Steelconstruction 01/2015 free sample copy

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Steel Construction

Volume 8 Februar 2015 ISSN 1867-0520

Design and Research

– Non-linear seismic response of vehicle-bridge system – Comparison of traffic vibrations in steel and concrete bridges – Safety assessment of bridge with fatigue crack – Sandwich plate decks for new and existing bridges – Steel bridges – service life simulation with fracture mechanics – Tensile load-carrying behaviour of elastomeric bearings – Tests and a unified design method for beam-columns – Formula for “true” shear buckling stresses in cold-formed channels – Butyl rubber tapes as corrosion protection for bridge cables – Complex geometry – Heydar Aliyev Centre 01_SC_U1_Titelseite_1-15.indd 1

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Content

The Acropolis Museum in Athens is a fine example of a seismically isolated structure. Unlike other structural protection systems against earthquake, a seismic isolation offers the possibility that the structure stays intact during an event of earthquake. Moreover even the objects within and on the seismically isolated structure can be protected from damaging. These special properties of seismic isolation are especially attractive for the application to important infrastructures such as bridges, hospitals or fire departments as well as museums because the historical priceless objects can be protected with a high safety. The earthquake protection system of the Acropolis Museum is realized by 94 friction pendulum bearings. In addition to protection function the bearings provide a recentering of the structure after occurrence of a seismic event (see pp. 33–41). (© Maurer AG, Munich)

Steel Construction 1 Volume 8 Februar 2015, No. 1 ISSN 1867-0520 (print) ISSN 1867-0539 (online)

Editorial 1

Articles 2

Sudanna Borjigin, Chul-Woo Kim, Kai-Chun Chang, Kunitomo Sugiura Non-linear seismic response analysis of vehicle-bridge interactive systems

9

Masahiko Tsubomoto, Mitsuo Kawatani, Kengo Mori Traffic-induced vibration analysis of a steel girder bridge compared with a concrete bridge

15

Kunitaro Hashimoto, Makio Kayano, Yasuo Suzuki, Kunitomo Sugiura, Eiichi Watanabe Structural safety assessment of continuous girder bridge with fatigue crack in web plate

21

Stephen J. Kennedy, Aldo E. Martino SPS bridge decks for new bridges and strengthening of existing bridge decks

28

Gerhard Lener Steel bridges – numerical simulation of total service life including fracture mechanic concepts

33

Toshihisa Mano, Ingbert Mangerig Tensile load-carrying behaviour of elastomeric bearings

42

Torsten Höglund Cold-formed members – comparison between tests and a unified design method for beam-columns

53

Osama Bedair An analytical expression to determine “realistic” shear buckling stress in cold-formed lipped channels Reports

http://wileyonlinelibrary.com/journal/stco 59

Oswald Nützel, Reiner Saul Long-term corrosion protection for bridge cables with butyl rubber tapes using the ATIS Cableskin® system

65

Thomas Winterstetter, Mustafa Alkan, Radu Berger, Maiko Watanabe, Agatha Toth, Werner Sobek Engineering complex geometries – the Heydar Aliyev Centre in Baku

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Oliver Fischer, Ingbert Mangerig, Martin Mensinger, Geralt Siebert, Susumu Inoue, Kunitomo Sugiura, Takashi Yamaguchi, Osamu Ohyama 10th Japanese-German Bridge Symposium

Regular Features 14 41 72 76

News (see 52, 58, 71, 74) People ECCS news Announcements

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Products & Projects

29.01.15 14:25

Products & Projects

Enovos Car Park At first glance the Enovos Car Park seems to be a classical, natural ventilated car park in steel. But at closer observation a special open and transparent aesthetics becomes apparent, achieved thanks to the use of the new flooring system Cofraplus 220 in combination with AngelinaTM beams. Furthermore, the car park convinces with various technical performance features like reduced weight of the beams, precise precambering and crack width control on the concrete surface, which could be easily accomplished with Cofraplus 220 system.

In course of the construction of the new headquarters of Luxembourg’s energy provider Enovos an open car park with a steel composite structure was planned. The multi-storey car park, designed in split-level layout, offers around 400 parking places arranged on 5 levels and is accessible through 3 exterior staircases towers.

In order to avoid indirect actions, the staircase towers were arranged outside of the main steel structure. With floor plan dimensions of 32 m × 60 m and a typical grid size of 15,75 m × 5 m, the car park generally complies with established concepts and benefits from the flexible design possibilities of steel composite construction avoiding any obstructive columns in the traffic zone of the car park.

Since the redesign of the area was not finished when the construction of the project started, many boundary conditions and future options had to be considered in the planning process. The construction site required a foundation on piles due to the difficult soil conditions. Thanks to the beam distance of 5 m, the total number of bored piles could be reduced significantly.

In an early planning stage an additional entrance to the car park on level 1 was foreseen at the south end. Therefore, this option was considered in the organization of the inner ramps from half level to half level. Furthermore, an old high voltage power line is crossing the construction site at its southern end reducing the final building height in this area to only 3 levels.

New flooring system and cellular beams with sinusoidal openings The innovation in this car park project lies in the use of the new flooring system Cofraplus 220® in combination with AngelinaTM beams. The distance of the web openings of the innovative cellular beams are adjusted to the cover width of the flooring deck to create a slender structure with new aesthetics. Compared to

traditional beams with solid webs, the large, sinusoidal openings allow a line of sight across various floor sectors.

The transparency gained in the floor beams and the reduced shadows grant the car park a very open and bright interior space despite of the limited height of only 2, 20 m (lower end of the beam).

Reduced steel tonnage and accurate cambering The fabrication of AngelinaTM beams is similar to that of traditional castellated and cellular beams by cutting a hot rolled steel section along its web and subsequent welding of the two resulting T sections in their web post. But in the case of this beam, the cut follows a continuous sinusoidal line that is adapted individually to the requirements of the project. In this process, the resulting height of the beams might increase to ca. 1, 5 times of the original girder height. Furthermore, the usual material loss due to the cutting is reduced to the cutting of the beam ends, which makes AngelinaTM a highly optimized castellated beam.

These beams used in the Enovos project are based on IPEO 400 in S460M grade for the longer spans and IPEA 330 in S460M for the shorter beams connected to the ramp columns. The cutting line, which ultimately decides the geometry of the beam’s openings and its new height, considers the cover width of 750 mm for the floor decking and thus the rip distance of the floor as well as the structural design requirements and the constructive height of the entire floor. The final beam height of 575 mm can be compared with the load bearing capacity of an IPE 550. The legally stipulated drainage on both sides required, in addition, a cambering of 210 mm which, after pouring of the concrete, declined to remaining 110 mm.

Wide spans and low crack widths The technically approved flooring system Cofraplus 220 (German Technical Approval Z-26.1-55) is based on the traditional additive design concept. According to this concept, after its assembly the 220 mm profile provides a working platform between the beams and takes the loads of the reinforcements and the concrete during construction. Furthermore, the profile sheet participates to the resistance of the bending moment and the shear force resistance in the final stage.

Depending on its thickness of 1,0 mm, 1,13 mm or 1,25 mm and the height of the concrete, spans of more than 5,50 m can be covered without additional propping. Spans of up to 9 m can be achieved using a specially designed support system. The Enovos Car Park required no props for the spans of 5 m. The height of the floor decking is 80 mm. Thanks to the offset of the “wing

Fig. 1. Bottom view of floor slab – AngelinaTM-beam with sinusoidal web opening and Cofraplus 220® floor decking as continuous ripped slab additive load bearing c­ apacity of the profile sheet

A4

Fig. 2. Detail of the connection between AngelinaTM-beam and Cofraplus 220 floor decking – the wings are welded to the web of the beam and filled with concrete permitting to consider it as a continuous ripped slab.

Steel Construction 8 (2015), No. 1

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Products & Projects

Structural Analysis and Design

The Structural Beam Analysis Program

The Ultimate FEA Program

BIM / Eurocodes

3D Finite Elements

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Steel Construction

Fig. 3. Assembly car park Enovos – AngelinaTM-beam with welded wings and shear connectors supporting bundles of Cofraplus 220 profile sheets which get installed manually. (© ArcelorMittal)

Dipl.-Ing./MBA Christoph Radermacher, Product Manager, ArcelorMittal Construction, Dipl.-Ing. Marc May, Senior Engineer, ArcelorMittal Europe – Long Products Further information: ArcelorMittal Construction France, Zone Industrielle – Site 1, 55800 Contrisson, France Tel. +33 (0)3 2979 8585, info.construction@arcelormittal.com, www.arcelormittal.com/construction

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Footings

Regarding durability, it was the client’s wish to limit the calculated average crack width above the beams to 0,1 mm.

These additional requirements could be realized by simple reinforcement above the beams, amongst others thanks to the continuous effect of the flooring system.

This way, also after shot blasting of the concrete surface in preparation for the final epoxy coating, no cracks appeared above the beams and no special post treatment (sealing) at this point was necessary.

The Enovos Car Park has already been opened although the façade has not been completely assembled. Thanks to the steel structure, the client could make use of the building even before it is completely finished. Finally, about 6 month after the start of the steel construction, the car park was operational by end of September 2014.

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20” by 20 mm, as described in the approval, the resulting total concrete height over the beam is thus 100 mm.

For assembly the profiles were inserted into these so-called wings of the beams and subsequently fixed with self-drilling screws and stitched together from below in the longitudinal overlap at the bottom of the ribs. The wings allow achieving a continuous slab across the beam. The concrete ribs are in direct contact with the beam’ web, which significantly increases the negative moment capacity at this point. Due to this type of the profile’s support the shear connectors can be freely arranged. The wings are simple formed parts made of 3,0 mm thick steel plates in conventional S235JR steel grade that were welded to the beam in course of the finishing process at the workshop and exposed to the same corrosion protection as the beam itself. The whole structure of the Enovos car park was hot-dip galvanized as common in car park construction.

The load bearing characteristics of the continuous flooring system, which despite a concrete cover of cnom = 50 mm does not require additional stainless steel reinforcements, convinces with its optimized crack behaviour, especially in the area of the hogging moment above the beams. Cofraplus 220’s load bearing characteristics are similar to these of a continuous ribbed slab. In non-cracked state, the concrete presents approximately the same stiffness in the floor slab area and above the supports.

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Products & Projects

Safe and secure – Wazirabad Signature Bridge

Sapa sells HatiCon to Mounting Systems GmbH

A new cable stayed bridge is currently under construction across the Yamuna River in Wazirabad, Delhi. Its dramatic inclined steel pylon, at 154 metres high, and elegant stay cable design, will make it a particularly attractive addition to the Wazirabad skyline.

Sapa has sold its HatiCon operations to the German company Mounting Systems GmbH. HatiCon produces, markets and sells aluminium extrusion-based mounting systems for the ­solar industry. The agreement reached earlier in January means that Mounting Systems GmbH with immediate effect takes over the operations for HatiCon Germany GmbH including the US company HatiCon Solar, LLC.

As well as its pleasing aesthetic impact, the shape of the pylon enables it to provide, to a substantial extent, the stress balance required to support the deck. The construction of this remarkable structure is being supported by the real-time data provided by a mageba ROBO®CONTROL structural health monitoring (SHM) system, and when the bridge is in use, the same system will support maintenance activities and provide constant safety monitoring.

The monitoring system, in accordance with specifications written by the client’s consultant and tendered internationally, consists of more than 100 measuring points with data management and display facilities. The installation of the system is taking place in parallel with the bridge construction process, with its completion and commissioning scheduled for 2015.

Fig. 1. The new cable stayed bridge’s steel pylon, at 154 metres high, and it’s elegant stay cable design, will make it a particularly attractive addition to the Wazirabad skyline.

Fig. 2. A sensor on a stay cable, measuring high-frequency vibrations (up to 200 Hz). (© mageba)

In particular, the system is designed to monitor the effects of weather, earthquakes and other environmental influences, and to detect and report any damage that may occur. The precisely measured data is made available to the bridge’s engineers in real time, via a user-friendly interface, greatly improving the efficiency of monitoring work compared to manual methods.

Further Information: mageba sa – engineering connections®, Solistrasse 68, 8180 Bülach, Switzerland Tel. +41-44-872 40 73, Fax +41-44-872 40 59, inf@mageba.ch, www.mageba.ch

A6

The divestment concludes a process in which the management of Sapa’s aluminium building systems business area also had evaluated new restructuring measures following challenging market conditions in the solar industry in Europe.

“Combining Mounting Systems and HatiCon will be an opportunity to create on strong and competitive player in the photovoltaic and solar thermal mounting systems industry”, says Karsten Lundgaard, executive vice president and head of Sapa Building Systems.

Sapa delivers aluminium solutions to customers in the solar industry across the world, however, HatiCon has been the only unit in Sapa delivering branded systems to this industry. “Going forward Sapa will not be operating with branded systems in this industry but rather continue as a supplier of aluminium extrusions to companies like Mounting Systems and Haticon”, concludes Lundgaard.

For over 20 years Mounting Systems develops and manufactures innovative racking system solutions for photovoltaic and solar thermal applications. With acquiring HatiCon, Mounting Systems continues growing as a specialist for innovative and high-quality racking system solutions for photovoltaic and solar thermal systems, both nationally and internationally.

“Uniting Mounting Systems and HatiCon is an important milestone for our company”, says Stefan Spork, Managing Director of Mounting Systems. “With acquiring HatiCon, we gain valuable know-how in racking systems solutions, especially for onroof systems. This fits perfectly in our product portfolio and the services we offer and will benefit our customers”, adds Stefan Spork.

HatiCon’s production activities and head office are in Pinnow, Germany. The company also has offices in Güterfelde, Germany, and Ontario, California. HatiCon employs about 100 people.

The companies agreed on keeping the purchase price confidential. The brand “HatiCon” and all associated functions, like administration, management and infrastructure, will be continued for now.

Sapa is the world leader in aluminium solutions, shaping a lighter future through a global reach and local presence within extrusions, building systems, and precision tubing. The company has 23,000 employees in more than 40 countries, and the headquarters are located in Oslo, Norway.

Mounting Systems GmbH is one of the largest manufacturers of fastening systems for photovoltaic and solar-thermal power plants in the world and module frames. With over 20 years of experience in the market, the company is a highly skilled developer and manufacturer in this business segment, headquartered in Rangsdorf near Berlin. Mounting Systems is also serving its customers from its own sales and production site in West Sacramento, USA and sales offices in UK, France and Japan.

Further information: Mounting Systems GmbH, Mittenwalder Straße 9a, 15834 Rangsdorf, Germany, Tel. +49 (0)337 08 – 529-0, Fax +49 (0)337 08 – 529-199, info@mounting-systems.com, www.mounting-systems.com

Steel Construction 8 (2015), No. 1

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Design Nicola Russo

If you are organising your trip to Italy on the occasion of Expo 2015, and are planning to follow in the footsteps of Wolfgang Goethe to appreciate its beauty, don't forget to visit the National Archaeological Museum of Reggio Calabria where you can admire the “Bronzi di Riace� statues, which are resting on a seismic isolator base, designed by ENEA, that is unique in the world. http://www.archeocalabria.beniculturali.it

Bronzi di Riace Bronzi di Riace

Bronzi di Riace Bronzi di Riace

Italian National Agency for new technologies, Energy and Sustainable Economic Development

Italian National Agency for new technologies, Energy and Sustainable Economic Development

Advertisement sponsored by HSH srl, national distributor of the Straus7 software, which was used to simulate and analyse the seismic isolator.

Courtesy of Ministero dei Beni e delle Attivita' Culturali e del Turismo - Authorization n. 2 - 8/01/2015 - Soprintendenza per i Beni Archeologici della Calabria.

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Products & Projects

Structural Award 2014 for Elbe Bridge at Schönebeck, Germany The 1129 m long Elbe Bridge at Schönebeck has gained the Strucutural Award 2014 of the London Institution of Structural Engineers.

The new Elbe Bridge at Schönebeck consists of a 309 m long southern approach bridge, a 489 m long main bridge across the Elbe River and a 331 m long northern approach bridge.

The main span across the river is cable-stayed and comprises a 185 m span of steel-concrete composite construction and an A-shaped pylon. The bridge has been constructed to relieve the City of Schönebeck from the considerable increase of through traffic it has experienced in recent years.

Judge’s comment: The judges were impressed by the elegant simplicity of the bridge which has been thoughtfully detailed to fit perfectly into the ­surrounding landscape whilst, at the same time, creating a landmark structure. The steel box superstructure was well chosen to suit the segmental erection methodology, to provide aerodynamic stability and to provide smooth lines to the deck, reducing its apparent depth.

Gained the renowned Structural Award 2014: Elbe Bridge at Schönebeck, Germany

(© LAP)

Further Information: Leonhardt, Andrä und Partner Beratende Ingenieure VBI AG, Heilbronner Straße 362, Nordtor Plaza, 70469 Stuttgart, Tel. +49 (0)711 – 25 06-0, Fax +49 (0)711 – 25 06-205, stuttgart@lap-consult.com, www.lap-consult.com

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16.12.14 12:20 09:20 29.01.15

Editorial

10 th Japanese-German Bridge Symposium

In September 2014 Universität der Bundeswehr München und Technische Universität München play host to the 10th edition of the Japanese-German Bridge Symposium, a biennial event which alternates between Japan and Germany. Over the years the symposium has established itself as an important meeting between bridge engineering experts from throughout Asia and Europe. If it was the bond of friendship between Professor Y. Maeda (Osaka City University) and Professor K. Roik (Ruhr-Universität Bochum) that promoted exchange between Japanese and German academics from the early 1980s onwards, it was the subsequent dedication of Professor H. Nakai (Osaka City University), Professor A. Kurita (Osaka Institute of Technology) and Professor G. Albrecht (Technische Universität München) that turned those early get-togethers into a leading bridge engineering symposium. Today, that tradition is continued by a group of professors from Kyoto University, the Osaka Institute of Technology, Osaka City University, Technische Universität München and Universität der Bundeswehr München.

Hosted by Technische Universität München and Universität der Bundeswehr München, the 2014 symposium featured contributions focusing on the preservation of built infrastructure (subtopics: load-bearing capacity, fa-

tigue, maintaining the durability of load-bearing bridge structures) and the planning of structural measures aimed at protecting buildings against the effects of earthquakes.

This journal includes a selection of contributions presented during the course of the symposium.

The organisers were equally as committed to the provision of a platform for the discussion of specialist subjects as the use of professional exchange to strengthen social ties – a principle passed down to them by their predecessors. After the symposium, participants who had travelled from Japan were joined on a joint trip to inspect a number of bridge structures currently under construction. The destination of this post-symposium tour was the Mosel Valley – a region well-known for fulfilling all the prerequisites for a long evening of lively conversation.

What began with the modest hopes of like-minded bridge engineers from different cultural backgrounds has long since become a true story of success. A number of fruitful partnerships have been established, and exchange between young academics from Asian and European universities is now the norm. Doctoral candidates from Japan and Germany are jointly supervised, and upon receiving their doctorates they represent highly qualified experts whose services are in high demand at global companies.

Prof. Dr.-Ing. Oliver Fischer, TU München

Prof., Dr. Eng. Susumu Inoue, O.I.T.

Prof. Dr.-Ing. Ingbert Mangerig, UniBw München

Prof., Ph.D., Kunitomo Sugiura, Kyoto University

Prof. Dr.-Ing. Martin Mensinger, TU München

Prof., Dr. Eng., Takashi Yamaguchi, Osaka City University

Prof. Dr.-Ing. Geralt Siebert, UniBw München

Assoc. Prof., Dr. Eng., Osamu Ohyama, O.I.T.

© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Steel Construction 8 (2015), No. 1

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Articles Sudanna Borjigin Chul-Woo Kim* Kai-Chun Chang Kunitomo Sugiura

DOI: 10.1002/stco.201510006

Non-linear seismic response analysis of vehicle-bridge interactive systems The intention of this study is to investigate how vehicles on highway bridges affect the seismic responses of the bridges under strong ground motions. Most highway bridge ­design codes do not consider the live load in the seismic design of highway bridges because of the low probability of the two events of the critical live load and an earthquake occurring at the same time. As a result, little attention has been paid to the influence of vehicle loads on the seismic responses of highway bridges. However, considering the high probability of traffic jams on urban roads, it is preferable to examine and clarify the dynamic interaction effect of vehicles on road bridges while subjected to seismic loads.

In this study, the vehicle-bridge-ground motion interactions are realized by combining ABAQUS and MATLAB. ABAQUS provides a GUI environment to establish the numerical bridge model and apply the seismic forces, while MATLAB provides a platform to control the iterations in both time and force increments. As a preliminary study, a simplified 3D pier-beam bridge model loaded with multiple vehicles with two degrees of freedom ­moving at a constant speed has been considered. When subjected to identical, strong seismic loadings, it was observed that the transverse accelerations of the bridge with moving vehicles are smaller than those without moving vehicles. Further, permanent deformation occurs after earthquakes because of yielding at the bottom of the pier; it was observed that the permanent deformations of the bridge with moving vehicles tend to be smaller than those without moving vehicles.

1 Introduction The seismic design of bridges is an issue of great concern in earthquake-­ prone countries such as Japan. However, in most countries, design procedures for earthquake-resistant bridges do not consider the presence of live loads when an earthquake occurs.

This decision is based on two major assumptions: firstly, it is assumed that the full design live load will not be on the bridge at the time of the design earthquake and, secondly, the seismic response of a bridge is dominated by its dead load, and inertia effects associated with live loads are negligible by comparison [1]. For bridges in urban areas, it is necessary to consider vehiSelected and reviewed by the Scientific Committee of the 10th JapaneseGerman Bridge Symposium, 16 to 19 September 2014, Munich, Germany * Corresponding author: kim.chulwoo.5u@kyoto-u.ac.jp

2

cle-bridge interaction when subjected to the ground motion that occurs with high probability, since the bridges in urban areas frequently experience traffic jams. Kameda et al. [2], [3] consider a vehicle standing on an urban highway bridge during a strong earthquake.

For monorail viaducts, Kim et al. [4] examined the effect of a stationary train on the seismic responses of the bridge under strong earthquakes. For the seismic responses of bridges under moving vehicles, the only results reported are those considering vehicle-bridge vibration under moderate earthquakes which lead to linear behaviour [5], [6], [7]. However, very little research has been carried out regarding the effects of moving vehicles on the seismic responses of highway bridges subjected to strong earthquakes.

This study aims to clarify the dynamic responses of a highway bridge under vehicles during a strong earthquake. It is important to mention that there is no guarantee that the bridge

will behave linearly during the application of vehicle and strong seismic loads. In other words, needless to say, a linear dynamic analysis may consequently be inadequate for a strong earthquake. This study is an attempt to investigate the non-linear dynamic responses of a highway bridge considering the vehicle-bridge interaction under strong earthquakes by a means of a three-dimensional (3D) dynamic response analysis. A vehicle is modelled with a rigid body, springs and dashpots with two degrees of freedom (DOF), considering sway and bouncing motions. The bridge is assembled from 3D beam elements. Equations of motion for the vehicle-bridge-ground motion interaction system, taking the road surface into account, are solved by Newmark’s β method [8]. The algorithm is implemented with ABAQUS [9], commercial FE software, and MATLAB [10], numerical computing software.

2 Vehicle-bridge system modelling The interaction between a bridge and moving vehicles is a special branch of structural dynamics. As the vehicle travels over the bridge, the dynamic tyre/wheel forces of a vehicle can lead to additional dynamic effects on the bridge. The vibration of the bridge also has a reciprocal effect on moving vehicles. This interaction problem between vehicles and bridge is called vehicle-bridge interaction (VBI). The coupled vehicles and bridge are classified as the vehicle-bridge interaction system.

2.1 Equations of motion for VBI system The Lagrange equation of motion is known to be one of the most popular

© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Steel Construction 8 (2015), No. 1

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S. Borjigin/C.-W. Kim/K.-C. Chang/K. Sugiura · Non-linear seismic response analysis of vehicle-bridge interactive systems

methods of formulating a dynamic system. Therefore, the governing equations for the VBI system are derived from the energy method using the Lagrange equation of motion [11], [12]. Equations of motion governing the vehicle and the bridge can be written as follows: Mvü + Cvu˙ + Kvu = Fbv (1) Mbv + Cbv + Kbv = Fvb (2) where: mass of vehicle and Mv and Mb bridge respectively Cv and Cb damping constant of vehicle and bridge respectively Kv and Kb spring stiffness of vehicle and bridge respectively Fvb force exerted by vehicle on bridge force exerted by bridge Fbv on vehicle v, v and v global vectors of nodal bridge displacements and rotations, their velocities and accelerations respectively u, u˙ and ü global vectors of vehicle displacements and rotations, their velocities and accelerations respectively The equations of motion for the bridge and vehicle models are combined to guarantee equilibrium of forces and compatibility of displacements at the contact points. The equilibrium of forces are the interaction forces existing at the contact points between the two subsystems. The fundamental problem in VBI modelling is that the contact points move with time and, for each point in time, the displacements of the vehicle are influenced by the displacements of the bridge. The latter affect the vehicle forces applied to the bridge, which in turn again alter the bridge displacements and interaction forces.

2.2 Numerical method In the VBI problem, two critical problems need to be solved: 1) movement of vehicle on bridge and 2) interaction between bridge and vehicle. For the bridge modelling process, FE software is adopted to run the structural analysis. On the other hand, external software is needed to analyse the dynamic

b

Satisfy Tolerance?

Fig. 1. Numerical method procedure

responses of vehicles considering road roughness, and to control the step-bystep analysis when solving the equations of motion of the VBI system.

Therefore, software coupling is needed and has been facilitated. Such tasks are realized by combining MATLAB and ABAQUS. MATLAB controls the entire process and ABAQUS provides the structure analysis environment.

The bridge displacements at time t+∆t are estimated with ABAQUS by Table 1. Classes of road roughness Class

Sd (f0) [× 10–6 m3/cycle] Min.

Mean

Max.

A

0

16

32

B

32

64

128

C

128

256

512

D

512

1024

2048

E

2048

4096

8192

F

8192

16384

32768

applying force {Fvb}t at the contact points during the time step ∆t. Next, the vehicle displacement is derived from the bridge displacements at time t+∆t. Finally, ut+∆t and {Fvb}t+∆t are computed with MATLAB. The above algorithm is illustrated as a flow chart in Fig. 1.

2.3 Road surface roughness The characteristics of road surface roughness are generally expressed by the power spectral density (PSD) function based on the ISO standard [13], in which paved roads are considered to be among road classes A–G. Some of these classes are given in Table 1. In ISO specifications, the general form of the displacement PSD of the road surface roughness is expressed as follows:

 f S d f = Sd f0    f0 

()

( )

−a

Steel Construction 8 (2015), No. 1

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(3)

3

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S. Borjigin/C.-W. Kim/K.-C. Chang/K. Sugiura · Non-linear seismic response analysis of vehicle-bridge interactive systems

where: f0 = 0.1 cycles/m reference spatial frequency and a exponent of PSD f spatial frequency (cycles/m)

Fig. 2. Elevation on bridge model

This surface roughness classification is based on a constant vehicle velocity PSD and by taking a = 2. The road surface roughness function r(x) in the time domain can be indicated by [14], [15]

() ∑

r x =

N i =1

()

(

4Sd fi ∆f cos 2 π fi x + θ

)

(4) where: fi = iDf, Df = 1/(ND)

1st mode: 2.1969Hz a) first vertical bending mode (girder)

2nd mode: 2.1986Hz b) second vertical bending mode (girder)

3rd mode: 2.2829Hz c) first lateral bending (pier)

4th mode: 2.7041Hz d) first pier bending in longitudinal bending

and D distance between successive ordinates on surface profile N number of data points θi set of independent random phase angles uniformly distributed between 0 and 2π

3 Model adjustment and verification 3.1 FE model of bridge The FE method and direct integration method were adopted to idealize bridges for dynamic response analysis. Beam elements with six DOFs at each node were used to idealize girders and piers. A 3D two-span simply-­ supported bridge model, as shown in Fig. 2, was used in this study and developed with ABAQUS. The length of each span is 40.4 m. Each girder was discretized into 20 elements. The substructure of the bridge model includes the concrete piers 10.2 m high. For the boundary condition, the piers were fully fixed at the foundation. Young’s modulus and Poisson’s ratio of the pier concrete were assumed to be 30 GPa and 0.167 respectively. The elastic modulus of the steel girders was taken as 210 GPa and Poisson’s ratio was assumed to be 0.2. To simplify the problem, damping constants were not considered in the bridge model in this preliminary study. Fig. 2 also shows observation points, denoted as B1, B2, C1, C2, C3, C4, C5 and C6; B1 and B2 are at mid-span of the girders, C1, C2 and C3 are at the top of the piers and C4, C5 and C6 are at the bottom of the piers. Fig. 3 shows the first four

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Fig. 3. Mode shapes and natural frequencies of the bridge

Fig. 4. Motions of the vehicle

mode shapes and natural frequencies obtained by eigenvalue analysis.

3.2 Vehicle model A single cargo truck was idealized as the sprung-mass model of two DOFs with bouncing and sway modes (Fig. 4). The vehicle body itself was

considered to be rigid and supported by a set of linear springs and dashpots.

In Fig. 5, Kv, Cv are the spring constant and damping coefficient of the vehicle corresponding to the bounce and KH and CH are spring constant and damping coefficient corresponding to the sway motion. Table 2 lists the vehicle model parameters.

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Table 2. Parameters of vehicle model Parameter

Notation

Unit

Value

Mass

m

kg

17 870

Vertical spring constant

KV

N/m

5.33 × 106

Lateral spring constant

KH

N/m

1.67 × 106

Vertical damping coefficient

CV

N · s/m

2.78 × 104

Lateral damping coefficient

CH

N · s/m

2.78 × 104

4 Numerical examples The analysis was conducted with the time step of 0.001 s and a class A road roughness profile was used. The assumptions considered in this study were: vehicle speed and path are constant; four vehicles pass over the bridge successively at a constant speed of 10.1 m/s; headway distance is 10.1 m. The Level-II ground motion of the JRA code [16] was adopted. The Level-II ground motion indicates the extreme design ground motion with a low probability of occurrence, which is caused by plate boundary and inland earthquakes such as the Kobe earthquake in 1995. Fig. 6 shows the ground acceleration time history. The sampling frequency of the time history is 100 Hz. Worthy of mention is

that, according to the JRA code, it is necessary to consider vertical ground motion as well as lateral ground motion. Therefore, the strong vertical ground motion with an amplitude of half the lateral ground motion is also applied to the bridge. The seismic responses of the bridge in the transverse direction are most critical in the seismic design; transverse seismic responses are therefore discussed here.

The time of vehicles on the bridge is about 11 s, so the results of dynamic responses during this period are shown and discussed here.

4.1 Non-linear components In ductile structures, damage due to strong earthquakes is associated with significant non-linear effects. There-

fore, any analysis of structures for severe ground motions should consider inelastic behaviour of structural components. This section describes a numerical analysis considering the inelastic behaviour of structural components to predict the dynamic response of a bridge.

Flexural failure was considered in this study and the shear resistance was assumed to be sufficiently large to prevent shear failure. In bridges with single-column piers, the maximum bending moment usually occurs at the ­bottom of the pier. The non-linear behaviour is therefore assumed to be concentrated at the base of the pier [17]. At the piers, three rotational springs were assumed as shown in Fig. 7. The rotational springs were assumed to be non-linear with respect to the longitudinal axis. Other possible degrees of freedom were restrained because they are not expected to be significant.

To determine stiffness variations upon unloading and reloading after load reversal, the bilinear model shown in Fig. 8 was considered. Here, My and Φy indicate the yielding moment and yielding rotation respectively, Mu and Φu the ultimate moment and ultimate rotation.

Acc (m/s^2)

Max = 6.87 m/s^2

Time(sec)

Fig. 5. Vehicle model with two DOFs

Fig. 6. Modified ground motion

My = 7.69 × 106 N·m qy = 0.001078 l/m Mu = 1.15 × 107 N·m qu = 0.008093 l/m

Fig. 7. Idealized bridge structure

Fig. 8. Bilinear model for nonlinear spring

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4.2 Seismic responses of the bridge Comparisons of transverse absolute accelerations, corresponding Fourier spectra and transverse deformations of observation points B1, C1, C2 and C3 due to the strong earthquake are shown in Figs. 9 to 14. It can be seen that the transverse accelerations of the bridge with moving vehicles are smaller than those without the mov-

ing vehicles even though the difference is small. However, no obvious variation in PSD is observed between accelerations with and without moving vehicles except at 6.5 Hz as shown in Figs. 10 and 12. The reason for the dominant frequency near 6.5 Hz in the PSDs of Fig. 10 (observation point C1) and Fig. 12 (observation point C3), which does not appear in the PSD of Fig. 11 (observation point C2), is not

known yet and now under investigation. However, the moving vehicles might act as a potential reason for the phenomenon, since the dominant frequency was observed at the accelerations of the piers at the entrance (C1) and exit (C3) of the bridge model, whereas the PSD in Fig. 11 is estimated from the acceleration of the intermediate pier (C2). From the consequent vibration after all vehicles

Fig. 9. Transverse absolute accelerations and corresponding Fourier spectra at B1

Fig. 10. Transverse absolute accelerations and corresponding Fourier spectra at C1

Fig. 11. Transverse absolute accelerations and corresponding Fourier spectra at C2

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Fig. 12. Transverse absolute accelerations and corresponding Fourier spectra at C3

Fig. 13. Transverse permanent displacements at B1 (left) and C1 (right)

Fig. 14. Transverse permanent displacements at C2 (left) and C3 (right)

have left the bridge, it was observed that the permanent deformations of the bridge with moving vehicles tend to be smaller than those without moving vehicles (see Figs. 13 and 14).

