. 9.3.2. Revisions to the Contract are also implemented by change order, extra work order, or notations on the shop and erection drawings when returned from approval. However, revisions implemented in this manner must be incorporated subsequently as revisions to the plans and/or specifications and re-issued in accordance with Section 9.3.1. 9.3.3. The issuance of revisions authorizes the fabricator and erector to incorporate the revisions into the work. This authorization obligates the owner to pay the fabricator and erector for costs associated with changed and/or additional work. 9.6. Terms of Payment These terms include such items as progress payments for material, fabrication, erection, retainage, performance and payment bonds and final payment. If a performance or payment bond, paid for by the owner, is required by contract, then no retainage shall be required.
SECTION 10. ARCHITECTURALLY EXPOSED STRUCTURAL STEEL The rapidly increasing use of exposed structural steel as a medium of architectural expression has given rise to a demand for closer dimensional tolerances and smoother finished surfaces than required for ordinary structural steel framing. This section of the Code establishes standards for these requirements which take into account both the desired finished appearance and the abilities of the fabrication shop to produce the desired product. These requirements were previously contained in the AISC Specification for Architecturally Exposed Structural Steel which architects and engineers have specified in the past. It should be pointed out that the term â&#x20AC;&#x153;Architecturally Exposed Structural Steelâ&#x20AC;? (AESS), as covered in this section, must be specified in the contract documents if the fabricator is required to meet the fabricating standards of Section 10, and applies only to that portion of the structural steel so identified. In order to avoid misunderstandings and to hold costs to a minimum, only those steel surfaces and connections which will remain exposed and subject to normal view by pedestrians or occupants of the completed structure should be designated as AESS.
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AISC Quality Certification Program
AMERICAN INSTITUTE OF STEEL CONSTRUCTION, INC. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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AISC Quality Certification Program In recent years. the quality of construction methods and materials has become the subject of increasing concern to building officials, highway officials, and designers. One result of this concern has been the enactment of ever more demanding inspection requirements intended to ensure product quality. In many cases, however, these more demanding inspection requirements have not been based upon demonstrated unsatisfactory performance of structures in service. Rather, they have been based upon the capacity of sophisticated test equipment. or upon standards developed for nuclear construction rather than conventional construction. Adding to the problem, arbitrary interpretation of specifications by inspectors has too often been made without rational consideration of the type of construction involved. The result has been spiraling increases in the costs of fabrication of structural steel and of inspection, which must be paid by owners without necessarily assuring that the product quality required has been improved. Product inspection. although it has a valid place in the construction process, is not the most logical or practical way to assure that structural steelwork will conform to he requirements of contract documents and satisfy the intended use. A better solution can be found in the exercise of good quality control and quality assurance by the fabricator throughout the entire production process. Recognizing this fact, and seeking some valid, objective method whereby a fabricator’s capability for assuring a quality product could be evaluated, a number of code authorities have, in recent years, instituted steps to establish fabricator registration programs. However, these independent efforts resulted in extremely inconsistent criteria. They were developed primarily by inspectors or inspection agencies who were experienced in testing, but were not familiar with the complexities of the many steps, procedures, techniques, and controls required to assure quality throughout the fabricating process. Neither were these inspection agencies qualified to determine the various levels of quality required to assure satisfactory performance in meeting the service requirements of the many different types of steel structures. Recognizing the need for a comprehensive national standard for fabricator certification, and concerned by the trend toward costly inspection requirements that could not be justified by rational quality standards, the American Institute of Steel Construction has developed and implemented a voluntary Quality Certification Program, whereby any structural steel fabricating plant—whether a member of AISC or not—can have its capability for assuring quality production evaluated on a fair and impartial basis.
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AISC QUALITY CERTIFICATION PROGRAM
THE AISC PROGRAM
The AISC Quality Certification Program does not involve inspection and/or judgment of product quality on individual projects. Neither does it guarantee the quality of specific fabricated steel products. Rather, the purpose of the AISC Quality Certification Program is to confirm to the construction industry that a Certified structural steel fabricating plant has the personnel, organization, experience, procedures, knowledge, equipment, capability and commitment to reproduce fabricated steel of the required quality for a given category of structural steelwork. The AISC Quality Certification Program was developed by a group of highly qualified shop operation personnel from large, medium, and small structural steel fabricating plants throughout the United States. These individuals all had extensive experience and were fully aware of where and how problems can arise during the production process and of the steps and procedures that must be followed during fabrication to assure that the finished product meets the quality requirements of the contract. The program was reviewed and strongly endorsed by an Independent Board of Review comprised of 17 prominent structural engineers from throughout the United States, who were not associated with the steel fabricating industry, but were well qualified in matters of quality requirements for reliable service of all types of steel structures. CATEGORIES OF CERTIFICATION
A fabricator may apply for certification of a plant in one of the following categories of structural steelwork: I: Conventional Steel Structures — Small Public Service and Institutional
Buildings, (Schools, etc.), Shopping Centers, Light Manufacturing Plants, Miscellaneous and Ornamental Iron Work, Warehouses, Sign Structures, Low Rise, Truss Beam/Column Structures, Simple Rolled Beam Bridges. II: Complex Steel Building Structures — Large Public Service and Institutional
Buildings, Heavy Manufacturing Plants, Powerhouses (fossil, non-nuclear), Metal Producing/Rolling Facilities, Crane Bridge Girders, Bunkers and Bins, Stadia, Auditoriums, High Rise Buildings, Chemical Processing Plants, Petroleum Processing Plants. III: Major Steel Bridges — All bridge structures other than simple rolled beam
bridges. MB: Metal Building Systems — Pre-engineered Metal Building Structures. Supplement: Auxiliary and Support Structures for Nuclear Power Plants — This
supplement, applicable to nuclear plant structures designed under the AISC Specification, but not to pressure-retaining structures, offers utility companies and designers of nuclear power plants a certification program that will eliminate the need for many of the more costly, conflicting programs now in use. A fabricator must hold certification in either Category I, II or III prior to application for certification in this category. Certification in Category II automatically includes Category I. Certification in Category III automatically includes Categories I and II. Certification in Category MB is not transferable to any other Category. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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INSPECTION-EVALUATION PROCEDURE
An outside, experienced, professional organization, ABS Quality Evaluations, Inc. (a subsidiary of American Bureau of Shipping) has been retained by AISC to perform the plant Inspection-Evaluation in accordance with a standard check list and rating procedure established by AISC for each certification category in the program. Upon completion of this Inspection-Evaluation, ABS Quality Evaluations, Inc. (commonly known as ABSQE) will recommend to AISC that a fabricator be approved or disapproved for certification. ABS-QE’s Inspection-Evaluation is totally independent of the fabricator’s and AISC’s influence, and their evaluation is not subject to review by AISC. At a time mutually agreed upon by the fabricator, AISC, and ABS-QE, the Inspection-Evaluation team visits the plant to investigate and rate the following basic plant functions directly and indirectly affecting quality assurance: General Management, Engineering and Drafting, Procurement, Shop Operations, and Quality Control. The Inspection-Evaluation team will perform the following: 1. Confirm data submitted with the Application for Certification. 2. Interview key supervisory personnel and subordinate employees. 3. Observe and rate the organization in operation, including procedures used in functions affecting quality assurance. 4. Inspect and rate equipment and facilities. 5. At an “exit interview,” review with plant management the completed check list observations and evaluation scoring, including discussions of deficiencies and omissions, if any. The number of days required for Inspection-Evaluation varies according to the size and complexity of the plant, but usually requires two to five days. CERTIFICATION
Following recommendation for Certification by the Inspection-Evaluation team, AISC will issue a certificate identifying the fabricator, the plant, and the Category of Certification. The certificate is valid for a three year period, subject to annual review in the form of unannounced inspections early in the second and third year periods. The certificate is endorsed annually, provided there is successful completion of the unannounced second and third year inspection. An annual self-audit, based on the standard check list, must be made by plant management during the 11th and 23rd months after initial Certification. This self-audit must be retained at the plant and made available to the Inspection-Evaluation team during the unannounced second and third year inspections. At the end of the third year, the cycle begins again with a complete prescheduled Inspection-Evaluation and the issuance of a new certificate.
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Part 7 MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION MISCELLANEOUS DATA Wire and Sheet Metal Gages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-3 AISI Standard Nomenclature for Flat Rolled Carbon Steel . . . . . . . . . . . . . . . . . 7-3 Coefficients of Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-4 Weights and Specific Gravities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-5 Weights of Building Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-7 SI UNITS FOR STRUCTURAL STEEL DESIGN . . . . . . . . . . . . . . . . . . . . . . 7-8 SI (Metric) Weights and Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-10 U.S. Weights and Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-11 SI Conversion Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-12 GEOMETRIC AND TRIGONOMETRIC DATA Bracing Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-14 Properties of the Parabola and Ellipse . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-15 Properties of the Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-16 Properties of Geometric Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-17 Trigonometric Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-24 DECIMAL EQUIVALENTS Decimals of an Inch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-25 Decimals of a Foot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-26
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Table 7-1. WIRE AND SHEET METAL GAGES Equivalent thickness in decimals of an inch
Gage No.
U.S. Standard Galvanized Sheet Gage Gage for for HotUncoated Dipped Hot & ColdZinc Coated Rolled Sheetsb Sheetsb
7/0 6/0 5/0 4/0 3/0 2/0 1/0 1 2 3 4 5 6 7 8 9 10 11 12
USA Steel Wire Gage
.490 .462a .430a .394a .362a .331 .306 .283 .262a .244a .225a .207 .192 .177 .162 .148a .135 .120a .106a
— — — — — — — — — — — — — — .1681 .1532 .1382 .1233 .1084
— — — — — — — — — .2391 .2242 .2092 .1943 .1793 .1644 .1495 .1345 .1196 .1046
Gage No.
13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
U.S. Standard Galvanized Gage for Sheet Gage Uncoated for HotHot & ColdDipped Rolled Zinc Coated Sheetsb Sheetsb
.0897 .0747 .0673 .0598 .0538 .0478 .0418 .0359 .0329 .0299 .0269 .0239 .0209 .0179 .0164 .0149 — —
.0934 .0785 .0710 .0635 .0575 .0516 .0456 .0396 .0366 .0336 .0306 .0276 .0247 .0217 .0202 .0187 .0172 .0157
USA Steel Wire Gage
.092a .080 .072 .062a .054 .048a .041 .035a — — — — — — — — — —
aRounded value. The steel wire gage has been taken from ASTM A510 “General Requirements for Wire Rods
and Coarse Round Wire, Carbon Steel.” Sizes originally quoted to four decimal equivalent places have been rounded to three decimal places in accordance with rounding procedures of ASTM “Recommended Practice” E29. bThe equivalent thicknesses are for information only. The product is commonly specified to decimal thickness, not to gage number.
Table 7-2. AISI STANDARD NOMENCLATURE FOR FLAT ROLLED CARBON STEEL Width (Inches) Thickness (Inches)
To 31⁄2 incl.
Over 31⁄2 To 6
Over 6 To 8
Over 8 To 12
Over 12 To 48
Over 48
0.2300 & thicker
Bar
Bar
Bar
Plate
Plate
Plate
0.2299 to 0.2031
Bar
Bar
Strip
Strip
Sheet
Plate
0.2030 to 0.1800
Strip
Strip
Strip
Strip
Sheet
Plate
0.1799 to 0.0449
Strip
Strip
Strip
Strip
Sheet
Sheet
0.0448 to 0.0344
Strip
Strip
0.0343 to 0.0255
Strip
0.0254 & thinner
Hot-rolled sheet and strip not generally produced in these widths and thicknesses
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Table 7-3. COEFFICIENTS OF EXPANSION The coefficient of linear expansion (ε) is the change in length, per unit, for a change of one degree of temperature. The coefficient of surface expansion is approximately two times the linear coefficient, and the coefficient of volume expansion, for solids, is approximately three times the linear coefficient. A bar, free to move, will increase in length with an increase in temperature and will decrease in length with a decrease in temperature. The change in length will be εtl, where ε is the coefficient of linear expansion, t the change in temperature and l the length. If the ends of a bar are fixed, a change in temperature (t ) will cause a change in the unit stress of E εt, and in force of AE εt, where A is the cross-sectional area of the bar and E the modulus of elasticity. The following table gives the coefficient of linear expansion for 100°, or 100 times the value indicated above. Example: A piece of medium steel is exactly 40 ft long at 60°F. Find the length at 90°F assuming the ends free to move. change of length = εt l =
.00065 × 30 × 40 = .0078 ft 100
The length at 90° is 40.0078 ft
Example: A piece of medium carbon steel is exactly 40 ft long and the ends are fixed. If the temperature increases 30°F, what is the resulting change in the unit stress? change in unit stress = E εt =
29,000 × .00065 × 30 = 5.7 ksi 100
COEFFICIENTS OF EXPANSION FOR 100 DEGREES = 100ε Linear Expansion
Linear Expansion Centigrade
Fahrenheit
METALS AND ALLOYS Aluminum, wrought Brass Bronze Copper Iron, cast, gray Iron, wrought Iron, wire Lead Magnesium, various alloys Nickel Steel , mild Steel, stainless, 18-8 Zinc, rolled
.00231 .00188 .00181 .00168 .00106 .00120 .00124 .00286 .0029 .00126 .00117 .00178 .00311
.00128 .00104 .00101 .00093 .00059 .00067 .00069 .00159 .0016 .00070 .00065 .00099 .00173
TIMBER Fir Maple parallel to fiber Oak Pine
.00037 .00064 .00049 .00054
.00021 .00036 .00027 .00030
Materials
Centigrade
Fahrenheit
STONE AND MASONRY Ashlar masonry Brick Masonry Cement, portland Concrete Granite Limestone Marble Plaster Rubble masonry Sandstone Slate
.00063 .00061 .00126 .00099 .00080 .00076 .00081 .00166 .00063 .00097 .00080
.00035 .00034 .00070 .00055 .00044 .00042 .00045 .00092 .00035 .00054 .00044
TIMBER Fir Maple perpendicular to Oak fiber Pine
.0058 .0048 .0054 .0034
.0032 .0027 .0030 .0019
Materials
EXPANSION OF WATER Maximum Density = 1 C°°
Volume
0 1.000126 4 1.000000
C°°
Volume
10 1.000257 20 1.001732
C°°
Volume
30 1.004234 40 1.007627
C°°
Volume
50 1.011877 60 1.016954
C°°
Volume
C°°
Volume
70 1.022384 90 1.035829 80 1.029003 100 1.043116
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
MISCELLANEOUS DATA
7-5
Table 7-4. WEIGHTS AND SPECIFIC GRAVITIES Weight lb per Specific Gravity cu ft
Substance ASHLAR, MASONRY Granite, syenite, gneiss . . . . Limestone, marble . . . . . . . Sandstone, bluestone . . . . .
165 160 140
2.3–3.0 2.3–2.8 2.1–2.4
MORTAR RUBBLE MASONRY Granite, syenite, gneiss . . . . Limestone, marble . . . . . . . Sandstone, bluestone . . . . .
155 150 130
2.2–2.8 2.2–2.6 2.0–2.2
DRY RUBBLE MASONRY Granite, syenite, gneiss . . . . Limestone, marble . . . . . . . Sandstone, bluestone . . . . .
130 125 110
1.9–2.3 1.9–2.1 1.8–1.9
BRICK MASONRY Pressed brick . . . . . . . . . Common brick . . . . . . . . . Soft brick . . . . . . . . . . . .
140 120 100
2.2–2.3 1.8–2.0 1.5–1.7
CONCRETE MASONRY Cement, stone, sand . . . . . Cement, slag. etc. . . . . . . . Cement, cinder, etc. . . . . . .
144 130 100
2.2–2.4 1.9–2.3 1.5–1.7
40–45 90 183 53–64 103 67–72 98–117 96 49–55
— — 2.7–3.2 — 1.4–1.9 — — — —
VARIOUS BUILDING MATERIALS Ashes. cinders . . . . . Cement, portland, loose Cement, portland, set . Lime, gypsum, loose . . Mortar, set . . . . . . . Slags, bank slag . . . . Slags, bank screenings Slags, machine slag . . Slags, slag sand . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
EARTH, ETC., EXCAVATED Clay, dry . . . . . . . . . . Clay, damp, plastic . . . . Clay and gravel, dry . . . . Earth, dry, loose . . . . . . Earth, dry, packed . . . . . Earth, moist, loose . . . . . Earth, moist, packed . . . . Earth, mud, flowing . . . . Earth, mud, packed . . . . Riprap, limestone . . . . . Riprap, sandstone . . . . . Riprap, shale . . . . . . . Sand, gravel, dry, loose . . Sand, gravel, dry, packed . Sand, gravel, wet . . . . .
. . . . . . . . . . . . . . .
. 63 . 110 . 100 . 76 . 95 . 78 . 96 . 108 . 115 . 80–85 . 90 . 105 . 90–105 . 100–120 . 118–120
— — — — — — — — — — — — — — —
EXCAVATIONS IN WATER Sand or gravel . . . . . . . Sand or gravel and clay . . Clay . . . . . . . . . . . . River mud . . . . . . . . . Soil . . . . . . . . . . . . . Stone riprap . . . . . . . .
. . . . . .
. . . . . .
— — — — — —
60 65 80 90 70 65
Weight lb per Specific cu ft Gravity
Substance MINERALS Asbestos . . . . . . . Barytes . . . . . . . . Basalt . . . . . . . . . Bauxite . . . . . . . . Borax . . . . . . . . . Chalk . . . . . . . . . Clay, marl . . . . . . . Dolomite . . . . . . . . Feldspar, orthoclase . . Gneiss, serpentine . . Granite, syenite . . . . Greenstone, trap . . . Gypsum, alabaster . . Hornblende . . . . . . Limestone, marble . . . Magnesite . . . . . . . Phosphate rock, apatite Porphyry . . . . . . . . Pumice, natural . . . . Quartz, flint . . . . . . Sandstone, bluestone . Shale, slate . . . . . . Soapstone, talc . . . .
. . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . .
153 281 184 159 109 137 137 181 159 159 175 187 159 187 165 187 200 172 40 165 147 175 169
2.1–2.8 4.50 2.7–3.2 2.55 1.7–1.8 1.8–2.6 1.8–2.6 2.9 2.5–2.6 2.4–2.7 2.5–3.1 2.8–3.2 2.3–2.8 3.0 2.5–2.8 3.0 3.2 2.6–2.9 0.37–0.90 2.5–2.8 2.2–2.5 2.7–2.9 2.6–2.8
STONE, QUARRIED, PILED Basalt, granite, gneiss . . . Limestone, marble, quartz . Sandstone . . . . . . . . . Shale . . . . . . . . . . . Greenstone, hornblende .
. . . . .
. . . . .
96 95 82 92 107
— — — — —
BITUMINOUS SUBSTANCES Asphaltum . . . . . . . . . . Coal, anthracite . . . . . . . Coal, bituminous . . . . . . Coal, lignite . . . . . . . . . Coal, peat, turf, dry . . . . . Coal, charcoal, pine . . . . . Coal, charcoal, oak . . . . . Coal, coke . . . . . . . . . . Graphite . . . . . . . . . . . Paraffine . . . . . . . . . . . Petroleum . . . . . . . . . . Petroleum, refined . . . . . . Petroleum, benzine . . . . . Petroleum, gasoline . . . . . Pitch . . . . . . . . . . . . . Tar, bituminous . . . . . . .
. . . . . . . . . . . . . . . .
81 97 84 78 47 23 33 75 131 56 54 50 46 42 69 75
1.1–1.5 1.4–1.7 1.2–1.5 1.1–1.4 0.65–0.85 0.28–0.44 0.47–0.57 1.0–1.4 1.9–2.3 0.87–0.91 0.87 0.79–0.82 0.73–0.75 0.66–0.69 1.07–1.15 1.20
COAL AND COKE, PILED Coal, anthracite . . . . . Coal, bituminous, lignite . Coal, peat, turf . . . . . . Coal charcoal . . . . . . Coal coke . . . . . . . .
. . . . .
47–58 40–54 20–26 10–14 23–32
— — — — —
. . . . .
. . . . .
The specific gravities of solids and liquids refer to water at 4°°C, those of gases to air at 0°°C and 760 mm pressure. The weights per cubic foot are derived from average specific gravities, except where stated that weights are for bulk, heaped, or loose material, etc.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7-6
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
Table 7-4 (cont.). WEIGHTS AND SPECIFIC GRAVITIES Weight lb per Specific Gravity cu ft
Substance METALS, ALLOYS, ORES Aluminum, cast, hammered Brass, cast, rolled . . . . . Bronze, 7.9 to 14% Sn . . . Bronze, aluminum . . . . . Copper, cast, rolled . . . . Copper ore, pyrites . . . . Gold, cast, hammered . . . Iron, cast, pig . . . . . . . Iron, wrought . . . . . . . . Iron, speigel-eisen . . . . . Iron, ferro-silicon . . . . . . Iron ore, hematite . . . . . Iron ore, hematite in bank . Iron ore, hematite loose . . Iron ore, limonite . . . . . . Iron ore, magnetite . . . . Iron slag . . . . . . . . . . Lead . . . . . . . . . . . . Lead ore, galena . . . . . . Magnesium, alloys . . . . . Manganese . . . . . . . . Manganese ore, pyrolusite Mercury . . . . . . . . . . Monel Metal . . . . . . . . Nickel . . . . . . . . . . . Platinum, cast, hammered . Silver, cast, hammered . . Steel, rolled . . . . . . . . Tin, cast, hammered . . . . Tin ore, cassiterite . . . . . Zinc, cast, rolled . . . . . . Zinc ore, blende . . . . . .
VARIOUS SOLIDS Cereals, oats . . . . Cereals, barley . . . Cereals, corn, rye . . Cereals, wheat . . . . Hay and Straw . . . . Cotton, Flax, Hemp . Fats . . . . . . . . . Flour, loose . . . . . Flour, pressed . . . . Glass, common . . . Glass, plate or crown Glass, crystal . . . . Leather . . . . . . . Paper . . . . . . . . Potatoes, piled . . . . Rubber, caoutchouc . Rubber goods . . . . Salt, granulated, piled Saltpeter . . . . . . . Starch . . . . . . . . Sulphur . . . . . . . Wool . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 165 2.55–2.75 . 534 8.4–8.7 . 509 7.4–8.9 . 481 7.7 . 556 8.8–9.0 . 262 4.1–4.3 . 1205 19.25–19.3 . 450 7.2 . 485 7.6–7.9 . 468 7.5 . 437 6.7–7.3 . 325 5.2 . 160–180 — . 130–160 — . 237 3.6–4.0 . 315 4.9–5.2 . 172 2.5–3.0 . 710 11.37 . 465 7.3–7.6 . 112 1.74–1.83 . 475 7.2–8.0 . 259 3.7–4.6 . 849 13.6 . 556 8.8–9.0 . 565 8.9–9.2 . 1330 21.1–21.5 . 656 10.4–10.6 . 490 7.85 . 459 7.2–7.5 . 418 6.4–7.0 . 440 6.9–7.2 . 253 3.9–4.2
bulk bulk bulk bulk bales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32 39 48 48 20 93 58 28 47 156 161 184 59 58 42 59 94 48 67 96 125 82
Weight lb per Specific Gravity cu ft
Substance TIMBER, U.S. SEASONED Moisture content by weight: Seasoned timber 15 to 20% Green timber up to 50% Ash, white, red . . . . . . Cedar, white, red . . . . . Chestnut . . . . . . . . . Cypress . . . . . . . . . Fir, Douglas spruce . . . Fir, eastern . . . . . . . . Elm, white . . . . . . . . Hemlock . . . . . . . . . Hickory . . . . . . . . . . Locust . . . . . . . . . . Maple, hard . . . . . . . Maple, white . . . . . . . Oak, chestnut . . . . . . Oak, live . . . . . . . . . Oak, red, black . . . . . . Oak, white . . . . . . . . Pine, Oregon . . . . . . . Pine, red . . . . . . . . . Pine, white . . . . . . . . Pine, yellow, long-leaf . . Pine, yellow, short-leaf . . Poplar . . . . . . . . . . Redwood, California . . . Spruce, white, black . . . Walnut, black . . . . . . . Walnut, white . . . . . . .
VARIOUS LIQUIDS Alcohol, 100% . . . . . . Acids, muriatic 40% . . . Acids, nitric 91% . . . . . Acids, sulphuric 87% . . — Lye, soda 66% . . . . . — Oils, vegetable . . . . . . — Oils, mineral, lubricants . — Water, 4°°C max. density — Water, 100°°C . . . . . . 1.47–1.50 Water, ice . . . . . . . . 0.90–0.97 Water, snow, fresh fallen 0.40–0.50 Water, sea water . . . . 0.70–0.80 2.40–2.60 2.45–2.72 2.90–3.00 0.86–1.02 GASES 0.70–1.15 Air, 0°°C 760 mm . . . . . — Ammonia . . . . . . . . 0.92–0.96 Carbon dioxide . . . . . 1.0–2.0 Carbon monoxide . . . . — Gas, illuminating . . . . . — Gas, natural . . . . . . . 1.53 Hydrogen . . . . . . . . 1.93–2.07 Nitrogen . . . . . . . . . 1.32 Oxygen . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . .
40 22 41 30 32 25 45 29 49 46 43 33 54 59 41 46 32 30 26 44 38 30 26 27 38 26
0.62–0.65 0.32–.038 0.66 0.48 0.51 0.40 0.72 0.42–0.52 0.74–0.84 0.73 0.68 0.53 0.86 0.95 0.65 0.74 0.51 0.48 0.41 0.70 0.61 0.48 0.42 0.40–0.46 0.61 0.41
. . . . . . . . . . . .
. . . . . . . . . . . .
. . . . . . . . . . . .
49 75 94 112 106 58 57 62.428 59.830 56 8 64
0.79 1.20 1.50 1.80 1.70 0.91–0.94 0.90–0.93 1.0 0.9584 0.88–0.92 .125 1.02–1.03
. . . . . . . . .
. . . . . . . . .
1.0 . .08071 0.5920 . .0478 .1234 1.5291 . 0.9673 . .0781 . .028–.036 0.35–0.45 . .038–.039 0.47–0.48 0.0693 . .00559 0.9714 . .0784 1.1056 . .0892
The specific gravities of solids and liquids refer to water at 4°°C, those of gases to air at 0°°C and 760 mm pressure. The weights per cubic foot are derived from average specific gravities, except where stated that weights are for bulk, heaped, or loose material, etc.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
WEIGHTS, MEASURES, AND CONVERSION FACTORS
7-7
Table 7-5. WEIGHTS OF BUILDING MATERIALS Materials CEILINGS Channel suspended system Lathing and plastering Acoustical fiber tile
FLOORS Steel Deck Concrete-Reinforced 1 in. Stone Slag Lightweight Concrete-Plain 1 in. Stone Slag Lightweight Fills 1 inch Gypsum Sand Cinders Finishes Terrazzo 1 in. Ceramic or Quarry Tile 3⁄4-in. Linoleum 1⁄4-in. Mastic 3⁄4-in. Hardwood 7⁄8-in. Softwood 3⁄4-in.
ROOFS Copper or tin Corrugated steel 3-ply ready roofing 3-ply felt and gravel 5-ply felt and gravel Shingles Wood Asphalt Clay tile Slate 1⁄4 Sheathing Wood 3⁄4-in. Gypsum 1 in. Insulation 1 in. Loose Poured Rigid
Weight lb per sq ft
Materials
PARTITIONS Clay Tile 3 in. 4 in. 6 in. 8 in. 10 in. Gypsum Block 2 in. See Manufacturer 3 in. 4 in. 5 in. 121⁄2 111⁄2 6 in. 6 to 10 Wood Studs 2×4 12–16 in. o.c. Steel partitions 12 Plaster 1 inch 11 Cement 3 to 9 Gypsum Lathing Metal 6 Gypsum Board 1⁄2-in. 8 4 1 See Partitions 1
13 10 1 9 4 1 2 ⁄2
WALLS Brick 4 in. 8 in. 12 in. Hollow Concrete Block (Heavy Aggregate) 4 in. 1 6 in. See Manufactuer 8 in. 1 121⁄2-in. 1 Hollow Concrete Block 5 ⁄2 6 (Light Aggregate) 4 in. 6 in. 2 8 in. 3 12 in. 9 to 14 Clay tile (Load Bearing) 10 4 in. 6 in. 8 in. 3 12 in. 4 Stone 4 in. Glass Block 4 in. Window, Glass, Frame, & Sash 1⁄ Curtain Walls 2 2 Structural Glass 1 in. 1 1 ⁄2 Corrugated Cement Asbestos 1⁄4-in.
For weights of other materials used in building construction, see Table 7-4.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Weight lb per sq ft 17 18 28 34 40 91⁄2 101⁄2 121⁄2 14 181⁄2 2 4 10 5 1⁄ 2
2
40 80 120 30 43 55 80 21 30 38 55 25 30 33 45 55 18 8 See Manufacturer 15 3
7-8
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
SI UNITS FOR STRUCTURAL STEEL DESIGN
Although there are seven metric base units in the SI system, only four are currently used by AISC in structural steel design. These base units are listed in the Table 7-6.
Table 7-6. Base SI Units for Steel Design Quantity
Unit
Symbol
Length mass time temperature
meter kilogram second celcius
m kg s °C
Similarly, of the numerous decimal prefixes included in the SI system, only three are used in steel design; see Table 7-7.
Table 7-7. SI Prefixes for Steel Design Prefix
Order of Magnitude
Symbol
mega kilo milli
Expression
6
M k m
1,000,000 (one million) 1,000 (one thousand) 0.001 (one thousandth)
10 103 10− 3
In addition, three derived units are applicable to the present conversion. They are shown in Table 7-8.
Table 7-8. Derived SI Units for Steel Design Quantity
Name
Symbol
Expression
force stress energy
newton pascal joule
N Pa J
N = kg × m/s2 Pa = N/m2 J=N×m
Although specified in SI, the pascal is not universally accepted as the unit of stress. Because section properties are expressed in millimeters, it is more convenient to express stress in newtons per square millimeter (1 N/mm2 = 1 MPa). This is the practice followed in recent international structural design standards. It should be noted that the joule, as the unit of energy, is used to express energy absorption requirements for impact tests. Moments are expressed in terms of N×m. A summary of the conversion factors relating traditional U.S. units of measurement to the corresponding SI units is given in Table 7-9.
Table 7-9. Summary of SI Conversion Factors Multiply
by:
to obtain:
inch (in.) foot (ft) pound-mass (lb) pound-force (lbf) ksi ft-lbf psf plf
25.4 305 0.454 4.448 6.895 1.356 47.88 14.59
millimeters (mm) millimeters (mm) kilogram (kg) newton (N) N/mm2 joule (J)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
N / m2 N/m
WEIGHTS, MEASURES, AND CONVERSION FACTORS
7-9
Note that fractions resulting from metric conversion should be rounded to whole millimeters. Common fractions of inches and their metric equivalent are in Table 7-10.
Table 7-10. SI Equivalents of Fractions of an Inch Fraction, in. 1⁄
16 1⁄ 8 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8
1
Exact conversion, mm
Rounded to: (mm)
1.5875 3.175 4.7625 6.35 7.9375 9.525 1.1125 12.7 15.875 19.05 22.225 25.4
2 3 5 6 8 10 11 13 16 19 22 25
Bolt diameters are taken directly from the ASTM Specifications A325M and A490M rather than converting the diameters of bolts dimensioned in inches. The metric bolt designations are in Table 7-11.
Table 7-11. SI Bolt Designation Designation
Diameter, mm
Diameter, in.
M16 M20 M22 M24 M27 M30 M36
16 20 22 24 27 30 36
0.63 0.79 0.87 0.94 1.06 1.18 1.42
The yield strengths of structural steels are taken from the metric ASTM Specifications. It should be noted that the yield points are slightly different from the traditional values. See Table 7-12. The modulus of elasticity of steel E is taken as 200,000 N/mm2. The shear modulus of elasticity of steel G is 77,000 N/mm2.
Table 7-12. SI Steel Yield Stresses ASTM Designation
2
Yield stress, N/mm
Yield stress, ksi
A36M
250
36.26
A572M Gr. 345 A588M
345
50.04
A852M
485
70.34
A514M
690
100.07
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7 - 10
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
Table 7-13. WEIGHTS AND MEASURES International System of Units (SI)a (Metric practice) BASE UNITS
Quantity length mass time electric current thermodynamic temperature amount of substance luminous intensity
SUPPLEMENTARY UNITS
Unit
Symbol
metre kilogram second ampere kelvin mole candela
m kg s A K mol cd
Symbol plane angle solid angle
Unit
Symbol
radian steradian
rad sr
DERIVED UNITS (WITH SPECIAL NAMES)
Quantity force pressure, stress energy, work, quantity of heat power
Unit
Symbol
Formula
newton pascal
N Pa
kg-m/s2 N/m2
joule watt
J W
N-m J/s
DERIVED UNITS (WITHOUT SPECIAL NAMES)
Quantity area volume velocity acceleration specific volume density
Unit
Formula
square metre cubic metre metre per second metre per second squared cubic metre per kilogram kilogram per cubic metre
m2 m3 m/s m/s2 m3/kg kg/m3
SI PREFIXES
Multiplication Factor 18
000 = 10 000 = 1015 000 = 1012 000 = 109 000 = 106 000 = 103 100 = 102 10 = 101 0.1 = 10−1 0.01 = 10−2 0.001 = 10−3 0.000 001 = 10−6 0.000 000 001 = 10−9 0.000 000 000 001 = 10−12 0.000 000 000 000 001 = 10−15 0.000 000 000 000 000 001 = 10−18
1 000 000 000 1 000 000 1 000 1
000 000 000 000 1
000 000 000 000 000 1
Prefix
Symbol
exa peta tera giga mega kilo hectob dekab decib centib milli micro nano pico femto atto
E P T G M k h da d c m µ n p f a
aRefer to ASTM E380 for more complete information on SI. bUse is not recommended.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
WEIGHTS, MEASURES, AND CONVERSION FACTORS
7 - 11
Table 7-14. WEIGHTS AND MEASURES United States System LINEAR MEASURE
Inches
Feet
Yards
.02778 .08333 = 1.0 = .33333 = 1.0 12.0 = 1.0 = 3.0 36.0 = 5.5 = 16.5 198.0 = = 220.0 7,920.0 = 660.0 = 1,760.0 63,360.0 = 5,280.0
Rods
Furlongs
.0050505 = = .0606061 = = .1818182 = = = = 1.0 = = 40.0 = = 320.0
.00012626 .00151515 .00454545 .025 1.0 8.0
Miles = = = = = =
.00001578 .00018939 .00056818 .003125 .125 1.0
SQUARE AND LAND MEASURE
Sq. Inches 1.0 = 144.0 = 1,296.0 = 39,204.0 =
Square Feet .006944 1.0 9.0 272.25 43,560.0
Square Yards = = = = =
Square Rods
.000772 .111111 1.0 30.25 4,840.0 3,097,600.0
Acres
.03306 = 1.0 = 160.0 = = 102,400.0
Sq. Miles
.000207 = .00625 = .0000098 = = .0015625 = 1.0 = 1.0 = 640.0
AVOIRDUPOIS WEIGHTS
Grains
Drams
Ounces
Pounds
.000143 .002286 = = .003906 .0625 = = .0625 = 1.0 = 1.0 = 16.0 = = 2,000.0 = 32,000.0
.03657 = 1.0 1.0 27.34375 = 16.0 = 437.5 256.0 = 7,000.0 = 512,000.0 140,000,000.0
DRY MEASURE
Pints 1.0 2.0 16.0 51.42627 64.0
Quarts = = = = =
.5 1.0 8.0 25.71314 32.0
Pecks
Cubic Feet
Bushels
= .0625 = .01945 = .01563 = .125 = .03891 = .03125 = .31112 = .25 = 1.0 = .80354 = 3.21414 = 1.0 = 1.2445 = 1.0 = 4.0
LIQUID MEASURE
Gills 1.0 4.0 8.0 32.0
= = = =
Pints
Quarts
.25 1.0 2.0 8.0
= .125 = .5 = 1.0 = 4.0
U.S. Gallons
Cubic Feet
= .03125 = .00418 = .125 = .01671 = .250 = .03342 = .1337 = 1.0 7.48052 = 1.0
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Tons = .0000000714 = .00000195 = .00003125 = .0005 = 1.0
7 - 12
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
Table 7-15. SI CONVERSION FACTORSa Quantity Length
Area
Volume
Mass
Multiply
by
to obtain
inch foot yard mile (U.S. Statute)
25.400 0.305 0.914 1.609
millimetre metre metre kilometre
millimetre metre metre kilometre
39.370×10−3 3.281 1.094 0.621
inch foot yard mile
square inch square foot square yard square mile (U.S. Statute) acre acre
0.645×103 0.093 0.836 2.590 4.047×103 0.405
square millimetre square metre square metre square kilometre square metre hectare
mm m m km in ft yd mi mm2 m2 m2 km2 m2
square millimetre square metre square metre square kilometre square metre hectare
1.550×10−3 10.764 1.196 0.386 0.247×10−3 2.471
square inch square foot square yard square mile acre acre
cubic inch cubic foot cubic yard gallon (U.S. liquid) quart (U.S. liquid)
16.387×103 28.317×10−3 0.765 3.785 0.946
cubic millimetre cubic metre cubic metre litre litre
cubic millimetre cubic metre cubic metre litre litre
61.024×10−6 35.315 1.308 0.264 1.057
cubic inch cubic foot cubic yard gallon (U.S. liquid) quart (U.S. liquid)
in3 ft3 yd3 gal qt
ounce (avoirdupois) pound (avoirdupois) short ton
28.350 0.454 0.907×103
gram kilogram kilogram
g kg kg
gram kilogram kilogram
35.274×10−3 2.205 1.102×10−3
ounce (avoirdupois) pound (avoirdupois) short ton
aRefer to ASTM E380 for more complete information on SI. The conversion factors tabulated herein have been rounded.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
in2 ft2 yd2 mi2
mm3 m3 m3 l l
oz av lb av
WEIGHTS, MEASURES, AND CONVERSION FACTORS
7 - 13
Table 7-15 (cont.). SI CONVERSION FACTORSa Quantity Force
Multiply 0.278 4.448
c
c
3.597 0.224
c
0.113 1.356
c
8.851 0.738
c
pound-force per square inch foot of water (39.2 F) c inch of mercury (32 F)
6.895 2.989 3.386
c
c
0.145
c
newton newton
c
pound-force-inch pound-force-foot
c c
newton-metre newton-metre
c
Pressure, Stress
to obtain
ounce-force c pound-force
c
Bending Moment
by
c
c c
kilopascal
newton c newton
c
c
c
ounce-force pound-force
N N
lbf
newton-metre newton-metre
N-m N-m
pound-force-inch pound-force-foot
lbf-in lbf-ft
kilopascal kilopascal c kilopascal c
kPa kPa kPa
lbf/in2 pound-force per square inch c foot of water (39.2 F) c inch of mercury (32 F) c
c
0.335 0.295
kilopascal kilopascal
c
Energy, Work, cfoot-pound-force b Heat British thermal unit b calorie c kilowatt hour
1.356 1.055×103 4.187 3.600×106
c
joule joule c joule c joule
0.738 0.948×10−3 0.239 0.278×10−6
c
c
foot-pound-force/second British thermal unit per hour c horsepower (550 ft lbf/s)
1.356 0.293 0.746
c
c
0.738
c
c c
Power
b
watt
joule joule c joule c joule c
foot-pound-force British thermal unit c calorie c kilowatt hour c
watt watt c kilowatt c
foot-pound-force/ second c British thermal unit c per hour c horsepower c (550 ft-lbf/s)
J J J J ft-lbf Btu kW-h W W kW ft-lbf/s
c c
3.412
kilowatt
1.341
watt
Angle
17.453×10−3 57.296
c
degree radian
c
Temperature
c
degree Fahrenheit degree Celsius
c
t°°C = (t°°F − 32)/1.8 t°°F = 1.8 × t°°C + 32
c c c c
radian degree degree Celsius degree Fahrenheit
aRefer to ASTM E380 for more complete information on SI. bInternational Table.
The conversion factors tabulated herein have been rounded.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Btu/h hp
rad
7 - 14
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
BRACING FORMULAS b
b
p
d
e
a
a
c
h
h
w
w
p
d
e
c
w
w
f
m
f m n
To Find Formula
Given bpw bw bp bp bfp bmp bpw afw cmw
( b + p )2 + w 2 √ √ b 2 +w 2 2 b ÷ (2b + p)
f m d e a c h h h
bpw bnw bnp bnp bfnp bmnp bnpw afw cmw
b (b + p ) ÷ (2 b + p ) bf ÷ (2b + p ) bm ÷ (2b + p ) bw ÷ (2b + p ) aw ÷ f cw ÷ m
(b + p )2 + w 2 √ √ (b − n )2 + w 2
b (b − n ) ÷ (2 b + p − n ) b (b + p ) ÷ (2 b + p − n ) bf ÷ (2b + p − n ) bm ÷ (2b + p − n ) bw ÷ (2b + p − n ) aw ÷ f cw ÷ m
k = (log B − log T) ÷ no. of panels. Constant k plus the logarithm of any line equals the log of the corresponding line in the next panel below.
p
d
e a
f m d e a c h h h
PARALLEL BLOCKING
b k
To Find Formula
Given
c
h
v
m
w
f
a = TH ÷ (T + e + p ) b = Th ÷ (T + e + p )
bpw bkv
T
Formula
f
√ ( b + p )2 + w 2
m
√ (b + k) + v 2
A
a
2
bkpvw
d
bw (b + k) ÷ [v (b + p ) + w (b + k )]
bkpvw
e
bv (b + p ) ÷ [v (b + p ) + w (b + k )]
bfkpvw
a
fbv ÷ [v (b + p ) + w (b + k )]
bkmpvw
c
bmw ÷ [v (b + p ) + w (b + k )]
bkpvw
h
bvw ÷ [v(b + p ) + w (b + k )]
afw
h
aw ÷ f
cmv
h
cv ÷ m
d = ce ÷ (T + e)
b
d
Given
c=√ (1 ⁄2 T + 1 ⁄2 e )2 + a 2
To Find
c e A H
f
g
h
n m
log e = k + log T log f = k + log a log g = k + log b log m = k + log c log n = k + log d log p = k + log e
p A
B
The above method can be used for any number of panels. In the formulas for ‘‘a’’ and ‘‘b’’ the sum in parenthesis, which in the case shown is (T + e + p), is always composed of all the horizontal distances except the base.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
GEOMETRIC AND TRIGONOMETRIC DATA
7 - 15
PROPERTIES OF PARABOLA AND ELLIPSE PARABOLA
ELLIPSE (x 2 ÷ H 2) + (y 2 ÷ B 2) = 1
Abscissa = x
¼
pe c. of g.
0.424H
.375B
Ordinate = y Abscissa = x
c. of g.
r ete
r
Major semi-axis = H
Ordinate = y
rim pe
ete rim
0.6H
½
Height = H
Apex
.424B
½ base = B Minor semi-axis = B 2 Parameter P = B H y2 x= P y = xP
a
b
Area =
HB
D
Area = .7854Dd
d
c
d
e a
1
b
Construction
1
2 H
c
2 H
3
3
B
e
Construction 4
4
B
B
5
AREA BETWEEN PARABOLIC CURVE AND SECANT Apex Center of gravity (shaded area)
Any secant
m .4m
H h
b
b
2
2
b B
B
Length b may vary from 0 to 2B
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7 - 16
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
PROPERTIES OF THE CIRCLE Circumference = 6.28318 r = 3.14159 d Diameter = 0.31831 circumference Area = 3.14159r 2
x
π rA° = 0.017453 rA° 180 ° 180 ° a a Angle A ° = = 57.29578 r πr 4 b 2 + c2 Radius r = 8b A Chord c = 2 √ 2 br − b 2 = 2 r sin 2 1 c A Rise b = r − √ 4 r 2− c2 = tan 2 2 4 2 A 2 r − x 2 = 2 r sin =r+y−√ 4 y=b−r+√ r 2− x 2 Arc a =
b
y c A°
r
d
x=√ r 2− (r + y − b )2
Diameter of circle of equal periphery as square Side of square of equal periphery as circle Diameter of circle circumscribed about square Side of square inscribed in circle
= 1.27324 side of square = 0.78540 diameter of circle = 1.41421 side of square = 0.70711 diameter of circle
CIRCULAR SECTOR
r = radius of circle y = angle ncp in degrees Area of Sector ncpo = 1 ⁄2 (length of arc nop x r)
o n
p
y
= Area of Circle ×
r
c
y 360
= 0.0087266 × r 2 × y CIRCULAR SEGMENT
r = radius of circle x = chord b = rise Area of Segment nop = Area of Sector ncpo − Area of triangle ncp
o b n
c
p
=
x
(Length of arc nop × r) − x (r − b) 2
Area of Segment nop = Area of Circle − Area of Segment nop
s
VALUES FOR FUNCTIONS OF π π = 3.14159265359, log = 0.4971499 _ _ 1 = 0.3183099, log = 1.5028501 1π = 0.5641896, log = 1.7514251 √ π _ _ π 1 π3 = 31.0062767, log = 1.4914496 = 0.1013212, log = 1.0057003 = 0.0174533, log = 2.2418774 180 π2 _ 1 180 = 0.0322515, log = 2.5085504 = 57.2957795, log = 1.7581226 π = 1.7724539, log = 0.2485749 √ π π3 _ _ Note: Logs of fractions such as 1 .5028501 and 2 .5085500 may also be written 9.5028501 − 10 and 8.5085500 − 10 respectively π2 = 9.8696044, log = 0.9942997
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
GEOMETRIC AND TRIGONOMETRIC DATA
7 - 17
PROPERTIES OF GEOMETRIC SECTIONS A = d2
SQUARE
c=
Axis of moments through center
I= c
S=
d
r= d
Z=
SQUARE
d 2
d4 12
d3 6
d
= .288675 d
√ 12
d3 4
A = d2 c=d
Axis of moments on base
I= d
c
S= r=
d4 3
d3 3
d = .577350 d 3 √
d
SQUARE
A = d2
Axis of moments on diagonal
c= I= c
S= r=
d4 12
d3 = .117851 d 3 6 √2 d
d
A = bd
RECTANGLE Axis of moments through center
c= I=
c
S= r= b
= .707107 d
= .288675 d √ 12 3 2c d3 = = .235702 d 3 Z= 3 3√ 2
d
d
d 2 √
Z=
d 2
bd 3 12
bd 2 6
d
= .288675 d
√ 12
bd
2
4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7 - 18
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
PROPERTIES OF GEOMETRIC SECTIONS (cont.) RECTANGLE
A = bd c=d
Axis of moments on base
bd 3
I=
3
S=
c
d
bd 2 3
d
r=
3 √
= .577350 d
b
RECTANGLE
A = bd
Axis of moments on diagonal
bd √ b2 + d 2 b3 d 3
c=
c
I=
S= b d
RECTANGLE
c a
d
b
6√ b2 + d 2
bd √ 6 (b 2 + d2 )
r=
Axis of moments any line through center of gravity
6(b 2 + d 2) b2 d 2
A = bd b sin a + d cos a c= 2 bd (b 2 sin2 a + d 2cos2 a ) I= 12 bd (b 2 sin2 a + d 2cos2 a ) S= 6 (b sin a + d cos a ) r=
√
b2 sin2 a + d 2cos2 a 12
A = bd − b 1 d 1
Axis of moments through center
I= c
d
d1
12
S=
b1
r= b
d 2 bd 3− b 1d13
c=
HOLLOW RECTANGLE
Z=
bd 3− b 1d13 6d
√
bd 3− b1d13 12 A
bd 2 b 1d 12 4
−
4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
GEOMETRIC AND TRIGONOMETRIC DATA
7 - 19
PROPERTIES OF GEOMETRIC SECTIONS (cont.) A = b(d − d 1 ) EQUAL RECTANGLES
d
c=
Axis of moments through center of gravity
2
b(d 3− d 13 )
I=
d
d1
r= b
Axis of moments through center of gravity
d
d 3− d 13
12(d − d1)
b
t
b
2
y
c
y1
c1
t1 b1
2
4
r=
√
Z=
TRIANGLE
(d 2− d 12 )
A = bt + b 1 t1 1⁄ bt 2+ b t (d − 1 ⁄ t ) 11 2 21 c= A b 1t13 bt 3 I= + bty 2 + + b1 t1 y 12 12 12 l l S= S1 = c c1
d1
t1
√
Z=
UNEQUAL RECTANGLES
t
12
b(d 3− d 13 ) S= 6d
c
I A
t + t1 A d − 2 2
bd 2 2d c= 3 bd 3 I= 36 bd 2 S= 24 d r= = .235702 d √ 18 A=
Axis of moments through center of gravity
c d
b
TRIANGLE
c
d
b
bd 2 c=d bd 3 I= 12 bd 2 S= 12 d r= = .408248 d 6 √ A=
Axis of moments on base
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7 - 20
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
PROPERTIES OF GEOMETRIC SECTIONS (cont.) TRAPEZOID Axis of moments through center of gravity b1
c
A=
d (b + b 1) 2
c=
d (2 b + b 1 ) 3 (b + b 1 )
I=
d 3(b 2 + 4 bb1 + b 21 ) 36 (b + b1)
d
S= b
d 2(b 2 + 4 bb1 + b 21 )
12 (2 b + b 1)
d r= √ 2(b 2 + 4bb1 + b 21 ) 6(b + b 1) A=
πd 2 = π R 2 = .785398 d 2= 3.141593 R 2 4
c=
d =R 2
I=
π d 4 π R4 = = .049087 d 4= .785398 R 4 64 4
CIRCLE Axis of moments through center
c
R
S=
d
π d 3 π R3 = = .098175 d 3= .785398 R 3 32 4
r=
d R = 4 2
Z=
d3 6
π(d 2− d 12 ) = .785398 (d 2− d 12 ) 4 d c= 2 π(d 4− d 14 ) I= = .049087 (d 4− d 14 ) 64 π(d 4− d 14 ) d 4− d 14 S= = .098175 32 d d
A= HOLLOW CIRCLE Axis of moments through center
c d
d1
r=
HALF CIRCLE
√ d 2+ d 12 4
Z=
d 13 d − 6 6
A=
πR 2 = 1.570796 R 2 2
3
4 = .575587 R C = R 1 − 3π
Axis of moments through center of gravity
π
R
d
c
I = R4
8
S=
−
8
9π
= .109757 R 4
2 R 3 (9π − 64 ) = .190687 R 3 24 (3π − 4)
r=R
√ 9π 2 − 64 6π
= .264336 R
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
GEOMETRIC AND TRIGONOMETRIC DATA
7 - 21
PROPERTIES OF GEOMETRIC SECTIONS (cont.) 4 ab 3 2 m= a 5 16 3 I1 = a b 175 4 ab 3 I2 = 15 32 3 I3 = a b 105
A=
PARABOLA 2
a 1 m 3
1 3 b 2
2 ab 3 2 m= a 5 3 n= b 8 8 I1 = a3b 175 19 ab 3 I2 = 480 16 3 I3 = a b 105 2 I4 = ab 3 15
A=
HALF PARABOLA 4
2
n apex
a 1 m 3
1 3
2 b 4
COMPLEMENT OF HALF PARABOLA 2
1 ab 3 7 m= a 10 3 n= b 4 37 a3b I1 = 2,100 1 I2 = ab 3 80
A=
n apex
1
1
a
m
2 b
PARABOLIC FILLET IN RIGHT ANGLE 2
t 2√ 2 t b= 2 √ 1 A = t2 6 A=
m
1
1
b
n
t 2
m=n=
a
I 1 = I2 =
4 t 5 11
2,100
t4
t
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7 - 22
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
PROPERTIES OF GEOMETRIC SECTIONS (cont.) * HALF ELLIPSE
A=
1 π ab 2
m=
4a 3π
2
a 1
1 m 3
3
π 8 I1 = a 3 b − 8 9π I2 =
1 πab3 8
I3 =
1 a3 π 8 b
b 2
1 πab 4 4a m= 3π 4b n= 3π
A=
* QUARTER ELLIPSE 2
4
n
π 4 I1 = a 3 b − 16 9π
a 1 3
1 m 3
2 b
π 4 I2 = ab 3 − 16 9π I3 =
4
1 πa3b 16
I4 = π ab3
* ELLIPTIC COMPLEMENT 2
n
π A = ab 1 − 4
1
1 a
m=
a π 6 1 − 4
n=
b π 6 1 − 4
m
2 b
1
I1 = a 3 b
3
−
π − 16
1 π 36 1 − 4
1 π 1 I2 = ab 3 − − π 3 16 36 1 − 4
*To obtain properties of half circle, quarter circle, and circular complement, substitute a = b = R.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
GEOMETRIC AND TRIGONOMETRIC DATA
7 - 23
PROPERTIES OF GEOMETRIC SECTIONS (cont.) n = Number of sides 180 º φ=
REGULAR POLYGON
n
Axis of moments through center
1
a = 2√ R2 − R 21 a R= 2 sin φ a R1 = 2 tan φ 1 1 A = na 2 cot φ = nR 2 sin 2φ = nR 12 tan φ 4 2 A (6 R 2− a 2 ) A (12 R 12 + a 2 ) I1 = I2 = = 24 48
a
2
φ R R1
2 1
r1 = r2 =
√ √ 6 R 2− a 2
24
=
12 R 12 + a 2
48
ANGLE
tan 2φ =
Axis of moments through center of gravity
2K Iy − Ix
b 2 + ct d 2 + at y= 2 (b + c ) 2(b + c ) K = Product of Inertia about XjX and YjY A = t (b + c ) x =
b
=±
a
t
Z
1 3 1 IY = 3 I z = Ix Iw = Ix Ix =
Y W
90° φ
X y
c
d
X
t
Z
Y
(t (d − y)3 + by 3 − a (y − t)3) (t (b − x)3 + dx 3 − c (x − t)3 ) sin 2 φ + IY cos 2 φ + K sin2 φ cos 2 φ + IY sin 2 φ − K sin2 φ
K is negative when heel of angle, with respect to center of gravity, is in 1st or 3rd quadrant, positive when in 2nd or 4th quadrant.
W
x
abcdt 4(b + c)
BEAMS AND CHANNELS Transverse force oblique through center of gravity F
F
Y
Y x
x
φ
φ X
3
X 3
3
3
I3 = Ix sin2 φ + IY cos 2 φ I4 = Ix cos2 φ + IY sin2 φ y x fb = M sin φ + cos φ I I x Y
where M is bending moment due to force F.
X
X y
y Y
Y 4
4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7 - 24
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
TRIGONOMETRIC FORMULAS Radius AF = 1 TRIGOMETRIC FUNCTIONS G
H
sin A cos A
D L
tan A
B
cot A
c
a
b
C
sec A A
F
cosec A
RIGHT ANGLED TRIANGLES
a 2= c 2− b 2 b 2= c 2− a 2 c 2= a 2+ b 2
B c b
A
= sin 2 A + cos 2 A = sin A cosec A = cos A sec A = tan A cot A 1 cos A = = = cos A tan A = √ 1 − cos 2 A = BC cot A cosec A sin A 1 = = = sin A cot A = √ 1 − sin2 A = AC tan A sec A sin A 1 = = = sin A sec A = FD cos A cot A cos A 1 = = = cos A cosec A = HG sin A tan A tan A 1 = = = AD sin A cos A cot A 1 = = = AG cos A sin A
a C
Required Known
A
B
a tan A = b a sin A = c
b tan B = a a cos B = c
√ c −a
A, a
90° − A
a cot A
A, b
90° − A
b tan A
A, c
90° − A
c sin A
a, b a, c
OBLIQUE ANGLED TRIANGLES
a
c b
C
b
2
s=
a+b+c 2
K=
√
B
A
a
c
Area
√ a 2+b 2
ab
2 a√ c 2− a 2 2
2
a sin A
a 2cot A 2
b cos A
b2 tan A 2 c2 sin 2A 4
c cos A
a 2= b 2+ c 2− 2bc cos A b 2= a 2+ c 2− 2ac cos B c 2= a 2+ b 2− 2 ab cos C
( s − a ) (s − b ) ( s − c ) s
Required Known
A
a, b , c
K 1 tan A = 2 s−a
B
C
180° − (A + B )
a, A, B sin B =
a , b, A a, b, C tan A =
a sin C b − a cos C
b
c
K K 1 1 tan B = tan C = 2 2 s−b s−c
b sin A
a
Area
√ s (s − a) (s − b) (s − c) a sin B sin A
a sin C sin A b sin C sin B
√ a 2+ b 2− 2 ab cos C
ab sin C
2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DECIMAL EQUIVALENTS
7 - 25
DECIMALS OF AN INCH For each 64th of an inch With millimeter equivalents Fractions
1⁄ ths 64
Decimal
Millimeters (Approx.)
—
1 2 3 4
.015625 .03125 .046875 .0625
0.397 0.794 1.191 1.588
5 6 7 8
.078125 .09375 .109375 .125
1.984 2.381 2.778 3.175
9 10 11 12
.140625 .15625 .171875 .1875
3.572 3.969 4.366 4.763
13 14 15 16
.203125 .21875 .234375 .250
5.159 5.556 5.953 6.350
17 18 19 20
.265625 .28125 .296875 .3125
6.747 7.144 7.541 7.938
21 22 23 24
.328125 .34375 .359375 .375
8.334 8.731 9.128 9.525
25 26 27 28
.390625 .40625 .421875 .4375
9.922 10.319 10.716 11.113
29 30 31 32
.453125 .46875 .484375 .500
11.509 11.906 12.303 12.700
1⁄ 32
—
1⁄ 16
—
3⁄ 32
— 1⁄ 8
—
5⁄ 32
—
3⁄ 16
—
7⁄ 32
— 1⁄ 4
—
9⁄ 32
—
5⁄ 16
— 11⁄
32
— 3⁄ 8 — 13⁄ 32
— 7⁄ 16
— 15⁄ 32
— 1⁄ 2
Decimal
Millimeters (Approx.)
33 34 35 36
.515625 .53125 .546875 .5625
13.097 13.494 13.891 14.288
37 38 39 40
.578125 .59375 .609375 .675
14.684 15.081 15.478 15.875
41 42 43 44
.640625 .65625 .671875 .6875
16.272 16.669 17.066 17.463
45 46 47 48
.703125 .71875 .734375 .750
17.859 18.256 18.653 19.050
49 50 51 52
.765625 .78125 .796875 .8125
19.447 19.844 20.241 20.638
53 54 55 56
.828125 .84375 .859375 .875
21.034 21.431 21.828 22.225
57 58 59 60
.890625 .90625 .921875 .9375
22.622 23.019 23.416 23.813
61 62 63 64
.953125 .96875 .984375 1.000
24.209 24.606 25.003 25.400
Fractions
1⁄ ths 64
— 17⁄ 32
— 9⁄ 16
— 19⁄ 32
— 5⁄ 8 — 21⁄ 32
— 11⁄ 16
— 23⁄ 32
— 3⁄ 4 — 25⁄ 32
— 13⁄ 16
— 27⁄ 32
— 7⁄ 8 — 29⁄ 32
— 15⁄ 16
— 31⁄ 32
— 1
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7 - 26
MISCELLANEOUS DATA AND MATHEMATICAL INFORMATION
DECIMALS OF A FOOT For each 32nd of an inch Inch
0
1
2
3
4
5
0
0 .0026 .0052 .0078
.0833 .0859 .0885 .0911
.1667 .1693 .1719 .1745
.2500 .2526 .2552 .2578
.3333 .3359 .3385 .3411
.4167 .4193 .4219 .4245
.0104 .0130 .0156 .0182
.0938 .0964 .0990 .1016
.1771 .1797 .1823 .1849
.2604 .2630 .2656 .2682
.3438 .3464 .3490 .3516
.4271 .4297 .4323 .4349
5⁄ 16 11⁄ 32
.0208 .0234 .0260 .0286
.1042 .1068 .1094 .1120
.1875 .1901 .1927 .1953
.2708 .2734 .2760 .2786
.3542 .3568 .3594 .3620
.4375 .4401 .4427 .4453
3⁄ 8 13⁄ 32 7⁄ 16 15⁄ 32
.0313 .0339 .0365 .0391
.1146 .1172 .1198 .1224
.1979 .2005 .2031 .2057
.2812 .2839 .2865 .2891
.3646 .3672 .3698 .3724
.4479 .4505 .4531 .4557
1⁄ 2 17⁄ 32 9⁄ 16 19⁄ 32
.0417 .0443 .0469 .0495
.1250 .1276 .1302 .1328
.2083 .2109 .2135 .2161
.2917 .2943 .2969 .2995
.3750 .3776 .3802 .3828
.4583 .4609 .4635 .4661
5⁄ 8 21⁄ 32 11⁄ 16 23⁄ 32
.0521 .0547 .0573 .0599
.1354 .1380 .1406 .1432
.2188 .2214 .2240 .2266
.3021 .3047 .3073 .3099
.3854 .3880 .3906 .3932
.4688 .4714 .4740 .4766
3⁄ 4 25⁄ 32 13⁄ 16 27⁄ 32
.0625 .0651 .0677 .0703
.1458 .1484 .1510 .1536
.2292 .2318 .2344 .2370
.3125 .3151 .3177 .3203
.3958 .3984 .4010 .4036
.4792 .4818 .4844 .4870
7⁄ 8 29⁄ 32 15⁄ 16 31⁄ 32
.0729 .0755 .0781 .0807
.1563 .1589 .1615 .1641
.2396 .2422 .2448 .2472
.3229 .3255 .3281 .3307
.4063 .4089 .4115 .4141
.4896 .4922 .4948 .4974
1⁄
1⁄ 3⁄
32 16 32
1⁄ 8
5⁄ 3⁄ 7⁄
32 16 32
1⁄ 4
9⁄
32
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DECIMAL EQUIVALENTS
7 - 27
DECIMALS OF A FOOT (cont.) For each 32nd of an inch Inch
6
7
8
9
10
11
0 1⁄ 32 1⁄ 16 3⁄ 32
.5000 .5026 .5052 .5078
.5833 .5859 .5885 .5911
.6667 .6693 .6719 .6745
.7500 .7526 .7552 .7578
.8333 .8359 .8385 .8411
.9167 .9193 .9219 .9245
1⁄ 8 5⁄ 32 3⁄ 16 7⁄ 32
.5104 .5130 .5156 .5182
.5938 .5964 .5990 .6016
.6771 .6797 .6823 .6849
.7604 .7630 .7656 .7682
.8438 .8464 .8490 .8516
.9271 .9297 .9323 .9349
1⁄ 4 9⁄ 32 5⁄ 16 11⁄ 32
.5208 .5234 .5260 .5286
.6042 .6068 .6094 .6120
.6875 .6901 .6927 .6953
.7708 .7734 .7760 .7786
.8542 .8568 .8594 .8620
.9375 .9401 .9427 .9453
3⁄
.5313 .5339 .5365 .5391
.6146 .6172 .6198 .6224
.6979 .7005 .7031 .7057
.7813 .7839 .7865 .7891
.8646 .8672 .8698 .8724
.9479 .9505 .9531 .9557
.5417 .5443 .5469 .5495
.6250 .6276 .6302 .6328
.7083 .7109 .7135 .7161
.7917 .7943 .7969 .7995
.8750 .8776 .8802 .8828
.9583 .9609 .9635 .9661
.5521 .5547 .5573 .5599
.6354 .6380 .6406 .6432
.7188 .7214 .7240 .7266
.8021 .8047 .8073 .8099
.8854 .8880 .8906 .8932
.9688 .9714 .9740 .9766
.5625 .5651 .5677 .5703
.6458 .6484 .6510 .6536
.7292 .7318 .7344 .7370
.8125 .8151 .8177 .8203
.8958 .8984 .9010 .9036
.9792 .9818 .9844 .9870
.5729 .5755 .5781 .5807
.6563 .6589 .6615 .6641
.7396 .7422 .7448 .7474
.8229 .8255 .8281 .8307
.9063 .9089 .9115 .9141
.9896 .9922 .9948 .9974
13⁄
8 32
7⁄ 16 15⁄ 32 1⁄
17⁄
2 32
9⁄ 16 19⁄ 32 5⁄
21⁄
8 32
11⁄ 16 23⁄ 32 3⁄
25⁄ 13⁄ 27⁄ 7⁄
29⁄ 15⁄ 31⁄
4 32 16 32 8 32 16 32
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8-1
PART 8 BOLTS, WELDS, AND CONNECTED ELEMENTS OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-3 BOLTED CONSTRUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-7 High-Strength Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-7 Non-High-Strength Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19 Design Strength of Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19 ECCENTRICALLY LOADED BOLT GROUPS . . . . . . . . . . . . . . . . . . . . . . . 8-28 ANCHOR RODS OR THREADED RODS . . . . . . . . . . . . . . . . . . . . . . . . . 8-88 OTHER MECHANICAL FASTENERS . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-92 WELDED CONSTRUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-98 Fillet Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-118 Complete-Joint-Penetration Groove Welds . . . . . . . . . . . . . . . . . . . . . . . . 8-122 Partial-Joint-Penetration Groove Welds . . . . . . . . . . . . . . . . . . . . . . . . . . 8-125 Flare Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-127 Plug and Slot Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-128 Design Strength of Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-129 Prequalified Welded Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-131 ECCENTRICALLY LOADED WELD GROUPS . . . . . . . . . . . . . . . . . . . . . . 8-154 CONSTRUCTION COMBINING BOLTS AND WELDS . . . . . . . . . . . . . . . . . 8-211 CONNECTED ELEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-212 Design Strength of Connecting Elements . . . . . . . . . . . . . . . . . . . . . . . . . 8-212 Members with Copes, Blocks, or Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-225 Other Elements in Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-237 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-238
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8-2
BOLTS, WELDS, AND CONNECTED ELEMENTS
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
8-3
OVERVIEW
Part 8 contains general information, design considerations, examples, and design aids for the design of bolts, anchor rods, other mechanical fasteners, welds, and connected elements in connections. It is based on the provisions of the 1993 LRFD Specification. Supplementary information may also be found in the Commentary on the LRFD Specification. Following is a detailed overview of the topics addressed. BOLTED CONSTRUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-7 High-Strength Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-7 Alternative Design Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-7 Compatible Nuts and Washers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-8 Economical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-8 Dimensions and Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-9 Entering and Tightening Clearances . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-12 Snug-Tightened and Fully Tensioned Installation . . . . . . . . . . . . . . . . . . . . 8-12 Inspection of Fully Tensioned High-Strength Bolts . . . . . . . . . . . . . . . . . . . 8-15 Galvanizing High-Strength Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-18 Reuse of High-Strength Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19 Non-High-Strength Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19 Dimensions and Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19 Entering and Tightening Clearances . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19 Design Strength of Bolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-19 Bolt Shear Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-22 Bearing Strength at Bolt Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-23 Bolt Tensile Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-23 Slip Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-25 ECCENTRICALLY LOADED BOLT GROUPS . . . . . . . . . . . . . . . . . . . . . . . 8-28 Eccentricity in the Plane of the Faying Surface . . . . . . . . . . . . . . . . . . . . . . 8-28 Instantaneous Center of Rotation Method . . . . . . . . . . . . . . . . . . . . . . . . 8-28 Elastic Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-33 Eccentricity Normal to the Plane of the Faying Surface . . . . . . . . . . . . . . . . . . 8-36 Case I窶年eutral Axis Not at Center of Gravity . . . . . . . . . . . . . . . . . . . . . 8-37 Case II窶年eutral Axis at Center of Gravity . . . . . . . . . . . . . . . . . . . . . . . 8-38 ANCHOR RODS OR THREADED RODS . . . . . . . . . . . . . . . . . . . . . . . . . 8-88 Minimum Edge Distance and Embeddment Length . . . . . . . . . . . . . . . . . . . . 8-88 Welding to Anchor Rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-89 AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8-4
BOLTS, WELDS, AND CONNECTED ELEMENTS
Hooked Anchor Rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-89 Headed Anchor Rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-90 OTHER MECHANICAL FASTENERS . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-92 Clevises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-92 Turnbuckles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-92 Sleeve Nuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-93 Recessed-Pin Nuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-93 Cotter Pins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-93 WELDED CONSTRUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-98 Weldability of Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-98 Chemical Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-99 Grain Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-100 Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-100 Structural Welding Materials and Processes . . . . . . . . . . . . . . . . . . . . . . . 8-101 SMAW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-102 SAW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-105 GMAW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-106 FCAW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-106 ESW and EGW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-107 Thermal Cutting and Air-Arc Gouging . . . . . . . . . . . . . . . . . . . . . . . . . 8-108 Inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-108 VT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-109 DPT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-109 MT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-109 RT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-110 UT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-110 Economical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-111 Welding Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-112 Weld Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-112 Weld Metal Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-112 Deposit Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-113 Prior Qualification of Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-113 Minimizing Weld Repairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-113 Lamellar Tearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-113 Fatigue Cracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-113 AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
8-5
Notch Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-114 Impact Toughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-114 Arc Strikes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-114 Other Considerations in Welded Construction . . . . . . . . . . . . . . . . . . . . . . . 8-115 Matching Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-115 Welding Shapes from ASTM A6 Groups 4 and 5 . . . . . . . . . . . . . . . . . . . . 8-115 Intersecting Welds and Triaxial Stresses . . . . . . . . . . . . . . . . . . . . . . . . . 8-116 Painting Welded Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-117 Clearances for Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-118 Fillet Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-118 Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-118 Minimum Effective Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-119 Minimum Fillet Weld Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-119 Maximum Fillet Weld Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-119 End Returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-120 Fillet Welds in Holes or Slots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-121 Other Limitations on Fillet Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-121 Minimum Shelf Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-122 Complete-Joint-Penetration Groove Welds . . . . . . . . . . . . . . . . . . . . . . . . 8-122 Extension, Runoff, Backing, and Spacer Bars . . . . . . . . . . . . . . . . . . . . . . 8-122 Weld Access Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-125 Partial-Joint-Penetration Groove Welds . . . . . . . . . . . . . . . . . . . . . . . . . . 8-125 Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-127 Intermittent Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-127 Flare Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-127 Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-128 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-128 Plug and Slot Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-128 Design Strength of Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-129 Weld Metal Design Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-129 Base Metal Design Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-129 Prequalified Welded Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-131 ECCENTRICALLY LOADED WELD GROUPS . . . . . . . . . . . . . . . . . . . . . . 8-154 Eccentricity in the Plane of the Faying Surface . . . . . . . . . . . . . . . . . . . . . . 8-154 Instantaneous Center of Rotation Method . . . . . . . . . . . . . . . . . . . . . . . . 8-154 AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8-6
BOLTS, WELDS, AND CONNECTED ELEMENTS
Elastic Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-159 Eccentricity Normal to the Plane of the Faying Surface . . . . . . . . . . . . . . . . . 8-211 CONSTRUCTION COMBINING BOLTS AND WELDS . . . . . . . . . . . . . . . . . 8-211 CONNECTED ELEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-212 Economical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-212 Design Strength of Connected Elements . . . . . . . . . . . . . . . . . . . . . . . . . 8-212 Shear Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-212 Shear Rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-212 Block Shear Rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-212 Tension Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-225 Tension Rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-225 Members with Copes, Blocks, or Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . 8-225 Flexural Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-225 Local Web Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-226 Lateral Torsional Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-229 Other Elements In Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-237 Shims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-237 Fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-237 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-238
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BOLTED CONSTRUCTION
8-7
BOLTED CONSTRUCTION High-Strength Bolts
LRFD Specification Section A3.3 permits the use of ASTM A325 and A490 high-strength bolts. ASTM A325 bolts are available in diameters from 1⁄2-in. to 11⁄2-in. in two types. Type 1 medium-carbon-steel bolts are for general purpose use and use in elevated temperatures; they may be galvanized. Type 3 bolts offer improved atmospheric corrosion resistance and weathering characteristics similar to those of ASTM A242 or A588 steels. ASTM A490 bolts are available in diameters from 1⁄2-in. to 11⁄2-in. in two types. Type 1 bolts are alloy-steel bolts. Type 3 are alloy-steel bolts with improved atmospheric corrosion resistance and weathering characteristics similar to those of ASTM A242 or A588 steels. ASTM A490 bolts should not be galvanized and caution should be exercised if used in highly corrosive environments. Type 2 (martensite) bolts, popular for many years, have been discontinued. Information on this type can be found in previous editions of the AISC Manual of Steel Construction. When bolts of diameter larger than 11⁄2 in. are required, ASTM A449 bolts are permitted to be used for snug-tightened and fully tensioned bearing-type connections; this material is not recognized in LRFD Specification Section A3.3 for use in slip-critical connections nor for use as bolts in diameters not greater than 11⁄2 in. ASTM A449 bolts may be galvanized. When an ASTM A449 bolt is used in tension or bearing and is tightened in excess of 50 percent of its minimum specified tensile strength, LRFD Specification Section J3.1 requires that an ASTM F436 washer be installed under the head of the bolt. The nut must be from the approved list in RCSC Specification Section 2(c). Since ASTM A325 nuts and washers for use with high-strength bolts are available only up to 11⁄2-in. diameter, reference should be made to ASTM A563 for nuts and ASTM F436 for washers to select suitable sizes and grades for the intended application. While ASTM A449 seems to be the equal of ASTM A325, there are two important differences which should be noted. First, ASTM A449 bolts are not produced to the same inspection and quality assurance requirements as ASTM A325 bolts. Second, ASTM A449 bolts are not produced to the same heavy-hex head and nut dimensions. Alternative Design Bolts
RCSC Specification Section 2d permits the use of other fasteners when they meet the requirements as outlined therein. Figure 8-1 shows a tension-control or “twist-off” bolt which is installed with a special tool which twists off the splined end when the proper
Fig. 8-1. Tension-control or “twist-off” bolt. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8-8
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-1. Compatability of High-Strength Bolts, Nuts, Washers F436 Washer Grade
ASTM Bolt Desig.
Type
Coating
Recommended
Suitable
Recommended
A325
1
plain
C
C3, D, DH, DH3
1
galvanized
DH
—
1
3
plain
C3
DH3
3
1
plain
DH
DH3
1
3
plain
DH3
—
3
1
plain
A
C, C3, D, DH, DH3
1
galvanized
DH
D
1
A490
A449
A563 Heavy Hex Nut Grade
bolt tension is achieved. Tension-control bolts are commonly available to meet the specifications of ASTM A325 and A490. Compatible Nuts and Washers
The compatibility of ASTM A563 nuts and F436 washers with the aforementioned high-strength bolt specifications is as listed in Table 8-1. Alternatively, appropriate ASTM A194 nuts may be used. RCSC Specification Section 7c gives general requirements for when washers are required for high-strength bolts. Economical Considerations
Since the material cost per unit of strength of ASTM A490 bolts is comparable with that of ASTM A325 bolts, it might seem more cost effective to reduce the number of bolts in a given connection by specifying ASTM A490 bolts. However, ASTM A490 bolts are more difficult to tighten and raise inventory and quality control issues associated with the use of multiple fastener grades; mixing of ASTM A325 and A490 bolts of the same diameter should be avoided to assure that the ASTM A490 bolts are installed in the proper location. Thus, the net benefit of specifying ASTM A490 bolts may be less than expected; cost ratios should be considered by the designer. Similarly, cost ratios between grades of alternative design bolts will vary from those of conventional high-strength bolts. Thus, the decision regarding fastener selection will vary accordingly. Regardless of the bolt type selected, the normal sizes of 3⁄4-in., 7⁄8-in., and 1-in. diameter are usually preferred. Diameters above one inch are not commonly available, nor are they practical since special tools may be required to achieve fully tensioned installation. Bearing-type connections should be specified whenever possible. Slip-critical connections with coatings other than clean mill scale incur appreciable extra costs associated with blasting, painting, drying, assembling, reblasting, and abrasion touch-up. If slipcritical connections are required for the proper serviceablity of the structure, care should be taken to avoid requiring the faying surfaces to be masked as this also contributes great AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BOLTED CONSTRUCTION
8-9
expense; coatings which provide a Class A or Class B slip coefficient may be an economical alternative to masking. Dimensions and Weights
ASTM A325 and A490 bolts, A563 nuts, and F436 washers are given identifying marks as illustrated in Figure 8-2. A detailed description of identifying marks may be found in the RCSC Specification. Dimensions of ASTM A325 and A490 bolts, A563 nuts, and F436 washers are given and illustrated in Table 8-2. Threading dimensions of highstrength bolts are given in Table 8-7. Weights of conventional ASTM A325 and A490 bolts, A563 nuts, and F436 washers are given in Table 8-3. For dimensions and weights of tension-control ASTM A325 and A490 bolts, refer to manufacturers’ literature or IFI. For dimensions and weights of ASTM A449 bolts, refer to Table 8-6. Threads for high-strength bolts may be rolled or cut. Note that thread lengths for high-strength bolts are shorter than those for non-high-strength bolts. This allows the threads to be excluded from the shear plane when the thickness of the connected ply closest to the nut is as shown in Figure 8-3. While the RCSC Specification permits some thread run-out into the shear plane, it is important to provide sufficient thread to avoid jamming the nut into the run-out when tightening the bolt. Inspection controversy will be reduced by recognizing that bolts intentionally have a limited thread length, a manufacturing tolerance, and limited length increments; as with all manufactured items, dimensional tolerances must be considered. The RCSC Specification recognizes these tolerances in two ways. First, additional washers are permitted to be used under the nut or under the head when circumstances permit. Second, there is no specified bolt “stick-through” requirement since only fullthread engagement of the nut is required; from RCSC Specification Section 2(b), “…The length of bolts shall be such that the end of the bolt will be flush with or outside the face of the nut when properly installed.” A requirement for “stick-through”, sometimes written in project specifications, increases the risk of jamming the nut on the thread run-out, and thus, of preventing tightening. A “stick-through” requirement will not enhance the performance of the bolt and should not be included in a project specification. Alternatively, ASTM A325 bolts with length less than or equal to four times the nominal diameter may be ordered as fully threaded with the designation ASTM A325 T. Fully threaded ASTM A325 T bolts are not for use in bearing-type X connections since it would be impossible to exclude the threads from the shear plane. While this supplementary provision exists for ASTM A325 bolts, there is no similar supplementary provision made in ASTM A490 for full-length threading. The ordered length of ASTM A325 and A490 bolts should be calculated as the grip (see Figure 8-2) plus the thickness of the washer(s) plus the allowance from Table 8-2. A thickness of 5⁄32-in. for circular washers and 5⁄16-in. for beveled washers should be provided per washer used; refer to the RCSC Specification for washer requirements. This total should be rounded to the next higher one-quarter inch. Note that bolts longer than five inches are generally available only in 1⁄2-in. increments, except by special arrangement with the manufacturer or vendor. While longer lengths may be ordered, an 8-in. length is generally the maximum stock length available. Clipped washers are available for use in areas of tight clearance.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Type 1
Type 3*
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
HARDENED WASHER (Beveled) 2
12
3
Hex head
Marking for washer used with Type 3 bolt
ASTM A490 BOLT
Grip
ASTM A325 BOLT
Washer face
Type 1 NUT MARKING
Type 3*
3
Alt. marking “D” or “DH” for type 1 “DH3” for Type 3
Nut marking “DH” for Type 1 “DH3” for Type 3
X
*Bolt heads, nuts, & washers shall include manuf. identification symbol. The manuf. may also add other marks indicating weathering grade.
X Hex Nut* Type 1 and 3*
See RCSC Specification for rules governing use of hardened washers
Hex nut
Standard marking indicates Grade C
Fig. 8-2. Identifying high-strength bolts, nuts, and washers.
HARDENED* WASHER (Plain)
Type 1
Type 3* Optional Clip
A490
A490
Standard bolt marking
BOLT HEAD MARKING
A325
A325
Three radial lines @ 120°, optional
See RCSC Specification for rules governing use of washers Grip
Dia. Dia.
8 - 10 BOLTS, WELDS, AND CONNECTED ELEMENTS
BOLTED CONSTRUCTION
8 - 11
Table 8-2. Dimensions of High-Strength Fasteners, in. E I.D.
Thread Length
O.D.
T
A325 E I.D.
H
F
Bolt Length
H W Nut may be chamfered on both faces
A T
A
Nominal Bolt Diameter, in.
A563 Nutsb
A325 and A490 Boltsa
Measurement Width Across Flats F Height H Thread Length Bolt Lengthf =Grip + → Width Across Flats W Height H
F436 Square or Rect. Washersc,e
F436 Circular Washersc
Nom. Outside Diameter OD
a b c
d e f
Nom. Inside Diameter ID Thckns. T
1⁄ 2
5⁄ 8
3⁄ 4
7⁄ 8
7⁄
11 ⁄16
11 ⁄4
16
25 ⁄
15 ⁄
1
11 ⁄4
13 ⁄8
11 ⁄2
13 ⁄4
2
2
21 ⁄4
21 ⁄4
7⁄
1
11 ⁄8
11 ⁄4
11 ⁄2
15 ⁄8
13 ⁄4
17 ⁄8
5⁄
11⁄
8
16
7⁄ 31 ⁄
64
8
32
1
1 1 ⁄8
17 ⁄16
15 ⁄8
113 ⁄16
35 ⁄
39 ⁄
64
64
11⁄
16
1 1 ⁄4
1 3 ⁄8
2
23⁄16
23 ⁄8
27 ⁄
15 ⁄
25 ⁄
32
32
1 1 ⁄2
16
8
11 ⁄16
11 ⁄4
17 ⁄16
15 ⁄8
113 ⁄16
2
23⁄16
23 ⁄8
64
39 ⁄
47 ⁄
55 ⁄
64
63 ⁄
17⁄64
17⁄32
111⁄32
115 ⁄32
13 ⁄4
2
21 ⁄4
21 ⁄2
23 ⁄4
3
11 ⁄8
11 ⁄4
13 ⁄8
11 ⁄2
15 ⁄8
64
11 ⁄16
15 ⁄16
17 ⁄
11⁄
32
16
64
115 ⁄32 13 ⁄
16
15 ⁄
16
64
Max.
0.097
0.122
0.122
0.136
0.136
0.136
0.136
0.136
0.136
Min.
0.177
0.177
0.177
0.177
0.177
0.177
0.177
0.177
0.177
1
1 3⁄32
17⁄32
15⁄16
Min. Edge Distance E d
7⁄
Min. Side Dimension A
13⁄4
13 ⁄4
13 ⁄4
13 ⁄4
13 ⁄4
21 ⁄4
21 ⁄4
21 ⁄4
21 ⁄4
5⁄
5⁄
5⁄
5⁄
5⁄
5⁄
5⁄
5⁄
5⁄
Mean Thckns. T Taper in Thickness Min. Edge Distance E d
16
16
2:12 7⁄
16
9⁄
16
16
2:12 9⁄
16
21 ⁄
32
16
25 ⁄
32
16
2:12
2:12
21 ⁄
25 ⁄
32
32
7⁄
8
16
2:12 7⁄
8
16
16
16
16
2:12
2:12
2:12
2:12
1
13⁄32
17⁄32
15⁄16
Tolerances as specified in ASTM A325 and A490. Tolerances as specified in ASTM A563. ASTM F436 Washer Tolerances, in.: Nominal Outside Diameter Nominal Diameter of Hole Flatness: max. deviation from straight-edge placed on cut side shall not exceed Concentricity: center of hole to outside diameter (full indicator runout) Burr shall not project above immediately adjacent washer surface more than For clipped washers only. For use with American standard beams (S) and channels (C). Tabular value does not include thickness of washer(s).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
−1/32; +1/32 −0; +1/32 0.010 0.030 0.010
8 - 12
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-3. Weights of High-Strength Fasteners, pounds per 100 count Nominal Bolt Diameter, in. 1⁄ 2
5⁄ 8
3⁄ 4
7⁄ 8
1
1 1 ⁄8
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
1 11 ⁄4 11 ⁄2 13 ⁄4
16.5 17.8 19.2 20.5
29.4 31.1 33.1 35.3
47.0 49.6 52.2 55.3
— 74.4 78.0 81.9
— 104 109 114
— — 148 154
— — 197 205
— — — 261
— — — 333
2 21 ⁄4 21 ⁄2 23 ⁄4
21.9 23.3 24.7 26.1
37.4 39.8 41.7 43.9
58.4 61.6 64.7 67.8
86.1 90.3 94.6 98.8
119 124 130 135
160 167 174 181
212 220 229 237
270 279 290 300
344 355 366 379
3 31 ⁄4 31 ⁄2 33 ⁄4
27.4 28.8 30.2 31.6
46.1 48.2 50.4 52.5
70.9 74.0 77.1 80.2
103 107 111 116
141 146 151 157
188 195 202 209
246 255 263 272
310 321 332 342
391 403 416 428
4 41 ⁄4 41 ⁄2 43 ⁄4
33.0 34.3 35.7 37.1
54.7 56.9 59.0 61.2
83.3 86.4 89.5 92.7
120 124 128 133
162 168 173 179
216 223 230 237
280 289 298 306
353 363 374 384
441 453 465 478
5 51 ⁄4 51 ⁄2 53 ⁄4
38.5 39.9 41.2 42.6
63.3 65.5 67.7 69.8
95.8 98.9 102 105
137 141 146 150
184 190 196 201
244 251 258 265
315 324 332 341
395 405 416 426
490 503 515 527
6 61 ⁄4 61 ⁄2 63 ⁄4
44.0 — — —
71.9 74.1 76.3 78.5
108 111 114 118
154 158 163 167
207 212 218 223
272 279 286 293
349 358 367 375
437 447 458 468
540 552 565 577
7 71 ⁄4 71 ⁄2 73 ⁄4
— — — —
80.6 82.8 84.9 87.1
121 124 127 130
171 175 179 183
229 234 240 246
300 307 314 321
384 392 401 410
479 489 500 510
589 602 614 626
8 81 ⁄4 81 ⁄2 83 ⁄4
— — — —
89.2 — — —
133 — — —
187 192 196 —
251 257 262 —
328 335 342 —
418 427 435 444
521 531 542 552
639 651 664 676
9
—
—
—
—
—
—
453
563
689
100, Conventional A325 or A490 Bolts with A563 Nuts
Bolt Length, in.
Per inch add’tl. add
5.5
8.6
12.4
16.9
22.1
28.0
34.4
42.5
49.7
100, F436 Circular Washers
2.1
3.6
4.8
7.0
9.4
11.3
13.8
16.8
20.0
100, F436 Square Washers
23.1
22.4
21.0
20.2
19.2
34.0
31.6
31.2
32.9
This table conforms to weight standards adopted by the Industrial Fasteners Institute (IFI), updated for washer weights.
Entering and Tightening Clearances
The assembly of high-strength bolted connections requires clearance for entering and tightening the bolts with an impact wrench. The clearance requirements for conventional high-strength bolts are as given in Table 8-4. When high-strength tension-control bolts are specified, the entering and tightening clearances are as specified in Table 8-5. Snug-Tightened and Fully Tensioned Installation
When subjected to shear only, high-strength bolts may be used in snug-tightened bearing-type, fully tensioned bearing-type, and slip-critical connections. When subjected AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BOLTED CONSTRUCTION
8 - 13
Table 8-4. Entering and Tightening Clearances, in. Conventional ASTM A325 and A490 Bolts Aligned Bolts
C2
socket H1 C1
Nominal Bolt Dia., Socket in. Dia., in.
H2 C1 C1
5⁄ 8 3⁄ 4 7⁄ 8
H2
1
C3
11⁄
8
fillet
11⁄
4
1 3 ⁄8 1 1 ⁄2
13 ⁄4 21 ⁄4 21 ⁄2 25 ⁄8 27 ⁄8 31 ⁄8 31 ⁄4 31 ⁄2
C3 H1 25 ⁄
15 ⁄ 35 ⁄ 39 ⁄ 11⁄
64 32 64 64
16 25 ⁄ 32 27 ⁄ 32 15 ⁄ 16
H2
C1
11 ⁄4 13 ⁄8 11 ⁄2 15 ⁄8 17 ⁄8 2 21 ⁄8 21 ⁄4
1 11 ⁄4 13 ⁄8 17 ⁄16 19 ⁄16 111⁄16 13 ⁄4 15 ⁄16
C2 11⁄
16 3⁄ 4 7⁄ 8 15 ⁄ 16 1 1 ⁄16 1 1 ⁄8 11 ⁄4 15 ⁄16
Circular Clipped 11⁄
16 3⁄ 4 7⁄ 8
9⁄ 16 11⁄ 16 13 ⁄ 16 7⁄ 8
1 11 ⁄8 11 ⁄4 13 ⁄8 11 ⁄2
1 11 ⁄8 11 ⁄4 15 ⁄16
Staggered Bolts Stagger P, in. Nominal Bolt Diameter, in.
F
5⁄ 8
3⁄ 4
7⁄ 8
1
1 1 ⁄8 1 1 ⁄4 1 3 ⁄8
15 ⁄8 11 ⁄2 11 ⁄2 17 ⁄16
115 ⁄16 17 ⁄8
23 ⁄16
11⁄
11 ⁄
113 ⁄
2
C1 P
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
2
2 1 ⁄8 2 1 ⁄4 2 3 ⁄8 2 1 ⁄2 2 5 ⁄8 2 3 ⁄4 2 7 ⁄8
F
3
3 1 ⁄8 3 1 ⁄4 3 3 ⁄8
C1 = tightening clearance
4
11 ⁄4 13 ⁄16 11 ⁄8 1
13 ⁄
16
16
13 ⁄4 111⁄16 19 ⁄16 11 ⁄
2
13 ⁄8 11 ⁄4 11 ⁄8 7⁄
8
1
11⁄8
11⁄4
1 3 ⁄8
1 1 ⁄2
21 ⁄8 21 ⁄16 2 115 ⁄16
25 ⁄16 25 ⁄16 21 ⁄4 23 ⁄16
29 ⁄16 29 ⁄16 21 ⁄2
213 ⁄16 23 ⁄4
3 3
33 ⁄4
113 ⁄
21 ⁄
27 ⁄
16
8
16
215 ⁄16 27 ⁄8 213 ⁄16
31 ⁄4 33 ⁄16 33 ⁄16 31 ⁄8
27 ⁄16 25 ⁄16 21 ⁄8 21 ⁄16
23 ⁄4 27 ⁄8 21 ⁄2 23 ⁄8
31 ⁄16 3 27 ⁄8 213 ⁄16
2 17 ⁄8 13 ⁄4 15 ⁄8
21 ⁄4 21 ⁄8 2 115 ⁄16
211⁄16 21 ⁄2 23 ⁄8 21 ⁄4
13 ⁄8 11 ⁄16
13 ⁄4 19 ⁄16 15 ⁄16
21 ⁄8 2 17 ⁄8 11 1 ⁄16
4
111⁄16 19 ⁄16 11 ⁄2
2 17 ⁄8 13 ⁄4
23 ⁄8 21 ⁄4 21 ⁄8
211⁄16 25 ⁄8 21 ⁄2
13 ⁄8 13 ⁄16
15 ⁄8 11 ⁄2 13 ⁄8 13 ⁄16
2 115 ⁄16 17 ⁄8 13 ⁄4
7⁄
15 ⁄8 11 ⁄2 11 ⁄4
15 ⁄
16
8
15 ⁄
16
31⁄
2
standard socket
23 ⁄
3 5 ⁄8 3 3 ⁄4 3 7 ⁄8
4 Notes: H1 = height of head, in. H2 = maximum shank extension,* in. C1 = clearance for tightening, in. C2 = clearance for entering, in. C3 = clearance for fillet,* in. P = bolt stagger, in. F = clearance for tightening staggered bolts, in. *Based on one standard hardened washer.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
215 ⁄
16
13 ⁄8
8 - 14
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-5. Entering and Tightening Clearances, in. Tension-Control ASTM A325 and A490 Bolts Aligned Bolts Nominal Bolt Dia, in.
Tools
C3 H1
3⁄ 4 7⁄ 8
C1
H2
1
1
2 /2
C1
C2
Circular Clipped
2
16 5⁄ 8
13 ⁄8 11 ⁄2 13 ⁄4
17 ⁄8 17 ⁄8 17 ⁄8
7⁄
8
1 11 ⁄8
3⁄
7⁄
4 8
1
— — —
2 1 ⁄2-in. Diameter Critical
2 3⁄ 4 7⁄ 8
1 C3
1⁄
9⁄
1⁄
9⁄
2
16 5⁄ 8
Small Tools
fillet
13 ⁄8 11 ⁄2 13 ⁄4
13 ⁄8 13 ⁄8 13 ⁄8
7⁄
8
1 11 ⁄8
3⁄
7⁄
4 8
1
— — —
3-in. Diameter Critical 5⁄ 8 3⁄ 4 7⁄ 8
3
21/2 2
C2
H2 C1
1 1 1 /2 3 /8
33/8
H1 C1
H2
3 3 ⁄8-in. Diameter Critical
Large Tools
7⁄
16 1⁄ 2 9⁄ 16
11 ⁄4 13 ⁄8 11 ⁄2
15 ⁄8 15 ⁄8 15 ⁄8
13 ⁄ 7⁄
16 8
1
11⁄
— — —
11⁄
— — —
16 3⁄ 4 7⁄ 8
2 3 ⁄16-in. Diameter Critical
3 2 /16
5⁄ 8 3⁄ 4 7⁄ 8
2
7⁄
16 1⁄ 2 9⁄ 16
11 ⁄4 13 ⁄8 11 ⁄2
11 ⁄8 11 ⁄8 11 ⁄8
13 ⁄ 7⁄
16 8
1
16 3⁄ 4 7⁄ 8
Staggered Bolts Stagger P, in. Nominal Bolt Diameter, in. C1
F
5⁄ 8
11⁄
4
113 ⁄
3⁄ 4
7⁄ 8
1
2
111⁄
21 ⁄16
21 ⁄4
27 ⁄16
19 ⁄16 11 ⁄2 17 ⁄16
2 17 ⁄8 13 1 ⁄16 13 ⁄4
23 ⁄
21 ⁄16 2 17 ⁄8
23 ⁄8 21 ⁄4 23 ⁄16 21 ⁄8
2
15 ⁄16 11 ⁄4 13 ⁄16 11 ⁄8
15 ⁄8 19 ⁄16 11 ⁄2 13 ⁄8
13 ⁄4 111⁄16 19 ⁄16 11 ⁄2
2 115 ⁄16 17 ⁄8 13 ⁄4
2 1 ⁄2 2 5 ⁄8 2 3 ⁄4 2 7 ⁄8
1
15 ⁄16 13 ⁄16 11 ⁄8
13 ⁄8 15 ⁄16 13 ⁄16 11 ⁄8
111⁄16 19 ⁄16 11 ⁄2 13 ⁄8
1 3 ⁄8 11⁄
P
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8 2 1 ⁄8 2 1 ⁄4 2 3 ⁄8
F
C1 = tightening clearance
installation tool
16
13 ⁄4
3
3 3 ⁄8
16
16
15 ⁄16 15 ⁄16
Notes: H1 = height of head, in. H2 = maximum shank extension,* in. C1 = clearance for tightening, in. C2 = clearance of entering, in. C3 = clearance for fillet,* in. P = bolt stagger, in. F = clearance for tightening staggered bolts, in. *Based on one standard hardened washer.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BOLTED CONSTRUCTION
8 - 15
to tension or combined shear and tension, high-strength bolts must be used in fully tensioned bearing-type or slip-critical connections. Bearing-type connections are typically used for shear, moment, and diagonal bracing connections in buildings. Bolts in bearing-type connections are installed in the snug-tightened condition unless required in LRFD Specification Section J1.11 to be fully tensioned. Note that bolts in bearing-type connections required to be fully tensioned must not be confused with fully tensioned bolts in slip-critical connections. Fully tensioned bolts in bearing-type connections have no requirements regarding the slip resistance of the contact surfaces. Thus, painted surfaces in fully tensioned bearing-type connections need not meet the slip resistance requirements of slip-critical connections. Slip-critical connections are used when slip would be detrimental to the serviceability of the structure; this is essentially fatigue related and is primarily of concern in bridge design. From LRFD Specification Section K3, “The occurrence of full design wind or earthquake loads is too infrequent to warrant consideration in fatigue design.” Consequently, slip-critical connections are not normally required or used for wind or seismic loading in buildings. Slip-critical shear connections are required, however, in applications such as those involving oversized holes, fatigue loading, or in craneway and bridge connections. High-strength bolts in slip-critical connections are always fully tensioned to resist slip on the faying surface(s) of the connection. While faying surfaces in slip-critical connections are not normally painted, painted surfaces in accordance with RCSC Specification Section 3(b) are permitted. When subjected to tension only or combined shear and tension, high-strength bolts must be used in fully tensioned bearing-type or slip-critical connections. Examples of these applications are hanger connections, extended end-plate FR moment connections, and diagonal bracing connections. Fully tensioned bolts in bearing-type or slip-critical connections must meet the minimum tensioning requirements for ASTM A325 and A490 bolts as specified in Table 4 of the RCSC Specification. Fully tensioned bolts in either case may be tightened by the same methods. The methods approved by the RCSC are: (1) turn-of-nut method; (2) calibrated wrench method; (3) alternative design bolt method; and, (4) direct tension indicator method. It is important to note that the RCSC prohibits the use of any published relationship between torque and tension. Inspection of Fully Tensioned High-Strength Bolts
When a joint with fully tensioned high-strength bolts is assembled, the RCSC Specification requires that all joint surfaces, including surfaces adjacent to the bolt head and nut be free of scale, except tight mill scale, and of dirt or other foreign material. Burrs need not be removed unless they prevent solid seating of the connected parts in the snug-tightened condition. ASTM A6 lists tolerances for straightness and flatness. These tolerances can prevent the faying surfaces from sufficiently contacting in medium- to large-size connections. Section C8 of the Commentary on the RCSC Specification states: “…Even after being fully tightened, some thick parts with uneven surfaces may not be in contact over the entire faying surface. In itself, this is not detrimental to the performance of the joint. As long as the specified bolt tension is present in all bolts of the completed connection, the clamping force equal to the total of the tensions in all bolts will be transferred at the locations that are in contact and be fully effective in resisting slip through friction.” AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 16
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-6. Dimensions of Non-High-Strength Bolts and Nuts, in. F
db
db
H Square
Bolt Dia. d b, in. 1⁄ 4 3⁄ 8
C, in. 1⁄ 2
78
Hex
H Countersunk
Heavy Hex
C
Countersunk Min. Thrd. Length, in.
H, in. C, in. H, in. L ≤ 6 in. L > 6 in.
H, in.
F, in.
C, in.
H, in.
F, in.
C, in.
3⁄ 16 1⁄ 4 5⁄ 16 7⁄ 16 1⁄ 2 5⁄ 8 11⁄ 16 3⁄ 4 7⁄ 8 15⁄ 16
7⁄ 16 9⁄ 16 3⁄ 4 15⁄ 16 1 1 ⁄8 5 1 ⁄16 11⁄2 111⁄16 17⁄8 21⁄16 21⁄4 25⁄8
1⁄ 2 5⁄ 8 7⁄ 8 1 1 ⁄16 5 1 ⁄16 11⁄2 13⁄4 115⁄16 23⁄16 23⁄8 25⁄8
3⁄ 16 1⁄ 4 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 11⁄ 16 3⁄ 4 7⁄ 8 15⁄ 16
— —
— —
— —
7⁄ 8 11⁄16 1 1 ⁄4 17⁄16
1 11⁄4 7 1 ⁄16 111⁄16
3⁄ 8 11⁄8 1⁄ 2 9⁄ 16
15⁄8 113⁄16 2 23⁄16
17⁄8 21⁄16 25⁄16 21⁄2
11⁄
16 3⁄ 4 7⁄ 8 15⁄ 16
3 33⁄8
3 37⁄16 37⁄8
1 13⁄16 13⁄8 11⁄2
23⁄8 23⁄4 31⁄8 31⁄2
23⁄4 33⁄16 35⁄8 41⁄16
1 13⁄16 13⁄8 11⁄2
1⁄ 2 11⁄ 16 7⁄ 8 11⁄8 3 1 ⁄8 19⁄16 113⁄16 21⁄16 21⁄4 21⁄2 211⁄16
1⁄ 8 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4
— — —
3⁄ 4
1
1 11⁄4
11⁄4 11⁄2 13⁄4 2
11⁄2 13⁄4 2 21⁄4
21⁄4 21⁄2 23⁄4 3
21⁄2 23⁄4 3 31⁄4
— — —
31⁄4 33⁄4 41⁄4 43⁄4
31⁄2 4 41⁄2 5
3⁄ 4 15⁄ 16 1 1 ⁄8 5 1 ⁄16 11⁄2 111⁄16 17⁄8 21⁄16 21⁄4
13⁄ 16 11⁄16 5 1 ⁄16 19⁄16 17⁄8 21⁄8 23⁄8 25⁄8 215⁄16 33⁄16
— — —
— — —
1 — — —
21⁄2 23⁄4
— —
— —
— —
33⁄4 41⁄8
45⁄16 43⁄4
111⁄16 113⁄16
37⁄8 41⁄4
41⁄2 415⁄16
111⁄16 113⁄16
— —
— —
51⁄4 53⁄4
51⁄2 6
3 31⁄4
— —
— —
— —
41⁄2 47⁄8
53⁄16 55⁄8
2 23⁄16
45⁄8 —
55⁄16 —
2 —
— —
— —
6 6
61⁄2 7
31⁄2 33⁄4
— —
— —
— —
51⁄4 55⁄8
61⁄16 61⁄2
25⁄16 21⁄2
— —
— —
— —
— —
— —
6 6
71⁄2 8
4
—
—
—
6
615⁄16
211⁄16
—
—
—
—
—
6
81⁄2
1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8
Bolts
Square
F, in. 3⁄ 8 9⁄ 16
db
C
H F Hex, Heavy Hex
C
1 11⁄8 11⁄4 13⁄8 11⁄2 13⁄4 2 21⁄4
W
C N C Square, Heavy Square
Nuts
Nut Size, in.
