1

Steel Construction

Volume 9 February 2016 ISSN 1867-0520

Design and Research

– Single-span beams with semi-continuous beam/column joints – Pt. 1: constant EI – Circular hollow through plate connections – Lateral-torsional buckling of I-section beam-columns – Underpressure-induced deformations of steel tanks – Curtain wall under lateral actions at ULS/SLS – Extended stiffened end plate link-column connections – Connection ﬂexibility in bridge girders – Simple bridges

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The corporate headquarters of the Belgian mechanical engineering group, Cockerill Maintenance & Ingénierie in Seraing, blossoms through its golden champagne skin. In the course of the renovation of the former industrial warehouse to the company headquarters, the façade was clad with Novelis J57S® aluminium anodised in a golden champagne in order to create an innovative building housing more than 600 employees. The name “L’Orangerie” was chosen as a reminiscence of the Cockerill Castle’s history. In the 18th century, the Castle was known for its unique garden with exotic greenhouses and the orangery, supplying the court with fruit and vegetables (see p. A4). (© Novelis)

Steel Construction 1 Volume 9 February 2016, No. 1 ISSN 1867-0520 (print) ISSN 1867-0539 (online)

Articles 1

Matthias Braun, Job Duarte da Costa, Renata Obiala, Christoph Odenbreit Design of single-span beams for SLS and ULS using semi-continuous beam-to-column joints

16

Andrew Voth, Jeffrey Packer Circular hollow through plate connections

24

Harald Unterweger, Andreas Taras, Zoltan Feher Lateral-torsional buckling behaviour of I-section beam-columns with one-sided rotation and warping restraint

33

Jerzy Ziółko, Tomasz Mikulski, Ewa Supernak Deformations of the steel shell of a vertical cylindrical tank caused by underpressure

37

Barbara Gorenc, Darko Beg † Curtain wall façade system under lateral actions with regard to limit states

46

Akbar Pirmoz, Parviz Ahadi, Vahid Farajkhah Finite element analysis of extended stiffened end plate link-to-column connections

58

Czesław Machelski, Robert Toczkiewicz Effects of connection ﬂexibility in bridge girders under moving loads

Reports 67

Andreas Keil, Sven Plieninger, Sebastian Linden, Christiane Sander Simple Bridges

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A4

Products & Projects

Products & Projects

A shiny homage to the Belgian Orangery From the seed a former industrial warehouse growing into a modern, multifunctional corporate headquarter – the new central of Cockerill Maintenance & Ingénierie blooms through a golden facade of Novelis J57S®. The corporate headquarters of the Belgian mechanical engineering group, Cockerill Maintenance & Ingénierie in Seraing, blossoms through its golden champagne skin. In the course of the renovation of the former industrial warehouse to the company headquarters, the facade was clad with Novelis J57S® aluminium anodised in a golden champagne in order to create an innovative building housing more than 600 employees.

Capacity for innovations The name “L’Orangerie” was chosen in conjunction with the corporate values of CMI. In the 18th century, the Cockerill Castle was known for its unique garden with exotic greenhouses and the orangery, supplying the court with fruit and vegetables. It is said that the existence of the garden was threatened by the war in 1784, so the gardener, Mr. Englebert, had to defend it with his heart and soul. Following this model, CMI intended to take that emotion with the new building, strengthening its values and generating capacity for innovations – a homage to the Belgian Orangery. For the design of the headquarters which has around 6,500 m² of façade surface, the architect, Nina Ghorbal, of Reichen et Robert Associate, Paris, chose Novelis J57S® in anodising quality for a high-quality aluminium surface with metallic brilliance and consistency of colour and gloss levels. Particularly noticea-

Fig. 3. Creative constructive ideas

(© 1 u. 3 Desmoulins, 2 Novelis)

ble is the three-dimensional cladding. The combination of glass elements and batch-anodised aluminium in 2.0 mm thickness with the J57S® in a golden champagne colour, provides a lively play of natural light and shadow. A second layer of suspended, perforated aluminium in the same color provides a visual highlight due to the reﬂection from the exterior façade. The weather-resistant properties of the anodised aluminium, in this instance processed by Metal Yapi (Istanbul), has already proved itself globally for both interior and exterior architectural projects.

High load capacity

Fig. 1. A lively play of natural light and shadow

Fig. 2. A visual highlight due to the reﬂection from the exterior façade

A4

Steel Construction 9 (2016), No. 1

Additionally, the team of architects had creative constructive ideas for the construction of the building too. The combination of unalloyed and thermodynamic steel for the basic structure enabled a highly durable construction of lattice girders with a high load capacity. With a large span width of some 35 m, the construction was prepared for installation in a nearby production hall which meant the steel girders had to be transported by crossing the river Meuse to the site where they were installed onto the building complex. An exposed atrium in the outdoor area as well as an overhanging building edge, underline the modern architectural style and this is demonstrated with the large structural dimensions and intelligent use of space. Thus the innovative building complex provides capacities for a reception, meeting rooms, an auditorium and a company restaurant which is all contained within this inspiring facade, emphasizing and promoting the character of CMI.

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Products & Projects

Roof and facade made from innovative ﬂat steel The extension of the museum of technology in Freudenberg marks the ﬁrst time that not just the roof but also a facade has been constructed with press-braked panels made of the innovative ﬂat steel. The modern extension forms an interesting contrast to the existing historical timber-framed building – making the museum a real eye-catcher. The facade is

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But why Pladur StandingSeam? “There were several reasons for choosing the steel facade and steel roof,” says architect Berthold Strauch from architectural ﬁrm Hein & Helsper. “Aesthetics were one factor: The matt panels have a beautiful elegant appearance. Then there’s the cost-effectiveness and durability of Pladur StandingSeam, meaning it’s a long time before any maintenance is required. And ﬁnally the ventilated facade and standing seam roof enabled us to meet thermal insulation requirements in an optimum way.” Local links were another consideration: There are many steel processing companies in the Siegerland area – and Pladur StandingSeam was developed at ThyssenKrupp’s Kreuztal-Eichen site in the region. The steel exterior of the extension is also a perfect ﬁt with the exhibits inside the museum – many of which are made of or were used in the production of steel. For example, visitors can view a steam engine built in 1904 that was employed in the steel mills. The ﬂat steel is distributed by Netphen-based Wolfgang Fischer Stahl GmbH. “We fabricate Pladur StandingSeam exactly the way customers want,” says Wolfgang Fischer, managing partner of Fischer Stahl. “We respond to the speciﬁc requirements of architects and tradespeople.”

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Tiles, slates, thatch – all these are familiar roof materials. Building owners wanting something less conventional now have another alternative in the area of metal rooﬁng: steel, or to be more precise Pladur StandingSeam ﬂat carbon steel from ThyssenKrupp Steel Europe. This material oﬀers numerous advantages. “It looks elegant and unusual and is more cost-effective than most building materials thanks to its extreme longevity,” says Christian Lukas, an employee of ThyssenKrupp Steel Europe. To make the steel weather-resistant it is coated with a special zinc-magnesium alloy oﬀering outstanding corrosion protection. Color and texture are provided by a high-quality organic coating that protects the material from UV radiation, makes it scratch-resistant and adds to the anticorrosion properties of the zinc-magnesium coating.

grey and the roof anthracite, blending perfectly with the slate shingles of the timber-framed main building. Wolfgang Leh, the director of the museum, is extremely satisﬁed: “We would choose this material again every time.”

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Pladur StandingSeam ﬂat carbon steel from ThyssenKrupp Steel Europe offers numerous advantages – here at the new extension of the Museum of Technology in Freudenberg (© ThyssenKrupp)

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Contrasts between the old and the new often give buildings a particular charm. That’s deﬁnitely the case with the museum of technology in Freudenberg: The historical timber-framed building was recently ﬁtted with a modern extension. Both the roof and facade are made of ﬂat carbon steel from ThyssenKrupp Steel Europe. The advantages: The material is cost-eﬀective, long-lasting and gives the building an elegant appearance.

Structural Analysis and Design

Stability and Dynamics

Freudenberg museum of technology shines in elegant new steel exterior

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Products & Projects

Noise Protection Hangar for Airliners at Zurich Airport, Switzerland Regular maintenance and repairs of an aircraft includes performing aircraft engine testing. For the protection of residents in nearby communities, Flughafen Zürich AG (FZAG) commissioned the planning of a noise protection hangar which goes beyond the legal requirements for noise protection. The Dlubal customer WTM Engineers was in charge of this project, together with Suisseplan, Zurich, GAC German Airport Consulting as well as with LSB Gesellschaft für Lärmschutz and brought it to a successful conclusion in June 2014. WTM Engineers calculated the spatial supporting structure of the noise protection hangar statically with RSTAB and designed it with STEEL SIA according to the Swiss steel construction standard SIA 263.

Fig. 1 3D model of the noise protection hangar with visualized deformations

Fig. 2 Noise protection hangar during construction (© 1 Dlubal, 2 WTM Engineers)

The roof construction with an area of 5,200 m² is supported by an external steel construction consisting of both spatial and ﬂat trusses as well as support elements across a maximum span of 78.5 m. The hangar can accommodate aircraft up to the size of a Boeing 747-8 with a wing span of 68.5 m. The main supporting elements are two truss frames with ridge releases which span the whole hangar and support it in the trans-verse direction. The frames are restrained to foundation blocks on the support nodes. A truss girder spans the rear opening which is integrated into the gable wall. In the longitudinal direction, trusses are placed in the apex zone at the side walls of the enclosure which are attached to the main truss frames. They cantilever about 34 m to the top of the hangar. External spatial three-chord truss girders are linked to the main supporting structure to hold the trapezoidal cross-sections of the roof. With the noise protection hangar at the Zurich Airport, a building with appealing architecture has been created. www.dlubal.com

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A6

Steel Construction 9 (2016), No. 1

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Articles Matthias Braun* Job Duarte da Costa Renata Obiala Christoph Odenbreit

DOI: 10.1002/stco.201610007

Design of single-span beams for SLS and ULS using semi-continuous beam-to-column joints Part 1: Beams with constant bending stiffness and joints according to EN 1993-1-8 This article explains a method for determining how semi-continuous joints inﬂuence the deﬂection, natural frequency and bending moment distribution of single-span beams with constant inertia under uniformly distributed load. The method is adequate for simple hand calculations, allowing the structural engineer to assess potential savings already in the pre-design phase. Further, the economical potential of semi-continuous joints according to EN 1993-1-8 [1] is demonstrated by an application example.

1 Introduction Modern construction demands long-span structures that allow huge spaces free from columns, easily convertible for future use. Further, the structures have to be economic, which requires low material consumption and simple erection processes, and they have to be sustainable. To satisfy such demand for economic structures with long beam spans, ﬂoor beams need a high loadbearing resistance and stiﬀness. The utilization of high-strength steel grades fulﬁls the requirement of a high loadbearing resistance, but it does not improve the bending stiﬀness. It is the activation of a composite action between steel beam and concrete slab that increases the beam stiﬀness signiﬁcantly [2], [3]; further optimization of the ﬂoor beam cross-section can be achieved by using semi-continuous beam-to-column joints. Semi-continuous joints inﬂuence the distribution of the bending moment along the beam, leading to the desired decrease in the beam deﬂection and increase in the natural frequency of the beam in comparison with simple, hinged beam-to-column joints. Design rules for semi-continuous beam-to-column joints in steel are given in [1]. Standard design software allows the moment–rotation characteristic of the joint to be quickly determined. But to assess the inﬂuence of those joints on the beam behaviour at ULS and SLS, the moment–rotation characteristic has to be implemented in the global analyses, which requires additional eﬀort by the structural engineer. This article gives formulae that allow easy determination of the inﬂuence of semi-continuous joints on the beam

* Corresponding author: mathias.braun@arcelormittal.com

deﬂection, natural frequency and distribution of the internal forces in a single-span ﬂoor beam with constant bending stiﬀness and subjected to a uniformly distributed load. The formulae derived can help engineers, practitioners and students to reach a better understanding of the inﬂuence of semi-continuous joints on the beam behaviour at ULS and SLS. The analytical equations given were used to determine factors, thus allowing quick, easy and safe application. Further contributions are planned, covering the use of semi-continuous joints for beams with partially constant stiﬀness (composite beams) and composite beam-to-column joints.

2 Global analysis In a global analysis, the eﬀects of the behaviour of the joints on the distribution of internal forces within a structure, and on the overall deformations of the structure, should generally be taken into account. However, as these eﬀects are suﬃciently small for nominally pinned and rigid/full-strength joints, they may therefore be neglected. Three basic methods of global analysis exist: Elastic global analysis The distribution of the internal forces within the structure only depends on the stiﬀness of the members in the structure. Therefore, joints should be classiﬁed according to their stiﬀness. In the case of a semi-rigid joint, the rotational stiﬀness Sj corresponding to the bending moment Mj,Ed should generally be used in the analysis. As a simpliﬁcation, the rotational stiﬀness may be taken as Sj,ini/M in the analysis for all values of the moment Mj,Ed f Mj,Rd, where a value of 2.0 for the stiﬀness modiﬁcation coeﬃcient M can be used for typical beam-to-column joints. For other types of joint, see Table 5.2 in [1]. If Mj,Ed does not exceed 2/3 of Mj,Rd, the initial rotational stiﬀness Sj,ini may be used in the global analysis. Rigid–plastic global analysis Using rigid–plastic global analysis, the distribution of the internal forces within the structure only depends on the strength of the members in the structure. Therefore, joints should be classiﬁed according to their strength. The rotational capacity of a joint should be suﬃcient to accommodate the rotations resulting from the analysis.

© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Steel Construction 9 (2016), No. 1

1

M. Braun/J. Duarte da Costa/R. Obiala/C. Odenbreit · Design of single-span beams for SLS and ULS using semi-continuous beam-to-column joints

provided that the approximate curve lies entirely below the design moment–rotation characteristic.

Mj Mj,Rd

3 Economical structures with semi-continuous joints

Sj,ini/η

As shown in section 2, the type of beam-to-column joint has a signiﬁcant inﬂuence on the distribution of the internal forces along the beam and, consequently, on the beam design. Whereas nominally pinned beam-to-column joints lead to a higher bending moment at mid-span, they are popular in buildings due to their low fabrication cost. A comparison of the bending moments for simple, hinged beam-to-column joints with fully rigid joints is given in Fig. 2. The rotational stiﬀness of the semi-continuous joint is represented at its adjacent support A and B by a rotational spring Sj,A and Sj,B respectively. As shown, fully rigid joints reduce the bending moment at mid-span by a factor of three by creating a bending moment at the supports. Hence, they lead to a more economic distribution of the internal forces along the beam span, enabling the use of a smaller beam section and thus reducing material consumption and costs. On the other hand, however, the fabrication costs for fully rigid joints are much higher than that for pinned joints. The economic optimum between fabrication and material costs is achieved by using semi-continuous joints, see Fig. 3. Semi-continuous joints allow for the transmission of a bending moment via the joint and for a certain rotation of the joint, which – compared with rigid joints – leads to a higher bending moment at mid-span, requiring a bigger beam section. But they are much more economic than rigid joints. An optimum (" minimum total cost) has to be calculated for each structure individually.

ϕj ϕCd

Fig. 1. Simpliﬁed bi-linear design moment–rotation characteristic for elastic–plastic global analysis

Elastic–plastic global analysis The distribution of the internal forces within the structure depends on the stiﬀness and strength of the structural members. Therefore, joints should be classiﬁed according to both stiﬀness and strength. The moment–rotation characteristic of the joints should be used to determine the distribution of internal forces. As a simpliﬁcation to the non-linear moment–rotation behaviour of a joint, a bi-linear design moment–rotation characteristic may be adopted, see Fig. 1. For the determination of the stiﬀness coeﬃcient M, see Table 5.2 in [1]. The appropriate type of joint model should be determined from Table 1, depending on the classiﬁcation of the joint and on the chosen method of analysis. The design moment–rotation characteristic of a joint used in the analysis may be simpliﬁed by adopting any appropriate curve, including a linearized approximation (e.g. bi- or tri-linear), Table 1. Type of joint model for global analysis according to [1] Method of global analysis

Classiﬁcation of joint

Elastic

Nominally pinned

Rigid

Semi-rigid

Rigid-Plastic

Nominally pinned

Full-strength

Partial-strength

Elastic-Plastic

Nominally pinned

Rigid and full-strength

Semi-rigid and partial-strength Semi-rigid and full-strength Rigid and partial-strength

Type of joint model

Simple

Continuous

Semi-continuous

Structural System

Bending Moment Distribution Sj,A

Sj,A= Sj,B= 0 → hinged joint

Sj,B

q = const. Sj,B

Sj,A

MEd = 3 qL2/24 L EI=constant

MEd = - 2 qL2/24 Sj,A

Sj,A= Sj,B= ∞ → rigid joint MEd = qL2/24

Fig. 2. Bending moment distribution for nominally pinned and rigid joints

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Steel Construction 9 (2016), No. 1

Sj,B

M. Braun/J. Duarte da Costa/R. Obiala/C. Odenbreit · Design of single-span beams for SLS and ULS using semi-continuous beam-to-column joints

Cost K

Sj,ini ≥ Kb EIb/Lb

Mj Rigid

Total cost

Semi - rigid

Fabrication cost

Sj,ini Material cost hinge

Joint stiffness

Fig. 3. Total cost as a function of the joint stiﬀness according to [4]

Mj

Stiffness boundaries Initial rotational stiffness

Fig. 5. Classiﬁcation of beam-to-column joints by stiﬀness

where: Kb " 8 for frames where the bracing system reduces the horizontal displacement by at least 80 % E elastic modulus of beam material Ib second moment of area of beam Lb beam span (distance between centres of supporting columns)

Sj,ini

Mj,Rd Mj

Sj,ini ≤ 0.5 EIb/Lb ϕj

rigid Kopt

Pinned

2/3 Mj,Rd

Sj

ϕj ϕXd

ϕCd

Fig. 4. Design moment–rotation characteristic for a joint

4 Joint design according to EN 1993-1-8 4.1 Design moment–rotation characteristic of a joint A joint is classiﬁed using its design moment–rotation curve, which is characterized by its rotational stiﬀness Sj, its design moment resistance Mj,Rd with corresponding rotation KXd and its design rotational capacity KCd, see Fig. 4. – The rotational stiﬀness Sj is the secant stiﬀness as indicated in Fig. 4. The deﬁnition of Sj applies up to the rotation KXd at which Mj,Ed ﬁrst reaches Mj,Rd. The initial stiﬀness Sj,ini is the slope of the elastic range of the design moment–rotation characteristic. – The design moment resistance Mj,Rd is equal to the maximum moment of the design moment–rotation characteristic. – The design rotation capacity KCd is equal to the maximum rotation of the design moment–rotation characteristic.

Nominally pinned joints transmit the internal forces without developing signiﬁcant moments and they should be capable of accepting the resulting rotations under the design loads. For rigid joints it is assumed that their rotational behaviour has no signiﬁcant inﬂuence on the distribution of internal forces. Semi-rigid joints have a rotational stiﬀness that allows the transmission of a moment based on their design moment–rotation characteristic and their initial joint stiﬀness Sj,ini, see Fig. 5. Classiﬁcation by strength According to its strength, a joint may be classiﬁed as fullstrength, nominally pinned or partial-strength by comparing its design moment resistance Mj,Rd with the design moment resistance of the members it connects, see Fig. 6. Nominally pinned joints transmit the internal forces without developing signiﬁcant moments and should be capable of accepting the resulting rotations under the design loads. A joint may be classiﬁed as nominally pinned if its design moment resistance Mj,Rd is not greater than 0.25 times the design moment resistance required for a full-strength joint, provided it also has suﬃcient rotational capacity. A joint may be classiﬁed as full-strength if it meets the criteria given in Fig. 6. A joint may be classiﬁed as a partial-strength joint if it does not meet the criteria for a full-strength or a nominally pinned joint.

Rules for calculating those values are given in [1].

4.2 Classiﬁcation of joints Joints may be classiﬁed by their rotational stiﬀness Sj,ini, their strength Mj,Rd and their rotational capacity KCd, see section 5.2 of [1] and Table 1. Classiﬁcation by stiﬀness Classifying a joint by its rotational stiﬀness is performed by comparing its initial rotational stiﬀness Sj,ini with the classiﬁcation boundaries given in Fig. 5.

Classiﬁcation by rotational capacity Using rigid–plastic global analysis and with the joint at a plastic hinge location, then for joints with a bending resistance Mj,Rd ! 1.2 times the design plastic bending moment Mpl,Rd of the cross-section of the connected member, the rotational capacity of the joint has to be checked. If the design resistance Mj,Rd of a bolted joint is not governed by the design resistance of its bolts in shear or the design resistance of the welds and local instability does not occur, it may be assumed to have adequate rotational capacity for plastic global analysis. For more details, see 6.4 of [1] and

Steel Construction 9 (2016), No. 1

3

M. Braun/J. Duarte da Costa/R. Obiala/C. Odenbreit · Design of single-span beams for SLS and ULS using semi-continuous beam-to-column joints

Mj

Full - strength Mj,Rd ≥ Mpl,Rd

Mpl,Rd Partial - strength 0.25 Mpl,Rd < Mj,Rd < Mpl,Rd Mj,Rd 0.25 Mpl,Rd Pinned

Mj,Rd ≤ 0.25 Mpl,Rd

Strength boundaries Joint moment resistance

ϕj

a) Top of column Mj,Rd

Either Mj,Rd ≥ Mb,pl,Rd or Mj,Rd ≥ Mc,pl,Rd

b) within column height

Mj,Rd

Either Mj,Rd ≥ Mb,pl,Rd or Mj,Rd ≥ 2 Mc,pl,Rd

Mb,pl,Rd is the design plastic moment resistance of a beam Mc,pl,Rd is the design plastic moment resistance of a column Fig. 6. Classiﬁcation of joints by strength

[5]. The rules given in [1] are valid for steel grades S235, S275 and S355 and for joints for which the design value of the axial force NEd in the connected member does not exceed 5 % of the plastic design resistance Npl,Rd of its cross-section.

4.3 Simpliﬁed prediction of the initial joint stiffness The rotational stiﬀness of a joint can be calculated with the rules given in section 6.3 of [1]. But to apply them, the joint ﬁrst has to be deﬁned, which requires knowledge about the distribution of the internal forces in the structure and especially at the positions of the joints. As the stiﬀness of the joint inﬂuences the distribution of the internal forces, the aforementioned process for determining the internal forces and the joint design is iterative. This process could be simpliﬁed if the designer could assess the initial joint stiﬀness adequately before the distribution of the internal forces is calculated, or at least when the basic dimensions of the sections are known. A method described in [6] allows the initial stiﬀness of a joint to be assessed, which can be used in the preliminary design phase using simpliﬁed formulae. The designer can determine the stiﬀness of a joint just by selecting the basic joint conﬁguration and taking account of some ﬁxed choices regarding the connection detailing, e.g. for endplate connections: – The connection has only two bolt rows in tension. – The bolt diameter is approx. 1.5 times the column ﬂange thickness.

4

Steel Construction 9 (2016), No. 1

– The location of the bolt is as close as possible to the root radius of the column ﬂange, the beam web and beam ﬂange (about 1.5 times the thickness of the column ﬂange). – The end-plate thickness is similar to the column ﬂange thickness. For other joint types see [6]. The approximate value of the initial joint stiﬀness Sj,app is expressed by

S j,app =

E ⋅ z2 ⋅ t fc C

(1)

where the values of C for diﬀerent joint conﬁgurations and loadings are given in Table 2, parameter z is the distance between the compression and tensile resultants and tfc is the column ﬂange thickness. After calculating the distribution of the internal forces in the structure using Sj,app, it is necessary to check if this assumption was adequate. Fig. 7 shows the upper and lower boundaries for semi-continuous joints in braced frames. If the re-calculated value of Sj,ini is within the given boundaries, the diﬀerence between stiﬀness Sj,app and Sj,ini aﬀects the frame’s loadbearing capacity by no more than 5 %. If Sj,ini is not within the given boundaries, the calculation of the internal forces has to be repeated with an adapted joint stiﬀness.

5 Analytical investigations of the inﬂuence of semicontinuous joints on the behaviour of single-span beams 5.1 Assumptions The equations for estimating the inﬂuence of semi-continuous beam-to-column joints on the overall beam behaviour

Table 2. Approximate determination of joint stiﬀness Sj,app according to [6] Joints with extended, unstiﬀened end-plate

Factor C

Single sided, (G ~ 1)

13

Double sided, (G ~ 0)

7.5

Note: For the rare cases of double-sided joint conﬁgurations where G " 2 (unbalanced moments), the value of the factor C is obtained by adding 11 to the relevant value for symmetrical conditions (balanced moments).

(ULS – distribution of inner forces, SLS – deﬂection and natural frequency) are derived in this section. Based on the equations obtained, factors are determined which simplify the use of semi-continuous joints, see Tables 3, 4 and 5. The rotational restraints at supports are represented by Sj,A and Sj,B. The following assumptions were made, see Fig. 8: – single-span beam – constant bending stiﬀness EI – uniformly distributed constant load and uniform mass distribution – Euler-Bernoulli beam theory, shear deformations not considered – ﬁrst-order theory – only vertical, harmonic vibration – damping not considered – linear moment–rotation (Mj-Kj) relationship of rotational restraints

Fig. 7. Boundaries for discrepancy between Sj,app and Sj,ini for braced frames [6]

Table 3. Factors a and b for determining the maximum bending moment in the span and its position kA

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.50 0.50

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

0.10

1.45 0.51

1.40 0.50

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

0.20

1.40 0.52

1.35 0.51

1.30 0.50

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

0.30

1.35 0.53

1.30 0.52

1.25 0.51

1.20 0.50

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

0.40

1.31 0.53

1.25 0.53

1.20 0.52

1.15 0.51

1.10 0.50

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

0.50

1.26 0.54

1.21 0.53

1.15 0.52

1.10 0.52

1.05 0.51

1.00 0.50

Sym.

Sym.

Sym.

Sym.

Sym.

0.60

1.22 0.55

1.16 0.54

1.11 0.53

1.05 0.53

1.00 0.52

0.95 0.51

0.90 0.50

Sym.

Sym.

Sym.

Sym.

0.70

1.17 0.56

1.12 0.55

1.06 0.54

1.01 0.53

0.95 0.53

0.90 0.52

0.85 0.51

0.80 0.50

Sym.

Sym.

Sym.

0.80

1.13 0.57

1.07 0.56

1.02 0.55

0.96 0.54

0.91 0.53

0.85 0.53

0.80 0.52

0.75 0.51

0.70 0.50

Sym.

Sym.

0.90

1.08 0.58

1.03 0.57

0.97 0.56

0.92 0.55

0.86 0.54

0.81 0.53

0.75 0.53

0.70 0.52

0.65 0.51

0.60 0.50

Sym.

1.00

1.04 0.58

0.98 0.58

0.93 0.57

0.87 0.56

0.82 0.55

0.76 0.54

0.71 0.53

0.65 0.53

0.60 0.52

0.55 0.51

0.50 0.50

1.10

1.00 0.59

0.94 0.58

0.88 0.58

0.83 0.57

0.77 0.56

0.72 0.55

0.66 0.54

0.61 0.53

0.55 0.53

/

/

1.20

0.96 0.60

0.90 0.59

0.84 0.58

0.78 0.58

0.73 0.57

0.67 0.56

0.62 0.55

/

/

/

/

1.30

0.92 0.61

0.86 0.60

0.80 0.59

0.74 0.58

0.68 0.58

/

/

/

/

/

/

1.40

0.88 0.62

0.82 0.61

0.76 0.60

/

/

/

/

/

/

/

/

1.50

0.84 0.63

/

/

/

/

/

/

/

/

/

/

kB 0.00

a" b"

With M A = −

q ⋅ L2 q ⋅ L2 q ⋅ L2 ⋅ k A; MB = − ⋅ kB; max. MSpan = ⋅ a at x max = b ⋅ L 12 12 12

Steel Construction 9 (2016), No. 1

5

Table 4. Factors c and d for determining the maximum beam deﬂection and its position kA

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

5.00 0.50

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

0.10

4.80 0.50

4.60 0.50

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

0.20

4.60 0.51

4.40 0.50

4.20 0.50

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

0.30

4.40 1.35

4.20 0.51

4.00 0.50

3.80 0.50

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

0.40

4.20 0.51

4.00 0.51

3.80 0.51

3.60 0.50

3.40 0.50

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

0.50

4.01 0.52

3.80 0.51

3.60 0.51

3.40 0.51

3.20 0.50

3.00 0.50

Sym.

Sym.

Sym.

Sym.

Sym.

0.60

3.81 0.52

3.61 0.52

3.40 0.52

3.20 0.51

3.00 0.51

2.80 0.50

2.60 0.50

Sym.

Sym.

Sym.

Sym.

0.70

3.61 0.53

3.41 0.52

3.21 0.52

3.00 0.52

2.80 0.51

2.60 0.51

2.40 0.50

2.20 0.50

Sym.

Sym.

Sym.

0.80

3.42 0.53

3.21 0.53

3.01 0.52

2.81 0.52

2.60 0.52

2.40 0.51

2.20 0.51

2.00 0.51

1.80 0.50

Sym.

Sym.

0.90

3.22 0.54

3.02 0.53

2.81 0.53

2.61 0.53

2.41 0.52

2.21 0.52

2.00 0.52

1.80 0.51

1.60 0.51

1.40 0.50

Sym.

1.00

3.03 0.54

2.82 0.54

2.62 0.54

2.42 0.53

2.21 0.53

2.01 0.53

1.81 0.52

1.60 0.52

1.40 0.51

1.20 0.51

1.00 0.50

1.10

2.83 0.55

2.63 0.55

2.43 0.54

2.22 0.54

2.02 0.54

1.81 0.54

1.61 0.53

1.41 0.53

1.20 0.52

/

/

1.20

2.64 0.55

2.44 0.55

2.23 0.55

2.03 0.55

1.82 0.55

1.62 0.54

1.42 0.54

/

/

/

/

1.30

2.45 0.56

2.25 0.56

2.04 0.56

1.84 0.56

1.63 0.56

/

/

/

/

/

/

1.40

2.27 0.57

2.06 0.57

1.86 0.57

/

/

/

/

/

/

/

/

1.50

2.08 0.58

/

/

/

/

/

/

/

/

/

/

kB 0.00

c" d"

With max . w =

c q ⋅ L4 ⋅ at x w = d ⋅ L 384 E ⋅ I

5.2 Determination of bending moment distribution The bending moments at supports A and B can be expressed as follows:

For n q h and m q 0, then kA q 1.5 and kB q 0. This presents the standard case of a single-span beam with a hinged support on one side and rigid support on the other. q ⋅ L2 and MB " 0 is ob8

MA = −

q ⋅ L2 ⋅ kA 12

(2)

The well-known solution M A = − tained.

MB = −

q ⋅ L2 ⋅ kB 12

(3)

For a beam with rigid supports at both ends, then kA q 1.0 and kB q 1.0, and the solution is

where kA =

m+6 n+6 ; kB = m 12 n 12 m+ 4+4⋅ + n+4+4⋅ + n n m m

and n =

6

M A = MB = −

S j,A ⋅ L E ⋅I

;m=

S j,B ⋅ L E ⋅I

Steel Construction 9 (2016), No. 1

q ⋅ L2 . 12

The vertical support reaction A as a function of kA and kB can be expressed as follows: A=

q⋅L q ⋅L + ⋅ k A − kB 2 12

(

)

(4)

Table 5. Factor e for determining the natural frequency kA kB 0.00

e"

0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.00

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

1.02

1.04

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

0.20

1.04

1.07

1.09

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

0.30

1.07

1.09

1.12

1.15

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

0.40

1.09

1.12

1.15

1.18

1.22

Sym.

Sym.

Sym.

Sym.

Sym.

Sym.

0.50

1.12

1.15

1.18

1.22

1.25

1.30

Sym.

Sym.

Sym.

Sym.

Sym.

0.60

1.15

1.18

1.22

1.25

1.30

1.34

1.39

Sym.

Sym.

Sym.

Sym.

0.70

1.18

1.21

1.25

1.30

1.34

1.39

1.45

1.52

Sym.

Sym.

Sym.

0.80

1.21

1.25

1.29

1.34

1.39

1.45

1.52

1.59

1.68

Sym.

Sym.

0.90

1.25

1.29

1.34

1.39

1.45

1.52

1.59

1.68

1.79

1.91

Sym.

1.00

1.29

1.34

1.39

1.45

1.51

1.59

1.68

1.78

1.91

2.07

2.27

1.10

1.34

1.39

1.45

1.51

1.59

1.68

1.78

1.91

2.06

/

/

1.20

1.38

1.44

1.51

1.58

1.67

1.77

1.90

/

/

/

/

1.30

1.44

1.50

1.58

1.66

1.77

/

/

/

/

/

/

1.40

1.50

1.57

1.66

/

/

/

/

/

/

/

/

1.50

1.56

/

/

/

/

/

/

/

/

/

/

With f1 = e ⋅

E ⋅I π2 , with m = uniform mass ⋅ m 2 ⋅ π ⋅ L2

where a =

and the bending moment as a function of x:

()

M x = A ⋅ x + MA −

1 ⋅ q ⋅ x2 2

(5)

Using Eqs. (2) and (4) with Eq. (5), the following expression is derived for the bending moment as a function of x and the stiﬀness coeﬃcients kA and kB:

()

M x = −

q⋅L q⋅L ⋅x + ⋅ k A − kB ⋅ x 12 2

(

)

q ⋅ L2 1 ⋅ kA − ⋅ q ⋅ x2 12 2

()

(6)

⇒x=

q⋅L q⋅L + ⋅ k A − kB − q ⋅ x = 0 ⇒ 2 12

(

L L + ⋅ k A − kB 2 12

)

)

(

)

q ⋅ L2 ⋅a 12

2

− kA (10)

Values for factors a and b, as a function of stiﬀness coeﬃcients kA and kB, are given in Table 3.