5 Conclusions The non-linear dynamic responses of a VBI system under strong earthquakes are investigated in this study.

ABAQUS was adopted to model the bridge and conduct a dynamic analysis of the bridge. MATLAB was adopted for the dynamic analysis of vehicles and to control the entire computing process. Equations of motion for the vehicle-bridge-ground motion interactive system are solved by Newmark’s β method.

From the analysis it was observed that the transverse accelerations of

the bridge with moving vehicles are smaller than those without moving vehicles. Further, permanent deformation occurred after earthquakes because of yielding at the pier bottom.

Vehicle loadings were likely to cause changes in seismic behaviour. From the consequent vibration after all vehicles have left the bridge, it was observed that the permanent deformations of the bridge with moving vehi-

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cles tend to be smaller than those without moving vehicles.

Further comprehensive studies are necessary to clarify reasons for the appearance of the dominant frequency near 6.5 Hz at the top of the piers at the bridge entrance/exit. This dominant frequency was not observed at the top of the intermediate pier. The next step for the study should be to consider structural damping of the bridge – a factor omitted from this study which focused on the how vehicles on the bridge affect the seismic responses of the bridge by comparing relative responses to simplify the problem.

References [1] Wibowo, H., Sanford, D. M., Buckle, I. G., Anders, D. H.: Effect of live load on seismic response of bridges: a preliminary study. Civil Engineering Dimension 14 (2012), pp. 166–172.

[2] Kameda, H., Kita, H., Morikawa, H.: Seismic Load of Highway Bridges under Dynamic Effect of Vehicle Loading.

Journal of Structural Engineering 36 (1990), pp. 791–801 (in Japanese).

[3] Kameda, H., Murono, Y., Nanjou, A., Sasaki, N.: Earthquake Response of Highway Bridges under Bridge-Vehicle System. Journal of JSCE 626/I-48 (1997), pp. 93–106 (in Japanese).

[4] Kim, C. W., Kawatani, M., Kambara, T., Nishimura, N.: Seismic behavior of

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steel monorail bridges under train load during strong earthquakes. Journal of Earthquake and Tsunami 7 (2013), pp. 1350006-1–1350006-17.

[5] Kim, C. W., Kawatani, M., Konaka, S., Kitaura, R.: Seismic Responses of a Highway Viaduct Considering Vehicles of Design Live Load as Dynamic System during Moderate Earthquakes.

Structure and Infrastructure Engineering 7 (2011), pp. 523–534.

[6] Kawatani, M., Kim, C. W., Yasui, K.: Seismic Response of a Highway Bridge under Traffic Loadings. Proc. of Pacific Structural Steel Conf. 2007: Steel Structures in Natural Hazards, Wairakei, New Zealand, 13–16 Mar 2007.

[7] Kim, C. W., Kawatani, M.: Effect of train dynamics on seismic response of steel monorail bridges under moderate ground motion. Earthquake Engng Struct. Dyn. 35 (2006), pp. 1225–1245.

[8] Newmark, N.: A method of computation for structural dynamics. J Eng Mech Div, ASCE 85 (1959), pp. 67–94.

[9] ABAQUS (2011), Dassault Systèmes, Providence, RI, USA. [10] MATLAB and Statistics Toolbox Release 2012b, The MathWorks, Inc., Natick, MA, USA. [11] Hutton, S. G., Cheung, Y. K.: Dynamic response of single span highway bridges. Earthq Eng Struct Dyn 7 (1979), pp. 543–553.

[12] Hurty, W. C., Rubinstein, M. F.: Dynamics of structures, Prentice-Hall, 1960, pp. 90–103.

[13] ISO 8608: Mechanical vibration – Road surface profiles – reporting of measured data, 1995(E).

[14] Henchi, K., Fafard, M., Talbot, M., Dhatt, G.: An efficient algorithm for dynamic analysis of bridges under moving vehicles using a coupled modal and physical components approach. J of Sound and Vib. 212 (1998), pp. 663–683.

[15] Jones, R. T., Pretlove, A. J.: Vibration Absorbers and Bridges. The Highway Engineer 26 (1979), pp. 2–9.

[16] Japan Road Association: Specifications for Highway Bridges, Part V: Seismic Design. JRA, Tokyo, Japan, 2002.

[17] Saiidi, M., Hart, J. D.: Non-linear Seismic Response of Short Reinforced Concrete Highway Bridges. Proc. of 8th World Conf. on Earthquake Engineering, San Francisco, CA, Jul 1984.

Keywords: moving vehicle; seismic response; strong ground motion; vehicle-bridge interaction

Authors: Sudanna Borjigin, PhD student, su.danna.52r@st.kyoto-u.ac.jp Chul-Woo Kim, Professor, kim.chulwoo.5u@kyoto-u.ac.jp Kai-Chun Chang, Researcher, chang.kaichun.4z@kyoto-u.ac.jp Kunitomo Sugiura, Professor, sugiura.kunitomo.4n@kyoto-u.ac.jp All authors: Kyoto University, Kyoto 615-8540, Japan

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Articles Masahiko Tsubomoto Mitsuo Kawatani* Kengo Mori

DOI: 10.1002/stco.201510010

Traffic-induced vibration analysis of a steel girder bridge compared with a concrete bridge At the preliminary design stage for a highway bridge 81 m long, a three-span continuous girder, including a span of about 30 m, is preferable from the point of construction cost. Generally, the concern is that girder bridges with spans of 30 m, which have a fundamental natural frequency of about 3 Hz, have large traffic-induced vibrations due to the coupling dynamic response with heavy vehicles having a bouncing natural frequency of about 3 Hz. Furthermore, large traffic-induced vibration in girder bridges causes low-frequency sound (LFS) as one of the environmental vibration problems. Two kinds of girder bridge with a length of 81 m – a concrete hollow slab bridge and an eight-girder steel bridge with the same spans – are proposed. For assessing the low-frequency sound radiated from bridges, firstly, the traffic-induced vibrations of two kinds of girder bridge are compared with each other by analysing the coupling dynamic response of bridges due to moving heavy vehicles in a dynamic system.

1 Introduction The low-frequency sound radiated from bridges carrying traffic is just one environmental problem, especially in the major cities of Japan where land is scarce, since in urban areas viaducts are even constructed alongside residential zones, and noise and vibration complaints arise. The sound radiated from the engines and tyres of heavy vehicles is usually regarded as one of the most typical environmental vibration problems [1]. Ground vibration is regarded as another major source of complaints related to the human reception of vibrations [2]. Compared with those two problems, the low-frequency sound due to the vibrations of bridges is really only a minor problem. However, the low-frequency sound, i.e. sound with frequencies < 100 Hz [3], causes extreme distress to a number of people who are sensitive to its effects. Such sensitivity may be a result of heightened sensory response within the whole or part of the auditory range. Historically, early work on low-frequency sound and its subjective effects was stimulated by the American space programme [4]. More recently, there have been media reports on the low-frequency sound radiated from

Selected and reviewed by the Scientific Committee of the 10th Japanese-German Bridge Symposium, 16–19 September 2014, Munich, Germany * Corresponding author: m-kawa@kobe-u.ac.jp

wind turbine generators [5]. Low-frequency sound can shake houses near the sound source and can also cause psychological and physiological effects in residents, even though these effects depend on intensity of the sound pressure level (SPL). Usually, psychological factors affect the physiological impact of noise [6]. The noise of doors or windows rattling is a typical effect in houses due to the SPL [7].

The physiological influences for residents include nausea, headaches, etc. It has also been reported that feelings of pressure and vibration are typical reactions of residents to low-frequency sound [8]. Constant low-frequency noise has been classified as background stresses, which are persistent events and may become routine elements in our lives [9].

Current bridge design adopts simplified bridge systems and light structures despite increasing truck weights and heavy traffic volumes. The current bridge design concept exposes bridges to the environmental vibration problem related to low-frequency sound [10]. However, very little research into the low-frequency sound radiated from highway bridges has been carried out. As a result, effective countermeasures as well as systematic approaches for reducing the vibration of bridges have not yet been established. Analytical approaches would be an important breakthrough in the research into the low-frequency sound radiated from bridges, provided proper numerical and simulation methods are available to examine the low-frequency sound around bridges. Recently, analytical studies were carried out to estimate the low-frequency sound due to traffic-induced vibration of bridges [11]–[15].

This study is intended to examine traffic-induced vibration of highway bridges with different girder types: a prestressed concrete (PC) hollow slab bridge and an eightgirder steel bridge. These bridges are 81 m long and have the same span lengths. For the first step in assessing the low-frequency sound radiated from a highway bridge, the traffic-induced vibrations of two kinds of girder bridge are compared with each other by analysing the coupling dynamic response of bridges due to moving heavy vehicles.

2 Analytical procedure The dynamic responses of the bridge are taken from a traffic-induced vibration analysis that is based on the finite element method for the modal analysis using three-dimensional models for both vehicle and bridge. The lumped mass and Rayleigh damping are adopted to form the mass and

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damping matrices respectively for the bridge model. The validity of the analytical method for the traffic-induced vibration of bridges was verified through the comparison with the field-test data [16]. Details of the traffic-induced vibration analysis can also be found in the previous study [16].

3 Analytical model 3.1 Bridge The objective bridge has the restriction of girder height up to 1.0 m, because under the first span of the bridge, there is a crossing surface road as shown in Fig. 1. Therefore, two kinds of girder, i. e. a PC hollow slab with a height of 1.0 m and eight steel plate girders with a height of 0.8 m, are adapted to examine the preferred type. The span lengths are 23.25 m + 28.5 m + 27.75 m. Each bridge is shown in Fig. 1. The second and third spans of the girder bridges were studied. The FE model of the concrete bridge consists of 216 nodes and 367 beam elements, whereas the steel girder bridge has 266 nodes and 465 beam elements. The damping ratio of the bridge for the first and second modes is taken as 0.02.

Table 1. Dynamic properties of vehicle Total Weight Axle Weight Logarithmic Decrement Natural Frequency

196.0 kN Front

49.0 kN

Rear

147.0 kN

Front

0.66

Rear

0.33

Front

1.9 Hz

Rear

3.2 Hz

3.2 Vehicle

Fig. 2. Dimensions of moving vehicle

The vehicle is composed of the body, tyres and suspension systems. It is simulated along with the eight degrees of freedom to describe its movement. The properties of the vehicle are summarized in Fig. 2 and Table 1.

on the PSD curve as shown in Fig. 3, in which the roadway roughness is assumed to be categorized as class A according to the ISO estimate [17].

3.3 Roughness In the traffic-induced vibration analysis of the bridge, the roadway roughness on the bridge surface is simulated based

4 Analytical results 4.1 Natural modes and frequencies Some of the natural modes and frequencies of each bridge estimated by the eigenvalue analysis are summarized in Table 2. The first mode of 2.22 Hz corresponds to the first Table 2. Natural frequencies of the bridges concrete hollow slab

(1) General layout of bridges

eight steel girder

1st (Bending)

2.22 Hz

1st (Bending)

2.48 Hz

2nd

3.09 Hz

2nd

3.52 Hz

3rd

3.89 Hz

3rd

3.75 Hz

4th

4.15 Hz

4th

4.46 Hz

5th

4.56 Hz

5th

4.79 Hz

(2) Section through PC hollow slab bridge

(3) Section through eight-girder steel bridge

Fig. 1. Bridges studied

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Fig. 3. PSD of roadway profile

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(1) PC hollow slab bridge, second span

(2) PC hollow slab bridge, third span

(3) Eight-girder steel bridge, second span

(4) Eight-girder steel bridge, third span

Fig. 4. Acceleration and FFT for vehicle speed of 45 km/h, second and third spans

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(1) PC hollow slab bridge

(2) Eight-girder steel bridge

Fig. 5. Acceleration and FFT for vehicle speed of 30 km/h third span

(1) PC hollow slab bridge

(2) Eight-girder steel bridge

Fig. 6. Acceleration and FFT for vehicle speed of 45 km/h, third span

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(1) PC hollow slab bridge

(2) Eight-girder steel bridge

Fig. 7. Acceleration and FFT for vehicle speed of 60 km/h, third span

bending mode of the concrete hollow bridge. On the other hand, the first mode of 2.48 Hz corresponds to the first bending mode of the eight-girder steel bridge.

4.2 Dynamic response of bridges Firstly, the observation points are the middle of the second span ( in Fig. 1) and the third span ( in Fig. 1) on the vehicle travel side. Fig. 4 shows the vertical acceleration responses and their Fourier amplitude spectra for a vehicle speed of 45 km/h. In the analytical results, the RMS values of acceleration response for the third span are larger than those for the second span. Therefore, traffic-induced vibrations in two kinds of girder bridge are compared for the third span. Figs. 5, 6 and 7 show the vertical acceleration responses and their Fourier amplitude spectra for vehicle speeds of 30, 45 and 60 km/h respectively. In the analytical results, the RMS values and the maximum acceleration response values of the eight-girder steel bridge are larger than those of the PC hollow slab bridge.

5 Conclusions This study is intended to assess the traffic-induced vibration of highway bridges with a length of 81 m, i.e. a PC hollow slab bridge and an eight-girder steel bridge with the same span lengths. The dynamic responses of the bridges are taken from a traffic-induced vibration analysis that is based on the finite element method for the modal analysis

using three-dimensional models for both vehicle and bridge. In a traffic-induced vibration analysis, the acceleration responses of the bridges in the third span are larger than those for the second span. Therefore, the observation point is the middle of the third span on the vehicle travel side. In the analytical results, the RMS values and the maximum acceleration response values of the steel girder bridge are larger than those of the concrete bridge. In particular, the maximum acceleration response values of the steel girder bridge are more than twice those of concrete bridge. The predominant frequency of the PC hollow slab bridge is slightly shorter than that of the eight-girder steel bridge. From the above, it is considered that the low-frequency sound of an eight-girder steel bridge is greater than that of a PC hollow slab bridge.

References [1] Eberhardt, J. L.: The influence of road traffic noise on sleep.

J. Sound Vibr., 127(3), 1988, pp. 449–455.

[2] Sheng, X., Jones, C. J. C., Thompson, D. J.: Prediction of ground vibration from trains using the wave number finite and boundary element methods. J. Sound Vibr., 293(3-5), 2006, pp. 575–586.

[3] ISO 7196: Frequency weighting characteristics for infrasound measurements, 1995.

[4] Mohr, G. C., Cole, J. N., Guild, E., von Gierke, H. E.: Effects of low frequency and infrasonic noise on man. Aerospace Medicine, 36, 1965, pp. 817–824.

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[5] Pedersen, E., Persson Waye, K.: Perception and annoyance due to wind turbine noise – a dose–response relationship. J. Acoust. Soc. Am., 116(6), 2004, pp. 3460–3470.

[6] Hatfield, J., Job, R., Carter, N., Peploe, P., Taylor, R., Morrell, S.: The influence of psychological factors on self-reported physiological effects of noise. Noise & Health, 3, 2001, pp. 1–13.

[7] Leventhall, G.: A Review of Published Research on Low Frequency Noise and its Effects. Department for Environment, Food & Rural Affairs, UK, 2003.

[8] Johnson, D. L.: Auditory and physiological effect of infrasound. Internoise 75, Proc. of Intl. Conf. on Noise Control Eng., 1975, pp. 475–482.

[9] Benton, S., Leventhall, H. G.: The role of “background stressors” in the formation of annoyance and stress responses.

J. Low Freq Noise Vibn., 13, 1994, pp. 95–102.

[10] Kim, C. W., Kawatani, M., Hwang, W. S.: Reduction of traffic-induced vibration of two-girder steel bridges seated on elastomeric bearings. Eng. Struct., 26(14), 2004, pp. 2185–2195.

[11] Kawatani, M., Kim, C. W., Nishitani, K., Kawada, N.: Low Frequency Sound due to Vibrations of a Bridge under Normal Traffic. Proc. of 8th Intl. Conf. on Structural Dynamics, EURODYN 2011, pp. 754–761.

[12] Wu, D., Xie, X., Yamashita, M.: Study on low-frequency noise radiated from steel multi-box girder bridge induced by traffic vibration. Proc. of 8th Intl. Conf. on Structural Dynamics, EURODYN 2011, pp. 785–790.

[13] Tsubomoto, M., Kawatani, M., Mori, K.: Prediction of Low-­ frequency sound of continuous girder highway bridges with

different span lengths. Proc. of 9th Intl. Conf. on Structural Dynamics, EURODYN 2014, pp. 1377–1382.

[14] Tsubomoto, M., Kawatani, M., Mori, K.: Traffic-induced vibration analysis of continuous girder highway bridges. Intl.

Conf. on Advances in Coupled Systems Mechanics, CD-ROM, 2014.

[15] Tsubomoto, M., Kawatani, M., Mori, K.: Estimation of traffic-induced vibration of continuous girder highway bridges.

4th Intl. Symp. on Life-Cycle Civil Engineering, 2014.

[16] Kim, C. W., Kawatani, M., Kim, K. B.: Three-dimensional dynamic analysis for bridge-vehicle interaction with roadway roughness. Computers Struct., 83(19-20), 2005, pp. 1627–1645.

[17] ISO 8606: Mechanical vibration-road surface profiles-reporting of measured data, 1995.

Keywords: traffic-induced vibration of bridges; steel girder; concrete hollow slab; dynamic analysis

Authors: Masahiko Tsubomoto, Bridge Engineer Kyowa Sekkei Co., Ltd., Ushitora, Ibaraki-si Osaka 567-0877, Japan Mitsuo Kawatani, Professor Kengo Mori, Graduate Student Department of Civil Engineering, Kobe University Kobedaigaku-rokkoudai, nada-ku, Kobe 657-8501, Japan

News Elbe Bridge at Schönebeck wins Structural Award 2014 in the category „Highway or Railway Bridge ­Structures“ The new 1129 m long Elbe Bridge at Schönebeck consists of a 309 m long southern approach bridge, a 489 m long main bridge across the Elbe River and a 331 m long northern approach bridge.

The main span across the river is cable-­ stayed and comprises a 185 m span of steel-concrete composite construction and an A-shaped pylon. The bridge has been constructed to relieve the City of Schönebeck from the considerable increase of through traffic it has experienced in recent years.

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Judge‘s comment: The judges were impressed by the elegant simplicity of the bridge which has been thoughtfully detailed to fit perfectly into the surrounding landscape whilst, at the same time, creating a landmark structure. The steel box superstructure was well chosen to suit the segmental erection methodology, to provide aerodynamic stability and to provide smooth lines to the deck, reducing its apparent depth.

Structural Designer: Leonhardt, Andrä und Partner Client Name: Landesstraßenbehörde Sachsen-Anhalt

Location: Schönebeck, Germany Architect: Manuela Theis, Leonhardt, Andrä und Partner Beratende Ingenieure VBI AG Principal Contractors: JV Hermann Kirchne Other Sub Contractors: Leonhardt, Andrä und Partner Further information: www.istructe.org/structuralawards/ 2014/winners www.lap-consult.com

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Articles Kunitaro Hashimoto* Makio Kayano Yasuo Suzuki Kunitomo Sugiura Eiichi Watanabe

DOI: 10.1002/stco.201510011

Structural safety assessment of continuous girder bridge with fatigue crack in web plate This paper, which focuses on a fatigue crack found in a main girder of a continuous steel girder bridge, assesses the remaining structural safety of the steel bridge with such a fatigue crack in order to judge whether or not urgent action such as closure to traffic or necessary temporary repairs and strengthening should be carried out. Therefore, an elastic-plastic finite displacement analysis is carried out for the continuous three-span non-composite steel girder bridge with four main girders in which a fatigue crack about 1.1 m long in the web plate of the main girder was discovered during an inspection. From the analysis results it is found that the load redistribution function of the multiple main girder system was effective and the remaining load-carrying capacity of such a bridge system is such that there will be no sudden collapse of the entire bridge.

1 Introduction In Japan, the “Regular Inspection Guidelines for Bridges (Draft)”, known as the “2004 Guidelines”, was published in March 2004. According to the “2004 Guidelines”, bridges must be inspected in the first two years after being opened to traffic and thereafter every five years, instead of every 10 years as given in the previous guidelines. Furthermore, inspection results must be recorded and stored as a “Management Record” according to the “System of maintenance management for Bridges and Preparation Guidelines for Bridge Management Record (Draft)”.

However, considering the damage typically found on steel bridge structures, assessing the structural integrity of the entire bridge or the residual load-carrying capacity is relatively difficult. For example, in the case of multiple main girder bridges, although the residual load-carrying capacity of one main girder could be reduced, it is understood that other girders may share such a reduction. Since the working stress state in service is different from that under the design loads, it may be necessary to assess the behaviour of the entire bridge including local fatigue and corrosion damage. In particular, it is important to provide any re-

Selected and reviewed by the Scientific Committee of the 10th Japanese-German Bridge Symposium, 16–19 September 2014, Munich, Germany * Corresponding author: hashimoto@person.kobe-u.ac.jp

sponse characteristics of structures under various actions in order to judge whether the road should be closed for any traffic and whether repairs and strengthening are needed and should be carried out urgently. Fatigue cracks and corrosion are well known as the main causes behind the deterioration of steel bridges. The main cause of fatigue cracks is the large number of vehicles passing over bridges and the numbers of heavy vehicles. On the other hand, corrosion could be caused by poor workmanship in waterproofing and drainage work.

This study focuses on fatigue cracks since many cracks have been found in old steel bridges during inspections in recent years. Generally speaking, fatigue cracks propagating in the primary members of steel bridges must be considered as dangerous because such fatigue cracks in the web or flange plates of a main girder may affect and reduce the load-carrying capacity of a girder or the bridge system, and cracks could grow rapidly due to cyclic vehicle loading, resulting in brittle failure. Therefore, focusing on a steel girder bridge with a very long fatigue crack in a web plate of a main girder, FE analyses are carried out in order to investigate its remaining loadbearing capacity. A typical steel girder bridge constructed in the 1970/1980s and crack damage found during a regular inspection are considered and modelled by using shell and solid elements.

Furthermore, some other types of crack are also modelled in FE analyses and the structural safety of steel bridges with fatigue cracks is assessed.

2 Bridge modelled and modelling of fatigue crack 2.1 Bridge modelled The design drawing and specifications of the target steel bridge are shown in Fig. 1 and Table 1. This bridge consists of three continuous spans and has four non-composite Table 1. Specification of bridge model Completion Year

1972

Length (m)

38.5 + 51.0 + 38.5

Width (m)

9.95

Specification Documents

Specifications for Highway Bridges (Japan, 1962)

Structural Summary

Steel 3 Span Non-composite Continuous Girder Bridge, 4 Girders

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Crack

(a) Elevation

Crack (b) Plan Fig. 1. Bridge modelled

steel I-section main girders. The bridge was built in 1971 and has been used for more than 40 years. This bridge is located in the national road network on the main route connecting Nagoya and Osaka. About 57 000 vehicles pass over the bridge every day, so it is thought that this heavy traffic may be the cause of this fatigue damage.

2.2 Fatigue crack The very long fatigue crack shown in Fig. 2 was found during a regular inspection in 2006. The crack started at a

Fig. 2. Real fatigue crack

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welded part of the gusset plate between the G3 main girder and the cross-beam, then propagated in the web plate of the G3 main girder towards the upper flange plate. The exact location of the crack is marked by red circles in Fig. 1. The crack was more than about 1.1 m long at the time of the inspection. Therefore, immediately after finding this crack, traffic was stopped for 23 h while temporary repairs were carried out. Permanent repairs and strengthening in the form of patching steel plates with high-strength bolts were carried out subsequently.

3 FE analysis model 3.1 FE modelling In order to assess the remaining load-carrying capacity of the entire bridge system or a main girder, an elastic-plastic finite displacement analysis is carried out using ABAQUS, which is known as a general-purpose FE analysis code in which a concrete slab, four main girders, vertical and horizontal stiffeners, cross-beams, lateral members and cross-frames are modelled by finite elements; however, gusset plates are not modelled in this analysis because stress concentrations at gusset plate welds are not the main goal. The concrete slab is discretized with solid elements, the main girders and the stiffeners are meshed by shell elements, and the cross-beams, lateral members and cross-frames are modelled by beam elements as shown in Fig. 3.

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Distributed Load

Elevation (a) Section Under Consideration

(b) Section Fig. 3. Analysis Model

3.2 Materials

3.4 Analysis cases

The elastic modulus and compressive strength of the concrete slab were set to 23 500 MPa and 21 MPa respectively – the lowest design values defined in Japanese specifications for highway bridges. The elastic modulus and yield strength of the steel members were set to 200 000 MPa and 315 MPa respectively. In the FE analysis, the steel material was defined by an elastic and perfectly plastic model. In order to make the analysis easy to converge, the softening behaviour after compressive strength is reached or the tensile strength of the concrete material are not considered.

The analysis cases are summarized in Table 3. Four analysis cases are considered in this research: case 1 is an INTACT bridge model without cracks for comparing with other analysis cases, cases 2, 3 and 4 are bridge models with fatigue crack. In case 2 the actual crack size and its location found in the inspection as shown in Fig. 4 are modelled by separating nodes of adjacent elements. The crack of case 3 is modelled as a case with a crack slightly shorter than the crack of case 2, but the crack of case 3 is assumed to propagate towards the lower flange and then penetrate that flange. Case 4 is set as the worst damage case. The crack of case 4 is extended to break through almost all the steel section of the main girder as shown in Fig. 4.

3.3 Support and loading conditions The loading conditions are also shown in Fig. 3. The support conditions of the FE model are also shown in Fig. 3 and summarized in Table 2. As a first step in the analysis procedure, the weight of the superstructure is applied as a dead load on the concrete slab. The next step is to place a uniformly distributed load on the middle span with the fatigue crack as shown in Fig. 3.

Table 2. Support condition of analysis Support

A1

P1

P2

A2

Support Condition

x, y, y, z

x, y, y, z

x, y, y, z

x, y, z, y, z

4 Results and discussion 4.1 Load-carrying capacity The cross-section defining a vertical displacement, the centre of the middle span (between pier P1 and pier P2) of the bridge, is marked by a red dashed line in Fig. 3a. The relationship between the sum of the reaction forces of all the ends of the G1, G2, G3 and G4 girders and the average vertical displacement of all the girders at the cross-section under consideration is drawn in Fig. 5. The relationship between the reaction force of both ends of a particular damaged girder, girder G3, and the vertical displacement

Fig. 4. Crack model of each analysis case

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of girder G3 at the cross-section under consideration is plotted in Fig. 6. Here, girder G3 is modelled with the fatigue crack in three different shapes.

It is understood from Fig. 5 that there exists only a little difference in the load-carrying capacity and the rigidity of the entire bridge system across the four cases. On the other hand, it can be seen from Fig. 6, which focuses on the response of girder G3, that the maximum reaction force of girder G3 in cases 2, 3 and 4 is smaller than that of case 1, i.e. a decrease of 2, 4 and 10 % in the maximum reaction forces for cases 2, 3 and 4 respectively compared with that of case 1.

The relationship between the reaction force of support P1 for girder G3 and the vertical displacement of girder G3 at the cross-section under consideration is drawn in Fig. 7. It is also understood from Fig. 7 that the differences in the maximum reaction force of case 1 and those of other cases are larger because the cracks are located between supports P1 and P2, a little closer to support P1. The decrease in the maximum reaction force of cases 2, 3 and 4 with respect to case 1 are about 3, 6 and 13 % respectively. As for the crack length, it is found that the maximum reaction force of case 3 is smaller than that of case 2 because the crack penetrates into the lower flange. It should be remembered that the load-carrying capacity of the steel girder bridge is influenced by the location of the crack and not only the length of the crack.

4.2 Load redistribution

Fig. 5. Relationship between total reaction force of all girders and average vertical displacement of all girders

Fig. 8. Share rate of all reaction forces of each girder for all reaction forces

Fig. 6. Relationship between total reaction force of girder G3 and vertical displacement of girder G3

Fig. 9. Share rate of P1 reaction force of each girder for P1 reation force

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Fig. 8 summarizes the load share rate of all the girders based on the summed reaction forces of each girder. The load share rate of P1 reaction force of each girder is compared in Fig. 9. It is understood from Fig. 8 that the load share rates of girders G2 and G3 in cases 2 and 3 decrease in comparison with the load share rate in case 1. On the contrary, the load share rates of girder G4 for case 2 and

Fig. 7. Relationships between P1 reaction force of girder G3 and vertical displacement of girder G3

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Fig. 10. Mises stress distribution of case 1 near support P1 (deformation ratio: 10 times)

case 3 increase compared with that of case 1. It can be seen that the variation in the load share rate of case 4 is the largest of all the cases.

4.3 Deformation and Mises stress distribution The deformation and Mises stress distribution of case 1 is drawn in Fig. 10. It is found from Fig. 10 that the buckling occurs at the lower flanges of all the girders near support P1 in the centre span because the girder at this cross-section is subjected to a negative bending moment. The buck-

ling also occurs at the same position in other analysis cases. This can be explained by the fact that the cause of the little difference in the load-carrying capacity of the entire bridge system is due to a failure mode that is the buckling of steel girders and not the extension of the yielding region due to cracking.

The deformation and Mises stress distribution near the middle of the span for all the analysis cases are shown in Fig. 11. The stress distribution of case 2 is similar to the stress distribution of case 1. However, the Mises stresses in girders G2 and G4 at the lower flange and the lower side of the web plate of cases 3 and 4 are higher than those of case 1, and the stresses in girder G3 in cases 3 and 4 are smaller than those of case 1 because the load redistribution at the cracked cross-section is expected in conjunction with a concrete slab.

The Mises stress distributions near the crack in cases 2, 3 and 4 are shown in Fig. 12. It is understood that the Mises stress can be largest at the crack tip for all the analysis cases. Therefore, it is necessary to assess the safety of the entire bridge system while the stress concentration at the crack tip causing brittle failure may not be reached due to the limited load-carrying capacity of steel girders in buckling failure.

5 Conclusion In this paper, an FE analysis is carried out in order to investigate the remaining load-carrying capacity of a steel girder

Fig. 11. Mises stress distribution in middle span at maximum load (deformation ratio: 10 times)

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Fig. 12. Mises stress distribution in girder G3 near crack at maximum load

bridge system with an extensive fatigue crack in a main girder and to assess its safety. The results obtained from a parametric analysis are summarized in the following: 1) There exist only little differences between the load-carrying capacities and rigidities of the steel girder bridge system with different fatigue cracks. However, focusing on the summed reaction force of girder G3 only or the reaction force of support P1 of girder G3, it is found that the maximum reaction forces in cases with the crack are smaller than those of the uncracked cases.

2) The load share rates of girders G2 and G3 with fatigue crack decrease in comparison to the share rates of girders G2 and G3 of the uncracked case.

3) Buckling occurs at the lower flanges of all the girders near support P1 in the centre span because the girder at this section is subjected to a negative bending moment.

4) The Mises stresses in girders G2 and G4 at the lower flange and the lower side of the web plate of the cracked analysis cases are higher than those of the uncracked analysis case, and the Mises stresses in girder G3 of case 3 and 4 are smaller than those of the uncracked analysis case because load redistribution can be expected.

References [1] Japan Road Association: Japanese Specifications for Highway Bridges, Part I, II (2012) (in Japanese).

[2] Road Bureau, Ministry of Land, Infrastructure, Transport & Tourism: Regular Inspection Guidelines for Bridges (Draft), 2007 (in Japanese).

[3] Road Bureau, Ministry of Land, Infrastructure, Transport and Tourism: System of maintenance management of Bridges and Preparation Guidelines for Bridge Management Record (Draft), 2004 (in Japanese).

[4] Yamaguchi, T., Kim, I., Kitada, T., Muramoto, K.: Analytical study on residual load-carrying capacity of damaged steel bridge with large crack. Steel Construction Engineering, vol. 16, No. 63 (2009), pp. 15–25 (in Japanese).

[5] Tachibana, Y., Tujikawa, M., Echigo, S., Takahashi, S., Miki, C.: A study of after-fracture redundancy for two girder bridges.

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Journal of Structural Mechanics and Earthquake Engineering (I), No. 647/I-51 (2000), pp. 241–251 (in Japanese).

[6] Ishikawa, T., Okura, I., Fujimori, Y.: Ultimate strength of cracked girders in bending. Journal of Structural Engineering, vol. 52A (2006), pp. 57–66 (in Japanese).

[7] Kim, I., Yamaguchi, T., Kitada, T., Nakamura, T.: Fundamental study on ultimate strength of plate girder ends with cracks around sole plates subjected to predominant shear force. Journal of Structural Mechanics and Earthquake Engineering (A), vol. 64, No. 4 (2008), pp. 841–856 (in Japanese).

[8] Japan Load Associations: Specifications for Highway Bridges, 2012 (in Japanese).

[9] Dassult Systemes Simulia: ABAQUS User’s Manual, version 6.12, 2012 (in Japanese).

[10] Fukumoto, Y., Yoshida, H.: Deflection stability of threespan continuous girder bridges under variable repeated loading. Proc. of Japan Society of Civil Engineering, No. 179 (1970), pp. 13–22 (in Japanese).