Square
W, in. C, in.
1⁄ 4 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8
7⁄ 16 5⁄ 8 4⁄ 5
1 11⁄8 5 1 ⁄16
1 11⁄8 11⁄4 13⁄8
11⁄2 111⁄16 17⁄8 21⁄16
11⁄2 13⁄4
21⁄4 —
2 21⁄4
5⁄ 8 7⁄ 8 11⁄8 17⁄16 19⁄16 17⁄8 21⁄8 23⁄8 25⁄8 215⁄16 33⁄16
Hex, Heavy Hex
Hex
N, in. W, in. C, in. 1⁄ 4 5⁄ 16 7⁄ 16 9⁄ 16 11⁄ 16 3⁄ 4 7⁄ 8
1 11⁄8 11⁄4
7⁄ 16 9⁄ 16 3⁄ 4 15⁄ 16 11⁄8 15⁄16 11⁄2 111⁄16 17⁄8 21⁄16 21⁄4
1⁄ 2 5⁄ 8 7⁄ 8 11⁄16 15⁄16 11⁄2 13⁄4 115⁄16 23⁄16 23⁄8 25⁄8
—
N
W
Heavy Square
N, in. W, in. C, in. 3⁄ 16 1⁄ 4 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 11⁄ 16 3⁄ 4 7⁄ 8 15⁄ 16
1⁄ 2 11⁄ 16 7⁄ 8 11⁄16 11⁄4 17⁄16 15⁄8 113⁄16
—
11⁄
11⁄4 11⁄2 13⁄4 21⁄16
1⁄ 4 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8
2 23⁄16
25⁄16 29⁄16 213⁄16 31⁄8
1 11⁄8 11⁄4 13⁄8
1 —
23⁄8 —
33⁄8 —
16
1
Heavy Hex
N, in. W, in. C, in. 1⁄ 2 11⁄ 16 7⁄ 8 11⁄16 11⁄4 17⁄16 15⁄8 113⁄16
9⁄ 16 13⁄ 16
N, in.
1 11⁄4 17⁄16 111⁄16
1⁄ 4 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8
2 23⁄16
17⁄8 21⁄16 25⁄16 21⁄2
1 11⁄8 11⁄4 13⁄8
11⁄2 —
23⁄8 23⁄4
23⁄4 33⁄16
11⁄2 13⁄4
—
15⁄16 —
— —
— —
— —
— —
— —
— —
— —
— —
— —
31⁄8 31⁄2
35⁄8 41⁄16
2 23⁄16
21⁄2 23⁄4
— —
— —
— —
— —
— —
— —
— —
— —
— —
37⁄8 41⁄4
41⁄2 415⁄16
27⁄16 211⁄16
3 31⁄4
— —
— —
— —
— —
— —
— —
— —
— —
— —
45⁄8 5
55⁄16 53⁄4
215⁄16 33⁄16
31⁄2 33⁄4
— —
— —
— —
— —
— —
— —
— —
— —
— —
53⁄8 53⁄4
63⁄16 65⁄8
37⁄16 311⁄16
4
—
—
—
—
—
—
—
—
—
61⁄8
71⁄16
315⁄16
Notes: For high-strength bolt and nut dimensions, refer to Table 8-2. Square, hex, and heavy hex bolt dimensions, rounded to nearest 1⁄16-in., are in accordance with ANSI B18.2.1. Countersunk bolt dimensions, rounded to the nearest 1⁄16-in., are in accordance with ANSI 18.5. Minimum thread length = 2db + 1⁄4-in. for bolts up to 6-in. long, and 2db + 1⁄2-in. for bolts longer than 6-in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BOLTED CONSTRUCTION
8 - 17
Table 8-7. Threading Dimensions for High-Strength and Non-High-Strength Bolts, in. SCREW THREADS Unified Standard Series-UNC/UNRC and 4UN/4UNR ANSI B1.1 Nominal size (basic major dia.) No. threads per inch (n)
H=0.866P
H /8
P/ 8
P
Thread series symbol c
Thread class symbol
60°
5/ 8H
H /4
Left hand thread. No symbol req’d for right hand thread.
db
P/ 4
K
3/ 4
- 10 UNC 2A LH
Thread Dimensions
Standard Designations
Diameter
Area
Bolt Diameter db, in.
Min. Root K, in.
Gross Bolt Area, in.2
Min. Root Area, in.2
Net Tensile Area, in.2 a
Threads per inch, n b
1⁄ 4 3⁄ 8
0.189 0.298
0.049 0.110
0.029 0.070
0.032 0.078
20 16
1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8
0.406 0.514 0.627 0.739
0.196 0.307 0.442 0.601
0.129 0.207 0.309 0.429
0.142 0.226 0.334 0.462
13 11 10 9
1 11⁄8 11⁄4 13⁄8
0.847 0.950 1.08 1.17
0.785 0.994 1.23 1.49
0.563 0.709 0.908 1.08
0.606 0.763 0.969 1.16
8 7 7 6
11⁄2 13⁄4
1.30 1.51
1.77 2.41
1.32 1.78
1.41 1.90
6 5
2 21⁄4
1.73 1.98
3.14 3.98
2.34 3.07
2.50 3.25
41⁄2 41⁄2
21⁄2 23⁄4
2.19 2.44
4.91 5.94
3.78 4.69
4.00 4.93
4 4
3 31⁄4
2.69 2.94
7.07 8.30
5.70 6.80
5.97 7.10
4 4
31⁄2 33⁄4
3.19 3.44
9.62 11.0
8.01 9.31
8.33 9.66
4 4
4
3.69
12.6
10.7
11.1
Notes:
aNet tensile area = 0.785 + d b
2
−
0.9743
n
bFor diameters listed, thread series is UNC (coarse). For larger diameters, thread series is 4UN. c2A denotes Class 2A fit applicable to external threads; c2B denotes corresponding Class 2B fit for internal threads.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4
8 - 18
BOLTS, WELDS, AND CONNECTED ELEMENTS
It should be noted that, even when bolts in bearing-type connections are required to be fully tensioned, high bolt tension is not normally required for proper connection performance. Thus, a significant reduction in inspection costs will be achieved by relying on visual inspection of the bolt head or nut to note the peening marks signifying that the tightening wrench was applied. From RCSC Specification Commentary Section C9, “It is apparent from the commentary on installation procedures that the inspection procedures giving the best assurance that bolts are properly installed and tensioned is provided by inspector observation of the calibration testing of the bolts using the selected installation procedure followed by monitoring of the work in progress to assure that the procedure which was demonstrated to provide the specified tension is routinely adhered to. When such a program is followed, no further evidence of proper bolt tension is required.” Galvanizing High-Strength Bolts
Galvanizing provides corrosion protection by applying zinc as a sacrificial metal to protect the base metal. As previously stated, ASTM A325 Type 1 high-strength bolts and A449 bolts are permitted to be galvanized; A490 bolts are not permitted to be galvanized. There are two methods of galvanizing: hot-dip galvanizing and mechanical galvanizing. Hot-dip galvanizing is a process whereby the bolt is dipped in molten zinc and spun in a centrifuge to remove the excess. This process is described in detail in ASTM A153. In contrast, mechanical galvanizing utilizes a combination of powdered zinc, chemicals, and water with the bolts in a spun hopper. As result of collisions between the bolts, zinc, and glass beads, the zinc is cold-welded to the surface of the bolts. This process is described in detail in ASTM B695. For more information, refer to AISC (1993).
Grip
Ply or plies closest to bolt head
Ply closest to nut
Nominal bolt diameter d b, in.
Min. thickness t of ply closest to nut to exclude threads from shear plane, in.*
3⁄ 4
1⁄ 4
7⁄ 8
1⁄ 4
1
3⁄ 8 5⁄ -in. 32
*Values shown assume one thick washer is present. If washer is not present, increase minimum thickness by 1⁄8-in.
Shear plane
stick-through 5/ 32
t Value from RCSC specification table C2
Fig. 8-3. Minimum thickness of ply closest to nut to exclude threads from shear plane. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BOLTED CONSTRUCTION
8 - 19
Reuse of High-Strength Bolts
From RCSC Specification Section 8f, ASTM A490 bolts and galvanized ASTM A325 bolts shall not be reused. Other A325 bolts are permitted to be reused if approved by the engineer of record. A simple rule based on the prevention of excessive plastic deformation of the bolt is that non-galvanized A325 bolts are satisfactory for reuse, regardless of previous use, if the nut can be placed on the threads and run down the full length of the thread by hand (AISC, 1988). Kulak, et al. (1987) recommends that non-galvanized ASTM A325 bolts may be reused once or twice, provided that proper control on the number of reuses can be established; adequate nut rotation capacity will be present as long as there is some lubricant on the bolt. This lubricant can be the original lubrication or oil, grease, or wax, or a lubricant that is added later. For a detailed assessment of the performance of repetitively tightened high-strength bolts, refer to Bowman and Betancourt (1991). Non-High-Strength Bolts
LRFD Specification Section A3.3 permits the use of ASTM A307 non-high-strength bolts for structural applications not requiring fully tensioned installation, that is, snug-tightened bearing-type connections. ASTM A307 bolts are available with both hex and square heads in diameters from 1⁄4-in. to four inches in two grades: Grade A for general applications and Grade B for cast-iron-flanged piping joints. ASTM A563 Grade A nuts are recommended for use with ASTM A307 bolts. Other suitable grades are listed in ASTM A563 Table X1.1. Dimensions and Weights
Typical non-high-strength bolt head and nut dimensions are given in Table 8-6. Thread lengths listed in this table may be calculated for non-high-strength bolts as 2db + 1⁄4-in. for bolts up to six inches long and 2db + 1⁄2-in. for bolts over six inches long, where db is the bolt diameter. Note that these thread lengths are longer than those given previously for high-strength bolts in Table 8-2. Threading dimensions are given in Table 8-7. Weights of non-high-strength bolts are given in Tables 8-8, 8-9, and 8-10. Entering and Tightening Clearances
As with high-strength bolts, clearance is required for entering and tightening the bolts with an impact wrench. The required clearances are the same as those given for high-strength bolts in Table 8-4. Design Strength of Bolts
The design strength of bolts is determined in accordance with the provisions of LRFD Specification Section J3. LRFD Specification requirements are based upon the provisions of the RCSC Specification. For bolts in bearing-type connections subjected to shear only, the limit states of bolt shear strength and bearing strength at bolt holes must be checked. For bolts in bearingtype connections subjected to tension only, the limit state of bolt tensile strength, including the effect of prying action, must be checked. For bolts in bearing-type connections subjected to combined shear and tension, the limit states of bolt tensile strength, including the effects of both the bolt shear stress present and prying action, and bearing strength at bolt holes must be checked. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 20
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-8. Weights of Non-High-Strength Fasteners, pounds Bolt Length, in.
3⁄ 8
1⁄ 2
5⁄ 8
3⁄ 4
7⁄ 8
1 1 ⁄8
1 1 ⁄4
— — — —
— — — —
104 109 114 119
143 149 155 161
— — 206 213
90.2 94.4 98.5 103
124 129 135 140
168 174 181 188
221 229 237 246
73.3 76.3 79.3 82.3
107 111 115 119
145 151 156 162
195 202 208 215
254 262 271 279
56.5 58.6 60.7 62.8
85.3 88.4 91.4 94.4
123 127 131 136
167 172 178 183
222 229 236 242
288 296 304 313
39.3 40.4 41.8 43.1
64.9 66.7 68.7 70.8
97.4 100 103 106
140 143 147 151
188 193 198 204
249 255 262 269
321 329 337 345
24.0 24.8 25.5 26.3
44.4 45.8 47.1 48.5
72.9 75.0 77.1 79.2
109 112 115 118
156 160 164 168
209 214 220 225
275 282 289 296
354 362 371 379
11.7 — — —
27.0 28.6 30.1 31.6
49.8 52.5 55.2 57.9
81.3 85.5 89.7 93.9
121 127 133 139
172 180 189 197
231 241 252 263
303 316 330 343
387 404 421 438
10
— —
66.1 34.6
60.6 63.3
98.1 102
145 151
205 213
274 284
357 371
454 471
11
— —
36.2 37.7
66.0 68.7
106 110
157 163
221 230
295 306
384 398
488 505
12
— —
39.2 —
71.3 74.0
115 119
170 176
238 246
316 327
411 425
522 538
13
— —
— —
76.7 79.4
123 127
182 188
254 263
338 349
439 452
556 572
14
— —
— —
82.1 84.8
131 135
194 200
271 279
359 370
466 479
589 605
15 1 ⁄2
15
— —
— —
87.5 90.2
140 144
206 212
287 296
381 392
493 507
622 639
16
—
—
92.9
148
218
304
402
520
656
Per inch add’tl. add
1.3
3.0
5.4
1
2.38 2.71 3.05 3.39
6.11 6.71 7.47 8.23
13.0 14.0 15.1 16.5
24.1 25.8 27.6 29.3
38.9 41.5 44.0 46.5
— — 67.3 70.8
2
3.73 4.06 4.40 4.74
8.99 9.75 10.5 11.3
17.8 19.1 20.5 21.8
31.4 33.5 35.6 37.7
49.1 52.1 55.1 58.2
74.4 77.9 82.0 86.1
3
5.07 5.41 5.75 6.09
12.0 12.8 13.5 14.3
23.2 24.5 25.9 27.2
39.8 41.9 44.0 46.1
61.2 64.2 67.2 70.2
4
6.42 6.76 7.10 7.43
15.1 15.8 16.6 17.3
28.6 29.9 31.3 32.6
48.2 50.3 52.3 54.4
5
7.77 8.11 8.44 8.78
18.1 18.9 19.6 20.4
33.9 35.3 36.6 38.0
6
9.12 9.37 9.71 10.1
21.1 21.7 22.5 23.3
7
10.4 10.7 11.0 11.4
8
1 1 ⁄4 1 1 ⁄2 1 3 ⁄4 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
100 Square Bolts with Hexagonal Nuts
Nominal Bolt Diameter, in. 1⁄ 4
3 1 ⁄4 3 1 ⁄2 3 3 ⁄4 4 1 ⁄4 4 1 ⁄2 4 3 ⁄4 5 1 ⁄4 5 1 ⁄2 5 3 ⁄4 6 1 ⁄4 6 1 ⁄2 6 3 ⁄4 7 1 ⁄4 7 1 ⁄2 7 3 ⁄4 8 1 ⁄2
9
9 1 ⁄2 10 1 ⁄2 111 ⁄2 12 1 ⁄2 13 1 ⁄2 14 1 ⁄2
8.4
12.1
16.5
1 — — 95.1 99.7
21.4
27.2
33.6
Notes: For weights of high-strength fasteners, see Table 8-3. This table conforms to weight standards adopted by the Industrial Fasteners Institute (IFI). *Square bolt per ANSI B18.2.1, hexagonal nut per ANSI B18.2.2. For other non-high-strength fasteners, refer to Tables 8-9 and 8-10.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BOLTED CONSTRUCTION
8 - 21
Table 8-9. Weight Adjustments for Combinations of Non-High-Strength Fasteners Other than Tabulated in Table 8-8
100, Square Bolts with Hexagonal Nuts*
Square Bolts with
Combinations of 100:
100, Hex Bolts
Nominal Bolt Diameter, in.
Add or Subtr.
1⁄ 4
3⁄ 8
1⁄ 2
5⁄ 8
3⁄ 4
7⁄ 8
1
11⁄8
11⁄4
3.5
5.5
8.0 12.2 16.3
Square Nuts
+
0.1
1.0
2.0
3.4
Heavy Square Nuts
+
0.6
2.1
4.1
7.0 11.6 17.2 23.2 32.1 41.2
Heavy Hex Nuts
+
0.4
1.5
2.8
4.6
7.6 10.7 14.2 18.9 24.3
Square Nuts
+
0.1
0.6
1.1
1.4
0.2
0.5 −0.2 −0.1 −1.7
Hex Nuts
−
0.0
0.4
0.9
2.0
3.3
5.0
Heavy Square Nuts
+
0.6
1.7
3.2
5.0
8.3 12.2 15.0 19.8 23.2
Heavy Hex Nuts
+
0.4
1.1
1.9
2.6
4.3
Heavy Square Nuts
+
—
—
4.7
7.3 11.3 16.5 20.7 27.0 33.6
Heavy Hex Nuts
+
—
—
3.4
4.9
5.7
8.2 12.3 18.0
6.0
6.6
6.3
7.3 10.0 11.7 13.8 16.7
Notes: For weights of high-strength fasteners, see Table 8-3. This table conforms to weight standards adopted by the Industrial Fasteners Institute (IFI). *Add or subtract value in this table to or from the value in Table 8-8.
Table 8-10. Weights of Non-High-Strength Bolts of Diameter Greater Than 11⁄4-in., pounds Nominal Bolt Diameter, in. 11⁄2
13⁄4
2
21⁄4
21⁄2
23⁄4
3
31⁄4
31⁄2
33⁄4
4
105
130
—
—
—
—
—
—
—
—
—
—
Hex Bolts
84.0 112
178
259
369
508
680
900
1120
1390
1730
2130
Heavy Hex Bolts
95.0 124
195
280
397
541
720
950
—
—
—
—
139
168
200
235
272
313
356
147
178
210
246
284
325
Heads of:
Weight of 100 Each: 13⁄8 Square Bolts
One Linear Inch, Unthreaded Shank
42.0
50.0
68.2
89.0 113
One Linear Inch, Threaded Shank
35.0
42.5
57.4
75.5
97.4 120
—
—
—
—
—
—
—
—
—
—
Square Nuts
94.5 122
Heavy Square Nuts
125
161
—
—
—
—
—
—
—
—
—
—
Heavy Hex Nuts
102
131
204
299
419
564
738
950
1190
1530
1810
2180
Notes: For weights of high-strength fasteners, see Table 8-3. This table conforms to weight standards adopted by the Industrial Fasteners Institute (IFI).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 22
BOLTS, WELDS, AND CONNECTED ELEMENTS
For bolts in slip-critical connections subjected to shear only, the limit states of slip resistance, bolt shear strength, and bearing strength at bolt holes must be checked. For bolts in slip-critical connections subjected to combined shear and tension, the limit states of slip resistance, including the effect of the tensile force present, bolt shear strength, and bearing strength at bolt holes must be checked. Bolt Shear Strength
As illustrated in Figure 8-4a, this limit state considers a shear failure of the bolt shank on plane cdef. Since there is one shear plane, the bolt is in single shear (S). Additional plies of material may increase the number of shear planes and, therefore, the shear strength of the bolt. This condition, as illustrated in Figure 8-4b, is called double shear (D). Additionally, high-strength bolts may be specified with the threads included (N) or excluded (X) from the shear plane of the connection. Note that the shear strength of bolts with the threads included is about 25 percent less than that of bolts with the threads excluded. In spite of this, many designers prefer to specify N bolts when possible due to the difficulty in assuring that threads are excluded from the shear plane in the as-built condition. If, however, the threads are to be excluded from the shear plane, care must be taken to specify a bolt of sufficient overall length given the thread length and required bolt length from Table 8-2. Note that additional washers may be required to accomplish this; refer to Figure 8-3. From LRFD Specification Section J3.6, the design bolt shear strength is φRn, where φ = 0.75 and: Rn = (Fv Ab)n
x ′,y ′,z ′
c,b
g,f
d,a
h,e x,y,z
x,x ′
Ru
e,f d,c
y,y ′
a,b
z,z ′
Ru 2
h,g
Ru Ru
Ru 2
(a) Single shear (S)
(b) Double shear (D)
Fig. 8-4. Bolt shear. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BOLTED CONSTRUCTION
8 - 23
In the above equation, n is the number of bolts in the connection, Fv is the nominal shear strength, and Ab is the nominal bolt area. For convenience, the design bolt shear strengths of various bolts are summarized in Table 8-11; design bolt shear strengths of vertical rows of n bolts are summarized in Table 8-12. Bearing Strength at Bolt Holes
As illustrated in Figure 8-5, this limit state considers both a tear fracture of the connected material and deformation around the bolt holes. Bearing strength is a function of the material being connected, the type of bolt hole, and the spacing and edge distance; it is independent of both the type of bolt and the presence or absence of threads on the bearing area. From LRFD Specification Section J3.10, when deformation around the bolt holes is a design consideration for standard holes, oversized holes, short-slotted holes, and longslotted holes parallel to the line of force, the design bearing strength at bolt holes is φRn, where φ = 0.75 and, for two or more bolts in the line of force, when Le ≥ 1.5d and s ≥ 3d: Rn = (2.4dtFu )n For a single bolt in the line of force or when Le < 1.5d or s < 3d: d Rn = Let + s − (n − 1)(tFu ) ≤ (2.4dtFu )n 2 In the above equations, n is the number of bolts in the connection, d is the nominal bolt diameter, t is the thickness in bearing, and Le is the edge distance. If deformation around the bolt hole is not a design consideration, or for long-slotted holes perpendicular to the line of force, refer to LRFD Specification Section J3.10. For convenience, the design bearing strength at bolt holes is tabulated for the foregoing conditions in Tables 8-13 and 8-14, respectively. Note that these tables may be applied to bolts with countersunk heads, by subtracting one-half the depth of the countersink from the material thickness t. As illustrated in Figure 8-6, this is equivalent to subtracting one-quarter the diameter of the bolt from the material thickness t. Bolt Tensile Strength
From LRFD Specification Section J3.6, when subjected to tension only, the design bolt tensile strength is φRn, where φ = 0.75 Rn = (Ft Ab)n In the above equation, n is the number of bolts in the connection. For convenience, the design bolt tensile strengths of various bolts is summarized in Table 8-15. When subjected to combined shear and tension, the design bolt tensile strength is reduced by a function of the shear stress present in the bolt as specified in LRFD Specification Section J3.7. LRFD Specification Section J3.6 states that any tension resulting from prying action must be considered in determining the required strength of the bolts. Prying action is a phenomenon (in bolted construction only) whereby the deformation of a fitting under a tensile force increases the tensile force in the bolt. The required strength per bolt is the AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 24
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-11. Design Shear Strength of One Bolt, kips Nominal Bolt Diameter d, in. 5⁄ 8
ASTM Desig.
Thread Cond.
φF v (ksi)
A325
N
36.0
X A490
A307
56.3
—
1 1 ⁄8
1
1 1 ⁄4
Loading 0.3068 0.4418 0.6013 0.7854 0.9940 1.227
45.0
X
7⁄ 8
1 3 ⁄8
1 1 ⁄2
1.485
1.767
Nominal Bolt Area, in.2
45.0
N
3⁄ 4
18.0
S
11.0
15.9
21.6
28.3
35.8
44.2
D
22.1
31.8
43.3
56.5
71.6
88.4
S
13.8
19.9
27.1
35.3
44.7
D
27.6
39.8
54.1
70.7
89.5
S
13.8
19.9
27.1
35.3
44.7
D
27.6
39.8
54.1
70.7
89.5
S
17.3
24.9
33.9
44.2
D
34.5
49.7
67.7
88.4
S D
5.52 11.0
7.95 15.9
56.0 112
55.2 110 55.2 110 69.1 138
53.5 107 66.8 134 66.8 134 83.6 167
63.6 127 79.5 159 79.5 159 99.5 199
10.8
14.1
17.9
22.1
26.7
31.8
21.6
28.3
35.8
44.2
53.5
63.6
N = Threads included in shear plane X = Threads excluded from shear plane S = Single shear D = Double shear
Table 8-12. Design Shear Strength of n Bolts in Double Shear* ASTM A325 N
ASTM A490 X
N
X
n
3⁄ 4
7⁄ 8
1
3⁄ 4
7⁄ 8
1
3⁄ 4
7⁄ 8
1
3⁄ 4
7⁄ 8
12
382
520
679
477
649
848
477
649
848
596
812
1060
11
350
476
622
437
595
778
437
595
778
547
744
972
10
318
433
565
398
541
707
398
541
707
497
676
884
9
286
390
509
358
487
636
358
487
636
447
609
795
8
254
346
452
318
433
565
318
433
565
398
541
707
7
223
303
396
278
379
495
278
379
495
348
474
619
6
191
260
339
239
325
424
239
325
424
298
406
530
5
159
216
283
199
271
353
199
271
353
249
338
442
4
127
173
226
159
216
283
159
216
283
199
271
353
130
170
119
162
212
119
162
212
149
203
265
108
141
108
141
135
177
3
95.4
2
63.6
86.6
1
31.8
43.3
113
79.5
56.5
39.8
54.1
70.7
79.5 39.8
54.1
N = Threads included in shear plane X = Threads excluded in shear plane *For design strength of bolts in single shear, divide tabular value by 2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
70.7
99.4 49.7
67.6
1
88.4
BOLTED CONSTRUCTION
8 - 25
sum of rut, the factored force per bolt due to the tensile force, and qu, the additional tension per bolt resulting from prying action produced by deformation of the connected parts. While the effect of prying action is considered in the design of the bolts, it is primarily a function of the connected elements; thus, the connected elements must possess adequate flexural strength and it is their stiffness which is the key to satisfactory performance. Refer to “Hanger Connections” in Part 11 for treatment of prying action. Slip Resistance
In slip-critical connections, the fully tensioned bolt creates resistance to slip through friction on the faying surface between two connected parts. This slip resistance is a function of the slip coefficient µ of the faying surface. Clean mill scale with no coating is defined as a Class A surface with µ = 0.33. Blast-cleaned surfaces with no coatings are defined as Class B surfaces with µ = 0.50. Hot-dip galvanized and roughened surfaces are defined as Class C surfaces with µ = 0.40.
Ru
Ru
Splitting of plate
(a) Tear fracture for smaller end distance
Ru
Ru
Tearout of Plate
(b) Tear fracture for longer end distance
Ru
Ru
Deformation
(c) Deformation of material at bolt hole Fig. 8-5. Bearing strength at bolt holes. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 26
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-13. Design Bearing Strength at Bolt Holes, kips/in. thickness Two or more holes in line of force with Le ≥ 1.5d and s ≥ 3d; hole deformation considered* Nominal Bolt Diameter d, in. 5⁄ 8
3⁄ 4
7⁄ 8
1
15⁄ 16
11⁄8
15⁄16
11⁄2
Fu, ksi
17⁄8
21⁄4
25⁄8
3
STD, OVS SSL, LSLP
58 65 70
65.3 73.1 78.8
78.3 87.8 94.5
91.4 102 110
LSLT
58 65 70
54.4 60.9 65.6
65.3 73.1 78.8
76.1 85.3 91.9
11⁄8
11⁄4
13⁄8
11⁄2
111⁄16
17⁄8
21⁄16
21⁄4
33⁄8
33⁄4
41⁄8
41⁄2
1.5d
Hole Type
3d 104 117 126
117 132 142
131 146 158
144 161 173
157 176 189
87.0 97.5 105
97.9 110 118
109 122 131
120 134 144
131 146 158
STD = Standard Hole OVS = Oversized Hole SSL = Short-Slotted Hole LSLP = Long-Slotted Hole parallel to line of force LSLT = Long-Slotted Hole transverse to line of force *When s < 3d, or when hole deformation is not a design consideration, refer to LRFD Specification Section J3.10. When Le < 1.5d or for one hole in the line of force, refer to Table 8-14.
Table 8-14. Design Bearing Strength at Bolt Holes, kips/in. thickness One hole in line of force or top bolt with Le < 1.5d* Nominal Bolt Diameter d, in.
Fu, ksi
1
11⁄8
11⁄4
13⁄8
11⁄2
15⁄8
13⁄4
17⁄8
58 65 70
43.5 48.8 52.5
48.9 54.8 59.1
54.4 60.9 65.6
59.8 67.0 72.2
65.3 73.1 78.8
70.7 79.2 85.3
76.1 85.3 91.9
81.6 91.4 98.4
*Design strength from Table 8-14 shall not exceed tabular value from Table 8-13. For remaining bolts, when s − d / 2 > 2.4d, refer to Table 8-13; otherwise refer to LRFD Specification Section J3.10.
Slip coefficients for all other coated blast-cleaned surfaces must be determined by the Testing Method to Determine the Slip Coefficient Used in Bolted Joints; refer to Appendix A of the RCSC Specification. When the tests results in 0.33 ≤ µ < 0.50, the coating is a Class A coating and the design slip coefficient is µ = 0.33. If the test results in µ ≥ 0.50, the coating is a Class B coating and the design slip coefficient is µ = 0.50. The surface requirements for slip-critical connections apply only to the faying surfaces and do not include the surfaces under the bolt, washer, or nut. Bolts in slip-critical connections may be designed at either service loads or factored loads with the provisions of LRFD Specification Section J3.8. From LRFD Specification Section J3.8a, when subjected to shear only, the resistance to slip for comparison with service loads is φRn, where Rn = (Fv Ab)n AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BOLTED CONSTRUCTION
8 - 27
Table 8-15. Design Tensile Strength of Bolts, kips Nominal Bolt Diameter d, in. 5⁄ 8
3⁄ 4
7⁄ 8
1
11⁄8
11⁄4
13⁄8
11⁄2
1.227
1.485
1.767
2
Nominal Bolt Area, in.
ASTM Desig.
φFt, ksi
A325
67.5
A490 A307
84.8 33.8
0.3068
0.4418
0.6013
20.7
29.8
40.6
41.4
59.6
81.2
26.0
37.4
52.0
74.9
51.0 102
0.7854 53.0 106 66.6 133
0.9940 67.1
82.8
134
166
84.2 169
100
119
200
239
104
126
150
208
252
300
10.4
14.9
20.3
26.5
33.5
41.4
20.7
29.8
40.6
53.0
67.1
82.8
50.1 100
59.6 119
and φ = 1.0 for standard holes, oversized holes, short-slotted holes, and long-slotted holes perpendicular to the direction of the load; φ = 0.85 for long-slotted holes parallel to the direction of the load. In the above equation, n is the number of bolts in the connection. In general, slip is likely to occur at 1.4 to 1.5 times the service loads. Note that the values of Fv tabulated in LRFD Specification Table J3.6 for bolts in slip-critical connections assume Class A surfaces with µ = 0.33. As stated in LRFD Specification Section J3.8a, it is permissible to increase Fv to the applicable value in the RCSC Specification for other surfaces. When subjected to combined shear and tension, the slip capacity for comparison with service loads must be reduced by the factor: T 1 − Tb as specified in LRFD Specification Section J3.9a, where T is the unfactored force on the connection and Tb is the minimum bolt tension from LRFD Specification Table J3.1. From LRFD Specification Appendix J3.8a, the design slip resistance for comparison with factored loads is φRstr, Effective thickness in bearing db 2
db 4
Ru Ru db
Fig. 8-6. Effective thickness for bearing of countersunk bolts. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 28
BOLTS, WELDS, AND CONNECTED ELEMENTS
where Rstr = 1.13µTm Nb Ns and φ is equal to 1.0 for standard holes, 0.85 for oversized and short-slotted holes, 0.70 for long-slotted holes perpendicular to the direction of the load, and 0.60 for long-slotted holes parallel to the direction of the load. When subjected to combined tension and shear, the design slip resistance for comparison with factored loads must be reduced by the factor: Tu 1 − 1.13Tm Nb as specified in LRFD Specification Appendix J3.8b. In the above equations, Tu is the factored force on the connection, Tm is the minimum bolt tension from LRFD Specification Table J3.1, and Nb is the number of bolts in the connection. For convenience, slip capacities for comparison with service loads and design slip resistances for comparison with factored loads are tabulated in Tables 8-16 and 8-17, respectively. ECCENTRICALLY LOADED BOLT GROUPS
When the line of action of an applied load does not pass through the center of gravity (CG) of a bolt group, the load is eccentric and results in a moment which must be considered in the design of the connection. Eccentricity in the Plane of the Faying Surface
Eccentricity in the plane of the faying surface produces additional shear. The bolts must be designed to resist the combined effect of the direct shear from the applied load Pu and the additional shear from the induced moment Pu e. Two methods of analysis for this type of eccentricity will be discussed: (1) the instantaneous center of rotation method; and, (2) the elastic method. Instantaneous Center of Rotation Method
Also known as the ultimate strength method (Crawford, 1968), this method considers the load-deformation relationship of each bolt and, thus, more accurately predicts the ultimate strength of the eccentrically loaded connection. Eccentricity produces both a rotation about the centroid of the bolt group and a translation of one connected element with respect to the other. The combined effect of this rotation and translation is equivalent to a rotation about a point defined as the instantaneous center of rotation (IC) as illustrated in Figure 8-7a. The location of the IC depends on the geometry of the bolt group as well as the direction and point of application of the load. The individual resistance of each bolt is assumed to act on a line perpendicular to a ray passing through the IC and the centroid of that bolt as illustrated in Figure 8-7b. The load-deformation relationship of one bolt is illustrated in Figure 8-8, where R = Rult(1 − e−10∆)0.55 In the above equation, AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 29
Table 8-16. Slip-Critical Connections Design Resistance to Shear at Service Loads,* kips (Class A faying surface, µ = 0.33) Nominal Bolt Diameter, in. 5⁄ 8
ASTM Desig.
Hole Type
A325
STD
A490
3⁄ 4
7⁄ 8
1
11⁄8
11⁄4
13⁄8
11⁄2
Nominal Bolt Area, in.2 Loading
0.3068 0.4418 0.6013 0.7854 0.9940
1.227
1.485
1.767
S D
5.22 10.4
7.51 15.0
10.2 20.4
13.4 26.7
16.9 33.8
20.9 41.7
25.2 50.5
30.0 60.1
OVS SSL
S D
4.60 9.20
6.63 13.3
9.02 18.0
11.8 23.6
14.9 29.8
18.4 36.8
22.3 44.5
26.5 53.0
LSLP
S D
3.13 6.26
4.51 9.01
6.13 12.3
8.01 16.0
10.1 20.3
12.5 25.0
15.1 30.3
18.0 36.0
LSLT
S D
3.68 7.36
5.30 10.6
7.22 14.4
9.42 18.8
11.9 23.9
14.7 29.5
17.8 35.6
21.2 42.4
STD
S D
6.44 12.9
9.28 18.6
12.6 25.3
16.5 33.0
20.9 41.7
25.8 51.5
31.2 62.4
37.1 74.2
OVS SSL
S D
5.52 11.0
7.95 15.9
10.8 21.6
14.1 28.3
17.9 35.8
22.1 44.2
26.7 53.5
31.8 63.6
LSLP
S D
3.93 7.85
5.65 11.3
7.70 15.4
10.1 20.1
12.7 25.4
15.7 31.4
19.0 38.0
22.6 45.2
LSLT
S D
4.60 9.20
6.63 13.3
9.02 18.0
11.8 23.6
14.9 29.8
18.4 36.8
22.3 44.5
26.5 53.0
STD = Standard Hole OVS = Oversized Hole SSL = Short-Slotted Hole LSLP = Long-Slotted Hole parallel to line of force LSLT = Long-Slotted Hole transverse to line of force S = Single Shear D = Double Shear *For design slip resistance at factored loads, refer to Table 8-17.
R = shear force in one bolt at a deformation ∆, kips. Rult = ultimate shear strength of one bolt, kips. ∆ = total deformation of a bolt, including shearing, bearing, and bending deformation, plus local bearing deformation of the plate, in. e = 2.718…, base of the natural logarithm. Applying a maximum deformation ∆max to the bolt most remote from the IC, the maximum shear strength of that bolt may be determined. For other bolts, deformations are assumed to vary linearly with distance from the IC, and shear strengths can be obtained from this relationship. The strength of the bolt group is, then, the sum of the
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 30
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-17. Slip-Critical Connections Design Slip Resistance at Factored Loads, kips (Class A faying surface, µ = 0.33) Nominal Bolt Area, in.2 5⁄ 8
ASTM Desig.
Hole Type
A325
STD
3⁄ 4
7⁄ 8
1
11⁄8
11⁄4
13⁄8
11⁄2
Minimum ASTM A325 Bolt Tension, kips Loading
19.0
28.0
39.0
51.0
56.0
71.0
85.0
103
S D
7.09 14.2
10.4 20.9
14.5 29.1
19.0 38.0
20.9 41.8
26.5 53.0
31.7 63.4
38.4 76.8
OVS SSL
S D
6.02 12.0
8.88 17.8
12.4 24.7
16.2 32.3
17.8 35.5
22.5 45.0
26.9 53.9
32.6 65.3
LSLP
S D
4.25 8.50
6.26 12.5
8.73 17.5
11.4 22.8
12.5 25.1
15.9 31.8
19.0 38.0
23.0 46.1
LSLT
S D
4.96 9.92
7.31 14.6
10.2 20.4
13.3 26.6
14.6 29.2
18.5 37.1
22.2 44.4
26.9 53.8
Minimum ASTM A490 Bolt Tension, kips
A490
24.0
35.0
49.0
64.0
80.0
102
121
148
STD
S D
8.95 17.9
13.1 26.1
18.3 36.5
23.9 47.7
29.8 59.7
38.0 76.1
45.1 90.2
55.2 110
OVS SSL
S D
7.61 15.2
11.1 22.2
15.5 31.1
20.3 40.6
25.4 50.7
32.3 64.7
38.4 76.7
46.9 93.8
LSLP
S D
5.37 10.7
7.83 15.7
11.0 21.9
14.3 28.6
17.9 35.8
22.8 45.6
27.1 54.1
33.1 66.2
LSLT
S D
6.26 12.5
9.14 18.3
12.8 25.6
16.7 33.4
20.9 41.8
26.6 53.3
31.6 63.2
38.6 77.3
STD = Standard Hole OVS = Oversized Hole SSL = Short-Slotted Hole LSLP = Long-Slotted Hole parallel to line of force LSLT = Long-Slotted Hole transverse to line of force S = Single Shear D = Double Shear
individual strengths of all bolts. If the correct location of the IC has been selected, the three equations of in-plane statics will be satisfied; i.e., ΣFx = 0, ΣFy = 0, and ΣM = 0. Tables 8-18 through 8-25 employ the instantaneous center of rotation method for the bolt patterns and eccentric conditions indicated and inclined loads at 0°, 15°, 30°, 45°, 60°, and 75°. The load-deformation relationship is based on data obtained experimentally for 3⁄4-in. diameter ASTM A325 bolts, where Rult = 74 kips, and ∆max = 0.34 in. The non-dimensional coefficient C is obtained by dividing the factored eccentric force Pu by Rult.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 31
For any of the bolt group geometries shown, the design strength of the eccentrically loaded bolt group is φRn, where φRn = C × φrn
lo e
Pu
IC
CG
(a) Instantaneous center of rotation (IC)
e
lo
Pu CG
IC lrm
ax
ru max
(b) Forces on bolts in group Fig. 8-7. Instantaneous center of rotation method. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 32
BOLTS, WELDS, AND CONNECTED ELEMENTS
In the above equation, φrn is the least design strength of one bolt determined from the limit states of bolt shear strength, bearing strength at bolt holes, and slip resistance (if the connection is to be slip-critical). The design strength φRn must be greater than or equal to the required strength Pu. Thus, by dividing Pu by φrn, the minimum coefficient C is obtained, and a bolt group can be selected for which the coefficient is of that magnitude or greater. These tables may be used with any bolt diameter and are conservative when used with ASTM A490 bolts. Linear interpolation within a given table between adjacent values of ex is permitted. Design strengths determined with these tables provide a factor of safety equivalent to that for bolts in connections less than 50 inches long, subjected to shear produced by a concentric load in either bearing-type or slip-critical connections. Although this procedure is based on connections which may experience slip under load, both load tests and analytical studies (Kulak, 1975) indicate that it may be conservatively extended to slip-critical connections. A convergence criterion of one percent was employed for the tabulated iterative solutions. Straight line interpolation between values for loads at different angles may be significantly unconservative. Therefore, unless a direct analysis is performed, use only the values for the next lower angle for design. For bolt group patterns not treated by these tables, a special ultimate strength analysis is required if the instantaneous center of rotation method is to be used.
Example 8-1
Given:
Refer to Figure 8-9. Determine the largest eccentric force Pu for which the design shear strength of the bolts in the connection is adequate using the instantaneous center of rotation method. Use 7⁄8-in. diameter A325-N bolts, φrn = 21.6 kips/bolt. A. Assume the load is vertical as illustrated in Figure 8-9 (θ = 0°°) B. Assume the load acts at an angle of 75°° with respect to vertical (θ = 75°°)
Solution A:
From Table 8-20 with θ = 0°, with s = 3 in., e = 16 in., and n = 6: C = 3.55 Design Shear Strength φRn = C × φrn = 3.55 × 21.6 kips/bolt = 76.7 kips Thus, Pu must be less than or equal to 76.7 kips.
Comment:
Note that this eccentricity has effectively reduced the shear strength of this bolt group by about 70 percent when compared with the concentrically loaded case.
Solution B:
From Table 8-20 with θ = 75°°, s = 3 in., e = 16 in., and n = 6: AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 33
C = 7.90 Design shear strength φRn = C × φrn = 7.90 × 21.6 kips/bolt = 171 kips Thus, Pu must be less than or equal to 171 kips. Comment:
In Solution B, the vertical component of the design strength is φRn sin75°° = (171 kips)(0.966) = 165 kips and the horizontal component of the design strength is φRn cos75°° = (171 kips)(0.259) = 44.3 kips
Elastic Method
Alternatively, the elastic method may be used to analyze eccentrically loaded bolt groups. It offers a simplified, conservative approach but does not render a consistent factor of safety and, in some cases, provides excessively conservative results. Furthermore, the elastic method ignores both the ductility of the bolt group and the load redistribution which occurs. Refer to Higgins (1971). In the elastic method, for a force applied parallel to the Y principal axis of the bolt group as illustrated in Figure 8-10, the eccentric force Pu is resolved into a force Pu acting through the center of gravity (CG) of the bolt group and a moment Pu e where e is the eccentricity. Each bolt is then assumed to support an equal share of the concentric force Pu, and a share of the eccentric moment Pu e which is proportional to its distance from the
80
R, kips
60 R = Rult (1 – e
–10 ∆ 0.55
)
40
20
0
0.10
0.20
0.30
∆, in.
Fig. 8-8. Load-deformation relationship for bolts. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 34
BOLTS, WELDS, AND CONNECTED ELEMENTS
CG. The bolt most remote from the CG, then, is the most highly stressed. The resultant vectorial sum of these forces ru is the required strength for the bolt. The direct shear force per bolt due to the concentric force Pu is r1, where r1 =
Pu n
and n is the number of bolts. The shear force in each bolt due to the moment Pu e varies with distance from the CG and will be maximum in the bolt which is must remote from the CG. The maximum shear due to the moment Pu e is rm, where Y e = 16 in. Pu =60 kips
X
CG
1½
5@3=1 ′-3
W14x82 A572 gr. 50
X PL 7/8, A36
2¾
2¾
5½ Y
Fig. 8-9. Bolted bracket plate for Examples 8-1 and 8-2. Y
Pu
e CG
X
Figure 8-10 AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
rm =
8 - 35
Pu ec Ip
In the above equation, c = distance from CG to center of bolt most remote from CG, in. Ip = polar moment of inertia of the bolt group, in.4 per in.2 (see any text on statics). To determine the resultant force on the most highly stressed bolt, rm must be resolved into vertical component r2 and horizontal component r3, where Pu ecx Ip Pu ecy r3 = Ip
r2 =
In the above equation, cx and cy are the horizontal and vertical components of the diagonal distance c. Thus, the resultant factored force is ru, where r2 r1
ru = √ (r1 + r2)2 + (r3)2
r3 rm ru
and the bolts must be chosen such that the design strength φrn exceeds the required strength ru. For the more general case of an inclined eccentric force, i.e., not parallel to the Y principal axes of the bolt group, the effect of the X-direction component of the direct shear must also be included. Refer to Iwankiw (1987).
Example 8-2
Given:
Refer to Example 8-1. Recalculate the largest eccentric force Pu for which the design shear strength of the bolts in the connection is adequate using the elastic method. Compare the result with that of Example 8-1. Use 7⁄8-in. diameter A325-N bolts, φrn = 21.6 kips. Ip = 406 in.4 per in.2
Solution:
Direct shear force per bolt: r1 =
Pu n
=
Pu 12
Additional shear force on bolt due to eccentricity: r2 =
Pu ecx Ip AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 36
BOLTS, WELDS, AND CONNECTED ELEMENTS
51⁄2−in. Pu (16 in.) 2 = 406 in.4 per in.2 = 0.108 Pu Pu ecy r3 = Ip Pu (16 in.) (71⁄2− in.) = 406 in.4 per in.2 = 0.296 Pu Resultant shear force: (r1 + r2)2 + (r3)2 ru = √
√ 2
Pu 2 12 + 0.108Pu + (0.296Pu ) = 0.352 Pu =
Since ru must be less than or equal to φrn, φrn 0.352 21.6 kips ≤ 0.352 ≤ 61.3 kips
Pu ≤
This 20 percent reduction in the strength predicted by the instantaneous center of rotation method in Example 8-1a is indicative of the conservatism of the elastic method. Eccentricity Normal to the Plane of the Faying Surface
Eccentricity normal to the plane of the faying surface produces tension above and compression below the neutral axis of the bracket connection illustrated in Figure 8-11. The eccentric load Pu can be resolved into a concentric force Pu acting at the faying surface of the connection and a moment Pu e normal to the plane of the faying surface where e is the eccentricity. Each bolt is then assumed to support an equal share of the concentric force Pu, and the moment is resisted by tension in the bolts above the neutral axis and compression between the lower part of the bracket and the column flange. The forces for which the bolts in this connection must be designed must be determined by balancing the tensile forces in the bolts above the neutral axis with the resultant compressive force below the neutral axis. The analysis of such a connection is straightforward and usually begins with one of two assumptions: Case I assumes the neutral axis is not at the center of gravity (CG) while Case II assumes the neutral axis is at the CG. For a bearing-type connection, the limit state of bolt tension, including the effect of prying action and the shear stress present, must still be checked as specified in LRFD Specification Section J3.7. For a slip-critical connection, the bolts above the neutral axis subject to tension would lose a portion of their clamping force. The overall connection, however, would experience no reduction in total clamping force because the clamping AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 37
force below the neutral axis is increased by an equivalent amount. Therefore, it would be unnecessary to reduce the strength of this connection for the interaction of tension and shear above the neutral axis. However, the limit state of bolt tension, including the effect of prying action and the shear stress present, must still be checked as specified in LRFD Specification Section J3.9. Case I窶年eutral Axis Not at Center of Gravity
The shear force per bolt due to the concentric force Pu is ruv, where ruv =
Pu n
and n is the number of bolts in the connection. To determine the location of the neutral axis, assume a trial position of the neutral axis at one-sixth of the total bracket depth, measured upward from the bottom. In Figure 8-12a, this is indicated by the line X-X. To provide for reasonable proportions and to recognize that the effective bearing area will depend upon the bracket flange or support flange bending stiffness, the effective width of the compression block Weff should be taken as: Weff = 8tf 竕､ bf where tf = lesser of bracket flange and support flange thicknesses, in. bf = bracket flange width, in. This effective width is valid for bracket flanges made from W or S shapes, welded plates, and angles. Where the bracket flange thickness is not constant, the average flange thickness should be used. Having assumed the width of the compression block, it is possible to check an assumed location of the neutral axis by checking static equilibrium assuming an elastic stress
e
Pu
Tee Bracket
Fig. 8-11. Bolts subjected to eccentricity normal to the plane of the faying surface. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BOLTS, WELDS, AND CONNECTED ELEMENTS
distribution. Equating the moment of the bolt area above the neutral axis with the moment of the compression block area below the neutral axis, ΣAb × y = Weff × d ×
d 2
In the above equation, ΣAb = sum of the areas of all bolts above the neutral axis, in.2 y = distance from line X-X to CG of of the bolt group above neutral axis, in. d = depth of compression block, in. The value of d may then be adjusted until a reasonable equality exists. Once the neutral axis has been located, the tensile force per bolt rut, as illustrated in Figure 8-12b may be determined as: rut =
Pu ec × Ab Ix
where c = distance from neutral axis to most remote bolt in group, in. Ix = combined moment of inertia of bolt group and compression block about neutral axis, in.4 Bolts above the neutral axis are subjected to the shear force ruv, the tensile force rut, and the effect of prying action; bolts below the neutral axis are subjected to the shear force ruv only. Case II—Neutral Axis at Center of Gravity
This method provides a more direct, but also a more conservative result. As for Case I, the shear force per bolt due to the concentric force Pu is ruv, where
tf
Pu n
CG (tension group)
2rut
y
d = Depth/6
Depth
ruv =
X
NA X
Weff (a) Initial approximation of location of NA
(b) Force diagram with final location of NA
Fig. 8-12. Case I—Neutral axis (NA) not at center of gravity (CG). AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 39
and n is the number of bolts in the connection. The neutral axis is assumed to be located at the CG of the bolt group as illustrated in Figure 8-13. The bolts above the neutral axis are in tension and the bolts below the neutral axis are said to be in “compression.” To obtain a more accurate result, a plastic stress distribution is assumed; this assumption is justified because this method is still more conservative than Case I. Accordingly, the tensile force rut in each bolt above the neutral axis due to the moment Pue is: rut =
Pu e n′dm
where n′ = number of bolts above the neutral axis dm = moment arm between resultant tensile force and resultant compressive force, in.
tf
Bolts above the neutral axis are subjected to the shear force ruv, the tensile force rut, and the effect of prying action; bolts below the neutral axis are subjected to the shear force ruv only.
2rut
NA
Fig. 8-13. Case II—Neutral axis (NA) at center of gravity (CG). AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-18. Coefficients C for Eccentrically Loaded Bolt Groups Angle = 0°° C req =
Pu
φrn
or φR n = C × φ rn
where
ex = e
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
s
s
s
Pu
Number of bolts in one vertical row, n
s, in. ex, in.
3
6
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.18 0.88 0.69 0.56 0.48
2.23 1.75 1.40 1.15 0.97
3.32 2.81 2.36 2.01 1.73
4.39 3.90 3.40 2.96 2.59
5.45 4.98 4.47 3.98 3.55
6.48 6.06 5.56 5.05 4.57
7.51 7.12 6.64 6.13 5.63
8.52 8.17 7.72 7.22 6.70
9.53 9.21 8.78 8.30 7.79
10.5 10.2 9.84 9.38 8.87
11.5 11.3 10.9 10.4 9.96
7 8 9 10 12
0.41 0.36 0.32 0.29 0.24
0.83 0.73 0.65 0.59 0.49
1.51 1.34 1.21 1.09 0.92
2.28 2.04 1.83 1.66 1.40
3.17 2.85 2.59 2.36 2.00
4.13 3.75 3.42 3.14 2.68
5.15 4.72 4.34 4.00 3.44
6.20 5.73 5.31 4.92 4.27
7.28 6.78 6.32 5.89 5.15
8.36 7.85 7.36 6.90 6.09
9.44 8.93 8.42 7.94 7.06
14 16 18 20 24
0.21 0.18 0.16 0.15 0.12
0.42 0.37 0.33 0.29 0.25
0.79 0.70 0.62 0.56 0.47
1.21 1.06 0.95 0.85 0.71
1.74 1.53 1.37 1.24 1.03
2.33 2.06 1.84 1.67 1.40
3.01 2.67 2.39 2.16 1.82
3.75 3.33 3.00 2.72 2.29
4.55 4.06 3.66 3.33 2.81
5.41 4.85 4.38 3.99 3.37
6.31 5.68 5.15 4.70 3.99
28 32 36
0.11 0.09 0.08
0.21 0.18 0.16
0.40 0.35 0.31
0.61 0.54 0.48
0.89 0.78 0.69
1.20 1.05 0.94
1.57 1.37 1.22
1.97 1.73 1.54
2.42 2.13 1.90
2.92 2.57 2.29
3.45 3.04 2.72
2 3 4 5 6
1.63 1.39 1.18 1.01 0.88
2.71 2.48 2.23 1.98 1.75
3.75 3.56 3.32 3.07 2.81
4.77 4.60 4.39 4.15 3.90
5.77 5.63 5.45 5.23 4.98
6.77 6.65 6.48 6.28 6.06
7.76 7.65 7.51 7.33 7.12
8.75 8.66 8.52 8.36 8.17
9.74 9.66 9.53 9.38 9.21
10.7 10.7 10.5 10.4 10.2
11.7 11.6 11.5 11.4 11.2
7 8 9 10 12
0.77 0.69 0.62 0.56 0.48
1.56 1.40 1.26 1.15 0.97
2.58 2.36 2.17 2.01 1.73
3.64 3.40 3.17 2.96 2.59
4.73 4.47 4.22 3.98 3.55
5.81 5.56 5.30 5.05 4.57
6.89 6.64 6.39 6.13 5.63
7.95 7.72 7.47 7.22 6.70
9.00 8.78 8.55 8.30 7.79
10.1 9.84 9.61 9.38 8.87
11.1 10.9 10.7 10.4 9.96
14 16 18 20 24
0.41 0.36 0.32 0.29 0.24
0.83 0.73 0.65 0.59 0.49
1.51 1.34 1.21 1.09 0.92
2.28 2.04 1.83 1.66 1.40
3.17 2.85 2.59 2.36 2.00
4.13 3.75 3.42 3.14 2.68
5.15 4.72 4.34 4.00 3.44
6.20 5.73 5.31 4.92 4.27
7.28 6.78 6.32 5.89 5.15
8.36 7.85 7.36 6.90 6.09
9.44 8.93 8.42 7.94 7.06
28 32 36
0.21 0.18 0.16
0.42 0.37 0.33
0.79 0.70 0.62
1.21 1.06 0.95
1.74 1.53 1.37
2.33 2.06 1.84
3.01 2.67 2.39
3.75 3.33 3.00
4.55 4.06 3.66
5.41 4.85 4.38
6.31 5.68 5.15
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 41
Table 8-18 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 15°° C req =
Pu
φ rn
or φ R n = C × φrn
where
ex
Pu 15°
s
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
s
s
e
Number of bolts in one vertical row, n
s, in. ex, in.
3
6
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.15 0.86 0.67 0.55 0.47
2.20 1.76 1.42 1.17 0.99
3.28 2.78 2.35 2.00 1.73
4.34 3.85 3.36 2.94 2.58
5.39 4.92 4.41 3.94 3.52
6.42 5.98 5.48 4.98 4.52
7.45 7.03 6.55 6.04 5.55
8.46 8.08 7.61 7.11 6.61
9.47 9.11 8.67 8.18 7.67
10.5 10.1 9.72 9.24 8.74
11.5 11.2 10.8 10.3 9.81
7 8 9 10 12
0.41 0.36 0.32 0.29 0.24
0.86 0.75 0.67 0.61 0.51
1.52 1.35 1.22 1.10 0.93
2.30 2.06 1.86 1.69 1.43
3.16 2.86 2.60 2.38 2.03
4.11 3.74 3.43 3.16 2.71
5.10 4.69 4.32 4.00 3.46
6.13 5.68 5.27 4.90 4.28
7.18 6.70 6.26 5.85 5.15
8.24 7.74 7.28 6.84 6.06
9.30 8.80 8.31 7.85 7.01
14 16 18 20 24
0.21 0.19 0.17 0.15 0.12
0.43 0.38 0.34 0.30 0.25
0.81 0.71 0.63 0.57 0.48
1.24 1.09 0.97 0.88 0.73
1.76 1.56 1.39 1.26 1.06
2.37 2.10 1.88 1.70 1.43
3.04 2.70 2.43 2.20 1.86
3.78 3.37 3.04 2.76 2.33
4.57 4.09 3.70 3.37 2.86
5.41 4.87 4.42 4.03 3.43
6.30 5.69 5.18 4.74 4.04
28 32 36
0.11 0.09 0.08
0.22 0.19 0.17
0.41 0.36 0.32
0.63 0.55 0.49
0.91 0.80 0.71
1.23 1.08 0.96
1.60 1.41 1.26
2.02 1.77 1.58
2.47 2.18 1.95
2.97 2.62 2.34
3.51 3.10 2.78
2 3 4 5 6
1.61 1.36 1.15 0.98 0.86
2.69 2.45 2.20 1.96 1.76
3.72 3.52 3.28 3.03 2.78
4.74 4.56 4.34 4.10 3.85
5.74 5.59 5.39 5.16 4.92
6.74 6.60 6.42 6.21 5.98
7.73 7.61 7.45 7.25 7.03
8.73 8.61 8.46 8.28 8.08
9.71 9.61 9.47 9.30 9.11
7 8 9 10 12
0.75 0.67 0.61 0.55 0.47
1.57 1.42 1.29 1.17 0.99
2.55 2.35 2.16 2.00 1.73
3.60 3.36 3.14 2.94 2.58
4.66 4.41 4.17 3.94 3.52
5.73 5.48 5.23 4.98 4.52
6.80 6.55 6.30 6.04 5.55
7.85 7.61 7.36 7.11 6.61
8.90 8.67 8.43 8.18 7.67
9.94 9.72 9.49 9.24 8.74
11.0 10.8 10.5 10.3 9.81
14 16 18 20 24
0.41 0.36 0.32 0.29 0.24
0.86 0.75 0.67 0.61 0.51
1.52 1.35 1.22 1.10 0.93
2.30 2.06 1.86 1.69 1.43
3.16 2.86 2.60 2.38 2.03
4.11 3.74 3.43 3.16 2.71
5.10 4.69 4.32 4.00 3.46
6.13 5.68 5.27 4.90 4.28
7.18 6.70 6.26 5.85 5.15
8.24 7.74 7.28 6.84 6.06
9.30 8.80 8.31 7.85 7.01
28 32 36
0.21 0.19 0.17
0.43 0.38 0.34
0.81 0.71 0.63
1.24 1.09 0.97
1.76 1.56 1.39
2.37 2.10 1.88
3.04 2.70 2.43
3.78 3.37 3.04
4.57 4.09 3.70
5.41 4.87 4.42
6.30 5.69 5.18
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10.7 10.6 10.5 10.3 10.1
11.7 11.6 11.5 11.3 11.1
8 - 42
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-18 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 30°° C req =
Pu
φrn
or φ R n = C × φ rn
where
ex
Pu
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
s
30°
s
s
e
Number of bolts in one vertical row, n
s, in. ex, in.
3
6
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.14 0.86 0.69 0.57 0.49
2.20 1.80 1.50 1.27 1.09
3.25 2.79 2.40 2.08 1.82
4.30 3.83 3.39 3.00 2.68
5.33 4.87 4.41 3.98 3.60
6.36 5.92 5.45 4.99 4.57
7.38 6.96 6.49 6.02 5.58
8.39 7.99 7.53 7.06 6.60
9.40 9.02 8.57 8.11 7.64
10.4 10.0 9.61 9.15 8.68
11.4 11.1 10.6 10.2 9.72
7 8 9 10 12
0.43 0.38 0.34 0.31 0.26
0.95 0.83 0.75 0.67 0.56
1.61 1.44 1.30 1.19 1.01
2.40 2.17 1.98 1.82 1.55
3.27 2.98 2.74 2.52 2.17
4.20 3.86 3.57 3.31 2.87
5.17 4.79 4.46 4.15 3.64
6.17 5.76 5.39 5.05 4.46
7.18 6.75 6.35 5.98 5.33
8.21 7.77 7.34 6.95 6.24
9.25 8.79 8.35 7.93 7.17
14 16 18 20 24
0.23 0.20 0.18 0.16 0.14
0.48 0.42 0.38 0.34 0.28
0.87 0.77 0.69 0.62 0.52
1.35 1.20 1.07 0.97 0.81
1.90 1.69 1.52 1.37 1.16
2.53 2.26 2.04 1.85 1.57
3.23 2.89 2.62 2.38 2.02
3.98 3.58 3.25 2.97 2.53
4.78 4.33 3.94 3.61 3.09
5.63 5.11 4.67 4.30 3.69
6.51 5.94 5.45 5.02 4.33
28 32 36
0.12 0.10 0.09
0.24 0.21 0.19
0.45 0.40 0.35
0.70 0.61 0.55
1.00 0.88 0.78
1.36 1.19 1.07
1.75 1.54 1.38
2.20 1.94 1.74
2.69 2.38 2.13
3.22 2.85 2.56
3.79 3.37 3.03
2 3 4 5 6
1.59 1.34 1.14 0.98 0.86
2.66 2.43 2.20 1.99 1.80
3.69 3.48 3.25 3.02 2.79
4.70 4.52 4.30 4.06 3.83
5.71 5.54 5.33 5.11 4.87
6.70 6.55 6.36 6.14 5.92
7.70 7.55 7.38 7.17 6.96
8.69 8.56 8.39 8.20 7.99
9.68 9.55 9.40 9.22 9.02
7 8 9 10 12
0.77 0.69 0.63 0.57 0.49
1.64 1.50 1.37 1.27 1.09
2.59 2.40 2.23 2.08 1.82
3.60 3.39 3.19 3.00 2.68
4.64 4.41 4.19 3.98 3.60
5.68 5.45 5.22 4.99 4.57
6.73 6.49 6.26 6.02 5.58
7.77 7.53 7.30 7.06 6.60
8.80 8.57 8.34 8.11 7.64
9.83 9.61 9.38 9.15 8.68
10.9 10.6 10.4 10.2 9.72
14 16 18 20 24
0.43 0.38 0.34 0.31 0.26
0.95 0.83 0.75 0.67 0.56
1.61 1.44 1.30 1.19 1.01
2.40 2.17 1.98 1.82 1.55
3.27 2.98 2.74 2.52 2.17
4.20 3.86 3.57 3.31 2.87
5.17 4.79 4.46 4.15 3.64
6.17 5.76 5.39 5.05 4.46
7.18 6.75 6.35 5.98 5.33
8.21 7.77 7.34 6.95 6.24
9.25 8.79 8.35 7.93 7.17
28 32 36
0.23 0.20 0.18
0.48 0.42 0.38
0.87 0.77 0.69
1.35 1.20 1.07
1.90 1.69 1.52
2.53 2.26 2.04
3.23 2.89 2.62
3.98 3.58 3.25
4.78 4.33 3.94
5.63 5.11 4.67
6.51 5.94 5.45
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10.7 10.6 10.4 10.2 10.0
11.7 11.5 11.4 11.2 11.1
ECCENTRICALLY LOADED BOLT GROUPS
8 - 43
Table 8-18 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 45°° C req =
Pu
φrn
or φ R n = C × φ rn
where
ex 45°
Pu
s
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
s
s
e
Number of bolts in one vertical row, n
s, in. ex, in.
3
6
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.17 0.92 0.75 0.64 0.55
2.23 1.89 1.63 1.42 1.25
3.26 2.87 2.54 2.25 2.01
4.28 3.87 3.50 3.17 2.88
5.29 4.88 4.49 4.13 3.80
6.30 5.90 5.49 5.11 4.76
7.31 6.91 6.51 6.11 5.73
8.32 7.93 7.52 7.11 6.73
9.32 8.94 8.53 8.12 7.73
10.3 9.95 9.55 9.14 8.73
11.3 11.0 10.6 10.2 9.74
7 8 9 10 12
0.49 0.44 0.40 0.36 0.31
1.11 0.99 0.90 0.81 0.68
1.81 1.64 1.49 1.37 1.17
2.63 2.41 2.22 2.06 1.79
3.51 3.25 3.02 2.82 2.47
4.43 4.14 3.87 3.63 3.22
5.38 5.06 4.77 4.50 4.02
6.36 6.01 5.69 5.39 4.87
7.34 6.98 6.64 6.32 5.74
8.34 7.96 7.61 7.27 6.65
9.34 8.96 8.58 8.23 7.58
14 16 18 20 24
0.27 0.24 0.21 0.19 0.16
0.59 0.52 0.46 0.41 0.35
1.03 0.91 0.82 0.74 0.63
1.58 1.41 1.27 1.16 0.98
2.20 1.97 1.78 1.62 1.38
2.88 2.60 2.36 2.16 1.85
3.62 3.29 3.00 2.76 2.37
4.41 4.03 3.70 3.41 2.94
5.24 4.81 4.43 4.10 3.56
6.11 5.63 5.21 4.84 4.22
6.99 6.48 6.02 5.61 4.92
28 32 36
0.14 0.12 0.11
0.30 0.26 0.23
0.54 0.48 0.43
0.85 0.75 0.67
1.19 1.05 0.94
1.61 1.43 1.28
2.08 1.84 1.65
2.58 2.30 2.07
3.14 2.80 2.53
3.73 3.34 3.02
4.37 3.92 3.55
2 3 4 5 6
1.57 1.35 1.17 1.03 0.92
2.64 2.43 2.23 2.05 1.89
3.66 3.46 3.26 3.06 2.87
4.67 4.48 4.28 4.07 3.87
5.67 5.49 5.29 5.09 4.88
6.66 6.49 6.30 6.10 5.90
7.66 7.50 7.31 7.12 6.91
8.65 8.49 8.32 8.13 7.93
9.64 9.49 9.32 9.13 8.94
10.6 10.5 10.3 10.1 9.95
11.6 11.5 11.3 11.1 11.0
7 8 9 10 12
0.83 0.75 0.69 0.64 0.55
1.75 1.63 1.52 1.42 1.25
2.70 2.54 2.39 2.25 2.01
3.68 3.50 3.33 3.17 2.88
4.68 4.49 4.30 4.13 3.80
5.69 5.49 5.30 5.11 4.76
6.71 6.51 6.30 6.11 5.73
7.72 7.52 7.31 7.11 6.73
8.74 8.53 8.33 8.12 7.73
9.75 9.55 9.34 9.14 8.73
10.8 10.6 10.4 10.2 9.74
14 16 18 20 24
0.49 0.44 0.40 0.36 0.31
1.11 0.99 0.90 0.81 0.68
1.81 1.64 1.49 1.37 1.17
2.63 2.41 2.22 2.06 1.79
3.51 3.25 3.02 2.82 2.47
4.43 4.14 3.87 3.63 3.22
5.38 5.06 4.77 4.50 4.02
6.36 6.01 5.69 5.39 4.87
7.34 6.98 6.64 6.32 5.74
8.34 7.96 7.61 7.27 6.65
9.34 8.96 8.58 8.23 7.58
28 32 36
0.27 0.24 0.21
0.59 0.52 0.46
1.03 0.91 0.82
1.58 1.41 1.27
2.20 1.97 1.78
2.88 2.60 2.36
3.62 3.29 3.00
4.41 4.03 3.70
5.24 4.81 4.43
6.11 5.63 5.21
6.99 6.48 6.02
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 44
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-18 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 60°° C req =
Pu
φrn
or φR n = C × φ rn
where
ex 60°
Pu
s
e
s
s
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
Number of bolts in one vertical row, n
s, in. ex, in.
3
6
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.27 1.05 0.89 0.77 0.68
2.32 2.05 1.83 1.65 1.49
3.32 3.02 2.77 2.54 2.34
4.31 4.00 3.72 3.47 3.24
5.30 4.98 4.69 4.41 4.16
6.30 5.97 5.66 5.37 5.10
7.29 6.96 6.64 6.34 6.06
8.27 7.94 7.62 7.32 7.02
9.27 8.94 8.61 8.29 7.99
10.3 9.93 9.60 9.28 8.97
11.3 10.9 10.6 10.3 9.95
7 8 9 10 12
0.61 0.56 0.51 0.47 0.40
1.37 1.26 1.16 1.07 0.93
2.17 2.01 1.87 1.74 1.52
3.03 2.83 2.66 2.50 2.22
3.93 3.71 3.51 3.32 3.00
4.85 4.61 4.39 4.19 3.82
5.79 5.54 5.30 5.08 4.67
6.74 6.48 6.23 5.99 5.55
7.71 7.43 7.17 6.92 6.45
8.67 8.39 8.12 7.86 7.37
9.64 9.35 9.07 8.81 8.30
14 16 18 20 24
0.35 0.32 0.29 0.26 0.22
0.81 0.72 0.65 0.58 0.49
1.35 1.21 1.09 1.00 0.85
2.00 1.81 1.66 1.53 1.32
2.73 2.49 2.30 2.12 1.84
3.50 3.23 2.98 2.77 2.41
4.32 4.00 3.72 3.47 3.05
5.16 4.81 4.50 4.21 3.73
6.03 5.65 5.31 4.99 4.45
6.92 6.51 6.14 5.80 5.21
7.83 7.40 7.00 6.63 5.99
28 32 36
0.19 0.17 0.15
0.42 0.37 0.33
0.74 0.65 0.59
1.15 1.02 0.92
1.61 1.43 1.29
2.13 1.91 1.72
2.71 2.44 2.21
3.34 3.02 2.74
4.00 3.63 3.31
4.70 4.28 3.92
5.44 4.97 4.57
2 3 4 5 6
1.60 1.42 1.27 1.15 1.05
2.65 2.48 2.32 2.18 2.05
3.65 3.48 3.32 3.17 3.02
4.64 4.48 4.31 4.15 4.00
5.64 5.47 5.30 5.14 4.98
6.63 6.46 6.30 6.13 5.97
7.62 7.45 7.29 7.12 6.96
8.61 8.44 8.27 8.11 7.94
9.60 9.44 9.27 9.10 8.94
10.6 10.4 10.3 10.1 9.93
11.6 11.4 11.3 11.1 10.9
7 8 9 10 12
0.96 0.89 0.83 0.77 0.68
1.93 1.83 1.73 1.65 1.49
2.89 2.77 2.65 2.54 2.34
3.86 3.72 3.59 3.47 3.24
4.83 4.69 4.55 4.41 4.16
5.81 5.66 5.51 5.37 5.10
6.80 6.64 6.49 6.34 6.06
7.78 7.62 7.47 7.32 7.02
8.77 8.61 8.45 8.29 7.99
9.76 9.60 9.43 9.28 8.97
10.8 10.6 10.4 10.3 9.95
14 16 18 20 24
0.61 0.56 0.51 0.47 0.40
1.37 1.26 1.16 1.07 0.93
2.17 2.01 1.87 1.74 1.52
3.03 2.83 2.66 2.50 2.22
3.93 3.71 3.51 3.32 3.00
4.85 4.61 4.39 4.19 3.82
5.79 5.54 5.30 5.08 4.67
6.74 6.48 6.23 5.99 5.55
7.71 7.43 7.17 6.92 6.45
8.67 8.39 8.12 7.86 7.37
9.64 9.35 9.07 8.81 8.30
28 32 36
0.35 0.32 0.29
0.81 0.72 0.65
1.35 1.21 1.09
2.00 1.81 1.66
2.73 2.49 2.30
3.50 3.23 2.98
4.32 4.00 3.72
5.16 4.81 4.50
6.03 5.65 5.31
6.92 6.51 6.14
7.83 7.40 7.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 45
Table 8-18 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 75°° C req =
Pu
φ rn
or φ R n = C × φrn
where
ex 75°
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
s
Pu
s
s
e
Number of bolts in one vertical row, n
s, in. ex, in.
3
6
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.49 1.32 1.18 1.07 0.98
2.51 2.33 2.18 2.04 1.92
3.49 3.30 3.14 2.99 2.85
4.46 4.27 4.09 3.93 3.79
5.44 5.24 5.05 4.88 4.73
6.42 6.21 6.01 5.84 5.67
7.40 7.18 6.98 6.79 6.62
8.38 8.15 7.95 7.75 7.57
9.36 9.13 8.92 8.72 8.53
10.3 10.1 9.89 9.68 9.49
11.3 11.1 10.9 10.7 10.5
7 8 9 10 12
0.90 0.84 0.78 0.73 0.65
1.82 1.72 1.63 1.55 1.41
2.73 2.62 2.51 2.41 2.23
3.65 3.52 3.40 3.29 3.08
4.58 4.44 4.31 4.19 3.95
5.52 5.37 5.23 5.10 4.84
6.46 6.30 6.16 6.02 5.75
7.40 7.24 7.09 6.94 6.66
8.36 8.19 8.03 7.88 7.59
9.31 9.14 8.97 8.81 8.51
10.3 10.1 9.92 9.76 9.45
14 16 18 20 24
0.58 0.53 0.48 0.44 0.38
1.30 1.20 1.11 1.03 0.89
2.06 1.92 1.78 1.66 1.46
2.88 2.70 2.53 2.38 2.12
3.73 3.52 3.33 3.16 2.85
4.60 4.38 4.17 3.97 3.63
5.50 5.26 5.03 4.82 4.44
6.40 6.15 5.91 5.69 5.27
7.31 7.05 6.80 6.56 6.13
8.23 7.96 7.70 7.45 6.99
9.16 8.88 8.61 8.35 7.87
28 32 36
0.34 0.30 0.27
0.79 0.70 0.62
1.29 1.16 1.05
1.90 1.73 1.58
2.59 2.38 2.19
3.33 3.08 2.85
4.11 3.81 3.55
4.91 4.58 4.28
5.73 5.37 5.05
6.57 6.19 5.84
7.43 7.02 6.65
2 3 4 5 6
1.71 1.60 1.49 1.40 1.32
2.72 2.61 2.51 2.42 2.33
3.70 3.59 3.49 3.39 3.30
4.69 4.57 4.46 4.37 4.27
5.67 5.55 5.44 5.34 5.24
6.66 6.53 6.42 6.31 6.21
7.64 7.52 7.40 7.29 7.18
8.79 8.50 8.38 8.26 8.15
9.78 9.48 9.36 9.24 9.13
10.8 10.5 10.3 10.2 10.1
11.7 11.5 11.3 11.2 11.1
7 8 9 10 12
1.25 1.18 1.13 1.07 0.98
2.25 2.18 2.11 2.04 1.92
3.22 3.14 3.06 2.99 2.85
4.18 4.09 4.01 3.93 3.79
5.14 5.05 4.97 4.88 4.73
6.11 6.01 5.92 5.84 5.67
7.07 6.98 6.88 6.79 6.62
8.05 7.95 7.85 7.75 7.57
9.01 8.92 8.81 8.72 8.53
10.0 9.89 9.78 9.68 9.49
11.0 10.9 10.8 10.7 10.5
14 16 18 20 24
0.90 0.84 0.78 0.73 0.65
1.82 1.72 1.63 1.55 1.41
2.73 2.62 2.51 2.41 2.23
3.65 3.52 3.40 3.29 3.08
4.58 4.44 4.31 4.19 3.95
5.52 5.37 5.23 5.10 4.84
6.46 6.30 6.16 6.02 5.75
7.40 7.24 7.09 6.94 6.66
8.36 8.19 8.03 7.88 7.59
9.31 9.14 8.97 8.81 8.51
10.3 10.1 9.92 9.76 9.45
28 32 36
0.58 0.53 0.48
1.30 1.20 1.11
2.06 1.92 1.78
2.88 2.70 2.53
3.73 3.52 3.33
4.60 4.38 4.17
5.50 5.26 5.03
6.40 6.15 5.91
7.31 7.05 6.80
8.23 7.96 7.70
9.16 8.88 8.61
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 46
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-19. Coefficients C for Eccentrically Loaded Bolt Groups Angle = 0°° C req =
Pu
φrn
or φR n = C × φ rn ex = e
where
s, in.
3
6
Pu
s
s
s
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
3
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
0.84 0.65 0.54 0.45 0.39
2.54 2.03 1.67 1.42 1.22
4.48 3.68 3.06 2.59 2.25
6.59 5.67 4.86 4.21 3.69
8.72 7.77 6.84 6.01 5.32
10.8 9.91 8.93 8.00 7.17
12.9 12.1 11.1 10.1 9.16
15.0 14.2 13.2 12.2 11.2
17.0 16.3 15.4 14.4 13.4
19.0 18.3 17.5 16.5 15.5
21.0 20.4 19.6 18.7 17.7
23.0 22.5 21.7 20.8 19.8
7 8 9 10 12
0.35 0.31 0.28 0.26 0.22
1.08 0.96 0.86 0.78 0.66
1.99 1.78 1.60 1.46 1.24
3.27 2.93 2.65 2.42 2.06
4.74 4.27 3.87 3.53 3.01
6.46 5.86 5.34 4.90 4.19
8.33 10.3 12.4 7.60 9.50 11.5 6.97 8.75 10.7 6.42 8.10 9.91 5.51 7.01 8.63
14.5 13.6 12.7 11.8 10.4
16.7 15.7 14.7 13.8 12.2
18.8 17.8 16.8 15.9 14.2
14 16 18 20 24
0.19 0.17 0.15 0.14 0.12
0.57 0.51 0.45 0.41 0.34
1.08 0.95 0.85 0.77 0.65
1.78 1.57 1.41 1.27 1.07
2.62 2.32 2.07 1.88 1.58
3.66 3.24 2.90 2.63 2.21
4.82 4.27 3.83 3.48 2.93
6.15 5.47 4.92 4.47 3.77
7.61 6.79 6.11 5.55 4.69
9.19 10.9 12.7 8.23 9.78 11.4 7.43 8.85 10.4 6.76 8.07 9.48 5.72 6.85 8.06
28 32 36
0.10 0.09 0.08
0.29 0.26 0.23
0.56 0.49 0.43
0.92 0.80 0.72
1.36 1.19 1.06
1.90 1.67 1.49
2.53 2.22 1.98
3.25 2.86 2.55
4.05 3.57 3.18
4.95 4.36 3.90
2 3 4 5 6
0.84 0.65 0.54 0.45 0.39
3.24 2.79 2.41 2.10 1.85
5.39 4.93 4.44 3.97 3.55
7.47 7.08 6.60 6.11 5.62
9.51 9.17 8.75 8.27 7.77
11.5 11.2 10.9 10.4 9.93
13.5 13.3 12.4 12.5 12.1
15.5 15.3 15.0 14.6 14.2
17.5 17.3 17.0 16.7 16.3
19.5 19.3 19.1 18.7 18.4
21.5 21.3 21.1 20.8 20.4
23.4 23.3 23.1 22.8 22.5
7 8 9 10 12
0.35 0.31 0.28 0.26 0.22
1.64 1.47 1.34 1.22 1.04
3.18 2.87 2.61 2.39 2.04
5.17 4.75 4.39 4.06 3.52
7.27 6.79 6.34 5.92 5.20
9.43 8.92 8.43 7.96 7.10
11.6 11.1 10.6 10.1 9.12
13.7 13.3 12.7 12.2 11.2
15.9 15.4 14.9 14.4 13.4
18.0 17.5 17.1 16.6 15.6
20.1 19.6 19.2 18.7 17.7
22.1 21.7 21.3 20.9 19.9
14 16 18 20 24
0.19 0.17 0.15 0.14 0.12
0.90 0.80 0.71 0.64 0.54
1.77 1.57 1.41 1.28 1.07
3.09 2.75 2.48 2.25 1.90
4.61 4.12 3.72 3.38 2.86
6.36 5.74 5.21 4.77 4.06
8.27 10.3 12.4 7.52 9.44 11.7 6.87 8.68 10.6 6.31 8.02 9.85 5.40 6.91 8.55
14.5 13.5 12.6 11.8 10.3
16.7 15.7 14.7 13.8 12.2
18.9 17.8 16.8 15.9 14.1
28 32 36
0.10 0.09 0.08
0.46 0.41 0.36
0.93 0.81 0.73
1.64 1.44 1.29
2.47 2.18 1.94
3.52 3.11 2.78
4.70 4.16 3.72
6.05 5.37 4.81
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.52 6.69 6.02
5.93 5.23 4.67
7.00 6.18
5.52
9.12 10.8 12.6 8.15 9.71 11.4 7.34 8.78 10.3
ECCENTRICALLY LOADED BOLT GROUPS
8 - 47
Table 8-19 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 15°° C req =
Pu
φrn
or φR n = C × φ rn ex
where
s, in.
3
6
15°
s
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
Pu
s
s
e
3
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
2 3 4 5 6
0.87 0.68 0.55 0.47 0.41
2.54 2.04 1.69 1.44 1.25
4.47 3.71 3.11 2.66 2.31
6.54 5.63 4.85 4.21 3.70
8.63 7.69 6.79 6.00 5.34
7 8 9 10 12
0.36 0.32 0.29 0.27 0.23
1.10 0.98 0.88 0.81 0.68
2.04 1.83 1.65 1.51 1.28
3.29 2.96 2.68 2.45 2.09
4.79 4.32 3.94 3.61 3.08
6.46 5.87 5.37 4.93 4.24
8.30 10.2 12.3 7.60 9.45 11.4 6.99 8.74 10.6 6.45 8.11 9.88 5.58 7.05 8.66
14 16 18 20 24
0.20 0.17 0.16 0.14 0.12
0.59 0.52 0.47 0.42 0.35
1.11 0.98 0.88 0.79 0.67
1.82 1.61 1.44 1.31 1.10
2.69 2.38 2.13 1.93 1.62
3.71 3.29 2.96 2.68 2.26
4.90 4.36 3.92 3.56 3.00
6.21 5.54 4.99 4.54 3.84
7.67 6.86 6.20 5.65 4.79
9.23 10.9 12.7 8.29 9.83 11.5 7.51 8.93 10.4 6.85 8.17 9.57 5.82 6.96 8.17
28 32 36
0.10 0.09 0.08
0.30 0.27 0.24
0.57 0.50 0.45
0.94 0.83 0.74
1.40 1.23 1.10
1.95 1.72 1.53
2.60 2.28 2.04
3.32 2.93 2.61
4.15 3.66 3.27
5.05 4.46 3.98
2 3 4 5 6
0.87 0.68 0.55 0.47 0.41
3.21 2.76 2.38 2.07 1.83
5.35 4.88 4.40 3.96 3.56
7.42 7.00 6.53 6.04 5.56
9.45 9.09 8.65 8.17 7.67
11.5 11.1 10.7 10.3 9.80
7 8 9 10 12
0.36 0.32 0.29 0.27 0.23
1.63 1.47 1.34 1.23 1.05
3.22 2.92 2.66 2.45 2.09
5.12 4.73 4.37 4.05 3.53
7.19 6.72 6.29 5.90 5.21
9.30 11.4 8.81 10.9 8.33 10.4 7.88 9.95 7.06 9.04
14 16 18 20 24
0.20 0.17 0.16 0.14 0.12
0.91 0.81 0.72 0.66 0.55
1.83 1.62 1.45 1.32 1.11
3.11 2.78 2.50 2.28 1.93
4.64 4.17 3.77 3.45 2.93
6.35 5.75 5.24 4.80 4.10
8.22 10.2 12.2 7.51 9.38 11.4 6.88 8.66 10.5 6.34 8.02 9.82 5.46 6.95 8.57
28 32 36
0.10 0.09 0.08
0.48 0.42 0.37
0.96 0.84 0.75
1.67 1.47 1.32
2.54 2.24 2.00
3.57 3.16 2.83
4.78 4.24 3.80
6
7
10.7 12.8 9.80 11.9 8.84 10.9 7.94 9.98 7.15 9.09
13.5 13.2 12.8 12.4 11.9
8
9
10
11
12
14.8 14.0 13.0 12.1 11.1
16.9 16.1 15.2 14.2 13.2
18.9 18.2 17.3 16.3 15.3
20.9 20.2 19.4 18.4 17.4
22.9 22.3 21.5 20.5 19.6
14.3 13.4 12.6 11.8 10.4
16.4 15.5 14.6 13.7 12.2
18.6 17.6 16.6 15.7 14.1
6.05 5.34 4.78
7.12 6.29 5.64
15.5 15.2 14.9 14.5 14.0
17.4 17.2 16.9 16.5 16.1
19.4 19.2 18.9 18.6 18.2
21.4 21.2 20.9 20.6 20.3
23.4 23.2 22.9 22.6 22.3
13.6 13.1 12.6 12.1 11.1
15.7 15.2 14.7 14.2 13.2
17.8 17.3 16.8 16.3 15.3
19.9 19.4 18.9 18.5 17.5
21.9 21.5 21.0 20.6 19.6
14.3 13.4 12.5 11.7 10.3
16.5 15.5 14.5 13.7 12.1
18.6 17.6 16.6 15.7 14.0
6.11 5.44 4.89
7.58 6.77 6.10
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9.15 10.8 12.6 8.21 9.75 11.4 7.42 8.85 10.4
8 - 48
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-19 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 30°° C req =
Pu
φrn
or φR n = C × φ rn ex
where
Pu
s, in.
3
6
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
s
30°
s
s
e
3
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
0.97 0.75 0.62 0.52 0.45
2.60 2.12 1.78 1.53 1.34
4.52 3.83 3.29 2.85 2.51
6.54 5.71 4.99 4.39 3.89
8.59 7.71 6.88 6.16 5.54
10.6 9.75 8.87 8.06 7.33
12.9 11.8 10.9 10.0 9.23
14.7 13.9 13.0 12.1 11.2
16.7 15.9 15.1 14.1 13.2
18.8 18.0 17.1 16.2 15.3
20.8 20.0 19.2 18.3 17.3
22.8 22.1 21.3 20.4 19.4
7 8 9 10 12
0.40 0.36 0.32 0.30 0.25
1.19 1.07 0.97 0.88 0.75
2.23 2.00 1.81 1.66 1.41
3.48 3.15 2.87 2.64 2.27
5.01 4.57 4.19 3.87 3.34
6.70 6.14 5.66 5.24 4.54
8.51 10.4 7.86 9.68 7.28 9.02 6.77 8.43 5.92 7.43
12.4 11.6 10.9 10.2 9.04
14.4 13.6 12.8 12.0 10.8
16.4 15.6 14.7 13.9 12.5
18.5 17.6 16.7 15.9 14.4
14 16 18 20 24
0.22 0.19 0.17 0.16 0.13
0.65 0.58 0.52 0.47 0.39
1.23 1.08 0.97 0.88 0.74
1.98 1.76 1.58 1.43 1.21
2.93 2.60 2.34 2.12 1.79
3.99 3.56 3.21 2.92 2.48
5.24 4.69 4.24 3.87 3.29
6.61 5.94 5.38 4.92 4.18
8.09 7.30 6.64 6.08 5.19
9.67 11.4 8.77 10.3 8.00 9.45 7.34 8.70 6.29 7.48
28 32 36
0.12 0.10 0.09
0.34 0.30 0.26
0.64 0.56 0.50
1.04 0.92 0.82
1.55 1.36 1.21
2.14 1.89 1.69
2.85 2.51 2.25
3.63 3.21 2.87
4.52 4.00 3.59
5.49 4.87 4.37
2 3 4 5 6
0.97 0.75 0.62 0.52 0.45
3.20 2.75 2.39 2.10 1.87
5.31 4.86 4.42 4.02 3.67
7.37 6.95 6.49 6.04 5.61
9.39 9.01 8.57 8.11 7.66
11.4 11.1 10.6 10.2 9.73
7 8 9 10 12
0.40 0.36 0.32 0.30 0.25
1.69 1.53 1.40 1.29 1.12
3.36 3.08 2.84 2.63 2.28
5.21 4.84 4.51 4.21 3.70
7.21 6.79 6.40 6.04 5.39
9.27 11.4 8.82 10.9 8.39 10.4 7.98 9.99 7.23 9.16
14 16 18 20 24
0.22 0.19 0.17 0.16 0.13
0.98 0.87 0.79 0.71 0.60
2.00 1.78 1.60 1.45 1.23
3.29 2.95 2.68 2.45 2.08
4.86 4.40 4.02 3.70 3.17
6.57 6.01 5.52 5.09 4.39
8.41 10.3 7.75 9.60 7.17 8.93 6.65 8.33 5.79 7.32
28 32 36
0.12 0.10 0.09
0.52 0.46 0.41
1.06 0.93 0.83
1.82 1.61 1.44
2.77 2.45 2.20
3.85 3.42 3.08
5.11 4.56 4.12
13.4 13.1 12.7 12.3 11.8
6.54 5.81 5.22
13.1 12.0 11.0 10.1 8.75 7.68 6.83 6.15
15.4 15.1 14.7 14.3 13.9
17.4 17.1 16.8 16.4 16.0
19.4 19.1 18.8 18.4 18.0
21.3 21.1 20.8 20.4 20.1
23.3 23.1 22.8 22.5 22.1
13.4 13.0 12.5 12.0 11.2
15.5 15.1 14.6 14.1 13.2
17.6 17.1 16.7 16.2 15.3
19.6 19.2 18.7 18.3 17.3
21.7 21.3 20.8 20.4 19.4
12.3 11.5 10.8 10.1 8.95
14.4 13.5 12.7 12.0 10.7
16.4 15.5 14.7 13.9 12.5
18.5 17.6 16.7 15.9 14.4
6.49 5.82 5.27
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.99 7.20 6.53
9.59 11.3 13.0 8.68 10.3 11.9 7.91 9.37 10.9
ECCENTRICALLY LOADED BOLT GROUPS
8 - 49
Table 8-19 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 45°° C req =
Pu
φ rn
or φ R n = C × φrn ex
where
Pu
3
6
s
s
45°
s
e
s, in.
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
3
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.17 0.92 0.75 0.64 0.55
2.79 2.32 1.99 1.74 1.54
4.67 4.06 3.57 3.17 2.84
6.62 5.92 5.31 4.78 4.33
8.61 7.86 7.16 6.53 5.98
10.6 9.83 9.09 8.39 7.76
12.6 11.8 11.1 10.3 9.63
14.6 13.9 13.1 12.3 11.6
16.6 15.9 15.1 14.3 13.5
18.6 17.9 17.1 16.3 15.5
20.6 19.9 19.1 18.3 17.5
22.6 21.9 21.1 20.3 19.5
7 8 9 10 12
0.49 0.44 0.40 0.36 0.31
1.38 1.25 1.14 1.05 0.90
2.57 2.33 2.13 1.96 1.68
3.93 3.60 3.31 3.06 2.65
5.49 5.06 4.69 4.36 3.83
7.20 6.70 6.25 5.85 5.17
9.00 10.9 8.43 10.3 7.91 9.67 7.44 9.14 6.63 8.20
12.8 12.1 11.5 10.9 9.86
14.8 14.0 13.4 12.7 11.6
16.8 16.0 15.3 14.6 13.4
18.7 18.0 17.2 16.5 15.2
14 16 18 20 24
0.27 0.24 0.21 0.19 0.16
0.78 0.69 0.62 0.56 0.48
1.47 1.31 1.17 1.06 0.90
2.33 2.08 1.88 1.71 1.45
3.40 3.05 2.76 2.52 2.14
4.61 4.16 3.77 3.45 2.94
5.95 5.38 4.91 4.51 3.87
7.41 6.74 6.18 5.69 4.91
8.97 10.6 12.3 8.20 9.75 11.4 7.55 9.00 10.5 6.97 8.34 9.80 6.04 7.26 8.57
28 32 36
0.14 0.12 0.11
0.41 0.36 0.32
0.77 0.68 0.61
1.26 1.11 0.99
1.86 1.64 1.47
2.56 2.27 2.03
3.38 3.00 2.70
4.30 3.82 3.44
5.30 4.73 4.26
2 3 4 5 6
1.17 0.92 0.75 0.64 0.55
3.24 2.84 2.51 2.24 2.03
5.30 4.90 4.52 4.17 3.86
7.32 6.93 6.53 6.15 5.78
9.33 8.96 8.56 8.15 7.76
11.3 11.0 10.6 10.2 9.77
13.3 13.0 12.6 12.2 11.8
15.3 15.0 14.6 14.2 13.8
17.3 17.0 16.6 16.2 15.8
19.3 19.0 18.6 18.3 17.9
21.3 21.0 20.6 20.3 19.9
23.2 23.0 22.6 22.3 21.9
7 8 9 10 12
0.49 0.44 0.40 0.36 0.31
1.85 1.70 1.57 1.46 1.28
3.59 3.35 3.13 2.94 2.60
5.45 5.13 4.85 4.58 4.11
7.39 7.03 6.70 6.38 5.81
9.38 9.00 8.63 8.28 7.64
11.4 11.0 10.6 10.2 9.54
13.4 13.0 12.6 12.2 11.5
15.4 15.0 14.6 14.2 13.5
17.5 17.1 16.7 16.3 15.6
19.5 19.1 18.7 18.3 17.5
21.5 21.1 20.7 20.3 19.5
14 16 18 20 24
0.27 0.24 0.21 0.19 0.16
1.13 1.01 0.92 0.84 0.72
2.32 2.09 1.90 1.73 1.47
3.71 3.36 3.07 2.83 2.43
5.31 4.88 4.50 4.18 3.64
7.06 6.55 6.09 5.69 5.00
8.89 10.8 8.31 10.2 7.78 9.56 7.31 9.02 6.48 8.08
12.7 12.0 11.4 10.8 9.76
14.7 14.0 13.3 12.7 11.5
16.7 15.9 15.2 14.6 13.3
18.7 17.9 17.2 16.5 15.2
28 32 36
0.14 0.12 0.11
0.62 0.55 0.49
1.28 1.13 1.01
2.13 1.90 1.71
3.22 2.88 2.61
4.45 3.99 3.62
5.80 5.24 4.77
8.86 10.5 12.2 8.09 9.65 11.3 7.43 8.90 10.4
14.0 13.0 12.0
7.28 6.62 6.05
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.41 5.73 5.17
7.59 6.80 6.15
14.1 13.1 12.1 11.3 9.95 8.85 7.94 7.20
8 - 50
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-19 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 60°° C req =
Pu
φrn
or φR n = C × φ rn ex
where
3
6
s s
60°
s
e
s, in.
Pu
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
3
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.51 1.24 1.04 0.89 0.77
3.17 2.76 2.43 2.16 1.95
4.97 4.47 4.04 3.70 3.40
6.85 6.30 5.81 5.39 5.01
8.77 8.19 7.65 7.17 6.73
10.7 10.1 9.53 9.01 8.52
12.7 12.0 11.5 10.9 10.4
14.6 14.0 13.4 12.8 12.3
16.6 16.0 15.3 14.7 14.2
18.6 17.9 17.3 16.7 16.1
20.6 19.9 19.3 18.6 18.0
22.5 21.9 21.2 20.6 20.0
7 8 9 10 12
0.68 0.61 0.56 0.51 0.43
1.77 1.62 1.49 1.38 1.20
3.13 2.90 2.70 2.52 2.21
4.67 4.37 4.09 3.84 3.40
6.33 5.96 5.62 5.31 4.76
8.07 7.65 7.26 6.89 6.25
9.88 9.42 8.98 8.58 7.85
11.7 11.2 10.8 10.3 9.53
13.6 13.1 12.6 12.1 11.3
15.5 15.0 14.5 14.0 13.0
17.4 16.9 16.3 15.8 14.9
19.4 18.8 18.2 17.7 16.7
14 16 18 20 24
0.38 0.34 0.30 0.27 0.23
1.06 0.95 0.85 0.78 0.66
1.96 1.76 1.60 1.46 1.24
3.05 2.75 2.51 2.30 1.97
4.30 3.92 3.59 3.32 2.87
5.71 5.24 4.84 4.48 3.90
7.23 6.68 6.19 5.76 5.04
8.83 10.5 8.20 9.79 7.64 9.16 7.14 8.60 6.29 7.64
12.2 11.5 10.8 10.1 9.06
14.0 13.2 12.4 11.7 10.6
15.8 14.9 14.1 13.4 12.1
28 32 36
0.20 0.18 0.16
0.57 0.50 0.45
1.07 0.95 0.85
1.72 1.52 1.37
2.52 2.24 2.02
3.44 3.07 2.77
4.47 4.01 3.63
5.61 5.06 4.59
2 3 4 5 6
1.51 1.24 1.04 0.89 0.77
3.39 3.08 2.80 2.57 2.37
5.36 5.04 4.73 4.45 4.20
7.33 7.01 6.69 6.39 6.11
9.31 8.98 8.66 8.35 8.05
7 8 9 10 12
0.68 0.61 0.56 0.51 0.43
2.19 2.04 1.91 1.80 1.60
3.98 3.77 3.59 3.42 3.11
5.85 5.61 5.38 5.17 4.78
7.76 7.49 7.24 7.00 6.54
9.70 9.41 9.13 8.87 8.37
14 16 18 20 24
0.38 0.34 0.30 0.27 0.23
1.44 1.31 1.20 1.10 0.95
2.85 2.63 2.43 2.26 1.97
4.43 4.12 3.84 3.58 3.15
6.13 5.74 5.40 5.08 4.53
7.91 7.48 7.08 6.71 6.06
9.74 9.27 8.84 8.43 7.69
28 32 36
0.20 0.18 0.16
0.84 0.74 0.67
1.73 1.54 1.39
2.80 2.52 2.28
4.08 3.71 3.39
5.52 5.05 4.65
7.06 6.51 6.02
11.3 11.0 10.6 10.3 10.0
6.85 6.20 5.65
8.17 7.41 6.77
9.55 11.0 8.70 10.1 7.98 9.26
13.3 12.9 12.6 12.3 12.0
15.2 14.9 14.6 14.3 13.9
17.2 16.9 16.6 16.2 15.9
19.2 18.9 18.6 18.2 17.9
21.2 20.9 20.5 20.2 19.9
23.2 22.8 22.5 22.2 21.8
11.7 11.6 11.1 10.8 10.2
13.6 13.3 13.0 12.7 12.1
15.6 15.3 15.0 14.7 14.1
17.6 17.2 16.9 16.6 16.0
19.5 19.2 18.9 18.6 18.0
21.5 21.2 20.9 20.5 19.9
11.6 11.1 10.7 10.2 9.39
13.5 13.0 12.5 12.0 11.2
15.4 14.9 14.4 13.9 12.9
17.4 16.8 16.3 15.7 14.8
19.3 18.7 18.2 17.6 16.6
8.68 10.4 12.1 8.05 9.66 11.3 7.49 9.03 10.7
13.9 13.1 12.3
15.7 14.8 14.0
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 51
Table 8-19 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 75°° C req =
Pu
φ rn
or φ R n = C × φrn ex
where
75°
3
6
s
Pu
s
s
e
s, in.
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
3
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.84 1.71 1.57 1.44 1.31
3.63 3.41 3.19 2.98 2.79
5.44 5.17 4.90 4.65 4.41
7.29 6.97 6.67 6.39 6.12
9.17 8.82 8.50 8.19 7.90
11.1 10.7 10.4 10.0 9.71
13.0 12.6 12.2 11.9 11.6
14.9 14.5 14.1 13.8 13.4
16.9 16.4 16.0 15.7 15.3
18.8 18.4 18.0 17.6 17.2
20.8 20.3 19.9 19.5 19.1
22.7 22.3 21.8 21.4 21.0
7 8 9 10 12
1.20 1.10 1.01 0.93 0.81
2.61 2.45 2.31 2.18 1.95
4.19 3.99 3.81 3.63 3.33
5.88 5.65 5.43 5.23 4.86
7.62 7.37 7.14 6.91 6.49
9.42 9.14 8.89 8.65 8.19
11.3 11.0 10.7 10.4 9.94
13.1 12.8 12.5 12.2 11.7
15.0 14.7 14.3 14.1 13.5
16.9 16.5 16.2 15.9 15.3
18.8 18.4 18.1 17.8 17.2
20.7 20.3 20.0 19.6 19.0
14 16 18 20 24
0.71 0.63 0.57 0.52 0.44
1.77 1.61 1.48 1.36 1.18
3.06 2.83 2.63 2.45 2.15
4.53 4.23 3.96 3.72 3.30
6.11 5.75 5.42 5.12 4.60
7.76 7.36 6.98 6.63 6.02
9.47 11.2 9.03 10.8 8.61 10.3 8.23 9.88 7.53 9.12
13.0 12.5 12.0 11.6 10.8
14.8 14.3 13.8 13.3 12.4
16.6 16.1 15.6 15.1 14.2
18.4 17.9 17.4 16.9 15.9
28 32 36
0.38 0.34 0.30
1.04 0.92 0.83
1.91 1.71 1.55
2.95 2.67 2.43
4.16 3.78 3.47
5.49 5.04 4.65
6.93 6.41 5.94
11.7 10.9 10.3
13.3 12.6 11.9
15.0 14.2 13.5
2 3 4 5 6
1.84 1.71 1.57 1.44 1.31
3.66 3.49 3.32 3.16 3.02
5.55 5.36 5.18 5.01 4.84
7.48 7.27 7.08 6.89 6.72
9.42 9.20 9.00 8.81 8.62
11.4 11.2 10.9 10.7 10.5
13.3 13.1 12.9 12.7 12.5
15.3 15.1 14.8 14.6 14.4
17.6 17.0 16.8 16.6 16.3
19.6 19.0 18.7 18.5 18.3
21.5 21.0 20.7 20.5 20.2
23.5 22.9 22.7 22.4 22.2
7 8 9 10 12
1.20 1.10 1.01 0.93 0.81
2.88 2.75 2.63 2.52 2.32
4.69 4.54 4.40 4.27 4.03
6.55 6.39 6.24 6.09 5.82
8.44 8.27 8.11 7.95 7.66
10.4 10.2 10.0 9.83 9.52
12.3 12.1 11.9 11.7 11.4
14.2 14.0 13.8 13.6 13.3
16.1 15.9 15.7 15.6 15.2
18.1 17.9 17.7 17.5 17.1
20.0 19.8 19.6 19.4 19.0
22.0 21.8 21.5 21.3 20.9
14 16 18 20 24
0.71 0.63 0.57 0.52 0.44
2.15 2.00 1.87 1.75 1.55
3.82 3.62 3.44 3.28 2.98
5.57 5.35 5.14 4.94 4.57
7.38 7.13 6.90 6.67 6.24
9.22 8.95 8.69 8.45 7.98
11.1 10.8 10.5 10.3 9.75
13.0 12.7 12.4 12.1 11.6
14.9 14.5 14.2 13.9 13.4
16.7 16.4 16.1 15.8 15.2
18.7 18.3 18.0 17.7 17.1
20.6 20.2 19.9 19.5 18.9
28 32 36
0.38 0.34 0.30
1.40 1.27 1.16
2.74 2.52 2.33
4.24 3.95 3.68
5.85 5.49 5.16
7.54 7.13 6.75
9.28 11.1 8.83 10.6 8.41 10.1
12.9 12.4 11.9
14.7 14.1 13.7
16.5 16.0 15.4
18.3 17.8 17.3
8.45 10.0 7.86 9.37 7.32 8.78
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 52
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-20. Coefficients C for Eccentrically Loaded Bolt Groups Angle = 0°° C req =
Pu
φrn
or φR n = C × φ rn ex = e
where
s, in.