5.3 Inﬂuence of semi-continuous joints on beam deﬂection

()

()

M x

(11)

E ⋅I

After applying Eq. (5) in place of M(x), Eq. (11) takes the following form:

()

(7)

()

1 ⋅ q ⋅ x2 2 1 1 −E ⋅ I ⋅ w′ x = A ⋅ ⋅ x 2 + M A ⋅ x − ⋅ q ⋅ x 3 + C1 6 2 1 2 1 3 −E ⋅ I ⋅ w x = A ⋅ ⋅ x + M A ⋅ ⋅ x 2 6 1 4 − ⋅ q ⋅ x + C1 ⋅ x + C 2 24

()

()

(8)

Using Eqs. (7) and (6), the maximum bending moment in the span MSpan can be expressed as max. MSpan =

)

−E ⋅ I ⋅ w′′ x = M x = A ⋅ x + M A −

Eq. (7) can be expressed in a dimensionless format: x 1 1 b= = + ⋅ k A − kB L 2 12

(

x max = b ⋅ L

w′′ x = −

(

)

The beam deﬂection is expressed by the well-known linear diﬀerential equation

The position of the maximum bending moment can be calculated with Me(x) " 0, which leads to M′ x = 0 ⇒

(

1 3 1 + ⋅ k A − kB + ⋅ k A − kB 24 2 2

(9)

(12)

Constants C1 and C2 are determined with the boundary conditions: 1 1 1 ⋅ A ⋅ L2 − ⋅ M A + ⋅ q ⋅ L3 ( ) 24 2 6 w ( x = 0) ⇒ C2 = 0 w x = L ⇒ C1 = −

Steel Construction 9 (2016), No. 1

7

q = const. Sj,B

Sj,A EI = constant

x

B

A L

Sj,B

Sj,A

Eq. (15) has three real solutions. The solution gives the position of the maximum beam deﬂection and can be expressed as a factor d. By using the now known position of the maximum vertical beam deﬂection with Eq. (14), the value of the maximum deﬂection can be calculated. Hence, the maximum vertical beam deﬂection w can be calculated using max. w =

c q ⋅ L4 ⋅ 384 E ⋅ I

(17)

w,v(x)

and the position of the maximum deﬂection with

x Fig. 8. Simply supported beam with rotational springs at the supports

xw = d ⋅ L

(18)

Pre-calculated values for factors c and d as a function of the stiﬀness coeﬃcients kA and kB are given in Table 4. Finally, the beam deﬂection as a function of the stiﬀness of the rotational springs is deﬁned as follows:

()

( (

()

) )

(

1 1 ⋅ A ⋅ x 3 − L2 ⋅ x + ⋅ M A ⋅ x 2 − L ⋅ x 2 6 1 4 3 − ⋅q⋅ x − L ⋅x 24

−E ⋅ I ⋅ w x =

)(

(

)

) (13)

1 1 ⋅ q ⋅ k A − kB + 6 ⋅ L ⋅ x 3 − L3 ⋅ x − 24 72 1 ⋅ q ⋅ k A ⋅ L2 ⋅ x 2 − L3 ⋅ x − ⋅ q ⋅ x 4 − L3 ⋅ x (14) 24

−E ⋅ I ⋅ w x =

(

)

(

)

5.4 Inﬂuence of semi-rigid joints on the natural frequency of the beam The natural frequency of the beam is of signiﬁcant interest for the structural engineer. Based on the diﬀerential equation of the harmonic vibration, a factor e, which allows a quick determination of the natural frequency, is given in Table 5. ⎛ x⎞ ⎛ x⎞ v x = C1 ⋅ cos ⎜ λ ⋅ ⎟ + C 2 ⋅ sin ⎜ λ ⋅ ⎟ ⎝ L⎠ ⎝ L⎠

()

⎛ x⎞ ⎛ x⎞ + C 3 ⋅ cosh ⎜ λ ⋅ ⎟ + C 4 ⋅ sinh ⎜ λ ⋅ ⎟ L ⎝ ⎠ ⎝ L⎠

The design value and position of the maximal vertical deﬂection is of key interest for the designer. It is derived from

()

()

v′ x =

()

1 −E ⋅ I ⋅ w′ x = ϕ x = 0 ⇒ A ⋅ ⋅ x 2 + M A ⋅ x 2 1 3 − ⋅ q ⋅ x + C1 = 0 6

(15)

This equation of the third order is solved by using the formulae from Cardan: ⎡L 3 ⎤ ϕ x = x 3 + x 2 ⋅ ⎢ ⋅ kB − k A − ⋅ L ⎥ 2 4 ⎣ ⎦

()

(

⎛ x⎞ ⎛ x⎞ λ ⎡ ⋅ ⎢ − C ⋅ sin ⎜ λ ⋅ ⎟ + C 2 ⋅ cos ⎜ λ ⋅ ⎟ L ⎣ 1 ⎝ L⎠ ⎝ L⎠ ⎛ x⎞⎤ ⎛ x⎞ + C 3 ⋅ sinh ⎜ λ ⋅ ⎟ + C 4 ⋅ cosh ⎜ λ ⋅ ⎟ ⎥ ⎝ L⎠⎦ ⎝ L⎠

()

v′′ x =

)

r

L3 L2 + x⋅ ⋅ kA + ⋅ 3 − 2 ⋅ k A − kB = 0 12 2

(

s

)

(16)

()

v′′′ x =

t

⎛ x⎞ ⎛ x⎞ λ2 ⎡ ⋅ ⎢ − C1 ⋅ cos ⎜ λ ⋅ ⎟ − C 2 ⋅ sin ⎜ λ ⋅ ⎟ 2 ⎝ L⎠ ⎝ L⎠ L ⎣ ⎛ x⎞ ⎛ x⎞⎤ + C 3 ⋅ cosh ⎜ λ ⋅ ⎟ + C 4 ⋅ sinh ⎜ λ ⋅ ⎟ ⎥ ⎝ L⎠ ⎝ L⎠⎦ ⎛ x⎞ ⎛ x⎞ λ3 ⎡ ⋅ ⎢C1 ⋅ sin ⎜ λ ⋅ ⎟ − C 2 ⋅ cos ⎜ λ ⋅ ⎟ 3 L ⎝ ⎠ ⎝ L⎠ L ⎣ ⎛ x⎞ ⎛ x⎞⎤ + C 3 ⋅ sinh ⎜ λ ⋅ ⎟ + C 4 ⋅ cosh ⎜ λ ⋅ ⎟ ⎥ L ⎝ ⎠ ⎝ L⎠⎦

(19)

(20)

(21)

(22)

Substituting x " y – r/3, the reduced form is obtained: 2 ⋅ r3 r ⋅ s 3 ⋅ s − r2 and q = y 3 + p ⋅ y + q = 0 with p = − +t 27 3 3 The discriminant D can be expressed as 3

⎛ p⎞ ⎛ q⎞ D=⎜ ⎟ +⎜ ⎟ ⎝ 3⎠ ⎝ 2⎠

2

For the given application range of the rotation (0 f x f L) and for the stiﬀness coeﬃcients kA and kB (0 f kA, kB f 1.5), the discriminant is always D f 0 and p ! 0. Therefore,

8

Steel Construction 9 (2016), No. 1

The constants are determined with the boundary conditions:

( ) v ( x = L) =

v x = 0 = 0 ⇒ C1 + C 3 = 0

(

0 ⇒ C1 ⋅ cos λ − cosh λ

)

+ C 2 ⋅ sin λ + C 4 ⋅ sinh λ = 0

(

– v′′ x = 0

)

S j,A ⋅ L n ⋅ C2 · v′ (x = 0) = 0 ⇒ 2 ⋅ C1 ⋅ λ + E ⋅I L S j,A ⋅ L + ⋅ C4 = 0 E ⋅I

+

M. Braun/J. Duarte da Costa/R. Obiala/C. Odenbreit · Design of single-span beams for SLS and ULS using semi-continuous beam-to-column joints HE320A S355

C30/37

m · v′ (x = L) = 0 ⇒ C1 ⋅ [λ ⋅ (cos λ + cosh λ) L S j,B ⋅ L ⋅ (sin λ + sinh λ)] + E ⋅I ⎡ ⎤ S j,B ⋅ L ⋅ cos λ ⎥ + C 2 ⋅ ⎢ λ ⋅ sin λ – E ⋅I ⎢⎣ ⎥⎦

220

310

40

a

130

)

350

(

– v′′ x = L –

⎡ S j,B ⋅ L ⎤ ⋅ cosh λ + λ ⋅ sinh λ ⎥ = 0 – C4 ⋅ ⎢ ⎢⎣ E ⋅ I ⎥⎦

25

Cofraplus 220

50

450x25, S355

25 50

300

a

[mm]

450

which leads to the following linear equation system: B · C = 0 mit

Section a-a:

⎞ ⎛ C ⎞ ⎟ ⎜ 1⎟ ⎟ und C = ⎜ C ⎟ ⎟ ⎜ 2⎟ ⎟ ⎜ C ⎟ ⎝ 4⎠ ⎠

Cofraplus 220

C30/37

b11 = cos λ – cosh λ

80 160

b12 = sin λ

beff = 750

b13 = sinh λ b21 = 2λ

220

⎛ b b b ⎜ 11 12 13 B = ⎜ b21 b22 b23 ⎜ ⎜ b b b ⎝ 31 32 33

130

(23)

[mm]

Fig. 9b. Application example – SFB cross-section with slab

b22 = b23 = n b31 = λ (cos λ + cosh λ) + m (sin λ + sinh λ) b32 = λ sin λ – m · cos λ b33 = – m cosh λ – λ sinh λ The equation system is solved if the determinant of matrix B " 0. The lowest value for Qi for which the above equation system is solved (the trivial solution Q " 0 is forbidden) is required. The determinant of matrix B is expressed with

( )

(

)

Det B = n · m · 1 − cos λ ·cosh λ + λ · n ·

(cosh λ ·sin λ − cos λ ·sinh λ ) + λ · m · (cosh λ ·sin λ − cos λ ·sinh λ ) + 2· λ 2 · sin λ ·sinh λ = 0

(24)

Solutions for Q as a function of stiﬀness coeﬃcients kA and kB are given in Table 5. The natural frequency can be calculated with f1 =

λ 2i E ⋅I E ⋅I π2 · = e⋅ ⋅ 2 2 m m 2⋅π ⋅L 2· π ·L

(25)

where m " uniformly distributed constant mass. q = const. Sj,B

Sj,A L=9m EI = constant

Fig. 9a. Application example – structural system and loading

Note: As Eq. (24) is non-algebraic, it had to be solved by numerical iteration. Therefore, the given values for the factor e are an approximation. The given factors a, b, c and d (described in the previous sections) are precise results, rounded to two digits.

6 Application example – single-span slim-ﬂoor beam with semi-continuous joints 6.1 Structural system and loading The use of semi-continuous joints using elastic–plastic global analysis is demonstrated for a single-span slim-ﬂoor beam (SFB) with a beam span L " 9.00m and a beam distance a " 8.10 m (axis-to-axis). The beam is loaded with a uniformly distributed constant load q, has a constant bending stiﬀness EI and it is symmetrically supported in an internal bay, see Fig. 9a. The SFB cross-section consists of an HE320A hot-rolled section in grade S355 and a welded bottom plate, see Fig. 9b. The SFB section has an inertia Iy " 39 560cm4 with zel,top " 23.445 cm (measured from top of upper ﬂange downwards); possible participation of the concrete is not taken into account. The slab consists of Cofraplus 220 metal decking with 13 cm in situ concrete [7]. It is shown that the use of semi-continuous joints leads to an economical beam design for the ultimate limit state (ULS) and to improved deﬂection and vibration behaviour of the beam at the serviceability limit state (SLS). Safety factors: LM0 " 1.00; LM1 " 1.00; LM2 " 1.25 Yield strength of hot-rolled section, HE320A, S355: fyd " 355 N/mm2 Yield strength of bottom plate, 450 w 25 mm, S355: fyd " 345 N/mm2

Steel Construction 9 (2016), No. 1

9

Elastic bending resistance of SFB cross-section: Mel,Rd =

fyd ⋅ I y zel,top

=

35.5 kN/cm 2 ⋅ 39560 cm 4 23.445 cm

c 310 − 2 ⋅ 15.5 − 2 ⋅ 27 225 = = t 9 9 = 25.0 < 58.58 = 72 ⋅

= 599 kNm Plastic bending resistance of SFB cross-section: Mpl,Rd " 732 kNm with zpl " 30.75 cm from top of upper ﬂange downwards (by hand calculation). The beam-to-column joints are realized as end-plate connections with a rotational stiﬀness Sj,A " Sj,B. Load assumptions: Cofraplus 220 with 13 cm concrete: gC220 " 4.29 kN/m2 Additional dead load: )g " 1.20 kN/m2 Self-weight of SFB with concrete encasement: gSFB " 1.82 kN/m 2.75 kN/m " 4.57 kN/m Dead load (slab beam, self-weight):

Σg k = [1.1 ⋅ 4.29 kN/m 2 ⋅ (8.10 − 0.45 + 2 ⋅ 0.05) m + 1.1 ⋅ 1.20 kN/m 2 ⋅ 8.10 m] + 4.57 kN/m = 51.83 kN/m

The additional load on the beam due to continuity of the slab – perpendicular to beam span – is taken into account by a factor of 1.10. Load combinations: Total characteristic load: Ek " qSLS " ¨gk qek " 51.83 kN/m " 18.17 kN/m " 70.0 kN/m Design load: Ed " qULS " 1.35 · ¨gk 1.50 · qek " 1.35 · 51.83 kN/m 1.50 · 18.17 kN/m " 97.2 kN/m

6.2 Section classiﬁcation Cross-section at mid-span – pure bending, positive bending moment: Upper ﬂange in compression:

=

c 235 = 7.32 < = t 355

(

0.5 ⋅ 300 − 9 − 2 ⋅ 27 15.5

)

235 118.5 = 7.65 < 8.14 = 10 ⋅ = 10 ⋅ ε ⇒ class 2 355 15.5

Web in compression:

Bottom plate lower ﬂange in compression:

(

)

c 0.5 ⋅ 300 − 9 − 2 ⋅ 27 118.5 = = 2.93 < 7.43 = t 25.0 + 15.5 40.5 235 = 9 ⋅ ε ⇒ class 1 355

¡ At the supports the SFB section is classiﬁed as a class 1 section, which can form a plastic hinge with the rotational capacity required from plastic analysis without a reduction in the resistance.

6.3 Semi-continuous beam-to-column joint The design of the joint is not presented in detail in this article. The joint can be designed using standard software or even by hand calculation; reference is made to [1]. The joint is designed as semi-continuous with an extended end plate, see Fig. 10. Both beam ends are connected symmetrically to the columns with end plates (Sj,A " Sj,B, n " m, kA " kB). The design moment–rotation characteristic of the joint is presented in Fig. 11a and was calculated according to [1]. The initial stiﬀness Sj,ini is within the boundaries for a semi-rigid joint (see also Fig. 5). Its design moment resistance Mj,Rd " 360 kNm is within the limits given in Fig. 6 for a partial-strength joint (0.25 · Mpl,Rd f Mj,Rd f Mpl,Rd with Mpl,Rd " Mb,pl,Rd " 732 kNm). Therefore the joint is classiﬁed as semi-rigid and partial-strength and is modelled in design as semi-continuous joint. 125 105.5 45

5 10 m 2 ⋅ψ + = 0.64 7 0 9 ⋅ 8.10 m 2

Reduced live load: qek " ¨qk · FA " 28.51 kN/m · 0.64 " 18.17 kN/m

9⋅ε = 9⋅

235 c 75 = = 3.00 < 7.43 = 9 ⋅ = 9 ⋅ ε ⇒ class 1 345 t 25

189

Reduction factor: α A =

¡ At mid-span the SFB section is classiﬁed as a class 2 section. A class 2 section can develop its plastic cross-sectional resistance, but has not enough rotational capacity to allow for a plastic hinge. Cross-section at supports – pure bending, negative bending moment: Edge of bottom plate in compression:

= 9⋅

Live load (category B1, oﬃce use, ^0 " 0.70): 2.00 kN/m2 Partitions: 1.20 kN/m2 ¨qk " 1.1 · (2.00 1.20) kN/m2 · 8.10 m " 28.51 kN/m

235 = 72 ⋅ ε ⇒ class 1 355

HE320A S355

6M30, 10.9 45 10

5

450x25 S355

10 450x300x20 S355

[mm]

Fig. 10. Application example – basic components of semi-continuous joint

10

Steel Construction 9 (2016), No. 1

For the following analysis of the SFB for SLS and ULS, a tri-linear approximation of the moment–rotation characteristic is used in accordance with 5.1.1(4) of [1], see Fig. 11b. It is divided into three areas: – An elastic area for a joint rotation Kj within the range 0 f Kj f Kj,el – A second area for a joint rotation Kj within the range Kj,el f Kj f KXd – A plastic area for a joint rotation Kj within the range KXd f Kj f KCd Note: Using Eq. (1) and Table 2 of section 4.3, an approximate joint stiﬀness Sj,app could be calculated as follows:

S j,app

(

E ⋅ z2 ⋅ t fc 210000 MN/m 2 ⋅ 0.307 m = = C 7.5

)

2

⋅ 0.0215 m

Calculation of qj,el 2 Up to a bending moment M j,Ed ≤ ⋅ M j,Rd , the initial joint 3 stiﬀness Sj,ini can be used in the calculation, see 5.1.2(3) in [1]. 2 2 ⋅ M j,Rd = ⋅ 360 kNm = 240 kNm 3 3 ⇒ S j,ini = 51.6 MNm/rad Using the equations given in section 5, it is possible to calculate the values for n " m and kA " kB: n=m =

S j,ini ⋅ L E ⋅I

= 5.59

= 56.7 MNm/rad = 56.7 kNm/mrad Based on the given SFB section, the structural system and the design moment–rotation characteristic (Fig. 11b), the corresponding load levels qj,el and qj,Rd are calculated for the joint rotations Kj,el and KXd.

k A = kB =

=

51.6 MNm/rad ⋅ 9.0 m 210000 MN/m 2 ⋅ 39560 ⋅ 10−8 m 4

[− ] rad

5.59 + 6 m+6 = 5.59 12 m 12 5.59 + 4 + 4 ⋅ m+ 4+ 4⋅ + + 5.59 5.59 n n

= 0.74

And using Eq. (2) we get qj,el:

Mj

(

q j,el ⋅ 9 m q j,el ⋅ L2 2 ⋅ M j,Rd = 240 kNm = ⋅ kA = 12 12 3

8 EIb / Lb = 73.8 kNm/mrad

Mj,Rd = 360 kNm 2/3 Mj,Rd = 240 kNm

)

2

⋅ 0.74

⇒ q j,el = 48.0 kN/m

Sj,ini = 51.6 kNm/mrad 0.5 EIb / Lb= 4.6 kNm/mrad

ϕj ϕCd

ϕXd = 20.9 mrad

Fig. 11a. Application example – design moment–rotation characteristic of semi-continuous joint

Calculation of qj,Rd For a bending moment Mj,Ed in the range 2 ⋅ M j,Rd < M j,Ed ≤ M j,Rd 3 we use the joint stiﬀness Sj,2 " 7.4 MNm/rad, see Fig. 11b.

Mj Mj,Rd = 360 kNm

ad m/mr N k 4 7. S j,2 =

Sj,2 =

qj,Rd = 110.0 kN/m

qEd= 97.2 kN/m

qSLS = 70.0 kN/m

Sj

,in i

=5 1.6 kN m/ mr ad qj,el= 48.0 kN/m

2/3 Mj,Rd = 240 kNm

Mj,Rd - 2/3 Mj,Rd ϕXd - ϕj,el

ϕj ϕj,el = 4.6 mrad "Elastic" (Area 1)

ϕj,SLS "Non-linear" (Area 2)

ϕj,Ed

ϕXd = 20.9 mrad

ϕCd

"Plastic"

Fig. 11b. Application example – tri-linear approximation of design moment–rotation characteristic

Steel Construction 9 (2016), No. 1

11

First, factors n2 " m2 and kA,2 and kB,2 have to be calculated: n2 = m2 =

S j,2 ⋅ L E ⋅I

= 0.80

k A,2 = kB,2 =

=

=

7.4 MNm/rad ⋅ 9.0 m 210000 MN/m 2 ⋅ 39560 ⋅ 10−8 m 4

represents a suﬃciently precise approximation of the real joint behaviour. Total characteristic load: E k = Σg k + q′k = 51.83 kN/m + 18.17 kN/m = 70.0 kN/m

[− ] rad

Load combination for beam deﬂection at mid-span:

m2 + 6 m 12 m2 + 4 + 4 ⋅ 2 + n2 n2

qSLS = 1.0 ⋅ Σg k + 1.0 ⋅ q′k = 1.0 ⋅ 51.83 kN/m + 1.0 ⋅ 18.17 kN/m = 70.0 kN/m

0.80 + 6 = 0.29 12 0.80 0.80 + 4 + 4 ⋅ + 0.80 0.80

Load combination for natural frequency: qHz = 1.0 ⋅ Σg k + 0.20 ⋅ q′k = 1.0 ⋅ 51.83 kN/m + 1.0 ⋅ 18.17 kN/m = 55.5 kN/m

Using Eq. (2) we get

M j,Rd −

2 ⋅ M j,Rd = 360 kNm − 240 kNm = 120 kNm 3

(

Δq ⋅ 9 m Δq ⋅ L2 = ⋅ kA = 12 12

)

Calculation of SFB deﬂection at mid-span: As shown in Fig. 11b, the load qSLS is in “area 2” (qj,el f qSLS " 70.0 kN/m f qj,Rd), so the deﬂection wSLS has to be calculated in two steps.

2

⋅ 0.29

Step 1 – deﬂection wel with qj,el: For kA " kB " 0.74, factor c is taken from Table 4: c " 2.04 (by linear interpolation). Deﬂection wel is calculated using Eq. (17):

⇒ Δq = 62.0 kN/m and q j,Rd = q j,el + Δq = 48.0 kN/m + 62.0 kN/m = 110.0 kN/m

⇒ w el

6.4 Beam design for SLS The total vertical beam deﬂection and the natural frequency of the SFB are determined by using the equations and tables in section 5. In the absence of a more precise method for deﬁning the joint stiﬀness, the tri-linear design moment–rotation characteristic of Fig. 11b is used, which

(

)

4

4 −2 c q j,el ⋅ L 2.04 48.0 ⋅ 10 kN/cm ⋅ 900 cm = ⋅ = ⋅ 384 E ⋅I 384 21000 kN/cm 2 ⋅ 39560 cm 4

= 2.01 cm Step 2 – additional deﬂection )w with )qSLS: Taking the load )qSLS " qSLS – qj,el " 70 kN/m – 48 kN/m " 22 kN/m, a deﬂection )w is calculated using the joint stiﬀness Sj,2 " 7.4 kNm/mrad, see Fig. 11b.

Mj Mj,Rd Mj,Hz = 254.5 kNm Sj,Hz =

S

j,H

z

=

38

qHz = 55.5 kN/m

.5

kN /m

2/3 Mj,Rd

Mj,Hz ϕj,Hz

ϕj ϕj,el

ϕj,Hz = 6.6 mrad

ϕXd

Fig. 12. Application example – idealized joint stiﬀness for vibration analysis Sj,Hz

12

Steel Construction 9 (2016), No. 1

ϕCd

With kA,2 " kB,2 " 0.29, factor c2 is determined with Table 4: c2 " 3.84 (by linear interpolation). A deﬂection )w is calculated using Eq. (17):

nHz = mHz = =

Δq ⋅ L4 c ⇒ Δw = 2 ⋅ SLS 384 E ⋅I

(

)

= 1.74 cm

38.5 MNm/rad ⋅ 9.0m [− ] = 4.17 rad 210000 MN/m 2 ⋅ 39560 ⋅ 10−8 m 4

=

which leads to the following total vertical deﬂection of the SFB at mid-span: wSLS " wel )w " 2.01 cm 1.74 cm " 3.75 cm ~ L/240 ! L/200 ¡ The deﬂection is within acceptable limits. Note: With simple, hinged beam-to-column joints, the beam deﬂection at mid-span would be:

(

)

4

−2 5 qSLS ⋅ L4 5 70 ⋅ 10 kN/cm ⋅ 900 cm ⇒w = ⋅ = ⋅ 384 E ⋅I 384 21000 kN/cm 2 ⋅ 39560 cm 4

which is 1.92 times the deﬂection of the semi-continuous beam! A basic assumption of the calculation of the beam deﬂection is an elastic material behaviour; the strains in the cross-section do not exceed the yield strain. To verify this assumption, the bending moment of the joint Mj,SLS at SLS and the bending moment at mid-span MSLS are calculated and compared with the elastic bending resistance of the SFB cross-section:

12

⋅ kA +

4.17 + 6 = 0.68 4.17 12 + 4.17 + 4 + 4 ⋅ 4.17 4.17

From Table 5 we obtain e " 1.49 (by linear interpolation). Using Eq. (25), the natural frequency can be calculated as follows: f1 = e ⋅

π2 E ⋅I π2 ⋅ = 1.49 ⋅ 2 m 2⋅π ⋅L 2⋅π⋅ 9 m

(

)

2

·

21000 kN/m 2 ⋅ 39560 cm 4 ⋅ 10−4 55.5 kN/m/9.81 m/s2

(

22 kN/m ⋅ 9 m 2 = ⋅ 360 kNm + 12 3

)

2

⋅ 0.29

= 240 kNm + 43 kNm = 283 kNm

(

The value of 2.60 Hz as a minimum acceptable natural frequency of the ﬂoor beams is found in [8]. Even though the natural frequency is commonly used to assess ﬂoor vibrations, the authors recommend using more precise methods that take into account the natural frequency of the whole ﬂoor and its modal mass. For further information see [9] and [10]. Note: With simple, hinged beam-to-column joints, the natural frequency of the SFB would be only 2.35 Hz!

6.5 Beam design for ULS

ΔqSLS ⋅ L2 ⋅ k A,2 12

ΔqSLS ⋅ L2 2 = ⋅ M j,Rd + ⋅ k A,2 3 12

MSLS =

mHz + 6 m 12 mH2 + 4 + 4 ⋅ Hz + nHz nHz

= 3.50 Hz > 2.60 Hz

= 7.20 cm,

q j,el ⋅ L2

E ⋅I

k A,Hz = kB,Hz =

4

−2 3.84 22.0 ⋅ 10 kN/cm ⋅ 900 cm = ⋅ 384 21000 kN/cm 2 ⋅ 39560 cm 4

M j,SLS =

S j,Hz ⋅ L

70 kN/m ⋅ 9 m qSLS ⋅ L2 − M j,SLS = 8 8

)

Design checks for bending and shear with semi-continuous joints Based on the simpliﬁed tri-linear design moment–rotation characteristic given in Fig. 11b and a design load level qj,el ! qEd " 97.2 kN/m ! qj,Rd, the bending moment at the joint Mj,Ed and the one at mid-span MEd are calculated as follows:

2

− 283 kNm

M j,Ed =

= 426 kNm < Mel,Rd = 599 kNm = ¡ The SFB cross-section remains fully elastic at SLS, the assumption is correct. Calculation of the natural frequency of the SFB The natural frequency of the SFB is determined based on the equations in section 5. The load qHz is in “area 2” (qj,el f qHz " 55.5 kN/m f qj,Rd), and so an idealized joint stiﬀness Sj,Hz is used, see Fig. 12. For q Hz, the corresponding values of the joint rotation +j,Hz and the bending moment M j,Hz are: +j,Hz " 6.6 mrad and M j,Hz " 254.5 kNm ¡ Sj,Hz " Mj,Hz/+j,Hz " 254.5 kNm / 6.6 mrad " 38.5 kNm/mrad

q j,el ⋅ L2 12

⋅ kA +

(

(q

48 kN/m ⋅ 9 m 12

)

Ed

12

⋅ k A,2

2

⋅ 0.74

( 97.2 − 48) kN/m ⋅ ( 9 m ) + 12

)

− q j,el ⋅ L2

2

⋅ 0.29

= 240 kNm + 96 kNm = 336 kNm < M j,Rd

MEd

(

97.2 kN/m ⋅ 9 m q ⋅ L2 = Ed − M j,Ed = 8 8

)

2

− 336 kNm

= 984 kNm − 336 kNm = 648 kNm

Steel Construction 9 (2016), No. 1

13

336 kNm

984 kNm

648 kNm 9.00m Fig. 13. Application example – bending moment distribution for ULS

4M20, 8.8

Table 6. Application example – cost comparison: simple joints vs. semi-continuous joints Joint Type / Component

Simple

Semi-continuous

Cost Diﬀerence* €/SFB

Hot Rolled Section (Grade S355)

HE280M

HE320A

– 480 €

Weld size (Endplate to ﬂanges only)

5 mm

10 mm

100 €

Endplate (Grade S355)

300 w 300 w 20

450 w 300 w 20

20

Bolts

4 M 20, 8.8

6 M 30, 10.9

60 €

S355

5

Total )Cost:

5

450x25 S355

– 300 €

¡ Beam Design with semi-continuous joints is 300 € cheaper (per 9 m SFB)! * Estimated cost based on 2015 price level, including erection.

300x300x20 S355

[mm]

Fig. 14. Application example – nominally pinned joint conﬁguration

which leads to the bending moment distribution presented in Fig. 13. Veriﬁcation of the SFB cross-section for bending at midspan: MEd = 648kNm ≤ Mpl,Rd = 732 kNm ⇒ Verification is fulfilled! Note: With simple beam-to-column joints, the bending moment at mid-span MEd would exceed the bending resistance Mpl,Rd of the cross-section: MEd = 984 kNm > Mpl,Rd = 732 kNm! Veriﬁcation of the SFB cross section at the supports: Bending: M j,Rd = 336 kNm ≤ Mpl,Rd = 732 kNm Shear: VEd = qEd ⋅ L/2 = 97.2 kN/m ⋅ 9 m/2 = 437.4 kN ≤ Vpl,Rd = =

A vz 3

⋅ fyd

41.13 cm 2 ⋅ 35.5 kN/cm 2 = 843 kN 3

¡ Veriﬁcation is fulﬁlled! With a load ratio VEd/Vpl,Rd " 437.4 kN/843 kN " 0.52 # 0.50, the bending resistance has to be reduced due to the presence of a shear force. According to 6.2.8 of [11], this may be done by reducing the yield strength of the shear area by

14

Steel Construction 9 (2016), No. 1

2 ⎡ ⎛ ⎞ ⎤ 2 ⋅ VEd fyd,V = ⎢⎢1 − ⎜ − 1⎟ ⎥⎥ ⋅ fyd V ⎠ ⎥ ⎢⎣ ⎝ pl,Rd ⎦ 2 ⎡ ⎛ ⎞ ⎤ 2 ⋅ 437.4 kN = ⎢1 − ⎜ − 1⎟ ⎥ ⋅ 35.5 kN/cm 2 ⎠ ⎥ ⎢ ⎝ 843 kN ⎦ ⎣

= 35.45 kN/cm 2 As this reduction in the yield strength is ! 1 %, it is neglected in this example. The SFB cross-section is not plastiﬁed at the supports. At mid-span it is partially plastiﬁed, but there is still no development of a plastic hinge; therefore, the classiﬁcation of the cross-section in class 2 is suﬃcient for the chosen design method. Rotational capacity of the joint Elastic–plastic global analysis was used in the given example. The joint is not located at the position of a plastic hinge, and the acting design moment does not reach the value of the design moment resistance, Mj,Ed ! Mj,Rd. Therefore, the rotation KEd does not reach KXd and the rotational capacity of the joint does not have to be checked.

6.6 Economic evaluation of semi-continuous joints This section compares the cost of the SFB designed with semi-continuous joints with a beam design using simple joints. The design of the simply supported SFB was carried out with the software [12] and was based on the same assumptions as the design of the semi-continuous SFB (same load assumptions and L " 9.0 m, a " 8.10 m, hSlab " 350 mm). The basic components of the simple joint are shown in Fig. 14. The cost diﬀerence for the basic components is presented in Table 6. Only the direct costs of the non-identical parts are given; the possible inﬂuence of the joint design on the foundations, columns etc. was not taken into account.

7 Conclusion and outlook This article outlines the advantage of semi-continuous beam-to-column joints for the design of single-span beams (with constant inertia and subjected to a uniformly distributed constant load) at ULS and SLS. Factors for use in combination with standard design formulae were derived analytically. They allow the structural engineer to determine the inﬂuence of the joint stiﬀness on the beam deﬂection, its natural frequency and the distribution of the bending moment quickly and easily. Further, the application is shown in a design example for a slim-ﬂoor beam (SFB), which shows the economic potential of semi-continuous joints. Overall, such joints lead to a more economic, more sustainable structure. The inﬂuence of semi-continuous joints on the design of single-span beams with partially constant inertia will be investigated in a second article. References [1] CEN/TC250: Eurocode 3: Design of steel structures – Part 1-8: Design of joints, European Commission. [2] Braun, M., Hechler, O., Obiala, R.: Untersuchungen zur Verbundwirkung von Betondübeln. Stahlbau, 83 (2014), No. 5. DOI:10.1002/stab.201410154 [3] Deutsches Institut für Bautechnik: Allgemeine bauaufsichtliche Zulassung – CoSFB-Betondübel. ArcelorMittal Belval & Diﬀerdange S.A., approval No. Z-26.4-59, Berlin, 2014. [4] Ungermann, D., Weynand, K., Jaspart, J.-P., Schmidt, B.: Momententragfähige Anschlüsse mit und ohne Steifen. Stahlbau-Kalender 2005, Kuhlmann, U. (ed.), Ernst & Sohn, Berlin, ISBN 3-433-01721-2. [5] Jaspart, J.-P., Demonceau, J.-F.: European Design Recommendations for simple joints in steel structures. ArGEnCo Dept., Liège University. [6] Maquoi, R., Chabrolin, B.: Frame Design including joint behaviour. European Commission, contract No. 7210SA/212/320, 1998.

[7] Deutsches Institut für Bautechnik: Allgemeine bauaufsichtliche Zulassung – ArcelorMittal Systemdecke Cofraplus 220, approval No. Z-26.1-55, Berlin, 2013. [8] AFNOR: National annex to NF EN 1993-1-1, Eurocode 3: Design of steel structures – Part 1-1: General rules and rules for buildings. [9] Sedlacek, G., et al.: Generalization of criteria for ﬂoor vibrations for industrial, oﬃce, residential and public building and gymnastic halls. European Commission, ﬁnal report, 2006, EUR 21972 EN, ISBN 92-79-01705-5. [10] Hicks, S., Peltonen, S.: Design of slim-ﬂoor construction for human induced vibrations. Steel Construction, 8 (2015), No. 2. DOI:10.1002/stco.201510015 [11] CEN/TC250: Eurocode 3: Design of steel structures – Part 1-1: General rules and rules for buildings, European Commission. [12] CTICM France, ArcelorMittal R&D: ArcelorMittal Beam Calculator (ABC), version 3.30, ArcelorMittal Belval & Diﬀerdange S.A. http://sections.arcelormittal.com/download-center/design-software.html Keywords: semi-continuous steel beam-to-column joints; global analysis; approximate determination of the joint stiﬀness; economical design; slim-ﬂoor construction

Authors: Matthias Braun ArcelorMittal Europe – Long Products 66, rue de Luxembourg L-4009 Esch-sur-Alzette, Luxembourg Job Duarte da Costa Renata Obiala Christoph Odenbreit University of Luxembourg, FSTC ArcelorMittal Chair of Steel & Façade Engineering 6, rue de Richard Coudenhove Kalergi L-1359 Luxembourg, Luxembourg

News European design standards widespread in the building sector According to a new study of the EU’s Joint Research Centre (JRC), 23 out of the 28 EU countries, as well as Norway, have implemented the European Technical Standards (Eurocodes) for buildings and other civil engineering works, which have become national standards. The study also recommends speeding up their adoption or removing the legal restrictions that prevent their implementation in the remaining five countries, hence boosting the competitiveness of the industry and increasing the safety of the built environment. The JRC has played

an important role in the development and implementation of the Eurocodes. Malta, Portugal and Spain should speed up the adoption of country-speciﬁc values and procedures and their publication in the so-called national annexes, while Italy and Romania should remove the legal restrictions preventing the implementation of the Eurocodes. The report also ﬁnds that issuing a Commission Recommendation on the regulatory environment would facilitate the implementation of the Eurocodes in those countries where design rules are included directly in national legislation. The report presents the results of the enquiry on the implementation of

the Eurocodes in the EU Member States and Norway, which was performed by the JRC and the European Commission’s Directorate-General for Internal Market, Industry, Entrepreneurship and SMEs. It is part of the activities envisaged in the Commission’s “Strategy for the sustainable competitiveness of the construction sector and its enterprises”. The results reported will be used also in the analysis envisaged for the ﬁtness check of EU legislation related to the construction sector. Further information: www.steelconstruct.com

Steel Construction 9 (2016), No. 1

15

Articles Andrew Voth Jeffrey Packer*

DOI: 10.1002/stco.201610004

Circular hollow through plate connections This article reviews prior research on connections between through-plates and circular hollow sections (CHS) and presents a ﬁnite element (FE) study validated against laboratory experiments. The FE analysis indicates that, for a given geometric conﬁguration, the behaviour of through-plate-to-CHS connections closely matches the sum of branch-plate-to-CHS connection behaviour in plate tension and compression. A connection design strength, which is shown to be valid for a wide range of connection geometries and which is the sum of existing design recommendations for branch plate-to-CHS connections loaded in axial tension and compression, is hence proposed for through-plateto-CHS T-connections. This therefore enables maximum advantage to be taken of the capacity of this type of “reinforced” tubular connection.

1 Introduction A very common connection to a steel hollow section is one in which a branch (or gusset) plate is welded to the exterior face, usually parallel or transverse to the axis of the member. In particular, this form of connection is used for simple shear connections between I-section beams and hollow section columns, hanger connections to hollow sections, branch member-to-chord member connections in hollow section trusses, bracing connections to hollow section columns and even as a representation of a beam ﬂange-to-column moment connection. Design recommendations for longitudinal and transverse branch plate T-connections, with the plate subjected to a quasi-static load axial to the plate, are now well established in modern steel design codes, speciﬁcations and international guides [1], [2], [3], [4], [5], [6], [7], [8]. An important feature of all these, however, is that the connection design capacity is independent of the sense of the branch plate load, i.e. the same strength is assumed for both branch tension and compression loading cases, with a lower bound being taken to accommodate both load cases. The limit states resistance available for many axially loaded branch plate T-connections is frequently low, however, so strengthening or stiﬀening techniques are often required. Some of the more common methods include ring stiﬀeners on either the outside or inside of the CHS as

* Corresponding author: jeﬀrey.packer@utoronto.ca

16

annular ring plates and ﬁlling the chord with concrete or grout. Signiﬁcant research has been completed on both of these strengthening methodologies, where by plastiﬁcation of the chord is limited, which thus increases the connection resistance [9], [10], [11], [12], [13]. Another widely used stiﬀening and strengthening method is a plate-to-tube connection where the branch plate is slotted through the hollow section and welded to two opposing faces (Fig. 1). This has the advantage of engaging much more of the cross-section in load resistance, and hence has a higher capacity than the equivalent branch plate connection. However, the through-plate connection entails more diﬃcult and more expensive fabrication. Further, a part of the through-plate protrudes beyond the far side of the hollow section (Fig. 1b), which may aﬀect connections to that side of the hollow section. Research on longitudinal connections between through-plates and rectangular hollow section (RHS) members [14] has shown that the connection strength was double that of the equivalent branch plate connection, because two ﬂat RHS faces were engaged in relatively independent but identical ﬂat-plate ﬂexural mechanisms. This “double strength” has hence been adopted for RHS-to-longitudinal through-plate connections in numerous codes, speciﬁcations and guides [2], [4], [6], [7], [15], but none of these oﬀers a solution for CHS-to-through-plate connections. A recent experimental study of through-plate-to-CHS connections [16] indicated that through-plate-to-hollow section connection behaviour actually comprises two independent mechanisms, one in compression and one in tension, which occur on opposite sides of the hollow section chord during load application. Preliminary examination of

Fig. 1. Examples of through-plate connections: a) to RHS, b) to CHS

© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Steel Construction 9 (2016), No. 1

A. Voth/J. Packer · Circular hollow through plate connections

Table 1. CIDECT/ISO design resistance for branch plate-to-CHS T-connections under axial load [5], [8] Transverse plate Qu " 2.2(1

Longitudinal plate

6.8G2).L0.2

Chord plastiﬁcation

N1* " 1.16 b1 t0 fy0 for b1 f d0 – 2t0

Punching shear

Qu " 5(1 0.4M)

Qf " (1 – |n|)C1, where n " (N0 /Npl,0) (M0 /Mpl,0) for chord compression stress (n ! 0), C1 " 0.25 for chord tension stress (n v 0), C1 " 0.20 N1* " 1.16 h1 t0 fy0/sin261

Range of validity: compression chords must be class 1 or 2, but also 2L f 50 tension chords must be 2L f 50 transverse plates: 0.4 f G f 1.0; longitudinal plates: 1 f M f 4 fy1 f fy0 , fy /f u f 0.8 , fy0 f 460 MPa Note: 61 is the angle of the force on the plate

this behaviour also illustrated that the capacity of a through-plate connection is approximately the summation of the capacities of a branch plate-to-CHS connection tested in tension and a branch plate-to-CHS connection tested in compression, provided that the connection geometry for the branch connection and the through-connection are similar. The dual mechanism for plate-to-CHS connections diﬀers from the approach that has been previously applied to plate-to-RHS connections, where the latter exhibit the same yield line mechanism on both the top and bottom connection faces. As only a limited set of experimental and numerical results exists for through-plate-to-CHS T-connections [16], a parametric FE study was initiated to explore an expanded range of geometric parameters for such connections, with the aim of combining tension and compression branch plate-to-CHS capacities to develop through-plateto-CHS connection capacity. The following describes the numerical FE study and the resulting expressions proposed for the through-plate ultimate limit state.

inﬂuence of normal stress in the chord connecting face. These functions, along with the chord punching shear expressions, are summarized in Table 1. An extensive experimental and numerical study has been conducted [16], [19], [20] for X- and T-type branch plate-to-CHS connections in an eﬀort to reassess the current CIDECT/ISO chord plastiﬁcation partial design strength function Qu (Table 1). The numerical study of plate-to-CHS T-connections, which consisted of approximately 100 connection geometries [20], concluded that the behaviour of branch plate connections tested under plate axial compression load varied signiﬁcantly with respect to connections under branch plate axial tension load. Since the capacity of the tension-only connections was found to be under-utilized in the current CIDECT [5] and ISO [8] guidelines, a regression analysis of the numerical results was undertaken and new Qu functions were developed for branch plate-to-CHS T-connections as follows [21]: Qu,90,C " 2.9_ (1 3Ge2).L0.35 for transverse (90o) plate in compression

(2)

Qu,90,T " 2.6_ (1 2.5Ge2).L0.55 for transverse (90o) plate in tension

(3)

Qu,0,C " 7.2_ (1 0.7Me) for longitudinal (0o) plate in compression

(4)

Qu,0,T " 10.2_ (1 0.6Me) for longitudinal (0o) plate in tension

(5)

1.1 Design resistance of branch plate T-connections Branch plate-to-CHS connection resistance is currently determined in practice by using the lower of two limit states – chord plastiﬁcation and chord punching shear, assuming that both the branch plate and the weld are adequately designed and are non-critical. Calculation of the two limit states depends signiﬁcantly on connection geometry, particularly the orientation and dimensions of both the branch plate and the chord. Recent axially loaded branch plate-to-CHS T-connection design guidelines [5], [7], [8] were developed by adapting existing CHS-to-CHS design guidelines to a limited set of experimental results for branch plate-to-CHS [16], [17] using regression analysis [18]. The chord plastiﬁcation connection resistance, expressed as an axial force in the branch member, took the following general form [5], [7], [8]: N1* " Qu Qf fy0 t02 /sin61

(1)

where Qu is a partial design strength function that predicts non-dimensionalized connection resistance (N1*sin61/fy0 t02) without chord axial stress and Qf is a chord stress function that reduces connection resistance to account for the

A lower-bound reduction factor _ " 0.85 was used, based on a regression analysis of the numerical results, for application to limit states design.