Keywords: remaining load-carrying capacity; safety assessment; fatigue crack; steel girder bridge

Authors: Kunitaro Hashimoto, Associate Professor Kobe University, Department of Civil Engineering 1-1 Rokkodai-cho Nada-ku Kobe, 657-8501, Japan hashimoto@person.kobe-u.ac.jp Makio Kayano, Section Manager Ministry of Land, Infrastructure, Transport & Tourism 2-1-3 Kasumigaseki Chiyoda-ku, Tokyo, 100-8918, Japan Yasuo Suzuki, Assistant Professor Kyoto University, Department of Civil & Earth Resources Engineering Kyotodaigaku-Katsura, Nishikyo-ku, Kyoto, 615-8540, Japan Kunitomo Sugiura, Professor Kyoto University, Department of Civil & Earth Resources Engineering Kyotodaigaku-Katsura, Nishikyo-ku, Kyoto, 615-8540, Japan Eiichi Watanabe Komaihaltec Inc. 4-2-21 Tachiurihori Nishi-ku Osaka, 550-0012, Japan

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Articles Stephen J. Kennedy Aldo E. Martino*

DOI: 10.1002/stco.201510005

SPS bridge decks for new bridges and strengthening of existing bridge decks The sandwich plate system (SPS) is a structural composite material made up of two metal plates bonded to a polyurethane elastomer core. SPS delivers high strength and stiffness, making it an excellent alternative to conventional stiffened steel and reinforced concrete. For strengthening of orthotropic bridge decks, SPS Overlay can be used to create a stiff bridge deck without removing the original plates. The renewed deck improves the distribution of wheel loads across the longitudinal stiffening elements, decreases deck curvatures associated with large concentrated wheel loads, extends the fatigue life of fatigue-critical welds and increases the life of the wearing surface and the whole bridge.

For new bridge applications, prefabricated SPS bridge deck plates reduce the dead load by up to 70 % compared with concrete bridge decks, thus allowing bridges to carry significantly greater live load without the need for girder or pier strengthening.

Deck replacement can be completed while leaving the steel or concrete girders in place or, where speed of erection is critical, pre-assembled longitudinal deck-girder units can be used.

1 Introduction SPS (sandwich plate system) technology was originally developed in 1993 for demanding applications in the maritime industry such as ice strengthening on Arctic drilling platforms and supertanker hulls. Since then, development of SPS technology has seen significant progress: to date more than 390 projects across 30 countries have been designed, fabricated and delivered for maritime repair, maritime newbuild, offshore, industrial and civil engineering applications (buildings, bridges, stadia). Intelligent Engineering (IE) has conducted more than 12000 tests at internationally recognized labs and technical institutions in different parts of the world, proving all aspects of performance, economics, safety and sustainability. Tests conducted to establish performance across the necessary range of engineering characteristics include: flexural and compressive strength, fatigue resistance, bond strength, corrosion resistance, impact resistance, vibration performance, acoustic performance, thermal insulation and fire resistance. Approvals have been obtained from key mari-

Selected and reviewed by the Scientific Committee of the 10th Japanese-German Bridge Symposium, 16 to 19 September 2014, Munich, Germany * Corresponding author: martino@ie-sps.com

Fig. 1. Experimental testing and verification

time and civil engineering regulatory bodies around the world.

SPS is a heavy engineering material technology that delivers significant simplification, performance and safety benefits. Owners gain significant economic savings during construction and throughout the design life of the structure.

The SPS Overlay system provides a minimal-disruption solution for strengthening existing orthotropic bridge decks that exhibit fatigue-induced weld cracking. For new bridge decks, the use of prefabricated SPS plates significantly reduces structural complexity by eliminating the need for longitudinal stiffening elements, reducing the number of fatigue-prone details and simplifying maintenance operations. Prefabrication on dedicated production lines results in high-quality plates that are fabricated to tight tolerances. Erection is simple and fast – using a single trade, light equipment and industry standard steel practices. SPS bridge decks can be specified to use atmospheric corrosion-resistant steel where conditions permit, or standard steel with applied coatings that meet prescribed specifications and standards.

Fig. 2. SPS composite plate and structure

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2 Strengthening of existing bridge decks (SPS Overlay) The existing stock of orthotropic bridge decks has been exposed to increasing truck traffic, heavier trucks and the introduction of super single tyres (larger concentrated wheel loads) over the past few decades. The negative impacts arising from these changes include fatigue cracking of welds and delamination of the wearing surface due to the flexibility of the deck between longitudinal stiffening elements. IE has developed SPS Overlay, a deck strengthening solution that extends the life of bridge decks and increases their load-carrying capacity, in order to mitigate against issues associated with traditional orthotropic bridge decks.

The SPS Overlay process uses the existing stiffened steel plate as one side of the composite plate, which is formed by a new top faceplate and a polyurethane elastomer core. The renewed deck is a permanent repair that is extremely quick, uses a fraction of the man-hours required for other repair or strengthening methods and has been tested, verified and approved by regulatory bodies. The benefits associated with SPS Overlay include: –– increased sharing of wheel loads across stiffening elements, –– reduced local effects of wheel loads, –– reduced fatigue issues in longitudinal stiffeners-to-deck welds, and –– increased service life of asphalt wearing surfaces by reducing deck curvatures.

The SPS Overlay process is efficient as work on site is conducted within specialized rigid enclosures that provide a weathertight working area which moves along the length of the bridge as work progresses. This protective enclosure ensures that no quality problems arise as a result of poor climate conditions. The process is extremely versatile and can be applied to any fixed bridge geometry. The repair of existing fatigue cracks is integrated into the steelwork for the SPS Overlay process, thus providing a seamless workflow. SPS Overlay strengthens, rehabilitates and extends the fatigue life of orthotropic steel bridge decks.

Laboratory and field tests have been conducted for SPS bridge decks by RWTH Aachen University [1], [2] in Germany and Virginia Tech [3] in the USA. Testing covered all key aspects of fabrication, installation, verification, enhanced fatigue resistance and strengthening of both the bridge deck and the overall bridge. In addition, tests were

conducted to evaluate stress reductions, fatigue life extension and the determination of load distribution and dynamic load allowance. Corresponding finite element analytical studies were undertaken to confirm the test results and to calibrate finite element models such that investigative studies of fatigue performance can be conducted.

2.1 Schönwasserpark Bridge (Krefeld, Germany) SPS Overlay was used to strengthen the deck of Schönwasserpark Bridge, a dual carriageway bridge near Krefeld, Germany, as illustrated in Fig. 4. The bridge was built in 1972, is 11.5 m wide and spans 70 m over the busy A57 motorway.

As experienced on orthotropic bridge decks around the world, Schönwasserpark Bridge was exhibiting signs of fatigue-induced damage due to heavier truck loads, increased traffic volumes and larger concentrated wheel loads, all contributing to a decrease in the expected life of the bridge.

The SPS Overlay solution, consisting of a 30 mm polyurethane elastomer core and 6 mm thick steel top faceplate (SPS 6‑30‑Existing), provided a renewed stiffer deck that improves the distribution of wheel loads across the troughs, decreases deck curvatures and prolongs the life of the bridge. Deck renewal began with the removal of the asphalt layer and grit blasting of the existing steel deck over a two-day period. Both the steel cavities and elastomer injection were completed over the following two weeks. A new asphalt wearing surface was applied and the bridge

Fig. 4. Schönwasserpark Bridge

Fig. 3. Strengthening of existing bridge deck using SPS Overlay

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re-opened after only a five-week closure period. The effectiveness of the SPS Overlay solution was realized by halving the stresses in the fatigue-critical welds of the longitudinal stiffeners, thus increasing the fatigue life by a factor of 32 [4], [5].

2.2 Berlin U-Bahn (subway) Bridge (Berlin, Germany) This bridge for Berlin’s subway, built in 1910, is a riveted steel overhead rail bridge with barrel plates to support the ballast, see Fig. 5. Signs of fatigue-induced cracking were visible in the barrel plates. Conventional repairs would have required the removal of steel plates, rail track, sleepers and ballast, which would have taken considerable time and led to major public inconvenience.

The SPS Overlay solution, consisting of a 25 mm thick polyurethane elastomer core and a 6 mm thick steel top faceplate (SPS 6‑25‑Existing), allowed the operators, Berliner Verkehrsbetriebe (BVG), to repair the bridge with minimum disruption to the operation of the subway as the need to close the bridge was avoided [6]. The repair was applied to the underside of the viaduct between Kottbusser Tor and Prinzenstrasse station near Wassertorplatz on the U1 line. The riveted and curved architectural features of this historic bridge were retained. The fatigue life of the bridge was significantly extended, as verified by the research institute from RWTH Aachen University, which calculated the new fatigue life to be in excess of 3400 years!

2.3 Huskisson Canada Passage Bridge (Liverpool, UK) The Huskisson Canada Passage Bridge is a single-span, two-lane swing bridge and spans the passage between Huskisson Dock and Canada Dock on the Northern Liverpool Dock Estate, Sandhills. The bridge was constructed in 1965 and spans from east to west, carrying a 50 m long x 6 m wide road. This bridge is the only suitable access route for a busy port scrap depot and therefore is in continuous use. The bridge comprises deep longitudinal steel plate girders and a half-through deck supported on trough decking spanning between transverse steel cross-girders.

The depths of the longitudinal beams vary over their length, resulting in a tapered profile on elevation. The bridge deck structure has been upgraded to allow the transit of heavier excavator loads and a new 93 t face shovel from the east wall main dock area to the outer west wall.

Bridge deck replacement or strengthening using carbon fibre would have been expensive and slow, causing major disruption to the client as continuous access is required.

Fig. 6. Huskisson Canada Passage Bridge

The SPS Overlay solution consisted of a 20 mm thick polyurethane elastomer core and an 8 mm thick steel top faceplate (SPS 8-20-Existing) over the entire 300 m2 of the bridge deck [7]. A 10-day intensive work schedule was selected over a 28-day, 2 h/day bridge possession (with restricted width but full load capacity at all other times). The deck strengthening was completed ahead of schedule in just nine days. Restricted access below the deck meant that SPS Overlay was an easier and faster procedure than a carbon fibre solution as all work could be executed from above. This solution also resulted in a shorter schedule than conventional steel replacement. The strengthening of the bridge deck with SPS Overlay is illustrated in Fig. 6.

3 New bridge decks 3.1 Characteristics of SPS bridge decks Prefabricated SPS bridge decks offer an innovative solution for the repair of deficient bridges, which typically require extended design life, increased load-carrying and vehicle capacities and additional pedestrian or cycle capacities to deal with growing transportation demands. The rehabilitation of deficient bridges includes refurbishing the supporting structure, bridge deck replacement and replacement of deck attachments (expansion joints, drains, kerbs, crash barriers). For cases where total bridge replacement is required, piers and abutments are modified or upgraded to suit project specifications and site conditions and a new bridge superstructure with deck is installed. The character-

Fig. 5. Berlin subway Bridge

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Table 1. Characteristics of SPS bridge decks Characteristic

Description

lightweight relative to existing deck construction

–– up to 70 % lighter than concrete decks –– lighter equipment for deck installation

compatible with existing bridge components

–– bolted to supporting girders and stringers –– works compositely with superstructure –– integrated details (deck-girder connections, drains, guardrails, abutments, kerbs) –– option for lightweight or asphalt wearing surfaces

adaptable to multiple configurations

–– cambered girders –– constant cross-section (crowns, superelevations) –– vertical or horizontal curves

prefabrication changes on‑site construction to on‑site assembly

–– simple, prefabricated structural plates –– pre-assembled sections (girders/deck plate) –– on-site assembly (fast erection)

simple design and construction

–– demonstrated performance characteristics –– demonstrated longevity –– pre-engineered –– prefabricated high-quality product –– tested and proven performance

fewer construction constraints and economically viable alternative

–– single trade for deck and superstructure –– no delays due to concrete curing –– immediate structural capacity for construction loads –– fewer girders, piers, pile sizes and pile caps

readily maintained or replaceable in the case of extreme load events (fire, collisions, floods)

–– bolted construction allows easy removal and replacement –– weathering steel or standard steel with applied coatings to provide protection against corrosion (epoxy and polyurethane paints have a lifespan of 15 years to first major maintenance, thermal aluminium spray (metallization) has a lifespan of 40 years)

istics for SPS bridge decks are summarized in Table 1. Prefabricated SPS bridge decks have all the desired and optimum characteristics required so that bridge decks can accommodate the wide range of conditions encountered in bridge rehabilitation, deck replacement and total bridge replacement projects.

3.2 Design and performance Design codes: SPS bridge decks are readily designed in accordance with the requirements given in AASHTO LRFD, CAN/CSA S6 or the Eurocode to satisfy ultimate limit states (flexural and shear resistance, bond strength), serviceability limit states (deflections, vibrations if applicable), fatigue limit states (welded connections) and requirements for bolted connections (shear resistance, bearing resistance and sealing requirements for watertightness).

The fatigue life of the steel-elastomer bond for SPS plates was determined in tests that indicate that the bond strength and core material are not sensitive to fatigue and therefore

will have an infinite fatigue life. All steel bridge structures will have bolted or welded connections with a lesser fatigue category and so these will govern the fatigue resistance.

Core material: The polyurethane elastomer core has been engineered to provide a functional structural sandwich plate for a temperature range between –60 and +110 °C [8]. The modulus of elasticity of the core and the bond strength vary with temperature. There are two basic characteristics that must be checked to satisfy structural performance for the design temperature range: bond strength and minimum core modulus. A design equation for bond strength, which is a function of temperature and steel surface preparation, was developed and must be compared with the maximum interface shear stresses to ensure composite sandwich plate behaviour.

For design calculations, the modulus of elasticity of the elastomer core material is 750 MPa and Poisson’s ratio of the core material is 0.36. The elastomer stabilizes the steel faceplates, precludes local buckling and provides suf-

Fig. 7. SPS bridge deck-to-girder connection details

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ficient shear stiffness to allow the faceplates to reach their full plastic capacity in compression, flexure or a combination of the two. Since there is a large difference in stiffness between the elastomer core and the steel faceplates, calculations of global performance can be based on the steel faceplates alone. For local plate deflections and stresses in the plates, the composite plate behaviour must include the elastomer. In general, design is based on room temperature conditions and performance checked if required at extreme temperature ranges. Further consideration should be given to core thicknesses > 30 mm in an extreme cold temperature environment (–40 to –60 °C).

Bolted and welded connections: Connections between SPS bridge deck plates and the top flanges of supporting girders may be achieved by one of the following methods (illustrated in Fig. 7): a) bolted connection with splice plate (no welding), and b) field welding of adjacent top faceplates in combination with countersunk bolted connection to supporting girders (flush with deck).

The bolted connection with splice plate provides continuity between adjacent plates, does not require field welding and is used with asphalt wearing surfaces only. The field welding of adjacent top faceplates and countersunk bolted connection provides a flush watertight deck surface that allows lightweight or asphalt wearing surfaces to be specified.

The bolt spacing specified is based on providing composite action and is often governed by code requirements for sealing against the penetration of moisture at joints (between steel plates). All connections are pre-engineered to enhance the fatigue resistance of fatigue-critical details and provide an infinite life.

3.3 Fabrication and erection Fabrication: SPS bridge decks are prefabricated in accordance with IE specifications to ensure a proper bond between the steel faceplates and the elastomer core and that plates are dimensionally accurate within specified tolerances. The prefabrication process for SPS plates is highly automated and includes: a grinding machine for steel surface preparation, CNC machinery for drilling, robotic welding of perimeter or seam welds and a polyurethane injection machine for elastomer core injection. Quality assurance guidelines have been developed to ensure that specifications have been met prior to deck plates being shipped from the fabrication plant to site.

Factors governing the size of SPS plates include handling weight, available plate widths and shipping/transportation requirements. Typical SPS bridge deck plates vary in weight from 185 to 245 kg/m2. Widths range from 1800 to 3200 mm and lengths from 8000 to 10 000 mm for ease of handling, but max. 12 000 mm can be supplied. For shipping plates in a container, typical widths are generally limited to max. 2320 mm, but larger widths can be accommodated where alternate shipping arrangements are possible.

SPS bridge decks incorporate connection details, openings for drains, expansion joint details, abutment details and attachment details for barriers/guardrails. All

drawings for SPS are completed using the building information modelling (BIM) software Tekla. The supporting steel structure is also modelled using Tekla and match-fitting between the SPS and supporting steel models ensures accuracy for the erection and fit-up process.

Erection: Individual SPS bridge deck plates for new bridge structures are installed on site or assembled (pre-attached to girder) and installed on site. Industry-standard steel practices for handling and erection are applicable. As for any steel deck structure, waterproofing, drainage and management of water in design is necessary for a bridge with low maintenance and long lifespan. Components or parts susceptible to wear can be designed so that they can be readily replaced. Steel-to-steel bolted connections are typical, with field welds used only if required. Field welds must be designed to limit heat input adjacent to the bonded surfaces to a maximum of 200 °C, which is easily accommodated with standard SPS details. Lifting points are incorporated in the design to allow SPS deck plates to be: a) individually lifted into place or b) pre-attached to girders and erected as an assembly (see photo of a typical bridge application in Fig. 8).

A typical on-site installation procedure is summarized below: 1. Lifting eyes are screwed into pre-drilled holes at the quarter points of the SPS plates and chains are attached to lift them into place.

2. The SPS plates are moved into position using a crane 3. The pre-drilled holes in the SPS plates are aligned with the pre-drilled holes in the supporting girders. Drift pins are used to maintain the alignment until bolting is completed.

4. The adjacent SPS plates are positioned and aligned following the same procedure outlined in step 3.

5. The splice plates (if applicable) are placed in position.

6. The SPS plates are bolted to the supporting girders.

Wearing Surface: The behaviour of wearing surfaces on SPS bridge decks is no different to that on orthotropic steel decks. An asphalt wearing surface can be applied using the following process:

Fig. 8. Erection of SPS bridge deck plates

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a) place a waterproof membrane on the SPS deck, b) overlay with a membrane and tack coat, and c) apply the asphalt layer, where the asphalt mix selected will control the durability of the wearing surface.

Asphalt wearing surfaces have been used on SPS bridge decks, including Schönwasserpark Bridge (Germany) [4], [5], Mettlach Bridge (Germany) [9] and Dawson Bridge (Canada).

Alternatively, a lightweight wearing surface can be applied directly to the SPS bridge deck surface (e.g. Stirling Lloyd’s Safetrack HW anti-skid/slip-resistant surfacing).

This system works by applying a primer to the top surface of the SPS deck, overlaying an epoxy-based resin and applying the aggregate which binds itself to the resin to provide a slip-resistant surface. The lightweight wearing surface does not crack. The slip resistance of a lightweight wearing surface is generally renewed after 10–15 years using the following process: a) simply cleaning the deck to remove contaminants and oil products, and b) applying resin and casting a new layer of aggregate.

3.5 Martin Branch Bridge (Texas, USA) Martin Branch Bridge, located in Wise County, Texas, is a three-span structure carrying two lanes of traffic, with each span measuring 15 240 mm and a clear roadway width of 9144 mm. The existing bridge superstructure was replaced by an SPS 8-25-8 bridge deck cross-section with integrated longitudinal girders designed in accordance with the AASHTO LRFD Bridge Design Specifications [10]. The road surface is a lightweight wearing surface (Stirling Lloyd, applied on site) with four expansion joints dividing the deck into three equal simply supported spans. Each span of the bridge is comprised of three longitudinal plates, i.e. a total of nine plates. The centre plate includes a shop splice along the crown to achieve a 2 % crossfall. The plates are supported longitudinally on W27×114 girders, with the top flange flush with the bottom SPS faceplate. Atmospheric corrosion-resistant steel was specified for the steel faceplates, longitudinal girders and diaphragms. The installation of the deck with integrated longitudinal girders is illustrated in Fig. 9.

3.4 Longevity, durability The longevity of steel bridge decks is a function of their fatigue resistance, corrosion resistance and strict adherence to the specified maintenance programme. The design of SPS bridge deck plates and corresponding connection details are tailored to ensure the structural response is not sensitive to fatigue. The resistance to corrosion is a function of proper water management design, waterproofing details, coating system and installation procedures to guard against the possibility of water infiltration which accelerates corrosion. Industry-standard coating systems typically last 15 years to first major maintenance. Thermal aluminium spray (metallization) systems typically have a 40-year life, which can be extended by 20 years by re-coating. SPS bridge decks can also be specified to use atmospheric corrosion-resistant steel (weathering steel) for bridges where water drainage is controlled and there is no possibility of salt spray from underneath the bridge (i.e. due to traffic from below). Provided the wearing surface and the coatings on the bridge are maintained in accordance with best practices, it will not be necessary to replace SPS bridge deck plates. The only scenario where the plates would need to be replaced would be where an accidental or extreme load event resulted in permanent deformation. Since the SPS plates are modular, prefabricated and bolted in place, damaged plates on the deck can be easily and rapidly replaced.

Many historical steel bridges > 100 years old are still in existence today, which confirms the longevity and durability of steel structures. Concrete bridges and decks in particular are susceptible to cracking, spalling and water infiltration, leading to the corrosion of steel reinforcing bars, which all contribute to a short service life of anything from 15 to 25 years. The service life of SPS bridge decks is the minimum specified design life in the relevant code (75 years to satisfy the Canadian Highway Bridge Design Code, CHBDC), with the understanding that SPS deck plates can last significantly longer if the maintenance programme is followed.

26

Fig. 9. Martin Branch Bridge

3.6 Dawson Bridge (Edmonton, Canada) Dawson Bridge over the North Saskatchewan River in Edmonton consists of five simply supported through-trusses with the first three spans 43 300 mm in length and the last two 76 200 and 30 500 mm respectively. The deck width is approx. 7800 mm and the total deck area is approx. 1845 m2.

The existing concrete deck was replaced with prefabricated SPS 10-25-10 bridge deck plates, which reduced the extent of truss strengthening and expedited the construction schedule [11]. The structure had weakened with age and a load limit had been imposed. Replacing the existing deck with concrete and revoking the load limit would have required a substantial strengthening of the truss superstructure and would have been constrained by a short summer build period.

The new bridge deck, designed in accordance with the CHBDC, used prefabricated SPS plates bolted down to the top flanges of existing transverse members and new longitudinal stringers. The deck plates measured 8000 × 2000 mm on plan, weighed 3.5 t and were lifted into place using telehandlers and then bolted, which created an immediate working platform that could be used for installing

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Fig. 12. Modules pre-assembled for transportation References

Fig. 10. Dawson Bridge

adjacent deck plates. Field welding was not required, with plate continuity along the bridge created by upper and lower bolted splice plates. The deck was sealed with a Stirling Lloyd Eliminator waterproofing membrane prior to applying an asphalt wearing surface. The speed and simplicity of the installation allowed the deck to be replaced in one month as opposed to three, and helped the main contractor complete the whole project in one summer season. The full load capacity for this historic bridge was reinstated without major structural reinforcement. The installation of the deck is illustrated in Fig. 10.

3.7 Integrated SPS bridge deck plates and steel tub girders A design concept for short-span bridges which integrates SPS bridge deck plates with steel tub girders, allowing bridge replacements to be executed quickly and efficiently, is under development. The bridge deck plates are bolted to steel tub girders to create exterior modular units (with pre-attached guardrails) and interior modular units that can be interconnected on site, as illustrated in Fig. 11. The pre-assembled modules can be stacked on a truck bed for transportation to site as illustrated in Fig. 12. A single exterior module is lifted into place and is connected to the adjacent interior module using shaped splice plates. The exterior module on the opposite side must then be positioned, followed by the final interior module, which is shown being lowered into position in Fig. 11. After the modules have been installed, they are field-welded along the length of the bridge to seal the gap between adjacent deck plates. A waterproofing membrane and lightweight wearing surface can be applied to the individual modules during fabrication and between adjacent modules on site.

[1] Feldmann, M., Sedlacek G., Geßler A.: A system of steel-elastomer sandwich plates for strengthening orthotropic bridge decks. Mechanics of Composite Materials, vol. 43, No. 2, Mar2007, pp. 183–190.

[2] Feldmann, M., Geßler, A.: SPS Overlay für Stahlfahrbahn, Schönwasserpark-Brücke, Krefeld. RWTH Aachen University, Germany, Nov 2006.

[3] Martin, J. D., Murray, T. M.: Sandwich Plate System Bridge Deck Tests, Report No. CEE/VPI-ST04/07. Virginia Polytechnic Institute & State University, Blacksburg, VA, Apr 2005.

[4] Matuschek, J., Stihl, T., Bild, S.: Die Verstärkung der orthotropen Stahlfahrbahn der Schönwasserbrücke mittels Stahl-Elastomer-Sandwich (SPS). Stahlbau 76 (2007), No. 7, pp. 465–471.

[5] Heinz, F.: Untersuchungen zur thermischen Beanspruchung von SPS beim Einbau bituminöser Fahrbahnbeläge. Stahlbau 76 (2007), No. 7, pp. 472–477.

[6] Intelligent Engineering. SPS Overlay for the Berlin U-Bahn Viaduct. Ottawa, Canada, Aug 2004.

[7] Intelligent Engineering. Huskisson Canada Passage Bridge, SPS Overlay – Bridge Deck Strengthening. Ottawa, Canada, May 2006.

[8] Intelligent Engineering. Material Characterization: Report for Classification Societies and Regulatory Authorities. Ottawa, Canada, Oct 2002.

[9] Stihl, T., Chassard, C., Feldmann, M., Bild, S.: Neue Technologie für die Hängebrücke über die Saar in Mettlach – Brücken­ fahrbahn aus Sandwich Plate System (SPS). Stahlbau 76 (2013), No. 3, pp. 179–187.

[10] Intelligent Engineering. Martin Branch Bridge, SPS New Build Deck. Ottawa, Canada, Jun 2006.

[11] Intelligent Engineering. Dawson Bridge, SPS Deck Design Report. Ottawa, Canada, Aug 2010.

Keywords: sandwich; bridge deck; overlay; strengthening; lightweight; prefabricated; pre-engineered; longevity; economical

Authors: Stephen J. Kennedy, Dr., P.Eng. 14 Chamberlain Ave., Ottawa, Ontario, K1S 1V9 Canada Aldo E. Martino, P.Eng. 14 Chamberlain Ave., Ottawa, Ontario, K1S 1V9 Canada

Fig. 11. Integrated SPS bridge deck plates and steel tub girders

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Articles Gerhard Lener

DOI: 10.1002/stco.201510003

Steel bridges – numerical simulation of total service life including fracture mechanic concepts The assessment of the total service life of a steel structure should gain importance in the near future due to the increasing significance of building preservation and building modernization. The main cause of the failure of existing structural steelwork under cyclic loading effects is material fatigue. Most steel structures are, however, failure-tolerant.

For economic reasons, this behaviour can be considered by including the crack propagation phase in the assessment. This contribution presents newly developed software tools and the results of some simulations of the total lifetimes of existing structures.

1 Introduction It had already been recognized in the 19th century that metal structures under cyclic loading could fail under lower loads than under static conditions. In the field of mechanical engineering, reliable methods to predict the service life of a structure have always been important, as few machines have ever been designed to endure for an infinite service life. From a financial perspective, the ultimate aim is to design machines in such a way that they resist the expected stresses for a specified designed service life.

In civil engineering, fatigue assessment has achieved growing importance for existing steel and concrete composite bridges. This trend is especially true for road bridges, for which – according to most design standards before the new Eurocodes became valid – complete fatigue checks were not obligatory, as such checks were only specified for railway bridges.

In addition to these primary economic aspects, the sustainability aspect is gaining increasing importance in civil engineering, particularly for

Selected and reviewed by the Scientific Committee of the 10th Japanese-German Bridge Symposium, 16–19 September 2014, Munich, Germany

28

bridges. In the near future, much more of the budget will be spent on maintenance and modernization of the existing infrastructure than for upgrading and renewal [7].

Related to this task, the accurate detection of the residual service life of an existing structure is important.

This contribution reports on the state of development of software tools for determining the total service life of a cyclically stressed steel structure at the University of Innsbruck.

Neglecting corrosion effects, the total life of a structure is the sum of service life up to technical crack initiation and the remaining service life, as shown in Fig. 1. The first part is covered by the mathematical concepts of fatigue assessments. For the remaining

service life, the rules of macro crack growth are valid, where fracture mechanics concepts are appropriate.

This paper describes software developed at the Institute for Structural Engineering & Material Science at the Unit for Steel Construction of the University of Innsbruck. The software developed is based on the finite element method and allows the user to: – perform a fatigue calculation on the entire 3D structure, include multiple cracks in an existing global FE model, and to simulate the propagation of each crack, – consider a much more realistic stress distribution in complex areas of steel structures (e.g. joints) compared with the results available from beam models, – consider a mutual influence and stress redistribution through the propagation of cracks, and – perform a parallel fatigue lifetime and crack propagation simulation (total life).

This method requires a 3D shell model of the entire global structure. Most

Fig. 1. Total service life of a structure [6]

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G. Lener · Steel bridges – numerical simulation of total service life including fracture mechanic concepts

Fig. 2. Railway bridge – A14 structure BB 62

steel structures are built up with cross-sections of thin-walled sheet metal structures. The stress distribution in such structures can be computed very accurately with the finite element method (FEM) by means of 3D shell models. The method developed for computing the total service life is limited to 3D shell models and isotropic materials. The software has been implemented in the ANSYS FE program using the scripting language APDL (Ansys Parametric Design Language) and currently allows a semi-automatic process of crack propagation computation.

The use of the software, including the results obtained, is demonstrated by the example of the steel railway bridge shown in Fig. 2. A complete numerical simulation of the total service life was carried out for this railway bridge, which formed the basis for the design of a successful repair solution.

2 Fatigue – service life up to detectable cracks With the help of fatigue calculations, the repeatable numbers of load cycles are determined up to the occurrence of a technical incipient crack. Reversing this, the existing safety factors can be calculated for a given operational time. The latter method is primarily used for the fatigue assessment of new structures; conversely, the remaining load cycles up to the occurrence of the first cracks are of interest for the simulation of the overall service life of an existing structure.

Moreover, it is possible to identify critical areas of the structure in which the occurrence of fatigue damage is to be expected. The results of fatigue strength calculations also provide information for existing or expected fatigue damage, and help to design appropriate repaired structures.

The assessment of the fatigue strength of welded steel structures according to EN 1993-1-9 [1] is based on the evaluation of the stress ranges Ds:

∆σ = σ max − σ min

(1)

where: σ max maximum stress value (with sign) σ min minimum stress value (with sign) Owing to the major influence of the residual stresses introduced by welding, other parameters such as steel quality and mean stresses are neglected in EN 1993-1-9. Only for non-welded or stress-relieved details in compression may the mean stress influence be

taken into account by adding the tensile portion of the stress range and 60 % of the magnitude of the compressive portion of the stress range.

To determine the maximum stress ranges Dsn = max sn – min sn, software routines based on the theory of the critical cutting plane were developed, which allows a spatial analysis. In order to compute the maximum stress ranges Dsn occurring for each finite element, the stress tensor for each element of the entire structure and the load history are transformed into direction n as shown in Fig. 3. According to EN 1993-1-9, shear stresses may be ignored if Dτ < 0.15 · Dsn. This fully three-dimensional method is also applicable for 2D problems – with a significant reduction in computing time.

Knowledge of the stress ranges occurring in each finite element and the assignment of each element to the existing fatigue detail category enables the allowable stress cycles and the existing safety factors against fatigue damage to be computed.

The determination of the tolerable stress cycles for a variable amplitude can be performed based on linear damage accumulation (PalmgrenMiner):

D= =

n1 N1 n

+

n2 N2

+

n3 N3

+ .....

n

∑ Ni = ∫ dn N i i =1

To take into account variable amplitude loading in the field of civil engineering, the concept of damage-equivalent factors is common and is applied in the current stage of the software.

This concept transfers the responsibility of assuming the load history for the structure during its entire life to the

Fig. 3. Critical cutting planes to determine the maximum stress ranges Dsn

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(2)

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a)

b)

Fig. 4. a) Fatigue detail category, b) stress ranges Dσ based on critical cutting plane

code developers. The damage-equivalent factor l is defined as

λ=

γ Ff ⋅ ∆σ E,2 ∆σ( γ Ff ⋅ Q k )

(3)

where: gMf partial safety factor for fatigue strength, strategy and consequence of failure according to EN 1993-1-9 [1] equivalent constant amDsE,2 plitude stress range related to 2 million cycles Ds(gMf · Qk) stress range caused by the fatigue loads according to Eurocode 1 [4] or [5] The fatigue loads for civil engineering structures are defined in EN 1991-2 for bridges and in EN 1991-3 for crane support structures. The damage-equivalent factor l can be obtained from the specific Eurocodes related to the type of construction (i.e. [2], [3] or [5]).

The fatigue utilization of a crossbeam from the railway bridge is

shown in Fig. 5. The figure shows the simulation results of the fatigue veri­ fication executed according to Eq. (4) and the cracks observed during a regular inspection:

Dd =

γ Ff ⋅ ∆σ E,2 ∆σ C / γ Mf

(4)

3 Crack propagation simulation – remaining fatigue life Not every fatigue crack will necessarily indicate the end of the complete service life of a steel structure. In damage-tolerant structures, a redistribution of loads between components of structural elements will normally occur. A simulation of the crack propagation based on fatigue load effects on the structure is necessary to determine the remaining fatigue life. The calculation of the crack growth rate and the determination of the direction of crack evolution are the central

tasks and are executed by using a fracture mechanics approach. Besides the crack extensions, the evolution of appropriate crack deflection angles at the crack tips must be integrated into the existing FE model, see Fig. 8.

