steel construction 01/2016 free sample copy

Steel ConstructionDesign 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 fl exibility in bridge girders

– Simple bridges

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Content

Steel Construction1

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 fl exibility in bridge girders under moving loads

Reports

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

Regular Features

15 News (see 78)74 ECCS news77 Announcements

A4 Products & Projects

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)

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

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A4 Steel Construction 9 (2016), No. 1

Products & Projects

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 high-light due to the reflection from the exterior façade. The weath-er-resistant properties of the anodised aluminium, in this in-stance processed by Metal Yapi (Istanbul), has already proved it-self globally for both interior and exterior architectural projects.

High load capacityAdditionally, 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 en-abled a highly durable construction of lattice girders with a high load capacity. With a large span width of some 35 m, the con-struction was prepared for installation in a nearby production hall which meant the steel girders had to be transported by cross-ing 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 architec-tural style and this is demonstrated with the large structural di-mensions and intelligent use of space. Thus the innovative build-ing 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.

[email protected], www.novelis.com

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 engineer-ing group, Cockerill Maintenance & Ingénierie in Seraing, blos-soms 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® alumin-ium anodised in a golden champagne in order to create an inno-vative building housing more than 600 employees.

Capacity for innovationsThe name “L’Orangerie” was chosen in conjunction with the cor-porate 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 gen-erating capacity for innovations – a homage to the Belgian Or-angery. 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 qual-ity for a high-quality aluminium surface with metallic brilliance and consistency of colour and gloss levels. Particularly noticea-

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

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

Fig. 3. Creative constructive ideas (© 1 u. 3 Desmoulins, 2 Novelis)

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Freudenberg museum of technology shines in elegant new steel exterior

Contrasts between the old and the new often give buildings a particular charm. That’s definitely the case with the mu-seum 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 Thyssen Krupp Steel Europe. The advantages: The ma-terial is cost- effective, long-lasting and gives the building an elegant appear-ance.

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 Pla-dur StandingSeam flat carbon steel from ThyssenKrupp Steel Europe. This mate-rial offers numerous advantages. “It looks elegant and unusual and is more cost-ef-fective than most building materials thanks to its extreme longevity,” says Christian Lukas, an employee of Thyssen-Krupp Steel Europe. To make the steel weather-resistant it is coated with a spe-cial zinc-magnesium alloy offering out-standing corrosion protection. Color and texture are provided by a high-quality or-ganic coating that protects the material from UV radiation, makes it scratch-re-sistant and adds to the anticorrosion properties of the zinc-magnesium coating.

Roof and facade made from innova-tive flat steelThe extension of the museum of technol-ogy 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 interest-ing contrast to the existing historical tim-ber-framed building – making the mu-seum a real eye-catcher. The facade is

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 ex-tremely satisfied: “We would choose this material again every time.”

Development at Kreuztal-Eichen siteBut 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 fac-tor: The matt panels have a beautiful ele-gant appearance. Then there’s the cost-ef-fectiveness and durability of Pladur Stand-ingSeam, 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 Stand-ingSeam was developed at ThyssenK-rupp’s Kreuztal-Eichen site in the region. The steel exterior of the extension is also a perfect fit with the exhibits inside the mu-seum – 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 Net-phen-based Wolfgang Fischer Stahl GmbH. “We fabricate Pladur Standing-Seam exactly the way customers want,” says Wolfgang Fischer, managing partner of Fischer Stahl. “We respond to the spe-cific requirements of architects and tradespeople.”

info.steel-europe@thyssenkrupp.comwww.thyssenkrupp-steel-europe.com

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)

A6 Steel Construction 9 (2016), No. 1

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Noise Protection Hangar for Airliners at Zurich Airport, Switzerland

Regular maintenance and repairs of an aircraft includes per-forming 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.

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

Fig. 1 3D model of the noise protection hangar with visual-ized deformations

Fig. 2 Noise protec-tion hangar during construction (© 1 Dlubal, 2 WTM Engineers)

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

Matthias Braun*Job Duarte da CostaRenata ObialaChristoph Odenbreit

Articles

DOI: 10.1002/stco.201610007

Design of single-span beams for SLS and ULS using semi-continuous beam-to-column jointsPart 1: Beams with constant bending stiffness and joints according to EN 1993-1-8

deflection, natural frequency and distribution of the inter-nal forces in a single-span floor beam with constant bend-ing 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 de-termine factors, thus allowing quick, easy and safe applica-tion. Further contributions are planned, covering the use of semi-continuous joints for beams with partially constant stiffness (composite beams) and composite beam-to-col-umn 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 struc-ture, 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 analysisThe distribution of the internal forces within the structure only depends on the stiffness of the members in the struc-ture. Therefore, joints should be classified according to their stiffness. In the case of a semi-rigid joint, the rota-tional stiffness Sj corresponding to the bending moment Mj,Ed should generally be used in the analysis. As a simpli-fication, the rotational stiffness may be taken as Sj,ini/ in the analysis for all values of the moment Mj,Ed Mj,Rd, where a value of 2.0 for the stiffness modification coeffi-cient 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 analysisUsing 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 rota-tional capacity of a joint should be sufficient to accommo-date the rotations resulting from the analysis.

This article explains a method for determining how semi-continu-ous 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 sim-ple 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 erec-tion processes, and they have to be sustainable. To satisfy such demand for economic structures with long beam spans, floor beams need a high loadbearing resis tance and stiffness. The utilization of high-strength steel grades fulfils the requirement of a high loadbearing resis tance, 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 mo-ment–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 determina-tion of the influence of semi-continuous joints on the beam

* Corresponding author: [email protected]

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

2 Steel Construction 9 (2016), No. 1

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

3 Economical structures with semi-continuous joints

As shown in section 2, the type of beam-to-column joint has a significant influence on the distribution of the inter-nal 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 sup-ports. 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 be-tween 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 – com-pared with rigid joints – leads to a higher bending mo-ment at mid-span, requiring a bigger beam section. But they are much more economic than rigid joints. An opti-mum ( minimum total cost) has to be calculated for each structure individually.

Elastic–plastic global analysisThe 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 char-acteristic 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-lin-ear design moment–rotation characteristic may be adopted, see Fig. 1. For the determination of the stiffness coefficient

, see Table 5.2 in [1].The appropriate type of joint model should be deter-

mined 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 anal-ysis may be simplified by adopting any appropriate curve, including a linearized approximation (e.g. bi- or tri-linear),

ϕj

Mj

Mj,Rd

Sj,ini/η

ϕCd

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

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-strengthSemi-rigid and partial-strength

Semi-rigid and full-strengthRigid and partial-strength

Type of joint model Simple Continuous Semi-continuous

q = const.

L

EI=constant

Sj,A Sj,B

Sj,A Sj,B

Sj,A Sj,B

Sj,A= Sj,B= 0 → hinged joint

Sj,A= Sj,B= ∞ → rigid joint

Structural System Bending Moment Distribution

MEd = 3 qL2/24

MEd = - 2 qL2/24

MEd = qL2/24

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


3Steel Construction 9 (2016), No. 1

where:Kb 8 for frames where the bracing system reduces the

horizontal displacement by at least 80 % E elastic modulus of beam materialIb second moment of area of beamLb beam span (distance between centres of supporting col-

umns)

Nominally pinned joints transmit the internal forces with-out developing significant moments and they should be capable of accepting the resulting rotations under the de-sign loads. For rigid joints it is assumed that their rota-tional behaviour has no significant influence on the distri-bution 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 strengthAccording to its strength, a joint may be classified as full-strength, nominally pinned or partial-strength by compar-ing 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 with-out 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.

Classification by rotational capacityUsing rigid–plastic global analysis and with the joint at a plastic hinge location, then for joints with a bending resist-ance 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 re-sistance 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

4 Joint design according to EN 1993-1-84.1 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 ro-tation Xd and its design rotational capacity Cd, see Fig. 4.– The rotational stiffness Sj is the secant stiffness as indi-

cated in Fig. 4. The definition of Sj applies up to the rotation Xd at which Mj,Ed first reaches Mj,Rd. The ini-tial 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 max-imum moment of the design moment–rotation charac-teristic.

– The design rotation capacity Cd is equal to the maxi-mum rotation of the design moment–rotation character-istic.

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 Cd, see section 5.2 of [1] and Table 1.

Classification by stiffnessClassifying a joint by its rotational stiffness is performed by comparing its initial rotational stiffness Sj,ini with the clas-sification boundaries given in Fig. 5.

Fabrication cost

Material cost

Cost K

Total cost

hinge rigid

Kopt Joint stiffness

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

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

ϕj

MjMj,Rd

ϕCd

2/3 Mj,Rd

ϕXd

Sj,ini

Sj

Mj

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

Pinned

Semi - rigid

Stiffness boundariesInitial rotational stiffness

Sj,ini ≤ 0.5 EIb/Lb

Sj,ini ≥ Kb EIb/Lb

Sj,ini

Rigid

ϕj

Mj



– 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

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 calcu-lation of the internal forces has to be repeated with an adapted joint stiffness.

5 Analytical investigations of the influence of semi- continuous joints on the behaviour of single-span beams

5.1 Assumptions

The equations for estimating the influence of semi-contin-uous beam-to-column joints on the overall beam behaviour

SE z t

C(1)j,app

2fc=

⋅ ⋅

[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 ex-ceed 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 es-pecially 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 sim-plified 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 end-plate connections:– The connection has only two bolt rows in tension.– The bolt diameter is approx. 1.5 times the column flange

thickness.

Joint moment resistance

a) Top of column

b) within column height

Mb,pl,Rd is the design plastic moment resistance of a beamMc,pl,Rd is the design plastic moment resistance of a column

Full - strength Mj,Rd ≥ Mpl,Rd

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

Mj,Rd

Pinned Mj,Rd ≤ 0.25 Mpl,Rd

0.25 Mpl,Rd

Mpl,Rd

Strength boundaries

Mj,Rd

Mj,Rd

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

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

ϕj

Mj

Fig. 6. Classification of joints by strength

Table 2. Approximate determination of joint stiffness Sj,app according to [6]

Joints with extended, unstiffened end-plate Factor C

Single sided, ( 1)

13

Double sided, ( 0)

7.5

Note: For the rare cases of double-sided joint configurations where 2 (unbalanced moments), the value of the factor C is obtained by adding 11 to the relevant value for symmetrical con-ditions (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- j) relationship of rota-

tional restraintsFig. 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

kB0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.00 a b

1.500.50

Sym. Sym. Sym. Sym. Sym. Sym. Sym. Sym. Sym. Sym.

0.101.450.51

1.400.50

Sym. Sym. Sym. Sym. Sym. Sym. Sym. Sym. Sym.

0.201.400.52

1.350.51

1.300.50

Sym. Sym. Sym. Sym. Sym. Sym. Sym. Sym.

0.301.350.53

1.300.52

1.250.51

1.200.50

Sym. Sym. Sym. Sym. Sym. Sym. Sym.

0.401.310.53

1.250.53

1.200.52

1.150.51

1.100.50

Sym. Sym. Sym. Sym. Sym. Sym.

0.501.260.54

1.210.53

1.150.52

1.100.52

1.050.51

1.000.50

Sym. Sym. Sym. Sym. Sym.

0.601.220.55

1.160.54

1.110.53

1.050.53

1.000.52

0.950.51

0.900.50

Sym. Sym. Sym. Sym.

0.701.170.56

1.120.55

1.060.54

1.010.53

0.950.53

0.900.52

0.850.51

0.800.50

Sym. Sym. Sym.

0.801.130.57

1.070.56

1.020.55

0.960.54

0.910.53

0.850.53

0.800.52

0.750.51

0.700.50

Sym. Sym.

0.901.080.58

1.030.57

0.970.56

0.920.55

0.860.54

0.810.53

0.750.53

0.700.52

0.650.51

0.600.50

Sym.

1.001.040.58

0.980.58

0.930.57

0.870.56

0.820.55

0.760.54

0.710.53

0.650.53

0.600.52

0.550.51

0.500.50

1.101.000.59

0.940.58

0.880.58

0.830.57

0.770.56

0.720.55

0.660.54

0.610.53

0.550.53

/ /

1.200.960.60

0.900.59

0.840.58

0.780.58

0.730.57

0.670.56

0.620.55

/ / / /

1.300.920.61

0.860.60

0.800.59

0.740.58

0.680.58

/ / / / / /

1.400.880.62

0.820.61

0.760.60

/ / / / / / / /

1.500.840.63

/ / / / / / / / / /

With M q L12

k ; M q L12

k ; max. M q L12

a at x b LA

2

A B

2

B Span

2

max= − ⋅ ⋅ = − ⋅ ⋅ = ⋅ ⋅ = ⋅



For n and m 0, then kA 1.5 and kB 0. This presents the standard case of a single-span beam with a hinged support on one side and rigid support on the other.

The well-known solution M q L8A

2= − ⋅

and MB 0 is ob-tained.

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

M M q L12

.A B

2= = − ⋅

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

A q L2

q L12

k k (4)A B( )= ⋅ + ⋅ ⋅ −

5.2 Determination of bending moment distribution

The bending moments at supports A and B can be ex-pressed as follows:

where

M q L12

k (2)A

2

A= − ⋅ ⋅

M q L12

k (3)B

2

B= − ⋅ ⋅

k m 6

m 4 4 mn

12n

; k n 6

n 4 4 nm

12m

A B= +

+ + ⋅ += +

+ + ⋅ +

and nS L

E I; m

S L

E Ij,A j,B=

⋅⋅

=⋅

⋅

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

kA

kB0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.00 c d

5.000.50

Sym. Sym. Sym. Sym. Sym. Sym. Sym. Sym. Sym. Sym.

0.104.800.50

4.600.50

Sym. Sym. Sym. Sym. Sym. Sym. Sym. Sym. Sym.

0.204.600.51

4.400.50

4.200.50

Sym. Sym. Sym. Sym. Sym. Sym. Sym. Sym.

0.304.401.35

4.200.51

4.000.50

3.800.50

Sym. Sym. Sym. Sym. Sym. Sym. Sym.

0.404.200.51

4.000.51

3.800.51

3.600.50

3.400.50

Sym. Sym. Sym. Sym. Sym. Sym.

0.504.010.52

3.800.51

3.600.51

3.400.51

3.200.50

3.000.50

Sym. Sym. Sym. Sym. Sym.

0.603.810.52

3.610.52

3.400.52

3.200.51

3.000.51

2.800.50

2.600.50

Sym. Sym. Sym. Sym.

0.703.610.53

3.410.52

3.210.52

3.000.52

2.800.51

2.600.51

2.400.50

2.200.50

Sym. Sym. Sym.

0.803.420.53

3.210.53

3.010.52

2.810.52

2.600.52

2.400.51

2.200.51

2.000.51

1.800.50

Sym. Sym.

0.903.220.54

3.020.53

2.810.53

2.610.53

2.410.52

2.210.52

2.000.52

1.800.51

1.600.51

1.400.50

Sym.

1.003.030.54

2.820.54

2.620.54

2.420.53

2.210.53

2.010.53

1.810.52

1.600.52

1.400.51

1.200.51

1.000.50

1.102.830.55

2.630.55

2.430.54

2.220.54

2.020.54

1.810.54

1.610.53

1.410.53

1.200.52

/ /

1.202.640.55

2.440.55

2.230.55

2.030.55

1.820.55

1.620.54

1.420.54

/ / / /

1.302.450.56

2.250.56

2.040.56

1.840.56

1.630.56

/ / / / / /

1.402.270.57

2.060.57

1.860.57

/ / / / / / / /

1.502.080.58

/ / / / / / / / / /

With max. w c384

q LE I

at x d L4

w= ⋅ ⋅⋅

= ⋅



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

5.3 Influence of semi-continuous joints on beam deflection

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

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

Constants C1 and C2 are determined with the boundary conditions:

where a 32

12

k k 124

k k kA B A B2

A( ) ( )= + ⋅ − + ⋅ − −

x b L (10)max = ⋅

w xM x

E I(11)) )( (

′′ = −⋅

E I w x M x A x M 12

q x

E I w x A 12

x M x 16

q x C

E I w x A 16

x M 12

x

124

q x C x C (12)

A2

2A

31

3A

2

41 2

( ) ( )( )( )

− ⋅ ⋅ ′′ = = ⋅ + − ⋅ ⋅

− ⋅ ⋅ ′ = ⋅ ⋅ + ⋅ − ⋅ ⋅ +

− ⋅ ⋅ = ⋅ ⋅ + ⋅ ⋅

− ⋅ ⋅ + ⋅ +

w x L C 16

A L 12

M 124

q L

w x 0 C 0

12

A3

2

( )( )

= ⇒ = − ⋅ ⋅ − ⋅ + ⋅ ⋅

= ⇒ =

and the bending moment as a function of x:

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

The position of the maximum bending moment can be cal-culated with M (x) 0, which leads to

Eq. (7) can be expressed in a dimensionless format:

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

M x A x M 12

q x (5)A2( ) = ⋅ + − ⋅ ⋅

M x q L2

x q L12

k k x

q L12

k 12

q x (6)

A B

2

A2

( ) ( )= ⋅ ⋅ + ⋅ ⋅ − ⋅

− ⋅ ⋅ − ⋅ ⋅

M x 0 q L2

q L12

k k q x 0

x L2

L12

k k (7)

A B

A B

( ) ( )

( )

′ = ⇒ ⋅ + ⋅ ⋅ − − ⋅ = ⇒

⇒ = + ⋅ −

b xL

12

112

k k (8)A B( )= = + ⋅ −

max. M q L12

a (9)Span

2= ⋅ ⋅

Table 5. Factor e for determining the natural frequency

kA

kB0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

0.00 e 1.00 Sym. Sym. Sym. Sym. Sym. Sym. Sym. Sym. Sym. Sym.

0.10 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 f e2 L

E Im

, with m uniform mass1

2

2= ⋅ π

⋅ π ⋅⋅ ⋅ =



Eq. (15) has three real solutions. The solution gives the position of the maximum beam deflection and can be ex-pressed 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

and the position of the maximum deflection with

Pre-calculated values for factors c and d as a function of the stiffness coefficients kA and kB are given in Table 4.

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 equa-tion of the harmonic vibration, a factor e, which allows a quick determination of the natural frequency, is given in Table 5.

The constants are determined with the boundary condi-tions:

max. w c384

q LE I

(17)4

= ⋅ ⋅⋅

x d L (18)w = ⋅

v x C cos xL

C sin xL

C cosh xL

C sinh xL

(19)

1 2

3 4

( ) = ⋅ λ ⋅⎛⎝⎜

⎞⎠⎟

+ ⋅ λ ⋅⎛⎝⎜

⎞⎠⎟

+ ⋅ λ ⋅⎛⎝⎜

⎞⎠⎟

+ ⋅ λ ⋅⎛⎝⎜

⎞⎠⎟

v xL

C sin xL

C cos xL

C sinh xL

C cosh xL

(20)

1 2

3 4

( )′ = λ ⋅ − ⋅ λ ⋅⎛⎝⎜

⎞⎠⎟

+ ⋅ λ ⋅⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

+ ⋅ λ ⋅⎛⎝⎜

⎞⎠⎟

+ ⋅ λ ⋅⎛⎝⎜

⎞⎠⎟

⎤

⎦⎥

v xL

C cos xL

C sin xL

C cosh xL

C sinh xL

(21)

2

2 1 2

3 4

( )′′ = λ ⋅ − ⋅ λ ⋅⎛⎝⎜

⎞⎠⎟

− ⋅ λ ⋅⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

+ ⋅ λ ⋅⎛⎝⎜

⎞⎠⎟

+ ⋅ λ ⋅⎛⎝⎜

⎞⎠⎟

⎤

⎦⎥

v xL

C sin xL

C cos xL

C sinh xL

C cosh xL

(22)

3

3 1 2

3 4

( )′′′ = λ ⋅ ⋅ λ ⋅⎛⎝⎜

⎞⎠⎟

− ⋅ λ ⋅⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

+ ⋅ λ ⋅⎛⎝⎜

⎞⎠⎟

+ ⋅ λ ⋅⎛⎝⎜

⎞⎠⎟

⎤

⎦⎥

v x 0 0 C C 0

v x L 0 C cos cosh

C sin C sinh 0

– v x 0 nL

· v (x 0) 0 2 CS L

E IC

S L

E IC 0

1 3

1

2 4

1j,A

2

j,A4

( )( ) ( )

( )

= = ⇒ + =

= = ⇒ ⋅ λ − λ

+ ⋅ λ + ⋅ λ =

′′ = + ′ = = ⇒ ⋅ ⋅ λ +⋅

⋅⋅

+⋅

⋅⋅ =

Finally, the beam deflection as a function of the stiffness of the rotational springs is defined as follows:

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

This equation of the third order is solved by using the for-mulae from Cardan:

Substituting x y – r/3, the reduced form is obtained:

The discriminant D can be expressed as

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

E I w x 16

A x L x 12

M x L x

124

q x L x (13)

3 2A

2

4 3

( ) ( )( )

( )− ⋅ ⋅ = ⋅ ⋅ − ⋅ + ⋅ ⋅ − ⋅

− ⋅ ⋅ − ⋅

E I w x 172

q k k 6 L x L x 124

q k L x L x 124

q x L x (14)

A B3 3

A2 2 3 4 3

( )( ) ( )

( ) ( )− ⋅ ⋅ = ⋅ ⋅ − + ⋅ ⋅ − ⋅ −

⋅ ⋅ ⋅ ⋅ − ⋅ − ⋅ ⋅ − ⋅

E I w x x 0 A 12

x M x

16

q x C 0 (15)

2A

31

( ) ( )− ⋅ ⋅ ′ = ϕ = ⇒ ⋅ ⋅ + ⋅

− ⋅ ⋅ + =

x x x L4

k k 32

L

x L2

k L12

3 2 k k 0 (16)

3 2B A

r2

A

s

3

A B

t

� ��

��

( ) ( )

( )

ϕ = + ⋅ ⋅ − − ⋅⎡⎣⎢

⎤⎦⎥

+ ⋅ ⋅ + ⋅ − ⋅ − =

y p y q 0 with p 3 s r3

and q 2 r27

r s3

t32 3

+ ⋅ + = = ⋅ − = ⋅ − ⋅ +

D p3

q2

3 2

=⎛⎝⎜

⎞⎠⎟

+⎛⎝⎜

⎞⎠⎟

q = const.

L

EI = constant

Sj,A Sj,B

xA B

Sj,A Sj,B

xw,v(x)

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



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 dis-tance a 8.10 m (axis-to-axis). The beam is loaded with a uniformly distributed constant load q, has a constant bend-ing stiffness EI and it is symmetrically supported in an in-ternal 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: M0 1.00; M1 1.00; M2 1.25Yield strength of hot-rolled section, HE320A, S355: fyd 355 N/mm2

Yield strength of bottom plate, 450 25 mm, S355: fyd 345 N/mm2

which leads to the following linear equation system:

The equation system is solved if the determinant of ma-trix B 0. The lowest value for i for which the above equation system is solved (the trivial solution 0 is forbidden) is required. The determinant of matrix B is expressed with

Solutions for as a function of stiffness coefficients kA and kB are given in Table 5.

The natural frequency can be calculated with

where m uniformly distributed constant mass.

( )′′ = ′ = = ⇒ ⋅ λ ⋅ λ + λ

+⋅

⋅⋅ λ + λ

+ ⋅ λ ⋅ λ⋅

⋅⋅ λ

⎡

⎣⎢⎢

⎤

⎦⎥⎥

⋅⋅

⋅⋅ λ + λ ⋅ λ

⎡

⎣⎢⎢

⎤

⎦⎥⎥

=

– v x L – mL

· v (x L) 0 C [ (cos cosh )

S L

E I(sin sinh )]

C sin –S L

E Icos

– CS L

E Icosh sinh 0

1

j,B

2j,B

4j,B

· mit (23)

b b b

b b b

b b b

und

C

C

C

b cos – cosh

b sin

b sinh

b 2

b b n

b (cos cosh ) m (sin sinh )

b sin – m · cos

b – mcosh – sinh

11 12 13

21 22 23

31 32 33

1

2

4

11

12

13

21

22 23

31

32

33

B C 0

B C

=

=

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

=

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

= λ λ= λ= λ= λ= == λ λ + λ + λ + λ= λ λ λ= λ λ λ

Det B n·m· 1 cos ·cosh ·n ·

cosh ·sin cos ·sinh ·m·

cosh ·sin cos ·sinh 2· ·

sin ·sinh 0 (24)

2

( ) ( )( )( )

= − λ λ + λ

λ λ − λ λ + λ

λ λ − λ λ + λλ λ =

=λπ

⋅ = ⋅ π⋅ π ⋅

⋅ ⋅f2· ·L

· E Im

e2 L

E Im

(25)1i2

2

2

2

q = const.

L = 9 m

EI = constant

Sj,A Sj,B

Fig. 9a. Application example – structural system and load-ing

130

beff = 750

Cofraplus 220

220

30025

50 5025

450

310

40

022031

350

[mm]

[mm]

450x25, S355

C30/37 HE320A S355

Cofraplus 220

a

a

Section a-a:

C30/37

80160

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



At mid-span the SFB section is classified as a class 2 section. A class 2 section can develop its plastic cross-sec-tional 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:

Bottom plate lower flange in compression:

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 sym-metrically 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 resis-tance Mj,Rd 360 kNm is within the limits given in Fig. 6 for a partial-strength joint (0.25 · Mpl,Rd Mj,Rd 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.

ct

310 2 15.5 2 279

2259

25.0 58.58 72 235355

72 class1

= − ⋅ − ⋅ =

= < = ⋅ = ⋅ ε ⇒

ct

7525

3.00 7.43 9 235345

9 class 1= = < = ⋅ = ⋅ ε ⇒

ct

0.5 300 9 2 27

25.0 15.5118.540.5

2.93 7.43

9 235355

9 class 1

( )=

⋅ − − ⋅+

= = <

= ⋅ = ⋅ ε ⇒

Elastic bending resistance of SFB cross-section:

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: gC 220 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/mDead load (slab beam, self-weight):

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

Reduction factor: 57

10 m9 8.10 m

0.64A 0

2

2α = ⋅ ψ +

⋅=

Reduced live load: qk qk · A 28.51 kN/m · 0.64 18.17 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 qk

51.83 kN/m 18.17 kN/m 70.0 kN/m

Design load: Ed qULS 1.35 · gk 1.50 · qk 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:

Web in compression:

Mf I

z35.5 kN/cm 39560 cm

23.445 cm

599 kNm

el,Rdyd y

el,top

2 4=

⋅= ⋅

=

g [1.1 4.29 kN/m (8.10 0.45 2 0.05) m

1.1 1.20 kN/m 8.10 m]

4.57 kN/m 51.83 kN/m

k2

2

Σ = ⋅ ⋅ − + ⋅

+ ⋅ ⋅+ =

9 9 235355

7.32 ct

0.5 300 9 2 27

15.5

118.515.5

7.65 8.14 10 235355

10 class 2

( )⋅ ε = ⋅ = < =

⋅ − − ⋅

= = < = ⋅ = ⋅ ε ⇒

4510

5.5

189

456M30, 10.9

10

5

10450x300x20S355

125

[mm]

HE320A S355

450x25S355

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



Calculation of qj,elUp to a bending moment M 2

3M ,j,Ed j,Rd≤ ⋅ the initial joint

stiffness Sj,ini can be used in the calculation, see 5.1.2(3) in [1].

Using the equations given in section 5, it is possible to calculate the values for n m and kA kB:

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

Calculation of qj,RdFor a bending moment Mj,Ed in the range

we use the joint stiffness Sj,2 7.4 MNm/rad, see Fig. 11b.

23

M 23

360 kNm 240 kNm

S 51.6 MNm/radj,Rd

j,ini

⋅ = ⋅ =

⇒ =

n mS L

E I51.6 MNm/rad 9.0 m

210000 MN/m 39560 10 m

5.59 [ ]rad

j,ini2 8 4

= =⋅

⋅= ⋅

⋅ ⋅

= −

−

k k m 6

m 4 4 mn

12n

5.59 6

5.59 4 4 5.595.59

125.59

0.74

A B= = +

+ + ⋅ += +

+ + ⋅ +

=

23

M 240 kNmq L

12k

q 9 m

120.74

q 48.0 kN/m

j,Rdj,el

2

Aj,el

2

j,el

( )⋅ = =

⋅⋅ =

⋅⋅

⇒ =

23

M M Mj,Rd j,Ed j,Rd⋅ < ≤

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 j within the range

0 j j,el– A second area for a joint rotation j within the range j,el

j Xd– A plastic area for a joint rotation j within the range Xd

j Cd

Note: Using Eq. (1) and Table 2 of section 4.3, an approx-imate joint stiffness Sj,app could be calculated as follows:

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 j,el and Xd.

SE z t

C

210000 MN/m 0.307 m 0.0215 m

7.5

56.7 MNm/rad 56.7 kNm/mrad

j,app

2fc

2 2( )=

⋅ ⋅=

⋅ ⋅

= =

ϕj

Mj

Mj,Rd = 360 kNm

ϕCd

2/3 Mj,Rd = 240 kNm

ϕXd = 20.9 mrad

Sj,ini = 51.6 kNm/mrad

8 EIb / Lb = 73.8 kNm/mrad

0.5 EIb / Lb= 4.6 kNm/mrad

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

ϕϕXdXd = 20.9 mrad = 20.9 mradϕϕj,elj,el = 4.6 mrad = 4.6 mrad ϕϕCdCd

ϕϕjj

MMj,Rdj,Rd

MMjj

= 360 kNm = 360 kNm

2/3 M2/3 Mj,Rdj,Rd = 240 kNm = 240 kNm

SSj,2j,2 = 7.4 kNm/mrad

= 7.4 kNm/mrad

SS j,ini

j,ini

= 51

.6 kN

m/m

rad

= 51

.6 kN

m/m

rad

"Elastic" "Non-linear""Elastic" "Non-linear" "Plastic""Plastic"(Area 1) (Area 2)(Area 1) (Area 2)

qq j,e

lj,e

l= 4

8.0

kN/m

=

48.0

kN

/m

qq SLSSL

S = 7

0.0

kN/m

=

70.

0 kN

/m

qq EdEd=

97.2

kN

/m

= 97

.2 k

N/m

qq j,R

dj,R

d = 1

10.0

kN

/m =

110

.0 k

N/m

ϕϕj,SLSj,SLS ϕϕj,Edj,Ed

SSj,2j,2 = = MMj,Rdj,Rd - 2/3 M - 2/3 Mj,Rdj,Rd

ϕϕXdXd - - ϕϕj,elj,el

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



represents a sufficiently precise approximation of the real joint behaviour.

Total characteristic load:

Load combination for beam deflection at mid-span:

Load combination for natural frequency:

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

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):

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.

E g q 51.83 kN/m 18.17 kN/m 70.0 kN/mk k k= Σ + ′ = + =

q 1.0 g 1.0 q

1.0 51.83 kN/m 1.0 18.17 kN/m 70.0 kN/m

SLS k k= ⋅ Σ + ⋅ ′

= ⋅ + ⋅ =

q 1.0 g 0.20 q

1.0 51.83 kN/m 1.0 18.17 kN/m 55.5 kN/m

Hz k k= ⋅ Σ + ⋅ ′

= ⋅ + ⋅ =

w c384

q L

E I2.04384

48.0 10 kN/cm 900 cm

21000 kN/cm 39560 cm

2.01 cm

elj,el

4 2 4

2 4

( )⇒ = ⋅

⋅⋅

= ⋅⋅ ⋅

⋅

=

−

First, factors n2 m2 and kA,2 and kB,2 have to be calcu-lated:

Using Eq. (2) we get

6.4 Beam design for SLS

The total vertical beam deflection and the natural fre-quency 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

n mS L

E I7.4 MNm/rad 9.0 m

210000 MN/m 39560 10 m

0.80 [ ]rad

2 2j,2

2 8 4= =

⋅⋅

= ⋅⋅ ⋅

= −

−

k km 6

m 4 4mn

12n

0.80 6

0.80 4 4 0.800.80

120.80

0.29

A,2 B,22

22

2 2

= =+

+ + ⋅ +

= +

+ + ⋅ +=

M 23

M 360 kNm 240 kNm 120 kNm

q L12

kq 9 m

120.29

q 62.0 kN/m

j,Rd j,Rd

2

A

2( )− ⋅ = − =

= Δ ⋅ ⋅ =Δ ⋅

⋅

⇒ Δ =

and q q q 48.0 kN/m 62.0 kN/m

110.0 kN/m

j,Rd j,el= + Δ = +

=

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

ϕXdϕj,el ϕCd

ϕj

Mj,Rd

Mj

2/3 Mj,Rd

q Hz =

55.

5 kN

/m

ϕj,Hz = 6.6 mrad

Sj,Hz = Mj,Hz

ϕj,Hz

S j,Hz =

38.5

kN/m

Mj,Hz = 254.5 kNm



From Table 5 we obtain e 1.49 (by linear interpolation).Using Eq. (25), the natural frequency can be calcu-

lated as follows:

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 vi-brations, the authors recommend using more precise meth-ods 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

Design checks for bending and shear with semi-contin-uous jointsBased 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 fol-lows:

n mS L

E I

38.5 MNm/rad 9.0m210000 MN/m 39560 10 m

4.17 [ ]rad

Hz Hzj,Hz

2 8 4

= =⋅

⋅

= ⋅⋅ ⋅

= −−

k km 6

m 4 4mn

12n

4.17 6

4.17 4 4 4.174.17

124.17

0.68

A,Hz B,HzHz

H2Hz

Hz Hz

= =+

+ + ⋅ +

= +

+ + ⋅ +=

( )= ⋅ π

⋅ π ⋅⋅ ⋅ = ⋅ π

⋅ π ⋅

⋅ ⋅

= >

−

f e2 L

E Im

1.492 9 m

·

21000 kN/m 39560 cm 1055.5 kN/m/9.81 m/s

3.50 Hz 2.60 Hz

1

2

2

2

2

2 4 4

2

Mq L

12k

q q L

12k

48 kN/m 9 m

120.74

97.2 48 kN/m 9 m

120.29

240 kNm 96 kNm 336 kNm M

j,Edj,el

2

AEd j,el

2

A,2

2

2

j,Rd

( )

( )

( ) ( )

=⋅

⋅ +− ⋅

⋅

=⋅

⋅

+− ⋅

⋅

= + = <

Mq L

8M

97.2 kN/m 9 m

8336 kNm

984 kNm 336 kNm 648 kNm

EdEd

2

j,Ed

2( )=

⋅− =

⋅−

= − =

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):

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:

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 resis-tance of the SFB cross-section:

The SFB cross-section remains fully elastic at SLS, the assumption is correct.

Calculation of the natural frequency of the SFBThe natural frequency of the SFB is determined based on the equations in section 5. The load qHz is in “area 2” (qj,el qHz 55.5 kN/m qj,Rd), and so an idealized joint stiffness Sj,Hz is used, see Fig. 12. For qHz, the corre-sponding values of the joint rotation j,Hz and the bend-ing moment Mj,Hz are: j,Hz 6.6 mrad and Mj,Hz 254.5 kNm Sj,Hz Mj,Hz/ j,Hz 254.5 kNm / 6.6 mrad 38.5 kNm/mrad

wc

384q L

E I

3.84384

22.0 10 kN/cm 900 cm

21000 kN/cm 39560 cm

1.74 cm

2 SLS4

2 4

2 4

( )

⇒ Δ = ⋅Δ ⋅

⋅

= ⋅⋅ ⋅

⋅

=

−

( )⇒ = ⋅

⋅⋅

= ⋅⋅ ⋅

⋅

=

−w 5

384q L

E I5

384

70 10 kN/cm 900 cm

21000 kN/cm 39560 cm

7.20 cm,

SLS4 2 4

2 4

Mq L

12k

q L12

k

23

Mq L

12k

23

360 kNm22 kN/m 9 m

120.29

240 kNm 43 kNm 283 kNm

j,SLSj,el

2

ASLS

2

A,2

j,RdSLS

2

A,2

2( )

=⋅

⋅ +Δ ⋅

⋅

= ⋅ +Δ ⋅

⋅

= ⋅ +⋅

⋅

= + =

Mq L

8M

70 kN/m 9 m

8283 kNm

426 kNm M 599 kNm

SLSSLS

2

j,SLS

2

el,Rd

( )=

⋅− =

⋅−

= < =



As this reduction in the yield strength is 1 %, it is ne-glected 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 jointElastic–plastic global analysis was used in the given ex-ample. 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 Ed does not reach Xd 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 as-sumptions 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 foun-dations, columns etc. was not taken into account.

f 12 VV

1 f

1 2 437.4 kN843 kN

1 35.5 kN/cm

35.45 kN/cm

yd,VEd

pl,Rd

2

yd

22

2

= −⋅

−⎛

⎝⎜

⎞

⎠⎟

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

⋅

= − ⋅ −⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢⎢

⎤

⎦⎥⎥

⋅

=

which leads to the bending moment distribution presented in Fig. 13.

Verification of the SFB cross-section for bending at mid-span:

Note: With simple beam-to-column joints, the bending mo-ment at mid-span MEd would exceed the bending resist-ance Mpl,Rd of the cross-section:

Verification of the SFB cross section at the supports:

Bending: = ≤ =M 336 kNm M 732 kNmj,Rd pl,Rd

Shear:

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

M 648kNm M 732 kNm

Verification is fulfilled!Ed pl,Rd= ≤ =

⇒

M 984 kNm M 732 kNm!Ed pl,Rd= > =

V q L/2 97.2 kN/m 9 m/2

437.4 kN VA

3f

41.13 cm

335.5 kN/cm 843 kN

Ed Ed

pl,Rdvz

yd

22

= ⋅ = ⋅

= ≤ = ⋅

= ⋅ =

4M20, 8.8

5

5

300x300x20S355

[mm]

S355

450x25S355

Fig. 14. Application example – nominally pinned joint con-figuration

Table 6. Application example – cost comparison: simple joints vs. semi-continuous joints

Joint Type /Component

SimpleSemi-con-tinuous

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)

300 300 20

450 300 20

20

Bolts4 M 20,

8.86 M 30,

10.9 60 €

Total Cost: – 300 €

Beam Design with semi-continuous joints is 300 € cheaper (per 9 m SFB)!

* Estimated cost based on 2015 price level, including erection.

9.00m

984 kNm 336 kNm

648 kNm

Fig. 13. Application example – bending moment distribu-tion for ULS



[7] Deutsches Institut für Bautechnik: Allgemeine bauaufsicht-liche 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 vibra-tions 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 Commis-sion.

[12] CTICM France, ArcelorMittal R&D: ArcelorMittal Beam Calculator (ABC), version 3.30, ArcelorMittal Belval & Differ-dange S.A. http://sections.arcelormittal.com/down-load-center/design-software.html

Keywords: semi-continuous steel beam-to-column joints; global analysis; approximate determination of the joint stiffness; eco-nomical design; slim-floor construction

Authors:Matthias BraunArcelorMittal Europe – Long Products66, rue de LuxembourgL-4009 Esch-sur-Alzette, Luxembourg

Job Duarte da Costa Renata ObialaChristoph OdenbreitUniversity of Luxembourg, FSTCArcelorMittal Chair of Steel & Façade Engineering6, rue de Richard Coudenhove KalergiL-1359 Luxembourg, Luxembourg

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 distrib-uted constant load) at ULS and SLS. Factors for use in combination with standard design formulae were derived analytically. They allow the structural engineer to deter-mine the influence of the joint stiffness on the beam deflec-tion, its natural frequency and the distribution of the bend-ing 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 Ver-bundwirkung von Betondübeln. Stahlbau, 83 (2014), No. 5. DOI:10.1002/stab.201410154

[3] Deutsches Institut für Bautechnik: Allgemeine bauaufsicht-liche 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.: Mo-mententragfähige Anschlüsse mit und ohne Steifen. Stahl-bau-Kalender 2005, Kuhlmann, U. (ed.), Ernst & Sohn, Ber-lin, ISBN 3-433-01721-2.

[5] Jaspart, J.-P., Demonceau, J.-F.: European Design Recom-mendations for simple joints in steel structures. ArGEnCo Dept., Liège University.

[6] Maquoi, R., Chabrolin, B.: Frame Design including joint be-haviour. European Commission, contract No. 7210-SA/212/320, 1998.

the Eurocodes in the EU Member States and Norway, which was per-formed by the JRC and the European Commission’s Directorate-General for Internal Market, Industry, Entrepre-neurship and SMEs. It is part of the activities envisaged in the Commis-sion’s “Strategy for the sustainable competitiveness of the construction sector and its enterprises”. The results reported will be used also in the analy-sis envisaged for the fitness check of EU legislation related to the construc-tion sector.

Further information: www.steelconstruct.com

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 Techni-cal 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 restric-tions that prevent their implementation in the remaining five countries, hence boosting the competitiveness of the in-dustry 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-spe-cific values and procedures and their publication in the so-called national an-nexes, while Italy and Romania should remove the legal restrictions preventing the implementation of the Eurocodes. The report also finds that issuing a Com-mission Recommendation on the regula-tory 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

Articles

16

DOI: 10.1002/stco.201610004

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

Andrew VothJeffrey Packer*

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 experi-ments. The FE analysis indicates that, for a given geometric con-figuration, the behaviour of through-plate-to-CHS connections closely matches the sum of branch-plate-to-CHS connection be-haviour in plate tension and compression. A connection design strength, which is shown to be valid for a wide range of connec-tion geometries and which is the sum of existing design recom-mendations for branch plate-to-CHS connections loaded in axial tension and compression, is hence proposed for through-plate-to-CHS T-connections. This therefore enables maximum advan-tage to be taken of the capacity of this type of “reinforced” tubu-lar 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 exte-rior 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 sec-tion columns and even as a representation of a beam flange-to-column moment connection. Design recommen-dations for longitudinal and transverse branch plate T-con-nections, 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 inde-pendent of the sense of the branch plate load, i.e. the same strength is assumed for both branch tension and compres-sion loading cases, with a lower bound being taken to ac-commodate both load cases.

The limit states resistance available for many axially loaded branch plate T-connections is frequently low, how-ever, 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

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 connec-tion resistance [9], [10], [11], [12], [13]. Another widely used stiffening and strengthening method is a plate-to-tube con-nection where the branch plate is slotted through the hol-low section and welded to two opposing faces (Fig. 1). This has the advantage of engaging much more of the cross-sec-tion 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, be-cause two flat RHS faces were engaged in relatively inde-pendent but identical flat-plate flexural mechanisms. This “double strength” has hence been adopted for RHS-to-lon-gitudinal 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 connec-tions. A recent experimental study of through-plate-to-CHS connections [16] indicated that through-plate-to-hollow section connection behaviour actually comprises two inde-pendent mechanisms, one in compression and one in ten-sion, 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

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


influence of normal stress in the chord connecting face. These functions, along with the chord punching shear ex-pressions, 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 cur-rent CIDECT/ISO chord plastification partial design strength function Qu (Table 1). The numerical study of plate-to-CHS T-connections, which consisted of approxi-mately 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 3 2). 0.35 (2) for transverse (90o) plate in compression

Qu,90,T 2.6 (1 2.5 2). 0.55 (3) for transverse (90o) plate in tension

Qu,0,C 7.2 (1 0.7 ) (4) for longitudinal (0o) plate in compression

Qu,0,T 10.2 (1 0.6 ) (5) for longitudinal (0o) plate in tension

A lower-bound reduction factor 0.85 was used, based on a regression analysis of the numerical results, for appli-cation 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 nu-merically. The high ultimate capacity of the through-plate-to-CHS connections proved difficult to capture without causing non-converged solutions and chord end failures. Nevertheless, five transverse and 13 longitudinal through-

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 ge-ometry for the branch connection and the through-connec-tion are similar. The dual mechanism for plate-to-CHS connections differs from the approach that has been previ-ously applied to plate-to-RHS connections, where the lat-ter 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 ex-panded range of geometric parameters for such connec-tions, with the aim of combining tension and compression branch plate-to-CHS capacities to develop through-plate-to-CHS connection capacity. The following describes the numerical FE study and the resulting expressions proposed for the through-plate ultimate limit state.

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, as-suming that both the branch plate and the weld are ade-quately designed and are non-critical. Calculation of the two limit states depends significantly on connection geom-etry, 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, ex-pressed as an axial force in the branch member, took the following general form [5], [7], [8]:

N1* Qu Qf fy0 t02 /sin 1 (1)

where Qu is a partial design strength function that predicts non-dimensionalized connection resistance (N1

*sin 1/fy0 t02) without chord axial stress and Qf is a chord stress func-tion that reduces connection resistance to account for the

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

Transverse plate Longitudinal plate

Chord plastification

Qu 2.2(1 6.8 2). 0.2 Qu 5(1 0.4 )

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 0), C1 0.20

Punching shearN1

* 1.16 b1 t0 fy0for b1 d0 – 2t0

N1* 1.16 h1 t0 fy0/sin2

1

Range of validity:compression chords must be class 1 or 2, but also 2 50

tension chords must be 2 50transverse plates: 0.4 1.0; longitudinal plates: 1 4

fy1 fy0 , fy /f u 0.8 , fy0 460 MPa

Note: 1 is the angle of the force on the plate



porated by converting both and to effective values of (0.32, 0.51, 0.69) and (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 substan-tial resistance so that connection behaviour would govern.

2.1 FE modelling of connections

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

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, mod-elled by varying from 0.2 to 0.6, from 0.2 to 2.5 and 2 from 19.74 to 45.84, as shown in Tables 2 and 3, with the effective chord length parameter ( 2l0 /d0) indicated. Note that transverse connections with values of 0.8 are improbable, depending on chord wall thickness, as suffi-cient space for the plate to pass through the chord is re-quired. 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 load-ing only.

All connections were modelled with fillet welds and the effect of weld size on connection behaviour was incor-

Table 2. Values of effective chord length parameter for longitudinal through-plate-to-CHS T-connections

t0(mm)

2Nominal depth ratio, h1/d0

0.2 0.6 1.0 1.5 2.0 2.5

11.10 19.74 4 4 4 4

7.95 27.56 8 8 8 8 8 8

4.78 45.84 12 12 12

Table 3. Values of effective chord length parameter for transverse through-plate-to-CHS T-connections

t0(mm)

2Nominal width ratio, b1/d0

0.2 0.4 0.6

7.95 27.56 8 8

4.78 45.84 12 12 8

Fig. 3. Parametric transverse through-plate-to-CHS T-connection configura-tion

Fig. 2. Parametric longitudinal through-plate-to-CHS T-connection configura-tion



bility, lateral restraint was provided by the symmetric boundary. A high equilibrium-induced chord bending mo-ment (and hence chord normal stress) is created at the joint connecting face; this is undesirable for determining connection behaviour without chord stress and hence gen-erating 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 l0 /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 inde-pendent of the partial design strength function Qu (see Ta-ble 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 l0 . 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, de-pending on predicted connection capacity and chord length.

ii) To prevent non-convergent results, which are possible with load-controlled analysis (especially for connec-tions loaded in compression during periods of signifi-cant plastification and deformation), displacement-con-trolled 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-

marized below, with validation performed against labora-tory experiments (Fig. 4) [16].

FE models were constructed and analysed using the commercially available ANSYS software [22]. Both geom-etry 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 free-dom per node and reduced integration with hourglass con-trol, 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, typ-ically 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 allow-ance 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 prop-erties 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 cou-pons 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 mate-rial fracture, with the “death feature” of an element being activated by a maximum equivalent (von Mises) strain value ef 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 bend-ing where, for a quarter model, the chord end was sup-ported by a roller at the chord neutral axis (Figs. 2 and 3) and loaded using displacement control. To prevent insta-

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

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



ii) the maximum connection load N1,max (the global max-imum 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/fy0t0

2 as a function of or (which include the effect of weld size) for all 2 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 branch- plate-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-plate-to-CHS T-connections do not even come close to predict-ing 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 under-standable.

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-of-time-step correction and a small displacement rate based in part on the slope of the connection load–defor-mation 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 deter-mined 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),

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



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 recom-mendations, but the general behaviour of a through-plate-to-CHS T-connection has been established to be approximately equivalent to the addition of tension and compression branch-plate-to-CHS connection behav-iours. Thus, it is logical that the partial design strength function Qu for through-plate connections could be given by:

Qu Qu,90,C Qu,90,T (6) for transverse through-plate connections

Qu Qu,0,C Qu,0,T (7) for longitudinal through-plate connections

To determine whether the numerical results are rea-sonable and applicable to a wider range of connection ge-ometries, Fig. 8 examines the ratio of Qu,Through (the nor-malized connection capacity N1,u/fy0t02 for through-plate connections) and Qu,Branch (Tens Comp) (the summation of the normalized connection capacities N1,u/fy0t0

2 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 sin 1 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-to-CHS T-connection capacities still underestimates through-plate connection capacity.

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



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

Notation

Ai cross-sectional area of member ib1, b1 nominal, effective branch width (b1 b1 2w0),

90o to CHS longitudinal axisd0 external diameter of CHS memberfu ultimate stressfyi yield stress of member ih1, h1 nominal, effective branch depth (h1 h1 2w0),

parallel to CHS longitudinal axisi subscript denoting member (i 0 for chord, i 1

for branch)l0, l1 chord length, branch lengthM0 chord bending momentM0,END applied in-plane bending moment at chord endMpl,0 chord plastic moment capacityNi axial force in member iN1,3% branch load at 3 % d0 connection deformationN1,u connection ultimate limit state capacityN1

* connection resistance, expressed as an axial force in the branch member

Npl,i yield capacity of member i ( Ai fyi)Qf chord stress influence functionQu partial design strength functionti thickness of member iw0, w1 measured weld leg length along chord, branch

, chord length parameter ( 2l0 /d0), effective length parameter ( 2l0 /d0)

, nominal, effective connection width ratio ( b1/d0, b1

/d0) for transverse plates chord radius-to-thickness ratio ( d0/2t0)

ef maximum equivalent strain reduction factor, nominal, effective connection depth (length) ra-

tio ( h1/d0, h1 /d0) for longitudinal plates;

t1/d0 for transverse plates

1 included angle of inclination between branch and chord

References

[1] CEN: Eurocode 3: Design of steel structures – Part 1.1: Gen-eral rules and rules for buildings, EN 1993-1-1:2005. Euro-pean Committee for Standardization, Brussels, 2005.

[2] AISC: Specification for structural steel buildings, ANSI/AISC 360-10. American Institute of Steel Construction, Chi-cago, 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 sec-tion connections – Steel design guide No. 24, American Insti-tute 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 Dévelop-pement 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

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 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 through-plate-to-CHS connection results, these values are not sta-tistically significant, but are indicative of the suitability of Eq. (6). Similarly, for longitudinal through-plate connec-tions, the “actual” Qu (which is equivalent to the normal-ized FE connection capacity N1,u/fy0t02) is compared with the Qu value from Eq. (7) in Fig. 10. In this comparison the 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 approxima-tions 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 ana-lysed (varying values of from 0.2 to 0.6, from 0.2 to 2.5 and 2 from 20 to 46) using validated FE models in order to determine connection behaviour trends and develop de-sign guidelines. From the 18 numerical FE analyses, two proposed partial design strength functions Qu – repre-sented 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 3 2). 0.35 2.6 (1 2.5 2). 0.55]Qf

Longitudinal: (9) N1

* fy0 t02 [7.2 (1 0.7 ) 10.2 (1 0.6 )]Qf

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]. So-called effective values for the non-dimensional parame-ters and are used in the above equations, but the use of the regular variables and (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-to-CHS connections to be based on just one limit state check, unlike for branch plate connections, where there are typi-cally two limit states to be checked (Table 1). More impor-tantly, 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



[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 numeri-cal 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 sec-tion 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 Consho-hocken, 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.: Paramet-ric 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 ele-ment analysis; design

Authors:Andrew P. Voth, Dr., P.Eng.Read Jones Christoffersen Ltd.144 Front Street West, Suite 500Toronto, Ontario M5J 2L7 Canada

Jeffrey A. Packer, Prof., Dr., P.Eng.Department of Civil EngineeringUniversity of Toronto35 St. George StreetToronto, Ontario M5S 1A4 Canada

(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, Ge-neva, 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 Stand-ards Organization, Geneva, 2013.

[9] Alostaz, Y. M., Schneider, S. P.: Analytical behavior of con-nections to concrete-filled steel tubes. Journal of Construc-tional 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 Struc-tures, 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. Engineer-ing 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 Engi-neering, ASCE, vol. 129, No. 4, 2003, pp. 478–486.

[15] Kurobane, Y., Packer, J. A., Wardenier, J., Yeomans, N.: De-sign guide for structural hollow section column connections, CIDECT design guide No. 9, Comité International pour le Développement et l’Étude de la Construction Tubulaire, Ge-neva, 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 Engineer-ing, 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.: Exper-imental 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).

Articles

24

DOI: 10.1002/stco.201610009

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

Harald Unterweger*Andreas TarasZoltan Feher

In many practical applications, columns are often fixed to a prac-tically 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 de-sign 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 later-al-torsional buckling (LTB) of I-section beam-columns in Euro-code EN 1993-1-1 consists of comprehensive parametric numeri-cal 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 re-straints. 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 con-cept (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-mo-ment at the end restraint, which is to be used for designing the welded joint. Finally, an improved LTB design curve (buckling re-duction factor LT) is presented, developed at the authors’ institu-tion, which may be used for the cases studied.

1 Introduction and motivation

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 warp-ing 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 1993-1-1 (e.g. [1]).

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 col-umn 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 com-pressed 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 1993-1-1 [2], section 6.3.3, are often used. If the so-called “method 2” of Annex B is used (only this method is con-sidered 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).

Determination of the buckling reduction factors z, LT:

N

N(European buckling curves) (5)z

pl,R

crzλ = → χ

NN

kM

M1.0 (1)d

z pl,RdLT

yd

LT pl,y,Rdχ ⋅+ ⋅

χ ⋅≤

where: k 10.1 n

C 0.251

0.1 nC 0.25

(2)LTz z

mLT

z

mLT= −

⋅ λ ⋅−

≥ −⋅−

nNN

(3)zd

z pl,Rd=χ ⋅

C 0.6 0.4 0.4 (4)mLT = + ⋅ψ ≥


Lateral-torsional buckling behaviour of I-section beam-columns with one-sided rotation and warping restraint

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


So in this study the resistance Rpl is calculated in a simpli-fied 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 behaviour2.1 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 summa-rized in Fig. 2. Type S4R shell elements were used for the flanges and the web of the member. The fact that the addi-tional fillets in the rolled sections studied increase stiffness and strength was considered by adding beam elements with box cross-sections with equivalent torsional and lon-gitudinal 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 previ-ous linear buckling analysis (LBA) for each member ana-lysed. Two representative cross-sections were studied: a very slender IPE 500 section and a stocky HEB 300 sec-tion. 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].

R

R(8)op

ult,k

cr,op

pl

cropλ =

αα

= → χ

It is worth mentioning that the buckling reduction fac-tors z and LT are a function of the slenderness

–z or

LT, which in turn are based on the ideal buckling strength Ncr and Mcr. These values are strongly influ-enced 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 sec-tion 6.3.2.3 of that code, a user may consider the in-creased 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 mo-ment Mcr 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 in-creased by a factor of 2.0 at least (k kw 1.0 for the end fork condition).

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 verifica-tion, 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 op 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)):

M

M(general case / specific case) (6)LT

pl,y,R

crLTλ = → χ

M CE I

kL

kk

II

kL G I

E I(7)cr 1

2z

2w

2w

z

2t

2z

0.5

( )( )

= ⋅π ⋅ ⋅

⋅⎛

⎝⎜⎞

⎠⎟⋅ +

⋅ ⋅π ⋅ ⋅

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

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



It can be seen that, for a constant moment, the utili-zation 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 in-creased at the fixed end for the other moment distribu-tions.

3 Results for Mcr – bending My only

The ideal critical buckling moment Mcr affects the LTB capacity of the Eurocode ( LT · Mpl,y,Rd) because LT de-pends on the slenderness

–LT (see Eq. (6)). For the bound-

ary 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

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 right-hand 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

x in both flanges, with plastic zones shown in red.

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 ca-pacities, deformations and longitudi-nal stresses x at ultimate load



The results of C1 in Table 1 illustrate a very small influence of the slenderness of the beam, but significantly higher nu-merical 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

In the following, a yield strength fy 235 N/mm2 was as-sumed, without any partial safety factor M for all compar-isons 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 consid-ered in this section. The numerical results of the GMNIA analyses are expressed in terms of buckling reduction val-ues LT in order to compare them with the Eurocode pre-dictions. The numerical values Mcr,LBA for the correct boundary conditions with the fixed end (Fig. 1) are used for calculating the slenderness ratios

–LT.

To clarify the calculation of LT in detail, all the rele-vant parameters are given in Table 2. For the “specific case”, the beneficial effect of a non-uniform moment dis-tribution, based on Eq. (11), can be also used according to Eurocode 3, and was thus always considered in the

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.

Values for C1 can also be found in the pre-version of the Eurocode, ENV 1993-1-1 [3]. Another source is the Na-tional Annex of EN 1993-1-1 in Austria, ÖNORM B 1993-1-1 [7], as well as the ECCS recommendations [8].

In addition, the results of an LBA analysis are given for different member lengths (the slenderness

–z given in

Table 1 is based on pinned ends), based on the ABAQUS and LTBEAM [9] software packages. In these cases the nu-merical 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).

CM

E I

0.7 L

II

0.7L G I

E I

(10)1,LBAcr,LBA

2z2

w

z

2t

2z

0.5

( )( )

=

π ⋅ ⋅

⋅⋅ +

⋅ ⋅π ⋅ ⋅

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

C 1k

1/ 11.33 0.33

(9)1c2

2

= =− ⋅ψ

⎛⎝⎜

⎞⎠⎟

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)

–k (k 1.0)

S235ABAQUS LTBEAM 1/kc

2 ENVÖNORM B

(interpolated)ECCS

(interpolated)

5084 0.71 1.818 2.507

1.769 2.092 1.955 1.824

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

Table 2. LTB member capacity; details for calculating LT based on EN 1993-1-1

“General case” “Specific case”

Reduction factor LT

1

LT LT2

LT2φ + φ − λ

1

0 75LT LT2

LT2φ + φ − ⋅λ.

Factor LT 0 5 1 0 2LT LT2( )⋅ + α λ − + λ⎡

⎣⎢⎤⎦⎥

. . 0 5 1 0 4 0 75LT LT2( )⋅ + α λ − + ⋅λ⎡

⎣⎢⎤⎦⎥

. . .

Buckling curve for rolled I- or H-sections

h/b 2 (HEB 300) a ( 0.21) b ( 0.34)

h/b 2 (IPE 500) b ( 0.34) c ( 0.49)

Increase in LT (if M uniform) valid in EC3 for “special case” only:

ff 1 0 5 1 k 1 2 0 0 8 but f 1 0LT mod

LTc LT

2( )( )χ = χ = − − − λ −⎡⎣⎢

⎤⎦⎥

≤; . . . .,



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

–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 –

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 re-straint when it is present; owing to the restraint at one end of the member, a significantly higher LTB capacity can be used,

results presented here for the corresponding Eurocode predictions.

Fig. 4 shows the results for the two different sections as-suming 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 trian-gular moment distributions – a case often present in col-umns, e.g. in portal frames. Now the “specific case” also gives accurate, safe results.

f(11)LT,mod

LTχ =χ

f 1 0.5 1 k 1 2.0 0.8 1.0 (12) (12)c LT2( ) ( )= − ⋅ − ⋅ − ⋅ λ −⎡

⎣⎢⎤⎦⎥≤

where : k 11.33 0.33

(13)c = − ⋅ψ

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

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



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.

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”.

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; compari-son 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; compari-son of GMNIA calculations with Eurocode predictions based on the interaction concept



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

–z 1.0. It is

worth mentioning that the general method is applied in the more conservative way mentioned in the Eurocode,

Fig. 7 shows results for the member with –

z 1.0 for non-uniform moment distributions. For the typical triangu-lar 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

–z 1.0 and for constant and triangular

moment distributions. In this case the Eurocode predic-tions for the “specific case” are very accurate for constant moment and on the safe side for the triangular moment distribution.

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

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



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. How-ever, 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 im-plied ultimate limit state. The warping restraint leads to sig-nificant bi-moments (warping moments), which can be mod-ified 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 inter-nal forces NEd and My,Ed.

As an additional recommendation, and as a conse-quence 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.

MM

M1 1 M

M

M1 1

t b4

· f (14)

z,fl,EdEd,y

pl,y.Rd LTz,fl,pl

Ed,y

pl,y.Rd LT

fl fl2

yd

= ⋅χ

−⎛

⎝⎜⎞

⎠⎟⋅

= ⋅χ

−⎛

⎝⎜⎞

⎠⎟⋅

⋅

as the minimum of z and LT was used for the reduction factor op.

Fig. 10 compares the HEB 300 section (slenderness –

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 LT 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 LT (Table 1) are modified, as shown in Fig. 11. Now the slenderness

–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 LT 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 mo-ment and antimetric moment distribution. The GMNIA re-sults are nearly identical with the proposed formulas for LT. Owing to the very accurate results with this modified LT 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.

Fig. 11. Suggestion for improved LT curves for LTB member capacity and comparison with GMNIA results for IPE 500 sec-tion with different moment distributions



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

References

[1] Greiner, R., Lindner, J.: Interaction formulae for members sub-jected 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 struc-tures. General rules and rules for buildings, CEN, Brussels, 2005.

[3] Eurocode 3, ENV 1993-1-1: Eurocode 3. Design of steel struc-tures. 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 Univer-sity 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 Steel-work, 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 con-cerning 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 Méral-lique: LTBeam v. 1.0.10 Documentation, Saint-Aubin, France, CTICM, 2010.

[10] Taras, A.: Contribution to the Development of Consistent Sta-bility Design Rules for Steel Members. PhD thesis, Graz Univer-sity of Technology, Institute for Steel Structures & Shell Struc-tures, 2011.