2 Research programme and connection FE modelling To investigate the increase in connection capacity of through-plate-to-CHS connections relative to their branch plate counterparts, the same connection geometries used for the branch plate T-connections were investigated numerically. The high ultimate capacity of the through-plateto-CHS connections proved diﬃcult to capture without causing non-converged solutions and chord end failures. Nevertheless, ﬁve transverse and 13 longitudinal through-

Steel Construction 9 (2016), No. 1

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A. Voth/J. Packer · Circular hollow through plate connections

Table 2. Values of eﬀective chord length parameter Fe for longitudinal through-plate-to-CHS T-connections Nominal depth ratio, M " h1/d0

t0 (mm)

2L

11.10

19.74

7.95

27.56

8

4.78

45.84

12

0.2

0.6

1.0

1.5

4

4

4

4

8

8

8

12

12

2.0 8

2.5 8

Table 3. Values of eﬀective chord length parameter Fe for transverse through-plate-to-CHS T-connections t0 (mm)

2L

7.95 4.78

Nominal width ratio, G " b1/d0 0.2

0.4

27.56

8

8

45.84

12

12

0.6 8

Fig. 2. Parametric longitudinal throughplate-to-CHS T-connection conﬁguration

Fig. 3. Parametric transverse throughplate-to-CHS T-connection conﬁguration

plate-to-CHS connections produced results up to the stage of connection ultimate capacity. The resulting parametric numerical FE study thus consisted of 18 connections, modelled by varying G from 0.2 to 0.6, M from 0.2 to 2.5 and 2L from 19.74 to 45.84, as shown in Tables 2 and 3, with the eﬀective chord length parameter (Fe " 2l0e /d0) indicated. Note that transverse connections with values of G # 0.8 are improbable, depending on chord wall thickness, as suﬃcient space for the plate to pass through the chord is required. As the behaviour of these connections is the same for both through-plate tension and compression loads, the connections were tested using through plate tension loading only. All connections were modelled with ﬁllet welds and the eﬀect of weld size on connection behaviour was incor-

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Steel Construction 9 (2016), No. 1

porated by converting both G and M to eﬀective values of Ge (0.32, 0.51, 0.69) and Me (0.32, 0.72, 1.12, 1.62, 2.12, 2.62). A plate thickness t1 " 19.01 mm and chord diameter d0 " 219.1 mm were used for all numerical models, which were constructed with the geometry shown in Figs. 2 and 3. Where the branch plate was considered critical, the yield strength of the plate fy1 was increased to provide substantial resistance so that connection behaviour would govern.

2.1 FE modelling of connections The numerical analysis was carried out using the same general characteristics described in detail elsewhere [16], [20] for branch plate-to-CHS T-connections. These previously established, non-linear, FE modelling techniques are sum-

A. Voth/J. Packer · Circular hollow through plate connections

Fig. 4. Typical laboratory test for through-plate-to-CHS connection

marized below, with validation performed against laboratory experiments (Fig. 4) [16]. FE models were constructed and analysed using the commercially available ANSYS software [22]. Both geometry and measured material properties, including chord end conditions and ﬁllet weld details, were replicated within the FE model. Eight-node solid brick elements (SOLID45), each with three translational degrees of freedom per node and reduced integration with hourglass control, were used for each connection model along with three chord through-thickness elements. Uniform mesh density was used, except in locations where large deformations and/or peak stress concentrations – leading to cracking and eventually fracture – occurred. At those positions, typically at joint locations between plate and CHS, increased mesh density was used to capture this behaviour better. Symmetrical boundary conditions were used wherever possible, with only one quarter of the connection modelled when geometry, restraint and loading were all symmetrical. A non-linear time-step analysis was used incorporating non-linear material properties, large deformation allowance and full Newton-Raphson frontal equation solver. Multi-linear true stress–strain curves, converted from tensile coupon results of both the plate [23] and the A500 Grade C CHS [24] steels, were used for FE material properties up to the point of coupon necking. The post-necking tensile behaviour was determined by an iterative method developed by Matic [25] and modiﬁed by Martinez-Saucedo et al. [26], using direct FE modelling of experimental coupons over their full range. The steel plate had yield and ultimate strengths of 326 and 505 MPa respectively, and the CHS had yield and ultimate strengths of 389 and 527 MPa. The weld material was given the same properties as the plate. A failure criterion was imposed to emulate material fracture, with the “death feature” of an element being activated by a maximum equivalent (von Mises) strain value Jef " 0.2 previously determined for these types of connections [19], [20]. Once the maximum equivalent strain value was reached within an element, the stiﬀness and the stress in that element were reduced to near zero, allowing the element to deform freely. The T-connections were modelled in three-point bending where, for a quarter model, the chord end was supported by a roller at the chord neutral axis (Figs. 2 and 3) and loaded using displacement control. To prevent insta-

Fig. 5. Member end loading to exclude chord normal stress at joint face, with resulting bending moment diagrams

bility, lateral restraint was provided by the symmetric boundary. A high equilibrium-induced chord bending moment (and hence chord normal stress) is created at the joint connecting face; this is undesirable for determining connection behaviour without chord stress and hence generating design recommendations without a chord stress inﬂuence function Qf. To remove this chord normal stress due to bending at the joint face, counteracting in-plane bending moments (M0,END " N1 l0e /4) were applied to the rigid chord end plates, as shown in Fig. 5, thus allowing the chord normal stress inﬂuence function Qf to remain independent of the partial design strength function Qu (see Table 1). An in-plane bending moment applied to the chord ends does, however, cause two additional problems that need to be addressed: i) Connections with high ultimate capacities due to geometric conﬁguration (e.g. thick chords, large plate widths, longer connection lengths) produce high end moments that might exceed the yield strength of the chord, because the applied end moment M0,END is a function of the applied connection load N1 and the chord eﬀective length l0e. A reinforcement band of elements with higher yield strength at the CHS chord end (see Fig. 5) was used in such cases to prevent chord end failure prior to connection capacity. When reinforcement was required, the width of the band was determined on an individual connection basis, depending on predicted connection capacity and chord length. ii) To prevent non-convergent results, which are possible with load-controlled analysis (especially for connections loaded in compression during periods of signiﬁcant plastiﬁcation and deformation), displacement-controlled analysis was used. This makes the calculation of the applied end moment diﬃcult as the branch plate load for a given applied displacement is not known un-

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A. Voth/J. Packer · Circular hollow through plate connections

Fig. 6. Parametric FE results for transverse through-plate-to-CHS T-connections

Fig. 7. Parametric FE results for longitudinal through-plate-to-CHS T-connections a) Longitudinal plate-to-CHS connections b) Transverse plate-to-CHS connections

til the end of each time step. The applied end moment required for application at the start of each time step was determined by predicting the branch load using a Taylor series approximation and load information from the previous time step, in combination with an end-oftime-step correction and a small displacement rate based in part on the slope of the connection load–deformation curve.

3 Parametric study results compared with branch plate connections The load–deformation curve for each longitudinal and transverse through-plate-to-CHS T-connection was determined with the connection deformation deﬁned as the change in distance between point A in Figs. 2 and 3 and a point at the crown of the CHS chord, point B in Figs. 2 and 3. From these curves the connection ultimate capacity N1,u was determined as the minimum of: i) the load at a deformation of 3 % d0, called N1,3% (if this deformation preceded the deformation at N1,max),

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Steel Construction 9 (2016), No. 1

ii) the maximum connection load N1,max (the global maximum load) and iii) branch plate yielding. For all connections, the load at a deformation of 3 % d0 governed the connection capacity. Figs. 6 and 7 show the normalized ultimate load N1,u/fy0t02 as a function of Ge or Me (which include the eﬀect of weld size) for all 2L values, for longitudinal and transverse through-plate connections. The numerical results in those ﬁgures are compared with the current CIDECT chord plastiﬁcation function Qu for branchplate-to-CHS T-connections [5], calculated using eﬀective geometric properties. For both longitudinal and transverse through-plate-to-CHS connections, the current CIDECT design equations [5] presented in Table 1 for branch-plateto-CHS T-connections do not even come close to predicting connection ultimate capacity (see Figs. 6 and 7). As the CIDECT design equations for branch plates were not intended for through plates, such a diﬀerence is understandable.

A. Voth/J. Packer · Circular hollow through plate connections

a)

b)

Fig. 8. Comparison of through-plate and the summed branch-plate connection capacities (all determined by FE analysis), a) Longitudinal plate-to-CHS connections, b) Transverse plate-to-CHS connections

Fig. 9. Comparison of FE data with proposed Qu (Eq. (6)) for transverse through-plate-to-CHS T-connections

Fig. 10. Comparison of FE data with proposed Qu (Eq. (7)) for longitudinal through-plate-to-CHS T-connections

To determine whether the numerical results are reasonable and applicable to a wider range of connection geometries, Fig. 8 examines the ratio of Qu,Through (the normalized connection capacity N1,u/fy0t02 for through-plate connections) and Qu,Branch (TensComp) (the summation of the normalized connection capacities N1,u/fy0t02 for branch plate T-connections in tension and compression, as previously reported [20]). The partial strength function Qu is equivalent to the normalized connection capacity N1,u/ fy0t02 in this case as the chord stress function Qf and angle of inclination term sin61 are both equal to unity. Figs. 8a and 8b (for which the data have a mean and coeﬃcient of variation (CoV) of 1.22 and 6.32 % for longitudinal and 1.22 and 3.82 % for transverse respectively), show that the summation of tension and compression branch plate-toCHS T-connection capacities still underestimates throughplate connection capacity.

4 Design recommendations for through-plate connections There are no precedents or theoretical models that can be used as a basis for the development of design recommendations, but the general behaviour of a throughplate-to-CHS T-connection has been established to be approximately equivalent to the addition of tension and compression branch-plate-to-CHS connection behaviours. Thus, it is logical that the partial design strength function Q u for through-plate connections could be given by: Qu " Qu,90,C Qu,90,T for transverse through-plate connections

(6)

Qu " Qu,0,C Qu,0,T for longitudinal through-plate connections

(7)

Steel Construction 9 (2016), No. 1

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A. Voth/J. Packer · Circular hollow through plate connections

where Qu,90,C, Qu,90,T, Qu,0,C and Qu,0,T are given by Eqs. (2), (3), (4) and (5) respectively. For transverse through-plate connections, the “actual” Qu (which is equivalent to the normalized FE connection capacity N1,u/fy0t02) is compared with the Qu value from Eq. (6) in Fig. 9. In this comparison the L term in Eqs. (2) and (3) is set to unity. The ratio in Fig. 9 has a mean of 1.21 and CoV of 7.82 %. As there are limited transverse throughplate-to-CHS connection results, these values are not statistically signiﬁcant, but are indicative of the suitability of Eq. (6). Similarly, for longitudinal through-plate connections, the “actual” Qu (which is equivalent to the normalized FE connection capacity N1,u/fy0t02) is compared with the Qu value from Eq. (7) in Fig. 10. In this comparison the L term in Eqs. (4) and (5) is set to unity. The ratio in Fig. 10 has a mean of 1.27 and CoV of 8.54 %. It is evident that Eqs. (6) and (7) give reasonable lower-bound approximations for ultimate capacity and can be conservatively adopted to estimate through-plate connection capacity.

5 Summary and conclusions Through-plate-to-CHS connections were numerically analysed (varying values of G from 0.2 to 0.6, M from 0.2 to 2.5 and 2L from 20 to 46) using validated FE models in order to determine connection behaviour trends and develop design guidelines. From the 18 numerical FE analyses, two proposed partial design strength functions Qu – represented by Eqs. (6) and (7) – provide adequate correlation with the numerical FE results. It is thus recommended that the limit states design resistance (N1*) of axially loaded through-plate-to-CHS 90o T-connections be determined as follows: Transverse: (8) N1* " fy0 t02 _ [2.9 (1 3Ge 2).L0.35 2.6 (1 2.5Ge 2).L0.55]Qf Longitudinal: N1* " fy0 t02 _ [7.2 (1 0.7Me ) 10.2 (1 0.6Me )]Qf

(9)

where Qf is as given in Table 1. The reduction factor _ is analogous to a limit states design resistance factor (in North America) or the inverse of a partial safety factor (in Europe) and can be taken as 0.85, as previously recommended for branch plate T-connections [20]. Socalled eﬀective values for the non-dimensional parameters Ge and Me are used in the above equations, but the use of the regular variables G and M (which are lower since they do not include the weld sizes) is a conservative alternative. Although Eqs. (8) and (9) are clearly empirical, and veriﬁed for a limited parameter range and with limited data, the implementation of the _ factor should provide adequate conservatism somewhat beyond the geometric parameter range investigated. The use of Eq. (8) or Eq. (9), as appropriate, also enables the design of through-plate-toCHS connections to be based on just one limit state check, unlike for branch plate connections, where there are typically two limit states to be checked (Table 1). More importantly, these recommendations provide, for the ﬁrst time, a means of enabling through-plate-to-CHS connections to be designed while taking proper advantage of their very

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Steel Construction 9 (2016), No. 1

favourable strength characteristics and without resorting to treating them punitively as branch plate-to-CHS connections.

Notation Ai b1, b1e d0 fu fyi h1, h1e i l0, l1 M0 M0,END Mpl,0 Ni N1,3% N1,u N1* Npl,i Qf Qu ti w0, w1 F, Fe G, Ge L Jef _ M, Me

61

cross-sectional area of member i nominal, eﬀective branch width (b1e " b1 2w0), 90o to CHS longitudinal axis external diameter of CHS member ultimate stress yield stress of member i nominal, eﬀective branch depth (h1e " h1 2w0), parallel to CHS longitudinal axis subscript denoting member (i " 0 for chord, i " 1 for branch) chord length, branch length chord bending moment applied in-plane bending moment at chord end chord plastic moment capacity axial force in member i branch load at 3 % d0 connection deformation connection ultimate limit state capacity connection resistance, expressed as an axial force in the branch member yield capacity of member i (" Ai fyi) chord stress inﬂuence function partial design strength function thickness of member i measured weld leg length along chord, branch chord length parameter (F " 2l0 /d0), eﬀective length parameter (Fe " 2l0e /d0) nominal, eﬀective connection width ratio (G " b1/ d0, Ge " b1e /d0) for transverse plates chord radius-to-thickness ratio (" d0/2t0) maximum equivalent strain reduction factor nominal, eﬀective connection depth (length) ratio (M " h1/d0, Me " h1e /d0) for longitudinal plates; M " t1/d0 for transverse plates included angle of inclination between branch and chord

References [1] CEN: Eurocode 3: Design of steel structures – Part 1.1: General rules and rules for buildings, EN 1993-1-1:2005. European Committee for Standardization, Brussels, 2005. [2] AISC: Speciﬁcation for structural steel buildings, ANSI/ AISC 360-10. American Institute of Steel Construction, Chicago, USA, 2010. [3] Packer, J. A., Henderson, J. E.: Hollow structural section connections and trusses – A design guide, 2nd ed., Canadian Institute of Steel Construction, Toronto, 1997. [4] Packer, J. A., Sherman, D., Lecce, M.: Hollow structural section connections – Steel design guide No. 24, American Institute of Steel Construction, Chicago, USA, 2010. [5] Wardenier, J., Kurobane, Y., Packer, J. A., van der Vegte, G. J., Zhao, X.-L.: Design guide for circular hollow section (CHS) joints under predominantly static loading, CIDECT design guide No. 1, 2nd ed., Comité International pour le Développement et l’Étude de la Construction Tubulaire, Geneva, 2008. [6] Packer, J. A., Wardenier, J., Zhao, X.-L., van der Vegte, G. J., Kurobane, Y.: Design guide for rectangular hollow section

A. Voth/J. Packer · Circular hollow through plate connections

(RHS) joints under predominantly static loading, CIDECT design guide No. 3, 2nd ed., Comité International pour le Développement et l’Étude de la Construction Tubulaire, Geneva, 2009. [7] Wardenier, J., Packer, J. A., Zhao, X.-L., van der Vegte, G. J.: Hollow sections in structural applications, 2nd ed., Comité International pour le Développement et l’Étude de la Construction Tubulaire, Geneva, 2010. [8] ISO: Static design procedure for welded hollow-section joints – Recommendations, ISO 14346. International Standards Organization, Geneva, 2013. [9] Alostaz, Y. M., Schneider, S. P.: Analytical behavior of connections to concrete-ﬁlled steel tubes. Journal of Constructional Steel Research, vol. 40, No. 2, 1996, pp. 95–127. [10] Packer, J. A.: Concrete-ﬁlled HSS connections. Journal of Structural Engineering, ASCE, vol. 121, No. 3, 1995, pp. 458– 467. [11] Zhao, X.-L., Packer, J. A.: Tests and design of concrete-ﬁlled elliptical hollow section stub columns. Thin-Walled Structures, vol. 47, No. 6/7, 2009, pp. 617–628. [12] Lee, M. M. K., Llewelyn-Parry, A.: Strength prediction for ring-stiﬀened DT-joints in oﬀshore jacket structures. Engineering Structures, vol. 27, No. 3, 2005, pp. 421–430. [13] Willibald, S.: The static strength of ring-stiﬀened tubular T- and Y-joints. Proc. of 9th Intl. Symp. on Tubular Structures, Düsseldorf, 2001, pp. 581–588. [14] Kosteski, N., Packer, J. A.: Longitudinal plate and through plate-to-HSS welded connections. Journal of Structural Engineering, ASCE, vol. 129, No. 4, 2003, pp. 478–486. [15] Kurobane, Y., Packer, J. A., Wardenier, J., Yeomans, N.: Design guide for structural hollow section column connections, CIDECT design guide No. 9, Comité International pour le Développement et l’Étude de la Construction Tubulaire, Geneva, 2004. [16] Voth, A. P., Packer, J. A.: Branch plate-to-circular hollow structural section connections. I: Experimental investigation and ﬁnite-element modeling. Journal of Structural Engineering, ASCE, vol. 138, No. 8, 2012, pp. 995–1006. [16] Washio, K., Kurobane, Y., Togo, T., Mitsui, Y., Nagao, N.: Experimental study of ultimate capacity for tube to gusset plate joints – Part 1. Proc. of Annual Conf. of AIJ, Japan, 1970. [17] Akiyama, N., Yajima, M., Akiyama, H., Ohtake, A.: Experimental study on strength of joints in steel tubular structures. Journal of Society of Steel Construction. vol. 10, No. 102, 1974, pp. 37–68 (in Japanese).

[18] van der Vegte, G. J., Wardenier, J., Zhao, X.-L., Packer, J. A.: Evaluation of new CHS strength formulae to design strengths. Proc. of 12th Intl. Symp. on Tubular Structures, Shanghai, 2008, pp. 313–322. [19] Voth, A. P., Packer, J. A.: Branch plate-to-circular hollow structural section connections. II: X-type parametric numerical study and design. Journal of Structural Engineering, ASCE, vol. 138, No. 8, 2012, pp. 1007–1018. [20] Voth, A. P., Packer, J. A.: Numerical study and design of T-type branch plate-to-circular hollow section connections. Engineering Structures, vol. 41, 2012, pp. 477–489. [21] Voth, A. P.: Branch plate-to-circular hollow structural section connections. PhD thesis, University of Toronto, 2010. [22] ANSYS ver. 11.0. ANSYS Inc., Canonsburg, USA, 2007. [23] CSA: General requirements for rolled or welded structural quality steel, CAN/CSA-G40.20-13/G40.21-13. Canadian Standards Association, Toronto, 2013. [24] ASTM: Standard speciﬁcation for cold-formed welded and seamless carbon steel structural tubing in rounds and shapes, ASTM A500/A500M-10. ASTM International, West Conshohocken, USA, 2010. [25] Matic, P.: Numerically predicting ductile material behavior from tensile specimen response. Theoretical and Applied Fracture Mechanics, vol. 4, No. 1, 1985, pp. 13–28. [26] Martinez-Saucedo, G., Packer, J. A., Willibald, S.: Parametric ﬁnite element study of slotted end connections to circular hollow sections. Engineering Structures, vol. 28, No. 14, pp. 1956–1971. Keywords: tubes; connections; joints; through-plates; ﬁnite element analysis; design

Authors: Andrew P. Voth, Dr., P.Eng. Read Jones Christoffersen Ltd. 144 Front Street West, Suite 500 Toronto, Ontario M5J 2L7 Canada Jeffrey A. Packer, Prof., Dr., P.Eng. Department of Civil Engineering University of Toronto 35 St. George Street Toronto, Ontario M5S 1A4 Canada

Steel Construction 9 (2016), No. 1

23

Articles Harald Unterweger* Andreas Taras Zoltan Feher

DOI: 10.1002/stco.201610009

Lateral-torsional buckling behaviour of I-section beam-columns with one-sided rotation and warping restraint In many practical applications, columns are often ﬁxed to a practically rigid concrete structure at the column base. This additional restraint should increase the real load-carrying capacity if the section is susceptible to lateral-torsional buckling. However, this effect is rarely taken into account in design, as most current design rules do not provide sufﬁcient guidance on how to account for this additional rigidity, and so the column base ﬁxity is often ignored. The background to the veriﬁcation formulae for lateral-torsional buckling (LTB) of I-section beam-columns in Eurocode EN 1993-1-1 consists of comprehensive parametric numerical studies for members with “end fork” conditions only, i.e. for members with free rotational and warping deformations at both ends. However, these speciﬁc boundary conditions are not clearly mentioned in the code. In the study presented in this paper, a comprehensive series of numerical FEM analyses for the realistic lateral-torsional buckling behaviour of beam-columns with one-sided rotation and warping restraints was carried out and compared with the results based on the LTB resistance of the Eurocode, calculated with increased idealized buckling loads (Ncr, Mcr) that account for the end restraints. The most important results of this study are presented in this paper and the ultimate capacity is compared for two different beam-column design methods in Eurocode 3: the interaction concept (EN 1993-1-1, 6.3.3) and the general method (EN 1993-1-1, 6.3.4). In addition, a simpliﬁed formula is given for the additional bi-moment at the end restraint, which is to be used for designing the welded joint. Finally, an improved LTB design curve (buckling reduction factor HLT) is presented, developed at the authors’ institution, which may be used for the cases studied.

Columns with the simpliﬁed boundary conditions of Fig. 1 were considered in the study presented in this paper. At the column base, full restraint is assumed, preventing any end rotation and warping (rotation and warping are fully ﬁxed). At the top of the column, “end fork” conditions are assumed, preventing out-of-plane deformation of the ﬂanges and rotation of the section about its longitudinal axis, but allowing for free warping and rotation about both cross-section axes. The direct wind loads acting on the column are ignored, leading to a linear moment distribution My in the column. Fig. 1 also shows the deformation at ultimate load for one example, showing the typical deformation pattern in the case of LTB, i.e. out-of-plane buckling of the compressed ﬂange leading to additional torsional eﬀects in the column. The colour of the member shows the stress state, with red indicating yielding in the most highly stressed part of the ﬂange. When performing Eurocode 3 LTB veriﬁcations of I- and H-section beam-columns, the formulas of EN 19931-1 [2], section 6.3.3, are often used. If the so-called “method 2” of Annex B is used (only this method is considered in this study), only Eq. (6.62) is relevant for LTB behaviour. For a better understanding of the results in this paper, this design formulation and the important parameters are presented in Eqs. (1) to (6), albeit in a simpliﬁed form for the limited internal forces studied (N and My) and moment distributions (see Fig. 1).

1 Introduction and motivation

M yd Nd + kLT ⋅ ≤ 1.0 χ z ⋅ Npl,Rd χLT ⋅ Mpl,y,Rd

For I- and H-section beam-columns that are susceptible to torsional deformation, lateral-torsional buckling (LTB) is often the most critical buckling failure mode. In practical applications, beam-columns often do not feature “end fork” conditions with pinned ends and unrestrained warping at the member extremities, even though this condition was commonly assumed in the research studies that form the background to the LTB veriﬁcation rules in EN 19931-1 (e.g. [1]).

where: kLT = 1 − nz =

0.1 ⋅ λ z ⋅ n z 0.1 ⋅ n z ≥1− C mLT − 0.25 C mLT − 0.25

Nd χ z ⋅ Npl,Rd

C mLT = 0.6 + 0.4 ⋅ ψ ≥ 0.4

(1)

(2)

(3) (4)

Determination of the buckling reduction factors Hz, HLT: * Corresponding author: h.unterweger@tugraz.at

24

λz =

Npl,R Ncr

→ χ z (European buckling curves)

© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Steel Construction 9 (2016), No. 1

(5)

H. Unterweger/A. Taras/Z. Feher · Lateral-torsional buckling behaviour of I-section beam-columns with one-sided rotation and warping restraint

Fig. 1. Lateral-torsional buckling of I-section beam-columns; boundary conditions and loading in this study

λ LT =

Mpl,y,R Mcr

→ χLT (general case / specific case)

(6)

It is worth mentioning that the buckling reduction fac– tors Hz and HLT are a function of the slenderness Q z or QLT, which in turn are based on the ideal buckling strength Ncr and Mcr. These values are strongly inﬂuenced by the boundary conditions. As EN 1993-1-1 [2] gives no information about the appropriate boundary conditions to be used for LTB design according to section 6.3.2.3 of that code, a user may consider the increased values for the ﬁxed-end condition of Fig. 1 in the design. Therefore, compared with the “end fork” condition, Ncr is increased by a factor (1/0.7)2 " 2.04, due to a buckling length 0.7 · L instead of the member length L. Additionally, the ideal critical buckling moment M cr is higher. For example, if the well-known Eq. (7) (included in [3], for instance) is used, based on k " kw " 0.7 for the ﬁxed-end solution, Mcr is also increased by a factor of 2.0 at least (k " kw " 1.0 for the end fork condition).

Mcr = C1 ⋅

π2 ⋅ E ⋅ I

( kL )

2

z

2 2 ⎡ ⎤ kL ⋅ G ⋅ It ⎥ ⎛ k ⎞ Iw ⋅ + ⋅ ⎢⎢⎜ ⎟ π 2 ⋅ E ⋅ Iz ⎥ ⎝ k ⎠ Iz ⎢⎣ w ⎥⎦

( )

0.5

(7)

The objective for this paper is to answer the question of whether or not the application of the Eurocode member design rules (Eqs. (1)–(6)) gives accurate and safe results when considering the increased values of Ncr and Mcr for the ﬁxed end. In addition, the alternative approach for LTB veriﬁcation, based on the general method (EN 1993-1-1, section 6.3.4, Eq. (6.63)), is also considered and its applicability veriﬁed. In this case the overall reduction factor Hop is also inﬂuenced by the increased ideal buckling load Rcr due to the ﬁxed end – now calculated for the combined eﬀect of N and My (Eq. (8)):

λ op =

α ult,k α cr,op

=

R pl R cr

→ χop

(8)

So in this study the resistance Rpl is calculated in a simpliﬁed way, ignoring the second-order eﬀect in plane, which was negligible for the examples studied. Most of the work presented in this paper was carried out as part of the master thesis of the third author [4].

2 Accurate predictions of LTB behaviour 2.1 FEM model and numerical analyses FEM-based, numerical GMNIA analyses (geometric and material non-linear analyses with imperfections) allow for accurate predictions of the LTB behaviour. The software package ABAQUS was used in the study presented in this paper. All the details of the numeric model are summarized in Fig. 2. Type S4R shell elements were used for the ﬂanges and the web of the member. The fact that the additional ﬁllets in the rolled sections studied increase stiﬀness and strength was considered by adding beam elements with box cross-sections with equivalent torsional and longitudinal stiﬀness to both ﬂanges. The boundary conditions at both ends were fulﬁlled by a kinematic coupling of the elements at the member ends. The assumptions for the imperfections, shown in Figs. 2b and 2c, are in accordance with past research conducted for “end fork” conditions, which formed the background and led to the LTB veriﬁcation rules in the Eurocode (Eqs. (1)– (6)). A maximum geometric imperfection eo " L/1000 was applied and the imperfection shape was based on a previous linear buckling analysis (LBA) for each member analysed. Two representative cross-sections were studied: a very slender IPE 500 section and a stocky HEB 300 section. The full plastic capacity Mpl,Rd in Eq. (1) was utilized for both sections (at least class 2 sections were used in all cases). The residual stresses considered, shown in Fig. 2c, are based on [6].

Steel Construction 9 (2016), No. 1

25

H. Unterweger/A. Taras/Z. Feher · Lateral-torsional buckling behaviour of I-section beam-columns with one-sided rotation and warping restraint

Fig. 2. Numerical FEM study for LTB behaviour: a) details of FEM model, b) geometric imperfections, c) residual stresses, d) simpliﬁed material behaviour

Fig. 3. LTB behaviour for the case of bending moment My only; member capacities, deformations and longitudinal stresses Xx at ultimate load

A linear elastic – ideal plastic behaviour was assumed for the material (Fig. 2d).

2.2 Typical LTB behaviour for representative cases Fig. 3 shows the resulting LTB deformation and stress patterns at the ultimate limit state for some representative cases, including a case with isolated bending moment My (zero compression force). In all cases, the length of the member is L " 7.5 m and the ﬁxed end is on the righthand side of the ﬁgure. The deformations of both ﬂanges at ultimate load are plotted, showing large out-of-plane deformations for the compression ﬂange and almost no out-of-plane deformations for the tension ﬂange. Three diﬀerent moment distributions are shown for the IPE 500 section. The triangular moment distribution – typical for columns – gives higher end restraint for the compression ﬂange. The colours represent the level of the normal stresses Xx in both ﬂanges, with plastic zones shown in red.

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Steel Construction 9 (2016), No. 1

It can be seen that, for a constant moment, the utilization of the plastic section capacity is diﬀerent in the two sections. For the slender IPE 500 section, the plastic zones are very limited (only a small part of the ﬂange yields), but the size and spread of these zones are increased at the ﬁxed end for the other moment distributions.

3 Results for Mcr – bending My only The ideal critical buckling moment Mcr aﬀects the LTB capacity of the Eurocode (HLT · Mpl,y,Rd) because HLT de– pends on the slenderness Q LT (see Eq. (6)). For the boundary condition studied with one ﬁxed end and end moments only (Fig. 1), diﬀerent solutions for the calculation of Mcr are available in the literature. Table 1 compares the results of diﬀerent sources for Mcr for the HEB 300 section and the triangular moment distribution. Owing to the linear relationship between C1 and Mcr in Eq. (7), the comparison of the C1 values is equal to a

H. Unterweger/A. Taras/Z. Feher · Lateral-torsional buckling behaviour of I-section beam-columns with one-sided rotation and warping restraint

Table 1. Ideal buckling moment Mcr based on diﬀerent sources; comparison of equivalent factor C1 for HEB 300 section and triangular bending moment distribution ^"0

Results for comparison

HEB 300

k " kw " 0.7

L (mm)

– Qk (k " 1.0) S235

ABAQUS

LTBEAM

5084

0.71

1.818

2.507

7626

1.07

2.422

2.479

10 168

1.43

2.427

2.457

12 710

1.79

2.419

2.437

15 252

2.14

2.410

2.420

17 793

2.50

2.401

2.406

20 336

2.86

2.394

2.393

comparison of Mcr. In [5], C1 is deﬁned based on the factor kc, which can be rewritten in the form of Eq. (9) for the end moments studied. C1 =

⎛ ⎞ 1 1 =1/⎜ 2 ⎝ 1.33 − 0.33 ⋅ ψ ⎟⎠ kc

2

(9)

Mcr,LBA 2 ⎤ ⎡ 0.7L ⋅ G ⋅ It ⎥ π 2 ⋅ E ⋅ Iz ⎢ I w ⋅ + 2 ⎢I π 2 ⋅ E ⋅ Iz ⎥ 0.7 ⋅ L ⎢⎣ z ⎥⎦

(

(

)

ENV

ÖNORM B (interpolated)

ECCS (interpolated)

1.769

2.092

1.955

1.824

The results of C1 in Table 1 illustrate a very small inﬂuence of the slenderness of the beam, but signiﬁcantly higher numerical results compared with the diﬀerent sources in the literature. Similar results can be found for other sections and moment distributions, see [4].

4 Ultimate LTB capacity for bending – comparison with Eurocode prediction

Values for C1 can also be found in the pre-version of the Eurocode, ENV 1993-1-1 [3]. Another source is the National Annex of EN 1993-1-1 in Austria, ÖNORM B 19931-1 [7], as well as the ECCS recommendations [8]. In addition, the results of an LBA analysis are given – for diﬀerent member lengths (the slenderness Q z given in Table 1 is based on pinned ends), based on the ABAQUS and LTBEAM [9] software packages. In these cases the numerical result Mcr,LBA is applied in Eq. (7) – with k " kw " 0.7 – and then the tabulated values of C1 are based on Eq. (10). C1,LBA =

1/kc2

)

(10)

0.5

In the following, a yield strength fy " 235 N/mm2 was assumed, without any partial safety factor LM for all comparisons of the LTB load-carrying capacity (sections 4–6) based on GMNIA results and Eurocode predictions. In a ﬁrst step, only bending moments My are considered in this section. The numerical results of the GMNIA analyses are expressed in terms of buckling reduction values HLT in order to compare them with the Eurocode predictions. The numerical values Mcr,LBA for the correct boundary conditions with the ﬁxed end (Fig. 1) are used – for calculating the slenderness ratios Q LT. To clarify the calculation of HLT in detail, all the relevant parameters are given in Table 2. For the “speciﬁc case”, the beneﬁcial eﬀect of a non-uniform moment distribution, based on Eq. (11), can be also used according to Eurocode 3, and was thus always considered in the

Table 2. LTB member capacity; details for calculating HLT based on EN 1993-1-1 “General case” 1

Reduction factor HLT

φLT + φLT

(

1 2−λ

LT

)

2

φLT + φLT

2 − 0.75 ⋅ λ

(

)

LT

2

0.5 ⋅ ⎡⎢1 + α λ LT − 0.2 + λ LT 2 ⎤⎥ ⎣ ⎦

0.5 ⋅ ⎡⎢1 + α λ LT − 0.4 + 0.75 ⋅ λ LT 2 ⎤⎥ ⎣ ⎦

h/b ! 2 (HEB 300)

a (F " 0.21)

b (F " 0.34)

h/b # 2 (IPE 500)

b (F " 0.34)

c (F " 0.49)

Factor KLT Buckling curve for rolled I- or H-sections

“Speciﬁc case”

Increase in HLT (if M | uniform) valid in EC3 for “special case” only: χLT,mod =

χLT ; f = 1 − 0.5 1 − kc f

(

) ⎡⎢⎣1 − 2.0 ( λLT − 0.8) ⎤⎥⎦ but f ≤ 1.0 2

Steel Construction 9 (2016), No. 1

27

Fig. 4. LTB member capacities for bending moments My only; comparison of GMNIA calculations with Eurocode predictions for constant moment

Fig. 5. LTB member capacities for bending moments My only; comparison of GMNIA calculations with Eurocode predictions for triangular moment distribution

results presented here for the corresponding Eurocode predictions. χLT,mod =

χLT f

(11)

2⎤ ⎡ f = 1 − 0.5 ⋅ 1 − kc ⋅ ⎢1 − 2.0 ⋅ λ LT − 0.8 ⎥ ≤ 1.0 (12) ⎣ ⎦

(

where : kc =

)

(

1 1.33 − 0.33 ⋅ ψ

)

(12)

(13)

Fig. 4 shows the results for the two diﬀerent sections assuming a constant moment My. It can be seen that only the Eurocode prediction based on the “general case” leads to safe results when compared with the GMNIA results. Using the higher capacity of the “speciﬁc case”, unsafe results – increasing for smaller slenderness – are observed. Fig. 5 shows the same sections, but now with triangular moment distributions – a case often present in columns, e.g. in portal frames. Now the “speciﬁc case” also gives accurate, safe results.

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Steel Construction 9 (2016), No. 1

5 Ultimate LTB capacity of beam-columns – comparison with Eurocode prediction 5.1 Comparison with interaction concept To show the results for diﬀerent My-N ratios, the ultimate LTB capacity is plotted in the form of interaction diagrams (Figs. 6–8). On the horizontal axis, the moment capacity refers to the plastic moment capacity of the section and on the vertical axis the axial force also refers to the plastic section capacity. In most cases the results are shown for a – weak-axis ﬂexural buckling slenderness Q z " 1.0, calculated with the accurate boundary conditions (LK,z " 0.7 · L), leading to a length L " 5.8 m for the IPE 500 section (Figs. 6 and 7) and L " 10.2 m for the HEB 300 section (Fig. 8). In addition, the results for a more slender member with – Q z " 1.5 are shown in Fig. 6 for the IPE 500 section. The results in Figs. 6–8 also show the ultimate LTB load-carrying capacity for cases where the beneﬁcial eﬀect of the end restraint is either not present or would be ignored (circles and dotted lines, called “pinned”). This comparison shows the conservatism inherent in neglecting the end restraint when it is present; owing to the restraint at one end of the member, a signiﬁcantly higher LTB capacity can be used,

Fig. 6. LTB member capacities for IPE 500 section, with loadings My and N for constant moment distribution; comparison of GMNIA calculations with Eurocode predictions based on the interaction concept

Fig. 7. LTB member capacities for IPE 500 section, with loadings My and N for diﬀerent moment distributions; comparison of GMNIA calculations with Eurocode predictions, based on the interaction concept

Fig. 8. LTB member capacities for HEB 300 section, with loadings My and N for diﬀerent moment distributions; comparison of GMNIA calculations with Eurocode predictions based on the interaction concept

for small m/n ratios in particular. The GMNIA results are compared with the Eurocode predictions (Eqs. (1)–(6)), considering the higher moment capacities for the “speciﬁc case”.

It can be seen in Fig. 6 that the Eurocode prediction for a constant moment gives accurate results. Only for cases with very small normal forces – which will generally not be signiﬁcant for columns – are unsafe results observed.

Steel Construction 9 (2016), No. 1

29

Fig. 9. LTB member capacities for IPE 500 section, with loadings My and N for diﬀerent moment distributions; comparison of GMNIA calculations with Eurocode predictions based on the general method

Fig. 10. LTB member capacities for HEB 300 section, with loadings My and N for diﬀerent moment distributions; comparison of GMNIA calculations with Eurocode predictions based on the general method

– Fig. 7 shows results for the member with Q z " 1.0 for non-uniform moment distributions. For the typical triangular moment distribution of a column, the results based on the “speciﬁc case” are always on the safe side. Fig. 8 shows the same results for the HEB 300 sec– tion, again for Q z " 1.0 and for constant and triangular moment distributions. In this case the Eurocode predictions for the “speciﬁc case” are very accurate for constant moment and on the safe side for the triangular moment distribution.

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Steel Construction 9 (2016), No. 1

5.2 Comparison with the “ general method” of EN 1993-1-1, section 6.3.4 The GMNIA results for the cases presented are plotted again in Figs. 9 and 10, and in this case compared with the results of the so-called “general method” of EN 1993-1-1, section 6.3.4, see Eq. (8). Fig. 9 shows the results for – the IPE 500 section with a slenderness Q z " 1.0. It is worth mentioning that the general method is applied in the more conservative way mentioned in the Eurocode,

Fig. 11. Suggestion for improved HLT curves for LTB member capacity and comparison with GMNIA results for IPE 500 section with diﬀerent moment distributions

as the minimum of Hz and HLT was used for the reduction factor Hop. – Fig. 10 compares the HEB 300 section (slenderness Q z " 1.0) for the diﬀerent moment distributions. It is obvious that the accuracy of the general method is heavily inﬂuenced by the bending moment diagrams, leading to very conservative results for non-uniform bending moment diagrams. This can be attributed to the lack of a speciﬁc factor to account for non-uniform bending moment diagrams in the general method.