Routines were programmed to per­ form an automatic sequence through all individual simulation steps. Basic values of the crack growth calculation are the stress intensity factors K at the crack tips and the stress intensity ranges ∆K under cyclic loading conditions. ANSYS [16] includes commands that provide the stress intensity factors (SIF) for all three modes KI, KII and KIII, but without signs. The signs of SIFs are required to compute the angle of the crack propagation direction and in order to consider crack closure effects. The software developed contains its own routines that give the SIFs with signs. Based on the limitation to thin shell structures and through-thickness flaws, only KI and KII are relevant. The software includes four options for calculating the crack propagation direction: –– Maximum tangential stress criterion [8] –– Model after Richard [9] –– Energy release rate criterion after Hussain et al. [10] –– Plane with dominant mode I Comparative analyses have shown that the methods mentioned above provide similar results, but the latter two methods require longer computation times.

Based on the material parameters available and the stress ratio R, most types of common analytical crack growth laws can be selected within the software developed. If only a few material parameters are available and the stress ratio R is negligible, then the Paris crack growth law (Eq. (5)) can be chosen [11]:

da = C ⋅ ∆K m if ∆K > ∆K th dN da = 0 if ∆K ≤ ∆K th dN

Fig. 5. Computed utilization factors Dd and damage found on a bridge cross-beam

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(5)

In Eqs. (5) and (6) C and m, as well as the threshold value ∆Kth, are material-dependent parameters. The following crack growth law, developed by Forman, Newman and de Koning and published by Forman/Mettu [12], is also known as the “NASGRO equation”:

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Fig. 6. Unit crack model a)

b)

a)

b)

p  ∆K th  Fig. 8. a) 3D FE mesh of global structure and b) surface domain with cracks − 1 m  ∆K   1 − f    da = C ⋅  ⋅ ∆ K   q dN  1 − R    K max  − 1   Kc   (6) where: p, q empirical coefficients f Newman’s crack opening function [13] R Kmin/Kmax ratio

Eq. (6) describes all parts of the crack growth curve. In addition, crack closure effects and/or mean stress dependence can be considered in the crack propagation simulation. Furthermore, residual stresses are covered by Eq. (6) as this causes a shift in the R ratio. More detailed information about the software developed is available in [14] and [15].

When performing a numerical simulation of crack propagation by using the software tools developed, the structure needs to be remeshed for each increment of crack length. To prevent a complete remeshing of the entire structure at each crack length increment, a “unit crack model” was developed, which can be incorporated in the FE model arbitrarily as often as the designer needs.

This unit model is shown in Fig. 6 and consists of a transition region and

Fig. 7. Meshing of inner region including singular crack tip elements

Fig. 9. Linear elastic stress distribution: a) global structure, b) near crack tip

an inner region including the crack.

The transition region allows the transition between the fine element division in the inner region and the generally coarser finite element mesh in the global model.

The existing mesh of the global model is deleted in the area surrounding the crack tip and the unit crack model implemented automatically by the software. This can also be done on existing shell models without underlying solid model geometry data.

The frequent remeshing during each crack length increment during the crack propagation calculation is only performed in the unit crack models, while the mesh of the global structure remains unchanged. The finite element mesh of the inner region of the unit crack model including the singular crack tip elements is shown in Fig. 7.

Fig. 8 shows the finite element mesh of a cross-beam after approx. 40 crack length increments.

The local linear elastic von Mises stresses in the structure and those near the crack tips are shown in Fig. 9. When determining the remaining service life, the phase of stable crack growth is considered to reach a given limit state. The required maximum number of load cycles reaching the material toughness KIC, excessive

deformation or the exceeding of permissible plastic strain rates can be chosen as termination criteria for the calculation loop for the entire structure including the cracks. When calculating the remaining service life, the simulation model can be updated with fictive cracks or cracks detected during inspections.

The simulation results can be used to create a better realistic basis for determining the time up to reaching the ultimate limit of the structure.

In addition, the crack propagation for a certain time interval, e.g. for the time period between two inspections of the structure, can be computed in order to obtain information about safe periods of operation intervals.

4 Simultaneous calculation of fatigue strength and crack propagation If the occurrence of additional cracks could be expected during the crack propagation phase, simultaneous computation of fatigue strength and crack propagation is required. The structure without cracks is subjected to a fatigue calculation according to the linear damage accumulation theory. The result of this calculation is the number of load cycles that will probably cause initial cracking and will be expressed

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Fig. 10. Simultaneous fatigue strength and crack propagation simulation for a bridge deck

by a damage factor Dd = 1.0. At this point, a crack will be incorporated in the structure and the area around the crack tip will be remeshed.

In the next calculation step, the crack propagation is calculated with a predetermined crack growth increment according to fracture mechanics concepts. Subsequently, the determination of the cumulative load cycles is followed by a renewed strength fatigue calculation. If the damage factor reaches the magnitude Dd = 1 again, an additional crack will be incorporated in the model structure. This loop will be repeated until the predefined limit state of the structure is achieved. Fig. 10 shows an additional example of a bridge deck after inserting a second crack.

5 Conclusions The calculations performed have shown that the simulation results are much more sensitive to the scatter of the material parameters than the influence according to the inaccuracies of the different approaches to the crack propagation direction rule or crack propagation laws. This stochastically distributed input data (loads and material properties) and gross simplification of the calculation model have a significant influence on the results of the total lifetime simulation. Therefore, the plan is to extend the simulation tools developed, operating with probabilistic methods, sensitivity analysis and calibrating on the basis of experimental tests.

Studies performed with the software developed will provide im-

32

proved information for repair and maintenance programmes, optimization of inspection intervals, structure replacement and retrofitting. The fact that the software can be used for existing 3D shell models by making only minor adaptations opens up the possibility for total lifetime simulations to be performed in a very economical way. Without considering the other potential benefits, information on the appropriate selection of required execution classes of the structural components according to EN 1090-2 will be provided owing to the fact that the simulation shows the extent of damage tolerance.

It should be noted that the software developed is based on the simple linear damage accumulation rule (Palmgren-Miner). The order of occurrence of the stress ranges is ignored in this assumption. The software developed is therefore valid for structures without significant overloads, which is applicable for most civil engineering structures (bridges and cranes support structures); however, the length of the cracks is limited by this assumed precondition.

References [1] EN 1993-1-9, 2009, Eurocode 3: Design of steel structures – Part 1-9: Fatigue. European Committee for Standardization (CEN), Brussels.

[2] EN 1993-2, 2009, Eurocode 3: Design of steel structures – Part 2: Steel bridges.

European Committee for Standardization (CEN), Brussels.

[3] EN 1993-3-1, 2009, Eurocode 3: Design of steel structures – Part 3-1: Towers, masts and chimneys – Tower and

masts. European Committee for Standardization (CEN), Brussels.

[4] EN 1991-2, 2010, Eurocode 1 – Actions on structures – Part 2: Traffic loads on bridges. European Committee for Standardization (CEN), Brussels.

[5] EN 1991-3, 2006, Eurocode 1 – Actions on structures – Part 3: Actions induced by cranes and machinery. European Committee for Standardization (CEN), Brussels.

[6] Gudehus, H., Zenner, H.: Leitfaden für eine Betriebsfestigkeitsrechnung.

Stahleisen Verlag, Düsseldorf, 2000.

[7] Kühn, B., Lukic, M., Nussbaumer, A., Günther, H.-P., Helmerich, R., Herion, S., Kolstein, M. H., Walbridge, S., Androic, B., Dijkstra, O., Bucak, Ö.: Assessment of Existing Steel Structures: Recommendations for Estimation of Remaining Fatigue Life, JRC43401, JRC-ECCS, 1st ed., 2008.

[8] Erdogan, F., Sih, G. C.: On the crack extension in plates under plane loading and transverse shear. Journal of Basic Engineering, 85, 1963, pp. 519–525.

[9] Richard, H. A.: Bruchvorgänge bei Mixed-Mode-Beanspruchung von Rissen. VDI report No. 480, VDI-Verlag, Düsseldorf, 1983.

[10] Hussain, M. A., Pu, S. L., Underwood, J.: Strain energy rate for a crack under combined mode I and mode II. ASTM STP 560, American Society for Testing and Materials, 1993, pp. 2–28.

[11] Paris, P. C., Erdogan, F.: A critical analysis of crack propagation laws.

Journal of Basic Engineering, 85, 1963, pp. 528–534.

[12] NASA: Fatigue Crack Growth Computer Program “Nasgro”, ref. manual, 2002.

[13] Newman, J. C.: A crack-opening stress equation for fatigue growth. Int. Journal of Fracture, vol. 24, R131–135, 1984.

[14] Reiterer, D.: Ein Beitrag zur praxis­ gerechten numerischen Simulation der Restlebensdauer von Seilbahnkomponenten mit Hilfe bruchmechanischer Konzepte. PhD thesis, University of Innsbruck, 2012.

[15] Hauser, A.: Beiträge zur praxisge­ rechten Abschätzung der Gesamtlebensdauer und der Schwingungsantwort von Eisenbahnbrücken. PhD thesis, University of Innsbruck, 2013 (in preparation).

[16] ANSYS Inc., Release 15.0, 2014.

Keywords: life cycle; fatigue; crack pro­ pagation; fracture mechanics

Author: Univ. Prof. Dipl.-Ing. Dr. Gerhard Lener University of Innsbruck, Institute for Structural Engineering & Material Science Technikerstr. 13, Innsbruck, Austria Gerhard.Lener@uibk.ac.at

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Articles Toshihisa Mano* Ingbert Mangerig

DOI: 10.1002/stco.201510009

Tensile load-carrying behaviour of elastomeric bearings Elastomeric bearings for seismic isolation applications can be subjected to tensile loads depending on the geometrical configuration, high vertical seismic motion or excessive horizontal deformation due to the elongated-period horizontal motion. It is a known fact that cavities develop within elastomeric material when it undergoes a certain amount of tensile force in a very constrained condition since a high hydrostatic tensile stress builds up. Once these cavities have developed, the tensile stiffness of the bearing drops dramatically. This paper contributes to understanding this phenomenon itself and its influence on the basic properties of elastomeric bearings. For this purpose, two types of elastomeric bearing were tested and the cavitation phenomenon observed.

Moreover, those test results are compared with the FE simulation results from the modified hyperelastic material model with the cavity damage criterion. The two-phase softening model presented here can simulate the real softening behaviour of elastomeric bearings well, and it may even help us grasp a better insight into the cavitation phenomenon.

1 Introduction Among the increasing number of applications for seismic isolation, high-rise buildings are no exception. Owing to their aspect ratios, the overturning moment has been an obstacle for the realization of seismically isolated high-rise buildings, since the conventional seismic isolator bearings are not designed to accommodate tensile forces. The rubber isolator bearings are known to be capable of carrying a little tension, but their tensile capacity has not been utilized in practice because of the cavitation-induced softening that occurs when the rubber bearing is subjected to a certain degree of tension.

This phenomenon has been known for quite some time, but research associated with rubber bearings is rarely found. In this paper, therefore, rubber isolator bearings are investigated for their capacity to handle tensile forces, the aim being to gain insights into the cavitation phenomenon mechanism theoretically, analytically and experimentally.

As for the cavitation mechanism itself, it is generally agreed that cavities develop if the rubber contains micro-

Selected and reviewed by the Scientific Committee of the 10th Japanese-German Bridge Symposium, 16 to 19 September 2014, Munich, Germany * Corresponding author: mano@maurer-soehne.de

scopic voids of a certain size, e.g. air bubbles, and is subjected to a hydrostatic pressure of approx. 5G/2, where G is the shear modulus of the rubber material. However, as pointed out in the mathematical research work [1], the pressure required for cavitation would be higher if the balance in the purely hydrostatic pressure condition is not maintained.

Compared with the results of uniaxial tension cases, slight differences in the cavity-induced softening behaviour of the bearing are frequently observed in the majority of the offset tension tests, i.e. a shift in the onset of cavitation or the degree of softening. Part of the reason for this change is the internal rotation of the bearing [2], but it can be explained mainly by the cavitation instability surface criterion [1]. This damage criterion is implemented for the simulation and, once cavitation is triggered, the degree of softening is controlled by reducing the bulk modulus as introduced in other research work [3]. It can be so interpreted that rubber becomes a highly compressible or “expandable” porous medium. Based on the study of FE and test results, a second softening phase is suggested, and also introduced into the cavitation damage model implemented. Right after the onset of cavitation up until the fully cavitated state, the degree of softening is relatively mild, but when enough cavities spread through the rubber body, they may expand its size elastically instead of developing further cavities. In this second phase, the degree of softening is high and the stiffness may decrease almost to zero, although in many cases the rubber can be stretched further without break. Conducting a uniaxial tension test on a single small rubber disc glued between two steel plates, as in laminated rubber bearings, enables us to obtain the parameters necessary for this two-phase softening model, such as the second critical volume change ratio or the degrees of softening. Then, with those parameters, it should be possible to simulate the tensile load-carrying behaviour of a much larger rubber body as well. Those parameters of the cavitation model implemented were obtained by adjusting the FE results to the uniaxial tension tests of the isolator rubber bearings. Using the same parameters, the force–deformation relationship obtained by the offset tension tests was successfully predicted.

2 Simulation model 2.1 Hyperelastic material The Arruda-Boyce material model available in ADINA is used for simulating an elastomer, whose strain energy density function is expressed as

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1

(

)

(

1

)

11

(

2 I3 − 27 W = G  2 I1 − 3 + 20n I1 − 9 + 1050n 2 1 

+

(

)

(

)

(1)

)

 19 1 I14 − 81 + I15 − 243 +  3 4 7000n 673750n 

Only two input parameters are necessary – the initial shear modulus G and the locking stretch λ = n0.5. If only the first term is considered, the classical neo-Hookean material based on Gaussian chain statistics is obtained. In order to take the small compressibility of filled rubber into account, the strain invariants Ii are substituted by the reduced strain invariants Ji, where J1 = I1I3–1/3, J2 = I2I3–2/3 and J3 = I1/2 3 = det ot X , where X is the deformation gradient tensor in Cartesian coordinates, x i,j = X ij = ∂ x i / ∂ x j. The volumetric potential otWV, which is the function of both the displacement and the pressure interpolated separately, is also added:

(

)

( )

W = WD J1 , J 2 + WV J 3

(

)

(3)

Integrating this pressure with respect to J3 leads to the volumetric strain energy function:

Wv =

(

)

2 1 E J −1

2 b 3

(4)

A non-linear pressure function instead of the linear one above (Eq. (3)) is seemingly more appropriate and another function Wv is obtained by integrating the non-linear pressure function accordingly [4]. However, when the user-supplied material, with which users develop their own subroutine, is used, then ADINA seems to calculate the pressure with the linear expression above. If the non-linear function is adopted, an inconsistency appears between the subroutine and the source code. To avoid inconsistency in the calculation, users have to compromise and use the linear expressions (Eqs. (3) and (4)).

2.2 Cavitation damage model To include the aforementioned softening phenomenon caused by cavities, the hyperelastic material model provided by ADINA has to be modified. Its so-called user-supplied material model enables users to develop their own subroutine. Another research work [3] is cited for the definition of the post-cavitation behaviour of the hyperelastic

34

Wv =

(

)

1 E J −1 2 b 3,crit

2

+

(

1 E J 2 b,cav 3,cav

)

2

(5)

(2)

The pressure must be calculated from the derivative of the total potential with respect to the volume change ratio det X = J3, and only the volumetric part of the strain energy function should contribute to the pressure. Hence, the use of the reduced invariants Ji is necessary in order to eliminate the contribution of the deviatoric part of the strain energy function to the pressure.

Assuming a linear relationship between the pressure and the volume change ratio, the pressure function adopted in ADINA is expressed as

p = −E b J 3 − 1

body, due to its rather simple formulation where the cavity-induced softening is associated with a significant reduction in the bulk modulus to 1/200 of its original value. This factor of 1/200 seems to be merely an empirical value and has to be varied according to the rubber material, the degree of molecular cross-linking and the amount or type of reinforcement filler material. This must be the case since the degree of softening is affected by those factors as were seen, for instance, in other experiments [5]. In general form it is expressed as Eb,cav = Eb/κcav, with an arbitrary reduction factor κcav in this paper. This reduction in the bulk modulus affects the volumetric part of the strain energy density and its derivative with respect to the ratio of the volumetric change J3, namely pressure p. They modify the volumetric part of the strain energy density function thus

where : J 3,crit = J 3 , J 3,cav = 0 J 3,crit = E b,cav

when p < pcrit

pcrit

+ 1, J 3,cav = J 3 − J 3,crit Eb = E b /κ cav

when p ≥ pcrit

Similarly, the pressure function is modified to tp

(

)

= − E b J 3,crit. − 1 + E b,cav J 3,cav.   

(6)

Finally, the second derivative of Wv with respect to J3 becomes

∂2 Wv ∂ J 23

= Eb

when

p < pcrit

= E b,cav when

p ≥ pcrit

(7)

In the work of Dorfmann and Burtscher [3], the critical pressure pcrit was set to a constant value of 5G/2. The model worked well for simulating the simple tension test on a rubber pad from Pond and the elastomeric bearing.

Using this damage criterion, however, it is feared that the onset of cavitation would not be predicted correctly where elements are subjected to non-hydrostatic negative pressure. Therefore, the cavitation instability surface is implemented in the user-supplied material subroutine for the damage criterion. This cavitation instability surface is derived mathematically by representing the deformation field of the incompressible spherical neo-Hookean body through the radius of the body and the three parameters that represent the size and the aspect ratio of a spherical cavity within the body [1], [6]. The principle of virtual work is then applied to that body so the relationship between the critical stresses and the form of cavity is obtained. In the subroutine, three principal stresses are obtained from the main source and, using these stress values, Eq. (8) determines if a damage function is triggered:

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( 4σ − σ 1

2

)(

)(

− σ 3 4σ 2 − σ 3 − σ1 4σ 3 − σ1 − σ 2

)

(8)

−125G3 < 0 This equation represents the surface in the space defined by the three axes σ1 – σ2, σ1 – σ3 and σm = (σ1 + σ2 + σ3)/3, i.e. the difference between principal stress components and the volumetric stress component respectively. The mean stress value σm is calculated with the principal stresses at the moment when this condition is violated and is set as the critical pressure value of the element considered. Once this criterion is violated, the element in which cavitation is activated remains soft, unless the pressure of the element returns to a positive (compressive) value. Implementing this condition is especially necessary when analysing offset tension tests on rubber bearings. It is observed in FE results that, with a high shear deformation, the negative pressure of some elements after violating the criterion is reduced again to below the critical level due to the interaction between neighbouring elements. When that happens, the stress distribution between those elements becomes inconsistent.

Studying the test results in the next section or the test results of other research work [7], it seems that cavitation-­ induced softening can be categorized into two phases: at the onset of cavitation, the degree of softening is mild; a more radical softening follows after some further increment of loading. The first stage can probably be attributed to the cavity development phase and in this phase the softening is mild because the majority of the rubber is not yet cavitated. Volume change is low and therefore developed cavities cannot expand. The second phase begins when most of the rubber is cavitated and a larger volume change occurs. With enough cavities, the constraint to the rubber’s deformability is released and then cavities have the chance to expand further. In this phase it is the size of the cavities that increases rather than the number of cavities. As a result, radical softening occurs due to the reduction in effective planar area. The concept of the two-phase cavitation is based purely on the observation of the test and FE results and thus is merely a hypothesis. However, as will be shown later, the stress–strain curves obtained from this model correspond quite convincingly with the ones measured in experiments. For simplicity, the same principle is

applied for the second phase and then the modified functions for the volumetric strain energy and pressure in the second phase are calculated as Wv =

(

)

1 −1 E J 2 b 3,crit +

(

2

1 E J 2 b,exp 3,exp

)

+

(

1 E J* 2 b,cav 3,cav

)

2

(9)

2

where : J 3,crit = E b,cav

pcrit

+ 1, J*3,cav = J 3,crit2 − J 3,crit , J 3,exp = J 3 − J*3,cav Eb = E b /κ cav , E b,exp = E b,cav /κ exp

Similarly, the pressure function is modified to tp

(

)

= − E b J 3,crit − 1 + E b,cav J*3,cav + E b,exp J 3,exp   

(10)

The second derivative of Wv with respect to J3 in the second phase is therefore

∂2 Wv ∂ J 23

(11) = E b,exp

This concept is shown schematically in Fig. 1. Note that J3,crit2 and κexp are additional input parameters and have to be adjusted according to the material. In particular, the second critical volume change ratio J3,crit2 is here the criterion for the second softening phase and can be determined by checking the volume change ratio in the FE model when the cavitation development phase is completed. Alternatively, if the results of the uniaxial test on a rubber disc or rubber bearing are available, the axial strain at the onset of the second softening phase can be directly used as an input value because the axial strain is very close to the volume change ratio at the centre. This is an elaborate procedure and would be useful when the range of the critical volume change ratio is known approximately.

Hereinafter, the cavitation model implemented is referred

Fig. 1. The three phases of the cavitation criterion

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to as “two-phase softening model” or simply “two-phase model”.

3 Experiment A series of elastomeric bearing tests were carried out in the laboratory of the Chair of Construction, University of the Armed Forces, Munich (Universität der Bundeswehr München). Twelve bearings with the first shape factor of 18.8 and another twelve with S1 = 9.4 were prepared. For convenience, the former are denoted type 1 bearing and the latter type 2 bearing. All bearings were made from low-damping natural rubber and were subjected to either simple tension or shear and tension, the aim being to cause damage within the rubber. Both bearings tested have the same diameter (450 mm) and a total rubber thickness of 120 mm, but different first shape factors. The type 1 bearing consists of 20 layers of 6 mm thick rubber pads, whereas the type 2 bearing consists of 10 layers of 12 mm thick rubber pads. Bearings with a higher first shape factor (S1 > 15) are likely to be used for seismically isolated buildings, and bearings with a shape factor of up to 10 are for bridges. In this sense, the type 1 bearing is for seismic isolation applications in buildings and type 2 for bridges. Fur-

thermore, the same planar dimensions and the same total thickness of rubber layers enable us to observe the difference in the cavitation process due purely to a different first shape factor.

3.1 Test setup For the uniaxial tension test, four LUKAS LHC 60-35/25 actuators were installed between two load-transferring plates as shown in Fig. 2. These actuators apply the compression force so that these plates are pulled away from each other. The forces were measured by AST Gruppe KAF 250/500 kN load cells. Displacement was measured at two positions (see Fig. 2) by the displacement transducer that was calibrated by the Mitutoyo micrometer gauge.

This test configuration was slightly modified for the offset tension test. In order to prevent the bearing from rotating due to the initial shear deformation, a support construction was set up, which is indicated in Fig. 3. A tension rod was installed on the other side for the same purpose. Furthermore, two actuators on the left side were replaced by just one actuator with an ENERPAC P84 ULTIMA hydraulic steel hand pump since the tensile force required on this side is smaller due to the aforementioned rotation caused by the shear deformation. The two load-transferring plates were also kept parallel during the test by manually adjusting the loading on the left side by pumping by hand.

3.2 Test results and FE simulation results

Fig. 2. Test setup for uniaxial tension test

The series of experiments described in the previous section were simulated with the two-phase softening model implemented. As for the steel material, the plastic-multilinear model based on the steel properties of S235 was used. The dumbbell-shaped elastomer sample ISO 37 type 1 (dumbbell type S1) was tested in order to obtain the characteristic material values. Using manual curve-fitting, the shear modulus of 0.96 MPa and the locking stretch of 2.8 were obtained and the simulation model captures the real behaviour of bearing type 2. As for bearing type 1, the parametric study was carried out to fit the force–displacement curve of the test. From the test result it was also observed that the shear modulus for bearing type 1 is somewhat higher than

Fig. 3. Test setup for offset tension test

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that of bearing type 2. Therefore, the shear modulus G = 1.05 MPa was selected for simulating the type 1 bearing.

Apart from test bearing type 1-09, the adjustment results in a better fit and therefore the shear modulus of 1.05 MPa was set for the analysis of bearing type 1. For bearing type 2, the shear modulus should only be reduced a little for type 2-03. However, the shear modulus of 0.96 MPa was used for the analysis since with this value most of the test results are in good agreement with FE results. Another characteristic value for the Arruda-Boyce material, the bulk modulus, was also determined by the parametric study. The best fit simulation result for the compression stiffness was obtained with a bulk modulus of 500 MPa. Hence, this value was used for all simulations.

3.2.1 Results of uniaxial tension tests The force–displacement curves of both bearing types are shown with the simulation results in Figs. 4 and 5 as examples. For both cases, the expected softening is observed, although its degree and onset point are different. Softening of the type 2 bearings appears at a lower loading level than that of the type 1 bearings. This is because the distribution of negative pressure in the radial direction is not constant and a higher pressure occurs in the centre region. This distribution is flattened towards constant distribution as the first shape factor increases, which means that, for the same loading level, the type 2 bearings experience a higher negative pressure there than the type 1 bearings. Therefore, cavities should develop in the type 2 bearings earlier with a lower loading level than the type 1 bearings, and the test results justify this concept.

The performance of the cavitation simulation model implemented was checked with these test results. In order to distinguish the results, the red line always represents the result with the shear modulus G = 0.96 MPa and the green one the result with G = 1.05 MPa. The second softening phase is activated at the critical volume change ratio J3,crit2 = 1.03 and the second reduction factor for the bulk modulus κexp = 10 is selected. The former parameter is initially determined roughly by the deformation where the second softening phase seems to begin. Analysing all the results of uniaxial tension tests, that deformation point is

Fig. 5. Test and simulation results for bearing type 2-03

approx. 5 mm – equivalent to the vertical stretch ratio 1.04.

As explained in 2.2, this strain should be nearly equal to the volume change ratio due to the highly constrained rubber configuration in all three principal directions. The FE result shows that the J3 value is about 1.03 at the time step when most of the rubber is cavitated. As expected, these two values are very close to each other and the best fit to these curves is obtained with J3,crit2 = 1.03. All these parameters hold for all simulations here. For the type 2 bearing, the result is in good agreement as well. Note that the force-displacement curve calculated with the FE analysis almost coincides with the path generated by connecting the peaks of the second cycles of each loading level and this tendency is also true for the offset tension case in the next section. The difference in the forces between the first and the second cycle of each loading level is the softening caused by cavitation. It is assumed that the “delay” in the cavitation is due to rubber’s viscoelastic property. In the FE analysis this viscoelastic property is not taken into consideration and so this delay does not occur. If the viscoelastic property of rubber were to be considered in the FE analysis, the curves would be closer to each other.

Fig. 6 plots the critical pressure for both bearing types under the maximum tensile load of 636 kN. The yellow colour denotes the critical pressure range from 2.7 to 3.0 MPa and the light green colour denotes the critical pressure range from 2.4 to 2.7 MPa. Pressures 2.7 and 2.4 MPa are nearly equivalent to the pressure obtained by 5G/2 for bearing types 1 and 2 respectively. From these plots it is clear that almost all cavitated elements are subjected to the hydrostatic pressure. Bearing type 2 has more intact areas along the outer edge than bearing type 1 because of a higher deformability there.

3.2.2 Results of offset tension tests

Fig. 4. Test and simulation results for bearing type 1-02

The force–displacement curves of bearing types 1-07 and 2-05 from the tests and FE results are compared in Figs. 7 and 8. Under offset tension, softening begins at marginally lower loading levels than the simple tension case, and the initial stiffness seems to be generally lower as well. The compressive stiffness is also lower when the shear defor-

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Fig. 6. Plots of critical pressure pcrit – left: type 1; right: type 2

mation is present for the effective planar area resisting compression is reduced. This explanation is probably not valid for the tensile stiffness, but the rotation within the bearing [2] contributes to the lower stiffness. It is observed in all force–displacement curves for uniaxial tension and offset tension tests that the force required to reach the same level of displacement previously reached is lower. This difference in the forces required is most distinct between the first and second cycles. Furthermore, cyclic force–displacement curves under a small loading range in which they are nearly linear exhibit no such difference between consecutive loading cycles. From these observations it can be deduced that the difference in the force required between consecutive loading cycles is caused mostly by the cavitation, or perhaps delamination, but not by Mullin’s effect.

With the same input parameters as in the uniaxial case, the simulation model delivers results corresponding to the test results.

Fig. 9 shows the plots of the critical pressure for both bearing types under the maximum shear deformation of 100 mm and the maximum tensile load of 636 kN. The same band plot as in Fig. 6 is applied. Here again, the critical pressure values of bearing type 1 are generally higher than those of bearing type 2 because of the difference in the

shear modulus. The critical pressure distribution is not uniform and the critical pressure values are also higher than the ones in Fig. 6. The hydrostatic condition is disturbed by the existing shear deformation and therefore a higher pressure is required to initiate cavitation. The results correspond well with the theory. That is also why the intact areas are slightly larger than in the uniaxial tension case.

However, if the overall behaviour is compared, the vertical stiffnesses in these cases are lower than the uniaxial tension cases. That is probably because the effective area resisting tensile force is reduced due to the shear deformation.

The same parameters are used for the both bearing types and the results are all in good agreement. This means that the critical parameters are all material-dependent.

Only one uniaxial tension test on a small bonded rubber disc is then needed to determine the parameters required.

Using these parameters, very accurate simulation results for any other geometrical configuration can be expected.

Before closing this section, the FE results are compared in the Fig. 10, which helps to recognize how the first shape factor and the simultaneous shear deformation influence the cavitation process.

Indeed, the shear deformation of 100 mm has an influence on the cavitation process, but it is not as significant

Fig. 7. Test and simulation results for bearing type 1-07

Fig. 8. Test and simulation results for bearing type 2-05

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Fig. 9. Plots of critical pressure pcrit – left: type 1; right: type 2

though this may be a conservative statement. So it can be concluded that seismic isolator rubber bearings are on the safe side with this criterion because bearings with such high first shape factors are frequently used for seismic isolation purposes. For the type 2 bearings, cavities develop before reaching this allowable stress level, so the criteria for seismic isolator rubber bearings with lower first shape factors, which are often used for seismically isolated bridges or simply as bridge bearings, may need to be reconsidered.

3.3 Changes in bearing properties due to cavities

as the influence of the first shape factor. The “allowable” tensile stress specified in design standards [8], [9], i.e. equivalent to twice the shear modulus, is indicated in the same figure. For bearing type 1, this limit line seems to be below the onset of softening and then perhaps all bearings with even a higher first shape factor would be safe enough, al-

Before and after the tension/offset tension tests, the properties of the bearings were evaluated in an extra set of tests in order to examine the influence of cavities on the bearing characteristics. These properties are vertical stiffness, horizontal stiffness and damping. In order to exclude Mullin’s effect for the evaluation of the horizontal stiffness, the bearing is subjected to 10 cyclic loadings and the results from the 9th cycle are presented. All property values are summarized in Tables 1 to 3. Changes in horizontal and vertical stiffness are quite small despite the fact that not only cavitation but also delamination between shims and elastomer pads might have occurred. The change in damping varies, indicating that there is no logical pattern. The

Table 1. Change in horizontal stiffness (9th cycle) of type 1 bearing (f = 0.0664 Hz)

Table 2. Change in damping ratio (9th cycle) of type 1 bearing (f = 0.0664 Hz)

Fig. 10. Comparison of all force–displacement curves

Bearing No.

Kh before tension test [N/m] × 106

Kh after tension test [N/m] × 106

Deviation [%]

Bearing No.

ξ before tension test [%]

ξ after tension test [%]

1-01

1.32

1.28

–3.0

1-01

5.7

5.8

1.2

8.3

6.4

–22.9 –0

Deviation [%]

1-02

1.30

1.25

–3.8

1-02

1-03

1.31

–0

–0

1-03

7.0

–0

1-04

1.23

1.18

–4.1

1-04

7.5

7.7

2.7

1-05

1.29

1.24

–3.9

1-05

8.0

7.4

–7.5

1-06

1.34

1.30

–3.0

1-06

5.9

7.3

23.7

1-07

1.26

1.23

–2.4

1-07

8.0

8.1

1.3

1-08

1.26

1.16

–7.9

1-08

7.3

9.4

28.8

1-09

1.16

1.11

-–4.3

1-09

8.5

8.2

–3.5

Mean

1.27

1.22

–4.1

Mean

7.4

7.5

3.0

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Table 3. Change in vertical stiffness of type 1 bearing Bearing No.

Kv before tension test [N/m] × 108

Kv after tension test [N/m] × 108

Deviation [%]

1-01

4.22

3.91

–7.3

1-02

4.81

4.49

1-03

4.93

1-04

4.54

Table 5. Change in damping ratio (9th cycle) of type 2 bearing (f = 0.0664 Hz) Bearing No.

ξ before tension test [%]

ξ after tension test [%]

Deviation [%]

–6.7

2-01

9.4

8.8

–6.4

–0

–0

2-02

9.2

9.5

3.3

4.56

0.4

2-03

11.1

10.3

–7.2

9.9

10.3

4.0

1-05

4.65

4.48

–3.7

2-04

1-06

4.80

4.79

–0.2

2-05

10.8

11.2

3.7

1-07

4.74

5.14

8.4

2-06

10.2

11.3

10.8

Mean

10.1

10.2

1.4

1-08

4.76

4.72

–0.8

1-09

4.72

4.54

–3.8

Mean

4.69

4.58

–1.7

Table 4. Change in horizontal stiffness (9th cycle) of type 2 bearing (f = 0.0664 Hz)

Table 6. Change in vertical stiffness of type 2 bearing Bearing No.

Kv before tension test [N/m] × 108

Kv after tension test [N/m] × 108

Deviation [%]

Kh before tension test [N/m] × 106

Kh after tension test [N/m] × 106

2-01

3.14

3.03

-3.5

Bearing No.