3
6
Pu
s
s
s
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
5½
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.14 0.94 0.80 0.70 0.62
2.75 2.32 1.99 1.74 1.54
4.59 3.92 3.39 2.96 2.62
6.61 5.80 5.10 4.51 4.03
8.69 7.82 6.98 6.24 5.60
10.8 9.90 9.00 8.15 7.39
12.9 12.0 11.1 10.2 9.30
14.9 14.1 13.2 12.3 11.3
17.0 16.2 15.3 14.4 13.4
19.0 18.3 17.4 16.5 15.5
21.0 20.4 19.6 18.6 17.7
23.0 22.4 21.7 20.8 19.8
7 8 9 10 12
0.55 0.50 0.46 0.42 0.37
1.38 1.25 1.14 1.04 0.90
2.36 2.14 1.96 1.80 1.55
3.63 3.30 3.01 2.78 2.39
5.07 4.61 4.22 3.89 3.36
6.72 6.15 5.66 5.23 4.53
8.53 10.5 7.84 9.67 7.23 8.97 6.70 8.34 5.82 7.28
12.5 11.6 10.8 10.1 8.87
14.6 13.6 12.8 12.0 10.6
16.7 15.7 14.8 13.9 12.4
18.8 17.8 16.9 15.9 14.2
14 16 18 20 24
0.32 0.29 0.26 0.24 0.20
0.79 0.70 0.63 0.57 0.48
1.36 1.21 1.09 0.99 0.84
2.10 1.87 1.68 1.53 1.29
2.96 2.64 2.37 2.16 1.83
3.99 3.55 3.20 2.91 2.46
5.13 4.58 4.14 3.77 3.19
6.44 5.76 5.21 4.75 4.03
7.87 7.05 6.38 5.82 4.94
9.42 11.1 12.8 8.47 9.99 11.6 7.68 9.08 10.6 7.02 8.30 9.69 5.97 7.07 8.28
28 32 36
0.18 0.16 0.14
0.42 0.37 0.33
0.73 0.64 0.57
1.11 0.98 0.88
1.58 1.39 1.24
2.13 1.88 1.68
2.77 2.44 2.18
3.49 3.08 2.75
4.29 3.79 3.39
5.19 4.58 4.10
2 3 4 5 6
1.14 0.94 0.80 0.70 0.62
3.25 2.86 2.52 2.24 2.00
5.37 4.93 4.47 4.04 3.65
7.45 7.05 6.59 6.12 5.66
9.49 9.14 8.72 8.25 7.77
11.5 11.2 10.8 10.4 9.91
13.5 13.2 12.9 12.5 12.1
15.5 15.3 15.0 14.6 14.2
17.5 17.3 17.0 16.7 16.3
19.5 19.3 19.0 18.7 18.4
21.4 21.3 21.0 20.8 20.4
23.4 23.3 23.0 22.8 22.5
7 8 9 10 12
0.55 0.50 0.46 0.42 0.37
1.80 1.64 1.50 1.38 1.19
3.31 3.02 2.77 2.56 2.21
5.23 4.84 4.49 4.18 3.65
7.29 6.83 6.39 5.99 5.29
9.42 8.93 8.45 7.99 7.16
11.6 11.1 10.6 10.1 9.15
13.7 13.2 12.7 12.2 11.2
15.8 15.4 14.9 14.4 13.4
17.9 17.5 17.0 16.5 15.5
20.0 19.6 19.2 18.7 17.7
22.1 21.7 21.3 20.8 19.8
14 16 18 20 24
0.32 0.29 0.26 0.24 0.20
1.04 0.93 0.84 0.76 0.64
1.95 1.74 1.57 1.43 1.21
3.24 2.90 2.62 2.39 2.02
4.72 4.24 3.84 3.50 2.98
6.44 5.83 5.31 4.87 4.16
8.32 10.3 12.4 7.59 9.48 11.5 6.95 8.74 10.7 6.39 8.08 9.89 5.49 6.99 8.61
14.5 13.6 12.6 11.8 10.4
16.7 15.7 14.7 13.8 12.2
18.8 17.8 16.8 15.9 14.1
28 32 36
0.18 0.16 0.14
0.55 0.49 0.43
1.05 0.93 0.83
1.76 1.55 1.38
2.59 2.29 2.05
3.63 3.21 2.88
4.80 4.25 3.81
6.13 5.45 4.90
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.59 6.77 6.09
6.15 5.44 4.87
7.21 6.38 5.72
9.18 10.9 12.7 8.21 9.76 11.4 7.41 8.83 10.4
ECCENTRICALLY LOADED BOLT GROUPS
8 - 53
Table 8-20 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 15°° C req =
Pu
φ rn
or φ R n = C × φrn ex
where
Pu
s, in.
3
6
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
s
15°
s
s
e
1 5½
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.18 0.97 0.83 0.72 0.64
2.78 2.34 2.02 1.77 1.57
4.61 3.97 3.45 3.03 2.70
6.59 5.80 5.11 4.54 4.06
8.64 7.78 6.97 6.26 5.65
10.7 9.83 8.94 8.12 7.39
12.8 11.9 11.0 10.1 9.27
14.8 14.0 13.1 12.1 11.2
16.8 16.1 15.2 14.2 13.3
18.9 18.1 17.3 16.3 15.4
20.9 20.2 19.3 18.4 17.5
22.9 22.2 21.4 20.5 19.6
7 8 9 10 12
0.57 0.52 0.48 0.44 0.38
1.41 1.28 1.17 1.07 0.93
2.43 2.20 2.01 1.85 1.60
3.66 3.34 3.06 2.82 2.44
5.13 4.68 4.30 3.98 3.44
6.74 6.18 5.70 5.27 4.58
8.52 10.4 7.86 9.65 7.27 8.97 6.76 8.36 5.90 7.34
12.4 11.6 10.8 10.1 8.91
14.4 13.5 12.7 11.9 10.6
16.5 15.6 14.7 13.8 12.4
18.6 17.6 16.7 15.8 14.2
14 16 18 20 24
0.33 0.30 0.27 0.25 0.21
0.81 0.72 0.65 0.59 0.50
1.40 1.25 1.13 1.02 0.87
2.15 1.91 1.72 1.57 1.33
3.03 2.70 2.44 2.22 1.88
4.05 3.62 3.27 2.98 2.53
5.22 4.68 4.23 3.86 3.27
6.51 5.84 5.28 4.83 4.11
7.94 7.14 6.48 5.93 5.05
9.47 11.1 12.8 8.54 10.1 11.7 7.77 9.16 10.7 7.11 8.40 9.78 6.07 7.19 8.39
28 32 36
0.18 0.16 0.14
0.43 0.38 0.34
0.75 0.66 0.59
1.15 1.01 0.90
1.63 1.43 1.28
2.19 1.93 1.73
2.84 2.50 2.24
3.57 3.15 2.82
4.39 3.88 3.48
5.29 4.68 4.19
2 3 4 5 6
1.18 0.97 0.83 0.72 0.64
3.24 2.85 2.51 2.23 2.00
5.34 4.90 4.45 4.05 3.68
7.40 6.99 6.53 6.07 5.62
9.43 9.07 8.63 8.16 7.69
11.5 11.1 10.7 10.3 9.80
7 8 9 10 12
0.57 0.52 0.48 0.44 0.38
1.81 1.65 1.52 1.40 1.21
3.36 3.08 2.83 2.62 2.27
5.20 4.82 4.48 4.18 3.66
7.22 6.78 6.36 5.98 5.31
9.31 11.4 8.83 10.9 8.37 10.5 7.93 9.97 7.13 9.08
14 16 18 20 24
0.33 0.30 0.27 0.25 0.21
1.07 0.95 0.86 0.78 0.66
2.00 1.79 1.62 1.47 1.25
3.25 2.92 2.65 2.42 2.06
4.76 4.29 3.90 3.58 3.05
6.44 5.85 5.34 4.91 4.21
8.28 10.2 12.3 7.58 9.43 11.4 6.97 8.72 10.6 6.43 8.09 9.87 5.55 7.03 8.64
28 32 36
0.18 0.16 0.14
0.57 0.50 0.45
1.08 0.95 0.85
1.79 1.58 1.42
2.66 2.35 2.11
3.68 3.26 2.93
4.87 4.33 3.90
13.5 13.2 12.8 12.4 11.9
6.28 5.56 4.99
7.33 6.50 5.84
15.4 15.2 14.8 14.5 14.0
17.4 17.2 16.87 16.5 16.1
19.4 19.2 18.9 18.6 18.2
21.4 21.2 20.9 20.6 20.2
23.4 23.1 23.0 22.6 22.3
13.5 13.1 12.6 12.1 11.1
15.7 15.2 14.7 14.2 13.2
17.7 17.3 16.8 16.3 15.3
19.8 19.4 18.9 18.4 17.4
21.9 21.4 21.0 20.6 19.6
14.3 13.4 12.5 11.7 10.4
16.4 15.5 14.6 13.7 12.2
18.6 17.6 16.6 15.7 14.1
6.19 5.52 4.97
7.65 6.84 6.18
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9.22 10.9 12.6 8.27 9.81 11.4 7.49 8.91 10.4
8 - 54
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-20 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 30°° C req =
Pu
φrn
or φR n = C × φ rn ex
where
Pu
s, in.
3
6
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
s
30°
s
s
e
5½
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.30 1.08 0.92 0.80 0.71
2.90 2.47 2.14 1.89 1.69
4.72 4.13 3.64 3.24 2.91
6.66 5.94 5.30 4.76 4.29
8.65 7.86 7.12 6.46 5.88
10.7 9.85 9.04 8.29 7.61
12.7 11.9 11.0 10.2 9.45
14.7 13.9 13.0 12.2 11.4
16.7 16.0 15.1 14.2 13.4
18.7 18.0 17.1 16.3 15.4
20.8 20.0 19.2 18.3 17.4
22.8 22.1 21.2 20.4 19.5
7 8 9 10 12
0.64 0.58 0.53 0.49 0.42
1.53 1.39 1.28 1.18 1.02
2.63 2.40 2.20 2.03 1.76
3.90 3.57 3.29 3.04 2.65
5.38 4.95 4.58 4.26 3.72
7.01 6.49 6.02 5.61 4.92
8.76 10.6 8.14 9.92 7.59 9.29 7.09 8.72 6.25 7.73
12.5 11.8 11.1 10.4 9.31
14.5 13.7 12.9 12.2 11.0
16.5 15.7 14.9 14.1 12.8
18.6 17.7 16.8 16.0 14.6
14 16 18 20 24
0.37 0.33 0.30 0.27 0.23
0.90 0.80 0.72 0.66 0.56
1.55 1.38 1.25 1.13 0.96
2.34 2.09 1.89 1.73 1.46
3.29 2.95 2.67 2.43 2.07
4.37 3.92 3.55 3.25 2.77
5.58 5.03 4.57 4.19 3.57
6.93 6.26 5.70 5.23 4.47
8.38 7.59 6.93 6.36 5.47
9.93 11.6 9.03 10.6 8.27 9.70 7.62 8.95 6.56 7.73
28 32 36
0.20 0.18 0.16
0.48 0.43 0.38
0.83 0.73 0.66
1.27 1.12 1.00
1.79 1.58 1.42
2.41 2.13 1.91
3.11 2.76 2.47
3.90 3.46 3.10
4.78 4.25 3.81
5.75 5.11 4.59
2 3 4 5 6
1.30 1.08 0.92 0.80 0.71
3.27 2.89 2.56 2.29 2.08
5.33 4.91 4.50 4.13 3.80
7.36 6.96 6.53 6.10 5.69
9.38 9.01 8.58 8.14 7.70
11.4 11.0 10.6 10.2 9.75
13.4 13.1 12.7 12.3 11.8
15.4 15.1 14.7 14.3 13.9
17.4 17.1 16.8 16.4 15.9
19.3 19.1 18.8 18.4 18.0
21.3 21.1 20.8 20.4 20.0
23.3 23.0 22.8 22.5 22.1
7 8 9 10 12
0.64 0.58 0.53 0.49 0.42
1.89 1.74 1.61 1.49 1.30
3.51 3.25 3.02 2.81 2.47
5.31 4.96 4.64 4.35 3.85
7.27 6.86 6.49 6.13 5.51
9.30 8.86 8.44 8.04 7.31
11.4 10.9 10.5 10.0 9.22
13.4 13.0 12.5 12.1 11.2
15.5 15.0 14.6 14.1 13.2
17.6 17.1 16.7 16.2 15.3
19.6 19.2 18.7 18.3 17.3
21.7 21.3 20.8 20.4 19.4
14 16 18 20 24
0.37 0.33 0.30 0.27 0.23
1.15 1.03 0.93 0.85 0.72
2.19 1.96 1.78 1.62 1.38
3.44 3.11 2.83 2.60 2.23
4.98 4.54 4.16 3.83 3.30
6.67 6.12 5.63 5.21 4.51
8.49 10.4 7.83 9.66 7.26 9.00 6.74 8.41 5.89 7.40
12.4 11.6 10.8 10.2 9.02
14.4 13.5 12.8 12.0 10.7
16.4 15.6 14.7 13.9 12.5
18.5 17.6 16.7 15.9 14.4
28 32 36
0.20 0.18 0.16
0.63 0.55 0.50
1.20 1.06 0.95
1.95 1.73 1.55
2.89 2.57 2.31
3.96 3.53 3.18
5.21 4.67 4.22
6.59 5.92 5.36
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8.07 7.28 6.61
6.78 6.04 5.44
13.3 12.2 11.2 10.4 8.99 7.91 7.06 6.36
9.66 11.3 13.1 8.75 10.3 12.0 7.98 9.43 11.0
ECCENTRICALLY LOADED BOLT GROUPS
8 - 55
Table 8-20 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 45°° C req =
Pu
φ rn
or φ R n = C × φrn ex
where
Pu
3
6
s
s
45°
s
e
s, in.
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
5½
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.53 1.30 1.11 0.98 0.87
3.18 2.76 2.43 2.17 1.95
4.96 4.42 3.97 3.60 3.28
6.84 6.22 5.67 5.19 4.77
8.77 8.09 7.46 6.89 6.37
10.7 10.0 9.32 8.68 8.09
12.7 12.0 11.2 10.6 9.90
14.7 14.0 13.2 12.5 11.8
16.7 15.9 15.2 14.4 13.7
18.7 17.9 17.2 16.4 15.6
20.7 19.9 19.2 18.4 17.6
22.6 21.9 21.2 20.4 19.6
7 8 9 10 12
0.78 0.71 0.65 0.60 0.52
1.78 1.63 1.50 1.39 1.22
3.01 2.77 2.57 2.39 2.08
4.40 4.07 3.78 3.52 3.09
5.91 5.50 5.13 4.81 4.26
7.56 7.07 6.64 6.25 5.58
9.31 11.1 8.76 10.5 8.26 9.97 7.81 9.45 7.01 8.54
13.0 12.4 11.8 11.2 10.2
14.9 14.2 13.6 13.0 11.9
16.9 16.2 15.5 14.8 13.6
18.8 18.1 17.4 16.7 15.4
14 16 18 20 24
0.45 0.41 0.37 0.33 0.28
1.08 0.96 0.87 0.79 0.68
1.85 1.65 1.50 1.37 1.16
2.75 2.48 2.25 2.06 1.76
3.82 3.45 3.14 2.88 2.47
5.02 4.55 4.16 3.82 3.28
6.34 5.77 5.29 4.87 4.21
7.76 7.09 6.53 6.04 5.23
9.28 10.9 8.53 10.1 7.87 9.30 7.30 8.65 6.35 7.55
12.6 11.6 10.8 10.1 8.85
14.3 13.3 12.4 11.6 10.2
28 32 36
0.25 0.22 0.20
0.59 0.52 0.46
1.01 0.89 0.80
1.53 1.35 1.21
2.15 1.91 1.71
2.87 2.55 2.29
3.69 3.29 2.96
4.61 4.11 3.70
5.61 5.01 4.53
2 3 4 5 6
1.53 1.30 1.11 0.98 0.87
3.39 3.04 2.74 2.49 2.28
5.36 4.99 4.64 4.31 4.02
7.35 6.98 6.60 6.24 5.89
9.35 8.98 8.60 8.21 7.84
11.3 11.0 10.6 10.2 9.82
13.3 13.0 12.6 12.2 11.8
15.3 15.0 14.6 14.2 13.8
17.3 17.0 16.6 16.3 15.9
19.3 19.0 18.6 18.3 17.9
21.3 21.0 20.6 20.3 19.9
23.2 22.9 22.6 22.3 21.9
7 8 9 10 12
0.78 0.71 0.65 0.60 0.52
2.10 1.94 1.81 1.69 1.50
3.76 3.53 3.32 3.13 2.80
5.57 5.28 5.00 4.74 4.29
7.48 7.13 6.81 6.50 5.94
9.44 9.07 8.71 8.37 7.74
11.4 11.0 10.7 10.3 9.61
13.4 13.0 12.7 12.3 11.5
15.5 15.1 14.7 14.3 13.5
17.5 17.1 16.7 16.3 15.5
19.5 19.1 18.7 18.3 17.5
21.5 21.1 20.7 20.3 19.5
14 16 18 20 24
0.45 0.41 0.37 0.33 0.28
1.34 1.21 1.10 1.01 0.86
2.52 2.29 2.09 1.92 1.64
3.89 3.55 3.26 3.01 2.61
5.45 5.02 4.65 4.33 3.79
7.17 6.67 6.22 5.82 5.13
8.98 10.9 8.41 10.2 7.89 9.65 7.42 9.11 6.60 8.17
12.8 12.1 11.5 10.9 9.84
14.7 14.0 13.4 12.7 11.6
16.7 16.0 15.3 14.6 13.4
18.7 17.9 17.2 16.5 15.2
28 32 36
0.25 0.22 0.20
0.75 0.67 0.60
1.44 1.27 1.14
2.30 2.05 1.85
3.36 3.02 2.73
4.58 4.12 3.74
5.92 5.35 4.88
8.95 10.6 12.3 8.18 9.73 11.4 7.52 8.98 10.5
14.1 13.0 12.1
7.38 6.72 6.15
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.69 6.00 5.43
7.87 7.07 6.40
9.11 8.20 7.44
8 - 56
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-20 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 60°° C req =
Pu
φrn
or φR n = C × φ rn ex
where
3
6
s
s
60°
s
e
s, in.
Pu
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
5½
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.78 1.62 1.45 1.31 1.18
3.55 3.26 2.97 2.71 2.48
5.34 4.95 4.57 4.23 3.93
7.17 6.71 6.27 5.86 5.50
9.04 8.53 8.04 7.58 7.16
10.9 10.4 9.86 9.36 8.90
12.9 12.3 11.7 11.2 10.7
14.8 14.2 13.6 13.1 12.5
16.7 16.1 15.5 15.0 14.4
18.7 18.1 17.5 16.9 16.3
20.6 20.0 19.4 18.8 18.2
22.6 22.0 21.4 20.7 20.1
7 8 9 10 12
1.07 0.98 0.90 0.83 0.72
2.28 2.11 1.97 1.84 1.62
3.66 3.43 3.22 3.03 2.70
5.18 4.88 4.61 4.37 3.93
6.79 6.45 6.12 5.82 5.28
8.48 10.2 8.09 9.80 7.72 9.39 7.37 9.00 6.73 8.28
12.0 11.6 11.1 10.7 9.91
13.9 13.4 12.9 12.5 11.6
15.7 15.2 14.7 14.2 13.4
17.6 17.1 16.6 16.1 15.1
19.5 19.0 18.4 17.9 16.9
14 16 18 20 24
0.64 0.57 0.52 0.47 0.40
1.45 1.31 1.19 1.09 0.93
2.43 2.21 2.02 1.85 1.59
3.56 3.24 2.98 2.75 2.37
4.81 4.42 4.07 3.77 3.28
6.19 5.71 5.29 4.93 4.32
7.66 7.11 6.63 6.19 5.46
9.22 10.9 8.60 10.2 8.05 9.55 7.55 8.98 6.69 8.01
12.5 11.8 11.1 10.5 9.41
14.3 13.5 12.7 12.1 10.9
16.0 15.2 14.4 13.7 12.4
28 32 36
0.35 0.31 0.28
0.82 0.72 0.65
1.39 1.24 1.11
2.08 1.86 1.67
2.90 2.59 2.34
3.83 3.43 3.11
4.86 4.37 3.97
5.99 5.41 4.93
2 3 4 5 6
1.78 1.62 1.45 1.31 1.18
3.59 3.35 3.11 2.89 2.70
5.48 5.20 4.93 4.66 4.42
7.41 7.12 6.82 6.53 6.26
9.36 9.06 8.75 8.45 8.16
7 8 9 10 12
1.07 0.98 0.90 0.83 0.72
2.52 2.36 2.23 2.10 1.89
4.19 3.99 3.81 3.64 3.34
6.01 5.77 5.55 5.35 4.97
7.88 7.62 7.37 7.13 6.70
9.79 9.51 9.24 8.98 8.49
14 16 18 20 24
0.64 0.57 0.52 0.47 0.40
1.71 1.57 1.44 1.33 1.16
3.08 2.85 2.65 2.47 2.17
4.63 4.32 4.04 3.79 3.36
6.29 5.92 5.58 5.26 4.71
8.04 7.62 7.22 6.86 6.21
9.85 9.39 8.95 8.55 7.82
28 32 36
0.35 0.31 0.28
1.02 0.91 0.82
1.92 1.72 1.56
3.00 2.71 2.46
4.26 3.88 3.55
5.67 5.20 4.80
7.19 6.64 6.16
11.3 11.0 10.7 10.4 10.1
7.21 6.54 5.98
8.51 7.75 7.10
9.88 11.3 9.02 10.4 8.29 9.55
13.3 13.0 12.7 12.3 12.0
15.3 15.0 14.6 14.3 14.0
17.2 16.9 16.6 16.3 15.9
19.2 18.9 18.6 18.2 17.9
21.2 20.9 20.6 20.2 19.9
23.2 22.9 22.5 22.2 21.9
11.7 11.4 11.1 10.9 10.3
13.7 13.4 13.1 12.8 12.2
15.6 15.3 15.0 14.7 14.1
17.6 17.3 17.0 16.7 16.1
19.6 19.2 18.9 18.6 18.0
21.5 21.2 20.9 20.6 19.9
11.7 11.2 10.7 10.3 9.50
13.6 13.1 12.6 12.1 11.2
15.5 15.0 14.4 13.9 13.0
17.4 16.9 16.3 15.8 14.8
19.3 18.8 18.2 17.7 16.7
8.80 10.5 12.2 8.17 9.77 11.4 7.61 9.14 10.7
14.0 13.1 12.4
15.8 14.9 14.1
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 57
Table 8-20 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 75°° C req =
Pu
φ rn
or φ R n = C × φrn ex
where
3
6
s s s
e
s, in.
75° P u
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
5½
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.92 1.87 1.82 1.75 1.68
3.82 3.72 3.60 3.47 3.33
5.70 5.54 5.37 5.18 5.00
7.57 7.36 7.14 6.92 6.69
9.45 9.19 8.94 8.68 8.42
11.3 11.1 10.8 10.5 10.2
13.2 12.9 12.6 12.3 12.0
15.2 14.8 14.5 14.1 13.8
17.1 16.7 16.3 16.0 15.7
19.0 18.6 18.2 17.9 17.5
20.9 20.5 20.1 19.8 19.4
22.9 22.5 22.1 21.7 21.3
7 8 9 10 12
1.60 1.52 1.45 1.38 1.25
3.19 3.06 2.93 2.80 2.57
4.81 4.63 4.46 4.29 3.98
6.47 6.26 6.05 5.85 5.48
8.17 7.93 7.70 7.48 7.07
9.92 9.66 9.41 9.16 8.71
11.7 11.4 11.2 10.9 10.4
13.5 13.2 12.9 12.6 12.1
15.3 15.0 14.7 14.4 13.9
17.2 16.9 16.5 16.2 15.7
19.1 18.7 18.4 18.1 17.5
20.9 20.6 20.3 19.9 19.3
14 16 18 20 24
1.13 1.03 0.95 0.87 0.75
2.36 2.18 2.02 1.88 1.65
3.70 3.45 3.23 3.03 2.69
5.15 4.85 4.57 4.32 3.87
6.69 6.34 6.01 5.71 5.17
8.29 7.90 7.54 7.19 6.57
9.96 9.53 9.13 8.75 8.05
11.7 11.2 10.8 10.4 9.60
13.4 12.9 12.5 12.0 11.2
15.2 14.7 14.2 13.7 12.9
16.9 16.4 15.9 15.4 14.5
18.7 18.2 17.7 17.2 16.2
28 32 36
0.66 0.59 0.53
1.46 1.31 1.19
2.42 2.18 1.99
3.50 3.19 2.92
4.71 4.32 3.98
6.03 5.56 5.15
7.44 6.90 6.42
12.1 11.4 10.7
13.7 12.9 12.2
15.4 14.6 13.8
2 3 4 5 6
1.92 1.87 1.82 1.75 1.68
3.80 3.70 3.59 3.48 3.36
5.69 5.55 5.40 5.26 5.11
7.59 7.42 7.25 7.09 6.93
9.51 9.32 9.14 8.96 8.78
11.5 11.2 11.1 10.9 10.7
13.4 13.2 13.0 12.8 12.6
15.4 15.1 14.9 14.7 14.5
17.6 17.1 16.9 16.6 16.4
19.6 19.0 18.8 18.6 18.4
21.5 21.0 20.8 20.5 20.3
23.5 23.0 22.7 22.5 22.2
7 8 9 10 12
1.60 1.52 1.45 1.38 1.25
3.24 3.13 3.02 2.91 2.72
4.97 4.84 4.71 4.58 4.34
6.77 6.62 6.47 6.33 6.07
8.62 8.45 8.29 8.14 7.85
10.5 10.3 10.2 9.98 9.67
12.4 12.2 12.0 11.9 11.5
14.3 14.1 13.9 13.7 13.4
16.2 16.0 15.8 15.6 15.3
18.1 17.9 17.7 17.6 17.2
20.1 19.9 19.7 19.5 19.1
22.0 21.8 21.6 21.4 21.0
14 16 18 20 24
1.13 1.03 0.95 0.87 0.75
2.54 2.38 2.24 2.11 1.88
4.13 3.92 3.74 3.57 3.27
5.82 5.59 5.38 5.17 4.80
7.57 7.32 7.09 6.87 6.44
9.38 9.10 8.85 8.61 8.15
11.2 10.9 10.7 10.4 9.90
13.1 12.8 12.5 12.2 11.7
15.0 14.6 14.3 14.0 13.5
16.8 16.5 16.2 15.9 15.3
18.7 18.4 18.1 17.7 17.1
20.6 20.3 19.9 19.6 19.0
28 32 36
0.66 0.59 0.53
1.70 1.55 1.42
3.00 2.77 2.57
4.47 4.17 3.90
6.06 5.70 5.37
7.72 7.31 6.93
9.43 11.2 8.99 10.7 8.57 10.3
13.0 12.5 12.0
14.8 14.3 13.8
16.6 16.1 15.5
18.4 17.9 17.3
8.93 10.5 8.32 9.81 7.78 9.21
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 58
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-21. Coefficients C for Eccentrically Loaded Bolt Groups Angle = 0°° C req =
Pu
φrn
or φR n = C × φ rn ex = e
where
s, in.
3
6
Pu
s
s
s
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
8
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.31 1.12 0.98 0.87 0.79
2.91 2.54 2.24 1.99 1.80
4.71 4.14 3.66 3.27 2.95
6.66 5.95 5.33 4.80 4.35
8.69 7.90 7.15 6.48 5.90
10.8 9.93 9.10 8.33 7.63
12.8 12.0 11.1 10.3 9.49
14.9 14.1 13.2 12.3 11.5
16.9 16.2 15.3 14.4 13.5
18.9 18.2 17.4 16.5 15.6
21.0 20.3 19.5 18.6 17.7
23.0 22.4 21.6 20.7 19.8
7 8 9 10 12
0.71 0.65 0.60 0.56 0.49
1.63 1.49 1.38 1.28 1.11
2.68 2.46 2.27 2.11 1.84
3.97 3.65 3.37 3.13 2.73
5.40 4.97 4.59 4.27 3.73
7.02 6.48 6.01 5.59 4.90
8.77 10.7 8.13 9.91 7.55 9.24 7.04 8.64 6.19 7.63
12.6 11.8 11.1 10.4 9.18
14.6 13.8 13.0 12.2 10.9
16.7 15.8 14.9 14.1 12.6
18.8 17.9 17.0 16.1 14.5
14 16 18 20 24
0.44 0.39 0.36 0.33 0.28
0.99 0.89 0.80 0.73 0.63
1.64 1.47 1.33 1.22 1.04
2.42 2.17 1.97 1.80 1.53
3.31 2.98 2.70 2.47 2.10
4.36 3.91 3.55 3.25 2.77
5.50 4.95 4.50 4.12 3.51
6.80 6.13 5.57 5.10 4.35
8.20 7.40 6.73 6.17 5.28
9.73 11.4 13.1 8.80 10.3 11.9 8.02 9.39 10.9 7.35 8.62 9.99 6.30 7.39 8.59
28 32 36
0.25 0.22 0.20
0.55 0.48 0.43
0.91 0.80 0.72
1.33 1.18 1.06
1.83 1.62 1.45
2.41 2.13 1.91
3.06 2.71 2.43
3.79 3.36 3.01
4.60 4.08 3.66
5.50 4.87 4.37
2 3 4 5 6
1.31 1.12 0.98 0.87 0.79
3.28 2.93 2.63 2.37 2.15
5.35 4.94 4.52 4.13 3.78
7.42 7.03 6.59 6.15 5.72
9.47 9.12 8.70 8.25 7.78
11.5 11.2 10.8 10.4 9.90
13.5 13.2 12.9 12.5 12.0
15.5 15.3 14.9 14.6 14.1
17.5 17.3 17.0 16.6 16.2
19.5 19.3 19.0 18.69 18.3
21.4 21.3 21.0 20.7 20.4
23.4 23.3 23.0 22.8 22.4
7 8 9 10 12
0.71 0.65 0.60 0.56 0.49
1.97 1.81 1.67 1.55 1.35
3.47 3.19 2.95 2.75 2.40
5.32 4.95 4.62 4.33 3.82
7.33 6.89 6.48 6.10 5.43
9.43 8.95 8.49 8.05 7.25
11.6 11.1 10.6 10.1 9.21
13.7 13.2 12.7 12.2 11.3
15.8 15.4 14.9 14.4 13.4
17.9 17.5 17.0 16.5 15.5
20.0 19.6 19.1 18.7 17.7
22.1 21.7 21.3 20.8 19.8
14 16 18 20 24
0.44 0.39 0.36 0.33 0.28
1.20 1.08 0.97 0.89 0.76
2.14 1.92 1.75 1.60 1.37
3.41 3.07 2.79 2.56 2.18
4.86 4.40 4.00 3.67 3.14
6.56 5.96 5.46 5.02 4.32
8.40 10.4 12.4 7.69 9.56 11.5 7.06 8.83 10.7 6.52 8.18 9.97 5.62 7.11 8.71
14.5 13.6 12.7 11.9 10.4
16.7 15.7 14.7 13.9 12.3
18.8 17.8 16.8 15.9 14.2
28 32 36
0.25 0.22 0.20
0.66 0.58 0.52
1.19 1.05 0.95
1.90 1.68 1.51
2.75 2.44 2.19
3.78 3.35 3.01
4.93 4.38 3.94
6.26 5.58 5.02
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.70 6.88 6.21
6.46 5.73 5.15
7.51 6.67 5.99
9.27 11.0 12.7 8.31 9.85 11.5 7.52 8.93 10.4
ECCENTRICALLY LOADED BOLT GROUPS
8 - 59
Table 8-21 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 15°° C req =
Pu
φ rn
or φ R n = C × φrn ex
where
Pu
s, in.
3
6
15°
s
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
s
s
e
8
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.35 1.16 1.02 0.90 0.81
2.96 2.58 2.28 2.03 1.84
4.75 4.20 3.73 3.35 3.03
6.67 5.98 5.37 4.85 4.40
8.67 7.90 7.17 6.53 5.96
10.7 9.89 9.08 8.34 7.66
12.7 11.9 11.1 10.3 9.48
14.8 14.0 13.1 12.2 11.4
16.8 16.0 15.2 14.3 13.4
18.8 18.1 17.3 16.3 15.4
20.9 20.2 19.3 18.4 17.5
22.9 22.2 21.4 20.5 19.6
7 8 9 10 12
0.74 0.68 0.63 0.58 0.51
1.67 1.53 1.42 1.31 1.15
2.76 2.53 2.34 2.17 1.90
4.02 3.70 3.43 3.19 2.79
5.48 5.05 4.68 4.36 3.82
7.06 6.53 6.07 5.66 4.97
8.79 10.6 8.17 9.91 7.61 9.27 7.12 8.69 6.28 7.69
12.6 11.8 11.0 10.4 9.23
14.5 13.7 12.9 12.2 10.9
16.6 15.7 14.8 14.0 12.6
18.6 17.7 16.8 16.0 14.4
14 16 18 20 24
0.45 0.41 0.37 0.34 0.29
1.02 0.91 0.83 0.76 0.65
1.69 1.51 1.37 1.26 1.07
2.48 2.23 2.02 1.85 1.58
3.40 3.05 2.77 2.54 2.16
4.43 3.99 3.63 3.32 2.84
5.61 5.05 4.60 4.21 3.60
6.88 6.21 5.66 5.19 4.45
8.29 7.50 6.84 6.28 5.39
9.79 11.4 8.88 10.4 8.11 9.48 7.45 8.73 6.40 7.52
28 32 36
0.25 0.23 0.20
0.56 0.50 0.45
0.93 0.83 0.74
1.37 1.22 1.09
1.89 1.67 1.50
2.47 2.19 1.96
3.14 2.78 2.49
3.88 3.44 3.09
4.71 4.18 3.75
5.61 4.98 4.47
2 3 4 5 6
1.35 1.16 1.02 0.90 0.81
3.29 2.94 2.64 2.38 2.17
5.33 4.93 4.52 4.15 3.82
7.39 6.99 6.55 6.12 5.70
9.42 9.05 8.63 8.18 7.72
11.4 11.1 10.7 10.3 9.80
13.4 13.1 12.8 12.4 11.9
15.4 15.2 14.8 14.4 14.0
17.4 17.2 16.9 16.5 16.1
19.4 19.2 18.9 18.5 18.2
21.4 21.2 20.9 20.6 20.2
23.4 23.2 22.9 22.6 22.3
7 8 9 10 12
0.74 0.68 0.63 0.58 0.51
1.99 1.83 1.69 1.58 1.38
3.52 3.25 3.02 2.81 2.47
5.31 4.95 4.63 4.34 3.84
7.28 6.86 6.46 6.10 5.45
9.33 8.87 8.43 8.00 7.23
11.4 11.0 10.5 10.0 9.15
13.5 13.1 12.6 12.1 11.2
15.6 15.2 14.7 14.2 13.2
17.7 17.3 16.8 16.3 15.3
19.8 19.4 18.9 18.4 17.4
21.9 21.5 21.0 20.5 19.6
14 16 18 20 24
0.45 0.41 0.37 0.34 0.29
1.23 1.10 1.00 0.92 0.78
2.20 1.98 1.80 1.65 1.41
3.44 3.11 2.83 2.60 2.23
4.91 4.46 4.08 3.75 3.22
6.56 5.99 5.49 5.06 4.36
8.38 10.3 12.3 7.69 9.52 11.5 7.09 8.82 10.7 6.56 8.20 9.96 5.70 7.15 8.74
14.4 13.5 12.6 11.8 10.4
16.5 15.5 14.6 13.8 12.2
18.6 17.6 16.6 15.7 14.1
28 32 36
0.25 0.23 0.20
0.68 0.60 0.54
1.23 1.09 0.97
1.95 1.73 1.55
2.82 2.50 2.25
3.83 3.41 3.07
5.02 4.47 4.03
6.32 5.64 5.09
7.76 6.96 6.30
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.59 5.86 5.27
13.1 11.9 11.0 10.1 8.71 7.64 6.80 6.12
9.31 11.0 12.7 8.38 9.90 11.5 7.60 9.01 10.5
8 - 60
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-21 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 30°° C req =
Pu
φrn
or φR n = C × φ rn ex
where
s, in.
3
6
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
Pu
s
30°
s
s
e
8
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.49 1.29 1.13 1.00 0.90
3.12 2.74 2.43 2.18 1.98
4.91 4.39 3.95 3.58 3.26
6.80 6.16 5.60 5.10 4.67
8.75 8.04 7.37 6.77 6.23
10.7 9.98 9.24 8.55 7.93
12.7 12.0 11.2 10.4 9.72
14.7 14.0 13.2 12.4 11.6
16.7 16.0 15.2 14.3 13.5
18.7 18.0 17.2 16.3 15.5
20.8 20.0 19.2 18.4 17.5
22.7 22.1 21.3 20.4 19.5
7 8 9 10 12
0.82 0.75 0.70 0.65 0.57
1.81 1.67 1.55 1.44 1.26
2.99 2.76 2.56 2.38 2.09
4.30 3.97 3.69 3.44 3.03
5.76 5.35 4.98 4.66 4.13
7.37 6.87 6.42 6.02 5.34
9.08 10.9 8.49 10.2 7.96 9.62 7.49 9.07 6.66 8.12
12.8 12.0 11.4 10.8 9.67
14.7 13.9 13.2 12.5 11.3
16.7 15.9 15.1 14.4 13.0
18.7 17.8 17.0 16.2 14.8
14 16 18 20 24
0.50 0.45 0.41 0.38 0.32
1.12 1.01 0.92 0.84 0.72
1.86 1.67 1.52 1.39 1.19
2.71 2.44 2.22 2.03 1.74
3.69 3.33 3.03 2.78 2.38
4.78 4.33 3.95 3.62 3.11
5.99 5.44 4.97 4.57 3.93
7.33 6.66 6.10 5.62 4.84
8.75 10.3 11.9 7.98 9.39 10.9 7.32 8.64 10.1 6.75 7.98 9.30 5.83 6.92 8.08
28 32 36
0.28 0.25 0.23
0.63 0.56 0.50
1.04 0.92 0.83
1.52 1.35 1.21
2.08 1.84 1.66
2.72 2.41 2.17
3.44 3.06 2.75
4.24 3.77 3.40
5.13 4.57 4.11
2 3 4 5 6
1.49 1.29 1.13 1.00 0.90
3.36 3.02 2.73 2.48 2.27
5.36 4.97 4.60 4.26 3.96
7.37 6.99 6.58 6.18 5.80
9.38 9.01 8.61 8.18 7.76
11.4 11.0 10.7 10.2 9.79
13.4 13.1 12.7 12.3 11.8
15.4 15.1 14.7 14.3 13.9
17.4 17.1 16.7 16.4 15.9
19.3 19.1 18.8 18.4 18.0
21.3 21.1 20.8 20.4 20.0
23.3 23.1 22.8 22.4 22.1
7 8 9 10 12
0.82 0.75 0.70 0.65 0.57
2.09 1.93 1.80 1.68 1.49
3.68 3.43 3.21 3.01 2.67
5.44 5.11 4.81 4.53 4.05
7.36 6.97 6.61 6.27 5.67
9.35 8.93 8.53 8.14 7.43
11.4 11.0 10.5 10.1 9.31
13.5 13.0 12.6 12.1 11.3
15.5 15.1 14.6 14.2 13.3
17.6 17.1 16.7 16.2 15.3
19.6 19.2 18.7 18.3 17.4
21.7 21.2 20.8 20.4 19.4
14 16 18 20 24
0.50 0.45 0.41 0.38 0.32
1.33 1.20 1.09 1.00 0.86
2.39 2.16 1.97 1.81 1.55
3.65 3.31 3.03 2.80 2.41
5.15 4.71 4.34 4.01 3.48
6.81 6.27 5.79 5.37 4.68
8.60 10.5 7.96 9.76 7.39 9.12 6.89 8.53 6.04 7.53
12.4 11.7 10.9 10.3 9.14
14.4 13.6 12.8 12.1 10.8
16.5 15.6 14.8 14.0 12.6
18.5 17.6 16.8 15.9 14.5
28 32 36
0.28 0.25 0.23
0.75 0.67 0.60
1.35 1.20 1.08
2.12 1.89 1.70
3.06 2.73 2.46
4.13 3.69 3.34
5.36 4.81 4.36
6.72 6.05 5.50
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8.19 7.40 6.74
6.09 5.43 4.89
7.12 6.36 5.74
13.6 12.5 11.5 10.7 9.32 8.24 7.37 6.66
9.76 11.4 13.2 8.86 10.4 12.0 8.09 9.53 11.1
ECCENTRICALLY LOADED BOLT GROUPS
8 - 61
Table 8-21 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 45°° C req =
Pu
φ rn
or φ R n = C × φrn ex
where
Pu
3
6
s
s
45°
s
e
s, in.
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
8
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.70 1.51 1.35 1.21 1.10
3.43 3.09 2.78 2.52 2.30
5.22 4.76 4.34 3.97 3.67
7.06 6.52 6.01 5.57 5.17
8.95 8.35 7.78 7.25 6.78
10.9 10.2 9.60 9.01 8.47
12.8 12.2 11.5 10.8 10.2
14.8 14.1 13.4 12.7 12.1
16.8 16.1 15.3 14.6 13.9
18.7 18.0 17.3 16.6 15.9
20.7 20.0 19.3 18.5 17.8
22.7 22.0 21.3 20.5 19.8
7 8 9 10 12
1.00 0.92 0.85 0.79 0.69
2.12 1.96 1.82 1.70 1.50
3.40 3.17 2.96 2.78 2.46
4.82 4.51 4.23 3.97 3.54
6.35 5.96 5.60 5.28 4.73
7.97 7.51 7.08 6.70 6.04
9.67 11.5 9.15 10.9 8.68 10.4 8.24 9.86 7.46 8.97
13.3 12.7 12.1 11.5 10.6
15.2 14.5 13.9 13.3 12.2
17.1 16.4 15.7 15.1 14.0
19.0 18.3 17.6 17.0 15.7
14 16 18 20 24
0.61 0.55 0.50 0.46 0.40
1.34 1.21 1.11 1.02 0.87
2.21 2.00 1.82 1.67 1.43
3.18 2.88 2.64 2.42 2.09
4.27 3.89 3.56 3.29 2.84
5.48 5.01 4.60 4.25 3.68
6.80 6.23 5.74 5.31 4.62
8.21 7.54 6.97 6.47 5.65
9.70 11.3 8.95 10.4 8.30 9.71 7.73 9.06 6.77 7.96
12.9 12.0 11.2 10.5 9.23
14.6 13.6 12.7 11.9 10.6
28 32 36
0.35 0.31 0.28
0.76 0.68 0.61
1.26 1.12 1.00
1.83 1.63 1.46
2.49 2.22 2.00
3.24 2.89 2.60
4.07 3.64 3.29
5.00 4.47 4.04
6.00 5.38 4.87
2 3 4 5 6
1.70 1.51 1.35 1.21 1.10
3.52 3.23 2.96 2.72 2.51
5.44 5.11 4.79 4.48 4.20
7.40 7.06 6.70 6.36 6.03
9.37 9.03 8.67 8.30 7.94
11.4 11.0 10.7 10.3 9.90
13.3 13.0 12.7 12.3 11.9
15.3 15.0 14.6 14.3 13.9
17.3 17.0 16.6 16.3 15.9
19.3 19.0 18.6 18.3 17.9
21.3 21.0 20.6 20.3 19.9
23.2 22.9 22.6 22.3 21.9
7 8 9 10 12
1.00 0.92 0.85 0.79 0.69
2.33 2.18 2.04 1.92 1.71
3.96 3.73 3.53 3.35 3.02
5.73 5.45 5.19 4.94 4.50
7.60 7.27 6.96 6.67 6.13
9.53 9.17 8.83 8.50 7.88
11.5 11.1 10.8 10.4 9.73
13.5 13.1 12.7 12.4 11.6
15.5 15.1 14.7 14.3 13.6
17.5 17.1 16.7 16.3 15.5
19.5 19.1 18.7 18.3 17.5
21.5 21.1 20.7 20.3 19.5
14 16 18 20 24
0.61 0.55 0.50 0.46 0.40
1.55 1.41 1.29 1.19 1.03
2.75 2.51 2.31 2.13 1.84
4.12 3.78 3.49 3.24 2.82
5.65 5.22 4.85 4.53 3.99
7.33 6.83 6.39 6.00 5.32
9.11 11.0 8.55 10.3 8.04 9.77 7.57 9.25 6.76 8.32
12.9 12.2 11.6 11.0 9.97
14.8 14.1 13.4 12.8 11.7
16.8 16.0 15.3 14.7 13.5
19.8 18.0 17.3 16.6 15.3
28 32 36
0.35 0.31 0.28
0.90 0.80 0.72
1.62 1.44 1.30
2.50 2.24 2.02
3.56 3.20 2.90
4.76 4.30 3.92
6.09 5.52 5.04
9.08 10.7 12.4 8.32 9.85 11.5 7.66 9.10 10.6
14.2 13.1 12.2
7.53 6.86 6.30
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.08 6.37 5.78
8.24 7.43 6.75
9.47 8.56 7.79
8 - 62
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-21 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 60°° C req =
Pu
φrn
or φR n = C × φ rn ex
where
3
6
s
s
60°
s
e
s, in.
Pu
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
8
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.86 1.77 1.66 1.54 1.43
3.71 3.52 3.31 3.10 2.90
5.56 5.29 4.99 4.70 4.41
7.41 7.07 6.70 6.34 6.00
9.28 8.88 8.45 8.04 7.64
11.2 10.7 10.3 9.79 9.35
13.1 12.6 12.1 11.6 11.1
15.0 14.5 13.9 13.4 12.9
16.9 16.4 15.8 15.3 14.7
18.8 18.3 17.7 17.1 16.6
20.8 20.2 19.6 19.0 18.5
22.7 22.1 21.6 21.0 20.4
7 8 9 10 12
1.33 1.24 1.16 1.08 0.96
2.71 2.54 2.38 2.24 2.00
4.15 3.92 3.70 3.51 3.17
5.68 5.39 5.12 4.88 4.44
7.27 6.94 6.63 6.34 5.82
8.94 10.7 8.56 10.3 8.22 9.86 7.89 9.49 7.28 8.81
12.4 12.0 11.6 11.2 10.4
14.2 13.8 13.3 12.9 12.1
16.1 15.6 15.1 14.6 13.8
17.9 17.4 16.9 16.4 15.5
19.8 19.3 18.7 18.2 17.3
14 16 18 20 24
0.86 0.77 0.70 0.65 0.56
1.81 1.64 1.51 1.39 1.20
2.88 2.64 2.43 2.25 1.95
4.07 3.74 3.46 3.21 2.80
5.36 4.95 4.59 4.28 3.76
6.73 6.25 5.83 5.45 4.81
8.19 7.64 7.15 6.71 5.96
9.72 11.3 9.11 10.7 8.56 10.0 8.06 9.48 7.19 8.50
13.0 12.2 11.6 11.0 9.88
14.7 13.9 13.2 12.5 11.3
16.4 15.6 14.8 14.1 12.8
28 32 36
0.49 0.43 0.39
1.06 0.94 0.85
1.72 1.54 1.39
2.48 2.22 2.01
3.34 3.00 2.72
4.29 3.87 3.52
5.34 4.83 4.40
6.47 5.87 5.36
2 3 4 5 6
1.86 1.77 1.66 1.54 1.43
3.72 3.55 3.36 3.17 2.99
5.59 5.37 5.14 4.90 4.67
7.50 7.25 6.98 6.72 6.46
9.43 9.16 8.88 8.59 8.31
7 8 9 10 12
1.33 1.24 1.16 1.08 0.96
2.82 2.67 2.52 2.40 2.17
4.46 4.26 4.08 3.91 3.61
6.21 5.98 5.76 5.56 5.20
8.05 7.79 7.55 7.32 6.90
9.92 9.65 9.39 9.14 8.66
14 16 18 20 24
0.86 0.77 0.70 0.65 0.56
1.98 1.82 1.69 1.57 1.37
3.35 3.11 2.91 2.72 2.41
4.87 4.57 4.30 4.05 3.61
6.51 6.15 5.81 5.50 4.96
8.23 10.0 7.81 9.56 7.43 9.13 7.07 8.73 6.43 8.00
28 32 36
0.49 0.43 0.39
1.22 1.09 0.99
2.15 1.94 1.76
3.25 2.94 2.69
4.49 4.10 3.77
5.88 5.41 5.00
11.4 11.1 10.8 10.5 10.2
7.68 6.99 6.41
8.97 10.3 11.7 8.19 9.46 10.8 7.53 8.71 9.96
13.3 13.0 12.7 12.4 12.1
15.3 15.0 14.7 14.4 14.1
17.3 17.0 16.7 16.3 16.0
19.2 18.9 18.6 18.3 18.0
21.2 20.9 20.6 20.3 19.9
23.2 22.9 22.6 22.2 21.9
11.8 11.5 11.3 11.0 10.5
13.8 13.5 13.2 12.9 12.4
15.7 15.4 15.1 14.8 14.2
17.7 17.3 17.0 16.7 16.1
19.6 19.3 19.0 18.7 18.1
21.6 21.3 20.9 20.6 20.0
11.8 11.4 10.9 10.5 9.67
13.7 13.2 12.7 12.2 11.4
15.6 15.1 14.5 14.1 13.2
17.5 16.9 16.4 15.9 15.0
19.4 18.9 18.3 17.8 16.8
8.97 10.6 12.3 8.34 9.92 11.6 7.78 9.30 10.9
14.1 13.3 12.5
15.9 15.0 14.2
7.38 6.83 6.35
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 63
Table 8-21 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 75°° C req =
Pu
φr n
or φ R n = C × φrn ex
where
3
6
s s
s
e
s, in.
75° P u
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
8
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.94 1.92 1.89 1.85 1.81
3.87 3.82 3.75 3.67 3.59
5.79 5.70 5.60 5.48 5.35
7.70 7.58 7.43 7.28 7.11
9.61 9.45 9.26 9.07 8.87
11.5 11.3 11.1 10.9 10.6
13.4 13.2 12.9 12.7 12.4
15.3 15.1 14.8 14.5 14.2
17.3 17.0 16.7 16.4 16.1
19.2 18.9 18.5 18.2 17.9
21.1 20.8 20.4 20.1 19.8
23.0 22.7 22.3 22.0 21.6
7 8 9 10 12
1.76 1.71 1.66 1.61 1.51
3.50 3.40 3.30 3.20 3.01
5.22 5.08 4.94 4.80 4.53
6.94 6.76 6.59 6.42 6.08
8.67 8.46 8.26 8.06 7.67
10.4 10.2 9.96 9.73 9.30
12.2 11.9 11.7 11.4 11.0
14.0 13.7 13.4 13.2 12.7
15.8 15.5 15.2 14.9 14.4
17.6 17.3 17.0 16.7 16.2
19.4 19.1 18.8 18.5 17.9
21.3 21.0 20.6 20.3 19.7
14 16 18 20 24
1.41 1.31 1.23 1.15 1.01
2.82 2.65 2.48 2.34 2.08
4.27 4.03 3.80 3.60 3.23
5.76 5.47 5.19 4.93 4.48
7.31 6.96 6.64 6.34 5.80
8.90 10.5 8.52 10.1 8.16 9.73 7.82 9.36 7.20 8.67
12.2 11.8 11.3 10.9 10.2
13.9 13.4 13.0 12.6 11.8
15.6 15.2 14.7 14.2 13.4
17.4 16.9 16.4 15.9 15.0
19.2 18.6 18.1 17.7 16.7
28 32 36
0.90 0.81 0.73
1.87 1.69 1.54
2.93 2.67 2.45
4.08 3.75 3.45
5.33 4.91 4.55
6.65 6.17 5.74
12.6 11.9 11.2
14.2 13.5 12.8
15.9 15.1 14.3
2 3 4 5 6
1.94 1.92 1.89 1.85 1.81
3.86 3.80 3.74 3.66 3.58
5.77 5.68 5.57 5.46 5.35
7.68 7.55 7.42 7.29 7.15
9.60 9.45 9.29 9.14 8.98
11.5 11.4 11.2 11.0 10.8
13.5 13.3 13.1 12.9 12.7
15.4 15.2 15.0 14.8 14.6
17.6 17.2 16.9 16.7 16.5
19.6 19.1 18.9 18.7 18.5
21.5 21.1 20.8 20.6 20.4
23.5 23.0 22.8 22.6 22.3
7 8 9 10 12
1.76 1.71 1.66 1.61 1.51
3.49 3.40 3.31 3.22 3.05
5.23 5.12 5.00 4.89 4.67
7.01 6.88 6.74 6.61 6.36
8.83 8.68 8.53 8.38 8.10
10.7 10.5 10.4 10.2 9.89
12.5 12.4 12.2 12.0 11.7
14.4 14.3 14.1 13.9 13.6
16.3 16.2 16.0 15.8 15.4
18.3 18.1 17.9 17.7 17.3
20.2 20.0 19.8 19.6 19.2
22.1 21.9 21.7 21.5 21.1
14 16 18 20 24
1.41 1.31 1.23 1.15 1.01
2.88 2.73 2.58 2.45 2.21
4.46 4.26 4.08 3.90 3.59
6.12 5.89 5.68 5.47 5.10
7.84 7.59 7.35 7.13 6.71
9.61 9.33 9.08 8.84 8.38
11.4 11.1 10.8 10.6 10.1
13.3 12.9 12.7 12.4 11.9
15.1 14.8 14.5 14.2 13.6
17.0 16.6 16.3 16.0 15.5
18.9 18.5 18.2 17.9 17.3
20.8 20.4 20.1 19.7 19.1
28 32 36
0.90 0.81 0.73
2.01 1.84 1.70
3.32 3.08 2.87
4.77 4.47 4.19
6.32 5.97 5.64
7.96 7.56 7.19
9.65 11.4 9.21 10.9 8.80 10.5
13.1 12.7 12.2
14.9 14.4 13.9
16.7 16.2 15.7
18.5 18.0 17.5
8.06 7.51 7.01
9.52 11.0 8.91 10.4 8.36 9.77
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 64
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-22. Coefficients C for Eccentrically Loaded Bolt Groups Angle = 0°° C req =
Pu
φrn
or φR n = C × φ rn
ex = e
where
s, in.
3
6
s
Pu
s
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
3
3 6
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.71 1.42 1.21 1.05 0.92
4.07 3.40 2.90 2.51 2.21
6.81 5.79 4.97 4.34 3.85
9.86 8.61 7.53 6.64 5.91
13.0 11.7 10.4 9.24 8.27
16.1 14.8 13.4 12.1 11.0
19.3 18.0 16.6 15.2 13.9
22.3 21.1 19.8 18.3 16.9
25.4 24.3 23.0 21.5 20.0
28.5 27.4 26.1 24.7 23.2
31.5 30.5 29.3 27.9 26.4
34.5 33.6 32.5 31.1 29.7
7 8 9 10 12
0.81 0.72 0.64 0.58 0.49
1.96 1.76 1.60 1.46 1.24
3.44 3.11 2.83 2.59 2.21
5.31 4.80 4.38 4.02 3.44
7.46 6.78 6.20 5.71 4.91
9.95 12.7 9.09 11.6 8.34 10.7 7.70 9.91 6.65 8.59
15.6 14.4 13.3 12.4 10.8
18.6 17.3 16.1 15.0 13.2
21.8 20.4 19.1 17.9 15.7
25.0 23.5 22.1 20.8 18.5
28.2 26.7 25.2 23.8 21.3
14 16 18 20 24
0.42 0.37 0.33 0.29 0.24
1.08 0.95 0.85 0.77 0.64
1.92 1.70 1.52 1.37 1.15
3.00 2.66 2.39 2.16 1.82
4.30 3.82 3.43 3.11 2.62
5.83 5.19 4.67 4.24 3.57
7.57 6.75 6.08 5.53 4.67
9.53 11.7 8.51 10.5 7.68 9.45 6.99 8.61 5.92 7.30
14.0 12.6 11.4 10.4 8.8
16.5 14.9 13.5 12.3 10.5
19.2 17.3 15.8 14.4 12.3
28 32 36
0.21 0.18 0.16
0.55 0.49 0.43
0.99 0.87 0.77
1.57 1.38 1.23
2.26 1.98 1.77
3.08 2.71 2.42
4.04 3.55 3.17
5.12 4.51 4.03
2 3 4 5 6
1.71 1.42 1.21 1.05 0.92
4.85 4.24 3.72 3.29 2.93
8.04 7.36 6.66 6.00 5.41
11.2 10.6 9.86 9.14 8.44
7 8 9 10 12
0.81 0.72 0.64 0.58 0.49
2.63 2.38 2.17 2.00 1.71
4.90 4.46 4.09 3.78 3.27
7.79 10.9 7.20 10.2 6.67 9.54 6.20 8.94 5.41 7.88
14 16 18 20 24
0.42 0.37 0.33 0.29 0.24
1.49 1.32 1.19 1.08 0.91
2.87 2.55 2.30 2.09 1.76
4.78 4.28 3.86 3.51 2.97
7.01 6.29 5.70 5.20 4.42
9.61 12.4 8.69 11.3 7.91 10.4 7.25 9.54 6.19 8.19
28 32 36
0.21 0.18 0.16
0.78 0.69 0.61
1.52 1.33 1.19
2.57 2.27 2.03
3.84 3.39 3.03
5.39 4.77 4.27
14.2 13.7 13.1 12.4 11.6
6.33 5.58 4.99
7.67 6.77 6.05
9.13 10.7 8.06 9.47 7.21 8.48
17.3 16.8 16.2 15.6 14.9
20.3 19.9 19.4 18.7 18.1
23.2 22.9 22.4 21.9 21.2
26.2 25.9 25.5 25.0 24.4
29.2 28.9 28.5 28.1 27.5
32.2 31.9 31.6 31.1 30.6
35.1 34.9 34.6 34.2 33.7
14.1 13.4 12.6 12.0 10.7
17.3 16.6 15.8 15.1 13.7
20.6 19.8 19.1 18.3 16.8
23.7 23.0 22.3 21.6 20.0
26.9 26.2 25.5 24.8 23.3
30.0 29.4 28.7 28.0 26.5
33.2 32.6 31.9 31.2 29.8
15.4 14.2 13.1 12.1 10.4
18.6 17.2 15.9 14.8 12.9
21.8 20.3 18.9 17.7 15.5
25.0 23.5 22.0 20.7 18.3
28.2 26.7 25.2 23.8 21.2
9.15 11.4 13.7 8.13 10.1 12.3 7.30 9.10 11.1
16.3 14.6 13.2
19.0 17.1 15.5
7.14 6.33 5.67
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 65
Table 8-22 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 15°° C req =
Pu
φ rn
or φ R n = C × φrn
ex Pu
where
s, in.
3
6
s
15° e
s
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
3
3 6
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.77 1.47 1.25 1.08 0.94
4.10 3.45 2.95 2.57 2.26
6.84 5.86 5.07 4.44 3.93
9.82 8.61 7.55 6.67 5.96
12.9 11.6 10.4 9.26 8.33
16.0 14.7 13.3 12.1 11.0
19.1 17.8 16.4 15.1 13.8
22.2 20.9 19.5 18.1 16.8
25.2 24.1 22.7 21.3 19.8
28.3 27.2 25.8 24.4 23.0
31.3 30.3 29.0 27.6 26.1
34.3 33.3 32.1 30.7 29.3
7 8 9 10 12
0.83 0.74 0.66 0.60 0.50
2.01 1.81 1.64 1.50 1.28
3.52 3.18 2.90 2.65 2.27
5.37 4.87 4.45 4.10 3.52
7.55 6.88 6.31 5.81 5.01
9.97 12.7 9.13 11.7 8.40 10.8 7.77 9.99 6.74 8.71
15.5 14.4 13.3 12.4 10.9
18.5 17.2 16.1 15.0 13.2
21.5 20.2 18.9 17.8 15.8
24.7 23.2 21.9 20.7 18.4
27.8 26.4 25.0 23.6 21.2
14 16 18 20 24
0.43 0.38 0.34 0.30 0.25
1.11 0.98 0.88 0.79 0.67
1.98 1.75 1.57 1.42 1.19
3.08 2.73 2.45 2.22 1.87
4.40 3.91 3.52 3.19 2.69
5.93 5.29 4.77 4.33 3.66
7.69 6.87 6.20 5.65 4.78
9.62 11.8 8.62 10.6 7.80 9.59 7.12 8.76 6.04 7.45
14.1 12.7 11.5 10.5 8.99
16.5 15.0 13.6 12.5 10.7
19.1 17.4 15.9 14.6 12.5
28 32 36
0.22 0.19 0.17
0.57 0.50 0.45
1.02 0.90 0.80
1.61 1.42 1.26
2.32 2.04 1.82
3.17 2.79 2.49
4.14 3.65 3.26
5.24 4.62 4.13
2 3 4 5 6
1.77 1.47 1.25 1.08 0.94
4.83 4.22 3.71 3.28 2.94
7.98 7.31 6.64 6.01 5.45
11.1 10.5 9.77 9.06 8.38
7 8 9 10 12
0.83 0.74 0.66 0.60 0.50
2.65 2.40 2.20 2.02 1.74
4.97 4.55 4.18 3.86 3.34
7.75 10.8 7.17 10.1 6.66 9.49 6.20 8.92 5.43 7.91
14 16 18 20 24
0.43 0.38 0.34 0.30 0.25
1.52 1.35 1.22 1.10 0.93
2.94 2.62 2.36 2.14 1.81
4.82 4.32 3.91 3.57 3.03
7.07 6.38 5.79 5.30 4.52
9.60 12.4 8.71 11.3 7.95 10.4 7.31 9.60 6.26 8.28
28 32 36
0.22 0.19 0.17
0.80 0.71 0.63
1.56 1.37 1.23
2.63 2.32 2.08
3.93 3.47 3.11
5.47 4.85 4.35
14.1 13.6 12.9 12.2 11.5
6.47 5.72 5.11
7.82 6.92 6.20
9.31 10.9 8.24 9.66 7.38 8.66
17.2 16.7 16.1 15.4 14.7
20.2 19.7 19.2 18.5 17.8
23.2 22.8 22.3 21.7 21.0
26.1 25.8 25.3 24.8 24.1
29.1 28.8 28.3 27.8 27.2
32.1 31.8 31.4 30.9 30.3
35.0 34.8 34.4 33.9 33.4
13.9 13.2 12.5 11.9 10.6
17.1 16.4 15.6 14.9 13.6
20.3 19.6 18.8 18.1 16.6
23.5 22.7 22.0 21.3 19.8
26.6 25.9 25.2 24.5 23.0
29.7 29.1 28.4 27.6 26.1
32.8 32.2 31.5 30.8 29.3
15.3 14.1 13.0 12.1 10.5
18.4 17.0 15.8 14.8 12.9
21.5 20.1 18.8 17.6 15.5
24.6 23.2 21.8 20.5 18.2
27.3 26.3 24.9 23.5 21.1
9.24 11.4 13.8 8.23 10.2 12.4 7.41 9.23 11.2
16.3 14.7 13.3
18.9 17.1 15.6
7.26 6.45 5.80
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 66
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-22 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 30°° C req =
Pu
φrn
or φ R n = C × φ rn
ex Pu
where
s, in.
3
6
s
30°
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
s
e
3
3 6
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
1.94 1.61 1.37 1.19 1.04
4.26 3.63 3.15 2.77 2.45
6.99 6.09 5.35 4.74 4.23
9.90 8.80 7.83 7.00 6.30
12.9 11.7 10.6 9.54 8.67
16.0 14.7 13.5 12.3 11.3
19.0 17.7 16.5 15.2 14.1
22.0 20.8 19.5 18.2 17.0
25.1 23.9 22.6 21.2 19.9
28.1 27.0 25.7 24.3 23.0
31.1 30.0 28.7 27.4 26.0
34.1 33.1 31.8 30.5 29.1
7 8 9 10 12
0.92 0.82 0.74 0.67 0.56
2.19 1.98 1.80 1.65 1.41
3.81 3.45 3.16 2.90 2.49
5.71 5.22 4.79 4.42 3.82
7.92 10.4 7.27 9.58 6.71 8.88 6.22 8.26 5.41 7.22
13.0 12.1 11.2 10.5 9.23
15.8 14.8 13.8 12.9 11.5
18.7 17.6 16.5 15.5 13.8
21.7 20.5 19.3 18.2 16.4
24.7 23.4 22.2 21.1 19.0
27.8 26.4 25.2 24.0 21.8
14 16 18 20 24
0.48 0.42 0.38 0.34 0.28
1.23 1.08 0.97 0.88 0.74
2.18 1.93 1.73 1.57 1.32
3.36 2.99 2.69 2.44 2.06
4.78 4.26 3.85 3.50 2.96
6.40 5.73 5.18 4.73 4.01
8.22 10.3 12.4 7.40 9.25 11.3 6.71 8.41 10.3 6.14 7.70 9.42 5.22 6.58 8.08
14.8 13.4 12.3 11.3 9.72
17.2 15.7 14.4 13.3 11.5
19.8 18.2 16.7 15.4 13.4
28 32 36
0.24 0.21 0.19
0.64 0.56 0.50
1.14 1.00 0.89
1.78 1.57 1.40
2.56 2.26 2.02
3.48 3.07 2.75
4.54 4.01 3.59
2 3 4 5 6
1.94 1.61 1.37 1.19 1.04
4.86 4.27 3.78 3.39 3.06
7.96 7.32 6.70 6.14 5.64
11.0 10.4 9.75 9.10 8.48
7 8 9 10 12
0.92 0.82 0.74 0.67 0.56
2.78 2.54 2.34 2.16 1.87
5.19 4.80 4.45 4.14 3.61
7.91 10.9 7.38 10.3 6.90 9.67 6.46 9.14 5.71 8.20
14 16 18 20 24
0.48 0.42 0.38 0.34 0.28
1.65 1.47 1.33 1.21 1.02
3.20 2.86 2.58 2.35 2.00
5.10 4.60 4.19 3.84 3.29
7.41 6.74 6.17 5.68 4.89
28 32 36
0.24 0.21 0.19
0.88 0.78 0.70
1.73 1.52 1.36
2.86 2.54 2.27
4.28 3.80 3.41
14.1 13.5 12.9 12.2 11.5
5.73 5.07 4.54
7.05 6.25 5.61
8.51 10.1 11.8 7.55 8.96 10.5 6.78 8.06 9.44
17.1 16.6 15.9 15.3 14.6
20.1 19.6 19.0 18.4 17.7
23.1 22.6 22.1 21.5 20.8
26.0 25.6 25.1 24.5 23.9
29.0 28.6 28.1 27.6 27.0
32.0 31.6 31.1 30.6 30.1
35.0 34.6 34.2 33.7 33.1
13.9 13.3 12.6 12.0 10.9
17.0 16.3 15.7 15.0 13.8
20.1 19.4 18.7 18.1 16.8
23.2 22.6 21.9 21.2 19.8
26.3 25.7 25.0 24.3 22.9
29.4 28.8 28.1 27.4 26.0
32.5 31.9 31.2 30.5 29.1
9.95 9.12 8.39 7.75 6.71
12.7 11.7 10.8 10.1 8.78
15.6 14.5 13.5 12.6 11.1
18.5 17.3 16.2 15.2 13.5
21.5 20.3 19.1 18.0 16.1
24.6 23.3 22.0 20.9 18.8
27.7 26.4 25.0 23.8 21.6
5.90 5.25 4.73
7.77 6.95 6.28
9.83 12.1 14.5 8.83 10.9 13.1 8.00 9.88 11.9
17.0 15.4 14.1
19.6 17.9 16.4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 67
Table 8-22 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 45°° C req =
Pu
φrn
or φ R n = C × φ rn
ex Pu
s
where
3
6
s
e
s, in.
45°
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
3
3 6
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
2.23 1.89 1.63 1.42 1.25
4.67 4.06 3.57 3.17 2.84
7.33 6.50 5.84 5.27 4.78
10.2 9.19 8.36 7.63 6.99
13.1 12.0 11.1 10.2 9.40
16.0 14.9 13.9 12.9 12.0
19.0 17.9 16.8 15.7 14.7
22.0 20.9 19.7 18.6 17.6
25.0 23.9 22.7 21.5 20.4
28.0 26.9 25.7 24.5 23.4
31.0 29.9 28.7 27.5 26.3
33.9 32.9 31.7 30.5 29.3
7 8 9 10 12
1.11 0.99 0.90 0.81 0.68
2.57 2.33 2.13 1.96 1.68
4.36 3.99 3.68 3.40 2.95
6.42 5.92 5.49 5.10 4.46
8.70 11.2 8.09 10.5 7.54 9.80 7.05 9.21 6.22 8.19
13.8 13.0 12.2 11.6 10.4
16.6 15.7 14.8 14.0 12.7
19.4 18.4 17.5 16.6 15.1
22.3 21.2 20.3 19.3 17.7
25.2 24.1 23.1 22.1 20.3
28.2 27.0 26.0 24.9 23.0
14 16 18 20 24
0.59 0.52 0.46 0.41 0.35
1.47 1.31 1.17 1.06 0.90
2.59 2.31 2.08 1.89 1.60
3.95 3.54 3.20 2.92 2.48
5.55 4.99 4.54 4.15 3.54
7.35 6.65 6.06 5.56 4.76
9.34 11.5 8.49 10.5 7.77 9.64 7.15 8.90 6.15 7.70
13.8 12.7 11.7 10.8 9.39
16.2 14.9 13.8 12.8 11.2
18.7 17.3 16.1 15.0 13.1
21.3 19.8 18.5 17.2 15.2
28 32 36
0.30 0.26 0.23
0.77 0.68 0.61
1.38 1.22 1.08
2.15 1.90 1.69
3.08 2.72 2.44
4.16 3.68 3.30
5.39 4.79 4.30
2 3 4 5 6
2.23 1.89 1.63 1.42 1.25
5.02 4.50 4.05 3.68 3.36
8.01 7.44 6.89 6.40 5.96
11.0 10.4 9.86 9.30 8.78
7 8 9 10 12
1.11 0.99 0.90 0.81 0.68
3.09 2.86 2.65 2.47 2.16
5.57 5.22 4.90 4.61 4.11
8.29 11.2 7.84 10.6 7.43 10.2 7.04 9.69 6.35 8.85
14 16 18 20 24
0.59 0.52 0.46 0.41 0.35
1.92 1.72 1.56 1.43 1.22
3.69 3.34 3.04 2.79 2.38
5.76 5.25 4.82 4.44 3.84
8.11 10.7 7.47 9.94 6.91 9.26 6.43 8.66 5.62 7.64
28 32 36
0.30 0.26 0.23
1.06 0.94 0.84
2.08 1.84 1.65
3.37 3.00 2.71
4.98 4.46 4.04
14.0 13.5 12.9 12.3 11.7
6.77 6.03 5.42
8.28 7.39 6.66
9.91 11.7 8.87 10.5 8.02 9.49
13.5 12.2 11.1
17.0 16.5 15.9 15.3 14.7
20.0 19.5 18.9 18.3 17.7
23.0 22.5 21.9 21.3 20.7
25.9 25.5 24.9 24.4 23.8
28.9 28.4 27.9 27.4 26.8
31.9 31.4 30.9 30.4 29.8
34.8 34.4 33.9 33.4 32.8
14.1 13.6 13.0 12.5 11.6
17.1 16.5 16.0 15.4 14.4
20.1 19.5 19.0 18.4 17.3
23.2 22.6 22.0 21.4 20.2
26.2 25.6 25.0 24.4 23.2
29.2 28.6 28.0 27.4 26.2
32.3 31.7 31.1 30.4 29.2
13.4 12.6 11.8 11.1 9.84
16.2 15.3 14.4 13.6 12.2
19.1 18.1 17.2 16.3 14.7
22.1 21.0 20.0 19.0 17.3
25.0 23.9 22.9 21.9 20.0
28.0 26.9 25.8 24.7 22.8
8.82 11.0 13.4 7.97 10.0 12.2 7.27 9.18 11.2
15.8 14.6 13.4
18.4 17.0 15.7
21.1 19.5 18.1
6.81 6.12 5.56
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 68
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-22 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 60°° C req =
Pu
φrn
or φR n = C × φ rn
ex
where
3
6
s
60°
s
e
s, in.
Pu
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
3
3 6
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
2.59 2.32 2.07 1.84 1.65
5.21 4.73 4.29 3.90 3.56
7.88 7.27 6.69 6.18 5.73
10.6 9.91 9.23 8.63 8.08
13.4 12.7 11.9 11.2 10.6
16.3 15.5 14.6 13.9 13.2
19.2 18.3 17.5 16.6 15.9
22.1 21.2 20.3 19.5 18.7
25.0 24.1 23.2 22.3 21.5
28.0 27.0 26.1 25.2 24.3
30.9 30.0 29.0 28.1 27.2
33.9 32.9 32.0 31.0 30.1
7 8 9 10 12
1.49 1.35 1.23 1.12 0.95
3.27 3.01 2.78 2.58 2.25
5.32 4.95 4.63 4.34 3.84
7.59 10.0 7.13 9.48 6.71 8.98 6.33 8.52 5.67 7.70
12.6 12.0 11.4 10.9 9.91
15.2 14.5 13.9 13.3 12.3
17.9 17.2 16.5 15.9 14.7
20.7 19.9 19.2 18.5 17.3
23.5 22.7 22.0 21.2 19.9
26.3 25.5 24.7 24.0 22.6
29.2 28.4 27.6 26.8 25.3
14 16 18 20 24
0.83 0.73 0.65 0.59 0.49
1.98 1.77 1.60 1.46 1.24
3.43 3.09 2.81 2.57 2.20
5.11 4.64 4.24 3.90 3.35
7.00 6.40 5.89 5.44 4.72
9.08 11.3 8.36 10.5 7.73 9.74 7.19 9.09 6.27 7.99
13.7 12.7 11.9 11.1 9.85
16.1 15.1 14.2 13.3 11.9
18.7 17.5 16.5 15.6 14.0
21.3 20.1 19.0 17.9 16.2
23.9 22.6 21.5 20.4 18.5
28 32 36
0.42 0.37 0.33
1.07 0.95 0.85
1.91 1.69 1.51
2.93 2.60 2.34
4.15 3.70 3.34
5.55 4.97 4.49
12.6 11.5 10.5
14.7 13.4 12.3
16.8 15.4 14.2
2 3 4 5 6
2.59 2.32 2.07 1.84 1.65
5.32 4.94 4.57 4.25 3.95
8.17 7.73 7.31 6.91 6.55
11.1 10.6 10.2 9.73 9.32
14.0 13.5 13.1 12.6 12.2
17.0 16.5 16.0 15.5 15.1
19.9 19.4 19.0 18.5 18.0
22.9 22.4 21.9 21.4 20.9
25.8 25.4 24.9 24.4 23.9
28.8 28.3 27.8 27.4 26.9
31.8 31.3 30.8 30.3 29.8
34.7 34.3 33.8 33.3 32.8
7 8 9 10 12
1.49 1.35 1.23 1.12 0.95
3.69 3.46 3.25 3.06 2.73
6.22 5.92 5.64 5.39 4.92
8.94 8.58 8.25 7.94 7.37
11.8 11.4 11.0 10.6 9.97
14.6 14.2 13.8 13.4 12.7
17.5 17.1 16.7 16.3 15.5
20.5 20.0 19.6 19.1 18.3
23.4 22.9 22.5 22.0 21.2
26.4 25.9 25.4 24.9 24.1
29.3 28.8 28.4 27.9 27.0
32.3 31.8 31.3 30.8 29.9
14 16 18 20 24
0.83 0.73 0.65 0.59 0.49
2.46 2.23 2.04 1.88 1.63
4.52 4.18 3.87 3.60 3.15
6.85 6.39 5.97 5.59 4.94
9.36 8.80 8.28 7.81 6.99
12.0 11.4 10.8 10.2 9.25
14.7 14.0 13.4 12.8 11.7
17.5 16.8 16.1 15.4 14.2
20.3 19.6 18.8 18.1 16.8
23.2 22.4 21.6 20.9 19.5
26.1 25.3 24.4 23.7 22.2
29.0 28.1 27.3 26.5 25.0
28 32 36
0.42 0.37 0.33
1.43 1.27 1.15
2.79 2.49 2.25
4.41 3.97 3.61
6.31 5.74 5.26
8.44 10.7 13.1 7.74 9.90 12.2 7.13 9.17 11.4
15.7 14.6 13.7
18.2 17.1 16.1
20.9 19.7 18.6
23.6 22.3 21.1
7.10 6.38 5.79
8.81 10.7 7.95 9.65 7.23 8.81
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 69
Table 8-22 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 75°° C req =
Pu
φ rn
or φ R n = C × φrn
ex
where
3
6
s s
e
s, in.
75° P u
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
3
3 6
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
2.86 2.77 2.66 2.53 2.40
5.68 5.49 5.27 5.04 4.81
8.47 8.19 7.89 7.58 7.27
11.3 10.9 10.5 10.2 9.81
14.1 13.7 13.2 12.8 12.4
16.9 16.4 16.0 15.5 15.1
19.8 19.2 18.8 18.3 17.8
22.6 22.1 21.6 21.0 20.6
25.5 24.9 24.4 23.9 23.3
28.4 27.8 27.2 26.7 26.2
31.3 30.7 30.1 29.5 29.0
34.2 33.6 33.0 32.4 31.8
7 8 9 10 12
2.26 2.13 2.00 1.89 1.67
4.57 4.35 4.13 3.93 3.57
6.97 6.69 6.41 6.15 5.67
9.47 9.13 8.82 8.51 7.95
12.0 11.7 11.3 11.0 10.4
14.7 14.3 13.9 13.5 12.9
17.4 16.9 16.5 16.1 15.4
20.1 19.6 19.2 18.8 18.0
22.9 22.4 21.9 21.5 20.7
25.6 25.1 24.7 24.2 23.4
28.4 27.9 27.4 27.0 26.1
31.3 30.7 30.2 29.8 28.8
14 16 18 20 24
1.49 1.34 1.21 1.10 0.93
3.25 2.97 2.73 2.53 2.19
5.25 4.87 4.54 4.24 3.75
7.44 6.98 6.56 6.18 5.52
9.77 9.23 8.74 8.28 7.48
12.2 11.6 11.1 10.5 9.59
14.7 14.1 13.5 12.9 11.8
17.3 16.6 16.0 15.3 14.2
19.9 19.2 18.5 17.8 16.6
22.6 21.8 21.1 20.4 19.1
25.3 24.5 23.7 23.0 21.6
28.0 27.2 26.4 25.6 24.2
28 32 36
0.80 0.71 0.63
1.93 1.72 1.55
3.34 3.01 2.74
4.97 4.51 4.12
6.79 6.20 5.70
13.2 12.3 11.5
15.5 14.5 13.6
17.9 16.8 15.9
20.4 19.2 18.2
22.9 21.7 20.6
2 3 4 5 6
2.86 2.77 2.66 2.53 2.40
5.66 5.49 5.30 5.10 4.91
8.48 8.25 8.02 7.79 7.56
11.3 11.1 10.8 10.6 10.3
14.2 13.9 13.6 13.4 13.1
17.1 16.8 16.5 16.2 15.9
20.1 19.7 19.4 19.1 18.8
23.0 22.7 22.3 22.0 21.7
26.4 25.6 25.2 24.9 24.6
29.3 28.5 28.2 27.8 27.5
32.3 31.5 31.1 30.8 30.4
35.2 34.4 34.0 33.7 33.3
7 8 9 10 12
2.26 2.13 2.00 1.89 1.67
4.72 4.54 4.37 4.21 3.90
7.34 7.14 6.94 6.75 6.39
10.1 9.83 9.61 9.40 9.00
12.9 12.6 12.4 12.1 11.7
15.7 15.4 15.2 14.9 14.4
18.5 18.3 18.0 17.7 17.2
21.4 21.1 20.8 20.6 20.0
24.3 24.0 23.7 23.4 22.9
27.2 26.9 26.6 26.3 25.7
30.1 29.8 29.5 29.2 28.6
33.0 32.7 32.4 32.1 31.5
14 16 18 20 24
1.49 1.34 1.21 1.10 0.93
3.63 3.39 3.17 2.98 2.65
6.06 5.75 5.47 5.22 4.76
8.63 8.29 7.96 7.66 7.10
11.3 10.9 10.6 10.2 9.57
14.0 13.6 13.2 12.9 12.2
16.8 16.3 15.9 15.5 14.8
19.6 19.1 18.7 18.2 17.5
22.4 21.9 21.4 21.0 20.2
25.2 24.7 24.2 23.8 22.9
28.1 27.5 27.0 26.6 25.7
30.9 30.4 29.9 29.4 28.5
28 32 36
0.80 0.71 0.63
2.38 2.16 1.97
4.37 4.03 3.73
6.60 6.15 5.75
8.99 11.5 8.45 10.9 7.96 10.3
14.1 13.4 12.8
16.7 16.0 15.3
19.4 18.7 17.9
22.1 21.3 20.6
24.8 24.0 23.3
27.6 26.8 26.0
8.78 10.9 8.08 10.1 7.47 9.40
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 70
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-23. Coefficients C for Eccentrically Loaded Bolt Groups Angle = 0°° C req =
Pu
φrn
or φR n = C × φ rn
ex= e
where
s, in.
3
6
s
Pu
s
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
6
6 12
Number of bolts in one vertical row, n
ex, in.
1
2
3
2 3 4 5 6
2.15 1.91 1.71 1.55 1.42
4.55 4.06 3.65 3.31 3.02
7.17 6.43 5.80 5.27 4.82
7 8 9 10 12
1.31 1.21 1.12 1.05 0.92
2.77 2.56 2.38 2.21 1.94
4.44 4.10 3.81 3.55 3.12
6.34 5.87 5.46 5.09 4.48
8.46 10.8 7.85 10.1 7.31 9.39 6.84 8.79 6.03 7.78
14 16 18 20 24
0.81 0.72 0.64 0.58 0.49
1.72 1.53 1.38 1.26 1.06
2.77 2.48 2.25 2.05 1.73
3.99 3.58 3.25 2.96 2.52
5.38 4.84 4.40 4.02 3.42
6.95 6.27 5.70 5.21 4.45
8.69 10.6 12.7 7.85 9.60 11.5 7.15 8.75 10.5 6.55 8.03 9.65 5.60 6.88 8.29
28 32 36
0.42 0.37 0.33
0.92 0.81 0.72
1.50 1.32 1.18
2.19 1.93 1.72
2.97 2.63 2.35
3.87 3.42 3.06
4.88 4.32 3.87
2 3 4 5 6
2.15 1.91 1.71 1.55 1.42
4.94 4.48 4.07 3.71 3.40
7.98 7.39 6.81 6.27 5.79
11.1 10.5 9.86 9.22 8.61
7 8 9 10 12
1.31 1.21 1.12 1.05 0.92
3.13 2.90 2.69 2.51 2.21
5.35 4.97 4.64 4.34 3.85
8.05 11.0 7.53 10.4 7.07 9.78 6.64 9.24 5.91 8.27
14 16 18 20 24
0.81 0.72 0.64 0.58 0.49
1.96 1.76 1.60 1.46 1.24
3.44 3.11 2.83 2.59 2.21
5.31 4.80 4.38 4.02 3.44
7.46 6.78 6.20 5.71 4.91
9.95 12.7 9.09 11.6 8.34 10.7 7.70 9.91 6.65 8.59
28 32 36
0.42 0.37 0.33
1.08 0.95 0.85
1.92 1.70 1.52
3.00 2.66 2.39
4.30 3.82 3.43
5.83 5.19 4.67
4
5
10.0 13.0 9.06 11.9 8.23 10.9 7.51 9.97 6.88 9.16
14.2 13.6 13.0 12.3 11.7
6
7
8
9
10
11
12
16.0 14.9 13.7 12.7 11.7
19.1 17.9 16.7 15.5 14.4
22.2 21.0 19.8 18.5 17.3
25.3 24.1 22.9 21.5 20.3
28.3 27.2 26.0 24.7 23.3
31.4 30.3 29.1 27.8 26.4
34.4 33.4 32.3 31.0 29.6
13.4 12.5 11.7 10.9 9.70
16.1 15.1 14.1 13.3 11.8
19.0 17.9 16.8 15.8 14.1
22.0 20.7 19.6 18.5 16.6
25.1 23.7 22.5 21.3 19.1
28.2 26.8 25.5 24.2 21.9
14.9 13.6 12.4 11.4 9.82
17.3 15.8 14.4 13.3 11.5
19.9 18.1 16.6 15.3 13.2
6.00 5.32 4.77
7.24 6.42 5.76
8.59 10.1 11.6 7.62 8.93 10.3 6.84 8.02 9.29
17.2 16.7 16.1 15.5 14.8
20.2 19.8 19.3 18.6 18.0
23.2 22.8 22.3 21.8 21.1
26.2 25.8 25.4 24.9 24.3
29.2 28.9 28.5 28.0 27.4
32.1 31.9 31.5 31.0 30.5
35.1 34.8 34.5 34.1 33.6
14.1 13.4 12.8 12.1 11.0
17.3 16.6 15.9 15.2 13.9
20.5 19.8 19.0 18.3 16.9
23.6 23.0 22.2 21.5 20.0
26.8 26.1 25.4 24.7 23.2
29.9 29.3 28.6 27.9 26.4
33.1 32.5 31.8 31.1 29.7
15.6 14.4 13.3 12.4 10.8
18.6 17.3 16.1 15.0 13.2
21.8 20.4 19.1 17.9 15.7
25.0 23.5 22.1 20.8 18.5
28.2 26.7 25.2 23.8 21.3
9.53 11.7 14.0 8.51 10.5 12.6 7.68 9.45 11.4
16.5 14.9 13.5
19.2 17.3 15.8
7.57 6.75 6.08
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 71
Table 8-23 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 15°° C req =
Pu
φ rn
or φ R n = C × φrn
ex
Pu
where s
15°
s, in.
3
6
e
s
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
6
6 12
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
2.22 1.97 1.77 1.61 1.47
4.62 4.13 3.72 3.38 3.10
7.25 6.53 5.91 5.39 4.93
10.1 9.13 8.31 7.60 6.98
13.0 11.9 10.9 10.1 9.28
16.0 14.9 13.7 12.7 11.8
19.0 17.9 16.7 15.5 14.4
22.1 20.9 19.7 18.4 17.2
25.1 24.0 22.7 21.4 20.2
28.2 27.1 25.8 24.5 23.2
31.2 30.1 28.9 27.6 26.2
34.2 33.2 32.0 30.7 29.3
7 8 9 10 12
1.35 1.25 1.16 1.08 0.94
2.85 2.63 2.44 2.28 2.00
4.54 4.21 3.91 3.65 3.20
6.45 5.98 5.57 5.21 4.59
8.59 10.9 7.98 10.2 7.45 9.51 6.97 8.92 6.16 7.91
13.5 12.6 11.8 11.1 9.84
16.1 15.1 14.2 13.4 11.9
19.0 17.8 16.8 15.9 14.2
21.9 20.7 19.5 18.5 16.6
24.9 23.6 22.4 21.2 19.2
27.9 26.6 25.3 24.1 21.9
14 16 18 20 24
0.83 0.74 0.66 0.60 0.50
1.77 1.58 1.43 1.30 1.10
2.85 2.56 2.31 2.11 1.79
4.09 3.68 3.34 3.05 2.59
5.50 4.96 4.51 4.13 3.52
7.08 6.40 5.83 5.34 4.56
8.84 10.8 12.8 8.00 9.75 11.7 7.30 8.91 10.7 6.70 8.19 9.82 5.74 7.03 8.45
15.0 13.7 12.6 11.6 10.0
17.4 15.9 14.6 13.5 11.7
19.9 18.2 16.8 15.5 13.4
28 32 36
0.43 0.38 0.34
0.95 0.84 0.75
1.55 1.37 1.22
2.25 1.99 1.78
3.06 2.70 2.42
3.98 3.52 3.15
5.01 4.43 3.98
2 3 4 5 6
2.22 1.97 1.77 1.61 1.47
4.97 4.50 4.10 3.75 3.45
7.97 7.40 6.84 6.32 5.86
11.0 10.5 9.82 9.20 8.61
7 8 9 10 12
1.35 1.25 1.16 1.08 0.94
3.18 2.95 2.75 2.57 2.26
5.44 5.07 4.73 4.44 3.93
8.06 11.0 7.55 10.4 7.09 9.78 6.67 9.26 5.96 8.33
14 16 18 20 24
0.83 0.74 0.66 0.60 0.50
2.01 1.81 1.64 1.50 1.28
3.52 3.18 2.90 2.65 2.27
5.37 4.87 4.45 4.10 3.52
7.55 6.88 6.31 5.81 5.01
9.97 12.7 9.13 11.7 8.40 10.8 7.77 9.99 6.74 8.71
28 32 36
0.43 0.38 0.34
1.11 0.98 0.88
1.98 1.75 1.57
3.08 2.73 2.45
4.40 3.91 3.52
5.93 5.29 4.77
14.1 13.5 12.9 12.3 11.6
6.15 5.45 4.89
7.40 6.57 5.90
8.77 10.2 11.8 7.79 9.12 10.5 7.01 8.20 9.49
17.1 16.6 16.0 15.4 14.7
20.1 19.7 19.1 18.5 17.8
23.1 22.7 22.2 21.6 20.9
26.1 25.7 25.2 24.7 24.1
29.1 28.7 28.3 27.8 27.2
32.1 31.7 31.3 30.8 30.3
35.0 34.7 34.3 33.9 33.3
14.0 13.3 12.7 12.1 11.0
17.1 16.4 15.7 15.1 13.8
20.3 19.5 18.8 18.1 16.8
23.4 22.7 22.0 21.3 19.8
26.5 25.8 25.1 24.4 23.0
29.6 29.0 28.3 27.6 26.1
32.7 32.1 31.4 30.7 29.3
15.5 14.4 13.3 12.4 10.9
18.5 17.2 16.1 15.0 13.2
21.5 20.2 18.9 17.8 15.8
24.7 23.2 21.9 20.7 18.4
27.8 26.4 25.0 23.6 21.2
9.62 11.8 14.1 8.62 10.6 12.7 7.80 9.59 11.5
16.5 15.0 13.6
19.1 17.4 15.9
7.69 6.87 6.20
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 72
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-23 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 30°° C req =
Pu
φrn
or φR n = C × φ rn
ex Pu
where
s, in.
3
6
s
30°
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
s
e
6
6 12
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
2.40 2.15 1.94 1.76 1.61
4.89 4.40 3.99 3.65 3.35
7.53 6.84 6.24 5.74 5.29
10.3 9.45 8.69 8.02 7.42
13.2 12.2 11.3 10.5 9.72
16.1 15.1 14.0 13.1 12.2
19.1 18.0 16.9 15.8 14.8
22.1 21.0 19.8 18.7 17.6
25.1 24.0 22.8 21.6 20.4
28.1 27.0 25.8 24.6 23.4
31.1 30.0 28.8 27.6 26.3
34.1 33.0 31.9 30.6 29.3
7 8 9 10 12
1.49 1.37 1.28 1.19 1.04
3.10 2.87 2.67 2.49 2.19
4.90 4.55 4.24 3.97 3.50
6.89 6.42 6.00 5.63 4.98
9.06 11.4 8.47 10.7 7.94 10.1 7.47 9.49 6.64 8.48
13.9 13.1 12.4 11.7 10.5
16.6 15.6 14.8 14.0 12.6
19.3 18.3 17.4 16.5 14.9
22.2 21.1 20.0 19.1 17.3
25.1 23.9 22.8 21.8 19.9
28.1 26.9 25.7 24.6 22.5
14 16 18 20 24
0.92 0.82 0.74 0.67 0.56
1.95 1.75 1.58 1.44 1.22
3.12 2.81 2.55 2.33 1.98
4.46 4.03 3.66 3.35 2.86
5.97 5.40 4.92 4.52 3.87
7.64 6.93 6.33 5.82 5.00
9.46 11.4 8.61 10.4 7.89 9.59 7.27 8.85 6.26 7.65
13.6 12.4 11.4 10.6 9.16
15.8 14.5 13.4 12.4 10.8
18.2 16.7 15.5 14.4 12.5
20.7 19.1 17.7 16.4 14.4
28 32 36
0.48 0.42 0.38
1.06 0.93 0.83
1.72 1.52 1.36
2.49 2.20 1.97
3.37 2.99 2.68
4.37 3.88 3.48
5.48 4.87 4.38
2 3 4 5 6
2.40 2.15 1.94 1.76 1.61
5.11 4.66 4.26 3.92 3.63
8.05 7.51 6.99 6.52 6.09
11.1 10.5 9.90 9.34 8.80
7 8 9 10 12
1.49 1.37 1.28 1.19 1.04
3.38 3.15 2.95 2.77 2.45
5.70 5.35 5.03 4.74 4.23
8.30 11.1 7.83 10.6 7.40 10.0 7.00 9.54 6.30 8.67
14 16 18 20 24
0.92 0.82 0.74 0.67 0.56
2.19 1.98 1.80 1.65 1.41
3.81 3.45 3.16 2.90 2.49
5.71 5.22 4.79 4.42 3.82
7.92 10.4 7.27 9.58 6.71 8.88 6.22 8.26 5.41 7.22
28 32 36
0.48 0.42 0.38
1.23 1.08 0.97
2.18 1.93 1.73
3.43 2.99 2.69
4.78 4.26 3.85
14.1 13.5 12.9 12.3 11.7
6.71 5.97 5.38
8.06 7.18 6.47
9.51 11.1 8.49 9.91 7.66 8.95
12.8 11.4 10.3
17.1 16.5 16.0 15.3 14.7
20.1 19.6 19.0 18.4 17.7
23.0 22.6 22.0 21.5 20.8
26.0 25.6 25.1 24.5 23.9
29.0 28.6 28.1 27.6 27.0
32.0 31.6 31.1 30.6 30.0
34.9 34.6 34.1 33.6 33.1
14.1 13.5 12.9 12.3 11.3
17.1 16.5 15.8 15.2 14.1
20.2 19.5 18.8 18.2 17.0
23.2 22.6 21.9 21.2 19.9
26.3 25.7 25.0 24.3 23.0
29.4 28.7 28.1 27.4 26.0
32.5 31.8 31.2 30.5 29.1
13.0 12.1 11.2 10.5 9.23
15.8 14.8 13.8 12.9 11.5
18.7 17.6 16.5 15.5 13.8
21.7 20.5 19.3 18.2 16.4
24.7 23.4 22.2 21.1 19.0
27.8 26.4 25.2 24.0 21.8
8.22 10.3 12.4 7.40 9.25 11.3 6.71 8.41 10.3
14.8 13.4 12.3
17.2 15.7 14.4
19.8 18.2 16.7
6.40 5.73 5.18
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 73
Table 8-23 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 45°° C req =
Pu
φ rn
or φ R n = C × φrn
ex Pu
where
3
6
s s
e
s, in.
45°
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
6
6 12
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
2.64 2.43 2.23 2.05 1.89
5.30 4.90 4.52 4.17 3.86
8.01 7.44 6.89 6.40 5.96
10.8 10.1 9.38 8.75 8.20
13.6 12.8 12.0 11.2 10.6
16.4 15.6 14.7 13.9 13.1
19.3 18.4 17.5 16.6 15.7
22.3 21.3 20.3 19.3 18.4
25.2 24.2 23.2 22.2 21.2
28.1 27.2 26.1 25.0 23.99
31.1 30.1 29.0 27.9 26.9
34.0 33.1 32.0 30.9 29.8
7 8 9 10 12
1.75 1.63 1.52 1.42 1.25
3.59 3.35 3.13 2.94 2.60
5.57 5.22 4.90 4.61 4.11
7.70 7.25 6.83 6.45 5.78
9.99 9.43 8.91 8.44 7.60
12.4 11.7 11.1 10.6 9.58
14.9 14.2 13.5 12.8 11.7
17.5 16.7 15.9 15.2 14.0
20.2 19.3 18.5 17.7 16.3
23.0 22.1 21.2 20.3 18.8
25.8 24.8 23.9 23.0 21.3
28.7 27.7 26.7 25.7 23.9
14 16 18 20 24
1.11 0.99 0.90 0.81 0.68
2.32 2.09 1.90 1.73 1.47
3.69 3.34 3.04 2.79 2.38
5.21 4.74 4.33 3.98 3.42
6.90 6.29 5.77 5.33 4.60
8.73 10.7 8.00 9.85 7.36 9.10 6.81 8.44 5.91 7.35
12.8 11.8 10.96 10.2 8.91
15.0 13.9 12.9 12.1 10.6
17.4 16.1 15.0 14.1 12.4
19.8 18.5 17.3 16.2 14.3
22.3 20.9 19.5 18.4 16.3
28 32 36
0.59 0.52 0.46
1.28 1.13 1.01
2.08 1.84 1.65
2.99 2.65 2.38
4.03 3.59 3.23
5.20 4.63 4.17
12.8 11.6 10.5
14.6 13.3 12.1
2 3 4 5 6
2.64 2.43 2.23 2.05 1.89
5.38 5.02 4.67 4.34 4.06
8.22 7.78 7.33 6.90 6.50
11.1 10.7 10.2 9.66 9.19
14.1 13.6 13.1 12.5 12.0
17.0 16.6 16.0 15.5 14.9
20.0 19.5 19.0 18.4 17.9
22.97 22.5 22.0 21.4 20.9
25.9 25.5 25.0 24.4 23.9
28.9 28.5 28.0 27.4 26.9
31.9 31.4 31.0 30.4 29.9
34.8 34.4 34.0 33.4 32.9
7 8 9 10 12
1.75 1.63 1.52 1.42 1.25
3.80 3.57 3.36 3.17 2.84
6.16 5.84 5.54 5.27 4.78
8.76 8.36 7.99 7.63 6.99
11.5 11.1 10.6 10.2 9.40
14.4 13.9 13.4 12.9 12.0
17.3 16.8 16.2 15.7 14.7
20.3 19.7 19.2 18.6 17.6
23.3 22.7 22.1 21.5 20.4
26.3 25.7 25.1 24.5 23.4
29.3 28.7 28.1 27.5 26.3
32.3 31.7 31.1 30.5 29.3
14 16 18 20 24
1.11 0.99 0.90 0.81 0.68
2.57 2.33 2.13 1.96 1.68
4.36 3.99 3.68 3.40 2.95
6.42 5.92 5.49 5.10 4.46
8.70 11.2 8.09 10.5 7.54 9.80 7.05 9.21 6.22 8.19
13.8 13.0 12.2 11.6 10.4
16.6 15.7 14.8 14.0 12.7
19.4 18.4 17.5 16.6 15.1
22.3 21.2 20.3 19.3 17.7
25.2 24.1 23.1 22.1 20.3
28.2 27.1 26.0 24.9 23.0
28 32 36
0.59 0.52 0.46
1.47 1.31 1.17
2.59 2.31 2.08
3.95 3.54 3.20
5.55 4.99 4.54
9.34 11.5 13.8 8.49 10.5 12.7 7.77 9.64 11.7
16.2 14.9 13.8
18.7 17.3 16.1
21.3 19.8 18.5
7.35 6.65 6.06
6.49 5.80 5.23
7.90 7.07 6.40
9.42 11.1 8.46 9.95 7.67 9.04
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 74
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-23 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 60°° C req =
Pu
φrn
or φR n = C × φ rn
ex
where
3
6
s
60°
s
e
s, in.