6 Application of an improved LTB capacity for bending Improved reduction factors HLT for the LTB capacity, based on comprehensive numerical GMNIA analyses for members with “end-fork” conditions, were developed at the authors’ institution [10]. In the case of isolated bending, very accurate results will be obtained with this method if the Eurocode formulas for HLT (Table 1) are modiﬁed, as shown in Fig. 11. – Now the slenderness Q z is also accounted for, as well as the ratio of the section moduli for both axes of bending (Wy/Wz). This improved formulation of HLT gives very accurate results for the case studied (see Fig. 1) with one ﬁxed end. Owing to space limitations in this paper, Fig. 11 only shows the results for the IPE 500 section for constant bending moment and antimetric moment distribution. The GMNIA results are nearly identical with the proposed formulas for HLT. Owing to the very accurate results with this modiﬁed HLT formulation, shown in Fig. 11, this formulation may also be proposed as an amendment to Eurocode EN 1993-1-1 for the next edition of the code.

7 Additional bi-moment at end restraint – simpliﬁed rule for practical design Owing to the ﬁxed end of the member, there is a signiﬁcant increase in the LTB capacity, as shown in Figs. 6–10. However, taking into account this beneﬁcial end restraint also leads to the need to account for additional stresses at the welded joint, as these are required for equilibrium at the implied ultimate limit state. The warping restraint leads to signiﬁcant bi-moments (warping moments), which can be modiﬁed to additional bending moments on the ﬂanges (Mz,ﬂ,Ed) to keep the design work simple. Some calculations were carried out in [4] to quantify these bending moments Mz,ﬂ,Ed at the load level of ultimate LTB limit for bending moments My only. The elastic bending moment Mz,ﬂ,Ed at the ﬁxed end may be estimated in a conservative way using Eq. (14). For the design of the welded connection between member and end plate, this bending moment should be added to the internal forces NEd and My,Ed. As an additional recommendation, and as a consequence of Eq. (14), full penetration welds at the ﬂanges are necessary if the utilization for the LTB veriﬁcation is equal to or near 1.0.

Mz,fl,Ed = =

MEd,y Mpl,y.Rd MEd,y Mpl,y.Rd

⎛ 1 ⎞ ⋅⎜ − 1⎟ ⋅ Mz,fl,pl ⎝ χLT ⎠ ⎛ 1 ⎞ t ⋅ b2 ⋅⎜ − 1⎟ ⋅ fl fl · fyd 4 ⎝ χLT ⎠

Steel Construction 9 (2016), No. 1

(14)

31

The following assumptions constitute the background to Eq. (14): – Utilization of the section resistance at the ﬁxed end: MEd,y Mpl,y.Rd

+

Mz,fl,Ed Mz,fl,pl

= 1.0

(15)

– Rewritten, with MEd,y limited by the LTB capacity: Mz,fl,Ed Mz,fl,pl

=1−

MEd,y Mpl,y.Rd

=1−

χLT ⋅ Mpl,y,Rd Mpl,y.Rd

= 1 − χLT

References

(16)

– Linear reduction of Mz,ﬂ,Ed for reduced bending moment MEd,y: Mz,fl,Ed Mz,fl,pl

(

)

= 1 − χLT ⋅

MEd,y χLT ⋅ Mpl,y

=

MEd,y ⎛ 1 ⎞ ⋅⎜ − 1⎟ Mpl,y ⎝ χLT ⎠

(17)

8 Summary and conclusion The LTB behaviour and ultimate LTB load-carrying capacity of representative columns with I-sections and one-sided rotation and warping restraints was studied. The current Eurocode rules (EN 1993-1-1) appear to be applicable and generally on the safe side even if the increased ideal buckling loads for a ﬁxed end (Ncr, Mcr) are used in the design equations – i.e. if the end ﬁxity is taken into account – for the following cases: – Basic loading cases (My alone, as shown in section 4, as well as N alone – not presented in this paper). – The “interaction concept” buckling rules for beam-columns, with the coeﬃcients of method 2/Annex B, can be used for these boundary conditions. This should also be possible for semi-rigid joints as long as the reduced stiﬀness for the ULS is considered when calculating Mcr and Ncr. – The “general method”, even when used with the minimum value of Hz or HLT, is not always on the safe side. The accuracy is rather diﬀerent for diﬀerent load cases and bending moment diagrams. The new proposal for LTB curves (HLT values), developed by the second author, also gives very accurate results for the boundary condition studied with one ﬁxed end. Furthermore, in order to be able to take full advantage of the signiﬁcant increase in the LTB load-carrying capacity for the member due to the ﬁxed end, it is necessary to consider the additional bending moments on the ﬂanges Mz,ﬂ (eﬀect of bi-moment) at the joint (at least for the welds between end plate and member). A ﬁrst proposal for this additional moment Mz,ﬂ has been presented in this paper.

32

Steel Construction 9 (2016), No. 1

Finally, it should be stressed again that the study presented in this paper assumed full rigidity of the substructure (e.g. a concrete base or foundation). If this condition is not suﬃciently approximated by the real support conditions, the gain in load-carrying capacity will be reduced, and the semi-rigid characteristic of the base joint should then be taken into account.

[1] Greiner, R., Lindner, J.: Interaction formulae for members subjected to bending and axial compression in Eurocode 3 – the Method 2 approach. Journal of Constructional Steel Research 62, Elsevier, 2005, pp 757–770. [2] Eurocode 3, EN 1993-1-1: Eurocode 3. Design of steel structures. General rules and rules for buildings, CEN, Brussels, 2005. [3] Eurocode 3, ENV 1993-1-1: Eurocode 3. Design of steel structures. General rules and rules for buildings, CEN, Brussels, 1992. [4] Feher, Z.: Out of plane buckling behaviour of steel members with rotation and warping restraints. Master thesis, Graz University of Technology, 2012. [5] ECCS, Rules for Member Stability in EN 1993-1-1, Background documentation and design guidelines, Boissonade, N., Greiner, R., Jaspart, J. P., Lindner, J. (eds.), ECCS Technical Committee 8, pub. No. 119, European Convention for Constructional Steelwork, Brussels, 2006. [6] ECCS: Ultimate Limit State Calculations of Sway Frames with Rigid Joints, Vogel. U., et. al. (eds.), European Convention for Constructional Steelwork – TC8, Brussels, 1984. [7] ÖNORM B 1993-1-1: Eurocode 3: Design of steel structures – Part 1-1: General structural rules – National speciﬁcations concerning ÖNORM EN 1993-1-1, national comments and national supplements, Austrian Standards Institute, Vienna, 2007. [8] da Silva, Simoes L., Simoes, R., Gervásio, H.: Design of Steel Structures, ECCS Eurocode design Manuals; Part 1-1 – General rules and rules for buildings. Ernst & Sohn, Berlin, 2010. [9] CTICM, Centre Technique Industriel de la Construction Mérallique: LTBeam v. 1.0.10 Documentation, Saint-Aubin, France, CTICM, 2010. [10] Taras, A.: Contribution to the Development of Consistent Stability Design Rules for Steel Members. PhD thesis, Graz University of Technology, Institute for Steel Structures & Shell Structures, 2011. Keywords: lateral-torsional buckling; beam-columns; GMNIA analyses

Authors: Univ. Prof. Dipl.-Ing. Dr. Harald Unterweger Assistant Prof. Dipl.-Ing. Dr. Andreas Taras Dipl.-Ing. Zoltan Feher All authors: Institute of Steel Structures, Graz University of Technology Lessingstr. 25, A-8010 Graz, Austria

Articles Jerzy Ziółko* Tomasz Mikulski Ewa Supernak

DOI: 10.1002/stco.201610005

Deformations of the steel shell of a vertical cylindrical tank caused by underpressure Underpressure in a tank with a ﬁxed roof may arise in the ﬁnal stage of its construction as well as during its usage. After completing the construction, when the tank is empty and all manholes and valves, through which air could get into the tank, are tightly closed, underpressure may arise in the case of a sudden change in the weather (air pressure and temperature), which is particularly dangerous in spring or summer. When the tank is in use, underpressure may arise if breather valves are obstructed, e.g. covered by snow during pumping out a product stored in the tank. Underpressure may cause extensive deformations of the shell or the roof of the tank. However, the shell undergoes deformation more frequently, since the roof has a stiff supporting structure. This article presents stages of deformations of the tank shell and their development from the occurrence of the ﬁrst deformation to either removal of the causes of underpressure or cracking of the steel shell and thus automatic equalization of pressure inside the tank with atmospheric pressure.

a)

1 Introduction The authors of this article have already published a number of papers on the subject of underpressure in steel vertical tanks [1]–[6]. Refs. [1] and [2] present original methods of repairing the deformed tank shells, whereas [3] describes causes of underpressure (Fig. 1). Apart from breather valves being obstructed during pumping out liquids stored in the tank, underpressure may be caused by changes in weather conditions even if there is a constant level of stored liquid. An analysis of a tank with a capacity of 10 000 m3 (shell diameter d " 29.0 m) revealed that the ﬁrst deformations of the shell in the hermetically sealed tank occur in the case of a temperature drop of 10 ºC and a pressure diﬀerence of 32 hPa. Ref. [4] shows that the underpressure value causing the ﬁrst shell deformation depends not only on the thickness of the sheets from which the upper part of the shell is made (Fig. 2), but also on the level of liquid in the tank. The more liquid, the more underpressure is needed to cause deformations, which, however, should be less due to the amount of liquid (Figs. 3 and 4). Ref. [5] deals with

* Corresponding author: jziolko@pg.gda.pl

b) Fig. 1. Tanks damaged by underpressure: a) during the productivity test of the extraction pump on the product pipeline, b) due to freezing of the breather valves

theoretical issues and model research on local loss of stability of cylindrical shells caused by underpressure. This article is a summary of the above publications concerning underpressure in steel vertical cylindrical tanks. It analyses the behaviour of the tank shell after its ﬁrst deformation caused by underpressure. These deformations, however, do not represent a serviceability limit state of the tank as the shell is still sealed. Along with changes

33

J. Ziółko/T. Mikulski/E. Supernak · Deformations of the steel shell of a vertical cylindrical tank caused by underpressure

Fig. 2. How the depth H [m] of liquid in the tank inﬂuences the critical underpressure value pmax-1 [kPa] [4]

Fig. 4. State of tank shell deformation [m] – tank ﬁlled with a product to a maximum level [4]

Fig. 3. State of tank shell deformation [m] – empty tank [4]

in underpressure, there will be a change in the location and shape of deformations as well as deﬂection values.

2 Behaviour of the steel shell of a vertical cylindrical tank after the ﬁrst deformation caused by underpressure Underpressure in a steel vertical cylindrical tank with a ﬁxed roof arises when the tank is hermetically sealed (all manholes and valves tightly closed) and the product stored is being pumped out of the tank or there is an ad-

34

Steel Construction 9 (2016), No. 1

verse change in temperature and air pressure. When underpressure reaches the limit value (pmax-1, see Fig. 5), resulting in loss of stability of the cylindrical shell in the upper part of the shell made of the thinnest sheets, the ﬁrst deformations, i.e. deﬂections of the tank, occur. In the case of an ideally shaped tank, these deformations would be evenly spread around the tank perimeter. However, in reality they will be located in places with e.g. some angle imperfections of tank sheets at their welded vertical edges. Local deﬂections of the side surface of the tank cause a reduction in the steam and air area in the tank (area limited by the ﬁxed roof above and the surface of the stored liquid below). Such a reduction in the steam and air area will also cause a decrease in underpressure inside the tank (Fig. 5 – the part of the line from pmax-1 to pmin-1) and a temporary halt to new deformations or worsening of the existing ones. If the cause of underpressure increase is not eliminated, e.g. if pumping out a stored product continues, deformation of the shell will begin again (Fig. 5 – the part of the line from pmin-1 to pmax-2) and the number of deformations will grow or they will join together and change their location. This cycle of temporary stability of the deformed shell and further deformation of the shell will persist until a crack occurs at the crossings of sheet welds. The crack results in equalization of the underpressure in the tank with atmospheric pressure and thus no further deformations occur. This state of the tank represents a serviceability limit state. The tank will no longer be sealed and the hydrocarbon vapours (in case of tanks for liquid fuel) will be emitted

J. Ziółko/T. Mikulski/E. Supernak · Deformations of the steel shell of a vertical cylindrical tank caused by underpressure

Fig. 5. Value of underpressure p [kPa] during a non-linear static FEM analysis

Fig. 6. Deformations of tank shell corresponding to limit underpressure value pmax-1 " 2.750 kPa

into atmosphere, which is unacceptable (environment protection regulations). A recurring increase in deformation of the tank shell cannot usually be observed since the user of the tank, after the occurrence of the ﬁrst deformation, tries to eliminate the causes of that deformation as soon as possible and to have it repaired in order to restore the proper shape of the shell and enable its further use. Owing to a lack of possibilities to observe the behaviour of the shell after its ﬁrst deformation caused by underpressure, a computer simulation of the situation was carried out; MSC/Nastran for Windows [6], which uses the ﬁnite element method, was used for this purpose. The structural analysis of a model tank was conducted with the following types of element: – Shell elements – a shell, a perimeter ring supporting a loadbearing structure for the roof and wind ties – Beam elements – elements of the roof supporting structure The following data was adopted for the calculations: – E " 210 GPa – Young’s modulus of elasticity – S " 0.3 – Poisson’s ratio for steel – W " 78.5 kN/m3 – steel weight – Re " 235 MPa – yield strength of steel used The analysis was carried out: – for characteristic loads, – for an adopted model of an elastic – perfectly plastic body (non-linear material analysis), and – with regard to the inﬂuence of deformation on the internal force distribution (non-linear geometric analysis). The behaviour of the shell of a completely empty tank was analysed. The results of the simulation are shown in Figs. 6 to 9. Fig. 6 presents the ﬁrst deformations of the shell of the tank with V " 10 000 m3 caused by underpressure. Since the model tank has an ideal shape, deformations are evenly

Fig. 7. Deformations of tank shell corresponding to underpressure value pmin-1 " 2.254 kPa

spread around the perimeter. They are vertical. The spacing between deﬂections corresponds to the spacing between the radial ribs of the supporting structure for a ﬁxed dome roof. The ribs are attached to the inner perimeter ring located at the upper edge of the sheets of the tank shell (roof ribs are marked by a thin line). Fig. 7 shows the state of the shell deformation after its stabilization and after completion of the ﬁrst cycle of deformation (point pmin-1 in Fig. 5). The occurrence of densely arranged, local elliptic deformations can be seen. Fig. 8 presents the deformations after completion of the second cycle of underpressure increase in the tank (point pmax-2). There are fewer elliptic deformations. Neighbouring deformations have joined together and their extent is wider than earlier.

Steel Construction 9 (2016), No. 1

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J. Ziółko/T. Mikulski/E. Supernak · Deformations of the steel shell of a vertical cylindrical tank caused by underpressure

Fig. 10. Deformations of upper part of tank shell caused by underpressure Fig. 8. Deformations of tank shell corresponding to underpressure value pmax-2 " 2.450 kPa

ering a larger area of the shell). The cycle continues until the user of the tank eliminates the cause of underpressure, or the shell cracks, which will result in the pressure inside the tank equalizing with atmospheric pressure. References

Fig. 9. Deformations of tank shell corresponding to underpressure value pend " 2.436 kPa

Fig. 9 demonstrates deformations of the shell after 300 iterations (adopted end of numerical analysis). Deformations are still irregular, and take diﬀerent forms and values. Fig. 10 is a photograph of the deformation of the upper part of the tank shell, where underpressure was generated. These deformations are permanent – they remain unchanged after opening of manholes and equalizing the pressure inside the tank with atmospheric pressure.

3 Summary Deformations of the shell of a steel vertical cylindrical tank with a ﬁxed roof occur when underpressure inside the tank reaches a limit value after the cycle of underpressure decrease and increase. During the cycle, the deformations change their location and nature (local deformations or deformations cov-

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Steel Construction 9 (2016), No. 1

[1] Ziółko, J.: Die Instandsetzung durch Unterdruck beschädigter zylindrischer Stahlbehälter. Der Stahlbau, 49(1980), No. 11, pp. 347–348. [2] Ziółko, J.: Reparatur von Dächern und Mänteln durch Unterdruck verformter Stahltanks. Stahlbau, 70(2001), No. 5, pp. 357–361. [3] Supernak, E., Ziółko, J.: Podcis´nienie w zbiornikach. Wnioski ze zdarzen´ w ostatnich latach. (Vacuum in tanks. Conclusions from the events in recent years) XXVI Scientiﬁc-Technical Conf. “Structural Failures” Szczecin – Mie˛dzyzdroje, Poland, 21–24 May 2013, pp. 589–598. [4] Ziółko, J., Mikulski. T., Supernak, E.: Stability of the steel shell of a vertical cylindrical tank under vacuum. Scientific-Technical Conf. “Metal Structures”, 2–4 July 2014, Kielce – Suchedniów, Poland, Kielce University of Technology, Short papers, pp. 85–88. [5] Ziółko, J., Schneider, W., Białek, T., Heizig, T., Gettel, M.: Längenabhängigkeit des Beulwiderstandes umfangsdruckbeanspruchter stählerner Kreiszylinderschalen. Stahlbau, 78(2009), No. 12, pp. 947–951. DOI: 10.1002/stab.200910110 [6] MSC Nastran for Windows, MSC Software Corporation, Los Angeles, 2002. Keywords: cylindrical tank; steel; shell; underpressure; deformations

Authors: Prof. Jerzy Ziółko, PhD Professor at University of Science & Technology Al. prof. S. Kaliskiego 7 L85-796 Bydgoszcz, Poland Tomasz Mikulski, PhD Ewa Supernak, PhD, Eng. Both authors: Gdan´sk University of Technology ul. G. Narutowicza 11/12 80-952 Gdan´sk, Poland

Articles Barbara Gorenc* Darko Beg †

DOI: 10.1002/stco.201400001

Curtain wall façade system under lateral actions with regard to limit states During high wind or earthquake action, high-rise multi-storey buildings respond with relatively large storey drifts. The building envelope, in this case a curtain wall, exposed to this in-plane shear resists the action with its drift capacity. This paper describes tests on two different conﬁgurations of a newly developed unitized curtain wall, “Qbiss Air” (QAir), using three different cyclic protocols. The protocols were derived on the basis of the serviceability limit state for regions with moderate to high wind and seismicity. The details and conﬁguration inﬂuence the response of the system signiﬁcantly, so the design of the structure can provide accurate information for the design of such systems.

1 Introduction In the past, façade systems used to be a part of the loadbearing structure which also kept out the heat, rain and wind. As structural systems and materials have developed, so heavy façades have been replaced by lighter ones, including curtain walls with large glass panels, which have become especially desirable in high-rise buildings. The assembly has become simpler and new functionalities have been introduced (e.g. transparency, thermal and sound insulation). In the structural sense, only self-weight, wind action and temperature changes perpendicular to the façade plane [1] have been considered for the design of façades. Curtain walls are suspended from the edge of a concrete slab or steel edge beam and all dead loads are transferred to the structure through point anchorages. Over the last decade, research has started to focus on understanding façade behaviour under the in-plane shear that can be expected during high wind and earthquake action. There is a high risk of the glass panels in typical curtain walls breaking and

* Corresponding author: barbara.gorenc@trimo.si

falling out [2], depending on the placement within the frame, the oﬀset between two glass panels and the type of ﬁxing to the structure. According to some authors [3], typical curtain wall systems would reach this ultimate condition at an inter-storey drift of approx. 30–40 mm for a typical 4 m storey. This deﬁnes the drift capacity of façade elements as a property that can be determined and/or tested. Storey drift ratios and maximum deﬂections for serviceability (SLS) and ultimate (ULS) limit states for structures are well deﬁned in European standards for wind [4] and earthquake [5], but only a very general idea is given on the drift capacity of non-structural elements. The solution can be two-fold: Firstly, limits from the design of the structure can be adopted and used when testing or designing the façade system. The system should remain intact and retain its functionalities in SLS but suﬀer limited damage and stay ﬁxed to the structure in ULS, which would prevent components from falling onto areas below. Secondly, limits speciﬁc to the façade system for SLS and ULS can be deﬁned through loss and retention of its own functionalities during diﬀerent phases of testing. This could be used later in building design. A new type of unitized curtain wall, “Qbiss Air” (QAir), produced by

the Trimo d.d. company from Slovenia, was tested [6] in this study. Five tests were performed on a part of a façade wall comprising three façade panels (Table 1). Two tests employed monotonic loading, used to determine the general response of two diﬀerent conﬁgurations, and the other three employed cyclic loading derived from the response of the structure designed for moderate to strong wind and earthquake loads as well as a comparative protocol according to interim testing protocols in FEMA 461.

2 Testing facility, test setup and test specimens The tests were performed in the laboratory of the Faculty of Civil Engineering, University of Ljubljana, between May and June 2013. The QAir system used in this study is a unitized glass curtain wall, intended primarily for use as an energy-eﬃcient building envelope in highrise buildings. According to the manufacturer’s speciﬁcations, there are many diﬀerent materials to choose from [6], including toughened glass, sintered ceramics, high-pressure laminate, wood or stone. Individual components of the panel are shown on the left in Fig. 1. They comprise clear toughened ﬂoat glass (8 mm) for the outer skin, a ﬁve-chamber core made from aluminium foil and spacer bars and an inner skin consisting of 12 mm wood ﬁbre-reinforced gypsum board. An integrated substructure made of polyamide and glass-ﬁbre extruded proﬁles (PA-GF40) with inserted steel tubes (50 w 30 w 2.5 mm) is located on both vertical sides of the panel. Ethylene propylene diene monomer (EPDM) rubber gasket proﬁles are in-

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B. Gorenc/D. Beg · Curtain wall façade system under lateral actions with regard to limit states

Table 1. Test research programme on Qbiss Air façade system Test

Type

Base derivation

Specimen Type

Test Specimen

Rate of drift application v

No. of Cycles

Relative Sorey Drift Ratio 6 [mrad]

Relative Storey Drift uaxis

T1-m

Monotonic

Benchmark 1

QAir1

S1

0,2 mm/s

/

43

108 mm

T2-1

Cyclic

Wind – SLS

QAir1

S2

4 mm/s

500

3

t8,5 mm

T2-2

Cyclic

Wind – SLS

QAir2

S2

4 mm/s

500

3

t8,5 mm

T2-3

Cyclic

Wind – ULS

QAir2

S2

6 mm/s

20

5

t12,0 mm

T2-m

Monotonic

Benchmark 2

QAir2

S2

0,2 mm/s

/

34

85,2 mm

T3

Cyclic

Earthquake – MRF10 – acc

QAir1

S3

4 mm/s

154

19

t47,5 mm

T4

Cyclic

Earthquake – MRF10 – acc

QAir2

S4

4 mm/s

234

25

t62,5 mm

T5

Cyclic

FEMA 461

QAir2

S5

4 mm/s

58

74

t184,9 mm

serted along the length of the PA-GF40 and form part of the ﬁnished element (joint detail, QAir1, Fig. 2). Where the panel is anchored to the structure, steel hook elements are ﬁxed into the PA-GF40 profile. Self-weight and forces perpendicular to the plane (wind, temperature) are transferred through them directly into the supports. Façades are not normally designed for large in-plane shear resistance. Instead, the basic assumption is that the panels compensate for large storey drifts and the resulting forces with some damage. In this case, however, the basic assumption was that the system will respond with adapt-

ability on supports and that damage, if it occurs, will be minimal and localized. The system is designed to allow relative ﬂexibility during assembly, taking into account diﬀerent tolerances on the primary structure [7], [8] or at least t20 mm in the three main directions (Figs. 1 and 2). The specimen tested represents a part of the façade consisting of three 2.5 m high w 1 m wide panels with two intermediate vertical joints. Panels were hung from the upper support elements mounted on the test frame (Fig. 1) and slid on pins 70 t 10 mm on the bottom support element. When all

Fig. 1. Panel with components (bottom left), layout of assembled test specimen (TS) on test frame with pin joints (PJ) lateral sliding supports (LSS) with LCS (x-y) for joints and GCS (X-Z) for the elements used and the direction of displacement designated by t uaxis and support details (right)

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three panels were assembled on the pinned test frame, they were levelled with each other in the out-of-plane and horizontal directions with an accuracy of up to 1 mm. A ﬁnished joint between the panels was 20 t 1 mm wide. After levelling, ﬂame-retardant elastic PUR foam, a usual part of the system which ensures tertiary watertightness and thermal and sound insulation, was injected into the joint and left to cure for at least 12 hours prior to testing. Two system assembly conﬁgurations were tested (detail A – A, Fig. 2): a) QAir1 – vertical joint as per manufacturer’s speciﬁcation with EPDM and PUR materials [6] – “rigid joint” b) QAir2 – material removed from joint – “ﬂexible joint” Five groups of tests were performed (T1–T5): two monotonic (T1-m and T2m), one for each conﬁguration (QAir1, QAir2) and four cyclic, one for wind action at diﬀerent storey drift levels (T21, T2-2 and T2-3), two for seismic action (T3 and T4) and one (T5) according to FEMA 461 [9] (Table 1). The rectangular test frame was composed of four steel sections joined together at the corners with pin joints. The bottom section was attached to the ﬁxed-base steel section that was levelled on a cement bed on the strong concrete floor. Sliding supports mounted on top controlled out-of-plane movements. A hydraulic actuator was attached to the reaction wall on one side and to the test frame on the other. Pinned joints were used to reduce the inﬂuence of the primary structure

B. Gorenc/D. Beg · Curtain wall façade system under lateral actions with regard to limit states

Fig. 2. Vertical joint detail for QAir1, with gaskets (Nos. 11 and 12) and PUR foam (No. 10), and QAir2, without those materials, bill of materials for the assembled system and support proﬁle elements with tolerance ranges. Horizontally, tolerances are compensated through design of support elements, vertically, however, are only achieved with the panel sliding up and down the supports.

on the force–displacement response of test specimen. The frame without test specimens was tested to determine the level of inﬂuence (Fig. 3) for later use in the specimen response analysis. A maximum force of 1.2 kN was observed at a frame column rotation 6 " 0.048. At 6 " 0.02, which is double the SLS limit for structure under earthquake, the force was only 0.4 kN.

Displacements of the frame and specimens as well as slip and opening of joints were measured with displacement transducers (measuring range t25 mm and t50 mm, error t0.1 mm) and rotation with dual axis inclinometers (measuring range t15°, error t0.1°). The applied force was measured by the actuator load cell. Horizontal lines spaced at 100 mm inter-

vals were drawn along the length of the vertical joint between two panels on the front and the back as a visual control measure.

3 Testing protocols The test series and protocols were developed by ﬁrst designing a typical 10-storey 2D moment-resistant frame

Fig. 3. Measured residual force in the empty frame from imposed relative drift ratio 6 and position of measuring equipment (transducers – numbered, inclinometers – CL) on the test frame, including the measurement (H – horizontal, V – vertical)

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B. Gorenc/D. Beg · Curtain wall façade system under lateral actions with regard to limit states

Fig. 4. MRF conﬁguration used to deﬁne test protocols for wind and earthquake

(MRF) with three bays each spanning 6 m (Fig. 4) according to Eurocode standards [4], [5], [10], [11] and then analysing it using non-linear dynamic analysis based on three selected ground motion records. HEB sections were chosen for the structural members, with elastic plastic material law and a kinematic isotropic hardening and characteristic minimal yield strength of 355 N/mm2. The characteristic used in all test protocols was the relative storey drift ratio 6 (Fig. 4). Rate of drift application was 0.2 mm/s for monotonic and 4 mm/s for cyclic tests. The monotonic rate was intended to capture response and detect possible failures of the specimen in in-plane shear through instruments and observation. The cyclic rate was considered to be similar to the inﬂuence of gust or earthquake in order to avoid the inﬂuence of the viscoelasticity of the materials within the specimen and to be executed within a reasonable amount of time. The rates were conﬁrmed through the T1 and T2 tests. The stiﬀness of the sample through two diﬀerent types of test remained the same until very high drift ratios.

3.1 Deﬁning experimental test protocols for exposure to wind actions The raw data for the maximum average wind speed over 10 min and 3 s (gust) intervals were obtained from the national Agency of the Republic of Slovenia for Environment (ARSO). It conﬁrmed that the base wind speed vb,0 in the region of Slovenia, deﬁned in the national annex [10], was gener-

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Steel Construction 9 (2016), No. 1

ally higher than the statistical vb,0 from 15 years of data collected since 1997. Considering a characteristic combination, there is a 2 % probability of wind pressure at a level of SLS or higher each year, which would occur at least once in 50 years of the design life. This would cause a maximum structural relative storey drift 6SLS to be limited with 1/300 of the storey height according to Eq. 6.14b [11] and the values from Table A.1.4 [11]. However, from the frequent combination, the probability would be higher and would account for about 50 occurrences in the design life, but at a lower 6SLS. To be on the safe side, the benchmark amplitude taken was that of the characteristic 6SLS translated into deflection on the zaxis (Fig. 1), uSLS " t8.5 mm with 10 times the number of cycles (500) at the frequent combination. Since for ULS the characteristic combination is factored with 1.5 in unfavourable conditions, an additional 20 cycles were performed for uULS " t12.0 mm. The tests using these protocols were designated T2-1, T2-2 and T2-3 (see Table 1).

3.2 Deﬁning experimental test protocols for exposure to earthquake actions Testing protocols for earthquake actions vary, depending on the materials used [12]. To construct protocols, the non-linear dynamic analysis procedure was performed on an MRF building model (Fig. 4) using SAP 2000 software [13]. The target spectrum used for peak ground acceleration was ag,475 " 0.25 g (g " gravitational acceleration), with a return period TR,ULS "

475 years [14]. A weaker ag,SLS " 0.13 g with approx. TR,SLS " 50 years was chosen for damage limitation, and a stronger ag,1.3ULS " 0.33 g with approx. TR " 1300 years for the near-collapse situation, designated by SLS and 1.3 ULS respectively. Combined average response spectra with 5 % damping ratio, see section 3.2.3.1.2.(1) [5], were developed from 22 recorded accelerations taken from the European Strong Motion Database [15]. Records were sized to comply with the requirements of section 3.2.3.1.2(4) [5] for three different ground accelerations using a procedure similar to [16]. Out of 22 records analysed, three were selected as representative, i.e. 333X, 333Y (Korinthos-OTE Building) and 1230Y (Iznik-Karayollari Seﬁgi Muracaati) (Fig. 5). The highest average drift ratio 6 was obtained in the 3rd storey. The spectrum that became the basis for the protocol, designated by MRF10-acc, was constructed (Fig. 6a) from these responses by counting events when the storey peaked at an interval of )6I " t0.002 starting from 61 " t0.001. Within the spectrum ground accelerations were grouped together based on peak ground acceleration ranged from weakest to strongest, with ag,SLS first and ag,1.3ULS last. Within one group, the least intense protocol was the ﬁrst, followed by the most intense and the average last. Only one (1230Y) was used for ag,1.3ULS as it is less likely to occur more than once within the design life of the structure. After every group there was a short pause to check for possible damage. Two tests were carried out: the test on QAir1 was designated T3 and that on QAir2 as T4 (Table 1).

B. Gorenc/D. Beg · Curtain wall façade system under lateral actions with regard to limit states

Fig. 5. Deﬁning the number of cycles from the results of NDA by counting events at ag,475 " 0.25 g for 3rd storey for three chosen ground accelerations

3.3 Test protocol according to FEMA 461

4 Test results

For test T5 (Fig. 6b), the protocol from Table 2-1 in FEMA 461 [9] was used as a comparison. It is primarily intended to determine fatigue damage for non-structural elements exposed to earthquake loading. The protocol was started with 10 cycles of uel " t10 mm. This is a 25 % increase in 6SLS for wind, but it is lower than when the damage was ﬁrst observed in test T1m. This protocol has higher amplitudes but a lower cumulative number of cycles (Fig. 7) than the constructed MRF 10 – acc, attempting to represent the realistic frame response.

The designated SLS and ULS limits are shown in all the resulting diagrams (wSLS and wULS for wind and eSLS1, eSLS2 and eSLS3 according to section 4.4.3.2 [5] for earthquake).

a)

4.1 T1-m – monotonic test The ﬁrst test was monotonic, performed on the QAir1 conﬁguration. Throughout the test, elements moved and rotated as a rigid diaphragm, with joints holding the panels ﬁrmly together by cohesive (PUR) and friction (EPDM) forces. The resulting force

increased at a constant rate with the increase in relative storey drift until it reached its limit FULT,T1-m " 24.67 kN at 6ULT " 0.043. The polyamide proﬁle then delaminated from the core of P3 at the upper support where the force was concentrated (Fig. 9a and Fres in Fig. 9b). Panel P1 on the left side rose up and nearly unhooked from the upper support element. Opening (du,x) and slip (du,y) at the end of the test were only 3 and 8 mm respectively (Fig. 8b). At 6 " 0.02 (2xeSLS3), du,x is close to 0 and du,y is ! 2 mm. The ﬁrst change was observed as the initial stiﬀness fell by a 1/3 at 6"

b)

Fig. 6. Spectrum for relative storey drift ratio and consequent shape for both protocols used in tests: a) MRF10-acc, b) FEMA461.

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B. Gorenc/D. Beg · Curtain wall façade system under lateral actions with regard to limit states

Fig. 7. Comparing amplitudes and number of cycles for MRF10-acc and FEMA 461

0.007 (pt. 1 in Fig. 8a). The elements began to slide up the pins at the bottom (Fig. 9a) and longitudinally along the upper support (Figs. 9d and 9e). The joints compressed and slid imperceptibly to the naked eye. At 6 " 0.020 (pt. 2a in Fig. 8a), the upper support slipped and the gypsum board of element P3 (Fig. 1) pressed on the

bottom support and suﬀered damage (Fig. 9c). At 6 = 0.02 (2xeSLS3) joint opening du,x is close to 0 and slip du,y is < 2 mm (Fig. 8b). At 6 " 0.039 (pt. 3a in Fig. 8a), the hook element on the panel reached its extreme position on the support. The test was paused to check for damage visually. At that time the force in the system

a)

fell by 1/3 but quickly increased after restarting the test. At the end of the test (6ULT = 0.043) panel P1 on the left side rose up and nearly unhooked from the upper support element. The polyamide proﬁle then delaminated from the core of P3 at the upper support where the force was concentrated (Fig. 9a and Fres in Fig. 9b). Opening (du,x) and slip (du,y) were only 3 and 8 mm, respectively (Fig. 8b).

4.2 T2 test (QAir1 and QAir2 conﬁguration) – wind Test T2 involved three consecutive cyclic tests followed by one monotonic test (Table 1). The ﬁrst cyclic test on the QAir1 conﬁguration was designated T2-1. Similarly to T1-m, the specimen again responded as a rigid diaphragm

b)

Fig. 8. a) QAir1 (blue) and QAir2 (red) exposed to monotonic tests T1-m and T2-m, b) opening and slip diagram and in situ deﬁnition for du,x and du,y

a)

b)

d)

e)

c)

Fig. 9. a) slip of P1 from bottom pin, b) panels slip on intermediate support (marked by arrows), c) gypsum board pressing on bottom support, d) delamination of PA+40GF from core, e) damage on PA element from excessive shear force

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Steel Construction 9 (2016), No. 1

B. Gorenc/D. Beg Âˇ Curtain wall faĂ§ade system under lateral actions with regard to limit states

a)

Fig. 10. QAir1 (blue) and QAir2 specimen through each phase of T2 test

and compensated amplitude merely through rotation and drift on supports, with no visible slip or opening of intermediate joints. The maximum force in the specimen was 5 kN and â€“7.2 kN. Even after 500 cycles, all F-6 loops remained the same, the force in the specimen decreased slightly; the specimenâ€™s mechanical properties did not degrade (Fig. 10). As the upper and bottom supports permitted the sliding of the elements, a relative drift of the panels was 0.001 rad smaller than the one induced in the frame. In T2-2, material was removed from joints and the test repeated. Since panels were no longer connected through joints, they did not inďŹ‚uence each other directly and so they swayed individually. Compared with T2-1, the resistance or the force was lower by 1/3 for the same 6 and the drift capacity was consequently higher. There was no perceptible change during 500 cycles in the characteristic loop. The last leg of the cyclic test, designated T2-3, consisted of 20 cycles at uaxis " t12.0 mm, consistent with ULS. The increased amplitude only caused a linear increase in force in the specimen and the shape of the loop remained similar to T2-2 (Fig. 10). No cracking, loss of stiďŹ€ness or any other damage were detected during the cyclic phases of T2 on QAir1 or QAir2. At the end of test T2-3, a monotonic test was performed on QAir2 (T2-m). The results are presented alongside those from T1-m (Fig. 8a). The initial response of QAir2 was similar to QAir1 until 6 " .0 when the force in the specimen decreased. The vertical joints that were cleared of material oďŹ€ered no resistance to imposed shear, so the force

could not transfer from one panel to the next via a longitudinal joint, but only indirectly through the supports. The panels stopped sliding with an induced drift but began rotating individually. With this movement, the shear capacity in the sample stabilized until 6 " 0.034 (FULT,T2-m " 3.49 kN), when delamination of panel P1 at the upper left support was observed. The specimen returned to its original starting position after the test. Force FULT,T2-m was less than 1/6 of FULT,T1-m.