Deviation [%]

2-02

3.56

3.40

-4.5

2-03

3.36

3.11

-7.4

2-01

1.22

1.18

–3.3

2-04

3.53

3.30

-6.5

2-02

1.15

1.11

–3.5

2-05

3.22

3.05

-5.3

2-03

1.08

1.04

–3.7

2-06

3.34

3.15

-5.7

2-04

1.16

1.11

–4.3

Mean

3.36

3.17

-5.5

2-05

1.15

1.10

–4.3

2-06

1.12

1.06

–5.4

Mean

1.15

1.10

–4.1

measurement and evaluation of such small damping is not quite accurate since, admittedly, the sampling frequency during measurement or rounding the number during the evaluation process can affect the results and might lead to an error.

The same sets of figures for the type 2 bearing are given in Tables 4 to 6. For bearing type 2, the change in characteristic values is in the same order of magnitude as bearing type 1. It can thus be concluded that the influence of cavities or delamination on the properties of both types of rubber bearing is minor within the loading or displacement range tested.

4 Conclusion The load-carrying behaviour of elastomeric bearings under tension was studied by means of numerical and experimental analysis. Tension and offset tension tests were carried out for two types of elastomeric bearing with different shape factors: bearing type 1 has a higher shape factor and represents the isolator for buildings, and bearing type 2 represents the isolator for bridges. Differences in the softening behaviour were observed between the two shape factors as well as between the tests with and without shear deformation. This is explained by the negative pressure distribution and the concept of the cavitation instability surface [1]. Bearing properties such as horizontal stiffness,

40

damping and vertical stiffness were evaluated by a series of tests before and after the tension/offset tension tests. Comparing both sets of results indicated no major differences in those properties due to cavities.

The cavitation damage model implemented for this study is also based on the cavitation criterion from [1] and the softening definition from [3]. Furthermore, the concept of two softening phases was introduced from the observation of test results. The model implemented delivered results corresponding to the test ones once the input parameters were fitted to one result. This indicates that the tensile load-carrying behaviour of elastomeric bearings can be simulated if the extra material inputs for the cavitation model are available from a test on a small single elastomeric pad. There is, however, some margin for improvement in this cavitation damage model, such as automating the criterion of the second softening phase by checking the proportion of the damaged elements with respect to the intact elements.

References [1] Hou, H. S., Abeyarante, R.: Cavitation in elastic and elastic-plastic solids. Journal of Mechanics and Physics of Solids 26 (3) (1992), pp. 571–592.

[2] Kelly, M. J., Takhirov, M. S.: Tension buckling in multilayer elastomeric isolation bearings. Journal of Mechanics of Material and Structures 2 (8) (2007), pp. 1591–1605.

[3] Dorfmann, A., Burtscher, L. S.: Aspects of cavitation damage in seismic bearings. Journal of Structural Engineering 126 (5) (2000), pp. 573–579.

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T. Mano/I. Mangerig · Tensile load-carrying behaviour of elastomeric bearings

[4] Boyce, M. C., Arruda, E. M.: Constitutive models of rubber elasticity: A review. Rubber Chemistry and Technology 73 (2000), pp. 504–522.

[5] Pond, T. J.: Cavitation in bonded natural rubber cylinder repeatedly loaded in tension. Journal of Natural Rubber Research 10 (1995), pp. 14–25.

[6] Hou, H. S.: Cavitation instability in solids. Dissertation, Massachusetts Institute of Technology, Cambridge (MA), 1990.

[7] Furuta, T., Araki, S., Kanamori, S.: Finite Element Analysis for Shear-Tensile Characteristics of Natural Rubber Bearings.

Journal of Structural Engineering B, Architectural Institute of Japan 51B (2005), pp. 231–236 (in Japanese).

[8] European Committee for Standardization (CEN): Anti-Seismic Devices, EN 15129:2009.

[9] Japan Road Association: Japanese specifications for highway bridges bearings, Apr 2004.

Keywords: elastomeric bearing; tension test; cavitation; FE simulation

Authors: Toshihisa Mano Maurer Söhne Munich GmbH & Co. KG Frankfurter Ring 193, 80807 Munich, Germany mano@maurer-soehne.de Univ.-Prof. Dr.-Ing. Ingbert Mangerig Universität der Bundeswehr München Chair of Construction Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany ingbert.mangerig@unibw.de

People Prof. Udo Peil awarded honorary ­doctorate Even though there are about 300 kilometres separating Ruhr-Universität Bochum and TU Braunschweig, the two universities are closely connected. Prof.

Dr.-Ing. Udo Peil, who was the head of the TU Department of Steel Structures between 1992 and 2012, has been making important contributions to the two universities scientific cooperation for years now. On 17th October 2014, Bochum’s Faculty of Civil and Environmental Engineering Sciences awarded him an honorary doctorate for his extraordinary academic merits.

“Professor Peil is an outstanding, internationally recognized researcher who has been serving as a role model for many”, the justification for the honorary doctorate said. Due to his charisma and his convincibility Peil helped to considerably and permanently shape the fields of steel construction, leight weight metal construction and constructive engineer-

ing, both in terms of research and teaching. The close contact to the RUB Faculty of Civil and Environmental Engineering Sciences was mainly established on the basis of joint fundamental research within collaborative research centers, research groups and individual projects. The successful cooperation between the SFB 477 “Life Cycle Assessment of Strcutures” at TU Braunschweig and the Bochum SFB 398 “Lifetime-Oriented Structural Design Concepts” was especially fruitful for RUB. Further synergies in the area of wind engineering originated from joint research at the RUB boundary layer wind tunnel.

Within its almost fifty years of history the RUB Faculty of Civil and Environmental Engineering Sciences only awarded the honorary doctorate to a researcher for the eleventh time, most recently in 2008 to Prof. Gerhard Schuëller (Dr. h. c.). The laudatory speech for Udo Peil was held by Prof. Rüdiger Höffer (Wind Engineering and Fluid Mechanics, RUB) and one of Prof Peil’s

Prof. Udo Peil receiving the honorary doctorate from Vice Dean Prof. Martin Radenberg (© RUB, photo by Schirdewahn)

oldest companions, Prof. Wilfried B. Krätzig, who holds several honorary doctorates himself.

Udo Peil was born on 20th April 1944 in Oldenburg (Lower Saxony). After completing his high school diploma he studied Civil Engineering at TU Braunschweig between 1965 and 1971, and in 1976 he completed his PhD there. After several other positions he was offered a professorship for Steel and Light Weight Metal Construction at the University of Karlsruhe. In 1992 he accepted a professorship at TU Braunschweig, where he was the Head of the Institute of Steel Construction until his retirement in 2012. Peil was the President of the Wind Engineering Society (Ger-Aus-Swi) and a member of several expert committees. In 2008 he founded the “Peil Ummenhofer company mbh” as a partner with its headquarters in Braunschweig.

Further information: www.massivbau.rub.de

Professors Elmar Weiler, Hans-Jürgen Niemann, Udo Peil, Martin Radenberg, Wilfried B. Krätzig, Rüdiger Höffer (from left to right; © RUB, photo by Schirdewahn)

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Articles Torsten Höglund

DOI: 10.1002/stco.201510002

Cold-formed members – comparison between tests and a unified design method for beam-columns In [1] a unified method for the design of steel beam-columns is presented. The method has been checked for rolled steel beam-columns and extruded aluminium beam-columns. It is included in Eurocode 9 [19] for aluminium members and it is proposed to be included also in Eurocode 3 Part 1-3 [16] as well, but then it needs to be checked for typical cold-formed sections.

Cold-formed sections are usually un-symmetric and thin-walled, for instance channel sections or C-shaped sections (lipped channels). When used as compression members, local buckling causes a redistribution of the longitudinal stress which leads to a shift of the effective centroid. The shift causes overall bending and reduces the column strength when the member is compressed between pinned ends. In fixed-ended columns, however, the shift of the effective centroid is balanced by a shift of the ­applied force and bending is not introduced [6]. As a result, the strength of fixed-ended channel column exceeds that of a pinended column of the same effective length [7].

Using effective width for the flanges of channels e.g. according to EN 1993-1-5 [17] gives conservative result as the centroid of the effective section is too close to the web. The mixed effective width/ effective thickness method for outstand elements given in Annex D of EN 1993-1-3 [16] is the basis in the following interpretations.

1 Flexural-torsional buckling For members susceptible to torsional deformation, flexural-torsional buckling is often the decisive buckling mode. For un-symmetrical cross-sections like channels the following criterion should be satisfied according to [1] for My,Ed = 0.

 N  Ed    N z,b,Rd 

ηc

 M z,Ed  +   M z,b,Rd 

ξ zc

≤ 1.00 (1)

where Mz,Ed = DMz,Ed for pin-ended column loaded in the centroid of the gross cross section, whereas for fixed-ended columns Mz,Ed = 0. For eccentrically loaded column

Fig. 1. Plain and lipped channel (U- and C-section)

Nz,b,Rd = wx cz Aefffy/gM1 is the lesser of the axial force resistance for buckling in the xy plane and the axial force resistance for flexural-torsional buckling. cz is the reduction factor for z-axis buckling or flexural-torsional buckling and wx in Nz,b,Rd is a factor to allow for the design section of the member. For axially loaded members, wx = 1.

Mz,Rd = α z Wzfy / γ M1 is the bending moment resistance with respect to the z-z axis, where az is the shape factor for z-axis bending, Wz is the elastic section modulus and fy the yield strength. For class 4 cross sections, az ≤ 1.0 and for class 1, 2 and 3 sections az ≥ 1.0.

The exponents are:

ηc = η0 χ z but ηc ≥ 0.8 (2) ξ zc = ξ 0 χ z but ξ zc ≥ 0.8 (3) where h0 and x0 are defined by Eqs. (4) and (5).

η0 = α 2z but 1 ≤ η0 ≤ 2 (4)

Mz,Ed = NEde + DMz,Ed

ξ 0 = α 2y but 1 ≤ ξ 0 ≤ 1.56

DMz,Ed = NEdeNy where eNy is the shift of the centroid.

As the exponents are depending on the reduction factor cz for z-axis or flexural-torsional buckling they will be = 1.0 for members with small slenderness and 0.8 for slender members and between 0.8 and 1.0 for intermediate slenderness. For simplicity, h0 and ξ0 may be taken as 1.0 and h0 and ξzc may be taken as 0.8.

Received 2 April 2014, revised 17 September 2014, accepted 24 September 2014

42

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Extensive research was performed on channel columns tested between pinned ends during the 1970s and 80s.

Tests of pin-ended cold-formed plain channel columns were performed by Klöppel and Bilstein (1976) [11], Rhodes and Harvey (1977) [22] and Batista et al. (1987) [19].

Cold-formed lipped channel columns were tested between pinned ends by Klöppel and Bilstein [11], Thomasson (1978) [26], Rhodes and Loughlan (1980) [23], Mulligan and Peköz (1984) [10], Batista et al. [19] and Weng and Peköz (1990) [9]. The failure modes observed in these tests were overall flexural and flexural-torsional buckling as well as local buckling. However, the focus of the tests was on the strength and behaviour of pin-ended channel columns.

Tests on fixed-ended channel columns have been reported for plain aluminium and carbon steel channels by Rothwell (1974) [24] and Lim (1987) [20] respectively and on cold-formed sections by Lau and Hancock (1990) [12] and Young and Rasmussen (1998) [7]. Some of all these tests are compared with the proposed method in the following.

2 Channel sections in bending To be able to use interaction formulae for beam-columns, the resistances for axial compression and bending moment separately are needed. For channel sections in minor axis bending with compression at the flange tips there are a series of tests in Beale et al. (2001) [3] which is used for this check.

As mentioned, using effective width for the flanges of channels may give very conservative result, which is especially true for members in bending [2]. The mixed effective width/effective thickness method for outstand elements in Annex D of EN 1993-1-3 [16] is therefore used in the following; see Fig. 2(a).

If the effective section modulus Weff is equal to the elastic section modulus Wel then the bending moment resistance according to expression (6.5) in EN 1993-1-3 is modified to

(

)

Mc,Rd = Wel fyb + (Wpl fya − Wel fyb )3(1 − λ e,max / λ e0 ) / γ M0 but not more than

Mc,Rd = Wpl fya / γ M0 (6) Compared to expression (6.5) in EN 1993-1-3 two changes have been made: The digit 4 is replaced by 3 and Wplfyb is

replaced by Wplfya where fyb is the yield strength of the sheeting before cold-forming and fya is the increased average yield strength due to cold working. le,max is the slenderness of the cross-section part with the largest le/le,0 and le is the limits for the slenderness for which no reduction for local or distortional buckling is needed.

The justification of the change from 4 to 3 is the tests below and also comparison with Eq. (7) from Greiner et al.

[28]

(

Mc,Rd = fy / γ M0 Wpl − (Wpl − Wel )c/t ref

)

If the notations b = c/t, b2 = c/t-limit for class 2 (83e for web in bending and 34e for internal cross-section part in compression) and b3 = c/t-limit for class 3 (124e for web in bending and 38e for internal cross-section part in compression) then

 β − β2  c/t ref = max  ; 0 ≤ 1

 β3 − β2 

Mc,Rd =

fy  fy β3 − β  W (7b)  Wel + (Wpl − Wel ) ≤ γ M0  β 3 − β 2  γ M0 pl

This is identical to expressions (6.25) + (6.26) in EN1999-1-1 for aluminium.

Noting that le/le,0 has the same value as b/b3, the digit 3 correspond to k = 1/(1 – b2/b3). For web in bending k = 1/(1 – 83e/124e) = 3.02 and for internal cross-section part in compression k = 1/(1 – 34e/38e) = 9.5. The agreement for web in bending is very good, but for internal cross-section part in compression the value is very conservative. Note however that the plastic resistance in (6) is Wpl times the increased yield strength fya due to cold-working.

The limit β 2 = 34 ε should therefore be smaller. β 2 = 26ε gives k = 3.17. Note that no cross section classification is given for cold-formed sections in EN 1993-1-3 and is not needed if Eq. (6) is used. Another reason why there is no classification is that it is difficult to find limits for distortional buckling e.g. for stiffened flanges.

As there are no cold working at the tip of the flanges of channel sections fya = fyb is used in the interpretation of the tests in Beale et al. [3]. However, for the smallest sections, fya = 1.15fyb is used for the plastic moment resistance as bending of the web is a large part of the resistance [3].

If the effective section modulus Weff is less than the elastic section modulus Wel then the bending moment resistance according to expression (6.4) in EN 1993-1-3 is (8)

The effective section is based on the mixed effective width/ effective thickness method in Annex D of EN 1993-1-3, but with the following changes.

Instead of the reduction factor r according to expression (4.3) in EN 1993-1-5 [17], an expression proposed by Brune (see e.g. [4]) is used which gives increased values for

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(7a)

Eq. (7) including the b-expression in (7a) can be rearranged, starting from Wel in the interpolation. The result is

Mc,Rd = Weff fyb / γ M0

Fig. 2. (a) Channel section in minor axis bending; (b) Reduction factor

(7)

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large slenderness. Of practical reason the originally expression (9)

ρ=

1 0.22 − 2 + 0.05λ p if λ p ≥ 0.749 λp

λp

(9)

is slightly modified to (10)

ρ=

0.77 1 0.188 but not less than if λ p ≥ 0.749 − 2 λp λp λp (10)

For small slenderness lp < 1.2, r is then the same as in EN 1993-1-5. The difference between Eqs. (9) and (10) is illustrated in Fig. 2(b). The reduced value of r in the region 1 < lp < 1.5 gives better agreement with the tests of Beale et al.

[3], see below.

The calculation of the buckling coefficient ks is based on the stress distribution for bending of the gross cross section and takes the elastic restraint of the web into account. Using CUFSM [14] the coefficient is found to be 1.614 for h/b = 1.5, 1.559 for h/b = 3 and 1.558 for h/b = 5 or approximately

h

≥ 1.5 for compression at the tip of the –– ks = 1.56 for b flange (11) Accordingly

b

–– ks = 5.5 for 0.2 ≤ ≤ 0.8 for compression in the web h (12)

Fig. 3. Cross-section of test specimens in bending [3]. For upper row fyb = 232.5 MPa and for ­bottom row fyb = 183 MPa

In the interpretation, the corner radii were modelled with the “two line model”, see below. The flange widths b, bp and effective width be0 are measured from the mid plane of the web (b = bp = B – 0.5t for the flanges).

Sections with b/t < 14 are able to carry the full plastic moment of the section. For 14 < b/t < 20 partial yielding of the flange tips can develop and for larger slenderness the moment resistance is based on the effective cross section.

The b/t ratio for the most slender sections is larger than the limit 50 according to the Eurocode. Nevertheless the predicted ultimate loads agree very good with the tests except two tests where shear lag of the web in tension might have reduced the load as L/b is very small (1.85 and 1.67 respectively). These two tests are omitted.

Comparison with the tests is given in Fig. 4. The mean value of test/calculated load is 1.014 and the standard deviation is 0.067.

The buckling factor for hinged supported edge according to Table D.1 in EN 1993-1-3 [16] is ks = 0.61 for y = 0.2 for compression at the tip of the flange and ks = 4 is usually used for the web in compression.

The part be0 with un-reduced thickness and the effective thickness of the remaining part of the flange are according to Annex D of EN 1993-1-3 [16] (see Fig. 2(a))

be0 =

0.42bp (1 − ψ )

+ b t < bp

t eff = (1.75ρ − 0.75 − 0.15ψ )t

(13) (14)

where bt is the part in tension.

For very slender flanges the effective thickness may be negative. Although a negative thickness seems somewhat odd, this negative value should be used. It corresponds to the tension stresses that may occur at the flange tip for large deformations.

3 Bending tests on channel sections by Beale et al [3] Channel section specimens were all manufactured from mild steel plate 1.6 mm thick by cold-forming. The inner radii of all bends were 1.6 mm. The beams were tested in four point bending. The load was applied through a screw jack and distributed by means of a spreader beam to two rollers. The distance between the rollers was 200 mm for the 500 mm specimens and 300 mm for the 1000 mm specimens (see Fig. 3).

44

Fig. 4. Test load Mtest and predicted load MR based on reduction factor r according to Eq. (10). Mel = Wel fyb = elastic section modulus times yield strength

4 Axial force resistance of channel sections If the effective area Aeff is equal to the gross area Ag then the compression force resistance according to expression (6.3) in EN 1993-1-3 [13] is

(

)

Nc,Rd = A eff fyb + 4(A g fya − A eff fyb )(1 − λ e,max / λ e0 ) / γ M0 but not more than

(15)

Nc,Rd = A g fya / γ M0 (16) If the effective area Aeff is less than the gross area Ag then the bending moment resistance according to expression (6.2) in EN 1993-1-3 is

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T. Höglund · Cold-formed members – comparison between tests and a unified design method for beam-columns

Nc,Rd = A eff fyb / γ M0

(17)

The effective section of the flanges is based on the mixed effective width/effective thickness method in Annex D of EN 1993-1-3, but with r according to expression (10).

For the web, r according to expression (4.2) in EN 1993-1-5 [17] is used.

ρ=

1 0.22 if λ ≥ 0.673 (18) − 2 p λp λp

be0 = 0.42bp

(21)

t eff = (1.75ρ − 0.75)t

(22)

For very slender flanges the effective thickness may be negative. This negative value is used in the following interpretations of tests.

5 Influence of rounded corners

Eq. (19) gives correct values for b/h = 0, 0.25, 0.5, 0.75 and 0.8 and the difference is less than 1 % in between; see Fig. 6.

The critical stress is the same for the flanges and the web and then also the slenderness lp but the reduction factors are not the same.

The part be0 with un-reduced thickness and the effective thickness of the remaining part of the flange are according to Annex D of EN 1993-1-3 [16] (see Fig. 2(a))

In EN 1993-1-3 [16] Fig. 5.1 the width bp is defined as the distance between the midpoints of the bent corners. However, these points do not define the supports of the flanges or web. When the flange and the web deflects they does not move in their plane which mean that the intersections of the extensions does not move, which in turn means that the corners rotate around the sharp corner A and B of a section with sharp corners (see Fig. 5).

From the figure it is clear that the middle of the bent corners is moved downwards and outwards corresponding to rotation around A and B. However, the developed width of the flange is less than the distance between these points why the starting points for bp and beff may be reduced.

In order to find out the best method to calculate bp, two examples are studied in Table 1; one with small radii and one with large radii. The correct values are found using the Finite Strip program CUFSM [14]. The result is depending on the slenderness of the plate. For small radii, bp is close to the distance between the sharp corners. For large radii the equivalent width is very much depending on the slenderness of the plate. For b/t = 100 the equivalent width is close to the flat part bflat of the flange whereas for b/t = 50 it is close to the distance between the centre of the bent corners.

The distances gr in EN 1993-1-3, Fig. 3.1 and x of the two line method (see Fig. 6) give very similar values. They don’t depend on the thickness. For small radii the values

Fig. 5. Rotation of rounded corners, definition of bp , starting points of beff and the two line model of rounded corners

Fig. 6. Curves for buckling coefficient [K1]min according to [5] and ksw according to Eq. (19)

ρ = 1.00 if λ p < 0.673 The buckling coefficient ks can be found in a diagram in Fig. 7.9 in Bulson (1970) [5], see Fig. 6. A polynomial fit to the curve for t1 = t2 gives –– for the web: 2

kσw = 4 + 10.335

3

 b  b b − 43.433   + 43.780   −  h  h h

−13.781  b 

4

 h 

(19)

– for the flanges: k σf = (b/h)2 k σw (20)

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Table 1. Equivalent bp of a flange between rounded corners Radii

r = 0.05 b

r = 0.10 b

Width of flat part

bflat = 0.9 b

bflat = 0.8 b

CUFSM (b/t = 100)

bp = 0.985 b

bp = 0.838 b

CUFSM (b/t = 83)

bp = 0.992 b

bp = 0.876 b

CUFSM (b/t = 50)

bp = 1.000 b

bp = 0.953 b

EN 1993-1-3, Figure 5.1

bp = 0.971 b

bp = 0.942 b

Two line method

bp = 0.974 b

bp = 0.948 b

of bp are too small and for large radii considerably too large for slender plates. For small radii the best, but somewhat conservative, results are given by bp = b. For large radii the two line method gives best result although conservative for large radii.

As the radii of the test profiles are small in most cases, bp = b is used in the interpretation of the tests in the following.

The corner itself is replaced by two lines where the midpoint is placed so that the length of the two lines is the same as the bow. For adjoining parts in right angle this gives

x=

r r − 2 2

π2 − 1 ≈ 0.258 r 8

(23)

and for an angle f according to Fig. 5(d)

x = s1s2 − (s1s2 )2 − s12s2 + (r 2φ2 /4)s2  φ

(24)

 φ

where s1 = r tan   and s2 = sin 2    2  2

6 Tests on channels according to Young and Rasmussen [7] The tests were performed on lipped and plain channels brake-pressed from zinc-coated Grade G450 structural steel sheets with nominal yield stress 450 MPa. Two series of lipped channels and two series of plane channels were tested with a nominal thickness of 1.5 mm and a nominal width of the web of 96 mm. The flange width was either 36 mm or 48 mm. The base metal thickness was measured by removing the zinc coating by acid-etching. The length of the specimens ranged from about 300 mm to 3000 mm.

Lipped channels (C-sections) Resistance of tests and calculated resistance of lipped channels (also denoted C-sections) are given in Figs. 7, 8 and 9 as function of the length of the specimens. For the pin-ended tests the buckling length used in the calculation is the member length for z-axis buckling but half the length for flexural-torsional buckling. For the fixed-ended tests the buckling length is half the length for all buckling modes [7].

According to Fig. 8, for pin-ended tests the calculated resistance is in agreement with the ultimate test loads. For fixed-ended tests the calculated loads underestimate the strength considerably, see dashed line in the diagrams in Fig. 7. The reason may be that the coupling between distortional buckling (see 5.5.3 in EN 1993-1-3 [16]), and flexural-torsional buckling is weak for slender members. Therefore, instead of using the effective cross-section (including reduction of thickness due to distortional buckling), the gross cross-section was used for the flexural-torsional buckling load NR,ft for large slenderness, and distortional buckling load NR,dist = Aefffy for small slenderness. In-between, the resistance was reduced according to Eq. (25b).

NR = NR,dist

NR =

1.65 1/NR,dist + 1/NR,ft

NR = NR,ft

for short columns

(25a)

for intermediate length (25b) for long columns

(25c)

The resistance is the smallest of the three resistances above. Resulting resistance are solid curve N2 in Fig. 7 giving better agreement with the test results.

The strength for axial force Nz,b,Rd is based on the effec­tive cross-section for compression force only e.g. without stress gradient. This effective cross-section is also the basis of the shift of the centroid for the pin-ended tests. For the ben­ding moment due to this shift, the web is in tension and the flanges are in partial compression with a stress gradient based on the gross cross section as stated in Annex D of EN 1993-1-3.

The agreement between the test strength and the calculated strength is generally very good if the improved method is used for the fix-ended tests. The mean value for test strength over calculated strength is 1.104 for the fixed tests and 1.026 for the pin-ended tests. Corresponding standard deviations are 0.073 and 0.041.

Plain channels (U-sections) Test strength and calculated strength for plain channels are given in Figs. 9 and 10 as function of the length of the

Fig. 7. Tests on fixed-ended lipped channels [7]

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Fig. 8. Tests on pin-ended lipped channels [7]

specimens. For the pin-ended tests the buckling length used in the calculation is the member length for z-axis buckling but half the length for flexural-torsional buckling [7]. For the fixed-ended tests the buckling length is half the length for all buckling modes. For the fixed-ended tests the agreement between test and calculation is very good; see the diagrams in Fig. 9. For the pin-ended tests the predictions are also reasonable good, see Fig. 10.

The mean value for test strength/calculated strength is 1.071 for these eight tests and the corresponding standard deviation is 0.109.

7 Eccentrically loaded U-sections by Zhang [8] In [8] two series of tests on eccentric loaded plane channels are presented. For both test series the width of the web is 100 mm. The width of the flanges is 75 mm and the thickness is 2 mm for one series and 40 mm and 1 mm respectively for the other. Comparisons are presented in Fig. 11. The agreement is reasonably good considering that the spread of the test results for the same sample is fairly large.

8 Pin-ended C-sections by Weng and Pekoz [9] In [9] a total of 68 tests on pin-ended column are presented, 23 tests on roll-formed lipped channels (R) and the rest on press-braked lipped channels (P). Here the tests with simple lips RFC and P1 – P4 are studied. The result is presented in Fig. 12. In the design of the test specimens, it was intended to have sections that were fully effective, and all column failures were due to flexural buckling around the weak axis of the sections. In many cases predictions according to the AISI specifications were un-conservative [9]. According to Eurocode 3 some sections were not fully effective. However, the main reason for too large predicted resistance is the AISI column curve which is more optimistic than curve b according to Eurocode 3.

For small sections and small buckling length the Eurocode 3 predictions are somewhat conservative. The reason might be increased material strength due to cold-working in large parts of the section with large corner radii in comparison with the width of flat remaining parts illustrated by cross-sections in Fig. 12.

Fig. 9. Tests on fix-ended plain channels [7]. Diamonds are ultimate test load; solid curves are calculated resistance

Fig. 10. Tests on pin-ended plain channels [7]. Diamonds are test loads and solid curves are calculated resistance

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Fig. 11. Tests [8] on pin-ended plain channels as function of eccentricity e. Diamonds are ultimate test load and solid lines are calculated resistances

Fig. 12. Tests [8] on pin-ended lipped channels made by press-­ braking as function of span. Diamonds are ultimate test load; solid curves calculated resistances

The mean value for test strength over calculated strength is 1.108 and the standard deviation is 0.072. No discernible difference between press-braked and roll-formed sections is found.

9 C-sections with bracing between lips by Mulligan and Pekoz [10] 22 lipped channel steel columns were tested to failure under concentric and eccentric loading conditions. All specimens were fabricated out of thin sheets of 1.2 mm steel.

Included in the interpretation here are only the results of the five eccentrically loaded tests where the flanges were braced against each other. The distortional buckling was then prevented so no reduction for such buckling was made in the interpretation. The design method seems to give reasonable results also for such a case, mean value 1.16 and standard deviation 0.11.

have been copied and curves for the design method have been included (see Fig. 13). The cross-section and span are given in these diagrams. A guessed yield stress of 240 MPa was used.

The predicted failure loads are very good in view of scatter of test results.

11 Rack column uprights by Lau and Hancock [12] Tests were made on fix-ended lipped channels of different material according to Australian standards HR340 (t = 1.7 mm), HR2 (t = 2.0 mm and G450 (t = 2.4 mm) with yield strength around 400, 220 and 480 MPa respectively.

Four types of section were tested, see Fig. 14: simple lipped channels (CH), rack column uprights (RA), rack column

10 Eccentrically loaded U-and C-sections by Klöppel and Bilstein [11] Tests on plane and lipped channels are briefly referred to in [11] and presented in diagrams only. These diagrams

Fig. 14. Test sections [12]

Fig. 13. Tests on eccentric loaded pin-ended plain and lipped channels [11]

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Figs. 15 and 16. Tests on fix-ended rack column uprights made by brake-pressing [12] as function of span. Diamonds are ultimate test loads and solid curves are according to Eq. (25)

uprights with additional lip stiffeners (RL) and hat (HA).

The tests are treated in Figs. 15 and 16.

The overall picture of the consistency of the predictions is the same as for the previously treated experiments.

Mean value and standard deviation are: –– lipped channel section CH 1.024 and 0.043 –– hat section HA 1.112 and 0.052 –– rack column uprights RA 1.069 and 0.050 –– column uprights RL 1.062 and 0.037 For all type of sections the predictions are conservative especially for slender columns.

12 Channels with inclined lips by Young and Hancock [13] Tests were performed on channels with inclined edge stiffeners compressed between fixed ends. The specimens were brake-pressed from high strength zinc-coated Grade G450 structural steel sheets having nominal yield stress of 450 MPa and specified according to the Australian Standard AS 1397 (1993). The test program comprised six series with different cross-sections, referred to as ST15, ST19, ST24, LT15, LT19, and LT24. The nominal flange width of the sections was either 50 or 100 mm, and the nominal plate thickness was 1.5, 1.9, and 2.4 mm. A nominal width of the web of 100 mm and a nominal width of the lip (edge stiffener) of 12 mm was used for all channel sections. The LT sections were basically square with the flange width equalling the web depth whereas the ST sections had a web depth twice the flange width. The edge stiffeners were inclined at different angles 30°≤ θ ≤ 150° measured from the plane of the flanges as shown in Fig. 17. Both outward and inward edge stiffeners were considered. The nominal

angle of 150° was not achieved in the brake-pressing process, and it was measured approximately 140°. The nominal length of each specimen was 1500 mm as supplied from the manufacturer in an uncut length.

Both ends of each specimen were milled flat by an electronic milling machine to ensure full contact between specimen and end bearings. The largest value of ley/ry ratios for Series ST15, ST19, and ST24 was approximately 45, while that for Series LT15, LTI9, and LT24 was approximately 20. The parameter ley is the effective length for buckling about the minor y-axis, which was assumed to be equal to one half of the column length.

The Eurocode design method using ks = 4 for local buckling results in rather conservative resistance for the ST series (mean Ntest/Ntheor = 1.30, see Table 2) but non-conservative resistance for the LT series (mean Ntest/Ntheor = 0.96). The obvious reason is that the web is elastically restrained by the flanges in the ST series which is not the

Fig. 17. Sections with outward and inward edge stiffeners

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Fig. 18. Critical stress as function of buckling length for ST15 and LT15, q = 90°, from CUFSM [14] Table 2. Mean values and coefficient of variation for test over predicted load based on ks = 4

Table 3. Mean values and coefficient of variation for test over predicted load based on ks from finite strip method

Series

ST15

ST19

ST24

LT15

LT19

LT24

Series

ST15

ST19

ST24

LT15

LT19

LT24

Mean Ntest/Ncalc

1.21

1.33

1.39

0.93

0.096

0.95

Mean Ntest/Ncalc

1.11

1.16

1.14

1.06

1.07

1.037

Coefficient of variation

0.088

0.071

0.051

0.020

0.060

0.065

Coefficient of variation

0.074

0.060

0.039

0.036

0.044

0.039

case for the LT series. Compare the two curves in Fig. 18 from CUFSM [14].

It is noted that the dimensional limits for the flat portion of the flange width to thickness ratio is approximately 65 for Series LT15 and 52 for Series LT19. The value for LT15 is larger than the maximum value of 60 as specified in the Eurocode.

Using local buckling stress according to numerical method gives much better agreement with the tests for the ST series (ks > 4). However, for the LT series the predictions are still un-conservative (ks < 4). The reason might be that the post-buckling strength cannot develop in the web and flanges as the flange lips are not rigid enough to act as support in the post-buckling range. The effective width factor ρ of the web and flange parts close to the web is therefore limited to the critical stress for distortional buckling increased with a factor 1.4 for LT15, 1.15 for LT19 and 1.0 for LT24 series, which means that there are some limited post-buckling strength for very slender flanges (see Fig. 19 and Table 3).

In the Australian/New Zealand standard AS/NZS 4600 [18] referred to in [13] the direct strength method is

Table 4. Mean values and coefficient of variation for test over load according to AS/AZS 4600 [13] Series

ST15

ST19

ST24

LT15

LT19

LT24

Mean Ntest/Ncalc

1.22

1.28

1.28

1.05

1.10

1.12

Coefficient of variation

0.129

0.082

0.084

0.069

0.089

0.098

optional e.g. a single reduction factor for the whole cross-section is used (see Table 4). It can be noted that for the LT series this model gives good results whereas for the series ST the prediction is conservative. For the LT series the result is non-conservative for outward bent lips but conservative for inward bent lips.