Pu
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
6
6 12
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
2.83 2.72 2.59 2.46 2.32
5.64 5.43 5.18 4.92 4.66
8.45 8.13 7.77 7.40 7.03
11.3 10.8 10.4 9.92 9.46
14.1 13.6 13.0 12.5 12.0
16.9 16.3 15.7 15.1 14.5
19.8 19.1 18.5 17.8 17.1
22.6 21.9 21.2 20.5 19.8
25.5 24.8 24.0 23.2 22.5
28.4 27.6 26.8 26.0 25.2
31.3 30.5 29.7 28.9 28.0
34.2 33.4 32.5 31.7 30.8
7 8 9 10 12
2.19 2.07 1.95 1.84 1.65
4.41 4.17 3.95 3.74 3.38
6.68 6.35 6.04 5.75 5.22
9.02 8.61 8.22 7.86 7.19
11.4 11.0 10.5 10.1 9.28
13.9 13.4 12.9 12.4 11.5
16.5 15.9 15.3 14.8 13.8
19.1 18.4 17.8 17.3 16.2
21.8 21.1 20.4 19.8 18.6
24.5 23.7 23.0 22.4 21.1
27.2 26.5 25.7 25.0 23.7
30.0 29.2 28.5 27.7 26.3
14 16 18 20 24
1.49 1.35 1.23 1.12 0.95
3.06 2.79 2.55 2.35 2.02
4.76 4.37 4.02 3.72 3.22
6.61 6.09 5.64 5.24 4.57
8.58 10.7 7.95 9.93 7.39 9.28 6.90 8.69 6.06 7.68
12.9 12.0 11.3 10.6 9.43
15.2 14.2 13.4 12.6 11.3
17.5 16.5 15.6 14.8 13.3
20.0 18.9 17.9 17.0 15.4
22.5 21.3 20.3 19.3 17.5
25.0 23.8 22.7 21.7 19.8
28 32 36
0.83 0.73 0.65
1.76 1.56 1.40
2.84 2.53 2.27
4.04 3.61 3.26
5.39 4.84 4.38
12.0 11.0 10.1
14.0 12.8 11.7
16.0 14.7 13.5
18.1 16.7 15.4
2 3 4 5 6
2.83 2.72 2.59 2.46 2.32
5.64 5.44 5.21 4.97 4.73
8.47 8.19 7.88 7.57 7.27
11.3 11.0 10.6 10.3 9.91
14.2 13.8 13.4 13.1 12.7
17.1 16.7 16.3 15.9 15.5
20.0 19.6 19.2 18.8 18.3
23.0 22.6 22.1 21.7 21.2
25.9 25.5 25.0 24.6 24.1
28.9 28.4 28.0 27.5 27.0
31.8 31.4 30.9 30.4 30.0
34.8 34.3 33.9 33.4 33.0
7 8 9 10 12
2.19 2.07 1.95 1.84 1.65
4.51 4.29 4.09 3.90 3.56
6.97 6.69 6.43 6.18 5.73
9.56 9.23 8.92 8.63 8.08
12.3 11.9 11.5 11.2 10.6
15.0 14.6 14.3 13.9 13.2
17.9 17.5 17.0 16.6 15.9
20.8 20.3 19.9 19.5 18.7
23.7 23.2 22.8 22.3 21.5
26.6 26.1 25.6 25.2 24.3
29.5 29.0 28.6 28.1 27.2
32.4 32.0 31.5 31.0 30.1
14 16 18 20 24
1.49 1.35 1.23 1.12 0.95
3.27 3.01 2.78 2.58 2.25
5.32 4.95 4.63 4.34 3.84
7.59 10.0 7.13 9.48 6.71 8.98 6.33 8.52 5.67 7.70
12.6 12.0 11.4 10.9 9.91
15.2 14.5 13.9 13.3 12.3
17.9 17.2 16.5 15.9 14.7
20.7 19.9 19.2 18.5 17.3
23.5 22.7 22.0 21.2 19.9
26.3 25.5 24.7 24.0 22.6
29.2 28.4 27.6 27.0 25.3
28 32 36
0.83 0.73 0.65
1.98 1.77 1.60
3.43 3.09 2.81
5.11 4.64 4.24
9.08 11.3 13.7 8.36 10.5 12.7 7.73 9.74 11.9
16.1 15.1 14.2
18.7 17.5 16.5
21.3 20.1 19.0
23.9 22.6 21.5
7.00 6.40 5.89
6.86 6.19 5.62
8.47 10.2 7.66 9.26 6.98 8.46
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 75
Table 8-23 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 75°° C req =
Pu
φ rn
or φ R n = C × φrn
ex
where
3
6
s s
e
s, in.
75° P u
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
6
6 12
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
2.92 2.89 2.86 2.82 2.77
5.83 5.77 5.70 5.61 5.51
8.73 8.63 8.51 8.38 8.23
11.6 11.5 11.3 11.1 10.9
14.5 14.3 14.1 13.9 13.6
17.4 17.2 16.9 16.6 16.3
20.3 20.0 19.7 19.4 19.0
23.1 22.8 22.5 22.1 21.8
26.0 25.7 25.3 24.9 24.5
28.9 28.5 28.1 27.7 27.2
31.8 31.4 30.9 30.5 30.0
34.7 34.2 33.7 33.3 32.8
7 8 9 10 12
2.72 2.66 2.60 2.53 2.40
5.40 5.29 5.16 5.04 4.78
8.06 7.89 7.71 7.53 7.16
10.7 10.5 10.3 10.1 9.57
13.4 13.1 12.8 12.6 12.0
16.0 15.7 15.4 15.1 14.5
18.7 18.3 18.0 17.7 17.0
21.4 21.0 20.6 20.3 19.6
24.1 23.7 23.3 22.9 22.1
26.8 26.4 26.0 25.6 24.8
29.6 29.1 28.7 28.3 27.4
32.3 31.9 31.4 31.0 30.1
14 16 18 20 24
2.26 2.13 2.00 1.89 1.67
4.52 4.27 4.03 3.81 3.41
6.80 6.45 6.12 5.80 5.24
9.12 8.68 8.27 7.88 7.18
11.5 11.0 10.5 10.1 9.22
13.9 13.3 12.8 12.3 11.4
16.4 15.8 15.2 14.6 13.6
18.9 18.2 17.6 17.0 15.9
21.4 20.7 20.1 19.4 18.2
24.0 23.3 22.6 21.9 20.7
26.6 25.9 25.1 24.4 23.1
29.3 28.5 27.7 27.0 25.6
28 32 36
1.49 1.34 1.21
3.06 2.77 2.52
4.75 4.33 3.97
6.56 6.02 5.56
12.6 11.8 11.1
14.9 13.9 13.1
17.1 16.1 15.2
19.5 18.4 17.4
21.9 20.7 19.7
24.3 23.1 22.0
2 3 4 5 6
2.92 2.89 2.86 2.82 2.77
5.82 5.76 5.68 5.59 5.49
8.71 8.60 8.47 8.34 8.19
11.6 11.4 11.3 11.1 10.9
14.5 14.3 14.1 13.9 13.7
17.4 17.1 16.9 16.7 16.4
20.3 20.0 19.8 19.5 19.2
23.5 22.9 22.6 22.4 22.1
26.4 25.8 25.5 25.2 24.9
29.3 28.7 28.4 28.1 27.8
32.3 31.7 31.3 31.0 30.7
35.2 34.6 34.2 33.9 33.6
7 8 9 10 12
2.72 2.66 2.60 2.53 2.40
5.39 5.27 5.16 5.04 4.81
8.04 7.89 7.74 7.58 7.27
10.7 10.5 10.4 10.2 9.81
13.4 13.2 13.0 12.8 12.4
16.2 16.0 15.8 15.5 15.1
19.0 18.8 18.5 18.3 17.8
21.8 21.6 21.3 21.0 20.6
24.6 24.4 24.1 23.9 23.3
27.5 27.2 27.0 26.7 26.2
30.4 30.1 29.8 29.5 29.0
33.3 33.0 32.7 32.4 31.8
14 16 18 20 24
2.26 2.13 2.00 1.89 1.67
4.57 4.35 4.13 3.93 3.57
6.97 6.69 6.41 6.15 5.67
9.47 9.13 8.82 8.51 7.95
12.0 11.7 11.3 11.0 10.4
14.7 14.3 13.9 13.5 12.9
17.4 16.9 16.5 16.1 15.4
20.1 19.6 19.2 18.8 18.0
22.9 22.4 21.9 21.5 20.7
25.6 25.1 24.7 24.2 23.4
28.4 27.9 27.4 27.0 26.1
31.3 30.7 30.2 29.8 28.8
28 32 36
1.49 1.34 1.21
3.25 2.97 2.73
5.25 4.87 4.54
7.44 6.98 6.56
9.77 12.2 9.23 11.6 8.74 11.1
14.7 14.1 13.5
17.3 16.6 16.0
19.9 19.2 18.5
22.6 21.8 21.1
25.3 24.5 23.7
28.0 27.2 26.4
8.49 10.5 7.84 9.77 7.27 9.10
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 76
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-24. Coefficients C for Eccentrically Loaded Bolt Groups Angle = 0°° C req =
Pu
φrn
or φR n = C × φ rn
ex = e
where
s, in.
3
6
s
Pu
s
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
3
3
3
9
Number of bolts in one vertical row, n
ex, in.
1
2
2 3 4 5 6
2.60 2.23 1.94 1.69 1.49
5.70 4.92 4.30 3.79 3.37
9.24 13.2 8.05 11.7 7.09 10.4 6.30 9.29 5.65 8.37
7 8 9 10 12
1.32 1.18 1.07 0.98 0.83
3.03 2.74 2.50 2.29 1.96
5.10 4.63 4.24 3.89 3.34
7.59 10.4 6.92 9.56 6.35 8.81 5.86 8.15 5.06 7.06
14 16 18 20 24
0.73 0.65 0.58 0.53 0.44
1.72 1.52 1.37 1.24 1.04
2.92 2.59 2.33 2.11 1.78
4.44 3.95 3.55 3.23 2.72
6.21 5.54 4.99 4.53 3.83
8.27 10.6 13.2 7.39 9.48 11.9 6.67 8.57 10.7 6.07 7.81 9.77 5.14 6.62 8.30
28 32 36
0.38 0.34 0.30
0.90 0.79 0.71
1.54 1.36 1.21
2.35 2.07 1.85
3.31 2.91 2.60
4.45 3.92 3.50
2 3 4 5 6
2.60 2.23 1.94 1.69 1.49
6.48 5.75 5.12 4.58 4.13
10.7 9.79 8.91 8.10 7.37
7 8 9 10 12
1.32 1.18 1.07 0.98 0.83
3.74 3.41 3.13 2.89 2.50
6.74 10.5 6.20 9.73 5.73 9.05 5.31 8.45 4.63 7.43
14 16 18 20 24
0.73 0.65 0.58 0.53 0.44
2.19 1.95 1.76 1.60 1.35
4.09 3.65 3.29 2.99 2.53
6.60 5.93 5.37 4.90 4.16
9.53 12.9 8.59 11.7 7.81 10.8 7.15 9.85 6.10 8.44
28 32 36
0.38 0.34 0.30
1.17 1.03 0.92
2.19 1.93 1.72
3.61 3.19 2.85
5.31 4.69 4.20
3
4
14.9 14.0 13.1 12.2 11.3
5
6
7
8
9
10
11
12
17.3 15.6 14.0 12.6 11.5
21.4 19.7 18.0 16.4 14.9
25.6 23.9 22.1 20.3 18.7
29.7 28.1 26.3 24.4 22.7
33.8 32.3 30.5 28.6 26.7
37.9 36.5 34.7 32.9 30.9
41.9 40.6 38.9 37.1 35.2
45.9 44.7 43.1 41.4 39.4
13.7 12.6 11.6 10.8 9.37
17.2 15.9 14.7 13.7 12.0
21.0 19.5 18.1 16.9 14.9
24.9 23.3 21.7 20.3 17.9
29.0 27.3 25.6 24.1 21.3
33.2 31.4 29.6 27.9 24.9
37.5 35.5 33.7 31.9 28.6
16.0 14.4 13.1 11.9 10.2
19.1 17.2 15.7 14.3 12.2
22.4 20.2 18.4 16.9 14.4
25.8 23.4 21.4 19.6 16.8
5.73 5.05 4.51
7.20 6.35 5.68
8.82 10.6 12.6 7.79 9.38 11.1 6.96 8.39 9.95
14.7 13.0 11.6
18.9 18.2 17.4 16.5 15.5
23.0 22.3 21.6 20.7 19.7
27.0 26.4 25.7 24.9 24.0
31.0 30.5 29.9 29.1 28.3
34.9 34.5 33.9 33.2 32.5
38.9 38.5 38.0 37.4 36.7
42.9 42.5 42.0 41.4 40.8
46.8 46.5 46.1 45.5 44.9
14.5 13.6 12.8 12.1 10.7
18.8 17.8 16.9 16.0 14.3
23.1 22.1 21.1 20.1 18.3
27.4 26.4 25.4 24.4 22.5
31.6 30.6 29.7 28.7 26.7
35.8 34.9 34.0 33.0 31.0
40.0 39.1 38.3 37.3 35.3
44.1 43.3 42.5 41.5 39.6
16.7 15.2 14.0 12.9 11.1
20.6 19.0 17.5 16.2 14.0
24.7 22.9 21.3 19.8 17.3
29.0 27.1 25.3 23.6 20.8
33.3 31.3 29.4 27.6 24.5
37.6 35.5 33.6 31.7 28.3
9.69 12.3 15.2 8.61 11.0 13.6 7.73 9.89 12.3
18.4 16.5 14.9
21.8 19.6 17.8
25.3 22.9 20.8
7.37 6.53 5.85
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 77
Table 8-24 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 15°° C req =
Pu φ rn
or φ R n = C × φrn
ex Pu
where s
15°
s, in.
3
6
e
s
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
3
3
3 9
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
2.68 2.30 1.99 1.74 1.53
5.77 5.00 4.38 3.88 3.45
9.31 8.17 7.22 6.43 5.77
13.2 11.7 10.4 9.37 8.47
17.2 15.6 14.1 12.8 11.6
21.3 19.6 17.9 16.4 15.0
25.4 23.7 22.0 20.2 18.6
29.5 27.9 26.0 24.2 22.5
33.6 32.0 30.2 28.3 26.6
37.7 36.2 34.4 32.5 30.6
41.7 40.2 38.5 36.7 34.8
45.7 44.3 42.7 40.9 39.0
7 8 9 10 12
1.36 1.22 1.11 1.01 0.86
3.10 2.81 2.57 2.36 2.02
5.21 4.74 4.34 4.00 3.44
7.71 10.6 7.05 9.70 6.48 8.95 5.98 8.29 5.18 7.21
13.7 12.7 11.8 10.9 9.52
17.2 15.9 14.8 13.8 12.2
20.9 19.5 18.1 17.0 15.0
24.8 23.2 21.7 20.4 18.1
28.8 27.1 25.5 24.0 21.4
32.9 31.1 29.4 27.7 24.9
37.1 35.2 33.4 31.6 28.5
14 16 18 20 24
0.75 0.67 0.60 0.54 0.46
1.77 1.57 1.41 1.28 1.08
3.01 2.68 2.40 2.18 1.84
4.55 4.05 3.65 3.32 2.80
6.36 5.67 5.12 4.66 3.94
8.43 10.8 13.3 7.54 9.66 12.0 6.81 8.74 10.9 6.21 7.98 9.95 5.26 6.78 8.47
16.1 14.6 13.3 12.1 10.4
19.2 17.3 15.8 14.5 12.4
22.4 20.3 18.6 17.1 14.6
25.8 23.5 21.5 19.8 17.0
28 32 36
0.40 0.35 0.31
0.93 0.82 0.73
1.59 1.40 1.25
2.43 2.14 1.91
3.41 3.00 2.68
4.56 4.03 3.60
12.8 11.3 10.2
14.9 13.2 11.9
2 3 4 5 6
2.68 2.30 1.99 1.74 1.53
6.48 5.75 5.13 4.61 4.17
10.6 9.75 8.91 8.14 7.45
7 8 9 10 12
1.36 1.22 1.11 1.01 0.86
3.79 3.46 3.19 2.94 2.55
6.84 10.4 6.30 9.71 5.83 9.05 5.42 8.47 4.73 7.47
14 16 18 20 24
0.75 0.67 0.60 0.54 0.46
2.24 2.00 1.80 1.64 1.39
4.18 3.74 3.38 3.08 2.60
6.66 6.00 5.45 4.98 4.25
9.62 12.9 8.71 11.8 7.94 10.8 7.28 9.92 6.23 8.54
28 32 36
0.40 0.35 0.31
1.20 1.06 0.94
2.26 1.99 1.78
3.69 3.26 2.92
5.43 4.81 4.31
14.7 13.9 13.0 12.1 11.2
5.89 5.19 4.65
7.37 6.51 5.83
9.02 10.9 7.98 9.59 7.15 8.59
18.8 18.1 17.2 16.3 15.3
22.9 22.2 21.4 20.5 19.5
26.9 26.3 25.5 24.7 23.7
30.9 30.3 29.7 28.9 27.9
34.9 34.4 33.7 33.0 32.2
38.8 38.3 37.7 37.1 36.3
42.8 42.4 41.8 41.2 40.4
46.7 46.3 45.8 45.2 44.5
14.5 13.6 12.8 12.1 10.7
18.6 17.6 16.8 15.9 14.3
22.8 21.8 20.9 20.0 18.2
27.0 26.0 25.1 24.1 22.2
31.3 30.3 29.3 28.3 26.4
35.4 34.5 33.5 32.6 30.6
39.6 38.7 37.8 36.8 34.8
43.7 42.9 42.0 41.0 39.1
16.6 15.2 14.0 13.0 11.2
20.5 18.9 17.5 16.2 14.1
24.5 22.8 21.2 19.8 17.3
28.6 26.8 25.1 23.5 20.8
32.9 30.9 29.1 27.4 24.4
37.1 35.1 33.2 31.4 28.1
9.85 12.5 8.77 11.1 7.89 10.0
15.4 13.8 12.5
18.5 16.6 15.1
21.8 19.7 17.9
25.3 22.9 20.9
7.48 6.65 5.97
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 78
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-24 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 30°° C req =
Pu
φrn
or φR n = C × φ rn
ex Pu
s
where
s, in.
3
6
30°
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
s
e
3
3
3
9
Number of bolts in one vertical row, n
ex, in.
1
2
2 3 4 5 6
2.90 2.50 2.18 1.91 1.69
6.06 5.31 4.70 4.18 3.75
9.59 13.4 8.52 12.1 7.62 10.9 6.85 9.86 6.19 8.98
7 8 9 10 12
1.51 1.36 1.23 1.13 0.96
3.38 3.07 2.81 2.59 2.23
5.63 5.14 4.73 4.37 3.78
8.21 11.2 7.55 10.3 6.97 9.54 6.46 8.88 5.62 7.78
14 16 18 20 24
0.84 0.74 0.67 0.61 0.51
1.95 1.73 1.56 1.42 1.20
3.32 2.96 2.66 2.42 2.04
4.96 4.43 4.00 3.65 3.09
6.90 6.19 5.60 5.11 4.34
9.08 11.6 8.17 10.4 7.41 9.46 6.77 8.67 5.77 7.41
28 32 36
0.44 0.39 0.35
1.03 0.91 0.81
1.77 1.56 1.39
2.68 2.36 2.11
3.77 3.32 2.97
5.01 4.43 3.97
2 3 4 5 6
2.90 2.50 2.18 1.91 1.69
6.59 5.88 5.30 4.81 4.38
10.6 9.83 9.05 8.35 7.72
7 8 9 10 12
1.51 1.36 1.23 1.13 0.96
4.01 3.69 3.41 3.16 2.76
7.15 10.7 6.64 10.0 6.19 9.41 5.79 8.85 5.09 7.88
14 16 18 20 24
0.84 0.74 0.67 0.61 0.51
2.44 2.18 1.97 1.80 1.53
4.54 4.08 3.70 3.38 2.87
7.08 10.1 6.41 9.21 5.85 8.45 5.37 7.80 4.61 6.74
28 32 36
0.44 0.39 0.35
1.32 1.17 1.05
2.49 2.20 1.97
4.02 3.57 3.21
3
4
14.7 13.9 13.0 12.3 11.4
5
6
7
8
9
10
11
12
17.3 15.8 14.4 13.2 12.1
21.3 19.8 18.2 16.8 15.5
25.3 23.8 22.1 20.6 19.1
29.4 27.8 26.1 24.5 22.9
33.4 31.9 30.1 28.4 26.8
37.5 35.9 34.2 32.5 30.7
41.4 40.0 38.3 36.6 34.8
45.4 44.0 42.4 40.7 38.9
14.4 13.3 12.4 11.6 10.2
17.8 16.6 15.5 14.6 12.9
21.4 20.0 18.8 17.7 15.8
25.2 23.7 22.3 21.1 18.9
29.1 27.5 26.1 24.7 22.2
33.1 31.4 29.9 28.3 25.7
37.1 35.4 33.7 32.2 29.3
14.2 12.9 11.8 10.8 9.22
17.1 15.5 14.2 13.1 11.2
20.2 18.4 16.9 15.5 13.4
23.4 21.4 19.7 18.2 15.7
26.8 24.6 22.7 21.0 18.2
13.9 12.3 11.1
16.1 14.4 13.0
6.46 5.71 5.12
8.05 7.14 6.40
9.83 11.8 8.72 10.5 7.84 9.41
18.7 18.0 17.1 16.3 15.4
22.7 22.0 21.2 20.4 19.5
26.7 26.1 25.4 24.5 23.6
30.8 30.1 29.4 28.6 27.8
34.7 34.1 33.5 32.7 31.9
38.7 38.2 37.5 36.8 35.9
42.6 42.2 41.5 40.8 40.0
46.6 46.1 45.5 44.9 44.1
14.6 13.8 13.0 12.4 11.2
18.6 17.7 16.9 16.2 14.7
22.7 21.8 20.9 20.1 18.5
26.9 25.9 25.0 24.1 22.4
31.0 30.0 29.1 28.2 26.4
35.1 34.2 33.3 32.4 30.6
39.2 38.3 37.4 36.5 34.6
43.3 42.4 41.6 40.6 38.8
13.4 12.3 11.4 10.5 9.16
17.0 15.7 14.6 13.6 11.9
20.9 19.4 18.1 16.9 14.9
24.7 23.2 21.8 20.4 18.1
28.8 27.1 25.6 24.1 21.5
32.9 31.1 29.4 27.9 25.1
36.9 35.1 33.4 31.8 28.8
8.07 10.5 13.3 7.20 9.45 11.9 6.49 8.55 10.9
16.3 14.6 13.4
19.4 17.6 16.0
22.7 20.7 18.9
26.2 23.9 22.0
5.91 5.26 4.73
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 79
Table 8-24 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 45°° C req =
Pu φ rn
or φ R n = C × φrn
ex Pu
s
where
3
6
s
e
s, in.
45°
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
3
3
3
9
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
3.26 2.87 2.54 2.25 2.01
6.62 5.92 5.31 4.78 4.33
10.2 9.19 8.36 7.63 6.99
13.9 12.7 11.7 10.8 9.94
17.7 16.4 15.2 14.1 13.1
21.6 20.2 18.9 17.6 16.5
25.5 24.0 22.6 21.3 20.1
29.4 27.96 26.5 25.1 23.8
33.4 32.0 30.5 29.0 27.5
37.4 35.9 34.4 32.9 31.4
41.3 39.9 38.4 36.9 35.3
45.3 43.9 42.4 40.8 39.3
7 8 9 10 12
1.81 1.64 1.49 1.37 1.17
3.93 3.60 3.31 3.06 2.65
6.42 5.92 5.49 5.10 4.46
9.20 8.55 7.96 7.44 6.55
12.2 11.4 10.7 10.1 8.93
15.5 14.6 13.7 13.0 11.6
18.9 17.9 16.9 16.0 14.4
22.5 21.3 20.3 19.2 17.5
26.2 24.9 23.8 22.7 20.7
30.0 28.6 27.4 26.2 24.0
33.9 32.4 31.1 29.9 27.5
37.7 36.3 34.9 33.6 31.1
14 16 18 20 24
1.03 0.91 0.82 0.74 0.63
2.33 2.08 1.88 1.71 1.45
3.95 3.54 3.20 2.92 2.48
5.83 5.24 4.75 4.35 3.71
8.00 10.5 7.23 9.47 6.59 8.66 6.04 7.96 5.18 6.84
13.1 12.0 10.9 10.1 8.71
15.9 14.6 13.5 12.5 10.8
19.0 17.5 16.1 15.0 13.0
22.1 20.4 18.9 17.6 15.4
25.4 23.6 21.9 20.5 18.0
28.8 26.8 25.0 23.5 20.7
28 32 36
0.54 0.48 0.43
1.26 1.11 0.99
2.15 1.90 1.69
3.23 2.86 2.56
4.52 4.00 3.59
13.7 12.3 11.2
16.0 14.4 13.1
18.5 16.7 15.2
2 3 4 5 6
3.26 2.87 2.54 2.25 2.01
6.89 6.28 5.74 5.27 4.85
10.8 10.1 9.38 8.75 8.20
7 8 9 10 12
1.81 1.64 1.49 1.37 1.17
4.49 4.16 3.87 3.62 3.19
7.70 11.3 7.25 10.7 6.83 10.2 6.45 9.65 5.78 8.75
14 16 18 20 24
1.03 0.91 0.82 0.74 0.63
2.84 2.56 2.33 2.13 1.82
5.21 4.74 4.33 3.98 3.42
7.97 11.1 7.30 10.3 6.72 9.48 6.21 8.83 5.38 7.74
28 32 36
0.54 0.48 0.43
1.59 1.41 1.26
2.99 2.65 2.38
4.74 4.22 3.81
14.8 14.0 13.3 12.6 11.9
5.99 5.31 4.77
7.65 6.81 6.13
9.50 11.5 8.48 10.3 7.64 9.30
18.7 18.0 17.3 16.5 15.7
22.7 22.0 21.2 20.4 19.7
26.6 26.0 25.3 24.5 23.7
30.6 30.0 29.2 28.5 27.7
34.6 33.9 33.2 32.5 31.7
38.5 37.9 37.2 36.5 35.7
42.5 41.9 41.2 40.5 39.7
46.5 45.9 45.2 44.5 43.8
15.1 14.4 13.8 13.1 12.0
19.0 18.2 17.5 16.9 15.6
22.9 22.2 21.4 20.7 19.3
26.9 26.1 25.4 24.6 23.2
30.9 30.1 29.4 28.5 27.0
34.9 34.1 33.3 32.5 31.0
39.0 38.2 37.4 36.6 35.0
43.0 42.2 41.4 40.6 39.0
14.5 13.5 12.6 11.8 10.4
18.1 16.9 15.9 15.0 13.4
21.8 20.6 19.4 18.4 16.5
25.6 24.3 23.0 21.9 19.8
29.5 28.1 26.7 25.5 23.2
33.4 32.0 30.6 29.2 26.8
37.4 35.9 34.4 33.1 30.5
9.30 12.0 14.9 8.38 10.9 13.6 7.62 9.89 12.5
18.0 16.5 15.2
21.3 19.5 18.0
24.7 22.8 21.1
28.2 26.1 24.3
6.87 6.17 5.59
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 80
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-24 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 60°° C req =
Pu
φrn
or φR n = C × φ rn
ex
where
3
6
s
60°
s
e
s, in.
Pu
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
3
3
3
9
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
3.63 3.38 3.10 2.84 2.60
7.25 6.77 6.27 5.80 5.36
10.9 10.3 9.55 8.92 8.33
14.6 13.8 13.0 12.2 11.5
18.3 17.4 16.5 15.6 14.8
22.1 21.1 20.1 19.1 18.2
25.9 24.8 23.7 22.7 21.7
29.7 28.6 27.5 26.4 25.4
33.6 32.4 31.3 30.1 29.1
37.5 36.3 35.1 33.9 32.8
41.4 40.2 38.9 37.8 36.6
45.3 44.1 42.8 41.6 40.4
7 8 9 10 12
2.38 2.19 2.02 1.87 1.62
4.96 4.60 4.28 3.99 3.51
7.79 10.9 7.30 10.2 6.85 9.68 6.45 9.17 5.75 8.27
14.1 13.4 12.7 12.1 11.0
17.4 16.7 15.9 15.2 13.9
20.9 20.0 19.2 18.4 17.0
24.4 23.5 22.6 21.8 20.3
28.0 27.1 26.1 25.3 23.6
31.8 30.7 29.7 28.8 27.0
35.5 34.4 33.4 32.4 30.6
39.3 38.2 37.1 36.1 34.1
14 16 18 20 24
1.43 1.27 1.15 1.04 0.88
3.12 2.81 2.56 2.34 2.00
5.18 4.70 4.29 3.95 3.39
7.50 10.1 6.85 9.23 6.28 8.52 5.80 7.89 5.01 6.87
12.9 11.9 11.0 10.2 8.98
15.8 14.7 13.7 12.8 11.3
18.9 17.6 16.5 15.5 13.8
22.1 20.7 19.5 18.4 16.4
25.4 24.0 22.6 21.4 19.2
28.9 27.3 25.9 24.5 22.1
32.4 30.7 29.1 27.7 25.2
28 32 36
0.76 0.67 0.60
1.74 1.54 1.38
2.96 2.63 2.36
4.39 3.91 3.52
12.3 11.2 10.2
14.8 13.5 12.3
17.4 15.9 14.5
20.1 18.4 16.9
23.0 21.1 19.4
2 3 4 5 6
3.63 3.38 3.10 2.84 2.60
7.29 6.88 6.46 6.06 5.69
11.1 10.6 10.0 9.55 9.09
14.9 14.3 13.8 13.2 12.7
18.8 18.2 17.6 17.0 16.4
22.7 22.1 21.5 20.9 20.3
26.6 26.0 25.4 24.7 24.2
30.5 29.9 29.3 28.7 28.1
34.5 33.9 33.3 32.6 31.9
38.4 37.8 37.2 36.5 35.9
42.4 41.8 41.1 40.4 39.8
46.3 45.7 45.1 44.4 43.8
7 8 9 10 12
2.38 2.19 2.02 1.87 1.62
5.34 5.03 4.74 4.47 4.01
8.66 8.27 7.90 7.55 6.93
12.2 11.7 11.3 10.9 10.1
15.9 15.4 14.9 14.5 13.6
19.7 19.1 18.6 18.1 17.2
23.6 22.9 22.4 21.9 20.8
27.4 26.8 26.2 25.7 24.5
31.3 30.7 30.1 29.5 28.3
35.2 34.6 34.0 33.4 32.2
39.2 38.5 37.9 37.3 36.0
43.1 42.4 41.8 41.2 39.9
14 16 18 20 24
1.43 1.27 1.15 1.04 0.88
3.63 3.31 3.04 2.81 2.44
6.38 5.91 5.49 5.12 4.49
9.46 8.84 8.28 7.77 6.90
12.8 12.1 11.3 10.8 9.62
16.2 15.4 14.6 13.9 12.6
19.9 18.9 18.0 17.2 15.8
23.5 22.6 21.6 20.8 19.1
27.3 26.3 25.2 24.3 22.6
31.0 30.0 28.9 28.0 26.1
34.9 33.8 32.7 31.7 29.8
38.7 37.6 36.5 35.4 33.4
28 32 36
0.76 0.67 0.60
2.15 1.91 1.73
3.99 3.58 3.24
6.18 5.58 5.08
8.70 11.5 14.5 7.93 10.6 13.4 7.27 9.76 12.5
17.7 16.5 15.4
21.1 19.7 18.4
24.5 23.0 21.6
28.0 26.4 24.9
31.6 29.9 28.3
6.07 5.43 4.91
7.97 10.1 7.15 9.06 6.48 8.22
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 81
Table 8-24 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 75°° C req =
Pu
φ rn
or φ R n = C × φrn
ex
where
3
6
s
Pu
s
e
s, in.
75°
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
3
3
3
9
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
3.86 3.79 3.70 3.59 3.47
7.69 7.53 7.34 7.13 6.89
11.5 11.2 11.0 10.6 10.3
15.3 14.9 14.6 14.2 13.8
19.1 18.6 18.2 17.7 17.2
22.9 22.4 21.9 21.3 20.8
26.7 26.1 25.5 24.9 24.4
30.5 29.9 29.2 28.6 28.0
34.3 33.6 33.0 32.3 31.7
38.2 37.5 36.7 36.1 35.4
42.1 41.3 40.6 39.8 39.1
45.9 45.1 44.3 43.6 42.9
7 8 9 10 12
3.34 3.20 3.07 2.94 2.68
6.65 6.40 6.16 5.91 5.45
9.98 9.64 9.31 8.98 8.36
13.4 12.9 12.6 12.2 11.5
16.8 16.4 15.9 15.4 14.6
20.3 19.8 19.3 18.8 17.9
23.8 23.3 22.8 22.2 21.3
27.4 26.9 26.3 25.7 24.8
31.1 30.4 29.9 29.3 28.3
34.8 34.1 33.5 32.9 31.8
38.5 37.8 37.1 36.6 35.4
42.2 41.5 40.8 40.2 39.0
14 16 18 20 24
2.45 2.24 2.06 1.90 1.63
5.03 4.65 4.31 4.01 3.51
7.79 10.7 7.28 10.1 6.81 9.55 6.40 9.03 5.69 8.13
13.9 13.2 12.5 11.9 10.8
17.1 16.3 15.5 14.9 13.6
20.4 19.6 18.8 18.0 16.6
23.8 22.9 22.0 21.2 19.7
27.3 26.3 25.4 24.5 22.9
30.8 29.8 28.8 27.9 26.2
34.3 33.2 32.2 31.3 29.5
37.9 36.8 35.8 34.8 32.9
28 32 36
1.43 1.27 1.14
3.11 2.79 2.53
5.11 4.62 4.22
12.5 11.5 10.7
15.4 14.3 13.3
18.3 17.1 16.0
21.4 20.0 18.9
24.6 23.2 21.8
27.8 26.3 24.9
31.1 29.5 28.0
2 3 4 5 6
3.86 3.79 3.70 3.59 3.47
7.67 7.51 7.32 7.12 6.92
11.5 11.2 11.0 10.7 10.4
15.3 15.0 14.7 14.4 14.1
19.1 18.8 18.4 18.1 17.7
23.0 22.6 22.2 21.9 21.5
26.9 26.4 26.0 25.6 25.3
30.8 30.4 29.9 29.5 29.1
35.2 34.3 33.8 33.3 32.9
39.1 38.1 37.7 37.3 36.8
43.0 42.1 41.6 41.1 40.7
47.0 46.0 45.5 45.0 44.6
7 8 9 10 12
3.34 3.20 3.07 2.94 2.68
6.70 6.49 6.28 6.08 5.69
10.2 9.92 9.66 9.42 8.95
13.8 13.5 13.2 12.9 12.4
17.4 17.1 16.8 16.5 15.9
21.1 20.8 20.5 20.2 19.5
24.9 24.5 24.2 23.9 23.2
28.7 28.3 28.0 27.6 26.9
32.6 32.1 31.8 31.4 30.7
36.4 36.0 35.6 35.2 34.5
40.2 39.8 39.5 39.0 38.3
44.1 43.7 43.3 42.9 42.1
14 16 18 20 24
2.45 2.24 2.06 1.90 1.63
5.33 4.99 4.69 4.42 3.95
8.51 8.10 7.72 7.36 6.74
11.9 11.5 11.0 10.6 9.83
15.4 14.9 14.4 13.9 13.1
19.0 18.5 17.9 17.4 16.5
22.6 22.1 21.5 21.0 20.0
26.3 25.7 25.1 24.6 23.6
30.1 29.4 28.8 28.2 27.1
33.8 33.1 32.5 31.9 30.7
37.6 36.9 36.2 35.6 34.4
41.4 40.7 40.0 39.3 38.1
28 32 36
1.43 1.27 1.14
3.57 3.25 2.98
6.21 5.74 5.33
9.16 12.4 8.56 11.6 8.02 11.0
15.7 14.9 14.1
19.0 18.2 17.3
22.5 21.6 20.7
26.1 25.1 24.1
29.7 28.6 27.6
33.3 32.2 31.2
36.9 35.9 34.8
7.36 6.71 6.15
9.83 9.02 8.31
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 82
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-25. Coefficients C for Eccentrically Loaded Bolt Groups Angle = 0°° C req =
Pu φ rn
or φR n = C × φ rn
ex= e
where
s, in.
3
6
s
Pu
s
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
4
4
4
12
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
2.82 2.50 2.23 2.01 1.81
5.98 5.31 4.74 4.27 3.86
9.46 8.43 7.58 6.86 6.24
13.3 12.0 10.8 9.82 8.96
17.3 15.7 14.3 13.1 12.0
21.3 19.7 18.2 16.7 15.4
25.5 23.8 22.2 20.5 19.0
29.6 28.0 26.3 24.5 22.9
33.7 32.2 30.4 28.6 26.9
37.7 36.3 34.6 32.8 31.0
41.8 40.4 38.8 37.0 35.2
45.8 44.6 43.0 41.3 39.4
7 8 9 10 12
1.64 1.49 1.36 1.25 1.07
3.52 3.22 2.96 2.73 2.37
5.70 5.24 4.83 4.47 3.89
8.22 11.1 7.57 10.2 7.01 9.48 6.51 8.83 5.68 7.74
14.2 13.2 12.3 11.4 10.1
17.6 16.4 15.3 14.3 12.6
21.3 19.9 18.6 17.5 15.5
25.2 23.6 22.1 20.8 18.5
29.2 27.5 25.9 24.4 21.8
33.3 31.5 29.8 28.2 25.3
37.5 35.6 33.8 32.1 29.0
14 16 18 20 24
0.94 0.83 0.75 0.68 0.58
2.08 1.86 1.67 1.52 1.29
3.42 3.05 2.75 2.50 2.12
5.02 4.49 4.06 3.70 3.14
6.86 6.15 5.56 5.07 4.30
8.95 11.3 8.04 10.2 7.29 9.22 6.65 8.43 5.66 7.18
13.8 12.5 11.4 10.4 8.88
16.6 15.0 13.7 12.6 10.8
19.6 17.8 16.3 14.9 12.8
22.8 20.7 19.0 17.5 15.0
26.2 23.9 21.9 20.2 17.4
28 32 36
0.50 0.44 0.40
1.12 0.98 0.88
1.84 1.62 1.45
2.72 2.40 2.15
3.73 3.30 2.95
4.92 4.34 3.89
13.1 11.6 10.4
15.2 13.5 12.1
2 3 4 5 6
2.82 2.50 2.23 2.01 1.81
6.54 5.90 5.33 4.84 4.42
10.6 9.81 9.01 8.27 7.60
7 8 9 10 12
1.64 1.49 1.36 1.25 1.07
4.05 3.73 3.45 3.20 2.80
7.02 10.6 6.51 9.94 6.06 9.30 5.66 8.72 4.98 7.73
14 16 18 20 24
0.94 0.83 0.75 0.68 0.58
2.47 2.21 2.00 1.82 1.55
4.43 3.98 3.60 3.29 2.79
6.92 6.25 5.68 5.21 4.45
28 32 36
0.50 0.44 0.40
1.34 1.18 1.06
2.42 2.14 1.92
3.87 3.43 3.07
14.8 14.0 13.1 12.2 11.4
6.24 5.51 4.94
7.73 6.84 6.13
9.37 11.2 8.29 9.90 7.43 8.88
18.9 18.1 17.3 16.4 15.5
22.9 22.3 21.5 20.6 19.7
26.9 26.4 25.7 24.8 24.0
30.9 30.4 29.8 29.0 28.2
34.9 34.5 33.9 33.2 32.4
38.9 38.5 37.9 37.3 36.6
42.8 42.5 42.0 41.4 40.7
46.8 46.5 46.0 45.5 44.8
14.6 13.7 13.0 12.2 10.9
18.8 17.8 16.9 16.1 14.5
23.0 22.0 21.1 20.2 18.4
27.3 26.3 25.3 24.4 22.5
31.5 30.6 29.6 28.6 26.7
35.7 34.8 33.9 32.9 30.9
39.9 39.1 38.2 37.2 35.2
44.1 43.3 42.4 41.5 39.5
9.81 8.90 8.13 7.47 6.40
13.2 12.0 11.0 10.1 8.72
16.8 15.4 14.2 13.1 11.3
20.7 19.1 17.7 16.4 14.3
24.8 23.0 21.4 20.0 17.5
29.0 27.1 25.3 23.7 20.9
33.2 31.3 29.4 27.7 24.5
37.5 35.5 33.6 31.7 28.3
5.59 4.95 4.44
7.64 6.79 6.10
9.96 12.6 8.87 11.2 7.98 10.1
15.5 13.8 12.5
18.6 16.7 15.1
21.9 19.7 17.9
25.5 23.0 20.9
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 83
Table 8-25 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 15°° C req =
Pu
φ rn
or φ R n = C × φrn
ex Pu
where
s, in.
3
6
s
15° e
s
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
4
4
4
12
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
2.91 2.57 2.30 2.06 1.86
6.06 5.40 4.84 4.37 3.96
9.56 8.57 7.72 6.99 6.37
13.3 12.0 10.9 9.93 9.09
17.2 15.8 14.4 13.2 12.1
21.3 19.7 18.2 16.7 15.5
25.3 23.7 22.1 20.5 19.0
29.4 27.8 26.1 24.4 22.8
33.5 31.9 30.2 28.5 26.7
37.5 36.1 34.3 32.6 30.8
41.6 40.2 38.5 36.7 34.9
45.6 44.3 42.6 40.9 39.0
7 8 9 10 12
1.69 1.53 1.40 1.29 1.11
3.61 3.31 3.04 2.81 2.44
5.83 5.36 4.95 4.59 4.00
8.36 11.2 7.72 10.4 7.15 9.64 6.65 9.00 5.82 7.90
14.3 13.3 12.4 11.6 10.2
17.7 16.5 15.4 14.5 12.8
21.3 19.9 18.7 17.6 15.6
25.1 23.6 22.2 20.9 18.7
29.0 27.4 25.8 24.4 21.9
33.1 31.3 29.7 28.1 25.3
37.2 35.3 33.6 31.9 28.9
14 16 18 20 24
0.97 0.86 0.78 0.71 0.60
2.15 1.92 1.73 1.57 1.33
3.52 3.15 2.84 2.59 2.19
5.15 4.61 4.17 3.80 3.23
7.02 6.30 5.71 5.21 4.43
9.12 11.5 8.21 10.3 7.45 9.41 6.81 8.61 5.80 7.36
14.0 12.7 11.6 10.6 9.07
16.8 15.2 13.9 12.8 11.0
19.8 18.0 16.5 15.2 13.0
22.9 20.9 19.2 17.7 15.3
26.3 24.0 22.1 20.4 17.6
28 32 36
0.52 0.46 0.41
1.15 1.02 0.91
1.90 1.68 1.50
2.80 2.48 2.22
3.85 3.40 3.04
5.05 4.46 4.00
13.4 11.9 10.7
15.5 13.8 12.4
2 3 4 5 6
2.91 2.57 2.30 2.06 1.86
6.57 5.93 5.37 4.89 4.48
10.6 9.81 9.04 8.33 7.70
7 8 9 10 12
1.69 1.53 1.40 1.29 1.11
4.12 3.80 3.52 3.27 2.86
7.13 10.6 6.62 9.95 6.17 9.32 5.77 8.76 5.09 7.80
14 16 18 20 24
0.97 0.86 0.78 0.71 0.60
2.54 2.27 2.06 1.88 1.59
4.53 4.08 3.70 3.38 2.88
7.00 6.34 5.78 5.30 4.54
9.92 9.02 8.26 7.60 6.54
28 32 36
0.52 0.46 0.41
1.38 1.22 1.09
2.50 2.21 1.98
3.96 3.51 3.15
5.72 5.08 4.56
14.7 13.9 13.0 12.2 11.4
6.41 5.67 5.08
7.91 7.01 6.29
9.59 11.4 8.50 10.1 7.63 9.09
18.8 18.0 17.2 16.3 15.4
22.8 22.1 21.3 20.5 19.5
26.8 26.2 25.5 24.6 23.7
30.8 30.3 29.6 28.8 27.9
34.8 34.3 33.6 32.9 32.1
38.8 38.3 37.7 37.0 36.2
42.7 42.3 41.7 41.1 40.3
46.7 46.3 45.8 45.1 44.4
14.5 13.7 12.9 12.2 11.0
18.6 17.7 16.8 16.0 14.5
22.8 21.8 20.9 20.0 18.3
27.0 26.0 25.1 24.1 22.3
31.2 30.2 29.3 28.3 26.4
35.4 34.4 33.5 32.5 30.6
39.5 38.6 37.7 36.8 34.8
43.7 42.8 41.9 41.0 39.0
13.2 12.0 11.1 10.2 8.84
16.8 15.4 14.2 13.2 11.5
20.6 19.0 17.7 16.4 14.4
24.6 22.9 21.3 19.9 17.5
28.7 26.9 25.2 23.6 20.9
32.8 30.9 29.1 27.5 24.5
37.1 35.1 33.2 31.4 28.2
7.77 10.1 12.7 6.92 9.03 11.4 6.23 8.15 10.3
15.6 14.0 12.7
18.7 16.8 15.3
22.0 19.9 18.1
25.4 23.1 21.1
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 84
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-25 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 30°° C req =
Pu
φrn
or φR n = C × φ rn
ex Pu
where
s, in.
3
6
s
30°
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
s
e
4
4
4
12
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
3.14 2.79 2.50 2.25 2.04
6.41 5.75 5.19 4.71 4.29
9.91 8.95 8.16 7.45 6.83
13.6 12.4 11.4 10.5 9.65
17.5 16.1 14.9 13.7 12.7
21.4 20.0 18.5 17.2 16.0
25.4 23.9 22.4 20.9 19.6
29.4 27.9 26.3 24.7 23.3
33.4 31.9 30.3 28.6 27.1
37.4 35.9 34.3 32.6 31.0
41.4 40.0 38.4 36.7 35.0
45.4 44.0 42.4 40.7 39.0
7 8 9 10 12
1.85 1.69 1.55 1.43 1.23
3.93 3.61 3.33 3.08 2.68
6.28 5.80 5.38 5.00 4.37
8.92 11.8 8.27 11.0 7.70 10.3 7.19 9.64 6.32 8.52
15.0 14.0 13.1 12.3 11.0
18.3 17.2 16.2 15.3 13.6
21.9 20.6 19.4 18.4 16.5
25.6 24.2 22.9 21.7 19.6
29.4 27.9 26.5 25.2 22.8
33.3 31.7 30.2 28.8 26.2
37.3 35.6 34.0 32.5 29.8
14 16 18 20 24
1.08 0.96 0.87 0.79 0.67
2.36 2.11 1.91 1.74 1.48
3.88 3.47 3.14 2.86 2.43
5.62 5.05 4.57 4.18 3.56
7.61 6.86 6.24 5.71 4.88
9.83 12.3 8.89 11.1 8.10 10.2 7.43 9.35 6.36 8.03
14.9 13.6 12.4 11.5 9.87
17.8 16.2 14.9 13.8 11.9
20.8 19.0 17.5 16.2 14.1
24.0 22.0 20.3 18.9 16.4
27.3 25.2 23.3 21.6 18.9
28 32 36
0.58 0.51 0.46
1.28 1.13 1.01
2.11 1.87 1.67
3.10 2.74 2.45
4.25 3.76 3.37
5.55 4.92 4.41
14.5 12.9 11.7
16.7 14.9 13.5
2 3 4 5 6
3.14 2.79 2.50 2.25 2.04
6.75 6.12 5.58 5.13 4.73
10.7 9.94 9.23 8.58 8.00
7 8 9 10 12
1.85 1.69 1.55 1.43 1.23
4.38 4.06 3.78 3.53 3.10
7.47 10.9 6.98 10.3 6.55 9.72 6.15 9.18 5.47 8.25
14 16 18 20 24
1.08 0.96 0.87 0.79 0.67
2.76 2.48 2.25 2.06 1.76
4.90 4.43 4.04 3.70 3.17
7.46 10.4 6.79 9.55 6.22 8.79 5.72 8.14 4.93 7.06
28 32 36
0.58 0.51 0.46
1.53 1.35 1.21
2.76 2.45 2.19
4.32 3.84 3.46
14.7 13.9 13.1 12.4 11.6
7.02 6.23 5.60
8.65 10.4 12.4 7.69 9.29 11.0 6.91 8.36 9.95
18.7 18.0 17.2 16.3 15.5
22.7 22.0 21.2 20.4 19.5
26.7 26.1 25.3 24.5 23.6
30.7 30.1 29.4 28.6 27.7
34.7 34.1 33.4 32.7 31.8
38.6 38.1 37.5 36.7 35.9
42.6 42.1 41.5 40.8 40.0
46.6 46.1 45.5 44.8 44.1
14.7 14.0 13.3 12.6 11.4
18.7 17.9 17.1 16.3 14.9
22.7 21.9 21.0 20.2 18.6
26.8 25.9 25.1 24.2 22.5
31.0 30.1 29.2 28.3 26.5
35.1 34.2 33.3 32.4 30.6
39.2 38.3 37.4 36.5 34.7
43.3 42.4 41.5 40.6 38.8
13.7 12.6 11.7 10.9 9.48
17.2 16.0 14.9 13.9 12.2
21.0 19.6 18.3 17.1 15.2
24.9 23.3 21.9 20.6 18.3
28.8 27.2 25.7 24.2 21.7
32.9 31.2 29.5 28.0 25.3
37.0 35.2 33.5 31.9 28.9
8.38 10.8 13.5 7.50 9.73 12.2 6.77 8.82 11.1
16.5 14.9 13.6
19.6 17.8 16.3
22.9 20.9 19.1
26.3 24.1 22.2
6.22 5.54 5.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 85
Table 8-25 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 45°° C req =
Pu
φ rn
or φ R n = C × φrn
ex Pu
s
where
3
6
s
e
s, in.
45°
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
4
4
4
12
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
3.46 3.15 2.87 2.61 2.39
6.96 6.38 5.84 5.36 4.93
10.5 9.73 8.97 8.30 7.69
14.2 13.2 12.3 11.4 10.7
18.0 16.8 15.7 14.7 13.9
21.8 20.6 19.3 18.2 17.2
25.7 24.4 23.1 21.8 20.7
29.6 28.2 26.9 25.5 24.3
33.5 32.1 30.7 29.3 28.0
37.4 36.1 34.6 33.2 31.8
41.4 40.0 38.6 37.1 35.6
45.3 44.0 42.5 41.0 39.5
7 8 9 10 12
2.19 2.01 1.86 1.72 1.49
4.55 4.21 3.90 3.63 3.18
7.15 6.66 6.21 5.82 5.14
9.98 9.34 8.76 8.24 7.33
13.0 12.2 11.5 10.9 9.76
16.2 15.3 14.5 13.8 12.4
19.6 18.6 17.7 16.8 15.2
23.1 22.0 21.0 20.0 18.3
26.7 25.5 24.4 23.3 21.4
30.4 29.2 27.9 26.8 24.7
34.2 32.9 31.6 30.4 28.1
38.1 36.7 35.3 34.0 31.6
14 16 18 20 24
1.32 1.17 1.06 0.96 0.82
2.82 2.53 2.29 2.10 1.79
4.59 4.14 3.76 3.44 2.94
6.58 5.95 5.43 4.98 4.26
8.81 11.3 8.00 10.3 7.32 9.44 6.74 8.71 5.81 7.53
13.9 12.7 11.7 10.9 9.43
16.7 15.4 14.2 13.2 11.5
19.7 18.2 16.9 15.7 13.8
22.8 21.2 19.7 18.4 16.2
26.1 24.3 22.7 21.2 18.7
29.5 27.5 25.7 24.2 21.4
28 32 36
0.71 0.63 0.56
1.56 1.38 1.23
2.56 2.26 2.03
3.73 3.31 2.97
5.09 4.52 4.06
14.4 12.9 11.7
16.7 15.1 13.7
19.2 17.3 15.8
2 3 4 5 6
3.46 3.15 2.87 2.61 2.39
7.09 6.58 6.09 5.66 5.26
10.9 10.3 9.65 9.07 8.54
14.8 14.1 13.4 12.8 12.1
18.7 18.1 17.3 16.6 15.9
22.7 22.0 21.3 20.6 19.8
26.7 26.0 25.3 24.5 23.8
30.6 30.0 29.3 28.5 27.8
34.6 33.9 33.3 32.5 31.8
38.5 37.9 37.3 36.5 35.8
42.5 41.9 41.2 40.5 39.8
46.5 45.9 45.2 44.5 43.8
7 8 9 10 12
2.19 2.01 1.86 1.72 1.49
4.91 4.59 4.30 4.04 3.59
8.07 7.63 7.23 6.85 6.19
11.6 11.0 10.5 10.0 9.14
15.3 14.6 14.0 13.4 12.4
19.1 18.4 17.7 17.1 15.9
23.0 22.3 21.5 20.8 19.5
27.0 26.2 25.5 24.7 23.3
31.0 30.2 29.4 28.6 27.2
35.0 34.2 33.4 32.6 31.1
39.0 38.2 37.4 36.6 35.1
43.0 42.2 41.4 40.6 39.1
14 16 18 20 24
1.32 1.17 1.06 0.96 0.82
3.22 2.91 2.66 2.44 2.10
5.62 5.13 4.71 4.35 3.76
8.38 11.4 7.71 10.6 7.12 9.87 6.61 9.22 5.76 8.11
14.8 13.8 12.9 12.1 10.8
18.3 17.2 16.2 15.3 13.7
22.0 20.8 19.6 18.6 16.7
25.8 24.4 23.2 22.1 20.0
29.6 28.2 26.9 25.7 23.4
33.5 32.1 30.7 29.4 27.0
37.5 36.0 34.6 33.2 30.6
28 32 36
0.71 0.63 0.56
1.83 1.63 1.46
3.30 2.94 2.64
5.08 4.54 4.11
9.64 12.3 8.71 11.2 7.93 10.2
15.2 13.9 12.7
18.3 16.7 15.4
21.5 19.8 18.3
24.9 23.0 21.3
28.4 26.3 24.5
7.22 6.50 5.90
6.61 5.89 5.30
8.31 10.2 12.2 7.42 9.11 11.0 6.69 8.23 9.91
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 86
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-25 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 60°° C req =
Pu
φrn
or φR n = C × φ rn
ex
where s
Pu
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
3
6
s s
e
s, in.
60°
4
4
4
12
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
3.74 3.57 3.38 3.17 2.97
7.46 7.12 6.75 6.36 5.99
11.2 10.7 10.2 9.61 9.09
14.9 14.3 13.6 12.9 12.3
18.6 17.9 17.1 16.4 15.6
22.4 21.6 20.7 19.8 19.0
26.2 25.3 24.3 23.4 22.5
30.0 29.0 28.0 27.0 26.1
33.9 32.8 31.8 30.7 29.7
37.7 36.7 35.6 34.5 33.4
41.6 40.5 39.4 38.2 37.1
45.5 44.4 43.2 42.0 40.9
7 8 9 10 12
2.78 2.60 2.44 2.28 2.02
5.63 5.29 4.98 4.69 4.18
8.59 8.13 7.69 7.28 6.56
11.7 11.1 10.6 10.1 9.16
14.9 14.2 13.6 13.0 11.9
18.2 17.5 16.8 16.1 14.9
21.6 20.8 20.1 19.3 18.0
25.1 24.3 23.4 22.7 21.2
28.7 27.8 26.9 26.1 24.5
32.3 31.4 30.4 29.5 27.8
36.0 35.0 34.0 33.1 31.3
39.8 38.7 37.7 36.7 34.8
14 16 18 20 24
1.80 1.62 1.47 1.34 1.15
3.76 3.40 3.10 2.85 2.45
5.95 5.43 4.99 4.61 3.99
8.38 11.0 7.70 10.2 7.11 9.42 6.59 8.76 5.73 7.67
13.8 12.8 11.9 11.1 9.82
16.7 15.6 14.6 13.7 12.2
19.8 18.6 17.4 16.4 14.6
23.0 21.6 20.4 19.3 17.3
26.3 24.8 23.5 22.2 20.1
29.6 28.1 26.7 25.3 23.0
33.1 31.4 29.9 28.5 26.0
28 32 36
1.00 0.88 0.79
2.15 1.91 1.72
3.51 3.13 2.81
5.06 4.52 4.08
13.2 11.9 10.9
15.6 14.2 13.0
18.2 16.6 15.3
20.9 19.2 17.7
23.8 21.8 20.2
2 3 4 5 6
3.74 3.57 3.38 3.17 2.97
7.47 7.16 6.82 6.47 6.14
11.2 10.8 10.4 9.94 9.52
15.0 14.6 14.1 13.6 13.1
18.9 18.4 17.8 17.3 16.7
22.8 22.2 21.7 21.1 20.5
26.7 26.1 25.5 24.9 24.3
30.6 30.0 29.4 28.8 28.2
34.5 33.9 33.3 32.7 32.1
38.5 37.9 37.3 36.6 36.0
42.4 41.8 41.2 40.5 39.9
46.4 45.8 45.1 44.5 43.8
7 8 9 10 12
2.78 2.60 2.44 2.28 2.02
5.82 5.52 5.24 4.98 4.51
9.11 8.73 8.37 8.03 7.41
12.6 12.1 11.7 11.3 10.6
16.2 15.7 15.2 14.8 14.0
19.9 19.4 18.9 18.4 17.5
23.7 23.2 22.6 22.1 21.1
27.6 27.0 26.4 25.8 24.8
31.5 30.8 30.2 29.7 28.5
35.3 34.7 34.1 33.5 32.3
39.3 38.6 38.0 37.4 36.2
43.2 42.5 41.9 41.3 40.1
14 16 18 20 24
1.80 1.62 1.47 1.34 1.15
4.10 3.76 3.46 3.21 2.79
6.86 6.37 5.94 5.56 4.91
9.91 9.29 8.74 8.23 7.34
13.2 12.4 11.8 11.2 10.1
16.6 15.8 15.0 14.3 13.0
20.1 19.2 18.4 17.6 16.2
23.8 22.8 21.9 21.0 19.5
27.5 26.5 25.5 24.6 22.9
31.2 30.2 29.2 28.2 26.4
35.0 33.9 32.9 31.9 30.0
38.9 37.7 36.6 35.6 33.6
28 32 36
1.00 0.88 0.79
2.47 2.21 2.00
4.38 3.95 3.58
6.61 5.99 5.46
9.13 11.9 8.33 11.0 7.65 10.1
14.9 13.8 12.8
18.1 16.8 15.7
21.4 20.0 18.7
24.7 23.2 21.9
28.2 26.6 25.1
31.8 30.1 28.5
6.80 6.11 5.53
8.76 10.9 7.89 9.83 7.16 8.95
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED BOLT GROUPS
8 - 87
Table 8-25 (cont.). Coefficients C for Eccentrically Loaded Bolt Groups Angle = 75°° C req =
Pu φ rn
or φ R n = C × φrn
ex
where
3
6
s s
e
s, in.
75° P u
s
Pu = factored force, kips φ rn = design strength per bolt, kips φ R n = design strength of bolt group, kips e = eccentricity of Pu with respect to centroid of bolt group, in. (not tabulated, may be determined by geometry.) e x = horizontal component of e, in. s = bolt spacing, in. C = coefficient tabulated below.
4
4
4
12
Number of bolts in one vertical row, n
ex, in.
1
2
3
4
5
6
7
8
9
10
11
12
2 3 4 5 6
3.89 3.84 3.79 3.72 3.65
7.75 7.66 7.54 7.40 7.25
11.6 11.5 11.3 11.1 10.8
15.5 15.2 15.0 14.7 14.4
19.3 19.0 18.7 18.3 17.9
23.1 22.7 22.4 21.9 21.5
26.9 26.5 26.1 25.6 25.1
30.8 30.3 29.8 29.3 28.7
34.6 34.1 33.5 32.9 32.4
38.5 37.9 37.3 36.7 36.1
42.3 41.7 41.0 40.4 39.8
46.2 45.5 44.8 44.1 43.5
7 8 9 10 12
3.56 3.47 3.37 3.27 3.07
7.08 6.90 6.71 6.52 6.14
10.6 10.3 10.0 9.77 9.23
14.1 13.7 13.4 13.1 12.4
17.6 17.2 16.8 16.4 15.6
21.1 20.6 20.2 19.8 18.9
24.6 24.1 23.7 23.2 22.3
28.2 27.7 27.2 26.7 25.7
31.8 31.3 30.7 30.2 29.1
35.5 34.9 34.3 33.7 32.6
39.1 38.5 37.9 37.3 36.2
42.8 42.2 41.6 41.0 39.8
14 16 18 20 24
2.87 2.68 2.50 2.34 2.06
5.76 5.40 5.07 4.76 4.23
8.71 8.22 7.76 7.33 6.57
11.8 11.1 10.6 10.0 9.10
14.9 14.2 13.5 12.9 11.8
18.1 17.3 16.6 15.9 14.7
21.4 20.5 19.7 19.0 17.6
24.7 23.8 23.0 22.2 20.7
28.1 27.2 26.3 25.5 23.9
31.6 30.6 29.7 28.8 27.1
35.1 34.1 33.1 32.2 30.4
38.7 37.6 36.6 35.6 33.8
28 32 36
1.82 1.63 1.48
3.78 3.41 3.11
5.94 5.41 4.95
13.5 12.6 11.7
16.4 15.3 14.3
19.3 18.1 17.0
22.4 21.0 19.8
25.5 24.1 22.8
28.7 27.2 25.8
32.0 30.4 28.9
2 3 4 5 6
3.89 3.84 3.79 3.72 3.65
7.74 7.64 7.52 7.38 7.23
11.6 11.4 11.2 11.0 10.8
15.4 15.2 14.9 14.7 14.4
19.3 19.0 18.7 18.4 18.1
23.1 22.8 22.5 22.1 21.8
27.0 26.6 26.3 25.9 25.6
30.9 30.5 30.1 29.7 29.3
35.2 34.4 34.0 33.6 33.2
39.1 38.3 37.8 37.4 37.0
43.0 42.2 41.7 41.3 40.8
47.0 46.1 45.6 45.2 44.7
7 8 9 10 12
3.56 3.47 3.37 3.27 3.07
7.07 6.90 6.73 6.56 6.21
10.6 10.4 10.1 9.92 9.48
14.2 13.9 13.6 13.4 12.9
17.8 17.5 17.2 16.9 16.4
21.5 21.2 20.8 20.5 19.9
25.2 24.9 24.5 24.2 23.6
29.0 28.6 28.3 27.9 27.3
32.8 32.4 32.0 31.7 31.0
36.6 36.2 35.8 35.5 34.7
40.4 40.0 39.6 39.3 38.5
44.3 43.9 43.5 43.1 42.3
14 16 18 20 24
2.87 2.68 2.50 2.34 2.06
5.88 5.57 5.27 4.99 4.50
9.07 8.67 8.29 7.94 7.29
12.4 11.9 11.5 11.1 10.3
15.9 15.4 14.9 14.4 13.6
19.4 18.8 18.3 17.8 16.9
23.0 22.4 21.9 21.3 20.4
26.6 26.0 25.5 24.9 23.9
30.3 29.7 29.1 28.5 27.4
34.1 33.4 32.8 32.2 31.0
37.8 37.1 36.5 35.8 34.7
41.6 40.9 40.2 39.6 38.3
28 32 36
1.82 1.63 1.48
4.08 3.73 3.43
6.73 6.25 5.82
9.67 12.8 9.06 12.1 8.51 11.4
16.1 15.3 14.5
19.4 18.6 17.8
22.9 22.0 21.1
26.4 25.4 24.5
30.0 29.0 28.0
33.6 32.5 31.5
37.2 36.1 35.1
8.30 10.9 7.61 10.0 7.01 9.26
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 88
BOLTS, WELDS, AND CONNECTED ELEMENTS
ANCHOR RODS OR THREADED RODS
Cast-in-place anchor rods, illustrated in Figure 8-14, are generally made from unheaded rod material or headed bolt material. Drilled-in anchor rods, illustrated in Figure 8-15, are not normally used; their design is governed by manufacturer’s specifications. Refer also to Cannon, Godfrey, and Moreadith (1981). LRFD Specification Section A3.4 permits the use of unheaded rod material from the following ASTM specifications as anchor rods or threaded rods: A36, A193, A354, A449, A572, A588, and A687. Additionally, LRFD Specification Section A3.4 permits the use of headed bolts conforming to the provisions of LRFD Specification Section A3.3 for use as anchor rods. Headed bolts, however, are generally available only in lengths up to about eight inches. Furthermore, designations such as ASTM A325, A490, and A307 apply only to bolts manufactured with a head and it is, therefore, improper to specify unheaded anchor rods or other similar threaded devices as ASTM A325, A490, or A307. The availability and strength of the aforementioned ASTM specifications for unheaded rod material and headed bolt material are summarized in Table 8-26. Suitable nuts may be selected from ASTM A563 or ASTM A194 grade 7. Because base plates typically have holes larger than oversized holes to allow for tolerances on the location of the anchor rod, washers are usually furnished from ASTM A36 steel plate; they may be round, square, or rectangular, are generally about 1⁄2-in. thick, and generally have holes which are 1⁄16-in. larger than the anchor rod diameter. Minimum Edge Distance and Embedment Length
The recommendations of Shipp and Haninger (1983) for minimum anchor-rod (concrete) edge distance and embedment length for tensile forces, adopted from ACI 349, are summarized in Table 8-26. The edge distance requirement is intended to prevent blow-out of the side of the concrete foundation and is based on concrete with fc′ = 3,000 psi. For edge distance requirements for shear, refer to Shipp and Haninger (1983). In addition to providing the recommended minimum embedment length, anchor rods must extend a distance above the foundation that is sufficient to permit full thread engagement of the nut; from RCSC Specification Section 2(b), “…the end of the [anchor rod] will be flush with or outside the face of the nut when properly installed.”
Lh
(a) Hooked
(b) Headed
(c) Threaded with Nut
Fig. 8-14. Typical cast-in-place anchor rods. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ANCHOR RODS OR THREADED RODS
8 - 89
Note that it is seldom possible to fully tension anchor rods since the concrete usually cannot provide the necessary anchorage. Welding to Anchor Rods
Though not typical, welds must sometimes be used in lieu of nuts to attach anchor rods to base plates. The use of weldable steels such as ASTM A36 or A572 is recommended for this purpose; anchor-rod material which is quenched and tempered should not be welded. Hooked Anchor Rods
Hooked anchor rods should be used only for axially loaded columns to locate and prevent the displacement or overturning of columns due to erection loads or accidental collisions during erection. Additionally, high-strength steels are not recommended for use in hooked rods since bending with heat may materially affect their strength. For the hooked rod of Figure 8-14a, the tensile force is resisted through bond development along the length and the mechanical anchorage of the hook. However, because smooth rods do not always form a reliable bond (due to oil used in threading among other things), the design of such anchor rods should be based upon the anchorage provided by the hook only. To prevent the anchor rod from pulling out and straightening, the hook should be designed to resist one-half the design tensile strength of the anchor rod φRn, where φ = 0.75 Rn = φtFu Ag In the above equation, φt = 0.75. From Fisher (1981), the bearing strength of the concrete is: 0.7fc′dLh
Grout
Fig. 8-15. Drilled-in anchor rods. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 90
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-26. Anchor Rod Material Availability and Strength Availability
Headed Bolt Mat. (Only)
Headed Bolt or Unheaded Rod Material
Unheaded Rod Material (Only)
Type
ASTM Design.
Material Typeb
Strength
Grade
Diameter, d, in.
Proof Load
Min. Yield, ksi
Minimum Min. Embdmt. Minimum Tensile, Length, Edge Dist., in.e ksi in.
A36
C
—
to 8
—
36
58
12d
5d
A572
HSLA
42
to 2
—
42
60
12d
5d
50
to 6
—
50
65
17d
7d
—
to 4
—
50
70
17d
7d
over 4 to 5
—
46
67
17d
7d
over 5 to 8
—
42
63
17d
7d
to 3
—
105
150c
19d
7d
to 21 ⁄2
120
130
150
19d
7d
105
115
140
19d
7d
105
109
125
17d
7d
95
99
115
17d
7d
85
92
120
17d
7d
11 ⁄8 to 11 ⁄2
74
81
105
17d
7d
13 ⁄4 to 3
55
58
90
17d
7d
to 4
—
—
60
12d
5d
85
92
120
17d
7d
74
81
105
17d
7d
120
—
150
19d
7d
A588
HSLA, ACR
A687
A, QT, NT
—
A354
A, QT
BD
5⁄ 1⁄
4
8
over 21 ⁄2 to 4 BC
1⁄
4
to 21 ⁄2
over 21 ⁄2 to 4 A449d
C, QT
—
A307
C
—
A325a,d
C, QT
—
1⁄
1⁄
4
2
to 1
to 1
11 ⁄8 to 11 ⁄2 A490a,d
A, QT
—
1⁄
2
to 11 ⁄2
aAvailable with weathering (atmospheric corrosion resistance) characteristics comparable to ASTM A242 and
A588 steels. bA = Alloy Steel bACR = Atmospheric-Corrosion-Resistant Steel bC = Carbon Steel bHSLA = High-Strength Low-Alloy Steel bNT = Notch-Tough Steel (CVN 15 @ −20°°F) bQT = Quenched and Tempered Steel cMaximum (ultimate tensile strength) dThreaded rod material with properties meeting ASTM A325, A490, and A449 specifications may be obtained
with the use of an appropriate steel (such as ASTM A193, grade B7), quenched and tempered after fabrication. eNot less than 4 in.
Thus, the minimum hook length Lh min is: φRn 2 Lh min = 0.7fc′d where fc′ is the specified strength of the concrete, ksi. The total embedded anchor rod length is then the hook length Lh plus the minimum embedment length from Table 8-26. Headed Anchor Rods
When anchor rods are required for a calculated tensile force Tu, a more positive anchorage is formed when headed anchor rods, illustrated in Figure 8-14b, are used. With adequate embedment and edge distance, the limit state is either a tensile failure of the anchor rod or the pull-out of a cone of concrete radiating outward from the head (Marsh and Burdette, 1985a) as illustrated in Figure 8-16. The design tensile strength of the anchor rod is φRn, AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ANCHOR RODS OR THREADED RODS
8 - 91
where φ = 0.75 Rn = φtFu Ag In the above equation, φt = 0.75. Using the projected surface area of the concrete cone and a limiting average stress on this area of 4√ fc′ , the minimum anchor rod length Lmin is Lmin =
√
Acp 3.14
where Acp =
Tu φt√ fc′
fc′ = specified strength of the concrete, psi
Tu
45° L
Failure Plane
Projected Surface
Fig. 8-16. Concrete cone subject to pull-out. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 92
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-27. Dimensions and Weights of Clevises
D
p
w
b
a
n
t Grip Grip = plate thickness + ¼ in.
t
Thread: UNC Class 2B
Dimensions, in. Clevis Number
Max. D
2
5⁄
2 1 ⁄2
3
3 1 ⁄2
4 5 6 7 8
7⁄
8
8 13 ⁄8 11 ⁄2 13 ⁄4
2 21 ⁄2 3 4
Max. p 3⁄
4
11 ⁄2 13 ⁄4 2 21 ⁄4 21 ⁄2 3 33 ⁄4 4
b
n
17 ⁄16 5⁄8 21 ⁄2 11⁄8 3 15 ⁄16 31 ⁄2 15⁄8 4 13⁄4 21⁄4 5 6 23⁄4 3 7 4 8
a
w
37 ⁄8 4 5 6 6 7 8 9 10
11 ⁄16 11 ⁄4 11 ⁄2 13 ⁄4 2 21 ⁄2 3 31 ⁄2 4
t
Weight, pounds
Design Strength φR n*, kips
(+ 1 ⁄32, −0) 1 16 (+ ⁄32, −0) 1 ⁄ (+ 1 ⁄ 2 32, −0) 1 ⁄ (+ 1 ⁄ 2 32, −0) 1 ⁄ (+ 1 ⁄ 2 32, −0) 5 ⁄ (+ 1 ⁄ 8 16, −0) 3 ⁄ (+ 3 ⁄ 4 32, −0) 7 ⁄ (+ 1 ⁄ −0) 8 8, 1 1 1 ⁄2 (+ ⁄8, −0)
1 2 4 6 8 16 26 36 80
5.25 11.3 22.5 27.0 31.5 56.4 81.0 103 203
5⁄ 5⁄
16
Notes: Weights and dimensions of clevises are typical; products of all suppliers are essentially similar. User shall verify with the manufacturer that product meets design-strength specifications above. *Tabulated design strengths for comparison with factored loads are based on φ=0.3. To determine safe working load (kips) for comparison with service loads, divide tabular design strength by 1.5. Safe working load, then, corresponds to a 5:1 factor of safety using maximum pin diameter.
Tu = tensile force in the anchor rod, kips When the concrete cone intersects an edge of the pedestal or the cone from another anchor rod, the effective area of concrete is reduced; refer to the AISC Design Guide Column Base Plates (DeWolf and Ricker, 1990) and Marsh and Burdette (1985). Marsh and Burdette (1985) showed that the head of the anchor rod usually provides sufficient anchorage and the use of an additional washer or plate does not add significantly to the anchorage. The nut and threading shown in Figure 8-14c is acceptable in lieu of a bolt head. The nut should be welded to the rod to prevent the rod from turning out when the top nut is tightened. For the design of anchor rods for shear or a combination of tension and shear, see AISC Design Guide Column Base Plates (DeWolf and Ricker, 1990), Fisher (1981), Shipp and Haninger (1983), and ACI 349. OTHER MECHANICAL FASTENERS Clevises
Dimensions, weights, and design strengths of clevises are listed in Table 8-27. Compatability of clevises with various rods and pins is given in Table 8-28. Turnbuckles
Dimensions, weights, and design strengths of turnbuckles are listed in Table 8-29. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OTHER MECHANICAL FASTENERS
8 - 93
Table 8-28. Clevis Numbers Compatible with Various Rods and Pins Diameter of Pin, in.
Dia. of Tap, in.
5⁄ 8
5⁄ 8 3⁄ 4 7⁄ 8
2 — —
2 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 — 21⁄2 21⁄2 21⁄2 21⁄2
1 11⁄4 13⁄8
— — —
— — —
— — —
11⁄2 13⁄4
— —
— —
— —
31⁄2 31⁄2 31⁄2 — 4 4
4 5
4 5
5 5
5
2 21⁄4
— —
— —
— —
— —
— —
5 —
5 —
5 6
5 6
5 6
6 6
6 6
7
7
21⁄2 23⁄4
— —
— —
— —
— —
— —
— —
— —
6 —
6 —
6 7
7 7
7 7
7 7
7 8
7 8
3 31⁄4
— —
— —
— —
— —
— —
— —
— —
— —
— —
7 —
8 8
8 8
8 8
8 8
8 8
8 8
31⁄2 33⁄4
— —
— —
— —
— —
— —
— —
— —
— —
— —
— —
8 8
8 8
8 8
8 8
8 8
8 8
4
—
—
—
—
—
—
—
—
—
—
8
8
8
8
8
8
3⁄ 4
7⁄ 8
1
3 3 3
11⁄4 11⁄2 13⁄4
3 3 3
3 3 3
2
3 3 31⁄2 31⁄2 31⁄2
21⁄4 21⁄2 23⁄4
3
31⁄4 31⁄2 33⁄4
4
4
Notes: Tabular values assume that the net area of the clevis through the pin hole is greater than or equal to 125 percent of the net area of the rod, and is applicable to round rods without upset ends. For other net area ratios, the required clevis size may be calculated by reference to the dimensions tabulated in Tables 8-7 and 8-27.
Sleeve Nuts
Dimensions and weights of sleeve nuts are listed in Table 8-30. Recessed-Pin Nuts
Dimensions and weights of recessed-pin nuts are listed in Table 8-31. Cotter Pins
Dimensions and weights of cotter pins are listed in Table 8-32.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 94
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-29. Dimensions and Weights of Turnbuckles c a
n
n
g
e
D
Threads: UNC and 4UN Class 2B
Weight (pounds) for Length a, in.
Dimensions, in. Diameter D, in.
a
3⁄ 8
6
9⁄
1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8
6 6 6 6
3⁄
32 11⁄16 7 1 ⁄32
1 1 ⁄8 1 1 ⁄4 1 3 ⁄8
1
6 6 6 6
13 ⁄8 19⁄16 13 ⁄4 115 ⁄16
1 1 ⁄2 1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
6 6 6 6
2 1 ⁄4
2
n 16
29 ⁄
4
c
g
6
11 ⁄32
0.41
71 ⁄2 11⁄16 15 ⁄16 713 ⁄16 13 ⁄16 11 ⁄2 81 ⁄8 15 ⁄16 123 ⁄32 87 ⁄16 13 ⁄32 17 ⁄8
0.75 1.00 1.45 1.85
71 ⁄8
83 ⁄4 91 ⁄8 91 ⁄2 97 ⁄8
e 9⁄
16
9
12
18
24
26
Design Strength, φR n *, kips 1.80
0.80 1.38 1.63
1.00 1.50 2.13 2.83
2.43 3.06 4.20
3.30 5.25 7.80 10.8
4.25 5.43
19 ⁄32 21 ⁄32 113 ⁄32 29 ⁄32 19 ⁄16 217 ⁄32 111⁄16 23 ⁄4
2.60 2.72 3.58 4.50
3.20 4.70 4.70
4.40 6.10 7.13
6.85
10.0
11.3
13.1
21 ⁄8 21 ⁄4 21 ⁄2 23 ⁄4
101 ⁄4 127 ⁄32 31 ⁄32 101 ⁄2 131 ⁄32 39 ⁄32 11 21 ⁄8 39 ⁄16 111 ⁄2 23 ⁄8 4
5.50 7.50 9.50 11.5
8.00
9.13
16.8
19.4
15.3
16.0
19.5
6 6
23 ⁄4 33 ⁄8
111 ⁄2 23 ⁄8 123 ⁄4 211⁄16
4 45 ⁄8
11.5 18.0
15.3 35.3
27.5 43.5
55.8 72.0
2 1 ⁄2 2 3 ⁄4
6 6
33 ⁄4 41 ⁄8
131 ⁄2 141 ⁄4
3 31 ⁄4
5 55 ⁄8
23.3 31.5
33.6
42.4 54.0
90.0 113
3 1 ⁄4
3
6 6
41 ⁄2 51 ⁄4
15 161 ⁄2
35 ⁄8 37 ⁄8
61 ⁄8 63 ⁄4
39.5 60.5
145 183
3 1 ⁄2 3 3 ⁄4
6 6
51 ⁄4 6
161 ⁄2 18
37 ⁄8 45 ⁄8
63 ⁄4 81 ⁄2
60.5 95.0
183 252
4 1 ⁄4
4
6 9
6 63 ⁄4
18 221 ⁄2
45 ⁄8 51 ⁄4
81 ⁄2 93 ⁄4
95.0
4 1 ⁄2 4 3 ⁄4
9 9
63 ⁄4 63 ⁄4
221 ⁄2 221 ⁄2
51 ⁄4 51 ⁄4
5
9
71 ⁄2
24
6
14.0 17.4 22.8 26.1 31.5 36.8 42.5 55.8
152
252 351
93 ⁄4 93 ⁄4
152 152
351 351
10
200
442
Notes: Weights and dimensions of turnbuckles are typical; products of all suppliers are essentially similar. User shall verify with the manufacturer that product meets design strength specifications above. *Tabulated design strengths for comparison with factored loads are based on φ = 0.3. To determine safe working load (kips) for comparison with service loads, divide tabular design strength by 1.5. Safe working load, then, corresponds to a 5:1 factor of safety using maximum pin diameter.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OTHER MECHANICAL FASTENERS
8 - 95
Table 8-30. Dimensions and Weights of Sleeve Nuts l
4
½
D
n
Long Dia.
½
Short Dia.
n
c
Inspection hole (optional)
Thread: UNC and 4 UN Class 2B Screw Dia. D, in. 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4 7⁄ 8
1 11⁄8 11⁄4 13⁄8 11⁄2 15⁄8 13⁄4 17⁄8 2 21⁄4 21⁄2 23⁄4 3 31⁄4 31⁄2 33⁄4 4 41⁄4 41⁄2 43⁄4 5 51⁄4 51⁄2 53⁄4 6
Dimensions, in. Short Dia.
Long Dia.
Length l
Nut n
Clear c
Weight, pounds
11⁄ 16 25⁄ 32 7⁄ 8 15⁄ 16 11⁄16 11⁄4 17⁄16 15⁄8 113⁄16
25⁄ 32 7⁄ 8
4 4 4 5 5 5 7 7 71⁄2 71⁄2 8 8 81⁄2 81⁄2 9 9 91⁄2 10 101⁄2 11 111⁄2 12 121⁄2 13 131⁄2 14 141⁄2 15 151⁄2 16 161⁄2 17
— — — — — — 17⁄16 17⁄16 15⁄8 15⁄8 17⁄8 17⁄8 21⁄16 21⁄16 25⁄16 25⁄16 21⁄2 23⁄4 215⁄16 33⁄16 33⁄8 35⁄8 313⁄16 41⁄16 43⁄4 5 51⁄4 51⁄2 53⁄4 6 61⁄4 61⁄2
— — — — — — 1 11⁄8 11⁄4 13⁄8 11⁄2 15⁄8 13⁄4 17⁄8 2 21⁄8 23⁄8 25⁄8 27⁄8 31⁄8 33⁄8 35⁄8 37⁄8 41⁄8 43⁄8 43⁄4 5 51⁄4 51⁄2 53⁄4 6 61⁄4
0.27 0.34 0.43 0.64 0.93 1.12 1.75 2.46 3.10 4.04 4.97 6.16 7.36 8.87 10.4 12.2 16.2 21.1 26.7 33.2 40.6 49.1 58.6 69.2 75.0 90.0 98.0 110 122 142 157 176
2 23⁄16 23⁄8 29⁄16 23⁄4 215⁄16 31⁄8 31⁄2 37⁄8 41⁄4 45⁄8 5 53⁄8 53⁄4 61⁄8 61⁄2 67⁄8 71⁄4 75⁄8 8 83⁄8 83⁄4 91⁄8
1 11⁄16 17⁄32 17⁄16 15⁄8 113⁄16 21⁄16 21⁄4 21⁄2 211⁄16 215⁄16 31⁄8 35⁄16 31⁄2 315⁄16 43⁄8 413⁄16 51⁄4 55⁄8 6 63⁄8 67⁄8 71⁄2 715⁄16 83⁄8 87⁄8 91⁄4 93⁄4 101⁄8 105⁄8
Notes: Weights and dimensions of sleeve nuts are typical; products of all suppliers are essentially similar. User shall verify with the manufacturer that strengths of sleeve nut are greater than the corresponding connecting rod when the same material is used.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 96
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-31. Dimensions and Weights of Recessed-Pin Nuts
Short Dia.
Long Dia.
Tc
Grip
d
D s t
Material: Steel
Thread: 6 UN Class 2A/2B
Pin Dimensions, in. Thread
Pin Dia. d, in.
D
T
2, 2 1 ⁄4 2 1 ⁄2 , 2 3 ⁄4 3, 3 1 ⁄4 , 3 1 ⁄2 3 3 ⁄4 , 4 4 1 ⁄4 , 4 1 ⁄2 , 4 3 ⁄4 5, 5 1 ⁄4 5 1 ⁄2 , 5 3 ⁄4 , 6 6 1 ⁄4 , 6 1 ⁄2 6 3 ⁄4 , 7 7 1 ⁄4 , 7 1 ⁄2 7 3 ⁄4 , 8, 81 ⁄4 8 1 ⁄2 , 8 3 ⁄4 , 9 9 1 ⁄4 , 9 1 ⁄2 9 3 ⁄4 , 10
11 ⁄2 2 21 ⁄2 3 31 ⁄2 4 41 ⁄2 5 51 ⁄2 51 ⁄2 6 6 6 6
1 11 ⁄8 11 ⁄4 13 ⁄8 11 ⁄2 15 ⁄8 13 ⁄4 17 ⁄8 2 2 21 ⁄4 21 ⁄4 23 ⁄8 23 ⁄8
c
Grip
½
d+1
d Bolt ¾
1⁄ 1⁄ 1⁄ 1⁄ 1⁄ 1⁄ 1⁄ 3⁄
3⁄ 3⁄ 3⁄ 3⁄ 3⁄ 3⁄
8 8 8 4 4 4 4 8 8 8 8 8 8 8
Nut Dimensions, in. Thickness t 7⁄
8
1 11 ⁄8 11 ⁄4 13 ⁄8 11 ⁄2 15 ⁄8 13 ⁄4 17 ⁄8 17 ⁄8 21 ⁄8 21 ⁄8 21 ⁄4 21 ⁄4
Diameter Short Dia. 3 35 ⁄8 43 ⁄8 47 ⁄8 53 ⁄4 61 ⁄4 7 75 ⁄8 81 ⁄8 85 ⁄8 93 ⁄8 101 ⁄4 111 ⁄4 111 ⁄4
Recess
Long Dia. Rough Dia. 33 ⁄8 41 ⁄8 5 55 ⁄8 65 ⁄8 71 ⁄4 81 ⁄8 87 ⁄8 93 ⁄8 10 107 ⁄8 117 ⁄8 13 13
25 ⁄ 8 31 ⁄ 8 37 ⁄ 8 43 ⁄ 8 51 ⁄ 4 53 ⁄ 4 61 ⁄ 2 7 71 ⁄ 2 8 83 ⁄ 4 95 ⁄ 8 105⁄8 105⁄8
s 1⁄ 1⁄ 3⁄ 3⁄ 1⁄ 1⁄ 5⁄
5⁄ 3⁄
3⁄ 3⁄ 3⁄ 3⁄ 3⁄
4 4 8 8 2 2 8 8 4 4 4 4 4 4
Weight, pounds 1 2 3 4 5 6 8 10 12 14 19 24 32 32
Notes: Although nuts may be used on all sizes of pins as shown above, a detail similar to that shown at the left is preferrable for pin diameters over 10 inches. In this detail, the pin is held in place by a recessed cap at each end and secured by a bolt passing completely through the caps and pin. Suitable provisions must be made for attaching pilots and driving nuts.
¾
Typical Pin Cap Detail for Pins over 10 in. in dia. Dimensions shown are approximate
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OTHER MECHANICAL FASTENERS
8 - 97
Table 8-32. Dimensions and Weights of Cotter Pins HORIZONTAL OR VERTICAL PIN 3/8
HORIZONTAL PIN 1″
1
GRIP + ½
p
d
h
GRIP + 1 ″
1″
d
c
l l = Length of pin, in.
Pins with Heads Head Diameter h, Pin Diameter d, in. in.
11⁄4 11⁄2 13⁄4 2 21⁄4 21⁄2 23⁄4 3 31⁄4 31⁄2 33⁄4
11⁄2 13⁄4 2 23⁄8 25⁄8 27⁄8 31⁄8 31⁄2 33⁄4 4 41⁄4
Weight of One, pounds
0.19 + 0.35l 0.26 + 0.50l 0.33 + 0.68l 0.47 + 0.89l 0.58 + 1.13l 0.70 + 1.39l 0.82 + 1.68l 1.02 + 2.00l 1.17 + 2.35l 1.34 + 2.73l 1.51 + 3.13l
Cotter Length c, in.
Diameter p, in.
Weight per 100, pounds
7⁄
1⁄ 4 1⁄ 4 1⁄ 4 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2
2.64 3.10 3.50 9.00 9.40 10.9 11.4 28.5 28.5 33.8 33.8
8
1 11⁄8 11⁄4 13⁄8 11⁄2 15⁄8 13⁄4 17⁄8 17⁄8 21⁄4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 98
BOLTS, WELDS, AND CONNECTED ELEMENTS
WELDED CONSTRUCTION
While AWS D1.1 is the traditional design specification for weld stresses in both buildings and bridges, AASHTO/AWS D1.5 also exists for dynamically loaded structures. There are significant differences between the two codes and, in the case of building structures, AWS D1.1 is normally used unless contract documents state otherwise. Welds in building structures are predominantly designed for static loading. Some parts, however, such as crane runways and machinery supports, are subjected to dynamic loading. When this is the case, additional requirements and special joint details may be necessary. This may include reinforcing fillet welds at tee and corner joints, radius cuts on terminations of gusset type connections, radiographic or ultrasonic testing for quality control, or joint details in accordance with LRFD Specification Appendix K3. The contract documents should specifically enumerate these additional requirements when they are determined to be necessary. Weldability of Steel
AWS has defined weldability as the capacity of a metal to be welded, under the fabrication conditions imposed, into a specific, suitably designed structure, and to perform satisfactorily in the intended service. AWS D1.1 is based on certain weldable grades of steel as listed therein by ASTM designation. It contains all of the steels permitted by LRFD Specification Section A3.1a. The effect a steelâ&#x20AC;&#x2122;s properties have upon its weldability relates to the reaction of the steel to the drastic heating and cooling cycle of welding. This weld quench can range from the practically instantaneous cooling of an accidental arc strike to the 10 minutes required to cool a high-heat-input electroslag weld. Due to the rapid cooling of the arc strike, the full-quench hardness for the carbon equivalent of the steel may be realized, resulting in brittleness and the potential for cracking. In contrast, the slower cooling rate of the electroslag weld may produce a more ductile and lower-strength metallurgical structure in the heat-affected zone (HAZ) of the base metal. As they cool, welds develop residual shrinkage strains that can approach the yield strain as a limit; ductility and notch resistance are needed to accommodate these strains. Since chemical composition, grain size, and thickness affect ductility and notch resistance, they are the most important properties for weldability. These factors, discussed below, assume greater significance as the structure becomes large and must store greater elastic energy. Table 8-33 summarizes several ASTM specifications and their requirements for the aforementioned properties. Note that there is a greater flexibility in grain size and carbon equivalents in these specifications for shapes, plates, and bars. Also, maximum tensile strength requirements are listed to exclude steels from the upper end of the chemical composition range which might require special welding procedures or weld repairs. In contrast, the requirements for structural tubing, pipe, sheet, and strip do not limit grain size or maximum tensile strength, but generally impose smaller limits on thickness. Chemical analysis of a heat of steel is usually made during the processing as a control and upon completion after it has been tapped into a ladle. This heat analysis is used to compile a mill test report which also lists the customerâ&#x20AC;&#x2122;s order number, steel grade, quantity and dimension of pieces shipped, and the results of any mechanical testing (tensile, flexural, Charpy impact, or other). This information may be obtained by request from the steel supplier when placing an order and is essential for good control of welded fabrication. It is imperative that the grade of steel to be welded is known since the proper welding procedure depends upon this information. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
WELDED CONSTRUCTION
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Table 8-33. ASTM Requirements for Properties Affecting Weldability of Steels Max. Carbon content, % by weight (heat analysis)
Max. tensile strength, ksi
Grain Size
Max. thickness, in.
80
—*
none
ASTM Specification
Products Covered
A36
shapes
0.26
plates
0.25–0.29
A242 A514
bars
0.26–0.29
shapes, plates, bars
type 1, 0.15
plates—quenched varies among 13 and tempered grades, 0.14–0.21
none
—
4
130
fully killed, fine grain
6 1⁄
A529
shapes, plates, bars
0.27
85
—
A572
shapes, plates, bars, sheet piling
varies among grades, 0.21–0.26
none
—*
Gr. 42: 6 Gr. 50: 4 Gr. 60, 65: 11 ⁄4
A588
shapes, plates, bars
varies among 5 grades, 0.15–0.20
none
fine grain
F y = 50: 4 F y = 42: 8
2
A852
plates
0.19
110
fine grain
4
A53 Grade B
tubing, pipe
0.30
none
—
2.344, 24 dia.
A500
tubing, pipe
Gr. A, B: 0.26 Gr. C: 0.23
none
—
A501
tubing, pipe
0.26
none
—
1
A618
tubing, pipe
Gr. Ia: 0.15 Gr. Ib: 0.20 Gr. II: 0.22 Gr. III: 0.23
none
—
11 ⁄2
A570, Gr. 36, 50
sheet, strip
0.25
none
—
0.23
A606
sheet, strip
0.22
none
—
none
A607
sheet, strip
0.22–0.26
none
—
none
1⁄
2
*Supplemental requirements can specify killed fine grain.
Chemical Composition
The most important element affecting weldability is carbon, however, the effect of other elements on weldability is related through a carbon equivalent formula. Weldability is enhanced as carbon equivalent decreases because the maximum hardness and consequent brittleness that a steel may reach after rapid liquid quenching from high temperature is directly proportional to the carbon equivalent. This relationship is illustrated in Figure 8-17 and is applicable to the surface in contact with the quench liquid where the quench rate is greatest. Although no liquid is present in welding, the HAZ is subject to rapid cooling and consequent hardening by conduction of weld heat into the base metal. As the thickness of the section increases, so does the cooling rate, producing progressively harder and less ductile metallurgical constituents. Alloys such as Ni, Cr, and Mo in the steel permit hardening at slower cooling rates and at depths below the surface where the cooling rate is slower; pre-heat is the common remedy for reducing the cooling rate and hardness. As the carbon content increases from 0.10 percent to 0.20 percent by weight, the maximum as-quenched hardness increases from 40 to 50 Rockwell C. Using the known hardness-strength relationship, it can be shown that the maximum as-quenched tensile AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 100
BOLTS, WELDS, AND CONNECTED ELEMENTS
strength increases from 180 to 260 ksi. Welding procedures are designed to keep weld quench rates far below these maximum rates. Also, electrodes are usually designed to deposit weld metal containing about 0.008 to 0.12 percent carbon to avoid cracking. Grain Size
In general, weldability will be enhanced by steel with a finer grain size. As illustrated in Figure 8-18, grain size is a prime variable affecting the ductility and impact resistance for a wide variety of steel compositions. The grain size of weld metal also varies and has a similar effect. Because they experience a slower cooling rate, high-heat-input welds show a larger grain size than the same process and electrode at a lower heat input. This is one reason the AWS D1.1 limits multi-pass SAW groove weld layers to a maximum size of 1â &#x201E;4-in. Also, a subsequent pass will refine the grain of a previous pass. Thickness
In general, as the thickness to be welded decreases, the weldability of the material is enhanced. Because of their greater mass, thick plates extract heat from and quench the weld more rapidly than thin plates with the identical weld. As a partial remedy, the plates may be pre-heated and held at temperatures of a few hundred degrees Fahrenheit for the welding operation. This pre-heat appreciably slows the quench rate and reduces weld hardness, as does post-heating. As plate thickness increases, the notch impact resistance decreases as shown in Figure 8-19. This test was conducted on American Bureau of Shipping (ABS) class C ship plate in 3â &#x201E;4-in., 1-in., 2-in., and 3-in. thicknesses using a severe crack-like notch in the ASTM A208 drop-weight test. The use of fine-grain steelmaking practice as specified by ASTM can improve notch toughness where required by the service of a particular structure.
60 255
50
Maximum hardness for carbon and alloy steels
40
180 140
30 20
Equivalent tensile strength, ksi
Maximum hardness, Rockwell, C
70
10
0
0.20
0.40
0.60
0.80
1.0
Carbon, per cent
Fig. 8-17. Influence of carbon content on the maximum hardness of steel as quenched (Stout and Doty, 1978), courtesy Welding Research Council. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
WELDED CONSTRUCTION
8 - 101
Structural Welding Materials and Processes
Filler metal and flux specifications are exclusively AWS specifications, having been removed from ASTM specifications. Additionally, AWS uses a coding system for consumable electrodes to designate the tensile strength and coating or flux combination. Since the coding for the several filler/flux combinations are consistent only with respect to the types of electrode used, it is very important that the applicable specifications be reviewed when specifying such welding requirements. The welding processes discussed in this text are: shielded metal arc welding (SMAW), submerged arc welding (SAW), gas-metal arc welding (GMAW), flux-cored arc welding (FCAW), electroslag welding (ESW) and electrogas welding (EGW). Except for electroslag welding, each of these processes use electrical energy from an arc discharge between a steel-wire electrode and the base metal to provide heat for fusion. Electroslag welding uses a high-electrical-resistance molten-slag bath which occupies the entire joint. This slag melts both the electrode and the base metal.
40
CVN Transition Temperature, °F
0
– 40
– 80
c c c
–120
–160
— Plain Carbon c — Nickel — Manganese — Molybdenum — Chromium
c
–200
(After Kottcamp and Stout) 9
8
7
6
5
4
ASTM Ferrite-grain Size Number
Fig. 8-18. Effect of ferrite-grain size on CVN transitional temperature (Stout and Doty, 1978), courtesy Welding Research Council. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3
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BOLTS, WELDS, AND CONNECTED ELEMENTS
Each of the aforementioned processes will be summarized here; a full description may be found in AWS (1978). Additionally, thermal cutting and air arc gouging will be discussed. SMAW
There are two AWS Specifications for SMAW electrodes: AWS A5.1 and AWS A5.5. A condensation of the provisions of these specifications is given in Table 8-34. AWS notation for SMAW electrodes is illustrated in Figure 8-20. This has also been extended to other processes. The welding positions noted in Figure 8-20 (flat, horizontal, vertical, and overhead) are illustrated in Figure 8-21. SMAW (stick) electrodes are made in a variety of low-carbon compositions. The extruded coatings contain aluminum, silicon, and other deoxidizers; the deposited weld is a mini-electric-furnace-killed steel with excellent ductility and resistance to cracking from weld shrinkage strains. In the arc stream, moisture breaks down and liberates atomic hydrogen which is readily soluble in molten iron (Stout and Doty, 1978); see Figure 8-22. As the weld solidifies,
70
Increase in NDT Transition Temperature, 째F
60
50
40
30
20
ABS-C, Drop-Weight NDT
10
0 0
1
2 Plate Thickness, in.
3
Fig. 8-19. Effect of plate thickness on the drop-weight NDT ductility transition temperature (Stout and Doty, 1978), courtesy Welding Research Council. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
WELDED CONSTRUCTION
8 - 103
Table 8-34. Condensed AWS Specifications for SMAW Electrodes Electrode
Type
AWS Spec.
Carbon Steel
A5.1
Low Alloy
A5.5
Impact Test Criteria Criteria for Min. Criteria for Tensile Composition Strength, of Deposited Charpy V- Weld Metal Radiographic Grades Weld Metal Notch Test Condition Soundness ksi 60
62
70
72
70 80 90 100 110 120
70 80 90 100 110 120
Not stipulated Required for As-welded some grades Stipulated only Stipulated (all grades)
Required for Some assome grades welded, only some stressrelieved
Stipulated for all but E6012, E6022 Stipulated for all grades
Note: A particular production welding condition may be more severe than the test conditions specified for the above.
hydrogen becomes much less soluble and the atoms are rejected into voids where pairs combine to form a much less mobile molecular H2. This molecular hydrogen can then exert pressure in lattice imperfections which is sufficient, when combined with weld shrinkage strains, to cause “fisheyes” or cracking in the weld material. This can be prevented by maintaining the moisture content of consumable electrodes below specified levels and through proper pre-heat. E7015, E7016, E7018, and E7028 low-hydrogen electrodes have specially compounded and baked extruded coatings containing a limited moisture (hydrogen) content by weight. Coatings for the E70 electrode series can contain a maximum of 0.04 percent moisture, while the E120 electrode series is limited to only 0.015 percent. As the tensile strength of the base metal increases, electrodes with lower moisture content must be selected to avoid weld cracking. Since the electrode coating will absorb moisture when stored in damp or humid conditions, drying ovens near points of use in the shop are necessary for low-hydrogen electrodes.