Keywords: lateral-torsional buckling; beam-columns; GMNIA analyses

Authors:Univ. Prof. Dipl.-Ing. Dr. Harald UnterwegerAssistant Prof. Dipl.-Ing. Dr. Andreas TarasDipl.-Ing. Zoltan Feher

All authors:Institute of Steel Structures, Graz University of TechnologyLessingstr. 25, A-8010 Graz, Austria

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

– Rewritten, with MEd,y limited by the LTB capacity:

– Linear reduction of Mz,fl,Ed for reduced bending mo-ment MEd,y:

8 Summary and conclusion

The LTB behaviour and ultimate LTB load-carrying capac-ity 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 in-creased 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-co-

lumns, 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 mini-mum value of z or LT, 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 ( LT 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 con-sider the additional bending moments on the flanges Mz,fl (effect of bi-moment) at the joint (at least for the welds be-tween end plate and member). A first proposal for this addi-tional moment Mz,fl has been presented in this paper.

M

M

M

M1.0 (15)Ed,y

pl,y.Rd

z,fl,Ed

z,fl,pl+ =

M

M1

M

M1

M

M1 (16)z,fl,Ed

z,fl,pl

Ed,y

pl,y.Rd

LT pl,y,Rd

pl,y.RdLT= − = −

χ ⋅= − χ

M

M1

M

M

M

M1 1 (17)z,fl,Ed

z,fl,plLT

Ed,y

LT pl,y

Ed,y

pl,y LT( )= − χ ⋅

χ ⋅= ⋅

χ−

⎛

⎝⎜⎞

⎠⎟


Jerzy Ziółko*Tomasz MikulskiEwa Supernak

Articles

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 com-pleting 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 particu-larly 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.

1 Introduction

The authors of this article have already published a num-ber of papers on the subject of underpressure in steel ver-tical 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 deforma-tions 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 thick-ness 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

theoretical issues and model research on local loss of sta-bility 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 deforma-tions, however, do not represent a serviceability limit state of the tank as the shell is still sealed. Along with changes


Fig. 1. Tanks damaged by underpressure: a) during the pro-ductivity test of the extraction pump on the product pipe-line, b) due to freezing of the breather valves

a)

b)

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


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-

verse change in temperature and air pressure. When un-derpressure 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. How-ever, 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 underpres-sure 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 equal-ization 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

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

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

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



spread around the perimeter. They are vertical. The spac-ing between deflections corresponds to the spacing be-tween 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. Neigh-bouring deformations have joined together and their ex-tent is wider than earlier.

into atmosphere, which is unaccep table (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 possi-bilities to observe the behaviour of the shell after its first deformation caused by underpressure, a computer simula-tion 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 struc-

ture

The following data was adopted for the calculations:– E 210 GPa – Young’s modulus of elasticity– 0.3 – Poisson’s ratio for steel– 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 inter-

nal 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. 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

Fig. 7. Deformations of tank shell corresponding to under-pressure value pmin-1 2.254 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

[1] Ziółko, J.: Die Instandsetzung durch Unterdruck beschädig-ter zylindrischer Stahlbehälter. Der Stahlbau, 49(1980), No. 11, pp. 347–348.

[2] Ziółko, J.: Reparatur von Dächern und Mänteln durch Un-terdruck verformter Stahltanks. Stahlbau, 70(2001), No. 5, pp. 357–361.

[3] Supernak, E., Ziółko, J.: Podcisnienie w zbiornikach. Wni-oski ze zdarzen w ostatnich latach. (Vacuum in tanks. Conclu-sions from the events in recent years) XXVI Scientific-Techni-cal Conf. “Structural Failures” Szczecin – Miedzyzdroje, Po-land, 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. Scientif-ic-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 umfangsdruckbe-anspruchter 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; defor-mations

Authors:Prof. Jerzy Ziółko, PhDProfessor at University of Science & TechnologyAl. prof. S. Kaliskiego 7 L85-796 Bydgoszcz, Poland

Tomasz Mikulski, PhD Ewa Supernak, PhD, Eng. Both authors: Gdansk University of Technology ul. G. Narutowicza 11/12 80-952 Gdansk, Poland

Fig. 9 demonstrates deformations of the shell after 300 iterations (adopted end of numerical analysis). Deforma-tions are still irregular, and take different forms and values.

Fig. 10 is a photograph of the deformation of the up-per part of the tank shell, where underpressure was gener-ated. 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-

Fig. 8. Deformations of tank shell corresponding to under-pressure value pmax-2 2.450 kPa

Fig. 9. Deformations of tank shell corresponding to under-pressure value pend 2.436 kPa

Fig. 10. Deformations of upper part of tank shell caused by underpressure


Articles

DOI: 10.1002/stco.201400001

During high wind or earthquake action, high-rise multi-storey buildings respond with rel-atively 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 de-sign 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 mate-rials have developed, so heavy façades have been replaced by lighter ones, including curtain walls with large glass panels, which have become es-pecially desirable in high-rise build-ings. The assembly has become sim-pler 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 per-pendicular to the façade plane [1] have been considered for the design of façades. Curtain walls are sus-pended 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

the Trimo d.d. company from Slove-nia, 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 compar-ative protocol according to interim testing protocols in FEMA 461.

2 Testing facility, test setup and test specimens

The tests were performed in the labo-ratory of the Faculty of Civil Engi-neering, University of Ljubljana, be-tween May and June 2013.

The QAir system used in this study is a unitized glass curtain wall, intended primarily for use as an ener-gy-efficient building envelope in high-rise buildings. According to the man-ufacturer’s specifications, there are many different materials to choose from [6], including toughened glass, sintered ceramics, high-pressure lami-nate, wood or stone. Individual com-ponents 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 30 2.5 mm) is located on both vertical sides of the panel. Ethy lene propylene diene monomer (EPDM) rubber gasket profiles are in-

Barbara Gorenc*Darko Beg †

Curtain wall façade system under lateral actions with regard to limit states

falling out [2], depending on the place-ment within the frame, the offset be-tween 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 ap-prox. 30–40 mm for a typical 4 m sto-rey. 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 Euro-pean standards for wind [4] and earth-quake [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 functional-ities in SLS but suffer limited damage and stay fixed to the structure in ULS, which would prevent components from falling onto areas below. Sec-ondly, limits specific to the façade sys-tem 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


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


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 ac-curacy of up to 1 mm. A finished joint between the panels was 20 1 mm wide. After levelling, flame-retardant elastic PUR foam, a usual part of the system which ensures tertiary water-tightness and thermal and sound insu-lation, was injected into the joint and left to cure for at least 12 hours prior to testing.

Two system assembly configura-tions were tested (detail A – A, Fig. 2):a) QAir1 – vertical joint as per manu-

facturer’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 T2-m), one for each configuration (QAir1, QAir2) and four cyclic, one for wind action at different storey drift levels (T2-1, T2-2 and T2-3), two for seismic ac-tion (T3 and T4) and one (T5) accord-ing 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 lev-elled 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

ability on supports and that damage, if it occurs, will be minimal and local-ized.

The system is designed to allow relative flexibility during assembly, taking into account different toler-ances on the primary structure [7], [8] or at least 20 mm in the three main directions (Figs. 1 and 2). The speci-men tested represents a part of the façade consisting of three 2.5 m high 1 m wide panels with two intermedi-ate vertical joints. Panels were hung from the upper support elements mounted on the test frame (Fig. 1) and slid on pins 70 10 mm on the bottom support element. When all

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 sup-ports. Façades are not normally de-signed for large in-plane shear resist-ance. Instead, the basic assumption is that the panels compensate for large storey drifts and the resulting forces with some damage. In this case, how-ever, the basic assumption was that the system will respond with adapt-

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 [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 8,5 mm

T2-2 Cyclic Wind – SLS QAir2 S2 4 mm/s 500 3 8,5 mm

T2-3 Cyclic Wind – ULS QAir2 S2 6 mm/s 20 5 12,0 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 47,5 mm

T4 Cyclic Earthquake – MRF10 – acc

QAir2 S4 4 mm/s 234 25 62,5 mm

T5 Cyclic FEMA 461 QAir2 S5 4 mm/s 58 74 184,9 mm

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 displace-ment designated by uaxis and support details (right)

39


Steel Construction 9 (2016), No. 1

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 de-veloped by first designing a typical 10-storey 2D moment-resistant frame

Displacements of the frame and specimens as well as slip and opening of joints were measured with displace-ment transducers (measuring range 25 mm and 50 mm, error 0.1 mm)

and rotation with dual axis inclinom-eters (measuring range 15°, error 0.1°). The applied force was mea-

sured by the actuator load cell. Hori-zontal lines spaced at 100 mm inter-

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 ob-served at a frame column rotation 0.048. At 0.02, which is double the SLS limit for structure under earthquake, the force was only 0.4 kN.

Fig. 2. Vertical joint detail for QAir1, with gaskets (Nos. 11 and 12) and PUR foam (No. 10), and QAir2, without those ma-terials, 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.

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



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 accelera-tions 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 dif-ferent 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 aver-age drift ratio 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 count-ing events when the storey peaked at an interval of I 0.002 starting from 1 0.001. Within the spectrum ground accelerations were grouped to-gether based on peak ground accelera-tion 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).

ally higher than the statistical vb,0 from 15 years of data collected since 1997. Considering a characteristic combination, there is a 2 % probabil-ity of wind pressure at a level of SLS or higher each year, which would oc-cur at least once in 50 years of the design life. This would cause a maxi-mum structural relative storey drift

SLS 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 com-bination, the probability would be higher and would account for about 50 occurrences in the design life, but at a lower SLS. To be on the safe side, the benchmark amplitude taken was that of the characteristic SLS trans-lated into deflection on the zaxis (Fig. 1), uSLS 8.5 mm with 10 times the number of cycles (500) at the fre-quent combination. Since for ULS the characteristic combination is factored with 1.5 in unfavourable conditions, an additional 20 cycles were per-formed for uULS 12.0 mm. The tests using these protocols were designated T2-1, T2-2 and T2-3 (see Table 1).

3.2 Defining experimental test proto-cols for exposure to earthquake actions

Testing protocols for earthquake ac-tions vary, depending on the materials used [12]. To construct protocols, the non-linear dynamic analysis proce-dure was performed on an MRF build-ing model (Fig. 4) using SAP 2000 software [13]. The target spectrum used for peak ground acceleration was ag,475 0.25 g (g gravitational accel-eration), with a return period TR,ULS

(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 mem-bers, 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 (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 speci-men in in-plane shear through instru-ments and observation. The cyclic rate was considered to be similar to the influence of gust or earthquake in or-der to avoid the influence of the visco-elasticity 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 re-mained the same until very high drift ratios.

3.1 Defining experimental test proto-cols for exposure to wind actions

The raw data for the maximum aver-age 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-

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

41



3.3 Test protocol according to FEMA 461

For test T5 (Fig. 6b), the protocol from Table 2-1 in FEMA 461 [9] was used as a comparison. It is primarily in-tended to determine fatigue damage for non-structural elements exposed to earthquake loading. The protocol was started with 10 cycles of uel 10 mm. This is a 25 % increase in SLS for wind, but it is lower than when the damage was first observed in test T1-m. This protocol has higher ampli-tudes but a lower cumulative number of cycles (Fig. 7) than the constructed MRF 10 – acc, attempting to represent the realistic frame response.

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

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

a) b)

4 Test results

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

4.1 T1-m – monotonic test

The first test was monotonic, per-formed on the QAir1 configuration. Throughout the test, elements moved and rotated as a rigid diaphragm, with joints holding the panels firmly to-gether 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 ULT 0.043. The polyamide pro-file 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 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



fell by 1/3 but quickly increased after restarting the test.

At the end of the test ( ULT = 0.043) panel P1 on the left side rose up and nearly unhooked from the up-per 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 mono-tonic 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

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

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

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

b)a)

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) c)

d) e)

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

43



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 defor-mations of the joint. The difference is very small, however, and does not outweigh the drift capacity achieved. A distinct pinching effect as well as shift of response loop centre to {F,

–4.4 kN, –0.005} in the third phase are visible globally and locally in all diagrams. The joint slip and opening were small – between 0.5 and 1.3 mm (Figs. 11b and 11c).

The SLS phase passed without any significant change and QAir1 re-turned to its initial position. Halfway through ULS, the end of the second phase, the specimen became stuck with the hook on the upper left sup-port in an elevated position (Fig. 12a) at 0.013. The elements remained fixed on the test frame so the test continued. The specimen was subse-

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 indi-vidually. With this movement, the shear capacity in the sample stabi-lized until 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 configuration) – seismic action

The test was performed on the QAir1 specimen (S3) using the MRF10-acc protocol. It responded as a rigid dia-phragm, much the same as in T1-m. The forces (Fmax 10 kN) were con-centrated 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- dia-gram (Fig. 11a with a larger surface in one (positive) and smaller in the other (negative) direction. The rea-son for this is rather difficult to deter-mine. It is evident when comparing the three diagrams in Fig. 10 that the difference 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 different in two directions. The system may have been too sensitive. The test rig or the samples may not have been assem-bled perfectly so the force needed for pushing the frame was greater than

and compensated amplitude merely through rotation and drift on sup-ports, with no visible slip or opening of intermediate joints. The maximum force in the specimen was 5 kN and –7.2 kN. Even after 500 cycles, all F- loops remained the same, the force in the specimen decreased slightly; the specimen’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 in-duced in the frame.

In T2-2, material was removed from joints and the test repeated. Since panels were no longer con-nected through joints, they did not influence 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 and the drift capacity was consequently higher. There was no perceptible change during 500 cycles in the char-acteristic loop. The last leg of the cy-clic test, designated T2-3, consisted of 20 cycles at uaxis 12.0 mm, con-sistent with ULS. The increased am-plitude 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 stiffness or any other damage were detected during the cyclic phases of T2 on QAir1 or QAir2.

At the end of test T2-3, a mono-tonic 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 .0 when the force in the specimen de-creased. The vertical joints that were cleared of material offered no resis-tance to imposed shear, so the force

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

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

b)

a)

c)



test, S4 returned to its original posi-tion 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 up-per support, but the form of the loop remained the same. The joint open-ing of 11 mm was the only residual deformation in the system after the test.

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 0.0075 ( 7 kN) the specimen exhibited a linear F- ratio due to the interaction between panel and supports, after which the drift in-creased with the increase in ampli-tude as well, but the force in the sys-tem remained the same. It increased only at very high drift (beyond 0.05), where the physical limit on sup-ports was reached. At 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

been reached. The test was stopped after ULS and 1.3ULS was not per-formed.

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 individu-ally (Fig. 13). As the drift ratio in-creased, so a steady increase in force was observed in the SLS phase until

0.0075 ( 6 kN). After that, the force stabilized even though the am-plitude increased. Every loop fol-lowed an almost identical path at the same amplitude. The entire MRF10-acc test protocol was run. After the

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

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

a) b)

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

a)

b)

c)

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

a) b) c)

45



formity assessment of structural com-ponents, 2009.

[8] EN 13670:2010: Execution of con-crete structures, 2010.

[9] FEMA 461: Interim Testing Protocols for Determining the Seismic Perfor-mance Characteristics of Structural and Nonstructural Components, Fed-eral Emergency Management Agency, 2007.

[10] SIST EN 1991-1-4:2004/oA101. Eurocode 1: Actions on structures – Part 1-4: General actions – Wind ac-tions – National annex, 2008.

[11] SIST EN 1990:2004. Eurocode – Ba-sis 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 Experi-mental Structural Engineering, San Francisco, 2009.

[13] SAP2000 (2002): Analysis reference manual, Computers and Structures, Inc., Berkeley.

[14] SIST EN 1998-1-4:2005/A101. Euro-code 8: Design of structures for earth-quake 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-Mo-tion Data. <http://www.isesd.cv.ic.ac.uk>, EVR1-CT-1999-40008, Euro-pean Commission, Directorate-General XII, Environmental and Climate Pro-gramme, Brussels, Belgium, Jan 2013.

[16] Reyes, J., Kalkan, E.: How Many Re-cords 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; service-ability limit state; in-plane shear; drift ca-pacity; wind; earthquake; relative storey drift ratio; testing protocols; experimen-tal test

Authors:Barbara Gorenc, BScTrimo d.d., Prijateljeva c. 128210 Trebnje Slovenia

Prof. Dr. Darko Beg †University of LjubljanaFaculty of Civil & Geodetic EngineeringChair for Metal StructuresJamova 21000 Ljubljana Slovenia

Slip and opening of joints in QAir1 were 1 mm and had no ad-verse effect on the joint functionality, e.g. watertightness, at normal drift ra-tios. 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 , 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, water-tightness, thermal and sound insula-tion should also be preserved.

Acknowledgements

The authors gratefully acknowledge the support of the Public Agency for Technology of the Republic of Slove-nia through its programme of funding “Young Researchers from the Eco-nomic 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 Engi-neering, 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 Engi-neering Society, Albury, NSW, 2005, pp. 35-1–35-8.

[4] SIST EN 1991-1-4:2005. Eurocode 1: Actions on structures – Part 1-4: Gen-eral 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 cur-tain 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 struc-tures – Part 1: Requirements for con-

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 dam-age to the individual panels (delami-nation, 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 toler-ances, help increase the drift capacity of the system. The resulting force in the system is in the range of 10 kN for QAir1 and 5 kN for QAir2 at 0.02. This is much lower than the to-tal 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 compo-nents in façade systems.

Storey drift ratios are very im-portant for façade design under any lateral action. Considering SLS in [5], the maximum inter-storey drift de-mand on the system for regular build-ings in the region of moderate wind and high seismicity is 0.02. Both QAir1 and QAir2 were able to com-pensate small ( 0.005) and moder-ate ( 0.01) relative storey drift ra-tios with no damage to the elements or components. This was especially true in the T2 test, where the capac-ity was large enough to compensate for 1/300 of the storey height even after 500 cycles. Damage was de-tected only at very large amplitudes ( 0.02) and only in the QAir1 con-figuration. Cohesive (PUR) and fric-tion (EPDM) forces held panels to-gether in the joints, which then re-sulted 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, pro-gressing slowly. At no time did the panels or any part of the system col-lapse. Glass layers were not in dan-ger of colliding or breaking.

Articles

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

1 Introduction

In recent years, EBFs have been widely used in steel structures in dif-ferent countries. These systems are known to fulfil the seismic design pa-rameters, providing relatively high ductility, strength and stiffness, and also offer architectural flexibility. Suc-cessful seismic performance of an EBF necessitates that all its compo-nents 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 spe-cial 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 re-strained (FR) connection. Owing to the severe loading conditions of link-to-column connections and the poten-tial for premature connection failure, the 2010 AISC Seismic Provisions [1]require qualification testing of link-to-column connections. However, the provisions do not introduce a prequal-ified link-to-column connection for

Akbar Pirmoz*Parviz AhadiVahid Farajkhah

DOI: 10.1002/stco.201350003


The applicability of extended stiffened end plate (ESEP) connections used as link-to-co-lumn 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 con-nection 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 mo-ment 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.

practical use, and the issue of the seis-mic link-to-column connection is still unresolved for researchers and engi-neers. Early tests by Malley and Popov [2] on short shear-controlled link-to-column connections with welded flange-bolted webs demonstrated the poor performance of these connec-tions. The tests by Engelhardt and Popov [3] demonstrated that the dom-inant failure mode of the long links connected to the columns was frac-ture of the link flanges prior to ade-quate rotation. As a result they pro-posed 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 connec-tions, five of which were extended end-plate (EEP) connections. The re-sults of their study demonstrated that a well-designed EEP link-to-column connection can withstand the severe forces of the active link until the re-quired 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 interme-diate links with a free flange detail achieved the required rotation and fractured immediately after this rota-

tion. Drolias [6] tested eight large-scale welded link-to-co lumn connec-tions in two phases. Six of the eight specimens achieved the required ine-lastic rotations with acceptable safety margins.

2 Aim of the current study

The recent experimental studies on link-to-column connections cover dif-ferent types of welded FR connec-tions. In those studies, the applicabil-ity of ESEP connections as link-to-column connections for long link beams was evaluated using non-linear FEM. First, the connection is de-signed according to the recent seismic design rules for the special moment frames. It is then subjected to the con-ditions of the link-to-column connec-tions 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 re-gard, non-linear FEM could be a rig-orous tool for evaluating the connec-tion and examining the proposed de-sign 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 in-vestigators and engineers to search for new connection configurations that exhibited favourable perfor-mance. The ESEP connection was among the connection types studied

Finite element analysis of extended stiffened end plate link-to-column connections

47

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


for special moment frames. Experi-mental studies [7–12] demonstrated that well-designed end-plate connec-tions exhibit ductile performance in moment frame applications. There have not been any studies performed regarding the performance of ESEP connections as link-to-column con-nections in EBFs for the long flexural links.

Some advantages of the ESEP connections as a link-to-column con-nection, 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 enhance-ment of the connection using rib stiffeners.

– Beneficial stiffness of the end-plate stiffeners (ribs) can decrease the panel zone distortions and the im-posed stresses in the panel zone.

– Contribution of the end plate to the strength capacity of the panel zone.

– Relatively higher ductility with re-spect to welded rigid connections.

– During an earthquake, probable slippage of the connection compo-nents may increase the damping of the system.

– Ease of replacing damaged links after a severe earthquake.

Since the ESEP connections are de-signed to remain mainly elastic, and also due to the time-consuming com-putational burden of the FEM in pre-dicting the response of the bolted con-

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

4 Study methodology4.1 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 geomet-ric characteristics of the specimens. The section depth, web thicknesses and flange thicknesses of the columns and beams are 300, 8 and 12 mm re-spectively, the flange widths 250 mm (column) and 200 mm (beam) [13].

4.2 FE modelling

The ANSYS multi-purpose finite ele-ment 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 col-umn 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 cre-ated which includes the out-of-the-link segment of the beam and the full-depth 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-of-the-link beam and the web stiffeners. This model represented the test speci-mens used for validation of the nu-merical models. The finite element mesh pattern of the link-to-column connection (corresponding to speci-men 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 con-

nection (e.g. beam, column, end-plate and bolts) were modelled us-ing 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: transla-tions in the nodal x, y and z direc-tions.

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

SpecimenBolt 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

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



– No weld failure was detected dur-ing the tests. It is expected that the effect of the welds on the response of the connection components is negligible. Accordingly, for simplic-ity, the FE modelling did not ex-plicitly include the welds.

– To achieve a precise through-thick-ness stress distribution and flexural deformations of the end plate, the end plate was divided into four seg-ments through its thickness.

– The cylindrical bolt shank was ap-proximated by a 12-sided prismatic volume and divided into six ele-ments in the radial and longitudi-nal directions to capture the flex-ural deformations and the prying actions more accurately.

– The effects of adjacent surface in-teractions were modelled using

contact elements. ANSYS can model contact problems using con-tact pair elements CONTA174 and TARGE170, which pair together in such a way that no penetration oc-curs 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 consid-ered in the FEM. The effects of fric-tion were modelled using the con-tact elements mentioned. To con-sider 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-criti-cal connections for ESEP connec-tions, 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 con-traction was applied to the shanks through a negative thermal gradi-ent. The magnitude of the thermal gradient needed for the bolt preten-sioning depends on several factors such as the stiffness of the plates and the adjacent areas, assumed normal stiffness for the contact ele-ments, assumed penetration toler-ance, the length of the shank and the thermal coefficient assigned to the material of the bolt shank. Ac-cordingly, the target value was fixed through a trial-and-error pro-cess. Once the shank of the bolts contract due to this thermal change, the nut and head make contact with the column flange and

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)

49



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 preten-sioning represents the actual condi-tions of bolt pretensioning during construction and has been success-fully 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 numeri-cal modelling of the bolted connec-tions under cyclic loading demon-strated that although the FEM yields adequate results for estimating the force–deflection response of the con-nection, the procedure is very time-consuming and cannot accu-rately simulate low-cyclic fatigue phe-nomenon (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 ef-fects of cyclic fatigue (which is crucial for higher levels of stress and strain) should be negligible. The models were then subjected to a displacement-con-trolled 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 simultane-ously. 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 sec-tion 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 repre-sents the location of the brace) and the beam end in accordance with AISC 341 [1]. Both ends of the col-umn flanges are restrained in all direc-tions 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 co lumn. For the models of the test specimens, the reaction force corres ponding to the applied displacement at the beam tip was multiplied by the beam length (1.2 m) to give the connection mo-ment.

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 hard-ening rule with the von Mises yielding criterion was applied to simulate plas-tic deformations of the connection components. Steel of grade Q345 was used for the plates with high-strength grade 10.9 bolts. The reported me-chanical 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 imper-fections. Here, the connection was modelled to capture the local buck-ling 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 direc-tion 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 im-perfection 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 ap-pearance of the panel zone of the test specimen. The moment–rotation re-sponses 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 dis-placement of the beam top and bot-tom 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]

MaterialMeasured yield strength

(MPa)Measured tensile strength

(MPa)Measured elastic modulus

(MPa)

Plate (thk. 16 mm) 391 559 190 707

Plate (thk. 16 mm) 363 537 204 228

M20 bolts 995 1160 –

M24 bolts 975 1188 –



joint rotation is depicted using the solid lines in Fig. 6. The line that de-fines the joint rotation passes through the top and bottom beam flange-web intersection points. The joint rotation is the rotation of this line. This defini-tion of the joint rotation has been used previously by other researchers for other types of PR connection. The ro-tation 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 col-umn flanges at the levels of the beam flanges (in the direction of the longitu-dinal beam axis) is divided by the beam depth. The middle solid line in Fig. 6 defines the shear rotation. This line

passes through the points on the col-umn flange for which coordinates cor-respond to the top and bottom flanges of the beam. The difference between the joint rotation and the shearing ro-tation gives the gap rotation. Gap ro-tation is due to deformations of the connection components such as the axial deformations of the bolts or flex-ural 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 rela-tionships, which were considered to be bilinear in the FE models. Al-though there was a slight difference between the FEM and the test in the non-linear range of the connection be-haviour, the average difference be-tween the two methods within the non-linear range was limited to 6.4 % for specimen EPC-4 and 8.1 % for

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

51



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 accu-rate enough to simulate the connec-tion behaviour before large rotations or joint failure.

5 Design of link-to-column connections5.1 Basic rules

AISC 358 [15] rovides a method for the seismic design of ESEP connec-tions 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 mo-ment 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 re-sponse below the yield point until the ultimate strength of the link is achieved.

5.2 A design method for ESEP link-to-column connections

In AISC 358 [15], the design formulas of ESEP connections are based on yield line theory and the plastic mo-ment 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 plas-tic moment capacity of the strain-hard-ened beam Mpu is compared with Mnp. To overcome the statistical dispersion of the material and geometric proper-ties of the frame components and achieve a prescribed reliability level, the resistance reduction factors are ap-plied in design (Pirmoz and Marefat, [24]). These factors, n for bolts and d for end plate, have a probabilistic na-ture, and assuming that the calculated values for the connection are used ex-actly in practice, these reduction fac-tors could be dropped. As a result, the difference between Mpu and Mpl would be exactly 10 % for optimal design.

where:Z plastic section modulus of link

beamFye expected yield strength of steelCpr 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-

C ZF 0.9M (1)pr ye pl

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 yield-ing 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 cur-rent study, which should be elastic when the link has fully yielded. Ac-cordingly, a load factor SC is intro-duced for the design of the connec-tions 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 connec-tion region, e.g. the link-to-end plate joint vicinity and through the link it-self, cyclic response is the controlling factor.

Although very thick end plates with very large bolts may remain elas-tic, 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 as-sessed here. Five connections, re-ferred to as S1 to S5, were designed and analysed with various SC factors.

Conforming to the load and re-sistance factor design principles, AISC 358 [15] applies two resistance factors (for the end plate and the bolts) when designing the connec-tions. These factors are expected to cover the uncertainties inherent in the assumed design values and achieve a desired performance for practical connections.

5.3 Design of connections

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

Fig. 6. Definition of gap rotation



the assumption of St37 steel does not affect the fundamentals of the pro-posed design procedure. The material for the connection bolts was the same as the test bolts. In addition to the ge-ometric 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 sec-tion 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 con-nection is estimated according to Eqs. (2) and (3):

where Lp is the distance of the as-sumed lumped plastic hinge from the column face and e the link length. Other parameters were already de-fined in previous sections.

6 Performance of designed ESEP link-to-column connections

The models were loaded (using dis-placement control) until rotations 0.02 rad for inelastic rotation of the link were achieved. The total rotation of the link includes the rotation of the link itself, and the joint rotation

joint was measured using Eq. (4):

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

M SC C M2M

eL (2)u pr p

pp= +

⎡

⎣⎢⎢

⎤

⎦⎥⎥

M ZF (3)p y

e(4)jointγ = δ − ψ

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 plas-tic deformation of the link flange ad-jacent to the rib stiffener was concen-trated 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 per-formance, and the yielding was re-stricted 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 assum-ing 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

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

No. SC Cpr Fu/Fy

Bolt dia. AISC 358 (2010),

Eq. (6.10-3)

End plate thickness AISC 310 (2010),

Eq. (6.10-5) Rib thickness Lp

calculated implemented calculated implemented

S1 1.0 1.0* 14.5 16 15.5 16 12 100

S2 1.25 1.5 19.4 20 19.4 20 12 100

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.

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

53



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 dis-tribution 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 connec-tion 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 deforma-tions 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 in-terfaces. This limited amount of yield-ing 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 re-mained 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

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 in-creased 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 Ft

4(5a)p yp

p2

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

Fig. 9. Von Mises stress distributions in model S3



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.

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].

m Ft

6(5b)y yp

p2

The PEEQ Index, which represents the local strain demand, is defined as the plastic equivalent strain divided by the yield strain y. 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 fail-ure mode indicates that these con-nections, 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 stiff-ness 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 In-dex 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.

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)

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

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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 connec-tion directly affect its moment–rota-tion 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 dis-cussed in section 5.1. As shown in these plots, connection S1 cannot achieve the plastic moment capacity of the beam. However, the other con-nections have a moment capacity greater than the plastic moment ca-pacity 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 connec-tions 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 connec-tion energy denotes the area under the moment versus gap rotation curve. The ratio of the initial rota-tional stiffness of the connection (ob-tained from the moment–gap rotation curves) to the effective flexural stiff-ness 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 en-ergy 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 stiff-ness increase, so the contribution of the connection to the energy dissipa-tion decreases, which indicates greater activation of the link. For specimens S3 and S4, the contribu-tion of the connection to energy ab-sorbance was 3 %, and most of the energy was dissipated by the link beam.

7 Summary and conclusion

The performance of the ESEP con-nections as link-to-column connec-tions 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–ro-tation response to the tests resulted in good agreement between models and tests. The FE models of the ESEP link-to-column connections were cre-ated and analysed based on the veri-fied FE models. These link-to-column connections were designed for 1.0, 1.25 and 1.5 times the maximum mo-ment capacity of the link to identify a convenient load factor for the connec-tion design moment for which the connection can remain elastic. The finite element analysis of the designed ESEP link-to-column connections un-der the loading conditions of the link-to-column connections demonstrated that a connection that is designed for 1.5 times the expected applied mo-ment at a connection can behave in a primarily elastic manner. This load factor results in a connection that ex-hibits the required strength and stiff-ness to yield the link, whereas the brittle parts (bolts) remain elastic. Among the analysed models, the stiff-ness 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 demon-strated that, as the connection stiff-ness increases, so the local ductility decreases, and so the larger load fac-tors (SC) may result in brittle perfor-mance of the link-rib region. Further,

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



the connection shear force is inde-pendent of its moment–rotation re-sponse and is controlled by the shear strength of the link. A comparison of the energy dissipated by the connec-tion and the total input energy demon-strated that the (namely) elastic con-nections 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 con-nection is in agreement with the AISC 341 [1] provisions, which state that most of the energy should be dissi-pated by the link.

The numerical study in this paper analysed the performance of the ESEP connections for long link-to-

column connections and demon-strated that this type of connection has the potential to be used as the link-to-column connections.

To support the results of the cur-rent numerical study, further experi-mental studies are required to evalu-ate the cyclic performance of this type of connection and for other link lengths and the effects of low cyclic fatigue – especially the reduced fa-tigue 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 Construc-tion, 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.: Ex-perimental 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., Na-kashima, M., Suita, K.: Experimental Performance of Link-to-Column Con-nections in Eccentrically Braced Frames. Journal of Structural Engineer-ing, 132(8), 2006, pp. 1201–1211.

[6] Drolias, A.: Experiments on Link-to-Column Connections in Steel Eccentri-

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

Table 4. General characteristics of the connections

ModelInitial rotational stiffness of con-

nection (kNm/mrad)Stiffness ratio Total energy (kJ)

Connection en-ergy (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

57



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 Be-haviour of Steel Beam to Column Joints. Experimental Research, Con-struzioni Metalliche No. 2, (1987), pp. 69–90.

[8] Tsai, K. C., Popov, E.: Cyclic behavior of end-plate moment connections. Jour-nal 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. En-gineering Structures, 12 (1), 1990, pp. 15–27.

[10] Adey, B. T., Grondin, G. Y., Cheng, J. J. R.: Cyclic loading of end plate mo-ment connections. Canadian Journal of Civil Engineering, 27 (2000), pp. 683–701.

[11] Sumner, E.: Unified design of ex-tended end plate moment connections subject to cyclic loading. PhD disserta-tion, Virginia Polytechnic Institute and State University, 2003.

[12] Shi, G., Shi, Y., Wamg Y.: Behaviour of end-plate moment connections un-der earthquake loading. Engineering Structures, 29 (2007), pp. 703–716.

[13] Shi, Y., Shi, G., Wamg, Y.: Experi-mental and theoretical analysis of the moment–rotation behaviour of stiff-ened extended end-plate connections. Journal of Constructional Steel Re-search, 63 (2007), pp. 1279–1293.

[14] ANSYS User’s manual.[15] American Institute of Steel Con-

struction, Inc.: Prequalified Connec-tions for Special and Intermediate Steel Moment Frames for Seismic Ap-plications. Standard ANSI/AISC 358-10 (2010), AISC, Chicago.

[16] Pirmoz, A.: Evaluation of nonlinear behavior of bolted connections under dy-namic loads. MSc thesis (in Persian), Teh-ran, Iran, K. N. Toosi University, 2006.

[17] Danesh, F., Pirmoz, A., Saedi Dar-yan, A.: Effect of shear force on the initial stiffness of top and seat angle connections with double web angles. Journal of Constructional Steel Re-search, 63 (2007), pp. 1208–1218.

[18] Pirmoz, A., Saedi Daryan, A., Maza-heri, A., Ebrahim Darbandi, H.: Behav-ior of bolted angle connections sub-jected to combined shear force and moment. Journal of Constructional Steel Research, 64 (2008), pp. 436–446.

[19] Salajegheh, E., Gholizadeh, S., Pir-moz, A.: Self-organizing back propaga-tion networks for predicting the mo-ment–rotation behavior of bolted con-nections. Asian Journal of Civil Engineering (Building and Housing), 9 (2008), pp. 629–645.

[20] Pirmoz, A., Danesh, F.: The seat an-gle 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., Mo-hammadrezapour, E., Saedi Daryan, A.: Moment–rotation behavior of bolted top-seat angle connections. Jour-nal 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 De-sign of Tall and Special Buildings, 20 (7), 2011, pp. 767–783.

[23] Pirmoz, A.: Performance of bolted angle connections in Progressive col-lapse of steel frames. The Structural Design of Tall and Special Buildings, 20 (3), 2011, pp. 349–370.

[24] Pirmoz, A., Marefat, M. S.: Reliabil-ity assessment of compression columns in seismic EBFs. Journal of Construc-tional 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 un-reinforced 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-col-umn connections; EBFs; extended stiff-ened end-plate connections; non-linear finite elements

Authors:Akbar PirmozDepartment of Civil EngineeringThe Catholic University of America620 Michigan Avenue, NEWashington, DC 20064, USA

Parviz AhadiDepartment of Civil Engineering, Germi BranchIslamic Azad University, GermiArdebil, Iran

Vahid FarajkhahDalhousie UniversityDepartment of Civil and Resource Engineering1360 Barrington St.Halifax, NS, Canada B3J 1Z1

Articles

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

DOI: 10.1002/stco.201400005

This paper looks at the problem of connection flexibility in steel- concrete bridge girders under moving loads. The static action of the load changing location on the structure is considered. An an-alytical 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 mate-rials with different physical characteristics interacting due to the specially designed connectors assuring their perma-nent cooperation [1]. A typical composite bridge girder consists of a steel beam and a concrete plate. Perfect beam-plate interaction is a theoretical case that would require the use of non-deformable connecting elements. The con-nection is thus always deformable (flexible), resulting in partial interaction of the girder’s elements. Headed shear studs, very common in bridge structures, can be consid-ered deformable connectors, as their rigidity does not pre-vent shear slip at the steel-concrete interface. A stiffer con-nection 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:

k Ts =

δ (1)

As the shear force is distributed along the interface

t dTdx

=

(2)

so the connection stiffness is defined as

Czesław MachelskiRobert Toczkiewicz*

k t=δ

(3)

In the general case relation T( ) is non-linear and the stiffness of a connector decreases along with the load in-crement. In the range of forces resulting from live loads on bridges, these changes are not significant and a con-stant stiffness ks can be assumed. The stiffness of the beam-plate connection is influenced by many factors, including type of connector, concrete properties [4], con-figuration 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 connec-tion 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 di-rected 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 dis-placements does not allow for an assessment of beam-plate interaction due to the change in flexural stiffness of the girders, resulting, among other things, from the coop-eration of non-structural elements [14]. In this case strain measurements in beams are relevant, which is not com-mon practice. Further, with few exceptions [15], no stud-ies 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]. Anal-yses 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].

Effects of connection flexibility in bridge girders under moving loads


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


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

aA

A Aad

pn

b pn=

+ (4)

and the moment of inertia of a fully composite girder is

I I I aa Ay0

b pn d b= + +

(5)

In the case analysed, the resultant internal forces are sep-arated into two subsystems: beam and plate. Internal forces are equivalent to the external global bending mo-ment M, meeting the conditions of static equilibrium [19]. Using the condition of strain discontinuity in the beam-plate interface

– ddx

1k

dtdxbp b

gpdΔε = ε ε = δ =

(6)

the following equation is obtained:

NE A

–M v

E I–

N

E A–

M y

E I1k

dtdx

.b

b b

b g

b b

p

p p

p d

p p=

(7)

It is also assumed that all elements of the girder have the same radius of curvature:

ME I

ME I

M

E Ib y

b

b b

p

p p= =

(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):

tdNdx

b=

(9)

Hence, the equation that combines axial force Nb with bending moment M takes the following form:

Ek

·I I

ad N

dx– 1

kdNdx

dkdx

–I

a AN M 0 (10)b b pn

2b

2b y

0

d bb

+ ⎛

⎝⎜

⎞

⎠⎟ + =

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 repre-senting the ratio between the internal forces Nb and Mb in the steel part of the girder is defined as

aNM

b

bμ =

(11)

In order to obtain a dimensionless value of index , axial force Nb is multiplied by distance a.

A typical diagram of internal forces in the girder cross-section versus index is shown in Fig. 2. The charac-teristics of the girder’s elements are given in Table 1. A

Analytical models often aim at obtaining exact rela-tionships that allow for the determination of displacements and forces for basic load cases only and for specific func-tions 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 beam-plate 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 con-cerning the action of moving forces changing their location on the structure, the use of influence functions is proposed.

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 com-posite 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 con-sidered in this paper. After the modular ratio implementa-tion, transformed values for cross-sectional area of con-crete plate Apn Ap/nbp and moment of inertia of concrete

Op

Ob

vd

Eb, Ab, Ibvg

ydyg

O

εb

a'dad

aag

∆εbp

Ep, Ap, Ip

Mb

Nb

M

Mp

Np

d

εbg

εpd

εpg

y

z

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



Eq. (10), providing the solution for the partially com-posite girder subjected to bending, is solved in the analysis using the finite difference method [19]. This method allows the function (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 char-acteristics Ib and Ab (and hence distance a) and connec-tion 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 connec-tion 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 (k, x) are shown in Fig. 3. It can be seen that along the whole length of the girder, index values fulfil the relationship (x) 0. Both the decrease in index and the range of de-

crease along the girder depend on the connection stiffness k(x). The lowest values of are obtained in the section where force P is applied. Function (k, x) results directly from the functions of internal forces Nb(x) and Mb(x) de-termined 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 (x) 0.

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-

bending moment M 1 MNm is assumed. The diagram shows that the increase in 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 and stabi-lize as increases.

The index has two characteristic values [15]: – in the case of full beam-plate interaction, then

a · a · AI0d b

bμ = μ =

(12)

– in the case of no interaction (when Nb 0), then 0 according to Eq. (11).

Values of 0 mean that there is partial beam-slab inter-action and that shear slip occurs at the steel-concrete in-terface. Examples of functions (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 depends lin-early on the position of the girder’s neutral axis described by distance a d (see Fig. 1), according to the relationship

a· I

a · Aad

b

bd

0′ =

μ= μ

μ

(13)

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

4 Function of partial interaction (x)

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 .

0.400

0.8 1.61.2 2.0 2.4μ0

=2.0

36

1.0

Mb

a·Nb [MNm]

a·Nb

Mb

μ

0.2

0.4

0.6

0.8

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

Table 1. Geometrical and physical characteristics of girder analysed

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

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

0 2 4 6 8 10 12 14

x [m]

1000

2000

5000

10000

20000

k [MN/m2]

x=L

/2

μ = μ0

P

L/2 L/2

k P

L/2 L/2

k

μ [-

]

Fig. 3. Effect of a single point load



distance xP from the support. Fig. 6 shows (x) diagrams generated for three positions of the vehicle on the girder. The graphs indicate a local reduction in value in sections where the forces are applied, depending on the load posi-tion. The results were obtained assuming a constant con-nection stiffness k and constant flexural stiffness of the girder. In real bridge structures these assumptions are usu-ally not satisfied.

Fig. 7 shows diagrams of function (x) for two posi-tions 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

lope of shear force t, resulting in a higher connection stiff-ness in the support zones. Therefore, the connection stiff-ness function k(x) usually changes along the girder.

The example considers a girder with a constant con-nection stiffness k 1000 MN/m2, which increases in the support zones to k 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 beam-plate interface – in the upper flange of the beam b

g and on the lower edge of the plate p

d. The values of pd 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 ( 0) appears over the whole depth of the beam in the range of connection stiffness change.

Fig. 5 shows (x) diagrams obtained for the case illus-trated in Fig. 4 for different values of nc. The analyses con-ducted show that a step change in k along the girder re-sults in local extreme values of in the zone of the connec-tion stiffness change. The results indicate an increase in along with an increasing change in the connection stiffness expressed by nc. The (x) diagrams show that in the zone of the connection stiffness change, values 0 appear which are higher than in the case of full steel-concrete in-teraction. 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 dec-rement in shear slip in the support zones of the girder – an effect of larger connection stiffness k k · nc in these parts of the beam.

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 (x) pre-sented in Fig. 6. A three-axle vehicle (front axle load P/2, rear axles load P) is considered in this example [15]. Con-figuration of axle loads and their values make the resultant load coincident with the position of the middle axle at

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14x [m]

Nb

[MN

]

Mb

[MN

m]

Nb

Mb

x=L/

2

bc

Nb

Mb

P

L/2 L/2

nc kk

bC bC

nc k

-10

-8

-6

-4

-2

0

20 1 2 3 4 5 6 7 8 9 10 11 12 13 14

x [m]

σ [M

Pa]

x=L/

2

bc

σbg

nbpσpd

P

L/2 L/2

nc kk

bC bC

nc k

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

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

x [m]

μ [-

]

nc=1

nc=2

nc=5

nc=20

change of connection stiffness

x=L/

2

bc

P

L/2 L/2

nc kk

bC bC

nc k

Fig. 5. Diagram of (x) for beam with step change in con-nection stiffness

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28x [m]

μ [-

]

xp=10 m

xp=14 m

xp=18 m

x=L/

2

PP 0.5P

xp

k b 2b

μ=μ

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



From Eq. (11), the value of ip at section i for any configu-ration of forces Ps and for any function k(x) can be calcu-lated thus [15]:

aN

M

N (P )

M (P )a s 1, 2, , nip

bip

bip

bi

ss

bi

ss

∑∑μ = = = …

(21)

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

N (P )

M (P )aij

bi

j

bi

j

μ =

(22)

– in the case of two forces Pj and Pk

N (P ) N (P )

M (P ) M (P )ai

jk bi

j bi

k

bi

j bi

k

μ =+

+

(23)

Introducing forces Nb0ik and Mb0

ik at section i resulting from unit force Pk0 1 at point k, for any force Pk, we ob-tain

M (P ) M · Pbi

k b0ik

k=

(24)

and

N (P ) N · Pbi

k b0ik

k=

(25)

and hence Eq. (23) is transformed into

N P N P

M P M Pai

jk b0ij

j b0ik

k

b0ij

j b0ik

k

μ =+

+

(26)

When Pj Pk, it can be seen that index does not depend on the value of P

N N

M Mai

jk b0ij

b0ik

b0ij

b0ik

μ =++

(27)

Introducing Eq. (11) transformed into

aN · Mb0ij

ij b0ij= μ

(28)

From the diagrams we reach the conclusion that in a pris-matic girder with constant connection stiffness, the follow-ing principle is valid:

(P ) (P )i j j iμ = μ

(14)

and hence the value of 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

N (P )

M (P )

N (P )

M (P )bi

j

bi

j

bj

j

bj

i

=

(15)

also appears when Pi Pj.In the girder with a step change in connection stiff-

ness, the diagrams indicate a lack of the principle described by Eq. (14). The difference

(P ) – (P )ij i j j iΔμ = μ μ

(16)

in the example given in Fig. 7 is equal to

ij 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:

N (P ) N (P ) N (P P )bi

j bi

k bi

j k+ = +

(17)

and

M (P ) M (P ) M (P P )bi

j bi

k bi

j k+ = +

(18)

The application of influence functions is thus valid in the case of moving loads.

Using the principle of the additivity of effects of sev-eral point loads, the values of Nb

i(p) Nbip and Mb

i(p) Mb

ip, as in Eqs. (17) and (18), can be calculated for sec-tion i according to

N N (P ) s 1, 2, 3, , mbip

bi

ss

∑= = …

(19)

and

M M (P ) s 1, 2, 3, , mbip

bi

ss

∑= = …

(20)

1.4

1.6

1.8

2.0

2.2

2.4

2.6

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28x [m]

μ [-

]

Pi

Pj

x jx i

μj(Pi)=2.028

μi(Pj)=2.028 Pj k

i j

Pi

1.4

1.6

1.8

2.0

2.2

2.4

2.6

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28x [m]

μ [-

]

Pi

Pj

x jx i

μj(Pi)=2.006

μi(Pj)=2.096

Pj

k1k2

k3

i j

Pi

μ=μ

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



Fig. 9 shows typical diagrams of influence lines for index

i(x0) at section i and j(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 (x0) 0 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 (x0) 0, especially at section j, which is situated in the zone of connection stiffness change.

Live loads on bridges consist of groups of forces mov-ing along the span. In the case of several point loads, the value of index i(xp) ip at point i (xp indicates the posi-tion of the load) is calculated according to Eq. (21), which after substitution of Eq. (28) is transformed into

M · P ·

M · Ps 1, 2, 3, , mip

b0is

s iss

b0is

ss

∑∑μ =

μ= …

(36)

Typical influence functions i(xp) and j(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

and

aN · Mb0ik

ik b0ik= μ

(29)

then Eq. (27) depends on the values of ij and ik calcu-lated for the individual components of the load Pj and Pk when Pj Pk:

M M

M Mijk ij b0

ijik b0

ik

b0ij

b0ik

μ =μ + μ

+

(30)

In the case of any value of forces Pj Pk, from Eq. (26), using Eqs. (28) and (29), we obtain the following relation-ship, depending on the values of index ij and ik:

M P M P

M P M Pijk ij b0

ijj ik b0

ikk

b0ij

j b0ik

k

μ =μ + μ

+

(31)

On the basis of Eq. (31), the calculated value iik at the

point of acting force Pi with additional symmetrical load Pk Pi

M P M P

M P M Piik i b0

iii ik b0

ikk

b0ii

i b0ik

k

μ =μ + μ

+

(32)

is different from the value of kki (at the point of acting

force Pk)

M P M P

M P M Pkki kk b0

kkk ki b0

kii

b0kk

k b0ki

i

μ =μ + μ

+

(33)

despite the load symmetry and thus conformity ii kk and Mb0

ii Mb0kk, and according to Eq. (14) Mb0

ik Mb0ki.

This is illustrated in Fig. 8, where the difference

–M M

M M–

M M

M Miik

kki ii b0

iiik b0

ik

b0ii

b0ik

ii b0ii

ik b0ik

b0ii

b0ik

Δ = μ μ =μ + αμ

+ ααμ + μ

α + (34)

is marked for Pk Pi. In the case analysed (girder with constant stiffness of connection k(x) k 2000 MN/m2 and assuming 0.5), this difference is equal to i

ik –

kki 1.610 – 1.724 0.114. The proportion of the forces

is therefore important.

6 Influence functions of index

Influence functions are a useful tool for illustrating the ef-fects 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 compos-ite 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 func-tion (x) required, being the influence line of the partial interaction index, is composed of values i(x0) i0 (x0 indicates position of force P0), defined as [15]

(x )aN (x )

M (x )i 0bi

0

bi

0

μ =

(35)

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28x [m]

μ [-

]

Pi

Pk

Pi+Pk

Pi+0.5Pk

x kx iμi(Pi)=1.550 μi(Pi+0.5Pk)=1.610

μi(Pi+Pk)=1.656

μk(Pi)=1.550

μk(Pi+0.5Pk)=1.724

μk(Pi+Pk)=1.656

∆

Pkk

i k

Pi

c c

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

1.2

1.4

1.6

1.8

2.0

2.2

2.4

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28x0 [m]

μ [-

]

a)

a)

b)

b)

k1k2

k3

i j

k

i j

P=1 P=1

x0 x0

xjxi

μi(xj)=2.096

μi(xj)=2.028μj(xi)=2.006

μj(xi)=2.028

μi(x0)

μj(x0)

μi(x0)

μj(x0)

a) b)

μ=μ

Fig. 9. Influence lines of index



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 were calculated according to the transformed Eq. (13). In this way, in situ influence functions of index (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 defor-mation 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 characteris-tics 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

lines i(x0) and j(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 val-ues than a group of forces.

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 four-axle 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 sup-port P, equal to xp 4.25 3(n – 1) , are considered. To determine the forces in the structure, the spans were dis-cretized as a grillage consisting of bar elements with a deck slab discretized as plate elements. FEM calculations re-sulted 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 (x, xp) were calculated.

Diagrams of the index (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 de-sign 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 index are visible. The results can be arranged in specific groups: in the area of acting load (x, xp) 0 and in the areas of connection stiffness change (x, xp) 0.

Fig. 11b presents influence functions of the index (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

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

xp [m]x0 [m]

μ [-

]

a)

a)

b)

b)

k1k2

k3

i ji j

P=1k1

k2k3b 2b

x0 xp

xjxi

μi(x0)

μj(x0)

μi(xp)

μj(xp)

a) b)

μ=μ

Fig. 10. Comparison of influence lines and influence func-tions of index [15]

1.6

1.8

2.0

2.2

2.4

5 10 15 20 25 30xp [m]

μ [-

]

x=4m

x=10m

x=12m(measurementsection)x=16m

1.6

1.8

2.0

2.2

2.4

2.6

2.8

0 2 4 6 8 10 12 14 16 18 20 22 24x [m]

μ [-

]

n=3

n=4

n=5

n=6

n=7

μ0=2.070

μ0=2.070

k1=4000 MN/m2

3

k2=2500 MN/m2k3=1000 MN/m2

4 5 6 721

mea

sure

men

tse

ctio

n

24.0 m

P F

4.25xP [m]:n:

7.25 10.25 13.25 16.25 19.25 22.25

xp

n

k2=2500 MN/m2

mea

sure

men

tse

ctio

n

a)

b)

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



Only a load moving along the structure (generation of in-fluence function) gives information on the range of partial interaction characterized by the proposed index .

The index used in the analyses is sensitive to the local effects of flexible connection. It is not possible to identify these local effects by measuring deflection, which depends on the global flexural stiffness of a girder, and in real struc-tures is often influenced by the cooperation of non-struc-tural elements.

It should be mentioned that results in the form of a range of index values (influence function) do not allow us to estimate the connection stiffness k. The influence function of index obtained as a result of the analysis under load changing its position on the structure shows whether the connection stiffness k is constant along the girder (then 0) or changes along the girder, which is indicated by the relationship 0. The basis for the iden-tification 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 cross-sectional area of beam / plateIb/Ip moment of inertia of beam / plateEb/Ep modulus of elasticity of steel (beam) / concrete

(plate)Iy moment of inertia of partially composite girderIy

0 moment of inertia of fully composite girderL spanM external bending moment in girderMb/Mp bending moment in beam / plateNb/Np axial force in beam / platea distance from centroid of beam to centroid of

platea d distance from neutral axis of girder to centroid of

beam in partially composite girderk connection stiffnessvg/vd distance from centroid of beam to top / bottom

edge of beamyg/yd distance from centroid of plate to top / bottom

edge of platet 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 Scientific Publishers, Oxford, 2004.[2] Galjaard, H. J. C., Walraven, J. C.: Behavior of different types

of shear connectors for composite structures. Proc. of Intl. Conf. on Structural Engineering, Mechanics & Computation “SEMC 2001”, Cape Town, South Africa, 2–4 Apr 2001, pp. 385–392.

[3] Lorenc, W.: Boundary approach in shape study of composite dowel shear connector. Archives of Civil and Mechanical En-gineering, IX(4) (2009), pp. 55–66.

[4] Hegger, J., Goralski, C., Rauscher, S., Kerkeni, N.: Finite-Elemente-Berechnungen zum Trag- und Verformungsverhal-ten von Kopfbolzenduebeln. Stahlbau, 73(1) (2004), pp. 20–25.

higher flexural stiffness of the girders. Even between the test results of both identical structures (viaduct N and via-duct S), considerable differences were noticed [15]. An-other problem is the estimation of actual connection stiff-ness k(x) taken into account in the analyses, which de-pends 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 specific feature of composite structures with flexible 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 stiff-ness. To identify the effects of flexible connection, a dimen-sionless index , defined 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 equili-brated with forces acting in two subsystems of different physical and geometrical characteristics (steel beam and concrete plate). Numerical analyses illustrating the effects of quasi-static loads changing location along the girder al-low us to formulate the following detailed conclusions: – The value of index at the point of acting force is re-

duced locally ( 0), which depends on the beam-plate connection stiffness k.

– A change in connection stiffness along the beam results in the local extreme value of the index 0 in the zone of the stiffness change.

– The function (x) is subjected to local fluctuations along the girder, taking both values x 0 and (x) 0, depending on the connection stiffness function k(x).

– It is advisable to take into account a load changing its position along the girder, which allows a full range of values to be obtained; the use of the influence function is effective in this case.

– The function (x) is related to the location and configu-ration 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 infor-mation on the partial interaction at the section analysed.

1.6

1.8

2.0

2.2

2.4

2.6

5 10 15 20 25 30x p [m]

μ [-

]

Viaduct S

Viaduct N

xp

μ0=2.070

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



[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 flexi-bility in steel-concrete composite beams due to live loads. Ar-chives 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 Construc-tional Steel Research, 36 (1996), pp. 15–29.

[21] Kim, B., Wright, H., Cairns, R.: The behaviour of through-deck welded shear connectors: an experimental and numeri-cal study. Journal of Constructional Steel Research, 57 (2001), pp. 1359–1380.

[22] Shim, C. S., Lee, P. G., Chang, S. P.: Design of shear con-nection 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 Engi-neering, 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 TechnologyWybrzez·e Wyspianskiego 27, 50-370 Wrocław, [email protected]

Robert Toczkiewicz, PhD, Civ. Eng.Research & Design Office Mosty-WrocławKrakowska 19-23, 50-424 Wrocław, [email protected]

[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 Engineer-ing, 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 consider-ing 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 inter-action stresses in continuous composite beams under service-ability 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 Re-search, 49 (1999), pp. 241–254.

[12] Nie, J., Fan, J., Cai, C. S.: Stiffness and deflection of steel-concrete composite beams under negative bending. Jour-nal 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 ef-fects in steel-concrete girders according to in-situ tests of a road bridge. Proc. of 5th European Conf. on Steel & Compos-ite 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.


DOI: 10.1002/stco.201620009

Reports

Simple Bridges

Andreas KeilSven PlieningerSebastian LindenChristiane 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 berger-mann 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 pre-stressed 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 structur-ally 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 appro-priate appearance in its particular context, the local situ-ation 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 some-times a simple approach, carefully executed, can produce interesting and innovative solutions.

2 Three footbridges across the Emscher in Dortmund2.1 Scope

Between 2005 and 2011 an artificial shallow lake of 24 ha was created on the area of the former steel mill Her-mannshütte PHOENIX Ost in Dortmund. This lake forms the centre of a new recreational area with residen-tial and commercial buildings. The uncovering and re-turning 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.

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 connec-tion 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. Construc-tion tolerances can be compensated by these rotatable

Fig. 1. Emschersteg (© sbp)

Reports


connections which also guarantee a smooth load applica-tion 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 trans-verse 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

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 unobtru-sive from a distance, emerging cautiously and unimpos-ingly from the shallow meadow. At a closer view, however, the technological character and the sophisticated connec-tion details stand out, particularly the hanger details.

3 Fehrlesteg in Schwäbisch Gmünd3.1 Design

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

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 devi-ation, creating a balcony-shaped cantilever on the central island.

At both ends the stress ribbons rest on slender con-crete saddles which protrude from the abutments that are concealed by the river banks.

3.2 Construction

The stress ribbons consist of two parallel 400 40 mm steel plates in grade S355, which were pre-curved in the work-shop and anchored at the abutments and the central sup-port. With a sag of 40 and 19cm respectively, the maxi-mum 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

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

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

Reports


back-anchored in cast-in steel parts. The hammer-head-shaped anchorage allows for adjusting the final length to the nearest millimetre.

At the central support, the stress ribbons are con-nected 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 dimen-sions of 290 80 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 neo-prene insert within the joints to improve the damping be-haviour 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 individ-ual handrail segment having sliding joints towards the ad-jacent one (Fig. 6). The friction in these sliding joints has a

positive impact on the damping behaviour of the light-weight 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 sophisti-cated and innovative structure. With its slenderness, trans-

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

Fig. 5. Fehrlesteg – section (© sbp)

Fig. 6 7. Fehrlesteg – railing and bridge lighting (© sbp/Michael Zimmermann)

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 out-standing 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 Esslingen4.1 Scope

In 2009 a bridge design competition was tendered in Ess-lingen, 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 mu-nicipal 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.


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 struc-turally and architecturally on the eastern bank of the ca-nal. Facing to the west at the connection to the Maille-Park the bridge only lightly rests on the bank like a canti-levered 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 in-serted into a steel crown that has been cast into the abut-ment.

The pendulums on the back side of the abutment con-nect 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 superstruc-ture to slide in the horizontal direction. These are inserted into a prefabricated steel abutment block that had previ-ously been aligned and cast in its exact position.

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

4.3 Finishing and Installation

The unobtrusive filled-rod railing was welded to the super-structure in the workshop. Through numerous small slid-ing 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 prefab-ricated superstructure, including railing, corrosion pro-tection 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. 8. Margarethe-Müller-Bull-Steg (© Ingolf Pompe)

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

Reports


5 Gert-Schwämmle-Steg in Hamburg5.1 Scope

From 2006 to 2013, Hamburg’s largest river island Wil-helmsburg 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 redevel-oped park area to the centre of Wilhelmsburg. Then it crosses the approx. 25 m wide river Rathauswettern just north of the lake Rathaussee.


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 sec-tion 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 con-straints 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

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

into consideration with regard to the soil–structure inter-action of this integral bridge.

5.3 Finishing and Installation

A steel box section connected to the face side of the super-structure 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 super-structure were all cast in-situ. This implied that the super-structure had to remain in the formwork until the con-crete had cured and all pre-stressing works had been com-pleted.

5.4 Summary

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 sus-tainable construction with minimal maintenance require-ments.

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.

6 Bleichwiesensteg in Backnang6.1 Scope

The new Bleichwiesensteg in Backnang connects the rede-signed Bleichwiese with the tree-covered rear of the Stifts-hof. As an attractive link it thus establishes a direct con-nection between the historic centre of the city and the re-cently 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.

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

Reports


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.

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 abut-ments 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 stabi-lized through an orthotropic deck.

The bridge’s structural and creative characteristics be-come apparent in the division of the superstructure into two almost identical parts. These are completely prefabri-cated, separately delivered, lifted and then assembled to form a whole system on site.

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

The distinctive central opening is therefore not an only eye-catching design but particular intelligent, offering effi-cient fabrication and installation procedures (Fig. 14).

Using a compression strut as top chord and visible pinned connections, the maximum bending moment is vis-ually 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).

6.3 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).

Fig. 13. Bleichwiesensteg (© sbp/Michael Zimmermann) Fig. 14. Bleichwiesensteg – central connection detail(© sbp/Michael Zimmermann)

Reports


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. Striv-ing 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. 15. Bleichwiesensteg – section (© sbp)

Fig. 16 17. 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; connec-tion details

AuthorsDipl.-Ing. Andreas Keil Dipl.-Ing. Sven Plieninger Dipl.-Ing. Sebastian Linden Dipl.-Des. (FH) Christiane Sander

schlaich bergermann partner Schwabstraße 43 70197 Stuttgart

ECCS news


Events

SDSS 2016 – the International Colloquium on Stability and Ductility of Steel Structures30 May–1 June 2016, Timisoara, Romania

The series of International Colloquia on Stability and Ductility of Steel Struc-tures has been supported by the Struc-tural Stability Research Council (SSRC) for many years and is intended to sum-marize the progress in theoretical, nu-merical 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 develop-ment and application of rules and rec-ommendations either appearing in re-cently published codes or specifications or about to be included in their upcom-ing versions. This international collo-quium series began in Paris in 1972.

SDSS 2016 is being jointly organized by the Politehnica University of Timisoara, Department of Steel Struc-tures and Structural Mechanics, in co-operation with the Romanian Academy, Timisoara Branch, with the support of the European Convention of Construc-tional Steelwork (ECCS), through the Structural Stability Technical Commit-tee (TC8), and the SSRC.

Further information: www.ct.upt.ro/sdss2016

8th International Conference on Bridge Maintenance, Safety and Management26–30 June 2016, Foz do Iguaçu, Brazil

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 mil-lion litres per second, is near the conflu-

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 In-dians since ancient times. The triple bor-der between Brazil, Argentina and Para-guay is a melting pot for Lebanese, Chi-nese, Germans, Italians, French, Swedes, Portuguese and Ukrainians, also for Christians, Muslims and Bud-dhists. Foz do Iguaçu is home to the Itaipu Dam, the world’s largest hydro-electric 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 BoardChair: Prof. M. Veljkovic

PMB – Promotional Management BoardChair: Mr. Yener Ger’es

TC3 – Fire SafetyChair: Prof. Paulo Vila RealSecretary: Martin MensingerNext meeting: 22–23 September 2016, Istanbul, Turkey

TC6 – Fatigue & FractureChair: Dr. M. LukicSecretary: Stephen Lochte-HoltgrevenNext meeting: Spring 2016, venue will be announced later

TC7 – Cold-formed Thin-walled Sheet Steel in BuildingsChair: Prof. J. Lange

TWG 7.5 – Practical Improvement of Design ProceduresChair: Prof. Bettina BruneNext meeting: June 2016, Manchester, UK

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

TC8 – Structural StabilityChair: Prof. Bert SnijderVice-Chair: Richard StroetmannSecretary: Dr. Markus Knobloch

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

TWG 8.3 – Plate BucklingChair: Prof. U. KuhlmannSecretary: Dr. B. Braun

TWG 8.4 – Buckling of ShellsChair: Prof. J. M. RotterSecretary: Prof. S. Karamanos

TC9 – Execution & Quality ManagementChair: Mr. Kjetil MyrheNext meeting: 26 April 2016, Brussels

TC10 – Structural ConnectionsChair: Prof. Thomas UmmenhoferSecretary: Mr. Edwin BelderNext meeting: 10–11 March 2016, Ljubljana, Slovenia

TC11 – CompositeChair: Prof. Riccardo ZandoniniVice-Chair: Prof. Jean-François DemonceauSecretary: Prof. Graziano LeoniNext meeting: 29 April 2016, Warsaw, Poland

TC13 – Seismic DesignChair: Prof. R. LandolfoSecretary: Dr. Aurel StratanNext meeting: 7–8 April, Naples, Italy

TC14 – Sustainability & Eco-Efficiency of Steel ConstructionChair: Prof. Luís BragançaSecretary: Ms. Heli Koukkari

TC16 – Wind Energy support structuresChair: Prof. Peter SchaumannVice-Chair: Prof. Milan VeljkovicSecretary: Ms. Anne Bechtel

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 orga-nized 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 morn-ings 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, acknowl-edged the work of Prof. Peter Schau-

ECCS news


tects and engineers to use more steel within the bridge construction sector, thus making the steel industry more competitive.

The European Convention for Con-structional 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 struc-tures were primarily designed or fabri-cated in the ECCS Full Member coun-tries. 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 outstand-ing steel bridge project submitted from ECCS Full Member countries and inter-national contestants in order to credit their collaboration and the excellence of their work. The national member is re-sponsible for approving each entry sub-mitted to indicate that it complies with the regulations of the awards.

For the first time this year, interna-tional contestants are also invited to submit their entries for a special Inter-national Bridge Award. For interna-tional entries, the ECCS Architecture and Awards Committee is responsible for ratifying each international bridge entry submitted to indicate that it com-plies with the regulations of the awards.

The ECCS International Jury will se-lect 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 2016Press release and documentation: by end of June 2016Presentations and additional files: by 20 August 2016Awards ceremony: Stockholm, Sweden, 14 November 2016

Regulations

1. Operation of the AwardsThe Awards are open to steel and com-posite 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 sub-mission procedure stated below.

Steel bridge projects located outside the member country are eligible if they have been designed or fabricated in an

experimental campaign carried out on a special slim-floor system. Gianluca Ranzi reported on models for servicea-bility 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 pro-gress in the revision of Eurocode 4; fu-ture work and possible collaboration with the ECCS-TC11 were discussed.

TC13

TC13 consists of 19 full and 15 corre-sponding 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: Earth-quake resistance design of structures”.

There are four Technical Working Groups operating within the committee: – TWG1 Members and connections

(convenor Dan Dubina) – TWG2 Traditional typologies (conve-

nor 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 sys-tematic review process. Cooperation was also strengthened with TC11 “Com-posite Structures”, with a view to im-proving seismic design rules for compos-ite construction.

Further ECCS news

European Steel Bridge Awards 2016

Call for Entries

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 re-cognition to steel and composite bridges while emphasizing the various advan-tages of steel in construction, produc-tion, economy, sustainability and archi-tecture, and to encourage clients, archi-

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 infor-mation for young engineers and begin-ners.

Recent topics discussed within TC3 include the following: – Fire resistance of composite inte-

grated 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 com-posite 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 in-

tumescent coatings – Behaviour of cold-formed steel ele-

ments 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 asso-ciations 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 commit-tee 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 cur-rently monitoring progress in relevant research.

During the meeting, five other pres-entations were delivered by members and guests. Roland Abspoel talked about recent research into composite slabs carried out at TU Delft. Jean-François Demonceau presented an in-vestigation about effective width of slabs in composite beam-to-column joints. Simo Peltonen showed the results of an

ECCS news


ECCS Full Member (National Associa-tion).

In cases where the partners of the project (project owner, general contrac-tor, architectural firm, structural engi-neering 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, the Full Members may submit the

entry together; one of Full Members may submit

in coordination with the other; the fabricator for the project shall

be the determining factor for se-lecting 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 con-testants for an International Bridge Spe-cial Award.

The structure must have been com-pleted and gone into service within the last three years, in the period between 31 May 2013 and 31 May 2016. Previ-ous entries are not eligible.

2. Jury and evaluationThe 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 representa-tive 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 con-struction.

– To encourage clients, architects and engineers to use more steel within the entire steel construction sector,

thus making the steel industry com-petitive.

– To emphasize the advantages of steel for construction, production, econ-omy and architecture.

– To adhere to the principles of sustain-ability 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 Mem-bersECCS Full Members have the responsi-bility: – 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 publica-tions and press releases on a national level (linking to the ECCS website).

4. AwardsAwards will be made in two main cate-gories 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, refurbish-ment 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 En-

tries 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 Inter-national Jury by 17 June 2016.

– Official information and press release by ECCS/National Associations re-lated to the winning entries by the end of June 2016.

– Uploading of presentations and docu-mentation for the ceremony and the publication by 20 August 2016.

– ECCS Steel Bridges Awards Cere-mony held in Stockholm, Sweden, on 14 November 2016.

6. Submission of entriesEntries 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 men-tioned above may submit entries directly to the ECCS by uploading entries that comply with the rules stated in this doc-ument.

7. Submittal requirementsThe entry documents have to be up-loaded to the ECCS website (www.steel-construct.com) by the Full Member or international contestants prior to 27 May 2016. The application scheme will be online by March 2016 at www.steel-construct.com.

The submission must contain key in-formation, a brief description, high-reso-lution photographs, design drawings and technical data. These documents are for publication and must therefore be of the highest quality and free of copy right charges. The material submit-ted 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, per-son to contact, phone, fax and e-mail)

– Name and location of fabricators, structural engineering firm, architec-tural firm, general contractor and project owner

– Main key data and technical informa-tion such as names of companies in-volved, date of completion, dimen-sions, tonnage, main structural con-cept, etc.

7.2 Project descriptionIncludes a brief description of the loca-tion, the function, an explanation of how the structure satisfies the design


ECCS news/Announcements

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

Announcements

International Colloquium on Stability and Ductility of Steel Structures 2016

Location and date:Timisoara, Romania, 30 May 1 June 2016

Information and registration:www.ct.upt.ro

XIII International Conference on Metal Structures

Location and date: Zielona Góra, Poland, 15 17 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, 26 30 June 2016

Information and registration:www.iabmas2016.org

ISMA Noise and Vibration Engineering Conference – ISMA2016

Location and date:Leuven, Belgium, 19 21 September 2016

Information and registration:www.isma-isaac.be

INALCO 2016 – 13th International Aluminium Conference

Location and date:Naples, Italy, 21 23 September 2016

Information and registration:www.inalco2016.it

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 reha-bilitation of existing structures were pre-sented. 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 con-trol (OPUS)

– Prefabricated steel structures for low-rise buildings in seismic areas (PRE-CASTEEL)

– Steel solutions for seismic retrofit and upgrading of existing structures (STEELRETRO)

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

brief and distinguishing/unique aspects of the structural system, aesthetic con-siderations 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 up-loaded for publication by 20 August 2016.

7.3 PhotographsA minimum of 12 high-resolution photo-graphs in electronic format (minimum 3600 x 2400 pixel or 300 dpi resolution, .eps, .jpg or .tif) taken during construc-tion and after completion must be up-loaded. The entrant must clear copy-right regarding photos, slides and draw-ings 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 mate-rials submitted for promotional pur-poses.

7.4 DrawingsProvide a site plan, principal elevations, sections (1:100 or 1:200) and general ar-rangement. In addition, show typical and innovative details (1:50), typical steel construction detail (1:20) with leg-ends apart in English. All drawings should be provided in electronic format (600 dpi, .eps or vectorized .pdf (possi-bly .dxf), black/white; without descrip-tion and measure layer).

7.5 PresentationsPowerPoint or PDF presentations or film clips to be used during the Awards Ceremony must be uploaded by 20 Au-gust 2016, together with any additional material that should be included with the press package. Presentations are lim-ited to 3 minutes for each entry. They may include incidental music to be played during the Awards Ceremony

8. ContactFor further information, contact the ECCS Design Award Committee (AC-4), Chair Lasse Kilvær (Norway): [email protected].

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

Madrid, Spain

Cluj-Napoca, Romania

Coimbra, Portugal


News

operational in 2018 and will consist of three or four wind turbines on floating foundations, accounting for a total ca-pacity of 25 MW. The project is led by a consortium of companies including French gas and power group Engie, Por-tugal’s EDP Renewables (EDPR), Ja-pan’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 oper-ation, 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 in-dustry companies, including Nippon Steel & Sumitomo Metal Corporation, and is funded by the Ministry of Econ-omy, Trade and Industry. In this project, three floating wind turbines and one floating power sub-station will be in-stalled 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 tur-bines 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 cylin-drical spar buoy or a triangular platform moored by catenary cables. So far, both technologies have shown promising re-sults 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

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 show-ing positive results and they may be-come a cost and energy effective solu-tion in areas lacking the appropriate geological conditions for the construc-tion of conventional offshore wind farms.

Floating turbines can be placed in areas with the best possible wind condi-tions rather than primarily basing the lo-cation selection on the depth of the wa-ters (max. 50 m for conventional off-shore wind turbines) or the quality of the seabed. Japan, the US and some parts of Europe, for example, could be-nefit 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, fea-turing 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 diffe-rent regions of the world.

On 3 November 2015, the Scottish Government gave approval to the Nor-wegian energy company Statoil, who is behind the Hywind project, to start a second project off Peterhead in Aber-deenshire, 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 ex-pected to provide electricity to around 20,000 households. Production is plan-ned for 2017. The turbines will be at-tached 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 Peter-head.

Five km off the coast of Aguçadoura, Portugal, another pilot project, known as the WindFloat Atlantic project, is be-ing tested under plans set out in Novem-ber 2015. The project is planned to be

Hywind Scotland pilot park overview (© Scottish Government)


The international journal “Steel Construction – Design and Research” publishes peer-reviewed papers covering the entire field of steel con-struction research and engineering practice, focusing on the areas of composite construction, bridges, buildings, cable and membrane struc-tures, façades, glass and lightweight constructions, also cranes, masts, towers, hydraulic structures, vessels, tanks and chimneys plus fire pro-tection. “Steel Construction – Design and Research” is the en gineer-ing science journal for structural steelwork systems, which embraces the following areas of activity: new theories and testing, design, analy-sis 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 structu ral engineers, and also other engineers active in the relevant industries and authori-ties.

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• 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

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Preview

Steel Construction 2/2016*

Günter Seidl, Mathias DaßlerPractical experience and economical aspects of bridges with composite dowel strips

Markus FeldmannFirst experience with the German „General Approval Composite Dowel Strips“

Pavel SimonR&D of composite dowel strips in Czech Republic

Wojciech LorencSteel design concept for composite dowel shear connection and Non-linear behaviour of steel dowels in composite dowels: design models and approach by finite elements

Maciej Koz·uch, Slawomir RowinskiElastic behaviour of steel part of shear connection by MCL composite dowels: design basis for serviceability and fatigue limit states

Maik KoppEffects on the static capacity and fati-gue resistance of composite dowels due to transversal tension load

Martin Mensinger, Luo GuoqingAnchorage of external reinforcement in case of rigid clamping

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Steel Construction

Composite con-structions integrate the advantages of steel and concrete. Recently an inven-tive composite connection, the so-called composite dowel strip, was created in several research projects. It is characterized by a high bearing ca-pacity combined with a ductile be-havior and favora-ble fatigue resist-ance 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 addi-tion to the research results, the best practice of construction implementing com-posite dowel strips will be highlighted. Innovative cross-sections of girders find their introduction in a wide range of application for composite bridges.

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

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

Dieter Ungermann, Svenja HoltkampHot dip galvanized composite dowel strips

Daniel PakCondition monitoring of two slab track VFT-Rail railway bridges

(subject to change without notice)* Selected and updated papers from the workshop “Composite dowels”, 25−26 November 2015, Berlin

From geometry principles to transparency and lightness

Hans Schober

Transparent Shells

Form, Topology, Structure

2015. approx. 272 pages.

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The book describes the design, detailing and structural design of filigree, double-curved and long-span glazed shells with min-imal weight and ingenious details. Innovative, clear and understandable geometric principles for the design of double-curved shell structures are explained in a practical manner. The principles are simple to use with the modules now available for the usual CAD programs. The author demonstrates how flowing and homogeneous structures can be created on these „free“ forms, particularly framed structures of planar rectangles, which are especially suitable for glazing with flat panes and offer constructional, economic and architectural advantages. Examples are provided to explain in a simple way the latest methods of form finding calculation and holistic op-timisation through the complex interaction of structure, form and topology. Numerous examples built all over the world in the period 1989 to 2014 offer orientation and assistance in the design of such double-curved shells. Essential design parameters, constructed net structures and their node connections are presented and evaluated. These structures have been built all over the world in close partnership with renowned architects.

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Annual table of contentsEditor-in-chief:Karl-Eugen Kurrer

Editorial boardChair: 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)

2015Volume 8No. 1–4ISSN 1867-0520

Steel ConstructionDesign and Research

2 Steel Construction 8 www.ernst-und-sohn.de

Aarønæs, Anton; Nilsson, Hanna;Neumann, Nicolas: Dynamicresponse of steel pipe rack struc-tures subjected to explosionloads Issue 3 162–166 A

Alkan, Mustafa; s. Winterstetter,Thomas

Andreassen, Michael Joachim;Jönsson, Jeppe: Joint and col-umn behaviour of slotted cold-formed steel studs Issue 3 155–161 A

Beccarelli, Paolo; Maffei, Roberto;Galliot, Cédric; Luchsinger,Rolf H.: A new generation oftemporary pavilions based onTensairity girders Issue 4 259–264 A

Bedair, Osama: An analyticalexpression to determine “realis-tic” shear buckling stress in cold-formed lipped channels Issue 1 53–58 A

Beguin, Philippe; s. Lawson, MarkBerger, Radu; s. Winterstetter,

ThomasBjörk, Timo; s. Hämäläinen, Olli-

PekkaBorjigin, Sudanna; Kim, Chul-

Woo; Chang, Kai-Chun; Sugiu-ra, Kunitomo: Non-linear seis-mic response analysis of vehicle-bridge interactive systems Issue 1 2–8 A

Botti, Andrea; s. Döring, BerndBraun, Matthias; Obiala, Renata;

Odenbreit, Christoph: Analysesof the loadbearing behaviour ofdeep-embedded concrete dowels,CoSFB Issue 3 167–173 A

Braun, Matthias; s. Lam, DennisBraun, Matthias; s. Lawson, MarkBraun, Matthias; s. Romero,

Manuel L.Cajot, Louis-Guy; s. Romero,

Manuel L.Chang, Kai-Chun; s. Borjigin,

SudannaConan, Yves; s. Romero,

Manuel L.Cywinski, Zbigniew; s. Kido, Ewa

MariaDai, Xianghe; s. Lam, DennisDe Laet, Lars; s. Mollaert, MarijkeDevos, Rika; s. Mollaert, MarijkeDöring, Bernd; Reger, Vitali;

Kuhnhenne, Markus; Feld-mann, Markus; Kesti, Jyrki;Lawson, Mark; Botti, Andrea:Steel solutions for enabling zero-energy buildings Issue 3 194–200 A

Feldmann, Markus; s. Döring,Bernd

Feldmann, Markus; s. Schillo,Nicole

Fischer, Oliver; Mangerig, Ing-bert; Mensinger, Martin;Siebert, Geralt; Inoue, Susumu;Sugiura, Kunitomo; Yam-aguchi, Takashi; Ohyama,Osamu: 10th Japanese-GermanBridge Symposium Issue 1 1 E

Galliot, Cédric; s. Beccarelli,Paolo

Gibson, Nick D.: How to get amembrane structure off thedrawing board Issue 4 244–250 A

Grabe, Jürgen; s. Kuhlmann,Ulrike

Gunalan, Shanmuganathan; s.Janarthanan, Balasubramaniam

Göppert, Knut; Paech, Christoph:High-performance materials infaçade design – Structural mem-branes used in the building enve-lope Issue 4 237–243 A

Hashimoto, Kunitaro; Kayano,Makio; Suzuki, Yasuo; Sugiura,Kunitomo; Watanabe, Eiichi:Structural safety assessment ofcontinuous girder bridge withfatigue crack in web plate Issue 1 15–20 A

Hauf, Gunter; Kuhlmann, Ulrike:Deformation calculation meth-ods for slim floors Issue 2 96–101 A

Heinisuo, Markku; Mäkinen, Jari:Nordic Steel Construction Con-ference 2015 Issue 3 145 E

Helbig, Thorsten; Kamp, Florian;Oppe, Matthias: An Eye to theSky – Inclined grid shell dome of90 m in Astana, Kazakhstan Issue 2 133–138 B

Hicks, Stephen; Peltonen, Simo:Design of slim-floor constructionfor human-induced vibrations Issue 2 110–117 A

Hämäläinen, Olli-Pekka; Björk,Timo: Fretting fatigue phenome-non in bolted high-strength steelplate connections Issue 3 174–178 A

Höglund, Torsten: Cold-formedmembers – comparison betweentests and a unified designmethod for beam-columns Issue 1 42–52 A

Inoue, Susumu; s. Fischer, OliverJanarthanan, Balasubramaniam;

Mahendran, Mahen; Gunalan,Shanmuganathan: Bearingcapacity of cold-formed unlippedchannels with restrained flangesunder EOF and IOF load cases Issue 3 146–154 A

Jungbluth, Dominik; s.Stranghöner, Natalie

Steel Construction: Annual table of contents Volume 8 (2015)

List of authors(A = Topics/Aufsatz, B = Report/Bericht, E = Editorial)

Annual table of contents 2014

3


www.ernst-und-sohn.de Steel Construction 8

Just, Adrian; s. Kuhlmann, UlrikeJönsson, Jeppe; s. Andreassen,

Michael JoachimKamp, Florian; s. Helbig, ThorstenKawatani, Mitsuo; s. Tsubomoto,

MasahikoKayano, Makio; s. Hashimoto,

KunitaroKennedy, Stephen J.; Martino,

Aldo E.: SPS bridge decks fornew bridges and strengtheningof existing bridge decks Issue 1 21–27 A

Kesti, Jyrki; s. Döring, BerndKido, Ewa Maria; Cywinski, Zbig-

niew: The new steel-glass archi-tecture of passenger service cen-tres on expressways in Japan Issue 3 210–215 B

Kim, Chul-Woo; s. Borjigin,Sudanna

Kuhlmann, Ulrike; Just, Adrian;Leitz, Bernadette; Grabe, Jür-gen; Schallück, Christoph: Sim-plified criteria and economicdesign for king piles in com-bined steel pile walls accordingto Eurocode 3, part 1-1 Issue 2 122–132 A

Kuhlmann, Ulrike; Zandonini,Riccardo: Slim floors – a chancefor high permance Issue 2 77–78 E

Kuhlmann, Ulrike; s. Hauf,Gunter

Kuhlmann, Ulrike; s. Lam, DennisKuhnhenne, Markus; s. Döring,

BerndLam, Dennis; Dai, Xianghe;

Kuhlmann, Ulrike; Raichle,Jochen; Braun, Matthias: Slim-floor construction – design forultimate limit state Issue 2 79–84 A

Lawson, Mark; Beguin, Philippe;Obiala, Renata; Braun,Matthias: Slim-floor construc-tion using hollow-core and com-posite decking systems Issue 2 85–89 A

Lawson, Mark; s. Döring, BerndLeitz, Bernadette; s. Kuhlmann,

UlrikeLener, Gerhard: Steel bridges –

numerical simulation of totalservice life including fracturemechanic concepts Issue 1 28–32 A

Leskela, Matti V.; Peltonen, Simo:Effect of unzipping connectionbehaviour on the compositeinteraction of shallow floorbeams Issue 2 118–121 A

Leskela, Matti V.; Peltonen, Simo;Obiala, Renata: Compositeaction in shallow floor beamswith different shear connections Issue 2 90–95 A

Luchsinger, Rolf H.; s. Beccarelli,Paolo

Maffei, Roberto; s. Beccarelli,Paolo

Mahendran, Mahen; s.Janarthanan, Balasubramaniam

Mangerig, Ingbert; s. Fischer,Oliver

Mangerig, Ingbert; s. Mano, Toshi-hisa

Mano, Toshihisa; Mangerig, Ing-bert: Tensile load-carryingbehaviour of elastomeric bear-ings Issue 1 33–41 A

Martino, Aldo E.; s. Kennedy,Stephen J.

Mensinger, Martin; s. Fischer,Oliver

Mollaert, Marijke; De Laet, Lars;Pyl, Lincy; Devos, Rika: Thedesign of tensile surface struc-tures – From a hand calculationin 1958 to a contemporarynumerical simulation Issue 4 251–258 A

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 protectionfor bridge cables with butyl rub-ber tapes using the ATIS Cable-skin® system Issue 1 59–64 B

Obiala, Renata; s. Braun,Matthias

Obiala, Renata; s. Lawson, MarkObiala, Renata; s. Leskela,

Matti V.Odenbreit, Christoph; s. Braun,

MatthiasOhyama, Osamu; s. Fischer, Oliv-

erOppe, Matthias; s. Helbig,

ThorstenPaech, Christoph; s. Göppert,

KnutPeltonen, Simo; s. Hicks, StephenPeltonen, Simo; s. Leskela,

Matti V.Peltonen, Simo; s. Leskela,

Matti V.Pyl, Lincy; s. Mollaert, MarijkeRaichle, Jochen; s. Lam, DennisReger, Vitali; s. Döring, BerndRomero, Manuel L.; Cajot, Louis-

Guy; Conan, Yves; Braun,Matthias: Fire design methodsfor slim-floor structures Issue 2 102–109 A

Saul, Reiner; s. Nützel, OswaldSaxe, Klaus; s. Uhlemann, JörgSchallück, Christoph; s.

Kuhlmann, UlrikeSchillo, Nicole; Feldmann,

Markus: Local buckling behav-iour of welded box sectionsmade of high-strength steel –Comparing experiments withEC3 and general method Issue 3 179–186 A

Siebert, Geralt; s. Fischer, OliverSobek, Werner; s. Winterstetter,

Thomas



Steige, Yvonne; Weynand, Klaus:Design resistance of end platesplices with hollow sections Issue 3 187–193 A

Stimpfle, Bernd: The Nuvola forthe Nuovo Centro Congressi inRome Issue 4 230–236 A

Stranghöner, Natalie: Tensilemembrane structures Issue 4 221 E

Stranghöner, Natalie; Jungbluth,Dominik: Fatigue strength ofmarked steel components –Influence of durable markingmethods on the fatigue strengthof steel components Issue 3 201–209 A

Stranghöner, Natalie; s. Uhle-mann, 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

Tsubomoto, Masahiko; Kawatani,Mitsuo; Mori, Kengo: Traffic-induced vibration analysis of asteel girder bridge comparedwith a concrete bridge Issue 1 9–14 A

Uhlemann, Jörg; Stranghöner,Natalie; Saxe, Klaus: Compari-son of stiffness properties ofcommon coated fabrics Issue 4 222–229 A

Watanabe, Eiichi; s. Hashimoto,Kunitaro

Watanabe, Maiko; s. Winterstet-ter, Thomas

Weynand, Klaus; s. Steige,Yvonne

Winterstetter, Thomas; Alkan,Mustafa; Berger, Radu; Watan-abe, Maiko; Toth, Agatha;Sobek, Werner: Engineeringcomplex geometries – the Hey-dar Aliyev Centre in Baku Issue 1 65–71 B

Yamaguchi, Takashi; s. Fischer,Oliver

Zandonini, Riccardo; s.Kuhlmann, Ulrike

Subject codes and keywords

Cable structures

Nützel, Oswald; Saul, Reiner:Long-term corrosion protectionfor bridge cables with butylrubber tapes using the ATISCableskin® system [buthyl rub-ber tapes; long term corrosionprotection; bridge ropes andcables; automatic visual andmagnetic induction testing; scaf-folding free application; dehu-midification of cables] Issue 1 59–64

Composite construction

Braun, Matthias; Obiala, Renata;Odenbreit, Christoph: Analysesof the loadbearing behaviour ofdeep-embedded concrete dow-els, CoSFB [Composite design;slim-floor; CoSFB; CoSFB-Betondübel; ABAQUS] Issue 3 167–173

Hauf, Gunter; Kuhlmann, Ulrike:Deformation calculation meth-ods for slim floors [slim-floorgirder; deflection; girder stiff-ness] Issue 2 96–101

Hicks, Stephen; Peltonen, Simo:Design of slim-floor construc-tion for human-induced vibra-

tions [slim-floor construction;human-induced vibrations; vibra-tions; dynamic response; multi-plying factor; frequency; EN1990; ISO 10137] Issue 2 110–117

Lam, Dennis; Dai, Xianghe;Kuhlmann, Ulrike; Raichle,Jochen; Braun, Matthias: Slim-floor construction – design forultimate limit state [slim floor;composite beam; shallow floorconstruction; steel section; com-posite decking; bending resist-ance; horizontally lying studs;CoSFB; CoSFB concrete dowels] Issue 2 79–84

Lawson, Mark; Beguin, Philippe;Obiala, Renata; Braun, Matthias:Slim-floor construction usinghollow-core and compositedecking systems [slim floor; inte-grated beam; composite action;shallow floor structure; steel sec-tion; reinforced concrete; deepcomposite decking; floor stiff-ness; bending resistance] Issue 2 85–89

Leskela, Matti V.; Peltonen, Simo:Effect of unzipping connectionbehaviour on the compositeinteraction of shallow floorbeams [shallow floor beams;composite interaction; non-duc-tile connections; unzipping

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behaviour; hollow-core deckingsupported on beams] Issue 2 118–121

Leskela, Matti V.; Peltonen, Simo;Obiala, Renata: Compositeaction in shallow floor beamswith different shear connec-tions [composite interaction;shallow floor beams; shear con-nection behaviour; effectivebending stiffness; bending resis -tance; partial connection theory] Issue 2 90–95

Romero, Manuel L.; Cajot, Louis-Guy; Conan, Yves; Braun,Matthias: Fire design methodsfor slim-floor structures [slimfloors; fire resistance; simplifiedmethods; composite steel-con-crete structures; shallow floorbeams] Issue 2 102–109

Design

Gibson, Nick D.: How to get amembrane structure off thedrawing board [tensile mem-brane structures; compensation] Issue 4 244–250

Helbig, Thorsten; Kamp, Florian;Oppe, Matthias: An Eye to theSky – Inclined grid shell domeof 90 m in Astana, Kazakhstan[dome; steel; grid shell; Kaza-khstan; global buckling; imper-fections; material toughness] Issue 2 133–138

Kido, Ewa Maria; Cywinski, Zbig-niew: The new steel-glass archi-tecture of passenger servicecentres on expressways inJapan [Steel-glass architecture;expressways; passenger servicecentres; Japan] Issue 3 210–215

Lawson, Mark; Beguin, Philippe;Obiala, Renata; Braun, Matthias:Slim-floor construction usinghollow-core and compositedecking systems [slim floor; inte-grated beam; composite action;shallow floor structure; steel sec-tion; reinforced concrete; deepcomposite decking; floor stiff-ness; bending resistance] Issue 2 85–89

Stimpfle, Bernd: The Nuvola forthe Nuovo Centro Congressi inRome [nurbs geometry; form-finding; patterning; seam layout;silicone glass membrane] Issue 4 230–236

Winterstetter, Thomas; Alkan,Mustafa; Berger, Radu; Watan-abe, Maiko; Toth, Agatha;Sobek, Werner: Engineeringcomplex geometries – the Hey-dar Aliyev Centre in Baku[freeform geometry; parametricdesign; 3D engineering; complexgeometry] Issue 1 65–71

Fastener

Andreassen, Michael Joachim;Jönsson, Jeppe: Joint and col-umn behaviour of slotted cold-formed steel studs [slotted, load-bearing; cold-formed steel mem-bers; joints; experiments;columns; channel sections;studs] Issue 3 155–161

Hämäläinen, Olli-Pekka; Björk,Timo: Fretting fatigue phenom-enon in bolted high-strengthsteel plate connections [Frettingfatique; bolted joint; double-lapjoint; high-strength steel] Issue 3 174–178

Steige, Yvonne; Weynand, Klaus:Design resistance of end platesplices with hollow sections[Rectangular hollow section;bolted end plate splices; steeljoints] Issue 3 187–193

Façade and roof sheeting

Göppert, Knut; Paech, Christoph:High-performance materials infaçade design – Structuralmembranes used in the build-ing envelope [membrane;façade; lightweight; ETFE;ECTFE; mesh membrane; shad-ing] Issue 4 237–243

Helbig, Thorsten; Kamp, Florian;Oppe, Matthias: An Eye to theSky – Inclined grid shell domeof 90 m in Astana, Kazakhstan[dome; steel; grid shell; Kaza-khstan; global buckling; imper-fections; material toughness] Issue 2 133–138

General

Döring, Bernd; Reger, Vitali; Kuhn-henne, Markus; Feldmann,Markus; Kesti, Jyrki; Lawson,Mark; Botti, Andrea: Steel solu-tions for enabling zero-energybuildings [Nearly zero-energybuildings (nZEB); steel energypiles; double-layer flooring ele-ment; thermo-active deck ele-ment; natural night cooling] Issue 3 194–200

Stranghöner, Natalie; Jungbluth,Dominik: Fatigue strength ofmarked steel components –Influence of durable markingmethods on the fatigue strengthof steel components [Fatiguedesign; fatigue strength; fatiguelife; hard stamping; plasmamarking; needling; durablemarking; soft stamping; identifi-cation; traceability; scribing] Issue 3 201–209



Light metal construction

Bedair, Osama: An analyticalexpression to determine “real-istic” shear buckling stress incold-formed lipped channels[cold-formed steel; channel sec-tions; shear buckling] Issue 1 53–58

Höglund, Torsten: Cold-formedmembers – comparisonbetween tests and a unifieddesign method for beam-columns [Cold-formed members;tests; beam-columns; Eurocode3; interaction formulae] Issue 1 42–52

Materials

Schillo, Nicole; Feldmann,Markus: Local buckling behav-iour of welded box sectionsmade of high-strength steel –Comparing experiments withEC3 and general method [Localbuckling; general method; high-strength steel] Issue 3 179–186

Uhlemann, Jörg; Stranghöner,Natalie; Saxe, Klaus: Compari-son of stiffness properties ofcommon coated fabrics [tensilemembrane structures; architec-tural fabric; synthetic fibres; uni-axial tensile tests; stiffness prop-erties; Young’s modulus; Pois-son’s ratio] Issue 4 222–229

Methods of analysis and design

Aarønæs, Anton; Nilsson, Hanna;Neumann, Nicolas: Dynamicresponse of steel pipe rackstructures subjected to explo-sion loads [Dynamic response;steel structures; explosion; sin-gle-degree-of-freedom system;multi-degree-of-freedom system;finite element analysis] Issue 3 162–166

Beccarelli, Paolo; Maffei, Roberto;Galliot, Cédric; Luchsinger, RolfH.: A new generation of tempo-rary pavilions based on Ten-sairity girders [Tensairity®; coat-ed fabrics; pavilion; pneumatic;beams] Issue 4 259–264

Bedair, Osama: An analyticalexpression to determine “real-istic” shear buckling stress incold-formed lipped channels[cold-formed steel; channel sec-tions; shear buckling] Issue 1 53–58

Borjigin, Sudanna; Kim, Chul-Woo; Chang, Kai-Chun; Sugiura,Kunitomo: Non-linear seismicresponse analysis of vehicle-bridge interactive systems [mov-ing vehicle; seismic response;

strong ground motion; vehicle-bridge interaction] Issue 1 2–8

Hashimoto, Kunitaro; Kayano,Makio; Suzuki, Yasuo; Sugiura,Kunitomo; Watanabe, Eiichi:Structural safety assessment ofcontinuous girder bridge withfatigue crack in web plate[remaining load-carrying capaci-ty; safety assessment; fatiguecrack; steel girder bridge] Issue 1 15–20


Hicks, Stephen; Peltonen, Simo:Design of slim-floor construc-tion for human-induced vibra-tions [slim-floor construction;human-induced vibrations; vibra-tions; dynamic response; multi-plying factor; frequency; EN1990; ISO 10137] Issue 2 110–117

Höglund, Torsten: Cold-formedmembers – comparisonbetween tests and a unifieddesign method for beam-columns [Cold-formed members;tests; beam-columns; Eurocode3; interaction formulae] Issue 1 42–52

Janarthanan, Balasubramaniam;Mahendran, Mahen; Gunalan,Shanmuganathan: Bearingcapacity of cold-formedunlipped channels withrestrained flanges under EOFand IOF load cases [Cold-formed unlipped channel sec-tions; bearing capacity; EOF andIOF load cases; fastened andunfastened to supports; experi-mental study; design rules; directstrength method] Issue 3 146–154

Kennedy, Stephen J.; Martino,Aldo E.: SPS bridge decks fornew bridges and strengtheningof existing bridge decks [SPScomposite plate; design; per-formance; fabrication; erection] Issue 1 21–27

Kuhlmann, Ulrike; Just, Adrian;Leitz, Bernadette; Grabe, Jürgen;Schallück, Christoph: Simplifiedcriteria and economic designfor king piles in combined steelpile walls according toEurocode 3, part 1-1 [combinedsteel pile wall; king piles; stabili-ty; flexural buckling; lateral tor-sional buckling; combined steelpiling] Issue 2 122–132

Lam, Dennis; Dai, Xianghe;Kuhlmann, Ulrike; Raichle,Jochen; Braun, Matthias: Slim-floor construction – design forultimate limit state [slim floor;composite beam; shallow floorconstruction; steel section; com-posite decking; bending resist-

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ance; horizontally lying studs;CoSFB; CoSFB concrete dowels] Issue 2 79–84

Lener, Gerhard: Steel bridges –numerical simulation of totalservice life including fracturemechanic concepts [life cycle;fatigue; crack propagation; frac-ture mechanics] Issue 1 28–32

Leskela, Matti V.; Peltonen, Simo:Effect of unzipping connectionbehaviour on the compositeinteraction of shallow floorbeams [shallow floor beams;composite interaction; non-duc-tile connections; unzippingbehaviour; hollow-core deckingsupported on beams] Issue 2 118–121

Leskela, Matti V.; Peltonen, Simo;Obiala, Renata: Compositeaction in shallow floor beamswith different shear connec-tions [composite interaction;shallow floor beams; shear con-nection behaviour; effectivebending stiffness; bending resist-ance; partial connection theory] Issue 2 90–95

Mano, Toshihisa; Mangerig, Ing-bert: Tensile load-carryingbehaviour of elastomeric bear-ings [elastomeric bearing; ten-sion test; cavitation; FE simula-tion] Issue 1 33–41

Mollaert, Marijke; De Laet, Lars;Pyl, Lincy; Devos, Rika: Thedesign of tensile surface struc-tures – From a hand calcula-tion in 1958 to a contemporarynumerical simulation [tensilesurface structures; form-finding;force density method; cable nets] Issue 4 251–258

Romero, Manuel L.; Cajot, Louis-Guy; Conan, Yves; Braun,Matthias: Fire design methodsfor slim-floor structures [slimfloors; fire resistance; simplifiedmethods; composite steel-con-crete structures; shallow floorbeams] Issue 2 102–109

Tsubomoto, Masahiko; Kawatani,Mitsuo; Mori, Kengo: Traffic-induced vibration analysis of asteel girder bridge comparedwith a concrete bridge [traffic-induced vibration of bridges;steel girder; concrete hollowslab; dynamic analysis] Issue 1 9–14

Preservation

Kennedy, Stephen J.; Martino,Aldo E.: SPS bridge decks fornew bridges and strengtheningof existing bridge decks [SPScomposite plate; design; per-formance; fabrication; erection] Issue 1 21–27

Protection against corrosionNützel, Oswald; Saul, Reiner:

Long-term corrosion protection

for bridge cables with butylrubber tapes using the ATISCableskin® system [buthyl rub-ber tapes; long term corrosionprotection; bridge ropes andcables; automatic visual andmagnetic induction testing; scaf-folding free application; dehu-midification of cables] Issue 1 59–64

Steel bridges

Borjigin, Sudanna; Kim, Chul-Woo; Chang, Kai-Chun; Sugiura,Kunitomo: Non-linear seismicresponse analysis of vehicle-bridge interactive systems [mov-ing vehicle; seismic response;strong ground motion; vehicle-bridge interaction] Issue 1 2–8

Hashimoto, Kunitaro; Kayano,Makio; Suzuki, Yasuo; Sugiura,Kunitomo; Watanabe, Eiichi:Structural safety assessment ofcontinuous girder bridge withfatigue crack in web plate[remaining load-carrying capaci-ty; safety assessment; fatiguecrack; steel girder bridge] Issue 1 15–20

Lener, Gerhard: Steel bridges –numerical simulation of totalservice life including fracturemechanic concepts [life cycle;fatigue; crack propagation; frac-ture mechanics] Issue 1 28–32


Tsubomoto, Masahiko; Kawatani,Mitsuo; Mori, Kengo: Traffic-induced vibration analysis of asteel girder bridge comparedwith a concrete bridge [traffic-induced vibration of bridges;steel girder; concrete hollowslab; dynamic analysis] Issue 1 9–14

Tests

Andreassen, Michael Joachim;Jönsson, Jeppe: Joint and col-umn behaviour of slotted cold-formed steel studs [slotted, load-bearing; cold-formed steel mem-bers; joints; experiments;columns; channel sections;studs] Issue 3 155–161

Braun, Matthias; Obiala, Renata;Odenbreit, Christoph: Analysesof the loadbearing behaviour ofdeep-embedded concrete dow-els, CoSFB [Composite design;slim-floor; CoSFB; CoSFB-Betondübel; ABAQUS] Issue 3 167–173



Döring, Bernd; Reger, Vitali; Kuhn-henne, Markus; Feldmann,Markus; Kesti, Jyrki; Lawson,Mark; Botti, Andrea: Steel solu-tions for enabling zero-energybuildings [Nearly zero-energybuildings (nZEB); steel energypiles; double-layer flooring ele-ment; thermo-active deck ele-ment; natural night cooling] Issue 3 194–200


Hämäläinen, Olli-Pekka; Björk,Timo: Fretting fatigue phenom-enon in bolted high-strengthsteel plate connections [Frettingfatique; bolted joint; double-lapjoint; high-strength steel] Issue 3 174–178

Janarthanan, Balasubramaniam;Mahendran, Mahen; Gunalan,Shanmuganathan: Bearingcapacity of cold-formedunlipped channels withrestrained flanges under EOFand IOF load cases [Cold-formed unlipped channel sec-tions; bearing capacity; EOF andIOF load cases; fastened andunfastened to supports; experi-mental study; design rules; directstrength method] Issue 3 146–154


Schillo, Nicole; Feldmann,Markus: Local buckling behav-iour of welded box sectionsmade of high-strength steel –Comparing experiments withEC3 and general method [Localbuckling; general method; high-strength steel] Issue 3 179–186

Stranghöner, Natalie; Jungbluth,Dominik: Fatigue strength ofmarked steel components –Influence of durable markingmethods on the fatigue strengthof steel components [Fatiguedesign; fatigue strength; fatiguelife; hard stamping; plasmamarking; needling; durablemarking; soft stamping; identifi-cation; traceability; scribing] Issue 3 201–209

Uhlemann, Jörg; Stranghöner,Natalie; Saxe, Klaus: Compari-son of stiffness properties ofcommon coated fabrics [tensilemembrane structures; architec-tural fabric; synthetic fibres; uni-axial tensile tests; stiffness prop-erties; Young’s modulus; Pois-son’s ratio] Issue 4 222–229

Columns

Book review

Hyperbolic structures. Shukhov’sLattice Towers – Forerunners ofModern Lightweight Construc-tion. From Beckh, M. Issue 2 143–144

People

Prof. Udo Peil awarded honorarydoctorate Issue 1 41

Luís Simões da Silva Issue 3 161The European Prize for Architec-

ture 2015: Laureate SantiagoCalatrava Issue 4 229

steel construction 01/2016 free sample copy

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