4.3 T3 test (QAir1 conďŹ guration) â€“ seismic action The test was performed on the QAir1 specimen (S3) using the MRF10-acc protocol. It responded as a rigid diaphragm, much the same as in T1-m. The forces (Fmax " t10 kN) were concentrated at the outside corners where the specimen was attached to the frame. The horizontal drift ratio translated to the vertical through specimen rotation. The specimen formed a distinct loop in the F-6 diagram (Fig. 11a with a larger surface in one (positive) and smaller in the other (negative) direction. The reason for this is rather diďŹƒcult to determine. It is evident when comparing the three diagrams in Fig. 10 that the diďŹ€erence is entirely in the force measured in the actuator. It could be that the actuator used in this testing had a capacity that was too high (250 kN) and the forces generated in the sample were too low, creating an additional error that was diďŹ€erent in two directions. The system may have been too sensitive. The test rig or the samples may not have been assembled perfectly so the force needed for pushing the frame was greater than

b)

c)

Fig. 11. Response of QAir1 conďŹ guration (last loop before shift is red) during ULS phase of T3 test: a) global response of S3, b) joint slip, c) joint opening

the one for pulling. There may also have been a greater resistance in the joints to the compression than to the tension, thus reducing the force in the negative direction. But that would have been visible in the deformations of the joint. The diďŹ€erence is very small, however, and does not outweigh the drift capacity achieved. A distinct pinching eďŹ€ect as well as shift of response loop centre to {F, 6b "`â€“4.4 kN, â€“0.005} in the third phase are visible globally and locally in all diagrams. The joint slip and opening were small â€“ between 0.5 and 1.3 mm (Figs. 11b and 11c). The SLS phase passed without any signiďŹ cant change and QAir1 returned to its initial position. Halfway through ULS, the end of the second phase, the specimen became stuck with the hook on the upper left support in an elevated position (Fig. 12a) at 6 " 0.013. The elements remained ďŹ xed on the test frame so the test continued. The specimen was subse-

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B. Gorenc/D. Beg · Curtain wall façade system under lateral actions with regard to limit states

test, S4 returned to its original position without visible damage. Slip (du,y) and opening (du,x) of the joints can be seen in Figs. 13b and 13c. The opening of the joint increased with every loop due to the slip on the upper support, but the form of the loop remained the same. The joint opening of 11 mm was the only residual deformation in the system after the test. a)

b)

Fig. 12. Steel hook detail on P1 panel at end of second part and during third part of ULS phase of test T3: a) pinned at upper left corner of P1 in elevated position on support, b) bent out of shape permanently at end of second part of test

quently irreversibly damaged when the steel hook on the left corner deformed (Fig. 12b) and the PA proﬁle on the right upper corner cohesively delaminated away from the gypsum board, core and glass layer. The loadbearing capacity of the specimen had

been reached. The test was stopped after ULS and 1.3ULS was not performed.

4.4 T4 test (QAir2 conﬁguration) – seismic actions Test T4 is a repetition of test T3 but on the QAir2 specimen. During the test, the façade elements reacted individually (Fig. 13). As the drift ratio 6 increased, so a steady increase in force was observed in the SLS phase until 6 " 0.0075 (t6 kN). After that, the force stabilized even though the amplitude increased. Every loop followed an almost identical path at the same amplitude. The entire MRF10acc test protocol was run. After the

a)

4.5 T5 test (QAir2 conﬁguration) – FEMA 461 Similarly to the T2-2 and T4 tests, the elements in T5 responded individually (Fig. 14a). Slip and opening of joints were not hindered (Figs. 14b and 14c). The amplitudes tested were 2.5 times higher than the highest limit for SLS under earthquake (Fig. 14a). At every loop until 6 " 0.0075 (t7 kN) the specimen exhibited a linear F-6 ratio due to the interaction between panel and supports, after which the drift increased with the increase in amplitude as well, but the force in the system remained the same. It increased only at very high drift (beyond 6 " 0.05), where the physical limit on supports was reached. At 6 " 0.065, the panels unhooked in the upper corner and the force decreased. The other three corners were still attached to the frame so they did not fall out. As the

b)

c)

Fig. 13. Response of QAir2 conﬁguration during all three phases of T4 test: a) global response of S4, b) joint slip, c) joint opening

44

Steel Construction 9 (2016), No. 1

a)

b)

c)

Fig. 14. a) response of S5, b) drift between P2 and P3, c) lift of panel P2 at upper support

B. Gorenc/D. Beg · Curtain wall façade system under lateral actions with regard to limit states

direction of the drift changed, so all the panels re-hooked back into the support proﬁles. After the test had been concluded and sample S5 closely inspected visually, no permanent damage to the individual panels (delamination, cracks) was found.

5 Conclusions The “Qbiss Air” system responded to drift rather than with its loadbearing capacity with ﬂexibility of the system on supports. The assumption that the damage would not occur, except at very high levels of storey drift, was conﬁrmed. Panels never fell out of the frame. The drift capacity observed is much higher than in some existing curtain wall systems [2], [3]. Supports, intended to compensate for tolerances, help increase the drift capacity of the system. The resulting force in the system is in the range of t10 kN for QAir1 and t5 kN for QAir2 at 6 " 0.02. This is much lower than the total horizontal force expected in one storey of the frame from wind or earthquake. Nevertheless, it cannot be entirely neglected and should be considered when designing components in façade systems. Storey drift ratios 6 are very important for façade design under any lateral action. Considering SLS in [5], the maximum inter-storey drift demand on the system for regular buildings in the region of moderate wind and high seismicity is 0.02. Both QAir1 and QAir2 were able to compensate small (6 f 0.005) and moderate (6 f 0.01) relative storey drift ratios with no damage to the elements or components. This was especially true in the T2 test, where the capacity was large enough to compensate for 1/300 of the storey height even after 500 cycles. Damage was detected only at very large amplitudes (6 v 0.02) and only in the QAir1 conﬁguration. Cohesive (PUR) and friction (EPDM) forces held panels together in the joints, which then resulted in a rigid diaphragm response. Damage was localized where stresses concentrated in the panels around supports (see T1-m and T3 tests), but was more ductile than brittle, progressing slowly. At no time did the panels or any part of the system collapse. Glass layers were not in danger of colliding or breaking.

Slip and opening of joints in QAir1 were ! 1 mm and had no adverse eﬀect on the joint functionality, e.g. watertightness, at normal drift ratios. In QAir2, slip and opening of the joints were larger, ranging from a few millimetres up to 20 mm for slip and 12 mm for the opening. In the extreme conditions at very high levels of 6, the function can become compromised unless the gaskets are ﬂexible. Based on the results, joints could be redesigned to be more ﬂexible, thus increasing the drift capacity of the existing system. Several options are currently under consideration at Trimo, ranging from softer materials to diﬀerent frames to diﬀerent shapes for the joint. However, if any changes are made, the basic functions of the system, loadbearing capacity, watertightness, thermal and sound insulation should also be preserved.

Acknowledgements The authors gratefully acknowledge the support of the Public Agency for Technology of the Republic of Slovenia through its programme of funding “Young Researchers from the Economic Sector – Generation 2009”, contract No. 3211-09-100049, which made this research possible. References [1] Davies, J. M.: Lightweight sandwich construction, Blackwell Science, 2001, pp. 311–314. [2] Memari, A. M., Behr, R. A., Kremer, P. A.: Seismic Behaviour of Curtain Walls Containing Insulating Glass Units. Journal of Architectural Engineering, vol. 9, No. 2, 2003, pp. 70–85. [3] McBean, P.: Drift Intolerant Façade Systems and Flexible Shear Walls. Do we have a Problem? Annual Tech. Conf. of Australian Earthquake Engineering Society, Albury, NSW, 2005, pp. 35-1–35-8. [4] SIST EN 1991-1-4:2005. Eurocode 1: Actions on structures – Part 1-4: General actions – Wind actions, 2007. [5] SIST EN 1998-1. Eurocode 8: Design of structures for earthquake resistance – Part 1: General rules, seismic actions and rules for buildings, 2006. [6] Unbeatable energy eﬃcient glass curtain wall system: http://www.trimo.si/ media/qbiss-air-brochure-en_23006.pdf, 2012. [7] SIST EN 1090-1:2009: Execution of steel structures and aluminium structures – Part 1: Requirements for con-

formity assessment of structural components, 2009. [8] EN 13670:2010: Execution of concrete structures, 2010. [9] FEMA 461: Interim Testing Protocols for Determining the Seismic Performance Characteristics of Structural and Nonstructural Components, Federal Emergency Management Agency, 2007. [10] SIST EN 1991-1-4:2004/oA101. Eurocode 1: Actions on structures – Part 1-4: General actions – Wind actions – National annex, 2008. [11] SIST EN 1990:2004. Eurocode – Basis of structural design, 2004. [12] Krawinkler, H.: Loading histories for cyclic tests in support of performance assessment of structural components. 3rd Intl. Conf. on Advances in Experimental Structural Engineering, San Francisco, 2009. [13] SAP2000 (2002): Analysis reference manual, Computers and Structures, Inc., Berkeley. [14] SIST EN 1998-1-4:2005/A101. Eurocode 8: Design of structures for earthquake resistance – Part 1: General rules, seismic actions and rules for buildings – National annex, 2009. [15] Ambraseys, N., Smit, P., Sigbjörnsson, R., Suhadolc, P., Margaris, B. (2001): Internet-Site for European Strong-Motion Data. <http://www.isesd.cv.ic. ac.uk>, EVR1-CT-1999-40008, European Commission, Directorate-General XII, Environmental and Climate Programme, Brussels, Belgium, Jan 2013. [16] Reyes, J., Kalkan, E.: How Many Records Should Be Used in ASCE/SEI-7 Ground Motion Scaling Procedure. Earthquake Spectra, vol. 28, No. 3, 2012, pp. 1223–1242. Keywords: unitized curtain wall; serviceability limit state; in-plane shear; drift capacity; wind; earthquake; relative storey drift ratio; testing protocols; experimental test

Authors: Barbara Gorenc, BSc Trimo d.d., Prijateljeva c. 12 8210 Trebnje Slovenia Prof. Dr. Darko Beg † University of Ljubljana Faculty of Civil & Geodetic Engineering Chair for Metal Structures Jamova 2 1000 Ljubljana Slovenia

Steel Construction 9 (2016), No. 1

45

Articles Akbar Pirmoz* Parviz Ahadi Vahid Farajkhah

DOI: 10.1002/stco.201350003

Finite element analysis of extended stiffened end plate link-to-column connections The applicability of extended stiffened end plate (ESEP) connections used as link-to-column connections in eccentrically braced frames (EBFs) with long (ﬂexural yielding) links is examined in this paper. A ﬁnite element method (FEM) is used for this purpose, based on a validated parametric FE benchmark. Analysing the numerical model of an ESEP connection designed to the recent seismic design rules for special moment frames reveals that the link-to-column connections of EBFs sustain more severe conditions than the moment connections of moment-resisting systems. The design approach implemented is examined and the results are discussed. The results demonstrate that ESEP connections can be used as a successful alternative for the link-to-column connections of EBFs and the system with this type of connection can achieve the required rotations for long or ﬂexural links.

1 Introduction In recent years, EBFs have been widely used in steel structures in different countries. These systems are known to fulﬁl the seismic design parameters, providing relatively high ductility, strength and stiﬀness, and also oﬀer architectural ﬂexibility. Successful seismic performance of an EBF necessitates that all its components have suﬃcient resistance to carry the forces imposed by the active link. Accordingly, failure of any of these components can interrupt the energy dissipation mechanism. A special conﬁguration of this system, the K-type, includes only a single brace and its link is directly connected to the adjacent column by a fully restrained (FR) connection. Owing to the severe loading conditions of linkto-column connections and the potential for premature connection failure, the 2010 AISC Seismic Provisions [1] require qualiﬁcation testing of link-tocolumn connections. However, the provisions do not introduce a prequaliﬁed link-to-column connection for

* Corresponding author: a.pirmoz@ut.ac.ir

46

practical use, and the issue of the seismic link-to-column connection is still unresolved for researchers and engineers. Early tests by Malley and Popov [2] on short shear-controlled link-tocolumn connections with welded ﬂange-bolted webs demonstrated the poor performance of these connections. The tests by Engelhardt and Popov [3] demonstrated that the dominant failure mode of the long links connected to the columns was fracture of the link ﬂanges prior to adequate rotation. As a result they proposed that long links connected to the column should be avoided in EBFs until further research was available. Ghobarah and Ramadan [4] tested six short shear link-to-column connections, ﬁve of which were extended end-plate (EEP) connections. The results of their study demonstrated that a well-designed EEP link-to-column connection can withstand the severe forces of the active link until the required inelastic rotations are achieved. Okazaki et al. [5] tested 12 large-scale link-to-column connections with four diﬀerent details and three diﬀerent link lengths. Only one of the intermediate links with a free ﬂange detail achieved the required rotation and fractured immediately after this rota-

tion. Drolias [6] tested eight largescale welded link-to-column connections in two phases. Six of the eight specimens achieved the required inelastic rotations with acceptable safety margins.

2 Aim of the current study The recent experimental studies on link-to-column connections cover different types of welded FR connections. In those studies, the applicability of ESEP connections as link-tocolumn connections for long link beams was evaluated using non-linear FEM. First, the connection is designed according to the recent seismic design rules for the special moment frames. It is then subjected to the conditions of the link-to-column connections and analysed. The results are discussed and the design method is modiﬁed to achieve a connection that can sustain the forces imposed by the fully yielded active link. It is anticipated that limiting the connection behaviour to the elastic response can make the eﬀects of the cyclic loading tolerable. In this regard, non-linear FEM could be a rigorous tool for evaluating the connection and examining the proposed design method.

3 ESEP link-to-column connections During the Northridge (1994) and Kobe (1995) earthquakes, the poor performance of the FR pre-Northridge moment connections compelled investigators and engineers to search for new connection conﬁgurations that exhibited favourable performance. The ESEP connection was among the connection types studied

A. Pirmoz/P. Ahadi/V. Farajkhah · Finite element analysis of extended stiffened end plate link-to-column connections

Fig. 1. Test setup (left) and details of test specimens (right)

for special moment frames. Experimental studies [7–12] demonstrated that well-designed end-plate connections exhibit ductile performance in moment frame applications. There have not been any studies performed regarding the performance of ESEP connections as link-to-column connections in EBFs for the long ﬂexural links. Some advantages of the ESEP connections as a link-to-column connection, compared with a welded FR connection, could be: – Applicability of the full penetration groove welds or high-quality shop ﬁllet welds. – Reduced eﬀort for quality control and decreased construction time. – Strength and stiﬀness enhancement of the connection using rib stiﬀeners. – Beneﬁcial stiﬀness of the end-plate stiﬀeners (ribs) can decrease the panel zone distortions and the imposed stresses in the panel zone. – Contribution of the end plate to the strength capacity of the panel zone. – Relatively higher ductility with respect to welded rigid connections. – During an earthquake, probable slippage of the connection components may increase the damping of the system. – Ease of replacing damaged links after a severe earthquake. Since the ESEP connections are designed to remain mainly elastic, and also due to the time-consuming computational burden of the FEM in predicting the response of the bolted con-

nections under cyclic loads (Pirmoz, 2006), this study is limited to examining the connection response under monotonic loading.

4 Study methodology 4.1 Benchmark test results To assess the validity of the numerical models, the results of the FEM were compared with the test results of Shi et al. [13]. In that study, ﬁve full-scale ESEP connections were tested under monotonic loading. Fig. 1 shows the test setup and Table 1 lists the geometric characteristics of the specimens. The section depth, web thicknesses and ﬂange thicknesses of the columns and beams are 300, 8 and 12 mm respectively, the ﬂange widths 250 mm (column) and 200 mm (beam) [13].

4.2 FE modelling The ANSYS multi-purpose ﬁnite element modelling code [14] was used for the numerical modelling (Fig. 2) of the test specimens of [13], which were selected as the benchmark specimens. The connections consisted of a column with a cantilever beam mounted on the column by means of an ESEP connection. The models were created using the ANSYS Parametric Design Language. Since the aim of this study is to assess the link-to-column ESEP connections (for which the boundary conditions are different from the tested models), a Base Model was created which includes the out-of-thelink segment of the beam and the fulldepth web stiﬀeners of the link (Fig.

3). It should be noted that the model presented in Fig. 2 is created using the Base Model (shown in Fig. 3), which eliminates the elements of the out-ofthe-link beam and the web stiﬀeners. This model represented the test specimens used for validation of the numerical models. The ﬁnite element mesh pattern of the link-to-column connection (corresponding to specimen EPC-1 from [13]) is shown in Fig. 2 (left). The geometry and mechanical properties of the connection models were deﬁned as parameters to reduce the amount of time needed to create new models. The numerical model of the connection included the following considerations: – All of the components of the connection (e.g. beam, column, endplate and bolts) were modelled using solid elements. The SOLID45 element was used for this purpose. This element is deﬁned by eight nodes that contained three degrees of freedom at each node: translations in the nodal x, y and z directions.

Table 1 Geometric characteristics of the specimens tested by Shi et al. [13] Specimen

Bolt dia. (mm)

End plate thk. (mm)

EPC-1

20

20

EPC-2

25

20

EPC-3

20

24

EPC-4

25

24

EPC-5

16

20

Steel Construction 9 (2016), No. 1

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A. Pirmoz/P. Ahadi/V. Farajkhah · Finite element analysis of extended stiffened end plate link-to-column connections

Fig. 2. FE mesh pattern of EPC-1 (left) and contact elements between adjacent surfaces (right)

Fig. 3. FE mesh pattern of Base Model with 51 834 elements (left) and boundary conditions (right)

– No weld failure was detected during the tests. It is expected that the eﬀect of the welds on the response of the connection components is negligible. Accordingly, for simplicity, the FE modelling did not explicitly include the welds. – To achieve a precise through-thickness stress distribution and ﬂexural deformations of the end plate, the end plate was divided into four segments through its thickness. – The cylindrical bolt shank was approximated by a 12-sided prismatic volume and divided into six elements in the radial and longitudinal directions to capture the ﬂexural deformations and the prying actions more accurately. – The eﬀects of adjacent surface interactions were modelled using

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Steel Construction 9 (2016), No. 1

contact elements. ANSYS can model contact problems using contact pair elements CONTA174 and TARGE170, which pair together in such a way that no penetration occurs during the loading process. Thus, interaction of the adjacent surfaces, including nut/head-end plate, bolt shank-bolt hole and end plate-column (Fig. 2), are considered in the FEM. The eﬀects of friction were modelled using the contact elements mentioned. To consider the frictional forces, Coulomb’s coeﬃcient was assumed to be 0.44, as reported in [13]. – Although AISC 358 (2010) does not necessitate the use of slip-critical connections for ESEP connections, the bolts of the models are pretensioned to simulate the test

specimens more precisely. In order to simulate the pretensioning forces in the bolts, an initial contraction was applied to the shanks through a negative thermal gradient. The magnitude of the thermal gradient needed for the bolt pretensioning depends on several factors such as the stiﬀness of the plates and the adjacent areas, assumed normal stiﬀness for the contact elements, assumed penetration tolerance, the length of the shank and the thermal coeﬃcient assigned to the material of the bolt shank. Accordingly, the target value was ﬁxed through a trial-and-error process. Once the shank of the bolts contract due to this thermal change, the nut and head make contact with the column ﬂange and

A. Pirmoz/P. Ahadi/V. Farajkhah · Finite element analysis of extended stiffened end plate link-to-column connections

the end plate. The contact elements prevent shortening of the bolt and penetration of the nut/head into the body of the adjacent plates. Preventing shortening of the shank strains it and imposes a tension force in it. This method of pretensioning represents the actual conditions of bolt pretensioning during construction and has been successfully used in numerical modelling of bolted angle connections with/ without web angles in [16–23].

4.3 Boundary conditions of FE models Previous numerical studies performed by Pirmoz [16] regarding the numerical modelling of the bolted connections under cyclic loading demonstrated that although the FEM yields adequate results for estimating the force–deﬂection response of the connection, the procedure is very time-consuming and cannot accurately simulate low-cyclic fatigue phenomenon (crack propagation). On the other hand, the target connection (S3 and S4 introduced in the following sections) is expected to behave in an elastic manner and therefore the effects of cyclic fatigue (which is crucial for higher levels of stress and strain) should be negligible. The models were then subjected to a displacement-controlled monotonic loading. Fig. 3 (right) shows the boundary conditions of the models. To simulate the loading condition, the end nodes of the beam were vertically restrained and the loading was applied by a downward displacement on the nodes of the last two adjacent stiffeners simultaneously. These stiﬀeners correspond to the stiﬀeners of the gusset plate in the brace-to-link connection region. As a result, the curvature of the link section adjacent to the left end stiﬀener is zero. The out-of-plane restraints were applied by constraining the out-

of-plane movement of the nodes at the location of the loads (which represents the location of the brace) and the beam end in accordance with AISC 341 [1]. Both ends of the column ﬂanges are restrained in all directions to provide the necessary support conditions as shown in Fig. 3 (left). The applied moment at the ESEP connection was calculated satisfying the static equilibrium conditions in Fig. 3 (left) excluding the column. For the models of the test specimens, the reaction force corresponding to the applied displacement at the beam tip was multiplied by the beam length (1.2 m) to give the connection moment.

4.4 Material properties The stress–strain relationship for all the connection components of the FE models was represented by a bilinear constitutive model. An isotropic hardening rule with the von Mises yielding criterion was applied to simulate plastic deformations of the connection components. Steel of grade Q345 was used for the plates with high-strength grade 10.9 bolts. The reported mechanical properties of the material [13] are listed in Table 2. In the FE modelling, a modulus of elasticity of 200 GPa was assumed for the bolts and an ultimate strain of 0.2 considered for the material of the plates and 0.1 for the bolts.

4.5 Modelling local buckling Local buckling in the steel members is one of the causes of the strength and stiﬀness degradation, which is initiated by residual stresses and initial imperfections. Here, the connection was modelled to capture the local buckling of both the beam and the panel zone observed in the tests. To achieve this, an initial imperfection was ap-

plied in the models. This imperfection was imposed applying some initial loads on the locations conforming to the buckled regions observed in the tests. These areas include one edge of the beam ﬂange (near the end plate) and the panel zone. The loading direction is perpendicular to the plane of the ﬂange and panel zone plates. This loading results in relatively low stress levels (almost 0.1 times the yield point of the steel) in the beam and column. In this method, not only the initial imperfection but also the residual stresses (somewhat) are considered approximately through the deﬁnition of this ﬁctive initial imperfection. Both the imperfection loads and the pretension loads were applied in the same load case.

4.6 Validation of FE models The deformed shape of the EPC-4 specimen at the failure rotation is compared with the test specimen in Fig. 4. As shown in this ﬁgure, the buckling of the beam ﬂange on the compression side and the separation of the end plate from the column ﬂange on the tension side of the FE model are in good agreement with the test specimen. The distorted elements in the panel zone represent the shear deformation of the panel zone, which can be identiﬁed from the ﬂaked appearance of the panel zone of the test specimen. The moment–rotation responses of specimens EPC-1 and EPC-4 obtained from the FEM are compared with the test results in Fig. 5. In the tests, the joint rotation >joint was deﬁned as the relative displacement of the beam top and bottom ﬂanges in the direction of the longitudinal beam axes (measured by displacement transducers at the beam-column interface) divided by the beam depth. The concept of the

Table 2. Reported mechanical properties of the material [13] Material

Measured yield strength (MPa)

Measured tensile strength (MPa)

Measured elastic modulus (MPa)

Plate (thk. f 16 mm)

391

559

190 707

Plate (thk. # 16 mm)

363

537

204 228

M20 bolts

995

1160

–

M24 bolts

975

1188

–

Steel Construction 9 (2016), No. 1

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Fig. 4. Deformed shape of FE model (left) for EPC-3 and test specimen (right)

Fig. 5. Comparison of the moment–rotation response of the tests and the FE models

joint rotation is depicted using the solid lines in Fig. 6. The line that deﬁnes the joint rotation passes through the top and bottom beam ﬂange-web intersection points. The joint rotation is the rotation of this line. This deﬁnition of the joint rotation has been used previously by other researchers for other types of PR connection. The rotation >joint includes two exponents: the shearing of the panel zone and the gap rotation. The shearing rotation of the panel zone is measured similarly to the joint rotation. For this purpose, the relative displacement of the column ﬂanges at the levels of the beam ﬂanges (in the direction of the longitudinal beam axis) is divided by the beam depth. The middle solid line in Fig. 6 deﬁnes the shear rotation. This line

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Steel Construction 9 (2016), No. 1

passes through the points on the column ﬂange for which coordinates correspond to the top and bottom ﬂanges of the beam. The diﬀerence between the joint rotation and the shearing rotation gives the gap rotation. Gap rotation is due to deformations of the connection components such as the axial deformations of the bolts or ﬂexural deformations of the plate. Fig. 5 compares the calculated moment–rotation curves with those of the tests. According to this ﬁgure, the moment–rotation curves resulting from the numerical models are in good agreement with the test results within the linear range of the loading. However, in the non-linear range of the response, the diﬀerence between the FE model and the test increases,

and the FEM slightly overestimates the connection capacity. This might be due to several factors such as the exact values of the imperfections of the specimens and residual stresses, which were not considered for the sake of simplicity. Other factors that might have aﬀected the connection response in the non-linear range are the non-linear constitutive laws for materials and the stress–strain relationships, which were considered to be bilinear in the FE models. Although there was a slight diﬀerence between the FEM and the test in the non-linear range of the connection behaviour, the average diﬀerence between the two methods within the non-linear range was limited to 6.4 % for specimen EPC-4 and 8.1 % for

Fig. 6. Deﬁnition of gap rotation

specimen EPC-1. By considering the accurate estimation of the failure mode of the connection, its deformed shape and the close prediction of the moment–rotation response by the FEM, the parametric model was accurate enough to simulate the connection behaviour before large rotations or joint failure.

5 Design of link-to-column connections 5.1 Basic rules AISC 358 [15] rovides a method for the seismic design of ESEP connections for moment frames. The design parameters include the diameter of the bolts and the thickness of the end plate. These parameters are designed for the plastic moment capacity of the fully yielded strain-hardened beam Mpu increased by the resulting moment of the eccentric shear force at the rib end. The basic design philosophy aimed at in this study is to limit the ESEP link-to-column connection response below the yield point until the ultimate strength of the link is achieved.

5.2 A design method for ESEP link-tocolumn connections In AISC 358 [15], the design formulas of ESEP connections are based on yield line theory and the plastic moment capacity of the end plate, and Mpl is estimated assuming that the end

plate has fully yielded within some lines. The moment capacity of the end plate is determined to be greater than the moment capacity corresponding to the ultimate capacity of the bolts Mnp increased by 10 %. The expected plastic moment capacity of the strain-hardened beam Mpu is compared with Mnp. To overcome the statistical dispersion of the material and geometric properties of the frame components and achieve a prescribed reliability level, the resistance reduction factors are applied in design (Pirmoz and Marefat, [24]). These factors, +n for bolts and +d for end plate, have a probabilistic nature, and assuming that the calculated values for the connection are used exactly in practice, these reduction factors could be dropped. As a result, the diﬀerence between Mpu and Mpl would be exactly 10 % for optimal design. C prZFye " 0.9Mpl

pected that when the beam reaches its maximum strength, the yield lines of the end plate reach 0.9 of their full plastic capacity and surpass their yielding moment by far. In other words, when the link beam approaches its maximum strength, the stress levels at the yield lines of the end plate will pass the yield point. However, this contrasts with the target connection of the current study, which should be elastic when the link has fully yielded. Accordingly, a load factor SC is introduced for the design of the connections to keep the stress levels below the yield point. Since the end plate and the bolts are designed to be elastic, the eﬀects of the cyclic loading should be negligible on their response. Beyond the connection region, e.g. the link-to-end plate joint vicinity and through the link itself, cyclic response is the controlling factor. Although very thick end plates with very large bolts may remain elastic, their minimum acceptable values should be known for engineering practice in order to satisfy economic aspects and fabrication requirements. The lower limit of the loads for which the ESEP connection will be in its elastic range (close to the yield stress) when the link is fully yielded is assessed here. Five connections, referred to as S1 to S5, were designed and analysed with various SC factors. Conforming to the load and resistance factor design principles, AISC 358 [15] applies two resistance factors (for the end plate and the bolts) when designing the connections. These factors are expected to cover the uncertainties inherent in the assumed design values and achieve a desired performance for practical connections.

(1)

where: Z plastic section modulus of link beam Fye expected yield strength of steel Cpr strain hardening ratio Owing to the deterministic nature of the FEM, the nominal yield strength of the material Fy is taken to be identical to Fye in the design and the models. Tracing the above design sequence for an optimally designed connection (modelled using FEM), it can be ex-

5.3 Design of connections Since the magnitude of the design loads is large with respect to the design loads of traditional ESEP connections in moment frames, grade St37 steel with 240 MPa yield stress and 360 MPa tensile strength Fu was considered for the link material instead of the original Q345 material of the tests in order to control the magnitude of the imposed load on the connection. It should be noted that any other material can be used and

Steel Construction 9 (2016), No. 1

51

Table 3. Geometric properties of the designed connections for scaled moments (mm)

No.

Bolt dia. AISC 358 (2010), Eq. (6.10-3)

End plate thickness AISC 310 (2010), Eq. (6.10-5)

SC

Cpr " Fu/Fy

calculated

implemented

calculated

implemented

Rib thickness

Lp

S1

1.0

1.0*

14.5

16

15.5

16

12

S2

1.25

1.5

19.4

20

19.4

20

12

100 100

S3

1.5

1.5

21.2

24

23.2

25

12

100

S4

1.5

1.5

21.2

24

23.2

25

20

100

S5

1.25

1.5

19.4

20

18.9

25

12

100

* Strain hardening is not considered in the design of S1.

the assumption of St37 steel does not aﬀect the fundamentals of the proposed design procedure. The material for the connection bolts was the same as the test bolts. In addition to the geometric properties listed in Table 3, other geometric properties of the ESEP connections, including plate width/height and bolt locations, are shown in Fig. 1. Further, the link section is the same as the beam section of the tested specimens with a plastic section modulus of 843.55 cm3 and link length e " 1.60 m. The moment imposed on the link-to-column connection is estimated according to Eqs. (2) and (3): ⎡ ⎤ 2Mp Mu = SC ⎢C prMp + Lp ⎥ e ⎢⎣ ⎥⎦

(2)

Mp " ZFy

(3)

where Lp is the distance of the assumed lumped plastic hinge from the column face and e the link length. Other parameters were already deﬁned in previous sections.

6 Performance of designed ESEP link-to-column connections

column attained for a moment of 200 kNm at the ESEP connection was about 0.00175 rad and overlooked when calculating the total rotation of the link (Eq. (4)).

6.1 Yielding mechanisms Fig. 7 presents the von Mises stress distribution in the link and end plate for the FE model of specimen S1 at 0.005 rad of the total link rotation. This rotation is achieved through yielding of the link, the end plate and the rib stiﬀener. Owing to diﬃculties in the solution convergence (large plastic strain in end plate and bolt shanks), the analysis was stopped at a link rotation of 0.005 rad. According to Fig. 7, the ﬂexural plastic hinge, distinguished by the von Mises stress contour, only formed on one side (the left side) of the link, and the end plate yielded instead of the link ﬂange at the right end. The plastic deformation of the link ﬂange adjacent to the rib stiﬀener was concentrated in a small region at the toe of the rib. Further, the von Mises stress level in the end plate was higher than that of the link. This ﬁgure also shows

the von Mises stress distribution in the bolts. The bolts were highly stressed beyond their yield stress. This was primarily due to the prying action of the highly deformed end plate. According to these results, the link did not exhibit the desired performance, and the yielding was restricted to a limited portion of the link and the connection. Yielding of the end plate prevents yielding of the link and leads to poor performance of the system. The von Mises stress level in the link web was between 214 and 249 MPa. Fig. 8 presents the von Mises stress distribution in the link and the end plate for the model of specimen S2. This specimen is designed assuming SC " 1.25 and considering the stain hardening of the link (Table 3). As shown in this ﬁgure, the ﬂexural plastic hinge formed at the location of the gusset plate (left end of the link, far from the connection, and at the bottom ﬂange of the link, adjacent to the connection). The von Mises stresses in the middle of the upper rib and the rib-end plate interface were also within the inelastic limit. The von Mises stress distribution in the bolts is

The models were loaded (using displacement control) until rotations # 0.02 rad for inelastic rotation of the link were achieved. The total rotation of the link L includes the rotation of the link itself, and the joint rotation >joint was measured using Eq. (4): γ=

δ − ψ jo int e

(4)

In the above equation, I and e are the vertical displacement of the link end and the length of the link respectively. The maximum rotation of the elastic

52

Steel Construction 9 (2016), No. 1

Fig. 7. Von Mises stress distribution in S1 (MPa) at the ultimate limit state

Fig. 8. Von Mises stress distribution in link, end plate and bolts for S2 (MPa); a) before link buckling; b) after link buckling

rather high, and some portions of the shank have entered the inelastic range. Specimen S3 was designed for SC " 1.5 and strain hardening eﬀects. Fig. 9 shows the von Mises stress distribution in the link, the end plate and the bolts for S3 at 0.0106 rad (prior to local buckling of the link ﬂange) and 0.0256 rad of link rotation, which is 28 % greater than the limit rotation of 0.02 rad speciﬁed in AISC 341 [1]. As shown in Fig. 9, the connection exhibits enough stiﬀness to yield the link, and therefore the ﬂexural plastic hinges form at both ends of the link. A clear inelastic local buckling at the brace (gusset plate) location and some inelastic local ﬂexural deformations of the bottom ﬂange near the end plate are visible in Fig. 9. The strength of the connection was high enough for the magnitude of the von Mises stress in the end plate to be less than the von Mises stress in the link. Although the magnitude of the stress in the end plate was lower than that of the link, the plate yielded along the link ﬂange-end plate and ﬂange-rib interfaces. This limited amount of yielding dissipates some of the energy and can be beneﬁcial. The rib stiﬀener, a major component in the connection responsible for the stiffness, also yielded and the von Mises stress in the rib is as high as that in the link ﬂange. As expected, the other segments of the system such as the bolts and the out-of-link segment of the beam remained elastic clearly below the yield point (Fig. 9b). This ﬁgure also shows the von Mises stress distribution in the upper ﬂange bolts. As shown in

Fig. 9. Von Mises stress distributions in model S3

this ﬁgure, the maximum stress level is below the yield stress, and so the bolts are totally elastic. To study the eﬀects of the rib thickness on the connection response, another model of S3 was created (named S4) with a rib thickness of 20 mm. The von Mises stress distribution in the link and bolts is shown in Fig. 10. By comparing Figs. 9 and 10, only a slight reduction in the von Mises

stress in the bolts and the rib stiﬀener and a slight increase in the link stress level were achieved due to the increased rib thickness. The plastic moment strength mp and the yielding moment strength my of the end plate per unit length are presented in Eq. (5): m p " Fyp

t 2p 4

Steel Construction 9 (2016), No. 1

(5a)

53

Fig. 10. Von Mises stress distribution in S4 at link rotation of 0.0254 rad (MPa); a) at link rotation of 0.0112 rad (MPa); b) at link rotation of 0.0244 rad (MPa)

m y " Fyp

t 2p 6

(5b)

where Fyp and tp denote the yield stress and the thickness of the end plate respectively. According to Eq. (5), the plastic moment capacity of the end plate would be 1.5 times its yielding moment capacity. Therefore, it is expected that a link-to-column ESEP connection designed with a load factor of 1.5 will remain elastic until it achieves the ultimate strength of the link. Fig. 11 shows the von Mises stress distributions in the link, the end plate and the bolts of connection S5 at a total link rotation of 0.0244 rad. Some portions of the shank were in the inelastic range and achieved the yield stress. This connection was designed for a load factor of 1.25. This connection was similar to S2, but its end plate was thicker. The thick plate caused a low level of stress in the bolt shanks by reducing the prying action. As shown in Fig. 11a, at a link rotation of almost 0.011 rad, the beam ﬂange buckled at the point of maximum moment. After yielding of the link and plastic hinge formation, the stress levels in the shanks of the bolts remained almost constant.

The PEEQ Index, which represents the local strain demand, is deﬁned as the plastic equivalent strain divided by the yield strain Jy. The contours of the PEEQ Index for the ﬂange-to-rib connection region are presented in Fig. 12. This region is prone to frac-

ture and was the observed failure mode of the specimens reinforced with a single rib (SR30 and SR20) which underwent cyclic testing by Chen and Jhang [26]. The similar failure mode indicates that these connections, which were designed for large forces, exhibit a performance similar to the rib-reinforced welded moment connections. As shown in this ﬁgure, as the connection stiﬀness increases, so the magnitude of the peak PEEQ Index also increases. This may be due to a decrease in the deformations at the end plate, bolts and stiﬀeners, which results in a stress concentration at the toe of the rib. A comparison of the PEEQ Index contours for S3 and S4 shows that the rib thickness has only a small eﬀect on the local ductility of the connection. Generally, as the stiﬀness of a connection increases, so the PEEQ index increases, and thus the local ductility of the connection decreases.

6.2 Local ductility of connections The PEEQ Index was employed to evaluate the eﬀects of the connection parameters on the local ductility of the connections. This parameter has been used by previous investigators for the ductility evaluation of rigid welded-bolted connections [25, 26].

54

Steel Construction 9 (2016), No. 1

Fig. 11. Von Mises stress distributions in the link and connection components of S5

Fig. 12. PEEQ index contours in the rib and link ﬂange region during their ﬁnal stage

6.3 Global behaviour of connections Although the yielding mechanism of the models and the moment–rotation responses of the connections were considerably diﬀerent, they sustained a shear force around the expected value of 321 kN due to plastic hinge formation at both ends of the link. The applied shear force was primarily controlled by the moment at both ends of the link (which are similar) and its shear strength. However, the geometric properties of the connection directly aﬀect its moment–rotation response. The gap rotation in Fig. 13 only includes the deformations of the end plate and was calculated by subtracting the panel zone rotation from the joint rotation. The panel zone rotation and the joint rotation were measured directly from the ﬁnite element models. The moment versus gap rotation response of each of the connections is compared with the plastic moment capacity of the beam, plotted by dashed lines in Fig. 13. The results are in agreement with the yielding mechanisms, which were discussed in section 5.1. As shown in these plots, connection S1 cannot achieve the plastic moment capacity of the beam. However, the other connections have a moment capacity greater than the plastic moment capacity of the beam. As discussed in section 5.1, the specimens were able to yield the beam. These connections were designed for load factors # 1.25. The peak moments in the response plots of S2, S3 and S4 correspond to the onset of buckling at the link ﬂange.

The stiﬀnesses of the connections and the energy absorbed by the system and its connection are listed in Table 4. In this table, total energy corresponds to the area under the load versus vertical deﬂection curve (of the loaded point) and the connection energy denotes the area under the moment versus gap rotation curve. The ratio of the initial rotational stiﬀness of the connection (obtained from the moment–gap rotation curves) to the eﬀective ﬂexural stiﬀness of the link (FEMA-273 [27], Eq. C5-41), is # 1.0 for all the models. As shown in Table 4, S3 and S4 have stiﬀness ratios # 3. Table 4 also presents the total energy absorbed by the system and the energy absorbed by the connection itself. The energy ratio, which is the ratio of the energy absorbed by the connection to the total energy, shows that as connection strength and stiﬀness increase, so the contribution of the connection to the energy dissipation decreases, which indicates greater activation of the link. For specimens S3 and S4, the contribution of the connection to energy absorbance was ! 3 %, and most of the energy was dissipated by the link beam.

7 Summary and conclusion The performance of the ESEP connections as link-to-column connections for EBFs with long links was evaluated numerically in this paper. This study was performed using a non-linear FEM. Reﬁned parametric models of ESEP connections were

created and validated based on the experimental tests from other studies dealing with moment connections. A comparison of the deformed shape of the FE models and their moment–rotation response to the tests resulted in good agreement between models and tests. The FE models of the ESEP link-to-column connections were created and analysed based on the veriﬁed FE models. These link-to-column connections were designed for 1.0, 1.25 and 1.5 times the maximum moment capacity of the link to identify a convenient load factor for the connection design moment for which the connection can remain elastic. The ﬁnite element analysis of the designed ESEP link-to-column connections under the loading conditions of the linkto-column connections demonstrated that a connection that is designed for 1.5 times the expected applied moment at a connection can behave in a primarily elastic manner. This load factor results in a connection that exhibits the required strength and stiﬀness to yield the link, whereas the brittle parts (bolts) remain elastic. Among the analysed models, the stiﬀness ratios of the accepted models were in the range of 3 to 4. As a result, considering only the strain hardening eﬀects is not suﬃcient for the design of ESEP link-to-column connections for long links. An evaluation of the local ductility of the rib-ﬂange region based on the PEEQ Index demonstrated that, as the connection stiﬀness increases, so the local ductility decreases, and so the larger load factors (SC) may result in brittle performance of the link-rib region. Further,

Steel Construction 9 (2016), No. 1

55

Fig. 13. Moment–rotation response of the connections and the plastic moment capacity of the beam

Table 4. General characteristics of the connections Model

Initial rotational stiﬀness of connection (kNm/mrad)

Stiﬀness ratio

Total energy (kJ)

Connection energy (kJ)

Energy ratio (%)

S1

66.9

0.8

7

1.48

21.06

S2

128

1.5

18.9

1.38

7.3

S3

270

3.2

12.5

0.33

2.6

S4

324

3.8

10.9

0.33

2.96

S5

210

2.5

9.13

0.42

4.57

the connection shear force is independent of its moment–rotation response and is controlled by the shear strength of the link. A comparison of the energy dissipated by the connection and the total input energy demonstrated that the (namely) elastic connections dissipated ! 3 % of the total energy and were able to yield the link. This energy dissipation was due to some plastic deformations of the rib stiﬀeners and limited plastiﬁcation of the end plate. The low percentage of the dissipated energy from the connection is in agreement with the AISC 341 [1] provisions, which state that most of the energy should be dissipated by the link. The numerical study in this paper analysed the performance of the ESEP connections for long link-to-

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Steel Construction 9 (2016), No. 1

column connections and demonstrated that this type of connection has the potential to be used as the link-to-column connections. To support the results of the current numerical study, further experimental studies are required to evaluate the cyclic performance of this type of connection and for other link lengths and the eﬀects of low cyclic fatigue – especially the reduced fatigue life of the bolts due to prying forces – on the performance of the connection and the brittle response of the welds and the welded parts (which are not considered in this study). References [1] American Institute of Steel Construction, Inc.: Seismic Provisions for struc-

tural steel buildings. Standard ANSI/ AISC 341-10 (2010), AISC, Chicago. [2] Malley, J. O., Popov, E. P.: Shear links in eccentrically braced frames. Journal of Structural Engineering, 110(9), 1984, pp. 2275–2295. [3] Engelhardt, M. D., Popov, E. P.: Experimental performance of long links in eccentrically braced frames. Journal of Structural Engineering, 118(11), 1992, pp. 3067–3088. [4] Ghobarah, A., Ramadan, T.: Bolted link-to-column joints in eccentrically braced frames. Engineering Structures, 16 (1), 1994, pp. 33–41. [5] Okazaki, T., Engelhardt, M. D., Nakashima, M., Suita, K.: Experimental Performance of Link-to-Column Connections in Eccentrically Braced Frames. Journal of Structural Engineering, 132(8), 2006, pp. 1201–1211. [6] Drolias, A.: Experiments on Link-toColumn Connections in Steel Eccentri-

cally Braced Frames. MSc dissertation, The University of Texas at Austin, 2007. [7] Ballio, G., Calado, L., De Martina, A., Faella, C., Mazzollani, F. M.: Cyclic Behaviour of Steel Beam to Column Joints. Experimental Research, Construzioni Metalliche No. 2, (1987), pp. 69–90. [8] Tsai, K. C., Popov, E.: Cyclic behavior of end-plate moment connections. Journal of Structural Engineering, 116(11), 1990, pp. 2917–2930. [9] Ghobarah, A., Osman, A., Korol, R. M.: Behaviour of extended end-plate connection under seismic loading. Engineering Structures, 12 (1), 1990, pp. 15–27. [10] Adey, B. T., Grondin, G. Y., Cheng, J. J. R.: Cyclic loading of end plate moment connections. Canadian Journal of Civil Engineering, 27 (2000), pp. 683– 701. [11] Sumner, E.: Uniﬁed design of extended end plate moment connections subject to cyclic loading. PhD dissertation, Virginia Polytechnic Institute and State University, 2003. [12] Shi, G., Shi, Y., Wamg Y.: Behaviour of end-plate moment connections under earthquake loading. Engineering Structures, 29 (2007), pp. 703–716. [13] Shi, Y., Shi, G., Wamg, Y.: Experimental and theoretical analysis of the moment–rotation behaviour of stiﬀened extended end-plate connections. Journal of Constructional Steel Research, 63 (2007), pp. 1279–1293. [14] ANSYS User’s manual. [15] American Institute of Steel Construction, Inc.: Prequaliﬁed Connections for Special and Intermediate Steel Moment Frames for Seismic Applications. Standard ANSI/AISC 35810 (2010), AISC, Chicago.

[16] Pirmoz, A.: Evaluation of nonlinear behavior of bolted connections under dynamic loads. MSc thesis (in Persian), Tehran, Iran, K. N. Toosi University, 2006. [17] Danesh, F., Pirmoz, A., Saedi Daryan, A.: Eﬀect of shear force on the initial stiﬀness of top and seat angle connections with double web angles. Journal of Constructional Steel Research, 63 (2007), pp. 1208–1218. [18] Pirmoz, A., Saedi Daryan, A., Mazaheri, A., Ebrahim Darbandi, H.: Behavior of bolted angle connections subjected to combined shear force and moment. Journal of Constructional Steel Research, 64 (2008), pp. 436–446. [19] Salajegheh, E., Gholizadeh, S., Pirmoz, A.: Self-organizing back propagation networks for predicting the moment–rotation behavior of bolted connections. Asian Journal of Civil Engineering (Building and Housing), 9 (2008), pp. 629–645. [20] Pirmoz, A., Danesh, F.: The seat angle role on moment-rotation response of bolted angle connections. Electronic Journal of Structural Engineering, 9 (2009), pp. 73–79. [21] Pirmoz, A., Seyed Khoei, A., Mohammadrezapour, E., Saedi Daryan, A.: Moment–rotation behavior of bolted top-seat angle connections. Journal of Constructional Steel Research, 65 (2009), pp. 973–984. [22] Pirmoz, A., Danesh, F., Farajkhah, V.: The eﬀect of axial beam force on moment–rotation curve of top and seat angles connections. The Structural Design of Tall and Special Buildings, 20 (7), 2011, pp. 767–783. [23] Pirmoz, A.: Performance of bolted angle connections in Progressive collapse of steel frames. The Structural Design of Tall and Special Buildings, 20 (3), 2011, pp. 349–370.

[24] Pirmoz, A., Marefat, M. S.: Reliability assessment of compression columns in seismic EBFs. Journal of Constructional Steel Research, 104 (2015), pp. 274–281. [25] El-Tawil, S., Vidarsson, E., Tameka, M., Kunnath, S. K.: Inelastic behavior and design of steel panel zones. Journal of Structural Engineering, 125(2), 1999, pp. 183–193. [26] Chen, C. C., Chen, S. W., Chung, M. D., Lin, M. C. L.: Cyclic behavior of unreinforced and rib-reinforced moment connections. Journal of Constructional Steel Research, 61 (2005), pp. 1–21. [27] Federal Emergency Management Agency: NEHRP Guidelines for the Seismic Rehabilitation of Buildings, FEMA-273, Washington, D.C., 1997. Keywords: seismic design; link-to-column connections; EBFs; extended stiﬀened end-plate connections; non-linear ﬁnite elements

Authors: Akbar Pirmoz Department of Civil Engineering The Catholic University of America 620 Michigan Avenue, NE Washington, DC 20064, USA Parviz Ahadi Department of Civil Engineering, Germi Branch Islamic Azad University, Germi Ardebil, Iran Vahid Farajkhah Dalhousie University Department of Civil and Resource Engineering 1360 Barrington St. Halifax, NS, Canada B3J 1Z1

Steel Construction 9 (2016), No. 1

57

Articles Czesław Machelski Robert Toczkiewicz*

DOI: 10.1002/stco.201400005

Effects of connection ﬂexibility in bridge girders under moving loads This paper looks at the problem of connection ﬂexibility in steelconcrete bridge girders under moving loads. The static action of the load changing location on the structure is considered. An analytical model of the girder is used assuming strain discontinuity at the steel-concrete interface as a result of beam-plate partial interaction. The effects of a ﬂexible connection are characterized by the proposed index deﬁned on the basis of the internal forces in the girder. This index can be calculated during loading tests on the basis of the neutral axis position at the section of the girder considered. Numerical analyses show that values of the index characterizing beam-plate interaction depend on the position of the load on the structure and the function describing connection stiffness.

1 Introduction A composite structure consists of elements made of materials with diﬀerent physical characteristics interacting due to the specially designed connectors assuring their permanent cooperation [1]. A typical composite bridge girder consists of a steel beam and a concrete plate. Perfect beamplate interaction is a theoretical case that would require the use of non-deformable connecting elements. The connection is thus always deformable (ﬂexible), resulting in partial interaction of the girder’s elements. Headed shear studs, very common in bridge structures, can be considered deformable connectors, as their rigidity does not prevent shear slip at the steel-concrete interface. A stiﬀer connection is obtained by using perfobond connectors or composite dowels [2], [3]. The stiﬀness of a single connector ks is deﬁned as the ratio of force T acting on the connector to the value of displacement along the steel-concrete interface: ks =

T δ

(1)

As the shear force is distributed along the interface t=

dT dx

so the connection stiﬀness is deﬁned as * Corresponding author: robert.toczkiewicz@mosty-wroclaw.com.pl

58

(2)

k=

t δ

(3)

In the general case relation T(I) is non-linear and the stiﬀness of a connector decreases along with the load increment. In the range of forces resulting from live loads on bridges, these changes are not signiﬁcant and a constant stiﬀness ks can be assumed. The stiﬀness of the beam-plate connection is inﬂuenced by many factors, including type of connector, concrete properties [4], conﬁguration of beam-plate connection [5] and load type [5], [6]. Partial interaction of the girder’s elements results in redistribution of the internal forces between the steel and concrete parts of the section and strain discontinuity at the steel-concrete interface. The ﬂexural stiﬀness of the girder is reduced, resulting in an increase in deﬂection. Several analytical models have been developed to describe the problem of partial interaction [7]–[10]. They assume a linear load-slip relationship (constant connection stiﬀness k) suﬃcient for the analysis of serviceability load eﬀects. Despite the large number of studies, which indicates that this issue is one of the most interesting problems in composite structures, a lack of analyses directed towards bridge structures as well as in situ research in this ﬁeld is evident. Many studies focus on assessing the inﬂuence of connection ﬂexibility on the deﬂection of composite girders [11], [12]. However, as load tests show [13], in the case of bridges, measurement of vertical displacements does not allow for an assessment of beamplate interaction due to the change in ﬂexural stiﬀness of the girders, resulting, among other things, from the cooperation of non-structural elements [14]. In this case strain measurements in beams are relevant, which is not common practice. Further, with few exceptions [15], no studies or research projects have been carried out with the aim of identifying the eﬀects of moving loads changing their location on the structure, which are typical bridge loads. The conclusions regarding the eﬀectiveness of beam-plate interaction are, as a rule, drawn on the basis of test results conducted with stationary loads [13]. Analyses concerning the eﬀects of moving loads have been carried out in the case of soil-steel composite structures [16]. Full-scale load tests indicate that in the case of those structures, the results are also inﬂuenced by the direction of the moving load [17].

C. Machelski/R. Toczkiewicz · Effects of connection flexibility in bridge girders under moving loads

Analytical models often aim at obtaining exact relationships that allow for the determination of displacements and forces for basic load cases only and for speciﬁc functions of connection stiﬀness. It seems that the introduction of simple indices characterizing the eﬀects of connection ﬂexibility, e.g. deﬁned on the basis of strain values, might be advisable. Little attention has been paid to attempting to relate the analytical models to the results of in situ bridge tests. The scope of this paper is the analysis of partial beamplate interaction in steel-concrete composite girders with ﬂexible connection subjected to the action of short-term live loads (vehicles). The static action of the load changing its position on the structure is considered. The analyses, aimed at determining the eﬀects of connection ﬂexibility in girders loaded by vehicles, taking into account diﬀerent connection stiﬀness functions, were conducted using the proposed index of partial interaction. In the analysis concerning the action of moving forces changing their location on the structure, the use of inﬂuence functions is proposed.

plate Ipn " Ip/nbp are obtained. The location of the centre of gravity of a fully composite section is given by ad =

A pn A b + A pn

(4)

a

and the moment of inertia of a fully composite girder is I0y = I b + Ipn + aad A b

(5)

In the case analysed, the resultant internal forces are separated into two subsystems: beam and plate. Internal forces are equivalent to the external global bending moment M, meeting the conditions of static equilibrium [19]. Using the condition of strain discontinuity in the beamplate interface Δε bp = ε gb – εdp =

dδ 1 dt = dx k dx

(6)

the following equation is obtained:

2 Analytical model The analytical model describing the problem is based on the classic approach [18]. The following assumptions have been made: – Normals to the neutral surface remain normal during the deformation, separately in each element of the composite steel-concrete girder. – All elements of the girder (beam and plate) have the same radius of curvature. – Internal forces in the elements of the girder meet the conditions of static equilibrium. – There is strain discontinuity at the beam-slab interface. The geometry of the cross-section relates to the centres of gravity of its elements (steel beam and concrete plate), as shown in Fig. 1. Beam and plate are characterized by their cross-sectional areas (Ab and Ap) and moments of inertia (Ib and Ip). The distance between the centres of gravity of the girder elements a is constant and does not depend on beam-plate interaction. Geometrical characteristics of the composite section are related to the parameters of the beam material by applying a modular ratio nbp " Eb/Ep, which is constant in the case of the short-term loads considered in this paper. After the modular ratio implementation, transformed values for cross-sectional area of concrete plate Apn " Ap/nbp and moment of inertia of concrete Ep, Ap, Ip

Mp Np

Op

yg yd

εdp

ag

M

O vg

Mb Nb

ad Ob

∆εbp

εbg

a

y Eb, Ab, Ib

εgp

a'd

εdb

Fig. 1. Axial strain, internal forces and geometry of a girder cross-section

(7)

It is also assumed that all elements of the girder have the same radius of curvature: Mp Mb M = = E bI y E bI b E pIp

(8)

The shear force t at the interface is a result of the change in axial force Nb in the beam (and simultaneously Np in the plate): t=

dN b dx

(9)

Hence, the equation that combines axial force Nb with bending moment M takes the following form: I0y E b I b + Ipn ⎛ d 2N b 1 dN b dk ⎞ N + M = 0 (10) – – · ⎜ ⎟ k dx dx ⎠ ad A b b a k ⎝ dx 2

Eq. (10) provides the solution for the partially composite girder, bent with moment M(x) [19].

3 Index of partial interaction A change in connection stiﬀness results in redistribution of internal forces in the beam and the plate. The index representing the ratio between the internal forces Nb and Mb in the steel part of the girder is deﬁned as μ=

vd z

Mpy d 1 dt Np M bv g Nb . – – – = E pIp k dx E bA b E bI b E pA p

aN b Mb

(11)

In order to obtain a dimensionless value of index R, axial force Nb is multiplied by distance a. A typical diagram of internal forces in the girder cross-section versus index R is shown in Fig. 2. The characteristics of the girder’s elements are given in Table 1. A

Steel Construction 9 (2016), No. 1

59

C. Machelski/R. Toczkiewicz · Effects of connection flexibility in bridge girders under moving loads

Mb a·Nb

Table 1. Geometrical and physical characteristics of girder analysed

[MNm]

Element

Ab/Ap [m2]

Ib/Ip [m4]

vg/yg [m]

vd/yd [m]

Eb/Ep [GPa]

Steel beam

0.0448

0.0191

0.990

0.640

205

Concrete plate

0.5820

0.0020

0.095

0.145

32.6

μ =2.036

1.0

0

0.8

Mb 0.6

0.2

μ 0 0

0.4

0.8

1.2

1.6

2.0

2.4

Fig. 2. Internal forces in steel beam versus value of index R

bending moment M " 1 MNm is assumed. The diagram shows that the increase in R value is associated with an increase in axial force Nb (multiplied in the example by distance a) and with a decrease in bending moment Mb. These changes are signiﬁcant at low values of R and stabilize as R increases. The index R has two characteristic values [15]: – in the case of full beam-plate interaction, then μ = μ0 =

a · ad · A b Ib

(12)

– in the case of no interaction (when Nb " 0), then R " 0 according to Eq. (11). Values of R | R0 mean that there is partial beam-slab interaction and that shear slip occurs at the steel-concrete interface. Examples of functions R(x) created for diﬀerent cases of connection stiﬀness function k(x) are given and commented on later in this paper. In the case of partial interaction, index R depends linearly on the position of the girder’s neutral axis described by distance aed (see Fig. 1), according to the relationship a′d =

μ · Ib μ = ad μ0 a · Ab

(13)

Eq. (10), providing the solution for the partially composite girder subjected to bending, is solved in the analysis using the ﬁnite diﬀerence method [19]. This method allows the function R(x) to be analysed for arbitrary functions of variables included in Eq. (10). Values of Eb, Ipn and Apn are usually constant in bridge structures, whereas beam characteristics Ib and Ab (and hence distance a) and connection stiﬀness k are most often constant only along sections of a girder. All the analyses described below were conducted for a typical steel-concrete girder of a beam bridge with a span L " 28 m. The geometrical and material characteristics of the girder are given in Table 1.

4.1 Local effect of concentrated load For the girder analysed here (simply supported beam loaded with single force at mid-span and constant connection stiﬀness), the problem was solved several times, each time changing the connection stiﬀness constant along the girder k(x) " k. The resulting diagrams of the function R(k, x) are shown in Fig. 3. It can be seen that along the whole length of the girder, index values fulﬁl the relationship R(x) f R0. Both the decrease in index R and the range of decrease along the girder depend on the connection stiﬀness k(x). The lowest values of R are obtained in the section where force P is applied. Function R(k, x) results directly from the functions of internal forces Nb(x) and Mb(x) determined from the solution of Eq. (10) and is connected with changes in slip increments at the beam-plate interface [19]. In the case of constant stiﬀness k(x) " k, the result is R(x) f R0.

4.2 Change in connection stiffness along beam In real composite girders, connection stiﬀness results from the distribution and type of connector (e.g. headed shear studs). The connectors are arranged according to the enve-

If there is no interaction (R " 0), the neutral axis coincides with the axis of inertia of the beam Ob (aed " 0), and in the case of full interaction (R " R0), the relation aed " ad is obtained. After transformation, Eq. (13) allows the value of R to be calculated on the basis of the position of the neutral axis that can be determined in loading tests [15].

2.1 2.0

μ = μ0 k [MN/m 2]

1.9

μ [-]

4 Function of partial interaction R(x)

2.2

x=L /2

a·Nb

0.4

1000

P

k

1.8

2000

1.7

The analytical model of a girder with partial interaction described in section 2 was used in the numerical analyses given below. The main aim of the analysis was to illustrate the inﬂuence of moving loads, changing their position on the structure, on the beam-plate interaction characterized by the proposed index R.

60

Steel Construction 9 (2016), No. 1

5000

1.6

L/2

10000

L/2

20000

1.5

x [m]

1.4 0

2

4

6

8

Fig. 3. Eﬀect of a single point load

10

12

14

bC

bC

nc k

0.5

nc k

P

-10

x=L / 2

0.6

bC k

-6 L/2

σ [MP a]

0.4

N b [MN]

nc k

P

k

M b [MNm]

bC

nc k

-8

x=L/ 2

C. Machelski/R. Toczkiewicz · Effects of connection flexibility in bridge girders under moving loads

L/2

0.3

bc

L/2

L/2

-4

bc

σbg d nbpσp

-2

0.2

Nb Nb 0.1

0

Mb Mb x [m]

0.0

0

1

2

3

4

5

6

7

8

9

10

11

12

13

x [m]

2

14

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

Fig. 4. Diagrams of forces and stresses in girder with step change in connection stiﬀness

5 Effect of moving group of forces Typical loads on bridges are vehicles, consisting of groups of forces changing position on the structure. The inﬂuence of such a load type is discussed below. A group of forces generates the function R(x) presented in Fig. 6. A three-axle vehicle (front axle load P/2, rear axles load P) is considered in this example [15]. Conﬁguration of axle loads and their values make the resultant load coincident with the position of the middle axle at

bc

nc=1 4.5

change of connection stiffness

nc=2

bC

4.0

μ [-]

bC

nc k

nc=5 3.5

x=L / 2

5.0

nc k

P k

nc=20

3.0 L/2

L/2

2.5 2.0 1.5

x [m]

1.0 0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

Fig. 5. Diagram of R(x) for beam with step change in connection stiﬀness

2.1

μ=μ

2.0

xp=10 m

1.9

μ [-]

xp=14 m xp=18 m

1.8

P

1.7

k

1.6 1.5

x=L /2

lope of shear force t, resulting in a higher connection stiﬀness in the support zones. Therefore, the connection stiﬀness function k(x) usually changes along the girder. The example considers a girder with a constant connection stiﬀness k " 1000 MN/m2, which increases in the support zones to ke " k · nc (nc " 1, 2, ... , 20), loaded with a single force resulting in a bending moment M(x " L/2) " 1 MNm. Connection stiﬀness increases along the section with length bc. Fig. 4 presents diagrams of internal forces Nb(x) and Mb(x) in the beam (see Fig. 1) and stress along the beamplate interface – in the upper ﬂange of the beam Xbg and on the lower edge of the plate Xpd. The values of Xpd are multiplied by the ratio nbp " Eb/Ep. A connection stiﬀness increment nc " 5 is considered. The diagrams indicate a local inﬂuence of the concentrated load and the change in connection stiﬀness. Characteristic ﬂuctuations of forces Mb and Nb can be noticed in both zones. Tension (X # 0) appears over the whole depth of the beam in the range of connection stiﬀness change. Fig. 5 shows R(x) diagrams obtained for the case illustrated in Fig. 4 for diﬀerent values of nc. The analyses conducted show that a step change in k along the girder results in local extreme values of R in the zone of the connection stiﬀness change. The results indicate an increase in R along with an increasing change in the connection stiﬀness expressed by nc. The R(x) diagrams show that in the zone of the connection stiﬀness change, values R # R0 appear which are higher than in the case of full steel-concrete interaction. This eﬀect results directly from the change in internal forces ratio in the beam (increase in axial force Nb and decrease in bending moment Mb) in the vicinity of the connection stiﬀness change. It is connected with the decrement in shear slip I in the support zones of the girder – an eﬀect of larger connection stiﬀness ke " k · nc in these parts of the beam.

1.4 0

2

4

6

8

10

12

14

0.5P

P b

2b

xp x [m] 16

18

20

22

24

26

28

Fig. 6. Diagram of R(x) for girder loaded by a group of forces [15]

distance xP from the support. Fig. 6 shows R(x) diagrams generated for three positions of the vehicle on the girder. The graphs indicate a local reduction in R value in sections where the forces are applied, depending on the load position. The results were obtained assuming a constant connection stiﬀness k and constant ﬂexural stiﬀness of the girder. In real bridge structures these assumptions are usually not satisﬁed. Fig. 7 shows diagrams of function R(x) for two positions of a point load: sections i (Pi) and j (Pj). The following functions of connection stiﬀness are considered: a) constant value k(x) " k " 2000 MN/m2 b) step change: k1 " 1000 MN/m2, k2 " 2000 MN/m2, k3 " 5000 MN/m2

Steel Construction 9 (2016), No. 1

61

C. Machelski/R. Toczkiewicz · Effects of connection flexibility in bridge girders under moving loads 2.6

2.6

2.4

Pi

μj (Pi )=2.028

2.4

Pi

μi (Pj )=2.096

Pj

Pj 2.2

μ=μ μ [-]

μ [-]

2.2 2.0

Pj k

Pi

1.8 μi (Pj )=2.028

2.0

k1

μj (Pi )=2.006

1.6

j

i xi

1.4 0

2

4

6

8

1.6

xj 10

12

x [m] 14

16

18

20

22

24

26

1.4

28

0

2

4

6

xj

8

10

12

k2

j

i xi

k3

Pj

Pi

1.8

x [m] 14

16

18

20

22

24

26

28

Fig. 7. Diagrams of R(x) for girder loaded with a single force: a) constant connection stiﬀness, b) step change in connection stiﬀness

From the diagrams we reach the conclusion that in a prismatic girder with constant connection stiﬀness, the following principle is valid: μ i(Pj) = μ j(Pi )

(14)

and hence the value of R at section i resulting from force P acting at section j is the same as at section j when the force is applied at section i. Thus, the proportion of internal forces Nib(Pj) Mib(Pj)

=

N jb(Pj)

(15)

M jb(Pi )

also appears when Pi | Pj. In the girder with a step change in connection stiﬀness, the diagrams indicate a lack of the principle described by Eq. (14). The diﬀerence Δμ ij = μ i(Pj) – μ j(Pi )

(16)

in the example given in Fig. 7 is equal to )Rij " 2.096 – 2.006 " 0.090. For any given function of connection stiﬀness k(x), it is possible to add the eﬀects of single point loads, e.g. Pj and Pk, according to the following relationship: Nib(Pj) +

Nib(Pk ) =

From Eq. (11), the value of Rip at section i for any conﬁguration of forces Ps and for any function k(x) can be calculated thus [15]:

Nib(Pj

+ Pk )

(17)

μ ip =

aNip b Mip b

∑ Nib(Ps) a = s ∑ Mib(Ps)

s = 1, 2, … , n

(21)

s

From the general Eq. (21), we get the following particular formulas: – in the case of a single force Pj μ ij =

Nib(Pj) Mib(Pj)

(22)

a

– in the case of two forces Pj and Pk μ ijk =

Nib(Pj) + Nib(Pk ) Mib(Pj) + Mib(Pk )

a

(23)

Introducing forces Nb0ik and Mb0ik at section i resulting from unit force Pk0 " 1 at point k, for any force Pk, we obtain Mib(Pk ) = Mik b0 · Pk

(24)

and

and Mib(Pj) + Mib(Pk ) = Mib(Pj + Pk )

(18)

∑ Nib(Ps)

s = 1, 2, 3, … , m

(19)

s

and

μ ijk =

Nijb0Pj + Nik b0Pk Mijb0Pj + Mik b0Pk

a

(26)

When Pj " Pk, it can be seen that index Rdoes not depend on the value of P μ ijk =

Nijb0 + Nik b0 Mijb0 + Mik b0

a

(27)

Introducing Eq. (11) transformed into

Mip b =

∑ Mib(Ps)

s = 1, 2, 3, … , m

s

62

(25)

and hence Eq. (23) is transformed into

The application of inﬂuence functions is thus valid in the case of moving loads. Using the principle of the additivity of eﬀects of several point loads, the values of Nbi(p) " Nbip and Mbi(p) " Mbip, as in Eqs. (17) and (18), can be calculated for section i according to Nip b =

Nib(Pk ) = Nik b0 · Pk

Steel Construction 9 (2016), No. 1

(20)

aNijb0 = μ ij · Mijb0

(28)

C. Machelski/R. Toczkiewicz · Effects of connection flexibility in bridge girders under moving loads

and

Pi

Pk

k

2.2

ik aNik b0 = μ ik · M b0

(29)

i

2.1

c

k

c

2.0

μ ijk =

μ ijMijb0 + μ ikMik b0 Mijb0

Pk Pi+Pk

1.8

Pi+0.5Pk

∆

1.7

+ Mik b0

μi (Pi )=1.550 0

ki Mkk b0 Pk + M b0Pi

8

10

12

(at the point of acting

k

14

16

18

20

x [m]

22

24

26

28

k3

P=1

b)

k1

j

i

k2

j

i

x0

2.4 μi (xj )=2.096

μj (xi )=2.028

μ=μ

2.0

μ [-]

ki

1.8

μi (xj )=2.028

μj (xi )=2.006

a) μi (x0) a) μj (x0)

1.6

b) μi (x0) b) μj (x0)

1.4

xi

(33)

ii ik μ iiMiib0 + αμ ikMik b0 – αμ iiM b0 + μ ikM b0 – μ ki (34) k = Miib0 + αMik αMiib0 + Mik b0 b0

is marked for Pk " FPi. In the case analysed (girder with constant stiﬀness of connection k(x) " k " 2000 MN/m2 and assuming F " 0.5), this diﬀerence is equal to ) " Riik – Rkki " 1.610 – 1.724 " 0.114. The proportion of the forces is therefore important.

6 Inﬂuence functions of index R Inﬂuence functions are a useful tool for illustrating the effects of moving loads. They show the changes in a selected internal force, reaction force or displacement versus the position of a moving unit force. In a similar way, inﬂuence functions can be used in the analysis of a partially composite girder. In the static method of inﬂuence line generation, we use a unit force P0 " 1 moving along a structure (e.g. acting at point x0 when section i is analysed). Therefore, the function R(x) required, being the inﬂuence line of the partial interaction index, is composed of values Ri(x0) " Ri0 (x0 indicates position of force P0), deﬁned as [15] aNib(x 0 ) μ i(x 0 ) = Mib(x 0 )

6

x0

(32)

despite the load symmetry and thus conformity Rii " Rkk and Mb0ii " Mb0kk, and according to Eq. (14) Mb0ik " Mb0ki. This is illustrated in Fig. 8, where the diﬀerence Δ = μ ik i

P=1

a)

μ iMiib0Pi + μ ikMik b0Pk ii ik M b0Pi + M b0Pk

ki μ kkMkk b0 Pk + μ kiM b0Pi

4

μk(Pi )=1.550

xk

Fig. 8. Diagram of R(x) for girder loaded by one force and two forces

2.2

μ ki k =

2

μi (Pi +0.5Pk)=1.610

(31)

Mijb0Pj + Mik b0Pk

is diﬀerent from the value of Rk force Pk)

xi

1.4

μ ijMijb0Pj + μ ikMik b0Pk

μk(Pi +Pk)=1.656

μi (Pi +Pk)=1.656 1.5

On the basis of Eq. (31), the calculated value Riik at the point of acting force Pi with additional symmetrical load Pk | Pi μ ik i =

μk(Pi +0.5Pk)=1.724

1.6

(30)

In the case of any value of forces Pj | Pk, from Eq. (26), using Eqs. (28) and (29), we obtain the following relationship, depending on the values of index Rij and Rik: μ ijk =

Pi

1.9

μ [-]

then Eq. (27) depends on the values of Rij and Rik calculated for the individual components of the load Pj and Pk when Pj " Pk:

(35)

xj

x 0 [m]

1.2 0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

Fig. 9. Inﬂuence lines of index R

Fig. 9 shows typical diagrams of inﬂuence lines for index Ri(x0) at section i and Rj(x0) at section j of the girder using the data from the example illustrated in Fig. 7. Two cases are considered: constant connection stiﬀness (girder a) and connection stiﬀness changing along the beam (girder b). The diagrams indicate a local decrease in index value as the moving unit force is near the section analysed. In girder a we get the relationship R(x0) f R0 for both sections analysed, i and j, for all load positions. In girder b the eﬀect of connection stiﬀness change is visible; for some positions of the force we get values R(x0) # R0, especially at section j, which is situated in the zone of connection stiﬀness change. Live loads on bridges consist of groups of forces moving along the span. In the case of several point loads, the value of index Ri(xp) " Rip at point i (xp indicates the position of the load) is calculated according to Eq. (21), which after substitution of Eq. (28) is transformed into

∑ Misb0 · Ps · μ is μ ip = s ∑ Misb0 · Ps

s = 1, 2, 3, … , m

(36)

s

Typical inﬂuence functions Ri(xp) and Rj(xp) at sections i and j of the girder with connection stiﬀness changing along the beam are presented in Fig. 10 (girder b). The load is considered as in the example illustrated in Fig. 6. Inﬂuence

Steel Construction 9 (2016), No. 1

63

C. Machelski/R. Toczkiewicz · Effects of connection flexibility in bridge girders under moving loads b

b)

k1

j

i

2b

i

x0

a) 2.8

k3 k2

2.6

j

2.4

xp

μ [-]

k1

k2

2.2

μ=μ

2.1

n=3 n=4 n=5

2.2

μ0=2.070

n=6

2.0 n=7

2.0 1.9

a) μi (x0)

1.8

a) μj (x0)

1.7

b) μi (xp)

1.6

b) μj (xp)

1.8 1.6

x [m] 0

2

4

6

8

10

12

14

16

18

20

P

24 F

xp k1=4000 MN/m2

1.5

xi

xj

1.4 0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

x p [m] x 0 [m]

k2=2500 MN/m2

k2=2500 MN/m2 k3=1000 MN/m2

n: 1 xP [m]: 4.25

Fig. 10. Comparison of inﬂuence lines and inﬂuence functions of index R [15]

2 7.25

3 10.25

4 13.25

5 16.25

6 19.25

6.1 Analysis of sample bridge Fig. 11 shows the results of calculations obtained for the girder of a sample composite viaduct loaded with a fouraxle vehicle used in testing this viaduct under moving loads [15]. The positions of the load changing along the span, denoted with numbers n " 1…9, corresponding to the distance of the vehicle’s front axle from the side support P, equal to xp " 4.25 3(n – 1) , are considered. To determine the forces in the structure, the spans were discretized as a grillage consisting of bar elements with a deck slab discretized as plate elements. FEM calculations resulted in bending moments M(x, xp) in the main girders. As a result of numerical analysis, forces Nb(x, xp) and Mb(x, xp) and values of index R(x, xp) were calculated. Diagrams of the index R(x, xp) for selected positions of the load are presented in Fig. 11a. The ﬁgure also shows the scheme of the moving load and connection stiﬀness k(x) assumed in the analysis, estimated on the basis of design documentation for the viaduct and other data [20]– [24]. The inﬂuence of the load position and the function of the connection stiﬀness k(x) on the diagrams of R index are visible. The results can be arranged in speciﬁc groups: in the area of acting load R(x, xp) ! R0 and in the areas of connection stiﬀness change R(x, xp) # R0. Fig. 11b presents inﬂuence functions of the index R(xp), generated on the basis of analysis results, for three sections of the girder, x " 4 m, x " 10 m, x " 16 m, and for the measurement section of the test viaduct, x " 12 m [15]. The load changes its position along the span, as shown in Fig. 11a. How the position of the load on the structure inﬂuences the values of the index can be seen. It is possible to compare the analysis results described above with the results of in situ load testing of the sample bridge. The test included recording strains at selected measurement sections of steel beams on the viaduct. The structure tested consisted of two parallel viaducts (denoted N and S) with the same conﬁguration, which enabled the

Steel Construction 9 (2016), No. 1

x=4m

2.2

x=10m

μ0=2.070 μ [-]

lines Ri(x0) and Rj(x0) resulting from the action of a unit force (girder a) are also presented. It can be seen that a single force generates a larger local decrease in index values than a group of forces.

7 22.25

24.0 m

b) 2.4

64

22

n

measurement section

μ [-]

measurement section

k3

P=1

a)

2.0

x=12m (measurement section) x=16m

1.8

x p [m]

1.6 5

10

15

20

25

30

Fig. 11. Results of analysis: a) diagram of R(x, n) for girder of test viaduct, b) inﬂuence functions R(xp) for selected sections of girder

results in the structures of the same conﬁguration to be compared, under similar conditions and with the same load [15]. The viaduct was loaded with a single vehicle moving along the side span, along the marked line. At certain points on the deck (positions n " 1…9 at distance xp from side support, see Fig. 11), the truck stopped and values of measured quantities were recorded. On the basis of the strains recorded in the beams, the position of the neutral axis was determined and values of index Rwere calculated according to the transformed Eq. (13). In this way, in situ inﬂuence functions of index R(xp) were created. Direct comparison between the results of the analysis presented in Fig. 11b (at measurement section x " 12 m) and the results of the loading tests illustrated in Fig. 12 is diﬃcult, as the bridge tests are inﬂuenced by a number of factors, including: – Transverse connections between girders, which thus form a grid and restrict ideally free longitudinal deformation of individual beams. – Friction forces on bearings, which generate additional internal forces in girders. – Cooperation of non-structural elements (e.g. concrete sidewalks) with deck plate [14]. – Random values of geometrical and material characteristics of girders. It is often hardly possible to evaluate or eliminate these factors during the tests. It can be seen that values of the index calculated on the basis of measurements are higher than those determined in the analysis, which may indicate

C. Machelski/R. Toczkiewicz Âˇ Effects of connection flexibility in bridge girders under moving loads 2.6 Viaduct S

2.4

Viaduct N

Îź [-]

2.2

Îź0=2.070

2.0 1.8

xp x p [m]

1.6 5

10

15

20

25

30

Fig. 12. Test results: inďŹ‚uence function of index R(xp) for measurement section of a girder of the test viaduct [15]

higher ďŹ‚exural stiďŹ€ness of the girders. Even between the test results of both identical structures (viaduct N and viaduct S), considerable diďŹ€erences were noticed [15]. Another problem is the estimation of actual connection stiďŹ€ness k(x) taken into account in the analyses, which depends not only on the characteristics of connectors, but also on other random factors [1], e.g. bond and friction.

7 Conclusions The analyses conducted have shown that a speciďŹ c feature of composite structures with ďŹ‚exible connectors (e.g. steel-concrete girders connected with welded shear studs) is how the results depend on the type and position of the load as well as the function describing the connection stiďŹ€ness. To identify the eďŹ€ects of ďŹ‚exible connection, a dimensionless index R, deďŹ ned on the basis of internal forces in the beam, was used. This index can be obtained during in situ load testing of a bridge on the basis of a neutral axis position in the section of the girder considered. An analytical model of a partially composite girder was used in which the global bending moment is equilibrated with forces acting in two subsystems of diďŹ€erent physical and geometrical characteristics (steel beam and concrete plate). Numerical analyses illustrating the eďŹ€ects of quasi-static loads changing location along the girder allow us to formulate the following detailed conclusions: â€“ The value of index R at the point of acting force is reduced locally (RÂ !Â R0), which depends on the beam-plate connection stiďŹ€ness k. â€“ A change in connection stiďŹ€ness along the beam results in the local extreme value of the index RÂ #Â R0 in the zone of the stiďŹ€ness change. â€“ The function R(x) is subjected to local ďŹ‚uctuations along the girder, taking both values R xÂ !Â R0 and R(x)Â #Â R0, depending on the connection stiďŹ€ness function k(x). â€“ It is advisable to take into account a load changing its position along the girder, which allows a full range of R values to be obtained; the use of the inďŹ‚uence function is eďŹ€ective in this case. â€“ The function R(x) is related to the location and conďŹ guration of forces forming the load and does not simply depend on the function k(x). The analysis conducted leads to a general observation that considering a single load position does not give full information on the partial interaction at the section analysed.

Only a load moving along the structure (generation of inďŹ‚uence function) gives information on the range of partial interaction characterized by the proposed index R. The index used in the analyses is sensitive to the local eďŹ€ects of ďŹ‚exible connection. It is not possible to identify these local eďŹ€ects by measuring deďŹ‚ection, which depends on the global ďŹ‚exural stiďŹ€ness of a girder, and in real structures is often inďŹ‚uenced by the cooperation of non-structural elements. It should be mentioned that results in the form of a range of index R values (inďŹ‚uence function) do not allow us to estimate the connection stiďŹ€ness k. The inďŹ‚uence function of index R obtained as a result of the analysis under load changing its position on the structure shows whether the connection stiďŹ€ness k is constant along the girder (thenRÂ !Â R0) or changes along the girder, which is indicated by the relationship RÂ #Â R0. The basis for the identiďŹ cation of partial interaction proposed in this paper is the analysis of the variation of the index, which is only possible when a moving load is considered.

Notation Ab/Ap Ib/Ip Eb/Ep Iy Iy0 L M Mb/Mp Nb/Np a aed k vg/vd yg/yd t I J R X

cross-sectional area of beam / plate moment of inertia of beam / plate modulus of elasticity of steel (beam) / concrete (plate) moment of inertia of partially composite girder moment of inertia of fully composite girder span external bending moment in girder bending moment in beam / plate axial force in beam / plate distance from centroid of beam to centroid of plate distance from neutral axis of girder to centroid of beam in partially composite girder connection stiďŹ€ness distance from centroid of beam to top / bottom edge of beam distance from centroid of plate to top / bottom edge of plate shear force shear slip at beam-plate interface axial strain index of partial interaction normal stress

References [1] Johnson, R. P.: Composite structures of steel and concrete, Blackwell ScientiďŹ c Publishers, Oxford, 2004. [2] Galjaard, H. J. C., Walraven, J. C.: Behavior of diďŹ€erent types of shear connectors for composite structures. Proc. of Intl. Conf. on Structural Engineering, Mechanics & Computation â€œSEMC 2001â€?, Cape Town, South Africa, 2â€“4 Apr 2001, pp. 385â€“392. [3] Lorenc, W.: Boundary approach in shape study of composite dowel shear connector. Archives of Civil and Mechanical Engineering, IX(4) (2009), pp. 55â€“66. [4] Hegger, J., Goralski, C., Rauscher, S., Kerkeni, N.: FiniteElemente-Berechnungen zum Trag- und Verformungsverhalten von Kopfbolzenduebeln. Stahlbau, 73(1) (2004), pp. 20â€“ 25.

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C. Machelski/R. Toczkiewicz · Effects of connection flexibility in bridge girders under moving loads

[5] Ohyama, O., Okubo, N., Kurita, A.: Fatigue strength of grouped shear studs. Proc. of 5th European Conf. on Steel & Composite Structures “Eurosteel 2008”, Graz, Austria, 3–5 Sept 2008, pp. 219–224. [6] Civjan, S. A., Singh, P.: Behavior of shear studs subjected to fully reversed cyclic loading. Journal of Structural Engineering, 129(11) (2003), pp. 1466–1474. [7] Luan, N. K., Ronagh, H. R.: In-plane behavior of composite beams with partial shear interaction. Proc. of 3rd Intl. Conf. on Structural Engineering, Mechanics & Computation “SEMC 2007”, Cape Town, South Africa, 10–12 Sept 2007, pp. 1121–1126. [8] Nie, J., Cai, C. S.: Steel-concrete composite beams considering shear slip eﬀects. Journal of Structural Engineering, 129(4) (2003), pp. 495–506. [9] Seracino, R., Chow, T. L., Tze, C. L., Iwo, Y. L.: Partial interaction stresses in continuous composite beams under serviceability loads. Journal of Constructional Steel Research, 60 (2004), pp. 1525–1543. [10] Seracino, R., Oehlers, D. J., Yeo, M. F.: Partial-interaction ﬂexural stresses in composite steel and concrete bridge beams. Engineering Structures, 23 (2001), pp. 1186–1193. [11] Jasim, N. A.: Deﬂections of partially composite beams with linear connector density. Journal of Constructional Steel Research, 49 (1999), pp. 241–254. [12] Nie, J., Fan, J., Cai, C. S.: Stiﬀness and deﬂection of steel-concrete composite beams under negative bending. Journal of Structural Engineering, 130(11) (2004), pp. 1842–1851. [13] Bien´, J., Rawa, P.: Proof load tests of highway composite bridges. Proc. of Congress of the American Society of Civil Engineers “Structural Engineering in the 21st Century”, New Orleans, USA, 1999, pp. 520–523. [14] Machelski, C., Toczkiewicz, R.: Connection ﬂexibility effects in steel-concrete girders according to in-situ tests of a road bridge. Proc. of 5th European Conf. on Steel & Composite Structures “Eurosteel 2008”, Graz, Austria, 3–5 Sept 2008, pp. 225–230. [15] Machelski, C., Toczkiewicz, R.: Identiﬁcation of connection ﬂexibility eﬀects based on load testing of a steel-concrete bridge. Journal of Civil Engineering and Architecture, 6(11) (2012), pp. 1504–1513. [16] Sobótka, M.: Numerical simulation of hysteretic live load eﬀect in a soil-steel bridge. Studia Geotechnica et Mechanica, XXXVI(1) (2014), pp. 103–109.

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[17] Machelski, C., Antoniszyn, G.: Inﬂuence of live loads on the soil-steel bridges. Studia Geotechnica et Mechanica, XXVI(3-4) (2004), pp. 91–119. [18] Newmark, N. M.: Tests and analysis of composite beams with incomplete interaction. Proc. Soc. Experimental Stress Analysis, 9(1) (1951), pp. 75–92. [19] Machelski, C., Toczkiewicz, R.: Eﬀects of connection ﬂexibility in steel-concrete composite beams due to live loads. Archives of Civil and Mechanical Engineering, VI(1) (2006), pp. 65–86. [20] An, L., Cederwall, K.: Push out tests on studs in high strength and normal strength concrete. Journal of Constructional Steel Research, 36 (1996), pp. 15–29. [21] Kim, B., Wright, H., Cairns, R.: The behaviour of throughdeck welded shear connectors: an experimental and numerical study. Journal of Constructional Steel Research, 57 (2001), pp. 1359–1380. [22] Shim, C. S., Lee, P. G., Chang, S. P.: Design of shear connection in composite steel and concrete bridges with precast decks. Journal of Constructional Steel Research, 57 (2001), pp. 203–219. [23] Shim, C. S., Lee, P. G., Yoon, T. Y.: Static behavior of large stud shear connectors. Engineering Structures, 26 (2004), pp. 1853–1860. [24] Lam, D., El-Lobody, E.: Behavior of Headed Stud Shear Connectors in Composite Beams. Journal of Structural Engineering, 131(1) (2005), pp. 96–107. Keywords: steel-concrete composite bridge; partial interaction; movable load; inﬂuence line

Authors: Czesław Machelski, Prof., PhD, Civ. Eng. Wrocław University of Technology Wybrzez·e Wyspian´skiego 27, 50-370 Wrocław, Poland czeslaw.machelski@pwr.edu.pl Robert Toczkiewicz, PhD, Civ. Eng. Research & Design Ofﬁce Mosty-Wrocław Krakowska 19-23, 50-424 Wrocław, Poland robert.toczkiewicz@mosty-wroclaw.com.pl

Reports DOI: 10.1002/stco.201620009

Simple Bridges Andreas Keil Sven Plieninger Sebastian Linden Christiane Sander

Many famous footbridges show a spectacular, eye-catching design or functionality. They feature extravagant structures, large spans or outstanding locations and they are globally published and widely discussed amongst professionals and laymen. However, there are smaller and simpler bridges, whose good and appropriate design, structural behaviour and sustainability can only be seen at the second look. While not having showy features they are beautiful, reasonable, efﬁcient, sometimes trendsetting but always interesting enough to justify careful attention. This paper presents ﬁve bridges – designed by schlaich bergermann partner, completed within the past few years – that are characterized especially by their apparent simplicity: a simple beam bridge in Backnang, three arch bridges in Dortmund, a prestressed concrete beam bridge in Hamburg, a two-span stress ribbon bridge in Schwäbisch Gmünd and a ﬁxed-end beam bridge in Esslingen.

1 Introduction Small and supposedly simple footbridges interact with their particular surroundings architecturally and structurally just as do larger, more prominent ones. Especially with inner-city and urban crossings a bridge can appear unobtrusive and integrated, but also intrusive, clumsy or misplaced. In order to give a bridge the right and appropriate appearance in its particular context, the local situation should be studied thoroughly. The ﬁve following bridges designed by schlaich bergermann partner show the result of a sophisticated consideration of each location. And they show that sometimes a simple approach, carefully executed, can produce interesting and innovative solutions.

2 Three footbridges across the Emscher in Dortmund 2.1 Scope Between 2005 and 2011 an artiﬁcial shallow lake of 24 ha was created on the area of the former steel mill Hermannshütte PHOENIX Ost in Dortmund. This lake forms the centre of a new recreational area with residential and commercial buildings. The uncovering and returning to nature of the river Emscher was an integral part of the redevelopment scheme for the old steel mill. Being a tributary river to the Rhine, the Emscher had partially been used as an underground sewer for the past 100 years.

Fig. 1. Emschersteg (© sbp)

Above ground the Emscher-meadow is up to 50 m wide deﬁning the northern edge of the Phoenix Lake. A group of three bridges was built to provide crossings over the approximately 3 m deep water-meadow in the course of a loop-walkway around the lake (Fig. 1).

2.2 Design and Concept The selected bridge type is an integral bowstring bridge with lateral steel arches and a suspended concrete deck. All three bridges have similar dimensions, spanning roughly 30 m with a total length of 40 m and a width of 3–5 m The lateral steel arches made of layered steel plates, with dimensions of w/h"250/180 mm, are rigidly ﬁxed to the boxed abutments below the deck level. The maximum arch rise of 2.40 m was chosen to ensure that the arches do not rise above the railings and thus do not disturb the view from the bridge. Due to the “lowered” lateral arches the system lengths of the hanger rods were extremely short. Hence a connection detail was designed where the 36 stainless steel hanger rods were inserted right through the cross-section of the arches and anchored at the top. The welded heads are ﬁxed in stainless steel conical sockets. Tubular sleeves at the front face of the transverse beams guide the hanger rods before they are screw-ﬁtted on the bottom by using two-piece spherical washers and conical sockets. Construction tolerances can be compensated by these rotatable

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Fig. 2. Emschersteg – elevation and section (© sbp)

connections which also guarantee a smooth load application to the hanger rods. The reinforced concrete slab of the superstructure with a depth of only 20 cm is monolithically connected to the abutments and suspended from the arches via transverse beams in the hanger axes (Fig. 2). The transverse beams, welded T-beams with a construction height of 170 mm, are connected via shear studs to the slab of the superstructure and function as composite beams. The closed boxed abutments are anchored with bored piles in a deep foundation. A ﬂexible geotextile drainage layer on the back sides of the abutments reduces thermal strains in the superstructure.

2.3 Finishing Fig. 3. Emschersteg – modular railing system (© sbp)

The railing is a modular system of horizontal bars. The bolted connection details were made of minimalist design using countersunk bolts that do not protrude the railing posts (Fig. 3). An additional handrail cantilevering towards the walkway prevents children from climbing the railing, and it contains a linear LED system illuminating the bridge at night.

2.4 Summary Due to the reduced construction height, the ﬁligree railing and the slender, lateral arches the bridges appear unobtrusive from a distance, emerging cautiously and unimposingly from the shallow meadow. At a closer view, however, the technological character and the sophisticated connection details stand out, particularly the hanger details.

3 Fehrlesteg in Schwäbisch Gmünd 3.1 Design The new Fehrlesteg in Schwäbisch Gmünd is a key connection for pedestrians as it links the inner city to the main railway station and the urban district Taubental. The twospan stress ribbon bridge was designed to cross the river Rems featuring a total length of 58 m with spans of 27 and

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19 m respectively. With its minimalist design, the new 2.50 m wide bridge follows the directions of the approaching walkways with a sharp bend at the central support (Fig. 4). The shape of the central support, which is located on an island between the two arms of the river, clearly shows the horizontal forces deriving from the redirection of the stress ribbons. Thus the abutment “leans” against the deviation, creating a balcony-shaped cantilever on the central island. At both ends the stress ribbons rest on slender concrete saddles which protrude from the abutments that are concealed by the river banks.

3.2 Construction The stress ribbons consist of two parallel 400w40 mm steel plates in grade S355, which were pre-curved in the workshop and anchored at the abutments and the central support. With a sag of 40 and 19cm respectively, the maximum inclination is at around 6%. The abutments serve to anchor, adjust and hence for pre-stress the steel plates. Following a speciﬁc curvature the stress ribbons are pulled over the concrete saddles and

Reports

Fig. 4. Fehrlesteg (© sbp/Michael Zimmermann)

back-anchored in cast-in steel parts. The hammerhead-shaped anchorage allows for adjusting the ﬁnal length to the nearest millimetre. At the central support, the stress ribbons are connected as ﬁxed anchors to a cast-in steel part with shear connectors on the bottom to transfer the high horizontal loads into the concrete structure. The solid abutment blocks are resting on rectangular pile caps that transfer the loads via inclined micropiles into deeper and sound soil layers (Fig. 5). The slab elements, comprising 12 cm thick cut and grit-blasted Alpendorada granite (Portugal) with dimensions of 290w80 cm, are placed on elastomeric strips onto the two steel stress ribbons. The slabs are laid with gaps, invisibly fastened to the stress ribbons by grouted stud shear connectors. Adjacent slabs are separated by a neoprene insert within the joints to improve the damping behaviour of the bridge.

3.3 Finishing The guardrail on both sides of the walkway is a 1.20 m high modular railing made of vertical stainless steel rods. The posts are bolted to the granite slabs with each individual handrail segment having sliding joints towards the adjacent one (Fig. 6). The friction in these sliding joints has a

Fig. 67. Fehrlesteg – railing and bridge lighting (© sbp/Michael Zimmermann)

positive impact on the damping behaviour of the lightweight stress ribbon structure. The handrail itself allowed for the integration of LED strip, illuminating the walkway, emphasizing the form and structure of the stress ribbon and reﬂecting the layout of the bridge at night (Fig. 7).

3.4 Summary The construction of the Fehrlesteg represents a sophisticated and innovative structure. With its slenderness, trans-

Fig. 5. Fehrlesteg – section (© sbp)

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Reports parency and shape being deﬁned by the ﬂow of forces, this exemplary structure meets high aesthetic and economic standards. The bridge is intrinsically connected with the urban setting. Despite its modest appearance, the outstanding structure makes it a unique and distinctive bridge. Its grace is underlined by the granite walkway and the stainless steel railing.

4 Margarethe-Müller-Bull-Steg in Esslingen 4.1 Scope In 2009 a bridge design competition was tendered in Esslingen, close to Stuttgart. The objective included a better connection between the inner city and the Maille-Park as well as the redesign of the public space in front of the listed Eichamt building. For crossing the Rossneckarkanal – and the canal is also listed – the objective called for a slender ﬁligree form that smoothly integrates into the historic ensemble of the old municipal park, without impinging on walls along the river banks, or the adjacent historic buildings. However, it was just as important that the design kept to the given budget.

Fig. 8. Margarethe-Müller-Bull-Steg (© Ingolf Pompe)

The deliberate use of stainless steel in critical areas reduces maintenance requirements to a minimum and produces a durable and sustainable structure.

4.3 Finishing and Installation 4.2 Design and Concept The realized structure meets these requirements in a very satisfactory manner. With an overall length of 29 m and a ﬁxed end on one side only, the new bridge focuses structurally and architecturally on the eastern bank of the canal. Facing to the west at the connection to the MaillePark the bridge only lightly rests on the bank like a cantilevered leaf spring (Fig. 8). The ﬁxed support has been conclusively realized by splitting the ﬁxed-end moment into a pair of compression and tension forces: the compression force is supported on the front side of the abutment block, while the tension force is anchored on the back side of the abutment with a pendulum. The 3 m wide steel superstructure, fabricated as a steel hollow section in monocoque-style, has a variable height following the size of the bending moment. Hence the depth decreases from 65 cm at the ﬁxed end to a mere 23 cm on the park side (Fig. 9). In order to reduce the weight of the structure, the complete superstructure has been manufactured using 10–12 mm thick metal plates. However, areas prone to buckling or wheel loads are strengthened with transverse stiﬀeners. The loads are transferred via micro piles into deeper and sound soil layers. The compression bearing at the front side of the eastern abutment is the longitudinally ﬁxed point of the bridge. It consists of a robust stainless steel contact plate, welded to the superstructure, which is inserted into a steel crown that has been cast into the abutment. The pendulums on the back side of the abutment connect the superstructure and the abutment with stainless steel pins. Facing the park, at the western end of the bridge, stainless steel shear dowels 70 mm allow the superstructure to slide in the horizontal direction. These are inserted into a prefabricated steel abutment block that had previously been aligned and cast in its exact position.

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The unobtrusive ﬁlled-rod railing was welded to the superstructure in the workshop. Through numerous small sliding connection details a constraint-free installation and later use of the bridge is guaranteed. Due to its relatively short length, the installation of the bridge was remarkably simple: the completely prefabricated superstructure, including railing, corrosion protection and walking surface, was lifted from a ﬂat-bed truck and set onto the prepared substructure in just 3 h (Fig. 10).

4.4 Summary The slender steel bridge across the Rossneckar provides a solution that naturally blends into the surrounding of both new and historic buildings. Conceptional design, material and choice of colour contribute to an impressive structure of high workmanship.

Fig. 9. Margarethe-Müller-Bull-Steg – section (© Ingolf Pompe)

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Fig. 10. Margarethe-Müller-Bull-Steg – Installation (© Ingolf Pompe)

Fig. 11. Footbridge Gert-Schwämmle-Weg (© sbp)

5 Gert-Schwämmle-Steg in Hamburg 5.1 Scope

into consideration with regard to the soil–structure interaction of this integral bridge.

From 2006 to 2013, Hamburg’s largest river island Wilhelmsburg was a project area of the International Building Exhibition IBA Hamburg. In the course of a sustainable, ecological and socially balanced urban development and in preparation for the international garden exhibition igs 2013 the infrastructure was one of the items to be redeveloped. With the promise of a homogeneous design concept, several small bridge structures were completed up to 2013, being part of the network of foot and cycle paths within the Wilhelmsburg Inselpark. The Gert-Schwämmle-Weg leads across the redeveloped park area to the centre of Wilhelmsburg. Then it crosses the approx. 25 m wide river Rathauswettern just north of the lake Rathaussee.

5.3 Finishing and Installation

5.2 Design and Concept

5.4 Summary

Completed in 2011, the Gert-Schwämmle-Steg spans 32 m across the waterway. Designed as an integral pre-stressed frame bridge made of reinforced concrete, the cross section of the superstructure has the shape of a sharp-edged T-beam. With an eﬀective width of 4 m, the depth of the superstructure reduces from 1.25 m at the abutments to just 37 cm at the centre of the bridge (Fig. 11). To achieve this extreme slenderness of approx. L/90 the deck was pre-stressed using internal parabolic strands. These internal forces caused by the pre-stress counteract the self-weight and the working load. Furthermore, the eccentric pre-stress manipulates the stiﬀness of the superstructure in a way that only minor bending moments occur at midspan. The superstructure is monolithically connected to the box abutments. Despite increasing the span length, the abutments have deliberately been oﬀset as far as possible to show the slope edges of the canal, thus making the bridge appear modest and delicate (Fig. 12). To reduce constraints resulting from thermal expansion, the soil behind the abutments has been ﬁlled with stabilized foamed clay. The foundation has been established using 80cm driven piles. Variations of soil parameters had to be taken

Due to the absence of maintenance-intensive components, such as bearings or transition joints, this integrated design made it possible to render an extremely durable and sustainable construction with minimal maintenance requirements. The delicate character distinguishes the bridge to serve as a role model and a basis for other bridges to follow in the parkland. The bridge appears to be an unobtrusive continuation of the park’s footpath, rather than a staged bridge structure.

A steel box section connected to the face side of the superstructure connects the hairpin shaped railing. To link the individual hairpins and to serve as an additional handrail they are connected by a continuous metal bar on the inside of the walkway. The superstructure is complemented by a bituminous sealing and a 4 cm thick mastic asphalt layer as walking surface. The concrete structures, the abutment and the superstructure were all cast in-situ. This implied that the superstructure had to remain in the formwork until the concrete had cured and all pre-stressing works had been completed.

6 Bleichwiesensteg in Backnang 6.1 Scope The new Bleichwiesensteg in Backnang connects the redesigned Bleichwiese with the tree-covered rear of the Stiftshof. As an attractive link it thus establishes a direct connection between the historic centre of the city and the recently ﬁnished Schweizerbau, a modern shopping facility. The new bridge crosses the river Murr with a span of approx. 27 m, fulﬁlling an important function in traﬃc. As it connects two urban districts it is also of signiﬁcance in terms of urban development and landscape design.

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Fig. 12. Footbridge Gert-Schwämmle-Weg – elevation and section (© sbp)

Fig. 13. Bleichwiesensteg (© sbp/Michael Zimmermann)

Fig. 14. Bleichwiesensteg – central connection detail(© sbp/ Michael Zimmermann)

The brief was complex. The main requirements were to reuse the existing abutments and foundations (the bridge replaces a wooden truss-girder bridge), as well as the demand for a high level of prefabrication and an easy and eﬃcient means of erecting the bridge.

The distinctive central opening is therefore not an only eye-catching design but particular intelligent, oﬀering eﬃcient fabrication and installation procedures (Fig. 14). Using a compression strut as top chord and visible pinned connections, the maximum bending moment is visually divided into a pair of forces, thus making the structure comprehensible. Also, the emerging triangular recess makes the bridge appear light and graceful at its highest point. Via elastomeric bearings it is supported on the in-situ enlarged abutments and the existing pile foundation. As the new bridge is very much lighter than the previous wooden one, the existing piles could be used without any additional measures (Fig. 15).

6.2 Design Hence, a simple and yet outstanding single-span girder with an eﬀective width of 2.50 m was designed. Two lateral box sections increase in depth from 30 cm at the abutments to 1.30 m towards the middle of the bridge, serving both as the primary structural element and as railings (Fig. 13). The two box sections are interconnected and stabilized through an orthotropic deck. The bridge’s structural and creative characteristics become apparent in the division of the superstructure into two almost identical parts. These are completely prefabricated, separately delivered, lifted and then assembled to form a whole system on site.

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6.3 Finishings Seemingly detached from the superstructure the delicate railing ﬂoats above the lateral box sections. It comprises 4 mm horizontally pre-stressed stainless steel cables that accentuate the dynamic linearity of the bridge (Fig. 16).

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Fig. 15. Bleichwiesensteg – section (© sbp)

In the dark, the walkway with its light-toned surfacing is illuminated by LED lighting strips integrated into the lower edges of the box sections (Fig. 17). In the daytime too, the light hue of the walkway creates a contrast to the signiﬁcantly darker box sections.

6.4 Summary The new Bleichwiesensteg is a striking demonstration of how an innovative structure can be realised in a very short construction time by pursuing a straightforward approach to structural design. Moreover, the visualization of the ﬂow of forces within the structure, generated by the opening of the superstructure at the bridge centre, makes it tangible for the user and thus contributes to its acceptance by the public. The innovative steel structure across the river Murr provides a graceful bridging between a modern residential area and the historic Stiftshof. With their ﬁligree railing contrasting the sculptural shape, the structure gains an air of elegance and distinction.

7 Conclusion The paper shows that the architectural motto “less is more” especially applies to the design of small footbridges. Striving for simplicity and reducing bridge design to the very necessary is always a desirable goal. At best, every single element is structurally essential, reasonably shaped and well proportioned. The ﬁve bridges introduced in this paper show that following these principles leads to quite satisfying and yet individual designs. Consequently all of these bridges show

Fig. 1617. Bleichwiesensteg – railing and lighting (© sbp/Michael Zimmermann)

the desire for a simple appearance, an eﬃcient structural behaviour, careful detailing and a sustainable construction. The combination of these leads to the overriding goal that bridge design should focus on: ﬁnding an appropriate and self-evident solution for each particular situation. Keywords: footbridge; design; sustainability; simplicity; connection details

Authors Dipl.-Ing. Andreas Keil Dipl.-Ing. Sven Plieninger Dipl.-Ing. Sebastian Linden Dipl.-Des. (FH) Christiane Sander schlaich bergermann partner Schwabstraße 43 70197 Stuttgart

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ECCS news

Events SDSS 2016 – the International Colloquium on Stability and Ductility of Steel Structures 30 May–1 June 2016, Timisoara, Romania

The series of International Colloquia on Stability and Ductility of Steel Structures has been supported by the Structural Stability Research Council (SSRC) for many years and is intended to summarize the progress in theoretical, numerical and experimental research in the ﬁeld of stability and ductility of steel and composite steel-concrete structures. Special emphasis is always given to new concepts and procedures concerning the analysis and design of steel structures and the background to and development and application of rules and recommendations either appearing in recently published codes or speciﬁcations or about to be included in their upcoming versions. This international colloquium series began in Paris in 1972. SDSS 2016 is being jointly organized by the Politehnica University of Timisoara, Department of Steel Structures and Structural Mechanics, in cooperation with the Romanian Academy, Timisoara Branch, with the support of the European Convention of Constructional Steelwork (ECCS), through the Structural Stability Technical Committee (TC8), and the SSRC. Further information: www.ct.upt.ro/sdss2016

ence of the Paraná and Iguaçu rivers. The waterfall is listed as one of the “New7Wonders of Nature” and has been a place of worship for Guarani Indians since ancient times. The triple border between Brazil, Argentina and Paraguay is a melting pot for Lebanese, Chinese, Germans, Italians, French, Swedes, Portuguese and Ukrainians, also for Christians, Muslims and Buddhists. Foz do Iguaçu is home to the Itaipu Dam, the world’s largest hydroelectric plant for power generation. In June 2016 Foz do Iguaçu will be the place where academics, researchers and practitioners of bridge maintenance, safety and management converge, and a place for you to merge with nature and other cultures. Further information: www.iabmas2016.org

Technical Committees (TC) activities TC meetings agenda TMB – Technical Management Board Chair: Prof. M. Veljkovic

PMB – Promotional Management Board Chair: Mr. Yener Ger’es

TC3 – Fire Safety Chair: Prof. Paulo Vila Real Secretary: Martin Mensinger Next meeting: 22–23 September 2016, Istanbul, Turkey Chair: Dr. M. Lukic Secretary: Stephen Lochte-Holtgreven Next meeting: Spring 2016, venue will be announced later

26–30 June 2016, Foz do Iguaçu, Brazil

TWG 7.5 – Practical Improvement of Design Procedures

Chair: Prof. J. Lange

Chair: Prof. Bettina Brune Next meeting: June 2016, Manchester, UK

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Chair: Prof. U. Kuhlmann Secretary: Dr. B. Braun

TWG 8.4 – Buckling of Shells Chair: Prof. J. M. Rotter Secretary: Prof. S. Karamanos

TC9 – Execution & Quality Management Chair: Mr. Kjetil Myrhe Next meeting: 26 April 2016, Brussels

TC10 – Structural Connections Chair: Prof. Thomas Ummenhofer Secretary: Mr. Edwin Belder Next meeting: 10–11 March 2016, Ljubljana, Slovenia Chair: Prof. Riccardo Zandonini Vice-Chair: Prof. Jean-François Demonceau Secretary: Prof. Graziano Leoni Next meeting: 29 April 2016, Warsaw, Poland

TC13 – Seismic Design Chair: Prof. R. Landolfo Secretary: Dr. Aurel Stratan Next meeting: 7–8 April, Naples, Italy

TC14 – Sustainability & Eco-Efficiency of Steel Construction Chair: Prof. Luís Bragança Secretary: Ms. Heli Koukkari

TC16 – Wind Energy support structures Chair: Prof. Peter Schaumann Vice-Chair: Prof. Milan Veljkovic Secretary: Ms. Anne Bechtel

TC6 – Fatigue & Fracture

TC7 – Cold-formed Thin-walled Sheet Steel in Buildings

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TC11 – Composite

8th International Conference on Bridge Maintenance, Safety and Management

The conference will be held in Foz do Iguaçu, Paraná, Brazil. Foz do Iguaçu is a place where rivers, borders, nature, technology and people converge. The Iguaçu Falls, with a ﬂow of up to 45 million litres per second, is near the conﬂu-

Next meetings: 1 June 2016, Timisoara, Romania (in conjunction with SDSS 2016 conference) and 4 Nov 2016, Barcelona

TWG 7.9 – Sandwich Panels & Related Subjects Chair: Dr. Thomas Misiek

TC8 – Structural Stability Chair: Prof. Bert Snijder Vice-Chair: Richard Stroetmann Secretary: Dr. Markus Knobloch

TC news TC3 – Fire Safety Currently, TC3 consists of one honorary, 22 full and 21 corresponding members. The committee meets once a year and its annual meeting is now jointly organized with the Working Groups of EN 1993-1-2 and EN 1994-1-2 because most of the members of those groups are also members of TC3. The afternoons of the two days of each meeting are devoted to the ECCS-TC3 meeting and the mornings to the Working Groups. This format worked very well with 20 participants at the last ECCS TC3 Annual Meeting in Manchester on 1 and 2 October 2015. During the meeting, Prof. Paulo Vila Real, the new Chair of TC3, acknowledged the work of Prof. Peter Schau-

ECCS news mann over the last 13 years as Chair of TC3. It was decided to publish a new publication entitled “Fire Design of Steel Structures using FEM” with the support of TC3. This publication will contain some theoretical background, examples for validation and benchmarks with a special focus on relevant information for young engineers and beginners. Recent topics discussed within TC3 include the following: – Fire resistance of composite integrated beams (slim-ﬂoor beams) – Temperature assessment of a vertical steel member subjected to localized ﬁre – Emissivity of hot-dip galvanized steel members – Fire scenarios in suspended ceilings and hollow ﬂoors – Fire behaviour of prefabricated composite ﬂoors with steel dowels – High-strength steel members in ﬁre – Default critical temperatures of steel members with class 4 cross-section – Fire design of steel structures with intumescent coatings – Behaviour of cold-formed steel elements in ﬁre – Assessment of existing structures in ﬁre

TC11 – Composite The last meeting of TC11 took place in Bradford, UK, on 30 October 2015. Two new members have joined the TC11: Roland Abspoel and Markus Knobloch, representing Dutch and Swiss steel associations respectively. Twenty-ﬁve full and 12 corresponding members from 15 European countries as well as Algeria, Australia, Brazil, China, New Zealand and the USA currently constitute the TC11. The agenda included a discussion about progress with a state of the art document on shear connections; this has been circulated among the committee and should be approved at the next meeting. A second document about composite beam-to-column connections is in preparation. A working group on shallow ﬂoors is also active and is currently monitoring progress in relevant research. During the meeting, ﬁve other presentations were delivered by members and guests. Roland Abspoel talked about recent research into composite slabs carried out at TU Delft. JeanFrançois Demonceau presented an investigation about eﬀective width of slabs in composite beam-to-column joints. Simo Peltonen showed the results of an

experimental campaign carried out on a special slim-ﬂoor system. Gianluca Ranzi reported on models for serviceability limit state design of composite steel-concrete slabs. Finally, Florian Eggert gave a presentation of SLIMAPP, a research project funded by RFCS that began recently. Graham Couchman, as Chair of CEN\TC250\SC4, presented the progress in the revision of Eurocode 4; future work and possible collaboration with the ECCS-TC11 were discussed.

TC13 TC13 consists of 19 full and 15 corresponding members. The next meeting of TC13 is scheduled for 7–8 April 2016 in Naples, Italy. The most recent meeting took place on 30 October 2015 in Paris, jointly with Working Group 2 (WG2) “Steel and Composite Structures” of CEN/TC250/SC8 “Eurocode 8: Earthquake resistance design of structures”. There are four Technical Working Groups operating within the committee: – TWG1 Members and connections (convenor Dan Dubina) – TWG2 Traditional typologies (convenor Ahmed Elghazouli) – TWG3 Innovative systems (convenor Federico M. Mazzolani) – TWG4 Low dissipative structures (convenor André Plumier) The main activity of TC13 consists of working jointly with CEN/TC250/SC8/ WG2 to prepare a set of background documents and proposals for improving Eurocode 8, which is undergoing a systematic review process. Cooperation was also strengthened with TC11 “Composite Structures”, with a view to improving seismic design rules for composite construction.

Further ECCS news European Steel Bridge Awards 2016

tects and engineers to use more steel within the bridge construction sector, thus making the steel industry more competitive. The European Convention for Constructional Steelwork has the pleasure of inviting its Full Members to submit their entries for the European Steel Bridges Awards 2016. The awards are open to steel and composite bridges for which steel structures were primarily designed or fabricated in the ECCS Full Member countries. If the project is multinational, it can also be submitted in accordance with the submission procedure stated below. The awards go to the owner, general contractor, architects, engineers and steelwork contractors of each outstanding steel bridge project submitted from ECCS Full Member countries and international contestants in order to credit their collaboration and the excellence of their work. The national member is responsible for approving each entry submitted to indicate that it complies with the regulations of the awards. For the ﬁrst time this year, international contestants are also invited to submit their entries for a special International Bridge Award. For international entries, the ECCS Architecture and Awards Committee is responsible for ratifying each international bridge entry submitted to indicate that it complies with the regulations of the awards. The ECCS International Jury will select the winning projects.

Key dates Last date for submission of entries: 27 May 2016 – uploading of entry form and documentation (available online from 1 March 2016 at www.steelconstruct.com) Award decision by ECCS International Jury: by 17 June 2016 Press release and documentation: by end of June 2016 Presentations and additional ﬁles: by 20 August 2016 Awards ceremony: Stockholm, Sweden, 14 November 2016

Call for Entries

Regulations

The European Steel Bridge Awards are presented by ECCS every two years to encourage the creative and outstanding use of steel in the construction of bridges. The objective is to give European recognition to steel and composite bridges while emphasizing the various advantages of steel in construction, production, economy, sustainability and architecture, and to encourage clients, archi-

1. Operation of the Awards The Awards are open to steel and composite bridges for which steel structures were designed or fabricated in the ECCS Full Member countries. If the project is multinational, it can also be submitted in accordance with the submission procedure stated below. Steel bridge projects located outside the member country are eligible if they have been designed or fabricated in an

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ECCS news ECCS Full Member (National Association). In cases where the partners of the project (project owner, general contractor, architectural ﬁrm, structural engineering ﬁrm and fabricators) are from diﬀerent countries, then … – If some partners are from an ECCS Full Member country and others are from a Non-Member country, the Full Member may apply. – If they are from diﬀerent ECCS Full Members countries, z the Full Members may submit the entry together; z one of Full Members may submit in coordination with the other; z the fabricator for the project shall be the determining factor for selecting the Full Member making the submission (should there be any disagreement). In addition, steel and composite bridges that were designed or fabricated in countries without ECCS representation may be submitted by international contestants for an International Bridge Special Award. The structure must have been completed and gone into service within the last three years, in the period between 31 May 2013 and 31 May 2016. Previous entries are not eligible. 2. Jury and evaluation The Jury consists of the following seven members: – A representative of the Hosting Full Member, – Veronique Dehan, ECCS Secretary General, – Lasse Kilvaer, Chair of Awards and Architecture Committee, representing PMB, – Oliver Hechler, representing AC3 Bridge Advisory Committee, – An architect from the hosting nation and – Two international representatives. The Chair of the jury is the representative of the Hosting Full Member, and the Jury Reporter/Jury Secretary shall be determined by the ECCS prior to 31 December 2015. The Jury shall select award-winners after assessing all entrants against the following criteria: – To have an internationally recognized standard. – To be of outstanding quality in terms of its architecture, structure and construction. – To encourage clients, architects and engineers to use more steel within the entire steel construction sector,

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thus making the steel industry competitive. To emphasize the advantages of steel for construction, production, economy and architecture. To adhere to the principles of sustainability and quality of steel bridges. To disseminate the knowledge of steel and its many-facetted uses and to draw attention to its development. To improve the image of steel.

3. Responsibilities of ECCS Full Members ECCS Full Members have the responsibility: – To call for entries according to ECCS criteria for their national/member participants. – To approve entries that comply with the regulations of the Awards. – To upload the entries to the ECCS website (online). – To invite nominated teams to attend the European Steel Bridges Award Ceremony. – To disseminate promotional publications and press releases on a national level (linking to the ECCS website). 4. Awards Awards will be made in two main categories of bridges: – Road and railway bridges – Bridges for cyclists and pedestrians In addition, the Jury may grant Special Awards such as: – Refurbishment of an existing bridge (major retroﬁt, expansion, refurbishment or partial replacement) using steel – Bridge constructed using weathering steel – Floating bridge – Crazy design and realization – International Bridge Entries that have received a Category Award may also be selected to receive a Special Award. An entry may receive more than one Special Award should the Jury decide to do so. The Awards will be presented during a special session at the ECCS Annual Meeting in Sweden on 14 November 2016. 5. Timetable – Dissemination of SBA Call for Entries 2016 by the end of October 2015. – Announcement of Jury Members on ECCS website prior to 14 December 2015. – Submission by uploading to ECCS website (www.steelconstruct.com) prior to 27 May 2016.

– Evaluation of entries by ECCS International Jury by 17 June 2016. – Oﬃcial information and press release by ECCS/National Associations related to the winning entries by the end of June 2016. – Uploading of presentations and documentation for the ceremony and the publication by 20 August 2016. – ECCS Steel Bridges Awards Ceremony held in Stockholm, Sweden, on 14 November 2016. 6. Submission of entries Entries can be submitted to the NAMs by either architects, engineering oﬃces, fabricators or clients, or the national jury itself. The entries will be approved and submitted to the ECCS by the ECCS National Full Members in order to comply with the regulations of the Awards. Full Members are entitled to approve more than one entry. The international contestants mentioned above may submit entries directly to the ECCS by uploading entries that comply with the rules stated in this document. 7. Submittal requirements The entry documents have to be uploaded to the ECCS website (www.steelconstruct.com) by the Full Member or international contestants prior to 27 May 2016. The application scheme will be online by March 2016 at www.steelconstruct.com. The submission must contain key information, a brief description, high-resolution photographs, design drawings and technical data. These documents are for publication and must therefore be of the highest quality and free of copyright charges. The material submitted can be utilized by ECCS and ECCS members in press releases, publications and on websites to promote the use of steel in steel bridges and structures. 7.1 Entry form – Name and location of project (name of ﬁrm submitting entry, address, person to contact, phone, fax and e-mail) – Name and location of fabricators, structural engineering ﬁrm, architectural ﬁrm, general contractor and project owner – Main key data and technical information such as names of companies involved, date of completion, dimensions, tonnage, main structural concept, etc. 7.2 Project description Includes a brief description of the location, the function, an explanation of how the structure satisﬁes the design

ECCS news/Announcements brief and distinguishing/unique aspects of the structural system, aesthetic considerations and sustainability criteria. The text must be no longer than one A4 page and must be written in English. In addition, a brief project description not exceeding 150 words must be uploaded for publication by 20 August 2016. 7.3 Photographs A minimum of 12 high-resolution photographs in electronic format (minimum 3600 x 2400 pixel or 300 dpi resolution, .eps, .jpg or .tif) taken during construction and after completion must be uploaded. The entrant must clear copyright regarding photos, slides and drawings for presentation and publication. Any fees or royalties connected with such releases are the responsibility of the entrant. ECCS reserves the right to unrestricted use of all photos and materials submitted for promotional purposes. 7.4 Drawings Provide a site plan, principal elevations, sections (1:100 or 1:200) and general arrangement. In addition, show typical and innovative details (1:50), typical steel construction detail (1:20) with legends apart in English. All drawings should be provided in electronic format (600 dpi, .eps or vectorized .pdf (possibly .dxf), black/white; without description and measure layer). 7.5 Presentations PowerPoint or PDF presentations or ﬁlm clips to be used during the Awards Ceremony must be uploaded by 20 August 2016, together with any additional material that should be included with the press package. Presentations are limited to 3 minutes for each entry. They may include incidental music to be played during the Awards Ceremony 8. Contact For further information, contact the ECCS Design Award Committee (AC-4), Chair Lasse Kilvær (Norway): lasse@ stalforbund.com.