6
—
A1 Weld metal composition
1
Coating characteristics**
70 70,000 psi min. tensile
Electrode
E
Position code*
ELECTRODE PROPERTIES
**1 = All flat, vertical, overhead, and horizontal **2 = Flat and horizontal only **5, 6, 8 = Low hydrogen
Fig. 8-20. AWS classification system for SMAW electrodes. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BOLTS, WELDS, AND CONNECTED ELEMENTS
Fillet Welds
Groove Welds
(a) Flat
(b) Horizontal
(c) Vertical
(d) Overhead Fig. 8-21. Welding positions. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
WELDED CONSTRUCTION
8 - 105
The electrodes to be used with various base metals are shown in AWS D1.1 Table 4.1. Low-hydrogen electrodes are used with ASTM A572 and A588 steels among others. Filler metal matching the color of ASTM A588 steel is listed in AWS D1.1 Table 4.2. SAW
The automatic and semi-automatic SAW processes provide consistent, high quality, and economical deposits which are particularly suitable for long welds. Their major limitation is that the work must be positioned to allow for near flat or horizontal welding. In the SAW process, fluxes may be fused or agglomerated (finely powdered constituents bonded together with silicates), but are classified in AWS specifications only according to the weld metal properties produced in the standard specified weld tests. The applicable specifications are: AWS A5.17 and AWS A5.23. AWS notation for SAW electrodes and fluxes is illustrated in Figure 8-23. Fluxes must be kept dry in storage to avoid an increase in moisture content and subsequent chance of hydrogen cracking in steels with higher yield strengths or highly restrained joints in thick members.
Hydrogen, cm.3 per 100 g. of iron 5
10
15
20
25
30
2100
2500 Austenite
Delta Iron
1 atmos.
1100
1500
600 Ferrite
Temperature, 째C.
1600
500
100 0
0.00075
0.0015 Hydrogen, percent
0.00225
Fig. 8-22. Solubility of hydrogen in iron (Stout and Doty, 1978), courtesy Welding Research Council. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
0.003
Temperature, 째F.
Liquid
3500
8 - 106
BOLTS, WELDS, AND CONNECTED ELEMENTS
GMAW
The GMAW process can be used with mixtures of argon and two percent oxygen, argon and carbon dioxide, or pure carbon dioxide. While argon is inert, carbon dioxide can react with the weld metal and result in a reduction in ductility and impact properties at low temperatures. Despite this, 70 ksi electrodes have commonly been used with carbon dioxide gas with good results; a CVN 20 (20 ft-lb Charpy V-notch impact value) at −20°F is specified in the AWS tests. Alloy electrodes producing up to 120 ksi minimum tensile strength with CVN 20 at −60°F, and three percent nickel electrodes producing 80 ksi minimum tensile strength with CVN 20 at −100°F are available. There are two AWS Specifications for GMAW electrodes: A5.18 and A5.28. Identification of these electrodes is illustrated in Figure 8-24. FCAW
FCAW electrodes are made by forming a thin sheet strip into a U-shape and filling it with flux. After closing the tube, it is drawn to size as a continuous coil. AWS classifies these
M
12
K
Silicon killed
Medium Mn (1.00% ± )
E
Nominal carbon (0.12%)
6
Electrode
A
ELECTRODE PROPERTIES
CVN 20 @ − 60° F
7
Tested as welded
Flux
F
70,000 psi min. tensile
FLUX CAPABILITY
Fig. 8-23. AWS classification system for SAW materials.
ELECTRODE PROPERTIES B2
L Low carbon (0.05% max.)
—
Cr (11/ 4 %); Mo (1/ 2 %)
S
Solid electrode
80 80,000 psi min. tensile
R
Rod*
Electrode
E
*Can be used as feed rod with independent heat source (e.g., tungsten arc)
Fig. 8-24. AWS classification system for GMAW electrodes. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
WELDED CONSTRUCTION
8 - 107
electrodes according to: (1) whether or not carbon dioxide is used as a separate shielding gas; (2) suitability for either single or multiple pass applications; (3) the type of current; (4) the welding position; and, (5) the as-welded mechanical properties of the weld metal. High weld-production rates may be attained with semi-automatic equipment which may be used in any position with the appropriate electrode. Where required by service conditions, flux-cored electrode grades can provide weld metal with CVN 20 impact values at temperatures in steps from 20°F to −100°F. Some of the deposits of the carbon steel electrodes will develop CVN 20 at −20°F, while the low alloy electrodes will develop CVN 20 at −100°F. The applicable specifications are AWS A5.20 and AWS 5.29 (symbols are similar to AWS 5.20 with the addition of an alloy composition at the extreme right). The AWS classification system is illustrated in Figure 8-25. ESW and EGW
With the ESW and EGW processes, 18-in. and greater thicknesses may be welded in one pass, using multiple electrodes, with the joint in a vertical plane. A single-electrode, semi-portable welding machine can join plates up to five inches thick. Furthermore, using either of these processes, it is possible to make girder flanges by welding mill-width plates and subsequently longitudinally cutting out three or more flange widths. Note that AWS prohibits the use of these welding processes on quenched and tempered steels. The composition of cored electrodes is based on weld-metal analysis, and the composition of solid electrodes is based on wire analysis. The coarse grains in the slow-cooled electroslag weld may make it difficult to test ultrasonically and the minimum size flaw detectable by RT is about 11⁄2 percent of the thickness. This creates difficulty in the inspection of electroslag welding. AWS A5.25 requires electrodes which contain nickel to provide CVN 15 impact values at either 0°F or −20°F. This specification is patterned after AWS A5.17 and A5.18 insofar as the electrodes are concerned; refer to Figure 8-26.
1
—
2 Usability code**
T
Position code*
70 70,000 psi min. tensile
Electrode
E
Tubular (flux cored)
ELECTRODE PROPERTIES
**2 = Flat and horizontal only **1 = All position **2 = Single pass CO2 shielded only
Fig. 8-25. AWS classification system for FCAW electrodes. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BOLTS, WELDS, AND CONNECTED ELEMENTS
Thermal Cutting and Air-Arc Gouging
Thermally cut welding bevels are required to be smooth and free of notches or grooves in which weld slag may be trapped. Two cutting systems, oxy-fuel gas and plasma arc, are available. Oxy-fuel gas cutting may be used to cut almost any plate thickness commercially available except in stainless steel which must be plasma cut. Plasma arc cutting will cut thicknesses only up to about 11⁄2-in., but is much faster than oxy-fuel gas cutting. This speed advantage increases as the plate thickness decreases; at a thickness of one inch, the cutting speed is over 300 percent faster with a water-injection plasma torch. The plasma arc cutting process, however, also leaves a slight taper in the cut as it descends. If the plate being cut contains large discontinuities or non-metallic inclusions, turbulence may be created in the oxy-fuel cutting stream. As result, this may cause notches or gouges in the edge of the cut. The plasma arc stream is less susceptible to this as it moves with a higher velocity. Within the depth limits of the specifications, it is usually better practice to remove these by grinding than to weld repair and grind. Additionally, re-entrant thermal cuts should provide a smooth transition. Carbon-air-arc gouging is a convenient method for removing weld defects, gouging the weld root to sound metal, or forming a U-groove on one side of a square butt joint. The carbon arc travels over the work and melts a weld-nugget-shaped area of the metal. This molten material is then blown away by a jet of compressed air, directed from the holder, parallel to the carbon electrode. Thus, air-arc gouging may be considered the opposite of welding in that each pass removes approximately one weld pass. Because the arc quench is similar in both air-arc gouging and welding, any pre-heat required for welding should also be used for air-arc gouging. Inspection
The five most commonly used testing methods for welding inspection are: visual (VT), dye penetrant (DPT), magnetic particle (MT), radiographic (RT), and ultrasonic (UT). These methods are discussed in the following sections; refer also to AWS B1.0. Visual inspection is the most commonly specified procedure. Other, more stringent methods can
Electrode
W
Fig. 8-26. AWS classification system for ESW materials. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
T
1
CNV 15 @ 20°F
E
70,000 psi min. tensile
2
Weld metal tested as deposited
7
CNV 15 @ 20°F
ES
Electroslag flux
Flux
F
ELECTRODE PROPERTIES
70,000 psi min. tensile
FLUX CAPABILITY
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add significant cost to the project and, therefore, should be specified only when essential to the integrity of the structure. The engineer of record (EOR) must specify in the contract documents which type of weld inspection is required as well as the extent and application of each type. In the absence of instruction, AWS D1.1, paragraph 6.6.5 states that the fabricator or erector is responsible only for those weld discontinuities found by visual inspection. If additional inspection more stringent than visual is later required, the owner is normally responsible for the cost of weld repairs other than those identified by the visual inspection. VT
Visual testing provides the most economical approach to checking weld quality. It is particularly good for inspecting single-pass welds, but is limited in that only surface imperfections may be detected. This type of inspection is especially effective when it includes both a check of the joint for accuracy and cleanliness before welding and an observation of the welding procedure. Acceptance criteria are specified in the AISC Code of Standard Practice and Quality Criteria and Inspection Standards (AISC, 1988), as well as AWS D1.1. DPT
A red dye penetrant is applied to the work and penetrates any crack or crevice open to the surface. After removing excess dye, a white developer is applied. Where cracks are present, the red dye seeps through the developer, producing a visible red image. This process is summarized in Figure 8-27. DPT may be used to detect tight cracks as long as they are open to the surface. Like VT, however, only surface cracks are detectable. Furthermore, deep weld ripples and scratches may give a false indication when DPT is used. MT
A magnetizing current is introduced into the weldment to be inspected as shown in Figure 8-28. The magnetic field induced in the work will be distorted by any cracks, seams, inclusions, etc., located on or within approximately 1â &#x201E;10-in. of the surface. A dry magnetic powder spread lightly on the surface will gather at such discontinuities, leaving a distinct mark. These magnetically held particles then show the size, location, and shape of the discontinuity. This method will detect surface cracks filled with slag or contaminants which dye in DPT could not enter. Additionally, the powder may be picked up and preserved with clear
Visible Indication
Subvisible Crack
Cleaned Surface
Penetrant Applied
Excess Removed
Fig. 8-27. Schematic diagram of DPT. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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tape, providing accurate and detailed records of inspection results. However, this method requires relatively smooth surfaces and while cleanup is easy, demagnetization, when necessary, may not be. RT
This method uses a radioactive source and an X-ray film process. RT can detect porosity, slag, voids, cracks, irregularities, and lack of fusion. To be detected, the imperfection must be oriented roughly parallel to the impinging radiation beam and occupy about 11⁄2 percent of the metal thickness along that beam. The film negative provides a permanent record of the inspection. Defects smaller than about 11⁄2 percent of the metal thickness and defects not parallel to the beam may not register. RT of closed, inaccessible pipe joints is difficult to obtain and interpret and should be discouraged. Additionally, when the particle beam must penetrate varying thicknesses, as at fillets and tee or corner joints, RT is not readily interpreted and the resulting inspection may be less consistent. When this is the case, other inspection methods should be used. Other limitations of RT are that the required exposure time increases with material thickness and there is a worker hazard due to the radiation used in the method. The precautions for avoiding these hazards and the equipment and film costs make this method the most expensive inspection method. UT
This process, illustrated in Figure 8-29, is analogous to radar and operates on a principle called pulse-echo. A short pulse of high-frequency sound is introduced into the metal. The reflection of this sound wave from the far end of the member and any voids encountered along the way may then be detected. Any reflections are displayed as pips on a display in which the horizontal grid represents the distance through the metal, and the vertical scale represents the area, and therefore the strength, of the reflecting surface. The point of origin of the sound wave can be readily moved around to check many orientations and can project the wave into the metal at angles of 90°, 70°, 60°, and 45°. While UT can detect favorably oriented, flat discontinuities smaller than 1⁄64-in. in carbon and low-alloy structural steels, austenitic stainless steels and extremely coarse-
Current
Part
Magnetic Field
Fig. 8-28. Schematic diagram of MT. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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grained steels such as electroslag weld metal are difficult to inspect. Also, certain joint geometry limits the use of UT and it is difficult to inspect members less than 5⁄16-in. thick because there is a “dead area” at the origin of the sound wave. The accuracy of UT depends upon the skill and training of the operator and frequent calibration of the instrument. ASNT has set training standards for UT operators. Despite the fact that UT is a more versatile, expedient, and economical inspection method than RT, it does not provide a permanent record like the X-ray negative in MT. Instead the operator must make a written record of discontinuity indications. For more information, see Krautkramer (1977) and Institute of Welding (1972). Economical Considerations
On a weight basis, the cost of weld metal far exceeds the cost of any other material in a structure. Therefore, in addition to designing joints for the best welding position, significant economy can be achieved by selecting the proper weld type and an arrangement for the welds which requires a minimum amount of weld metal and the least amount of deposit time. Acceptance of prior qualification of welding procedures can also result in a more economical structure.
Good Bond
Slag Inclusion
Crack or Incomplete Fusion Fig. 8-29. Variations in UT reflections due to differences in acoustic properties caused by defects at the boundary. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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Welding Position
When weld metal is deposited in the flat position, it can be deposited more quickly since gravity does not adversely affect the deposit. As a result, large electrodes and high currents may be used. In the vertical and overhead positions, electrode diameters above 5⁄ -in. produce weld pools with surface tensions and arc forces which are unable to 32 overcome the pull of gravity, causing the weld metal to run. Since the deposition rate in the flat position and in the horizontal position for single-pass fillet welds (not greater than 5⁄ -in.) is approximately four times faster than that in the vertical or overhead position, 16 there is strong economic incentive to design and position work for welding in the flat or horizontal position. Weld Type
In general, in the flat position, the SAW, GMAW, or FCAW processes will be more economical than the SMAW process. However, the selection of the welding process should be left to the fabricator since the equipment and training of personnel will vary from one shop to another. It is appropriate, though, for the designer to specify the type of weld to be used, e.g., fillet, groove, etc. The fillet weld will be most economical and should generally be selected instead of the groove weld in applications for which groove welds are not required. Additionally, fillet welds result in lesser distortion of the connected material. There are, however, situations, such as joints subjected to fatigue loading, in which the performance of the groove weld is superior. Complete-joint-penetration groove welds may incur the additional costs of non-destructive testing, backgouging, or backing bars; refer to Alexander (1991). Fillet welds around the inside of a hole or slot require less weld metal than plug or slot welds of the same size. It should be noted, however, that the diameters of holes and widths of slots for fillet welds should be somewhat larger than those for plug and slot welds in metal of the same thickness to accommodate the necessary tilt of the electrode. Weld Metal Volume
Welds which are oversized waste weld metal and labor time, resulting in an unnecessary increase in the cost of the connection. Thus, it is important to use the proper weld size required for strength or based upon the minimum weld size from the LRFD Specification and to not over-specify weld size. While the strength of a fillet weld is in direct proportion to its size, the volume of the weld metal increases as the square of the weld size. Thus, a 5⁄8-in. fillet weld is twice as strong as a 5⁄16-in. fillet weld but also four times more costly. For this reason, it is more desirable to specify a smaller-sized and longer weld than a larger-sized and shorter weld. In groove welds, double-bevel, double-V, double-J, and double-U welds are typically more economical than single welds of the same type since they use less weld metal. As an added benefit, the resulting symmetry results in less rotational distortion strain. Double welds, however, require more labor in edge preparation and proper cleaning of the weld root prior to commencing the weld on the second side. There may also be added cost if the piece must be repositioned to perform the weld on the second side. For this reason, many fabricators prefer a single weld in thicknesses up to about one inch. Where single- or double-groove welds are to be used, bevel- and V-groove welds are usually less expensive since they may be flame cut; J- and U-groove welds are more expensive since they must be planed or air-arc gouged. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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Deposit Time
Fillet welds sizes up to 5â &#x201E;16-in. may be deposited in a single pass when deposited in the flat or horizontal position. Larger-size welds must be deposited in multiple passes which will require appreciably more time and weld metal. Thus, fillet welds sized not greater than 5â &#x201E;16-in., where possible, will result in a significant savings in deposit time, weld material, and cost. Prior Qualification of Procedures
Evidence of prior qualification of welding procedures, welders, welding operators, or tackers may be accepted at the discretion of the engineer of record (EOR). Fabricators certified in the AISC Quality Certification Program have the experience and documentation necessary to assure that the EOR could accept such prior qualifications (refer to Part 6 for a description of the AISC Quality Certification Program). Significant economic savings may be achieved by accepting such prior qualifications. Minimizing Weld Repairs
Added cost in the form of weld repairs or replacement may be minimized if the designer considers the possibilities of lamellar tearing, fatigue cracking, notch development, and reduced impact toughness when designing welded connections. Lamellar Tearing
A lamellar tear is a separation or crack in the base metal caused by through-thickness weld shrinkage strains. When steel is hot-rolled, sulphides or other inclusions are elongated to form microscopic platelets in the plane of the steel plate. These inclusions reduce the strength of the steel in the through-thickness direction below that in the longitudinal or transverse direction. While special practices are available to produce low-sulphur steel which is resistant to lamellar tearing and ASTM A770 provides a testing method by which the throughthickness strength of the base metal may be measured, it is difficult to assure freedom from the possibility of lamellar tearing. Lamellar tearing is a phenomenon which can occur even in material with superior mechanical properties. Instead, the joint detail is most important in preventing lamellar tearing. Some joint designs are inherently susceptible to lamellar tearing (AISC, 1973). For example, the complete-joint-penetration groove-welded tee joints in thick sections shown in Figure 8-30 can develop lamellar tears in the crossbar of the tee flange. Such tears can be detected with UT. Other susceptible joints are shown with improved details in Figures 8-31 and 8-32. The probability of lamellar tearing may be minimized through good joint design and proper welding procedures. The joint design should minimize the weld size and, therefore, the resulting shrinkage strains. Additionally, the design should reduce the restraint which intensifies the local strains. The welding procedure should then establish a sequence to minimize component and internal restraint. Welding with low-hydrogen processes and effective pre-heat has also been shown to minimize lamellar tearing (Kaufmann, Pense, and Stout, 1981). Fatigue Cracking
Because of their inherent rigidity, welded members are subjected to severe restrictions at service loads if subjected to the repeated variations in stress (fatigue loading). In a AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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dynamically loaded structure, fatigue cracks at notches progress at a rate proportional to the stress range and to the number of stress cycles. Gradual transitions of sections will help to alleviate these concentrations. The fatigue resistance of a butt weld in a tension member, for example, can be improved approximately 25 percent by grinding the weld reinforcement flush. Thus, any notches in the tension areas should be ground out. Additionally, all grinding should be done in the direction of the stress. Refer to LRFD Specification Appendix K3 for further information. Notch Development
When subjected to lateral movement, a severe notch can result at locations of one-sided welds. For the fillet-welded joint subjected to lateral loading in Figure 8-33, the unwelded side has no strength in tension and a notch may form from the unwelded side. Using one fillet weld on each side will eliminate this condition. This is also true with partial-jointpenetration groove welds. In the case of the backing bar of Figure 8-34a, the location of the tack welds may cause fatigue notches. An improved detail would be as shown in Figure 8-34b, where the backing bar is tack welded inside the groove. Any undercut would then be filled, or at least backed up, by the final weld joint. This is also applicable in the case of box members with corner backup. Note that backing bars should also be continuous throughout the length to avoid discontinuities at the base of the weld profile. Impact Toughness
Different classifications of alloy electrodes and fluxes can produce welds with CVN 20 at selected temperatures between 0°F and −150°F. Arc Strikes
Arc strikes may occur during welding procedures if the welding rod is lifted from the work while the current is on, or during magnetic particle testing if the magnetizing prod is lifted from the work while the current is on. As stated in Quality Criteria and Inspection Standards (AISC, 1988), arc strikes need not be removed in statically loaded structures.
Fig. 8-30. Lamellar tear resulting from shrinkage of large welds in thick material under high restraint. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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Other Considerations in Welded Construction
Matching Electrodes
AWS D1.1 Table 4.1 lists matching electrodes for various steels by ASTM Specification and is referenced in LRFD Specification Table J2.5. Use of electrodes one strength-level higher than matching is permitted. Typical structural steel grades with Fy equal to 36 ksi and 50 ksi are normally welded with electrode material of 70 ksi nominal strength, indicated as E70XX for SMAW or its equivalent. Welding Shapes from ASTM A6 Groups 4 and 5
When heavy shapes are spliced, extremely high shrinkage strains may develop in the base metal, inhibiting ductile deformation in the material and increasing the possibility of brittle fracture. Additionally, interior portions of heavy hot-rolled shapes and plates may contain a coarser grain structure and/or lower notch-toughness properties than other areas of the product.
(a)
Susceptible Detail
Improved Detail
Susceptible Detail
Improved Detail
Susceptible Detail
Improved Detail
(b)
(c)
Fig. 8-31. Susceptibility to lamellar tearing can be reduced by careful detailing of welded connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BOLTS, WELDS, AND CONNECTED ELEMENTS
LRFD Specification Sections A3.1c, J1.5, J1.6, J2.8, and M2.2 contain special material and fabrication requirements for ASTM A6 Groups 4 and 5 rolled shapes, shapes built-up from plates more than two inches thick, welded together to form the cross section, and shapes where the cross section is to be spliced by welding and subjected to primary tensile stress due to tension or flexure. These special requirements address notch toughness, access hole profiles, welding procedures, pre-heat, thermal cutting, grinding, and inspection requirements and are intended to minimize the possibility of cracking. The corresponding sections of the Commentary on the LRFD Specification provide further information, including alternative splice details and details for weld-access holes and beam copes. Intersecting Welds and Triaxial Stresses
If a stiffener were to be welded into and around the corner as it meets two elements of a shape (i.e., the flange and web of a column), the welding arc would take the path of least resistance to the three plates meeting at the corner and a lack of fusion or slag pocket would result in that corner. In addition to creating a discontinuity, this would add to the weld shrinkage strains in that corner. Corners of stiffeners, then, should be clipped generously to preclude this problem.
Susceptible Detail
Improved Detail Figure 8-32. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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In general, a 3⁄4-in. clip will be adequate. In small stiffeners, where such a clip would remove a large portion of the effective area of the stiffener, and in shapes, the radii of which require a clip in excess of 3⁄4-in., the clip dimension may be adjusted to suit conditions. For further information, see Butler, Pal, and Kulak (1972) and Blodgett (1980). Painting Welded Connections
Paint is normally omitted in areas to be field welded. LRFD Specification Section M3.5 requires that, unless otherwise provided in the plans and specifications, surfaces within two inches of any field weld shall be free of materials that would prevent proper welding or produce objectionable fumes during welding. Since little is gained by an exhaustive identification of the small areas involved, most fabricators prefer to use the general note, “No paint on OSL of connection angles,” where OSL stands for outstanding leg. This
Weak
Strong
Notch
Fig. 8-33. One-sided fillet weld results in a severe notch. A similar effect exists with a one-sided partial-penetration groove weld.
Fillet weld tacks can result in notches that reduce fatigue resistance.
tacks are incorporated in weld
(a) Susceptible Detail
(b) Improved Detail
Fig. 8-34. Backing bar tack welds. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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“no paint” requirement does not apply to shop welding where painting is normally done after the welds are made. Clearances for Welding
Clearances are required to allow the welder to make proper welds. In the SMAW process, for example, the welder must hold an electrode, about 3⁄8-in. in diameter and 14 inches to 18 inches long, in full control, and in such a position that the far end of the rod is in near contact with the base metal. This welder must observe the weld through a protective window of very dark glass in a bulky protective hood. Furthermore, the welder must keep control of the stiff electrical cable which powers the welding process. These conditions make welding difficult and it is imperative that other factors do not further hamper the welder. Ample room must be provided so that the welder or welding operator may manipulate the electrode and observe the weld as it is being deposited. The preferred position of the electrode when welding in the horizontal position is in a plane forming 30° with the vertical side of the fillet weld being made. However, this angle, shown as angle x in Figure 8-35, may be varied somewhat to avoid contact with some projecting part of the work. A simple rule which may be used to provide adequate clearance for the electrode in horizontal fillet welding is that the clear distance to a projecting element should be at least one-half its height; distance y / 2 in Figure 8-35b. A special case of minimum clearance for welding with a straight electrode is illustrated in Figure 8-36. The 20° angle is the minimum which will allow satisfactory welding along the bottom of the angle and therefore governs the setback with respect to the end of the beam. If a 1⁄2-in. setback and 3⁄8-in. electrode diameter were used, the clearance between the angle and the beam flange could be no less than 11⁄4-in. for an angle with a leg dimension w of three inches, nor less than 15⁄8-in. with a w of four inches. When it is not possible to provide this clearance, the end of the angle may be cut as noted by the optional cut in Figure 8-36 to allow the necessary angle. However, this secondary cut will increase the cost of fabricating the connection. Fillet Welds
In Figure 8-37a, fillet welds A are loaded in longitudinal shear and fillet weld B is loaded in transverse shear. If the force Ru is increased to exceed the strength of the welds, rupture will occur on the planes of least resistance. As shown in Figure 8-37b, this is assumed to take place in the weld throat where the least cross-sectional area is present. Tests of fillet welds using matching electrodes have demonstrated that the weld will fail through its effective throat before the material will fail along the weld leg. Fillet welds are approximately one-third stronger in the transverse direction than in the longitudinal direction. While this increased strength is ignored in LRFD Specification Section J2.4, the provisions of LRFD Specification Appendix J2.4 may be used to take advantage of this increased strength. Effective Area
The effective area of a fillet weld Aw is the product of the effective length of the fillet weld times the effective throat thickness of the fillet weld. The effective length l of the fillet weld is the overall length of the full-sized fillet weld. Except for fillet welds made with the SAW process, the effective throat thickness of the fillet weld is 0.707w, where w is the weld size. The deep penetration of fillet welds made by the SAW process is recognized in the LRFD Specification Section J2.2a wherein the effective throat thickAMERICAN INSTITUTE OF STEEL CONSTRUCTION
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ness is considered to be equal to the weld size for 3⁄8-in. and smaller welds, and equal to the effective throat thickness plus 0.11 in. for fillet welds sizes over 3⁄8-in. Minimum Effective Length
The minimum effective length of a fillet weld when used alone and not as a part of a continuing joint boundary (i.e., an end return or corner) must be greater than or equal to four times the nominal weld size. Thus, the shortest length of 5⁄16-in. fillet weld which is permitted to be considered to transmit load is 11⁄4-in. Conversely, regardless of the fillet-weld size used, the maximum effective size is limited to one-fourth the weld length. Intermittent fillet welds likewise are subject to this provision with the added requirement that the incremental length of weld must not be less than 11⁄2-in; refer to LRFD Specification Section J2.2b. Minimum Fillet Weld Size
When very small fillet-weld sizes are used, rapid cooling after welding creates internal stresses which, in turn, may lead to cracking of the weld. To preclude this, the minimum fillet-weld size is established in LRFD Specification Section J2.2b as a function of the thickness of the thicker of the parts joined. From this, if two 7⁄8-in. plates are joined, the minimum permissible fillet-weld size is 5⁄16-in., even if a 1⁄4-in. weld might provide adequate strength. Where different thicknesses are joined, the weld size need not exceed the thickness of the thinner part, unless a larger size is required for strength. If this is the case, adequate pre-heat must be provided to assure soundness of the weld. Maximum Fillet-Weld Size
The maximum fillet-weld size on the edge of the material is limited in LRFD Specification Section J2.2b to the thickness of the element for material less than 1⁄4-in. thick and 1⁄ -in. less than the thickness of the element for material greater than or equal to 1⁄ -in. 16 4 thick, unless the drawing is specially noted to build up the weld to achieve full throat size. This limitation recognizes that the exposed corner of the welded edge tends to melt Electrode x
END VIEW
PLAN VIEW
(a) y
Electrode A x
y /2
A PLAN VIEW
SECTION A-A (b)
Fig. 8-35. Clearances for welding. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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into the weld as illustrated in Figure 8-38, thereby reducing the leg dimension and the weld throat. Additionally, the toes of most rolled shapes do not have an ideal 90° corner. Thus the actual thickness of material at the weld is less than the nominal thickness t of the member. While the LRFD Specification permits the use of a larger weld size if the weld is built up to the full throat size, this is difficult to achieve. End Returns
LRFD Specification Section J2.2b gives requirements on when fillet weld terminations must be returned around ends or sides. This is illustrated in Figure 8-39. Weld returns reinforce the effective weld where it is most highly stressed and, thus, inhibit cracking and progressive tearing throughout the length of the weld. Thus, they are required in fatigue applications and for connections which assume flexibility exists in the connected part or parts (e.g., the support legs of a double angle connection). If welds are not returned, they must terminate not less than two times the nominal weld size from the sides or ends. Also, based upon LRFD Specification Section J2.2b, Figures 8-40 and 8-41 indicate examples where welds must be interrupted or should not be returned. In these instances, the welds, while in the same plane, lie on opposite sides of the contact surfaces. An attempt to weld around the corner will melt the corner material, creating a reduced thickness and notch. Furthermore, such welds cannot be made with a fully effective throat. Welding around such a corner should be avoided. It is not recommended that weld be applied in the gap at the end of the beam web between the heels of the angles, as this reduces the flexibility of the connection angles. Furthermore, the setback of the beam web is not a controlled dimension as it may be used to account for the tolerance in length of the beam and may vary from zero in. to 1⁄2-in. or
Setback
w
Optional cut
20° PLAN VIEW Electrode
45° to 50°
ELEVATION
END VIEW
Fig. 8-36. Clearances for welding. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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more. In any case, most beam webs are too thin for an effective minimum weld size to be applied along such an edge. Fillet Welds in Holes or Slots
The recommended minimum hole diameters or slot widths for fillet welding are shown in Table 8-35. It is important to distinguish between plug or slot welds and fillet welds placed around the inside of a hole or slot. In the case of such fillet welds, the shear strength is the product of the effective throat thickness and the weld length measured along the line bisecting the throat area. If this effective area should exceed the area of the hole or slot, it cannot be considered to be a fillet weld and must be designed as a plug or slot weld. Other Limitations on Fillet Welds
In concentrically loaded welded joints, the stresses are assumed to be uniformly distributed throughout the length of the welds. The design strength of a concentrically loaded fillet-weld group, then, is the sum of the design strengths of each weld in the group. LRFD Specification Section J1.8 provides that the center of gravity of a weld group should coincide with the gravity axis of an axially loaded member, or provision must be made for the resulting eccentricity. Certain welded members not subject to fatigue loading are excluded from this provision: “Eccentricity between gravity axes of such members…may be neglected in statically loaded members, but shall be considered in members subject to fatigue loading.” This provision permits very significant cost savings in weld material
Ru
Ru
Welds A Weld B
Ru
Ru (a)
(b)
t
1/16
t
1/16
Fig. 8-37. Fillet welds.
(a)
(b)
Figure 8-38. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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and labor in the fabrication and erection of such statically loaded members as roof and floor trusses, bracing, etc. Additionally, LRFD Specification Section J2.2b imposes other limitations on proportions of lap joints. Minimum Shelf Dimensions
In Figure 8-42, the recommended minimum shelf dimensions for normal size SMAW fillet welds are summarized. This dimension is critical to the deposition of the weld. SAW fillet welds would require a greater shelf dimension to contain the flux, although this is sometimes provided by clamping auxiliary material to the member. In Figure 8-43, the distance b must be large enough so that a full-size weld may be deposited on it. Select a gage that will permit enough clearance b to deposit an effective weld. The dimension b should be sufficient to accommodate the combined tolerances of the framing-angle length, the cope depth, and the beam mill over/underrun as well as the specified weld size. Complete-Joint-Penetration Groove Welds
Assuming compliance with LRFD Specification Section J2, the design strength of complete-joint-penetration groove welds is equal to that of the base metal in all respects. Therefore, no allowance for the presence of such welds need be made in proportioning the connections of structural members for any type of static loading. Where members are of unequal cross section or different material strength, the strength of the complete-jointpenetration groove weld is limited to the strength of the weaker member. Extension, Runoff, Backing, and Spacer Bars
When groove welds are used to splice plate girders and beams, LRFD Specification Section J7 requires that the splice be capable of developing the full strength of the smaller spliced section or 100 percent of the full section if the spliced sections are of the same size. To obtain a fully welded cross section, the termination at either end of the joint must Provide end returns having length = twice nominal weld size if subjected to cyclical (fatigue) loading or = four times nominal weld size if needed for connection flexibility. Otherwise, terminate welds not less than nominal weld size from ends with no end returns.
1
2 x nominal weld size
/4 for Pts. 1 1 for Pts. 2 2
5 /16
Note: Locations of Pts. 1 and Pts. 2 are shown on the erection diagram (not included).
Fig. 8-39. Weld returns. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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be of sound weld metal. Extension or runoff bars are usually used to assure the soundness of the end of the weld. Frequently, the joint will require a backing or spacer bar which can be extended to serve as the extension or runoff bar. Figure 8-44 demonstrates the application of extension, backing, and spacer bars in a splice or moment connection. Extension and backing bars should be of approved weldable material as specified in AWS D1.1, Section 8.2.4; spacer bars must be of the same material specification as the base metal. This can create a procurement problem since small tonnage requirements may make them difficult to obtain in the specified ASTM designation. Also indicated in Figure 8-44 is the use of a cover plate or seat angle for backing the weld.
Do not tie welds together here terminate welds 2 x nominal weld size from end.
Do not tie welds together here
Fig. 8-40. Fillet welds on opposite sides of a common plane should not be continuous. Do not return welds here terminate welds 2 x nominal weld size from end.
Fig. 8-41. Fillet welds should not be returned across thickness of material. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-35. Recommended Minimum Hole Diameters or Slot Widths for Fillet Welding, in. Plate Thickness, in. 3⁄
16
Min. Diameter or Width, in.
and 1⁄4
11⁄ 16 13⁄ 16 15⁄ 16 11⁄16 13⁄16 15⁄16
5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8
Shown in Figure 8-45 are flat-type extension bars, normally used with beveled grooves, and contour-type extension bars, normally used with J-grooves or U-grooves and shaped to follow the contour of the joint geometry. While the contour-type extension bar is shown as though it were comprised of two pieces, some fabricators might elect to mill the full contour in one piece and subsequently cut it to suit job requirements. AWS D1.1, Section 3.12 states that runoff and extension bars need not be removed in statically loaded structures unless required by the engineer of record (EOR). Such might be the case where these bars would create an interference with other work. In dynamically and cyclically loaded structures, however, they must be removed and the welds made smooth and flush to the base metal abutting edges.
Vertical or horizontal section
Fillet Weld Size (in.)
Min. Shelf Dim. (in.)
3
/16
7
1
1
5
9
3
5
7
11
1
3
/4
/16 /8 /16 /2
/16 /2
/16
/8 /16
/4
Fig. 8-42. Recommended minimum shelf dimensions for SMAW fillet welds. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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According to AWS D1.1, Section 3.13, backing bars on groove-welded joints must be fully spliced to avoid stress concentrations or discontinuities and should be thoroughly fused with the weld metal. It is further required on dynamically loaded structures that the backing bars be removed and the surfaces finished smooth when they are transverse to the direction of stress. If this were the case for the flange splice of Figure 8-44, removal of the backing bars would be required and, therefore, the splice might be made more economically with another joint profile. Weld Access Holes
The beam web is provided with an access hole or â&#x20AC;&#x153;ratholeâ&#x20AC;?, as illustrated in Figure 8-44, to permit down-hand welding to the backing bars located below both the top and bottom flanges. The weld-access hole also provides increased relief from concentrated weld shrinkage strains and prevents the intersection or close juncture of welds in orthogonal directions. Weld-access holes should not be filled with weld metal since it is difficult to provide sound weld metal to fill such a void and doing so may introduce a state of triaxial stress under loading. Partial-Joint-Penetration Groove Welds
b
b
b
Gage
Gage
Partial-joint-penetration groove welds are used primarily for welded compression splices, the connection of elements in heavy box sections and pedestals, and, in general, for joints where the stress to be transferred is substantially less than that which would require complete-joint-penetration groove welds. This type of weld is not, however, recom-
Figure 8-43 AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BOLTS, WELDS, AND CONNECTED ELEMENTS
1
t
Extension bars
/8 ″ Min.
w
L
W
8 - 126
Extension bars Backing bar Backing bar
Col.
Beam access hole
Access Hole
Seat angle
Spacer bar (when req’d)
Beam flange Overlapping cover plate Note: Extension bars should be at least ¼ ″ thick to reduce hazard of weld “blow through.” Figure 8-44 AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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mended in joints subject to dynamic or cyclical loading, except for joining the components of built-up members. Effective Area
The effective area of a partial-joint-penetration groove weld Aw is the product of the effective length of the weld times the effective throat thickness of the fillet weld. These quantities are determined as follows. The effective length is the width of the part joined. The effective throat thickness E is as determined from LRFD Specification Table J2.1, but not less than specified in LRFD Specification Table J2.3. Nomenclature of partial-joint-penetration welds is shown in Figure 8-46. Note that the effective throat thickness shown is less than the dimensioned groove-weld size. AWS prequalified partial-joint-penetration welds establish for each joint an effective throat E as a function of the material thickness, weld-preparation size, or depth S. Thus, the design drawings should specify the effective weld length and the required effective throat. The shop drawings should then show the groove depth S and geometry which will provide for the specified effective throat E. Some fabricators may indicate both the weld size and the effective throat on the shop drawings to eliminate confusion. The comments on “Extension, Runoff, Backing, and Spacer Bars” and “Weld Access Holes” for complete-joint-penetration groove welds also apply to partial-joint-penetration groove welds. Intermittent Welds
In preparing the joint profile for intermittent partial-joint-penetration groove welds, a transition or “faring-in” of the joint at beginning and termination must be provided to ensure proper fusion with the base metal. The nominal angular value of this transition should be 45°as shown in Figure 8-46. Flare Welds
A flare weld is a special case of the partial-joint-penetration groove weld wherein the convex surface of the connected part creates the joint preparation. This convexity may be the result of an edge preparation, but more often results when one (or both) joint component consists of a round rod or a shape with a rounded bend or corner radius created by bending or rolling as shown in Figure 8-47.
Extension bars Runout plate or backing bar extension
Figure 8-45. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BOLTS, WELDS, AND CONNECTED ELEMENTS
Effective Area
The effective area of a flare weld Aw is the product of the effective length of the weld times the effective throat thickness of the flare weld; the effective length is the width of the part joined and the effective throat thickness E is as determined from LRFD Specification Table J2.2. Limitations
The deposition of effective weld metal to the bottom of the flare groove is very difficult because the welding arc short-circuits across the surfaces due to the sharp angular slopes. Thus, the quality of this weld is difficult to control; LRFD Specification Section J2.1a permits examination and adjustment of the weld strength based on random testing and special qualification. Note that weldability of concrete reinforcing bars is not a part of ASTM specifications. In past experience, improperly welded concrete reinforcing bars have cracked and separated under no-load conditions. Typical deformed-type concrete reinforcing bars, such as ASTM A615, A616, and A617, are not produced to a controlled chemistry and their weldability must be carefully evaluated; refer to AWS D1.4. Plug and Slot Welds
The use of plug and slot welds for stress transfer is limited to resisting shear loads in joint planes parallel to the faying surfaces. These welds should not be subjected to tensile stresses and are limited when subjected to stress reversal. Furthermore, some specificaEffective A
Transition
length
T
S
E
45째 Min.
A
SECTION A-A
Fig. 8-46. Partial-joint-penetration groove weld nomenclature.
Flare-V-groove effective throat=R/2
R
R Flare-bevel groove effective throat = 5R/16
Fig. 8-47. Flare weld nomenclature. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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tions do not permit their use as load-carrying welds. Because of these limitations, plug and slot welds are more frequently employed as stitch welds rather than as a means of primary stress transfer. The effective area of a plug or slot weld Aw is the nominal cross-sectional area of the hole or slot. The proportions and spacing of holes and slots and the depth of weld are stipulated in LRFD Specification Section J2.3b and illustrated in Figure 8-48. Design Strength of Welds
The design strength of welds is determined in accordance with LRFD Specification Sections J2.2 and J2.4. LRFD Specification requirements are based upon the provisions of AWS D1.1, except as noted in LRFD Specification Section J2. For welds, the limit states of the weld-metal strength and the base-metal strength must be checked as applicable in LRFD Specification Table J2.5. These limit states assume that the matching electrode requirements of LRFD Specification Section J2.6 and Table J2.1 are met. Weld Metal Design Strength
From LRFD Specification Section J2.4, the weld metal design strength is φRn, where φ is a resistance factor from LRFD Specification Table J2.5 and: Rn = Fw Aw In the above equation, Fw = 0.60FEXX Aw = effective area of the weld, in.2 and φ is determined as follows: For a fillet weld loaded in shear on its effective area, φ = 0.75; For a complete-joint-penetration groove weld loaded in shear on its effective area, φ = 0.80; For a partial-joint-penetration groove weld loaded in shear parallel to the axis of the weld, φ = 0.75; For a partial-joint-penetration groove weld loaded in tension normal to the effective area, φ = 0.80; For a plug or slot weld loaded in shear on its effective area, φ = 0.75. Base Metal Design Strength
From LRFD Specification Section J2.4, the base metal design strength is φRn, where φ is a resistance factor from LRFD Specification Table J2.5 and: Rn = FBM ABM AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BOLTS, WELDS, AND CONNECTED ELEMENTS
In the above equation, ABM is the cross-sectional area of the base metal. For a fillet weld loaded in tension or compression parallel to the axis of the weld, φ = 0.90 FBM = Fy For a complete-joint-penetration groove weld loaded in tension or compression normal to its effective area, φ = 0.90 FBM = Fy For a complete-joint-penetration groove weld loaded in shear on its effective area, φ = 0.90 FBM = 0.60Fy d
l
l
R′
d
d
S′
t
W
W
W
S
W
S
R
Plate thickness, in. 3/16 & 1/4
Min. hole dia. or slot width, d, in. 9/16
5/16 & 3/8
11/16
7/16 & 1/2
13/16
9/16 & 5/8
15/16
Hole and slot proportions, spacing and depth of weld d ≥ (t + 5/16), round to next higher odd 1/16; also d ≤ 2 1/4W S ≥ 4d S ′≥ 2 l l ≤ 10W R = d/2 R≥t
Where t ≤ 5/8, W = t Where t > 5/8, W = t/2 but, not less than 5/8
Fig. 8-48. Plug and slot welds. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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For a partial-joint-penetration groove weld loaded in tension or compression normal to its effective area or tension or compression parallel to the axis of the weld, φ = 0.90 FBM = Fy Prequalified Welded Joints
AWS D1.1 contains provisions for prequalified welded joints which provide joint geometries, such as root openings, angles, and clearances, as illustrated in Figures 8-49 and 8-50, that will permit a qualified welder to deposit sound weld material. Thus, prequalified joints are concerned almost exclusively with the welding process as a method of joining metal and deal with welded joints only from fusion boundary to fusion boundary. The designer must satisfy all provisions of AWS D1.1 Sections 2, 3, and 4 before a joint is considered prequalified. Prequalified welded joints are not, in themselves, adequate consideration of welded design details. To emphasize this, the AWS D1.1 Section 1.1 states: “…The use of prequalified joints is not intended as a substitute for engineering judgment with respect to the suitability of application of these joints to a weld assembly.” The design and detailing for successful welded construction requires consideration of factors which include, but are not limited to, the magnitude, type, and distribution of forces to be transmitted, access, restraint against weld shrinkage, thickness of connected materials, residual stress, and distortion. Accordingly, the design and detailing must also satisfy the requirements of LRFD Specification Section J2. The prequalified welded joints in Table 8-36 meet the requirements of the 1992 version of AWS D1.1 as well as the 1993 LRFD Specification. Because AWS D1.1 is revised every other year, designers and fabricators should verify this information with the latest issue of AWS D1.1. The designations such as B-L1a, B-U2, and B-P3 are those used in AWS standards. Note that lowercase letters, e.g., a, b, c, etc., are often used to differentiate between joints that would otherwise have the same joint designation. These prequalified welded joints are limited to those made by the SMAW, SAW, GMAW (except short circuit transfer), and FCAW procedures. Small deviations from dimensions, angles of grooves, and variation in depth of groove joints are permissible within the tolerances given. In general, all fillet welds, whether illustrated or not, are prequalified, provided they conform to the requirements of AWS D1.1. Groove welds are classified using the conventions indicated in the tables. Welded joints other than those prequalified by AWS may be qualified, provided they are tested and qualified in accordance with AWS D1.1.
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BOLTS, WELDS, AND CONNECTED ELEMENTS
ctive Effe ength dL Wel
Weld face Throat area (shaded)
45째
45째
t line
e
tiv
Roo
c ffe
E Leg size
h
gt
d
el
n le
/12 N o Th rma r o Siz at l e
W al rm at o N ro Th ze Si
Root
Size 135째 max.
60째 min.
Penetration
t
roa
Th
t
oa
r Th
t oa
r
Th
Normal Throat Size
p
e De
CONVEX
n tio e tra iz ne t S Pe hroa T
al e rm Siz No at ro Th Fig. 8-49. Fillet weld nomenclature. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONCAVE
WELDED CONSTRUCTION
Groove face
8 - 133
Groove (and bevel) angle
Groove angle Bevel angle
Groove radius
Root
Root opening
Spacer bar
Root Root Root face opening
Backing bar
Root opening
PREPARATION Penetration (fusion zone)
Weld face
Root Backing bead
Weld size
Reinforcement
Weld throat= Weld size
Root opening
0
Root face
PARTIAL-JOINT-PENETRATION
COMPLETE-JOINT-PENETRATION
Groove size Root face
Groove angle Fillet size
1/8
Effective throat
Eff. at thro
PARTIAL-JOINT-PENETRATION (When Reinforcing Fillet is Specified) Fig. 8-50. Groove weld nomenclature. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-36. Prequalified Welded Joints Symbols for Joint Types B C T
butt joint corner joint T-joint
L U P
limited thickness, complete-joint-penetration unlimited thickness, complete-joint-penetration partial-joint-penetration
1 2 3 4 5
square-groove single-V-groove double-V-groove single-bevel-groove double-bevel-groove
S G F
submerged arc welding SAW gas metal arc welding GMAW flux cored arc welding FCAW
BC butt or corner joint TC T- or corner joint BTC butt, T-, or corner joint
Symbols for Base Metal Thickness and Penetration
Symbols for Weld Types 6 7 8 9 10
single-U-groove double-U-groove single-J-groove double-J-groove Flare-bevel-groove
Symbols for Welding Processes if not Shielded Metal Arc welding (SMAW):
Symbols for Welding Positions F flat H horizontal V vertical OH overhead The lower case letters, e.g., a, b, c, d, etc., are used to differentiate between joints that would otherwise have the same joint designation.
Notes to Prequalified Welded Joints A B Br C E J
J2 L M Mp N
Q Q2 R
V
Not prequalified for GMAW using short circuiting transfer. Refer to AWS D1.1 Appendix A. Joints welded from one side only. Bridge applications limit the use of these joints to the horizontal position. Refer to AWS D1.1 Section 9.12.5. Back gouge root to sound metal before welding second side. Minimum effective throat (E) as shown in LRFD Specification Table J2.3; S as specified on drawings. If fillet welds are used in buildings to reinforce groove welds in corner and T-joints, they shall be equal to 1 ⁄4 T 1 , but need not exceed 3 ⁄8 -in. Groove welds in corner and T-joints in bridges shall be reinforced with fillet welds equal to 1 ⁄4 T 1 , but not more than 3 ⁄8 -in. If fillet welds are used in buildings to reinforce groove welds in corner and T-joints, they shall be equal to 1 ⁄4 T 1 , but not more than 3 ⁄8 -in. Butt and T-joints are not prequalified for bridges. Double-groove welds may have grooves of unequal depth, but the depth of the shallower groove shall be not less than one-fourth of the thickness of the thinner part joined. Double-groove welds may have grooves of unequal depth, provided they conform to the limitations of Note E. Also, the effective throat (E), less any reduction, applies individually to each groove. The orientation of the two members in the joints may vary from 135° to 180°, provided the basic joint configuration (groove angle, root face, root opening) remains the same and the design throat thickness is maintained. For corner and T-joints, the member orientation may be changed provided the groove dimensions are maintained as specified. The member orientation may be changed provided the groove dimensions are maintained as specified. The orientation of two members in the joint may vary from 45° to 135° for corner joints and from 45° to 90° for T-joints, provided the basic joint configuration (groove angle, root face, root opening) remains the same and the design throat thickness is maintained. For corner joints, the ouside groove preparation may be in either or both members, provided the basic groove configuration is not changed and adequate edge distance is maintained to support the welding operations without excessive edge melting.
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Table 8-36 (cont.). Prequalified Welded Joints Basic Weld Symbols
Back
Groove or Butt
Plug or Slot
Fillet
Square
V
Bevel
U
J
Flare Bevel
Flare V
Supplementary Weld Symbols
Backing
Weld All Around
Spacer
Contour Field Weld
Flush
Convex
For other basic and supplementary weld symbols, see AWS A2.4
Standard Location of Elements of a Welding Symbol Finish symbol
Groove angle or included angle or countersink for plug welds
Contour symbol Root opening, depth of filling for plug and slot welds
Length of weld in inches
Effective throat
Pitch (c. to c. spacing) of welds in inches
F
Depth of preparation or size in inches
A
S(E)
sides)
R
Specification, process, or other reference
(Both
T
Tail (omitted when reference is not used)
Field weld symbol
(Arrow (Other side ) side )
Reference line
Weld-all-around symbol
@P
Elements in this area remain as shown when tail and arrow are reversed.
Basic weld symbol or detail reference
A
B
Arrow connects reference line to arrow side of joint. Use break as at A or B to signify that arrow is pointing to the grooved member in bevel or J-grooved joints.
Note: Size, weld symbol, length of weld, and spacing must read in that order, from left to right, along the reference line. Neither orientation of reference nor location of the arrow alters this rule. The perpendicular leg of
,
,
,
, weld symbols must be at left.
Arrow and other side welds are of the same size unless otherwise shown. Dimensions of fillet welds must be shown on both the arrow side and the other side symbol. The point of the field weld symbol must point toward the tail. Symbols apply between abrupt changes in direction of welding unless governed by the ‘‘all around’’ symbol or otherwise dimensioned. These symbols do not explicitly provide for the case that frequently occurs in structural work, where duplicate material (such as stiffeners) occurs on the far side of a web or gusset plate. The fabricating industry has adopted this convention: that when the billing of the detail material discloses the existence of a member on the far side as well as on the near side, the welding shown for the near side shall be duplicated on the far side.
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BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-36 (cont.). Prequalified Welded Joints Fillet Welds
Notes: 1. En, En′ = effective throats dependent on magnitude of root opening Rn. See AWS D1.1 Section 3.3.1 Subscript n represents 1, 2, 3, or 4. 2. t = thickness of thinner part. 3. Not prequalified for gas metal arc welding using short circuitry transfer. Refer to AWS D1.1. 4. Part (f), apply Z loss factor of AWS D1.1 Table 2.4 to determine effective thrust. 5. Part (f), not prequalified for angles under 30°°. For welder qualfications, see AWS D1.1 Table 10.5, Column 10. *Angles smaller than 60°° are permissible, however, if the weld is considered to be a partial-joint-penetration groove weld.
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Table 8-36 (cont.). Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Square-groove weld (1) Butt joint (B) Corner Joint (C)
Welding Process
Joint Designation
SMAW
B-L1a
GMAW FCAW
Base Metal Thickness (U = unlimited)
Groove Preparation Tolerances
Gas Shielding for (FCAW)
T1
T2
Root Opening
As Detailed
As Fit Up
Permitted Welding Positions
1 ⁄4
max
—
R = T1
+ 1 ⁄16 , −0
+ 1 ⁄4 , − 1 ⁄16
All
—
N
C-L1a
1 ⁄4
max
U
R = T1
+ 1 ⁄16 , −0
+ 1 ⁄4 , − 1 ⁄16
All
—
—
B-L1a-GF
3 ⁄8
max
—
R = T1
+ 1 ⁄16 , −0
+ 1 ⁄4 , − 1 ⁄16
All
Not Required
A, N
Notes
Square-groove weld (1) Butt joint (B)
Base Metal Thickness (U = unlimited)
Welding Process
Joint Designation
SMAW
B-L1b
1 ⁄4
GMAW FCAW
B-L1b-GF
SAW SAW
Groove Preparation Tolerances
Gas Shielding for (FCAW)
T1
T2
Root Opening
As Detailed
As Fit Up
Permitted Welding Positions
max
—
R = T1 / 2
+ 1 ⁄16 , −0
+ 1 ⁄6 , − 1 ⁄8
All
—
C, N
3 ⁄8
max
—
R = 0 to 1 ⁄8
+ 1 ⁄16 ,
+ 1 ⁄6 ,
− 1 ⁄8
All
Not Required
A, C, N
B-L1-S
3 ⁄8
max
—
R=0
±0
+ 1 ⁄16 , −0
F
—
N
B-L1a-S
5 ⁄8
max
—
R=0
±0
+ 1 ⁄16 , −0
F
—
C, N
Gas Shielding for (FCAW)
Notes
−0
Notes
Square-groove weld (1) T-joint (T) Corner joint (C)
Welding Process
Joint Designation
SMAW
TC-L1b
GMAW FCAW SAW
Base Metal Thickness (U = unlimited)
Groove Preparation Tolerances
T1
T2
Root Opening
As Detailed
As Fit Up
Permitted Welding Positions
1 ⁄4
max
U
R = T1 / 2
+ 1 ⁄16 , −0
+ 1 ⁄16 , − 1 ⁄8
All
—
C, J
TC-L1-GF
3 ⁄8
max
U
R = 0 to 1 ⁄8
+ 1 ⁄16 , −0
+ 1 ⁄16 , − 1 ⁄8
All
Not Required
A, C, J
TC-L1-S
3 ⁄8
max
U
R=0
±0
+ 1 ⁄16 , −0
F
—
J, C
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BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-36 (cont.). Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Single-V-groove weld (2) Butt joint (B)
Welding Process
Joint Designation
SMAW
B-U2a
GMAW FCAW
B-U2a-GF
Tolerances
Base Metal Thickness (U = unlimited)
As Detailed
As Fit Up
R = +1 ⁄16 , −0
+ 1 ⁄4 , − 1⁄16
α = +10°°, − 0°°
+10°°, − 5°°
Groove Preparation
Gas Shielding for FCAW
Notes
T1
T2
Root Opening
Groove Angle
Permitted Welding Positions
U
—
R = 1 ⁄4
α = 45°°
All
—
N
R = 3 ⁄8
α = 30°°
F, V, OH
—
N
R = 1 ⁄2
α = 20°°
F, V, OH
—
N
R = 3 ⁄16
α = 30°°
F, V, OH
Required
A, N
R = 3 ⁄8
α = 30°°
F, V, OH
Not req.
A, N
R = 1 ⁄4
α = 45°°
F, V, OH
Not req.
A, N
U
—
SAW
B-L2a-S
2 max
—
R = 1 ⁄4
α = 30°°
F
—
N
SAW
B-U2-S
U
—
R = 5 ⁄8
α = 20°°
F
—
N
Tolerances
Single-V-groove weld (2) Corner joint (C)
Welding Process
Joint Designation
SMAW
C-U2a
Base Metal Thickness (U = unlimited)
As Detailed
As Fit Up
R = +1 ⁄16 , −0
+ 1 ⁄4 , − 1⁄16
α = +10°°, − 0°°
+10°°, − 5°°
Groove Preparation
Gas Shielding for FCAW
Notes
T1
T2
Root Opening
Groove Angle
Permitted Welding Positions
U
U
R = 1 ⁄4
α = 45°°
All
—
Q
R = 3 ⁄8
α = 30°°
F, V, OH
—
Q
R = 1 ⁄2
α = 20°°
F, V, OH
—
Q
R = 3 ⁄16
α = 30°°
F, V, OH
Required
A
R = 3 ⁄8
α = 30°°
F, V, OH
Not req.
A, Q
GMAW FCAW
C-U2a-GF
U
U
R = 1 ⁄4
α = 45°°
F, V, OH
Not req.
A, Q
SAW
C-L2a-S
2 max
U
R = 1 ⁄4
α = 30°°
F
—
Q
SAW
C-U2-S
U
U
R = 5 ⁄8
α = 20°°
F
—
Q
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Table 8-36 (cont.). Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Single-V-groove weld (2) Butt joint (B)
Welding Process
Joint Designation
SMAW
Base Metal Thickness (U = unlimited)
Groove Preparation Tolerances
Root Opening Root Face Groove Angle
As Detailed
As Fit Up
Gas Permitted Shielding Welding for Positions Notes FCAW
T1
T2
B-U2
U
—
R = 0 to 1⁄8 f = 0 to 1 ⁄8 α = 60°°
+1 ⁄16 , − 0 +1 ⁄16 , − 0 +10°°, − 0°°
+1 ⁄16 , − 1 ⁄8 Not limited +10°°, − 5°°
All
—
C, N
GMAW FCAW
B-U2-GF
U
—
R = 0 to 1⁄8 f = 0 to 1 ⁄8 α = 60°°
+1 ⁄16 , − 0 +1 ⁄16 , − 0 +10°, − 0°°
+1 ⁄16 , −1 ⁄8 Not limited +10°, − 5°°
All
Not required
A, C, N
SAW
B-L2c-S
Over 1 ⁄2 to 1
—
R = 0, α = 60°° f = 1 ⁄4 max
R = ±0 f = +0, − f α = +10°°, − 0°°
+1 ⁄16 , − 0
F
—
C, N
Over 1 to 11 ⁄2
—
R = 0, α = 60°° f = 1 ⁄2 max
Over 11 ⁄2 to 2
—
R = 0, α = 60°° f = 5 ⁄8 max
± 1 ⁄16 +10°°, − 5°°
Single-V-groove weld (2) Corner joint (C)
Welding Process
Joint Designation
SMAW
Base Metal Thickness (U = unlimited)
Groove Preparation Tolerances
Root Opening Root Face Groove Angle
As Detailed
As Fit Up
Gas Permitted Shielding Welding for Positions FCAW Notes
T1
T2
C-U2
U
U
R = 0 to 1 ⁄8 f = 0 to 1 ⁄8 α = 60°°
+1 ⁄16 , − 0 +1 ⁄16 , − 0 +10°°, − 0°°
+1 ⁄16 , − 1 ⁄8 Not limited +10°°, − 5°°
All
—
C, J, R
GMAW FCAW
C-U2-GF
U
U
R = 0 to 1 ⁄8 f = 0 to 1 ⁄8 α = 60°°
+1 ⁄16 , − 0 +1 ⁄16 , − 0 +10°, − 0°°
+1 ⁄16 , −1⁄8 Not limited +10°°, − 5°°
All
Not required
A, C, J, R
SAW
C-L2b-S
U
U
R=0 f = 1 ⁄4 max α = 60°°
±0 +0, − 1 ⁄4 +10° − 0°
+1 ⁄16 , − 0
F
—
C, J, R
± 1 ⁄16 +10°°, − 5°°
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 140
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-36 (cont.). Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Tolerances
Double-V-groove weld (3) Butt joint (B)
Welding Process SMAW
B-U3a
SAW
B-U3a-S
Base Metal Thickness (U = unlimited)
As Fit Up
R = ±0
+ 1 ⁄4 , −0
f = ±0
+1 ⁄16 , − 0
α = +10°°, − 0°°
+10°°, − 5°°
SAW
±0
+1 ⁄16 , − 0
SMAW
±0
+1 ⁄8 , − 0
Spacer
Joint Designation
As Detailed
Groove Preparation
Gas Permitted Shielding Welding for Positions (FCAW) Notes
T1
T2
Root Opening
Root Face
Groove Angle
U Spacer = 1 ⁄8 × R
—
R = 1 ⁄4
f = 0 to 1 ⁄8
α = 45°°
All
—
R = 3 ⁄8
f = 0 to 1 ⁄8
α = 30°°
F, V, OH
—
R = 1 ⁄2
f = 0 to 1 ⁄8
α = 20°°
F, V, OH
—
U Spacer = 1 ⁄4 × R
—
R = 5 ⁄8
f = 0 to 1 ⁄4
α = 20°°
F
—
C, M, N
C, M, N
Double-V-groove weld (3) Butt joint (B) For B-U3c-S only T1
Over 2 21 ⁄ 2 3 35 ⁄ 8 4 43 ⁄ 4 51 ⁄ 2
S1
to 21 ⁄2 3 35 ⁄8 4 43 ⁄4 51 ⁄2 61 ⁄4
13 ⁄8 13 ⁄4 21 ⁄8 23 ⁄8 23 ⁄4 31 ⁄4 33 ⁄4
For T 1 > 61⁄4, or T 1 ≤ 2 S 1 = 2 ⁄3 ( T 1 − 1 ⁄4 )
Welding Process
Joint Designation
SMAW
B-U3b
GMAW FCAW
B-U3-GF
SAW
B-U3c-S
Base Metal Thickness (U = unlimited) T1
T2
U
—
U
—
Groove Preparation Tolerances
Gas Permitted Shielding Welding for Positions FCAW
Root Opening Root Face Groove Angle
As Detailed
As Fit Up
R = 0 to 1 ⁄8 f = 0 to 1 ⁄8 α = β = 60°°
+1 ⁄16 , − 0 +1 ⁄16 , − 0 +10°°, − 0°°
+1 ⁄16 , − 1 ⁄8 Not limited +10°°, − 5°°
All
—
C, M, N
All
Not required
A, C, M, N
R=0 f = 1 ⁄4 min α = β = 60°°
+1 ⁄16 , − 0 +1 ⁄4 , − 0 +10°, − 0°°
+1 ⁄16 , − 0 +1 ⁄4 , − 0 +10°, − 5°°
F
—
C, M, N
To find S 1 see table above; S 2 = T 1 − (S 1 + f )
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Notes
WELDED CONSTRUCTION
8 - 141
Table 8-36 (cont.). Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Tolerances
Single-bevel-groove weld (4) Butt joint (B)
Welding Process
Joint Designation
SMAW
B-U4a
GMAW FCAW
Base Metal Thickness (U = unlimited)
B-U4a-GF
Welding Process SMAW
GMAW FCAW
SAW
As Fit Up
R = +1 ⁄16, − 0
+ 1 ⁄4 , − 1⁄16
α = +10°°, − 0°°
+10°°, − 5°°
Groove Preparation
Gas Shielding for FCAW
Notes Br, N
T1
T2
Root Opening
Groove Angle
Permitted Welding Positions
U
—
R = 1 ⁄4
α = 45°°
All
—
R = 3 ⁄8
α = 30°°
All
—
Br, N
R = 3 ⁄16
α = 30°°
All
Required
A, Br, N
R = 1 ⁄4
α = 45°°
All
Not req.
A, Br, N
R = 3 ⁄8
α = 30°°
F
Not req.
A, Br, N
U
—
Tolerances
Single-bevel-groove weld (4) T-joint (T) Corner joint (C)
Joint Designation
As Detailed
Base Metal Thickness (U = unlimited)
As Detailed
As Fit Up
R = +1 ⁄16, − 0
+ 1 ⁄4 , − 1⁄16
α = +10°°, − 0°°
+10°°, − 5°°
Groove Preparation
Gas Shielding for FCAW
Notes
—
J, Q, V
T1
T2
Root Opening
Groove Angle
Permitted Welding Positions
TC-U4a
U
U
R = 1 ⁄4
α = 45°°
All
R = 3 ⁄8
α = 30°°
F, V, OH
—
J, Q, V
TC-U4a-GF
U
U
R = 3 ⁄16
α = 30°°
All
Required
A, J, Q, V
R = 3 ⁄8
α = 30°°
F
Not req.
A, J, Q, V
R = 1 ⁄4
α = 45°°
All
Not req.
A, J, Q, V
R = 3 ⁄8
α = 30°°
F
—
J, Q, V
R = 1 ⁄4
α = 45°°
TC-U4a-S
U
U
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 142
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-36 (cont.). Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Single-bevel-groove weld (4) Butt joint (B)
Base Groove Preparation Metal Thickness Tolerances (U = unlimited) Root Opening As As Fit Root Face T1 T2 Groove Angle Detailed Up
Welding Process
Joint Designation
SMAW
B-U4b
U
—
GMAW FCAW
B-U4b-GF
U
—
R = 0 to 1 ⁄8 f = 0 to 1 ⁄8 α = 45°°
+1 ⁄16 , − 0 +1 ⁄16 , − 0 +10°°, − 0°°
+1 ⁄16 , − 1⁄8 Not limited +10°°, − 5°°
Permitted Welding Positions
Gas Shielding for FCAW
Notes
All
—
Br, C, N
All
Not required
A, Br, C, N
Single-bevel-groove weld (4) T-joint (T) Corner joint (C)
Base Groove Preparation Metal Thickness Tolerances (U = unlimited) Root Opening As As Fit Root Face T1 T2 Up Groove Angle Detailed
Welding Process
Joint Designation
SMAW
TC-U4b
U
U
GMAW FCAW
TC-U4b-GF
U
U
SAW
TC-U4b-S
U
U
Gas Permitted Shielding Welding for Positions FCAW
Notes
R = 0 to 1 ⁄8 f = 0 to 1 ⁄8 α = 45°°
+1 ⁄16 , − 0 +1 ⁄16 , − 0 +10°°, − 0°°
+1 ⁄16 , − 1 ⁄8 Not limited +10°°, − 5°°
All
—
C, J, R, V
All
Not required
A, C, J, R, V
R=0 f = 1 ⁄4 max α = 60°
±0 +0, − 1 ⁄8 +10°, − 0°
+1 ⁄4 , − 0
F
—
C, J, R, V
± 1⁄16 +10°, − 5°
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
WELDED CONSTRUCTION
8 - 143
Table 8-36 (cont.). Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Tolerances
Double-bevel-groove weld (5) Butt joint (B) T-joint (T) Corner joint (C)
Welding Process SMAW
Base Metal Thickness (U = unlimited)
Groove Preparation
As Fit Up
R = ±0
+ 1 ⁄4 , −0
f = 1 ⁄16 , − 0
± 1 ⁄16
α = +10°°, − 0°°
+10°, − 5°°
+1⁄16 , − 0
+1 ⁄8 , − 0
Spacer
Joint Designation
As Detailed
Gas Permitted Shielding Welding for Positions FCAW
T1
T2
Root Opening
Root Face
Groove Angle
B-U5b
U Spacer =1⁄8 × R
U
R = 1 ⁄4
f = 0 to 1 ⁄8
α = 45°°
All
—
Br, C, M, N
TC-U5a
U Spacer =1⁄4 × R
U
R = 1 ⁄4
f = 0 to 1 ⁄8
α = 45°°
All
—
C, J, M, R, V
R = 3 ⁄8
f = 0 to 1 ⁄8
α = 30°°
F, OH
—
C, J, M, R, V
Notes
Double-bevel-groove weld (5) Butt joint (B)
Base Groove Preparation Metal Thickness (U = unlimited) Root Opening Tolerances Joint As As Fit Welding DesigRoot Face T1 T2 Groove Angle Detailed Up Process nation SMAW
B-U5a
GMAW B-U5-GF FCAW
Gas Permitted Shielding Welding for Positions FCAW Notes
U
—
R = 0 to 1 ⁄8 f = 0 to 1⁄8 α = 45°° β = 0°° to 15°°
+1 ⁄16 , − 0 +1 ⁄16 , − 1⁄8 Not limited +1 ⁄16 , − 0 α + β , +10°°, − 0° α + β , +10°°, − 5°
All
—
Br, C, M, N
U
—
R = 0 to 1 ⁄8 f = 0 to 1⁄8 α = 45°° β = 0°° to 15°
+1 ⁄16 , − 0 +1 ⁄16 , − 0 α + β = +10°°, − 0°
All
Not req.
A, Br, C, M, N
+1 ⁄16 , − 1⁄8 Not limited α + β = +10°°, − 5°
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 144
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-36 (cont.). Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Double-bevel-groove weld (5) T-joint (T) Corner joint (C)
Welding Process
Joint Designation
SMAW
TC-U5b
GMAW TC-U5-GF FCAW SAW
TC-U5-S
Base Groove Preparation Metal Thickness Tolerances (U = unlimited) Root Opening As As Fit Root Face T1 T2 Groove Angle Detailed Up U
U
U
U
U
U
Permitted Welding Positions
Gas Shielding for (FCAW)
Notes
R = 0 to 1⁄8 f = 0 to 1 ⁄8 α = 45°
+1 ⁄16 , − 0 +1 ⁄16 , − 0 +10°°, − 0°
+1 ⁄16 , − 1 ⁄8 Not limited +10°°, − 5°
All
—
C, J, M, R, V
All
Not req.
A, C, J, M, R, V
R=0 f = 3 ⁄16 max α = 60°
±0 +0, − 3 ⁄16 +10°°, − 0°
+1 ⁄16 , − 0
F
—
C, J, M, R, V
± 1 ⁄16 +10°°, − 5°
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
WELDED CONSTRUCTION
8 - 145
Table 8-36 (cont.). Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Tolerances
Single-U-groove weld (6) Butt joint (B) Corner joint (C)
Welding Process
Joint Designation
SMAW
B-U6
GMAW FCAW
Base Metal Thickness (U = unlimited)
As Detailed
As Fit Up
R = +1 ⁄16, − 0
+ 1 ⁄16 , − 1⁄8
α = +10°°, − 0°°
+10°°, − 5°°
f = ± 1 ⁄16
Not limited
r = +1 ⁄8 , − 0
+1 ⁄8 , − 0
Groove Preparation Gas Shielding for FCAW
Notes C, N
T1
T2
Root Opening
Groove Angle
Root Face
Groove Radius
Permitted Welding Positions
U
U
R = 0 to 1 ⁄8
α = 45°°
f = 1 ⁄8
r = 1 ⁄4
All
—
R = 0 to 1 ⁄8
α = 20°°
f = 1 ⁄8
r = 1 ⁄4
F, OH
—
C, N
R = 0 to 1 ⁄8
α = 45°°
f = 1 ⁄8
r = 1 ⁄4
All
—
C, J, R
C-U6
U
U
R = 0 to 1 ⁄8
α = 20°°
f = 1 ⁄8
r = 1 ⁄4
F, OH
—
C, J, R
B-U6-GF
U
U
R = 0 to 1 ⁄8
α = 20°°
f = 1 ⁄8
r = 1 ⁄4
All
Not req.
A, C, N
C-U6-GF
U
U
R = 0 to 1 ⁄8
α = 20°°
f = 1 ⁄8
r = 1 ⁄4
All
Not req.
A, C, J, R
Double-U-groove weld (7) Butt joint (B)
Welding Process
Joint Designation
SMAW
Base Metal Thickness (U = unlimited) T1
T2
B-U7
U
—
GMAW FCAW
B-U7-GF
U
—
SAW
B-U7-S
U
—
Tolerances
Tolerances
For B-U7 and B-U7-GF
For B-U7-S
As Detailed
As Fit Up
R = +1 ⁄16, − 0
+ 1 ⁄16 , − 1⁄8
R = ±0
+ 1 ⁄16 , − 0
+10°°, − 5°°
α = +0°°, − 1 ⁄4 °
± 1 ⁄16
f = ± 1 ⁄16 , − 0
Not limited
r = +1 ⁄4 , − 0
± 1 ⁄16
Gas Permitted Shielding Groove Welding for Radius Positions FCAW
Groove Angle
Root Face
R = 0 to 1 ⁄8 α = 45°°
f = 1 ⁄8
r = 1 ⁄4
All
R = 0 to 1 ⁄8 α = 20°°
f = 1 ⁄8
r = 1 ⁄4
R = 0 to 1 ⁄8 α = 20°°
f = 1 ⁄8
r = 1 ⁄4 r = 1 ⁄4
R=0
As Fit Up
α = +10°°, − 0°°
Groove Preparation Root Opening
As Detailed
α = 20°° f = 1 ⁄4 max
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Notes
—
C, M, N
F, OH
—
C, M, N
All
Not required
A, C, M, N
F
—
C, M, N
8 - 146
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-36 (cont.). Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Tolerances
Single-J-groove weld (8) Butt joint (B)
Welding Process
Joint Designation
SMAW GMAW FCAW
Base Metal Thickness (U = unlimited)
As Detailed
As Fit Up
R = +1 ⁄16, − 0
+ 1 ⁄16 , − 1⁄8
α = +10°°, − 0°°
+10°°, − 5°°
f = ± 1 ⁄16 , − 0
Not limited
r = +1 ⁄4 , − 0
± 1 ⁄16
Groove Preparation Permitted Groove Welding Radius Positions
Notes
T1
T2
Root Opening
Groove Angle
Root Face
B-U8
U
—
R = 0 to 1 ⁄8
α = 45°°
f = 1 ⁄8
r = 3 ⁄8
All
—
Br, C, N
B-U8-GF
U
—
R = 0 to 1 ⁄8
α = 30°°
f = 1 ⁄8
r = 3 ⁄8
All
Not required
A, Br, C, N
Tolerances
Single-J-groove weld (8) T-joint (T) Corner joint (C)
Welding Process
Joint Designation
SMAW
TC-U8a
GMAW FCAW
Gas Shielding for FCAW
TC-U8a-GF
Base Metal Thickness (U = unlimited)
Groove Preparation
As Detailed
As Fit Up
R = +1 ⁄16, − 0
+ 1 ⁄16 , − 1⁄8
α = +10°°, − 0°°
+10°°, − 5°°
f = ± 1 ⁄16 , − 0
Not limited
r = +1 ⁄4 , − 0
± 1 ⁄16
Gas Permitted Shielding Groove Welding for Radius Positions FCAW
T1
T2
Root Opening
Groove Angle
Root Face
U
U
R = 0 to 1 ⁄8
α = 45°°
f = 1 ⁄8
r = 3 ⁄8
All
—
C, J, R, V
R = 0 to 1 ⁄8
α = 30°°
f = 1 ⁄8
r = 3 ⁄8
F, OH
—
C, J, R, V
R = 0 to 1 ⁄8
α = 30°°
f = 1 ⁄8
r = 3 ⁄8
All
Not required
A, C, J, R, V
U
U
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Notes
WELDED CONSTRUCTION
8 - 147
Table 8-36 (cont.). Prequalified Welded Joints Complete-Joint-Penetration Groove Welds Tolerances
Double-J-groove weld (9) Butt joint (B)
Welding Process
Joint Designation
SMAW GMAW FCAW
Base Metal Thickness (U = unlimited)
As Detailed
As Fit Up
R = +1 ⁄16, − 0
+ 1 ⁄16 , − 1⁄8
α = +10°°, − 0°°
+10°°, − 5°°
f = ± 1 ⁄16 , − 0
Not limited
r = +1 ⁄8 , − 0
± 1 ⁄16
Groove Preparation Permitted Groove Welding Radius Positions
T1
T2
Root Opening
Groove Angle
Root Face
B-U9
U
—
R = 0 to 1 ⁄8
α = 45°°
f = 1 ⁄8
r = 3 ⁄8
All
—
Br, C, M, N
B-U9-GF
U
—
R = 0 to 1 ⁄8
α = 30°°
f = 1 ⁄8
r = 3 ⁄8
All
Not required
A, Br, C, M, N
Welding Process
Joint Designation
SMAW
TC-U9a
TC-U9a-GF
Notes
Tolerances
Double-J-groove weld (9) T-joint (T) Corner joint (C)
GMAW FCAW
Gas Shielding for FCAW
Base Metal Thickness (U = unlimited)
Groove Preparation
As Detailed
As Fit Up
R = +1 ⁄16, − 0
+ 1 ⁄16 , − 1⁄8
α = +10°°, − 0°°
+10°°, − 5°°
f = +1 ⁄16 , − 0
Not limited
r = +1 ⁄8 , − 0
± 1 ⁄16
Gas Permitted Shielding Groove Welding for Radius Positions FCAW
T1
T2
Root Opening
Groove Angle
Root Face
U
U
R = 0 to 1⁄8
α = 45°°
f = 1 ⁄8
r = 3 ⁄8
All
—
C, J, M, R, V
R = 0 to 1⁄8
α = 30°°
f = 1 ⁄8
r = 3 ⁄8
F, OH
—
C, J, M, R, V
R = 0 to 1⁄8
α = 30°°
f = 1 ⁄8
r = 3 ⁄8
All
Not required
A, C, J, M, R, V
U
U
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Notes
8 - 148
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-36 (cont.). Prequalified Welded Joints Partial-Joint-Penetration Groove Welds Square-groove weld (1) Butt joint (B)
Base Metal Thickness (U = unlimited)
Welding Process
Joint Designation
T1
SMAW
B-P1a
1 ⁄8
max
B-P1c
1 ⁄4
max
Groove Preparation Tolerances
T2
Root Opening
As Detailed
As Fit Up
Permitted Welding Positions
Effective Throat (E)
Notes
—
R = 0 to 1⁄16
+1 ⁄16 , − 0
± 1 ⁄16
All
T 1 − 1 ⁄32
B
—
T1 R= min 2
+1 ⁄16 , − 0
± 1 ⁄16
All
T1 2
B
Square-groove weld (1) Butt joint (B)
E 1 + E 2 must not exceed
Welding Process
Joint Designation
SMAW
B-P1b
3T1 4
Base Metal Thickness (U = unlimited) T1
T2
max
—
1 ⁄4
Groove Preparation Tolerances Root Opening
As Detailed
As Fit Up
Permitted Welding Positions
Effective Throat (E)
T1 R= 2
± 1 ⁄16 , − 0
± 1 ⁄16
All
3T1
Notes
4
Single-V-groove weld (2) Butt joint (B) Corner joint (C)
Welding Process
Joint Designation
SMAW
BC-P2
GMAW FCAW
BC-P2-GF
SAW
BC-P2-S
Groove Preparation Base Metal Thickness Tolerances (U = unlimited) Root Opening Root Face As As Fit T1 T2 Up Groove Angle Detailed 1 ⁄4
1 ⁄4
7 ⁄16
min
min
min
U
U
U
R=0 f = 1⁄32 min α - 60°°
0, +1 ⁄16 +u, −0 +10°°, − 0°
+1 ⁄8 , − 1 ⁄16
R=0 f = 1 ⁄8 min α - 60°°
0, +1 ⁄16 +u, −0 +10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0 f = 1 ⁄4 min α - 60°°
±0 +u, −0 +10°°, − 0°°
+1 ⁄16 , − 0*
Permitted Welding Positions
Effective Throat (E)
All
S
B, E, Q2
All
S
A, B, E, Q2
F
S
B, E, Q2
± 1 ⁄16 +10°°, − 5° ± 1 ⁄16 +10°°, − 5°° ± 1 ⁄16 +10°°, − 5°°
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Notes
WELDED CONSTRUCTION
8 - 149
Table 8-36 (cont.). Prequalified Welded Joints Partial-Joint-Penetration Groove Welds Double-V-groove weld (3) Butt joint (B)
Welding Process
Joint Designation
SMAW
B-P3
GMAW FCAW
B-P3-GF
SAW
B-P3-S
Base Groove Preparation Metal Thickness Tolerances (U = unlimited) Root Opening Root Face As As Fit T1 T2 Groove Angle Detailed Up 1 ⁄2
1 ⁄2
3 ⁄4
min
min
min
—
—
—
R=0 f = 1 ⁄8 min α = 60°°
+1⁄16 , − 0 +u, −0 +10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0 f = 1 ⁄8 min α = 60°°
+1⁄16 , − 0 +u, −0 +10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0 f = 1 ⁄4 min α = 60°°
±0 +u, −0 +10°°, − 0°°
+1 ⁄16 , − 0*
Permitted Welding Positions
Effective Throat (E)
All
S
E, Mp, Q2
All
S
A, E, Mp, Q2
F
S
E, Mp, Q2
± 1 ⁄16
Notes
+10°°, − 5°° ± 1 ⁄16 +10°°, − 5°° ± 1 ⁄16 +10°°, − 5°°
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 150
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-36 (cont.). Prequalified Welded Joints Partial-Joint-Penetration Groove Welds Single-bevel-groove weld (4) Butt joint (B) T-joint (T) Corner joint (C)
Welding Process
Joint Designation
SMAW
BTC-P4
GMAW FCAW
BTC-P4-GF
SAW
TC-P4-S
Base Groove Preparation Metal Thickness Tolerances (U = unlimited) Root Opening Root Face As As Fit T1 T2 Groove Angle Detailed Up U
1 ⁄4
7 ⁄16
U
U
min
min
U
R=0 f = 1 ⁄8 min α = 45°°
+1 ⁄16 , − 0 unlimited +10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0 f = 1 ⁄8 min α = 45°°
+1 ⁄16 , − 0 unlimited* +10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0 f = 1 ⁄4 min α = 60°°
±0 +u, −0 +10°°, − 0°°
+1 ⁄16 , − 0
Permitted Welding Positions
Effective Throat (E)
All
S − 1⁄8
B, E, J2, Q2, V
F, H V, OH
S
S − 1 ⁄8
A, B, E, J2, Q2, V
F
S
Permitted Welding Positions
Effective Throat (E)
All
(S − 1 ⁄8 ) − 1 ⁄4
E, J2, L, Mp, Q2, V
All
(S 1 + S 2 )
A, E, J2, L, Mp, Q2, V
± 1 ⁄16 +10°°, − 5°° ± 1 ⁄16 +10°°, − 5°° ± 1 ⁄16 +10°°, − 5°°
Notes
B, E, J2, Q2, V
Double-bevel-groove weld (5) Butt joint (B) T-joint (T) Corner joint (C)
Welding Process
Joint Designation
SMAW
BTC-P5
GMAW FCAW
BTC-P5-GF
SAW
TC-P5-S
Base Groove Preparation Metal Thickness Tolerances (U = unlimited) Root Opening Root Face As As Fit T1 T2 Groove Angle Detailed Up 5 ⁄16
1 ⁄2
3 ⁄4
min
min
min
U
U
U
R=0 f = 1 ⁄8 min α = 45°°
+1 ⁄16 , − 0 unlimited +10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0 f = 1 ⁄8 min α = 45°°
+1 ⁄16 , − 0 unlimited +10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0 f = 1 ⁄4 min α = 60°°
±0 unlimited +10°°, − 0°°
+1 ⁄16 , − 0*
± 1 ⁄16
+10°°, − 5°° ± 1 ⁄16 +10°°, − 5°°
± 1 ⁄16 +10°°, − 5°°
*For flat and horizontal postiions f = + u , −0
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
− 1 ⁄4
F
S1 + S2
Notes
E, J2, L, Mp, Q2, V
WELDED CONSTRUCTION
8 - 151
Table 8-36 (cont.). Prequalified Welded Joints Partial-Joint-Penetration Groove Welds Single-U-groove weld (6) Butt joint (B) Corner joint (C)
Welding Process
Joint Designation
SMAW
BC-P6
GMAW FCAW
BC-P6-GF
SAW
BC-P6-S
Base Groove Preparation Metal Thickness Root Opening Tolerances (U = unlimited) Root Face Groove Radius As As Fit T1 T2 Groove Angle Detailed Up 1 ⁄4
1 ⁄4
7 ⁄16
U
min
U
min
min
U
R=0 f = 1 ⁄32 min r = 1 ⁄4 α = 45°°
+1 ⁄16 , − 0 +u, −0 +1 ⁄4 , − 0 +10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0 f = 1 ⁄8 min r = 1 ⁄4 α = 20°°
+1 ⁄16 , − 0 +u, −0 +1 ⁄4 , − 0 +10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0 f = 1 ⁄4 min r = 1 ⁄4 α = 20°°
±0 +u, −0 +1 ⁄4 , − 0 +10°°, − 0°°
+1 ⁄16 , − 0
Permitted Welding Positions
Effective Throat (E)
All
S
B, E, Q2
All
S
A, B, E, Q2
F
S
B, E, Q2
Permitted Welding Positions
Effective Throat (E)
All
S1 + S2
E, Mp, Q2
All
S1 + S2
A, E, Mp, Q2
F
S1 + S2
E, Mp, Q2
± 1 ⁄16 ± 1 ⁄16 +10°°, − 5°° ± 1 ⁄16 ± 1 ⁄16 +10°°, − 5°° ± 1 ⁄16 ± 1 ⁄16 +10°°, − 5°°
Notes
Double-U-groove weld (7) Butt joint (B)
Welding Process
Joint Designation
SMAW
B-P7
GMAW FCAW
B-P7-GF
SAW
B-P7-S
Base Groove Preparation Metal Thickness Root Opening Tolerances (U = unlimited) Root Face Groove Radius As As Fit T1 T2 Groove Angle Detailed Up 1 ⁄2
1 ⁄2
3 ⁄4
min
min
min
—
—
—
R=0 f = 1 ⁄8 min r = 1 ⁄4 α = 45°°
+1 ⁄16 , − 0 +u, −0 +1 ⁄4 , − 0 +10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0 f = 1 ⁄8 min r = 1 ⁄4 α = 20°°
+1 ⁄16 , − 0 +u, −0 +1 ⁄4 , − 0 +10°°, − 0°°
+1 ⁄8 , − 1 ⁄16
R=0 f = 1 ⁄4 min r = 1 ⁄4 α = 20°°
±0 +u, −0 +1 ⁄4 , − 0 +10°°, − 0°°
+1 ⁄16 , − 0
± 1 ⁄16 ± 1 ⁄16 +10°°, − 5°° ± 1 ⁄16 ± 1 ⁄16 +10°°, − 5°° ± 1 ⁄16 ± 1 ⁄16 +10°°, − 5°°
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Notes
8 - 152
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-36 (cont.). Prequalified Welded Joints Partial-Joint-Penetration Groove Welds Single-J-groove weld (8) Butt joint (B) T-joint (T) Corner joint (C)
Welding Process SMAW
Joint Designation TC-P8*
SMAW
Base Metal Thickness (U = unlimited) T1
T2
1 ⁄4
min
U
BC-P8**
1 ⁄4
min
U
GMAW FCAW
TC-P8-GF*
1 ⁄4
min
U
GMAW FCAW
BC-P8-GF**
1 ⁄4
min
U
SAW
TC-P8-S*
7 ⁄16
min
U
SAW
C-P8-S**
7 ⁄16
min
U
Groove Preparation Root Opening Tolerances Root Face As As Fit Groove Radius Up Groove Angle Detailed R=0 +1 ⁄16 , − 0 +1 ⁄8 , − 1 ⁄16 1 f = ⁄8 min ± 1 ⁄16 +u, −0 r = 3 ⁄8 +1 ⁄4 , − 0 ± 1 ⁄16 α = 45°° +10°°, − 0°° +10°°, − 5°° R=0 +1 ⁄16 , − 0 +1 ⁄8 , − 1 ⁄16 f = 1 ⁄8 min ± 1 ⁄16 +u, −0 3 r = ⁄8 +1 ⁄4 , − 0 ± 1 ⁄16 α = 30°° +10°°, − 0°° +10°°, − 5°° R=0 +1 ⁄16 , − 0 +1 ⁄8 , − 1 ⁄16 f = 1 ⁄8 min ± 1 ⁄16 +u, −0 3 r = ⁄8 +1 ⁄4 , − 0 ± 1 ⁄16 α = 45°° +10°°, − 0°° +10°°, − 5°° 1 1 R=0 + ⁄16 , − 0 + ⁄8 , − 1 ⁄16 f = 1 ⁄8 min ± 1 ⁄16 +u, −0 r = 3 ⁄8 +1 ⁄4 , − 0 ± 1 ⁄16 α = 30°° +10°°, − 0°° +10°°, − 5°° 1 R=0 ±0 + ⁄16 , − 0 f = 1 ⁄4 min ± 1 ⁄16 +u, −0 r = 1 ⁄2 +1 ⁄4 , − 0 ± 1 ⁄16 α = 45°° +10°°, − 0°° +10°°, − 5°° R=0 ±0 +1 ⁄16 , 0 f = 1 ⁄4 min ± 1 ⁄16 +u, −0 r = 1 ⁄2 +1 ⁄4 , − 0 ± 1 ⁄16 α = 20°° +10°°, − 0°° +10°°, − 5°°
*Applies to inside corner joints. **Applies to outside corner joints.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Permitted Effective Welding Throat Positions (E) All S
Notes E, J2, Q2, V
All
S
E, J2, Q2, V
All
S
A, E, J2, Q2, V
All
S
A, E, J2, Q2, V
F
S
E, J2, Q2, V
F
S
E, J2, Q2, V
WELDED CONSTRUCTION
8 - 153
Table 8-36 (cont.). Prequalified Welded Joints Flare Welds Double-J-groove weld (9) Butt joint (B) T-joint ( T) Corner joint (C)
Welding Process SMAW
Joint Designation BTC-P9*
GMAW FCAW
Base Metal Thickness (U = unlimited) T1
T2
1 ⁄2
min
U
BTC-P9-GF**
1 ⁄2
min
U
SAW
C-P9-S*
3 ⁄4
min
U
SAW
C-P9-S**
3 ⁄4
min
U
SAW
T-P9-S
3 ⁄4
min
U
Groove Preparation Root Opening Tolerances Root Face As As Fit Groove Radius Up Groove Angle Detailed 1 1 R=0 + ⁄16 , − 0 + ⁄8 , − 1 ⁄16 f = 1 ⁄8 min ± 1 ⁄16 +u, −0 r = 3 ⁄8 ± 1 ⁄16 +1 ⁄4 , − 0 α = 45°° +10°°, − 0°° +10°°, − 5°° 1 1 R=0 + ⁄16 , − 0 + ⁄8 , − 1 ⁄16 f = 1 ⁄8 min ± 1 ⁄16 +u, −0 r = 3 ⁄8 +1 ⁄4 , − 0 ± 1 ⁄16 α = 30°° +10°°, − 0°° +10°°, − 5°° R=0 ±0 +1 ⁄16 , − 0 f = 1 ⁄4 min ± 1 ⁄16 +u, −0 r = 1 ⁄2 +1 ⁄4 , − 0 ± 1 ⁄16 α = 45°° +10°°, − 0°° +10°°, − 5°° R=0 ±0 − 1⁄16 , 0 f = 1 ⁄4 min ± 1 ⁄16 +u, −0 r = 1 ⁄2 +1 ⁄4 , − 0 ± 1 ⁄16 α = 20°° +10°°, − 0°° +10°°, − 5°° R=0 ±0 +1 ⁄16 , 0 f = 1 ⁄4 min ± 1 ⁄16 +u, −0 1 r = 1 ⁄2 + ⁄4 , − 0 ± 1 ⁄16 α = 45°° +10°°, − 0°° +10°°, − 5°°
Permitted Effective Welding Throat Positions (E) All S1 + S2
Notes E, J2, Mp, Q2, V
All
S1 + S2
A, J2, Mp, Q2, V
F
S1 + S2
E, J2, Mp, Q2, V
F
S1 + S2
E, J2, Mp, Q2, V
F
S1 + S2
E, J2, Mp, Q2
Single-J-groove weld (B) Butt joint (B) T-joint (T) Corner joint (C)
Welding Process SMAW
Joint Designation BTC-P10
Base Metal Thickness (U = unlimited) T1
T2
3 ⁄16
U
min GMAW FCAW
BTC-P10-GF
SAW
T-P10-S
3 ⁄16
U
min 1 ⁄2
1 ⁄2
min
min
Groove Preparation
Tolerances Root Opening As As Fit Root Face T3 Bend Radius Detailed Up 1 1 T 1 min R=0 + ⁄16 , − 0 + ⁄8 , − 1 ⁄16 f = 3⁄16 min +U, − 1 ⁄16 +U, −0 3T1 − 0, +Not- − 0, +NotC= min Limited Limited 2 T 1 min R=0 +1⁄16 , − 0 + 1 ⁄8, − 1⁄16 f = 3⁄16 min +U, − 1 ⁄16 +U, −0 3T 1 − 0, +Not- − 0, +NotC= min Limited Limited 2 N/A R=0 ±0 + 1 ⁄16, −0 1 f = ⁄2 min +U, − 1 ⁄16 +U, −0 3T1 − 0, +Not- − 0, +NotC= min Limited Limited 2
*Applies to inside corner joints. **Applies to outside corner joints.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Permitted Effective Welding Throat Positions (E) Notes 5 ⁄8 T 1 J2, All Q2, Z
All
5 ⁄8 T 1
A, J2, Q2, Z
F
5 ⁄8 T 1
J2, Q2, Z
8 - 154
BOLTS, WELDS, AND CONNECTED ELEMENTS
ECCENTRICALLY LOADED WELD GROUPS
When the line of action of an applied load does not pass through the center of gravity (CG) of a weld group, the load is eccentric and results in a moment which must be considered in the design of the connection. Eccentricity in the Plane of the Faying Surface
Eccentricity in the plane of the faying surface produces additional shear and the welds must then be designed to resist the combined effect of the direct shear from the applied load Pu and the additional shear from the induced moment Pu e. Two methods of analysis for this type of eccentricity will be discussed: (1) the instantaneous center of rotation method; and, (2) the elastic method. Instantaneous Center of Rotation Method
Also known as the ultimate strength method (Crawford, 1968), this method considers the load-deformation relationship of each weld element as well as the variation in weld strength with respect to the direction of the applied force and, thus, more accurately predicts the ultimate strength of the eccentrically loaded connection (Butler, Pal, and Kulak, 1972). Eccentricity produces both a rotation about the centroid of the weld group and a translation of one connected element with respect to the other. The combined effect of this rotation and translation is equivalent to a rotation about a point defined as the instantaneous center of rotation (IC) as illustrated in Figure 8-51a. The location of the IC depends on the geometry of the weld group as well as the direction and point of application of the load. The individual resistance of each unit weld element is assumed to act on a line perpendicular to a ray passing through the instantaneous center and the centroid of that element, as illustrated in Figure 8-51b. The load-deformation relationship of a single unit-weld element was originally given by Butler, Pal, and Kulak (1972) for E60 electrodes. New strength curves for E70 electrodes (Lesik and Kennedy, 1990) are illustrated in Figure 8-52, where: R = 0.60FEXX(1.0 + 0.50 sin1.5θ) [p (1.9 − 0.9p)]0.3 In the above equation, R FEXX θ p
= shear force per unit area in a single unit-weld element at a deformation ∆, kips = weld electrode strength, ksi = angle of loading measured from the weld longitudinal axis, degrees = ratio of element deformation to its deformation at maximum stress
Unlike the load-deformation relationship for bolts, strength and deformation of welds are dependent on the angle θ that the resultant elemental force makes with the axis of the weld element. The critical weld element is usually the weld element farthest from the IC. While this may not always be the case, for the purpose of explanation, this will be assumed. The maximum deformation ∆max may be determined as ∆max = 1.087w (θ + 6)−0.65 ≤ 0.17w where w is the leg size of the weld and θ is expressed in degrees. The deformation of other weld elements is assumed to vary linearly with distance from the IC as, AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
∆=
lr lr max
8 - 155
∆max
More discussion of this method is contained in LRFD Specification Appendix J2.4 and its Commentary. These new provisions permit, for the first time, weld strength to exceed the 0.6FEXX nominal value, which is the least strength applicable to longitudinally loaded (θ = 0°) elements. Load-deformation curves in Figure 8-52 for values of θ = 0°, 30°, 45°, Pu
e
lo
CG
IC
(a) Instantaneous center of rotation (IC)
lo e
IC
CG
l ax
rm
ru max
(b) Forces on weld elements Fig. 8-51. Instantaneous center of rotation method. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Pu
8 - 156
BOLTS, WELDS, AND CONNECTED ELEMENTS
60°, 75°, and 90° are shown relative to Ro = 0.6FEXX. The ductility of the weld group is governed by ∆max of the element that first reaches its limit. The total strength of all weld elements is the sum of the individual resistances of all welds in the group. If the correct location of the instantaneous center has been selected, the three equations of statics will be satisfied, i.e., ΣFx = 0, ΣFy = 0, ΣM = 0. Because of the non-linear nature of the requisite iterative solution, a minimum of twenty weld elements for the longest line segment is generally recommended for sufficient accuracy. Tables 8-38 through 8-45 employ the instantaneous center of rotation method in accordance with LRFD Specification Appendix J2.4 for the weld patterns and eccentric conditions indicated and inclined loads at 0°, 15°, 30°, 45°, 60°, and 75°. Thus, unlike the First Edition LRFD Manual, tabulated values are not limited to a maximum weld nominal strength of 0.6FEXX. For some cases, significant increases of up to 50 percent of values tabulated previously are possible; many values reflect more moderate but, nevertheless, substantial increases on the order of 10 to 30 percent. The traditional and more conservative designs based upon a constant fillet weld nominal strength of 0.6FEXX is also permitted, refer to AISC (1986). For any of the weld group geometrics shown, the design strength of the eccentrically loaded weld group is φRn, where In the above equation, 1.6
θ = 90° θ = 75°
1.4
θ = 60° θ = 45°
1.2 θ = 30°
θ = 0°
1.0
( RR ) o
0.8
0.6
0.4 Ro = 0.6Fexx
0.2
0 0.000
0.050
∆ w
0.100
Fig. 8-52. Fillet weld strength as a function of force angle, θ. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
0.150
ECCENTRICALLY LOADED WELD GROUPS
8 - 157
C = tabular value (which includes φ = 0.75) φRn = CC1Dl C1 = electrode coefficient from Table 8-37 which adjusts tabular value, which is based on E70XX electrodes, for other electrodes. Note that this coefficient includes an additional reduction factor of 0.90 for E80 and E90 electrodes and 0.85 for E100 and E110; this accounts for the uncertainty of extrapolation to the higher strength electrodes. D = number of sixteenths-of-an-inch in the weld size l = length of the reference weld, in. The first line in each table (a = 0) gives the design strength of a concentrically loaded weld group in accordance with LRFD Specification Appendix J2.2a. Linear interpolation within a given table between adjacent a and k values is permitted. Figure C-J2.5 from LRFD Specification Commentary Section J2 indicates that, for equal-leg fillet welds, the area of the fusion surface is always larger than the leg dimension times the weld length. Therefore, the tabulated values are based upon the strength through the throat of the weld of (0.75 × 0.6 × FEXX × 0.707 × 1⁄16) Tabulated values are valid for weld metal with a strength level equal to or matching the base material. A convergence criterion of less than 0.5 percent unbalanced force was employed for the tabulated iterative solutions. Straight line interpolation between these angles may be significantly unconservative. Therefore, unless a direct analysis is performed, use only the values tabulated for the next lower angle. Since the coefficients in these tables were derived from physical tests with loading at ultimate strength levels, they should be used only for the weld patterns indicated and not in combination with any additional loading. In cases not treated by these tables, a special ultimate strength analysis is required if the instantaneous center of rotation method is to be used.
Example 8-3
Given:
Refer to Figure 8-53. Determine the largest eccentric force Pu for which the design shear strength of the welds in the connection is adequate using the instantaneous center of rotation method. Use 3⁄8-in. fillet weld and 70 ksi electrode weld size. A. Assume the load is vertical as illustrated in Figure 8-53 (θ = 0°°) B. Assume the load acts at an angle of 75°° with respect to vertical (θ = 75°°)
Solution A:
l = 10 in. kl = 5 in. k = 0.5 From Table 8-42 with θ = 0°, x = 0.125 AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 158
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-37. Electrode Strength Coefficients Electrode
FEXX (ksi)
C1
E60 E70 E80 E90 E100 E110
60 70 80 90 100 110
0.857 1.00 1.03 1.16 1.21 1.34
xl + al = 10 in. 0.125(10 in.) + a (10 in.) = 10 in. a = 0.875 By interpolation from Table 8-42 with θ = 0°, C = 1.41 Design shear strength φRn = CC1Dl = 1.41(1.0)(6 sixteenths)(10 in.) = 84.6 kips Comment:
Note that this eccentricity has effectively reduced the shear strength of this weld group by 60 percent when compared with the eccentrically loaded case.
Solution B:
From Solution A, k = 0.5 a = 0.875 By interpolation from Table 8-42 with θ = 75°°, C = 2.59 Design shear strength φRn = CC1Dl = 2.59(1.0)(6 sixteenths)(10 in.) = 155 kips
Comment:
In Solution B, the vertical component of the design strength is φRn sin75°° = (155 kips)(0.966) = 150 kips and the horizontal component of the design strength is AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 159
φRn cos75°° = (155 kips)(0.259) = 40.1 kips Elastic Method
Alternatively, the elastic method may be used to analyze eccentrically loaded weld groups. It offers a simplified, conservative approach but does not render a consistent factor of safety and, in some cases, provides excessively conservative results. Furthermore, the elastic method ignores both the ductility of the weld group and the load redistribution which occurs. Refer to Higgins (1971). In the elastic method, for a force applied parallel to the Y principle axis of the weld group, the eccentric force Pu is resolved into a force Pu acting through the center of gravity (CG) of the weld group and a moment Pu e where e is the eccentricity. Each weld element is then assumed to support an equal share of the concentric force Pu, and a share of the eccentric moment Pu e which is proportional to its distance from the CG. The weld most remote from the CG, then, is the most highly stressed. The resultant vectorial sum of these forces ru is the required strength for the weld element. The shear force per linear inch of weld due to the concentric force Pu is r1, where r1 =
Pu l
and l is the total length of the weld measured along the axis of each element. The shear force per linear inch of weld due to the moment Pu e varies with distance from the CG and will be maximum in the weld element which is most remote from the CG. The maximum shear due to the moment Pu e is rm, where rm =
Pu ec Ip
In the above equation,
10 in.
Pu
k l = 5 in.
l = 10 in.
1.25 in.