13 Conclusions A comparison between the strength of tests reported in the literature and the design strength as proposed in [1] has been presented. The tests were performed on plain and

Fig. 19. Test/calculated load for fix-ended channels with inclined lips [13] versus angle θ of lips. Distortional buckling according to finite strip method and reduced effective width of flat cross-section parts

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lipped channels press-braked or roll-formed from steel sheets with nominal yield stress ranging from 220 MPa up to 480 MPa. Some columns were tested between fixed ends and some between pinned ends. Most of them were loaded at the centroid of the gross cross section, but also eccentrically loaded specimens were evaluated.

For the fixed-ended tests it was assumed in the calculation that loading passes through the centroid of the effective cross-section. The agreement between test and calculation is generally very good except for some tests where distortional buckling interact with flexural-torsional buckling where, for large slenderness, flexural-torsional buckling occur without interacting with distortional buckling, and vice-versa for short columns. However, if the buckling load for those two buckling modes is about the same there is some interaction. A possible reduction factor for this case is given in the text and used in the interpretation for comparison.

For the pin-ended tests on plain channel sections (U-sections), however, the calculation very conservatively predicts the resistance if it is assumed that the column is eccentrically loaded with an eccentricity equal to the shift of the effective centroid of the applied force eN,y, calculated as the distance between the geometric and the effective centroid. The conservatism is partly due to over-estimated value of the shift and partly from under-estimated values of the bending moment resistance [7]. If the mixed effective width/effective thickness method in Annex D of EN 1993-1-3 and an increased reduction factor ρ according to Brune [4] is used the agreement with the tests is much better. The scatter of test over predicted load is further reduced if a somewhat modified expression for ρ according to (10) is used.

Using the buckling coefficient ks = 4 for section parts with supported longitudinal edges may result in both safe and unsafe results. Using numerical methods to calculate the buckling stress improve the results considerably.

The influence of rounded corners on the elastic buckling stress is allowed for by using a notional width bp. In the Eurocode the distance between the midpoints of the corners is used, in other codes the flat part. The most correct values may be found by comparing the buckling stress based on bp with buckling stress found using a numerical method.

It was found that the result is not only depending on the radii but also on the slenderness b/t of the plate. For small radii, bp is close to the distance between the sharp corners.

For large radii and large b/t the equivalent width is close to the flat part bflat of the flange whereas for large radii and small b/t it is close to the distance between the centres of the bent corners. As the radii of the test profiles are small in most cases, bp = b is used in the interpretations of the tests.

The two line method is a convenient way to take rounded corners into account when calculating cross section constants.

During the years extensive research was performed on channel columns and other types of thin-walled columns.

References to papers with tests not evaluated in this paper are given at the end of the reference list. A special feature of the proposed method in [1] is the possibility to take account of varying bending moment along the beam-column in a simple way. However, no such tests were found in the literature so far.

References [1] Höglund, T.: A unified method for the design of steel beam-columns. Background document to Amendment to EN 1993-1-3. Steel Construction – Design and Research 7 (2014), No. 4, pp. 230–245.

[2] Heinisuo, M., Kukkonen, J.: Design of Cold-Formed Members Following New EN 1993-1-3. Tampere University of Technology, Structural Engineering Laboratory Research Report 132, 2005.

[3] Beale, R. G., Godley, M. H. R., Enjily, V.: A theoretical and experimental investigation into cold-formed channel sections in bending with the unstiffened flanges in compression. Computers and Structures 79 (2001), pp. 2403–2411.

[4] Brune, B.: Stabilitätsprobleme von Stahlbauteilen mit dünnwandigen ebenen Blechen. Universität Dortmund, Schriftenreihe Stahlbau, Heft 1, 2004.

[5] Bulson, Ph.: The stability of flat plates. London: Chatto and Windus, 1970.

[6] Rasmussen, K. J. R., Hancock, G. J.: The flexural buckling behaviour of fixed-ended channel section columns. ThinWalled Structures Vol. 17(1), 1993, pp. 45–63.

[7] Young, B., Rasmussen, J. R.: Tests of cold-formed channel columns. Fourteenth International Specialty Conference on Cold-Formed Steel Structures 1998, St. Louis, Missouri USA. [8] Zhang, X.: Ein Beitrag zur Bestimmung der Traglast dünnwandiger, durch Knicken und Beulen gefährdeter U-Profile unter Längsdruckbelastung in der Symmetrieebene. Bericht Nr. 8, Institut für Statik, Technische Hochschule Darmstadt, 1989.

[9] Weng, C. C., Peköz, T.: Compression Tests of Cold-Formed Steel Columns. Journal of Structural Engineering, ASCE, Vol. 116(5), 1990, pp. 1230–1246.

[10] Mulligan, G. P., Peköz, T.: Locally Buckled Thin-Walled Columns. Journal of Structural Engineering, ASCE, Vol. 110(11), 1984, pp. 2635–2654.

[11] Klöppel, K., Bilstein, W.: Untersuchungen zur linearen und nichtlinearen Beultheorie mit Beulwerttafeln für dünnwandige U, C- und Hut-Profile und Tafeln für mitwirkende Breiten und Tragspannungen von dreiseitig und vierseitig gelenkig gelagerten Reckteckplatten nach der nichtlinearen Beultheorie. Der Stahlbau 45 (1976), No. 2, pp. 33–38.

[12] Lau, S. C. W., Hancock, G. J.: Inelastic buckling of channel columns in the distortional mode. Thin-Walled Structures, Vol. 10, 1990.

[13] Young, B., Hancock, G. J.: Compression tests of channels with inclined simple edge stiffeners. Journal of Structural Engineering, ASCE, October 2003.

[14] Li, Z., Schafer, B. W.: Buckling analysis of cold-formed steel members with general boundary conditions using CUFSM: conventional and constrained finite strip methods. Proceedings of the 20th International Spec. Conf. on Cold-Formed Steel Structures, St. Louis, MO. November, 2010.

[15] Eurocode 3, EN 1993-1-1 – Design of Steel Structures, Part 1.1: General Rules and Rules for Buildings.

[16] Eurocode 3, EN 1993-1-3, Design of Steel Structures, Part 1.3: Supplementary Rules for Cold-Formed Members and Sheeting.

[17] Eurocode 3, EN 1993-1-5, Design of Steel Structures, Part 1.5: Plated Structural Elements.

[18] Australian/New Zealand Standard (NS/AZS) (2005). Coldformed steel structures. NS/AZS 4600:2005, Standards Australia, Sidney, Australia.

Papers presenting tests not evaluated in this report [19] Batista, B., Rondal, J., Maquoi, R.: Column Stability of Cold-Formed U and C Sections. Proc. Int. Conf. on Steel and Aluminium Structures, Cardiff, UK 1987, pp. 419–427.

[20] Lim, K. W.: Examination of the Effects of Local Buckling on the Behaviour of Fully-Fixed Thin-Walled Columns. MPhil.

Thesis, University of Strathclyde, Glasgow, UK 1987.

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[21] Rasmussen, K. J. R., Hancock, G. J.: Design of Thin-Walled Plain Channel Section Columns against Flexural Buckling.

Thin-Walled Structures, Vol. 20(1–4), 1994, pp. 219–240.

[22] Rhodes, J., Harvey, J. M.: Interaction Behaviour of Plain Channel Columns under Concentric or Eccentric Loading.

Proc. 2nd Int. Colloquium on the Stability of Steel Structures ECCS, Liege, Belgium, 1977, pp. 439–444.

[23] Rhodes, J., Loughlan, J.: Simple Design Analysis of Lipped Channel Columns. Proc. 5th Int. Specialty Conf. on ColdFormed Steel Structures, St. Louis, Mo, USA, 1980, pp. 241– 262.

[24] Rothwell, A.: An Experimental Investigation of the Efficiency of a Range of Channel Section Struts”, The Aeronautical Journal of the Royal Aeronautical Society, Vol. 78(9), 1974, pp. 426–430.

[25] Seah, L. K., Rhodes, J., Lim, B. S.: Collapse behaviour of edge stiffened thin-walled sections. Int. Conf. on Steel and Aluminium Structures ICSAS, Singapore 1991.

[26] Thomasson, P. O.: Thin-Walled C-shaped Panels in Axial Compression. Document D1: Swedish Council for Building Research, Stockholm, Sweden 1978.

[27] Ungermann, D., Brune, B., Lübke, S.: Experimental investigations on plain channels in coupled instabilities. Steel Construction Design and Research 5 (2012), No. 3, pp. 87–92.

Further reference [28] Greiner, R. et al.: Design guidelines for cross-section and member design according to Eurocode 3 with particular focus on semi-compact sections. Valorisation Project: SEMICOMP+, Research Programme of the Research Fund for Coal and Steel – RTD, 2011.

Keywords: Cold-formed members; tests; beam-columns; Eurocode 3; interaction formulae

Author: Torsten Höglund, Professor emeritus Steel Structures Royal Institute of Technology, KTH, Brinellvägen 23 SE-100 44 Stockholm torsten.hoglund@byv.kth.se

News Enercon wind turbine erected by ­Liebherr crane The Liebherr 1000 EC-B 125 Litronic was recently used to erect a new Enercon E-101 wind turbine with a hub height of 135 m in Wardenburg in the Rural District of Oldenburg (Germany).

An adjustable undercarriage with a sup-

52

port base measuring just 18.0 m × 18.0 m was designed for the 1000 EC-B especially for Enercon. The support struts can be adjusted on this special undercarriage from the 45° position by ±5° or ±10°. The support base is then 20.4 m × 15.2 m. For the job near Oldenburg the Liebherr crane was used on the undercarriage measuring 18.0 × 18.0 m. The crane range was erected on the 1000 HC tower system with conical bolt connections. The monoblock tower sections with system dimensions of 3.40 m × 3.40 m and a length of 5.80 m allow high free-standing erection heights with short erection times.

Wind turbines in areas with poor wind conditions are not generally used in large wind farms and instead are erected in wooded areas or areas with difficult access. The use of the Liebherr tower crane is particularly beneficial for these locations. Both the crane and the wind turbine can be erected on a comparatively small area. The area requirement for erecting the complete crane is approximately half of the normal standing area of other crane systems. In addition the logistics required to transport the crane are much less than comparable crane systems. One specific benefit of tower cranes is their operational

safety in wind speeds of up to 18 m/s.

Only when the wind reaches a speed of 120 km/h or more, the jib has to be released to turn freely.

Initially the crane was erected using a mobile Liebherr LR 1200 crawler crane to a basic hook height of 38 m. After this the crane climbed itself to a free-­ standing hook height of 108 m. In the second stage the Flat-Top crane was guyed to a level of approx. 87 m using the wind turbine tower. The guying so­ lution was used to securely anchor the crane to the tower. In principle the 1000 EC-B 125 Litronic can achieve a free-standing hook height of approx.

110 m. After guying the tower the crane climbed quickly and safely using the completely new climbing equipment in stages of 5.8 m to the required final hook height of 149 m for installing the nacelle and the rotor blades.

The Flat-Top crane can reach the lifting height of 149 m with a single guy on the tower of the wind turbine. It can operate in free-standing mode for such projects up to a lifting height of 108 m.

The crane has a lifting capacity of 125 tonnes.

Further information: www.liebherr.com

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Articles Osama Bedair

DOI: 10.1002/stco.201510007

An analytical expression to determine “realistic” shear buckling stress in cold-formed lipped channels Current North American and European design provisions ignore the rotational restraint when evaluating local web shear buckling stresses in cold-formed steel channels. This paper offers a new analytical expression for computing local buckling shear stresses in cold-formed channel members taking into account the rotational restraints imposed by the flanges and the lips. The expression ­derived is suitable for hand calculations and can replace current code expressions in order to achieve economical steel designs. Comparisons with existing design formulas currently used in practice for the limiting conditions show a difference within 5 %.

Fig. 1. Channels attached to wall cladding and roof sheeting

1 Introduction Cold-formed steel channels are very popular structural members that are commonly used in the construction of industrial and commercial facilities. For example, vertical channels (or studs) are extensively used in wall framing of commercial and residential buildings. Horizontal girts (or rails) are also used to connect the side cladding to the primary framing columns, as shown in Fig. 1a. Channel sections are also used to connect the roof cladding to the main rafters, as shown in Fig. 1b. The industrial applications for cold-formed steel structures are continuously increasing due to the ease of manufacturing and fabrication.

Despite the manufacturing simplicity of cold-formed channel members, their behaviour is difficult to predict, which is due to the many parameters involved and the varieties of loading. Owing to the small thicknesses of these sections, stability is a major governing design criterion.

Despite the wide industrial applications of coldformed channels, the shear buckling condition is hardly addressed in the literature. The majority of the research has focused on channel sections under pure compression or bending. Studies by the author in [1–4] detail the behaviour of lipped channel sections under combined axial compression and biaxial bending. Design guidelines were proposed which can be utilized by practising engineers to maximize the performance of the channel section. Pham and Hancock [5, 6] presented semi-analytical finite strip

Received 25 December 2013, revised 25 August 2014, accepted 19 October 2014

method (SAFSM) formulations for the buckling analysis of channels in pure shear parallel to the web. The section is idealized as infinitely long and ignoring the end restraints.

The procedure requires considerable computation effort to calculate the shear buckling loads due to the large number of degrees of freedom required, especially as the channel section length increases. In the numerical investigations presented in [5], unrealistic flange-to-web ratios (0.00005– 0.8) were used which are rarely encountered in practice, and contradicting the assumed boundary conditions. Other anomalies in the formulations and assumptions have been pointed out in detail by Bedair [7]. Further investigations have dealt with channel members under axial loads or bending. For example, Ren et al. [8] used the finite element method to analyse cold-formed steel channels subjected to pure bending. Tian et al. [9] presented a model for predicting the axial failure load of wall studs. Young [10] presented finite element investigations of cold-formed steel channel columns with inclined edge stiffeners. Liu and Day [11] studied the bending resistance of channel beam sections. Chu et al. [12] investigated the buckling behaviour of cold-formed steel channel beam sections under uniformly distributed lateral loads. Lange [13], using the results of several tests, developed an empirical procedure for the design of laterally supported cold-formed shear walls.

Stowell [14] presented formulations to compute the critical buckling shear stress for infinitely long plates with partial restraints; rotational springs were used in the model to measure restraint intensity. An extensive review of various modelling and idealization procedures for plates and shells is also presented in [15].

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O. Bedair · An analytical expression to determine “realistic“ shear buckling stress in cold-formed lipped channels

The objective of this paper is to furnish this class of stability problem with a closed-form solution for predicting the shear buckling of cold-formed channel sections taking rotational restraint into account. The paper enables practising engineers to predict the local shear buckling stress in the channel with the aid of a simple formula that, for design purposes, is suitable for hand calculation and avoids the excessive computer time and effort required by numerical finite element or finite strip procedures.

where Is is the second moment of inertia of the longitudinal stiffener. For unstiffened webs, kst = 0.

Other equations commonly used in practice for the clamped conditions are available in the structural stability research council (SSRC) handbook [19]. Approximate expressions are also provided for plates clamped on two opposite edges and simply supported on the other two using polynomial curve fitting to the numerical results obtained

by Cook and Rockey [20], given by

2 Existing design expressions

Kv =

The common procedure used in practice is to idealize the web by assuming hinged boundary conditions in the longitudinal direction. In doing so, the rotational restraints imposed by the flanges/lips are ignored. The North American cold-formed steel design specifications, AISI [16] and CSA-S136-07 [17] provide (in section C3.2) shear buckling coefficients based on simply supported web edges, ignoring the rotational restraints of flanges and lips. A constant value Kv = 5.34 is used for unreinforced webs. Eqs. C3.2.1-6 and C3.2.17 are used for webs with transverse stiffeners:

Kv = 4 +

5.34

(a/h )

K v = 5.34 +

2

4

(a/h )

2

for

(a/h ) ≤ 1

(1)

for

(a/h ) > 1

(2)

where a is the distance between shear stiffeners of reinforced webs and h is the web width.

Eurocode 3 [18] provides general shear buckling equations for webs with longitudinal and transverse stiffeners, given by

5.34 2 (a/h) 5.34 Kv = 4 + 4 K v = 5.34(a/h) + 2 2 (a/h) 4 K v = 5.34 + (a/h)2 Kv = 4 +

( ) for ( a/h ) < 1 for ( a/h ) ≥ 1 for ( a/h ) ≥ 1

+ kst for a/h < 1 + kst + kst + kst

(3)

(4)

8.98 + 5.61 − 1.99 α α2

K v = 8.98 +

5.61 1.99 − 3 α2 α

for for

(α ) ≤ 1 (α ) ≥ 1

(6)

(7)

where a is the web aspect ratio (a/h). Numerical values for simply supported and clamped web panel edges are also available in the Column Research Committee of Japan Handbook of Structural Stability [21].

3 Proposed design expression Let us consider the typical cold-formed lipped channel sections shown in Fig. 2 subjected to a shear loading t parallel to the web longitudinal edges. Fig. 2a illustrates a typical stiffened channel web section and section A-A shows the stiffener detail. The spacing between the stiffening angles is denoted by a, web width by h, flange width by b, lip width by D and channel thickness by t. The web local coordinate system is located at the centre of the panel and is defined by skewed non-dimensional parameters ξ = (x/a) and η = (y/a). The oblique (or prime) system is identified by the dashed arrows and is related to the skew coordinates by the phase angle f using the following relation:

x = x \ − y \ tan φ,

y = y \ sec φ

(8)

Note that the shear t acting on the web represents a resultant or total force. If the web, for example, is subjected to a variable shear distribution defined by f(x`), then the total shear force becomes 0.5x \

∫ ( )

τ = (9) f x \ dx \ where:

 h kst = 9    a

−0.5x \ 3

2 4

 Is  2.1 Is  3  > t h  t h

(5)

a) Stiffened Web

Fig. 2b shows a typical unstiffened channel. The notation is identical to Fig. 2a except that the web coordinate system is located at the centre of the channel.

b) Unstiffened Web

Fig. 2. Typical stiffened and unstiffened channels

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O. Bedair · An analytical expression to determine “realistic“ shear buckling stress in cold-formed lipped channels

In the present formulation it is assumed that the channel section is made of an isotropic, perfectly elastic material. The influence of the residual stresses is ignored. It is further assumed that the web is partially restrained against rotation by the attached flanges. The rotation angles are assumed to be identical at their junction lines. In addition, the flanges of the channel are not restrained by other members such as cladding. This restraint is mainly induced in the flanges when they are connected to the cladding. This assumption is conservative since this restraint will increase the web rotational restraint, thus resulting in a higher web shear buckling load.

The total strain energy of the system is composed of the web bending strain energy, the rotational strain energy of the flanges and the work done by the shear forces. This can be expressed in general terms as follows: F L

Π = Uw b + U R + U R − Tτ

(10)

where: Uw b web bending strain energy

The total strain energy can be written in the following compact matrix form:

[J]8×1

(11)

where the matrices [T] and [J] contain integral equations that depend on the shape functions used to approximate the shear displacement profile in the longitudinal and transverse directions. The form of these integrals is not given here due to space limitations. By minimizing the total strain energy of the system with respect to the displacement coefficients, the shear buckling stress of the web can be expressed as 2

τ = Kv

 t π 2E   2 12 1 − v  h 

(

)

(12)

where E is modulus of elasticity and ν is Poisson’s ratio.

Note that the buckling coefficient Kv is a function of the web displacement profile and geometric characteristics of the flange and lip sizes. For convenience, the buckling factor Kv is expressed in the following form:

K v = C1 C2

1  C3  θ1  θ2 

(13)

An approximation of the transverse web displacement profile can be obtained by combining the following quadratic polynomial and sinusoidal functions:

  cos( πη) F( η) = A  4 η2 − 1  +  A + B cos( πη) π  

2   Sec4 φ  h   λ  C1   −2   Cot φ   h C2  =   λ  2    C3   2  2 3Sec φ − 2  

()

()

(

() )

          

where λ represents the spacing between the nodal lines of the shear buckling mode. Similarly, when substituting Eq. (14) into (13), the constants {θ1 θ2} become

(14)

2 2   b + D  h   b + D  h   +1 2.17  1.2 +  h   λ    h   λ     θ2 = (17) 2  2   b + D  h   b + D  h 1.72  + 1.53 + 1  h   λ    h   λ    

The minimum buckling coefficient Kv is obtained by finding the minimum combination of ϕ and λ. The author performed a numerical study using mathematical programming techniques and found that the magnitude of the optimum combination of λ, ϕ is sensitive to small web aspect ratios a/h ≤ 1.5. The Kv values converge to the following expression when the channel web aspect ratio a/h > 1.5, as the case in most situations encountered in practice: 2

b+ D b+ D 14  + 15.2   + 4.24   h   h  K v = 1.58 + 2 b+ D b+ D

1.72  + 2.6    +1  h   h 

(18)

Therefore, for a given channel section size, the web shear buckling coefficient Kv can be computed using Eq. (18) by taking into account the rotational restraints imposed by the flanges and lips.

4 Comparison with the limiting conditions Table 1 compares the accuracy of the derived expression, Eq. (18), with available formulas and numerical data used in design codes and engineering manuals. The second column shows the cold-formed steel codes AISI [16], CSA-S136-07 [17] and Eurocode 3 [18] for the simply supported condi-

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(15)

2 2   b + D   h   b + D   h   9 + 0.91 + 1         h   λ   h   λ     (16) θ1 = 2  2   b + D   h   b + D   h  1.72  + 1.53 + 1  h   λ    h   λ    

URF flange rotational strain energy ULR lip rotational strain energy Tt work done by shear forces

Π = [T]3× 8

where A and B are the amplitudes of the displacement functions. Substituting into Eq. (13) and using ν = 0.3, the shear buckling constants C1, C2 and C3 become

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Table 1. Comparison of shear buckling Kv factor Boundary condition

Ref [16–18]

Ref [19]

Ref [21]

Average

Eq. [18]

Difference

5.8

5.8

6.1

5.95

5.82

2.2 %

N/A

9.5

9.61

9.60

9.71

0.2 %

Simply supported Clamped

tion using Eqs. (2) and (4), using a web aspect ratio a/h = 3.

Note that in Eurocode 3 [18], Eq. (4), Kst = 0. No provisions are available in theses codes for the clamped condition. The third column represents the Kv factor obtained from SSRC [19] for simply supported and clamped conditions. The fourth column shows numerical values reported in [21]. The fifth column shows the average values provided by the five references. The sixth column represents the Kv factor computed using the proposed expression, Eq. (18).

The simply supported condition is obtained by substitution (b = D = 0). This implies that the longitudinal web edges are free to rotate. The web shear buckling load factor in this case is K = 5.82. The clamped condition is obtained by substituting (b + D)/h → ∞ in Eq. (18). This implies that the flanges fully restrain the web rotation. The web shear buckling load factor in this case is Kv = 9.71. It can be seen that the prediction of Eq. (18) is in excellent agreement with available design data. It was found that the difference increases for shorter web aspect ratios. However, the prediction of Eq. (18) is on the safe side. For example, the average difference for web aspect ratios commonly used in practice (between 2 and 5) is 6 % for the simply supported condition and 4 % for the clamped condition. The accuracy of Eq. (18) was also verified using alternative numerical procedures and the results were in good agreement.

Existing design expressions used in practice are only applicable for the limiting simply supported or clamped conditions. This section illustrates the influence of the geometric proportions of the channel section on the shear buckling of cold-formed channels. Fig. 3 shows the variation of the web/lip width ratio h/D with the web shear buckling stress t for channels with h/t = 100. The solid line represents the web/flange ratio h/b = 1.5, the dashed one h/b = 3 and the

dotted one h/b = 4. Note that the comparison is made for the elastic critical buckling stress, not the shear resistance.

It can be seen that by increasing the h/D ratio, the web buckling shear stress decreases. In other words, as the width of the lip decreases (for the same web width), the buckling stress t decreases. This is due to the decrease in the web rotational restraint as a result of reducing the lip size. The average reduction in the t values is approx. 10 % for this h/D range. Furthermore, much of the reduction occurs in the early stage of the curves, (i.e. when h/D is between 3 and 8). It must be emphasized that the prediction of the buckling stress by cold-formed steel design specifications AISI [16], CSA-S136-07 [17] and Eurocode 3 [18] is independent of the lip and flange sizes. A constant value t = 103 MPa is used for all lip or flange sizes. The difference in t values between these curves and these code provisions ranges between 23 and 31 %. The figure shows that the web buckling stress is influenced by the lip size and is not a constant value as assumed by cold-formed steel codes.

Fig. 4 shows the variation in the web buckling stress t with the web/flange width ratio d/b. The channel h/t ratio = 100. The solid line represents the web/lip ratio d/D = 5, the dotted one h/D = 10 and the dashed one h/D = 25. The variation in the h/b ratio ranges between 2 and 10, which captures the majority of the cold-formed steel sections used in industry. The change in t values is approximately 10 % for h/D = 5. This difference increases to 12 % by increasing the h/D ratio to 10 and increases further to 14 % as h/D approaches 25. This indicates that as the flange width decreases, the shear buckling stress t decreases. Note that majority of the decrease in t values occurs when the h/d ratio is between 2 and 7. The difference in t used by AISI [13] and CSA-S136-07 [14] ranges between 15 and 27 %.

This shows the large influence of the flange and lip sizes on the web stability.

Fig. 3. Variation in the web shear buckling stress t with h/D

Fig. 4. Variation in the web shear buckling stress t with h/b

5 Influence of flange and lip rotational restraints

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O. Bedair · An analytical expression to determine “realistic“ shear buckling stress in cold-formed lipped channels

6 Economic aspects Taking into account the rotational restraints results in economical steel design. To provide an insight into the cost savings of using the proposed expression, Eq. (18), we shall assume an unsupported web length of 1500 mm, a web width h = 300 mm, a flange width b = 200 mm, a lip width D = 50 mm, a channel thickness t = 3.05 mm and yield stress σY = 300 MPa. The shear buckling stress determined using Eq. (18) is t = 144 MPa. The code prediction given

by Eqs. (2) and (4) is 102.8 MPa – a difference of almost 29 %. We shall assume that it is required to use a channel member with total length of 6 m in the construction of a commercial building. Fig. 5 shows a cost comparison when using the described procedure vs. AISI, CSA-S136-07 and Eurocode 3. The comparison is made for three sets, including the cost of fabrication. The cost of materials shown by the red bars represents the code values and the blue bars are the costs using the proposed design procedure, Eq. (18).

Three sets are compared using 100, 300 and 500 channel members in the building construction. It can be seen that the difference in cost becomes very pronounced as the number of members increases. For example, the difference in the cost of materials is approx. US$ 34,000 when using 500 members. Therefore, the form of the proposed Eq. (18) yields significant material savings. It should be noted that the comparison in this example is made for the elastic critical buckling stress, not the shear resistance.

7 Conclusions This paper has provided a closed-form expression to compute local shear buckling stresses in lipped channels with partial rotational restraints. Current North American and European provisions use simply supported web conditions, thus ignoring the flange/lip rotational restraints. The expression derived is suitable for hand calculation and avoids excessive efforts required by numerical procedures such as the finite element or finite strip method. In addition, significant material savings can result from using the proposed equation.

100 Members

300 Members

500 Member

Fig. 5. Cost comparison between code predictions and proposed expression

Notation a unsupported length of channel h width of web b width of flange D width of lip E elastic modulus Kv web and flange buckling coefficients x\, y\ oblique coordinate system t web buckling shear stress t thickness of channel section v Poisson’s ratio ξ, η non-dimensional web coordinates θ1, θ2, C1–C3, H1–H3 web displacement coefficients

References [1] Bedair, O.: Serviceability and Ultimate Limit States of Channels under Compression and Bi-axial Bending. Journal of Constructional Steel Research, vol. 67 (10), 2011, pp. 1415–1425.

[2] Bedair, O.: Practical Design Considerations for Light-Weight Channels under Combined Compression, Major and Minor Axes Bending. ASCE, Practice Periodical on Structural Design and Construction, vol. 16 (1), 2011, pp. 15–23.

[3] Bedair, O.: A Cost-Effective Design Procedure for ColdFormed Lipped Channels under Uniform Compression. ThinWalled Structures, vol. 47 (11), 2009, pp. 1281–1294.

[4] Bedair, O.: A Simplified Procedure for Prediction of Ultimate Strength of Beam-Column Channel Sections. Engineering Journal, vol. 3 (10), 2011, pp. 973–977.

[5] Pham, C., Hancock, G.: Shear buckling of thin-walled channel sections. Journal of Constructional Steel Research, vol. 65 (3), 2009, pp. 585–579.

[6] Hancock, G., Pham, C.: Shear buckling of channel sections with simply supported ends using the Semi-Analytical Finite Strip Method. Thin-Walled Structures, vol. 71, 2013, pp. 72–80.

[7] Bedair, O.: Discussion of Shear buckling of thin-walled channel sections. Journal of Constructional Steel Research, vol. 66 (1), 2010, pp. 136–137.

[8] Ren, W., Fang, S., Young, B.: Analysis and design of coldformed steel channels subjected to combined bending and web crippling. Thin-Walled Structures, vol. 44 (3), 2006, pp. 314–320.

[9] Tian, Y. S., Wang, J., Lu, T. J.: Axial load capacity of coldformed steel wall stud with sheathing. Thin Walled Structures, vol. 45 (5), 2007, pp. 537–551.

[10 Young, B.: Design of channel columns with inclined edge stiffeners. Journal of Constructional Steel Research, vol. 60 (2), 2004, pp. 183–197.

[11] Liu, Y., Day, M.: Multi-axis bending of channel section beam and modelling. Thin-Walled Structures, vol. 46 (11), 2008, pp. 1290–1303.

[12] Chu, X., Ye, Z., Kettle, R., Li, L.: Buckling behaviour of coldformed channel sections under uniformly distributed loads.

Thin-Walled Structures, vol. 43 (4), 2005, pp. 531–542.

[13] Lange, J., Naujoks, B.: Behaviour of cold-formed steel shear walls under horizontal and vertical loads. Thin-Walled Structures, vol. 44 (12), 2006, pp. 1214–1222.

[14] Stowell, E.: Critical Shear Stress of Infinitely Long Flat Plate with Equal Elastic Restraints Against Rotation Along The Parallel Edges. National advisory Committee for Aeronautics (NACA): Wartime Report 3K12. Langley & Washington, 1943.

[15] Bedair, O.: Analysis and Limit State Design of Stiffened Plates and Shells: A World View. Journal of Applied Mechanics Reviews, vol. 62 (2), 2009, pp. 1–16.

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[16] American Iron & Steel Institute (AISI): North American Specification for the Design of Cold Formed Steel Structural Members, Washington, D.C., USA, 2007.

[17] Canadian Standard Association (CSA-S136-07): North American Specification for the Design of Cold-Formed Steel Structural Members. Canadian Standard Steel Association, Mississauga, Ontario, 2007.

[18] Eurocode 3: Design of steel structures – Part 1-5: Plated structural elements; EN 1993-1-5, 2005.

[19] Ziemian, R.: Guide to Stability Design Criteria for Metal Structures, 6th ed., John Wiley & Sons Ltd., New York, USA, 2010.

[20] Cook, I. T., Rocky, K. C.: Shear Buckling Of Rectangular Plates With Mixed Boundary Conditions. Aeronaut. Q., vol. 14., 1963, pp. 349–356.

[21] Column Research Committee of Japan Handbook of Structural Stability. Corona Publishing Co., Tokyo, 1971.

Keywords: cold-formed steel; channel sections; shear buckling

Author: Osama Bedair, PhD, P.Eng Consultant 623-5330 58A Street, Red Deer, Alberta, Canada, T4N 3W1 obedair@gmail.com

News Phänomenta Science Center in ­Lüdenscheid, Germany As of next year, the Phänomenta Science Center in Lüdenscheid will extend its premises and add new content to its interior. An annex with around 2,000 m² of exhibition space will offer more room in future for all kinds of different things – even supporting one of the extensions on the roof designed by KKW Architects.

The 76 meter-high steel tower, replete with an inner membrane, touches the

sky as if with the point of a finger. This expressive design not only catches the eye: a Foucault pendulum swings within the interior.

The supporting frame of this distinctive structure consists of a spiral steel tower to which the inner helix membrane is anchored at a few points. This flexible structure consists of approximately 1,000 m² of membrane and three shape-giving ropes, which harness the textile fabric at nine points in the direction of the steel tower. The membrane

follows the tower structure, which rotates and tapers upwards in the form of a helix, creating a space of approximately 5,200 m³. Within this is to be found the pendulum tower, a roughly 26-meter-­ high tripod with a covering, wherein the Foucault pendulum swings. The outer shell protects the pendulum tower from the elements. In addition, the steel membrane sculpture, full of expression, forms a luminous body highly visible as evening turns to night. Backlit with light, it functions as an exhibit of the interactive Science Center, stimulating the viewer’s interest in the world of science.

Dimensions: Steel tower 76 m, base height 12 m Helix 58 m, base height 12 m Membrane surface area: 990 m² (helix) + 350 m² (pendulum tower)

Phänomenta Science Center with illuminated membrane helix; © Engel-Hähnel for KKW Architekten, formTL

58

Material: Membrane: PVC/PES Ferrari P ­ recontraint 1202S2 Supporting rope ∅ 26 mm Support structure: S355 steel Tower supporting structure planning: WERNER Bauingenieure, Germany Structural planning for the membrane helix supporting: formTL GmbH, G ­ ermany Steel construction: Heinrich Rohlfing GmbH, Germany Membrane: A. Arnegger GmbH, Germany Further information: www.form-tl.de

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Reports DOI: 10.1002/stco.201520004

Long-term corrosion protection for bridge cables with butyl rubber tapes using the ATIS Cableskin® system Oswald Nützel Reiner Saul

ATIS Cableskin® is a corrosion protection system for bridge cables which uses proven materials to strike out in a new direction. These innovative ideas mean that, for the first time, corrosion protection work on scaffolds and in enclosures will be a thing of the past, and the costs and traffic restrictions are massively reduced. It is worth highlighting the extremely long lifetime of this corrosion protection.