STEEL-EARTH workshops organized by ECCS The ECCS organized three workshops recently within the scope of the RFCS STEEL-EARTH project: – Madrid, Spain, 28 October 2015, – Cluj-Napoca, Romania, 20 November 2015 – Coimbra, Portugal, 27 November 2015

Pictures and proceedings of these workshops can be downloaded free of charge from www.steelconstruct.com < EVENTS (NATIONAL) >.

Announcements Madrid, Spain

International Colloquium on Stability and Ductility of Steel Structures 2016 Location and date: Timis¸oara, Romania, 30 May1 June 2016 Information and registration: www.ct.upt.ro

XIII International Conference on Metal Structures Cluj-Napoca, Romania

Location and date: Zielona Góra, Poland, 1517 June 2016 Information and registration: www.icms2016.uz.zgora.pl

8th International Conference on Bridge Maintenance, Safety and Management (IABMAS2016) Location and date: Foz do Iguaçu, Brazil, 2630 June 2016

Coimbra, Portugal

The aim was to explore material choices and structural solutions when dealing with seismic loads; cost-eﬀective and safe design solutions in high-risk seismic areas and steel-based solutions for rehabilitation of existing structures were presented. The building typologies covered industrial and commercial buildings. The workshop material was based on the results of three successful European RFCS projects: – Optimizing the seismic performance of steel and steel-concrete structures by standardizing material quality control (OPUS) – Prefabricated steel structures for lowrise buildings in seismic areas (PRECASTEEL) – Steel solutions for seismic retroﬁt and upgrading of existing structures (STEELRETRO)

Information and registration: www.iabmas2016.org

ISMA Noise and Vibration Engineering Conference – ISMA2016 Location and date: Leuven, Belgium, 1921 September 2016 Information and registration: www.isma-isaac.be

INALCO 2016 – 13th International Aluminium Conference Location and date: Naples, Italy, 2123 September 2016 Information and registration: www.inalco2016.it

Experts involved in the STEEL-EARTH project and prominent national experts organized the workshops.

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News

News Floating wind farms near Norway, Portugal and Japan Not so long ago, erecting a wind turbine farm in deep water would have seemed a futuristic idea, but not anymore. Pilot floating wind turbine projects are showing positive results and they may become a cost and energy effective solution in areas lacking the appropriate geological conditions for the construction of conventional offshore wind farms. Floating turbines can be placed in areas with the best possible wind conditions rather than primarily basing the location selection on the depth of the waters (max. 50 m for conventional oﬀshore wind turbines) or the quality of the seabed. Japan, the US and some parts of Europe, for example, could beneﬁt from the development of ﬂoating oﬀshore wind turbines due to their lack of shallow waters. It was in 2009 that the ﬁrst full-scale ﬂoating pilot platform Hywind, featuring a 2.3 MW Siemens turbine, was deployed 10 km oﬀ the south-west coast of Norway and has since produced

32.5 GWh of energy. Since then, several other successful full scale pilot projects have been given the green light in diﬀerent regions of the world. On 3 November 2015, the Scottish Government gave approval to the Norwegian energy company Statoil, who is behind the Hywind project, to start a second project oﬀ Peterhead in Aberdeenshire, Scotland. It is set to become the largest ﬂoating wind turbine farm in the world. The 30 MW pilot project will consist of ﬁve 6 MW ﬂoating Siemens turbines operating in waters exceeding 100 m of depth at Buchan Deep, 25 km oﬀshore Peterhead. The wind farm is expected to provide electricity to around 20,000 households. Production is planned for 2017. The turbines will be attached to the seabed by a three-point mooring spread and anchoring system. An export cable will transport electricity from the pilot park to shore at Peterhead. Five km oﬀ the coast of Aguçadoura, Portugal, another pilot project, known as the WindFloat Atlantic project, is being tested under plans set out in November 2015. The project is planned to be

operational in 2018 and will consist of three or four wind turbines on ﬂoating foundations, accounting for a total capacity of 25 MW. The project is led by a consortium of companies including French gas and power group Engie, Portugal’s EDP Renewables (EDPR), Japan’s Mitsubishi Corp and Chiyoda Corp, along with Spanish energy group Repsol. According to the consortium, the aim of the project is to demonstrate the economic potential and reliability of this technology, advancing it further in the path towards commercialisation. During phase one, a semi-submersible wind generator carrying a 2 MW Vestas turbine had produced more than 16 GWh over almost four years of operation, during which time it withstood extreme weather conditions. Oﬀ the coast of Fukushima in Japan another project launched in 2013 is also seeing the huge potential of ﬂoating wind farms. The demonstration project (Fukushima FORWARD) is led by a consortium of universities and heavy industry companies, including Nippon Steel & Sumitomo Metal Corporation, and is funded by the Ministry of Economy, Trade and Industry. In this project, three ﬂoating wind turbines and one ﬂoating power sub-station will be installed oﬀ the coast of Fukushima. The ﬁrst phase of the project was completed in November 2013 and consisted of one 2 MW ﬂoating wind turbine. Phase II began in June 2015 and should see two of the world’s largest 7 MW wind turbines being installed by the end of the year. The technologies enabling the wind turbines to stay aﬂoat typically consist either of a single central ﬂoating cylindrical spar buoy or a triangular platform moored by catenary cables. So far, both technologies have shown promising results even in severe weather conditions. The commercial development of this new technology could help further boost the use of renewables in lieu of fossil fuel energy. Steel plays a vital role in wind power generation. Steel represents on average 80 % of all materials used to construct a wind turbine. Further information: www.worldsteel.org

Hywind Scotland pilot park overview

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The international journal “Steel Construction – Design and Research” publishes peer-reviewed papers covering the entire ﬁeld of steel construction research and engineering practice, focusing on the areas of composite construction, bridges, buildings, cable and membrane structures, façades, glass and lightweight constructions, also cranes, masts, towers, hydraulic structures, vessels, tanks and chimneys plus ﬁre protection. “Steel Construction – Design and Research” is the engineering science journal for structural steelwork systems, which embraces the following areas of activity: new theories and testing, design, analysis and calculations, fabrication and erection, usage and conversion, preserving and maintaining the building stock, recycling and disposal. “Steel Construction – Design and Research” is therefore aimed not only at academics, but in particular at consulting structural engineers, and also other engineers active in the relevant industries and authorities. “Steel Construction – Design and Research” is published four times a year. Except for manuscripts, the publisher Ernst & Sohn purchases exclusive publishing rights. Ernst & Sohn accepts for publication only those works whose content has never appeared before in Germany or elsewhere. The publishing rights for the pictures and drawings made available are to be obtained by the author. The author undertakes not to reprint his or her article without the express permission of the publisher Ernst & Sohn. The “Notes for Authors” regulate the relationship between author and editorial staﬀ or publisher, and the composition of articles. “Notes for Authors” can be obtained from the publisher or via the Internet at www.ernst-und-sohn.de/zeitschriften. The articles published in the journal are protected by copyright. All rights are reserved, particularly those of translation into foreign languages. No part of this journal may be reproduced in any form whatsoever without the written consent of the publisher. Brand-names or trademarks published in the journal are to be considered as protected under the terms of trademark protection legislation, even if they are not individually identiﬁed as such. Manuscripts are to be sent to the editorial staﬀ or http://mc.manuscriptcentral.com/stco. If required, oﬀprints or run-ons can be made of single articles. Requests should be sent to the publisher. Current prices The journal “Steel Construction – Design and Research” comprises four issues per year. In addition to “Steel Construction – Design and Research print”, the PDF version “Steel Construction – Design and Research online” is available on subscription through the “Wiley Online Library” online service. Prices

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Steel Construction 8 (2015), No. 3

Preview

Steel Construction 2/2016* Günter Seidl, Mathias Daßler Practical experience and economical aspects of bridges with composite dowel strips Markus Feldmann First experience with the German „General Approval Composite Dowel Strips“ Pavel Simon R&D of composite dowel strips in Czech Republic Wojciech Lorenc Steel design concept for composite dowel shear connection and Nonlinear behaviour of steel dowels in composite dowels: design models and approach by ﬁnite elements Maciej Koz·uch, Slawomir Rowin´ski Elastic behaviour of steel part of shear connection by MCL composite dowels: design basis for serviceability and fatigue limit states

Composite constructions integrate the advantages of steel and concrete. Recently an inventive composite connection, the socalled composite dowel strip, was created in several research projects. It is characterized by a high bearing capacity combined with a ductile behavior and favorable fatigue resistance especially with the combination of high strength materials. In recent years the investigations reached a level which allows the design of a wide variety of building and bridge structures. Leading research institutes introduce their ﬁndings obtained in several articles in issue 2/2016 of “Steel Construction – Design and Research”. In addition to the research results, the best practice of construction implementing composite dowel strips will be highlighted. Innovative cross-sections of girders ﬁnd their introduction in a wide range of application for composite bridges.

Maik Kopp Eﬀects on the static capacity and fatigue resistance of composite dowels due to transversal tension load

Thomas Lechner, Sebastian Gehrlein Structural behaviour of composite dowels in thin UHPC-beams

Dieter Ungermann, Svenja Holtkamp Hot dip galvanized composite dowel strips

Martin Mensinger, Luo Guoqing Anchorage of external reinforcement in case of rigid clamping

Josef Hegger, Martin Claßen Shear behaviour of composite dowels in transversely cracked concrete

Daniel Pak Condition monitoring of two slab track VFT-Rail railway bridges

* Selected and updated papers from the workshop “Composite dowels”, 25−26 November 2015, Berlin

(subject to change without notice)

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2015 Steel Construction Volume 8 No. 1–4 ISSN 1867-0520

Design and Research

Annual table of contents Editor-in-chief: Karl-Eugen Kurrer

Editorial board Chair: Luís Simões da Silva (Portugal) Frans Bijlaard (The Netherlands) Luís Bragança (Portugal) Dinar Camotim (Portugal) S. L. Chan (P. R. China) Paulo Cruz (Portugal) Dan Dubina (Romania) László Dunai (Hungary) Morgan Dundu (Rep. of South Africa)

Markus Feldmann (Germany) Dan Frangopol (USA) Leroy Gardner (UK) Richard Greiner (Austria) Jerome Hajjar (USA) Markku Heinisuo (Finland) Jean-Pierre Jaspart (Belgium) Ulrike Kuhlmann (Germany) Akimitsu Kurita (Japan) Raffaele Landolfo (Italy) Guo-Qiang Li (P. R. China) Richard Liew (Singapore) Mladen Lukic (France) Enrique Mirambell (Spain)

Kjetil Myhre (Norway) Kim Rassmussen (Australia) John Michael Rotter (UK) Peter Schaumann (Germany) Bert Snijder (The Netherlands) Thomas Ummenhofer (Germany) Ioannis Vayas (Greece) Milan Veljkovic (Sweden) Pedro Vellasco (Brazil) Paulo Vila Real (Portugal) Frantisek Wald (Czech Republic) Riccardo Zandonini (Italy) Jerzy Ziółko (Poland)

Annual table of contents 2014

Steel Construction: Annual table of contents Volume 8 (2015) List of authors (A = Topics/Aufsatz, B = Report/Bericht, E = Editorial)

Aarønæs, Anton; Nilsson, Hanna; Neumann, Nicolas: Dynamic response of steel pipe rack structures subjected to explosion loads Issue 3 Alkan, Mustafa; s. Winterstetter, Thomas Andreassen, Michael Joachim; Jönsson, Jeppe: Joint and column behaviour of slotted coldformed steel studs Issue 3 Beccarelli, Paolo; Maffei, Roberto; Galliot, Cédric; Luchsinger, Rolf H.: A new generation of temporary pavilions based on Tensairity girders Issue 4 Bedair, Osama: An analytical expression to determine “realistic” shear buckling stress in coldformed lipped channels Issue 1 Beguin, Philippe; s. Lawson, Mark Berger, Radu; s. Winterstetter, Thomas Björk, Timo; s. Hämäläinen, OlliPekka Borjigin, Sudanna; Kim, ChulWoo; Chang, Kai-Chun; Sugiura, Kunitomo: Non-linear seismic response analysis of vehiclebridge interactive systems Issue 1 Botti, Andrea; s. Döring, Bernd Braun, Matthias; Obiala, Renata; Odenbreit, Christoph: Analyses of the loadbearing behaviour of deep-embedded concrete dowels, CoSFB Issue 3 Braun, Matthias; s. Lam, Dennis Braun, Matthias; s. Lawson, Mark Braun, Matthias; s. Romero, Manuel L. Cajot, Louis-Guy; s. Romero, Manuel L. Chang, Kai-Chun; s. Borjigin, Sudanna Conan, Yves; s. Romero, Manuel L. Cywin´ski, Zbigniew; s. Kido, Ewa Maria Dai, Xianghe; s. Lam, Dennis De Laet, Lars; s. Mollaert, Marijke Devos, Rika; s. Mollaert, Marijke Döring, Bernd; Reger, Vitali; Kuhnhenne, Markus; Feldmann, Markus; Kesti, Jyrki; Lawson, Mark; Botti, Andrea: Steel solutions for enabling zeroenergy buildings Issue 3 Feldmann, Markus; s. Döring, Bernd

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162–166

155–161

A

A

259–264

A

53–58

A

2–8

167–173

194–200

A

A

A

Feldmann, Markus; s. Schillo, Nicole Fischer, Oliver; Mangerig, Ingbert; Mensinger, Martin; Siebert, Geralt; Inoue, Susumu; Sugiura, Kunitomo; Yamaguchi, Takashi; Ohyama, Osamu: 10th Japanese-German Bridge Symposium Issue 1 Galliot, Cédric; s. Beccarelli, Paolo Gibson, Nick D.: How to get a membrane structure off the drawing board Issue 4 Grabe, Jürgen; s. Kuhlmann, Ulrike Gunalan, Shanmuganathan; s. Janarthanan, Balasubramaniam Göppert, Knut; Paech, Christoph: High-performance materials in façade design – Structural membranes used in the building envelope Issue 4 Hashimoto, Kunitaro; Kayano, Makio; Suzuki, Yasuo; Sugiura, Kunitomo; Watanabe, Eiichi: Structural safety assessment of continuous girder bridge with fatigue crack in web plate Issue 1 Hauf, Gunter; Kuhlmann, Ulrike: Deformation calculation methods for slim floors Issue 2 Heinisuo, Markku; Mäkinen, Jari: Nordic Steel Construction Conference 2015 Issue 3 Helbig, Thorsten; Kamp, Florian; Oppe, Matthias: An Eye to the Sky – Inclined grid shell dome of 90 m in Astana, Kazakhstan Issue 2 Hicks, Stephen; Peltonen, Simo: Design of slim-floor construction for human-induced vibrations Issue 2 Hämäläinen, Olli-Pekka; Björk, Timo: Fretting fatigue phenomenon in bolted high-strength steel plate connections Issue 3 Höglund, Torsten: Cold-formed members – comparison between tests and a unified design method for beam-columns Issue 1 Inoue, Susumu; s. Fischer, Oliver Janarthanan, Balasubramaniam; Mahendran, Mahen; Gunalan, Shanmuganathan: Bearing capacity of cold-formed unlipped channels with restrained flanges under EOF and IOF load cases Issue 3 Jungbluth, Dominik; s. Stranghöner, Natalie

1

E

244–250

A

237–243

A

15–20

A

96–101

A

145

E

133–138

B

110–117

A

174–178

A

42–52

A

146–154

A

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Annual table of contents 2015

Just, Adrian; s. Kuhlmann, Ulrike Jönsson, Jeppe; s. Andreassen, Michael Joachim Kamp, Florian; s. Helbig, Thorsten Kawatani, Mitsuo; s. Tsubomoto, Masahiko Kayano, Makio; s. Hashimoto, Kunitaro Kennedy, Stephen J.; Martino, Aldo E.: SPS bridge decks for new bridges and strengthening of existing bridge decks Issue 1 Kesti, Jyrki; s. Döring, Bernd Kido, Ewa Maria; Cywin´ski, Zbigniew: The new steel-glass architecture of passenger service centres on expressways in Japan Issue 3 Kim, Chul-Woo; s. Borjigin, Sudanna Kuhlmann, Ulrike; Just, Adrian; Leitz, Bernadette; Grabe, Jürgen; Schallück, Christoph: Simplified criteria and economic design for king piles in combined steel pile walls according to Eurocode 3, part 1-1 Issue 2 Kuhlmann, Ulrike; Zandonini, Riccardo: Slim floors – a chance for high permance Issue 2 Kuhlmann, Ulrike; s. Hauf, Gunter Kuhlmann, Ulrike; s. Lam, Dennis Kuhnhenne, Markus; s. Döring, Bernd Lam, Dennis; Dai, Xianghe; Kuhlmann, Ulrike; Raichle, Jochen; Braun, Matthias: Slimfloor construction – design for ultimate limit state Issue 2 Lawson, Mark; Beguin, Philippe; Obiala, Renata; Braun, Matthias: Slim-floor construction using hollow-core and composite decking systems Issue 2 Lawson, Mark; s. Döring, Bernd Leitz, Bernadette; s. Kuhlmann, Ulrike Lener, Gerhard: Steel bridges – numerical simulation of total service life including fracture mechanic concepts Issue 1 Leskela, Matti V.; Peltonen, Simo: Effect of unzipping connection behaviour on the composite interaction of shallow floor beams Issue 2 Leskela, Matti V.; Peltonen, Simo; Obiala, Renata: Composite action in shallow floor beams with different shear connections Issue 2 Luchsinger, Rolf H.; s. Beccarelli, Paolo Maffei, Roberto; s. Beccarelli, Paolo Mahendran, Mahen; s. Janarthanan, Balasubramaniam Mangerig, Ingbert; s. Fischer, Oliver

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21–27

A

210–215

B

122–132

A

77–78

E

79–84

A

85–89

A

28–32

A

118–121

A

90–95

A

Mangerig, Ingbert; s. Mano, Toshihisa Mano, Toshihisa; Mangerig, Ingbert: Tensile load-carrying behaviour of elastomeric bearings Issue 1 Martino, Aldo E.; s. Kennedy, Stephen J. Mensinger, Martin; s. Fischer, Oliver Mollaert, Marijke; De Laet, Lars; Pyl, Lincy; Devos, Rika: The design of tensile surface structures – From a hand calculation in 1958 to a contemporary numerical simulation Issue 4 Mori, Kengo; s. Tsubomoto, Masahiko Mäkinen, Jari; s. Heinisuo, Markku Neumann, Nicolas; s. Aarønæs, Anton Nilsson, Hanna; s. Aarønæs, Anton Nützel, Oswald; Saul, Reiner: Long-term corrosion protection for bridge cables with butyl rubber tapes using the ATIS CableIssue 1 skin® system Obiala, Renata; s. Braun, Matthias Obiala, Renata; s. Lawson, Mark Obiala, Renata; s. Leskela, Matti V. Odenbreit, Christoph; s. Braun, Matthias Ohyama, Osamu; s. Fischer, Oliver Oppe, Matthias; s. Helbig, Thorsten Paech, Christoph; s. Göppert, Knut Peltonen, Simo; s. Hicks, Stephen Peltonen, Simo; s. Leskela, Matti V. Peltonen, Simo; s. Leskela, Matti V. Pyl, Lincy; s. Mollaert, Marijke Raichle, Jochen; s. Lam, Dennis Reger, Vitali; s. Döring, Bernd Romero, Manuel L.; Cajot, LouisGuy; Conan, Yves; Braun, Matthias: Fire design methods for slim-floor structures Issue 2 Saul, Reiner; s. Nützel, Oswald Saxe, Klaus; s. Uhlemann, Jörg Schallück, Christoph; s. Kuhlmann, Ulrike Schillo, Nicole; Feldmann, Markus: Local buckling behaviour of welded box sections made of high-strength steel – Comparing experiments with EC3 and general method Issue 3 Siebert, Geralt; s. Fischer, Oliver Sobek, Werner; s. Winterstetter, Thomas

33–41

A

251–258

A

59–64

B

102–109

A

179–186

A

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Annual table of contents 2015

Steige, Yvonne; Weynand, Klaus: Design resistance of end plate splices with hollow sections Stimpfle, Bernd: The Nuvola for the Nuovo Centro Congressi in Rome Stranghöner, Natalie: Tensile membrane structures Stranghöner, Natalie; Jungbluth, Dominik: Fatigue strength of marked steel components – Influence of durable marking methods on the fatigue strength of steel components Stranghöner, Natalie; s. Uhlemann, Jörg Sugiura, Kunitomo; s. Borjigin, Sudanna Sugiura, Kunitomo; s. Fischer, Oliver Sugiura, Kunitomo; s. Hashimoto, Kunitaro Suzuki, Yasuo; s. Hashimoto, Kunitaro Toth, Agatha; s. Winterstetter, Thomas

Issue 3 187–193

A

Issue 4 230–236

A

Issue 4 221

E

Issue 3 201–209

A

Tsubomoto, Masahiko; Kawatani, Mitsuo; Mori, Kengo: Trafficinduced vibration analysis of a steel girder bridge compared with a concrete bridge Issue 1 9–14 Uhlemann, Jörg; Stranghöner, Natalie; Saxe, Klaus: Comparison of stiffness properties of common coated fabrics Issue 4 222–229 Watanabe, Eiichi; s. Hashimoto, Kunitaro Watanabe, Maiko; s. Winterstetter, Thomas Weynand, Klaus; s. Steige, Yvonne Winterstetter, Thomas; Alkan, Mustafa; Berger, Radu; Watanabe, Maiko; Toth, Agatha; Sobek, Werner: Engineering complex geometries – the Heydar Aliyev Centre in Baku Issue 1 65–71 Yamaguchi, Takashi; s. Fischer, Oliver Zandonini, Riccardo; s. Kuhlmann, Ulrike

A

A

B

Subject codes and keywords

Cable structures Nützel, Oswald; Saul, Reiner: Long-term corrosion protection for bridge cables with butyl rubber tapes using the ATIS Cableskin® system [buthyl rubber tapes; long term corrosion protection; bridge ropes and cables; automatic visual and magnetic induction testing; scaffolding free application; dehumidification of cables] Issue 1 59–64

Composite construction Braun, Matthias; Obiala, Renata; Odenbreit, Christoph: Analyses of the loadbearing behaviour of deep-embedded concrete dowels, CoSFB [Composite design; slim-floor; CoSFB; CoSFBBetondübel; ABAQUS] Issue 3 167–173 Hauf, Gunter; Kuhlmann, Ulrike: Deformation calculation methods for slim floors [slim-floor girder; deflection; girder stiffness] Issue 2 96–101 Hicks, Stephen; Peltonen, Simo: Design of slim-floor construction for human-induced vibra4

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tions [slim-floor construction; human-induced vibrations; vibrations; dynamic response; multiplying factor; frequency; EN 1990; ISO 10137] Issue 2 110–117 Lam, Dennis; Dai, Xianghe; Kuhlmann, Ulrike; Raichle, Jochen; Braun, Matthias: Slimfloor construction – design for ultimate limit state [slim floor; composite beam; shallow floor construction; steel section; composite decking; bending resistance; horizontally lying studs; CoSFB; CoSFB concrete dowels] Issue 2 79–84 Lawson, Mark; Beguin, Philippe; Obiala, Renata; Braun, Matthias: Slim-floor construction using hollow-core and composite decking systems [slim floor; integrated beam; composite action; shallow floor structure; steel section; reinforced concrete; deep composite decking; floor stiffness; bending resistance] Issue 2 85–89 Leskela, Matti V.; Peltonen, Simo: Effect of unzipping connection behaviour on the composite interaction of shallow floor beams [shallow floor beams; composite interaction; non-ductile connections; unzipping

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Annual table of contents 2015

behaviour; hollow-core decking supported on beams] Issue 2 118–121 Leskela, Matti V.; Peltonen, Simo; Obiala, Renata: Composite action in shallow floor beams with different shear connections [composite interaction; shallow floor beams; shear connection behaviour; effective bending stiffness; bending resistance; partial connection theory] Issue 2 90–95 Romero, Manuel L.; Cajot, LouisGuy; Conan, Yves; Braun, Matthias: Fire design methods for slim-floor structures [slim floors; fire resistance; simplified methods; composite steel-concrete structures; shallow floor beams] Issue 2 102–109

Design Gibson, Nick D.: How to get a membrane structure off the drawing board [tensile membrane structures; compensation] Issue 4 Helbig, Thorsten; Kamp, Florian; Oppe, Matthias: An Eye to the Sky – Inclined grid shell dome of 90 m in Astana, Kazakhstan [dome; steel; grid shell; Kazakhstan; global buckling; imperfections; material toughness] Issue 2 Kido, Ewa Maria; Cywin´ski, Zbigniew: The new steel-glass architecture of passenger service centres on expressways in Japan [Steel-glass architecture; expressways; passenger service centres; Japan] Issue 3 Lawson, Mark; Beguin, Philippe; Obiala, Renata; Braun, Matthias: Slim-floor construction using hollow-core and composite decking systems [slim floor; integrated beam; composite action; shallow floor structure; steel section; reinforced concrete; deep composite decking; floor stiffness; bending resistance] Issue 2 Stimpfle, Bernd: The Nuvola for the Nuovo Centro Congressi in Rome [nurbs geometry; formfinding; patterning; seam layout; silicone glass membrane] Issue 4 Winterstetter, Thomas; Alkan, Mustafa; Berger, Radu; Watanabe, Maiko; Toth, Agatha; Sobek, Werner: Engineering complex geometries – the Heydar Aliyev Centre in Baku [freeform geometry; parametric design; 3D engineering; complex geometry] Issue 1

www.ernst-und-sohn.de

Fastener Andreassen, Michael Joachim; Jönsson, Jeppe: Joint and column behaviour of slotted coldformed steel studs [slotted, loadbearing; cold-formed steel members; joints; experiments; columns; channel sections; studs] Issue 3 155–161 Hämäläinen, Olli-Pekka; Björk, Timo: Fretting fatigue phenomenon in bolted high-strength steel plate connections [Fretting fatique; bolted joint; double-lap joint; high-strength steel] Issue 3 174–178 Steige, Yvonne; Weynand, Klaus: Design resistance of end plate splices with hollow sections [Rectangular hollow section; bolted end plate splices; steel joints] Issue 3 187–193

Façade and roof sheeting 244–250

133–138

210–215

Göppert, Knut; Paech, Christoph: High-performance materials in façade design – Structural membranes used in the building envelope [membrane; façade; lightweight; ETFE; ECTFE; mesh membrane; shading] Issue 4 237–243 Helbig, Thorsten; Kamp, Florian; Oppe, Matthias: An Eye to the Sky – Inclined grid shell dome of 90 m in Astana, Kazakhstan [dome; steel; grid shell; Kazakhstan; global buckling; imperfections; material toughness] Issue 2 133–138

General

85–89

230–236

65–71

Döring, Bernd; Reger, Vitali; Kuhnhenne, Markus; Feldmann, Markus; Kesti, Jyrki; Lawson, Mark; Botti, Andrea: Steel solutions for enabling zero-energy buildings [Nearly zero-energy buildings (nZEB); steel energy piles; double-layer flooring element; thermo-active deck element; natural night cooling] Issue 3 194–200 Stranghöner, Natalie; Jungbluth, Dominik: Fatigue strength of marked steel components – Influence of durable marking methods on the fatigue strength of steel components [Fatigue design; fatigue strength; fatigue life; hard stamping; plasma marking; needling; durable marking; soft stamping; identification; traceability; scribing] Issue 3 201–209

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Annual table of contents 2015

Light metal construction Bedair, Osama: An analytical expression to determine “realistic” shear buckling stress in cold-formed lipped channels [cold-formed steel; channel sections; shear buckling] Issue 1 53–58 Höglund, Torsten: Cold-formed members – comparison between tests and a unified design method for beamcolumns [Cold-formed members; tests; beam-columns; Eurocode 3; interaction formulae] Issue 1 42–52

Materials Schillo, Nicole; Feldmann, Markus: Local buckling behaviour of welded box sections made of high-strength steel – Comparing experiments with EC3 and general method [Local buckling; general method; highstrength steel] Issue 3 179–186 Uhlemann, Jörg; Stranghöner, Natalie; Saxe, Klaus: Comparison of stiffness properties of common coated fabrics [tensile membrane structures; architectural fabric; synthetic fibres; uniaxial tensile tests; stiffness properties; Young’s modulus; Poisson’s ratio] Issue 4 222–229

Methods of analysis and design Aarønæs, Anton; Nilsson, Hanna; Neumann, Nicolas: Dynamic response of steel pipe rack structures subjected to explosion loads [Dynamic response; steel structures; explosion; single-degree-of-freedom system; multi-degree-of-freedom system; finite element analysis] Issue 3 162–166 Beccarelli, Paolo; Maffei, Roberto; Galliot, Cédric; Luchsinger, Rolf H.: A new generation of temporary pavilions based on Tensairity girders [Tensairity®; coated fabrics; pavilion; pneumatic; beams] Issue 4 259–264 Bedair, Osama: An analytical expression to determine “realistic” shear buckling stress in cold-formed lipped channels [cold-formed steel; channel sections; shear buckling] Issue 1 53–58 Borjigin, Sudanna; Kim, ChulWoo; Chang, Kai-Chun; Sugiura, Kunitomo: Non-linear seismic response analysis of vehiclebridge interactive systems [moving vehicle; seismic response;

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strong ground motion; vehiclebridge interaction] Issue 1 Hashimoto, Kunitaro; Kayano, Makio; Suzuki, Yasuo; Sugiura, Kunitomo; Watanabe, Eiichi: Structural safety assessment of continuous girder bridge with fatigue crack in web plate [remaining load-carrying capacity; safety assessment; fatigue crack; steel girder bridge] Issue 1 Hauf, Gunter; Kuhlmann, Ulrike: Deformation calculation methods for slim floors [slim-floor girder; deflection; girder stiffness] Issue 2 Hicks, Stephen; Peltonen, Simo: Design of slim-floor construction for human-induced vibrations [slim-floor construction; human-induced vibrations; vibrations; dynamic response; multiplying factor; frequency; EN 1990; ISO 10137] Issue 2 Höglund, Torsten: Cold-formed members – comparison between tests and a unified design method for beamcolumns [Cold-formed members; tests; beam-columns; Eurocode 3; interaction formulae] Issue 1 Janarthanan, Balasubramaniam; Mahendran, Mahen; Gunalan, Shanmuganathan: Bearing capacity of cold-formed unlipped channels with restrained flanges under EOF and IOF load cases [Coldformed unlipped channel sections; bearing capacity; EOF and IOF load cases; fastened and unfastened to supports; experimental study; design rules; direct strength method] Issue 3 Kennedy, Stephen J.; Martino, Aldo E.: SPS bridge decks for new bridges and strengthening of existing bridge decks [SPS composite plate; design; performance; fabrication; erection] Issue 1 Kuhlmann, Ulrike; Just, Adrian; Leitz, Bernadette; Grabe, Jürgen; Schallück, Christoph: Simplified criteria and economic design for king piles in combined steel pile walls according to Eurocode 3, part 1-1 [combined steel pile wall; king piles; stability; flexural buckling; lateral torsional buckling; combined steel piling] Issue 2 Lam, Dennis; Dai, Xianghe; Kuhlmann, Ulrike; Raichle, Jochen; Braun, Matthias: Slimfloor construction – design for ultimate limit state [slim floor; composite beam; shallow floor construction; steel section; composite decking; bending resist-

2–8

15–20

96–101

110–117

42–52

146–154

21–27

122–132

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Annual table of contents 2015

ance; horizontally lying studs; CoSFB; CoSFB concrete dowels] Lener, Gerhard: Steel bridges – numerical simulation of total service life including fracture mechanic concepts [life cycle; fatigue; crack propagation; fracture mechanics] Leskela, Matti V.; Peltonen, Simo: Effect of unzipping connection behaviour on the composite interaction of shallow floor beams [shallow floor beams; composite interaction; non-ductile connections; unzipping behaviour; hollow-core decking supported on beams] Leskela, Matti V.; Peltonen, Simo; Obiala, Renata: Composite action in shallow floor beams with different shear connections [composite interaction; shallow floor beams; shear connection behaviour; effective bending stiffness; bending resistance; partial connection theory] Mano, Toshihisa; Mangerig, Ingbert: Tensile load-carrying behaviour of elastomeric bearings [elastomeric bearing; tension test; cavitation; FE simulation] Mollaert, Marijke; De Laet, Lars; Pyl, Lincy; Devos, Rika: The design of tensile surface structures – From a hand calculation in 1958 to a contemporary numerical simulation [tensile surface structures; form-finding; force density method; cable nets] Romero, Manuel L.; Cajot, LouisGuy; Conan, Yves; Braun, Matthias: Fire design methods for slim-floor structures [slim floors; fire resistance; simplified methods; composite steel-concrete structures; shallow floor beams] Tsubomoto, Masahiko; Kawatani, Mitsuo; Mori, Kengo: Trafficinduced vibration analysis of a steel girder bridge compared with a concrete bridge [trafficinduced vibration of bridges; steel girder; concrete hollow slab; dynamic analysis]

Issue 2 79–84

Issue 1 28–32

Steel bridges

Issue 2 118–121

Issue 2 90–95

Issue 1 33–41

Issue 4 251–258

Issue 2 102–109

Borjigin, Sudanna; Kim, ChulWoo; Chang, Kai-Chun; Sugiura, Kunitomo: Non-linear seismic response analysis of vehiclebridge interactive systems [moving vehicle; seismic response; strong ground motion; vehiclebridge interaction] Hashimoto, Kunitaro; Kayano, Makio; Suzuki, Yasuo; Sugiura, Kunitomo; Watanabe, Eiichi: Structural safety assessment of continuous girder bridge with fatigue crack in web plate [remaining load-carrying capacity; safety assessment; fatigue crack; steel girder bridge] Lener, Gerhard: Steel bridges – numerical simulation of total service life including fracture mechanic concepts [life cycle; fatigue; crack propagation; fracture mechanics] Mano, Toshihisa; Mangerig, Ingbert: Tensile load-carrying behaviour of elastomeric bearings [elastomeric bearing; tension test; cavitation; FE simulation] Tsubomoto, Masahiko; Kawatani, Mitsuo; Mori, Kengo: Trafficinduced vibration analysis of a steel girder bridge compared with a concrete bridge [trafficinduced vibration of bridges; steel girder; concrete hollow slab; dynamic analysis]

Issue 1 2–8

Issue 1 15–20

Issue 1 28–32

Issue 1 33–41

Issue 1 9–14

Tests Issue 1 9–14

Preservation Kennedy, Stephen J.; Martino, Aldo E.: SPS bridge decks for new bridges and strengthening of existing bridge decks [SPS composite plate; design; performance; fabrication; erection] Issue 1 21–27 Protection against corrosion Nützel, Oswald; Saul, Reiner: Long-term corrosion protection

www.ernst-und-sohn.de

for bridge cables with butyl rubber tapes using the ATIS Cableskin® system [buthyl rubber tapes; long term corrosion protection; bridge ropes and cables; automatic visual and magnetic induction testing; scaffolding free application; dehumidification of cables] Issue 1 59–64

Andreassen, Michael Joachim; Jönsson, Jeppe: Joint and column behaviour of slotted coldformed steel studs [slotted, loadbearing; cold-formed steel members; joints; experiments; columns; channel sections; studs] Issue 3 155–161 Braun, Matthias; Obiala, Renata; Odenbreit, Christoph: Analyses of the loadbearing behaviour of deep-embedded concrete dowels, CoSFB [Composite design; slim-floor; CoSFB; CoSFBBetondübel; ABAQUS] Issue 3 167–173 Steel Construction 8

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Annual table of contents 2015

Döring, Bernd; Reger, Vitali; Kuhnhenne, Markus; Feldmann, Markus; Kesti, Jyrki; Lawson, Mark; Botti, Andrea: Steel solutions for enabling zero-energy buildings [Nearly zero-energy buildings (nZEB); steel energy piles; double-layer flooring element; thermo-active deck element; natural night cooling] Issue 3 Hauf, Gunter; Kuhlmann, Ulrike: Deformation calculation methods for slim floors [slim-floor girder; deflection; girder stiffness] Issue 2 Hämäläinen, Olli-Pekka; Björk, Timo: Fretting fatigue phenomenon in bolted high-strength steel plate connections [Fretting fatique; bolted joint; double-lap joint; high-strength steel] Issue 3 Janarthanan, Balasubramaniam; Mahendran, Mahen; Gunalan, Shanmuganathan: Bearing capacity of cold-formed unlipped channels with restrained flanges under EOF and IOF load cases [Coldformed unlipped channel sections; bearing capacity; EOF and IOF load cases; fastened and unfastened to supports; experimental study; design rules; direct strength method] Issue 3

194–200

96–101

174–178

146–154

Mano, Toshihisa; Mangerig, Ingbert: Tensile load-carrying behaviour of elastomeric bearings [elastomeric bearing; tension test; cavitation; FE simulation] Issue 1 Schillo, Nicole; Feldmann, Markus: Local buckling behaviour of welded box sections made of high-strength steel – Comparing experiments with EC3 and general method [Local buckling; general method; highstrength steel] Issue 3 Stranghöner, Natalie; Jungbluth, Dominik: Fatigue strength of marked steel components – Influence of durable marking methods on the fatigue strength of steel components [Fatigue design; fatigue strength; fatigue life; hard stamping; plasma marking; needling; durable marking; soft stamping; identification; traceability; scribing] Issue 3 Uhlemann, Jörg; Stranghöner, Natalie; Saxe, Klaus: Comparison of stiffness properties of common coated fabrics [tensile membrane structures; architectural fabric; synthetic fibres; uniaxial tensile tests; stiffness properties; Young’s modulus; Poisson’s ratio] Issue 4

33–41

179–186

201–209

222–229

Columns

Book review

People

Hyperbolic structures. Shukhov’s Lattice Towers – Forerunners of Modern Lightweight Construction. From Beckh, M. Issue 2 143–144

Prof. Udo Peil awarded honorary doctorate Luís Simões da Silva The European Prize for Architecture 2015: Laureate Santiago Calatrava

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Issue 1 41 Issue 3 161 Issue 4 229

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