Figure 8-53. Illustration for Example 8-3 and 8-4. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 160
BOLTS, WELDS, AND CONNECTED ELEMENTS
c = distance from CG to point on weld most remote from CG, in. Ip = polar moment of inertia of the weld group, in.4 per in.2 (Ip = Ix + Iy). Refer to Figure 8-54. For section moduli and torsional constants of various welds treated as line elements, refer to Table 5 (page 7.4–7) of Blodgett (1966). To determine the resultant force on the most highly stressed weld element, rm must be resolved into vertical component r2 and horizontal component r3, where Pu ecx Ip Pu ecy r3 = Ip
r2 =
In the above equations, cx and cy are the horizontal and vertical components of the diagonal distance c. Thus, the resultant force is ru, where r2 r1
ru = √ (r1 + r2)2 + (r3)2
r3 rm ru
and the weld size must be chosen such that the design strength of the weld exceeds the required strength ru. For the more general case of an inclined eccentric force, i.e., not parallel to the Y principle axis of the bolt group, the effect of the X-direction component of the direct shear must also be included. Refer to Iwankiw (1987).
Example 8-4
Given:
Refer to Example 8-3a. Recalculate the largest eccentric force Pu for which the design shear strength of the welds in the connection is adequate using the elastic method. Compare the result with that of Example 8-3a. Use 3⁄8-in. weld size, E70XX electrodes Ip = 385 in.4 per in.2
Solution:
Direct shear force per inch of weld Pu l Pu = 20 in.
r1 =
Additional shear force on weld due to eccentricity Pu ecx Ip Pu (8.75 in.) (3.75 in.) = 385 in.4 per in.2 = 0.0852Pu
r2 =
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
r3 =
8 - 161
Pu ecy
Ip
Pu (8.75 in.) (5 in.) = 385 in.4 per in.2 = 0.114Pu Resultant shear force per inch of weld (r1 + r2)2 + (r3)2 ru = √
y
(p) x
xo cg (po )
x
yo
y
xo
xo
x
yo
y
l = 6.283R
x (p)
x
n
y
x (p)
ln2 12
ln2 + l(dy)2 12 lm2 Iyo = 12 lm2 Iy = + l(dx)2 12 Ix =
yo a
xo
cg (po ) xo
dx
y
xo
R
dy
yo
xo
m
Ixo =
y
a = 0.637R l = 3.142R
Ixo = πR 3 Ix = πR 3 + l(dy)2 Iyo = πR 3 Iy = πR 3 + l(dx)2
(p) x
yo
R
a
R
xo cg (po ) x
yo d y x
cg (po )
dy
xo
dx
xo
Ixo = 0 Ix = l(dy)2 l3 Iyo = 12 l3 Iy = + l(dx)2 12
12 l3 Ix = + l(dy)2 12 Iyo = 0 Iy = l(dx)2
cg (po )
y
yo
l3
l /2
/2
dy
xo
y
dx
dy
Ixo =
l l
a
yo
yo
y
dx
l
dy
xo x
yo
y
dy
dx cg (po )
l/ 2
l
yo
x (p)
x yo
y
x (p)
a = 0.637R l = 1.571R
Ix =
π 3 R + l(dy)2 2 π 4 Iyo = − R 3 2 π
π 2 Ixo = − R 3 4 π π 2 3 Ix = − R + l(dy)2 4 π π 2 Iyo = − R 3 4 π
π 4 Iy = − R 3 2 π
π 2 Iy = − R 3 + l(dx)2 4 π
Ixo =
π 3 R 2
Fig. 8-54. Moments of inertia of various weld segments. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 162
BOLTS, WELDS, AND CONNECTED ELEMENTS
√
Pu 2 20 + 0.0852Pu + (0.114Pu ) = 0.177Pu 2
=
Since ru must be less than or equal to φrn, φrn 0.177 1.392D ≤ 0.177 1.392 (6 sixteenths) ≤ 0.177 ≤ 47.2 kips
Pu ≤
This is a 44 percent reduction in the strength predicted by the instantaneous center of rotation method in Example 8-3a.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 163
Table 8-38. Coefficients C for Eccentrically Loaded Weld Groups Angle = 0°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D ex = a l Pu
l
where Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
kl ex = a l
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes
P
Special Case
u
(Load not in plane of weld group) Use C-values for k = 0 Any equal distances
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
2.78 2.78 2.75 2.64 2.48
2.78 2.78 2.75 2.63 2.48
2.78 2.78 2.74 2.63 2.48
2.78 2.78 2.73 2.62 2.47
2.78 2.78 2.71 2.60 2.47
2.78 2.77 2.70 2.59 2.46
2.78 2.75 2.69 2.58 2.46
2.78 2.74 2.67 2.57 2.45
2.78 2.73 2.66 2.56 2.45
2.78 2.71 2.64 2.55 2.44
2.78 2.70 2.63 2.54 2.44
2.78 2.67 2.60 2.52 2.43
2.78 2.64 2.58 2.50 2.41
2.78 2.61 2.55 2.48 2.40
2.78 2.59 2.53 2.46 2.39
2.78 2.78 2.50 2.44 2.38
0.30 0.40 0.50 0.60 0.70
2.32 2.00 1.72 1.50 1.32
2.32 2.00 1.72 1.50 1.32
2.32 2.01 1.74 1.52 1.34
2.32 2.03 1.77 1.55 1.38
2.33 2.05 1.80 1.59 1.42
2.33 2.07 1.83 1.63 1.47
2.33 2.08 1.86 1.67 1.51
2.33 2.10 1.89 1.71 1.55
2.33 2.11 1.91 1.74 1.59
2.33 2.12 1.93 1.77 1.62
2.33 2.14 1.95 1.79 1.65
2.33 2.15 1.99 1.84 1.71
2.33 2.16 2.01 1.87 1.75
2.32 2.17 2.03 1.90 1.79
2.32 2.18 2.05 1.92 1.81
2.31 2.18 2.06 1.94 1.84
0.80 0.90 1.00 1.20 1.40
1.17 1.05 0.957 0.806 0.695
1.18 1.06 0.963 0.812 0.701
1.20 1.08 0.986 0.835 0.724
1.24 1.12 1.02 0.872 0.758
1.28 1.17 1.07 0.916 0.799
1.33 1.22 1.12 0.963 0.844
1.38 1.27 1.17 1.01 0.889
1.42 1.31 1.21 1.06 0.932
1.46 1.35 1.26 1.10 0.973
1.50 1.39 1.29 1.14 1.01
1.53 1.43 1.33 1.17 1.05
1.59 1.49 1.40 1.24 1.12
1.64 1.54 1.45 1.30 1.18
1.68 1.59 1.50 1.35 1.23
1.71 1.62 1.54 1.40 1.28
1.74 1.66 1.58 1.44 1.32
1.60 1.80 2.00 2.20 2.40
0.611 0.544 0.491 0.447 0.410
0.616 0.550 0.496 0.452 0.415
0.638 0.570 0.515 0.470 0.431
0.670 0.600 0.542 0.495 0.455
0.708 0.635 0.576 0.526 0.484
0.750 0.674 0.612 0.560 0.516
0.792 0.714 0.650 0.596 0.550
0.833 0.753 0.687 0.631 0.583
0.873 0.791 0.723 0.665 0.616
0.911 0.828 0.758 0.699 0.648
0.947 0.863 0.792 0.731 0.679
1.01 0.928 0.855 0.792 0.738
1.07 0.987 0.912 0.848 0.792
1.13 1.04 0.964 0.899 0.842
1.17 1.09 1.01 0.945 0.887
1.22 1.13 1.05 0.988 0.929
2.60 0.379 0.384 0.399 0.421 0.448 0.478 0.510 0.542 0.573 0.604 0.634 0.691 0.743 0.791 0.836 0.877 2.80 0.352 0.357 0.371 0.392 0.417 0.446 0.476 0.506 0.536 0.565 0.594 0.649 0.699 0.746 0.790 0.830 3.00 0.329 0.333 0.347 0.366 0.390 0.417 0.446 0.474 0.503 0.531 0.559 0.611 0.661 0.706 0.748 0.788
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 164
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-38 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 15°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D ex = a l Pu
15° l
where Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
kl ex = a l Pu
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
15°
Special Case
(Load not in plane of weld group) Use C-values for k = 0 Any equal distances
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
2.97 2.84 2.76 2.63 2.48
2.97 2.84 2.76 2.63 2.48
2.97 2.84 2.75 2.63 2.48
2.97 2.83 2.75 2.62 2.48
2.97 2.82 2.74 2.62 2.49
2.97 2.82 2.73 2.62 2.49
2.97 2.81 2.72 2.61 2.49
2.97 2.80 2.72 2.61 2.49
2.97 2.80 2.71 2.61 2.49
2.97 2.79 2.70 2.61 2.50
2.97 2.78 2.70 2.60 2.50
2.97 2.77 2.69 2.60 2.50
2.97 2.75 2.68 2.59 2.51
2.97 2.74 2.67 2.59 2.51
2.97 2.73 2.66 2.58 2.51
2.97 2.72 2.65 2.58 2.51
0.30 0.40 0.50 0.60 0.70
2.32 2.01 1.74 1.52 1.34
2.32 2.01 1.74 1.52 1.35
2.32 2.02 1.76 1.54 1.37
2.33 2.04 1.78 1.57 1.40
2.34 2.06 1.82 1.62 1.45
2.35 2.09 1.86 1.66 1.50
2.36 2.12 1.89 1.70 1.54
2.37 2.14 1.93 1.75 1.59
2.38 2.16 1.96 1.78 1.63
2.39 2.18 1.99 1.82 1.67
2.39 2.19 2.01 1.85 1.70
2.41 2.22 2.05 1.90 1.77
2.42 2.25 2.09 1.95 1.82
2.43 2.27 2.12 1.99 1.87
2.43 2.28 2.15 2.02 1.90
2.43 2.30 2.17 2.05 1.94
0.80 0.90 1.00 1.20 1.40
1.20 1.08 0.979 0.826 0.714
1.20 1.08 0.985 0.832 0.719
1.22 1.11 1.01 0.856 0.743
1.26 1.15 1.05 0.893 0.778
1.31 1.19 1.09 0.938 0.820
1.36 1.24 1.15 0.987 0.866
1.41 1.30 1.20 1.04 0.913
1.46 1.34 1.25 1.09 0.960
1.50 1.39 1.29 1.13 1.00
1.54 1.43 1.33 1.17 1.05
1.58 1.47 1.37 1.21 1.09
1.65 1.54 1.45 1.29 1.16
1.71 1.60 1.51 1.35 1.23
1.76 1.66 1.57 1.41 1.28
1.80 1.70 1.62 1.46 1.34
1.84 1.74 1.66 1.51 1.39
1.60 1.80 2.00 2.20 2.40
0.628 0.560 0.506 0.461 0.423
0.633 0.566 0.511 0.466 0.428
0.656 0.587 0.530 0.484 0.445
0.688 0.617 0.558 0.510 0.469
0.727 0.653 0.592 0.541 0.499
0.770 0.693 0.630 0.577 0.532
0.815 0.735 0.669 0.613 0.566
0.859 0.777 0.708 0.650 0.601
0.901 0.817 0.746 0.687 0.636
0.941 0.855 0.783 0.722 0.670
0.980 0.893 0.819 0.757 0.703
1.05 0.963 0.887 0.822 0.765
1.12 1.03 0.949 0.882 0.824
1.18 1.09 1.01 0.938 0.878
1.23 1.14 1.06 0.989 0.928
1.28 1.19 1.11 1.04 0.974
2.60 0.391 0.396 0.412 0.434 0.462 0.493 0.526 0.559 0.591 0.624 0.656 0.716 0.772 0.825 0.873 0.918 2.80 0.363 0.368 0.383 0.404 0.430 0.460 0.491 0.522 0.553 0.584 0.614 0.672 0.727 0.778 0.825 0.869 3.00 0.339 0.344 0.358 0.378 0.403 0.430 0.460 0.489 0.519 0.549 0.578 0.634 0.686 0.736 0.781 0.824
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 165
Table 8-38 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 30°° φ R n = CC1Dl
C min =
Pu
D min =
C1Dl
Pu
Pu
lmin =
CC 1 l
CC 1 D
ex = a l
Pu 30° l
where Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
kl ex = a l
Pu
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
30°
Special Case
(Load not in plane of weld group) Use C-values for k = 0 Any equal distances
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
3.28 3.03 2.87 2.72 2.57
3.28 3.03 2.87 2.73 2.57
3.28 3.04 2.87 2.73 2.57
3.28 3.04 2.87 2.73 2.58
3.28 3.04 2.88 2.74 2.59
3.28 3.05 2.88 2.74 2.61
3.28 3.05 2.88 2.75 2.62
3.28 3.06 2.89 2.76 2.63
3.28 3.06 2.90 2.76 2.64
3.28 3.06 2.90 2.77 2.66
3.28 3.07 2.91 2.78 2.67
3.28 3.07 2.92 2.79 2.68
3.28 3.07 2.94 2.81 2.70
3.28 3.06 2.94 2.82 2.72
3.28 3.06 2.95 2.83 2.73
3.28 3.05 2.95 2.84 2.74
0.30 0.40 0.50 0.60 0.70
2.41 2.11 1.84 1.62 1.44
2.41 2.11 1.85 1.63 1.45
2.42 2.12 1.86 1.65 1.47
2.43 2.14 1.89 1.68 1.51
2.45 2.17 1.93 1.73 1.56
2.47 2.20 1.98 1.78 1.61
2.49 2.24 2.02 1.83 1.66
2.51 2.28 2.06 1.88 1.72
2.53 2.30 2.10 1.92 1.77
2.54 2.33 2.13 1.96 1.81
2.56 2.35 2.17 2.00 1.85
2.59 2.40 2.22 2.07 1.92
2.61 2.43 2.27 2.12 1.99
2.63 2.46 2.31 2.17 2.04
2.64 2.49 2.34 2.21 2.09
2.66 2.51 2.37 2.25 2.13
0.80 0.90 1.00 1.20 1.40
1.30 1.17 1.07 0.907 0.786
1.30 1.18 1.08 0.913 0.792
1.33 1.20 1.10 0.939 0.817
1.37 1.24 1.14 0.979 0.855
1.42 1.29 1.19 1.03 0.901
1.47 1.35 1.25 1.08 0.951
1.52 1.41 1.30 1.14 1.00
1.58 1.46 1.36 1.19 1.05
1.63 1.51 1.41 1.24 1.10
1.68 1.56 1.46 1.29 1.15
1.72 1.61 1.51 1.33 1.20
1.80 1.69 1.59 1.42 1.28
1.87 1.76 1.66 1.49 1.35
1.93 1.82 1.73 1.56 1.42
1.98 1.88 1.78 1.62 1.49
2.02 1.92 1.84 1.68 1.54
1.60 1.80 2.00 2.20 2.40
0.693 0.619 0.559 0.510 0.469
0.699 0.625 0.565 0.516 0.474
0.723 0.648 0.587 0.536 0.493
0.759 0.681 0.617 0.564 0.520
0.801 0.721 0.655 0.599 0.552
0.848 0.765 0.696 0.638 0.589
0.897 0.811 0.740 0.679 0.628
0.946 0.857 0.783 0.720 0.667
0.993 0.901 0.825 0.761 0.705
1.04 0.945 0.866 0.800 0.743
1.08 0.987 0.907 0.838 0.779
1.16 1.07 0.984 0.912 0.850
1.24 1.14 1.05 0.981 0.917
1.31 1.21 1.12 1.04 0.978
1.37 1.27 1.18 1.10 1.04
1.42 1.32 1.24 1.16 1.09
2.60 0.433 0.439 0.456 0.481 0.512 0.546 0.583 0.620 0.657 0.693 0.728 0.795 0.860 0.920 0.975 1.03 2.80 0.403 0.408 0.424 0.448 0.477 0.509 0.544 0.579 0.614 0.649 0.683 0.748 0.809 0.867 0.922 0.972 3.00 0.376 0.382 0.397 0.419 0.446 0.477 0.510 0.543 0.577 0.610 0.642 0.705 0.764 0.821 0.873 0.923
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 166
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-38 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 45°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
ex = a l 45°
Pu
l
where Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
kl ex = a l
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
45° Pu
Special Case
(Load not in plane of weld group) Use C-values for k = 0 Any equal distances
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
3.61 3.37 3.13 2.94 2.77
3.61 3.37 3.13 2.94 2.77
3.61 3.38 3.15 2.95 2.78
3.61 3.38 3.17 2.97 2.80
3.61 3.40 3.20 2.99 2.83
3.61 3.42 3.23 3.03 2.86
3.61 3.43 3.25 3.06 2.89
3.61 3.44 3.28 3.10 2.93
3.61 3.46 3.30 3.13 2.97
3.61 3.47 3.33 3.17 3.01
3.61 3.48 3.35 3.20 3.04
3.61 3.50 3.38 3.25 3.11
3.61 3.51 3.41 3.29 3.16
3.61 3.52 3.43 3.33 3.21
3.61 3.52 3.45 3.35 3.25
3.61 3.52 3.46 3.38 3.28
0.30 0.40 0.50 0.60 0.70
2.61 2.32 2.06 1.84 1.66
2.61 2.32 2.07 1.85 1.66
2.63 2.34 2.09 1.87 1.69
2.65 2.37 2.12 1.91 1.73
2.68 2.41 2.17 1.96 1.79
2.71 2.45 2.22 2.02 1.85
2.75 2.50 2.27 2.08 1.91
2.79 2.54 2.33 2.14 1.97
2.83 2.59 2.38 2.19 2.03
2.86 2.63 2.42 2.25 2.09
2.90 2.66 2.47 2.30 2.14
2.97 2.73 2.54 2.38 2.23
3.04 2.80 2.61 2.45 2.31
3.09 2.87 2.68 2.52 2.38
3.14 2.92 2.74 2.58 2.44
3.18 2.97 2.79 2.63 2.50
0.80 0.90 1.00 1.20 1.40
1.50 1.37 1.26 1.08 0.938
1.51 1.38 1.26 1.08 0.946
1.54 1.40 1.29 1.11 0.975
1.58 1.45 1.34 1.16 1.02
1.64 1.51 1.40 1.21 1.07
1.70 1.57 1.46 1.28 1.13
1.76 1.64 1.53 1.34 1.19
1.83 1.70 1.59 1.40 1.25
1.89 1.76 1.65 1.46 1.31
1.95 1.82 1.71 1.52 1.37
2.00 1.88 1.77 1.58 1.42
2.10 1.98 1.87 1.68 1.52
2.18 2.07 1.96 1.77 1.62
2.26 2.14 2.04 1.85 1.70
2.32 2.21 2.11 1.93 1.77
2.38 2.27 2.17 2.00 1.84
1.60 1.80 2.00 2.20 2.40
0.831 0.745 0.675 0.617 0.568
0.838 0.752 0.682 0.624 0.574
0.866 0.779 0.707 0.647 0.596
0.908 0.817 0.743 0.681 0.628
0.958 0.864 0.787 0.722 0.667
1.01 0.917 0.836 0.768 0.710
1.07 0.972 0.888 0.818 0.756
1.13 1.03 0.941 0.868 0.804
1.19 1.08 0.992 0.917 0.851
1.24 1.13 1.04 0.964 0.897
1.29 1.19 1.09 1.01 0.941
1.39 1.28 1.18 1.10 1.03
1.48 1.37 1.27 1.18 1.11
1.56 1.45 1.35 1.26 1.18
1.64 1.52 1.42 1.33 1.25
1.71 1.59 1.49 1.40 1.32
2.60 0.526 0.532 0.553 0.583 0.619 0.660 0.703 0.749 0.794 0.838 0.881 0.963 1.04 1.12 1.18 2.80 0.489 0.496 0.515 0.544 0.578 0.617 0.658 0.701 0.743 0.786 0.827 0.906 0.982 1.05 1.12 3.00 0.458 0.464 0.482 0.509 0.542 0.579 0.618 0.658 0.699 0.739 0.779 0.856 0.929 0.998 1.06
1.25 1.18 1.12
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 167
Table 8-38 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 60°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D ex = a l 60° P
u
l
where Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
kl ex = a l
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
60° Pu
Special Case (Load not in plane of weld group) Use C-values for k = 0 Any equal distances
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
3.91 3.65 3.46 3.27 3.10
3.91 3.66 3.47 3.28 3.10
3.91 3.68 3.49 3.30 3.13
3.91 3.71 3.53 3.35 3.17
3.91 3.74 3.58 3.40 3.23
3.91 3.78 3.63 3.47 3.30
3.91 3.80 3.68 3.54 3.38
3.91 3.83 3.73 3.60 3.46
3.91 3.84 3.76 3.65 3.53
3.91 3.85 3.79 3.69 3.58
3.91 3.86 3.80 3.73 3.63
3.91 3.86 3.83 3.78 3.70
3.91 3.87 3.84 3.80 3.75
3.91 3.86 3.85 3.82 3.78
3.91 3.86 3.85 3.83 3.80
3.91 3.86 3.86 3.84 3.82
0.30 0.40 0.50 0.60 0.70
2.95 2.68 2.44 2.24 2.05
2.95 2.69 2.45 2.24 2.06
2.98 2.71 2.48 2.27 2.09
3.02 2.76 2.53 2.32 2.15
3.07 2.81 2.59 2.39 2.21
3.14 2.88 2.66 2.46 2.29
3.22 2.95 2.73 2.54 2.37
3.31 3.03 2.80 2.62 2.45
3.39 3.12 2.88 2.69 2.53
3.46 3.21 2.96 2.77 2.60
3.53 3.29 3.05 2.84 2.67
3.62 3.43 3.22 3.01 2.82
3.68 3.53 3.36 3.17 2.98
3.73 3.61 3.46 3.29 3.12
3.76 3.66 3.54 3.39 3.24
3.78 3.70 3.60 3.47 3.34
0.80 0.90 1.00 1.20 1.40
1.89 1.75 1.62 1.42 1.25
1.90 1.76 1.63 1.43 1.26
1.93 1.79 1.67 1.46 1.30
1.99 1.85 1.73 1.52 1.36
2.06 1.92 1.80 1.59 1.42
2.14 2.00 1.88 1.67 1.50
2.22 2.08 1.96 1.75 1.57
2.30 2.16 2.04 1.83 1.65
2.38 2.24 2.12 1.91 1.73
2.45 2.32 2.20 1.98 1.81
2.52 2.39 2.27 2.06 1.88
2.66 2.53 2.41 2.19 2.01
2.81 2.65 2.53 2.32 2.13
2.95 2.80 2.66 2.43 2.25
3.08 2.93 2.79 2.54 2.35
3.20 3.05 2.91 2.66 2.45
1.60 1.80 2.00 2.20 2.40
1.12 1.01 0.922 0.847 0.782
1.13 1.02 0.932 0.856 0.791
1.17 1.06 0.964 0.887 0.820
1.22 1.11 1.01 0.932 0.863
1.28 1.17 1.07 0.986 0.914
1.35 1.24 1.13 1.05 0.971
1.43 1.31 1.20 1.11 1.03
1.50 1.38 1.27 1.18 1.10
1.58 1.45 1.34 1.25 1.16
1.65 1.52 1.41 1.31 1.22
1.72 1.59 1.47 1.37 1.28
1.85 1.72 1.60 1.49 1.40
1.98 1.84 1.72 1.61 1.51
2.09 1.95 1.82 1.71 1.62
2.19 2.05 1.92 1.81 1.71
2.29 2.14 2.02 1.90 1.80
2.60 0.726 0.734 0.762 0.803 0.852 0.907 0.964 1.03 1.09 1.15 2.80 0.677 0.686 0.712 0.750 0.797 0.849 0.905 0.963 1.02 1.08 3.00 0.635 0.643 0.668 0.704 0.749 0.799 0.852 0.906 0.963 1.02
1.21 1.14 1.07
1.32 1.24 1.18
1.43 1.35 1.28
1.53 1.45 1.37
1.62 1.54 1.46
1.71 1.62 1.55
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 168
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-38 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 75°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
ex = a l
75°
Pu l
where Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
kl ex = a l
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
75° Pu
Special Case (Load not in plane of weld group) Use C-values for k = 0
Any equal distances
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
4.11 3.88 3.76 3.64 3.53
4.11 3.90 3.77 3.65 3.54
4.11 3.95 3.83 3.71 3.60
4.11 4.00 3.90 3.79 3.69
4.11 4.04 3.96 3.88 3.78
4.11 4.07 4.01 3.94 3.87
4.11 4.08 4.04 3.99 3.93
4.11 4.09 4.06 4.03 3.98
4.11 4.09 4.08 4.05 4.01
4.11 4.09 4.08 4.06 4.03
4.11 4.09 4.09 4.07 4.05
4.11 4.09 4.09 4.08 4.07
4.11 4.09 4.09 4.09 4.08
4.11 4.09 4.09 4.09 4.08
4.11 4.09 4.09 4.09 4.09
4.11 4.09 4.09 4.09 4.09
0.30 0.40 0.50 0.60 0.70
3.43 3.24 3.07 2.91 2.77
3.44 3.25 3.08 2.92 2.78
3.49 3.29 3.12 2.97 2.82
3.58 3.38 3.20 3.05 2.90
3.69 3.50 3.32 3.15 3.00
3.78 3.62 3.45 3.29 3.13
3.86 3.72 3.57 3.42 3.27
3.92 3.80 3.67 3.54 3.40
3.97 3.86 3.75 3.63 3.51
4.00 3.91 3.82 3.71 3.60
4.02 3.95 3.87 3.78 3.68
4.05 4.00 3.94 3.88 3.80
4.07 4.03 3.99 3.94 3.88
4.07 4.05 4.02 3.98 3.93
4.08 4.06 4.04 4.01 3.97
4.08 4.07 4.05 4.03 4.00
0.80 0.90 1.00 1.20 1.40
2.63 2.50 2.38 2.17 1.99
2.64 2.52 2.40 2.18 2.00
2.69 2.57 2.45 2.24 2.05
2.77 2.64 2.53 2.32 2.13
2.87 2.74 2.63 2.41 2.23
2.99 2.86 2.74 2.52 2.33
3.13 3.00 2.87 2.64 2.45
3.26 3.13 3.01 2.78 2.57
3.39 3.26 3.14 2.91 2.71
3.49 3.38 3.26 3.04 2.84
3.58 3.48 3.37 3.16 2.96
3.72 3.64 3.55 3.37 3.18
3.81 3.75 3.68 3.52 3.36
3.88 3.83 3.77 3.64 3.50
3.93 3.88 3.83 3.73 3.61
3.96 3.93 3.88 3.80 3.69
1.60 1.80 2.00 2.20 2.40
1.83 1.69 1.57 1.46 1.37
1.84 1.70 1.58 1.48 1.38
1.89 1.75 1.63 1.52 1.43
1.97 1.83 1.70 1.59 1.49
2.06 1.92 1.79 1.68 1.57
2.17 2.02 1.89 1.77 1.67
2.28 2.13 1.99 1.87 1.76
2.39 2.24 2.10 1.97 1.86
2.52 2.35 2.21 2.08 1.97
2.65 2.48 2.33 2.19 2.07
2.78 2.61 2.45 2.30 2.18
3.01 2.84 2.68 2.54 2.40
3.20 3.05 2.89 2.75 2.61
3.36 3.22 3.08 2.94 2.81
3.49 3.36 3.23 3.10 2.98
3.59 3.48 3.36 3.24 3.13
2.60 2.80 3.00
1.28 1.21 1.14
1.30 1.22 1.15
1.34 1.27 1.20
1.40 1.33 1.26
1.48 1.40 1.33
1.57 1.49 1.41
1.66 1.58 1.49
1.76 1.67 1.59
1.86 1.77 1.68
1.96 1.86 1.77
2.07 1.96 1.87
2.28 2.16 2.06
2.49 2.37 2.26
2.68 2.56 2.45
2.85 2.73 2.62
3.01 2.89 2.78
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 169
Table 8-39. Coefficients C for Eccentrically Loaded Weld Groups Angle = 0°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
Pu
kl
l
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
4.18 3.24 2.92 2.65 2.41
4.18 3.27 2.95 2.68 2.44
4.18 3.36 3.03 2.75 2.50
4.18 3.48 3.15 2.85 2.60
4.18 3.61 3.29 2.99 2.73
4.18 3.73 3.43 3.15 2.88
4.18 3.83 3.56 3.30 3.04
4.18 3.91 3.68 3.43 3.19
4.18 3.97 3.77 3.55 3.33
4.18 4.01 3.84 3.65 3.44
4.18 4.05 3.90 3.73 3.54
4.18 4.09 3.98 3.85 3.70
4.18 4.12 4.04 3.93 3.81
4.18 4.13 4.07 3.99 3.89
4.18 4.14 4.09 4.03 3.95
4.18 4.15 4.11 4.06 3.99
0.30 0.40 0.50 0.60 0.70
2.20 1.86 1.60 1.40 1.24
2.23 1.88 1.62 1.42 1.26
2.29 1.95 1.68 1.47 1.30
2.39 2.03 1.76 1.54 1.37
2.50 2.14 1.85 1.63 1.45
2.64 2.26 1.96 1.73 1.54
2.81 2.39 2.08 1.84 1.64
2.96 2.55 2.21 1.96 1.75
3.11 2.71 2.36 2.08 1.86
3.24 2.86 2.51 2.22 1.98
3.36 2.99 2.66 2.36 2.11
3.54 3.22 2.91 2.63 2.38
3.68 3.40 3.12 2.86 2.61
3.79 3.55 3.29 3.05 2.81
3.86 3.66 3.43 3.21 2.99
3.92 3.74 3.55 3.34 3.14
0.80 0.90 1.00 1.20 1.40
1.11 1.00 0.914 0.777 0.674
1.13 1.02 0.929 0.789 0.685
1.17 1.06 0.965 0.821 0.713
1.23 1.11 1.02 0.866 0.753
1.30 1.18 1.08 0.920 0.802
1.39 1.26 1.15 0.984 0.856
1.48 1.35 1.23 1.05 0.918
1.58 1.44 1.31 1.13 0.982
1.68 1.53 1.40 1.20 1.05
1.79 1.63 1.49 1.28 1.12
1.90 1.73 1.59 1.36 1.19
2.15 1.96 1.79 1.53 1.34
2.39 2.19 2.02 1.72 1.50
2.60 2.40 2.22 1.92 1.68
2.78 2.59 2.41 2.11 1.85
2.95 2.76 2.59 2.28 2.02
1.60 1.80 2.00 2.20 2.40
0.594 0.531 0.481 0.439 0.404
0.604 0.541 0.489 0.446 0.410
0.629 0.563 0.509 0.465 0.427
0.665 0.595 0.538 0.492 0.452
0.709 0.635 0.574 0.524 0.483
0.759 0.680 0.616 0.562 0.517
0.812 0.729 0.661 0.604 0.555
0.871 0.780 0.708 0.647 0.596
0.931 0.836 0.757 0.693 0.638
0.993 0.892 0.810 0.740 0.681
1.06 0.950 0.862 0.789 0.727
1.19 1.07 0.971 0.890 0.820
1.33 1.20 1.09 0.994 0.917
1.48 1.33 1.21 1.10 1.02
1.64 1.47 1.33 1.22 1.12
1.80 1.62 1.47 1.34 1.23
2.60 0.374 0.379 0.396 0.419 0.447 0.479 0.514 0.552 0.592 0.632 0.674 0.760 0.850 0.941 1.04 1.14 2.80 0.348 0.353 0.368 0.390 0.416 0.446 0.479 0.514 0.551 0.589 0.628 0.709 0.793 0.878 0.966 1.06 3.00 0.325 0.330 0.344 0.364 0.389 0.417 0.448 0.481 0.516 0.552 0.588 0.664 0.742 0.822 0.904 0.989
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 170
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-39 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 15°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
Pu
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
15° kl
l
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
4.11 3.29 2.97 2.70 2.46
4.11 3.30 2.99 2.71 2.48
4.11 3.34 3.03 2.76 2.53
4.11 3.43 3.11 2.84 2.61
4.11 3.55 3.22 2.94 2.71
4.11 3.66 3.35 3.07 2.82
4.11 3.76 3.48 3.20 2.95
4.11 3.83 3.59 3.34 3.09
4.11 3.89 3.68 3.45 3.22
4.11 3.94 3.76 3.55 3.34
4.11 3.97 3.82 3.64 3.44
4.11 4.02 3.90 3.76 3.61
4.11 4.04 3.96 3.85 3.72
4.11 4.06 4.00 3.91 3.81
4.11 4.07 4.02 3.95 3.87
4.11 4.07 4.04 3.98 3.91
0.30 0.40 0.50 0.60 0.70
2.25 1.91 1.65 1.44 1.28
2.27 1.93 1.66 1.46 1.29
2.32 1.98 1.71 1.50 1.34
2.40 2.05 1.79 1.57 1.40
2.50 2.15 1.87 1.65 1.48
2.61 2.25 1.97 1.75 1.56
2.73 2.37 2.08 1.85 1.66
2.87 2.49 2.19 1.95 1.76
3.00 2.62 2.30 2.06 1.85
3.13 2.75 2.42 2.17 1.96
3.25 2.87 2.55 2.28 2.06
3.44 3.10 2.79 2.51 2.27
3.58 3.29 2.99 2.72 2.48
3.69 3.44 3.17 2.91 2.67
3.77 3.56 3.32 3.08 2.85
3.83 3.65 3.44 3.22 3.00
0.80 0.90 1.00 1.20 1.40
1.15 1.04 0.945 0.803 0.697
1.16 1.05 0.958 0.814 0.707
1.20 1.09 0.993 0.846 0.735
1.26 1.14 1.05 0.892 0.776
1.33 1.21 1.11 0.946 0.825
1.41 1.29 1.18 1.01 0.881
1.50 1.37 1.26 1.08 0.942
1.59 1.45 1.34 1.15 1.01
1.69 1.54 1.42 1.22 1.07
1.78 1.63 1.50 1.30 1.14
1.88 1.72 1.59 1.37 1.21
2.07 1.90 1.75 1.52 1.34
2.27 2.08 1.92 1.67 1.47
2.45 2.26 2.10 1.82 1.61
2.63 2.43 2.26 1.97 1.74
2.79 2.59 2.42 2.12 1.87
1.60 1.80 2.00 2.20 2.40
0.615 0.550 0.497 0.454 0.418
0.624 0.559 0.505 0.461 0.424
0.649 0.581 0.526 0.480 0.442
0.686 0.614 0.556 0.508 0.467
0.731 0.655 0.593 0.542 0.499
0.781 0.701 0.635 0.580 0.534
0.835 0.751 0.681 0.623 0.573
0.894 0.802 0.729 0.667 0.615
0.954 0.858 0.778 0.713 0.657
1.01 0.913 0.830 0.760 0.700
1.08 0.968 0.881 0.808 0.745
1.20 1.08 0.985 0.904 0.834
1.32 1.19 1.09 0.999 0.924
1.44 1.30 1.19 1.10 1.01
1.56 1.41 1.29 1.19 1.10
1.68 1.52 1.39 1.28 1.19
2.60 0.387 0.392 0.409 0.433 0.462 0.495 0.531 0.570 0.609 0.650 0.691 0.775 0.859 0.942 1.03 1.11 2.80 0.360 0.365 0.381 0.403 0.430 0.461 0.494 0.530 0.568 0.606 0.644 0.724 0.802 0.881 0.959 1.03 3.00 0.336 0.341 0.356 0.377 0.402 0.431 0.463 0.496 0.532 0.568 0.604 0.678 0.753 0.827 0.900 0.972
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 171
Table 8-39 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 30°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
Pu
30° kl
l
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
3.91 3.37 3.07 2.82 2.60
3.91 3.38 3.07 2.83 2.61
3.91 3.40 3.10 2.85 2.63
3.91 3.45 3.14 2.89 2.68
3.91 3.50 3.20 2.94 2.73
3.91 3.56 3.27 3.01 2.80
3.91 3.62 3.35 3.09 2.87
3.91 3.67 3.43 3.17 2.94
3.91 3.71 3.50 3.26 3.03
3.91 3.75 3.56 3.35 3.12
3.91 3.77 3.61 3.42 3.21
3.91 3.81 3.69 3.54 3.36
3.91 3.83 3.74 3.62 3.48
3.91 3.84 3.77 3.68 3.56
3.91 3.85 3.79 3.72 3.62
3.91 3.85 3.81 3.75 3.67
0.30 0.40 0.50 0.60 0.70
2.40 2.06 1.80 1.58 1.41
2.41 2.07 1.80 1.59 1.42
2.44 2.10 1.84 1.62 1.45
2.49 2.16 1.89 1.68 1.51
2.55 2.22 1.97 1.75 1.58
2.62 2.30 2.04 1.83 1.66
2.69 2.38 2.13 1.91 1.74
2.76 2.46 2.21 2.00 1.82
2.84 2.54 2.29 2.07 1.90
2.92 2.61 2.36 2.15 1.97
3.01 2.69 2.44 2.23 2.05
3.18 2.83 2.57 2.36 2.18
3.32 2.99 2.70 2.49 2.30
3.43 3.14 2.85 2.61 2.42
3.51 3.25 2.98 2.74 2.53
3.57 3.35 3.10 2.86 2.64
0.80 0.90 1.00 1.20 1.40
1.26 1.15 1.05 0.891 0.774
1.27 1.15 1.06 0.900 0.783
1.31 1.19 1.09 0.932 0.812
1.37 1.25 1.14 0.979 0.855
1.43 1.31 1.20 1.03 0.906
1.51 1.38 1.27 1.10 0.963
1.59 1.46 1.35 1.17 1.02
1.66 1.53 1.42 1.23 1.09
1.74 1.61 1.49 1.30 1.15
1.82 1.68 1.57 1.37 1.21
1.89 1.75 1.63 1.43 1.27
2.03 1.88 1.76 1.56 1.39
2.15 2.01 1.88 1.67 1.50
2.26 2.12 1.99 1.78 1.60
2.36 2.22 2.09 1.88 1.70
2.46 2.32 2.19 1.97 1.79
1.60 1.80 2.00 2.20 2.40
0.684 0.612 0.554 0.506 0.465
0.692 0.620 0.562 0.513 0.472
0.719 0.644 0.584 0.534 0.491
0.757 0.679 0.616 0.563 0.519
0.805 0.723 0.655 0.600 0.553
0.857 0.771 0.700 0.641 0.591
0.913 0.823 0.749 0.686 0.633
0.972 0.876 0.799 0.733 0.676
1.03 0.931 0.848 0.779 0.720
1.09 0.985 0.899 0.826 0.764
1.14 1.04 0.949 0.874 0.808
1.26 1.14 1.05 0.965 0.896
1.36 1.24 1.14 1.05 0.979
1.46 1.33 1.23 1.14 1.06
1.55 1.42 1.31 1.22 1.14
1.64 1.51 1.39 1.30 1.21
2.60 0.431 0.437 0.455 0.481 0.512 0.548 0.587 0.628 0.669 0.711 0.752 0.835 0.915 0.992 1.07 1.14 2.80 0.401 0.406 0.423 0.448 0.477 0.511 0.547 0.585 0.625 0.664 0.704 0.782 0.858 0.931 1.00 1.07 3.00 0.375 0.380 0.396 0.419 0.447 0.478 0.513 0.548 0.586 0.623 0.661 0.734 0.808 0.878 0.946 1.01
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 172
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-39 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 45°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
45° Pu
kl
l
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
3.61 3.37 3.13 2.94 2.77
3.61 3.37 3.13 2.94 2.77
3.61 3.38 3.15 2.95 2.78
3.61 3.38 3.17 2.97 2.80
3.61 3.40 3.20 2.99 2.83
3.61 3.42 3.23 3.03 2.86
3.61 3.43 3.25 3.06 2.89
3.61 3.44 3.28 3.10 2.93
3.61 3.46 3.30 3.13 2.97
3.61 3.47 3.33 3.17 3.01
3.61 3.48 3.35 3.20 3.04
3.61 3.50 3.38 3.25 3.11
3.61 3.51 3.41 3.29 3.16
3.61 3.52 3.43 3.33 3.21
3.61 3.52 3.45 3.35 3.25
3.61 3.52 3.47 3.38 3.28
0.30 0.40 0.50 0.60 0.70
2.61 2.32 2.06 1.84 1.66
2.61 2.32 2.07 1.85 1.66
2.63 2.34 2.09 1.87 1.69
2.65 2.37 2.12 1.91 1.73
2.68 2.41 2.17 1.96 1.79
2.71 2.45 2.22 2.02 1.85
2.75 2.50 2.27 2.08 1.91
2.79 2.54 2.33 2.14 1.97
2.83 2.59 2.38 2.19 2.03
2.86 2.63 2.42 2.25 2.09
2.90 2.66 2.47 2.30 2.14
2.97 2.73 2.54 2.38 2.23
3.04 2.80 2.61 2.45 2.31
3.09 2.87 2.68 2.52 2.38
3.14 2.92 2.74 2.58 2.44
3.18 2.97 2.79 2.63 2.50
0.80 0.90 1.00 1.20 1.40
1.50 1.37 1.26 1.08 0.938
1.51 1.38 1.26 1.08 0.946
1.54 1.40 1.29 1.11 0.975
1.58 1.45 1.34 1.16 1.02
1.64 1.51 1.40 1.21 1.07
1.70 1.57 1.46 1.28 1.13
1.76 1.64 1.53 1.34 1.19
1.83 1.70 1.59 1.40 1.25
1.89 1.76 1.65 1.46 1.31
1.95 1.82 1.71 1.52 1.37
2.00 1.88 1.77 1.58 1.42
2.10 1.98 1.87 1.68 1.52
2.18 2.07 1.96 1.77 1.62
2.26 2.14 2.04 1.85 1.70
2.32 2.21 2.11 1.93 1.77
2.38 2.27 2.17 2.00 1.84
1.60 1.80 2.00 2.20 2.40
0.831 0.745 0.675 0.617 0.568
0.838 0.752 0.682 0.624 0.574
0.866 0.779 0.707 0.647 0.596
0.908 0.817 0.743 0.681 0.628
0.958 0.864 0.787 0.722 0.667
1.01 0.917 0.836 0.768 0.710
1.07 0.972 0.888 0.818 0.756
1.13 1.03 0.941 0.868 0.804
1.19 1.08 0.992 0.917 0.851
1.24 1.13 1.04 0.964 0.897
1.29 1.19 1.09 1.01 0.941
1.39 1.28 1.18 1.10 1.03
1.48 1.37 1.27 1.18 1.11
1.56 1.45 1.35 1.26 1.18
1.64 1.52 1.42 1.33 1.25
1.71 1.59 1.49 1.40 1.32
2.60 0.526 0.532 0.553 0.583 0.619 0.660 0.703 0.749 0.794 0.838 0.881 0.963 1.04 1.12 1.18 2.80 0.489 0.496 0.515 0.544 0.578 0.617 0.658 0.701 0.743 0.786 0.827 0.906 0.982 1.05 1.12 3.00 0.458 0.464 0.482 0.509 0.542 0.579 0.618 0.658 0.699 0.739 0.779 0.856 0.929 0.998 1.06
1.25 1.18 1.12
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 173
Table 8-39 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 60°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
60°
Pu
kl
l
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
3.28 3.20 3.10 2.98 2.89
3.28 3.19 3.09 2.98 2.89
3.28 3.19 3.10 2.98 2.89
3.28 3.19 3.10 2.98 2.89
3.28 3.19 3.10 2.98 2.89
3.28 3.19 3.10 2.99 2.90
3.28 3.19 3.10 2.99 2.90
3.28 3.19 3.10 3.00 2.91
3.28 3.18 3.10 3.01 2.91
3.28 3.18 3.10 3.01 2.92
3.28 3.18 3.10 3.02 2.92
3.28 3.17 3.10 3.02 2.94
3.28 3.16 3.10 3.03 2.95
3.28 3.15 3.09 3.03 2.96
3.28 3.14 3.09 3.02 2.96
3.28 3.13 3.08 3.02 2.96
0.30 0.40 0.50 0.60 0.70
2.80 2.63 2.44 2.27 2.09
2.80 2.63 2.44 2.27 2.10
2.80 2.63 2.45 2.28 2.11
2.81 2.64 2.47 2.29 2.13
2.81 2.65 2.48 2.32 2.16
2.82 2.66 2.50 2.35 2.19
2.82 2.67 2.52 2.37 2.23
2.83 2.68 2.54 2.40 2.27
2.83 2.69 2.55 2.42 2.29
2.84 2.70 2.57 2.44 2.32
2.85 2.71 2.58 2.46 2.34
2.86 2.73 2.61 2.49 2.39
2.87 2.74 2.63 2.52 2.42
2.89 2.76 2.65 2.55 2.45
2.89 2.77 2.66 2.57 2.48
2.90 2.78 2.68 2.59 2.50
0.80 0.90 1.00 1.20 1.40
1.94 1.80 1.67 1.46 1.28
1.94 1.80 1.67 1.46 1.29
1.96 1.82 1.69 1.48 1.31
1.98 1.85 1.73 1.52 1.35
2.02 1.89 1.77 1.57 1.40
2.06 1.93 1.82 1.62 1.46
2.10 1.98 1.87 1.67 1.51
2.14 2.02 1.92 1.73 1.57
2.18 2.06 1.96 1.78 1.62
2.21 2.10 2.00 1.82 1.67
2.23 2.13 2.04 1.86 1.71
2.29 2.19 2.10 1.93 1.79
2.33 2.24 2.15 2.00 1.86
2.37 2.28 2.20 2.05 1.92
2.40 2.32 2.24 2.10 1.97
2.42 2.34 2.27 2.14 2.01
1.60 1.80 2.00 2.20 2.40
1.15 1.03 0.940 0.861 0.794
1.15 1.04 0.946 0.867 0.800
1.18 1.06 0.971 0.892 0.825
1.22 1.11 1.01 0.932 0.863
1.27 1.16 1.06 0.979 0.909
1.32 1.21 1.11 1.03 0.959
1.38 1.27 1.17 1.09 1.01
1.44 1.32 1.22 1.14 1.06
1.49 1.37 1.28 1.19 1.11
1.54 1.42 1.32 1.24 1.16
1.58 1.47 1.37 1.28 1.21
1.66 1.55 1.45 1.37 1.29
1.73 1.63 1.53 1.44 1.36
1.80 1.69 1.60 1.51 1.43
1.85 1.75 1.66 1.57 1.49
1.90 1.80 1.71 1.63 1.55
2.60 0.736 0.743 0.767 0.804 0.848 0.896 0.946 0.997 1.05 1.09 1.14 2.80 0.686 0.693 0.716 0.752 0.794 0.841 0.889 0.937 0.985 1.03 1.07 3.00 0.643 0.649 0.672 0.706 0.746 0.792 0.838 0.885 0.931 0.975 1.02
1.22 1.16 1.10
1.29 1.23 1.17
1.36 1.30 1.24
1.42 1.36 1.30
1.48 1.42 1.36
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 174
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-39 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 75°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l 75°
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
Pu kl
l
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
2.97 2.86 2.89 2.88 2.87
2.97 2.86 2.89 2.88 2.87
2.97 2.87 2.89 2.88 2.87
2.97 2.87 2.89 2.88 2.87
2.97 2.88 2.89 2.88 2.86
2.97 2.88 2.89 2.87 2.86
2.97 2.88 2.89 2.87 2.85
2.97 2.89 2.89 2.86 2.85
2.97 2.89 2.88 2.86 2.84
2.97 2.89 2.88 2.85 2.84
2.97 2.89 2.87 2.85 2.83
2.97 2.88 2.86 2.84 2.81
2.97 2.87 2.85 2.82 2.80
2.97 2.85 2.83 2.81 2.79
2.97 2.84 2.82 2.80 2.78
2.97 2.55 2.81 2.78 2.76
0.30 0.40 0.50 0.60 0.70
2.86 2.84 2.79 2.74 2.66
2.86 2.83 2.79 2.73 2.66
2.86 2.83 2.78 2.73 2.66
2.85 2.82 2.77 2.72 2.66
2.85 2.82 2.77 2.72 2.65
2.84 2.81 2.76 2.71 2.65
2.84 2.80 2.76 2.70 2.64
2.83 2.79 2.75 2.70 2.64
2.82 2.79 2.74 2.69 2.64
2.82 2.78 2.73 2.68 2.63
2.81 2.77 2.73 2.68 2.63
2.80 2.76 2.71 2.67 2.62
2.78 2.74 2.70 2.66 2.61
2.77 2.73 2.69 2.65 2.61
2.76 2.72 2.68 2.64 2.60
2.74 2.71 2.67 2.63 2.59
0.80 0.90 1.00 1.20 1.40
2.59 2.51 2.42 2.25 2.08
2.59 2.51 2.42 2.25 2.08
2.59 2.51 2.43 2.25 2.09
2.58 2.51 2.43 2.27 2.11
2.58 2.51 2.43 2.28 2.13
2.58 2.51 2.44 2.30 2.15
2.58 2.51 2.44 2.31 2.18
2.58 2.51 2.45 2.32 2.19
2.58 2.52 2.45 2.33 2.21
2.58 2.52 2.46 2.34 2.23
2.58 2.52 2.46 2.35 2.24
2.57 2.52 2.47 2.37 2.27
2.57 2.52 2.48 2.38 2.29
2.56 2.52 2.48 2.39 2.31
2.56 2.52 2.48 2.40 2.32
2.56 2.52 2.48 2.40 2.33
1.60 1.80 2.00 2.20 2.40
1.92 1.78 1.65 1.54 1.44
1.93 1.78 1.66 1.54 1.44
1.94 1.80 1.67 1.56 1.46
1.96 1.83 1.70 1.60 1.50
1.99 1.86 1.74 1.64 1.54
2.02 1.89 1.78 1.68 1.59
2.05 1.93 1.82 1.72 1.63
2.08 1.96 1.86 1.76 1.68
2.10 1.99 1.89 1.80 1.71
2.12 2.02 1.92 1.83 1.75
2.14 2.04 1.95 1.86 1.78
2.17 2.08 2.00 1.92 1.84
2.20 2.12 2.04 1.96 1.89
2.22 2.15 2.07 2.00 1.93
2.24 2.17 2.10 2.03 1.97
2.26 2.19 2.12 2.06 2.00
2.60 2.80 3.00
1.35 1.26 1.19
1.35 1.27 1.20
1.37 1.29 1.22
1.41 1.33 1.26
1.45 1.37 1.30
1.50 1.42 1.35
1.55 1.47 1.40
1.60 1.52 1.45
1.64 1.56 1.50
1.67 1.60 1.54
1.71 1.64 1.58
1.77 1.71 1.64
1.82 1.76 1.70
1.87 1.81 1.75
1.91 1.85 1.79
1.94 1.88 1.83
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 175
Table 8-40. Coefficients C for Eccentrically Loaded Weld Groups Angle = 0°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
l
Pu
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
0.00 0.10 0.15 0.20 0.25
2.78 2.78 2.75 2.64 2.48
3.20 3.07 3.05 2.95 2.79
3.62 3.42 3.37 3.25 3.10
4.04 3.78 3.71 3.57 3.40
4.45 4.15 4.06 3.91 3.72
4.87 4.53 4.42 4.25 4.04
5.29 4.91 4.78 4.59 4.38
5.71 5.30 5.15 4.94 4.71
6.12 5.69 5.52 5.30 5.06
6.54 6.08 5.89 5.66 5.40
6.96 6.47 6.27 6.02 5.75
7.80 7.25 7.02 6.75 6.46
8.63 8.03 7.78 7.49 7.18
9.47 10.3 11.1 8.82 9.61 10.4 8.54 9.31 10.1 8.23 8.98 9.74 7.91 8.65 9.39
0.30 0.40 0.50 0.60 0.70
2.32 2.00 1.72 1.50 1.32
2.61 2.26 1.95 1.70 1.50
2.92 2.54 2.20 1.92 1.70
3.22 2.83 2.47 2.17 1.93
3.52 3.12 2.75 2.44 2.17
3.83 3.41 3.03 2.70 2.43
4.15 3.71 3.31 2.97 2.68
4.47 4.01 3.59 3.24 2.93
4.80 4.32 3.89 3.52 3.20
5.14 4.64 4.19 3.80 3.47
5.48 4.96 4.50 4.09 3.75
6.17 5.62 5.13 4.70 4.33
6.88 6.30 5.78 5.33 4.93
7.59 6.99 6.46 5.98 5.56
8.32 7.70 7.14 6.64 6.20
9.05 8.42 7.84 7.32 6.86
0.80 0.90 1.00 1.20 1.40
1.17 1.05 0.957 0.806 0.695
1.33 1.20 1.09 0.916 0.790
1.52 1.37 1.24 1.05 0.908
1.73 1.56 1.42 1.21 1.05
1.95 1.77 1.62 1.38 1.20
2.20 2.00 1.83 1.57 1.37
2.43 2.23 2.05 1.76 1.54
2.67 2.45 2.26 1.95 1.72
2.92 2.69 2.49 2.15 1.89
3.18 2.93 2.72 2.36 2.08
3.45 3.18 2.96 2.57 2.27
4.00 3.71 3.45 3.02 2.68
4.58 4.26 3.98 3.50 3.12
5.18 4.84 4.53 4.00 3.58
5.80 5.44 5.10 4.53 4.06
6.44 6.05 5.69 5.08 4.57
1.60 1.80 2.00 2.20 2.40
0.611 0.544 0.491 0.447 0.410
0.694 0.619 0.558 0.509 0.467
0.800 0.714 0.645 0.588 0.540
0.923 0.825 0.746 0.680 0.625
1.06 0.950 0.860 0.785 0.721
1.21 1.09 0.984 0.898 0.827
1.37 1.23 1.12 1.02 0.939
1.53 1.37 1.25 1.14 1.05
1.69 1.52 1.38 1.27 1.17
1.86 1.68 1.53 1.40 1.29
2.03 1.84 1.67 1.54 1.42
2.40 2.18 1.99 1.83 1.69
2.80 2.54 2.33 2.14 1.99
3.23 2.93 2.69 2.48 2.30
3.67 3.35 3.08 2.84 2.64
4.15 3.79 3.49 3.22 3.00
2.60 0.379 0.431 0.499 0.578 0.667 0.765 0.869 0.977 1.09 1.20 2.80 0.352 0.401 0.464 0.538 0.621 0.712 0.809 0.911 1.01 1.12 3.00 0.329 0.375 0.434 0.503 0.580 0.666 0.757 0.853 0.949 1.05
1.32 1.23 1.16
1.57 1.47 1.38
1.85 1.73 1.62
2.15 2.01 1.89
2.46 2.31 2.17
2.80 2.63 2.47
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.8
2.0
8 - 176
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-40 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 15°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
15°
l
Pu
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
0.00 0.10 0.15 0.20 0.25
2.97 2.84 2.76 2.63 2.48
3.38 3.16 3.10 2.96 2.79
3.79 3.52 3.44 3.30 3.12
4.20 3.89 3.79 3.64 3.45
4.61 4.28 4.14 3.98 3.78
5.02 4.66 4.51 4.32 4.11
5.43 5.05 4.87 4.67 4.45
5.84 5.43 5.24 5.02 4.78
6.25 5.83 5.61 5.37 5.13
6.66 6.22 5.98 5.73 5.47
7.07 6.62 6.35 6.09 5.82
7.89 7.41 7.11 6.82 6.53
8.71 8.20 7.86 7.55 7.25
9.54 10.4 11.2 8.99 9.79 10.6 8.63 9.41 10.2 8.30 9.05 9.81 7.98 8.72 9.46
0.30 0.40 0.50 0.60 0.70
2.32 2.01 1.74 1.52 1.34
2.61 2.26 1.96 1.72 1.52
2.92 2.54 2.21 1.94 1.72
3.24 2.84 2.48 2.19 1.95
3.57 3.15 2.77 2.46 2.19
3.89 3.46 3.07 2.74 2.46
4.22 3.77 3.37 3.03 2.73
4.54 4.08 3.66 3.30 3.00
4.88 4.39 3.96 3.59 3.27
5.21 4.71 4.27 3.88 3.55
5.55 5.04 4.58 4.18 3.83
6.24 5.70 5.21 4.79 4.42
6.95 6.38 5.87 5.42 5.03
7.66 7.07 6.54 6.07 5.66
8.39 7.78 7.23 6.74 6.31
9.13 8.50 7.93 7.43 6.97
0.80 0.90 1.00 1.20 1.40
1.20 1.08 0.979 0.826 0.714
1.36 1.22 1.11 0.938 0.810
1.54 1.39 1.27 1.07 0.930
1.75 1.58 1.45 1.23 1.07
1.98 1.80 1.65 1.41 1.23
2.22 2.03 1.87 1.60 1.40
2.48 2.27 2.09 1.81 1.58
2.74 2.52 2.32 2.01 1.77
3.00 2.76 2.55 2.21 1.95
3.26 3.01 2.79 2.43 2.14
3.53 3.26 3.03 2.65 2.34
4.09 3.80 3.54 3.10 2.76
4.67 4.36 4.07 3.59 3.20
5.28 4.94 4.63 4.10 3.67
5.91 5.54 5.21 4.64 4.16
6.55 6.16 5.81 5.19 4.68
1.60 1.80 2.00 2.20 2.40
0.628 0.560 0.506 0.461 0.423
0.713 0.636 0.575 0.524 0.481
0.820 0.733 0.663 0.605 0.556
0.946 0.846 0.766 0.699 0.643
1.09 0.974 0.882 0.805 0.741
1.24 1.11 1.01 0.922 0.849
1.41 1.26 1.15 1.05 0.965
1.57 1.42 1.29 1.18 1.09
1.74 1.57 1.43 1.31 1.21
1.91 1.73 1.57 1.45 1.33
2.09 1.89 1.73 1.59 1.47
2.48 2.24 2.05 1.89 1.75
2.89 2.62 2.40 2.21 2.05
3.32 3.02 2.77 2.56 2.38
3.78 3.45 3.17 2.93 2.72
4.26 3.89 3.59 3.32 3.09
2.60 0.391 0.445 0.514 0.595 0.686 0.786 0.894 1.01 1.12 1.24 2.80 0.363 0.414 0.478 0.554 0.638 0.732 0.832 0.938 1.05 1.16 3.00 0.339 0.386 0.447 0.518 0.597 0.684 0.779 0.878 0.981 1.09
1.36 1.27 1.19
1.63 1.52 1.43
1.91 1.79 1.68
2.22 2.07 1.95
2.54 2.38 2.24
2.89 2.71 2.55
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.8
2.0
ECCENTRICALLY LOADED WELD GROUPS
8 - 177
Table 8-40 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 30°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
30°
l
Pu
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
3.28 3.03 2.87 2.72 2.57
3.67 3.45 3.25 3.07 2.88
4.06 3.85 3.63 3.43 3.22
4.45 4.24 4.02 3.80 3.57
4.84 4.62 4.40 4.17 3.93
5.23 5.00 4.77 4.53 4.29
5.62 5.38 5.15 4.89 4.65
6.01 5.76 5.52 5.25 4.99
6.40 6.14 5.89 5.61 5.34
6.79 6.52 6.26 5.97 5.69
7.18 6.90 6.64 6.34 6.05
7.96 7.67 7.39 7.09 6.77
8.74 8.44 8.15 7.84 7.52
9.53 10.3 9.22 10.0 8.93 9.70 8.60 9.37 8.27 9.04
11.1 10.8 10.5 10.2 9.81
0.30 0.40 0.50 0.60 0.70
2.41 2.11 1.84 1.62 1.44
2.70 2.36 2.07 1.83 1.63
3.02 2.64 2.32 2.06 1.84
3.35 2.95 2.60 2.31 2.07
3.70 3.27 2.90 2.59 2.33
4.05 3.60 3.21 2.88 2.60
4.40 3.94 3.53 3.18 2.89
4.75 4.28 3.86 3.50 3.19
5.09 4.61 4.19 3.82 3.50
5.43 4.94 4.50 4.12 3.79
5.77 5.27 4.83 4.43 4.09
6.48 5.95 5.48 5.07 4.70
7.21 6.65 6.16 5.73 5.33
7.95 7.36 6.85 6.40 5.99
8.71 8.09 7.56 7.09 6.66
9.48 8.85 8.28 7.79 7.35
0.80 0.90 1.00 1.20 1.40
1.30 1.17 1.07 0.907 0.786
1.46 1.32 1.21 1.03 0.890
1.65 1.50 1.37 1.17 1.02
1.87 1.70 1.56 1.34 1.17
2.11 1.93 1.78 1.53 1.34
2.37 2.18 2.01 1.73 1.52
2.64 2.43 2.25 1.95 1.72
2.93 2.70 2.51 2.18 1.93
3.22 2.98 2.77 2.41 2.14
3.50 3.25 3.02 2.65 2.34
3.79 3.52 3.28 2.88 2.56
4.38 4.08 3.82 3.37 3.01
4.98 4.67 4.38 3.89 3.49
5.61 5.28 4.97 4.44 3.99
6.26 5.90 5.57 5.00 4.52
6.93 6.55 6.20 5.59 5.07
1.60 1.80 2.00 2.20 2.40
0.693 0.619 0.559 0.510 0.469
0.785 0.703 0.635 0.579 0.533
0.901 0.808 0.731 0.668 0.614
1.04 0.931 0.844 0.771 0.710
1.19 1.07 0.970 0.887 0.818
1.36 1.22 1.11 1.01 0.935
1.53 1.38 1.26 1.15 1.06
1.72 1.55 1.41 1.30 1.20
1.91 1.73 1.57 1.45 1.34
2.10 1.90 1.74 1.60 1.48
2.30 2.08 1.91 1.75 1.62
2.72 2.47 2.26 2.08 1.93
3.16 2.88 2.64 2.44 2.27
3.62 3.31 3.05 2.82 2.62
4.12 3.77 3.48 3.22 3.00
4.63 4.25 3.93 3.64 3.40
2.60 0.433 0.493 0.569 0.658 0.758 0.867 0.984 1.11 1.24 2.80 0.403 0.458 0.529 0.613 0.706 0.808 0.918 1.03 1.16 3.00 0.376 0.428 0.495 0.573 0.661 0.757 0.860 0.969 1.08
1.37 1.28 1.20
1.51 1.41 1.32
1.80 1.68 1.58
2.11 1.98 1.86
2.45 2.29 2.16
2.80 2.63 2.48
3.18 2.99 2.82
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 178
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-40 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 45°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
45°
l
Pu
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
3.61 3.37 3.13 2.94 2.77
3.97 3.74 3.52 3.29 3.10
4.33 4.11 3.89 3.65 3.44
4.70 4.48 4.26 4.02 3.79
5.06 4.84 4.62 4.38 4.14
5.42 5.21 4.99 4.75 4.51
5.78 5.58 5.36 5.12 4.87
6.14 5.94 5.74 5.50 5.25
6.50 6.31 6.11 5.88 5.63
6.86 6.68 6.49 6.26 6.01
7.22 7.04 6.86 6.64 6.40
7.95 7.78 7.61 7.39 7.16
8.67 8.52 8.36 8.15 7.92
9.39 10.1 9.25 9.99 9.11 9.85 8.91 9.66 8.68 9.45
10.8 10.7 10.6 10.4 10.2
0.30 0.40 0.50 0.60 0.70
2.61 2.32 2.06 1.84 1.66
2.91 2.59 2.30 2.06 1.86
3.24 2.87 2.57 2.30 2.08
3.57 3.18 2.86 2.58 2.34
3.92 3.51 3.16 2.87 2.61
4.27 3.85 3.49 3.17 2.91
4.63 4.20 3.82 3.50 3.22
5.00 4.55 4.17 3.83 3.54
5.38 4.92 4.52 4.18 3.88
5.76 5.29 4.89 4.53 4.22
6.15 5.67 5.26 4.89 4.56
6.91 6.42 5.97 5.57 5.22
7.67 7.18 6.71 6.28 5.90
8.44 7.95 7.47 7.02 6.62
9.21 8.72 8.24 7.78 7.35
9.98 9.50 9.01 8.54 8.10
0.80 0.90 1.00 1.20 1.40
1.50 1.37 1.26 1.08 0.938
1.69 1.54 1.41 1.21 1.06
1.90 1.74 1.60 1.38 1.21
2.13 1.96 1.81 1.57 1.38
2.40 2.21 2.05 1.78 1.57
2.68 2.48 2.30 2.01 1.78
2.98 2.76 2.58 2.26 2.01
3.29 3.06 2.86 2.52 2.24
3.61 3.37 3.15 2.78 2.49
3.93 3.68 3.45 3.06 2.74
4.27 4.00 3.76 3.34 3.00
4.91 4.62 4.35 3.90 3.52
5.56 5.25 4.97 4.48 4.06
6.25 5.91 5.61 5.07 4.62
6.97 6.61 6.28 5.70 5.21
7.70 7.32 6.97 6.35 5.81
1.60 1.80 2.00 2.20 2.40
0.831 0.745 0.675 0.617 0.568
0.939 0.843 0.764 0.699 0.644
1.07 0.966 0.877 0.804 0.741
1.23 1.11 1.01 0.925 0.854
1.41 1.27 1.16 1.06 0.981
1.60 1.45 1.32 1.21 1.12
1.80 1.63 1.49 1.37 1.27
2.02 1.83 1.67 1.54 1.43
2.24 2.04 1.87 1.72 1.59
2.48 2.25 2.06 1.90 1.77
2.71 2.48 2.27 2.10 1.95
3.20 2.93 2.69 2.49 2.32
3.70 3.40 3.14 2.91 2.71
4.23 3.90 3.60 3.35 3.13
4.78 4.42 4.09 3.81 3.57
5.36 4.96 4.61 4.30 4.03
2.60 0.526 0.597 0.687 0.792 0.911 1.04 1.18 2.80 0.489 0.556 0.641 0.739 0.850 0.972 1.10 3.00 0.458 0.520 0.600 0.693 0.796 0.911 1.03
1.33 1.24 1.17
1.48 1.39 1.30
1.65 1.54 1.45
1.82 1.70 1.60
2.16 2.03 1.91
2.54 2.38 2.24
2.93 2.75 2.60
3.35 3.15 2.97
3.78 3.57 3.37
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 179
Table 8-40 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 60°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
60°
l
Pu
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
3.91 3.65 3.46 3.27 3.10
4.23 3.97 3.78 3.60 3.42
4.56 4.30 4.11 3.92 3.74
4.89 4.64 4.45 4.26 4.07
5.22 4.99 4.80 4.61 4.41
5.54 5.35 5.17 4.97 4.78
5.87 5.70 5.53 5.35 5.15
6.20 6.05 5.90 5.72 5.53
6.53 6.40 6.26 6.09 5.92
6.85 6.74 6.61 6.46 6.29
7.18 7.08 6.97 6.82 6.67
7.84 7.75 7.66 7.54 7.40
8.49 8.42 8.34 8.24 8.12
9.15 9.08 9.02 8.93 8.83
9.80 9.74 9.69 9.61 9.52
10.5 10.4 10.4 10.3 10.2
0.30 0.40 0.50 0.60 0.70
2.95 2.68 2.44 2.24 2.05
3.25 2.96 2.70 2.47 2.28
3.57 3.26 2.98 2.74 2.53
3.89 3.57 3.29 3.04 2.81
4.23 3.90 3.61 3.35 3.12
4.59 4.24 3.95 3.69 3.45
4.97 4.61 4.31 4.04 3.79
5.35 4.99 4.68 4.40 4.14
5.74 5.38 5.06 4.77 4.50
6.12 5.77 5.45 5.15 4.87
6.50 6.16 5.84 5.54 5.25
7.25 6.93 6.61 6.31 6.02
7.98 7.69 7.37 7.08 6.79
8.70 8.43 8.12 7.83 7.55
9.41 10.1 9.16 9.87 8.87 9.60 8.58 9.31 8.30 9.04
0.80 0.90 1.00 1.20 1.40
1.89 1.75 1.62 1.42 1.25
2.10 1.95 1.81 1.59 1.41
2.34 2.18 2.03 1.79 1.59
2.62 2.44 2.29 2.02 1.81
2.92 2.73 2.56 2.28 2.04
3.23 3.04 2.86 2.55 2.30
3.56 3.36 3.17 2.84 2.57
3.91 3.69 3.49 3.15 2.85
4.26 4.03 3.82 3.46 3.14
4.62 4.38 4.17 3.78 3.45
4.99 4.74 4.52 4.11 3.76
5.75 5.49 5.24 4.80 4.41
6.51 6.24 5.98 5.50 5.07
7.27 6.99 6.72 6.21 5.75
8.02 7.74 7.46 6.93 6.44
8.76 8.48 8.20 7.66 7.16
1.60 1.80 2.00 2.20 2.40
1.12 1.01 0.922 0.847 0.782
1.26 1.14 1.04 0.956 0.884
1.43 1.30 1.19 1.09 1.01
1.63 1.48 1.36 1.25 1.16
1.85 1.69 1.55 1.43 1.33
2.09 1.91 1.75 1.62 1.51
2.34 2.14 1.97 1.83 1.70
2.60 2.39 2.20 2.04 1.91
2.88 2.65 2.45 2.27 2.12
3.16 2.92 2.70 2.51 2.35
3.46 3.20 2.97 2.76 2.58
4.08 3.78 3.52 3.28 3.08
4.69 4.36 4.08 3.82 3.59
5.34 4.97 4.65 4.37 4.11
6.01 5.61 5.26 4.94 4.66
6.70 6.27 5.90 5.55 5.24
2.60 0.726 0.821 0.943 1.08 1.24 2.80 0.677 0.767 0.881 1.01 1.16 3.00 0.635 0.719 0.827 0.952 1.09
1.41 1.32 1.24
1.59 1.49 1.40
1.78 1.67 1.58
1.99 1.87 1.76
2.20 2.07 1.95
2.42 2.28 2.15
2.89 2.73 2.58
3.38 3.20 3.03
3.88 3.68 3.49
4.40 4.18 3.97
4.96 4.70 4.47
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 180
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-40 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 75°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
75°
l
Pu
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
0.00 0.10 0.15 0.20 0.25
4.11 3.88 3.76 3.64 3.53
4.40 4.17 4.04 3.92 3.80
4.70 4.49 4.36 4.23 4.11
5.00 4.81 4.69 4.57 4.45
5.29 5.14 5.03 4.92 4.81
5.59 5.45 5.36 5.26 5.16
5.89 5.76 5.69 5.60 5.50
6.18 6.07 6.00 5.92 5.84
6.48 6.36 6.31 6.24 6.16
6.78 6.66 6.61 6.55 6.48
7.07 6.96 6.91 6.86 6.80
7.67 7.53 7.50 7.46 7.41
8.26 8.11 8.09 8.05 8.01
8.85 8.69 8.67 8.64 8.60
9.45 10.0 9.27 9.84 9.25 9.83 9.23 9.81 9.19 9.78
0.30 0.40 0.50 0.60 0.70
3.43 3.24 3.07 2.91 2.77
3.70 3.51 3.34 3.17 3.02
4.00 3.80 3.63 3.46 3.31
4.34 4.14 3.95 3.78 3.63
4.70 4.49 4.31 4.13 3.97
5.05 4.86 4.67 4.49 4.33
5.40 5.22 5.04 4.86 4.70
5.75 5.57 5.40 5.23 5.07
6.08 5.91 5.75 5.60 5.44
6.41 6.25 6.10 5.95 5.80
6.72 6.57 6.43 6.30 6.16
7.35 7.22 7.08 6.96 6.84
7.96 7.85 7.71 7.60 7.50
8.56 8.46 8.34 8.23 8.13
9.16 9.07 8.96 8.84 8.75
9.75 9.67 9.57 9.46 9.36
0.80 0.90 1.00 1.20 1.40
2.63 2.50 2.38 2.17 1.99
2.87 2.74 2.62 2.39 2.20
3.16 3.02 2.89 2.66 2.45
3.48 3.34 3.20 2.96 2.74
3.81 3.67 3.53 3.28 3.05
4.17 4.02 3.87 3.61 3.38
4.53 4.38 4.23 3.96 3.71
4.91 4.75 4.60 4.32 4.06
5.28 5.13 4.98 4.69 4.42
5.65 5.50 5.35 5.06 4.79
6.01 5.87 5.72 5.44 5.16
6.72 6.58 6.45 6.18 5.91
7.39 7.27 7.15 6.90 6.64
8.04 7.93 7.83 7.60 7.36
8.66 8.57 8.48 8.28 8.06
9.27 9.20 9.11 8.93 8.74
1.60 1.80 2.00 2.20 2.40
1.83 1.69 1.57 1.46 1.37
2.03 1.88 1.75 1.63 1.53
2.27 2.11 1.97 1.84 1.73
2.54 2.37 2.22 2.08 1.96
2.84 2.66 2.49 2.34 2.21
3.16 2.96 2.79 2.63 2.48
3.49 3.28 3.10 2.92 2.77
3.82 3.61 3.41 3.23 3.07
4.17 3.95 3.74 3.55 3.37
4.53 4.29 4.08 3.88 3.69
4.90 4.65 4.43 4.22 4.02
5.64 5.39 5.15 4.92 4.71
6.39 6.13 5.88 5.64 5.42
7.12 6.87 6.62 6.37 6.14
7.83 7.59 7.34 7.10 6.87
8.53 8.30 8.07 7.83 7.59
2.60 2.80 3.00
1.28 1.21 1.14
1.44 1.36 1.28
1.63 1.54 1.46
1.85 1.75 1.66
2.09 1.98 1.88
2.35 2.23 2.12
2.62 2.50 2.38
2.91 2.78 2.65
3.21 3.07 2.92
3.52 3.36 3.22
3.84 3.67 3.52
4.51 4.32 4.14
5.20 5.00 4.80
5.91 5.70 5.49
6.63 6.41 6.19
7.36 7.13 6.91
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2.0
ECCENTRICALLY LOADED WELD GROUPS
8 - 181
Table 8-41. Coefficients C for Eccentrically Loaded Weld Groups Angle = 0°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
Pu
kl
l
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
4.18 3.24 2.92 2.65 2.41
4.45 3.51 3.18 2.89 2.64
4.73 3.81 3.49 3.19 2.93
5.01 4.15 3.81 3.52 3.25
5.29 4.51 4.16 3.85 3.58
5.57 4.87 4.53 4.21 3.92
5.85 5.22 4.89 4.58 4.28
6.12 5.55 5.25 4.95 4.65
6.40 5.87 5.60 5.31 5.02
6.68 6.17 5.94 5.67 5.39
6.96 6.47 6.27 6.02 5.75
7.52 7.03 6.89 6.69 6.45
8.07 7.56 7.47 7.32 7.12
8.63 8.08 8.03 7.92 7.76
9.19 8.59 8.58 8.50 8.37
9.74 9.09 9.11 9.06 8.96
0.30 0.40 0.50 0.60 0.70
2.20 1.86 1.60 1.40 1.24
2.43 2.07 1.79 1.57 1.39
2.70 2.31 2.01 1.77 1.58
3.00 2.59 2.27 2.01 1.79
3.33 2.90 2.55 2.26 2.03
3.66 3.22 2.85 2.54 2.28
4.01 3.54 3.16 2.83 2.56
4.37 3.88 3.48 3.13 2.84
4.74 4.23 3.80 3.44 3.13
5.11 4.60 4.15 3.76 3.44
5.48 4.96 4.50 4.09 3.75
6.20 5.70 5.22 4.79 4.40
6.90 6.43 5.95 5.50 5.09
7.57 7.14 6.68 6.22 5.80
8.21 7.83 7.39 6.95 6.51
8.83 8.49 8.09 7.66 7.23
0.80 0.90 1.00 1.20 1.40
1.11 1.00 0.914 0.777 0.674
1.25 1.13 1.03 0.880 0.764
1.42 1.29 1.18 1.01 0.879
1.62 1.48 1.35 1.16 1.01
1.84 1.68 1.54 1.32 1.16
2.07 1.89 1.74 1.50 1.31
2.32 2.13 1.96 1.69 1.48
2.59 2.38 2.19 1.89 1.67
2.87 2.64 2.44 2.11 1.86
3.15 2.91 2.69 2.34 2.06
3.45 3.18 2.96 2.57 2.27
4.07 3.77 3.51 3.08 2.73
4.72 4.39 4.10 3.61 3.21
5.41 5.05 4.73 4.18 3.73
6.11 5.73 5.38 4.78 4.28
6.82 6.42 6.06 5.40 4.86
1.60 1.80 2.00 2.20 2.40
0.594 0.531 0.481 0.439 0.404
0.675 0.604 0.547 0.499 0.459
0.777 0.696 0.630 0.576 0.530
0.895 0.803 0.728 0.665 0.612
1.03 0.921 0.836 0.765 0.705
1.17 1.05 0.953 0.873 0.805
1.32 1.19 1.08 0.990 0.913
1.48 1.34 1.22 1.11 1.03
1.66 1.49 1.36 1.25 1.15
1.84 1.66 1.51 1.39 1.28
2.03 1.84 1.67 1.54 1.42
2.44 2.21 2.02 1.86 1.72
2.89 2.62 2.39 2.20 2.04
3.36 3.06 2.80 2.58 2.39
3.87 3.52 3.23 2.97 2.76
4.39 4.00 3.67 3.39 3.14
2.60 0.374 0.425 0.491 0.567 0.653 0.747 0.847 0.955 1.07 1.19 2.80 0.348 0.396 0.457 0.529 0.608 0.696 0.790 0.890 0.998 1.11 3.00 0.325 0.370 0.428 0.495 0.569 0.651 0.740 0.834 0.935 1.04
1.32 1.23 1.16
1.60 1.49 1.40
1.90 1.77 1.66
2.22 2.08 1.95
2.57 2.40 2.25
2.93 2.74 2.57
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 182
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-41 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 15°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
Pu
ex = a l
15°
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
kl
l
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
0.00 0.10 0.15 0.20 0.25
4.11 3.29 2.97 2.70 2.46
4.40 3.56 3.24 2.95 2.70
4.70 3.85 3.53 3.24 2.98
5.00 4.19 3.85 3.56 3.29
5.29 4.55 4.20 3.89 3.63
5.59 4.91 4.56 4.25 3.97
5.89 5.26 4.93 4.62 4.33
6.18 5.61 5.30 4.99 4.70
6.48 5.95 5.66 5.37 5.08
6.78 6.29 6.01 5.73 5.45
7.07 6.62 6.35 6.09 5.82
7.67 7.26 7.01 6.78 6.54
8.26 7.88 7.65 7.45 7.23
8.85 8.49 8.27 8.08 7.90
9.45 10.0 9.09 9.69 8.89 9.51 8.71 9.31 8.54 9.17
0.30 0.40 0.50 0.60 0.70
2.25 1.91 1.65 1.44 1.28
2.48 2.12 1.83 1.61 1.43
2.75 2.36 2.06 1.82 1.62
3.05 2.65 2.32 2.06 1.84
3.38 2.95 2.60 2.32 2.08
3.71 3.27 2.90 2.60 2.34
4.06 3.61 3.22 2.89 2.62
4.43 3.95 3.54 3.20 2.91
4.80 4.30 3.88 3.52 3.21
5.17 4.67 4.22 3.84 3.51
5.55 5.04 4.58 4.18 3.83
6.29 5.78 5.31 4.88 4.49
7.01 6.52 6.04 5.60 5.19
7.70 7.25 6.78 6.33 5.90
8.36 7.95 7.51 7.06 6.62
9.01 8.64 8.23 7.78 7.34
0.80 0.90 1.00 1.20 1.40
1.15 1.04 0.945 0.803 0.697
1.29 1.17 1.07 0.908 0.789
1.46 1.33 1.22 1.04 0.907
1.67 1.52 1.39 1.19 1.04
1.89 1.72 1.59 1.36 1.19
2.13 1.95 1.79 1.54 1.35
2.38 2.19 2.02 1.74 1.53
2.65 2.44 2.25 1.95 1.72
2.93 2.70 2.50 2.17 1.91
3.23 2.98 2.76 2.40 2.12
3.53 3.26 3.03 2.65 2.34
4.15 3.86 3.60 3.16 2.80
4.82 4.49 4.19 3.70 3.30
5.50 5.15 4.83 4.27 3.82
6.21 5.83 5.48 4.86 4.35
6.92 6.52 6.15 5.48 4.92
1.60 1.80 2.00 2.20 2.40
0.615 0.550 0.497 0.454 0.418
0.698 0.625 0.565 0.516 0.475
0.803 0.719 0.651 0.595 0.548
0.924 0.829 0.752 0.687 0.633
1.06 0.951 0.863 0.790 0.728
1.21 1.08 0.984 0.902 0.832
1.36 1.23 1.12 1.02 0.943
1.53 1.38 1.26 1.15 1.06
1.71 1.54 1.40 1.29 1.19
1.90 1.71 1.56 1.43 1.32
2.09 1.89 1.73 1.59 1.47
2.51 2.28 2.08 1.91 1.77
2.97 2.69 2.47 2.27 2.10
3.45 3.13 2.87 2.65 2.45
3.93 3.58 3.29 3.04 2.82
4.45 4.06 3.73 3.45 3.20
2.60 0.387 0.440 0.508 0.586 0.675 0.772 0.875 0.987 1.11 1.23 2.80 0.360 0.409 0.473 0.546 0.629 0.719 0.817 0.921 1.03 1.15 3.00 0.336 0.383 0.442 0.511 0.589 0.674 0.765 0.863 0.967 1.08
1.36 1.27 1.19
1.65 1.54 1.44
1.96 1.83 1.72
2.28 2.14 2.01
2.63 2.46 2.31
2.99 2.80 2.63
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2.0
ECCENTRICALLY LOADED WELD GROUPS
8 - 183
Table 8-41 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 30°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
Pu
30° kl
l
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
3.91 3.37 3.07 2.82 2.60
4.23 3.70 3.38 3.11 2.87
4.56 4.02 3.71 3.42 3.16
4.89 4.36 4.03 3.74 3.47
5.22 4.71 4.38 4.07 3.80
5.54 5.08 4.74 4.42 4.14
5.87 5.45 5.12 4.80 4.51
6.20 5.81 5.50 5.18 4.88
6.53 6.18 5.88 5.57 5.27
6.85 6.55 6.26 5.96 5.66
7.18 6.90 6.64 6.34 6.05
7.84 7.61 7.37 7.10 6.82
8.49 8.30 8.10 7.85 7.58
9.15 8.98 8.80 8.58 8.33
9.80 9.65 9.50 9.30 9.06
10.5 10.3 10.2 10.0 9.79
0.30 0.40 0.50 0.60 0.70
2.40 2.06 1.80 1.58 1.41
2.65 2.29 2.00 1.76 1.57
2.93 2.55 2.23 1.98 1.77
3.24 2.83 2.50 2.23 2.01
3.56 3.14 2.79 2.50 2.26
3.89 3.46 3.10 2.79 2.54
4.25 3.81 3.42 3.10 2.82
4.62 4.16 3.76 3.42 3.13
5.00 4.52 4.11 3.75 3.44
5.39 4.89 4.46 4.09 3.76
5.77 5.27 4.83 4.43 4.09
6.55 6.04 5.57 5.15 4.77
7.31 6.81 6.33 5.88 5.47
8.06 7.57 7.09 6.61 6.18
8.81 8.32 7.84 7.35 6.90
9.55 9.06 8.58 8.09 7.63
0.80 0.90 1.00 1.20 1.40
1.26 1.15 1.05 0.891 0.774
1.42 1.29 1.18 1.01 0.875
1.60 1.46 1.34 1.15 1.00
1.82 1.66 1.53 1.32 1.15
2.06 1.89 1.74 1.50 1.32
2.31 2.13 1.96 1.70 1.49
2.59 2.38 2.20 1.91 1.69
2.87 2.65 2.46 2.14 1.89
3.17 2.93 2.72 2.38 2.10
3.47 3.22 3.00 2.62 2.33
3.79 3.52 3.28 2.88 2.56
4.44 4.14 3.87 3.42 3.05
5.10 4.77 4.47 3.97 3.56
5.78 5.42 5.09 4.54 4.08
6.48 6.09 5.74 5.13 4.63
7.19 6.79 6.41 5.76 5.20
1.60 1.80 2.00 2.20 2.40
0.684 0.612 0.554 0.506 0.465
0.774 0.694 0.629 0.574 0.528
0.889 0.798 0.723 0.662 0.609
1.02 0.919 0.834 0.763 0.703
1.17 1.05 0.957 0.877 0.809
1.33 1.20 1.09 1.00 0.924
1.51 1.36 1.24 1.14 1.05
1.69 1.53 1.39 1.28 1.18
1.88 1.70 1.55 1.43 1.32
2.09 1.89 1.73 1.59 1.47
2.30 2.08 1.91 1.75 1.62
2.75 2.50 2.29 2.11 1.95
3.22 2.94 2.69 2.48 2.30
3.70 3.38 3.11 2.87 2.67
4.21 3.86 3.55 3.29 3.06
4.74 4.35 4.01 3.72 3.47
2.60 0.431 0.489 0.565 0.652 0.750 0.857 0.972 1.10 1.23 2.80 0.401 0.456 0.526 0.608 0.699 0.800 0.908 1.02 1.15 3.00 0.375 0.426 0.492 0.569 0.654 0.749 0.851 0.959 1.07
1.36 1.27 1.20
1.51 1.41 1.32
1.82 1.70 1.60
2.15 2.01 1.89
2.49 2.34 2.20
2.86 2.68 2.52
3.24 3.05 2.87
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 184
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-41 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 45°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
45° Pu
kl
l
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
3.61 3.37 3.13 2.94 2.77
3.97 3.74 3.52 3.29 3.10
4.33 4.11 3.89 3.65 3.44
4.70 4.48 4.26 4.02 3.79
5.06 4.84 4.62 4.38 4.14
5.42 5.21 4.99 4.75 4.51
5.78 5.58 5.36 5.12 4.87
6.14 5.94 5.74 5.50 5.25
6.50 6.31 6.11 5.88 5.63
6.86 6.68 6.49 6.26 6.01
7.22 7.04 6.86 6.64 6.40
7.95 7.78 7.61 7.39 7.16
8.67 8.52 8.36 8.15 7.92
9.39 10.1 9.25 9.98 9.11 9.85 8.91 9.67 8.68 9.45
10.8 10.7 10.6 10.4 10.2
0.30 0.40 0.50 0.60 0.70
2.61 2.32 2.06 1.84 1.66
2.91 2.59 2.30 2.06 1.86
3.24 2.87 2.57 2.30 2.08
3.57 3.18 2.86 2.58 2.34
3.92 3.51 3.16 2.87 2.61
4.27 3.85 3.49 3.17 2.91
4.63 4.20 3.82 3.50 3.22
5.00 4.55 4.17 3.83 3.54
5.38 4.92 4.52 4.18 3.88
5.76 5.29 4.89 4.53 4.22
6.15 5.67 5.26 4.89 4.56
6.91 6.42 5.97 5.57 5.22
7.67 7.18 6.71 6.28 5.90
8.44 7.95 7.47 7.02 6.62
9.21 8.72 8.24 7.78 7.35
9.98 9.50 9.01 8.54 8.10
0.80 0.90 1.00 1.20 1.40
1.50 1.37 1.26 1.08 0.938
1.69 1.54 1.41 1.21 1.06
1.90 1.74 1.60 1.38 1.21
2.13 1.96 1.81 1.57 1.38
2.40 2.21 2.05 1.78 1.57
2.68 2.48 2.30 2.01 1.78
2.98 2.76 2.58 2.26 2.01
3.29 3.06 2.86 2.52 2.24
3.61 3.37 3.15 2.78 2.49
3.93 3.68 3.45 3.06 2.74
4.27 4.00 3.76 3.34 3.00
4.91 4.62 4.35 3.90 3.52
5.56 5.25 4.97 4.48 4.06
6.25 5.91 5.61 5.07 4.62
6.97 6.61 6.28 5.70 5.21
7.70 7.32 6.97 6.35 5.81
1.60 1.80 2.00 2.20 2.40
0.831 0.745 0.675 0.617 0.568
0.939 0.843 0.764 0.699 0.644
1.07 0.966 0.877 0.804 0.741
1.23 1.11 1.01 0.925 0.854
1.41 1.27 1.16 1.06 0.981
1.60 1.45 1.32 1.21 1.12
1.80 1.63 1.49 1.37 1.27
2.02 1.83 1.67 1.54 1.43
2.24 2.04 1.87 1.72 1.59
2.48 2.25 2.06 1.90 1.77
2.71 2.48 2.27 2.10 1.95
3.20 2.93 2.69 2.49 2.32
3.70 3.40 3.14 2.91 2.71
4.23 3.90 3.60 3.35 3.13
4.78 4.42 4.09 3.81 3.57
5.36 4.96 4.61 4.30 4.03
2.60 0.526 0.597 0.687 0.792 0.911 1.04 1.18 2.80 0.489 0.556 0.641 0.739 0.850 0.972 1.10 3.00 0.458 0.520 0.600 0.693 0.796 0.911 1.03
1.33 1.24 1.17
1.48 1.39 1.30
1.65 1.54 1.45
1.82 1.70 1.60
2.16 2.03 1.91
2.54 2.38 2.24
2.93 2.75 2.60
3.35 3.15 2.97
3.78 3.57 3.37
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 185
Table 8-41 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 60°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l 60°
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
Pu
kl
l
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
3.28 3.20 3.10 2.98 2.89
3.67 3.59 3.50 3.38 3.27
4.06 3.98 3.90 3.79 3.66
4.45 4.37 4.29 4.17 4.04
4.84 4.76 4.67 4.56 4.43
5.23 5.14 5.05 4.94 4.80
5.62 5.53 5.43 5.31 5.17
6.01 5.92 5.82 5.69 5.55
6.40 6.30 6.20 6.07 5.92
6.79 6.69 6.58 6.45 6.29
7.18 7.08 6.96 6.83 6.67
7.96 7.86 7.74 7.59 7.43
8.74 8.63 8.51 8.36 8.19
9.53 10.3 9.41 10.2 9.29 10.1 9.13 9.91 8.96 9.74
11.1 11.0 10.9 10.7 10.5
0.30 0.40 0.50 0.60 0.70
2.80 2.63 2.44 2.27 2.09
3.16 2.96 2.74 2.54 2.35
3.54 3.30 3.06 2.84 2.63
3.92 3.66 3.40 3.16 2.93
4.29 4.02 3.75 3.49 3.25
4.66 4.38 4.10 3.83 3.58
5.02 4.74 4.46 4.18 3.92
5.39 5.09 4.80 4.53 4.26
5.76 5.44 5.14 4.86 4.59
6.13 5.80 5.49 5.20 4.92
6.50 6.16 5.84 5.54 5.25
7.25 6.89 6.54 6.23 5.93
8.01 7.64 7.28 6.93 6.63
8.77 8.40 8.02 7.66 7.34
9.55 10.3 9.17 9.94 8.78 9.56 8.42 9.18 8.07 8.82
0.80 0.90 1.00 1.20 1.40
1.94 1.80 1.67 1.46 1.28
2.18 2.02 1.88 1.64 1.45
2.44 2.27 2.11 1.85 1.64
2.73 2.54 2.37 2.09 1.86
3.03 2.83 2.65 2.35 2.10
3.35 3.14 2.95 2.62 2.35
3.68 3.46 3.26 2.91 2.63
4.01 3.78 3.58 3.21 2.91
4.34 4.11 3.90 3.52 3.20
4.66 4.43 4.21 3.82 3.48
4.99 4.74 4.52 4.11 3.76
5.65 5.40 5.16 4.73 4.35
6.34 6.07 5.82 5.36 4.96
7.04 6.76 6.50 6.02 5.58
7.75 7.46 7.19 6.69 6.23
8.49 8.18 7.90 7.38 6.89
1.60 1.80 2.00 2.20 2.40
1.15 1.03 0.940 0.861 0.794
1.30 1.17 1.06 0.974 0.899
1.47 1.33 1.21 1.11 1.03
1.67 1.51 1.39 1.27 1.18
1.89 1.72 1.58 1.46 1.35
2.13 1.95 1.79 1.65 1.54
2.39 2.19 2.01 1.86 1.73
2.66 2.44 2.25 2.09 1.94
2.93 2.69 2.49 2.31 2.15
3.19 2.94 2.72 2.53 2.36
3.46 3.20 2.97 2.76 2.58
4.01 3.72 3.47 3.24 3.03
4.60 4.28 3.99 3.74 3.52
5.20 4.85 4.55 4.27 4.02
5.82 5.45 5.12 4.82 4.55
6.47 6.07 5.72 5.40 5.11
2.60 0.736 0.834 0.956 1.10 1.26 2.80 0.686 0.778 0.893 1.03 1.18 3.00 0.643 0.729 0.837 0.964 1.11
1.43 1.34 1.26
1.62 1.52 1.43
1.82 1.70 1.61
2.02 1.89 1.79
2.22 2.08 1.97
2.42 2.28 2.15
2.86 2.69 2.55
3.32 3.13 2.97
3.80 3.60 3.41
4.31 4.08 3.88
4.84 4.59 4.37
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 186
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-41 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 75°° φ R n = CC 1 D l
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
75° Pu
kl
l
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
2.97 2.86 2.89 2.88 2.87
3.38 3.27 3.24 3.19 3.17
3.79 3.67 3.65 3.61 3.57
4.20 4.08 4.06 4.02 3.98
4.61 4.49 4.47 4.43 4.38
5.02 4.90 4.87 4.83 4.79
5.43 5.31 5.28 5.24 5.19
5.84 5.72 5.69 5.64 5.59
6.25 6.14 6.10 6.05 5.99
6.66 6.55 6.50 6.45 6.39
7.07 6.96 6.91 6.86 6.80
7.89 7.78 7.72 7.67 7.60
8.71 8.60 8.54 8.48 8.40
9.54 9.42 9.36 9.29 9.21
10.4 10.2 10.2 10.1 10.0
11.2 11.1 11.0 10.9 10.8
0.30 0.40 0.50 0.60 0.70
2.86 2.84 2.79 2.74 2.66
3.17 3.16 3.13 3.07 3.00
3.54 3.51 3.47 3.42 3.34
3.93 3.88 3.83 3.76 3.68
4.33 4.26 4.19 4.11 4.02
4.73 4.64 4.56 4.47 4.37
5.13 5.02 4.93 4.83 4.72
5.53 5.41 5.30 5.19 5.07
5.93 5.79 5.68 5.56 5.43
6.33 6.18 6.05 5.93 5.79
6.73 6.57 6.43 6.30 6.16
7.52 7.36 7.20 7.04 6.89
8.32 8.15 7.96 7.80 7.63
9.12 8.94 8.75 8.56 8.38
9.92 9.73 9.53 9.33 9.14
10.7 10.5 10.3 10.1 9.90
0.80 0.90 1.00 1.20 1.40
2.59 2.51 2.42 2.25 2.08
2.91 2.82 2.73 2.53 2.35
3.25 3.15 3.05 2.84 2.63
3.59 3.49 3.38 3.15 2.94
3.93 3.82 3.71 3.48 3.25
4.26 4.15 4.03 3.80 3.57
4.61 4.49 4.37 4.12 3.88
4.95 4.83 4.70 4.44 4.19
5.30 5.17 5.03 4.77 4.51
5.66 5.52 5.38 5.10 4.83
6.01 5.87 5.72 5.44 5.16
6.74 6.58 6.42 6.12 5.83
7.47 7.30 7.14 6.82 6.52
8.21 8.04 7.86 7.53 7.22
8.96 8.78 8.60 8.26 7.93
9.71 9.52 9.34 8.99 8.65
1.60 1.80 2.00 2.20 2.40
1.92 1.78 1.65 1.54 1.44
2.17 2.01 1.87 1.74 1.63
2.44 2.26 2.11 1.97 1.84
2.73 2.54 2.37 2.22 2.08
3.04 2.84 2.65 2.49 2.34
3.35 3.14 2.95 2.77 2.61
3.65 3.43 3.24 3.06 2.89
3.95 3.73 3.53 3.34 3.17
4.26 4.04 3.82 3.63 3.44
4.58 4.34 4.12 3.92 3.73
4.90 4.65 4.43 4.22 4.02
5.55 5.30 5.05 4.83 4.62
6.23 5.96 5.70 5.47 5.24
6.92 6.63 6.37 6.12 5.89
7.62 7.33 7.05 6.79 6.55
8.33 8.03 7.75 7.48 7.23
2.60 2.80 3.00
1.35 1.26 1.19
1.52 1.43 1.35
1.73 1.63 1.53
1.95 1.84 1.74
2.20 2.08 1.97
2.47 2.34 2.22
2.74 2.60 2.48
3.01 2.86 2.73
3.28 3.13 2.99
3.56 3.40 3.25
3.84 3.67 3.52
4.43 4.25 4.07
5.04 4.84 4.66
5.67 5.46 5.26
6.32 6.10 5.89
6.98 6.75 6.53
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 187
Table 8-42. Coefficients C for Eccentrically Loaded Weld Groups Angle = 0°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
Pu
l
c.g.
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
1.39 1.39 1.37 1.32 1.24
1.81 1.71 1.69 1.63 1.56
2.28 2.09 2.05 1.98 1.88
2.65 2.48 2.43 2.33 2.22
3.06 2.88 2.81 2.70 2.57
3.48 3.28 3.20 3.08 2.93
3.90 3.69 3.60 3.46 3.29
4.32 4.10 4.00 3.84 3.65
4.73 4.51 4.40 4.23 4.03
5.15 4.92 4.80 4.62 4.40
5.57 5.33 5.21 5.01 4.77
6.40 6.16 6.02 5.80 5.53
7.24 6.99 6.84 6.58 6.30
8.07 7.82 7.65 7.38 7.07
8.91 8.65 8.47 8.17 7.84
9.74 9.48 9.28 8.97 8.62
0.30 0.40 0.50 0.60 0.70
1.16 0.998 0.860 0.748 0.659
1.46 1.27 1.09 0.952 0.838
1.77 1.55 1.35 1.17 1.04
2.09 1.84 1.61 1.41 1.25
2.42 2.13 1.87 1.65 1.46
2.76 2.43 2.14 1.89 1.68
3.10 2.74 2.41 2.14 1.91
3.45 3.06 2.70 2.40 2.15
3.81 3.38 3.00 2.67 2.40
4.16 3.71 3.30 2.95 2.66
4.53 4.04 3.61 3.24 2.93
5.26 4.73 4.25 3.84 3.50
6.00 5.43 4.92 4.47 4.09
6.75 6.14 5.60 5.13 4.72
7.51 6.87 6.30 5.80 5.36
8.27 7.61 7.01 6.49 6.03
0.80 0.90 1.00 1.20 1.40
0.586 0.527 0.478 0.403 0.348
0.746 0.671 0.609 0.512 0.441
0.922 0.829 0.752 0.633 0.546
1.11 1.00 0.909 0.766 0.661
1.31 1.18 1.08 0.910 0.787
1.51 1.37 1.25 1.06 0.922
1.72 1.56 1.43 1.22 1.06
1.94 1.77 1.62 1.39 1.21
2.17 1.98 1.82 1.56 1.36
2.42 2.21 2.03 1.75 1.53
2.67 2.44 2.25 1.94 1.70
3.20 2.95 2.73 2.36 2.08
3.77 3.48 3.23 2.81 2.48
4.36 4.05 3.77 3.29 2.92
4.98 4.64 4.33 3.80 3.38
5.62 5.25 4.92 4.34 3.86
1.60 1.80 2.00 2.20 2.40
0.305 0.272 0.245 0.223 0.205
0.387 0.345 0.311 0.283 0.260
0.479 0.427 0.385 0.350 0.321
0.581 0.518 0.467 0.425 0.390
0.692 0.618 0.558 0.508 0.467
0.813 0.727 0.657 0.599 0.551
0.938 0.840 0.760 0.694 0.639
1.07 0.958 0.868 0.793 0.729
1.21 1.09 0.983 0.897 0.826
1.36 1.22 1.10 1.01 0.929
1.51 1.36 1.23 1.13 1.04
1.85 1.66 1.51 1.38 1.27
2.21 1.99 1.81 1.66 1.53
2.61 2.35 2.14 1.97 1.82
3.03 2.74 2.50 2.30 2.12
3.48 3.15 2.88 2.65 2.46
2.60 0.189 0.240 0.297 0.360 0.431 0.509 0.591 0.675 0.765 0.860 0.961 1.18 2.80 0.176 0.223 0.276 0.335 0.401 0.474 0.550 0.628 0.712 0.801 0.895 1.10 3.00 0.164 0.208 0.257 0.313 0.375 0.443 0.514 0.588 0.666 0.749 0.838 1.03
1.42 1.33 1.24
1.69 1.57 1.48
1.98 1.85 1.73
2.29 2.14 2.01
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 188
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-42 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 15°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
15°
Pu l
c.g.