1 Development In the beginning there was the butyl rubber. When it was first manufactured on an industrial scale, people were excited by its physical and chemical properties, which made a broad range of applications accessible. One use of butyl rubber is in tyre production, so that tyres retain their air and the embedded steel cord is protected against moisture.

In the 1960s, PE films were inserted into the soft butyl rubber material to prevent overstretching, which massively increased its stability. DENSO Leverkusen developed a procedure in which coextruded interlayers generated a perfect bond between these two different materials. That was crucial for its use as corrosion protection applied in the form of wrapping.

Butyl rubber tapes have been successfully used commercially since 1970, initially for gas and other pipelines underground and open to the weather. Since then, more than 107 million square metres of surface have been protected globally, with no significant cases of damage known.

In 2006 this success gave DYWIDAG-Systems International GmbH (DSI), one of the leading global companies for prestressing and stay cable systems, the idea to use these tapes for protecting the stay cables of bridges against corrosion.

Alpin Technik und Ingenieurservice GmbH (ATIS) in Leipzig delivered the necessary equipment for the automated application of the tapes on the cables. Today, this company markets and develops this wrapping method globally under the name of ATIS Cableskin®. It has been officially approved in Germany since 2010 and in Europe since 2013 [1], [2].

2 Brief description of ATIS Cableskin® corrosion protection system

–– The base layer is directly on the cable surface and consists of a three-ply tape, which is wound around with approx. 50 % overlap, Fig. 2a.

–– The top layer constitutes the outer corrosion protection and is a two-ply tape, whose outer ply is made of robust UV-stabilized PE film, Fig. 2b. It comes in different colours depending on the owner’s specification and forms mechanical protection for the layers underneath. The overlap is also approx. 50 %, so there is a total layer thickness of approx. 2.6 mm.

Interdiffusion of the butyl rubber molecules, so-called cold welding, Fig. 2c, forms a tube-like encasement, which adheres very well to the cable surface and meshes with it, Fig. 3.

It is practically impermeable to oxygen and water vapour.

3 Approval tests In order to obtain official approvals in Germany and Europe, extensive tests were required, which were carried out

cable

base layer

top layer

Fig. 1. ATIS Cableskin® corrosion protection system

base layer

top layer

butyl rubber PE film coextruded layer

PE film coextruded layer butyl rubber

butyl rubber

2nd layer 1st layer

Cableskin®

The ATIS corrosion protection system consists of two layers of butyl rubber tape wrapped around the cable, Fig. 1.

Fig. 2. Make-up of corrosion protection tapes: a) base layer, b) top layer, c) cold welding (interdiffusion)

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Fig. 3. How the base layer adheres to and meshes with the cable surface

Fig. 5. Visual inspection with high-speed camera

–– Direct visual inspection –– Inspection with video –– Inspection with high-resolution, high-speed cameras, Fig. 5

Fig. 4. Samples in the salty fog test

at the Otto Graf Institute of the University of Stuttgart. The test criteria were set in compliance with the corresponding guidelines for coatings [4], [5], [6].

All tests were passed successfully – the most important being: –– Resistance to salty fog, Fig. 4 –– Resistance to condensed water –– Resistance to chemicals –– Artificial weathering with xenon radiation –– Artificial weathering in UV test –– Resistance to water vapour The results were either in line with the requirements or exceeded them by far. They fulfilled the conditions for corrosion protection for industrial and coastal atmospheres C5-I and C5-M according to EN ISO 12944-6 [7], [8].

4 Preliminary investigation of the cables 4.1 Visual inspection Normally, visual inspection of the cables is carried out with cameras before corrosion protection work starts.

There are different systems for this on the market:

60

The advantage of the third procedure is that it supplies a sharp panorama image whose quality is equivalent to an on-site inspection and which captures the whole scale of the cable. The evaluation takes place with the help of a special analysis and comparison program.

4.2 Magnetic induction (MI) tests In order to check whether there are any internal wire fractures in the free cable length, there are two MI procedures that differ considerably in significance: Magnetisation of outer wire layers only Owing to the low output of the devices, only the outer wires of the cable are magnetised, which means that wire fractures in the interior cannot be detected.

Magnetisation of whole cable cross section High-performance devices are needed for this. Wire fractures across the entire cross-section are recorded, Fig. 6.

4.3 Ultrasonic tests In places that cannot be checked with the MI procedure due to geometric design, e.g. anchorages areas, the ultrasonic procedure is employed, which allows wire fractures along a length of approx. 1.40 m to be detected with the help of a transducer placed on the end surface of each individual wire, Fig.7.

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Fig. 8. Test sample subjected to 30 bar interior pressure under the wrapping

Fig. 6. Magnetic induction (MI) unit

Fig. 9. Wrapping robot on painted cables

Fig. 7. Ultrasonic test

Fig. 10. Wrapping with hand unit

5 Application of tapes 5.1 Surface preparation

under slight tension. Depending on the length and diameter of the cable, joints may be required, which are also produced automatically by the robot. All working steps are controlled from the ground by a monitoring unit and can be saved and archived so that the owner is able to closely monitor what is or was happening.

In the meantime, robots that wrap both the base and top layer in one process have been specially developed for large projects. They are loaded with butyl rubber tapes in place with the help of rope access technology. By this, the wrapping is accelerated considerably.

At places where the geometry does not allow the use of robots, the tape can be wrapped using a manually operated unit, Fig. 10 or directly by hand.

No special pre-treatment of the cable surface, e.g. blasting or sweeping, is required for the wrapping procedure. Any existing coatings may remain in place, too. The surface must only be dry and free from serious contamination and loose material.

Cable filling material that has leaked out must be removed mechanically. No further measures are required. In tests involving applying an internal pressure of 30 bar, it was shown that the wrapping remains tight even under this extreme load, Fig. 8.

5.2. Wrapping The butyl rubber tapes are usually applied to the cable automatically using a wrapping robot, Fig. 9. It moves along the cable independently and wraps the tape helically

6 Repairing damage If the wrapped protection is damaged, through vandalism, for example, it can be repaired without extensive base

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Fig. 11. Repairing damage

preparation. To do so, only the damaged area is cut out in circular shapes. The new tape is wrapped around by hand, overlapping the existing tapes, Fig. 11.

7 Control areas For long-term monitoring of the corrosion protection, control areas can be set up in accordance with the current guidelines [6].

If damage to the existing intact wrapping is to be avoided when carrying out such control tests, an alternative to this is available. An additional 50 cm long wrapping, which can be easily removed while taking appropriate precautions, is applied to the existing wrapping. This allows the corrosion protection performance to be assessed in an easy and careful way under the conditions prevailing at the structure, Fig. 12.

Fig. 13. Dehumidification channels under the wrapping to a cable bundle (mock-up)

9 Monitoring A monitoring system can be installed parallel to applying the ATIS Cableskin® corrosion protection system. This allows frequently updated information about temperatures, humidity and thus the dew point. To achieve this, sensors are mounted under the wrapping on the cable. Wherever the protected structure is located in the world, the data are transmitted by wireless technology to a server, then evaluated and displayed on a web-based page. The owner can check the condition of the structure anytime, anywhere.

Usually, this monitoring system is installed on bridges with bundles of ropes, where moisture inside the cable is more likely due to the complex cable structure, Fig. 14.

Fig. 14. ATIS monitoring system at Ophus suspension bridge, Norway Fig. 12. Control area on wrapping

10 Examples of applications

8 Dehumidification

The ATIS Cableskin® wrapping system has been employed for several large projects: First of all, in 2008 it was used for the 80 stay cables of the Passerelle des deux Rives pedestrian and cycle bridge over the Rhine at Kehl/Strasbourg (∅ 60 mm to ∅ 139 mm, total stay cable length approx. 3700 m). The works were performed four years after completing the bridge. No special preparation of the galvanized cable surface was carried out, Fig. 15a [9].

During recent years a procedure has been developed to dehumidify cross-sections of cable bundles on older suspension and cable-stayed bridges. This involves creating one or several channels on the cable surface under the wrapping with the help of mouldings into which dried air is fed. This can target the removal of any residual moisture that might be present in the inside of the cable bundle, Fig. 13.

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Reports In 2010 the Köhlbrand Bridge in the port of Hamburg followed with 88 cables (up to ∅ 118 mm, approx. 8700 m in total). The cables had been in use since 1978 and were PU-covered. The butyl rubber tapes were applied after manual removal of loose paint coats. Adhesive coating was not removed, Fig. 15b [10].

In 2012 the cables of the Obere Argen Bridge on the A96 motorway nearby Wangen, Allgäu, Germany, were wrapped (24 cables, ∅ 126 mm, total of approx. 1700 m).

The existing coating was not removed here, either, Fig. 15c [11].

A further development of the wrapping system was employed on the Ophus suspension bridge in Norway in 2013–14, where the loadbearing main cables were protected, Fig. 14 [12]. Their wrapping is tightly connected to the suspenders with the help of neoprene boots, which can be opened for inspection purposes at any time. The newly developed dehumidifier and monitoring systems were also successfully employed for the first time in this project.

Smaller projects, e.g. the wrapping of masts in Scandinavia and the corrosion protection of cable-supported structures at the airport in Johannesburg, South Africa, have been carried out recently.

The wrapping of the cables of two large cable-stayed bridges in Houston and Port Arthur, Texas/ USA (parallel wire cables with cement grout and PE pipes, total surface

13000 m2), with the main aim of improving their resistance against UV rays, has started in December 2014 and will take about six months, Fig. 15d.

11 Lifetime Tenders for cable-stayed bridges usually specify a lifetime of 100 years for the cables. That is a big challenge in view of corrosion protection, too.

In locked coil ropes, the individual wires are protected with zinc or galfan. If the surfaces are exposed to the weather, the SO2 content of the air will mean that the protective layer will be steadily eroded. The rate of erosion depends on the ambient atmosphere (sea, industry) and increases massively if dirt accumulates between the wires and form moisture pockets in combination with salt. The surface may also have been already damaged by mechanical impact during cable installation operations.

Therefore, another layer of protection is normally applied in order to shield the zinc or galfan from environmental factors – a duplex system with a total thickness of about 400 μm. However, the lifetime of the paint coating normally used has been limited up to now. In general, such a coating is assumed to last up to approx. 25 years.

The use of butyl rubber tapes leads to a significantly longer lifetime. According to the positive experiences col-

a)

b)

c)

d)

Fig. 15. Applications: a) Passerelle des deux Rives, Kehl/Strasbourg, b) Köhlbrand Bridge, Hamburg, c) Obere Argen Bridge on A96 motorway, Wangen/Allgäu, d) Veterans Memorial Bridge, Port Arthur, Texas, USA

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Reports lected over more than four decades since the 1970s as well as in new tests, such tapes are likely to last > 60 years. In 2013 the Otto Graf Institute at the University of Stuttgart undertook another set of tests with wrapped samples, which had already been exposed to tests in 2008 (see section 3) and were additionally exposed to environmental conditions for a further five years. Even after this extreme treatment, absolutely no changes to the material or the anti-corrosion effect were evident [13].

A further indication for the long lifetime is the fact that owing to this kind of tape wrapping, there is a total of eight barriers of butyl rubber and PE film to overcome before any damaging influences can get through to the cable surface. Even if the top layer breaks down for example due to vandalism, corrosion protection is still guaranteed, because even the base layer alone has passed the tests listed in section 3.

12 Summary of features The advantages for using butyl rubber tapes are as follows: –– Officially approved by authorities in Germany and Europe –– Quick, reasonably priced, VOC-free application –– Essentially independent of climatic conditions –– No scaffolds or enclosures, therefore minimal traffic restrictions –– No extensive preparation of the cable surface, e.g. blasting or sweeping, necessary and therefore no disposal of environmentally harmful materials –– Ability to wrap over existing coatings –– Simple repair of damaged areas –– Control areas for long-term monitoring –– Use of monitoring systems –– Use of dehumidifying systems in the case of rope bundles –– 100 % recyclable The technical features should also be cited, which account for the excellent long-term durability of this wrapping system: –– Lifetime > 60 years –– Robust, multi-layered system made of tough materials with approx. 2.6 mm layer thickness –– Very good adhesion and interlocking with cable surface –– Highly elastic behaviour, which accommodates all temperature and load movements –– No spalling or tearing of the wrapping in the case of possible discharges of cable filling materials or with relative displacements of the wires –– Approved to corrosion categories C5-I and C5-M according to EN ISO 12944-6

13 Concluding remarks The advantages of the ATIS Cableskin® wrapping system, which is officially approved for use across Europe, are not just the execution and short manufacturing times, but also the easy repair possibilities and the excellent long-term durability in particular. The system requires almost no maintenance. This makes it a high-quality alternative to the coating systems available up to now, which is reasonably priced, quick to apply and adapts optimally to the particular conditions.

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References [1] Deutsches Institut für Bautechnik (DIBt): Allgemeine bauaufsichtliche Zulassung für das Korrosionsschutzverfahren ATIS Cableskin® für vollverschlossene Seile (national technical approval for the corrosion protection system ATIS Cableskin® for locked coil ropes), Berlin, Nov 2010.

[2] Deutsches Institut für Bautechnik (DIBt): Europäische Technische Zulassung ETA-13/0171 für das Korrosionsschutzverfahren ATIS Cableskin® für tragende Seile (European Technical approval for the corrosion protection system ATIS Cableskin® for loadbearing cables), Berlin, Apr 2013.

[3] Bundesanstalt für Straßenwesen (BAST): Umwicklung von vollverschlossenen Seilen mit Korrosionsschutzbändern (wrapping of locked coil ropes with corrosion protective tapes) Bergisch Gladbach, Nov 2010.

[4] RKS-Seile: Richtlinien für den Korrosionsschutz von Seilen und Kabeln im Brückenbau (guidelines for the corrosion protection of ropes and cables in bridge construction), Verkehrsblatt Verlag, Dortmund, 1983.

[5] TLKS-Seile: Technische Lieferbedingungen für Beschichtungs-, Dicht- und Injizierstoffe an Seilen und Kabeln im Brückenbau (technical delivery conditions for material for coating, sealing and injecting for ropes and cables in bridge construction), Verkehrsblatt Verlag, Dortmund, 1983.

[6] ZTV-Kor Seile: Zusätzliche Technische Vertragsbedingungen und Richtlinien für den Korrosionsschutz von Seilen und Kabeln im Brückenbau (additional technical contract conditions and guidelines for the corrosion protection of ropes and cables in bridge construction), Verkehrsblatt Verlag, Dortmund, 1998.

[7] Nürnberger, U.: Stellungnahme zum Korrosionsschutzsystem ATIS Cableskin® mit Butylkautschukbändern (statement on the corrosion protection system ATIS Cableskin® with butyl rubber tapes), Stuttgart, Oct 2010.

[8] Materialprüfungsanstalt Universität Stuttgart: Untersuchungsbericht “Korrosionsschutzsystem mit Butylkautschuk für vollverschlossene Seile” (corrosion protection system with butyl rubber for locked coil ropes), Stuttgart, Sept 2007.

[9] Morgenthal, G., Saul, R.: Die Geh- und Radwegbrücke Kehl – Straßburg (The Pedestrian and Cycle Bridge Kehl – Strasbourg). Stahlbau 74 (2005), pp. 121–125.

[10] Zellner, W., Saul, R.: Über Erfahrungen beim Umbau und Sanieren von Brücken. Bautechnik 62 (1985), pp. 51–65.

[11] Schmid, H.: Wickeln von vollverschlossenen Seilen an der Talbrücke Obere Argen. Stahlbrückenbau, Expertengespräch, BAST, Bergisch Gladbach, 23 Sept 2014.

[12] Saul, R., Nützel, O.: Neuartige Sanierung der Tragkabel einer Hängebrücke in Norwegen (Innovative rehabilitation of the main cables of a suspension bridge in Norway). Stahlbau 83 (2014), pp. 96–100.

[13] Materialprüfanstalt Universität Stuttgart: report No. 902 4706 000, Stuttgart, 30 Apr 2013.

Keywords: buthyl rubber tapes; long term corrosion protection; bridge ropes and cables; automatic visual and magnetic induction testing; scaffolding free application; dehumidification of cables

Authors: Dipl.-Ing. Oswald Nützel Grellstr. 30, 81929 Munich oswald.nuetzel@gmx.de Dipl.-Ing. Dr.-Ing. E.h. Reiner Saul Riegeläckerstr. 60, 71229 Leonberg-Warmbronn saul.reger@gmail.com

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Reports DOI: 10.1002/stco.201520005

Engineering complex geometries – the Heydar Aliyev Centre in Baku Thomas Winterstetter Mustafa Alkan Radu Berger Maiko Watanabe Agatha Toth Werner Sobek

The present paper describes the engineering design by Werner Sobek for the new Heydar Aliyev Centre in Baku, a masterpiece of 3D freeform architecture by Zaa Hadid.

1 General The Heydar Aliyev Centre is the new national cultural centre of Azerbaijan, housing a museum, auditorium/opera house and related cultural facilities. It is located in the centre of the city, overlooking a large park. Its unique and iconic design by Zaha Hadid Architects is intended to serve as a memorial to the founder of modern Azerbaijan (Fig. 1).

1.1 Location Baku is the capital of Azerbaijan, a country on the southern side of the Caucasus Mountains, lying between Russia (north), Georgia (west), Turkey/Iran (south) and the Caspian Sea (east). The country is rich in natural resources, especially oil and natural gas. For centuries it was a hub on the Silk Road and preserves a rich Islamic cultural heritage.

The climate of Baku is relatively harsh, with strong winds, hot, dry summers with very little precipitation, and cold temperatures as low as –10 °C in winter. Another challenge for planners is the (decreasing, but still important) air pollution caused by industry, especially crude-oil refining.

Moreover, the city is subjected to a high risk of earthquakes since it lies on the Apseron peninsula, the eastern extension of one of the main Caucasus ridges marking a fault line between continental plates.

1.2 The project The project arose out of a competition won by Zaha Hadid Architects, London, in 2007. The Heydar Aliyev Centre consists of the following components (Fig. 2): –– A large park with a sculptured landscape connecting the above-ground facilities in a large, free-flowing gesture –– An underground car park –– A pond café –– An underground utilities and energy supply centre –– The main building housing a museum, an auditorium and other facilities The following article focuses on the main building.

Fig. 1. Exterior view of Heydar Aliyev Centre (© Helene Binet, London)

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Reports Table 1. Key figures

Fig. 2. Site plan

1.3 Basic design intent and figures The basic idea underlying the design is that the main building develops its form from the plaza in front of it. Architecturally, the plaza is divided into strips running from east to west; these strips wrap upwards around the main building and create a free-flowing 3D shape (Fig. 3). The geometry of the building envelope is reflected in the interior.

Max. height of roof

80 m

Max. span of roof

90 m

Area of roof covering

28 000 m2

Area of outer skin

40 000 m2

Area of glazed curtain-wall

8500 m2

Area of inner skin

22 000 m2

Area of plaza

10 000 m2

Seats in auditorium

960

Solid skin panels

16 150 pcs.

The building is subdivided into two areas: a museum and an auditorium. The auditorium area contains the auditorium itself, a library and a multipurpose hall (Fig. 4).

2 Main building 2.1 Structural design The structure of the main building consists of in situ reinforced concrete (RC) and a composite steel frame structure. The slabs in the museum and library areas are longspan composite beams with RC slabs cast on a metal deck.

The auditorium and the multipurpose hall consist of conventional RC slabs on RC beams.

The lateral stiffening system reacts to both the spatial limitations imposed by the architectural design and the high horizontal forces liable to be caused by earthquakes.

In the museum area there is a 3D free-form shear wall with a concrete core. In the auditorium and the multipurpose hall there are various RC shear walls. In the library (which is situated in the highest part of the building) the stiffness of a very slender concrete core and that of a steel section frame system were combined (Fig. 5).

Fig. 3. Detailed view of 3D curves of the building envelope (© Helene Binet, London)

Fig. 5. Section

2.2 Roof structure space frame

Fig. 4. Floor plan

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The design of the space frame for the roof was a multi-step process, starting with the definition of a structural zone between the architectural free-form shapes of the inner and outer skins. Afterwards, the space frame was aligned with the structural design of the main structure.

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Reports –– First, top and bottom chord grid-lines were defined along the number axes, with the structural grid-lines at 9 m offsets being multiples of these axes.

–– In a second step, a grid of three-dimensional diagonals was inserted, the geometry being constantly checked for clashes with the architectural shape.

–– An FE model was then generated and computed; the steel sections and quantities were calculated and optimized by MERO, the space frame fabricator, using specialist software.

–– Finally, the support forces and details were coordinated with the main structure.

During the computerized stress analysis, it was particularly important to include a correct model of the combined action of the space frame and the main concrete-steel frame structure underneath.

Erection had to follow a carefully planned installation sequence in order to achieve the schedule milestones, maintain structural safety under all temporary conditions and minimize the impact of dead load deflections and other issues during the erection process.

As a result of their involvement in the competition, the concept design for the concrete-and-composite main structure and the linear steel truss system roof were provided by AKT, London. Design development and final design of the main structure was carried out by Tuncel Mühendislik, Istanbul. The roof was erected as a unitized 3D space frame structure designed and fabricated by MERO, Würzburg, Germany.

The scope of work for Werner Sobek regarding the main structure comprised the following tasks: –– Coordinating the design of the space frame with other architecture-related issues such as the solid skin, curtain wall and interior 3D ceilings.

–– Coordinating the structural interfaces at the supports for the space frame on the main structure and the foundations.

–– Detailed structural design of all steel columns and steel frames supporting space frame roof and glazed curtain wall.

–– Checking and coordinating the 2D and 3D design submittals provided by MERO. –– Checking the structural calculations provided by MERO using two independent full 3D FE Etabs and Rstab models combining the main structure and the space frame.

a)

b)

–– Planning, managing and coordinating the various installation sequences, supervising the installation of the space frame and the steel columns and beams on site.

2.3 Solid skin The external solid skin is the most important architectural feature of the building. It has a 3D free-form geometry and is built up in several layers with different functions. Efforts were made to facilitate the design, production and logistics of the solid skin and to achieve the unique appearance proposed by the architects.

The functional and/or architectural layers of the external solid skin are shown in Fig. 6 and will be described in the following sections (Figs. 6a–6c).

The scope of Werner Sobek’s services included the design, engineering, tendering and installation management and supervision of the various components of the solid skin.

2.3.1 Weatherproofing The first layer is a prefabricated weatherproofing tray system, which rests on the top chord nodes of the main roof structure space frame and thus exhibits a faceted geometry.

The trays consist of two U-section purlins, a trapezoidal metal deck in between, a self-adhesive vapour barrier, a layer of rigid, non-flammable rockwool insulation boards and a weatherproofing membrane on top, in a special overlapping system covering the gaps between two adjacent trays.

Owing to the shape of the building and the space frame, all four corner bays to be covered by any given tray are not in one common plane, but twisted. Therefore, maximum acceptable warping criteria for the cold-bending of the four corner trays during installation were defined.

Trays exceeding these criteria were produced with a triangularized form, with two triangles and an additional U-section purlin in the middle. The support on the space frame stools and the fixing of the trays were achieved with spherical washers in order to accommodate the ever changing support angles.

All weatherproofing trays were pre-assembled on site, according to their actual dimensions, and lifted up to the roof as complete units. Therefore, most work could be carried out without having to face the very windy working conditions encountered several metres above ground. Only

c)

Fig. 6. a) Isometric view of layers of external skin, b) isometric view from below, c) isometric view from above

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Reports the mechanical fixings to the MERO stools and two membrane welding seams along the overlaps were installed on the roof.

The basic quantities for the building were tendered as follows: Metal deck purlins: 3607 pcs., 10 092 m total length Metal deck, insulation, weatherproofing: 3936 trays, 26 853 m2 total area The prefabricated tray system was invented and engineered entirely by Werner Sobek using parametric design software.

Fabrication and installation was carried out by LIMIT Müh., shop drawings were subcontracted by LIMIT to the engineering office Selcuk Iz.

2.3.2 Substructure to solid skin The white solid skin is an open-joint rain-screen cladding system, which required a secondary steel substructure to fix it to the space frame. The entire design, engineering, 3D parametric modelling, tendering, generation of fabrication data for the subcontractor LIMIT and installation supervision was part of Werner Sobek’s remit.

The secondary steel structure is attached to the nodes of the space frame by means of rods. From there, the secondary steel layer is responsible for interfacing between the faceted, nodal, regular space frame chord nodes geometry and the solid skin joint pattern defined by the architecture. This was accomplished by –– curving the tube elements of the secondary steel (overcoming the faceted node system), –– using a first array of transverse tubes (“primary tubes”) to span between nodes, and –– using a second array of longitudinal tubes (“secondary tubes”) to span between the first layer of tubes and to carry the actual panel fixings.

The build-up zone dimensions required that both arrays be in the same layer. Owing to the irregular shape of the building, all the elements of the steel substructure have unique dimensions. The theoretical spline shapes were optimized and approximated into circular tube bending using a fine-tuned stepping of radiuses to facilitate production and installation while not compromising the architectural appearance.

The substructure covers about 39 000 m2 of roof area and consists of more than 12 500 elements, all of which are individual. The precise design required considerable specialist engineering and 3D modelling, and the care during design paid off as erection proceeded virtually without any mismatch problems.

2.3.3 Solid skin panels The exterior skin is divided into the solid skin of the building (cladding the building’s roof and exterior walls and extending into interior ceilings as well) and the plaza, with a steady and invisible transition between. The total surface is about 39 100 m2 for the solid skin and another 9000 m2 for the plaza.

The solid skin and plaza panels are defined by architectural joint lines, which depend in turn on the limits imposed

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by the production and transportation of the panels. The joint lines create a unique and free-flowing pattern, enveloping the entire building and the plaza; at the same time each panel’s geometry is unique. In addition, the panels were to have the appearance of solid stone blocks. Therefore, they were required to have perpendicular “edge returns” 12 cm deep on all four edges. The main joints across the building had to be 40 mm wide to accentuate that direction and to be able to access the invisible fixings through them; the secondary joints in the other direction had to be 10 mm wide, placing high demands on precision in fabrication.

Up until the HAC project, panels had never been produced on such a scale and with such a geometrical complexity anywhere in the world. Most of the production methods and materials had to be invented and/or adapted specifically for the project. Therefore, a very long and extensive materials and production research and prequalification routine was conducted, including: –– Realization of small- and large-scale prototypes –– Factory visits to various potential producers all over Europe and the Middle East –– A pre-contract laboratory testing programme to identify key material and performance characteristics –– Assessment of experience and financial and output capabilities of the bidders One of the key architectural requirements was that the solid skin and plaza cladding look the same, and that the panels have an off-white concrete material appearance.

Therefore, research originally focused on fibre-reinforced concrete (FRC) cladding. As a technical alternative, some manufacturers offered fibre-reinforced plastic (FRP) panels for certain areas. which looked identical; these FRP panels were to overcome issues such as schedule constraints related to curing time, limited output capacity of FRC producers, cost impact, risk of fracture of brittle FRC panels and issues related to easy cleaning of roof and wall surfaces that were difficult to reach. As a result, a concept evolved in which FRP was ordered for the roof, up to a line about 3 m above ground, and FRC in a matching colour for the bottom part of the exterior walls and the plaza.

The production contract for the FRP/FRC panels was awarded to Arabian Profiles Ltd. in Sharjah, UAE. Production took place in their plant in Ajman, UAE, using a technique involving single-use plywood formwork mould-making. The colour match between FRP and FRC was established using a gelcoat layer with a special mixture for the visible faces of the FRP. The shop drawings for the production of the panels were prepared by London-based subcontractor Newtecnic.

Werner Sobek’s scope of work included consultancy for and participation in all of the aforementioned pre-contract research and engineering activities, coordination of the design criteria and technical performance requirements, tendering, post-contract coordination of 3D location of embedment points and design of special panels, checking panel 3D shop drawings, full continious factory inspection of panels produced in the plant in Ajman to a set of architectural inspection criteria before shipment, and installation management and supervision on behalf of the main contractor on site.

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Reports

Fig. 7. Main structure and space frame with roof covering at various stages

Fig. 9. Supporting structure in the interior (© Helene Binet, London)

Fig. 8. Installing the roof covering

Certain rows of panels were left open, to be closed at the end of installation, in order to eliminate any tolerances built up during installation or any other structural or thermal or survey deviation effects (Figs. 7 and 8).

2.4 Interior skin The interior skin of the building has the same geometrical complexity as the exterior skin. In addition, the architectural intention was also to divide the interior skin visually into “bands” in the cross-building direction, again emphasizing the theme of the plaza wrapping around the building (Figs. 9 and 10).

As for the exterior skin, Werner Sobek’s remit for the interior skin included consultancy for and participation in all pre-contract research and engineering activities, consulting of the design criteria and technical performance requirements and tendering, post-contract coordination of 3D shop design, checking 3D and 2D shop drawings, factory goods inspections prior to packing and shipment, and installation management and supervision on site on behalf of the main contractor.

Fig. 10. Interior view of Heydar Aliyev Cultural Centre (© Hufton + Crow, Hertford)

For the technical system, extensive research into the various options was needed to create these unique interiors. Two basic methods were investigated: a panel mould-making approach (as used for the exterior skin) and a cold-bending approach. For the latter, flat thin plates were bent on site during installation while fixing them to a pre-arranged substructure grid defininsg the free-flowing curvature.

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Reports Following several prototype inspections and further assessments, tests and negotiations, the second method was selected. Lindner AG of Arnstorf, Bavaria, was awarded the contract for production.

The system installed consists of a layer of purlins holding curved substructure tubes at a 50 cm spacing. The tubes have thin steel plate fixings attached to them on a 50 × 50 cm grid. The tubes and their fixings were designed to match the 3D curvature of the interior skin precisely.

The interior cladding, consisting of fibre-reinforced flexible boards, was attached to the fixings by site-drilled screws. After installing a larger area of boards, the architectural joints and the curved slots for lighting, spotlights, loudspeakers, etc. were cut out on site and filled with seam profiles. Skimming and painting provided the final touches.

Special care was necessary to phase the installation, because accessing the ceiling at a height of up to 40 m above floor level required extensive scaffolding. Fast removal of that scaffolding was crucial in order not to block the progress of the subsequent fitting-out trades.

2.5 Glazed curtain wall The glazed curtain wall is the “window” to the cultural centre and, given the specifics of the project, it has to fulfil a series of demanding requirements: –– Very high transparency, at the same time ensuring adequate thermal insulation –– Accommodation of large storey heights (sometimes > 7.50 m between supports) –– Accommodation of large horizontal inter-storey drifts due to wind and seismic impact on the main structure –– Flush exterior glazing effect with no pressure caps at mullions or slab edges –– Accommodation of a specific, stepped architectural transom pattern

–– Coordination with many different and varying interfaces such as floors (with trench heaters), interior skin, exterior skin, vestibules, MEP air ducts, etc.

Werner Sobek’s scope of work comprised the full engineering, detailed drawings, tender documents, shop drawings for the contractor and factory inspections plus site coordination and installation supervision on site for the entire glazed curtain wall.

Owing to quality and inter-storey drift considerations, it was decided to use a unitized, fixed-glazing curtain wall system with adapter frames bonded to the inside by means of structural silicone adhesive. The glazing units with these frames are attached to the split-mullions and split-transoms of the façade units by screws concealed by metal caps. Each unit, or façade panel, is suspended from its top; this support provides sufficient flexibility to accommodate tolerances, thermal and structural movements and especially the critical in-plane earthquake shear effects.

2.6 Miscellaneous In addition to the work mentioned above, Werner Sobek was also appointed for a series of other building engineering and supervision issues.

2.6.1 Glass balustrades Inside the museum there are approx. 1300 m of glass balustrades in a highly customized design that includes LED lighting to handrails. Their geometry is partly flat, partly 2D and even 3D curved, and inclined inwards or outwards.

The balustrades are in laminated safety glass produced

by Sunglass from Padova, Italy. Werner Sobek’s remit included engineering consultancy for the performance crite-

Fig. 11. View of completed building at night (© Hufton + Crow, Hertford)

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Reports ria, build-ups and support conditions at slabs and beams, 3D modelling definition of production geometry and factory inspections of the goods produced prior to packing and shipment.

2.6.2 Metal grilles along façade interfaces, trench heaters Along the curved lines where the glazed curtain wall meets the exterior and interior skins, there are curved metal grilles covering these gaps while providing permeability for MEP air duct outlets, the trench heaters at the floor interfaces and the solid skin cavity.

Werner Sobek engineered the details for these grilles, provided consultancy services during tendering and negotiations and performed factory inspections of the grilles (at SLT’s plant in Lingen, Germany) and the trench heaters (by MINIB near Prague, Czech Republic) prior to packing and shipment.

3 Outlook The Heydar Aliyev Centre represents a milestone in fasttrack free-form building engineering and construction. The flowing interior and exterior spaces create a stunning experience for everyone who visits the building. Innovative engineering and consulting, with a holistic view on optimizing the various trades and their interfaces, were key factors in turning this architectural masterpiece into reality (Fig. 11).

Keywords: freeform geometry; parametric design; 3D engineering; complex geometry

Authors: Dr. Thomas Winterstetter General Manager, Werner Sobek Stuttgart Mustafa Alkan General Manager, Werner Sobek Istanbul

2.6.3 Pond Café

Radu Berger Project Manager, Werner Sobek Stuttgart

At the bottom of the landscape flowing down from the main building, there is a large pond with a café and an auxiliary building next to it.

Werner Sobek’s scope of work included the full structural and façade engineering and all design and CA phases for all concrete and steel parts and the façade of the café building, the pond and the surrounding landscape structures.

Specific features of this part of the project are: –– A steel roof with a very long cantilever, supporting the green roof on top of the café building.

–– A 4.5 m tall café front façade made from insulated glass units that can be turned and moved entirely sideways (if the weather allows).

Maiko Watanabe Senior Designer, Werner Sobek New York Agatha Toth Architect, Werner Sobek Stuttgart Prof. Dr. Dr. E.h. Dr. h.c. Werner Sobek Founder of Werner Sobek Group Director of Institute of Lightweight Structures & Conceptual Design (ILEK), Stuttgart Address for all authors: Werner Sobek Group Albstr. 14, 70597 Stuttgart, Germany mail@wernersobek.com

News EUROFER: Chinese steel imports ­confuse buyers in Europe as Chinese steel producers exploit the export tax regime Steel supplied on the EU market by ­European steel producers complies with the European regulations and standards.

“Steel made in Europe means reliability in trade, stability of properties during processing and safety in the use of the material”, EUROFER Director General Axel Eggert says. This is not guaranteed in the case of Chinese steel imported in the EU, notably imports of wire rod, ­rebar and bar, as well as hot-rolled coil and heavy plate.

The Chinese government promotes exports of alloyed steels with tax rebates

of 9 to 13 percent on the general export tax of 17 percent. To get the most tax-­ beneficial classification as alloyed steels, Chinese steel producers add cheap alloy boron agent to steels specified by the customer as non-alloy qualities. Although the boron quantities are up to twice as high as permitted, Chinese steels are marketed in the EU as unalloyed steels.

Boron in steel improves the uniformity of the hardness of the steel. But if weld ability and elasticity are required, typically for unalloyed steel, a higher share of boron can be particularly harmful including welding cracks.

China’s steel exports are estimated to reach at least 85 million tonnes this year, up by 43 percent year-on-year. Chinese exports of steel products in which boron

is typically added represent more than 50 percent of the total Chinese export volume.

“Not only does China promote exports of its excess steel production by targeted product tax advantages, but Chinese steel qualities also confuse the markets as Chinese producers exploit the export tax regime. The EU market surveillance authorities are now required to eliminate the risk of misleading use of the CE mark,” Eggert says, “Steel processors must be protected from being exposed to wrongfully declared qualities to the risk of serious economic disadvantages.”

Further information: www.eurofer.be

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ECCS news

Events 15th International Symposium on Tubular Structures

27–29 May 2015, Rio de Janeiro, Brazil

The Subcommission for Tubular Structures XV-E of the International Institute of Welding (IIW) has decided that the 15th International Symposium on Tubular Structures (ISTS 15) will be hosted

by COPPE/UFRJ and UERJ, Brazil. In the past, 14 International Symposia have been successfully held in Boston, USA (1984), Tokyo, Japan (1986), Lappeenranta, Finland (1989), Delft, The Netherlands (1991), Nottingham, UK (1993), Melbourne, Australia (1994), Miskolc, Hungary (1996), Singapore (1998), Düsseldorf, Germany (2001), Madrid, Spain (2003), Québec, Canada (2006), Shanghai, China (2008), Hong Kong, China (2010) and London (2012).

The 15th International Symposium will take place at Hotel Pestana from Wednesday 27 to Friday 29 May 2015.

This symposium is considered to be the principal showcase for tubular structures and the prime international forum for the discussion of research, developments and applications in this field. The conference would be of interest to manufacturers of hollow sections or related construction products, architects, trade associations, design engineers, steel fabricators, owners or developers of tubular structures, researchers, academics and postgraduate students. www.labciv.eng.uerj.br/ists15/

8th International Conference on Advances in Steel Structures 21–24 July 2015, Lisbon, Portugal

The international conference series on Advances in Steel Structures was initiated in 1996 under the auspices of Hong Kong Polytechnic University, which remained instrumental in fostering its con-

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tinuation – joined a few years later by the Hong Kong Institute of Steel Construction. This will be the eighth conference in the series (ICASS 2015) and the first to take place outside Asia; indeed, the first, second, third and sixth conferences were held in Hong Kong, the fourth in Shanghai, the fifth in Singapore and the seventh in Nanjing. Like its predecessors, this conference aims to provide a forum where researchers and designers can discuss and disseminate the most recent advances in the analysis, behaviour, design and construction of steel, aluminium and steel-concrete composite structures. Abstracts of papers relating to all topics covered by the general themes of the conference are welcome. They will be considered for presentation at ICASS 2015 and publication in the conference proceedings. www.icass2015.ist.utl.pt/

8th International Symposium on Steel Bridges: Innovation & New Challenges 2015 (SBIC-2015) 14–16 September 2015, Istanbul, Turkey

The Turkish Constructional Steelwork Association (TUCSA) is organizing the 8th International Symposium on Steel Bridges: Innovation & New Challenges 2015 (SBIC-2015). It will be held in Istanbul between 14 and 16 September 2015 in cooperation with the European Convention for Constructional Steelwork (ECCS) and in conjunction with the ECCS Steel Design Awards Ceremony and ECCS Annual General Meetings to be held between 15 and 17 September 2015.

Istanbul is one of the best places to organize this bridge symposium. The city is a natural bridge between Europe and Asia and also has three steel bridges

over the Bosporus. We would like to invite architects, structural engineers, designers, steel fabricators and builders as well as environmental psychologists, urban planners and environmentalists to participate in the symposium and discuss new horizons for steel bridges.

The first announcement and call for papers have already been sent out. A list of the previous International Symposiums on Steel Bridges and other details related to the symposium are available at www.sbic2015.org.

13th Nordic Steel Construction Conference 2015 23–25 September 2015, Tampere, Finland

The Nordic Steel Construction Conference (NSCC) is an event with proud traditions. The conference was held for the first time in Stockholm in 1970 and since then it has circulated between the Nordic countries at intervals of about three years. The last conference was held in Oslo in 2012 and brought together scientists, representatives from steel producers, steel wholesalers, contractors, consultants, architects, etc. Finland is responsible for the event in 2015.

The last time the conference was organized in Finland was in 2001. The organizer then was the Finnish Constructional Steelwork Association (FCSA) together with Helsinki University of Technology (HUT). Now the baton has once again been handed to Finland. The FCSA will again be responsible for the administrative part of the event. But this time Tampere University of Technology (TUT) takes responsibility for the scientific side.

That scientific side will be led by Prof. Markku Heinisuo, TUT, chairman of the Scientific Committee, and Dr. Jari Mäkinen, the committee’s vice-chairman.

The Scientific Committee is composed of leading steel professors and researchers from the Nordic countries and the rest of Europe. www.tut.fi/nscc-2015

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1st International Conference on Steel & Composite Construction (CICOMM 2015)

XIII International Conference on Metal Structures

15–17 June 2016, Zielona Góra, Poland

12–13 October 2015, Algiers, Algeria

TC3 – Fire Safety Chairperson: Prof. Paulo Vila Real Secretary: Martin Mensinger Date: 1–2 October 2015, Manchester, UK

TC6 – Fatigue & Fracture Chairperson: Dr. M. Lukic Venue: Italian institute of Welding, Genoa This congress is being organized by the University of Tlemcen (Algeria) in collaboration with the University of Clermont-Ferrand and CNERIB (Algiers).

The aim of this conference is to bring together researchers, educators, engineers and owners to acknowledge the technological and scientific developments in Algeria and throughout the world in connection with the use of steel in construction (buildings, works of art, etc.).

More details are available on the conference website at www.univ-tlemcen.dz/ cicomm2015.

X Conference on Steel and ­Composite Construction

26–27 November 2015, Coimbra, P ­ ortugal

The International Conference on Metal Structures will be held in Zielona Góra, Poland, on 15–17 June 2016. It is the thirteenth conference in the series, which started in 1958. The last four conferences were organized in Kraków (1995), Gdan´sk (2001), Rzeszów (2006) and Wrocław (2011).

The Metal Structures Section of the Committee for Civil Engineering at the Polish Academy of Sciences (SMS CCE PAS) is the institution that organizes conferences in this series.

Zielona Góra has been selected as the venue for the Conference. The event is being organized by the Faculty of Civil and Environmental Engineering, Institute of Building Engineering, University of Zielona Góra.

The conference is intended to provide a forum for discussing and exchanging experience with recent developments in the areas related to the structural behaviour and modelling, analysis and design, manufacturing and construction, maintenance and rehabilitation of steel, aluminium and composite structures as well as standardization, education and innovations. www.uz.zgora.pl

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

TWG 7.5 – Practical Improvement of Design Procedures Chairperson: Prof. Bettina Brune

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

TC8 – Structural Stability Chairperson: Prof. H. H. Snijder Secretary: Dr. Markus Knobloch Date: 22 May 2015, Budapest, Hungary Date: 6 November 2015, Bochum, G ­ ermany

TWG 8.3 – Plate Buckling Chairperson: Prof. U. Kuhlmann Secretary: Dr. B. Braun

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

TC9 – Execution & Quality Management Chairperson: Mr. Kjetil Myrhe Date: 16 March 2015, Brussels

Announcements Following the success of the previous Conferences organized by CMM – Portuguese Steelwork Association, with the X Conference on Steel and Composite Construction, CMM intend to promote the most recent innovations in this type of construction, reveal the main guidelines of research in this field and disseminate the main innovations with the objective of promoting the potential of Steel and Composite Construction.

This year the X Conference on Steel and Composite Construction will take place in Coimbra, on 26 and 27 November 2015. The Conference will be a privileged encounter for the exchange of ideas and experiences among the different actors in the implementation of projects representing this construction sector (owners, designers, contractors, etc.).

Please find more details on www.cmm.pt/congresso.

Norwegian Steel Day 2015 Norwegian Steel Day 2015 will be held on Thursday, 19 November 2015 in the Grand Hotel, Oslo. For more details go to www.stalforbund.com.

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

TC10 – Structural Connections Chairperson: Prof. Thomas Ummenhofer Secretary: Mr. Edwin Belder

TC11 – Composite Chairperson: Prof. R. Zandonini Secretary: Prof. Graziano Leoni Date: 8 May 2015, Stuttgart

TC13 – Seismic Design Chairperson: Prof. R. Landolfo Secretary: Dr. Aurel Stratan

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

PMB – Promotional Management Board

TC16 – Wind Energy & Support ­Structures

Chairperson: Mr. Yener Ger’es

Chairperson: Prof. P. Schaumann

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TC News ECCS-TC11 – Composite ­Structures Chairperson: Prof. Riccardo Zandonini Vice-chairperson: Prof. Jean-François Demonceau Secretary: Prof. Graziano Leoni The most recent meeting of TC11 took place in Paris on 31 October 2014. During the meeting, Prof. Jean-François Demonceau was appointed as vice-­ chairperson of the committee.

In the first part of the meeting, some members presented advances in research into composite structures. Prof. JeanPaul Lebet talked about the latest developments in research on the lateral torsional buckling of steel bridge girders.

Prof. Mohammed Hjiaj gave an overview of the ongoing project SMARTCOCO (smart composite components – concrete structures reinforced by steel sections), the object of which is to draw up design guidance for “hybrid” structural systems.

Prof. Graziano Leoni presented the results of the INNO-HYCO project, which aims to develop innovative hybrid and composite steel concrete structural solutions for buildings in seismic areas. Furthermore, Graham Couchman, chairman of CEN TC 250/SC4, ­reported on the Eurocode 4 revision ­activities.

The second part of the meeting was devoted to discussing the publications being prepared within TC11. A draft of the publication on shear connections in composite elements, prepared by Matti Leskelä, was reviewed, and suggestions from TC members were collected. Pedro Vellasco and Luis Costas Neves presented a document containing test results and the proposed analytical method for characterizing perfor bond connections. Urike Kuhlmann had up-to-date news about the special issue of Steel Construction that will include seven papers by TC11 members about composite shallow floors. Finally, Jean-François Demonceau summarized the table of contents of a new publication that will be dedicated to composite joints.

The next meeting of ECCS-TC11 will be held in Stuttgart on 8 May 2015.

News Call for entries: European Steel Design Awards 2015 The European Steel Design Awards are given by ECCS every two years to en-

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courage the creative and outstanding use of steel in architecture and construction in Europe. The Awards are open to steel works designed or produced in the ECCS Full Member countries. If the project is multinational, it can also be submitted in accordance with the submission procedure stated in the following regulations.

Steel construction projects located outside the member country are eligible, if they have been designed or produced by members of the ECCS Full Member (National Association). Both new buildings or bridges, and renovation projects (major retrofit, expansion or rehabilitation) are eligible.

The awards are dedicated to the owner, general contractor, the architects, the engineers and the steelwork contractors of one outstanding national project per member country in order to esteem their collaboration and the excellence of their work. The national member is responsible for the evaluation and selection of the submitted project. ECCS International Jury will select the projects to be awarded with the awards of merit or awards of excellence in different categories. The European Convention for Constructional Steelwork has pleasure in inviting its Full Member Associations to submit their projects for the European Steel Design Awards 2015.

Key dates Last date for entry submission: by the end of April 2015 Uploading of entry-form and documentation online available from March 2015 on www.steelconstruct.com Award of Merit & Awards of Excellence Decision by ECCS International Jury: by 29 May 2015 Press-release and documentation: by the end of June 2015 Awards Ceremony: 15 September 2015, hosted by TUCSA in Istanbul, Turkey European Student Awards for Steel Design 2015 The Student Awards for Steel Design are a subcategory of European Steel ­Design Awards. The objective is to give European recognition to outstanding student projects in architectural design using structural steel as a prominent architectural feature. The Awards are open to all ECCS Full Member Associations, which organise contest for architectural students in their respective country. The Student Awards will be presented within the ECCS Award Ceremony. Key data and procedures are similar to the Steel Design Awards. Detailed entry conditions and forms are published on ECCS-website by March 2015.

Regulations (extracts) 1 Operation of the Awards […] In case of those partners of the project (project owner, general contractor, architectural firm, structural engineering firm and fabricators) are from different countries; –– If some partners are from an ECCS Full Member country and others are from 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 the Full Members may submit in coordination with the other –– Should there be disagreement, the fabricator of the project is the determining factor to select the submitting Full Member.

The building or construction must have been completed and be ready for occupation or use within the last three years, not later than 31 May 2015.

2 Jury and Evaluation The Jury consists of the following seven members: –– Nesrin Yardimci, representing Hosting Full Member, TUCSA –– Veronique Dehan, ECCS Secretary General –– Lasse Kilvaer, Chairman of Awards and Architecture Committee, representing PMB –– Harun Batirbaygil, Architect from Hosting Nation –– Nuran Kara Pilehvarian, Architect from Hosting Nation –– Kari Nissen Brodtkorb, international representative –– Paulo J. S. Cruz, international representative Chair of the jury is Prof. Dr. Nesrin Yardimci and Jury Reporter/Jury Secretary is Dr. Berna Aydöner. Entries are to be evaluated within three phases.

Phase-1 The National Association assesses the entries in its country in accordance to the following criteria, in order to select the best entry which will be submitted to ECCS: –– To have an international recognised standard, –– To be of outstanding quality in its architecture, structure and construction, –– To interest clients, architects and engineers in using more steel within the entire building sector, thereby making the steel industry competitive, –– To emphasise the advantages of steel in construction, production, economy and architecture,

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News –– To adhere to the principles of sustainability, –– To disseminate the knowledge of steel and its many-sides uses and to draw attention to its development, –– To improve the image of steel.

Phase-2 ECCS Awards Advisory Committee only approves the entries by their accordance to the ECCS Steel Design Awards Procedure.

Phase-3 ECCS International Jury evaluates the entries which were approved by the Awards Advisory Committee, according to criteria stated above. Therefore, ECCS International Jury is; –– To select up to 3 projects as category winners to be awarded by the ‘ECCS Steel Design Award of Excellence in (Specific) Category 2015’.

–– To keep this decision as confidential which will be publicised during the Awards Ceremony, but not before.

Until that time only Chairs of PMB and Awards Advisory Committee and Secretary General will be informed.

–– To clarify the justification of selecting projects and categories in its evaluation report.

3 Liabilities of Full Member ­Associations ECCS Full Members have; –– To Call for entries according to ECCS-criteria for their national / member participants, –– To assess the entries regarding ECCS Steel Design Awards Procedure, –– To establish a National Jury composed of representatives of Architecture and Civil Engineering in order to judge the quality of entries to select the best, –– To submit National Award winner to ECCS including the evaluation report of the national Jury (online), –– To invite Award winning team to ­European Award Ceremony –– To provide photographical and promotional material for publication –– To disseminate promotional publication / press-release on national level (linking to ECCS-website) 4 Awards Nominees may be awarded either by Award of Merit or by Award of Excellence stated below.

Award of Merit: Nominated projects that adhere to the standards of the ECCS Steel Design Awards Procedure are presented with the award ‘ECCS Steel Design Award of Merit 2015’.

Award of Excellence: Out of these projects, up to 3 projects will be selected by the jury as category winners and awarded the ‘ECCS Steel Design

Award of Excellence in (Specific) Category 2015’. Jury may decide the category among the followings or another category deemed appropriate by the jury; –– Public & Cultural –– Industrial & Commercial –– Façade & Surfaces (with steel structures) –– Bridges –– High-rise/tall buildings or towers.

The Awards are dedicated to the owner, the general contractor, the architects, the engineers and steelwork fabricators of one outstanding national project in order to esteem their collaboration and the excellence of the realised work, as stated below.

–– The ‘ECCS Steel Design Award of Merit’ winner teams receive a certificate each.

–– The ‘ECCS Steel Design Award of Excellence in (Specific) Category’­ winner teams receive trophies (up to five trophies for each of fabricator, structural engineering firm, architectural firm, general contractor and project owner).

The Awards will be presented during a special session at the ECCS Annual Meeting to be held in Istanbul on 15 September 2015.

5 Time-table –– Submission/Uploading of the national winner with documentation and evaluation report of the national Jury (online on www.steelconstruct. com) by the end of April 2015 –– Evaluation of entries by the ECCS International Jury by 29 May 2015 –– Official information and press-release

by ECCS/National Associations related to the awarded entries by the end of June 2015 but not mentioning the excellence award owners.

–– ECCS Steel Design Awards Ceremony held in Istanbul, Turkey on 15 September 2015 within the ECCS Annual General Meetings 2015 6 Submittal Requirements Each Full Member is entitled to submit one entry only. The documents are to be uploaded on ECCS-website before 30 April 2015. The application scheme will be online by March 2015 on www.steelconstruct.com The submission will contain key information, a short description and evaluation of the project by the National Associations Jury, high resolution photographs, design drawings and technical data. These documents are for publication and must therefore be of best quality and free of copyright charges.

6.1 Entry form –– Name and location of project (name of firm submitting entry, address, person to contact, phone, fax and e-mail), –– Name and location of fabricators, structural engineering firm, architectural firm, general contractor and project owner, –– Main key data and technical information like involved company names, date of completion, dimensions, tonnage, main structure concept, etc, –– Names/information on responsible national Jury.

6.2 Project description and Jury ­evaluation Include a short description of the site, the owner’s/architect’s building programme, an explanation of how the structure satisfies the Award criteria and the appreciation / validation of the national Jury why this project and the project team are to be awarded. The text must be no longer than one A4-page and be written in English.

6.3 Photographs A minimum of 12 high resolution photographs in electronic format (min. 300 dpi resolution, format 16 × 24, .eps, .jpg or .tif) of both construction and the completed project must be uploaded. Pictures should show both the interior and exterior of the building, captions should be included. Rights to photos, slides and plans must be cleared for presentation and publication (booklet and website) by the entrant. Any fees or royalties connected with such releases are the responsibility of the entrant. ECCS reserves the right to free use of all photos and materials submitted for promotional purposes.

6.4 Drawings Provide a site plan, principal elevations, cross sections and typical floor plans (1:100 or 1:200). In addition, show typical and innovative detail sections (1:50 connection area facade-ceiling-roofing), typical steel construction detail (1:20) with legends apart in English, eventually a 3D axonometry of the structure. All drawings should be presented in electronic format (600 dpi, .eps or vectorised .pdf (eventually.dxf), black-white; without description and measure layer).

6.5 Power Point or PDF Presentation Presentation is of 5 minutes length maximum. It will include a short comment and ideally musical background to be used during the Awards Ceremony.

7 Contact For further technical information contact ECCS Design Award Committee

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News / Announcements (AC-4) Chairman Lasse Kilvær (Norway): lasse@stalforbund.com. For further local information contact TUCSA representative Dr. Berna Aydöner (Turkey): berna@tucsa.org.

Announcements 2nd Young Engineers Colloquium 2015 Location and date: Stuttgart, Germany, 23 March 2015 Information and registration: www.iabse.de/YEC2015

5th International Congress on Construction History Location and date: Chicago, USA, 3–7 June 2015 Information and registration: http://5icch.org/

Russia Essen Welding & Cutting 2015 Location and date: Moscow, Russia, 25–28 June 2015 Information and registration: www.russia-essen-welding-cutting.com

Information and registration: www.fe.up.pt\mslb2015

13th International Probabilistic ­Workshop (IPW2015)

8th STESSA Conference on Behaviour of Steel Structures in Seismic Areas

Location and date: Liverpool, UK, 4–6 November 2015

Location and date: Shanghai, China, 1–3 July 2015

Information and registration: www.ipw2015.org

Information and registration: http://steelpro.net/stessa15

International Colloquium on Stability and Ductility of Steel Structures 2016

8th International Symposium on Steel Bridges

Location and date: Timis¸oara, Romania, 30 May to 1 June 2016

Innovation & New Challenges 2015 (SBIC-2015) Location and date: Istanbul, Turkey, 14–16 September 2015 Information and registration: www.sbic2015.org

International Symposium on Non-Destructive Testing in Civil Engineering (NDT­CE) 2015 Location and date: Berlin, Germany, 15–17 September 2015 Information and registration: www.ndt-ce2015.net/awards

Nordic Steel 2015 Construction Conference

Multi-Span Large Bridges

Location and date: Tampere, Finland, 23–25 September 2015

Location and date: Porto, Portugal, 1–3 July 2015

Information and registration: www.tut.fi/en/nordic-steelconstruction-conference-2015

Information and registration: www.ct.upt.ro

XIII International Conference on Metal Structures Location and date: Zielona Góra, Poland, 15–17 June 2016 Call for papers: deadline 28 February 2015 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 Call for abstracts: deadline 15 March 2015 Information and registration www.iabmas2016.org

ECCS individual membership 4

Steel Construction

Volume 7 November 2014 ISSN 1867-0520

Design and Research

– Cyclic behaviour of welded stiffened beam/column joints – A unified method for the design of steel beam-columns – The new steel-glass architecture of air terminals in Japan – “Carioca Wave” free-form steel/glass canopy – Material modelling for QA and product development of heavy plates – The grid-shell of Jinji Lake Mall – MAST multipurpose building – Design tool for end plate connections to EC 3 – Jörg Schlaich at 80

Individual members of ECCS will be part of a large international network and benefit from various services:

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–– An annual subscription to “Steel Construction – Design and Research” in paper and electronic format free of charge (otherwise available at 148 € per year); –– Free access to Wiley Online Library for the digital archive of Journal “Steel Construction”: you have ­access to all articles of the last 4 years; –– 20 % discount on ECCS publications, e.g. Eurocode Manuals, Conference Proceedings; –– Access to exclusive information via the ECCS homepage Member Area, e.g. Software Downloads, Calculator Apps; –– ECCS monthly newsletter;

–– Supply of news for potential inclusion in “Steel Construction”; –– ECCS conferences at reduced prices (Steel Bridges in Turkey – September 2015, Nordic Steel – September 2015).

All this is available for an annual fee of 148 € and all are welcome to apply for membership. Make your registration for 2015 now and you will receive for free the last issue of 2014 of the Journal Steel Construction.

Individual membership is open worldwide to all architects, engineers or anyone interested in steel construction subjects and in supporting the ECCS objectives. Find additional information at www.steelconstruct.com

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The international journal “Steel Construction – Design and Research” publishes peer-reviewed papers covering the entire field of steel construction research and engineering practice, focusing on the areas of composite construction, bridges, buildings, cable and membrane 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 en­gineer­ ing science journal for structural steelwork systems, which embraces the following areas of activity: new theories and testing, design, analysis and calculations, fabrication and erection, usage and conversion, preserving and maintaining the building stock, recycling and disposal.

“Steel Construction – Design and Research” is therefore aimed not only at academics, but in particular at consulting structu­ral engineers, and also other engineers active in the relevant industries and authorities.

“Steel Construction – Design and Research” is published four times a year.

Except for manuscripts, the publisher Ernst & Sohn purchases exclusive publishing rights. Ernst & Sohn accepts for publication only those works whose content has never appeared before in Germany or else­where.

The publishing rights for the pictures and drawings made available are to be obtained by the author. The author undertakes not to reprint his or her article without the express permission of the publisher Ernst & Sohn. The “Notes for Authors” regulate the relation­ship between author and editorial staff or publisher, and the composition of articles.

“Notes for Authors” can be obtained from the pub­lisher or via the Internet at www.ernst-und-sohn.de/zeitschriften.

The articles published in the journal are protected by copyright. All rights are reserved, particularly those of translation into foreign languages. No part of this journal may be reproduced in any form whatsoever without the written consent of the publisher. Brand-names or trademarks published in the journal are to be considered as protected under the terms of trademark protection legislation, even if they are not individually identified as such.

Manuscripts are to be sent to the editorial staff or http://mc.manuscriptcentral.com/stco.

If required, offprints or run-ons can be made of single articles. Requests should be sent to the publisher.

Current prices The journal “Steel Construction – Design and Research” comprises four issues per year. In addition to “Steel Construction – Design and Research print”, the PDF version “Steel Construction – Design and Research online” is available on subscription through the “Wiley Online Library” online service.

Prices print print + online

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Members of the ECCS – European Convention for Constructional Steelwork receive the journal Steel Construction as part of their mem­ bership.

Prices exclusive VAT and inclusive postage. Errors and omissions excepted. Subject to change without notice.

Prices are valid from 1st September 2014 until 31st August 2015.

Personal subscriptions may not be sold to libraries nor used as library copies.

A subscription lasts for one year. It can be terminated in writing at any time with a period of notice of three months to the end of the subscription year. Otherwise, the subscription extends for a further year without written notification.

Publisher Wilhelm Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG Rotherstrasse 21 10245 Berlin Germany Phone +49 (0)30 47031-200 Fax +49 (0)30 47031-270 info@ernst-und-sohn.de www.ernst-und-sohn.de Journal for ECCS members The ECCS – European Convention for Constructional Steelwork and Ernst & Sohn have agreed that from 2010 onwards Steel Construction is the official journal for ECCS members. www.steelconstruct.com Editorial staff Editor-in-chief: Dr.-Ing. Karl-Eugen Kurrer, Ernst & Sohn Phone +49 (0)30 47031-248, Fax -270 karl-eugen.kurrer@wiley.com Technical Editor: Jost Lüddecke, M. A. Phone +49 (0)30 47031-244, Fax -230 jost.lueddecke@wiley.com Editorial board Chair: Luís Simões da Silva (Portugal) • Frans Bijlaard • Guo-Qiang Li (P. R. China) (The Netherlands) • Richard Liew (Singapore) • Luís Bragança (Portugal) • Mladen Lukic (France) • Dinar Camotim (Portugal) • Enrique Mirambell (Spain) • S. L. Chan (P. R. China) • Kjetil Myhre (Norway) • Paulo Cruz (Portugal) • Kim Rassmussen (Australia) • Dan Dubina (Romania) • John Michael Rotter (UK) • László Dunai (Hungary) • Peter Schaumann (Germany) • Morgan Dundu • Bert Snijder (Rep. of South Africa) (The Netherlands) • Markus Feldmann (Germany) • Thomas Ummenhofer (Germany) • Dan Frangopol (USA) • Leroy Gardner (UK) • Ioannis Vayas (Greece) • Richard Greiner (Austria) • Milan Veljkovic (Sweden) • Jerome Hajjar (USA) • Pedro Vellasco (Brazil) • Markku Heinisuo (Finland) • Paulo Vila Real (Portugal) • Jean-Pierre Jaspart (Belgium) • Frantisek Wald (Czech Republic) • Ulrike Kuhlmann (Germany) • Akimitsu Kurita (Japan) • Riccardo Zandonini (Italy) • Raffaele Landolfo (Italy) • Jerzy Ziółko (Poland) Advertising manager Norbert Schippel, Ernst & Sohn Phone +49 (0)30 47031-252, Fax -230 norbert.schippel@wiley.com Services for customers and readers Wiley-VCH Customer Service for Ernst & Sohn Boschstrasse 12, D-69469 Weinheim Tel.: +49 (0)800 1800 536 (with Germany) Tel.: +44 (0)1865476721 (outside Germany) Fax: +49 (0)6201 606184 cs-germany@wiley.com Quicklink: www.wileycustomerhelp.com Layout and typesetting LVD I BlackArt, Berlin © 2015 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin

Bank details Dresdner Bank Weinheim, A/C No: 751118800 Bank sort code: 67080050, SWIFT: DRESDEFF670 “Steel Construction – Design and Research”, ISSN 1867-0520, is published quarterly. US mailing agent: SPP, PO Box 437, Emigsville, PA 17318. Periodicals postage paid at Emigsville PA. Postmaster: Send all address changes to “Steel Construction – Design and Research”, John Wiley & Sons Inc., C/O The Sheridan Press, PO Box 465, Hanover, PA 17331.

Inserts in this issue: Verlag Ernst & Sohn GmbH & Co. KG, 10245 Berlin

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Preview

Steel Construction 2/2015 Philippe Beguin, Mark Lawson, Renata Obiala, Matthias Braun Slim Floor Construction using ­Composite Decking Systems Dennis Lam, Xianghe Dai, Matthias Braun, Ulrike Kuhlmann, Florian Eggert Design methods for slim floor constructions Gunter Hauf, Dennis Lam, Xianghe Dai Deformation calculation methods for slim floor constructions Manuel L. Romero, Louis-Guy Cajot, Yves Conan, Matthias Braun Fire design methods for slim floor constructions Stephen Hicks, Simon Peltonen Design of Slim Floor Beams Against Human-induced Vibration Matti V. Leskelä, Simon Peltonen, Renata Obiala Composite interaction in shallow floor beams with different shear ­connections

The steadily growing world trade leads to a demand of increasing port facilities.

One of the most common construction types of deep harbour quays is the combined steel piling wall. It consists of up to 45 m long H-shaped king piles and ­Z-shaped intermediate infill elements. The intermediate elements and the quay both transfer all forces to the king piles, which as a result are loaded with (bi-)axial bending and axial force, so stability is a risk. Up to now, the effect of the soil surrounding the piles was used just in terms of best practise: buckling about the weak axis and lateral torsional buckling were neglected completely.

Ulrike Kuhlmann, Bernadette Leitz, Adrian Just, Jürgen Grabe, Christoph Schallück Simplified criteria and economic design for king piles of combined steel piling walls according to Eurocode 3, part 1-1

Matti V. Leskelä, Simon Peltonen Effect of unzipping connection behavior on the composite interaction of shallow floor beam (subject to change without notice)

Journal: Steel Construction

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Stahlbau-Kalender Die Stahlbau-Kalender dokumentieren den aktuellen Stand des StahlbauRegelwerkes. Herausragende Autoren vermitteln Grundlagen und geben praktische Hinweise für Konstruktion und Berechnung. Mit neuen Schwerpunkten in jeder Ausgabe! Die Herausgeberin: Ulrike Kuhlmann

Hrsg.: Ulrike Kuhlmann Stahlbau-Kalender 2015 Schwerpunkte: Eurocode 3 – Grundnorm, Leichtbau ca. € 144,–* Fortsetzungspreis: ca. € 124,–* ISBN 978-3-433-03104-9

Zur bauaufsichtlichen Einführung von Eurocode 3 werden ab Stahlbau-Kalender 2011 systematisch alle Normteile kommentiert.

In diesem Jahr mit Anwendungshinweisen zur Fertigungsnorm EN 1090. Außerdem: Leichtbau, Aluminiumtragwerke, Glasbau, Membrantragwerke, Faserverbundwerkstoffe.

Hrsg.: Ulrike Kuhlmann Stahlbau-Kalender 2014 Eurocode 3 – Grundnorm, Außergewöhnliche Einwirkungen € 144,–* Fortsetzungspreis: € 124,–* ISBN 978-3-433-03052-3

Hrsg.: Ulrike Kuhlmann Stahlbau-Kalender 2013 Eurocode 3 – Anwendungsnormen, Stahl im Industrieund Anlagenbau € 139,–* Fortsetzungspreis: € 119,–* ISBN 978-3-433-02994-7

Hrsg.: Ulrike Kuhlmann Stahlbau-Kalender 2012 Eurocode 3 – Grundnorm, Brücken € 79,–* Fortsetzungspreis: € 119,–* ISBN 978-3-433-02988-6

Hrsg.: Ulrike Kuhlmann Stahlbau-Kalender 2009 Schwerpunkt: Stabilität, Membrantragwerke € 79,–* Fortsetzungspreis: € 119,–* ISBN 978-3-433-02909-1

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