Substituting, φVcbg = 10.4
Av ψ 6 do Avo
Ncp = nominal concrete breakout strength in tension of a single anchor, kips f c′ c11.5
Avo = 4.5c12 (the area of the full shear cone for a single anchor as shown in View A-A of Figure 3.5.2) Av = the total breakout shear area for a single anchor, or a group of anchors ψ6 = a modifier to reflect the capacity reduction when side cover limits the size of the breakout cone It is recommended that the rod diameter, do, used in the square root term of the Vb expression, be limited to a maximum of 1.25 in., based on research results conducted at the University of Stuttgart. If the edge distance c1 is large enough, then the anchor rod shear strength will govern. The nominal shear strength of a single anchor rod equals 0.4FuAr, if the threads are not excluded from the shear plane, and 0.5FuAr, if the threads are included; φ = 0.55 and Ω = 2.75. ACI 318-02 Appendix D recognizes the benefit of the friction and allows the sharing of the anchor rod shear with the friction developed from factored axial and flexural load. In evaluating the concrete breakout strength, the breakout either from the most deeply embedded anchors or breakout on the anchors closer to the edge should be checked. When breakout is being determined on the inner two anchors (those farthest from the concrete edge) the outer two anchors (those closest to the concrete edge) should be considered to carry the same load. When the concrete breakout is considered from the outer two anchors, all of shear is to be taken by the outer anchors. Shown in Figure 3.5.3 are the two potential breakout surfaces and an indication of which will control, based on anchor location relative to the edge distance. In many cases it is necessary to use reinforcement to anchor the breakout cone to achieve the shear strength as well as the ductility desired. Ties placed atop piers as required in Section 7.10.5.6 of ACI 318-02 can also be used structurally to transfer the shear from the anchors to the piers. In addition to the concrete breakout strength, ACI also contains provisions for a limit state called pryout strength. The authors have checked several common situations and have not found pryout strength to control for typical anchor rod designs. ACI defines the pryout strength as
hef = effective anchor embedment length, in. 3.5.4 Interaction of Tension and Shear in the Concrete When the concrete is subjected to a combination of pullout and shear, ACI 318, Appendix D, uses an interaction equation solution. The reader is referred to ACI for further explanation. 3.5.5 Hairpins and Tie Rods To complete the discussion on anchorage design, transfer of shear forces to reinforcement using hairpins or tie rods will be addressed. Hairpins are typically used to transfer load to the floor slab. The friction between the floor slab and the subgrade is used in resisting the column base shear when individual footings are not capable of resisting horizontal forces. The column base shears are transferred from the anchor rods to the hairpin (as shown in Figure 3.5.4) through bearing. Problems have occurred with the eccentricity between the base plate and the hairpin due to bending in the anchor rods after the friction capacity is exceeded. This problem can be avoided as shown in Figure 3.5.5 or by providing shear lugs. Since hairpins rely upon the frictional restraint provided by the floor slab, special consideration should be given to the location and type of control and construction joints used in the floor slab to ensure no interruption in load transfer, yet still allowing the slab to move. In addition, a vapor barrier should not be used under the slab.
Vcp = kcp Ncp where kcp = 1.0 for hef ≤ 2.5 in. and = 2.0 for hef > 2.5 in. Figure 3.5.3. Concrete breakout surfaces for group anchors.
30 / DESIGN GUIDE 1, 2ND EDITION / BASE PLATE AND ANCHOR ROD DESIGN