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
1.48 1.42 1.38 1.32 1.24
1.89 1.77 1.73 1.66 1.56
2.31 2.15 2.09 2.01 1.91
2.72 2.55 2.47 2.37 2.25
3.13 2.96 2.86 2.74 2.60
3.54 3.38 3.25 3.11 2.96
3.95 3.79 3.64 3.49 3.32
4.36 4.20 4.04 3.87 3.68
4.77 4.61 4.44 4.25 4.05
5.18 5.02 4.84 4.64 4.41
5.59 5.43 5.24 5.02 4.79
6.41 6.25 6.05 5.80 5.53
7.23 7.08 6.85 6.57 6.29
8.05 7.90 7.66 7.36 7.06
8.87 8.73 8.46 8.15 7.82
9.69 9.55 9.28 8.94 8.60
0.30 0.40 0.50 0.60 0.70
1.16 1.00 0.869 0.759 0.670
1.46 1.27 1.10 0.961 0.849
1.79 1.56 1.35 1.18 1.05
2.12 1.85 1.62 1.42 1.26
2.45 2.16 1.89 1.67 1.48
2.79 2.46 2.17 1.92 1.72
3.13 2.77 2.45 2.18 1.95
3.48 3.09 2.74 2.44 2.20
3.83 3.41 3.04 2.72 2.45
4.19 3.74 3.34 3.00 2.71
4.54 4.07 3.65 3.29 2.98
5.27 4.76 4.30 3.90 3.55
6.01 5.46 4.96 4.53 4.15
6.75 6.17 5.64 5.18 4.78
7.51 6.90 6.34 5.86 5.43
8.27 7.63 7.06 6.55 6.10
0.80 0.90 1.00 1.20 1.40
0.598 0.539 0.490 0.413 0.357
0.758 0.683 0.621 0.524 0.452
0.934 0.842 0.766 0.646 0.558
1.12 1.02 0.924 0.781 0.675
1.33 1.20 1.10 0.928 0.804
1.54 1.40 1.28 1.09 0.943
1.76 1.60 1.47 1.25 1.09
1.99 1.81 1.66 1.42 1.24
2.22 2.03 1.87 1.61 1.40
2.47 2.26 2.08 1.80 1.57
2.72 2.50 2.31 1.99 1.75
3.26 3.01 2.79 2.42 2.13
3.83 3.55 3.30 2.88 2.54
4.43 4.12 3.84 3.36 2.99
5.06 4.71 4.41 3.88 3.45
5.70 5.33 5.00 4.42 3.95
1.60 1.80 2.00 2.20 2.40
0.314 0.280 0.253 0.230 0.211
0.398 0.355 0.320 0.291 0.267
0.491 0.438 0.395 0.360 0.330
0.595 0.531 0.479 0.437 0.401
0.708 0.633 0.572 0.522 0.479
0.833 0.746 0.675 0.616 0.566
0.967 0.867 0.784 0.717 0.659
1.10 0.988 0.896 0.819 0.753
1.25 1.12 1.01 0.926 0.853
1.40 1.26 1.14 1.04 0.959
1.56 1.40 1.27 1.16 1.07
1.90 1.71 1.55 1.43 1.31
2.27 2.05 1.87 1.71 1.58
2.67 2.42 2.20 2.03 1.87
3.11 2.81 2.57 2.37 2.19
3.56 3.24 2.96 2.73 2.53
2.60 0.195 0.247 0.305 0.370 0.444 0.524 0.610 0.697 0.790 0.889 0.993 1.22 2.80 0.182 0.230 0.284 0.344 0.412 0.487 0.568 0.649 0.736 0.827 0.925 1.14 3.00 0.170 0.214 0.265 0.321 0.386 0.456 0.531 0.607 0.688 0.774 0.866 1.06
1.47 1.37 1.28
1.74 1.62 1.52
2.04 1.90 1.79
2.36 2.20 2.07
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 189
Table 8-42 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 30°° φ R n = CC1Dl
C min =
Pu
D min =
C1Dl
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
30° Pu
l
c.g.
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
1.64 1.52 1.44 1.36 1.28
2.03 1.93 1.82 1.72 1.61
2.42 2.32 2.21 2.09 1.97
2.81 2.72 2.60 2.47 2.33
3.20 3.11 2.99 2.84 2.69
3.59 3.50 3.37 3.21 3.04
3.98 3.89 3.75 3.58 3.40
4.37 4.28 4.14 3.95 3.76
4.76 4.68 4.52 4.33 4.11
5.15 5.07 4.91 4.70 4.48
5.54 5.46 5.29 5.08 4.84
6.33 6.24 6.07 5.84 5.59
7.11 7.03 6.84 6.60 6.34
7.89 7.81 7.62 7.38 7.10
8.67 8.60 8.41 8.15 7.87
9.45 9.39 9.19 8.93 8.65
0.30 0.40 0.50 0.60 0.70
1.20 1.05 0.921 0.812 0.722
1.51 1.32 1.16 1.02 0.908
1.84 1.61 1.41 1.25 1.11
2.18 1.91 1.68 1.49 1.33
2.53 2.23 1.96 1.74 1.56
2.88 2.55 2.26 2.01 1.81
3.22 2.87 2.56 2.29 2.07
3.56 3.19 2.86 2.57 2.33
3.91 3.52 3.16 2.86 2.60
4.26 3.85 3.47 3.15 2.87
4.62 4.18 3.79 3.45 3.15
5.33 4.86 4.44 4.07 3.74
6.07 5.57 5.11 4.71 4.36
6.82 6.28 5.80 5.38 5.00
7.58 7.02 6.51 6.06 5.67
8.35 7.77 7.24 6.77 6.35
0.80 0.90 1.00 1.20 1.40
0.647 0.586 0.535 0.454 0.393
0.816 0.739 0.674 0.572 0.496
0.998 0.905 0.827 0.703 0.610
1.20 1.09 0.994 0.847 0.736
1.41 1.28 1.18 1.00 0.874
1.64 1.49 1.37 1.17 1.02
1.88 1.71 1.58 1.36 1.19
2.12 1.95 1.80 1.55 1.36
2.37 2.18 2.02 1.75 1.53
2.63 2.42 2.25 1.95 1.72
2.90 2.68 2.48 2.16 1.91
3.46 3.21 2.99 2.61 2.32
4.05 3.77 3.52 3.10 2.75
4.66 4.36 4.08 3.61 3.22
5.30 4.97 4.67 4.15 3.72
5.96 5.60 5.28 4.71 4.24
1.60 1.80 2.00 2.20 2.40
0.347 0.310 0.280 0.255 0.234
0.437 0.391 0.353 0.322 0.296
0.538 0.481 0.435 0.397 0.365
0.650 0.582 0.526 0.481 0.442
0.773 0.693 0.627 0.573 0.528
0.909 0.816 0.740 0.677 0.623
1.06 0.949 0.861 0.789 0.727
1.21 1.09 0.988 0.904 0.833
1.37 1.23 1.12 1.02 0.944
1.53 1.38 1.26 1.15 1.06
1.70 1.54 1.40 1.28 1.18
2.07 1.87 1.71 1.57 1.45
2.47 2.24 2.05 1.88 1.74
2.90 2.64 2.41 2.22 2.06
3.36 3.06 2.81 2.59 2.40
3.85 3.52 3.23 2.98 2.77
2.60 0.217 0.273 0.337 0.409 0.489 0.577 0.674 0.772 0.875 0.983 1.10 1.34 2.80 0.201 0.254 0.314 0.381 0.455 0.538 0.628 0.719 0.815 0.916 1.02 1.26 3.00 0.188 0.238 0.293 0.356 0.426 0.504 0.588 0.673 0.763 0.858 0.959 1.18
1.62 1.51 1.42
1.92 1.79 1.68
2.24 2.10 1.97
2.59 2.43 2.28
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 190
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-42 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 45°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
45°
l
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
Pu
c.g.
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
1.81 1.68 1.57 1.47 1.39
2.17 2.06 1.95 1.83 1.72
2.53 2.43 2.32 2.19 2.06
2.89 2.80 2.68 2.55 2.41
3.25 3.17 3.05 2.91 2.76
3.61 3.55 3.42 3.28 3.12
3.97 3.92 3.80 3.64 3.48
4.33 4.29 4.17 4.02 3.85
4.70 4.66 4.54 4.39 4.22
5.06 5.03 4.92 4.76 4.58
5.42 5.40 5.29 5.13 4.95
6.14 6.14 6.03 5.88 5.69
6.86 6.86 6.77 6.62 6.44
7.58 7.58 7.51 7.37 7.19
8.31 8.31 8.25 8.12 7.94
9.03 9.03 8.99 8.86 8.69
0.30 0.40 0.50 0.60 0.70
1.31 1.16 1.03 0.921 0.829
1.62 1.43 1.28 1.14 1.03
1.94 1.72 1.54 1.38 1.25
2.27 2.03 1.81 1.63 1.48
2.61 2.34 2.10 1.90 1.73
2.96 2.66 2.40 2.18 1.99
3.31 2.99 2.71 2.47 2.26
3.67 3.33 3.03 2.77 2.54
4.03 3.68 3.36 3.08 2.84
4.39 4.03 3.70 3.41 3.15
4.75 4.37 4.03 3.72 3.46
5.49 5.08 4.70 4.37 4.08
6.23 5.82 5.41 5.04 4.72
6.99 6.57 6.15 5.76 5.40
7.75 7.32 6.90 6.49 6.11
8.50 8.09 7.66 7.23 6.84
0.80 0.90 1.00 1.20 1.40
0.751 0.685 0.629 0.538 0.469
0.935 0.854 0.785 0.674 0.589
1.13 1.04 0.956 0.822 0.720
1.35 1.24 1.14 0.985 0.864
1.58 1.45 1.34 1.16 1.02
1.82 1.68 1.56 1.35 1.19
2.08 1.92 1.78 1.56 1.38
2.35 2.18 2.03 1.78 1.58
2.63 2.45 2.29 2.01 1.79
2.93 2.73 2.55 2.25 2.00
3.22 3.00 2.81 2.49 2.22
3.81 3.57 3.35 2.98 2.67
4.43 4.17 3.93 3.51 3.16
5.08 4.79 4.53 4.07 3.68
5.77 5.45 5.16 4.66 4.23
6.47 6.14 5.83 5.28 4.81
1.60 1.80 2.00 2.20 2.40
0.416 0.373 0.338 0.308 0.284
0.522 0.468 0.424 0.388 0.357
0.639 0.574 0.521 0.477 0.439
0.769 0.692 0.628 0.575 0.531
0.911 0.821 0.746 0.685 0.632
1.07 0.964 0.879 0.806 0.745
1.24 1.12 1.02 0.939 0.868
1.42 1.29 1.17 1.08 0.999
1.61 1.46 1.33 1.22 1.13
1.80 1.63 1.49 1.37 1.27
2.00 1.82 1.66 1.53 1.42
2.42 2.20 2.02 1.86 1.73
2.87 2.62 2.41 2.23 2.07
3.35 3.07 2.84 2.63 2.44
3.87 3.56 3.29 3.05 2.84
4.41 4.06 3.76 3.50 3.27
2.60 0.263 0.331 0.407 0.492 0.587 0.692 0.807 0.928 1.05 1.18 2.80 0.245 0.308 0.379 0.458 0.548 0.646 0.753 0.867 0.983 1.10 3.00 0.229 0.288 0.355 0.429 0.513 0.606 0.707 0.814 0.922 1.04
1.32 1.23 1.16
1.61 1.51 1.42
1.93 1.81 1.70
2.28 2.14 2.02
2.66 2.50 2.36
3.06 2.88 2.72
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 191
Table 8-42 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 60°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
60°
l
Pu
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
c.g.
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
1.95 1.82 1.73 1.63 1.55
2.28 2.15 2.05 1.96 1.87
2.61 2.48 2.38 2.28 2.18
2.94 2.82 2.71 2.61 2.50
3.26 3.16 3.06 2.94 2.83
3.59 3.51 3.41 3.29 3.17
3.92 3.86 3.76 3.65 3.53
4.25 4.21 4.12 4.01 3.89
4.57 4.56 4.47 4.37 4.25
4.90 4.90 4.83 4.73 4.62
5.23 5.24 5.18 5.09 4.98
5.88 5.88 5.87 5.80 5.70
6.54 6.54 6.54 6.49 6.41
7.19 7.19 7.19 7.18 7.11
7.85 7.85 7.85 7.85 7.79
8.51 8.51 8.51 8.51 8.47
0.30 0.40 0.50 0.60 0.70
1.47 1.34 1.22 1.12 1.03
1.78 1.62 1.48 1.36 1.25
2.09 1.91 1.75 1.61 1.49
2.40 2.20 2.03 1.88 1.74
2.72 2.51 2.32 2.15 2.00
3.05 2.83 2.63 2.44 2.28
3.40 3.16 2.95 2.75 2.58
3.76 3.52 3.28 3.07 2.89
4.13 3.88 3.63 3.41 3.22
4.50 4.24 4.00 3.76 3.56
4.87 4.61 4.36 4.13 3.91
5.60 5.36 5.10 4.86 4.62
6.32 6.09 5.84 5.59 5.33
7.02 6.82 6.57 6.32 6.05
7.72 7.53 7.30 7.03 6.78
8.40 8.23 8.01 7.75 7.50
0.80 0.90 1.00 1.20 1.40
0.945 0.874 0.812 0.709 0.626
1.16 1.07 0.999 0.875 0.776
1.38 1.28 1.20 1.06 0.939
1.62 1.51 1.41 1.25 1.12
1.87 1.75 1.64 1.46 1.31
2.14 2.01 1.89 1.69 1.52
2.42 2.28 2.15 1.93 1.75
2.72 2.57 2.43 2.19 1.98
3.04 2.87 2.72 2.46 2.23
3.36 3.18 3.02 2.74 2.49
3.70 3.51 3.34 3.03 2.76
4.39 4.17 3.97 3.62 3.31
5.09 4.85 4.63 4.23 3.89
5.80 5.55 5.32 4.89 4.50
6.52 6.26 6.02 5.56 5.15
7.24 6.98 6.73 6.26 5.82
1.60 1.80 2.00 2.20 2.40
0.560 0.506 0.461 0.423 0.391
0.696 0.630 0.575 0.528 0.489
0.845 0.766 0.701 0.645 0.597
1.01 0.916 0.839 0.774 0.718
1.18 1.08 0.993 0.917 0.851
1.38 1.26 1.16 1.07 0.999
1.59 1.46 1.34 1.24 1.16
1.81 1.66 1.53 1.42 1.33
2.04 1.88 1.74 1.61 1.51
2.28 2.11 1.95 1.81 1.69
2.54 2.34 2.17 2.02 1.89
3.05 2.82 2.62 2.44 2.29
3.59 3.33 3.11 2.90 2.72
4.17 3.88 3.62 3.39 3.19
4.79 4.46 4.17 3.91 3.68
5.43 5.07 4.75 4.47 4.21
2.60 0.363 0.454 0.556 0.669 0.794 0.932 1.08 1.24 2.80 0.339 0.424 0.519 0.625 0.744 0.875 1.02 1.17 3.00 0.317 0.398 0.488 0.587 0.700 0.824 0.956 1.10
1.41 1.33 1.25
1.59 1.49 1.41
1.77 1.66 1.57
2.15 2.02 1.91
2.56 2.42 2.29
3.01 2.84 2.69
3.48 3.29 3.12
3.98 3.77 3.58
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 192
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-42 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 75°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
75°
Pu l
c.g.
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
2.05 1.94 1.88 1.82 1.76
2.35 2.22 2.15 2.09 2.04
2.65 2.51 2.44 2.38 2.32
2.94 2.81 2.75 2.69 2.63
3.24 3.13 3.07 3.01 2.95
3.54 3.44 3.39 3.33 3.27
3.83 3.75 3.70 3.65 3.60
4.13 4.05 4.01 3.97 3.92
4.43 4.35 4.32 4.29 4.24
4.72 4.65 4.63 4.60 4.56
5.02 4.94 4.93 4.90 4.87
5.61 5.53 5.52 5.50 5.47
6.21 6.11 6.10 6.09 6.07
6.80 6.68 6.68 6.67 6.66
7.39 7.26 7.26 7.25 7.24
7.99 7.83 7.83 7.83 7.82
0.30 0.40 0.50 0.60 0.70
1.71 1.62 1.53 1.46 1.38
1.99 1.89 1.80 1.71 1.63
2.27 2.16 2.07 1.97 1.89
2.57 2.46 2.35 2.25 2.16
2.89 2.77 2.65 2.55 2.45
3.21 3.09 2.98 2.86 2.76
3.54 3.42 3.31 3.19 3.08
3.87 3.76 3.64 3.53 3.42
4.19 4.09 3.98 3.87 3.76
4.51 4.41 4.31 4.21 4.10
4.83 4.73 4.64 4.54 4.44
5.44 5.36 5.27 5.19 5.11
6.05 5.98 5.90 5.83 5.75
6.64 6.58 6.51 6.44 6.38
7.23 7.18 7.11 7.04 6.99
7.81 7.77 7.71 7.64 7.59
0.80 0.90 1.00 1.20 1.40
1.31 1.25 1.19 1.09 0.994
1.56 1.49 1.42 1.30 1.20
1.81 1.73 1.66 1.53 1.41
2.07 1.99 1.91 1.77 1.65
2.35 2.27 2.18 2.03 1.90
2.66 2.56 2.47 2.31 2.16
2.98 2.88 2.78 2.60 2.44
3.31 3.21 3.10 2.91 2.74
3.65 3.54 3.44 3.24 3.05
3.99 3.89 3.78 3.57 3.38
4.34 4.23 4.13 3.92 3.71
5.01 4.92 4.82 4.61 4.40
5.67 5.59 5.49 5.30 5.09
6.31 6.24 6.16 5.98 5.78
6.93 6.87 6.80 6.64 6.46
7.54 7.48 7.43 7.29 7.13
1.60 1.80 2.00 2.20 2.40
0.914 0.845 0.784 0.730 0.683
1.11 1.03 0.956 0.894 0.838
1.31 1.22 1.14 1.07 1.01
1.53 1.43 1.34 1.26 1.19
1.77 1.66 1.56 1.47 1.39
2.03 1.91 1.80 1.70 1.61
2.30 2.16 2.04 1.94 1.84
2.58 2.44 2.31 2.19 2.08
2.88 2.73 2.58 2.45 2.33
3.20 3.03 2.88 2.73 2.60
3.52 3.35 3.18 3.03 2.89
4.20 4.00 3.82 3.65 3.49
4.89 4.68 4.49 4.30 4.12
5.58 5.38 5.18 4.97 4.77
6.27 6.07 5.86 5.65 5.43
6.94 6.76 6.55 6.33 6.11
2.60 0.641 0.788 0.949 1.13 2.80 0.604 0.744 0.897 1.07 3.00 0.570 0.704 0.851 1.01
1.32 1.25 1.19
1.53 1.45 1.38
1.75 1.66 1.59
1.98 1.89 1.80
2.22 2.12 2.03
2.48 2.37 2.27
2.76 2.63 2.52
3.34 3.20 3.07
3.95 3.78 3.63
4.58 4.39 4.23
5.23 5.04 4.85
5.90 5.70 5.50
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 193
Table 8-43. Coefficients C for Eccentrically Loaded Weld Groups Angle = 0°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
Pu
l
c.g.
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
kl xl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
1.39 1.39 1.38 1.32 1.24
1.81 1.72 1.70 1.63 1.55
2.23 2.10 2.05 1.96 1.86
2.65 2.48 2.41 2.31 2.18
3.06 2.86 2.77 2.65 2.51
3.48 3.24 3.13 2.99 2.84
3.90 3.62 3.50 3.34 3.17
4.32 4.00 3.86 3.68 3.50
4.73 4.38 4.22 4.03 3.83
5.15 4.76 4.58 4.38 4.16
5.57 5.13 4.94 4.72 4.50
6.40 5.88 5.66 5.42 5.17
7.24 6.63 6.38 6.12 5.86
8.07 7.37 7.11 6.83 6.55
8.91 8.12 7.84 7.55 7.25
9.74 8.87 8.57 8.27 7.96
0.30 0.40 0.50 0.60 0.70
1.16 0.998 0.860 0.748 0.659
1.45 1.26 1.08 0.942 0.828
1.75 1.52 1.31 1.14 1.00
2.05 1.79 1.56 1.35 1.20
2.36 2.08 1.81 1.58 1.41
2.68 2.36 2.07 1.83 1.63
2.99 2.65 2.34 2.07 1.86
3.31 2.94 2.60 2.32 2.10
3.63 3.24 2.88 2.58 2.34
3.95 3.54 3.15 2.84 2.58
4.27 3.84 3.44 3.11 2.83
4.93 4.46 4.02 3.66 3.35
5.60 5.09 4.63 4.23 3.90
6.27 5.74 5.25 4.83 4.47
6.96 6.41 5.89 5.45 5.06
7.66 7.08 6.55 6.08 5.67
0.80 0.90 1.00 1.20 1.40
0.586 0.527 0.478 0.403 0.348
0.735 0.661 0.599 0.505 0.436
0.895 0.807 0.734 0.621 0.537
1.07 0.971 0.885 0.751 0.651
1.27 1.15 1.05 0.893 0.776
1.47 1.34 1.23 1.05 0.912
1.69 1.54 1.41 1.21 1.06
1.91 1.75 1.61 1.38 1.21
2.13 1.96 1.81 1.56 1.37
2.36 2.18 2.01 1.75 1.54
2.60 2.40 2.22 1.94 1.71
3.09 2.86 2.66 2.33 2.07
3.61 3.35 3.13 2.75 2.45
4.15 3.87 3.62 3.20 2.86
4.72 4.41 4.14 3.68 3.30
5.30 4.97 4.68 4.17 3.75
1.60 1.80 2.00 2.20 2.40
0.305 0.272 0.245 0.223 0.205
0.383 0.341 0.308 0.280 0.257
0.472 0.422 0.381 0.347 0.318
0.574 0.512 0.463 0.422 0.388
0.685 0.613 0.554 0.506 0.465
0.806 0.722 0.654 0.597 0.548
0.936 0.839 0.760 0.694 0.639
1.07 0.963 0.873 0.798 0.735
1.22 1.10 0.993 0.909 0.836
1.37 1.23 1.12 1.02 0.942
1.53 1.38 1.25 1.15 1.06
1.86 1.68 1.53 1.41 1.30
2.21 2.00 1.84 1.69 1.56
2.58 2.35 2.15 1.99 1.85
2.98 2.72 2.50 2.31 2.15
3.41 3.11 2.87 2.65 2.47
2.60 0.189 0.238 0.294 0.358 0.430 0.508 0.592 0.681 0.773 0.872 0.976 1.20 2.80 0.176 0.221 0.274 0.333 0.400 0.472 0.550 0.633 0.720 0.811 0.908 1.12 3.00 0.164 0.207 0.256 0.311 0.374 0.442 0.515 0.593 0.673 0.758 0.850 1.05
1.46 1.36 1.27
1.72 1.61 1.51
2.00 1.88 1.76
2.30 2.16 2.03
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 194
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-43 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 15°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
15°
Pu l
c.g.
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
1.48 1.42 1.38 1.32 1.24
1.89 1.77 1.73 1.65 1.55
2.31 2.15 2.09 1.99 1.87
2.72 2.53 2.45 2.33 2.20
3.13 2.91 2.80 2.67 2.53
3.54 3.29 3.16 3.01 2.85
3.95 3.66 3.52 3.35 3.17
4.36 4.04 3.87 3.69 3.50
4.77 4.41 4.22 4.03 3.82
5.18 4.78 4.58 4.36 4.15
5.59 5.14 4.93 4.70 4.47
6.41 5.89 5.64 5.38 5.13
7.23 6.63 6.36 6.08 5.80
8.05 7.38 7.08 6.78 6.49
8.87 8.14 7.81 7.49 7.18
9.69 8.90 8.54 8.21 7.89
0.30 0.40 0.50 0.60 0.70
1.16 1.00 0.869 0.759 0.670
1.45 1.25 1.09 0.950 0.838
1.75 1.51 1.31 1.14 1.01
2.06 1.78 1.55 1.35 1.20
2.37 2.06 1.80 1.58 1.41
2.68 2.35 2.05 1.81 1.62
3.00 2.64 2.32 2.06 1.86
3.31 2.94 2.60 2.33 2.10
3.62 3.23 2.88 2.59 2.35
3.93 3.53 3.17 2.87 2.61
4.25 3.82 3.45 3.14 2.87
4.89 4.43 4.03 3.69 3.40
5.54 5.05 4.63 4.27 3.95
6.21 5.69 5.25 4.86 4.52
6.89 6.35 5.89 5.47 5.10
7.58 7.03 6.54 6.11 5.71
0.80 0.90 1.00 1.20 1.40
0.598 0.539 0.490 0.413 0.357
0.747 0.672 0.611 0.516 0.446
0.905 0.818 0.746 0.633 0.548
1.08 0.980 0.896 0.763 0.663
1.27 1.15 1.06 0.905 0.789
1.47 1.34 1.23 1.06 0.925
1.68 1.54 1.42 1.22 1.07
1.91 1.75 1.61 1.39 1.22
2.15 1.97 1.82 1.58 1.39
2.39 2.20 2.04 1.77 1.56
2.64 2.44 2.26 1.97 1.74
3.14 2.92 2.72 2.39 2.12
3.66 3.41 3.19 2.82 2.52
4.21 3.94 3.69 3.27 2.93
4.77 4.48 4.21 3.75 3.38
5.36 5.04 4.75 4.25 3.84
1.60 1.80 2.00 2.20 2.40
0.314 0.280 0.253 0.230 0.211
0.393 0.351 0.317 0.289 0.265
0.484 0.432 0.391 0.356 0.327
0.586 0.524 0.474 0.433 0.398
0.698 0.626 0.567 0.518 0.476
0.820 0.737 0.668 0.611 0.562
0.951 0.854 0.776 0.710 0.654
1.09 0.981 0.891 0.816 0.753
1.24 1.11 1.01 0.929 0.857
1.39 1.26 1.14 1.05 0.967
1.56 1.41 1.28 1.18 1.09
1.91 1.73 1.58 1.45 1.34
2.27 2.06 1.89 1.74 1.61
2.65 2.42 2.22 2.05 1.90
3.06 2.80 2.57 2.38 2.21
3.49 3.19 2.95 2.73 2.54
2.60 0.195 0.245 0.303 0.368 0.441 0.521 0.606 0.698 0.795 0.898 1.01 1.24 2.80 0.182 0.228 0.282 0.343 0.410 0.485 0.565 0.650 0.741 0.837 0.937 1.16 3.00 0.170 0.213 0.263 0.320 0.384 0.453 0.528 0.609 0.694 0.782 0.877 1.08
1.50 1.40 1.31
1.77 1.66 1.56
2.06 1.93 1.82
2.37 2.23 2.10
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 195
Table 8-43 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 30°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
30°
Pu l
c.g.
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
1.64 1.52 1.44 1.36 1.28
2.03 1.92 1.81 1.70 1.60
2.42 2.30 2.17 2.04 1.91
2.81 2.66 2.53 2.37 2.22
3.20 3.02 2.87 2.70 2.53
3.59 3.38 3.21 3.02 2.83
3.98 3.74 3.55 3.35 3.14
4.37 4.10 3.90 3.67 3.45
4.76 4.46 4.24 4.00 3.77
5.15 4.83 4.59 4.34 4.09
5.54 5.19 4.94 4.68 4.42
6.33 5.93 5.66 5.37 5.10
7.11 6.67 6.39 6.09 5.79
7.89 7.43 7.13 6.82 6.51
8.67 8.19 7.88 7.56 7.24
9.45 8.96 8.64 8.32 8.00
0.30 0.40 0.50 0.60 0.70
1.20 1.05 0.921 0.812 0.722
1.49 1.30 1.14 1.01 0.895
1.79 1.56 1.36 1.20 1.07
2.08 1.82 1.59 1.41 1.26
2.37 2.08 1.83 1.63 1.47
2.66 2.35 2.09 1.87 1.69
2.96 2.63 2.35 2.12 1.93
3.25 2.92 2.63 2.39 2.17
3.56 3.22 2.92 2.66 2.43
3.89 3.52 3.21 2.94 2.70
4.21 3.84 3.51 3.23 2.98
4.86 4.46 4.12 3.82 3.55
5.53 5.10 4.73 4.41 4.11
6.23 5.77 5.37 5.01 4.69
6.95 6.45 6.03 5.64 5.30
7.68 7.15 6.70 6.30 5.93
0.80 0.90 1.00 1.20 1.40
0.647 0.586 0.535 0.454 0.393
0.803 0.726 0.663 0.563 0.489
0.966 0.878 0.805 0.687 0.599
1.15 1.05 0.960 0.825 0.721
1.34 1.23 1.13 0.973 0.855
1.54 1.42 1.31 1.13 0.997
1.76 1.62 1.50 1.30 1.15
2.00 1.84 1.71 1.48 1.31
2.24 2.07 1.92 1.68 1.49
2.49 2.31 2.15 1.88 1.67
2.75 2.56 2.39 2.10 1.86
3.30 3.08 2.88 2.55 2.28
3.85 3.61 3.39 3.02 2.72
4.41 4.15 3.91 3.50 3.16
4.99 4.71 4.45 4.01 3.63
5.60 5.30 5.02 4.53 4.12
1.60 1.80 2.00 2.20 2.40
0.347 0.310 0.280 0.255 0.234
0.432 0.386 0.349 0.319 0.293
0.530 0.475 0.430 0.393 0.361
0.639 0.574 0.521 0.476 0.439
0.760 0.684 0.620 0.568 0.524
0.890 0.802 0.729 0.668 0.616
1.03 0.928 0.846 0.776 0.716
1.18 1.06 0.969 0.890 0.823
1.33 1.21 1.10 1.01 0.936
1.50 1.36 1.24 1.14 1.06
1.68 1.52 1.39 1.28 1.19
2.06 1.87 1.71 1.58 1.46
2.46 2.25 2.06 1.91 1.77
2.88 2.63 2.42 2.25 2.09
3.31 3.04 2.80 2.60 2.42
3.77 3.47 3.21 2.98 2.78
2.60 0.217 0.271 0.335 0.406 0.486 0.572 0.665 0.765 0.870 0.983 1.10 1.36 2.80 0.201 0.252 0.311 0.378 0.453 0.534 0.621 0.714 0.813 0.919 1.03 1.28 3.00 0.188 0.236 0.291 0.354 0.424 0.500 0.582 0.669 0.763 0.862 0.967 1.20
1.65 1.55 1.45
1.95 1.83 1.72
2.27 2.13 2.00
2.60 2.45 2.31
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 196
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-43 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 45°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
45°
Pu l
c.g.
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
1.81 1.68 1.57 1.47 1.39
2.17 2.04 1.93 1.81 1.70
2.53 2.38 2.25 2.12 1.99
2.89 2.71 2.56 2.41 2.27
3.25 3.04 2.86 2.69 2.53
3.61 3.37 3.18 2.99 2.82
3.97 3.71 3.51 3.30 3.12
4.33 4.06 3.85 3.64 3.44
4.70 4.41 4.19 3.98 3.77
5.06 4.77 4.55 4.33 4.12
5.42 5.12 4.91 4.69 4.47
6.14 5.84 5.64 5.41 5.18
6.86 6.56 6.37 6.14 5.92
7.58 7.30 7.10 6.88 6.66
8.31 8.03 7.85 7.63 7.40
9.03 8.76 8.59 8.38 8.15
0.30 0.40 0.50 0.60 0.70
1.31 1.16 1.03 0.921 0.829
1.60 1.41 1.26 1.13 1.02
1.88 1.67 1.48 1.33 1.20
2.14 1.91 1.71 1.55 1.41
2.40 2.16 1.96 1.78 1.63
2.68 2.43 2.22 2.03 1.86
2.97 2.71 2.49 2.29 2.11
3.28 3.01 2.77 2.55 2.37
3.60 3.31 3.06 2.84 2.63
3.94 3.63 3.37 3.13 2.91
4.28 3.96 3.68 3.43 3.21
4.98 4.64 4.34 4.06 3.82
5.70 5.33 5.02 4.72 4.45
6.42 6.03 5.70 5.38 5.09
7.17 6.74 6.38 6.06 5.75
7.92 7.46 7.09 6.75 6.42
0.80 0.90 1.00 1.20 1.40
0.751 0.685 0.629 0.538 0.469
0.920 0.840 0.772 0.664 0.581
1.10 1.01 0.930 0.804 0.706
1.29 1.19 1.10 0.957 0.845
1.50 1.38 1.28 1.12 0.995
1.72 1.59 1.48 1.30 1.16
1.95 1.81 1.69 1.49 1.33
2.20 2.05 1.92 1.69 1.51
2.46 2.30 2.15 1.91 1.71
2.72 2.55 2.40 2.13 1.91
3.00 2.82 2.65 2.37 2.13
3.59 3.38 3.19 2.87 2.59
4.21 3.98 3.77 3.40 3.09
4.82 4.58 4.35 3.95 3.60
5.46 5.20 4.95 4.50 4.12
6.12 5.83 5.57 5.09 4.67
1.60 1.80 2.00 2.20 2.40
0.416 0.373 0.338 0.308 0.284
0.515 0.463 0.420 0.384 0.354
0.629 0.566 0.515 0.471 0.435
0.754 0.681 0.621 0.569 0.526
0.892 0.807 0.736 0.677 0.626
1.04 0.943 0.862 0.793 0.734
1.20 1.09 0.995 0.918 0.850
1.36 1.24 1.14 1.05 0.974
1.54 1.41 1.29 1.19 1.11
1.73 1.58 1.45 1.34 1.25
1.93 1.77 1.62 1.50 1.40
2.36 2.17 2.00 1.85 1.72
2.82 2.60 2.40 2.23 2.08
3.31 3.05 2.83 2.64 2.46
3.80 3.52 3.27 3.05 2.85
4.31 4.00 3.73 3.48 3.27
2.60 0.263 0.328 0.403 0.488 0.582 0.683 0.792 0.909 1.03 1.16 2.80 0.245 0.306 0.376 0.455 0.543 0.639 0.741 0.851 0.966 1.09 3.00 0.229 0.286 0.352 0.427 0.510 0.600 0.697 0.799 0.910 1.03
1.31 1.22 1.15
1.61 1.51 1.43
1.95 1.83 1.73
2.31 2.17 2.05
2.68 2.53 2.39
3.07 2.90 2.74
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 197
Table 8-43 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 60°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
60° Pu
l
c.g.
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
1.95 1.83 1.73 1.63 1.55
2.28 2.13 2.03 1.93 1.84
2.61 2.42 2.30 2.19 2.09
2.94 2.72 2.58 2.45 2.34
3.26 3.03 2.88 2.74 2.62
3.59 3.36 3.19 3.04 2.92
3.92 3.69 3.52 3.36 3.23
4.25 4.03 3.86 3.69 3.55
4.57 4.37 4.20 4.03 3.88
4.90 4.71 4.55 4.38 4.22
5.23 5.05 4.89 4.73 4.56
5.88 5.73 5.59 5.43 5.26
6.54 6.41 6.27 6.13 5.97
7.19 7.08 6.96 6.82 6.67
7.85 7.74 7.63 7.51 7.37
8.51 8.40 8.31 8.19 8.06
0.30 0.40 0.50 0.60 0.70
1.47 1.34 1.22 1.12 1.03
1.76 1.60 1.46 1.34 1.23
2.00 1.84 1.69 1.56 1.44
2.25 2.08 1.93 1.79 1.67
2.52 2.34 2.18 2.04 1.91
2.81 2.62 2.45 2.30 2.16
3.12 2.91 2.73 2.57 2.42
3.43 3.22 3.04 2.86 2.70
3.76 3.54 3.35 3.16 3.00
4.09 3.87 3.67 3.48 3.30
4.42 4.20 3.99 3.80 3.62
5.11 4.87 4.66 4.46 4.27
5.80 5.54 5.33 5.14 4.94
6.51 6.23 6.01 5.81 5.62
7.22 6.91 6.69 6.49 6.30
7.93 7.61 7.37 7.16 6.98
0.80 0.90 1.00 1.20 1.40
0.945 0.874 0.812 0.709 0.626
1.14 1.06 0.983 0.862 0.766
1.34 1.25 1.17 1.03 0.922
1.55 1.45 1.37 1.21 1.09
1.79 1.68 1.58 1.41 1.27
2.03 1.91 1.81 1.62 1.46
2.29 2.16 2.05 1.84 1.67
2.56 2.42 2.30 2.08 1.89
2.84 2.70 2.57 2.33 2.13
3.14 2.98 2.84 2.59 2.37
3.45 3.28 3.13 2.86 2.63
4.08 3.91 3.75 3.44 3.18
4.75 4.56 4.39 4.06 3.76
5.42 5.24 5.05 4.70 4.38
6.10 5.91 5.73 5.36 5.02
6.79 6.60 6.41 6.03 5.66
1.60 1.80 2.00 2.20 2.40
0.560 0.506 0.461 0.423 0.391
0.688 0.623 0.569 0.524 0.484
0.831 0.756 0.692 0.638 0.591
0.988 0.901 0.828 0.765 0.710
1.16 1.06 0.975 0.902 0.840
1.34 1.23 1.13 1.05 0.979
1.53 1.41 1.30 1.21 1.13
1.74 1.60 1.48 1.38 1.29
1.95 1.80 1.67 1.56 1.46
2.18 2.02 1.88 1.75 1.64
2.43 2.25 2.09 1.95 1.83
2.94 2.73 2.55 2.39 2.24
3.50 3.26 3.05 2.86 2.69
4.08 3.82 3.58 3.37 3.17
4.70 4.41 4.14 3.90 3.69
5.32 5.00 4.71 4.45 4.21
2.60 0.363 0.451 0.551 0.662 0.785 0.916 1.06 1.21 2.80 0.339 0.421 0.515 0.620 0.736 0.861 0.994 1.14 3.00 0.317 0.395 0.484 0.584 0.693 0.812 0.939 1.07
1.37 1.29 1.22
1.54 1.45 1.37
1.72 1.62 1.53
2.11 2.00 1.89
2.54 2.40 2.28
3.00 2.85 2.70
3.49 3.31 3.15
3.99 3.79 3.60
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 198
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-43 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = 75°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
75° Pu l
c.g.
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
2.05 1.94 1.88 1.82 1.76
2.35 2.21 2.14 2.07 2.01
2.65 2.48 2.40 2.32 2.26
2.94 2.77 2.67 2.59 2.53
3.24 3.06 2.96 2.88 2.82
3.54 3.37 3.26 3.18 3.11
3.83 3.68 3.58 3.48 3.41
4.13 3.99 3.89 3.78 3.71
4.43 4.31 4.20 4.10 4.02
4.72 4.60 4.51 4.42 4.32
5.02 4.88 4.82 4.73 4.63
5.61 5.46 5.42 5.35 5.26
6.21 6.04 6.00 5.96 5.88
6.80 6.61 6.58 6.54 6.49
7.39 7.19 7.16 7.12 7.08
7.99 7.77 7.74 7.70 7.67
0.30 0.40 0.50 0.60 0.70
1.71 1.62 1.53 1.46 1.38
1.95 1.86 1.77 1.69 1.61
2.20 2.10 2.01 1.93 1.85
2.47 2.36 2.27 2.18 2.09
2.76 2.65 2.55 2.45 2.36
3.05 2.95 2.84 2.74 2.65
3.36 3.25 3.15 3.05 2.95
3.66 3.56 3.46 3.36 3.26
3.96 3.86 3.77 3.67 3.57
4.26 4.16 4.07 3.98 3.89
4.56 4.46 4.38 4.29 4.21
5.17 5.06 4.98 4.91 4.83
5.79 5.66 5.58 5.51 5.44
6.42 6.26 6.17 6.10 6.05
7.03 6.88 6.76 6.69 6.64
7.62 7.49 7.35 7.28 7.22
0.80 0.90 1.00 1.20 1.40
1.31 1.25 1.19 1.09 0.994
1.54 1.47 1.40 1.29 1.18
1.77 1.70 1.63 1.50 1.39
2.01 1.94 1.87 1.73 1.61
2.28 2.19 2.12 1.98 1.85
2.56 2.47 2.39 2.24 2.10
2.85 2.76 2.68 2.51 2.36
3.16 3.07 2.98 2.80 2.64
3.48 3.38 3.29 3.11 2.94
3.79 3.70 3.60 3.42 3.24
4.11 4.02 3.93 3.74 3.56
4.75 4.66 4.57 4.39 4.21
5.37 5.29 5.21 5.04 4.86
5.98 5.92 5.84 5.69 5.52
6.58 6.52 6.46 6.32 6.17
7.17 7.13 7.07 6.95 6.80
1.60 1.80 2.00 2.20 2.40
0.914 0.845 0.784 0.730 0.683
1.10 1.02 0.947 0.886 0.832
1.29 1.21 1.13 1.06 0.996
1.50 1.41 1.32 1.25 1.18
1.73 1.63 1.53 1.45 1.37
1.97 1.86 1.75 1.66 1.57
2.23 2.10 1.99 1.89 1.79
2.50 2.36 2.24 2.13 2.03
2.78 2.64 2.50 2.38 2.27
3.08 2.93 2.78 2.65 2.53
3.39 3.23 3.07 2.93 2.80
4.02 3.85 3.68 3.53 3.38
4.68 4.50 4.33 4.16 3.99
5.34 5.16 4.98 4.81 4.64
6.00 5.82 5.65 5.47 5.29
6.65 6.49 6.31 6.13 5.96
2.60 0.641 0.782 0.940 1.11 2.80 0.604 0.738 0.890 1.06 3.00 0.570 0.699 0.844 1.00
1.30 1.23 1.17
1.49 1.42 1.36
1.71 1.62 1.55
1.93 1.84 1.76
2.17 2.07 1.98
2.42 2.31 2.22
2.68 2.57 2.46
3.24 3.11 2.99
3.84 3.70 3.56
4.47 4.31 4.16
5.12 4.95 4.79
5.78 5.61 5.44
x
0.000 0.008 0.029 0.056 0.089 0.125 0.164 0.204 0.246 0.289 0.333 0.424 0.516 0.610 0.704 0.800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 199
Table 8-44. Coefficients C for Eccentrically Loaded Weld Groups Angle = 0°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l Pu
yl
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
l
c.g.
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
1.39 1.39 1.38 1.32 1.24
1.60 1.53 1.52 1.47 1.39
1.81 1.71 1.69 1.63 1.55
2.02 1.90 1.87 1.80 1.71
2.23 2.09 2.05 1.98 1.88
2.44 2.29 2.24 2.15 2.04
2.65 2.48 2.43 2.33 2.21
2.85 2.68 2.62 2.52 2.39
3.06 2.88 2.82 2.70 2.57
3.27 3.08 3.01 2.89 2.74
3.48 3.29 3.21 3.08 2.93
3.90 3.70 3.61 3.46 3.30
4.32 4.11 4.01 3.85 3.68
4.73 4.52 4.42 4.25 4.06
5.15 4.94 4.83 4.65 4.46
5.57 5.35 5.26 5.05 4.85
0.30 0.40 0.50 0.60 0.70
1.16 0.998 0.860 0.748 0.659
1.30 1.12 0.965 0.840 0.739
1.45 1.25 1.08 0.935 0.822
1.61 1.39 1.20 1.04 0.913
1.77 1.54 1.32 1.15 1.01
1.92 1.68 1.46 1.27 1.12
2.08 1.82 1.60 1.40 1.24
2.25 1.97 1.73 1.53 1.36
2.42 2.13 1.87 1.66 1.48
2.59 2.29 2.02 1.80 1.61
2.77 2.45 2.17 1.94 1.74
3.13 2.79 2.50 2.24 2.03
3.50 3.15 2.84 2.57 2.34
3.88 3.51 3.19 2.90 2.66
4.26 3.89 3.55 3.26 3.00
4.65 4.27 3.92 3.62 3.35
0.80 0.90 1.00 1.20 1.40
0.586 0.527 0.478 0.403 0.348
0.658 0.591 0.536 0.452 0.389
0.732 0.658 0.597 0.503 0.433
0.813 0.731 0.663 0.558 0.481
0.901 0.811 0.736 0.620 0.535
1.00 0.900 0.818 0.690 0.596
1.11 0.999 0.909 0.769 0.665
1.22 1.11 1.01 0.856 0.743
1.34 1.21 1.11 0.947 0.824
1.45 1.32 1.21 1.04 0.904
1.58 1.44 1.32 1.13 0.990
1.85 1.69 1.56 1.35 1.18
2.14 1.97 1.82 1.58 1.39
2.45 2.26 2.10 1.83 1.62
2.77 2.57 2.40 2.10 1.86
3.11 2.90 2.71 2.38 2.12
1.60 1.80 2.00 2.20 2.40
0.305 0.272 0.245 0.223 0.205
0.342 0.305 0.275 0.250 0.229
0.381 0.339 0.306 0.278 0.255
0.423 0.377 0.340 0.309 0.284
0.470 0.419 0.378 0.344 0.316
0.525 0.468 0.423 0.385 0.354
0.586 0.524 0.473 0.431 0.396
0.655 0.585 0.529 0.483 0.443
0.728 0.652 0.590 0.539 0.495
0.800 0.717 0.649 0.593 0.546
0.877 0.787 0.713 0.652 0.600
1.05 0.941 0.854 0.780 0.719
1.24 1.11 1.01 0.927 0.855
1.44 1.30 1.19 1.09 1.00
1.67 1.51 1.38 1.26 1.17
1.91 1.73 1.58 1.45 1.34
2.60 0.189 0.212 0.236 0.262 0.292 0.327 0.366 0.410 0.458 0.505 0.555 0.667 0.792 0.933 1.09 1.25 2.80 0.176 0.197 0.219 0.244 0.271 0.304 0.340 0.381 0.426 0.470 0.517 0.621 0.739 0.870 1.01 1.17 3.00 0.164 0.184 0.204 0.228 0.254 0.284 0.318 0.356 0.398 0.440 0.483 0.581 0.692 0.815 0.950 1.10
x y
0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 200
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-44 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = ±15°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
15° yl
15°
c.g.
l
Pu
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
1.48 1.42 1.38 1.32 1.24
1.69 1.56 1.53 1.48 1.39
1.89 1.73 1.69 1.63 1.55
2.10 1.90 1.85 1.78 1.69
2.31 2.09 2.03 1.94 1.85
2.51 2.28 2.20 2.11 2.00
2.72 2.47 2.39 2.28 2.16
2.92 2.67 2.57 2.46 2.33
3.13 2.88 2.76 2.64 2.50
3.33 3.09 2.95 2.82 2.67
3.54 3.30 3.15 3.00 2.85
3.95 3.73 3.54 3.38 3.21
4.36 4.17 3.95 3.77 3.59
4.77 4.59 4.37 4.16 3.97
5.18 5.02 4.80 4.57 4.36
5.59 5.45 5.23 4.97 4.76
0.30 0.40 0.50 0.60 0.70
1.16 1.00 0.869 0.759 0.670
1.31 1.13 0.978 0.854 0.753
1.46 1.27 1.09 0.953 0.840
1.60 1.41 1.22 1.06 0.936
1.74 1.53 1.34 1.18 1.04
1.89 1.66 1.46 1.29 1.15
2.04 1.80 1.59 1.41 1.26
2.20 1.94 1.72 1.53 1.37
2.36 2.09 1.85 1.65 1.48
2.53 2.25 2.00 1.79 1.61
2.70 2.41 2.15 1.93 1.74
3.05 2.74 2.47 2.23 2.03
3.42 3.09 2.80 2.55 2.33
3.79 3.45 3.15 2.89 2.65
4.18 3.83 3.51 3.24 2.99
4.57 4.21 3.88 3.60 3.34
0.80 0.90 1.00 1.20 1.40
0.598 0.539 0.490 0.413 0.357
0.672 0.605 0.550 0.464 0.401
0.749 0.675 0.613 0.517 0.446
0.834 0.750 0.681 0.574 0.496
0.927 0.834 0.758 0.639 0.552
1.03 0.925 0.842 0.712 0.616
1.13 1.02 0.933 0.791 0.686
1.23 1.12 1.03 0.878 0.764
1.34 1.23 1.12 0.964 0.841
1.46 1.33 1.23 1.06 0.921
1.58 1.45 1.34 1.15 1.01
1.85 1.71 1.58 1.36 1.20
2.14 1.98 1.84 1.60 1.41
2.45 2.28 2.12 1.86 1.64
2.78 2.59 2.42 2.13 1.89
3.12 2.91 2.73 2.41 2.15
1.60 1.80 2.00 2.20 2.40
0.314 0.280 0.253 0.230 0.211
0.352 0.314 0.283 0.258 0.237
0.392 0.350 0.315 0.287 0.263
0.436 0.389 0.351 0.319 0.293
0.485 0.433 0.391 0.356 0.327
0.542 0.484 0.437 0.398 0.366
0.605 0.541 0.489 0.446 0.410
0.675 0.604 0.546 0.499 0.458
0.745 0.668 0.606 0.554 0.510
0.818 0.735 0.666 0.609 0.561
0.897 0.806 0.731 0.669 0.616
1.07 0.962 0.875 0.801 0.738
1.26 1.14 1.04 0.950 0.877
1.47 1.33 1.21 1.11 1.03
1.70 1.54 1.41 1.29 1.20
1.94 1.77 1.62 1.49 1.38
2.60 0.195 0.219 0.243 0.271 0.302 0.338 0.379 0.424 0.472 0.520 0.571 0.685 0.814 0.957 1.12 1.28 2.80 0.182 0.203 0.226 0.252 0.281 0.314 0.352 0.394 0.439 0.484 0.532 0.639 0.759 0.894 1.04 1.20 3.00 0.170 0.190 0.211 0.235 0.262 0.294 0.329 0.368 0.411 0.453 0.498 0.598 0.711 0.838 0.977 1.13
x y
0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 201
Table 8-44 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = ±30°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
30°
yl
30°
c.g.
l
Pu
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
1.64 1.52 1.44 1.36 1.28
1.83 1.68 1.60 1.51 1.43
2.03 1.85 1.76 1.67 1.58
2.22 2.03 1.91 1.83 1.73
2.42 2.21 2.08 1.98 1.88
2.61 2.39 2.25 2.14 2.03
2.81 2.58 2.42 2.30 2.18
3.01 2.77 2.60 2.47 2.34
3.20 2.97 2.78 2.64 2.51
3.40 3.16 2.97 2.82 2.68
3.59 3.36 3.16 3.00 2.85
3.98 3.77 3.55 3.37 3.21
4.37 4.18 3.95 3.76 3.59
4.76 4.59 4.37 4.16 3.98
5.15 5.00 4.79 4.57 4.37
5.54 5.41 5.20 4.98 4.78
0.30 0.40 0.50 0.60 0.70
1.20 1.05 0.921 0.812 0.722
1.34 1.18 1.03 0.910 0.811
1.49 1.31 1.15 1.02 0.908
1.63 1.44 1.27 1.13 1.01
1.78 1.58 1.40 1.25 1.12
1.92 1.71 1.52 1.36 1.22
2.06 1.84 1.64 1.47 1.33
2.22 1.98 1.77 1.59 1.44
2.37 2.13 1.91 1.72 1.56
2.54 2.28 2.06 1.86 1.69
2.71 2.44 2.21 2.00 1.83
3.06 2.78 2.53 2.31 2.12
3.43 3.13 2.87 2.64 2.43
3.81 3.50 3.23 2.98 2.77
4.20 3.88 3.60 3.34 3.12
4.60 4.27 3.98 3.71 3.48
0.80 0.90 1.00 1.20 1.40
0.647 0.586 0.535 0.454 0.393
0.729 0.660 0.601 0.510 0.441
0.815 0.736 0.671 0.568 0.492
0.908 0.820 0.747 0.632 0.547
1.01 0.912 0.831 0.704 0.610
1.11 1.01 0.920 0.783 0.680
1.21 1.10 1.01 0.868 0.756
1.31 1.20 1.11 0.952 0.835
1.43 1.31 1.21 1.04 0.916
1.55 1.42 1.31 1.14 1.00
1.67 1.54 1.43 1.24 1.10
1.95 1.81 1.68 1.47 1.30
2.25 2.10 1.96 1.72 1.53
2.58 2.41 2.25 1.99 1.77
2.91 2.73 2.56 2.28 2.04
3.26 3.07 2.89 2.58 2.32
1.60 1.80 2.00 2.20 2.40
0.347 0.310 0.280 0.255 0.234
0.389 0.347 0.314 0.286 0.263
0.433 0.387 0.349 0.318 0.292
0.482 0.430 0.389 0.354 0.325
0.537 0.480 0.433 0.395 0.363
0.600 0.536 0.485 0.442 0.406
0.668 0.599 0.542 0.495 0.455
0.742 0.666 0.604 0.552 0.508
0.814 0.733 0.666 0.610 0.562
0.893 0.805 0.732 0.670 0.618
0.978 0.882 0.802 0.735 0.679
1.16 1.05 0.958 0.880 0.813
1.37 1.24 1.13 1.04 0.963
1.60 1.45 1.33 1.22 1.13
1.84 1.67 1.54 1.42 1.31
2.10 1.92 1.76 1.63 1.51
2.60 0.217 0.243 0.270 0.301 0.335 0.376 0.421 0.471 0.521 0.573 0.630 0.754 0.896 1.05 1.22 2.80 0.201 0.226 0.251 0.280 0.312 0.349 0.392 0.438 0.486 0.535 0.588 0.704 0.836 0.984 1.15 3.00 0.188 0.211 0.235 0.261 0.292 0.327 0.366 0.410 0.455 0.501 0.550 0.660 0.784 0.924 1.08
1.41 1.32 1.24
x y
0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 202
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-44 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = ±45°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
45° yl
45°
c.g.
l
Pu
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
1.81 1.68 1.57 1.47 1.39
1.99 1.83 1.71 1.61 1.52
2.17 1.99 1.86 1.75 1.65
2.35 2.14 2.01 1.90 1.80
2.53 2.30 2.17 2.06 1.96
2.71 2.47 2.33 2.22 2.11
2.89 2.64 2.50 2.37 2.26
3.07 2.82 2.67 2.54 2.42
3.25 3.00 2.84 2.71 2.58
3.43 3.18 3.02 2.88 2.75
3.61 3.37 3.21 3.06 2.93
3.97 3.76 3.59 3.43 3.29
4.33 4.15 3.99 3.83 3.68
4.70 4.55 4.39 4.23 4.07
5.06 4.95 4.80 4.64 4.48
5.42 5.35 5.21 5.06 4.90
0.30 0.40 0.50 0.60 0.70
1.31 1.16 1.03 0.921 0.829
1.43 1.27 1.14 1.02 0.919
1.56 1.40 1.25 1.13 1.02
1.71 1.53 1.38 1.24 1.13
1.86 1.67 1.51 1.36 1.24
2.01 1.81 1.64 1.49 1.36
2.15 1.95 1.77 1.62 1.48
2.31 2.10 1.91 1.74 1.60
2.46 2.25 2.05 1.88 1.73
2.63 2.40 2.20 2.02 1.87
2.80 2.57 2.36 2.18 2.01
3.16 2.92 2.70 2.50 2.32
3.54 3.28 3.05 2.85 2.66
3.93 3.66 3.43 3.21 3.02
4.33 4.06 3.81 3.59 3.39
4.75 4.47 4.21 3.98 3.77
0.80 0.90 1.00 1.20 1.40
0.751 0.685 0.629 0.538 0.469
0.835 0.764 0.702 0.603 0.527
0.928 0.849 0.782 0.674 0.589
1.03 0.943 0.870 0.751 0.655
1.14 1.05 0.966 0.836 0.730
1.25 1.15 1.07 0.926 0.811
1.36 1.26 1.16 1.01 0.894
1.47 1.36 1.27 1.11 0.979
1.60 1.48 1.38 1.21 1.07
1.73 1.61 1.50 1.32 1.17
1.87 1.74 1.63 1.43 1.28
2.17 2.03 1.90 1.69 1.51
2.49 2.34 2.21 1.97 1.77
2.84 2.68 2.53 2.27 2.05
3.20 3.03 2.87 2.59 2.34
3.58 3.39 3.22 2.92 2.65
1.60 1.80 2.00 2.20 2.40
0.416 0.373 0.338 0.308 0.284
0.467 0.419 0.379 0.346 0.318
0.521 0.466 0.422 0.385 0.355
0.580 0.519 0.470 0.429 0.395
0.646 0.579 0.524 0.479 0.441
0.721 0.647 0.587 0.536 0.493
0.799 0.720 0.654 0.599 0.552
0.877 0.793 0.722 0.663 0.613
0.961 0.869 0.794 0.730 0.675
1.05 0.953 0.871 0.801 0.741
1.15 1.04 0.954 0.878 0.812
1.36 1.24 1.14 1.05 0.971
1.60 1.46 1.34 1.24 1.15
1.86 1.70 1.56 1.45 1.34
2.14 1.96 1.80 1.67 1.56
2.43 2.23 2.06 1.92 1.78
2.60 0.263 0.295 0.328 0.365 0.408 0.457 0.511 0.570 0.627 0.689 0.756 0.904 1.07 1.26 2.80 0.245 0.274 0.305 0.340 0.380 0.425 0.476 0.532 0.585 0.643 0.707 0.845 1.00 1.18 3.00 0.229 0.256 0.286 0.318 0.355 0.398 0.446 0.498 0.549 0.604 0.663 0.794 0.942 1.11
1.46 1.37 1.29
1.67 1.57 1.48
x y
0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 203
Table 8-44 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = ±60°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
60° yl
60°
c.g.
l
Pu
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
1.95 1.83 1.73 1.63 1.55
2.12 1.94 1.84 1.74 1.66
2.28 2.07 1.96 1.87 1.78
2.44 2.20 2.10 2.00 1.92
2.61 2.35 2.25 2.15 2.06
2.77 2.51 2.40 2.31 2.22
2.94 2.68 2.57 2.47 2.38
3.10 2.85 2.74 2.64 2.55
3.26 3.03 2.92 2.81 2.72
3.43 3.21 3.10 2.99 2.89
3.59 3.40 3.28 3.18 3.07
3.92 3.78 3.67 3.56 3.45
4.25 4.17 4.07 3.96 3.85
4.57 4.55 4.47 4.37 4.27
4.90 4.90 4.86 4.78 4.68
5.23 5.23 5.23 5.16 5.08
0.30 0.40 0.50 0.60 0.70
1.47 1.34 1.22 1.12 1.03
1.58 1.44 1.32 1.21 1.12
1.70 1.56 1.43 1.32 1.22
1.83 1.69 1.56 1.44 1.33
1.98 1.83 1.69 1.57 1.46
2.13 1.98 1.83 1.71 1.59
2.29 2.13 1.99 1.85 1.73
2.46 2.29 2.14 2.00 1.88
2.63 2.45 2.30 2.15 2.02
2.80 2.62 2.46 2.31 2.18
2.98 2.80 2.63 2.48 2.34
3.35 3.16 2.99 2.83 2.68
3.75 3.55 3.37 3.21 3.05
4.16 3.96 3.77 3.60 3.44
4.58 4.38 4.19 4.01 3.85
5.00 4.81 4.61 4.43 4.26
0.80 0.90 1.00 1.20 1.40
0.945 0.874 0.812 0.709 0.626
1.03 0.958 0.893 0.783 0.695
1.13 1.05 0.983 0.865 0.771
1.24 1.16 1.08 0.957 0.855
1.36 1.27 1.19 1.06 0.948
1.49 1.40 1.31 1.17 1.05
1.63 1.53 1.44 1.29 1.16
1.76 1.66 1.56 1.40 1.26
1.90 1.79 1.69 1.52 1.38
2.05 1.94 1.83 1.65 1.50
2.21 2.09 1.98 1.79 1.63
2.55 2.42 2.30 2.09 1.91
2.91 2.77 2.65 2.42 2.22
3.29 3.15 3.01 2.76 2.55
3.69 3.53 3.39 3.13 2.89
4.09 3.93 3.79 3.51 3.25
1.60 1.80 2.00 2.20 2.40
0.560 0.506 0.461 0.423 0.391
0.623 0.564 0.515 0.473 0.438
0.693 0.629 0.575 0.530 0.489
0.771 0.701 0.642 0.590 0.545
0.857 0.781 0.716 0.659 0.608
0.952 0.868 0.798 0.735 0.680
1.05 0.957 0.880 0.813 0.755
1.15 1.05 0.964 0.891 0.829
1.25 1.15 1.06 0.978 0.910
1.36 1.25 1.16 1.07 0.997
1.49 1.37 1.26 1.17 1.09
1.75 1.61 1.49 1.39 1.30
2.04 1.89 1.75 1.63 1.53
2.35 2.18 2.03 1.90 1.78
2.68 2.50 2.33 2.18 2.05
3.03 2.83 2.64 2.48 2.33
2.60 0.363 0.407 0.454 0.506 0.565 0.632 0.704 0.774 0.850 0.932 1.02 1.22 2.80 0.339 0.380 0.424 0.472 0.527 0.590 0.658 0.726 0.797 0.875 0.958 1.14 3.00 0.317 0.356 0.397 0.442 0.494 0.553 0.618 0.683 0.750 0.824 0.903 1.08
1.43 1.35 1.27
1.67 1.57 1.49
1.93 1.82 1.72
2.20 2.08 1.97
x y
0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 204
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-44 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = ±75°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
75°
75°
c.g.
l
Pu
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
2.05 1.94 1.88 1.82 1.76
2.20 2.01 1.95 1.90 1.84
2.35 2.11 2.05 2.00 1.95
2.50 2.23 2.17 2.12 2.07
2.65 2.37 2.31 2.26 2.21
2.79 2.52 2.47 2.41 2.36
2.94 2.69 2.63 2.58 2.53
3.09 2.87 2.81 2.76 2.71
3.24 3.05 3.00 2.95 2.89
3.39 3.24 3.19 3.14 3.09
3.54 3.44 3.39 3.34 3.29
3.83 3.80 3.77 3.73 3.69
4.13 4.09 4.09 4.09 4.06
4.43 4.38 4.38 4.38 4.38
4.72 4.67 4.67 4.67 4.67
5.02 4.96 4.96 4.96 4.96
0.30 0.40 0.50 0.60 0.70
1.71 1.62 1.53 1.46 1.38
1.79 1.70 1.62 1.54 1.47
1.90 1.81 1.72 1.64 1.57
2.02 1.93 1.84 1.76 1.69
2.16 2.07 1.98 1.90 1.82
2.31 2.22 2.13 2.05 1.97
2.48 2.39 2.30 2.21 2.13
2.66 2.56 2.47 2.38 2.30
2.84 2.75 2.66 2.57 2.48
3.04 2.94 2.85 2.76 2.67
3.24 3.14 3.04 2.95 2.86
3.65 3.54 3.44 3.34 3.25
4.03 3.95 3.85 3.75 3.65
4.38 4.32 4.25 4.16 4.07
4.67 4.66 4.61 4.54 4.46
4.96 4.96 4.94 4.90 4.84
0.80 0.90 1.00 1.20 1.40
1.31 1.25 1.19 1.09 0.994
1.40 1.34 1.28 1.17 1.07
1.50 1.44 1.38 1.27 1.17
1.62 1.55 1.49 1.38 1.28
1.75 1.68 1.62 1.50 1.40
1.90 1.83 1.76 1.64 1.53
2.06 1.98 1.91 1.79 1.67
2.22 2.15 2.08 1.95 1.83
2.40 2.33 2.25 2.11 1.98
2.59 2.51 2.43 2.28 2.14
2.77 2.69 2.60 2.45 2.31
3.16 3.07 2.98 2.82 2.67
3.56 3.47 3.38 3.21 3.04
3.97 3.88 3.79 3.61 3.44
4.38 4.29 4.20 4.02 3.85
4.76 4.68 4.60 4.43 4.26
1.60 1.80 2.00 2.20 2.40
0.914 0.845 0.784 0.730 0.683
0.992 0.920 0.857 0.801 0.751
1.08 1.01 0.941 0.881 0.828
1.19 1.11 1.04 0.973 0.916
1.30 1.22 1.14 1.08 1.01
1.43 1.34 1.26 1.19 1.12
1.57 1.47 1.39 1.31 1.24
1.72 1.62 1.52 1.44 1.36
1.86 1.76 1.66 1.57 1.49
2.02 1.90 1.80 1.70 1.62
2.18 2.06 1.95 1.85 1.76
2.53 2.39 2.27 2.16 2.06
2.89 2.75 2.62 2.50 2.39
3.28 3.13 2.99 2.86 2.73
3.68 3.52 3.37 3.23 3.10
4.10 3.93 3.77 3.62 3.48
2.60 0.641 0.706 0.781 0.865 0.960 1.07 1.18 2.80 0.604 0.666 0.738 0.819 0.910 1.01 1.12 3.00 0.570 0.631 0.700 0.777 0.863 0.961 1.07
1.29 1.23 1.17
1.41 1.34 1.28
1.54 1.46 1.39
1.67 1.59 1.52
1.96 1.87 1.79
2.28 2.18 2.09
2.62 2.51 2.41
2.97 2.86 2.74
3.35 3.22 3.10
x y
0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 205
Table 8-45. Coefficients C for Eccentrically Loaded Weld Groups Angle = 0°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
Pu
lmin =
CC 1 l
CC 1 D
where ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
yl
Pu
l
c.g.
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
1.39 1.39 1.38 1.32 1.24
1.60 1.55 1.53 1.47 1.38
1.81 1.74 1.71 1.63 1.52
2.02 1.93 1.88 1.79 1.66
2.23 2.12 2.06 1.94 1.80
2.44 2.31 2.22 2.09 1.94
2.65 2.49 2.38 2.23 2.07
2.85 2.66 2.54 2.37 2.21
3.06 2.83 2.69 2.52 2.35
3.27 2.99 2.83 2.67 2.51
3.48 3.14 2.98 2.81 2.66
3.90 3.45 3.28 3.12 2.96
4.32 3.76 3.59 3.42 3.27
4.73 4.08 3.91 3.75 3.59
5.15 4.42 4.24 4.08 3.91
5.57 4.76 4.58 4.41 4.25
0.30 0.40 0.50 0.60 0.70
1.16 0.998 0.860 0.748 0.659
1.29 1.11 0.958 0.833 0.733
1.42 1.22 1.05 0.913 0.805
1.54 1.32 1.14 0.998 0.884
1.67 1.42 1.24 1.09 0.967
1.79 1.54 1.34 1.18 1.06
1.92 1.66 1.46 1.29 1.15
2.06 1.80 1.58 1.41 1.26
2.20 1.94 1.72 1.54 1.38
2.35 2.09 1.86 1.67 1.51
2.51 2.24 2.01 1.81 1.64
2.82 2.55 2.31 2.10 1.92
3.12 2.85 2.61 2.40 2.21
3.44 3.16 2.91 2.69 2.50
3.76 3.48 3.22 2.99 2.79
4.10 3.81 3.54 3.31 3.09
0.80 0.90 1.00 1.20 1.40
0.586 0.527 0.478 0.403 0.348
0.652 0.586 0.532 0.448 0.387
0.719 0.648 0.589 0.497 0.430
0.791 0.715 0.651 0.551 0.476
0.868 0.786 0.717 0.609 0.528
0.951 0.864 0.791 0.674 0.586
1.04 0.949 0.870 0.744 0.648
1.14 1.04 0.957 0.820 0.716
1.25 1.15 1.05 0.904 0.790
1.37 1.26 1.16 0.997 0.874
1.50 1.38 1.27 1.10 0.963
1.77 1.63 1.51 1.31 1.16
2.05 1.90 1.77 1.55 1.37
2.32 2.17 2.03 1.80 1.60
2.61 2.44 2.29 2.04 1.83
2.90 2.73 2.57 2.30 2.07
1.60 1.80 2.00 2.20 2.40
0.305 0.272 0.245 0.223 0.205
0.340 0.303 0.273 0.249 0.228
0.378 0.337 0.304 0.277 0.254
0.419 0.374 0.338 0.308 0.283
0.466 0.416 0.376 0.343 0.315
0.518 0.463 0.419 0.382 0.351
0.573 0.514 0.465 0.425 0.391
0.634 0.569 0.516 0.472 0.434
0.702 0.630 0.572 0.523 0.482
0.776 0.697 0.633 0.579 0.534
0.856 0.771 0.700 0.641 0.591
1.03 0.932 0.848 0.778 0.718
1.23 1.11 1.02 0.932 0.861
1.44 1.31 1.20 1.10 1.02
1.66 1.51 1.39 1.28 1.18
1.88 1.72 1.58 1.47 1.36
2.60 0.189 0.211 0.235 0.261 0.291 0.325 0.362 0.402 0.446 0.495 0.548 0.667 0.800 0.945 1.10 1.27 2.80 0.176 0.196 0.218 0.243 0.271 0.302 0.337 0.375 0.416 0.461 0.511 0.622 0.747 0.882 1.03 1.18 3.00 0.164 0.183 0.204 0.227 0.253 0.282 0.315 0.350 0.389 0.431 0.478 0.582 0.700 0.825 0.962 1.11
x y
0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 206
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-45 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = ±15°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
yl
15° 15°
c.g.
l
Pu
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
1.48 1.42 1.38 1.32 1.24
1.69 1.57 1.54 1.47 1.39
1.89 1.74 1.70 1.63 1.54
2.10 1.92 1.86 1.78 1.68
2.31 2.09 2.02 1.94 1.81
2.51 2.27 2.19 2.09 1.94
2.72 2.44 2.35 2.22 2.07
2.92 2.61 2.51 2.36 2.21
3.13 2.78 2.67 2.51 2.35
3.33 2.95 2.83 2.66 2.50
3.54 3.12 2.98 2.82 2.66
3.95 3.45 3.30 3.13 2.98
4.36 3.78 3.62 3.45 3.30
4.77 4.12 3.95 3.78 3.63
5.18 4.46 4.29 4.12 3.96
5.59 4.81 4.64 4.46 4.30
0.30 0.40 0.50 0.60 0.70
1.16 1.00 0.869 0.759 0.670
1.30 1.12 0.970 0.847 0.746
1.43 1.23 1.06 0.926 0.820
1.55 1.33 1.15 1.01 0.899
1.68 1.44 1.25 1.10 0.983
1.80 1.55 1.36 1.20 1.07
1.93 1.68 1.48 1.31 1.18
2.06 1.81 1.60 1.43 1.29
2.21 1.95 1.74 1.56 1.41
2.36 2.10 1.88 1.69 1.53
2.51 2.25 2.02 1.83 1.67
2.83 2.57 2.33 2.12 1.95
3.15 2.88 2.64 2.43 2.25
3.48 3.20 2.95 2.74 2.54
3.81 3.53 3.28 3.05 2.84
4.15 3.87 3.61 3.37 3.15
0.80 0.90 1.00 1.20 1.40
0.598 0.539 0.490 0.413 0.357
0.666 0.600 0.545 0.461 0.398
0.734 0.663 0.604 0.511 0.442
0.807 0.730 0.666 0.565 0.490
0.885 0.803 0.734 0.625 0.543
0.969 0.881 0.807 0.690 0.601
1.06 0.968 0.888 0.761 0.664
1.17 1.06 0.979 0.840 0.734
1.28 1.17 1.08 0.927 0.812
1.40 1.28 1.18 1.02 0.897
1.52 1.40 1.30 1.12 0.988
1.79 1.66 1.54 1.34 1.19
2.08 1.93 1.80 1.58 1.40
2.37 2.21 2.08 1.84 1.64
2.66 2.49 2.34 2.09 1.88
2.96 2.78 2.63 2.35 2.12
1.60 1.80 2.00 2.20 2.40
0.314 0.280 0.253 0.230 0.211
0.350 0.312 0.282 0.257 0.236
0.389 0.347 0.313 0.286 0.262
0.432 0.386 0.348 0.318 0.292
0.479 0.429 0.388 0.354 0.325
0.532 0.476 0.431 0.393 0.362
0.589 0.528 0.479 0.438 0.403
0.651 0.585 0.531 0.486 0.447
0.721 0.649 0.589 0.538 0.496
0.798 0.718 0.652 0.597 0.550
0.879 0.793 0.721 0.660 0.609
1.06 0.958 0.873 0.801 0.740
1.26 1.14 1.04 0.958 0.886
1.48 1.34 1.23 1.13 1.05
1.70 1.55 1.43 1.32 1.22
1.93 1.77 1.63 1.51 1.40
2.60 0.195 0.218 0.242 0.270 0.301 0.335 0.373 0.415 0.460 0.510 0.565 0.687 0.824 0.975 1.13 1.31 2.80 0.182 0.203 0.225 0.251 0.280 0.312 0.348 0.386 0.428 0.476 0.527 0.641 0.770 0.910 1.06 1.22 3.00 0.170 0.189 0.211 0.234 0.261 0.291 0.325 0.361 0.401 0.445 0.494 0.601 0.722 0.852 0.993 1.15
x y
0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 207
Table 8-45 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = ±30°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
30°
yl
30°
c.g.
l
Pu
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
1.64 1.52 1.44 1.36 1.28
1.83 1.68 1.59 1.51 1.42
2.03 1.85 1.75 1.66 1.56
2.22 2.03 1.91 1.81 1.71
2.42 2.20 2.07 1.96 1.85
2.61 2.38 2.23 2.12 1.99
2.81 2.55 2.40 2.26 2.12
3.01 2.73 2.56 2.41 2.26
3.20 2.90 2.72 2.56 2.41
3.40 3.06 2.88 2.72 2.57
3.59 3.23 3.05 2.89 2.74
3.98 3.59 3.41 3.24 3.09
4.37 3.95 3.77 3.59 3.43
4.76 4.32 4.13 3.94 3.77
5.15 4.70 4.51 4.31 4.13
5.54 5.08 4.89 4.68 4.49
0.30 0.40 0.50 0.60 0.70
1.20 1.05 0.921 0.812 0.722
1.34 1.17 1.03 0.904 0.804
1.47 1.29 1.13 0.993 0.884
1.60 1.40 1.22 1.08 0.968
1.74 1.51 1.33 1.18 1.06
1.87 1.64 1.45 1.29 1.16
1.99 1.76 1.57 1.41 1.27
2.13 1.90 1.70 1.53 1.38
2.28 2.04 1.83 1.66 1.51
2.43 2.19 1.98 1.80 1.64
2.60 2.35 2.13 1.94 1.78
2.95 2.68 2.45 2.25 2.08
3.28 3.03 2.80 2.59 2.40
3.62 3.35 3.13 2.93 2.73
3.97 3.69 3.46 3.25 3.06
4.32 4.04 3.80 3.58 3.37
0.80 0.90 1.00 1.20 1.40
0.647 0.586 0.535 0.454 0.393
0.722 0.654 0.596 0.506 0.438
0.796 0.722 0.659 0.560 0.487
0.874 0.794 0.727 0.620 0.540
0.957 0.872 0.799 0.685 0.597
1.05 0.957 0.879 0.755 0.660
1.15 1.05 0.968 0.833 0.729
1.26 1.16 1.07 0.920 0.806
1.38 1.27 1.17 1.02 0.891
1.51 1.39 1.29 1.12 0.984
1.64 1.51 1.40 1.22 1.08
1.92 1.78 1.66 1.46 1.29
2.23 2.08 1.94 1.72 1.53
2.55 2.39 2.24 1.99 1.79
2.87 2.70 2.55 2.28 2.05
3.19 3.02 2.85 2.56 2.32
1.60 1.80 2.00 2.20 2.40
0.347 0.310 0.280 0.255 0.234
0.386 0.345 0.312 0.285 0.262
0.430 0.384 0.347 0.317 0.291
0.477 0.427 0.386 0.352 0.324
0.529 0.474 0.429 0.392 0.360
0.585 0.526 0.477 0.436 0.401
0.648 0.583 0.529 0.484 0.446
0.717 0.645 0.586 0.537 0.495
0.794 0.715 0.650 0.595 0.549
0.878 0.791 0.720 0.660 0.609
0.967 0.874 0.796 0.730 0.674
1.16 1.05 0.961 0.884 0.817
1.38 1.25 1.15 1.06 0.978
1.61 1.47 1.35 1.24 1.15
1.87 1.70 1.57 1.45 1.34
2.12 1.94 1.79 1.66 1.55
2.60 0.217 0.242 0.269 0.299 0.334 0.372 0.413 0.459 0.510 0.566 0.626 0.760 0.910 1.08 1.25 2.80 0.201 0.225 0.250 0.278 0.311 0.346 0.385 0.428 0.475 0.527 0.584 0.710 0.851 1.01 1.17 3.00 0.188 0.210 0.234 0.260 0.290 0.324 0.360 0.401 0.445 0.494 0.547 0.666 0.799 0.944 1.10
1.44 1.35 1.27
x y
0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 208
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-45 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = ±45°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
45° yl
45°
c.g.
l
Pu
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
1.81 1.68 1.57 1.47 1.39
1.99 1.83 1.71 1.60 1.51
2.17 1.99 1.86 1.74 1.64
2.35 2.15 2.02 1.88 1.77
2.53 2.32 2.18 2.04 1.92
2.71 2.50 2.36 2.21 2.07
2.89 2.67 2.53 2.38 2.24
3.07 2.85 2.69 2.54 2.41
3.25 3.02 2.86 2.71 2.58
3.43 3.19 3.03 2.88 2.75
3.61 3.37 3.21 3.06 2.93
3.97 3.74 3.58 3.42 3.29
4.33 4.10 3.95 3.80 3.66
4.70 4.48 4.33 4.18 4.04
5.06 4.85 4.71 4.56 4.42
5.42 5.21 5.08 4.94 4.80
0.30 0.40 0.50 0.60 0.70
1.31 1.16 1.03 0.921 0.829
1.43 1.27 1.13 1.01 0.911
1.55 1.38 1.23 1.11 1.00
1.67 1.49 1.35 1.22 1.11
1.81 1.63 1.48 1.34 1.21
1.95 1.77 1.61 1.46 1.33
2.11 1.92 1.74 1.58 1.45
2.28 2.07 1.88 1.72 1.58
2.45 2.23 2.03 1.86 1.71
2.62 2.39 2.19 2.01 1.86
2.80 2.57 2.36 2.18 2.01
3.16 2.92 2.72 2.52 2.35
3.54 3.27 3.06 2.87 2.70
3.91 3.64 3.40 3.21 3.04
4.29 4.03 3.76 3.55 3.37
4.66 4.41 4.14 3.91 3.71
0.80 0.90 1.00 1.20 1.40
0.751 0.685 0.629 0.538 0.469
0.828 0.757 0.696 0.598 0.523
0.915 0.839 0.773 0.666 0.582
1.01 0.927 0.854 0.735 0.644
1.11 1.02 0.938 0.810 0.712
1.22 1.12 1.03 0.892 0.786
1.33 1.22 1.14 0.985 0.868
1.45 1.34 1.25 1.09 0.960
1.58 1.47 1.36 1.20 1.06
1.72 1.60 1.49 1.31 1.16
1.87 1.74 1.63 1.43 1.28
2.19 2.05 1.92 1.70 1.52
2.53 2.38 2.24 2.00 1.80
2.88 2.73 2.58 2.31 2.09
3.21 3.05 2.91 2.64 2.40
3.54 3.38 3.23 2.96 2.71
1.60 1.80 2.00 2.20 2.40
0.416 0.373 0.338 0.308 0.284
0.464 0.416 0.377 0.344 0.317
0.516 0.463 0.419 0.383 0.353
0.572 0.513 0.466 0.426 0.392
0.633 0.570 0.518 0.474 0.436
0.700 0.631 0.574 0.526 0.485
0.774 0.699 0.636 0.583 0.538
0.857 0.775 0.705 0.647 0.598
0.948 0.858 0.782 0.718 0.664
1.05 0.947 0.865 0.795 0.736
1.15 1.04 0.954 0.878 0.812
1.38 1.25 1.15 1.06 0.983
1.63 1.49 1.37 1.26 1.17
1.90 1.74 1.60 1.49 1.38
2.19 2.02 1.86 1.73 1.61
2.50 2.31 2.14 1.99 1.85
2.60 0.263 0.293 0.327 0.363 0.405 0.450 0.500 0.555 0.617 0.684 0.756 0.916 1.09 1.29 2.80 0.245 0.273 0.304 0.338 0.377 0.420 0.467 0.518 0.576 0.638 0.707 0.857 1.03 1.21 3.00 0.229 0.256 0.285 0.317 0.353 0.393 0.437 0.486 0.540 0.599 0.663 0.805 0.964 1.14
1.50 1.41 1.33
1.73 1.62 1.53
x y
0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
ECCENTRICALLY LOADED WELD GROUPS
8 - 209
Table 8-45 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = ±60°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where ex = a l
Pu = factored force, kips
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
60° yl
60°
c.g.
l
Pu
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
1.95 1.83 1.73 1.63 1.55
2.12 1.94 1.84 1.74 1.65
2.28 2.07 1.96 1.86 1.76
2.44 2.21 2.09 1.98 1.88
2.61 2.36 2.24 2.12 2.02
2.77 2.53 2.40 2.28 2.18
2.94 2.70 2.57 2.45 2.35
3.10 2.88 2.75 2.63 2.53
3.26 3.06 2.94 2.82 2.72
3.43 3.24 3.13 3.00 2.90
3.59 3.41 3.31 3.20 3.08
3.92 3.76 3.67 3.57 3.46
4.25 4.11 4.03 3.94 3.84
4.57 4.45 4.38 4.30 4.21
4.90 4.78 4.72 4.65 4.56
5.23 5.12 5.06 4.99 4.91
0.30 0.40 0.50 0.60 0.70
1.47 1.34 1.22 1.12 1.03
1.58 1.44 1.31 1.20 1.11
1.68 1.54 1.41 1.30 1.20
1.80 1.66 1.53 1.42 1.32
1.94 1.79 1.67 1.55 1.45
2.09 1.94 1.81 1.69 1.59
2.26 2.10 1.97 1.85 1.74
2.44 2.27 2.13 2.01 1.90
2.62 2.45 2.30 2.17 2.06
2.81 2.64 2.48 2.35 2.23
2.99 2.83 2.66 2.52 2.40
3.36 3.20 3.04 2.89 2.75
3.73 3.56 3.42 3.27 3.12
4.11 3.93 3.78 3.64 3.50
4.48 4.29 4.14 4.00 3.87
4.83 4.65 4.49 4.36 4.23
0.80 0.90 1.00 1.20 1.40
0.945 0.874 0.812 0.709 0.626
1.02 0.950 0.886 0.777 0.690
1.12 1.04 0.973 0.858 0.765
1.23 1.15 1.08 0.952 0.852
1.35 1.27 1.19 1.06 0.945
1.49 1.40 1.32 1.17 1.04
1.64 1.54 1.45 1.28 1.15
1.79 1.68 1.58 1.41 1.26
1.95 1.83 1.73 1.54 1.39
2.11 1.99 1.88 1.68 1.52
2.28 2.16 2.05 1.84 1.66
2.63 2.51 2.40 2.17 1.97
2.99 2.87 2.75 2.52 2.31
3.36 3.23 3.10 2.87 2.66
3.73 3.60 3.46 3.21 3.00
4.10 3.96 3.83 3.56 3.34
1.60 1.80 2.00 2.20 2.40
0.560 0.506 0.461 0.423 0.391
0.619 0.561 0.512 0.471 0.436
0.689 0.626 0.573 0.527 0.487
0.769 0.697 0.636 0.585 0.541
0.850 0.771 0.705 0.649 0.600
0.938 0.853 0.780 0.719 0.666
1.04 0.943 0.864 0.797 0.738
1.14 1.04 0.957 0.883 0.819
1.26 1.15 1.06 0.977 0.907
1.38 1.27 1.17 1.08 1.00
1.52 1.39 1.28 1.19 1.10
1.81 1.66 1.53 1.43 1.33
2.12 1.96 1.82 1.69 1.58
2.46 2.28 2.12 1.98 1.85
2.80 2.61 2.44 2.28 2.14
3.13 2.94 2.77 2.60 2.44
2.60 0.363 0.405 0.452 0.502 0.558 0.620 0.687 0.763 0.847 0.937 1.03 1.25 2.80 0.339 0.379 0.422 0.469 0.521 0.580 0.644 0.715 0.793 0.878 0.969 1.17 3.00 0.317 0.355 0.395 0.440 0.489 0.545 0.605 0.672 0.746 0.826 0.913 1.10
1.48 1.39 1.31
1.74 1.63 1.54
2.01 1.90 1.79
2.30 2.17 2.06
x y
0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 210
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-45 (cont.). Coefficients C for Eccentrically Loaded Weld Groups Angle = ±75°° φ R n = CC1Dl
C min =
Pu
D min =
C 1D l
Pu
lmin =
CC 1 l
Pu
CC 1 D
where Pu = factored force, kips
ex = a l
D = number of sixteenths-of-an-inch in the fillet weld size l = characteristic length of weld group, in. a = e x / l, in. e x = horizontal component of eccentricity of Pu with respect to centroid of weld group, in.
75° yl
75°
c.g.
l
Pu
C = coefficient tabulated below which includes φ = 0.75 C 1 = electode strength coefficient from Table 8-37 (1.0 for E70XX electrodes)
xl kl
k a
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
0.00 0.10 0.15 0.20 0.25
2.05 1.94 1.88 1.82 1.76
2.20 2.01 1.94 1.89 1.83
2.35 2.08 2.03 1.97 1.92
2.50 2.20 2.15 2.09 2.04
2.65 2.34 2.29 2.24 2.19
2.79 2.49 2.44 2.39 2.35
2.94 2.65 2.61 2.56 2.52
3.09 2.81 2.77 2.73 2.69
3.24 2.97 2.94 2.90 2.86
3.39 3.13 3.10 3.07 3.03
3.54 3.28 3.25 3.23 3.20
3.83 3.59 3.56 3.53 3.51
4.13 3.93 3.87 3.84 3.81
4.43 4.25 4.20 4.15 4.11
4.72 4.57 4.52 4.48 4.42
5.02 4.88 4.84 4.80 4.75
0.30 0.40 0.50 0.60 0.70
1.71 1.62 1.53 1.46 1.38
1.78 1.69 1.61 1.53 1.46
1.87 1.79 1.70 1.63 1.56
2.00 1.91 1.83 1.75 1.68
2.14 2.05 1.97 1.89 1.82
2.30 2.21 2.12 2.05 1.97
2.47 2.38 2.29 2.21 2.14
2.65 2.56 2.47 2.39 2.31
2.82 2.74 2.66 2.57 2.49
3.00 2.92 2.84 2.76 2.68
3.17 3.10 3.03 2.95 2.87
3.49 3.43 3.38 3.31 3.25
3.79 3.75 3.70 3.65 3.60
4.09 4.05 4.02 3.97 3.93
4.39 4.35 4.32 4.28 4.24
4.70 4.65 4.61 4.58 4.55
0.80 0.90 1.00 1.20 1.40
1.31 1.25 1.19 1.09 0.994
1.39 1.33 1.27 1.16 1.07
1.49 1.43 1.37 1.26 1.16
1.61 1.54 1.48 1.37 1.27
1.75 1.68 1.62 1.50 1.40
1.90 1.83 1.77 1.64 1.54
2.06 1.99 1.93 1.80 1.69
2.24 2.16 2.10 1.97 1.85
2.41 2.34 2.27 2.14 2.01
2.60 2.52 2.45 2.31 2.19
2.79 2.71 2.64 2.50 2.36
3.17 3.10 3.03 2.87 2.73
3.54 3.47 3.41 3.26 3.12
3.88 3.82 3.76 3.64 3.50
4.20 4.16 4.10 3.99 3.87
4.51 4.47 4.43 4.34 4.23
1.60 1.80 2.00 2.20 2.40
0.914 0.845 0.784 0.730 0.683
0.987 0.915 0.852 0.797 0.748
1.08 1.00 0.937 0.878 0.825
1.18 1.11 1.04 0.972 0.915
1.30 1.22 1.15 1.08 1.02
1.44 1.35 1.27 1.20 1.13
1.58 1.49 1.40 1.33 1.26
1.74 1.64 1.55 1.46 1.39
1.90 1.80 1.70 1.60 1.52
2.07 1.95 1.84 1.74 1.65
2.24 2.11 2.00 1.89 1.80
2.59 2.45 2.33 2.21 2.10
2.97 2.82 2.69 2.56 2.44
3.36 3.21 3.06 2.92 2.80
3.74 3.61 3.46 3.31 3.17
4.11 3.99 3.85 3.71 3.56
2.60 0.641 0.704 0.778 0.865 0.963 1.07 1.19 2.80 0.604 0.664 0.736 0.819 0.913 1.02 1.13 3.00 0.570 0.628 0.698 0.777 0.867 0.966 1.07
1.32 1.25 1.18
1.44 1.37 1.30
1.57 1.49 1.42
1.71 1.62 1.55
2.00 1.91 1.82
2.33 2.23 2.13
2.68 2.57 2.46
3.05 2.93 2.81
3.42 3.30 3.18
x y
0.000 0.005 0.017 0.035 0.057 0.083 0.113 0.144 0.178 0.213 0.250 0.327 0.408 0.492 0.579 0.667 0.500 0.455 0.417 0.385 0.357 0.333 0.313 0.294 0.278 0.263 0.250 0.227 0.208 0.192 0.179 0.167
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONSTRUCTION COMBINING BOLTS AND WELDS
8 - 211
Eccentricity Normal to the Plane of the Faying Surface
Figure 8-55 shows a bracket welded to a column flange. The eccentric load Pu can be resolved into a concentric force Pu at the faying surface of the connection and a moment Pu e normal to the plane of the faying surface where e is the eccentricity. Each weld element is then assumed to support an equal share of the concentric force Pu, and the moment Pu e is resisted by tension in the welds above the neutral axis and compression below the neutral axis. In contrast to bolts, where the interaction of shear and tension must be considered, for welds, shear and tension may be combined vectorially for welds into a resultant shear. Thus, the solution of a weld loaded eccentrically normal to the plane of the faying surface is parallel to that discussed previously for welds loaded eccentrically in the plane of the faying surface; with the neutral axis assumed to be located at the CG of the weld group, this case is identical to that described previously for the elastic method. CONSTRUCTION COMBINING BOLTS AND WELDS
In bearing-type connections in new construction, the rigidity of the welds prevents the initial joint slippage necessary to develop the strength of all the bolts in a connection that might combine both welds and bolts. Thus, bearing-type connections combining welds and bolts are permissible only if the design strength of the welds Ď&#x2020;Rn alone exceeds the required strength of the connection Ru. However, in situations where it can safely be assumed that joint slippage has occurred before welding is performed, welds may be used to reinforce existing bolted or riveted joints. Such is the case with structures previously in service. In this case, the design strength of the original bolt group may be used to carry the existing dead loads and the design strength of the welds need be adequate only to carry additional loads. Refer to LRFD Specification Section J1.9. In slip-critical connections, since connection slip is neither expected nor required for the bolts to develop their strength, the design strengths of welds and high-strength bolts are additive. When high-strength bolts and welds are used together in a slip-critical connection, the bolts should preferably be fully tensioned before welding is performed. The design drawings should clearly indicate where this type of connection occurs.
Pu e
Fig. 8-55. Welds subjected to eccentricity normal to the plane of the faying surface. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BOLTS, WELDS, AND CONNECTED ELEMENTS
CONNECTED ELEMENTS
Connected elements are the angles, plates, tees, gussets, and other connecting elements used in connections to transfer load from one structural member to another as well as the affected elements of the connected members. Economical Considerations
Cost effective steel fabrication requires close cooperation between the designer, detailer, and fabricator. Effective communication and planning will allow the project to take full advantage of the strengths of all parties involved. Often, potential problems can be avoided through early consultation and good communication during the full life of a project. Designs and details should be suited to the shop practices and standards of the fabricator. The resulting similarity throughout the project will further lend itself to the minimization of errors. For example, once gage lines conforming to standard machine set-ups are determined, they should be utilized as much as possible throughout any one job. Furthermore, it is desirable to keep the same bolt spacing throughout a project. Longitudinal spacing should preferably be three inches or a multiple of three inches, since most shops consider this to be standard. At a minimum, gages and hole sizes on any one member should not be varied throughout the length of that member. This prevents unnecessary material re-handling and the need for multiple punching or drilling. Design Strength of Connected Elements
The design strength of connecting elements is determined in accordance with the provisions of LRFD Specification Sections J4 and J5; the applicable limit states are shear yielding, shear rupture, block shear rupture, tension yielding, and tension rupture. Shear Yielding
This limit state applies to the gross section of the connected element. From LRFD Specification Section J5.3, the design shear yielding strength is φRn, where φ = 0.90 Rn = 0.60Fy Ag Shear Rupture
This limit state applies to the net section From LRFD Specification Section J4.1, the design shear rupture strength is φRn, where φ = 0.75 Rn = 0.60Fu Anv Table 8-46 gives the reduction in area for standard, oversized, short-slotted, and long-slotted holes in material thicknesses from 3⁄16-in. to 1 in.; for other material thicknesses, multiply the tabular value for 1-in. thickness by the actual thickness. Block Shear Rupture
The term block shear rupture describes a material tearing limit state which occurs in a combination of shear and tension. This phenomenon can occur at the end of a coped beam, shown in Figure 8-56, or at the end of a tension connection, shown in Figure 8-57. This AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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Table 8-46. Reduction in Area for Holes, in.2 C
Thckns. t, in.
A
B
STD Standard Hole
OVS Oversized Hole
3⁄ 4
7⁄ 8
D
A
A
SSL Short-Slotted Hole
LSL Long-Slotted Hole
A ×t
B ×t
Bolt Diameter d b , in.
Bolt Diameter d b , in.
1
1 1 ⁄8
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
3⁄ 4
7⁄ 8
1
1 1 ⁄8
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
3⁄ 16 1⁄ 4
0.164 0.188 0.211 0.234 0.258 0.281 0.305 0.188 0.211 0.246 0.281 0.305 0.328 0.352 0.219 0.250 0.281 0.313 0.344 0.375 0.406 0.250 0.281 0.328 0.375 0.406 0.438 0.469
5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2
0.273 0.328 0.383 0.438
0.313 0.375 0.438 0.500
0.352 0.422 0.492 0.563
0.391 0.469 0.547 0.625
0.430 0.516 0.602 0.688
0.469 0.563 0.656 0.750
0.508 0.609 0.711 0.813
0.313 0.375 0.438 0.500
0.352 0.422 0.492 0.563
0.410 0.492 0.574 0.656
0.469 0.563 0.656 0.750
0.508 0.609 0.711 0.813
0.547 0.656 0.766 0.875
0.586 0.703 0.820 0.938
9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4
0.492 0.547 0.602 0.656
0.563 0.625 0.688 0.750
0.633 0.703 0.773 0.844
0.703 0.781 0.859 0.938
0.773 0.859 0.945 1.03
0.844 0.938 1.03 1.13
0.914 1.02 1.12 1.22
0.563 0.625 0.688 0.750
0.633 0.703 0.773 0.844
0.738 0.820 0.902 0.984
0.844 0.938 1.03 1.13
0.914 1.02 1.12 1.22
0.984 1.09 1.20 1.31
1.05 1.17 1.29 1.41
13⁄ 16 7⁄ 8 15⁄ 16
0.711 0.766 0.820 0.875
0.813 0.875 0.938 1.00
0.914 0.984 1.05 1.13
1.02 1.09 1.17 1.25
1.12 1.20 1.29 1.38
1.22 1.31 1.41 1.50
1.32 1.42 1.52 1.63
0.813 0.875 0.938 1.00
0.914 0.984 1.05 1.13
1.07 1.15 1.23 1.31
1.22 1.31 1.41 1.50
1.32 1.42 1.52 1.63
1.42 1.53 1.64 1.75
1.52 1.64 1.76 1.88
1 3 ⁄8
1 1 ⁄2
1
Thckns. t, in.
3⁄ 4
7⁄ 8
C ×t
D ×t
Bolt Diameter d b , in.
Bolt Diameter d b , in.
1
1 1 ⁄8
1 1 ⁄4
1 3 ⁄8
1 1 ⁄2
3⁄ 4
7⁄ 8
1
1 1 ⁄8
1 1 ⁄4
3⁄ 16 1⁄ 4
0.199 0.223 0.258 0.293 0.316 0.340 0.363 0.363 0.422 0.480 0.539 0.598 0.656 0.715 0.266 0.297 0.344 0.391 0.422 0.453 0.484 0.484 0.563 0.641 0.719 0.797 0.875 0.953
5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2
0.332 0.398 0.465 0.531
0.371 0.445 0.520 0.594
0.430 0.516 0.602 0.688
0.488 0.586 0.684 0.781
0.527 0.633 0.738 0.844
0.566 0.680 0.793 0.906
0.605 0.727 0.848 0.969
0.605 0.727 0.848 0.969
0.703 0.844 0.984 1.13
0.801 0.961 1.12 1.28
0.898 1.08 1.26 1.44
0.996 1.20 1.39 1.59
1.09 1.31 1.53 1.75
1.19 1.43 1.67 1.91
9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4
0.598 0.664 0.730 0.797
0.668 0.742 0.816 0.891
0.773 0.859 0.945 1.03
0.879 0.977 1.07 1.17
0.949 1.05 1.16 1.27
1.02 1.13 1.25 1.36
1.09 1.21 1.33 1.45
1.09 1.21 1.33 1.45
1.27 1.41 1.55 1.69
1.44 1.60 1.76 1.92
1.62 1.80 1.98 2.16
1.79 1.99 2.19 2.39
1.97 2.19 2.41 2.63
2.14 2.38 2.62 2.86
13⁄ 16 7⁄ 8 15⁄ 16
0.863 0.930 0.996 1.06
0.965 1.04 1.11 1.19
1.12 1.20 1.29 1.38
1.27 1.37 1.46 1.56
1.37 1.48 1.58 1.69
1.47 1.59 1.70 1.81
1.57 1.70 1.82 1.94
1.57 1.70 1.82 1.94
1.83 1.97 2.11 2.25
2.08 2.24 2.40 2.56
2.34 2.52 2.70 2.88
2.59 2.79 2.99 3.19
2.84 3.06 3.28 3.50
3.10 3.34 3.57 3.81
1
failure is usually the result of high reactions imposed on relatively thin material through a short connection. The design block shear rupture strength is φRn, where φ = 0.75 and Rn is determined as follows. For bolted connections, from LRFD Specification Section J4.3, when Fu Ant ≥ 0.6Fu Anv, shear yielding occurs in combination with tension rupture and, Rn = 0.6Fy Agv + Fu Ant AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BOLTS, WELDS, AND CONNECTED ELEMENTS
This case is the basis of Tables 8-47, where φFu Ant is tabulated per inch of material thickness in Table 8-47a and φ(0.6Fy Agv) is tabulated per inch of material thickness in Table 8-47b. When 0.6Fu Anv > Fu Ant , shear rupture occurs in combination with tension yielding and, Rn = 0.6Fu Anv + Fy Agt This case is the basis of Tables 8-48, where φ(0.6Fu Anv) is tabulated per inch of material thickness in Table 8-48a and φFy Agt is tabulated per inch of material thickness in Table 8-48b. For welded connections, block shear rupture is treated as for bolted connections; the only difference is that, in the absence of bolt holes, Anv = Agv and Ant = Agt. L eh
L ev n bolts @ s spacing
Shear Area
Shear Area
Tension Area
Tension Area
(a) Bolted Connections
(b) Welded Connections
Fig. 8-56. Block shear rupture in coped beams.
L eh
L ev Shear Area
n bolts @ s spacing
Tension Area
Fig. 8-57. Block shear rupture in ends of tension members. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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8 - 215
Table 8-47a. Block Shear Rupture Tension Rupture Component per inch of thickness, φ[FuAnt] / t, kips/in. L eh
Fu, ksi 58
65
70
Bolt Diameter db, in.
Bolt Diameter db, in.
Bolt Diameter db, in.
3⁄ 4
7⁄ 8
3⁄ 4
7⁄ 8
3⁄ 4
7⁄ 8
1
24.5
21.8
19.0
27.4
24.4
21.3
29.5
26.3
23.0
1 1 ⁄8 1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
29.9 35.3 40.8 46.2
27.2 32.6 38.1 43.5
24.5 29.9 35.3 40.8
33.5 39.6 45.7 51.8
30.5 36.6 42.7 48.8
27.4 33.5 39.6 45.7
36.1 42.7 49.2 55.8
32.8 39.4 45.9 52.5
29.5 36.1 42.7 49.2
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
51.7 57.1 62.5 68.0
48.9 54.4 59.8 65.3
46.2 51.7 57.1 62.5
57.9 64.0 70.1 76.2
54.8 60.9 67.0 73.1
51.8 57.9 64.0 70.1
62.3 68.9 75.5 82.0
59.1 65.6 72.2 78.8
55.8 62.3 68.9 75.5
78.8 89.7 101 111
76.1 87.0 97.9 109
73.4 84.3 95.2 106
88.4 101 113 125
85.3 97.5 110 122
82.3 94.5 107 119
95.2 108 121 135
91.9 105 118 131
88.6 102 115 128
Leh, in.
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
3
1
1
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-47b. Block Shear Rupture Shear Yielding Component per inch of thickness, φ[0.6FyAgv] / t, kips/in.
L ev n bolts @ 3 ″ spacing
Fy, ksi 36
50
Bolt Diameter db, in.
Bolt Diameter db, in.
n
Lev, in.
3⁄ 4
7⁄ 8
1
3⁄ 4
7⁄ 8
1
12
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
562 564 566
563 565 567
564 566 568
780 783 786
782 785 788
783 786 789
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
568 570 572 574
569 571 573 575
570 572 574 576
789 792 795 797
790 793 796 799
792 795 797 800
3
578 582 586 590
579 583 587 591
580 584 588 592
803 809 814 820
804 810 816 821
806 811 817 823
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
513 515 517
514 516 518
515 517 519
713 716 719
714 717 720
716 719 721
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
519 521 523 525
520 522 524 527
521 523 525 528
721 724 727 730
723 726 728 731
724 727 730 733
3
530 534 538 542
531 535 539 543
532 536 540 544
735 741 747 752
737 743 748 754
738 744 750 755
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
465 467 469
466 468 470
467 469 471
645 648 651
647 650 653
648 651 654
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
471 473 475 477
472 474 476 478
473 475 477 479
654 657 660 662
655 658 661 664
657 660 662 665
481 485 489 493
482 486 490 494
483 487 491 495
668 674 679 685
669 675 681 686
671 676 682 688
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
11
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
10
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
3
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8 - 217
Table 8-47b (cont.). Block Shear Rupture Shear Yielding Component per inch of thickness, φ[0.6FyAgv] / t, kips/in.
L ev n bolts @ 3 ″ spacing
Fy, ksi 36
50
Bolt Diameter db, in.
Bolt Diameter db, in.
n
Lev, in.
3⁄ 4
7⁄ 8
1
3⁄ 4
7⁄ 8
1
9
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
416 418 420
417 419 421
418 420 422
578 581 584
579 582 585
581 584 586
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
422 424 426 428
423 425 427 429
424 426 428 430
586 589 592 595
588 591 593 596
589 592 595 598
3
432 436 440 444
433 437 441 446
434 438 442 447
600 606 612 617
602 608 613 619
603 609 615 620
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
368 370 372
369 371 373
370 372 374
510 513 516
512 515 518
513 516 519
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
374 376 378 380
375 377 379 381
376 378 380 382
519 522 525 527
520 523 526 529
522 525 527 530
3
384 388 392 396
385 389 393 397
386 390 394 398
533 539 544 550
534 540 546 551
536 541 547 553
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
319 321 323
320 322 324
321 323 325
443 446 449
444 447 450
446 449 451
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
325 327 329 331
326 328 330 332
327 329 331 333
451 454 457 460
453 456 458 461
454 457 460 463
335 339 343 347
336 340 344 348
337 341 345 349
465 471 477 482
467 473 478 484
468 474 480 485
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
8
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
7
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
3
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BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-47b (cont.). Block Shear Rupture Shear Yielding Component per inch of thickness, φ[0.6FyAgv] / t, kips/in.
L ev n bolts @ 3 ″ spacing
Fy, ksi 36
50
Bolt Diameter db, in.
Bolt Diameter db, in.
n
Lev, in.
3⁄ 4
7⁄ 8
1
3⁄ 4
7⁄ 8
1
6
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
270 272 274
271 273 275
272 274 276
375 378 381
377 380 383
378 381 384
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
276 278 280 282
277 279 281 284
278 280 282 285
384 387 390 392
385 388 391 394
387 390 392 395
3
287 291 295 299
288 292 296 300
289 293 297 301
398 404 409 415
399 405 411 416
401 406 412 418
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
222 224 226
223 225 227
224 226 228
308 311 314
309 312 315
311 314 316
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
228 230 232 234
229 231 233 235
230 232 234 236
316 319 322 325
318 321 323 326
319 322 325 328
3
238 242 246 250
239 243 247 251
240 244 248 252
330 336 342 347
332 338 343 349
333 339 345 350
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
173 175 177
174 176 178
175 177 179
240 243 246
242 245 248
243 246 249
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
179 181 183 185
180 182 184 186
181 183 185 187
249 252 255 257
250 253 256 259
252 255 257 260
189 193 197 201
190 194 198 203
191 195 199 204
263 269 274 280
264 270 276 281
266 271 277 283
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
5
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
4
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONNECTED ELEMENTS
8 - 219
Table 8-47b (cont.). Block Shear Rupture Shear Yielding Component per inch of thickness, φ[0.6FyAgv] / t, kips/in.
L ev n bolts @ 3 ″ spacing
Fy, ksi 36
50
Bolt Diameter db, in.
Bolt Diameter db, in.
n
Lev, in.
3⁄ 4
7⁄ 8
1
3⁄ 4
7⁄ 8
1
3
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
125 127 129
126 128 130
127 129 131
173 176 179
174 177 180
176 179 181
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
131 133 135 137
132 134 136 138
133 135 137 139
181 184 187 190
183 186 188 191
184 187 190 193
3
141 145 149 153
142 146 150 154
143 147 151 155
195 201 207 212
197 203 208 214
198 204 210 215
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
76 78 80
77 79 81
78 80 82
105 108 111
107 110 113
108 111 114
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
82 84 86 88
83 85 87 89
84 86 88 90
114 117 120 122
115 118 121 124
117 120 122 125
92 96 100 104
93 97 101 105
94 98 102 106
128 134 139 145
129 135 141 146
131 136 142 148
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
2
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-48a. Block Shear Rupture Shear Rupture Component per inch of thickness, φ[0.6FuAnv] / t, kips/in.
L ev n bolts @ 3 ″ spacing
Fu, ksi 58
65
70
Bolt Diameter db, in.
Bolt Diameter db, in.
Bolt Diameter db, in.
n
Lev, in.
3⁄ 4
7⁄ 8
1
3⁄ 4
7⁄ 8
1
3⁄ 4
7⁄ 8
1
12
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
631 635 638
594 597 600
556 560 563
707 711 715
665 669 673
623 627 631
762 766 770
717 721 725
671 675 679
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
641 644 648 651
604 607 610 613
566 569 573 576
718 722 726 729
676 680 684 687
634 638 642 645
774 778 782 786
728 732 736 740
683 687 691 695
3
657 664 670 677
620 626 633 639
582 589 595 602
737 744 751 759
695 702 709 717
653 660 667 675
793 801 809 817
748 756 764 772
703 711 719 726
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
576 579 582
542 545 548
507 511 514
645 649 653
607 611 614
569 572 576
695 699 703
654 658 662
612 616 620
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
586 589 592 595
551 555 558 561
517 520 524 527
656 660 664 667
618 622 625 629
580 583 587 590
707 711 715 719
665 669 673 677
624 628 632 636
3
602 608 615 622
568 574 581 587
533 540 546 553
675 682 689 697
636 644 651 658
598 605 612 620
726 734 742 750
685 693 701 709
644 652 660 667
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
520 524 527
489 493 496
458 462 465
583 587 590
548 552 556
514 517 521
628 632 636
591 595 599
553 557 561
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
530 533 537 540
499 502 506 509
468 471 475 478
594 598 601 605
559 563 567 570
525 528 532 536
640 644 648 652
602 606 610 614
565 569 573 577
546 553 560 566
515 522 529 535
484 491 498 504
612 620 627 634
578 585 592 600
543 550 558 565
660 667 675 683
622 630 638 646
585 593 600 608
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
11
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
10
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONNECTED ELEMENTS
8 - 221
Table 8-48a (cont.). Block Shear Rupture Shear Rupture Component per inch of thickness, φ[0.6FuAnv ] / t, kips/in.
L ev n bolts @ 3 ″ spacing
Fu, ksi 58
65
70
Bolt Diameter db, in.
Bolt Diameter db, in.
Bolt Diameter db, in.
n
Lev, in.
3⁄ 4
7⁄ 8
1
3⁄ 4
7⁄ 8
1
3⁄ 4
7⁄ 8
1
9
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
465 468 471
437 440 444
409 413 416
521 525 528
490 494 497
459 463 466
561 565 569
528 532 536
494 498 502
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
475 478 481 484
447 450 453 457
419 422 426 429
532 536 539 543
501 505 508 512
470 473 477 481
573 577 581 585
539 543 547 551
506 510 514 518
3
491 498 504 511
463 470 476 483
436 442 449 455
550 558 565 572
519 527 534 541
488 495 503 510
593 600 608 616
559 567 575 583
526 534 541 549
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
409 413 416
385 388 392
361 364 367
459 463 466
431 435 439
404 408 411
494 498 502
465 469 473
435 439 443
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
419 422 426 429
395 398 401 405
370 374 377 380
470 473 477 481
442 446 450 453
415 419 422 426
506 510 514 518
476 480 484 488
447 451 455 459
3
436 442 449 455
411 418 424 431
387 393 400 406
488 495 503 510
461 468 475 483
433 441 448 455
526 534 541 549
496 504 512 520
467 474 482 490
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
354 357 361
333 336 339
312 315 318
397 400 404
373 377 380
349 353 356
427 431 435
402 406 410
376 380 384
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
364 367 370 374
343 346 349 352
321 325 328 331
408 411 415 419
384 388 391 395
360 364 367 371
439 443 447 451
413 417 421 425
388 392 396 400
380 387 393 400
359 365 372 378
338 344 351 357
426 433 441 448
402 410 417 424
378 386 393 400
459 467 474 482
433 441 449 457
408 415 423 431
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
8
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
7
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-48a (cont.). Block Shear Rupture Shear Rupture Component per inch of thickness, φ[0.6FuAnv ] / t, kips/in.
L ev n bolts @ 3 ″ spacing
Fu, ksi 58
65
70
Bolt Diameter db, in.
Bolt Diameter db, in.
Bolt Diameter db, in.
n
Lev, in.
3⁄ 4
7⁄ 8
1
3⁄ 4
7⁄ 8
1
3⁄ 4
7⁄ 8
1
6
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
299 302 305
281 284 287
263 266 269
335 338 342
314 318 322
294 298 302
360 364 368
339 343 347
317 321 325
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
308 312 315 318
290 294 297 300
272 276 279 282
346 349 353 356
325 329 333 336
305 309 313 316
372 376 380 384
350 354 358 362
329 333 337 341
3
325 331 338 344
307 313 320 326
289 295 302 308
364 371 378 386
344 351 358 366
324 331 338 346
392 400 408 415
370 378 386 394
348 356 364 372
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
243 246 250
228 232 235
214 217 220
272 276 280
256 260 263
239 243 247
293 297 301
276 280 284
258 262 266
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
253 256 259 263
238 241 245 248
223 227 230 233
283 287 291 294
267 271 274 278
250 254 258 261
305 309 313 317
287 291 295 299
270 274 278 282
3
269 276 282 289
254 261 268 274
240 246 253 259
302 309 316 324
285 293 300 307
269 276 283 291
325 333 341 348
307 315 323 331
289 297 305 313
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
188 191 194
176 179 183
165 168 171
210 214 218
197 201 205
185 188 192
226 230 234
213 217 221
199 203 207
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
197 201 204 207
186 189 192 196
175 178 181 184
221 225 229 232
208 212 216 219
196 199 203 207
238 242 246 250
224 228 232 236
211 215 219 222
214 220 227 233
202 209 215 222
191 197 204 210
239 247 254 261
227 234 241 249
214 221 229 236
258 266 274 282
244 252 260 268
230 238 246 254
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
5
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
4
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONNECTED ELEMENTS
8 - 223
Table 8-48a (cont.). Block Shear Rupture Shear Rupture Component per inch of thickness, φ[0.6FuAnv ] / t, kips/in.
L ev n bolts @ 3 ″ spacing
Fu, ksi 58
65
70
Bolt Diameter db, in.
Bolt Diameter db, in.
Bolt Diameter db, in.
n
Lev, in.
3⁄ 4
7⁄ 8
1
3⁄ 4
7⁄ 8
1
3⁄ 4
7⁄ 8
1
3
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
132 135 139
124 127 131
116 119 122
148 152 155
139 143 146
130 133 137
159 163 167
150 154 158
140 144 148
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
142 145 148 152
134 137 140 144
126 129 132 135
159 163 166 170
150 154 157 161
141 144 148 152
171 175 179 183
161 165 169 173
152 156 159 163
3
158 165 171 178
150 157 163 170
142 148 155 161
177 185 192 199
168 176 183 190
159 166 174 181
191 199 207 215
181 189 197 205
171 179 187 195
1 1 ⁄4 1 3 ⁄8 1 1 ⁄2
77 80 83
72 75 78
67 70 73
86 90 93
80 84 88
75 79 82
93 96 100
87 91 95
81 85 89
1 5 ⁄8 1 3 ⁄4 1 7 ⁄8
86 90 93 96
82 85 88 91
77 80 83 86
97 101 104 108
91 95 99 102
86 90 93 97
104 108 112 116
98 102 106 110
93 96 100 104
103 109 116 122
98 104 111 117
93 100 106 113
115 122 130 137
110 117 124 132
104 112 119 126
124 132 140 148
118 126 134 142
112 120 128 136
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
2
2 2 1 ⁄4 2 1 ⁄2 2 3 ⁄4
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 224
BOLTS, WELDS, AND CONNECTED ELEMENTS
Table 8-48b. Block Shear Rupture Tension Yielding Component per inch of thickness φ[FyAgt] / t, kips/in. L eh
Fy, ksi Leh, in.
36
50
1
27.0
37.5
11⁄8 11⁄4 13⁄8 11⁄2
30.4 33.8 37.1 40.5
42.2 46.9 51.6 56.3
15⁄8 13⁄4 17⁄8 2
43.9 47.3 50.6 54.0
60.9 65.6 70.3 75.0
21⁄4 21⁄2 23⁄4 3
60.8 67.5 74.3 81.0
84.4 93.8 103 113
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONNECTED ELEMENTS
8 - 225
Tension Yielding
From LRFD Specification Section J5.2, the design tension yielding strength is φRn, where φ = 0.90 Rn = Fy Ag Tension Rupture
From LRFD Specification Section J5.2, the design tension rupture strength is φRn, where φ = 0.75 Rn = Fu An In the above equation, An is the net area not to exceed 0.85Ag. Table 8-46 gives the reduction in area for standard, oversized, short-slotted, and long-slotted holes in material thicknesses from 3⁄16-in. to 1 in.; for material thicknesses not listed, multiply the tabular value for 1-in. thickness by the actual thickness. Members with Copes, Blocks, or Cuts
When structural members frame together, a minimum clearance of 1⁄2-in. should be provided, when possible. In cases where material removal is necessary to provide such a clearance, material may be removed by coping, blocking, or cutting as illustrated in Figures 8-58. Note the recommended practices for coping illustrated in Figure 8-59; the potential notch left by the first cut will occur in waste material which will subsequently be removed by the second cut. All re-entrant corners must be shaped notch-free per AWS D1.1 to a radius. An approximate minimum radius to which this corner must be shaped is 1⁄2-in. Material removal is costly, and should be avoided when possible. For example, the elevations of the tops of infill beams could be established at a sufficient distance below the tops of girders to clear the girder fillet. Alternatively, coping could be eliminated with a connection as illustrated in Figure 8-60; this detail also allows the use of a shorter beam length. When necessary, coping is usually the most economical method to remove material. Copes, blocks, and cuts can significantly reduce the design strengths of members and may require web reinforcement; it may be more economical to use a heavier member than to provide such reinforcement. The design strength of the unreinforced coped member is determined from the limit states of flexural yielding, local buckling, and lateral torsional buckling, if applicable. Web reinforcement of coped beams is discussed in Part 9. Flexural Yielding
The flexural yielding strength of a supported beam which is coped at the top and/or bottom is φbMn, where φb = 0.90 Mn = Fy Snet AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8 - 226
BOLTS, WELDS, AND CONNECTED ELEMENTS
In the above equation, Snet is the net elastic section modulus, in.3 Values of Snet are tabulated in Table 8-49. The beam-end reaction Ru must be such that: Ru ≤
φbMn e
where e is the distance from the face of the cope to the point of inflection of the beam, in. It is usually assumed that the point of inflection is located at the face of the supporting member and e is as shown in Figure 8-61. However, depending upon the connection type and stiffness and support condition, the point of inflection may move away from the face of the supporting member; when this is the case, a lesser value of e may be justified. In any case, the choice of e shown in Figure 8-61 will be conservative. Local Web Buckling
For short copes no greater than the length of the connection angle(s), plate, or tee, local web buckling will generally not occur. If, however, the depth of the cope were such that
c dc
c
Cut not grid preferred Cut and grid if surface must be flush with web
c dc
(a) Cope
(b) Blocks
(c) Cut
Fig. 8-58. Copes, blocks, and cuts.
first cut
resulting notch occurs in waste
0 to 15° as required second cut
second cut potential notch
AVOID
first cut
RECOMMENDED
Fig. 8-59. Recommended coping practice. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONNECTED ELEMENTS
8 - 227
dc > 0.2d, the unreinforced web could buckle between the top of the cope and the beam flange if the beam web were thin. In a reduced section, the design strength in local web buckling may be more critical than the design strength in flexural yielding. This design strength is critical at the compression zone of the web near the cope and is dependent on three parameters: (1) cope depth dc; (2) cope length c; and (3) web thickness tw. It should be noted that, for convenience, the dimension h0 in Figure 8-61 is used instead of the more correct dimension h1; this eliminates the detailed calculation required to locate the neutral axis of the coped beam. Alternatively, the dimension h1 may be substituted for h0 in the following local buckling calculations. The beam end reaction Ru must be such that: Ru ≤
φFbc Snet e
where Snet = elastic section modulus of the net section, in.3 from Table 8-49 e = distance from the end reaction to the face of the cope, in. and φFbc is determined as follows. When a beam is coped at the top flange only, the design recommendations are based on the classical plate buckling formula with a k-factor based on three edges simply supported and one free edge. An additional factor f, which generally accounts for stress concentration at the cope, was developed to correlate with the coped beam buckling solutions (Cheng, et. al., 1984). From Figure 8-61, when the c ≤ 2d and dc ≤ d / 2, 2
π2E tw fk Fcr = 12(1 − v2) ho where E = 29,000 ksi, modulus of elasticity of steel ν = 0.3, Poisson’s ratio f = plate buckling model adjustment factor
(a) Coping Required
(b) Coping Eliminated
Fig. 8-60. Minimizing coping requirements. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BOLTS, WELDS, AND CONNECTED ELEMENTS
k = plate buckling coefficient ho = d − dc, reduced beam depth, in. Thus, the design buckling stress φFbc for a beam coped at the top flange only is, 2
tw φFbc = 23,590 fk ho where f and k are determined from the following equations: c c f = 2 for ≤ 1.0 d d c c f = 1 + for > 1.0 d d ho c k = 2.2 for ≤ 1.0 ho c ho c k = 2.2 for > 1.0 ho c When a beam is coped at both flanges, the design recommendations are based on the lateral buckling model with an adjustment factor fd (Cheng, et al., 1984). From Figure 8-62, when at both flanges c ≤ 2d and dc ≤ 0.2d, Fcr = 0.62πE
t2w f cho d
Thus, the design buckling stress φFbc for a beam coped at both flanges is, φFbc = 50,840
t2w f cho d
and e c
Buckling checked here dc
Setback
ho
Ru
d
h1
tw
Simple shear connection
Fig. 8-61. Local buckling of beam web coped at top flange only. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
N.A.
CONNECTED ELEMENTS
8 - 229
d d
c fd = 3.5 − 7.5
where dc is the larger of the top cope depth dct and the bottom cope depth dcb. Lateral Torsional Buckling
In laterally unbraced beams, copes, blocks, and cuts further reduce the out-of-plane rotational restraint. Cheng, et al. (1984) discusses the design strength of laterally unbraced coped beams. For laterally unbraced beams coped at the top only, this design strength may be determined with this information and the provisions of LRFD Specification Section F1.2. For laterally unbraced beams coped at the top and bottom, this design strength may be determined with this information and the provisions of LRFD Specification Appendix F1. A detailed discussion of this topic is beyond the scope of this text.
e c
Buckling checked here
Simple shear connection
d
Ru
tw
d cb
d – d ct – dcb
d ct
Setback
Fig. 8-62. Local buckling of beam web coped at both flanges. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
N.A.
8 - 230
BOLTS, WELDS, AND CONNECTED ELEMENTS
So
Snet
d
Sx
d
d
dc
Table 8-49. Section Modulus of Coped W Shapes
Snet, in.3 dc, in.
Designation
d in.
tf in.
Sx in.3
So in.3
2
3
4
5
6
7
8
9
10
W44×335 W ×290 W ×262 W ×230
44.0 43.6 43.3 42.9
1.77 1.58 1.42 1.22
1410 1240 1120 969
492 417 374 330
451 382 342 301
431 365 327 288
411 348 312 274
392 332 297 261
373 316 283 249
355 300 269 236
337 285 255 224
320 270 241 212
303 255 228 200
W40×593 W ×503 W ×431 W ×372 W ×321 W ×297 W ×277 W ×249 W ×215 W ×199 W ×174
43.0 42.1 41.3 40.6 40.1 39.8 39.7 39.4 39.0 38.7 38.2
3.23 2.76 2.36 2.05 1.77 1.65 1.58 1.42 1.22 1.07 0.830
2340 1980 1690 1460 1250 1170 1100 992 858 769 639
810 673 567 480 406 374 335 299 256 247 234
— — — — 368 339 304 271 231 224 211
— 584 491 415 350 323 289 258 220 213 201
671 556 467 394 332 306 274 245 208 202 190
639 528 444 374 315 290 260 232 197 191 180
607 501 421 354 298 275 246 219 186 180 170
575 475 398 335 282 259 232 207 176 170 160
545 449 376 316 266 245 219 195 166 160 151
515 424 355 298 250 230 206 183 156 150 142
486 399 334 280 235 216 193 172 146 141 133
W40×466 W ×392 W ×331 W ×278 W ×264 W ×235 W ×211 W ×183 W ×167 W ×149
42.4 41.6 40.8 40.2 40.0 39.7 39.4 39.0 38.6 38.2
2.95 2.52 2.13 1.81 1.73 1.58 1.42 1.22 1.03 0.830
1710 1440 1210 1020 971 874 785 682 599 512
705 581 483 396 371 320 286 244 234 217
— — — 360 337 291 259 221 212 196
613 504 419 342 321 276 246 210 201 186
584 480 398 325 305 262 234 199 191 177
556 456 378 308 289 249 221 189 181 167
528 432 358 292 274 235 209 179 171 158
500 409 339 276 259 222 198 168 161 149
474 387 320 261 244 210 186 159 152 140
448 365 302 245 230 197 175 149 143 132
422 344 284 231 216 185 165 140 134 123
W36×848 W ×798 W ×650 W ×527 W ×439 W ×393 W ×359 W ×328 W ×300 W ×280 W ×260 W ×245 W ×230
42.5 42.0 40.5 39.3 38.3 37.8 37.4 37.1 36.7 36.5 36.3 36.1 35.9
4.53 4.29 3.54 2.91 2.44 2.20 2.01 1.85 1.68 1.57 1.44 1.35 1.26
3170 2980 2420 1950 1620 1450 1320 1210 1110 1030 953 895 837
1094 1016 794 618 503 443 400 360 328 305 285 269 253
— — — — — — — 324 295 274 256 241 227
— — — 531 430 378 341 307 279 259 242 228 214
903 836 649 503 407 358 322 290 264 245 228 215 202
858 794 615 476 384 338 304 273 249 230 215 203 190
813 752 582 449 362 318 286 257 234 217 202 190 179
770 712 550 423 341 299 269 242 220 203 190 178 168
728 673 518 398 320 281 252 226 206 190 177 167 157
687 634 487 374 300 263 236 212 192 178 166 156 146
647 597 457 350 280 246 220 197 179 165 154 145 136
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONNECTED ELEMENTS
8 - 231
So
Snet
d
Sx
d
d
dc
Table 8-49 (cont.). Section Modulus of Coped W Shapes
Snet, in.3 Designation
d in.
tf in.
Sx in.3
W36×256 W ×232 W ×210 W ×194 W ×182 W ×170 W ×160 W ×150 W ×135
37.4 37.1 36.7 36.5 36.3 36.2 36.0 35.9 35.6
1.73 1.57 1.36 1.26 1.18 1.10 1.02 0.940 0.790
895 809 719 664 623 580 542 504 439
W33×354 W ×318 W ×291 W ×263 W ×241 W ×221 W ×201
35.6 35.2 34.8 34.5 34.2 33.9 33.7
2.09 1.89 1.73 1.57 1.40 1.28 1.15
W33×169 W ×152 W ×141 W ×130 W ×118
33.8 33.5 33.3 33.1 32.9
W30×477 W ×391 W ×326 W ×292 W ×261 W ×235 W ×211 W ×191 W ×173 W30×148 W ×132 W ×124 W ×116 W ×108 W ×99 W ×90
So in.3
dc, in. 2
3
4
5
6
7
8
9
329 295 272 249 234 218 206 195 181
297 266 245 224 211 196 185 176 163
281 251 232 212 199 185 175 166 154
266 238 219 201 188 175 165 157 145
251 224 207 189 178 165 156 148 137
237 211 195 178 167 155 147 139 129
223 199 183 167 157 146 138 130 121
209 186 172 157 147 137 129 122 113
196 174 161 146 137 128 120 114 105
183 163 150 137 128 119 112 106 98.1
1230 1110 1010 917 829 757 684
373 330 300 268 250 230 209
— 295 268 239 223 205 186
315 278 253 226 210 193 175
297 262 238 212 197 181 165
279 246 223 199 185 170 154
262 230 209 186 173 159 144
245 216 195 174 162 148 135
229 201 182 162 150 138 125
213 187 169 151 140 128 116
198 173 157 139 129 118 107
1.22 1.06 0.960 0.855 0.740
549 487 448 406 359
191 176 165 155 143
170 157 147 138 128
161 148 139 130 120
151 139 130 122 113
141 130 122 114 106
132 122 114 107 98.6
124 114 106 100 91.9
115 106 98.8 92.5 85.4
107 97.9 91.6 85.7 79.1
98.6 90.5 84.6 79.2 73.0
34.2 33.2 32.4 32.0 31.6 31.3 30.9 30.7 30.4
2.95 2.44 2.05 1.85 1.65 1.50 1.32 1.19 1.07
1530 1250 1030 928 827 746 663 598 539
475 378 305 269 240 211 192 174 158
— — — 238 212 186 170 153 139
398 315 254 223 198 174 159 143 130
374 295 237 208 185 163 148 133 121
350 276 221 194 172 152 138 124 112
327 257 206 180 160 141 128 115 104
305 239 191 167 148 130 118 106 96.1
283 222 177 155 137 120 109 97.7 88.4
262 205 163 142 126 110 100 89.6 81.0
242 188 150 130 115 101 91.2 81.8 73.9
30.7 30.3 30.2 30.0 29.8 29.7 29.5
1.18 1.00 0.930 0.850 0.760 0.670 0.610
436 380 355 329 299 269 245
152 139 131 124 118 110 98.7
134 123 115 109 103 96.4 86.7
125 115 108 102 96.5 90.0 80.9
117 107 100 95.3 89.9 83.9 75.4
109 99.3 93.4 88.6 83.6 77.9 70.0
101 92.1 86.5 82.1 77.4 72.1 64.8
93.3 85.1 79.9 75.8 71.4 66.5 59.7
86.0 78.3 73.6 69.7 65.7 61.1 54.9
78.9 71.8 67.4 63.9 60.1 56.0 50.2
72.1 65.5 61.5 58.2 54.8 51.0 45.7
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10
8 - 232
BOLTS, WELDS, AND CONNECTED ELEMENTS
So
Snet
d
Sx
d
d
dc
Table 8-49 (cont.). Section Modulus of Coped W Shapes
Snet, in.3 Designation
d in.
tf in.
Sx in.3
So in.3
W27×539 W ×448 W ×368 W ×307 W ×281 W ×258 W ×235 W ×217 W ×194 W ×178 W ×161 W ×146
32.5 31.4 30.4 29.6 29.3 29.0 28.7 28.4 28.1 27.8 27.6 27.4
3.54 2.99 2.48 2.09 1.93 1.77 1.61 1.50 1.34 1.19 1.08 0.975
1570 1300 1060 884 811 742 674 624 556 502 455 411
W27×129 W ×114 W ×102 W ×94 W ×84
27.6 27.3 27.1 26.9 26.7
1.10 0.930 0.830 0.745 0.640
W24×492 W ×408 W ×335 W ×279 W ×250 W ×229 W ×207 W ×192 W ×176 W ×162 W ×146 W ×131 W ×117 W ×104
29.7 28.5 27.5 26.7 26.3 26.0 25.7 25.5 25.2 25.0 24.7 24.5 24.3 24.1
W24×103 W ×94 W ×84 W ×76 W ×68 W24×62 W ×55
dc, in. 2
3
4
5
6
7
8
9
10
509 404 321 259 233 212 193 174 155 145 131 118
— — — — 203 185 168 152 134 126 113 102
— — 262 211 189 172 156 141 125 117 105 95.0
394 310 244 196 176 159 145 130 115 108 97.2 87.7
367 288 226 181 162 147 134 120 106 100 89.5 80.7
341 267 209 167 150 136 123 111 97.6 91.5 82.0 74.0
316 247 193 154 137 124 113 101 89.3 83.6 74.9 67.5
292 227 177 141 126 114 103 92.3 81.3 76.1 68.1 61.3
269 209 162 128 114 103 93.2 83.7 73.6 68.8 61.5 55.3
247 191 147 116 104 93.3 84.2 75.5 66.3 61.9 55.3 49.7
345 299 267 243 213
117 106 94.2 88.0 80.5
101 91.6 81.6 76.2 69.6
94.0 84.9 75.6 70.6 64.5
86.9 78.4 69.8 65.1 59.5
80.1 72.2 64.3 59.9 54.7
73.5 66.2 58.9 54.9 50.1
67.2 60.5 53.7 50.1 45.7
61.1 54.9 48.8 45.4 41.4
55.3 49.6 44.0 41.0 37.3
49.7 44.6 39.5 36.8 33.5
3.54 2.99 2.48 2.09 1.89 1.73 1.57 1.46 1.34 1.22 1.09 0.960 0.850 0.750
1290 1060 864 718 644 588 531 491 450 414 371 329 291 258
420 331 261 210 184 167 149 136 124 115 104 94.4 84.4 75.4
— — — — 158 143 127 117 106 98.0 88.5 80.3 71.7 64.1
— — 209 167 146 132 117 107 97.6 90.0 81.2 73.7 65.7 58.7
316 247 193 154 134 121 107 98.2 89.4 82.3 74.2 67.3 60.0 53.5
292 227 177 141 123 111 98.0 89.5 81.4 74.9 67.5 61.1 54.5 48.6
269 209 162 128 112 101 89.0 81.2 73.8 67.9 61.1 55.3 49.2 43.8
247 191 147 116 101 91.0 80.4 73.3 66.5 61.1 54.9 49.7 44.2 39.3
226 173 133 105 91.2 81.8 72.2 65.8 59.6 54.7 49.1 44.3 39.4 35.0
205 157 120 94.3 81.7 73.1 64.4 58.6 53.0 48.6 43.6 39.3 34.8 30.9
186 141 108 84.0 72.6 64.9 57.0 51.8 46.8 42.8 38.3 34.5 30.5 27.1
24.5 24.3 24.1 23.9 23.7
0.980 0.875 0.770 0.680 0.585
245 222 196 176 154
82.9 76.2 68.3 62.6 57.5
70.7 64.9 58.0 53.2 48.8
64.9 59.5 53.2 48.7 44.7
59.3 54.3 48.6 44.5 40.8
53.9 49.4 44.1 40.4 37.0
48.8 44.6 39.8 36.4 33.4
43.9 40.1 35.8 32.7 29.9
39.2 35.8 31.9 29.1 26.6
34.8 31.7 28.2 25.8 23.5
30.6 27.9 24.8 22.6 20.6
23.7 23.6
0.590 0.505
131 114
56.9 51.1
48.3 43.4
44.3 39.7
40.4 36.2
36.7 32.9
33.1 29.7
29.7 26.6
26.5 23.7
23.4 20.9
20.5 18.3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CONNECTED ELEMENTS
8 - 233
So
Snet
d
Sx
d
d
dc
Table 8-49 (cont.). Section Modulus of Coped W Shapes
Snet, in.3 Designation
d in.
tf in.
W21×201 W ×182 W ×166 W ×147 W ×132 W ×122 W ×111 W ×101
23.0 22.7 22.5 22.1 21.8 21.7 21.5 21.4
W21×93 W ×83 W ×73 W ×68 W ×62
dc, in.
Sx in.3
So in.3
2
3
4
5
6
7
8
9
1.63 1.48 1.36 1.15 1.04 0.960 0.875 0.800
461 417 380 329 295 273 249 227
125 111 99.3 91.2 81.0 74.1 67.1 60.4
105 93.3 83.0 76.1 67.5 61.6 55.7 50.1
95.2 84.8 75.3 68.9 61.1 55.7 50.4 45.3
86.2 76.6 68.0 62.1 55.0 50.2 45.3 40.7
77.6 68.8 61.0 55.7 49.2 44.8 40.4 36.3
69.4 61.4 54.4 49.5 43.7 39.8 35.9 32.1
61.6 54.4 48.1 43.7 38.5 35.0 31.5 28.2
54.2 47.8 42.2 38.2 33.6 30.5 27.4 24.5
47.3 41.6 36.6 33.1 29.0 26.3 23.6 21.1
21.6 21.4 21.2 21.1 21.0
0.930 0.835 0.740 0.685 0.615
192 171 151 140 127
67.2 59.0 51.5 48.1 44.1
56.0 49.1 42.7 39.9 36.5
50.7 44.4 38.7 36.1 33.0
45.7 40.0 34.8 32.4 29.7
40.9 35.7 31.0 29.0 26.5
36.3 31.7 27.5 25.6 23.4
32.0 27.9 24.2 22.5 20.5
27.9 24.3 21.0 19.6 17.8
24.1 20.9 18.1 16.8 15.3
W21×57 W ×50 W ×44
21.1 20.8 20.7
0.650 0.535 0.450
111 94.5 81.6
43.4 39.2 35.2
36.1 32.5 29.1
32.6 29.4 26.3
29.3 26.4 23.6
26.2 23.6 21.0
23.2 20.8 18.6
20.4 18.3 16.3
17.7 15.9 14.1
15.2 13.6 12.1
W18×311 W ×283 W ×258 W ×234 W ×211 W ×192 W ×175 W ×158 W ×143 W ×130
22.3 21.9 21.5 21.1 20.7 20.4 20.0 19.7 19.5 19.3
2.74 2.50 2.30 2.11 1.91 1.75 1.59 1.44 1.32 1.20
624 564 514 466 419 380 344 310 282 256
186 166 148 130 115 102 92.1 81.7 72.5 65.2
— — — — 94.5 83.4 75.1 66.4 58.8 52.8
140 124 110 96.1 84.8 74.7 67.2 59.3 52.4 47.0
126 111 98.3 85.9 75.6 66.5 59.7 52.6 46.4 41.5
113 99.3 87.4 76.2 66.9 58.7 52.6 46.2 40.7 36.4
100 87.8 77.2 67.1 58.7 51.4 45.9 40.2 35.4 31.5
88.2 77.1 67.5 58.5 51.0 44.5 39.6 34.6 30.4 27.0
77.0 67.0 58.5 50.4 43.8 38.1 33.8 29.4 25.7 22.8
66.5 57.6 50.0 43.0 37.1 32.1 28.4 24.6 21.5 19.0
W18×119 W ×106 W ×97 W ×86 W ×76
19.0 18.7 18.6 18.4 18.2
1.06 0.940 0.870 0.770 0.680
231 204 188 166 146
61.7 54.4 48.9 43.1 37.6
49.8 43.8 39.3 34.6 30.1
44.3 38.9 34.9 30.6 26.7
39.1 34.3 30.7 26.9 23.4
34.2 29.9 26.8 23.4 20.3
29.5 25.8 23.1 20.2 17.5
25.2 22.0 19.6 17.1 14.8
21.2 18.5 16.4 14.3 12.3
W18×71 W ×65 W ×60 W ×55 W ×50
18.5 18.4 18.2 18.1 18.0
0.810 0.750 0.695 0.630 0.570
127 117 108 98.3 88.9
42.4 38.3 35.0 32.4 29.1
34.1 30.8 28.1 26.0 23.4
30.3 27.3 24.9 23.0 20.7
26.7 24.0 21.9 20.2 18.2
23.3 20.9 19.1 17.6 15.8
20.1 18.0 16.4 15.1 13.5
17.1 15.3 13.9 12.8 11.5
14.3 12.8 11.6 10.7 9.54
W18×46 W ×40 W ×35
18.1 17.9 17.7
0.605 0.525 0.425
78.8 68.4 57.6
28.9 24.9 22.7
23.2 20.0 18.2
20.6 17.7 16.1
18.1 15.5 14.1
15.7 13.5 12.3
13.5 11.6 10.5
11.5 9.80 8.88
9.56 8.16 7.37
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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8 - 234
BOLTS, WELDS, AND CONNECTED ELEMENTS
So
Snet
d
Sx
d
d
dc
Table 8-49 (cont.). Section Modulus of Coped W Shapes
Snet, in.3 dc, in.
Designation
d in.
tf in.
Sx in.3
So in.3
2
3
4
5
6
7
W16×100 W ×89 W ×77 W ×67
17.0 16.8 16.5 16.3
0.985 0.875 0.760 0.665
175 155 134 117
44.4 39.0 33.1 28.3
34.9 30.6 25.9 22.1
30.5 26.7 22.6 19.2
26.4 23.1 19.4 16.5
22.6 19.7 16.5 14.0
19.0 16.5 13.8 11.7
15.7 13.6 11.4 9.58
W16×57 W ×50 W ×45 W ×40 W ×36
16.4 16.3 16.1 16.0 15.9
0.715 0.630 0.565 0.505 0.430
92.2 81.0 72.7 64.7 56.5
29.4 25.6 22.9 20.1 18.8
23.0 20.0 17.9 15.6 14.6
20.1 17.4 15.5 13.6 12.7
17.3 15.0 13.4 11.7 10.9
14.8 12.7 11.3 9.89 9.21
12.4 10.7 9.47 8.24 7.67
10.2 8.74 7.75 6.73 6.25
W16×31 W ×26
15.9 15.7
0.440 0.345
47.2 38.4
17.1 14.9
13.3 11.6
11.6 10.1
10.0 8.64
8.44 7.31
7.03 6.08
5.73 4.95
W14×808 W ×730 W ×665 W ×605 W ×550 W ×500 W ×455
22.8 22.4 21.6 20.9 20.2 19.6 19.0
5.12 4.91 4.52 4.16 3.82 3.50 3.21
1400 1280 1150 1040 931 838 756
— — — — — — —
— — — — — — —
W14×426 W ×398 W ×370 W ×342 W ×311 W ×283 W ×257 W ×233 W ×211 W ×193 W ×176 W ×159 W ×145
18.7 18.3 17.9 17.5 17.1 16.7 16.4 16.0 15.7 15.5 15.2 15.0 14.8
3.04 2.85 2.66 2.47 2.26 2.07 1.89 1.72 1.56 1.44 1.31 1.19 1.09
707 656 607 559 506 459 415 375 338 310 281 254 232
164 150 135 122 107 94.4 83.1 73.2 64.9 57.6 52.2 45.7 40.9
— — — — — — 64.1 56.1 49.5 43.8 39.5 34.5 30.7
W14×132 W ×120 W ×109 W ×99 W ×90
14.7 14.5 14.3 14.2 14.0
1.03 0.940 0.860 0.780 0.710
209 190 173 157 143
38.1 34.2 30.0 27.2 24.3
28.6 25.5 22.3 20.2 18.0
24.3 21.7 18.9 17.0 15.2
W14×82 W ×74 W ×68 W ×61
14.3 14.2 14.0 13.9
0.855 0.785 0.720 0.645
123 112 103 92.2
28.0 24.4 22.2 19.7
20.9 18.2 16.5 14.6
17.7 15.4 13.9 12.3
451 365 317 275 238 208 182
— — — — 153 131 113
— 220 187 158 134 115 98.2
244 195 165 139 117 99.4 84.6
216 172 144 121 101 85.3 72.1
87.6 78.7 70.1 61.9 53.5 46.3 40.0 34.6 30.2 26.4 23.6 20.4 18.0
75.2 67.2 59.6 52.3 44.9 38.7 33.3 28.6 24.8 21.6 19.2 16.5 14.5
63.8 56.7 50.0 43.6 37.2 31.8 27.1 23.2 19.9 17.3 15.2 13.0 11.4
20.3 18.1 15.7 14.2 12.6
16.7 14.8 12.8 11.5 10.2
13.4 11.8 10.2 9.15 8.07
14.8 12.8 11.6 10.2
12.1 10.4 9.42 8.28
9.64 8.31 7.46 6.54
— 101 104 91.1 93.7 81.4 83.4 72.3 72.7 62.7 63.6 54.6 55.5 47.4 48.4 41.3 42.6 36.1 37.5 31.7 33.8 28.5 29.4 24.7 26.1 21.9
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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9
10
CONNECTED ELEMENTS
8 - 235
So
Snet
d
Sx
d
d
dc
Table 8-49 (cont.). Section Modulus of Coped W Shapes
Snet, in.3 dc, in.
Designation
d in.
tf in.
Sx in.3
So in.3
2
3
4
5
6
W14×53 W ×48 W ×43
13.9 13.8 13.7
0.660 0.595 0.530
77.8 70.3 62.7
19.1 17.3 15.3
14.2 12.8 11.3
12.0 10.8 9.50
9.93 8.93 7.84
8.07 7.23 6.34
6.39 5.71 4.99
W14×38 W ×34 W ×30
14.1 14.0 13.8
0.515 0.455 0.385
54.6 48.6 42.0
16.0 14.4 13.2
12.0 10.8 9.88
10.2 9.14 8.37
8.48 7.62 6.96
6.94 6.22 5.68
5.54 4.95 4.51
W14×26 W ×22
13.9 13.7
0.420 0.335
35.3 29.0
12.3 10.7
9.20 7.97
7.80 6.75
6.50 5.62
5.31 4.58
4.23 3.64
W12×336 W ×305 W ×279 W ×252 W ×230 W ×210 W ×190 W ×170 W ×152 W ×136 W ×120 W ×106 W ×96 W ×87 W ×79 W ×72 W ×65
16.8 16.3 15.9 15.4 15.1 14.7 14.4 14.0 13.7 13.4 13.1 12.9 12.7 12.5 12.4 12.3 12.1
3.00 2.71 2.47 2.25 2.07 1.90 1.74 1.56 1.40 1.25 1.105 0.990 0.900 0.810 0.735 0.670 0.605
— — — — — 49.0 42.3 36.5 31.6 27.5 23.7 19.8 17.4 15.8 14.1 12.6 11.2
83.1 71.4 63.1 54.2 47.5 41.6 35.7 30.7 26.5 22.9 19.7 16.3 14.3 13.0 11.5 10.3 9.16
71.4 61.0 53.5 45.7 39.9 34.7 29.7 25.3 21.7 18.7 16.0 13.2 11.5 10.4 9.23 8.24 7.28
60.6 51.4 44.8 38.0 32.9 28.5 24.2 20.5 17.5 14.9 12.6 10.4 9.03 8.11 7.16 6.37 5.61
50.8 42.7 36.9 31.0 26.7 22.9 19.3 16.2 13.7 11.6 9.70
W12×58 W ×53
12.2 12.1
0.640 0.575
78.0 70.6
14.8 13.9
10.4 9.74
8.52 7.94
6.79 6.31
5.24 4.85
W12×50 W ×45 W ×40
12.2 12.1 11.9
0.640 0.575 0.515
64.7 58.1 51.9
14.8 13.1 11.4
10.4 9.27 8.03
8.54 7.56 6.54
6.82 6.02 5.19
5.27 4.63 3.98
W12×35 W ×30 W ×26
12.5 12.3 12.2
0.52 0.44 0.38
45.6 38.6 33.4
12.3 10.5 9.08
8.85 7.47 6.47
7.30 6.15 5.32
5.89 4.94 4.27
4.61 3.86 3.32
W12×22 W ×19 W ×16 W ×14
12.3 12.2 12.0 11.9
0.425 0.350 0.265 0.225
25.4 21.3 17.1 14.9
9.60 8.39 7.43 6.61
6.89 6.01 5.30 4.71
5.69 4.95 4.36 3.86
4.59 3.98 3.50 3.10
3.59 3.11 2.72 2.41
483 123 435 108 393 96.1 353 83.7 321 74.2 292 65.6 263 57.0 235 49.6 209 43.3 186 37.9 163 32.8 145 27.6 131 24.3 118 22.2 107 19.9 97.4 17.9 87.9 16.0
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7
8
9
10
8 - 236
BOLTS, WELDS, AND CONNECTED ELEMENTS
So
Snet
d
Sx
d
d
dc
Table 8-49 (cont.). Section Modulus of Coped W Shapes
Snet, in.3 Designation
d in.
tf in.
dc, in.
Sx in.3
So in.3
2
3
4
25.7 22.3 19.1 16.2 13.9 12.1 10.5 9.46
17.5 15.0 12.8 10.7 9.13 7.88 6.79 6.10
13.9 11.9 10.0 8.35 7.10 6.09 5.22 4.68
10.8 9.12 7.62 6.29 5.30 4.52 3.86 3.44
W10×112 W ×100 W ×88 W ×77 W ×68 W ×60 W ×54 W ×49
11.4 11.1 10.8 10.6 10.4 10.2 10.1 8.00
1.25 126 1.12 112 0.990 98.5 0.870 85.9 0.770 75.7 0.680 66.7 0.615 60.0 0.560 54.6
W10×45 W ×39 W ×33
10.1 2.00 3.00
0.620 0.530 0.435
49.1 42.1 35.0
9.75 8.49 7.49
6.33 5.48 4.80
4.88 4.20 3.67
3.61 3.08 2.67
W10×30 W ×26 W ×22
10.5 10.3 10.2
0.510 0.440 0.360
32.4 27.9 23.2
8.64 7.33 6.51
5.75 4.86 4.29
4.51 3.80 3.34
3.41 2.85 2.50
W10×19 W ×17 W ×15 W ×12
10.2 10.1 9.00 7.00
0.395 0.330 0.270 0.210
18.8 16.2 13.8 10.9
6.52 6.01 5.52 4.43
4.33 3.98 3.64 2.91
3.39 3.10 2.83 2.26
2.55 2.33 2.12 1.68
W8×67 W ×58 W ×48 W ×40 W ×35 W ×31
0.00 5.00 0.00 5.00 2.00
0.935 0.810 0.685 0.560 0.495 0.435
60.4 52.0 43.3 35.5 31.2 27.5
12.2 10.4 7.89 6.71 5.66 5.06
7.42 6.24 4.63 3.89 3.24 2.88
5.44 4.52 3.32 2.74 2.28 2.01
W8×28 W ×24
6.00 3.00
0.465 0.400
24.3 20.9
5.04 4.23
2.89 2.40
2.02 1.67
W8×21 W ×18
8.00 4.00
0.400 0.330
18.2 15.2
4.55 4.02
2.67 2.35
1.91 1.66
W8×15 W ×13 W ×10
1.00 9.00 9.00
0.315 0.255 0.205
11.8 9.91 7.81
4.03 3.61 2.65
2.36 2.10 1.54
1.68 1.49 1.08
5
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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7
8
9
10
CONNECTED ELEMENTS
8 - 237
Other Elements in Connections
Shims
Shims are furnished to the erector for use in filling the spaces allowed for field clearance which might be present at connections such as simple shear connections, PR and FR moment connections, column base plates, and column splices. These shims, illustrated in Figure 8-63, may be either strip shims, with round punched holes, or finger shims, with slots cut through the edge. Whereas strip shims are less expensive to fabricate, finger shims may be laterally inserted and eliminate the need to remove erection bolts or pins already in place. Finger shims, when inserted fully against the bolt shank, are acceptable for slip-critical connections and are not to be considered as an internal ply with the slotted hole determining the design strength of the connection. This is because less than 25 percent of the contact surface is lost and this is not enough to affect the performance of the joint. Fillers
A filler is furnished to occupy spaces which will be present because of dimensional separations between elements of a connection across which load transfer occurs. Examples where fillers might be used are beams framing off center on a column and raised beams. From LRFD Specification Section J6, fillers in welded connections and fillers thicker than 3⁄4-in. in bolted bearing-type connections must be fully developed. In bolted bearing-type connections, fillers between 1⁄4-in. and 3⁄4-in. thick, inclusive, need not be developed, provided the design shear strength of the bolts is reduced by the factor 0.4(t − 0.25) where t is the total thickness of the fillers up to 3⁄4-in. In bolted slip-critical connections, fillers need not be fully developed.
Strip
Finger
Fig. 8-63. Shims. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BOLTS, WELDS, AND CONNECTED ELEMENTS
REFERENCES
Alexander, W. G., 1991, “Designing Longitudinal Welds for Bridge Members,” Engineering Journal, Vol. 28, No. 1, (1st Qtr.), pp. 29–36, AISC, Chicago, IL. American Concrete Institute, 1985, ACI 349 Code Requirements for Nuclear Safety Related Concrete Structures, Appendix B, ACI, Detroit, MI. American Institute of Steel Construction, Inc., 1993, Load and Resistance Factor Design Specification for Structural Steel Buildings, AISC, Chicago, IL. American Institute of Steel Construction, Inc., 1989, Manual of Steel Construction— Allowable Stress Design, 9th ed., AISC, Chicago, IL. American Institute of Steel Construction, Inc., 1988, Quality Criteria and Inspection Standards, 3rd ed., AISC, Chicago, IL. American Institute of Steel Construction, Inc., 1973, “Commentary on Highly Restrained Welded Connections,” Engineering Journal, Vol. 10, No. 3, (3rd Qtr.), pp. 61–73, AISC, Chicago, IL. American Welding Society, 1978, Welding Handbook—Volume 2, 7th ed., AWS, Miami, FL. American Welding Society, 1977, Guide for the Non-Destructive Inspection of Welds, (AWS B1.0-77), AWS, Miami, FL. Astaneh, A., 1985, “Procedure for Design and Analysis of Hanger-Type Connections,” Engineering Journal, Vol. 22, No. 2, (2nd Qtr.), pp. 63–66, AISC, Chicago, IL. Blodgett, O. W., 1966, Design of Welded Structures, James F. Lincoln Arc Welding Foundation, Cleveland, OH. Blodgett, O. W., 1980, “Detailing to Achieve Practical Welded Fabrication,” Engineering Journal, Vol. 17, No. 4, (4th Qtr.), pp. 106–119, AISC, Chicago, IL. Bowman, M. D. and M. Betancourt, 1991, “Reuse of A325 and A490 High-Strength Bolts,” Engineering Journal, Vol. 28, No. 3, (3rd Qtr.), pp. 110–118, AISC, Chicago, IL. Butler, L. J., S. Pal, and G. L. Kulak, 1972, “Eccentrically Loaded Welded Connections,” Journal of the Structural Division, Vol. 98, No. ST5, (May), pp. 989–1005, ASCE, New York, N.Y. Cannon, R. W., D. A. Godfrey, and F. L. Moreadith, 1981, “Guide to the Design of Anchor Bolts and Other Steel Embedments,” Concrete International, Vol. 3, No. 7, (July 1981), pp. 28–41, ACI, Detroit, MI.. Cheng, J. J., J. A. Yura, and C. P. Johnson, 1984, “Design and Behaviour of Coped Beams,” Department of Civil Engineering, The University of Texas at Austin, Austin, TX. Crawford, S. F. and G. L. Kulak, 1968, “Behavior of Eccentrically Loaded Bolted Connections,” Studies in Structural Engineering, (No. 4), Department of Civil Engineering, Nova Scotia Technical College, Halifax, Nova Scotia. DeWolf, J. T. and D. T. Ricker, 1990, Column Base Plates, AISC, Chicago, IL Fisher, J. M., 1981, “Structural Details in Industrial Buildings,” Engineering Journal, Vol. 18, No. 3, (3rd Qtr.), pp. 83–89, AISC, Chicago, IL. Fisher, J. W. and J. H. A. Struik, 1974, Guide to Design Criteria for Bolted and Riveted Joints, John Wiley & Sons, Inc., New York, NY. Grover, L., 1946, Manual of Design for Arc Welded Steel Structures, Air Reduction Sales Co., New York, NY. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
REFERENCES
8 - 239
Higgins, T. R., 1971, “Treatment of Eccentrically Loaded Connections in the AISC Manual,” Engineering Journal, Vol. 8, No. 2, (April), pp. 52–54, AISC, Chicago, IL. Institute of Welding, 1972, Procedures and Recommendations for the Ultrasonic Testing of Butt Welds, London, England. Iwankiw, N. R., 1987, “Design for Eccentric and Inclined Loads on Bolt and Weld Groups,” Engineering Journal, Vol. 24, No. 4, (4th Qtr.), pp. 164–171, AISC, Chicago, IL. Kaufmann, J., A. W. Pense, and R. D. Stout, 1981, “An Evaluation of Factors Significant to Lamellar Tearing,” Welding Journal Research Supplement, Vol. 60, No. 3, (March), AWS, Miami, FL. Krautkramer, J., 1977, Ultrasonic Testing of Materials, 2nd. ed., Springer-Verlag, Berlin, West Germany. Kulak, G. L., 1975, “Eccentrically Loaded Slip-Resistant Connections,” Engineering Journal, Vol. 12, No. 2, (2nd Qtr.), pp. 52–55, AISC, Chicago, IL. Lesik, D. F. and D. J. L. Kennedy, 1990, “Ultimate Strength of Fillet-Welded Connections Loaded in Plane,” Canadian Journal of Civil Engineering, Vol. 17, No. 1, National Research Council of Canada, Ottawa, Canada. Kulak, G. L. and Timler, 1984, “Tests on Eccentrically Loaded Fillet Welds,” Department of Civil Engineering, University of Alberta, Edmonton, Canada. Kulak, G. L., J. W. Fisher, and J. H. A. Struik, 1987, Guide to Design Criteria for Bolted and Riveted Joints, 2nd ed., John Wiley & Sons, New York, NY. Marsh, M. L., and E. G. Burdette, 1985a, “Anchorage of Steel Building Components to Concrete,” Engineering Journal, Vol. 15, No. 4, (4th Qtr.), pp. 33–39, AISC, Chicago, IL. Marsh, M. L., and E. G. Burdette, 1985b, “Multiple Bolt Anchorages: Method for Determining the Effective Projected Area of Overlapping Stress Cones,” Engineering Journal, Vol. 15, No. 4, (4th Qtr.), pp. 29–32, AISC, Chicago, IL. Research Council on Structural Connections, 1988, Load and Resistance Factor Design Specification for Structural Joints Using ASTM A325 or A490 Bolts, AISC, Chicago, IL. Shipp, J. G. and E. R. Haninger, 1983, “Design of Headed Anchor Bolts,” Engineering Journal, Vol. 20, No. 2, (2nd Qtr.), pp. 58–69, AISC, Chicago. IL. Stout, R. D. and W. D. Doty, 1978, Weldability of Steels, 3rd. ed., Welding Research Council, New York, NY Thornton, W. A., 1985, “Prying Action—A General Treatment,” Engineering Journal, Vol. 22, No. 2, (2nd Qtr.), pp. 67–75, AISC, Chicago, IL. Tide, R. H. R., 1980, “Eccentrically Loaded Weld Groups—AISC Design Tables,” Engineering Journal, Vol. 17, No. 4, (4th Qtr.), pp. 90–95, AISC, Chicago, IL.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9-1
PART 9 SIMPLE SHEAR AND PR MOMENT CONNECTIONS SIMPLE SHEAR CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-7 Double-Angle Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-11 Shear End-Plate Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-91 Unstiffened Seated Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-128 Stiffened Seated Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-138 Single-Plate Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-147 Single-Angle Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-161 Tee Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-170 SHEAR SPLICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-176 SPECIAL CONSIDERATIONS FOR SIMPLE SHEAR CONNECTIONS . . . . . . . . . 9-185 Web Reinforcement of Coped Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-185 Simple Shear Connections at Stiffened Column-Web Locations . . . . . . . . . . . . . 9-190 Eccentric Effect of Larger-Than-Normal Gages . . . . . . . . . . . . . . . . . . . . . . 9-192 Simple Shear Connections for Large End Reactions . . . . . . . . . . . . . . . . . . . . 9-196 Double Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-196 Beams Offset from Column Centerline . . . . . . . . . . . . . . . . . . . . . . . . . . 9-202 Connections for Raised Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-211 Connections for Tubular and Pipe Members . . . . . . . . . . . . . . . . . . . . . . . . 9-215 Non-Rectangular Simple Shear Connections
. . . . . . . . . . . . . . . . . . . . . . . 9-215
PR MOMENT CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-234 Flange-Plated PR Moment Connections . . . . . . . . . . . . . . . . . . . . . . . . . . 9-246 Flexible Wind Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-253 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-263
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9-2
SIMPLE SHEAR AND PR MOMENT CONNECTIONS
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
9-3
OVERVIEW Part 9 contains general information, design considerations, examples, and design aids for the design of simple shear connections, shear splices, PR moment connections, and special considerations in the aforementioned topics. It is based upon the provisions of the 1993 LRFD Specification. Supplementary information may also be found in the Commentary on the LRFD Specification. Following are the general topics addressed. SIMPLE SHEAR CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-7 Considerations for Economical Simple Shear Connections . . . . . . . . . . . . . . . . . 9-7 Comparing Two-Sided, Seated, and One-Sided Connections . . . . . . . . . . . . . . . . 9-8 Erectability Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-9 Computer Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-10 Double-Angle Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-11 Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-12 Recommended Angle Length and Thickness . . . . . . . . . . . . . . . . . . . . . . 9-12 Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-12 All-Bolted Double-Angle Connections . . . . . . . . . . . . . . . . . . . . . . . . . 9-13 Bolted/Welded Double-Angle Connections . . . . . . . . . . . . . . . . . . . . . . . 9-15 All-Welded Double-Angle Connections . . . . . . . . . . . . . . . . . . . . . . . . . 9-16 Shear End-Plate Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-91 Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-91 Recommended End-Plate Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . 9-91 Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-91 Bolted/Welded Shear End-Plate Connections . . . . . . . . . . . . . . . . . . . . . . 9-92 Unstiffened Seated Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-128 Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-129 Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-130 All-Bolted Unstiffened Seated Connections . . . . . . . . . . . . . . . . . . . . . . . 9-130 Bolted/Welded Unstiffened Seated Connections . . . . . . . . . . . . . . . . . . . . 9-132 All-Welded Unstiffened Seated Connections . . . . . . . . . . . . . . . . . . . . . . 9-132 Stiffened Seated Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-138 Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-139 Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-140 All-Bolted Stiffened Seated Connections . . . . . . . . . . . . . . . . . . . . . . . . 9-140 Bolted/Welded Stiffened Seated Connections . . . . . . . . . . . . . . . . . . . . . . 9-140 Single-Plate Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-147 Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-147
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9-4
SIMPLE SHEAR AND PR MOMENT CONNECTIONS
Recommended Plate Length and Thickness . . . . . . . . . . . . . . . . . . . . . . 9-148 Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-149 Bolted/Welded Single-Plate Connections . . . . . . . . . . . . . . . . . . . . . . . 9-149 Single-Angle Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-161 Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-161 Recommended Angle Length and Thickness . . . . . . . . . . . . . . . . . . . . . . 9-161 Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-161 All-Bolted Single-Angle Connections . . . . . . . . . . . . . . . . . . . . . . . . . 9-162 Bolted/Welded Single-Angle Connections . . . . . . . . . . . . . . . . . . . . . . . 9-163 Tee Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-170 Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-170 Recommended Tee Length and Flange and Web Thicknesses . . . . . . . . . . . . . 9-171 Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-171 SHEAR SPLICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-176 SPECIAL CONSIDERATIONS FOR SIMPLE SHEAR CONNECTIONS . . . . . . . . 9-185 Web Reinforcement of Coped Beams . . . . . . . . . . . . . . . . . . . . . . . . . . 9-185 Doubler Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-185 Longitudinal Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-185 Combination Longitudinal and Transverse Stiffening . . . . . . . . . . . . . . . . . 9-185 Simple Shear Connections at Stiffened Column-Web Locations . . . . . . . . . . . . . 9-190 Eccentric Effect of Larger-Than-Normal Gages . . . . . . . . . . . . . . . . . . . . . 9-192 Column-Web Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-192 Girder-Web Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-194 Alternative Treatment of Eccentric Moment . . . . . . . . . . . . . . . . . . . . . . 9-195 Simple Shear Connections for Large End Reactions . . . . . . . . . . . . . . . . . . . 9-196 Double Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-196 Supported Beams of Different Nominal Depths . . . . . . . . . . . . . . . . . . . . 9-196 Supported Beams Offset Laterally . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-200 Beams Offset from Column Centerline . . . . . . . . . . . . . . . . . . . . . . . . . . 9-202 Framing to the Column Flange from the Strong Axis . . . . . . . . . . . . . . . . . 9-202 Framing to Column Flange from the Weak Axis . . . . . . . . . . . . . . . . . . . . 9-204 Framing to the Column Web . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-209 Connections for Raised Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-211 Connections for Tubular and Pipe Members . . . . . . . . . . . . . . . . . . . . . . . 9-215 Non-Rectangular Simple Shear Connections . . . . . . . . . . . . . . . . . . . . . . . 9-215 AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
9-5
Skewed Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-215 Sloped Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-224 Canted Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-225 Inclines in Two or More Directions (Hip and Valley Framing) . . . . . . . . . . . . . 9-228 PR MOMENT CONNECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-234 Modeling PR Moment Connections for Gravity Loads . . . . . . . . . . . . . . . . . . 9-234 Deflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-237 The Beam Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-239 Elastic Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-240 Non-Rigid Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-242 Plastic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-244 Real Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-244 Flange Plated PR Moment Connections . . . . . . . . . . . . . . . . . . . . . . . . . . 9-246 Force Transfer in PR Moment Connections . . . . . . . . . . . . . . . . . . . . . . . 9-248 Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-248 Shop and Field Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-248 Flexible Wind Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-253 Design Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-254 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-263
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9-6
SIMPLE SHEAR AND PR MOMENT CONNECTIONS
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SIMPLE SHEAR CONNECTIONS
9-7
SIMPLE SHEAR CONNECTIONS
The ends of members with simple shear connections are assumed to be unrestrained or free to rotate under load as illustrated in Figure 9-1. While simple shear connections do actually possess some rotational restraint, as illustrated by curve A in Figure 9-2, this small amount is usually neglected and the connection is idealized to be completely flexible. Accordingly, simple shear connections are sized only for the end reaction or shear Ru of the supported beam. Note that simple shear connections must provide flexibility to accommodate the required end rotation of the supported beam. When members are designed with simple shear connections, provision must be made to stabilize the frame for gravity loads and also to resist lateral loads. A positive steel bracing system, such as X- or K-bracing, PR or FR construction, and concrete or masonry shear walls are three commonly used methods. PR moment connections (including flexible wind connections) are treated in this Part. FR moment connections are treated in Part 10. Bracing systems and connections are treated in Part 11. For the design of concrete or masonry shear walls, refer to ACI 318. Considerations for Economical Simple Shear Connections
The AISC Code of Standard Practice states that, after the engineer of record (EOR) designs the structural members, the EOR may design and detail the connections or the EOR may have the fabricator develop the detailed configuration of the simple shear connections. In both cases, the fabricator must submit shop drawings for approval and verification that the EOR’s design criteria and intent have been satisfied. Regardless of which approach is taken, the AISC Code of Standard Practice states that the EOR is responsible for the adequacy of these connections. The fabricator is responsible for the accuracy of the detail dimensions, clearances, and general fit-up of the structural steel members and connecting materials for field assembly (refer to the AISC Code of Standard Practice Section 2 for definition of which items are and are not considered structural steel). The latter approach is usually taken since there are economies inherent in allowing the fabricator to choose the most efficient connections for the fabricator’s shop and erection processes. Whenever possible, the designer should give the fabricator and erector the flexibility to choose the connection types which offer the most economical shop fabrication and safest and most economical erection. In taking this approach, however, some engineers of record specify general design criteria (e.g., one-half the total factored uniform load) from which the connections are to be developed without regard to the actual reactions. Thornton (1992) describes several of these practices and provides examples of the uneconomical and/or unsafe connections which can result from their use. Because of this, when the fabricator or detailer is to θ
θ No restraint Ends free to rotate
Note: top angle not shown for clarity.
Figure 9.1. Illustration of simple shear connection. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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SIMPLE SHEAR AND PR MOMENT CONNECTIONS
develop the detailed configuration of the connections, the EOR must indicate the actual design reactions on the contract drawings or provide the fabricator with a method to accurately determine the required strength. In the absence of such information, connections will be selected to support one-half the total factored uniform load for the given beam, span, and grade of steel specified; no consideration will be given for the effects of any other loads unless specified on the contract drawings. Comparing Two-Sided, Seated, and One-Sided Connections
Following is a general discussion of the advantages of two-sided, seated, and one-sided connections. Two-sided connections, such as double-angle and shear end-plate connections, offer the following advantages: (1) suitability for use when the end reaction is large; (2) compactness (usually, the entire connection is contained within the flanges of the supported beam); and, (3) eccentricity perpendicular to the beam axis need not be considered for usual gages. Unstiffened and stiffened seated connections offer the following advantages: (1) seats may be shop attached to the support, simplifying erection; (2) ample erection clearance is provided; (3) erection is fast and safe; and, (4) the bay length of the structure is easily maintained (seated connections may be preferable when maintaining bay length is a concern for repetitive bays of framing). Note that seated connections can cause erection
FR moment connections
Fixed end moment PR moment connections
End moment
Beam line
Simple shear connections A Simple beam rotation
Rotation
A
Figure 9-2. Simple shear connection behavior. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SIMPLE SHEAR CONNECTIONS
9-9
interference when floors are close, beams are deep, or seats protrude excessively from the column face; the practice of leaning or tilting the columns to erect a column-web connection is difficult, unsafe, and should always be avoided. One-sided connections such as single-plate, single-angle, and tee connections offer the following advantages: (1) shop attachment of connecting materials to the support, simplifying shop fabrication and erection; (2) reduced material and shop labor requirements; and, (3) excellent safety during erection since double connections may be eliminated. Erectability Considerations
In field-bolted connections, when beams or girders frame opposite each other and take the same open holes in the web of a column, as illustrated in Figure 9-3, the first member to be erected must be supported while the second member to be erected is brought into its final position. Note that hanging the beam on a partially inserted bolt or drift pin is dangerous; such a makeshift practice should not be attempted. A temporary erection seat, usually an angle, is sometimes provided in the column web and located to clear the bottom flange of the supported member by approximately 3â &#x201E;8-in. to accommodate mill, fabrication, and erection tolerances. The erection seat is sized and attached to the column web with sufficient bolts or welds to support the dead weight of the member, unless additional loading is indicated. The sequence of erection is most important in determining the need for erection seats. If the erection sequence is known, the erection seat is provided on the side needing the support. If the erection sequence is not known, a seat can be provided on both sides of the column web. Erection seats may be reused at other locations, but are not generally required to be removed unless they create an interference, detract from the architectural appearance, or such removal is required in the contract documents. In field-welded connections in which some means of temporary support must be provided until final welding is performed, temporary erection bolts are usually provided.
Column First beam to be erected
Clearance
Second beam to be erected
Temporary erection seat
Figure 9-3. Erection seat. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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SIMPLE SHEAR AND PR MOMENT CONNECTIONS
Note that it is not necessary that these bolts be removed subsequent to final welding. Subject to the provisions of LRFD Specification Section J1.9, erection bolts may also serve as permanent attachment; refer to “Construction Combining Bolts and Welds” in Part 8. Safety laws require that two bolts be placed for erection safety. As a general rule, then, two erection bolts are used for framing angles or similar connecting elements up to 12 inches long, four bolts are used for connecting elements up to 18 inches long, and six bolts are used for longer connecting elements. Additional erection bolts may be provided and serve two purposes: (1) they provide for the contingency of large temporary loads during erection; and, (2) they assist in pulling the connection angles up tightly against the web of the supporting beam prior to welding. Some engineers prefer to locate erection bolts below the mid-depth of the connection; theoretically, this provides the greatest possible flexibility near the top of the connection, where the angles are expected to flex away from the supporting member. However, this practice does not ensure a close fit-up of the angle before welding. Other engineers prefer the more general practice of spacing the bolts equally along the length of the angles. In this latter case, the bolts are placed as closely as practical to the toes of the outstanding leg to provide greater flexibility. Computer Software
CONXPRT is fully automated connection design software which provides for rapid design of economical simple shear connections. Based upon the AISC Manual of Steel Construction, Volume II—Connections and the engineering knowledge and experience of respected fabricators and design engineers, CONXPRT comes with preset guidelines, but can be modified to meet individual standards. It is menu-driven with a built-in shapes database and provides complete documentation of all design checks.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SIMPLE SHEAR CONNECTIONS
9 - 11
Double-Angle Connections
A double-angle connection is made with two angles, one on each side of the web of the beam to be supported, as illustrated in Figure 9-4. These angles may be bolted or welded to the supported beam as well as to the supporting member. When the angles are welded to the support, adequate flexibility must be provided in the connection. As illustrated in Figure 9-4c, line welds are placed along the toes of the angles with a return at the top per LRFD Specification Section J2.2b. Note that welding across the entire top of the angles must be avoided as it would inhibit the flexibility and, therefore, the necessary end rotation of the connection; the performance of the resulting connection is unpredictable.
(a) All-bolted
w
(b) Bolted/welded, angles welded to supported beam
w
2w Note: weld returns on top of angles per LRFD Specification Section J2.2b.
w
(c) Bolted/welded, angles welded to support Figure 9-4. Double-angle connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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SIMPLE SHEAR AND PR MOMENT CONNECTIONS
Table 9-1. Fillet Encroachment Chart k − tf, in. 5⁄
k
tf encr.
1
/32 in.
tw
encr., in.
16
1⁄ 8
3⁄ 8
3⁄ 16
7⁄
16
3⁄ 16
1⁄ 2
3⁄ 16
9⁄
16
1⁄ 4
5⁄ 8
1⁄ 4
11⁄ 16
1⁄ 4
3⁄ 4
1⁄ 4
13⁄ 16
1⁄ 4
7⁄ 8
5⁄ 16
1
5⁄ 16
Design Checks
The design strengths of the bolts and/or welds and connected elements must be determined in accordance with the LRFD Specification; the applicable limit states are discussed in Part 8. In all cases, the design strength φRn must equal or exceed the required strength Ru. For usual gages of three inches and standard or short-slotted holes, eccentricity in double-angle connections may be neglected, except in the case of a double vertical row of bolts through the web of the supported beam, as illustrated in Figure 9-5. Eccentricity should always be considered in the design of welds for double-angle connections. Recommended Angle Length and Thickness
To provide for stability during erection, it is recommended that the minimum angle length be one-half the T-dimension of the beam to be supported. The maximum length of the connection angles must be compatible with the T-dimension of an uncoped beam and the remaining web depth, exclusive of fillets, of a coped beam. Note that the angle may encroach on the fillet or fillets by 1⁄8-in. to 5⁄16-in., depending upon the radius of the fillets; refer to Table 9-1. To provide for flexibility, the maximum angle thickness for use with usual gages should be limited to 5⁄8-in. Shop and Field Practices
Double-angle connections may be made to the webs of supporting girders and to the flanges of supporting columns. Because of bolting and welding clearances, double-angle connections may not be suitable for connections to the webs of W8 columns, unless gages are reduced or bolts are staggered, and may be impossible for W6 columns. When framing to a girder web, both angles are usually shop attached to the web of the supported beam. When framing to a column web, both angles may be shop attached to AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SIMPLE SHEAR CONNECTIONS
9 - 13
the supported beam or to the column web. In the latter case, the bottom flange of the supported beam is coped to allow knifed erection (the beam web is lowered into place between the angles from above). Knifed erection requires that a total erection clearance of about 1⁄8-in. be provided between the angles as illustrated in Figure 9-6a. For bolted construction, this clearance may vary as gages will occur in minimum increments of 1⁄ -in. Shims must be furnished whenever measured clearances exceed 1⁄ -in. 16 8 When framing to a column flange, provision must be made for possible mill variation in the depth of the columns. If both angles are shop attached to the beam web, the beam length could be shortened to provide for mill overrun and shims could be furnished at the appropriate intervals to fill the resulting gaps or to provide for mill underrun; in general, shims are not required except for fairly long runs (i.e., six or more bays of framing). If both angles are shop attached to the column flange, the erected beam is knifed into place and play in the open holes usually furnishes the necessary adjustment to compensate for the mill variation in the columns; short slots can also be used. Alternatively, in any of the aforementioned cases, one angle could be shop attached to the support and the other shipped loose. In this case, the spread between the outstanding legs should equal the decimal beam web thickness plus a clearance which will produce an opening to the next higher 1⁄16-in. increment, as illustrated in Figure 9-6b; short slots in the support-leg of the angle eliminate the need to provide for variations in web thickness. However, shipping one angle loose is not a desirable practice since it requires additional material handling as well as added erection costs and difficulty. All-Bolted Double-Angle Connections
Tables 9-2 are design aids for all-bolted double-angle connections. Design strengths are tabulated for supported and supporting member material, as well as angle material with Supporting member
g1
g3
E
g2
E
E indicates that eccentricity must be considered in this leg. Gages g1, g2, g 3 are usual gages as shown below Usual gages* in angle legs, in. Leg
8
7
6
5
4
31⁄2
3
21⁄2
2
13⁄4
11⁄2
13⁄8
11⁄4
1
g1 g2 g3
41⁄2 3 3
4 21⁄2 3
31⁄2 21⁄4 21⁄2
3 2 13⁄4
21⁄2
2
13⁄4
13⁄8
11⁄8
1
7⁄ 8
7⁄ 8
3⁄ 4
5⁄ 8
*Other gages are permitted to suit specific requirements subject to clearances and edge distance limitations.
Figure 9-5. Eccentricity in double-angle connections. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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SIMPLE SHEAR AND PR MOMENT CONNECTIONS
Fy = 36 ksi and Fu = 58 ksi and with Fy = 50 ksi and Fu = 65 ksi. All values, including slip-critical bolt design strengths, are for comparison with factored loads. Tabulated bolt and angle design strengths consider the limit states of bolt shear, bolt bearing on the angles, shear yielding of the angles, shear rupture of the angles, and block shear rupture of the angles. Values are tabulated for 2 through 12 rows of 3⁄4-in., 7⁄8-in, and 1 in. diameter A325 and A490 bolts at 3 in. spacing. For calculation purposes, angle edge distances Lev and Leh are assumed to be 11⁄4-in. Tabulated beam web design strengths, per inch of web thickness, consider the limit state of bolt bearing on the beam web. For beams coped at the top flange only, the limit state of block shear rupture is also considered. Additionally, for beams coped at both the top and bottom flanges, the tabulated values consider the limit states of shear yielding gage
Provide approximately 1/8 in. erection clearance between angles; spread should be a multiple of 1/16 in.
(a) Both angles shop attached to the column flange (beam knifed into place)
gage
Provide erection clearance so that spread is the next larger multiple of 1/16 in. greater than the beam web thickness.
(b) One shop attached to the column flange, other shipped loose Figure 9-6. Double-angle connection erection clearances. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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and shear rupture of the beam web. Values are tabulated for beam web edge distances Leh from 11⁄4-in. to 3 in. and for beam end distances Leh of 11⁄2-in. and 13⁄4-in.; for calculation purposes, these end distances have been reduced to 11⁄4-in. and 11⁄2-in., respectively, to account for possible underrun in beam length. For coped members, the limit states of flexural yielding and local buckling must be checked independently. These limit states are discussed in Part 8; web reinforcement of coped members is treated in this Part under “Special Considerations”. Tabulated supporting member design strengths, per inch of flange or web thickness, consider the limit state of bolt bearing on the support. Bolted/Welded Double-Angle Connections
Table 9-3 (see page 9-88) is a design aid arranged to permit substitution of welds for bolts in connections designed with Tables 9-2. Electrode strength is assumed to be 70 ksi. All values are for comparison with factored loads. Holes for erection bolts may be placed as required in angle legs that are to be field welded. Welds A may be used in place of bolts through the supported-beam-web legs of the double angles or welds B may be used in place of bolts through the support legs of the double angles. Although it is permissible to use welds A and B from Table 9-3 in combination to obtain all-welded connections, it is recommended that such connections be chosen from Table 9-4. This table will allow increased flexibility in selection of angle lengths and connection strengths since Table 9-3 conforms to the bolt spacing and edge distance requirements for the bolted double-angle connections of Tables 9-2. Weld design strengths are tabulated for the limit state of weld shear. Design strengths for welds A are determined by the instantaneous center of rotation method using Table 8-42 with θ = 0°. Design strengths for welds B are determined by the elastic method. With the neutral axis assumed at one-sixth the depth of the angles measured downward and the tops of the angles in compression against each other through the beam web, the design strength of these welds is φRn, where φRn = 2 ×
1.392DL
√ 1+
12.96e2 L2
In the above equation, D is the number of sixteenths-of-an-inch in the weld size, L is the length of the connection angles, and e is the width of the leg of the connection angle attached to the support. The tabulated minimum thicknesses of the supported beam web for welds A and the support for welds B match the shear yielding strength of these elements with the strength of the weld metal. Given the design shear yielding strength per unit length from LRFD Specification Section J5.3 as 0.9(0.60Fy t) and the weld strength constant (unit length design strength per 1⁄16-in. weld size for 70 ksi electrodes) as 1.392 kips/in., the minimum supported beam web thickness for welds A (two lines of weld) is tmin =
D × 1.392 × 2 5.16D = Fy 0.9 × 0.60Fy
where D is the number of sixteenths in the weld size. Similarly for welds B (one line of weld) the minimum supporting flange or web thickness is AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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tmin =
SIMPLE SHEAR AND PR MOMENT CONNECTIONS
2.58D
Fy
When welds line up on opposite sides of the support, the minimum thickness is the sum of the thicknesses required for each weld. In either case, when less than the minimum material thickness is present, the tabulated weld design strength must be reduced by the ratio of the thickness provided to the minimum thickness. The minimum angle thickness when Table 9-3 is used is the weld size plus 1⁄16-in. but not less than the angle thickness determined from Table 9-2. The angle length L must be as tabulated in Table 9-3. In general, 2L4×31⁄2 will accommodate usual gages, with the 4 in. leg attached to the supporting member. Width of web legs in Case I may be optionally reduced from 31⁄2-in. to 3 in. Width of outstanding legs in Case II may be optionally reduced from 4 in. to 3 in. for values of L from 51⁄2 through 171⁄2-in. All-Welded Double-Angle Connections
Table 9-4 (see page 9-89) is a design aid for all-welded double-angle connections. Electrode strength is assumed to be 70 ksi. All values are for comparison with factored loads. Holes for erection bolts may be placed as required in angle legs that are to be field welded. Weld design strengths are tabulated for the limit state of weld shear. Design strengths for welds A are determined by the instantaneous center of rotation method using Table 8-42 with θ =0°. Design strengths for welds B are determined by the elastic method as discussed previously for bolted/welded double-angle connections. The tabulated minimum thicknesses of the supported beam web for welds A and the support for welds B match the shear yielding strength of these elements with the strength of the weld metal and are determined as discussed previously for bolted/welded double angle connections. When welds line up on opposite sides of the support, the minimum thickness is the sum of the thicknesses required for each weld. When less than the minimum material thickness is present, the tabulated weld design strength must be reduced by the ratio of the thickness provided to the minimum thickness. The minimum angle thickness when Table 9-4 is used must be equal to the weld size plus 1⁄16-in. The angle length L must be as tabulated in Table 9-4. Use 2L4×3 for angle lengths greater than or equal to 18 in.; use 2L3×3 otherwise.
Example 9-1
Given:
Refer to Figure 9-7. Use Table 9-2 to design an all-bolted double-angle connection for the W18×50 beam to W21×62 girder web connection. Ru = 60 kips W18×50 tw = 0.355 in. d = 17.99 in. Fy = 50 ksi, Fu = 65 ksi top flange coped 2 in. deep by 4 in. long, Lev = 11⁄4-in., Leh = 13⁄4-in. (Assumed to be 11⁄2-in. for calculation purposes to account for possible underrun in beam lengths) AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SIMPLE SHEAR CONNECTIONS
9 - 17
W21×62 tw = 0.400 in. Fy = 50 ksi, Fu = 65 ksi Use 3⁄4-in. diameter A325-N bolts in standard holes. Assume angle material with Fy = 36 ksi and Fu = 58 ksi. Solution:
Design bolts and angles (refer to Part 8) From Table 9-2, for 3⁄4-in. diameter A325-N bolts and angle material with Fy = 36 ksi and Fu = 58 ksi, select three rows of bolts and 1⁄4-in. angle thickness. φRn = 76.7 kips > 60 kips o.k. Check supported beam web From Table 9-2, for three rows of bolts, beam material with Fy = 50 ksi and Fu = 65 ksi, and Lev = 11⁄4-in. and Leh = 13⁄4-in. (Assumed to be 11⁄2-in. for calculation purposes to account for possible underrun in beam lengths) φRn = (204 kips/in.)(0.355 in.) = 72.4 kips > 60 kips o.k. Check flexural yielding on the coped section (refer to Part 8) From Table 8-49, Snet = 23.4 in.3 φRn =
φFy Snet
e 0.9 (50 ksi) (23.4 in.3) = (4 in. + 1⁄2jin.) = 234 kips > 60 kips o.k.
Check local web buckling at the cope (refer to Part 8) c 4 in. = = 0.222 d 17.99 in. 4 in. c = = 0.250 ho (17.99 in. − 2 in.) c Since ≤ 1.0, d c f =2 d = 2(0.222) = 0.444 c Since ≤ 1.0, ho AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9 - 18
SIMPLE SHEAR AND PR MOMENT CONNECTIONS
1.65
ho k = 2.2 c
1 = 2.2 0.250
1.65
= 21.7 2
tw φFbc = 23,590 fk ho 2
0.355 in. = 23,590 (0.444) (21.7) 17.99 in. − 2 in. = 112 ksi φFbc Snet φRn =
e (112 ksi) (23.4 in.3) = (4 in. + 1⁄2jin.) = 582 kips > 60 kips o.k.
Check supporting girder web From Table 9-2, for three rows of bolts and girder material with Fu = 65 ksi, φRn = (527 kips/in.)(0.400 in.) = 211 kips > 60 kips o.k. The connection, as summarized in Figure 9-7, is adequate.
Example 9-2
Given:
Refer to Figure 9-8. Use Table 9-2 to design an all-bolted double-angle connection for the W36×230 beam to W14×90 column-flange connection. Ru = 225 kips W36×230 tw = 0.760 in. Fy = 50 ksi, Fu = 65 ksi W14×90 tf = 0.710 in. Fy = 50 ksi, Fu = 65 ksi Use 3⁄4-in. diameter A325-N bolts in standard holes. Assume angle material with Fy = 36 ksi and Fu = 58 ksi.
Solution:
Design bolts and angles AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SIMPLE SHEAR CONNECTIONS
9 - 19
From Table 9-2, for 3⁄4-in. diameter A325-N bolts and angle material with Fy = 36 ksi and Fy = 58 ksi, select eight rows of bolts and 5⁄16-in. angle thickness. φRn = 254 kips > 225 kips o.k. Check supported beam web From Table 9-2, for eight rows of bolts, beam material with Fy = 50 ksi and Fu = 65 ksi, and Leh = 13⁄4-in., φRn = (702 kips/in.)(0.760 in.) = 534 kips > 225 kips o.k. Check supporting column flange From Table 9-2, for eight rows of bolts and column material with Fy = 50 ksi and Fu = 65 ksi, φRn = (1,404 kips/in.)(0.710 in.) = 997 kips 225 kips o.k.
Example 9-3
Given:
Refer to Example 9-1. Use Table 9-3 to substitute welds for bolts in the supported-beam-web legs of the double-angle connection (welds A).
Solution:
From Table 9-3, for three rows of bolts (an angle length of 81⁄2-in.), a 3⁄ -in. weld size provides φR = 110 kips. For beam web material with 16 n Fy = 50 ksi, the minimum web thickness is 0.31 in. Since tw = 0.355 in. > 0.31 in., no reduction in the tabulated value is required. φRn = 110 kips > 60 kips o.k. Check minimum angle thickness The minimum angle thickness for Table 9-3 is the weld size plus 1⁄16-in., but not less than the thickness determined from Table 9-2. tmin = 3⁄16-in. + 1⁄16-in. = 1⁄4-in. This thickness is equal to the thickness chosen previously from Table 9-2.
Example 9-4
Given:
Refer to Example 9-2. Use Table 9-3 to substitute welds for bolts in the support legs of the double-angle connection (welds B).
Solution:
From Table 9-3, for eight rows of bolts (an angle length of 231⁄2-in.), a 5⁄ -in. weld size provides φR = 279 kips. For beam web material with 16 n AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9 - 20
SIMPLE SHEAR AND PR MOMENT CONNECTIONS
Fy = 50 ksi, the minimum column flange thickness is 0.26 in. Since tf = 0.710 in. > 0.26 in., no reduction of the tabulated value is required. φRn = 279 kips > 225 kips o.k. Check minimum angle thickness The minimum angle thickness for Table 9-3 is the weld size plus 1⁄16-in., but not less than the thickness determined from Table 9-2. tmin = 5⁄16-in. + 1⁄16-in. = 3⁄8-in. Thus, the angle thickness must be increased to 3⁄8-in. to accommodate the welded legs of the double-angle connection. Example 9-5
Given:
Refer to Example 9-2. Use Table 9-4 to design an all-welded doubleangle connection for the W36×230 beam to W14×90 column-flange connection.
Solution:
Design supported-beam-web angle leg welds (welds A) From Table 9-4, for L = 24 in., a 3⁄16-in. weld A size provides φRn = 259 kips. For beam web material with Fy = 50 ksi, the minimum supported beam web thickness is 0.31 in. Since tw = 0.760 in. > 0.31 in., no reduction of the tabulated value is required. φRn = 259 kips > 225 kips o.k. Design support angle leg welds (welds B) From Table 9-4, for L = 24 in., a 1⁄4-in. weld B size provides φRn = 229 kips. For column flange material with Fy = 50 ksi, the minimum column flange thickness is 0.21 in. Since tf = 0.710 in. > 0.21 in., no reduction of the tabulated value is required. Check minimum angle thickness The minimum angle thickness for Table 9-4 is the weld size plus 1⁄16-in. tmin = 1⁄4-in. + 1⁄16-in. = 5⁄16-in. Use 2L4×3×5⁄16.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SIMPLE SHEAR CONNECTIONS
9 - 21
¾φ A325-N
/16*
¼ 1 3/8 max.
11/4 min.
W18×50
11/16
2 15/16
A
3
61/8 min. (use 6¼)
L ev = 1¼
3 3 3¼ 2
2¼ L eh = 1¾
2L 4×3½×¼×8½ (SLBB)
Section at A * This dimension (see sketch, section at A) is determined to be one-half of the decimal web thickness rounded to the next higher 1/16 in. Example: 0.355/2 = 0.1775; use 3/16 in. This will produce spacing of holes in the supporting beam slightly larger than detailed in the angles to per mit spreading of angles (angles can be spread but not closed) at time of erection to supporting member. Alternatively, consider using horizontal slots in the support legs of the angles. Fig. 9-7.
2½
¾φ A325-N /16 *
/16
7
2L 5×3× 5/16 ×1″-1½
Section at B * This dimension is one-half decimal web thickness rounded to the next higher 1/16 in., as in example 9-1. Fig. 9-8. AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 3/8 max.
1¼ min.
W36×230
3 9/16
5
B
1 7/16
7@3 = 1 ″-9
1¼
6¾ min. (use 8)
1¾
9 - 22
SIMPLE SHEAR AND PR MOMENT CONNECTIONS
Fy = 36 ksi Fu = 58 ksi
Table 9-2. All-Bolted Double-Angle Connections
3⁄ -in. 4
Bolts
Bolt and Angle Design Strength, kips
12 Rows
ASTM Thread Desig. Cond.
W44
1⁄ 4
5⁄ 16
3⁄ 8
1⁄ 2
N
—
326
382
382
382
X
—
326
408
477
477
SC
STD
251
251
251
251
OVS
213
213
213
213
SSLT
213
213
213
213
STD
326
380
380
380
OVS
307
323
323
323
SSLT
323
323
323
323
N
—
326
408
477
477
X
—
326
408
489
596
SC Class A
STD
313
313
313
313
OVS
266
266
266
266
SSLT
266
266
266
266
STD
326
408
475
475
OVS
307
383
403
403
SSLT
326
403
403
403
A325 Varies
t
11@3 = 33
Class A
SC Class B 2 1/ 4
L eh
Angle Thickness, in.
Hole Type
11@3 = 33
Lev
A490
Lev
SC Class B
Beam Web Design Strength per Inch Thickness, kips/in. Coped at Top Flange Only Hole Leh,* UnType in. coped 11⁄4 STD OVS SSLT
Coped at Both Flanges
Lev, in.
Lev, in.
13⁄8
11⁄2
15⁄8
2
3
11⁄4
13⁄8
11⁄2
15⁄8
2
3
11⁄2
940
665
668
672
675
685
711
653
659
666
672
685
711
13⁄4
940
672
675
678
682
691
717
653
659
666
672
691
717
11⁄2
940
628
631
634
637
647
673
613
620
626
633
647
673
13⁄4
940
634
638
641
644
654
680
613
620
626
633
653
680
11⁄2
940
665
668
672
675
685
711
653
659
666
672
685
711
13⁄4
940
672
675
678
682
691
717
653
659
666
672
691
717
Notes: Support Design STD = Standard holes Strength per Inch OVS = Oversized holes Thickness, kips/in. SSLT = Short-slotted holes transverse to direction of load
1879
N = Threads included X = Threads excluded SC = Slip critical
*Tabulated values include 1⁄4-in. reduction in end distance Leh to account f or possible underrun in beam length
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SIMPLE SHEAR CONNECTIONS
9 - 23
Fy = 50 ksi Fu = 65 ksi
Table 9-2 (cont.). All-Bolted Double-Angle Connections 3⁄ -in 4
Bolts
Bolt and Angle Design Strength, kips
12 Rows
ASTM Thread Desig. Cond.
W44
A325 Varies
t
1⁄ 4
5⁄ 16
3⁄ 8
1⁄ 2
N
—
366
382
382
382
X
—
366
457
477
477
SC
STD
251
251
251
251
OVS
213
213
213
213
SSLT
213
213
213
213
STD
366
380
380
380
OVS
323
323
323
323
SSLT
323
323
323
323
N
—
366
457
477
477
X
—
366
457
548
596
SC
STD
313
313
313
313
OVS
266
266
266
266
SSLT
266
266
266
266
STD
366
457
475
475
OVS
344
403
403
403
SSLT
366
403
403
403
11@3 = 33
Class A
SC Class B 2 1/ 4
L eh Lev
A490
Angle Thickness, in.
Hole Type
11@3 = 33
Class A
SC Lev
Class B
Beam Web Design Strength per Inch Thickness, kips/in. Coped at Top Flange Only Hole Leh,* UnType in. coped 11⁄4 STD OVS SSLT
11⁄
Coped at Both Flanges
Lev, in.
Lev, in.
13⁄8
11⁄2
15⁄8
2
3
11⁄4
13⁄8
11⁄2
15⁄8
2
3
2
1053
754
758
762
765
776
806
731
739
746
753
775
806
13⁄4
1053
764
767
771
775
786
815
731
739
746
753
775
815
11⁄
2
1053
712
716
720
723
734
764
687
695
702
709
731
764
13⁄4
1053
722
725
729
733
744
773
687
695
702
709
731
773
11⁄2
1053
754
758
762
765
776
806
731
739
746
753
775
806
13⁄
1053
764
767
771
775
786
815
731
739
746
753
775
815
4
Notes: Support Design STD = Standard holes Strength per Inch OVS = Oversized holes Thickness, kips/in. SSLT = Short-slotted holes transverse to direction of load
2106
N = Threads included X = Threads excluded SC = Slip critical
*Tabulated values include 1⁄4-in. reduction in end distance Leh to account for possible underrun in beam length.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9 - 24
SIMPLE SHEAR AND PR MOMENT CONNECTIONS
Fy = 36 ksi Fu = 58 ksi
Table 9-2 (cont.). All-Bolted Double-Angle Connections
3⁄ -in. 4
Bolts
Bolt and Angle Design Strength, kips
11 Rows
ASTM Thread Desig. Cond.
W44, 40
1⁄ 4
5⁄ 16
3⁄ 8
1⁄ 2
N
—
299
350
350
350
X
—
299
373
437
437
SC
STD
230
230
230
230
OVS
195
195
195
195
SSLT
195
195
195
195
STD
299
348
348
348
OVS
281
296
296
296
SSLT
296
296
296
296
N
—
299
373
437
437
X
—
299
373
448
547
SC Class A
STD
287
287
287
287
OVS
244
244
244
244
SSLT
244
244
244
244
STD
299
373
435
435
OVS
281
351
370
370
SSLT
299
370
370
370
A325 Varies
t
Class A 10@3 = 30
Angle Thickness, in.
Hole Type
SC Class B 2 1/ 4
L eh
10@3 = 30
Lev
A490
Lev
SC Class B
Beam Web Design Strength per Inch Thickness, kips/in. Coped at Top Flange Only Hole Leh,* UnType in. coped 11⁄4 STD OVS SSLT
Coped at Both Flanges
Lev, in.
Lev, in.
13⁄8
11⁄2
15⁄8
2
3
11⁄4
13⁄8
11⁄2
15⁄8
2
3
11⁄2
861
610
613
616
619
629
655
597
604
610
617
629
655
13⁄4
861
616
620
623
626
636
662
597
604
610
617
636
662
11⁄2
861
575
579
582
585
595
621
561
568
574
581
595
621
13⁄4
861
582
585
589
592
602
628
561
568
574
581
600
628
11⁄2
861
610
613
616
619
629
655
597
604
610
617
629
655
13⁄4
861
616
620
623
626
636
662
597
604
610
617
636
662
Notes: Support Design STD = Standard holes Strength per Inch OVS = Oversized holes Thickness, kips/in. SSLT = Short-slotted holes transverse to direction of load
1723
N = Threads included X = Threads excluded SC = Slip critical
*Tabulated values include 1⁄4-in. reduction in end distance Leh to account for possible underrun in beam length.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SIMPLE SHEAR CONNECTIONS
9 - 25
Fy = 50 ksi Fu = 65 ksi
Table 9-2 (cont.). All-Bolted Double-Angle Connections 3⁄ -in. 4
Bolts
Bolt and Angle Design Strength, kips
11 Rows
ASTM Thread Desig. Cond.
W44, 40
A325 Varies
t
1⁄ 4
5⁄ 16
3⁄ 8
1⁄ 2
N
—
335
350
350
350
X
—
335
418
437
437
SC
STD
230
230
230
230
OVS
195
195
195
195
SSLT
195
195
195
195
STD
335
348
348
348
OVS
296
296
296
296
SSLT
296
296
296
296
N
—
335
418
437
437
X
—
335
418
502
547
SC
STD
287
287
287
287
OVS
244
244
244
244
SSLT
244
244
244
244
STD
335
418
435
435
OVS
314
370
370
370
SSLT
335
370
370
370
Class A 10@3 = 30
Angle Thickness, in.
Hole Type
SC Class B 2 1/ 4
L eh
10@3 = 30
Lev
A490
Class A
Lev
SC Class B
Beam Web Design Strength per Inch Thickness, kips/in. Coped at Top Flange Only Hole Leh,* UnType in. coped 11⁄4 STD OVS SSLT
11⁄
Coped at Both Flanges
Lev, in.
Lev, in.
13⁄8
11⁄2
15⁄8
2
3
11⁄4
13⁄8
11⁄2
15⁄8
2
3
2
965
692
696
700
703
714
743
669
676
684
691
713
743
13⁄4
965
702
705
709
713
724
753
669
676
684
691
713
753
11⁄
2
965
654
657
661
665
676
705
629
636
644
651
673
705
13⁄4
965
663
667
671
674
685
714
629
636
644
651
673
714
11⁄2
965
692
696
700
703
714
743
669
676
684
691
713
743
13⁄
965
702
705
709
713
724
753
669
676
684
691
713
753
4
Notes: Support Design STD = Standard holes Strength per Inch OVS = Oversized holes Thickness, kips/in. SSLT = Short-slotted holes transverse to direction of load
1931
N = Threads included X = Threads excluded SC = Slip critical
*Tabulated values include 1⁄4-in. reduction in end distance Leh to account for possible underrun in beam length.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9 - 26
SIMPLE SHEAR AND PR MOMENT CONNECTIONS
Fy = 36 ksi Fu = 58 ksi
Table 9-2 (cont.). All-Bolted Double-Angle Connections
3⁄ -in. 4
Bolt
Bolt and Angle Design Strength, kips
10 Rows
ASTM Thread Desig. Cond.
W44, 40, 36
1⁄ 4
5⁄ 16
3⁄ 8
1⁄ 2
N
—
271
318
318
318
X
—
271
338
398
398
SC
STD
209
209
209
209
OVS
178
178
178
178
SSLT
178
178
178
178
STD
271
316
316
316
OVS
254
269
269
269
SSLT
269
269
269
269
N
—
271
338
398
398
X
—
271
338
406
497
SC Class A
STD
261
261
261
261
OVS
222
222
222
222
SSLT
222
222
222
222
STD
271
338
396
396
OVS
254
318
336
336
SSLT
271
336
336
336
A325 Varies
t
Class A 9@3 = 27
Angle Thickness, in.
Hole Type
SC Class B 2 1/ 4
Lev
L eh
Lev
9@3 = 27
A490
SC Class B
Beam Web Design Strength per Inch Thickness, kips/in. Coped at Top Flange Only Hole Leh,* UnType in. coped 11⁄4 STD OVS SSLT
Coped at Both Flanges
Lev, in.
Lev, in.
13⁄8
11⁄2
15⁄8
2
3
11⁄4
13⁄8
11⁄2
15⁄8
2
3
11⁄2
783
554
557
561
564
574
600
542
548
555
561
574
600
13⁄4
783
561
564
567
571
580
607
542
548
555
561
580
607
11⁄2
783
523
526
530
533
543
569
509
515
522
529
543
569
13⁄4
783
530
533
536
540
549
576
509
515
522
529
548
576
11⁄2
783
554
557
561
564
574
600
542
548
555
561
574
600
13⁄4
783
561
564
567
571
580
607
542
548
555
561
580
607
Notes: Support Design STD = Standard holes Strength per Inch OVS = Oversized holes Thickness, kips/in. SSLT = Short-slotted holes transverse to direction of load
1566
N = Threads included X = Threads excluded SC = Slip critical
*Tabulated values include 1⁄4-in. reduction in end distance Leh to account for possible underrun in beam length.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SIMPLE SHEAR CONNECTIONS
9 - 27
Fy = 50 ksi Fu = 65 ksi
Table 9-2 (cont.). All-Bolted Double-Angle Connections 3⁄ -in. 4
Bolts
Bolt and Angle Design Strength, kips
10 Rows
ASTM Thread Desig. Cond.
W44, 40, 36
A325 Varies
t
1⁄ 4
5⁄ 16
3⁄ 8
1⁄ 2
N
—
303
318
318
318
X
—
303
379
398
398
SC
STD
209
209
209
209
OVS
178
178
178
178
SSLT
178
178
178
178
STD
303
316
316
316
OVS
269
269
269
269
SSLT
269
269
269
269
N
—
303
379
398
398
X
—
303
379
455
497
SC
STD
261
261
261
261
OVS
222
222
222
222
SSLT
222
222
222
222
STD
303
379
396
396
OVS
285
336
336
336
SSLT
303
336
336
336
Class A 9@3 = 27
Angle Thickness, in.
Hole Type
SC Class B 2 1/ 4
Lev
L eh
9@3 = 27
A490
Lev
Class A
SC Class B
Beam Web Design Strength per Inch Thickness, kips/in. Coped at Top Flange Only Hole Leh,* UnType in. coped 11⁄4 STD OVS SSLT
11⁄
Coped at Both Flanges
Lev, in.
Lev, in.
13⁄8
11⁄2
15⁄8
2
3
11⁄4
13⁄8
11⁄2
15⁄8
2
3
2
878
630
634
637
641
652
681
607
614
622
629
651
681
13⁄4
878
639
643
647
650
661
691
607
614
622
629
651
691
11⁄
2
878
595
599
603
606
617
647
570
578
585
592
614
647
13⁄4
878
605
608
612
616
627
656
570
578
585
592
614
656
11⁄2
878
630
634
637
641
652
681
607
614
622
629
651
681
13⁄
878
639
643
647
650
661
691
607
614
622
629
651
691
4
Notes: Support Design STD = Standard holes Strength per Inch OVS = Oversized holes Thickness, kips/in. SSLT = Short-slotted holes transverse to direction of load
1755
N = Threads included X = Threads excluded SC = Slip critical
*Tabulated values include 1⁄4-in. reduction in end distance Leh to account for possible underrun in beam length.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION