Structural Concrete 01/2013

1Volume 14March 2013ISSN 1464-4177

- Focus: fib Model Code for Concrete Structures 2010- fib MC2010: mastering challenges, encountering new ones- Service life design – incorporating fib MC2010 rules in ISO 16204- Reliability-based non-linear analysis to fib MC2010- Global safety format for non-linear analysis of RC structures- Towards efficient structures: construction of an ellipsoidal concrete shell- Lattice equivalent continuum method for 3D FE analysis- Experimental appraisal of large circular RC columns in compression- How cover, φ/ρs,ef and stirrup spacing affects cracking –

tests and theory

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March 2013ISSN 1464-4177 (print)ISSN 1751-7648 (online)

Wilhelm Ernst & SohnVerlag für Architektur und technische Wissenschaften GmbH & Co. KGwww.ernst-und-sohn.de

3Bautechnik 81 (2004), Heft 1

Contents

Structural Concrete Vol. 14 / 1

Editorial

1 Joost Walraven, György L. Balázsfib Model Code for Concrete Structures 2010: a landmark in an ongoing development

Focus: fib Model Code for Concrete Structures 2010

3 Joost Walravenfib Model Code for Concrete Structures 2010: mastering challenges and encountering new ones

10 Steinar HellandDesign for service life: implementation of fib Model Code 2010 rules in the operational code ISO 16204

19 Vladimir CervenkaReliability-based non-linear analysis according to fib Model Code 2010

Technical Papers

29 Diego Lorenzo Allaix, Vincenzo Ilario Carbone, Giuseppe ManciniGlobal safety format for non-linear analysis of reinforced concrete structures

43 Aurelio Muttoni, Franco Lurati, Miguel Fernández RuizConcrete shells – towards efficient structures: construction of an ellipsoidalconcrete shell in Switzerland

51 Syed Ishtiaq Ahmad, Tada-aki TanabeThree-dimensional FE analysis of reinforced concrete structures using the lattice equivalent continuum method

60 Tai-Kuang Lee, Cheng-Cheng Chen, Austin D.E. Pan, Kai-Yuan Hsiue, Wei-Ming Tsai, Ken HwaExperimental evaluation of large circular RC columns under pure compression

69 Alejandro Pérez Caldentey, Hugo Corres Peiretti, Joan Peset Iribarren, Alejandro Giraldo SotoCracking of RC members revisited: influence of cover, φ/ρs,ef and stirrup spacing – an experimental and theoretical study

fib-news79 fib days in Chennai, India80 fibUK Technical Meeting in recognition of Andrew Beeby81 Design of Concrete Bridges: fib short course in Ankara, Turkey81 New fib officers81 Gordon Clark visits Japan82 Short notes83 Congresses and symposia84 fib membership benefits85 Acknowledgement

A5 Products and Projects

The photograph shows a newly completed mall in Chiasso, Switzerland. The shell has theform of an ellipsoid (93 × 52 × 22 m) and its thickness varies between 100 and 120 mm. Theshell was built using sprayed concrete and also ordinary concrete in some regions. A num-ber of tailored solutions were also adopted, such as post-tensioning, addition of fibres andshear studs, to ensure satisfactory performance at both the serviceability and ultimate limitstates. More information is provided on pages 43–50 of this issue (Photo: Simone Mengani,Chiasso, Switzerland)

fédération internationale du bétonInternational Federation for Structural Concrete www.fib-international.org

Journal of the fib

Peer reviewed journalSince 2009, Structural Concrete is indexedin Thomson Reuter’s Web of Knowledge(ISI Web of Science).

Impact Factor 2011: 0.270

The journal “Structural Concrete”, the official journal of the Inter -national Federation for Structural Concrete (fib – fédérationinternationale du béton), provides conceptual and proceduralguidance in the field of concrete construction, and features peer-reviewed papers, keynote research and industry news covering allaspects of the design, construction, performance in service anddemolition of concrete structures.

“Structural Concrete” is published four times per year completely inEnglish.

Except for a manuscript, the publisher Ernst & Sohn purchasesexclusive publishing rights. Only works are accepted for publication,whose content has never been published before. The publishingrights for the pictures and drawings made available are to beobtained from the author. The author undertakes not to reprint hisarticle without the express permission of the publisher Ernst & Sohn.The “Notes for authors” regulate the relationship between authorand editorial staff or publisher, and the composition of articles. Thesecan be obtained from the publisher or in the Internet at www.ernst-und-sohn.de/en/journals.

The articles published in the journal are protected by copyright. Allrights, particularly that of translation into foreign languages, arereserved. No part of this journal may be reproduced in any formwithout the written approval of the publisher. Names of brands ortrade names published in the journal are not to be considered freeunder the terms of the law regarding the protection of trademarks,even if they are not individually marked as registered trademarks.

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Publisherfib – International Federation for Structural ConcreteCase Postale 88, CH-1015 Lausanne,Switzerlandphone: +41 (0)21 693 2747, fax: +41 (0)21 693 6245e-mail: [email protected], Website: www.fib-international.org

Publishing houseWilhelm Ernst & SohnVerlag für Architektur und technische Wissenschaften GmbH & Co. KGRotherstraße 2112045 Berlin/Germanyphone: +49 (0)30/47031-200fax: +49 (0)30/47031-270e-mail: [email protected], Website: www.ernst-und-sohn.de

EditorDr.-Ing. Dirk Jesse, Verlag Ernst & SohnRotherstraße 21, D-10245 Berlinphone: +49 (0)30/47031-275, fax: +49 (0)30/47031-227e-mail: [email protected]

Technical editorFrancisco Velasco, Verlag Ernst & SohnRotherstraße 21, D-10245 Berlinphone: +49 (0)30/47031-277, fax: +49 (0)30/47031-227e-mail: [email protected]

Advertising managerFred Doischer, Verlag Ernst & Sohnphone: +49 (0)30/47031-234

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Editorial boardEditor-in-Chief� Luc Taerwe (Belgium), e-mail: [email protected]

Deputy Editor� Steinar Helland (Norway), e-mail: [email protected]

Members� György L. Balázs (Hungary)� Josée Bastien (Canada)� Mikael Braestrup (Denmark)� Tom d’ Arcy (USA)� Michael Fardis (Greece)� Stephen Foster (Australia)� Tim Ibell (UK)� S.G. Joglekar (India)� Akio Kasuga (Japan)� Gaetano Manfredi (Italy)� Pierre Rossi (France)� Guilhemo Sales Melo (Brazil)� Petra Schumacher (Secretary General fib)� Tamon Ueda (Japan)� Yong Yuan (China)

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Structural Concrete 14 (2013), No. 1

Inserts in this issue: Southeast University, Jiangsu Research Institute ofBuilding; Science Co. Ltd and The Hong Kong University of Science andTechnology; Tekna – The Norwegian Society of Graduate Technical andScientific Professionals, N-0201 Oslo, Norway; ORTRA LTD., Tel-Aviv61092, Israel; Verlag Ernst & Sohn GmbH & Co. KG, 10245 Berlin

The Rotterdam-based architect, RemKoolhaas, has given his high-rise en-semble a huge “jolt” – and as a resulthas placed high demands on the con-struction work. Therefore, the suppor-ting structure concept for realizing thecantilevers at a height of 86 m is an es-sential part of the comprehensive PERIoverall solution.

De Rotterdam will be the largest buildingin the Netherlands – situated in the im-mediate vicinity to other architecturalhighlights such as the Erasmus Bridge byVan Berkel & Bos, the inclined high-risebuilding by Renzo Piano and the WorldPort Center by Sir Norman Foster. Oncecompleted, the 150 m high multi-storeyensemble on Rotterdam´s Wilhelminapierpeninsula on the south bank of the riverMaas, will consist of three complex de-signed towers standing side by side andconnected to each other. The West Towerhas 45 residential levels, the 41-storeyCentral Tower is designed to be used asoffice facilities only whilst the 43 floors ofthe East Tower feature both office spaceas well as a hotel tract. In total, around250 apartments, 280 hotel rooms and60,000 m² of office space will be realised.The five-storey base section of the build-ing has retail stores, restaurants, confer-ence rooms and a fitness centre – as wellas three parking decks on the groundfloor and two basement levels.A native of Rotterdam, renowned archi-tect Rem Koolhaas has given his high-risecomplex a huge “jolt” – shifting the upperhalf of the building to the side with a hor-izontal offset to the west and north. In sodoing, at a height of 86 m, the 24th and26th floors respectively along with the re-maining upper storeys cantilever out-wards up to 9 m. The construction sitecrew of Ed. Züblin AG, Stuttgart, has vastexperience in realising high-rise buildingsand the structural work is scheduled tobe finished in early 2013 whilst the deRotterdam CV project group plans tohave all construction work completed bythe end of the year. The rapid construc-tion progress is supported through theuse of comprehensive and ideally com-bined PERI system solutions. In particu-lar, the supporting formwork solution forthe cantilevered sections is an importantcomponent of the PERI overall concept.

Supporting structure with systemFor realizing the huge cantilevers at thegreat heights, PERI engineers developeda supporting formwork solution on thebasis of the VARIOKIT engineering con-struction kit. For this, rentable systemcomponents are being used to a large ex-

tent, supplemented by a project-specificbracing construction. The flexiblearrangement of the shear frames is car-ried out here whilst taking into accountthe respective geometry and loads of thestructure as well as the range of mountingparts through to the masts of the towercranes positioned in the building itself.For dimensioning the beam heights in theWest Tower, transferring the large loadsfrom the 8.88 m cantilevers for two com-plete floors of the building and the low3.52 m height of the storey below, had tobe taken into consideration. For the Cen-tral and East Towers, a double-storey canbe used for this purpose – here, the sup-porting formwork solution not onlyserves for transferring the loads from thecantilevers but also as a supporting struc-ture between the floors.Extensive PERI know-how is used togood effect especially in the beam exten-sions when the inherent load-bearing ca-pacity of the building has been reached.The fact is that due to reasons of space,the shear frames cannot be simply retract-ed and disassembled within the storey it-self without requiring direct crane sup-port. For this purpose, the constructionsite crew is using the PERI lifting carriagethat is normally used in connection withSKYTABLE large slab tables. The advan-tage of the PERI method – which was de-veloped in and has been used for manyyears in North America – is that the shearframe is pulled horizontally from thebuilding by means of a crane lift, a spe-cial chain block system and rear carriage.

Faster working through enhancedsafetyWith the RCS P climbing protection pan-el from PERI, the two topmost floors un-der construction are completely enclosedeach time. As a result, site personnel areprevented from falling at all times andprotected from strong winds at greatheights – this means that forming opera-tions are accelerated and work perfor-mance is greatly enhanced. Züblin re-quires only eight days for one completestandard floor.Already during the planning phase, thegeometrical changes of the towers weretaken into consideration so that thoseprotection panel units affected by the off-set could be moved to other sectionswithout requiring any extensive modifica-tion work. The RCS solution demonstrat-ed its high level of flexibility in the areasclose to the slab edge where anchoringwas not an option. In this situation, too,the slab shoes are securely fixed and en-sure fast climbing procedures due to thecontinuing rail guidance.

Products & Projects

Accelerated and safe construction with systemcomponents

Crane-independent forming operationsWith the SKYDECK panel slab formwork, floor slabs can beformed without the need of a crane. System components madeof aluminum to facilitate the transport and, in particular, shut-tering and striking can be carried out manually. The systematicand therefore easy to-understand assembly sequence acceleratesthe construction processes and also ensures that time require-ments can be accurately estimated. In addition, through the useof the drophead and the possibility of early striking, this also re-duces the amount of panels and main beams required on site.For the floors in the base section, the systematic assembly se-quence and the high degree of safety for each standard bay hasalready been achieved using the SKYDECK platforms and thecantilevered 375 SLT main beams, also at the slab edges. For thelarge supporting heights reaching over several floors, the con-struction crew have combined SKYDECK with the MULTI-PROP load-bearing system. The lightweight aluminum individ-ual props can be vertically connected to each other by means ofthe MULTIPROP connector – and joined together using MULTI-PROP frames to form extremely stable shoring towers.De Rotterdam is encircled on all sides – longitudinally betweenthe road and the Maas river as well as between two neighboringbuildings at the ends. The narrow construction site thereforehas very limited storage space. As a result, PERI supplied theRCS protection panel units and VARIOKIT shear frames alreadypre-assembled to the construction site. This means that theseare lifted directly from the truck by crane and taken immediate-ly to the designated place of use. This saves valuable crane time;

in particular, no additional storage facilities and assembly areaare required.

Further Information:PERI GmbH, Schalung Gerüst Engineering, Rudolf-Diesel-Straße 19, 89264 Weißenhorn, Tel. +49 (0)7309.950-0, Fax +49 (0)7309.951-0, [email protected], www.peri.com

A6 Structural Concrete 14 (2013), No. 1 Responsible for Products & Projects: Publishing House Ernst & Sohn

Products & Projects

Fig. 1. The three towers of the 150 m high De Rotterdam multi-storey en-semble are positioned very close to each other and are offset halfway up.

Fig. 2. The striking procedure is an important component of the PERI solu-tion: with the help of the SKYTABLE moving technique, the truss girders canbe pulled horizontally from the building.

Fig. 3. The systematic assembly sequence along with the lightweight sys-tem components of the SKYDECK slab formwork accelerate constructionprogress; even obstructions are easily shuttered within the system itselfwithout requiring any additional formworking measures. (© PERI)

Design of Precast Concrete Componentswith RSTAB and RFEM

Due to their numerous advantages, precast parts consisting ofreinforced concrete have become indispensable at construc -tion sites because they can be applied in various ways. Pre-cast single foundations, columns, girders, floors, etc., allow forquick mounting, regardless of weather conditions. Thus, con-struction periods are short. Furthermore, accuracy of precastparts is given in millimeters and they have very smooth surfa-ces that are difficult to be produced in comparison to cast-in-place concrete components.

The design of such precast parts can be performed with RSTABand RFEM in combination with the appropriate add-on moduleaccording to Eurocode, ACI, DIN or SIA. Members and surfaces(only available in RFEM) for example can be designed in the

Fig. 1. Reinforcement output shown in table and graphic in CONCRETE

add-on module RF-/CONCRETE, columns are designed in theadd-on module RF-/CONCRETE Columns.

Nonlinear Calculation in CONCRETEThe RSTAB add-on module CON-CRETE offers you the optionto perform also non-linear calculations in cracked sections (stateII). Moreover, it is possible to apply the effect of Tension-Stiffen-ing (tension stiffening of concrete between cracks).When you want to design girders, a variety of cross-sections likeT-beams, rotated floor beams, rectangle-hollow cross-sectionsand I-beams are available for selection.The calculated required reinforcement is shown by membersand surfaces in the individual add-on modules. The provided reinforcement for members and columns can be viewed in 3Drendering mode. In this way, you can compare reinforcementdrawings created later with the calculation so that data can bechecked.In addition, individual cross-sections can be created and designed in the stand-alone program SHAPE-MASSIVE.

BIM-Oriented Planning is PossibleBecause of numerous interfaces with other programs, concretedesign of RSTAB/RFEM can be easily integrated into the BIMprocess. Models can be imported and exported in different fileformats such as dxf, ifc, stp and dgn. Moreover, RSTAB andRFEM provide direct interfaces with Tekla Structures as well asRevit Structures and Auto-CAD by Autodesk, enabling a bidirec-tional data exchange (data transfer in both directions).In addition, it is possible to transfer reinforcement specificationsincluding geometry directly from RF-CONCRETE Surfaces toAutoCAD Structural Detailing where reinforcement plans arecreated.

Further Information and Demo Versions:Dlubal Engineering Software, Am Zellweg 2, 93464 Tiefenbach, Tel. +49 (0)9673 – 92 03-0, Fax +49 (0)9673 – 92 03-51, [email protected], www.dlubal.de

Products & Projects

Fig. 2. Column reinforcement in CONCRETE Columns in 3D rendering (© Dlubal)

Reminiscence of Bruno Taut

The new headquarters of the French petroleum corporationTotal will be the first building block of the so-called Europa -city. The dominant feature of the slim and slightly bent buil-ding is its facade.

It consists of three-dimensional, sometimes very delicate curtainconcrete elements. In their form and details, the façade elementsremind of the famous architect Bruno Taut, who passed away in1967. They offer an impressive display of the unique shapingpossibilities of concrete – when design, execution, quality con-trol and formwork facing set the highest standards. The 1395precast concrete elements were manufactured by Dreßler BauGmbH in their precast plant in Stockstadt. This is also wherethe formwork facing of Westag & Getalit AG, the East-West-falian manufacturer of wood products, was implemented.The blueprint was developed by architects and then fine-tunedin several workshops procedures, together with a panel of devel-opers, users, external experts and representatives of the City andthe State of Berlin. In the end, concrete was preferred as build-ing material, for reasons of durability and appearance, to thedetriment of a less expensive façade version made of steel. The architects developed the so-called “K module”, as a basic el-ement of the facade of the 17-storey Tour Total building. Each ofthe 400 modules consists of two three-dimensional elements. A“K module” extends over two floors and measures 7.35 m ×2.40 m. The individual modules differ in the layout of their diag-onal edge which forms the “K” shape. The maximum depth of

an element varies by up to 25 cm. The three-dimensional struc-ture of the entire facade is created by the mirrored, staggeredpositioning the modules.

Greatest imaginable challengeEconomist Daniel Stanik, manager of the Dreßler precast plant:“In addition to the design and the manufacture of classic pre-cast concrete elements, we have successfully expanded the man-ufacture of special concrete facades into a stand-alone produc-tion line for multi-purpose architectural concrete. The Tour To-tal façade, however, was the greatest possible challenge for theDreßler team. Every single production stage – statics, produc-tion particularities, logistics and assembly – was defined inminute detail. The timely production and the high architecturalrequirements were supported by rigorous quality controls. Form-work manufacturing and logistics presented unusual challengesfor the team. For example, a new turning beam was bought forimproving the production process.”The basic elements of the facade were cast in a T-form. The ver-tical pilaster strip and the horizontal parapet were formed simul-taneously, thus preventing the twisting of the pilaster strips un-der the influence of horizontal wind loads.

Manufacturing tolerances of less than three millimetersPeter Zahn, carpentry and formwork technician at the pre-castplant Stockstadt: “Because of the dimensional accuracy, a lot ofthe difficult pointed forms, partly converging to 0, had to be cutout with the circular hand saw, from the 21 mm thick Magno-plan panels. From our experience, the high requirements interms of concrete surface quality were best met using this DUO360 5 ply plywood sheet”. The perfect sealing of the edges, theassembly, the thorough cleaning of the form and the precise in-sertion of the reinforcement were well documented. Manufactur-ing tolerances have to be under three millimeters, as the generaljoint pattern had to have a deviation of maximum +/–1.5 mm.“The abrasion-resistant film facing of the formwork also con-tributed to the outstanding results in terms of finish and lifes-pan”. The white cement-based architectural concrete of the moduleswas produced in a specially designed mixing plant, built on thepremises of the Stockstadt plant. The pouring and the subse-quent compaction of the concrete were done by means of vibra-tion tables and bottles but also by trowel, which required exquis-ite craftsmanship, due to the sometimes extreme geometries.The final procedure was the souring of the entire surface of ca.7.500 m2. The final souring gives the structure made of white ce-ment and quartz sand an elegant marble appearance. 450 of the almost 1395 elements were pre-produced within eightweeks, until the beginning of August 2011, and then stored onthe premises under weatherproof conditions. Subsequently, theywere transported to the building site on trailers, fastened andpadded, in special loading boxes. Subcontractors then startedthe assembling under the supervision of Dreßler Bau. The remaining façade elements (column claddings, parapets, T-columns, attics, etc.), were produced by the end of 2011. The assembling took place until early summer 2012.The specifications require that the dynamic façade should act asa medium, linking the building and the city. “Repetition andvariation of a precast concrete module breaks the rigidity of thegrid-like facade. The bright concrete elements cover the buildingin a three-dimensional line pattern, which enhances the effectsof light and shadow on the facade”.

Further information:Westag & Getalit AG, Hellweg 15, D-33378 Rheda-Wiedenbrück, Tel. +49/5242/17-0, Fax +49/5242/17-75000, [email protected], www.westag-getalit.de


Products & Projects

Fig 1. The dominant feature of the slim and slightly bent building is itsfaçade. It consists of three-dimensional, sometimes very delicate curtainconcrete elements.

Fig 2. 450 of the almost 1395 elements were pre-produced within eightweeks, until the beginning of August 2011, and then stored on the premisesunder weatherproof conditions. Magnoplan DU= 360 formwork panels wereused to meet the very tight tolerance levels. (© Westag & Getalit)

Doka has won another landmark, the super-high-rise Lokhandwala Minervabuilding in Mumbai

Looming out of a 12-storey parking podium, the skyscraper willtop out at 300 m and feature 82 storeys in two separate towers.Named the “Minerva” after the Roman goddess of wisdom, thedesign for the tower comes from Hafeez Contractors, and bearsa similarity to an oversized letter “M”.The tower will be for residential use only and aims to be one ofthe most luxurious addresses in Mumbai. For the core walls, au-tomatic climbing formwork SKE50 and SKE100 will be in use.In order to guarantee an optimal construction workflow, eachcore will be split into two individual working zones. This in-creases productivity and guarantees a smooth work-flow. Con-struction of the building is scheduled to be finished in 2014.With this project Doka continues its expansion strategy in thesegment of the world’s tallest buildings.

Further Information:Doka GmbH, Josef-Umdasch-Platz 1, 3300 Amstetten, Austria, Tel. +43 (0)7472 605-0, Fax +43 (0)7472 64430, www.doka.com


Products & Projects

The Minvera Tower in Mumbai will be formed with Doka’s automatic climb-ing formwork. (© Doka)

Structural Concrete 14 (2013), No. 1 A11

software

Ing.-Software DLUBAL GmbHAm Zellweg 293464 TiefenbachPhone +49 (0) 96 73 92 03-0Fax +49 (0) 96 73 92 03-51Mail: [email protected]: www.dlubal.de

stay cables

DYWIDAG-Systems International GmbHMax-Planck-Ring 140764 Langenfeld/GermanyPhone +49 (0)21 73/7 90 20Mail: [email protected]: www.dywidag-systems.de

vibration isolation

BSW GmbHAm Hilgenacker 24D-57319 Bad BerleburgPhone +49(0)2751 803-126Mail: [email protected]:www.bsw-vibration-technology.com

under-screed impact sound insulation with European TechnicalApproval, PUR foam & PUR rubbermaterials for vibration isolation

reinforcement technologies

HALFEN Vertriebsgesellschaft mbHKatzbergstraße 3D-40764 LangenfeldPhone +49 (0) 21 73 9 70-0Fax +49 (0) 21 73 9 70-2 25Mail: [email protected]: www.halfen.de

concrete: fixing systems facade: fastening technology framing systems: products and systems

Max Frank GmbH & Co. KGTechnologies for the construction industryMitterweg 194339 LeiblfingGermanyPhone +49 (0)94 27/1 89-0Fax +49 (0)94 27/15 88Mail: [email protected]: www.maxfrank.com

sealing technologies

Max Frank GmbH & Co. KGTechnologies for the construction industryMitterweg 194339 LeiblfingGermanyPhone +49 (0)94 27/1 89-0Fax +49 (0)94 27/15 88Mail: [email protected]: www.maxfrank.com

Provider directoryproducts & services

anchor channels

JORDAHL GmbHNobelstraße 51D-12057 BerlinTel. (0 30) 6 82 83-02Fax (0 30) 6 82 83-4 97e-Mail: [email protected]: www.jordahl.de

JORDAHL® anchor channels JORDAHL® screws Shear ReinforcementShear Connector

bridge accessories

Maurer Söhne GmbH & Co. KGFrankfurter Ring 193D-80807 MünchenPhone +49(0)89 32394-341Fax +49(0)89 32394-306Mail: [email protected]: www.maurer-soehne.de

Structural Protection Systems Expansion Joints Structural Bearings Seismic Devices Vibration Absorbers

literature

Ernst & SohnVerlag für Architektur und technische Wissenschaften GmbH & Co. KGRotherstraße 2110245 BerlinPhone +49 (0) 30 4 70 31-2 00Fax +49 (0) 30 4 70 31-2 70E-mail: [email protected]: www.ernst-und-sohn.de

anchored in quality

fastening technology

HALFEN Vertriebsgesellschaft mbHKatzbergstraße 3D-40764 LangenfeldPhone +49 (0) 21 73 9 70-0Fax +49 (0) 21 73 9 70-2 25Mail: [email protected]: www.halfen.de

concrete: fixing systems facade: fastening technology framing systems: products and systems

post-tensioning

DYWIDAG-Systems International GmbHMax-Planck-Ring 140764 Langenfeld/GermanyPhone +49 (0)21 73/7 90 20Mail: [email protected]: www.dywidag-systems.de

prestressed concrete

Paul Maschinenfabrik GmbH & Co. KGMax-Paul-Straße 188525 Dürmentingen/GermanyPhone +49 (0)73 71/5 00-0Fax +49 (0)73 71/5 00-1 11Mail: [email protected]: www.paul.eu

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This book provides the reader with a consistent approach to theory of structures on the basis of applied mechanics. It covers framed structures as well as plates and shells using elastic and plastic theory, and emphasizes the historical background and the relationship to practical engineering activities. This is the first comprehensive treatment of the school of structures that has evolved at the Swiss Federal Institute of Techno-logy in Zurich over the last 50 years. The many worked examples and exercises make this a textbook ideal for in-depth studies. Each chapter concludes with a summary that highlights the most important aspects in concise form. Specialist terms are defined in the appendix. There is an extensive index befitting such a work of reference. The structure

of the content and highlighting in the text make the book easy to use. The notation, properties of materials and geometrical properties of sections plus brief outlines of matrix algebra, tensor calculus and calculus of variations can be found in the appen-dices. This publication should be regarded as a key work of reference for students, teaching staff and practicing engineers. Its purpose is to show readers how to model and handle structures appropriately, to support them in designing and checking the structures within their sphere of responsibility.

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2013. approx. 750 pages, approx. 600 fi g., approx. 30 tab. Hardcover.approx. € 98,–*ISBN: 978-3-433-02991-6

Theory of StructuresFundamentals, Framed Structures, Plates and Shells

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The International Federation for Structural Concrete (fib) is a pre-normative organiza-tion. “Pre-normative” implies pioneering work in codification. This work has now been realized with the fib Model Code 2010. The objectives of the fib Model Code 2010 are to (a) serve as a basis for future codes for concrete structures, and (b) present new develop-ments with regard to concrete structures, structural materials and new ideas in order to achieve optimum behaviour.The fib Model Code 2010 is now the most comprehensive code on concrete structures, in-cluding their complete life cycle: conceptual design, dimensioning, construction, conserva-

tion and dismantlement. It is expected to become an important document for both national and internatio-nal code committees, practitioners and researchers.

The fib Model Code 2010 was produced during the last ten years through an exceptional effort by Joost Walraven (Convener; Delft University of Technology, The Netherlands), Agnieszka Bigaj-van Vliet (Technical Secretary; TNO Built Environment and Geosciences, The Netherlands) as well as experts out of 44 coun-tries from five continents.

E d . : f i b – I n t e r n a t i o n a l F e d e r a -

t i o n f o r S t r u c t u r a l C o n c re t e

fi b Model Code for Concrete Structures 2010

2013. approx. 550 pages, Hardcover.approx. € 199,–ISBN 978-3-433-03061-5Also available as Date of Publication: Spring 2013

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The design and analysis of concrete structures has a remarkablehistory. This starts with the concrete material itself, which has undergone a revolutionary metamorphosis, especially during thelast decades. Only a few decades ago, the maximum concretestrength achievable on a building site was about 35 N/mm2. Themixes had to be designed with a sufficient amount of water to ensure workability. Nobody cared about properties such as permeability, diffusion and chemical reactions leading to deterio-ration. As admixtures were developed, so lower water/cement ratios became daily practice and higher strengths could beachieved. The discovery of silica fume as a reactive filler enabledthe realization of concrete strengths up to C100, which was expe-rienced as a sensation – and only 15 years ago. Self-compactingconcrete and high-performance fibre concrete represented thenext steps, which went hand in hand with a more careful study ofthe question as to why these mixes function and how we can re-place empiricism by mix design methods based on knowledgeabout the interactions of the components. By virtue of the ongo-ing insight into aspects such as particle packing, optimizing the design of performance-based concrete became reality. In this respect, further leaps forward are expected in the forthcomingyears.

We have also witnessed considerable advances in the designand analysis of concrete structures, in conjunction with remark-able changes in priority. In the eighties and early nineties of thelast century, great effort was invested in developing viable modelsfor structural safety and serviceability. Many current code rulesgo back to the work carried out in those days. A daring prognosisin that period was that durability of concrete structures would be-come a design issue of the same importance as structural safetyand serviceability. Meanwhile, this is a matter of course: servicelife design is becoming the norm. In the early years of this centu-ry, major steps were taken to realize the international harmoniza-tion of building codes. Transparency and up-to-dateness of coderules were leading principles in this work. And, just a few yearslater, we have realized that the codes we have written focus onnew structures only. Nowadays, we are confronted with an enor-mous legacy of existing structures, exhibiting different degrees ofdeterioration and exposed to loads larger than those for whichthey were initially designed. So the focus changes again, and newchallenges beg serious consideration.

The Model Codes, published by CEB-FIP in the past andnow by fib, testify very clearly to these changes in priority. The fibModel Code 2010, too, now brand-new, will in future only be seenas an intermediate landmark. Nevertheless, it will fulfil an impor-tant duty: the creation of a sound basis to facilitate new and nec-

fib Model Code for Concrete Structures 2010: a landmark in an ongoing development

György L. Balázs

Joost Walraven

Editorial

1© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete 14 (2013), No. 1

essary developments, which will help the engineers of the futurein their responsibility towards meeting the demands of a chang-ing society.

We see it as a privilege that we could work together with somany esteemed colleagues on the realization of fib Model Code2010. It is a pleasure to announce a series of articles, starting inthis issue, on various new aspects of the design and analysis ofstructural concrete as published in the latest Model Code.

Joost Walraven György L. BalázsConvenor of fib SAG5 President of fib 2011–12“New Model Code”

2 Structural Concrete 14 (2013), No. 1

Editorial

3© 2013 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete 14 (2013), No. 1

The Model Code for Concrete Structures 2010 is a recommenda-tion for the design of structural concrete, written with the inten-tion of giving guidance for future codes. As such, the results ofthe newest research and development work are used to generaterecommendations for structural concrete at the level of the lateststate of the art. While carrying out this exercise, areas are in-evitably found where information is insufficient, thus inviting fur-ther study. This paper begins with a brief introduction to the newexpertise and ideas implemented in fib Model Code 2010, fol-lowed by a treatment of areas where knowledge appeared to beinsufficient or even lacking and where further research might beuseful.

Keywords: concrete, structures, codes, recommendations, futuredevelopments, fib Model Code 2010

1 Introduction

The fib Model Code for Concrete Structures is a set of rec-ommendations for the design of reinforced and pre-stressed concrete which is intended to be a guiding docu-ment for future codes. Model Codes have been publishedearlier, in 1978 and 1990. A Model Code not only func-tions as a reference document for new codes, but also of-fers the latest state-of-the-art information about the vari-ous methods of design and analysis, in line with the realneeds of society regarding the creation of an optimized liv-ing environment and infrastructure. When Model Code1990 appeared, it focused primarily on structural safetyand serviceability. An important new aspect in those dayswas the introduction of constitutive equations for con-crete. This was inspired by the emergence of new, power-ful non-linear finite element programs, which requirepreferably uniform input by users with regard to the rele-vant parameters. The maximum concrete strength class inMC 1990 was C80, which in those days was a significantstep forward, but turns out meanwhile to be only a mod-erate step in the direction of the ultra-high-performanceconcretes we know today. fib Model Code 2010, the finaldraft of which appeared in 2012, not only presents updat-ed methods of design and analysis, but also introducesnew elements, the need for which has developed over re-

cent years. During the preparation of fib MC 2010, newfindings from research and application have been synthe-sized to form up-to-date design methods and new con-cepts in structural design. It is inevitable that during thisprocess areas are found where information is incompleteor even missing, and where existing ideas seem to be con-flicting. The following overview starts with a brief look atthose areas in fib MC 2010 where progress has been madeand innovations have been introduced. Subsequently, theoverview turns to areas that can be seen as “white spots”that invite further investigation.

2 New elements in fib Model Code 2010

Looking at fib Model Code 2010 [1], the final draft ofwhich was edited in early 2012, we see quite a number ofnew aspects:– The most important new element in fib MC 2010 is the

introduction of “time” as an important design criterion[2]. This not only applies to traditional concrete proper-ties such as creep and shrinkage, but is aimed especiallyat design for service life. Whereas fib MC 1990 primari-ly focused on the design of concrete structures with suf-ficient safety and serviceability in the new state, the aimof fib MC 2010 is the design of concrete structures withsufficient safety and serviceability for a defined period oftime after delivery. This means that the structure shouldbe able to fulfil its function with low maintenance costsfor the period specified, which in turn requires an ade-quate strategy to be adopted right from the design stage.The structure of the code reflects this philosophy: thechapter on design is followed by chapters on construc-tion, conservation and dismantlement. The approach infib MC 2010 is considerably more analytical and maturethan that of MC 1990, where only general statementswere given.

– fib MC 2010 contains a chapter on conceptual designwhich provides many indications for realizing optimumdesign for given boundary conditions. Structures shouldnot only be aesthetic in order to gain long-term accep-tance; they should also be sustainable and be able to ful-fil their duty without constraints for the period envis-aged. Moreover, they should be robust and easy tomaintain, fit well into their environment and respect lo-cal traditions (Fig. 1). Aspects such as adaptation, dis-mantlement and recycling should be considered at the

Technical Paper

fib Model Code for Concrete Structures 2010: mastering challenges and encountering new ones

Joost Walraven DOI: 10.1002/suco.201200062

Corresponding author: [email protected]

Submitted for review: 16 December 2012Revised: 3 January 2013Accepted for publication: 3 January 2013

design stage, even if such aspects only become relevantfar in the future.

– fib MC 2010 introduces – further to the partial safety fac-tor format, which is generally used in daily practice now– the probabilistic safety format and the global resis-tance format. The probabilistic safety format is especial-ly relevant to a new task in structural engineering whichis very quickly gaining in importance: the assessment ofthe loadbearing capacity of existing structures whichwere designed to old codes but are now subjected toloads higher than those for which they were designedoriginally and are possibly in a state of developing or ad-vanced deterioration. The global safety format shouldsupport the application of non-linear calculations, e.g.with finite elements, with defined reliability levels.

– fib MC 2010 offers methods of analysis with various“levels of approximation”. In this way a distinction ismade between applications for daily use and applica-tions that require a more accurate analysis because of,for instance, considerable financial consequences, see[3], for example.

– A reliability concept is introduced for numerical calcula-tions. Up to now, numerical calculations have been usedwith the input of personal choices for the basis of thecalculation. In this way the results of the analysis, evencarried out by experts, are to a certain degree subjectiveand can vary substantially. Therefore, authorities are of-ten reluctant to accept the results obtained by thismethod since the reliability of the results is difficult toquantify. In fib MC 2010 a choice of methods is offered,which are linked to different levels of reliability.

– A design method for steel fibre-reinforced concrete isgiven. This recognizes fibre reinforcement as a seriousalternative or supplement to traditional reinforcing sys-tems. The design method offered is valid over the fullrange between conventional fibre-reinforced concreteand ultra-high-performance concrete.

4

J. Walraven · fib Model Code for Concrete Structures 2010: mastering challenges and encountering new ones


– Design principles for external reinforcement using fibre-reinforced polymers (FRP) are given, respecting the upcoming need to strengthen an increasing number of existing structures to enable them to carry higherloads.

– fib MC 2010 deals with a wide scope of loads that can berelevant during the life of a structure. It treats the designof concrete structures under static, cyclic, impact and fa-tigue loads. Moreover, it deals with fire, seismic loadsand imposed deformations in a harmonized way.

– fib MC 2010 gives principles for design by testing, not on-ly based on the statistical analysis of series of tests onsimilar specimens, but also respecting the combination ofshort series of tests with numerical methods of analysis,including the reliability principles mentioned previously.

– fib MC 2010 specifies maintenance strategies as a part ofthe design for service life.

– A first introduction is given on the expected growingrole of sustainability criteria in design. Only principlesare given, based on the expectation that there will beconsiderable development in this field in forthcomingyears, resulting in more specific methods.

3 Areas inviting further study3.1 Defined performance materials

In current codes, the properties of concrete are linked to itscompressive strength. This is a very practical arrangementsince cylinder or cube tests are carried out anyhow, and formost properties there is a reasonable correlation betweencompressive strength and properties such as creep, shrink-age, tensile strength, elastic modulus, coefficient of waterpermeability and diffusion coefficient. These relationshipsare valid for conventional concrete under certain restric-tions such as the condition of a minimum cement content(e.g. 260–280 kg/m3). Recent years, however, have shown aconsiderable evolution with regard to designing concretemixes. The knowledge about particle packing, fillers andadmixtures has opened the door to a considerable spec-trum of concretes with attractive properties. As an example,the development of low binder concretes is given. Research,e.g. that carried out by Fennis [4], has led to a method of de-signing low binder concretes with sufficient strength andworkability based on packing density considerations, waterdemand and the so-called cement-space factor CSF (Fig. 2).Concrete mixes with only 110 kg/m3 of cement showed a28-day cylinder strength of 32 N/mm2. Shrinkage andcreep tests showed lower values than obtained with con-ventional concretes of the same strength. Moreover, electricresistivity tests exhibited more favourable values, demon-strating that durability criteria are also satisfied. It is clearthat for such innovative concretes, the link between proper-ties and compressive strength is misleading and would pre-vent such mixes from being used. To give those mixes achance, an appropriate system of testing not only strength,but also other properties should be devised. Mixes can bedeveloped with particular properties, but should mean-while meet other demands. The equivalent performanceconcept, as generally defined in the European standardEN 206-1, is promising but should be worked out further:the question is “equivalent to what?”, and how to demon-strate this by means of tests.

Fig. 1. The Pantheon in Rome – an example of a structure that has survivedfor centuries

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3.2 Creep of concrete bridges

The creep functions in section 5.1 “Materials” in fib MC2010 have been upgraded to reflect the most recent state ofthe art. Nevertheless, it was claimed that those relation-ships would not be satisfactory because long-term deflec-tion measurements on a substantial number of long-spanconcrete bridges showed that the measured deflections canreach values about twice as large as those calculated. Aninteresting discussion on this topic at the fib conference inPrague in 2011 showed that there are quite different pointsof view with regard to the reason for this difference. Prof.Bazant (see [5], for example) argued that the creep expres-sions in fib MC 2010 were not correct, and proposed hisown B3 model as an improvement. Others, however, dis-agreed on the statement that the formulation of the creepfunction is the reason for the difference between calculatedand measured deflections. Several other potential reasonswere suggested, such as the role of cracking in the stiffness,insufficient regard for the construction history and the un-derestimation of temperature effects. Another aspect men-tioned was the definition of the notional size of the mem-ber assumed as Ac/u, where Ac is the cross-sectional areain mm2 and u is the perimeter of the member in contactwith the atmosphere in mm. It should be noted that in abridge built as a cantilever system, the lower flange of thecross-section at the central support often has a thickness ofabout 1 m, whereas the notional size factor has been veri-fied on prismatic specimens with a cross-section no largerthan 300 × 300 mm. A small error in the estimation of thecreep of the concrete in this lower flange could have a largeinfluence on the mid-span deflection because of the “multi-plier” 0.5 l/h, where l is the span and h the depth of thecross-section at the support. Anyhow, this question invitesfurther investigation.

3.3 Role of maximum allowable crack width for durability

Throughout history there have been many discussionswith regard to the question of which is the most appropri-ate crack width calculation model. However, it should benoted that in design, calculated crack widths are com-

pared with limit values in tables, the origins of which aresomewhat vague. The maximum crack width values areformulated depending on the exposure class and the typeof steel used (reinforcing or prestressing steel). Also, thedefinition of the load for which the maximum crack widthshould be calculated differs: some codes use the maxi-mum service load, whereas other codes use the frequentload combination. All tabulated maximum crack widthvalues are < 0.4 mm, whereas Schiessl [6], as long ago as1986, demonstrated that crack widths < 0.4 mm are harm-less as long as the thickness and quality of the concretecover meet certain standards. Nowadays, new questionsarise, associated with increased traffic loads on oldbridges: e.g. “Is it acceptable if the crack width in a bridgeunder traffic load occasionally reaches a value of0.5 mm?” Another interesting question was raised in rela-tion to the crack width control in the storm surge barrierat the Hook of Holland in The Netherlands. The maxi-mum crack width specified was 0.2 mm at maximum ser-vice load. The maximum service load is, however, onlyreached if the barrier is closed, which is expected to beonce in 10 years, and for only a few days. In such a situa-tion (see Fig. 3), the pressure of the high external waterlevel is transmitted through the 237 m long steel trusses totwo concrete foundation structures (length 30 m) throughwhich this force is transferred into the soil. When the bar-rier is open, which is about 99.9 % of the time, the serviceload is zero. Therefore, the logical question asked was:Could, under this maximum service load, the maximum al-lowable crack width in the foundation structures be in-creased to a value of, for example, 0.6 mm because nolarge deterioration is expected to occur in the short periodwhen the cracks are open? This would save a consider-able amount of reinforcing steel. The answer from the ex-perts in this particular case was that increasing the crackwidth to 0.6 mm would lead to significant microcrackingin the concrete cover, which could impair the durability.Anyhow, a sound basis for the definition of the maximumvalues of the allowable crack width, based on good argu-ments and test results, would be most welcome.

3.4 Shear capacity of solid slabs

Shear has been a topic of discussion for many decades al-ready. As an estimation, about 8000–10 000 shear tests

strengthwater

packingφ

mix/α

t

CSF

Mixture adjustm

ent

strengthwater

packingφ

mix/α

t

CSF

Mixture adjustm

ent

Fig. 2. Design procedure for developing low binder concrete based onpacking density, water demand and cement-space factor ([4])

Fig. 3. Storm surge barrier, Hook of Holland, The Netherlands, giving rise tointeresting discussions on crack width control

have been carried out in the meantime. Nowadays, theshear capacity of solid slab bridges is under discussion, asa result of the increased traffic loads for which bridgeswere not designed originally. It turned out that despite thelarge number of tests mentioned, the answers required forthe determination of the shear bearing capacity of solidslabs with large wheel loads near to line supports couldnot be found. Therefore, tests were carried out recentlyand these have formed the basis for a design recommen-dation introduced in fib MC 2010 (section 7.3.3.1), includ-ing an expression for the spreading of the load to the sup-port and a multiplication factor to consider the positiveeffect of direct load transfer. Another remarkable observa-tion is that the expressions for the shear bearing capacityof a slab have always been derived on the basis of tests onbeams without shear links, assuming that slabs and beamsbehave similarly. However, slabs may be expected to havea better residual capacity since weak spots are compensat-ed for by stronger areas and can carry the loads via an al-ternative loadbearing path. Special tests were recently car-ried out at TU Delft: solid slabs were tested which wereintentionally weakened by strips with a much lower con-crete strength than the basic concrete, Fig. 4. The slabswith a length of 4200 mm were supported on line supportsat their ends and subjected to line loads at distances of2.2d and 3.0d from the support.

The weak strips had no significant influence on theloadbearing capacity: the shear resistance agreed well withthe resistance calculated using the mean concrete com-pressive strength. Another remarkable further observationwas, however, that the shear capacity of the slabs tendedto be significantly higher than that of comparable beams.A higher mean value for the shear capacity of slabs incombination with a lower range of scatter of the resultscould lead to the introduction of a “slab factor” > 1.0,which would work out favourably for the assessment of ex-isting slab bridges. This possibility should be investigatedfurther.

Many old structures were reinforced with plain steelbars with a relatively low characteristic yield value(220–240 N/mm2). When the shear resistance of oldbridges has to be assessed, the question comes up as to

6



whether the shear resistance of slabs reinforced with plainsteel is reduced by the lower bond strength in comparisonto ribbed steel. In this respect, very interesting tests werecarried out by Leonhardt way back in the early 1960s [7].His tests showed, surprisingly, that the shear capacity ofbeams reinforced with plain bars was substantially largerthan that of similar beams with ribbed bars. This led to aninteresting discussion about this phenomenon [8] that wasdenied by some authors, including even Leonhard himself!A decade later, M. W. Kani [9] carried out shear tests onbeams with reinforcement, the bond properties of whichwere reduced stepwise. Those tests clearly demonstratedthe increasing effect of lowering the bond on the shear ca-pacity. This effect can be explained by the fact that in-clined cracks cannot occur if the reinforcement is smooth.Current expressions do not take account of this effect,which is important for bridge assessment. Moreover, noshear tests are known on members with staggered plain re-inforcement. In old structures with staggered plain bars,those bars often terminate in hooks, whose effect on theshear capacity is not known.

3.5 The effect of compressive membrane action on bendingand shear capacity

An effect that is still generally ignored in design is com-pressive membrane action in slabs. Although this effectwas demonstrated by Ockleston as long ago as 1955 [10],who tested the capacity of inner slabs in a large floor sys-tem of an old hospital that was about to be demolished, ithas scarcely been introduced in codes. Fig. 5 shows theprinciple of compressive membrane action [11]. The slab(Fig. 5, left) is loaded by a concentrated load at mid-span.This results in cracks under the load and at the supports.If the steel in those cracks yields, a kinematic mechanismforms. At the support, the lower part of the slab cannotmove horizontally because of the confinement by the ad-jacent part of the slab; this leads to the development ofcompression membrane action that substantially increas-es both the bending capacity and the punching shear ca-pacity. In situ tests were carried out by Taylor et al. [12] ona bridge deck subjected to a concentrated wheel load. The

Fig. 4. Geometry of a slab composed of high- and low-strength concrete strips

7



160 mm thick deck was supported by prestressed beamsspaced at 1500 mm c/c. Depending on the position of theconcentrated load, the measured loadbearing capacity wasa factor 1.6–5.2 times larger than the load predicted on thebasis of the unconfined situation. The increase in the loaddue to compressive membrane action depends on the con-fining action of the adjacent part of the structure. At thismoment, tests are being carried out at TU Delft on a 1:2size model of a bridge deck in order to verify the effect ofcompressive membrane action on the loadbearing capaci-ty. This bridge deck consists of prestressed beams withthin concrete slabs cast in between and connected bytransverse prestressing. The concentrated load will be ap-plied at various positions of the deck in order to quantifythe effect of compressive membrane action on the capaci-ty of this bridge prototype, representing 69 bridges in TheNetherlands. The tests are being carried out in order toverify whether those decks should be strengthened or havea sufficient loadbearing capacity. General rules with re-gard to this phenomenon are of great importance for de -cision-making when it comes to strengthening existingstructures.

3.6 Further development of the design recommendations for fibre-reinforced concrete

The provisions for the design of fibre-reinforced structuresgiven in fib MC 2010 are a step forward in various re-spects. The recommendations are valid for the wholerange between conventional fibre-reinforced concrete(FRC), with moderate strength and relatively low volumesof coarse fibres, to ultra-high-performance FRC, with avery high strength (180–200 N/mm2) and high volumes offine steel fibres. Moreover, a classification of FRC has beenintroduced with regard to its mechanical properties. Thismeans that design relationships can be assumed in ad-vance for carrying out the design, which are verified laterby tests on control specimens. Through this arrangement,the design of FRC basically follows the same pattern asthe design of reinforced concrete, where the concretestrength class is chosen in advance and verified by cylin-der or cube tests at a later stage. An objection that is some-times raised against such a harmonized approach – validfor all types of FRC – is that it may be too conservative for

special FRC mixtures such as ultra-high-strength FRC. Itmight therefore be worthwhile comparing the results ofthe harmonized approach according to fib MC 2010 withthose of tailor-made approaches in order to see if it makessense to distinguish different levels of approximation, asintroduced elsewhere in fib MC 2010. Another aspect thatshould be considered is the way in which the properties ofFRC are tested. In order to determine the mechanicalproperties of FRC, in most cases a series of small controlbeams is subjected to a load at mid-span (RILEM test).The stress-crack opening relationship is then derived fromthis series by inverse analysis. The tests show mostly aconsiderable scatter in load-deflection relations. This scat-ter, which is reflected as well by the stress-crack openingrelationship and as a consequence affects the designstress-strain relation derived afterwards, is rather a proper-ty of the test series than it is representative of the behav-iour of FRC in a structure. This should be given seriousconsideration. One possibility is to determine as accurate-ly as possible the mean stress-crack opening relationshipfrom tests with low variability, such as a bending test on acircular panel on three point supports (Fig. 6), where thescatter is small because of the compensating effect of thethree yield lines, and combine the stress-crack opening orstress-strain relations obtained in this way with the scatterto be expected in the real structure. In a structure the scat-ter decreases as the cracked area involved in the loadbear-ing mechanism increases. General rules could be derivedhere.

3.7 Reliability of non-linear finite element calculations

As mentioned before, fib MC 2010 offers various strategiesfor introducing reliability into numerical calculations.Three principles are given. The most practical strategy liesbetween the extremes of the “probabilistic method” andthe “partial factor method” and is known as the “global re-sistance method”, and under this heading the “method ofestimation of a coefficient of variation of resistance”. Thismethod can be seen as a compromise between accuracyand practical applicability. Further case studies to opti-mize this method would be worthwhile. It is a step in thedirection of tailor-made NLFEM analyses with the highestpossible reliability.

Fig. 5. Principle of compressive membrane action [11]

3.8 Verification of limit states associated with durability

Since structural safety is expressed in terms of reliability,which should be maintained over the full service life of astructure, it is logical that reliability considerations enterthe limit state conditions with regard to durability. A limitstate of durability is reached when a specified criterion fora certain type of deterioration is reached. For chloridepenetration and carbonation these criteria can be reason-ably well specified. For other deterioration mechanisms,e.g. freeze/thaw attack, sulphate attack, alkali aggregatereaction and delayed ettringite formation, the deteriora-tion mechanisms, and as such the limit state criteria, areless well defined. For a better specification of those crite-ria, an investigation of older structures with regard to theirstate of deterioration might be very instructive. Olderstructures offer an excellent opportunity to calibrate theresults of theoretical deterioration models!

3.9 Introducing a sound basis for making decisions with regard to sustainability

When the draft version of fib MC 2010 was published andexperts were invited to comment on it, several people won-dered whether sustainability should really be a part of amodern code on structural concrete. This doubt was certainly stimulated by the circumstance that the recom-mendations given in the area of sustainability were quitegeneral, which was partly due to the early stage of devel-opment of sustainability models. Actually, however, pre-liminary sustainability qualification models are already

8



used in various countries in the process of tendering fornew projects. It is therefore important that criteria in rela-tion to concrete are introduced in an appropriate way inorder to quantify the level of sustainability of designs fornew concrete structures. Providing sets of suitable criteriacan be a stimulus for the introduction of high-perfor-mance materials, as shown by Voo and Foster, Fig. 7 [14].They compared a bridge in conventional concrete with analternative in ultra-high-performance concrete (UHPC)with regard to sustainability, using the necessary volumeof material, the embodied energy, the CO2 emission andthe 100-year global warming potential (GWP). Remark-ably, this comparison was definitely in favour of the UHPCsolution, whereas a comparison on the basis of 1 m3 of

Fig. 6. Bending test on 3 fibre-reinforced concrete circular slabs supported at three points [13]

Fig. 7. Comparison of a conventional bridge with an alternative in UHPC onthe basis of sustainability criteria according to Voo and Foster [14]

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such concretes would erroneously give preference to theconventional material.

3.10 Dismantlement

The chapter entitled “Dismantlement” in fib MC 2010 isrelatively short. It marks the end of service life of a con-crete structure and for that reason alone its implementa-tion is justified in a document that tends to stimulate de-sign for service life. The chapter could just as well havebeen called “Demolition”, but the term “Dismantlement”was preferred since it suggests a controlled process, whichencourages designers to think about the end of service liferight from an early stage of design. It is hoped that thismight inspire the development of concepts for demount-able and adaptable structures (Figs. 8 and 9). For furtherdevelopment, cooperation between structural engineersand architects might be fruitful.

4 Conclusions

– fib MC 2010 offers modernized design recommenda-tions for many aspects of the design and analysis of con-crete structures.

– fib MC 2010 not only treats aspects of design and analy-sis, but also offers a more general philosophy, based onservice life design.

– During the work on fib MC 2010, a number of areas werefound where consistent information was lacking, or nomature ideas had been developed at all.

– The exercise of writing a new Model Code made surethat structural engineering is an area that is still showingsignificant evolution.

References

1. Model Code 2010, vols. 1 & 2, final draft, fib – Bulletins 65 &55, fib, Lausanne, www.fib-international.org

2. Walraven, J. C., Bigaj, A. J., The 2010 fib Model Code forConcrete Structures: a new approach to structural engineer-ing. Structural Concrete, Vol. 12, Nr. 3, pp. 139–147.

3. Muttoni, A., Fernández Ruiz, M., The levels-of-approxima-tion approach in MC 2010: application to punching shearprovisions. Structural Concrete 13 (2012), No. 1, pp. 32–41.

4. Fennis, S.: Design of Ecological Concrete by Particle Pack-ing Optimization. PhD thesis, Delft University of Technolo-gy, 2011.

5. Bazant, Z. P., Hubler, M. H., Yu, Q.: Pervasiveness of Exces-sive Segmental Bridge Deflections: Wake-Up Call for Creep.ACI Structural Journal, Nov–Dec 2011, pp. 766–774.

6. Schiessl, P.: Influence of cracks on the durability of rein-forced and prestressed concrete members. Deutscher Aus -schuss für Stahlbeton, No. 370, Beuth Verlag, Berlin, 1986(in German).

7. Leonhardt, F., Walther, R.: Shear tests on simply supportedreinforced concrete beams with and without shear reinforce-ment for the determination of the shear resistance and theupper limit of the shear stress. Deutscher Ausschuss fürStahlbeton, No. 151, Ernst & Sohn, Berlin, 1962 (in Ger-man).

8. Discussion of the paper by Kani, G. N. J.: The Riddle ofShear Failure and Its Solution. Journal of the ACI, Dec 1964,pp. 1587–1637

9. Kani, M. W., Huggins, M. W., Wittkopp, R. R.: Kani on Shearin Reinforced Concrete. University of Toronto, Departmentof Civil Engineering, 1979, 225 pp.

10. Ockleston, A. J.: Load tests on a three-storey reinforced con-crete building in Johannesburg. The Structural Engineer, vol.33, 1955, pp. 304–322.

11. Long, A. E., Basheer, P. A. M., Taylor, S. E., Rankin, B., Kirk-patrick, J.: Sustainable Bridge Construction Through Innov-ative Advances. Proc. of ICE Bridge Engineering, vol. 161,No. 4, Dec 2008, pp. 183–188.

12. Tailor, S. E., Rankin, B., Cleland, D. J., Kirkpatrick, J.: Ser-viceability of Bridge Deck Slabs with Arching Action. ACIJournal, Jan-Feb 2007, pp. 39–48.

13. Yang, Y.: Mechanical properties of steel fibre reinforced con-crete tested by statically determinate round panel tests. In-ternal report, TU Delft, Section of Concrete Structures,2008.

14. Voo, Y. L., Foster, S. J.: Characteristics of ultra-high perfor-mance ductile concrete and its impact on sustainable con-struction. IES Journal, Part A, Civil & Structural Engineer-ing, vol. 3, No. 3, Aug 2010, pp. 168–187.

Joost WalravenDelft University of TechnologyFaculty of Civil EngineeringSection GCTPO Box 50482600 GA Delft, The [email protected]

Fig. 9. Priority of dismantlement for optimum flexibility

Fig. 8. Part of a demountable office building in Delft, The Netherlands

10 © 2013 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete 14 (2013), No. 1

Technical Paper

DOI: 10.1002/suco.201200021

CEB/FIP Model Code 1990 (MC-1990) [1] did represent the tech-nology and focus some 20 years ago. However, it soon becameevident that the document had some notable lacunas. In 1995 thegeneral assemblies of the two organizations endorsed CEB/FIPbulletin No. 228 [2], extensions to MC 1990 for high-strength con-crete, and in 2000 a similar extension to MC 1990 for lightweightaggregate concrete as bulletin No. 4 [3].The fib approved bulletin No. 34 Model Code for Service Life De-sign (MC SLD) [4] in 2006. All these three additions have sincematured and are now incorporated in the new fib Model Code forConcrete Structures 2010 (MC-2010) [5, 6, 7].The main purpose of an fib Model Code is to act as a model foroperational standards. The obvious counterpart for a body suchas fib operating worldwide is ISO. The initiative taken by MC SLDhas therefore further matured in ISO TC-71/SC-3/WG-4 and it wasaccepted as ISO 16204 “Durability – Service Life Design of Con-crete Structures” [8] during the summer of 2012.According to the obligations given in the WTO Agreement onTechnical Barriers to Trade [9], it is hoped that these principleswill be further implemented in national and regional standards.This article describes the need for a transparent methodologywhen dealing with service life design, and the process – originat-ing from a group of enthusiasts one decade ago – through fib andfinally reaching international consensus in ISO.

Keywords: fib Model Code 2010, ISO 16204, service life design

1 Background

Durability of concrete structures, and in particular thelack of such, has been in the focus of society in generalover the last few decades. Excessive repair needs havechallenged our industry.

The traditional approach in most national and re-gional concrete standards is to specify the provisions toensure a certain design service life by limiting values formaterial composition and geometry based on the expertopinion of the code committee.

There are several weaknesses in this approach:– It is often unclear as to which condition represents the

end of the service life.

– The required level of reliability for the design is oftenunclear as well.

– The criteria should be based on long-term field experi-ence. Such experience is, however, not normally avail-able for modern materials and design concepts, and con-cepts with service records > 50 years are seldom in useany more.

In 1998 a group of 19 European enthusiasts, all of us witha long record within CEB and FIP, signed a contract withthe European Commission to develop a platform for dura-bility design of concrete structures that contained thesame elements and philosophy as that of modern structur-al design. This European network was named “Duranet”,and the contract lasted until 2001.

At DuraNet’s final workshop in Tromsø, Norway, in2001, attendees from Europe and North America workedout a plan for how to progress to get this methodologystandardized and implemented in the industry worldwide(Fig. 1). The obvious environment for this was ISO.

Some of us therefore met at the ISO TC-71 meetingin Norway that autumn and presented our visions. TC-71,responsible for concrete-related standardization withinISO, endorsed the initiative, but quite correctly made usaware of the fact that ISO normally starts its work on thebasis of existing documents. We therefore agreed to askthe International Federation for Structural Concrete, fib(formed by the merger of CEB and FIP) to work out such amodel for a standard.

Design for service life: implementation of fib Model Code 2010 rules in the operationalcode ISO 16204

Steinar Helland


Submitted for review: 03 August 2012Revised: 23 August 2012Accepted for publication: 23 August 2012

Fig. 1. The “Duranet” workshop in Tromsø, 2001, which came up with aroadmap for how to implement limit state and reliability-based service lifedesign in standards.

11

S. Helland · Design for service life: implementation of fib Model Code 2010 rules in the operational code ISO 16204


Thereupon, fib set up Task Group 5.6 with expertsfrom Europe, North and South America and Japan. In2006 fib “Model Code for Service Life Design” (bulletinNo. 34) was endorsed by the fib’s General Assembly inNaples, Italy. fib TG 5.6 was headed by Prof. PeterSchiessl from Germany. The other members were Gehlen(DE), Baroghel-Bouny (FR), Bamforth (UK), Corley (US)(present chair of ISO TC-71), Faber (DK), Helene (BR),Ishida (JP), Markeset (NO), Nilsson (SE), Rostam (DK)and Helland (NO).

The group decided early on to produce a documentfully parallel with ISO 2394 “General principles on relia-bility for structures” [10]. This standard today forms thereference for fib MC-2010 and most modern standards forstructural design. ISO 2394 is also the “parent document”for the European Eurocode 0 “Basis of structural design”(EN 1990) [11].

fib based its approach on a limit state (LS) and relia-bility-based concept. This approach recognizes that thenature of the deterioration of concrete structures overtime must be treated in a statistical way. This is due to thenatural spread in material characteristics and also to thespread in the mesoclimatic and microclimatic conditionsa concrete structure is exposed to.

Since 2006 this initiative has progressed in close co-operation between fib’s group working on fib MC-2010,Special Activity Group No. 5 (SAG-5) and ISO TC-71/SC-3/WG-4. fib MC-2010, including its elements for servicelife design, is currently being finalized. ISO 16204 “Dura-bility – Service life design of concrete structures” achieveda positive international vote in summer 2012. These twodocuments are today – except for the cover and references– close to being identical when it comes to service life design.

2 How service life design is handled in most standardstoday

Provisions to ensure sufficient durability are today nor-mally embedded in the concrete standards. In Europedurability is still regarded as coming under national au-thority and its provisions are expected to be given in a na-tional annex to the European standard. In CEN TR 15868[12], Tom Harrison has compared how the 31 Europeancountries cooperating in CEN have solved the request inEN 1992/EN 13670/EN 206-1 [13, 14, 15] to give nationalprovisions for a service life of 50 years based on require-ments mainly linked to maximum w/c ratio, minimumcover to the reinforcement and cement type.

The spread of requirements for structures expectedto be subject to similar conditions is striking. Some exam-

ples for exposure classes XC3 (exposed to carbonation –sheltered from rain), XC4 (exposed to carbonation – ex-posed to rain) and XS2 (submerged in sea water) for 50years design service life are given in Table 1.

The differences in actual performance for these ex-tremes are very large. Comparisons of durability-relatedprovisions from other parts of the world demonstrate asimilar spread.

Bearing in mind that the technical expertise on thesematters is more or less at the same level in these countries,the explanation must be that the different national stan-dardization bodies have different understandings of whatactually represents the “end of service life” as well as theintended level of reliability.

3 Limit state concept for service life design

The limit state concept recognizes the need to be specificabout what condition represents the “end of service life”.The application of reliability-based and LS-based servicelife design is specifically excluded from both ISO 2394and EN 1990. The task for fib TG 5.6 was therefore tocome up with the amendments needed in these referencedocuments.

At first sight these ideas might be considered as rev-olutionary, but actually that is not true. All code writersin the past must have had some idea of what they consid-ered to be the “end of service life” when they came upwith their provisions. They must have known whetherthey were considering just rust stains or full structural col-lapse. They then applied a “limit state” concept. Theymust also have had in mind whether they expected thestatistical average of the building population to stand thisdesign service life length, or whether they expected thegreat majority of the population to meet this requirement.They then applied a probabilistic approach. However, it isfair to say that these processes are very seldom applied ina transparent way.

ISO 2394 defines the serviceability limit state as “astate which corresponds to conditions beyond which spec-ified service requirements for a structure or structural ele-ment are no longer met”. fib MC SLD, fib MC-2010 andISO 16204 apply the same definition, but fib MC-2010 hasa further group “Limit states asso ciated with durability” asa separate category. In principle, this may be any condi-tion that makes the building owner feel uncomfortable.For concrete structures, corrosion of the reinforcement isoften the critical deterioration process. The LS could thenbe depassivation, cracking, spalling or collapse (ultimateLS). Due to the problem of developing reliable time-de-pendent models for the rate of corrosion (after depassiva-

Table 1. Comparison of some European durability requirements to ensure 50 years design service life (from [12])

Range of XC3 provisions for CEM I UK → w/c < 0.55 and 25 mm Germany → w/c < 0.65 and 20 mm in Europe minimum cover minimum cover

Range of XC4 provisions for CEM I Netherlands → w/c < 0.50 and 25 mm Germany → w/c < 0.60 and 25 mm in Europe minimum cover minimum cover

Range of XS2 provisions for CEM I UK → w/c < 0.50 and 35 mm Norway → w/c < 0.40 and 40 mm in Europe minimum cover minimum cover

12



tion), LS depassivation is the choice of convenience formost engineers.

4 Level of reliability – consequences of failure

fib MC SLD, fib MC-2010, EN 1990 and ISO 2394 all sug-gest a three-level differentiation of the consequences uponpassing an LS:a) risk to life low, economic, social and environmental

consequences small or negligibleb) risk to life medium, economic, social and environmen-

tal consequences considerablec) risk to life high, economic, social and environmental

consequences very great

Based on the relevant consequence class, combined with aconsideration of the cost of safety measures, a relevantlevel of reliability for not passing the LS during the designservice life should be selected.

Within the limitations normally found in nationalbuilding legislation, the reliability level used in the designshould be agreed with the owner of the structure.

fib and ISO suggest a probability of failure pf = 10–1

for depassivation of reinforcement (by carbonation oringress of chlorides) in cases where the presence of oxy-gen and moisture makes corrosion possible. If collapse isthe LS considered, pf = 10–4 to 10–6 may, as for traditionalstructural design, be the relevant level if the possible con-sequences are in classes b) and c).

5 End of service life

Based on the above, a main element in the fib and ISOdocuments is therefore an amended quantitative defini-tion to the qualitative one we find in traditional standardssuch as the ones in ISO 2394 or EN 1990:

Traditional qualitative definition: The design service lifeis the assumed period for which a structure or part of it isto be used for its intended purpose with anticipated main-tenance but without major repair being necessary.

Quantitative amendment by fib and ISO: The design service life is defined by: – A definition of the relevant LS– A number of years– A level of reliability for not passing the LS during this

period

Fig. 2 indicates how various limit states may be associatedwith corresponding levels of reliabilities for not passingthe LS within the design service life in the case where cor-rosion of reinforcement is the critical case.

In principle, the verification of the design has todemonstrate that the structure will satisfy all combina-tions of LS and pf. For practical design, however, we donot have time-dependent models with international con-sensus to predict the corrosion phase after depassivation.The calculation therefore often has to be based on thetime up to depassivation. The corresponding pf must thenbe sufficiently low to ensure that this LS results in equal orstricter requirements for material and depth of cover thanthe other combinations.

When considering the effect of corrosion of the rein-forcement after its depassivation, splitting stresses in thecover zone from the reinforcement due to the effects ofother mechanical actions/loads should also be consid-ered. Wherever there are bond stresses in the reinforce-ment there are also “bursting stresses” in the concrete ofthe same nature as those from the expanding corrosionproduct, ultimately leading to the same type of crackingand spalling of the cover.

This is another argument for avoiding the minefieldsof using cracking and spalling as the LS for service lifedeign.

If we are pursuing the example of depassivation dueto carbonation, all the characteristics that determine whenthe individual reinforcing bars will depassivate in a struc-ture will have a statistical spread. This includes the actualdepth of cover, the microclimatic conditions, the humidityof the concrete, its curing, etc. As a result, the initiation pe-riod will also exhibit a statistical spread.

Fig. 3, derived from Bamforth [16], indicates the ac-cumulative time for depassivation of the surface rebars ina structure subjected to carbonation. To assess the actualservice life of this structure, the depassivation LS has to be

15

20

(cor

rosi

on)

Spalling

Collapse of structurepf ≈ 10 -4- 10 -6

0

5

10

0 5 10 15 20 25 30 35

Det

erio

ratio

n (

Time

Depassivationpf ≈ 10 -1

Formation of cracks

Fig. 2. Various limit states and related reliability levels shown for corrosionof reinforcement

50

75

100

failu

re (

%)

B30%

C50%

0

25

50

0 50 100 150

cum

ula

tive

years

A2%

10%

Fig. 3. Time until depassivation of surface reinforcement (example derivedfrom [16]). The Norwegian Standardization body applied a 10 % acceptancefor depassivation as a criterion when determining its durability provisions,whereas countries A, B and C applied 2, 30 and 50 % respectively.

13



matched with a level of reliability. In fib Commission 5,TG.5.11, we are presently developing supporting docu-ments to fib MC-2010/ISO 16204. The work has revealedthat Norway applied a pf of 10–1 when working out its pre-sent deemed-to-satisfy requirement. In this case a servicelife of 70 years is reached. However, representatives fromthree other European countries stated that experts in theirstandardization bodies had in mind a pf of 2*10–2, 3*10–1

and 5*10–1 (2, 30 and 50 % respectively). This then gives arange of nominal service lives from 50 to 109 years for thesame structure exposed to the same environment.

This lack of consistent use of the reliability-basedlimit state concept is probably a main reason for the afore-mentioned major differences in durability provisionsamong the European standards. The present lack of trans-parency must also be very confusing for the stakeholderswhen service life design is discussed.

In Fig. 4 I have included an assumption often used of10 years active corrosion until cracking and spalling oc-curs. In this case the nation accepting a 50 % probabilityfor depassivation implicitly also accepts an approx. 35 %probability of cracking and spalling.

Although it might be easy for a client to accept a highprobability for passing an undramatic event such as depas-sivation during the design service life, it will be muchharder to accept excessive cracking and spalling. The im-plicit consequences of linking an excessively high proba-bility of failure for depassivation should therefore be clear-ly communicated.

6 What is the appropriate length of a design service life?

ISO 2394 gives guidance on the appropriate choice of thelength of the design service life (Table 2).

The same guidance is referred to in the Europeanstandard EN 1990 and in practice dominates the applica-tion in many parts of the world. However, the table pro-vides general guidance for all structural materials andshould be used with utmost care for concrete structures.This is particularly the case for class 3 comprising “build-ings”. This is a very diverse group. Some buildings, e.g. fac-tories, will often have an economic service life corre-sponding to the installed machinery. On the other hand,structural parts of residential buildings will, in general so-ciety, normally have an expected service life of much morethan the 50 years indicated in the table.

ISO 16204 therefore strongly advises users to bemore ambitions for at least those structural parts of a con-crete building where repairing or replacing elements willbe complicated and expensive.

7 Design of service life and its verification

“The design of a structure includes all activities needed todevelop a suitable solution, taking due account of func-tional, environmental and economical requirements.” (de-finition in fib MC-2010)

This implies that the flow of activities for service lifedesign will follow the flowchart given in Fig. 5.

A similar graph is given in fib MC SLD and in textform in fib MC-2010.

The serviceability (performance) criteria have to beagreed with the owner within boundaries given in the leg-islation.

The documents are not specific regarding how thedesigner comes up with a general layout, dimensions andmaterials. However, the verification of the proposed de-sign is strictly regulated. The fib and ISO documents offerfour formats for verifying the service life design:

The full probabilistic method: The time to reach the LSwith the required level of reliability is calculated based onstatistical data for the environmental load and structuralresistance.

The partial factor method: As for the full probabilisticmethod, but the statistical data for load and resistance aresubstituted by characteristic values and partial coeffi-cients.

Table 2. ISO 2394, Table 1 [10], gives examples of design service lives. The same table is given as guidance in EN 1990 [11]. ISO 16204 [8] states that class 3should be used with care for structural parts of buildings where repair is complicated or expensive.

Class Notional design working life Examples

1 1 to 5 Temporary structures

2 25 Replacement structural parts, e.g. gantry girders, bearings

3 50 Buildings and other structures, other than those listed below

4 100 or more Monumental buildings and other special or important structures, large bridges

50

75

100e

failu

re (

%)

0

25

0 50 100 150

cum

ula

tive

years

Fig. 4. The same example as in Fig. 3, but with10 years of active corrosionadded to reach cracking and spalling of the rebar cover. The limit state at50 % probability for depassivation then implicitly results in an approx. 35%probability of failure for the limit state of cracking and spalling.

14



The deemed-to-satisfy method: A set of requirements(normally w/c, cover to the reinforcement, crack width, airentrainment, etc.) that are prequalified by the code com-mittee to satisfy the design criteria.

The avoidance-of-deterioration method: This methodimplies that the deterioration process will not take placedue to, for instance: separation of load and structure by,for example, cladding or membrane, using non-reactivematerials, suppressing the reaction with electrochemicalmethods, etc.

The fifth format offered by fib MC-2010 for verifying thestructural capacity, the “global resistance”, is not mobi-lized for service life design.

The partial factor and deemed-to-satisfy methodsboth need to be calibrated, either by the full-probabilisticmethod or on the basis of long-term experience of buildingtraditions.

Of these four options, the full probabilistic method isobviously the most complicated and sophisticated. Forthis reason, many academics have regarded it as the mostprestigious and precise one. This is fundamentally wrong.Due to the normal lack of good and representative data,and uncertainty in modelling, the full probabilisticmethod will seldom be feasible for the design of new struc-tures; however, the method is well suited to assess the re-maining service life of existing structures where datamight be derived from the actual structure.

By assessing the remaining service life of existingstructures by means of the full-probabilistic method, we al-

so have a powerful tool for verifying deemed-to-satisfyprovisions for the design of new structures with similar ex-posure and design conditions.

The partial factor method is a semi-probabilistic ap-proach where the calculation is deterministic and the sta-tistical spread of the input parameters is taken care of bypartial factors. The calibration of these partial factors forservice life design for general use is very challenging, andits practical application is therefore not envisioned in thenear future.

Both MC-2010 and ISO 16204 assume that thedeemed-to-satisfy and avoidance-of-deterioration methodswill continue to dominate the practical service life designof new structures in the future, but the provisions for theformer will be linked to a specific LS and reliability. Thesetwo methods should be further verified by the code com-mittee and communicated to the stakeholders.

8 Modelling8.1 General

We need models describing the deterioration process overtime in order to be able to apply the full probabilistic andpartial factor methods. There are not too many of modelsin our field which enjoy general international consensus.

In fib MC SLD, fib MC-2010 and ISO 16204 we havedared to suggest Fick’s 2nd law, modified by a time-depen-dent diffusion coefficient, for the ingress of chlorides, andthe traditional square-root-of-time model for carbonation.These two models, as described and explained in the threedocuments, are described in sections 8.2 and 8.3.

Establishing the serviceability criteria

Establishing the general layout, the dimensions and selection of materials

Verification by the “Full probabilistic” method.Involving:• Probabilistic models

– resistance– loads/exposure– geometry

• Limit states

Verification by the “Partial factor” method.Involving:• Design values

– characteristic values– partial factors

• Design equations• Limit states

Execution specification Maintenance plan

Condition assessment plan

Execution of the structure

Inspection of execution

Maintenance Condition assessments during operational service life

Verification by the “Deemed-to-satisfy”method.Involving:Exposure classes,limit states and other design provisions

Verification by the “Avoidance of deterioration”method.Involving:Exposure classes, limitstates and other design provisions

In th

e ca

se o

f no

n-co

nfor

mity

to th

e pe

rfor

man

ce c

rite

ria,

th

e st

ruct

ure

beco

mes

obs

olet

e or

sub

ject

to f

ull o

r pa

rtia

l red

esig

n

Fig. 5. Flowchart for service life design (from [8])

15



However, the documents are also open for the use ofother models provided they are sufficiently validatedthrough full-scale experience.

8.2 Carbonation

The ingress of the carbonation front might be assumed toobey the following equation:

xc(t) = W · k √⎯ t (1)

wherek is a factor reflecting the basic resistance of the chosenconcrete mix (such as w/c ratio, cement type, additives)under reference conditions and the influence of the basicenvironmental conditions (such as mean relative humidityand CO2 concentration) against ingress of carbonation. Italso reflects the influence of the execution.

W takes into account the varying mesoclimatic con-ditions for the specific concrete member during the designservice life, such as humidity and temperature.

For the design of a new structure, the factors W andk might be derived from published data or existing struc-tures where the concrete composition, execution and ex-posure conditions are similar to those expected for thenew structure.

When assessing the remaining service life of an exist-ing structure, the product of W and k might be derived di-rectly from measurements on the structure.

8.3 Chloride ingress

The ingress of chlorides in a marine environment may beassumed to obey the following equation:

(2)

In this modified Fick’s 2nd law of diffusion, the factorsare:C(x,t) chlorides content in the concrete at depth x

(structure surface: x = 0 mm) and time t [% bywt./binder content]

Cs chlorides content at the concrete surface [% bywt./binder content]

Ci initial chlorides content of concrete [% bywt./binder content]

x depth with a corresponding chlorides contentC(x,t) [mm]

Dapp(t) apparent coefficient of chloride diffusionthrough concrete [mm2/year] at time t, see Eq.(3)

t time of exposure [years]erf error function

(3)

where:Dapp (t0) apparent diffusion coefficient measured at a

reference time t0

( ) ( )00D t D t

ttapp app=

⎛

⎝⎜⎞

⎠⎟

α

= − − ⋅⋅ ⋅

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥C x

s s iC(x, t) C ( C ) erf (2 D (t) t

)app

α ageing factor giving the decrease over time ofthe apparent diffusion coefficient – dependingon type of binder and micro-environmentalconditions, the aging factor is likely to lie be-tween 0.2 and 0.8

The “apparent” diffusion coefficient after a period t of ex-posure to chlorides Dapp(t) represents a constant equiva-lent diffusion coefficient giving a similar chloride profileas the measured one for a structure exposed to the chlo-ride environment over a period t.

The decrease in the apparent diffusion coefficient isdue to several reasons:– Ongoing reactions of the binder– Influence of reduced capillary suction of water in the

surface zone over time– Degree of saturation of concrete– Effect of penetrated chlorides from seawater or de-icing

salts (leading to ion exchange with subsequent blockingof pores in the surface layer)

For the design of a new structure, the parameters Cs, Ci, αand Dapp (t0) may be derived from existing structureswhere the concrete composition, execution and exposureconditions are similar to those relevant for the new struc-ture. When assessing the remaining service life of an exist-ing structure, the factors, with the possible exception of α,may be derived directly from measurements on the struc-ture.

For both the design of new structures and the assess-ment of the remaining service life of existing structures,the ageing factor α should be obtained from in situ obser-vations of structures where the concrete composition, exe-cution and exposure conditions are similar to those of theactual structure. Observations during at least two periodsof exposure (with a sufficient interval between the obser-vations) are needed for the calculation of the ageing fac-tor.

8.4 Other deterioration mechanisms

For acid and sulphate attack, as well as for alkali-aggregatereactions, fib MC-2010 and ISO 16204 conclude that notime-dependent models with general international consen-sus are available and that full probabilistic and partial fac-tor approaches for service life design are in these cases notfeasible at present.

For these mechanisms, deemed-to-satisfy and avoid-ance-of-deterioration approaches have to be applied.

We have formulated a general time-dependent modelfor freeze-thaw cases, but this will hardly be usable due tothe complexity of the input parameters. Therefore,deemed-to-satisfy and avoidance-of-deterioration willagain be the practical approaches here.

As mentioned above, the fib and ISO committees didhave problems with recommending time-dependent mod-els for the rate of corrosion after the steel is depassivated.Even if such models for predicting the total volume of cor-rosion products exist, they have problems in distinguish-ing between concentrated corrosion (pitting) and corro-sion spread over a greater area with less severeconsequences.

16



8.5 Influence of cracks

Intuitively, we assume that cracked structures will deterio-rate faster than uncracked structures. However, neitherthe fib nor the ISO committee was able to come up withany general model to take this effect into account.

The committees therefore decided to stick to the sim-plified approach used by most operational concrete stan-dards today. This implies that corrosion of the reinforce-ment is not influenced by crack widths below a certainsize. Depending on the severity of the environment andsensitivity of the structure, this limiting crack width is nor-mally given as a characteristic value (5 % upper fractile) inthe range of 0.2 to 0.4 mm.

In harsh exposure conditions (e.g. exposure classesXD3/XS3 as defined in ISO 22965-1 [17] and EN 206-1), iffunctionality or structural integrity is affected, and if in-spection and possible intervention is impossible, an avoid-ance-of-deterioration approach is recommended.

8.6 Uncertainties in model and data

As engineers, we should be humble and accept that themodels we are applying are only approximations of howthe real thing operates. As with traditional structural de-sign, model uncertainties must be taken into account inour calculations, and their consequences should be re-duced if possible. We also have an inherent problem whentrying to characterize a structure’s long-term resistance byway of accelerated testing on young concrete specimens inthe laboratory. fib MC-2010 and ISO 16204 thereforewarn the user not to rely, uncritically, on predictions basedon laboratory tests involving specimens just a few monthsold extrapolated to the end of the design service life with-out taking due account of the uncertainties in both modeland data.

One obvious way of reducing these influences is touse the models to extrapolate observations from struc-tures exposed in the field for a certain period. The Norwe-gian code committee used this approach when verifyingthe present deemed-to-satisfy requirements given in theNorwegian standards.

Maage and Smeplass [18] analysed and extrapolatedin situ observations of carbonation in structures with anage of about one decade. Helland, Aarstein and Maage[19] analysed the remaining service life of 10 North Seaconcrete structures based on 180 chloride profiles takenafter 2 to 26 years of exposure (Figs. 6 and 7). Both studieswere carried out according to the models and principlesbased on LS (depassivation) and level of reliability as de-scribed for the full probabilistic method in MC-2010 andISO 16204.

9 Design assumptions concerning execution,maintenance and repair

Some important assumptions have to be made when de-signing a new structure (or redesigning an existing one).

The execution of the structure must ensure that thefinished work achieves the properties on which the designis based. The quality level for the workmanship, and thequality management regime at the construction site, must

therefore be at a certain level. fib MC-2010 and ISO 16204have therefore assumed that the minimum requirementsgiven in ISO 22966 “Execution of concrete structures”[20] are complied with. This standard is more or less iden-tical to its European counterpart EN 13670.

It should be stressed that any special requirementsregarding materials or execution that affect durability andare not already covered by the execution standard shouldbe communicated from the designer to the constructor aspart of the “execution specification”. It is further anticipat-ed that the completed structure will be subject to an in-spection.

It is advised that the design and construction be pro-vided with “as-built” documentation. The part of this doc-umentation containing the direct input parameters for theservice life design, and therefore acting as a basis for con-dition assessments during the service life, is often calledthe structure’s “birth certificate”.

If inspections reveal deviations from the specifica-tions outside the given tolerances, a non-conformityprocess should be initiated.

Fig. 6. Oseberg A platform in stormy weather [19]

Fig. 7. An inspector assessing the condition of a concrete shaft on a NorthSea petroleum installation [19]

17



The assumptions concerning following up the struc-ture during its use are given in fib MC-2010 in chapter 9“Conservation”, and in ISO 16204 as the series of stan-dards to be denoted ISO 16311 [21].

The ISO 16311 series for maintenance and repair ofconcrete structures is under development in ISO TC-71/SC-7, chaired by Prof. Tamon Ueda, one of the mainauthors of chapter 9 of fib MC-2010. This is another exam-ple of fib MC-2010 provisions being implemented in oper-ational ISO standards, and vice versa.

Another requirement is that the designer shouldcommunicate a “maintenance plan” to the organizationthat manages the structure. This plan should give the in-structions on those activities assumed during the design,which may include activities such as general cleaning, en-suring that the drainage system works, applying sealants atregular intervals, etc.

The design work should also result in an inspectionplan to be applied by the operator. This plan should state:– what types of inspection are required,– what components of the structure are to be inspected,– the frequency of the inspections,– the performance criteria to be met,– how to record the results, and– the actions to be taken in the event of non-conformity

with the performance criteria.

Since the reliability level on which the verification of thedesign is based is chosen on the basis of the possible con-sequences if the structure does not satisfy the relevantLS, the extent of inspections during the service life is veryimportant. If the structure will be subjected to frequentdetailed inspections by qualified personnel, deficiencieswill be noticed at an early stage, enabling strengthen-ing/repair of the structure. Severe consequences will thenbe avoided. On the other hand, if the structure will not besubjected to any inspections (the case with many founda-tions), the possible consequences of underperformancewill be much more severe. This must be reflected in thedesign.

10 Differences between fib MC SLD, fib MC-2010 andISO 16204

In this suite of documents, the MC SLD was the first stage.Due to its mission to introduce a new concept, it containsan extensive commentary as well as a number of informa-tive annexes giving examples of applications. These exam-ples have been very helpful for readers, but some have mis-interpreted the examples and regarded them as generallyvalid. Such misuse has caused some disappointments as itoften produced results that were regarded as unrealistic.Some in our community have also incorrectly associatedMC SLD only with the use of modelling using the fullprobabilistic method. It is for these reasons that there issome scepticism of the concept in the industry and thestandardization bodies.

In contrast to the fib MC SLD, fib MC-2010 is a gen-eral document covering all aspects of design, execution,conservation and dismantling. The various elements ofrelevance for service life design here are spread and dealtwith fully in parallel with structural design and design for

sustainability. The main element for service life design is,however, found in section 7.8 “Verification of limit statesassociated with durability”. fib MC-2010 does not includethe informative annexes of fib MC SLD, but refers to thisdocument for interested readers.

The text in fib MC-2010 is basically the same as inthe normative part of fib MC SLD, but has somewhat ma-tured based on experience with fib MC SLD and the factthat the core of the old fib TG.5.6 was reinforced withsome additional 25 experts in the ISO committee workingin parallel with fib SAG-5 preparing fib MC-2010.

ISO 16204 is close to an equivalent to the elementson service life design in fib MC-2010, but contains lesscommentary. Owing to the fact that ISO 16204 is an oper-ational standard, its scope also differs from that of fib MC-2010:

“This International Standard specifies principles andrecommends procedures for the verification of the dura-bility of concrete structures subject to:– known or foreseeable environmental actions causing

material deterioration ultimately leading to failure ofperformance;

– material deterioration without aggressiveness from the external environment of the structure, termed self-ageing.

NOTE The inclusion of, for example, chlorides [in] theconcrete mix might cause deterioration over timewithout the ingress of additional chlorides fromthe environment.

“This International Standard is intended for the use by na-tional standardization bodies when establishing or validat-ing their requirements for durability of concrete struc-tures. The standard may also be applied:– for the assessment of remaining service life of existing

structures; and– for the design of service life of new structures provided

quantified parameters on levels of reliability and designparameters are given in a national annex to this Interna-tional Standard;

“In annex E to ISO 16204 we have given guidance for thecontent of such a national annex.”

11 Further fib activities regarding service life design

Commission 5 “Structural service life aspects” is the primefib committee dealing with this theme.

The Task Groups currently working on documentsproviding direct support for fib MC-2010 and ISO 16204are:– TG.5.08 “Condition control and assessment of rein-

forced concrete structures exposed to corrosive environ-ment”

– TG.5.09 “Model technical specifications for repair andinterventions”

– TG.5.10 “Birth and rebirth certificates and through-lifemanagement aspects”

– TG.5.11 “Calibration of code deemed-to-satisfy provi-sions for durability”

– TG-5.13 “Operational documents to support service lifedesign”

18



12 Conclusion

fib MC-2010 considers the design of a concrete structurefor loadbearing capacity, service life and sustainability inparallel. The main author of the sustainability related ele-ments in MC-2010 is Prof. Koji Sakai. He is also the chair-man of the parallel ISO TC-71 subcommittee implement-ing these provisions in the ISO 13315 [22] suite ofstandards ensuring compatibility between these two setsof documents.

The design service life of a structure is the prime de-nominator in all calculations regarding cost and sustain-ability as applied by the owner and society.

As chairman of ISO TC-71/SC-3/WG-4, it is my hopethat the LS and reliability-based concept developed by fiband implemented by ISO will improve the present situa-tion and enable the industry to make more rational deci-sions. In Europe we have started the process of revisingour main concrete-related standards. The result is expect-ed to appear at the end of this decade.

The joint working group from CEN TC-104 (materi-als and execution) and TC-250/SC-2 (design) dealing withoverlapping issues have already taken this methodologyon board in their discussions. A similar intention to in-clude the fib/ISO methodology on service life design wasexpressed by TC-250/SC-2 when starting the process of re-vising EN 1992 [23]. It is the author’s hope that thismethodology will also be included in the “light” revision ofthe European standard for concrete production, EN 206,scheduled for 2013, thus enabling the 31 national stan-dardization bodies in the CEN community to make theirnational annexes more harmonized and transparent thanis the case today.

References

1. CEB/FIP Model Code 90. fib – fédération internationale dubéton, International Federation for Structural Concrete.Lausanne, 1993.

2. FIP/CEB Bulletin No 228. High Performance Concrete. Ex-tensions to the Model Code 90. fib – fédération interna-tionale du béton, International Federation for StructuralConcrete. Lausanne, 1995.

3. fib Bulletin No. 4. Light Weight Aggregate Concrete – part 1:Recommended extensions to Model Code 90. fib – fédéra-tion internationale du béton, International Federation forStructural Concrete. Lausanne, 2000.

4. fib Bulletin No 34. Model Code for Service Life Design. fib –fédération internationale du béton, International Federationfor Structural Concrete. Lausanne, 2006.

5. fib Bulletin No. 65. Model Code 2010, Final draft, vol. 1. fib– fédération internationale du béton, International Federa-tion for Structural Concrete. Lausanne, 2012.

6. fib Bulletin No. 66. Model Code 2010, Final draft, Volume 2.fib – fédération internationale du béton, International Feder-ation for Structural Concrete. Lausanne, 2012.

7. Walraven, J., Bigaj-van Vliet, A.: The 2010 fib Model Codefor concrete structures: a new approach to structural engi-neering. Structural Concrete, Journal of the fib, vol. 12, No.3, Sept 2011.

8. ISO 16204 Durability – Service Life Design of ConcreteStructures. International Organization for Standardization,Geneva, 2012.

9. WTO Agreement on Technical Barriers to Trade (TBT),Uruguay Round Agreement, World Trade Organization,https://www.wto.org/english/docs_e/legal_e/17-tbt_e.htm.

10. ISO 2394 General Principles on reliability for structures. In-ternational Organization for Standardization. Geneva, 1998.

11. EN 1990, Eurocode – Basis of structural design. CEN – Eu-ropean Committee for standardization, Brussels, 2002.

12. Harrison, T.: CEN/TR 15868 Survey of national require-ments used in conjunction with EN 206-1:2000. CEN – Eu-ropean Committee for standardization, Brussels, 2009.

13. EN 1992-1-1, Eurocode 2: Design of concrete structures –Part 1-1: General – Common rules and rules for buildings.CEN – European Committee for standardization, Brussels,2004.

14. EN 13670 Execution of concrete structures. CEN – Euro-pean Committee for standardization, Brussels, 2009.

15. EN 206-1 Concrete – Part 1: Specification, performance, pro-duction and conformity. CEN – European Committee forstandardization, Brussels, 2000.

16. Bamforth, P.: Enhancing reinforced concrete durability.Concrete Society Technical Report No. 61. The ConcreteSociety, 2004.

17. ISO 22965-1 Concrete – Part 1: Methods of specifying andguidance for the specifier. International Organization forStandardization, Geneva, 2007.

18. Maage, M., Smeplass, S.: Carbonation – A probabilistic ap-proach to derive provisions for EN 206-1. DuraNet, 3rdworkshop, Tromsø, Norway, June 2001. Reported in “Be-tongkonstruksjoners Livsløp”, report No. 19, NorwegianRoad Administration, Oslo, 2001.

19. Helland, S., Aarstein, R., Maage, M.: In-field performance ofNorth Sea offshore platforms with regard to chloride resis-tance. Structural Concrete, Journal of the fib, vol. 11, No. 2,June 2010.

20. ISO 22966 Execution of concrete structures. InternationalOrganization for Standardization, Geneva, 2009.

21. ISO/DIS 16311 Maintenance and repair of concrete struc-tures. International Organization for Standardization, Gene-va, 2011.

22. ISO 13315 Environmental management for concrete andconcrete structures. International Organization for Stan-dardization, Geneva, 2012.

23. CEN TC250/SC2 document N 833 Future developmentneeds in EN 1992’s. Secretariat, DIN, Berlin.

Steinar HellandSkanska Norge asPost box 1175Sentrum0107 OsloNorway


The fib Model Code 2010 for Concrete Structures introduces numerical simulation as a new tool for designing reinforced con-crete structures. The model of resistance based on non-linearanalysis requires adequate model validation and a global safetyformat for verifying designs. The numerical simulations combinedwith random sampling offer the chance of an advanced safety as-sessment. Approximate methods of global safety assessment arediscussed and compared in a case study. An example of a bridgedesign supported by non-linear analysis is shown.

Keywords: non-linear analysis, safety formats, reliability, fib Model Code 2010

1 Introduction

Advanced non-linear analysis is becoming a useful tool forthe design of new and assessment of existing structures.This development is influenced by the general impact ofinformation technologies on society and the economy.The fast-developing industry of concrete structures yieldsnew structural solutions, which are often verified by nu-merical simulations based on non-linear analysis and thefinite element method. Examples of such applications canbe observed in integral bridge structures [1] and nuclearpower plants [2]. This trend is confirmed by several recentconferences devoted to computational mechanics, such asEuro-C 2010 and WCCM 2012, where special sectionswere devoted to concrete structures. The subject was re-cently dealt with in fib Task Group 4.4 [3].

Non-linear finite element analysis can be used in thedesign of concrete structures as an alternative to linearanalysis. The concept has been developed within the fieldof computational mechanics with the aim of simulating re-al structural behaviour. Although it was initially used in re-search studies to support experimental investigations andexplain observed structural behaviour, it has recently be-come a powerful design tool.

In the design process, non-linear analysis offers theengineer a refined verification of a structural solution bysimulating structural response under design actions. Sucha simulation can be regarded as a virtual test and does notfit into the traditional scope of the design process. This is

mainly due to the basic differences between linear andnon-linear approaches. In traditional design, distributionof internal forces is carried out by linear analysis and safe-ty is checked locally in sections. There are two importantdiscrepancies worth mentioning in this approach. First,the elastic force distribution is one of the many possiblestates of equilibrium, which can be realistic at low loadlevels only. A significant force redistribution can occur dueto inelastic response. Second, the local section safetycheck of limit states is made under the assumption of non-linear material behaviour (cracking, reinforcement yield-ing, etc.), which is not consistent with the elastic analysisof internal forces. Furthermore, the local safety checkdoes not provide any information about overall structuralsafety. Nevertheless, this approach represents a very ro-bust design method verified through many years of experi-ence, and is the basis of the partial factor design conceptcurrently in use.

In order to support a more rational safety assess-ment, fib Model Code 2010 [4] reflects new developmentsin safety formats based on probabilistic methods. Chapter4 “Principles of structural design” introduces the proba-bilistic safety format as a general and rational basis forevaluating safety. In addition to the partial factor format,which remains as the main safety format for most practi-cal cases, a “global resistance format” is recommended fornon-linear analysis. Section 7.11 “Verification assisted bynumerical simulations” outlines a guide for using non-lin-ear analysis for assessing resistance. This paper illustratesthe background to these innovative approaches.

2 Numerical simulation

The finite element method is typically used for the numer-ical solutions to continuum problems. Depending on thetype of formulation (stiffness, compliance and mixedmethods), the results are, by definition, different from theexact solution. In the stiffness formulation a best possibleequilibrium is found for a given approximation (finite ele-ment type and size). The finite element solution shouldsatisfy the requirement of convergence to the exact solu-tion by reducing the element size (and increasing thenumber of degrees of freedom). Thus, irrespective of thematerial model, the approximations introduced solely bythe finite element formulation can be a significant sourceof errors in numerical analysis and these errors should be

Technical Paper

Reliability-based non-linear analysisaccording to fib Model Code 2010

Vladimir Cervenka DOI: 10.1002/suco.201200022


Submitted for review: 06 August 2012Revised: 20 November 2012Accepted for publication: 25 November 2012

adequately controlled. Non-linear analysis introduces ad-ditional effects, e.g. material behaviour approximation,large deformations (change of geometry), or time-depen-dent behaviour (e.g. creep). The most significant effect inconcrete structures is the material behaviour.

The principles of non-linear analysis are illustrated inFig. 1. The non-linear solution is performed by a predictor-corrector iterative process (variations of the Newton-Raphson method). In the predictor (1), the solution is esti-mated by a linear analysis based, optionally, on tangent orinitial material stiffness. The solution is improved in thecorrector (2), based on non-linear constitutive laws. The it-erative process is stopped when the difference betweenpredictor and corrector is acceptably small. Appropriate it-erative techniques can be employed for chosen specificconstitutive laws. A balanced approximation of numericalmethods involved in all parts of the model, i.e. in structur-al discretization, element formulation and material laws,should be maintained.

3 Constitutive models

The material models used for concrete, reinforcement andtheir interaction should capture all significant and rele-

20

V. Cervenka · Reliability-based non-linear analysis according to fib Model Code 2010


vant features of material behaviour for the problem underconsideration. Constitutive laws should be based on theprinciples of continuum and failure mechanics and mustensure the objectivity of the solution in the context of nu-merical methods.

Models for material softening, i.e. materials exhibit-ing a decrease in strength after reaching a certain ultimatestress value, should include appropriate regularizationtechniques in order to reduce the mesh sensitivity ofstrain-based formulations of constitutive laws. An exampleof such a technique is the crack band method used formodelling cracks in concrete as shown in Figs. 2 and 3. Adiscrete crack is modelled by a band of smeared cracks.Owing to the softening of the stress–crack opening law,the strain localizes in a narrow band of elements but re-mains evenly distributed within one element. The crackband model ensures that the fracture energy required forcrack formation is dissipated within the crack band. Thistechnique significantly reduces the mesh effect [6, 7]. Ex-amples of crack pattern simulations are shown in Fig. 4.

One important property of concrete is its sensitivityto the multi-axial stress state, i.e. a significant strength in-crease under hydrostatic stress, referred to as the confine-ment effect, see Figs. 5 and 6. Two well-known models re-

Fig. 1. Typical algorithm for non-linear finite element analysis Fig. 2. Model of fracture energy-based crack band

PP Load P [kN]

400

300

200

100

0.0.0 0.2 0.4 0.6Displacement [mm]

Pu=309 kN

sym

Fig. 3. Example of a crack band in a shear wall [5]

flecting this effect are those of Willam [9] and Ottosen[10]; both supply satisfactory results for a wide range ofconcrete strengths (including HSC).

In numerical implementations, various effects inter-act and, in general, can form a complex non-linear prob-lem. Therefore, a strain decomposition method, where thetotal strain is the sum of strains due to fracture, plasticity,creep, etc., is often used in order to solve this problem. Anexample of such a constitutive model is the fracture-plas-tic model proposed in [11].

Only the most significant concrete properties werementioned in the above discussion. However, there aresome additional properties that are important as well,such as modelling of interfaces between two concrete sur-faces, steel-concrete contacts, bond between reinforce-ment and concrete and reinforcement itself. All should beconsidered in practical applications.

4 Model validation

Numerical models are more complex than simplified engi-neering methods and the associated uncertainty is poten-tially high. Therefore, numerical models must be validated

21



to ensure adequate safety. Such a validation should coverthe whole range of inherent approximations: constitutivemodels, numerical discretization and structural solution.

Basic material tests serve to validate the constitutiverelations and are performed on simple structures, with theaim of reducing the influence of geometry and boundaryconditions under well-defined stress and strain conditions.Examples of such tests are compressive tests on concretecylinders, fracture tests on concrete prismatic specimenssubjected to three-point loading and tension stiffeningtests in uniaxial tension for reinforcing bars embedded inconcrete members. These tests are typically described incodes for materials testing, such as those recommended byRILEM.

The aim of structural tests is to validate the abilityof the algorithm or software to reproduce certain struc-tural behaviour objectively. This is often accomplished byway of benchmark calculations. For example, if a shearwall is to be simulated, then validating the software bymeans of shear wall experiments should be ensured. Suchstudies can be considered to be a rational basis for choos-ing adequate material models and software for a givenstructure.

Fig. 4. Crack pattern simulation of beams (test by Braam [8])

hydrostaticaxis

deviatoricplane

- 3

- 1

- 2

0τ

0σ

σ

σ

σ

Fig. 5. Concrete failure surface in 3D stress state

concrete 30

Compression

Eurocode 2

Tension

0 -100 -200 -300 -400

-800

-700

-600

-500

-400

-300

-200

-100

0

Stre

ngth

[Mpa

] 3

σ

Confining stress [Mpa] 2 = 1 σ σ

Fig. 6. Example of confinement effect modelled by the Menetrey-Willamyield function

Mesh sensitivity tests should be performed in orderto validate the finite element mesh of the numerical mod-el. At least three mesh cases with different element sizesshould be tested and their effect on the resistance evaluat-ed. In the case of a significant mesh sensitivity, when atleast two different mesh sizes do not provide sufficientlysimilar results, the numerical model should be consideredas not objective. An example of a mesh sensitivity study ofa shear panel tested by the author is shown in Fig. 7, (formore details see [3], p. 168). It can be seen that the meshrefinement has an opposite effect on resistance (stiffness)in the ranges of crack formation (increased stiffness) andmaximum load (reduced strength). Thus, the principlesfrom elastic analysis based on displacement methods,where refining the mesh always reduces the stiffness, can-not be simply extended into a non-linear analysis andshould be applied with caution.

The errors of non-linear solutions are controlled byconvergence criteria. The solution convergence is satisfiedwhen the error lies within prescribed limits. In the case ofthe stiffness method, the most significant convergence cri-terion is the error in the force equilibrium (residualforces). In addition, increments in displacements or theresidual energy can be checked. The choice of an ade-quate error tolerance is an important aspect of non-linear

22



analysis. The admissible errors must be appropriately val-idated, e.g. by a convergence study in which the results ob-tained with different tolerances are compared.

Finally, the model performance on the structural lev-el should be checked. It should prove the capability of thechosen numerical model to reproduce the structural be-haviour under consideration.

An example of validation based on a shear test from[7] is shown in Fig. 8. The beam size tested by Collins andYoshida [12] exceeds the usual beam dimensions(span = 12 m, depth = 2 m). The failure was dominated bybrittle response, which contributed to the size effect andwhich could be well reproduced by the numerical modelbased on fracture mechanics. More about this study willbe show later in the examples of application.

5 Global safety format and model uncertainty

The usual design condition is considered as

Fd < Rd (1)

where Fd is the design action and Rd is the design resis-tance and both these entities cover safety margins. In thisformulation the safety of loading and resistance are treat-

Experimental crack pattern Analysis, mesh M20, cracks andcompressive stress

0 1 2 3 4 5Displacement [mm]

Experiment

Mesh 5

Mesh 10

Mesh 20

140

120

100

80

60

40

20

0

Forc

e P

[kN

]

Fig. 7. How mesh size affects of shear panels

23



ed separately, which is a certain approximation comparedwith a general probabilistic approach. In design practice(based on the partial safety factors) we accept this simpli-fication and consider Fd = F(S,γG,γQ,γP,..) where the repre-sentative load S is factorized by partial safety factorsγG,γQ,γP,.. for permanent load, imposed load, prestressing,etc.

In non-linear analysis Rd describes the global resis-tance (e.g. set of forces representing an imposed load,horizontal load, etc.). Note that in the partial safety fac-tor method we assume failure probabilities of separatematerials but do not evaluate the failure probability onthe structural level. Unlike in sectional design, the globalresistance reflects an integral response of the whole struc-ture in which all material points (or cross-sections) inter-act. The safety margin can be expressed by the safety factor

(2)

where Rm is the mean resistance (sometimes referred to asnominal resistance). The global safety factor γR covers alluncertainties and can be related to the coefficient of vari-ation of resistance VR (assuming a log-normal distributionaccording to Eurocode 2) as

γR = exp(αRβVR) (3)

RR

dm

Rγ=

where αR is the sensitivity factor for resistance and β is thereliability index. It is recognized that variability included inVR depends on uncertainties due to various sources: materi-al properties, geometry and resistance model. They can betreated as random effects and analysed by probabilisticmethods. Owing to the statistical data available, the proba-bilistic treatment of materials and geometry can be per-formed in a rational way. However, a random treatment ofmodel uncertainties is more difficult because of limited data.A simplified formulation was proposed in fib Model Code2010, where the denominator on the right-hand side ofEq. (2) is a product of two factors: γR = γmγRd (which followsfrom the determination of partial safety factors in fib ModelCode 2010, section 4.5.2.2.3). The first factor γm is related tomaterial uncertainty and can be established by a probabilis-tic analysis. The second factor γRd is related to model andgeometrical uncertainties and recommended values are inthe range 1.05–1.1 (as suggested by Eurocode 2-2).

Recent investigations by Schlune et. al. [13] foundsuch values to be unsafe and proposed a more generalmethod in which the overall coefficient of resistance vari-ation can be determined as

(4)

where variability due to specific sources are identified: VG– geometry, Vm – material strength, VRd – model. This ap-

2 2 2V V V VR G m Rd= + +

Load

[kN

]500

450

400

350

300

250

200

150

100

50

00 1 2 3 4 5 6 7 8 9 10

Displacement [mm]

ATENA analysis

Experiment Y0

Fig. 8. Comparison of load-displacement diagrams and crack patterns of large beams

Fig. 9. Safety formats for design resistance

24



the resistance properties. The randomization can becarried out by two methods: (1) random variables,where the parameter is constant within a sample(structure) but changes between samples; (2) randomfields, where the parameter is randomly variable with-in a sample. A correlation of random variables shouldbe considered appropriately.

(3) Probabilistic analysis of resistance. This can be per-formed by the numerical method of the Monte Carlo-type of sampling, such as the LHS sampling method.The results of this analysis provide random parametersof resistance, e.g. mean, standard deviation, etc., andthe type of distribution function for resistance (PDF).

(4) Evaluation of design resistance based on the reliabilityindex β or probability of failure. In this, a design point isfound by extrapolating a point around a central regionbased on the probability distribution function (PDF).

The advantage of a full probabilistic analysis is that it is in-dependent of a failure mode. The potentially higher safetymargins of some failure modes, e.g. shear failure, is auto-matically included in the higher sensitivity of numericalresistance to a brittle failure. A disadvantage of this ap-proach [16] is that the target value of design resistance islocated in the tail of the PDF. This function is determinedby the best fit from the available, and the design value isobtained by extrapolation and heavily depends on thechoice of PDF. On the other hand, the approach is numer-ically robust, computationally efficient and feasible forpractical application.

5.2 ECOV method – estimate of coefficient of variation

A simplified probabilistic analysis was proposed by theauthor [15], in which the random variation of resistance isestimated using two samples only. It is based on the ideathat the random distribution of resistance, which is de-scribed by the coefficient of variation VR, can be estimat-ed from the mean Rm and characteristic Rk values of re-sistance. The underlying assumption is that randomdistribution of resistance is in accord with a log-normaldistribution, which is typical for structural resistance. Inthis case it is possible to express the coefficient of varia-tion as

(5)

The global safety factor γR of resistance is then estimatedusing Eq. (3).

Using the typical values β = 3.8 (50 years) andαR = 0.8 (which corresponds to the failure probability Pf= 0.001), the global resistance factor can be directly relatedto the estimated coefficient of variation VR as γR ≅exp(3.04 VR), and the design resistance is obtained fromEq. (2).

The key element in this method is the determinationof the mean and characteristic values of the resistance,Rm, Rk. It is proposed to estimate them using two separatenon-linear analyses employing the mean and characteris-tic values of input material parameters respectively.

11.65

lnVRRR

m

k=

⎛

⎝⎜⎞

⎠⎟

proach allows the inclusion of all uncertainties in a morerational way. Based on a survey of various blind bench-mark studies, Schlune et al. concluded that the model un-certainties of non-linear analysis are much higher than instandard design based on engineering formulas and arestrongly dependent on modes of failure. Reported coeffi-cients of variation due to model uncertainty for bendingfailure are in the range 5–30 %, and 15–64 % for shear.Schlune et al. concluded that due to the lack of data, thechoice of the model uncertainty often depends on engi-neering judgment and can be subjective. However, theseconclusions do not recognize the effect of model valida-tion, which can decrease model uncertainties. Further re-search is needed to recommend appropriate values of themodel uncertainty for numerical simulations.

The assessment of the design resistance according toEq. (1) can be achieved by various methods, ranging froma full probabilistic analysis to the partial factor method,which differ in the level of approximations involved.These safety formats are briefly characterized below andare illustrated in Fig. 9 by comparing how they representfailure probability.

5.1 Full probabilistic analysis

In general, probabilistic analysis is the most rational toolfor assessing the safety of structures. It can be further re-fined by introducing non-linear structural analysis as alimit state function. The numerical simulation resemblesreal tests on structures by considering a representativegroup of samples, which can be analysed statistically forassessing safety. An approach applied in [16] will only bebriefly outlined here. More information on probabilisticanalysis can be found in [17].

The probabilistic analysis of resistance is performedby the LHS method, in which the material input parame-ters are varied in a systematic way. The resulting array ofresistance values is approximated by a distribution func-tion of global resistance and describes the random varia-tion of resistance. Finally, for a required reliability index β,or probability of failure Pf, the value of design resistanceRd should be calculated.

However, full probabilistic analysis is computational-ly demanding and requires good information about ran-dom properties of input variables. It is usually applied inspecial cases where the consequences of failure justify theeffort.

Probabilistic analysis based on numerical simulationwith random sampling can be briefly described as follows:

(1) Formulation of a numerical model based on the non-linear finite element method. Such a model describesthe resistance function and can perform a determinis-tic analysis of resistance for a given set of input vari-ables.

(2) Randomization of input variables (material properties,dimensions, boundary conditions, etc.). This can alsoinclude some effects that are not in the action function(e.g. prestressing, dead load, etc.). Random materialproperties are defined by a random distribution typeand its parameters (mean, standard deviation, etc.).They describe the uncertainties due to the variation of

25



Table 1. Case study description

No. Description Scheme

1 Beam in bending

2 Deep beam in shear

3 Bridge pier

Railway bridge test

5 Beam in shear without ties

6 Beam in shear with ties

The method is general and the reliability level β anddistribution type can be changed if required. It reflects alltypes of failure. The sensitivity to random variation of allmaterial parameters is automatically included. Thus, thereis no need for special modifications to the concrete prop-erties in order to compensate for the greater random vari-ation of certain properties as in the next method, EN1992-2.

A similar and refined method with more samples wasproposed by Schlune et al. [13].

5.3 Method based on EN 1992-2

Eurocode 2 for bridges introduced a concept for verifyingglobal safety based on non-linear analysis. Design resis-tance is calculated from

Rd = R(fym, f∼cm…)/γR (6)

where fym, f∼cm are the mean values of the material para-

meters of steel reinforcement and concrete fym = 1.1 fykand f

∼cm = 0.843 fck. Note that the mean value for concrete

is reduced to account for the higher variability of the con-crete property. The global factor of resistance should beγR = 1.27. The evaluation of the resistance function is ac-complished using non-linear analysis assuming the materi-al parameters according to the above rules.

5.4 Partial safety factors (PSFs)

The method of partial safety factors, which is used in mostdesign codes, can be directly applied to global analysis inorder to obtain the design resistance Rd = R(fd). The de-sign values of the material parameters fd = fk/γM are usedhere, where fk are characteristic values and γM partial safe-ty factors for materials.

It can be argued that design values represent extremely low material properties, which in turn do notrepresent real material behaviour and can thus lead to distorted failure modes. On the other hand, this methoddirectly addresses the target design value and thus no extrapolation is involved. However, the probability of global resistance is not evaluated and is therefore notknown.

6 Case study and applications6.1 Case study for safety formats

The author has initiated investigations with the aim ofcomparing the various safety formats. The study com-prised the six cases described in Table 1. It included a widerange of structures, including simple beam, laboratory testof a shear wall, laboratory test of a deep beam, in situ testof a real bridge and a bridge pier design case. A variety offailure modes covered ductile bending mode, brittle shearmodes and a concrete compression mode. Details of thisinvestigation can be found in [15]. A summary of the re-sults is shown in Table 2. Three approximate methods,namely the partial safety factors (PSF) method based onthe estimate of coefficient or variation of resistance(ECOV) and the method according to EN 1992-2 are eval-uated. The table shows the ratio of resistances Rd found

26



by approximate methods to the full probabilistic analysis(which is considered as the most exact for this purpose). Itshould be noted that the study does not reflect the modeluncertainty in a consistent way. The PSF and EN 1992-2methods include the model uncertainty as given by theEurocode, whereas in the ECOV and full probabilisticanalysis it is not considered in order to simplify the com-parison. This could explain why the average results of theECOV method are slightly higher than the other two meth-ods.

The study confirmed the feasibility of the approxi-mate methods for the safety assessment. The ECOVmethod is preferred since it relates the safety to the resis-tance random variation and is considered more rationalwhen compared with the EN 1992-2 method.

Multiple failure modes, which are typical features ofreinforced concrete structures, are inherently included inthe numerical models and thus they are reflected in re-sults of analysis and resistance variability. Therefore, theapproximate methods of safety verification are generallyapplicable in design. In significant cases, if justified by theconsequences of failure, a full probabilistic analysisshould be applied.

6.2 Large shear beam

To illustrate this, two applications of design verification bynon-linear analysis will be shown. The first example ap-plies the safety formats discussed above to a large beamtested in the laboratory by Collins et al. [12] and alreadymentioned in Fig. 8. Its size is large and exceeds usualbeam dimensions (span = 12 m, depth = 2 m). The shearfailure is apparently influenced by its large size and is verybrittle. The comparison of resistances obtained by varioussafety formats is shown in Fig. 10, which also shows thevalues of design resistance obtained with EN 1992-1 andACI 318.

This case reveals two remarkable features of numeri-cal simulation. First, a refined constitutive modellingbased on fracture mechanics can capture the size effect ofbrittle shear failure and provide a safer model of resis-

Table 2. Case study of safety formats

Rd/Rdprob.

PSF ECOV EN 1992-2

Example 1 1.04 1.04 0.99bending

Example 2 1.02 1.04 1.0deep beam

Example 3 0.98 1.04 vbridge pier

Example 4 0.99 0.96 0.92bridge frame

Example 5 1.03 0.98 1.02shear beam Y0

Example 6 0.81 1.04 0.82shear beam Y4

average 0.98 1.01 0.95

27



tance. Second, the global safety formats offer consistentsafety margins for the design verification.

6.3 Box girder bridge

The bridge over the River Berounka on the recentlyopened ring road around the city of Prague was designedwith the help of numerical simulation. It is a box girder in-tegral structure with complex geometry curved in three di-mensions and supported on slender piers. During con-struction stages when the girder was not yet integrallyconnected with other spans, it was very sensitive to stabil-ity conditions, see Fig. 11. The safety of construction phas-es was verified by numerical simulation and global safetyformat.

For illustration only, a result of the load case withproportionally increased uniform load is presented inFig. 12, showing cracks and plastic deformations. Thishelps to identify a mode of failure reached at the ultimatelimit state. The evidence of structural resistance is provid-ed by a load–displacement diagram (Fig. 13). The relativeload on the vertical axis is a non-dimensional overloading parameter representing the global safety factor γR fromEq. (2). In this case the analysis confirmed the safety fac-

tor γR = 1.7, which is well above the value of 1.27 requiredby the code. The global safety factors obtained for the oth-er load histories due to the construction phases of the bal-anced cantilever method were 6.2 for wind action and 5.5for formwork action during the cantilever construction. Asufficient safety margin was confirmed for all stages ofconstruction.

The shape of a descending branch in the load-dis-placement diagram provides additional information aboutthe ductile nature of the failure, which is an importantmeasure of robustness. The case observed indicates a rela-tively brittle behaviour, which in this case is due to a com-pressive failure of the concrete, which occurs in the boxgirder following cable yielding and excessive rotation, andin some load cases in the concrete of the pier. More de-tails can be found in [1].

Fig. 10. Comparison of safety margins in shear failure

Fig. 11. Bridge under construction, built using the balanced cantilevermethod

Fig. 12. Cracks and plastic strains at maximum uniform load

Fig. 13. Load-displacement diagram for bridge during construction

7 Closing remarks

Verification by numerical simulation is a powerful tool forthe design of concrete structures. It extends the range ofapplication beyond the scope of engineering methodsbased on the elastic distribution of internal forces andcross-section safety check. Owing to its general approach,it overcomes the limits of standard design based on beamsand columns. On the other hand, it introduces potentiallyhigher model uncertainties. Therefore, the model valida-tion becomes an important requirement for its applicationin engineering practice.

fib Model Code 2010 outlines the framework of limitstate verification by numerical simulations and introducesthe global safety formats suggested for this purpose.

Further research is needed in order to improve theguide for the validation of numerical models and the clas-sification of model uncertainties.

Acknowledgements

The author would like to acknowledge the fruitful cooper-ation of the colleagues who contributed to the new fibModel Code. The financial support of Czech ScienceFoundation project P105/12/2051 is greatly appreciated.

References

1. Cervenka, V., Cervenka, J., Sistek, M.: Verification of globalsafety assisted by numerical simulation. fib Symposium,Prague, 8–10 June 2011.

2. Cervenka, J., Proske, D., Kurmann, D., Cervenka, V.:Pushover analysis of nuclear power plant structures. fib Sym-posium, Stockholm, 11–14 June 2012, pp. 245–248, ISBN978-91-980098-1.

3. Foster, S. (ed.), Maekawa, K. (convenor), Vecchio, F. (deputychair): Practitioners’ guide to finite element modelling of re-inforced concrete structures. State of the art report by fibTask Group 4.4, Bulletin No. 45, 2008, ISBN 987-3-88394-085-7.

4. Walraven, J. (convener): Model Code 2010. Final draft, vols.1 & 2, 2012. fib Bulletin Nos. 65 & 66, ISBN 978-2-88394-105-2.

5. Asin, M.: The Behaviour of Reinforced Concrete ContinuousDeep Beams. PhD dissertation, Delft University Press,Netherlands, 1999, ISBN 90-407-2012-6.

6. Cervenka, V., Pukl, R., Ozbold, J., Eligehausen, R.: MeshSensitivity Effects in Smeared Finite Element Analysis ofConcrete Fracture, Proc. Fracture Mechanics of ConcreteStructure II, (FRAMCOS 2), Wittmann, F. H. (ed.). Zurich,25–28 July 1995, vol. II, pp. 1387–1396, ISBN 3-905088-12-6.

28



7. Cervenka, J., Cervenka,V.: On the uniqueness of numericalsolutions of shear failure of deep concrete beams: compari-son of smeared and discrete crack approaches. EURO-C2010. Computational Modeling of Concrete structures –Bicanic et. al. (eds.). Taylor & Francis Group, London, ISBN978-0-415-58479-1.

8. Braam C. R.: Control of crack width in deep reinforcedbeams. Heron 4 (35), 1990.

9. Menétrey, P., Willam, K. J.: Triaxial failure criterion for con-crete and its generalization. ACI Structural Journal 92 (3),pp. 311–318.

10. Ottosen, N.: A Failure Criterion for Concrete, Journal Engi-neering Mechanics Division, ASCE, vol. 103, EM4, Aug1977.

11. Cervenka, J., Pappanikolaou, V.: Three-dimensional com-bined fracture-plastic material model for concrete. Int. J. ofPlasticity, vol. 24, 12, 2008, pp. 2192–2220, ISSN 0749-6419.

12. Yoshida, Y.: Shear Reinforcement for Large Lightly Rein-forced Concrete Members, MS thesis under supervision ofProf. Collins, University of Toronto, 2000.

13. Schlune, H., Plos, M., Gylltoft, K.: Safety Formats for Non-linear Analysis of Concrete Structures. Engineering Struc-tures, Elsevier, vol. 33, No. 8, Aug 2011.

14. Novak, D., Vorechovsky, M., Lehky, D., Rusina, R., Pukl, R.,Cervenka, V.: Stochastic nonlinear fracture mechanics finiteelement analysis of concrete structures. Proceedings of 9thInt. conf. on Structural Safety & Reliability, Icossar, Rome,2005.

15. Cervenka, V.: Global Safety Format for Nonlinear Calcula-tion of Reinforced Concrete. Beton- und Stahlbetonbau 103(2008), special edition, Ernst & Sohn, pp. 37–42.

16. Cervenka, V. (ed.): SARA – Structural Analysis and Reliabili-ty Assessment. User’s manual. Cervenka Consulting, Prague,2003.

17. Vrouvenwelder, A. C. W. M.: Conclusions of the JCSS Work-shop on Semi-probabilistic FEM calculations, Delft, 1–2 Dec2009.

Vladimir Cervenka,President, Cervenka ConsultingNa Hrebenkach 55, 15000 Prague 5, Czech RepublicTel. +420 220 610 018, e-mail: [email protected]


Semi-probabilistic safety formats for the non-linear analysis ofreinforced concrete structures are of practical interest for struc-tural designers. The safety format proposed in EN 1992-2 enablesa safety assessment through a non-linear structural analysis andthe application of a global safety factor, which is defined as theratio between the representative and design values of the materi-al resistances. A more realistic estimate of the global safety fac-tor can be obtained from the distribution of the structural re-sponse. This paper proposes a safety format based on the meanvalues of the material resistances and a global resistance factor.Its practical application in the structural design of concretebeams and columns is also presented.

Keywords: safety format, non-linear analysis, reinforced concrete structures,global resistance factors, Monte Carlo method

1 Introduction

According to EN 1990 [1], the verification of structuresagainst failure due to lack of structural resistance is indi-cated at section level by the following inequality:

Ed ≤ Rd (1)

where Ed is the design value of the effects of actions andRd the corresponding resistance. EN 1992-1-1 [2] allowsthe designer of concrete structures to determine the de-sign value Ed by means of a linear elastic analysis, a linearelastic analysis with limited redistribution or a non-linearanalysis. The non-linear analysis is the most accuratemethod of those proposed because it makes use of the re-alistic constitutive laws of the materials and is based onthe concepts of equilibrium and compatibility of deforma-tions. Furthermore, it can be used to predict the structuralresponse at each load level, from serviceability to ultimateconditions.

As observed in [3], the non-linear analysis of concretestructures should be performed using the mean values of

the material resistances. The comparison of experimentalcould occur tests and non-linear finite element analyseshas shown that the actual structural behaviour can be re-produced only if the mean values of the material proper-ties are considered in the structural analysis. The use ofthe design values in the structural analysis leads to an er-roneous assessment of the load bearing capacity; for ex-ample, an unrealistic redistribution of internal actionscould occur in the case of beams. An even worse effectcould be observed in the case of slender columns. In fact,the design values of the material properties lead to anoverestimation of the deformability of a structure.

So for the sake of the accuracy of the distribution ofinternal forces, the term Ed should be estimated with themean values, whereas the semi-probabilistic approach re-quires an assessment of the resistance Rd using the designvalues. Therefore, the left- and right-hand sides of Eq. (1)should be determined using different values for the mater-ial properties.

Several safety formats have been proposed to solvethis inconsistency. A safety format based on the mean val-ues of the material resistances and a safety check in thedomain of the internal actions are proposed in this paper.The safety format is intended to be consistent with the Eurocodes. The procedure is developed and applied tobeams and columns subjected to a combination of axialforce and bending moment.

The safety formats already available in the literatureare analysed first. This is followed by a description of thenew proposal. Finally, examples of applications are pre-sented.

2 Safety formats in fib Model Code 2010

The design condition used in the safety format for non-lin-ear analysis proposed in fib Model Code 2010 [4] is writtenin the domain of the actions:

Fd ≤ Rd (2)

where Fd is the design value of the actions and Rd the de-sign resistance. Three different approaches can be usedfor evaluating the resistance Rd in Eq. (2):– the probabilistic method– the global resistance methods– the partial factor method

Technical Papers

Global safety format for non-linear analysisof reinforced concrete structures

Diego Lorenzo Allaix*Vincenzo Ilario CarboneGiuseppe Mancini

DOI: 10.1002/suco.201200017

* Corresponding author: [email protected]

Submitted for review: 17 July 2012Revised: 20 September 2012Accepted for publication: 30 September 2012

2.1 Probabilistic method

The design value Rd of the actual resistance is derivedfrom the distribution of the resistance R of the structure,which can be represented by the ultimate load. In generalterms, the design value Rd is expressed as

(3)

whereR resistance predicted by a mechanical modelαR resistance sensitivity factorβ reliability indexγRd model uncertainty factor.

As an example, the values αR = 0.8, β = 3.8 and γRd = 1.06 can be considered for the ultimate limit states,moderate consequences of failure and a reference periodof 50 years [1]. The two-parameter log-normal distributionis normally used to model the resistance of concrete struc-tures. Hence, Eq. (3) may be rewritten as

(4)

where μR and VR are the mean value and the coefficient ofvariation of the distribution respectively of the resistancepredicted by the model. These two parameters can be esti-mated by means of a Monte Carlo simulation. As de-scribed in [4], the probabilistic assessment of the structur-al resistance is based on two models; a non-linear finiteelement model is suggested to represent the response ofthe structure and a probabilistic model is required to ac-count for the uncertainty of the model parameters, e.g.material properties, geometrical dimensions, boundaryconditions, or other effects, e.g. prestressing.

2.2 Global resistance methods

The aim of the global resistance methods is to estimate thedesign resistance Rd by dividing the resistance computedwith properly chosen representative values frep for the ma-terial resistances and the global resistance factor γR:

(5)

Two alternative methods are mentioned in [4]: the globalresistance factor method and the method of estimating acoefficient of variation of resistance (ECOV). These meth-ods differ in their derivation of the global resistance factor.

In the former, the global resistance factor is definedas the ratio between the representative and the design val-ues of the material properties. The mean value of the yieldstress fym is considered for the reinforcing steel:

fym = 1.1 fyk (6)

where fyk is the characteristic yield stress. A reduced valuefcmd for the concrete compressive strength is used to takeinto account a reduction in the material resistance due toconcrete uncertainty:

1

RR

dR

Rd

Φ α βγ( )

=−⎡

⎣⎤⎦

−

μ α βγ( )

=−

RV

dR R R

Rd

exp

RR f

drep

R Rdγ γ( )

=

30

D. L. Allaix/V. I. Carbone/G. Mancini · Global safety format for non-linear analysis of reinforced concrete structures


fcmd = 0.85 fck (7)

where fck is the characteristic compressive strength. A value of 1.2 is proposed in [4] for the global resistance fac-tor γR.

In the ECOV method, the global resistance factor isestimated from

γR = exp(αRβVR) (8)

This relationship, too, relies on the hypothesis that the re-sistance R is modelled by a log-normal random variable.The coefficient of variation VR of the resistance is estimat-ed by means of two non-linear analyses performed usingthe mean and characteristic values of the material resis-tances. The coefficient of variation VR is derived under thehypothesis that the resistance follows a two-parameter log-normal distribution:

(9)

where Rm and Rk are the values of the structural resis-tance based on the mean and characteristic values of thematerial resistances respectively. The design resistance isthen calculated from

(10)

Although not included in fib Model Code 2010, the safetyformat proposed by Schlune et al. [5, 6] could be consid-ered as an improved ECOV method. Schlune et al. presentan investigation concerning beam sections subjected to acombination of bending moments and shear forces. Thedesign resistance Rd is derived from the global resistancefactor γR and the resistance is computed using the meanyield stress of the steel fym, the mean in situ concrete com-pressive strength fcm,is and the nominal values of the geo-metrical dimensions anom:

(11)

where:

(12)

and θm is the bias factor, which is defined as the mean ratio of experimental to predicted resistance. Its valuevaries between 0.7 and 1.2 for failure in compression,bending and shear. It is important to note the distinctionbetween the bias factor θm and the model uncertainty factor γRd, although both take into account model uncer-tainties.

Firstly, they correspond to different fractiles of thecorresponding distribution. The bias factor is a mean value, whereas the model uncertainty factor is a designvalue.

Secondly, they describe different types of uncertain-ties. The bias factor is directly related to the difference be-

11.65

lnVRRR

m

k=

⎛

⎝⎜⎞

⎠⎟

RR

dm

R Rdγ γ=

, ,,R

R f f ad

ym cm is nom

Rγ( )

=

exp VR

R R

mγ

α βθ( )

=

31



tween the experimental and the model results. The modeluncertainty factor also takes into account uncertainties re-lated to the position of the reinforcing bars in concretemembers.

The coefficient of variation VR is written by Schluneet al. [5] as follows:

(13)

where Vg, Vm and Vf are the coefficients of variation of thegeometrical, model and material uncertainties respective-ly. Suggestions for Vg and Vm are also proposed in [5, 6].When the main material parameters are the concrete com-pressive strength and the yield stress of the steel, the coef-ficient of variation Vf can be estimated by means of

(14)

whereσfc, σfy standard deviations of the concrete compres-

sive strength and the yield stress of the steel re-spectively

Δfc, Δfy finite variations of the material resistancesRΔfc, RΔfy results of non-linear analyses performed using

the values fcm – Δfc for the concrete compres-sive strength and fym – Δfy for the yield stress

The coefficient of variation VR can be estimated by meansof three non-linear analyses: one performed with the meanvalues of the material resistances, the other two with thevalues fcm – Δfc and fym – Δfy. As observed in [8], the para-meters Δfc and Δfy should be chosen with particular carein order to avoid unsafe results.

The most important improvement in this methodwith respect to the ECOV method is that the uncertaintyrelated to the numerical model can be taken into accountdirectly. This model uncertainty is taken into account inboth the numerator and the denominator of Eq. (12),which defines the global resistance factor γR.

As observed in [7], these two approaches lead to de-sign resistance values that do not differ significantly fromthe results of the probabilistic method.

2.3 Partial factor method

According to this method, the design resistance Rd is esti-mated by means of a non-linear analysis with the designvalues of the material resistances. However, it was men-tioned in the introduction that the choice of the designvalues should be avoided when evaluating the left-handside of Eq. (1) [3].

3 Safety format in EN 1992-2

According to the safety format proposed in EN 1992-2 [8],a non-linear analysis is performed using the following as-sumptions for the material properties. The concrete incompression is described by the Sargin constitutive law,assuming

2 2 2V V V VR g m f= + +

2

2

2

2

V

R R

f

R R

f

Rf

m f

cfc

m f

yfy

m

c y

Δσ

Δσ

≈

−⎛

⎝⎜⎜

⎞

⎠⎟⎟

+−⎛

⎝⎜⎜

⎞

⎠⎟⎟

Δ Δ

fc,rep = 0.843 fck (15)

as the compressive resistance value. A bilinear constitutivelaw is adopted for the reinforcing steel. The mean valuesof the yield stress fym and the tensile strength ftm are

fym = 1.1 fyk (16)

ftm = 1.1 ftk (17)

where fyk and ftk are the characteristic values of the yieldstress and tensile strength respectively. Once the non-lin-ear analysis has been performed, the following inequalityin terms of external and internal actions is checked for thecritical regions of the structure:

(18)

The left-hand side is the load effect evaluated for the de-sign load, where γG and γQ are the partial factors to be ap-plied to the characteristic values of the permanent actionsGk and variable actions Qk respectively. The resistance Rcorresponding to the load effect E is evaluated at the loadlevel qu/γO, where qu is the ultimate load level and γO isthe global safety factor. Suggested values for γO and γRdare 1.20 and 1.06 respectively [8]. Alternatively, the safetycheck can be written as

(19)

where γO′ = γO γRd = 1.27 [8]. The inequality (18) can be also rewritten as follows:

(20)

where γEd is the load effect uncertainty factor and γg and γqare the partial factors for the permanent and variable ac-tions respectively.

Concerning the evaluation of the action effects Ed, itshould be noted that the expression Eq. (20) is the mostgeneral. The relationships of Eqs. (18) and (19) are ap-proximations that may be unsafe if the action effects areunder-proportional functions of the actions [9].

Fig. 1 shows an application of this safety format forthe case of a scalar problem (i.e. beam in bending) usingEq. (19).

The term R(qu/γO′) is the point on the internal ac-tions path corresponding to the load level qu/γO′. Thestructure is safe if the point on the internal path at loadlevel γGGk + γQQk is below the point corresponding toR(qu/γO′).

The value γO′ = 1.27 is proposed in EN 1992-2 [8].This value is obtained as the ratio of the representative tothe design values of the material resistances. In the case ofconcrete failure

E G QR

q

G k Q k

u

O

Rdγ γ

γγ( )+ ≤

⎛

⎝⎜⎞

⎠⎟

γ γγ( )+ ≤

′⎛

⎝⎜⎞

⎠⎟E G Q R

qG k Q k

u

O

E G QR

q

Ed g k q k

u

O

Rdγ γ γ

γγ( )+ ≤

⎛

⎝⎜⎞

⎠⎟

(21)

and in the case of steel failure

(22)

the value of γO′ is not differentiated with respect to thelimit state condition and type of failure. This compromisehas the practical advantage that a single global safety fac-tor has to be applied to the resistance R.

4 Discussion

Four safety formats for the non-linear analysis of concretestructures were presented in sections 2 and 3. The safetyformats differ in terms of the values of the material prop-erties used in the calculations and in terms of the domainwhere the safety check is performed.

A new safety format, which could be used in the con-text of the Eurocodes, is proposed below. Therefore, theproposal should be consistent with the EN 1990 [1]. In thestructural design according to the STR limit state, the de-signer has to check that Eq. (1) is fulfilled. Hence, the pro-posed safety format is based on comparing the action ef-fects and corresponding resistances, as in the approach ofEN 1992-2 [6].

Concerning the material properties, the mean valuesof the resistances of steel and concrete should be used inthe non-linear analysis in accordance with the suggestionsof the CEB [3].

A comment is necessary regarding the global safetyfactor (or global resistance factor). The global safety factorused in EN 1992-2 is defined as the ratio between the rep-resentative values and the design values of the materialproperties. It would be more appropriate to derive this fac-tor from the resistance at cross-section level or from theload-carrying capacity of the structure.

γ = = ≈′f

ff

fOc rep

cd

ck

ck

0.843

1.5

1.27,

γ = = ≈′f

f

f

fOym

yd

yk

yk

1.1

1.15

1.27

32



Following this idea, the probabilistic derivation ofthe global resistance factor γR has been developed in a fewresearch papers [10–13]. This factor takes into account theeffect of the uncertainties of the structural parameters onthe global response and possibly the uncertainties relatedto the resistance model. For example, global resistancefactors for reinforced concrete beams and columns havebeen derived recently [10–12] considering the axial forceand bending moment resistance of the cross-section. Alter -natively, the global resistance factor can be estimated in terms of the ultimate load level [13]. This approach isrealistic because it also takes into account the type of failure.

5 Safety format based on mean values of materialresistances

The safety format proposed in the present paper is basedon the mean values of the material resistances and verify-ing safety in the domain of the internal actions. In order tobe easily applicable, the safety format is based on the glob-al resistance method.

The design resistance Rd is evaluated as follows:

(23)

where qum is the ultimate load level reached in a non-lin-ear analysis performed with the mean values of the mater-ial resistances. The global resistance factor γR is defined asthe ratio between the mean value and the design value ofthe distribution of the ultimate load level:

(24)

In the derivation of the global resistance factor γR it hasbeen assumed that the mean value μqu of the ultimate loadlevel can be approximated by the ultimate load level qumcomputed using the mean values of the material resis-tances. This assumption is an approximation because itcorresponds to the truncation at the first term of the Tay-lor series expansion of the ultimate load level about themean values of the material resistances:

(25)

where Xi is one of the material resistances. Although qumis an approximation of μqu, the assumption is of practicaluse for designers.

Considering that the resistance of reinforced con-crete members can be described by a two-parameter log-normal distribution, the design value qud is approximatedby

qud = μqu exp(–αRβ Vqu) (26)

RR

q

d

um

R

Rd

γγ

=

⎛

⎝⎜⎞

⎠⎟

qRqu

udγ

μ=

X

X

X

X

12

1

11

2

q q XqX

X Xq

X X

u um i Xu

ii

n

i X j Xj

n

i

nu

i j

i

i j…

∑

∑∑

μ

μ μ

( )

( )

= + −∂∂

+ − −⎛⎝

⎞⎠

∂∂ ∂

+

μμ

μμ

==

== =

Fig. 1. Application of the safety format of EN1992-2.

33



Therefore, the global resistance factor γR can be easily de-rived from the coefficient of variation Vqu:

γR = exp(αRβ Vqu) ≈ exp(3.04 Vqu) (27)

The coefficient of variation Vqu is estimated here using theMonte Carlo method. A non-linear analysis up to failure isperformed using an FE model for each sample of the ran-dom variables in order to obtain the ultimate load qu.

The results of the investigation heavily depend onthe assumptions underlying the models used in the non-linear analysis. Clearly, the approach is meaningful if thestructural model covers all relevant failure mechanisms.It is suggested to make reference to EN 1992-1-1 [2] andEN 1992-2 [8] for the constitutive laws and models forspecific situations, e.g. structures where the second-ordereffects are not negligible. In the case of beams andcolumns, the proper choice is to use the Sargin law forconcrete in compression and a bilinear constitutive lawwith inclined top branch.

The probabilistic model used for the uncertaintyanalysis of the structural response mainly covers the ma-terial resistances (concrete compressive strength, yieldstress and tensile strength of steel) and the model uncer-tainties. A probabilistic characterization of the geometri-cal dimensions of the cross-section and the positions ofthe reinforcing bars could also be considered.

The safety check becomes

(28)

The model uncertainty factor γRd is applied to the resis-

tance . According to the simplified level II

method [14], the limit state function concerning a ULSproblem is written as

g(X,ϑR,ϑE) = ϑRR(X) – ϑEE(X) (29)

where X is the vector of random parameters and ϑR andϑE are the resistance and load effects uncertainties respec-tively. As can be seen, these model uncertainties multiplythe resistance R and the load effects E.

Furthermore, the model uncertainty factor γRdshould account for the difference between the real behav-iour of a structure and the results of its numerical model.Therefore, its value should be derived from the compari-son of experimental tests and numerical calculations. Giv-en the distribution of the resistance model uncertainty ϑR,the model uncertainty factor γRd can be derived using thefollowing expression [14]:

(30)

where α∼R = 0.4αR = 0.32 is the sensitivity factor for the re-

sistance model uncertainty and VϑR is the coefficient ofvariation of the resistance model uncertainty ϑR.

E G QR

q

Ed g k q k

um

R

Rdγ γ γ

γγ( )+ ≤

⎛

⎝⎜⎞

⎠⎟

Rqum

Rγ⎛

⎝⎜⎞

⎠⎟

γα β( )=

− ϑVRdR R

1exp �

In accordance with EN 1990 [1], the safety check canbe rewritten as

(31)

or

(32)

The comparison between the action effects and the resis-tance in Eqs. (28), (31) and (32) automatically takes intoaccount the structural behaviour. The internal actionspath allows the designer to understand the structural be-haviour, including the redistribution of internal actions.

Concerning the evaluation of the actions effects Ed,the relationships of Eqs. (31) and (32) are an approxima-tion of Eq. (28), which may be unsafe if the action effectsare an under-proportional function of the actions [9].

The global resistance factor γR′ can be estimatedfrom the distribution of the actual ultimate load qu′:

qu′ = ϑRqu (33)

The coefficient of variation Vqu′ of the distribution of qu′can be estimated by means of a set of Monte Carlo simu-lations that explicitly include the resistance model uncer-tainty. Assuming that qu and ϑR are independent randomvariables, then the coefficient of variation Vqu′ can be ap-proximated as

(34)

The global resistance factor γR′ is derived as follows:

(35)

Alternatively, γR′ can be written as follows [1]:

γR′ = γRdγR (36)

where γRd is defined in Eq. (30) and γR in Eq. (27). Theglobal resistance factor γR′ can be expressed in terms ofthe coefficients of variation Vqu and VϑR:

γR′ = exp(α∼RβVϑR)exp(αRβVqu

) (37)

Eqs. (35) and (37) lead to slightly different expressions ofthe global resistance factor γR′. Eq. (35) is derived from thedistribution of the actual ultimate load qu′. Hence, the un-certainties related to the resistance model uncertainty ϑRand the ultimate load qu are taken into account accordingto Eq. (34).

A simplified approach is presented in Eq. (37), whichseparates the effects of the resistance model uncertaintyand the ultimate load on the global resistance factor. Giv-en the probabilistic characterization of the resistancemodel uncertainty, the contribution of γRd to γR′ is thesame irrespective of the uncertainty related to the ultimate

E G QR

q

G k Q k

um

R

Rdγ γ

γγ( )+ ≤

⎛

⎝⎜⎞

⎠⎟

γ γγ( )+ ≤

′⎛

⎝⎜⎞

⎠⎟E G Q R

qG k Q k

um

R

≈ +ϑ′V V Vq qu R u

2 2

γ α β α β( )′ = = +⎛⎝⎜

⎞⎠⎟ϑ′V V VR R q R qu R u

exp exp 2 2

load. The advantage of this approach is that it is straight-forward if global resistance factors have to be estimatedfor a class of structures, for examples according to the sim-plified level II approach [14].

The model uncertainty in Eq. (33) is related to the es-timation of the ultimate load by means of a non-linearanalysis. It has been observed [7] that the difference be-tween the results of FE models and experimental testsheavily depends on the type of structural problem and themodelling approach chosen. As discussed in [8], insuffi-cient data are available for quantifying the modelling un-certainty related to the results of a non-linear analysis inorder to establish a probabilistic model. In the present pa-per, the uncertainty concerning the resistance model inEq. (29) is also used for the ultimate load.

In the following section it is shown that the global re-sistance factors can be related to the critical regions of thestructure, for concrete beams and columns subjected toaxial force and bending moment. The case of a single fail-ure mode is considered.

5.1 Continuous beams

A comparison between the values of the global resistancefactors γR and γR′ obtained with respect to the distributionof the resistance at section and structure levels is pro-posed for a two-span continuous beam (Fig. 2).

The structure is loaded by a permanent load gk = 28kN/m and a variable load qk = 12 kN/m. The beam is de-signed using C25 concrete and S500reinforcing steel. Thecross-section is rectangular with a width b = 0.30 m anddepth h = 0.45 m (Fig. 3). The reinforcement areas havebeen designed using a linear elastic analysis, leading to theareas As = 710 mm2 and As′ = 1137 mm2.

34



The global resistance factors are estimated with theMonte Carlo method. For each sample, a non-linear analy-sis up to failure is performed using an FE model in orderto obtain the ultimate load (structural resistance). More-over, the resisting bending moment (sectional resistance)at the critical cross-section (inner support section) is alsoevaluated. The coefficients of variation of the distribu-tions of the ultimate load and resisting bending momentare computed at the end of the simulations. Two simula-tions are performed, as explained in the previous section.In the first one, the resistance model uncertainty is not in-cluded in the probabilistic model in order to assess γR. Inthe second one, the model uncertainty is modelled as arandom variable in order to estimate γR′.

A probabilistic model is derived from [15] for thecompressive strength of the concrete, the yield stress andtensile strength of the steel and the resistance model un-certainty. Details of the probabilistic model are given inTable 1.

The results of the investigation are shown in Table 2.The mean value μ, the standard deviation σ and the coef-ficient of variation V are estimated for the ultimate loadand the resisting bending moment. The global resistanceγR is evaluated with Eq. (27). In the case of the resistingbending moment, the coefficient of variation of the distri-bution of the ultimate load is replaced by the coefficient ofvariation of the resisting bending moment. The global re-sistance γR′ is evaluated in the same way as γR, but the re-sisting model uncertainty ϑR is considered directly in theMonte Carlo simulations, as expressed in Eq. (33).

It can be seen that the coefficients of variation of thedistributions of the ultimate load and resisting bendingmoment coincide. Therefore, the global resistance factorsγR and γR′ have the same value. This means that the struc-tural behaviour, in terms of redistribution of internal ac-tions, does not affect the global resistance factor. This fac-tor is only influenced by the material non-linearityconcerning the critical section, where failure occurs.

A parametric analysis of the global resistance factorγR′ has been performed for a section subjected to a bend-ing moment with respect to the amount of reinforcementarea. It was assumed that failure occurs with crushing ofthe concrete while the bottom reinforcement is in the plas-

Fig. 2. Structural scheme.

Fig. 3. Cross-section.

increment in the resultant F for the bottom reinforcementin order to satisfy equilibrium of internal forces, as shownin Fig. 7. If a reinforcement ratio equal or larger than 1.5 %is adopted, the size of the concrete compression zonereaching the peak stress fc increases. Hence, the smallincrement in C is due to the gradual broadening of thearea of the cross-section with a concrete deformation lessthan –0.002. Moreover, the distance bc decreases in themean value for the same reason.

In terms of the standard deviation of the resultant C,a more significant increment can be observed between thereinforcement ratios ρ = 1.5 % and ρ = 4.0 % (see Fig. 8).As previously mentioned, an increment in the reinforce-ment ratio leads to a larger number of fibres with deforma-tion less than –0.002. Consequently, the standard devia-tion of C increases. An increment in the standarddeviation of distance bc is observed at the same time. Thecoupling between the behaviour of the standard deviationof resultant C and the distance bc explains the incrementin the standard deviation of the contribution MC to the resisting bending moment.

The contribution MF of the bottom reinforcement isa linear function of the reinforcement area and the steelstress. Whereas the reinforcement ratio ρ varies between0.13 and 4 %, the bottom steel always yields because theincrement in the reinforcement area leads to a linear in-

35



tic range. The relative depth of the neutral axis x/d hasbeen limited to 0.45 in order to ensure enough ductility inhyperstatic beams, as required by EN 1992-1-1 [2].

Seven values of the reinforcement ratio ρ = As/(bd)varying between 0.13 % and 4 % are considered in the de-sign. The reinforcement areas are listed in Table 3. Theprobabilistic model [15] given in Table 4 has been used toevaluate the global resistance factors γR and γR′.

The behaviour of the coefficient of variation, themean value and the standard deviation of the distributionof the resisting bending moment is explained below. Thecoefficient of variation VMR of the distribution of the re-sisting bending moment is plotted in Fig. 4. The relativevariation of VMR is about 10 %. It induces a decrement inthe global resistance factor γR amounting to 3 %, which isconsidered negligible. The reason for such behaviour ofVMR is that the standard deviation and the mean value ofthe distribution increase with the reinforcement ratio withan approximately constant slope, as shown in Figs. 5 and 6.

The contribution MC of the concrete in compressionis equal to the product of the resultant C of the stress inthe concrete and the distance of this resultant from thecentre of gravity of the cross-section. The mean value ofthe compressive resultant C increases in absolute valuesfrom ρ = 0.13 % to ρ = 1.0 %, with the same rate of

Table 1. Probabilistic model

Variable Description Distribution Mean value Std. dev. C.o.v.

fc25 [MPa] Concrete compressive strength log-normal 33.7 5.7 0.17

fy [MPa] Yield stress log-normal 560.0 30.0 0.05

ft [MPa] Tensile strength log-normal 644.0 40.0 0.06

ϑR [–] Resistance model uncertainty log-normal 1.1 0.077 0.07

Table 2. Results

Parameter Ultimate load Resisting bending [kN/m] moment [kNm]

μ (without ϑR) 86.9 249.8

σ (without ϑR) 4.2 12.9

V (without ϑR) 0.05 0.05

γR 1.16 1.16

μ (with ϑR) 95.4 274.1

σ (with ϑR) 8.3 24.0

V (with ϑR) 0.09 0.09

γR′ 1.31 1.31

Table 3. Reinforcement areas

ρ [%] As,btm [mm2] As,top [mm2]

0.13 158 –

0.50 608 –

1.00 1215 –

1.50 1823 126

2.00 2430 733

2.50 3038 1341

3.00 3645 1948

3.50 4253 2556

4.00 4860 3163







36



Fig. 4. Coefficient of variation VMR.

Fig. 5. Mean value of the components of the resisting bending moment.

Fig. 6. Standard deviation of the components of the resisting bending moment.

37



crement in both the values μMF and σMF due to the con-stant value of the coefficient of variation of the distribu-tion of the area of the reinforcing bars.

The contribution MF′ of the top reinforcement is anincreasing function of the reinforcement ratio. The incre-ment in the reinforcement ratio leads to an increment inthe strain in the top reinforcing bars in order to satisfyequilibrium of the axial forces acting in the cross-section.Therefore, the stress in the reinforcing bars increases inabsolute terms. If the mean value of the stress in the topreinforcing bars is considered, it is noticeable that it de-creases due to the increment in the strain. For the samereason, the standard deviation is an increasing function ofthe reinforcement ratio.

After having performed the non-linear analysis withthe mean material resistances, the structural designerknows the value of the bending moment due to the ap-plied loads at the critical cross-section. By means of theproposed safety format, the designer performs the safetycheck according to Eqs. (28), (31) and (32). The global re-sistance factors γR and γR′ are plotted in Fig. 9. The differ-ence between the two diagrams simply depends on the re-

sistance model uncertainty, which is not considered in thederivation of γR.

5.2 Columns

The columns of non-sway frames and isolated slendercolumns are considered here.

5.2.1 Columns of non-sway frames

It is assumed that only the material non-linearity can af-fect the distribution of the internal actions, as in the caseof continuous beams. The failure load is the load thatleads to the attainment of the bending moment capacity atthe critical section of the column. Indeed, the safety checkis expressed by the following inequality:

MEd ≤ MRd for NRd = NEd (38)

where NEd and MEd are the design axial force and bendingmoment respectively. Given the interaction diagram (N,M) for the critical cross-section of the column, it is possi-

Fig. 7. Mean value of the internal forces.

Fig. 8. Standard deviation of the internal forces.

ble to estimate the global resistance factors γR and γR′ withrespect to the distribution of the resisting bending mo-ment for different axial force values. As an example, a con-crete column with a square cross-section is considered.Concrete class C35 and reinforcing steel grade S500 are used in the design. The width of the cross-section is0.30 m and the distance of the reinforcing bars from theconcrete surface is 0.045 m.

It is interesting to investigate the variation in theglobal resistance factors for different values of NR andMR, which represent the resistance of a cross-section subjected to axial force and bending moment respective-ly. The area of reinforcement has been varied betweenAs,min = 0.002 Ac and As,max = 0.04 Ac, where Ac is theconcrete area. An interaction diagram (NR, MR) is com-puted for each reinforcement area, considering the meanvalues of the material properties. The global resistancefactors are estimated for each point on this diagram. Theprobabilistic model listed in Table 4 has been used to

38



evaluate the global resistance factors γR and γR′. As a re-sult, the global resistance factors are plotted in Figs. 10and 11. With reference to the possible strain profiles, itcould be observed that γR shows a significant variability inthe part of the diagram where the steel deformation εsvaries between zero and the deformation at yield, which is0.0027.

The global resistance factor decreases with an incre-ment in the reinforcement area for a fixed value of the ax-ial force Ν. As the reinforcement area increases, so its con-tribution to the resisting bending moment also rises. Thevariability in the steel properties is limited and so an in-crement in the reinforcement area is associated with an in-crement in the mean value of the resisting bending mo-ment, which is larger than the increment in the standarddeviation. Therefore, the coefficient of variation and theglobal resistance factor decrease.

The structural engineer can plot the internal actionpath of the critical section of the column on this dia-

Fig. 9. Global resistance factors gammaR and gammaR’.

Fig. 10. Global resistance factor gammaR. Fig. 11. Global resistance factor gammaR’.

39



gram and can easily find the values of γR and γR′ to beused in the safety check according to Eqs. (28), (31) and(32).

5.2.2 Slender isolated columns

Let us consider a column fully restrained at the bottom,free at the top and bent in simple flexure subjected to the action of loads parallel with the axis, horizontal forcesand moments at the top. Under these hypotheses, the critical section is at the base of the column. As the load-carrying capacity of the structure is affected by the sec-ond-order effects, the global resistance factors should notrefer to the ultimate section capacity because buckling occurs.

The effect of slenderness on the global resistance fac-tors is analysed for a column with the same cross-sectionas that considered in the previous section. It has been as-sumed that the slenderness λ = 100, where λ is the ratio be-tween the effective buckling length of the column and theradius of gyration of the concrete section. A parametricanalysis of the global resistance factors with respect to thereinforcement area has been performed. As in the previ-ous section, the reinforcement area has been varied be-tween As,min = 0.002 Ac and As,max = 0.04 Ac. The reducedinteraction diagram is computed using the mean values ofthe material resistances for different amounts of reinforce-ment. Given the axial force N, the bending moment M rep-resents the maximum first-order moment that can be car-ried by the cross-section. This value decreases withrespect to the resisting bending moment of the cross-sec-tion as the column becomes more slender, except for thecase N = 0. The probabilistic model listed in Table 4 hasbeen used to evaluate the global resistance factors γR andγR′.

The global resistance factors γR and γR′ are plotted inFigs. 12 and 13. The shape of the diagrams differs signifi-cantly from those of Figs. 10 and 11 due to the slendernessof the column. However, the global resistance factors varyover the same range as that observed in the case ofcolumns of non-sway frames.

6 Comparison of safety formats

The safety formats proposed in EN 1992-2 and the oneproposed in this paper can be compared directly becauseboth are formulated in the domain of the internal actions.The first example concerns a two-span continuous beamand the second one is related to a slender column.

6.1 Continuous beam

The non-linear analysis concerns the concrete beam al-ready presented in section 5.1. The bending moment atthe inner support section is plotted as a function of theload level in Fig. 14.

The design value Ed of the bending moment due tothe applied loads is computed for γG = 1.35 and γQ = 1.5.The ultimate load level is 89.3 kN/m and corresponds to abending moment of –246 kNm at the inner support sec-tion.

Let us consider the design resistance Rd according toEqs. (31) and (32) of the safety format proposed in the pre-sent paper. According to Eq. (31), the ultimate load is di-vided by γR and then the corresponding bending momentis divided by γRd. The global resistance factor γR = 1.16 ac-cording to Eq. (27), whereas γRd is assumed to be 1.09from Eq. (30). If the safety check is performed using Eq.(32), the ultimate load is divided by γR′, which is 1.31.

The safety format according to EN 1992-2 is appliedby means of Eqs. (18) and (19), which are analogous toEqs. (31) and (32). According to Eq. (18), the ultimate loadis divided by γO and then the corresponding bending mo-ment is divided by γRd. The global safety factor γO and themodel uncertainty factor γRd are equal to 1.20 and 1.06 re-spectively. The safety verification according to Eq. (19) re-quires that the ultimate load is divided by γO′, which is1.27.

It can be seen in Fig. 14 that the safety formats ac-cording to Eqs. (19) and (32) lead to almost the same Rdvalue because the difference between γR′ and γO′ is negligi-ble. Further, the difference between the Rd values ob-tained from Eqs. (18) and (31) is insignificant. Therefore,

Fig. 12. Global resistance factor gammaR. Fig. 13. Global resistance factor gammaR’.

the two safety formats lead to similar results in this appli-cation example.

6.2 Slender column

A slender column is subjected to the vertical forces Ngk =280 kN and Nqk = 80 kN, a horizontal force Hqk = 10 kNand two moments Mgk = 27 kNm and Mqk = 8 kNm. Thecolumn is 8 m high and the square cross-section is 0.45 mwide. Fig. 15 shows the structural scheme and the section.The column is designed using C35 concrete and S500 re-inforcing steel. The reinforcement areas As1 and As2 areboth equal to 1527 mm2. The slenderness of this column isλ = 123.

The probabilistic model listed in Table 5 has beenused to evaluate the global resistance factors γR and γR′.The resistance model uncertainty is characterized by alarger mean and larger standard deviation with respect tothe probabilistic model of the first example. The presentmodel also takes into account the presence of the axialforce.

The internal actions path is plotted in Fig. 16. It canbe seen that the safety formats according to Eqs. (18) and(31) agree well. The global resistance factor γR and the

40








φ [rad] Out-of-plumb normal 0.0 0.0015 –


Fig. 15. Structural scheme.

Fig. 14. Example 1: Application of the safety format.

41



model uncertainty γRd applied in Eq. (28) are 1.18 and 1.20respectively.

The reader will notice a difference between the de-sign resistances Rd computed using Eqs. (19) and (32).The reason for this difference is the value of 1.61 used forthe global resistance factor γR′, whereas γO′ = 1.27 is usedin Eq. (19). The larger value of γR′ with respect to the pre-vious one is explained by the different probabilistic modelof the resistance model uncertainty ϑR.

7 Conclusions

This paper proposes a safety format for the non-linearanalysis of concrete structures. The safety check is per-formed in the domain of the internal actions. Followingthe suggestions of previous papers, the mean values of thematerial resistances are used in the non-linear analysis inorder to estimate the internal actions accurately. Twoglobal resistance factors γR and γR′ are applied on the re-sistance side of the safety check.

The global resistance factors depend on the coeffi-cient of variation of the actual resistance of the structure.The uncertainty of the resistance is related to the structur-al layout, the randomness of the material properties andgeometrical dimensions of the members and model uncer-tainties.

The results of the application examples are valid forthe particular beam in bending and column investigatedfor the combination of axial force and bending moment.The results presented in the paper cannot be directly ex-trapolated to other structures and failure modes. A broadnumerical investigation would be necessary in order to as-sess global resistance factors that can be used for several

types of structure that may fail according to different fail-ure modes.

The proposed safety format is compared with theone in EN 1992-2. Very close agreement for the resistanceRd is obtained in the first example (beam), whereas a dis-crepancy is observed in the second example (slender col-umn) due to the different assumptions concerning the re-sistance model uncertainties. A detailed comparisonbetween the method suggested in EN 1992-2 and themethod proposed in this paper would require an investiga-tion of several structures and failure modes.

References

1. CEN: EN 1990: Eurocode – Basis of structural design. CEN,Brussels, 2003.

2. CEN: EN 1992-1-1: Eurocode 2 – Design of concrete struc-tures. Part 1-1: general rules and rules for buildings. CEN,Brussels, 2004.

3. CEB: New developments in non-linear analysis methods.Bulletin d’Information No. 229. CEB, Lausanne, 1995.

4. fib: fib Bulletin 56: Model Code 2010, first complete draft,vol. 2, fib, Lausanne, 2010.

5. Schlune, H., Plos, M., Gylltoft, K.: Safety formats for nonlin-ear analysis tested on concrete beams subjected to shearforces and bending moments. Engineering Structures 33(2011), pp. 2350–2356.

6. Schlune, H., Gylltoft, K., Plos, M.: Safety formats for non-lin-ear analysis of concrete structures. Magazine of ConcreteResearch (2012), pp. 1–12.

7. Sykora, M., Holicky, M.: Safety format for non-linear analysisin the Model Code – Verification of reliability level. fib sym-posium proceedings, Prague, 2011.

8. CEN: EN 1992-2: Eurocode 2 – Design of concrete struc-tures. Part 2: concrete bridges. CEN, Brussels, 2005.

Fig. 16. Example 2: Application of the safety format.

9. fib: fib Bulletin 55: Model Code 2010, first complete draft,vol. 1. fib, Lausanne, 2010.

10. Holicky, M.: Probabilistic approach to the global resistancefactor for reinforced concrete members. In: Taerwe, Proske:5th International Probabilistic Workshop, Ghent, Acco,2007, pp. 209–218.

11. Allaix, D. L., Carbone, V. I., Mancini, G.: Global resistancefactor for reinforced concrete beams. In: Taerwe, Proske: 5thInternational Probabilistic Workshop, Ghent, Acco, 2007,pp. 195–208.

12. Allaix, D. L, Mancini, G.: Assessment of a global resistancefactor for reinforced concrete columns by parametric analy-sis. In: Shen, Li, Wu, Luo: International Symposium on In-novation & Sustainability of Structures in Civil Engineering,Shanghai, Southeast University Press, 2007, pp. 1–9.

13. Cervenka, V.: Global safety format for nonlinear calculationof reinforced concrete. In: Taerwe, Proske: 5th InternationalProbabilistic Workshop, Ghent, Acco, 2007, pp. 183–194.

14. König, G., Hosser, D.: The simplified level II method and itsapplication on the derivation of safety elements for level I.CEB, 1983.

15. Joint Committee on Structural Safety. Probabilistic ModelCode, Internet publication, 2001, www.jcss.byg.dtu.dk.

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Giuseppe ManciniDepartment of Structural, Building &Geotechnical EngineeringPolitecnico di TorinoCorso Duca degli Abruzzi 2410129 Torino, Italye-mail: [email protected]

Vincenzo Ilario CarboneDepartment of Structural, Building &Geotechnical EngineeringPolitecnico di TorinoCorso Duca degli Abruzzi 2410129 Torino, Italye-mail: [email protected]

Diego Lorenzo AllaixDepartment of Structural, Building & Geotechnical EngineeringPolitecnico di TorinoCorso Duca degli Abruzzi 2410129 Torino, Italye-mail: [email protected]: +39 011 090 4825Fax: +39 011 090 4899


Concrete shells have been widely used in the past as economicaland suitable solutions for a number of structures such as roofs,silos, cooling towers and offshore platforms. Taking advantage oftheir single or double curvature, bending moments and shearforces are limited, and the structures develop mostly membrane(in-plane) forces, allowing them to span large distances with limited thicknesses (typically just a few centimetres). In recentdecades, advances in numerical modelling, formwork erectionand concrete technology have opened up a new set of possibili-ties for the use of concrete shells. This paper describes the design and construction of a shell in the form of an ellipsoid(93 × 52 × 22 m) and with thickness varying between 100 and120 mm. The shell was built using sprayed concrete and also or-dinary concrete in some regions. A number of tailored solutionswere also adopted, such as post-tensioning, addition of fibresand shear studs, to ensure satisfactory performance at both theserviceability and ultimate limit states.

Keywords: shell, concrete structure, design, sprayed concrete, fibre-reinforced concrete, architecture

1 Introduction

Masonry arches and vaultsThe history of masonry arches and vaults is rich and em-braces a number of building traditions. Detailed sum-maries and analyses can be consulted elsewhere [1–5]. Ma-sonry arches were most probably the first structuresinvented by mankind to span significant distances acrossrivers or valleys. These structures, which might have beeninspired by natural shapes, appeared as early as the 2ndmillennium BC in Mesopotamia. They are composed of aset of prepared stones (voussoirs) arranged side by side indirect contact or with intermediate mortar. Taking advan-tage of the shape of the arch, external actions (gravity-in-duced forces and imposed loads) are carried by the com-pression forces that develop internally and at theinterfaces between the voussoirs (and sometimes throughthe spandrel walls and filling at the extrados of the ma-sonry works). The line defining the theoretical resultant ofthe compression forces equilibrating the external actions

is usually called the “thrust line” (comprising its associat-ed thickness referring to the material strength) and needsto remain inside the masonry since no tensile stresses areacceptable at the joints of such constructions [5]. Theshape of the arch is thus decisive. Shapes where the thrustline does not remain inside the masonry are not in equi-librium with the external actions and lead to the collapseof the structure.

Vaults are double-curvature surfaces assembled frommasonry voussoirs or bricks. They have traditionally beenused as roofs or to cover underground constructions. Asfor masonry arches, vaults need to develop the thrust sur-face within the masonry work. However, loads can be car-ried in more than one direction due to the double curva-ture of the vaults. For classical dome shapes, withspherical soffits, the pressure surface can be kept withinthe masonry by significantly increasing its thickness in se-lected zones (e.g. Pantheon dome, Rome). In these casesthe vaults exert a horizontal thrust at the bottom sup-ports. Another possibility is to provide the vault with tan-gential tensile forces, keeping the pressure surface withinthe masonry. St. Peter’s basilica (Vatican City) wasstrengthened in the mid-18th century with four iron chainsserving as a tension ring after large cracks in the domewere discovered [5].

Reinforced concrete shellsThe problems observed for masonry works, and in partic-ular for vaults (adequacy of the form for the actions lead-ing to significant thicknesses), can be mostly solved withthe addition of reinforcement, whose tensile forces can deviate the thrust surface, allowing it to lie within the concrete. As a consequence, reinforced double-curvaturestructures develop mostly membrane forces (in-plane axialand shearing forces) and very limited bending and out-of-plane shear forces. As a consequence, the required thick-ness can be significantly reduced, leading to double-curva-ture thin concrete shells.

Following this principle of membrane behaviour, thefirst concrete shells were built expressing this potential ina clear manner [6]. Designers in Europe (F. Dischinger, E.Torroja, R. Maillart) and America (A. Tedesko) experi-enced the advantages of such constructions with thick-nesses as low as 30–40 mm. These works, built mainly be-tween 1910 and 1940, typically used shapes defined byanalytical expressions (such as sections of spheres, cylin-

Technical Papers

Concrete shells – towards efficient structures:construction of an ellipsoidal concrete shell in Switzerland

Aurelio MuttoniFranco LuratiMiguel Fernández Ruiz*

DOI: 10.1002/suco.201200058


Submitted for review: 8 December 2012Accepted for publication: 12 December 2012

ders or hyperbolic paraboloids). They included stringersin the edges to ensure membrane behaviour as perfectly aspossible. The difficulties encountered in the analyticaltreatment of thin shells explains the rather limited numberof shapes used during this period and the low number ofdesigners using them. Following this period, interestingnew developments took place between 1940 and 1970 inAmerica, instigated by the Spanish architect F. Candelaand the Uruguayan engineer E. Dieste (the latter also in-volved with the development of masonry shells). Their ap-proach consisted of performing analyses that were as sim-ple as possible (Candela particularly) and combiningdifferent sections of previous shapes, preferring mostly hy-perbolic paraboloids due to their plastic qualities and easeof construction. Their approach led to a larger and richervariety of forms. In Switzerland, H. Isler [7, 8], too, built animpressive number of unusual shells between the 1960sand 1980s whose shape was obtained and optimized bydifferent mechanical analogies (pneumatic, gravity-shapedmembranes, etc.). It should be noted that, actually, the dif-ferent experiences with concrete shells were mostly linkedto the skills of their designers rather than to a continuousevolution in concrete shell design.

In the 1980s and 1990s, concrete shells were seldomused as a consequence of the large number of man-hoursrequired for building formwork and placing reinforcementwith respect to the material costs, which typically gave pri-ority to other structural solutions. In recent years, the situ-ation has changed somewhat. The possibilities offered bynew types of concrete (as fibre-reinforced concrete), rein-forcement, numerical cutting of formwork and its posi-tioning on the construction site as well as the new possi-bilities available for the analysis of these structures(related mostly to computer software) have allowed thedevelopment of a new approach to shells, with more free-dom in the choice of shape. Nevertheless, an understand-ing of the role of double curvature, the load-carryingmechanisms and the governing limit states of these struc-tures still remains essential to the design of shells. This isparticularly relevant with respect to the analysis of thebuckling behaviour of these structures. A state-of-the-artreview of this topic was published in 1979 [9] by the Inter-national Association for Shell & Spatial Structures, pro-viding guidance on such design. However, research is stillbeing performed in this area [10, 11] and remains neces-sary.

In the following, the most significant aspects of thedesign and construction for concrete shells will be dis-cussed with reference to a shell built recently in Switzer-land, a project in which the authors of this paper were in-volved.

2 Design of a concrete shell for covering a mall at Chiasso, Switzerland

Why a concrete shell?An ellipsoid-shaped roof was planned to cover a new mallto be constructed at Chiasso, Switzerland. This roof satis-fied the requirements of the client in terms of usability, ar-chitectural needs and image. The thickness of the ellip-soid was decisive since it directly influenced the amountof floor area that could be let, see Fig. 1a. Solutions were

44

A. Muttoni/F. Lurati/M. Fernández Ruiz · Concrete shells – towards efficient structures: construction of an ellipsoidal concrete shell in Switzerland


investigated using timber and steel linear elements. Localbuckling, however, was the governing factor for these solu-tions, requiring significant thicknesses in the most criticalparts. This led to uneconomical solutions for the client,with significant reductions in the lettable floor area. Bycontrast, a concrete shell was shown to be a suitable solu-tion. Its thickness was only 100 mm in the critical regionsinfluencing the lettable floor area. This allowed the clientto have sufficient space available and optimized the costof the mall (Fig. 1b).

Geometry and main properties of shellThe ellipsoid shell has axis dimensions of 92.8 m (majoraxis) and 51.8 m (minor axis) and is 22.5 m high. The ellipsoid is cut by a horizontal plane and is supported on aconcrete basement composed of transverse walls, leadingto a total height for the shell of 18.24 m, see Fig. 2. Thethickness of the shell varied. A value of 100 mm was se-lected as the default thickness. This was governed by con-structive issues (minimum thickness considering rein-forcement cover necessary) and also ensured adequatesafety against buckling.

Four layers of reinforcement were provided, two atthe intrados and two at the extrados of the shell. The rein-forcement layers were oriented following the radial(meridian) and tangential (parallel) directions. This wasselected as the most effective layout for structural reasons.The four-layer arrangement was needed to control thebending moments and shear forces that develop at thebasement connection, near the prestressed zone, and forconnecting to the steel structure at the zenith opening(Fig. 2). Bending moments and shear forces in other re-gions were very limited. Four reinforcement layers werenevertheless arranged in all regions for constructional rea-sons, to ensure suitable crack control (which may appeardepending on the load cases) and to ensure adequate safe-ty against buckling of the structure.

In addition to the ordinary reinforcement, 35 post-tensioned tendons (0.6 inch monostrand tendons) werearranged near the equator of the shell (from level +5.50 mto level +12.60 m, see Fig. 1) to carry membrane tension inthe horizontal direction. (They also presented a limited di-

Fig. 1. How the thickness of the roof influences the lettable floor area: (a)thick roof, and (b) thin concrete shell

(a)

(b)

45



mension for the plastic duct, thus minimizing the distur-bance in the compression field developing through theshell [12, 13].) The thickness of the shell was increased to 120 mm in this region (between levels +4.24 m and+13.35 m).

At the level of the connection to the concrete base-ment (between levels +4.24 m and +5.14 m), shear studswere also provided to ensure adequate shear strength anddeformation capacity in this region (subjected to parasiticshear forces and bending moments).

The thickness of the shell was also 120 mm from lev-el +21.60 m to the zenith opening. In the top part, the in-creased thickness allowed the concrete shell to be linkedto a steel structure at the zenith opening (10.21 × 5.70 m);this allows daylight to reach the inside of the mall. In ad-dition, between levels +4.81 m and +18.78 m, there are sev-eral circular openings (0.40 m dia.), see Fig. 2.

Concrete propertiesThe structure was cast using sprayed concrete from level+4.24 m to level +19.90 m. This allowed conventional(one-sided) formwork to be used for the entire shell.Where the slope was sufficiently limited (< 20°, from level+19.90 m to level +22.48 m), concrete was poured conven-tionally. For both concrete types, a characteristic compres-sive strength fck of 30 MPa at 28 days was specified.

Hooked metallic steel fibres (30 kg/m3) were used inthe sprayed concrete region between level +4.24 m andlevel +13.36 m. The fibres have a length of 30 mm and alength-to-diameter ratio of 80. The fibres were arranged toenhance crack control (in the post-tensioned region) andto improve the ductility of concrete under high normaland shear forces (at the junction with the basement). Thesprayed concrete contained 300 kg/m3 of cement and25 kg/m3 of lean lime (to enhance the workability of theconcrete). The aggregate sizes between 0 and 4 mm accounted for 70 % of the total, the rest ranging between 4and 8 mm. Addition of water was performed at the spray-ing gun.

3 Design aspects

Apart from some aspects that were governed by construc-tional issues (e.g. shell thickness, as explained previously),the design of the shell and its reinforcement was governedby three structural aspects: the membrane (in-plane) innerforces in the shell, the second-order effects and the non-membrane (parasitic) bending and shear forces at thejunction with the concrete basement. The structure wasmodelled using a 3D finite element model (using the com-mercial program ANSYS) capable of performing linearand non-linear analyses. A comparison of the software re-

Fig. 2. Main geometrical dimensions: (a) section along major axis, (b) section along minor axis

(a)

(b)

sults with some analytically solved cases such as spheres[14] was also performed in order to check the accuracyand relevance of the FEM results. This approach providedrefined solutions but with a means to control them andcheck the suitability of the results obtained.

Membrane inner forcesThe membrane (in-plane) tensile inner forces were gener-ally moderate or low and could be handled by the mini-mum reinforcement amount. The most significant excep-tion to this rule was the large tensile forces occurring atthe equator of the shell (see Fig. 3). Design was performedto ensure sufficient strength at the ultimate limit state aswell as to control crack widths at the serviceability limitstate. This required arranging post-tensioning in this re-gion (monostrand tendons). In other parts of the structureit was noted that the delayed strains in the concrete (main-ly shrinkage) led to tensile stresses in some regions (par-ticularly at the connection to the concrete basement)which required the provision of sufficient reinforcementfor crack control (spacing and crack opening).

46



Buckling behaviourBuckling governed the design of the top region of theshell, with minimum curvature and largest compressionforces. Design was performed according to IASS recom-mendations [9]. In order to determine the buckling behav-iour, non-linear analyses were performed considering theinitial imperfections, creep strains of concrete, the actualcracked stiffness and the non-linear behaviour [9]. In addi-tion, a sensitivity analysis was performed by assuminglarge reductions in the stiffness in some selected cases(cracking in selected regions of the shell, local imperfec-tions combined with snow cases or temperature). Thismodified the buckling modes (see Fig. 4), but with accept-able results in all cases.

Edge forcesNon-membrane inner forces developed mostly at the con-crete basement connection (edge forces due to compatibil-ity). Also, non-membrane inner forces were observed inthe post-tensioned region and zenith opening (neverthe-less, with a lower intensity than at the basement).

Fig. 3. Membrane (in-plane) inner forces: (a) equator region, where maximum tensile forces develop, (b) diagram of unitary force intensity

(a)

(b)

Fig. 4. Deformed shapes at buckling failure: (a) reduced stiffness at zenith opening connection, (b) reduced flexural stiffness at top of post-tensioned region, and (c) overall reduced flexural stiffness

(a) (b) (c)

47



The edge forces (bending and shear) typically appearat the boundaries of a shell and are well described in thescientific literature [14]. Both forces can be calculated onthe basis of the shell geometry as

vy = vy,0 · exp(–λvs) ·cos(ωvs)

my = my,0 · exp(–λms) ·cos(ωms)

wherevy, my unitary shear forces and bending moments

at a distance s (perpendicular to the edgedirection)

vy,0, my,0 unitary shear forces and bending momentsat the clamped edge

λv, λm, λv, λm parameters depending on geometry ofshell [14] (radius of curvature, thickness,Poisson’s coefficient, clamping conditions)

Both formulas lead to an exponential decay of the edgeforces modulated by a harmonic function. For the presentshell, the influence of the edge forces was almost negligi-ble at a distance > 40 times the thickness of the shell (seeFig. 5). Accounting for the various imposed strains andload cases, the bending moments and shear forces at thefree edges could act with both positive or negative values.

The significance of the edge forces of the boundaryconditions should also be noted. For clamped edges, abending moment appears (my,0,clamp), which becomes zerofor a hinged shell at the edge line, but with a maximumthereafter (with lowest absolute value anyway). Also, withrespect to the shear force, a shell supported on a clampededge exhibits a maximum shear force (at the supportededge, vy,0,clamp) double that of a hinged shell at the edgeline (vy,0,hinged). Fig. 5 plots the normalized inner forces inthe region near the basement for two cases. The differ-ences allow an appreciation of how the boundary condi-tions and deformation capacity influence these forces.

Different strategies are usually followed to providesuitable control of the edge forces. The first one consistsof increasing the thickness of the shell locally so that thethrust line can be better accommodated (an analogous ap-proach to that followed for stress ribbons [15]). Alterna-tively, the reinforcement can be designed at the service-ability limit state accounting for suitable crack control andat the ultimate limit state assuming a plastic redistributionof internal forces (plastic hinge, see Fig. 5, solution be-tween clamped and hinged structures). This latter solutionrequires a certain level of deformation capacity in theedge region which is influenced by shear forces [16].

For the present shell, the second strategy was adopt-ed to account for architectural and functional needs. The

Fig. 5. Comparison of non-membrane forces in vertical (radial) direction (normalized by maximum forces for a clamped case) as a function of the distanceto the clamped edge (s normalized by thickness of slab): (a) bending moments, and (b) shear forces

(b)(a)

Fig. 6. Shear and bending forces at the connection to the concrete basement: (a) location of theoretical thrust line, (b) behaviour of specimen tested withshear studs, and (c) behaviour of specimen tested without shear studs

(a) (b) (c)

solution selected was tested in the laboratory, see Fig. 6.Transverse reinforcement was provided (an amount equalto 0.5 % of the concrete transverse surface) allowing suffi-cient strength with a large deformation capacity (Fig. 6b).This was instrumental and led to behaviour significantlybetter than that of a reference control specimen (Fig. 6c)tested without shear studs, which failed at a lower strengthbut most significantly with a quite limited deformation ca-pacity.

4 Construction of the shell

Formwork was placed over timber falsework, Fig. 7a. Theformwork was composed of panels bent in situ andscrewed in their corresponding positions (Fig. 7b). Rein-forcement was then placed and concrete was sprayed orpoured in situ (Figs. 7c, 7d). Placing the reinforcementand concreting the shell took about three months in total.

Once concreting was finished, decentering of theshell was performed. This is probably the most criticalphase, and in some cases has led shells collapsing [17]. Forthe present shell, the work was performed in a number ofphases in order to avoid decentering being the governingdesign situation. Firstly, half of the post-tensioning forcewas applied (one out of two tendons post-tensioned).Then, the timber falsework in contact with the post-ten-

48



sioned zone was removed, followed by the post-tensioningof all tendons. This operation ensured correct post-ten-sioning transfer to the concrete. Finally, the vertical strutsof the falsework supporting the top region of the shellwere gradually released, leading to complete decenteringof the structure. Measured deflections were recorded dur-ing the process and were in good agreement with predict-ed values. Some pictures of the completed work can beseen in Fig. 8.

The cost of the concrete structure was 49 % for false-work and formwork, 21 % for ordinary reinforcement, 5 %for post-tensioning, 24 % for sprayed concrete and 1% forpoured in situ concrete. This reveals the relatively largecost of falsework and formwork for this type of structure,and points to the need for future research on more effi-cient techniques.

5 Conclusions

This paper has provided a summary of the most relevantaspects related to the design and construction of a con-crete shell built in Chiasso, Switzerland. Its main conclu-sions are:– Concrete shells are efficient structures and can be used

as durable solutions for roofs or for covering largespaces.

Fig. 7. Construction of shell: (a) temporary falsework, (b) placing of prestressing tendons, (c) spraying of concrete, and (d) pouring of concrete

(a) (b)

(c) (d)

49



– Concrete shells can be built with limited thicknesses,thus maximizing the space inside them. This fact alsopermits the amount of material and energy in their con-struction to be minimized, thus contributing to a sus-tainable construction approach.

– The design of concrete shells can be governed by as-pects that are not always critical in other types of con-crete structure, i.e. membrane forces, second-order ef-fects and edge forces (for compatibility reasons), whichare potentially governing criteria in different regions ofthe shell.

– Research and innovation are still required for formworkand falsework. Traditional approaches lead to good re-sults in terms of shape and quality, but double-curvaturesurfaces lead potentially to excessively complicated (andexpensive) systems.

– Design for buckling of concrete shell structures is acomplex topic and is not suitably covered by codes ofpractice. A review and update of such design provisionsshould help and encourage designers in the use of con-crete shell structures.

Credits

Structural design and engineering: Aurelio Muttoni, Fran-co Lurati, Miguel Fernández Ruiz (Mendrisio and Lau-sanne, Switzerland)Architecture: Elio Ostinelli (Chiasso, Switzerland)Client: Centro Ovale 1 SA, (Chiasso, Switzerland)Contractor: Muttoni SA, (Bellinzona, Switzerland)Cost: SFr 5,300,000 (VAT and design costs included)

Fig. 8. Completed structure

References

1. Arenas de Pablo, J. J.: Bridges (in Spanish: Caminos en elaire: los puentes). Colegio de ingenieros de Caminos,Canales y Puertos, Madrid, 2 vols., 2002.

2. Boothby, T. E.: Analysis of masonry arches and vaults. Prog.Struct. Engng. Mater., vol. 3, 2001, pp. 246–256.

3. Boyd, T. D.: The Arch and the Vault in Greek Architecture.American Journal of Archaeology, vol. 82, No. 1, 1978, pp.83–100.

4. Heyman, J.: The Stone Skeleton: structural engineering ofmasonry architecture. Cambridge University Press, 1995.

5. Muttoni, A.: The art of Structures – an introduction to thefunctioning of structures in architecture. EPFL Press, Lau-sanne, Switzerland, 2011.

6. Cassinello, P., Schlaich, M., Torroja, J. A.: Félix Candela. Inmemoriam (1910–97). From thin concrete shells to the 21stcentury’s lightweight structures (in Spanish: Félix Candela.En memoria (1910–1997). Del cascarón de hormigón a lasestructuras ligeras del s. XXI). Informes de la Construcción,vol. 62, No. 519, 2010, pp. 5–26.

7. Chilton, J., Isler, H.: Heinz Isler: The engineer’s contributionto contemporary architecture. RIBA Publications/ThomasTelford, 2000, pp. 20–29.

8. Kotnik, T., Schwartz, J.: The Architecture of Heinz Isler. Jour-nal of the International Association for Shell & SpatialStructures, vol. 52, No. 3, 2011, pp. 185–190.

9. IASS (International Association for Shell & Spatial Struc-tures), Working Group No. 5: Recommendations for rein-forced concrete shells and folded plates. Madrid, Spain,1979.

10. Espín, A.T.: Optimal design of shape and reinforcement inconcrete shells (in Spanish: Diseño óptimo de forma y arma-do de láminas de hormigón). PhD thesis, UniversidadPolitécnica de Cartagena – Departamento de estructuras yconstrucción, Spain, 2007.

11. Mungan, I.: A conceptual approach to shell buckling withemphasis on reinforced concrete shells. In: Proc. of Interna-tional Association for Shell & Spatial Structures (IASS),symposium, 2009, Valencia, pp. 39–50.

12. Muttoni, A., Burdet, O., Hars, E.: Effect of Duct Type on theShear Strength of Thin Webs. ACI Structural Journal, Farm-ington Hills, USA, 2006, pp. 729–735.

50



13. Fernández Ruiz, M., Muttoni, A.: Shear strength of thin-webbed post-tensioned beams. American Concrete Institute,Structural Journal, vol. 105, No. 3, 2008, pp. 308–317.

14. Timoshenko, S., Woinowsky-Krieger, S.: Theory of plates andshells, 2nd ed., McGraw-Hill, 1959.

15. Schlaich, J., Engelsmann, S.: Stress Ribbon ConcreteBridges, Structural Engineering International, 1996, pp.271–274.

16. Vaz Rodrigues, R., Muttoni, A., Fernández Ruiz, M.: Influ-ence of shear on the rotation capacity of R/C plastic hinges.American Concrete Institute, Structural Journal, vol. 107,No. 5, 2010, pp. 516–525.

17. Garlock, M., Billington, D.: Félix Candela. Engineer, Builder,Structural Artist. Yale University Press, New Haven, CT,2008.

Franco LuratiLurati Muttoni Partner SAVia Moree 3, CH-6850Mendrisio, [email protected]

Miguel Fernández RuizMuttoni & Fernández, ic SARoute du Bois 17, CH-1024Lausanne, [email protected]

Aurelio MuttoniMuttoni & Fernández, ic SARoute du Bois 17, CH-1024Lausanne, [email protected]


The lattice equivalent continuum model (LECM) has proved to bevery effective in analysing reinforced concrete structures in two-dimensional cases. That model is extended here to three dimen-sions and is fitted to a finite element formulation for analysingthree-dimensional reinforced concrete structures. In any of thethree principal directions, the stress–strain behaviour of con-crete will be affected by the stress state in the other two direc-tions. Consequently, stress-strain curves for concrete will shiftfrom a uniaxial pattern. This phenomenon is considered in thiswork by selecting concrete peak stresses in three alternative ap-proaches. The effectiveness of those approaches is also evaluat-ed. The results of the calculations show good reproduction of thetest data, which indicates the validity of this proposed 3D model-ling of reinforced concrete.

Keywords: finite element, three-dimensional model, simulation, reinforcedconcrete, ultimate strength, concrete structure, lattice, model

1 Introduction

Analysing reinforced concrete to simulate its three-dimen-sional behaviour under different types of loading has al-ways been a challenging issue for researchers, engineersand academics due to its complexity arising from the het-erogeneous concrete, reinforcement and presence ofcracking. Many constitutive models have been proposedto simulate this complex 3D behaviour of reinforced con-crete and are available in the literature. These constitutivemodels have used different approaches in their formula-tions. In one approach, some researchers have used latticeand particle models in which the continuum is replacedby a system of discrete elements. Van Mier et al. [1],Schlangen [2] and Niwa et. al. [3] were the first to use a lat-tice-type model for concrete. Further modification of thislattice-type model in later years can also be found else-where in the literature [4, 5, 6]. The smeared crack model,first introduced by Rashid [7] and Cervenka and Gerstle[8], is another approach that has been extensively used todevelop constitutive models for reinforced concrete. It isbased on the development of appropriate continuum ma-terial models in which cracks are smeared over a distinct

area, typically a finite element or an area corresponding toan integration point of the finite element. Many recent,successful models are based on this smeared crack ap-proach [9, 10]. Although a number of models are availablein the literature, the authors of this paper feel that there isroom for improvement in this area. The authors also be-lieve that any research in this area should benefit the pro-fession so that the existing gap between scientific activityand practice is narrowed. It is therefore of interest to de-velop constitutive laws for reinforced concrete which willnot only give reasonably accurate results but will also pro-vide a clear and easy understanding of the complex phe-nomenon occurring inside concrete elements with respectto stress and strain distribution, i.e. more engineering-ori-ented constitutive laws as opposed to the prevailing con-stitutive laws for reinforced concrete. To do this, the con-cept of the equivalent continuum of the lattice system [11,12] is used and extended to three dimensions.

The lattice equivalent continuum model (hereinaftercalled “LECM”) has its origins in the successful use of dis-crete lattice modelling of reinforced concrete elements byNiwa et al. [3]. The continuum model essentially retainsthe features of the uniaxiality of stress-bearing materials;however, combining those features alters their fundamen-tal characteristics from an initially orthotropic model andlater even to a general, anisotropic model. Conceptually,this model begins with lattice-type idealization but ulti-mately the governing equations represent equivalent con-tinuum of that lattice system, i.e. similar to a smear crack-type model. The concepts behind the formulation of theLECM are unique and different from other well-knownuniaxial-type models such as Bazant’s microplane model[13]. For instance, the number of microplanes used inBazant’s model is far more than the lattices used for mod-elling reinforced concrete in the LECM. Therefore, thepresent model is far easier to understand and apply. Fur-thermore, appropriate peak stress and strain criteria for in-dividual lattices distinguish the LECM model from the mi-croplane model, where the stress-strain laws are not theones for macroscopic concrete elements.

The paper begins with a brief introduction to the for-mulation to derive the constitutive equation in the LECM.That is followed by the modelling of the stress transfer be-tween cracked faces in concrete due to traction by intro-ducing shear lattices into the system. Since the choice ofthe ultimate stress in the concrete lattice system influ-

Technical Paper

Three-dimensional FE analysisof reinforced concrete structures usingthe lattice equivalent continuum method

Syed Ishtiaq Ahmad*Tada-aki Tanabe

DOI: 10.1002/suco.201100009


Submitted for review: 03 February 2011Revised: 11 July 2012Accepted for publication: 23 September 2012

ences the results of the computations, the analysis is per-formed using three different ways of selecting peak stress-es in a concrete lattice system, and a conclusion is drawnfrom the analysis results as to which system is closer to theactual concrete behaviour.

2 Formulation of the constitutive equation

The formulation of the lattice equivalent method is basedon the assumption that reinforced concrete is cracked andcomposed of two sets of lattices. One set of lattices is par-allel with the original discontinuous plane and lattices or-thogonal to it. We call these main lattices. Fig. 1 depictsschematically the concept of main lattice idealization inreinforced concrete. The other set is the one that consid-ers the shear transfer between main concrete lattices andwill be introduced in the next section. The stresses and direction of the steel main lattices are those of the steel reinforcement itself, whereas crack directions in the concrete, which are in turn fixed by principal stresses, determine the concrete main lattices and their orienta-tion.

We begin by assuming a uniformly strained 3D con-tinuum strain, which has the global coordinates

(1)

The strain in a lattice member in this strain field is as-sumed to be identical with the strain of Eq. (1). Therefore,for an inclined lattice member for which local coordinates(ξ, η, ζ) are taken such that the ξ coordinate coincideswith the lattice axis, the lattice strain εξ is

(2)

where a, b and c are the direction cosines of the lattice di-rection with respect to the x, y and z axes. For reinforcedconcrete, ξ, η and ζ are the directions of the principalstrains and can be computed using basic continuum me-chanics laws. If n number of lattices exists in the continu-um, we can write

(3)

where

Multiplying the strains by the stiffness of each lattice, theincremental stresses of the replaced continuum can beevaluated as

[ ]g x y z sy yz zxTε ε ε ε γ γ γ{ } =

[ ]2 2 2a b c a b b c c a

x

y

z

xy

yz

zx

ε

εεεγγγ

=

⎧

⎨

⎪⎪⎪

⎩

⎪⎪⎪

⎫

⎬

⎪⎪⎪

⎭

⎪⎪⎪

ξ

ε εεl gL{ } = ⎡⎣ ⎤⎦{ }

L

a b c a b b c c a

a b c a b b c c aj j j j j j j j jε⎡⎣ ⎤⎦ =

12

12

12

1 1 1 1 1 1

2 2 2� � � � � �

� � � ��

a b c a b b c c an n n n n n n n n2 2 2

⎡

⎣

⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥

52

S. I. Ahmad/T. Tanabe · Three-dimensional FE analysis of reinforced concrete structures using the lattice equivalent continuum method


(4)

where rj = ∂σj/∂εj denotes the tangential stiffness of indi-vidual lattices.

Continuum local stresses transformed into global co-ordinates have the following form:

Summing over all lattices gives us the expression

which can be written as

(5)

2

2

2

a

b

c

a b

b c

c a

x

y

z

xy

yz

zx

j

j

j

j j

j j

j j

l

ΔσΔσΔσΔτΔτΔτ

Δσ{ }

⎧

⎨

⎪⎪⎪

⎩

⎪⎪⎪⎪

⎫

⎬

⎪⎪⎪

⎭

⎪⎪⎪⎪

=

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥⎥⎥⎥

12 2 2

12 2 2

12 2 2

1 1

1 1

1 1

a a a

b b b

c c c

a b a b a b

b c b c b c

c a c a c a

g

x

y

z

xy

yz

zx

j n

j n

j n

j j n n

j j n n

j j n n

l

� �

� �

� ��

Δσ

ΔσΔσΔσΔτΔτΔτ

Δσ{ } { }=

⎧

⎨

⎪⎪⎪

⎩

⎪⎪⎪⎪

⎫

⎬

⎪⎪⎪

⎭

⎪⎪⎪⎪

=

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥⎥⎥⎥

L

L R L

D

gT

lT

n g

kin g

Δσ Δσ

Δε

Δε

{ }{ }

{ }

{ }= ⎡⎣ ⎤⎦

= ⎡⎣ ⎤⎦ ⎡⎣ ⎤⎦ ⎡⎣ ⎤⎦= ⎡⎣ ⎤⎦

ε

ε ε

{ }

ln

Δ

Δ

Δ

Δ

σ

σ

σ

σ

l

l

lj j

nn

r

r

r

=

⎧

⎨

⎪⎪

⎩

⎪⎪

⎫

⎬

⎪⎪

⎭

⎪⎪

=

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥

1 10

0

�

�

�

� ⎥⎥⎥

⎧

⎨

⎪⎪

⎩

⎪⎪

⎫

⎬

⎪⎪

⎭

⎪⎪

= ⎡⎣ ⎤⎦{ }

Δ

Δ

Δ

Δ

ε

ε

ε

ε

l

lj

n lR

1�

�

ln

latticesSteellatticesConcrete

RC block Lattice idealization

Fig. 1. Lattice idealization of reinforced concrete members

53



where

(6)

3 Crack surface modelling with shear lattices

The formulation developed here decomposes the incre-mental strain {ε} into the uncracked or elastic strains {εe}and the crack strain {εcr} in order to accommodate singu-larities in the strain field caused by cracking while usingthe continuum-based formulation.

(7)

Interlocking stress transfer between adjacent concrete mainlattice faces in a crack will depend on the actual contactarea between them. Contact surface is a complex functionof height of protruding elements, i.e. roughness in a crackedface and crack width. For simplicity, a relative contact den-sity factor t is introduced in this work and is linearly corre-lated with the tension strain softening curve of concrete.For zero or no crack strain εcr, relative contact density isunity or, in other words, complete contact is assumed. As εcrincreases, density factor t decreases linearly. An additionalfactor α is added to t to account for the effect of steel in theRC zone. These factors are illustrated in Figs. 2a and 2b. Ex-perience shows that an α value of 0.0001~0.0005 is suffi-cient and 0.0002 has been used in this work.

To model this contact zone on a cracked face, fourlattices are introduced for one cracked plane surface atany sampling point as shown in Figs. 2c and 2d. However,a modification factor in the form of a shear controllingmatrix [Ω] is necessary in Eq. (7) to account for the limitedvolumetric characteristics of these shear lattices aroundthe interlocking region. Therefore, we get, from the crackstrain,

(8)

where

e crΔε Δε Δε{ } { } { }= +

ε ε ε ε ε γ γ γ

ε γ γ

{ }{ }

{ } = Ω⎡⎣ ⎤⎦ −

=

ξ η ς ξη ης ςξ

η ξη ης

cr e

T

cr

T0 0 0

.

4

1

2 2

1

2 2

1

3

1

2

1

3

1

4

1

2 2

1

3

1

3

1

2

1

4

1

2

1

3

1

3

1

2 2

1

2

1

2 2

1

2 2

1

2

1

2 2

1

D

r a r a b r a b r a b r a b c r a c

r a rb c rb a rb c r a b c

r c r a b c r c b r c a

r a c r a b c r a b c

Sym rb c r c b a

r c a

main

j j

n

j j j

n

j j j

n

j j j

n

j j j j

n

j j j

n

j j

n

j j j

n

j j j

n

j j j

n

j j j j

n

j j

n

j j j j

n

j j j

n

j j j

n

j j j

n

j j j j

n

j j j j

n

j j j

n

j j j j

n

j j j

n

⎡⎣ ⎤⎦ =

∑ ∑ ∑ ∑ ∑ ∑

∑ ∑ ∑ ∑ ∑

∑ ∑ ∑ ∑

∑ ∑ ∑

∑ ∑

∑

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

Ω⎡⎣ ⎤⎦ =

⎡

⎣

⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥

0 0 0 0 0 00 1 0 0 0 00 0 0 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

Two lattices are introduced in each of the local coordinatedirections parallel with the cracked plane as shown inFig. 2c. Of these two, the lattice that is activated to trans-fer the stresses depends on the negative or positive trac-tion direction as shown in Fig 2d. Now, incrementalstresses in the shear lattice direction of S1 and S2 (inplane ξ – η) and S3 and S4 (in plane η – ς, not shown inthe figure) can be evaluated using the following relation:

(9)

where [Tε,s1,..,S4] is the matrix for transforming stress fromthe local direction to the shear lattice direction. This matrix is dependent on the angle of the protruding partof the crack surface θ, normally 45° as shown in Fig. 2d.In the matrix, ESi is the tangent elastic modulus fromthe uniaxial stress–strain relation of individual shear lattices. In this work the shape of the stress–strain curvefor the shear lattice is taken to be elastic – completelyplastic, as shown in Fig. 2e. The peak stress fs of thiscurve is taken as to be equal to 18fc0.33, which is in linewith the research findings of Okamura et al. [14]. The local stress increment can be evaluated using the follow-ing relation:

(10)

where [Tσ1,S1,..,S4] is the matrix for transforming stress fromthe shear lattice direction to the local coordinate direc-tion. Therefore, we get a constitutive matrix for the shearlattice in global coordinates:

(11)

where [Tσ] and [Tε] are transformation matrices from thelocal stress and strain to global direction respectively, andt is determined according to the procedure described be-fore. Further,

(12)

For a number of cracks n at a sampling point we get

(13)

Therefore, the completed constitutive equation will bethat of the combined influence of main and shear lattices,i.e.

or

(14)

σ Δσ{ }⎡⎣ ⎤⎦ = Ω⎡⎣ ⎤⎦ ⎡⎣⎤⎦σ−

Tl S S sl, 1,.., 4

1

1D t T D Tshear shear⎡⎣ ⎤⎦ = ⎡⎣ ⎤⎦ ⎡⎣ ⎤⎦ ⎡⎣ ⎤⎦σ ξηζ ε

−

⎡⎣ ⎤⎦ = Ω⎡⎣ ⎤⎦ ⎡⎣⎤⎦

⎡⎣

⎤⎦⎡⎣

⎤⎦ Ω⎡⎣ ⎤⎦ξης σ ε

−D T D Tshear S S shear uni S S, 1,.., 4

1

, , 1,.., 4

1

1

,D t T D Tshear i

n

shear unii i i∑⎡⎣ ⎤⎦ =

⎡⎣⎢

⎤⎦⎥

⎡⎣⎢

⎤⎦⎥

⎡⎣⎢

⎤⎦⎥σ ξης ε

−

0 0 00 0 00 0 00 0 0

1

2

3

4

, 1,.., 4

,

EE

EE

T

D

sl

s

s

s

s

S S cr

shear uni cr

Δσ Δε

Δε

{ } { }

{ }

=

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

⎡⎣

⎤⎦

= ⎡⎣

⎤⎦

ε

D D Dtotal main shear⎡⎣ ⎤⎦ = ⎡⎣ ⎤⎦ + ⎡⎣ ⎤⎦

1D D t T D Ttotal main i i

i

n

shear i i∑⎡⎣ ⎤⎦ = ⎡⎣ ⎤⎦ + ⎡

⎣⎤⎦

⎡⎣

⎤⎦

⎡⎣⎢

⎤⎦⎥σ ξηζ ε

−

54



Eq. (14) denotes the final form of the constitutive matrixfor reinforced concrete in the LECM.

4 Ultimate strength criterion for concrete lattices

In the 3D stress field, stress–strain behaviour in any prin-cipal direction of the concrete will shift from its uniaxialbehaviour due to the influence of stresses in the other twodirections. This means that a point may reach a failuresurface that is different from the uniaxial strength of con-crete due to stresses in other directions. But exactly wherethe stress state of a point will reach the failure surface isunknown beforehand. Additionally, changes in peak stresswill result in overall changes to the shape of the concrete

Fig. 2. Shear lattice on a crack surface

cf

tf

ipcσ

iptσ

/1E1E

Fig. 3. Concrete lattice stress–strain laws

55



lattice stress–strain curve and, consequently, the tangentmodulus to be incorporated in Eq. (14). Fig. 3 shows theconcrete lattice stress–strain diagram with modified tan-gent modulus and peak strains due to changes in peakstress. Since the tangent modulus to be incorporated inEq. (14) varies due to changes in peak stress, in the analy-sis it is important to predict correctly beforehand theprobable peak stress that a point will reach from the cur-rent stress state. However, it should be noted that thereare infinite paths in which the failure stress state (σp1, σp2,σp3) can be achieved by varying the current stresses (σ1,σ2, σ3) of three principal or lattice directions. Fig. 4 showsone of the numerous stress paths in which the currentstress state may reach the eventual failure stress. To over-come this problem, in this work three fundamentally dif-ferent ways of relating failure stresses to the current stresscondition are considered, a concept that was first used byOttosen [15]. These are:

Case 1: Concrete lattice peak stresses are taken as equalto the uniaxial stresses of concrete (Fig. 5a).

Case 2: Peak stresses are taken as the point on the failuresurface that is attained by proportionally increas-ing and/or decreasing the current stresses in allthree principal stresses, i.e. the lattice direction.This is elaborated in Fig. 5b, where point A repre-sents stresses at the current loading step in thenumerical computation. Point B is achieved byproportionally increasing the stresses up to thefailure surface.

Case 3: The failure stress of any principal stress or latticedirection is taken as the one achieved by decreas-ing (for tension, increasing) it up to the failuresurface parallel with the axis system. This meansthat stresses in the other two directions are keptunchanged while the peak stress is evaluated inany direction. This is illustrated in Fig. 5c, wherepoint A (σ1, σ2, σ3) represents the stress state atthe current loading step in the numerical compu-tation. Point B (σ1, σ2, σpc3), which lies on thefailure surface, is achieved by drawing a straightline from point A parallel with the σ3 direction,and σpc3

is the corresponding peak stress for thelattice in the direction of σ3. The same procedureis used to determine σpc1

and σpc2, the peak stress-

es in the other two lattice directions. The failuresurface used in this work is the one proposed byKang and Willam [16].

5 Analysis of reinforced concrete test specimen5.1 RC cantilever column

First, a simple case of an RC cantilever column is analysedusing the proposed LECM model. This column was testedby Hirasawa et al. [17]. The dimensions of and reinforce-ment in the column are shown in Fig. 6. The column was1440 mm high and supported on an RC block 400 mmdeep and 610 mm wide having a concrete compressivestrength of fc = 36.97 MPa. Other material properties are:Ec = 26 100 MPa, ft = 2.03 MPa and steel fy = 361 MPa.The mesh selected is shown in Fig. 7a and is composed of8-noded solid elements. Due to symmetry, only half of the

),,( 321 σσσ

),,( 321 ppp σσσ

Fig. 4. Stress path showing current stress state relative to failure stress

(a) Case1 of peak stress selection

(b) Case 2 of peak stress selection

(c) Case 3 of peak stress selection

A

B

),,( 321 σσσ

3σ

1σ

2σA

B3pσ

1σ

2σ

3σ

),,( 321 σσσ

),,( 321 ppp σσσ

),,( 321 ppp σσσ

2σ

cf

cfcf

tf

tf

tf

1σ3σ

Fig. 5. Concrete lattice stress–strain diagram with peak stress criteria

400

1190 1840

230

Actuator

150

610

100 25 25

D10

D6 @ 50 250

Fig. 6. Dimensions of specimen RC cantilever column

section need be considered in the analysis. At the line ofsymmetry, the horizontal direction facing the other part isrestrained for all points. For each element, at the calcula-tion point, three concrete lattices are formed in the direc-tion of the principal stresses as soon as cracks appear inthe concrete. Reinforcement in an element is smearedacross the section. The direction of these rebars is in effectthe direction of the steel lattices. Shear lattice parametersθ and α are taken as 45° and 0.002 respectively.Stress–strain behaviour for the concrete lattice in com-pression is taken to be parabolic. For tension, two types ofbehaviour are considered. Owing to the bond betweenconcrete and the reinforcing bars, the concrete will continue to support part of the tensile force even aftercracking has taken place. To account for this phenome-non, the tension stiffening model proposed by Okamura etal. [14] is taken as representative of concrete lattice behav-iour in those elements where a steel lattice is present. Forother elements, concrete lattice behaviour in tension isconsidered to follow softening model. The column assem-

56



bly is then analysed with a finite element analysis plat-form. Fig. 8 shows the load-deflection behaviour foundfrom both the test and the FE analysis. Three analysis re-sults were found using three peak stress criterions as de-scribed in the previous section. For Case 1, i.e. uniaxialconcrete strength for concrete lattices, the peak load isoverestimated by about 15 %. For Case 2 and Case 3, thepeak load estimation is much closer to the experimentalresults. Of the three response curves, it can be seen thatfixing two directions and considering peak stress in thethird direction produces the most reasonable result (i.e.Case 3).

5.2 Slab in punching

The simulation of slab punching behaviour, which is a tru-ly three-dimensional phenomenon, is presented in thissection. The slab taken considered was tested by Hoeggarand Beutel [18] and is shown in Fig. 9. The hexagonalspecimen was vertically supported by 12 tie rods andloaded on the centre column with a hydraulic jack. Afterreaching the service load, the slab was unloaded and re-loaded twice. The material properties and arrangement ofthe reinforcement are summarized in Table 1. No shear re-inforcement was provided in the slab.

The finite element mesh used in the simulation isshown in Fig. 10. For reasons of symmetry, only a quarterof the test slab was modelled. The spatial discretizationwas performed by 8-noded solid elements as in the previ-ous example. Load was applied by controlling the verticaldisplacement of the nodes at the bottom of the columnarea. To account for the confining effect, nodes adjacentto the column were kept fixed in the horizontal directions.

Table 1. Material Properties of Test Slab

Concrete Tension reinforcement Compression reinforcement

fc ft E GF fy Number Spacing fy Number Spacing

MPa MPa MPa N/mm MPa – mm MPa – mm

21.0 1.73 21697 0.10 569 ϕ14 10 569 ϕ10 17.5

(a) FE mesh (b) Deflected shape

Fig. 7. Finite element mesh and deflected shape of RC cantilever column

0 20 40 600

0.5

1

1.5

Load (tf)

Deflection (mm)

Test Case 1 Case 2 Case 3

Fig. 8. Experimental and analytical load-deflection behaviour of RC can-tilever column

Slab thickness h = 230 mm, effective depth d = 195mm

(all dimensions in mm)

275

80.5

80.5

113.9

300

300

150

275

9.113 5.805.80

Fig. 9. Dimensions of test specimen for slab in punching

57



The support points were exactly at the same location asthat of the experiment. To avoid local damage, the ele-ments around the supporting nodes were defined as linearelastic. Fig. 11 shows the comparison between calculatedand experimentally measured load-deflection curves withthree peak stress criteria. The load corresponds to the ver-

tical column force and the deflection is monitored on thecolumn loading surface. For Case 1, i.e. lattice peak stressequal to uniaxial concrete strength, the response curvepredicts a higher peak load with a steep decline inload–displacement response in the post-peak region,whereas the Case 2 and Case 3 response curves showgood representation of the experimental load-displace-ment behaviour. Case 3 exhibits the closest approximationto the test data. Therefore, it can said that the proposedconstitutive laws are able to predict the load-deformationresponse of a slab in punching with a good degree of ac-curacy provided the peak stress criterion is chosen appro-priately.

The exaggerated deformed mesh of the simulatedcrack is shown in Fig. 12, which verifies the punchingmode of failure as the deflections are localized along theinclined band of the element near the column. Fig. 13shows the simulated crack pattern at failure obtained inthe analysis for Case 3. The cracks are plotted in the direc-tion of and in proportion to the principal strains. Thecrack pattern of the experiments is also superposed in thisfigure. As in the experiment, failure is obtained in theanalysis due to punching shear with the formation of thecharacteristic punching cone, thus verifying the ability ofthe proposed constitutive laws to capture the three-dimen-sional behaviour of reinforced concrete accurately. Fig. 14ashows calculated and measured vertical deflections of theslab tension surface plotted for different load levels. Fur-thermore, Fig. 14b shows the calculated and measured ten-sile strains in the tension reinforcement. The tangentialand radial strains in the concrete compression zonearound the column for different load levels are shown in

Vertical supports

Load application 20 x 20 cm, 25 nodes

Fig. 10. Finite element mesh

0 10 200

200

400

600 Test Case 1 Case 2 Case 3

Deflection (mm)

Load (kN)

Fig. 11. Experimental and analytical load-deflection behaviour of slab inpunching

Deformed Zon

Colum

ne

mn

Fig. 12. Deflection pattern of the mesh representing the slab in punching

Columnn EExperimental ppunching cracck

Fig. 13. Crack pattern at failure for slab in punching

Figs. 15a and 15b respectively. All of these graphs representCase 3, where the response was closest to the test data. Fig.14a shows that the analysis is close to predicting the verti-cal displacement distribution characterized by pronouncedrotation at the column face and small rotation away fromthat face (Fig. 12). The calculation predicts the maximumdeflection at peak load effectively, but at service load thecalculated values are slightly lower. An improved predic-tion of the deflection at service load could be achieved byusing a finer FE mesh. Since reinforcement is smeared out,the calculated strain in the tension reinforcement shown inFig. 14b is that of steel lattices at sampling points at the lev-el of the reinforcement. It can be seen that at peak load inparticular, the predicted distribution agrees well with theexperimental data. The tangential and radial strains in con-crete are shown in Figs. 15a and 15b at the level of thecompression reinforcement. From these figures it can beseen that calculation and experiment exhibit good agree-ment. Whereas the calculated radial strains are slightlylower, strains in tangential direction are slightly highercompared with the test results.

From the comparison between calculated and test re-sults presented here it can be concluded that the latticeequivalent continuum method is able to provide a realisticprediction of the loadbearing behaviour, the deformationsand the failure mechanism of flat slab punching behav-

58



iour, which is a truly three-dimensional reinforced con-crete behaviour.

6 Conclusion

The application and effectiveness of the simple, engineer-ing-oriented three-dimensional LECM for analysing rein-forced concrete structures is presented in this paper. Basicinput parameters of the model include concrete uniaxialcompressive and tensile strength for construction of thefailure surface, reinforcement yield strength and initialstiffness for both concrete and steel. These can be ob-tained from standardized tests on concrete and steel spec-imens. Apart from these primary parameters, two sec-ondary input parameters for the shear lattice part of theconstitutive matrix are θ and α. A crack angle θ value of45° is a good approximation for the average of all cracksurface roughnesses. For α, a value within 0.0002~0.0005may be used. From the analysis results it is clear that load-deflection and other behaviour are influenced by thechoice of peak stress criterion for a concrete lattice sys-tem. Analysis results show keeping two directions fixedand checking for the peak stress in the third direction re-produces actual concrete behaviour reasonably (Case 3 inthis paper). Two examples provided in this paper showthat the LECM can capture the deformation characteris-

050010000

5

10

Experiment, P=345 Experiment, P=520 Experiment, P=615 Calculation, P=345 Calculation, P=520 Calculation, P=615

Def

lect

ion

(m

m)

Distance from Slab Center

200300400500600700800

-1

-0.5

0

Experiment, P=375 Experiment, P=520 Experiment, P=615 Calculation, P =375 Calculation, P =520 Calculation, P =615

Distance from Column Center (mm)

Tan

gen

tial

Co

ncr

ete

Str

ain

Fig. 14. Comparison of calculation and experiment: (a) deflection, (b)strains in tension reinforcement

0 500 10000

1

2

Experiment, 375 KN Experiment, 520 KN Experiment, 615 KN Calculation, 375 KN Calculation, 520 KN Calculation, 615 KN

Distance from Slab Center (mm)

Tens

ile R

einf

orce

men

t Str

ain

200 300 400 500 600 700 800

-1

-0.5

0

Experiment, P=375 Experiment, P=520 Experiment, P=615 Calculation, P=375 Calculation, P=520 Calculation, P=615

Rad

ial C

oncr

ete

Stra

in

Distance from Slab Center

Fig. 15. Comparison of calculation and experiment: (a) tangential strains,(b) radial strains in concrete compression zone

(a)

(b) (b)

(a)

59



tics, load-displacement relationship and cracking behav-iour of real three-dimensional reinforced concrete struc-tures effectively.

References

1. Van Mier, J. G. M., Vervuurt, A., Schlangen, E.: Boundaryand size effects in uniaxial tensile tests: a numerical and ex-perimental study. Fracture and Damage in QuasibrittleStructures, E&FN Spon, London, 1994, pp. 289–302.

2. Schlangen, E.: Computational aspects of fracture simula-tions with lattice models. Fracture mechanics of concretestructures (Proc., FraMCoS-2, Zurich), Wittmann, F. H.(ed.), pp. 913–928. Aedificatio Publ., Freiburg, Germany,1995.

3. Niwa, J., Choi, I. C., Tanabe, T.: Analytical Study for ShearResisting Mechanism using Lattice Model. JCI Int. Work-shop on Shear in Concrete Structures, 1994, pp. 130–145.

4. Van Mier, J. G. M., Van Vliet, M. R. A., Wang, T. K.: FractureMechanisms in Particle Composites: Statistical aspects inLattice Type Analysis. Mech. Mater., vol. 34, No. 11 (2002),pp. 705–724.

5. Lilliu, G., Van Mier, J. G. M.: 3D Lattice type Fracture Mod-el for Concrete. Eng. Fracture Mech., vol. 70, No. 7–8(2003), pp. 927–941.

6. Cusatis, G., Bazant, Z. P., Cedolin, L.: Confinement-ShearLattice Model for Concrete Damage in Tension and Com-pression: I. Theory. Journal of Engineering Mechanics, AS-CE, vol. 129, No. 12 (2003), pp. 1439–1448.

7. Rashid, Y. R.: Ultimate Strength Analysis of Pre-stressedConcrete Pressure Vessels. Nuclear Engineering and Design,vol. 7 (1968), pp. 334–344.

8. Cervenka, V., Gerstle, K.: Inelastic Analysis of ReinforcedConcrete Panels: Part I. Theory, Part II: Experimental Veri-fication. IABSE, Zurich, Part I: vol. 31 (1971), pp. 32–45,Part II: vol. 32 (1972), pp. 26–39.

9. Rots, J. G., De Borst, R.: Analysis of concrete fracture in ‘di-rect’ tension. International Journal of Solids and Structures25 (1989), pp. 1381–1394.

10. Barzegar, F., Maddipudi, S.: Three-dimensional Modeling ofConcrete Structures II: Reinforced Concrete. Journal ofStructural Engineering, vol. 123, No. 10 (1997), pp.1347–1356.

11. Tanabe, T., Ahmad, S. I.: Development of Lattice EquivalentContinuum Model for Analysis of Cyclic Behavior of Rein-forced Concrete, Modeling of Inelastic Behavior of RC struc-tures under Seismic Loads, ASCE (2000), pp. 297–314.

12. Ahmad, S. I., Tanabe, T.: Development of Concrete Consti-tutive Laws Based on 3D lattice Equivalent Continuum.Journal of Materials, Concrete Structures and Pavements,JSCE, vol. 58, No. 725 (2003), pp. 293–304.

13. Bazant, Z. P., Prat, P. C.: Microplane Model for Brittle-Plas-tic Material-parts I and II. Journal of Engineering Mechan-ics, ASCE, vol. 114, No. 10 (1988), pp. 1689–1702.

14. Okamura, H., Maekawa, K.: Nonlinear Analysis and Consti-tutive Models of Reinforced Concrete, Gihodo-Shuppan,Tokyo, 1991.

15. Ottosen, N. S.: Constitutive Model for Short-Time Loading ofConcrete. Journal of the Engineering Mechanics Division,ASCE, vol. 125, No. EM1 (1979), pp. 127–141.

16. Kang, H. D., Willam, K.: Mechanical Properties of Concretein Uniaxial Compression. Materials Journal, American Con-crete Institute, vol. 94, No.6 (1997), pp. 457–471.

17. Hirasawa, I., Kanoh, M., Fujishiro, M.: Basic Test on the Dy-namic Strength of R/C Square Columns under Biaxial Bend-ing. Journal of the Society of Material Science, vol. 45, No. 4(1996) pp. 423–429.

18. Hegger, J., Beutel, R.: Durchstanzen schubbewehrterFlachdecken im Bereich von Innenstutzen. Final report, AiFresearch project 10644N, Chair and Institute of ConcreteStrctures, RWTH Aachen University, 1998.

19. Okamura, H., Maekawa, K.: Nonlinear Analysis and Consti-tutive Models of Reinforced Concrete, Gihod-Shuppan,Tokyo, 1991.

Ahmad, Syed IshtiaqPhD, Professor, Department of CivilEngineering, Bangladesh Universityof Engineering and Technology,Dhaka 1000, Bangladesh.E-mail: [email protected]

Tanabe, Tada-akiPhD, Professor (retd.), Departmentof Civil Engineering, Nagoya University, Furo-cho, Chikusa-ku,Nagoya, 464-8603, Japan.E-mail: [email protected]

60 © 2013 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete 14 (2013), No. 1

Technical Paper

DOI: 10.1002/suco.201200012

Eight sets of large, circular, short reinforced concrete columnswere tested under monotonic axial compression. The primaryvariables are type of transverse reinforcement (spiral vs. circulartie), type of splice, end hook length and staggered length of adja-cent circular ties. The tests confirmed the acceptable perfor-mance of the circular tie newly proposed in ACI 318M-11. In addi-tion, the circular tie scheme in which the ends terminate withhooks that engage with a longitudinal steel bar and bend into theconcrete core is acceptable for performance and ease of con-struction. The effectiveness of its end hook length and the stag-gered length of adjacent circular ties is also investigated.

Keywords: reinforced concrete, circular column, spiral, circular tie

1 Introduction

Concrete confinement of the column core is important forenhancing ductility, and transverse reinforcement plays animportant role. The current provisions for spiral reinforce-ment require that the minimum volumetric ratios of suchreinforcement ρs for non-seismic and seismic design ofbuilding columns are given by Eqs. (10-5) and (21-3) in ACI318M-11 [5]:

(ACI Eq. 10-5)

ρs = 0.12fc′/fyt (ACI Eq. 21-3)

wherefc′ specified compressive strength of concreteAg gross area of concrete sectionAch cross-sectional area of a structural member measured

to outside edges of transverse reinforcementfyt specified yield strength of transverse reinforcement

For circular bridge columns, only spirals or complete cir-cular ties are permitted as confining steel in the USA [1].

ρ = −⎛

⎝⎜

⎞

⎠⎟

′A

Affs

g

ch

c

yt0.45 1

Some other countries, such as Korea [9] and Japan [8], per-mit lap-spliced confinement steel with adequate cross-ties.Since the 1995 Kobe earthquake in Japan, interlockingspiral columns have been recommended in the designcode [7]. Recently in Taiwan [6, 10, 11], a new type of five-spiral cage is approved as confining hoops for columns.

ACI 318M-08 [4] does not provide sufficient designdetails of transverse reinforcement for circular columns(unlike rectangular columns), especially for circular ties.Recently, a new type of transverse reinforcement and thecorresponding detailing of circular columns have beenadded by ACI [5]. In the additional section 7.10.5.4, a com-plete circular tie is permitted where longitudinal bars arelocated around a circular cross-section. The ends of thecircular tie should overlap by not less than 150 mm andterminate with standard hooks that engage with a longitu-dinal column bar. Overlaps at ends of adjacent circularties must be staggered around the perimeter enclosing thelongitudinal bars. Alternatively, the design concept of thedevelopment of standard hooks in tension in section 12.5in ACI 318M-11 may be adopted in the newly proposedcomplete circular tie. Table 1 summarizes the related de-sign concepts for circular transverse reinforcement.

ACI 318M-11 does not provide any references to ver-ify the performance of the new type of transverse rein-forcement. Furthermore, design details such as splice type,end hook length and staggered lengths of adjacent circularties still need to be clarified. To investigate these issues [2, 3], axial load tests were carried out on 16 large circularcolumns.

2 Experimental programme2.1 Test specimens

Eight sets of large circular concrete columns, each set withtwo identical specimens, were fabricated and tested undermonotonic axial compression. All 16 specimens had thesame cross-sectional dimensions, length, longitudinal bararrangement and amount of transverse steel.

The cross-section of the circular specimens was850 mm diameter with 24 metric No. 25 (nominal diame-ter 25.4 mm) longitudinal steel bars, as shown in Fig. 1(c).This resulted in a longitudinal steel ratio of 2.2 %. Steelbars with a specified yield strength of 420 MPa and con-crete with a specified compressive strength of 28 MPawere used. According to Eqs. (10-5) and (21-3) in ACI

Experimental evaluation of large circular RC columns under pure compression

Tai-Kuang Lee*Cheng-Cheng ChenAustin D.E. PanKai-Yuan HsiueWei-Ming TsaiKen Hwa

* Corresponding author: E-mail: [email protected]

Submitted for review: 21 May 2012Revised: 7 November 2012Accepted for publication: 6 December 2012

61

T.-K. Lee/C.-C. Chen/A. D.E. Pan/K.-Y. Hsiue/W.-M. Tsai/K. Hwa · Experimental evaluation of large circular RC columns under pure compression


Table 1. Design concepts for circular transverse reinforcement

ACI 318M-11 Class of transverse Type of transverse Length of lap Extension length of Overlaps at ends section reinforcement reinforcement splice or overlap 90° hook at end of adjacent circular

splice ties staggered?

7.10.4.5 spiral lap splice larger of (1) 300 mm – no

(2) 48db

7.10.5.4 complete circular tie overlap ≥ 150 mm larger of (1) 6db yes

(2) 75 mm

12.5 complete circular tie overlap calculated development 12db noof standard hooks in tension

7.10.5.3 rectilinear tie – – larger of (1) 6db no

(2) 75 mm

Note: db is the nominal diameter of spiral or circular tie reinforcement.

850

Unit mm

A A

3535

850850

850

2580

A572 Grade 50 steel plate(850 mm Diameter)


Top segment

Test segment

Bottom segment

14 @

60

mm

10 @

80

mm

14 @

60

mm

Unit mm

A A

3535

850850

850850

850850

2580

A572 Grade 50 steel plate(850 mm Diameter)A572 Grade 50 steel plate(850 mm Diameter)


Top segment

Test segment

Bottom segment

14 @

60

mm

10 @

80

mm

14 @

60

mm

14 @

60

mm

10 @

80

mm

14 @

60

mm

850

Unit mm

A A

3535

850850

850

2580



Top segment

Test segment

Bottom segment

14 @

60

mm

10 @

80

mm

14 @

60

mm

Unit mm

A A

3535

850850

850850

850850

2580



Top segment

Test segment

Bottom segment

14 @

60

mm

10 @

80

mm

14 @

60

mm

14 @

60

mm

10 @

80

mm

14 @

60

mm

85050

Note Spiral or circular tie 2-No.10 @ 60 mm for top and bottom segments

Concrete cover = 50 mm

24 Longitudinal reinforcement (No.25)

Spiral or circular tie 2-No.10 @ 80 mm

(a) Spiral elevation (b) Circular tie elevation

(c) Section A-A

Fig. 1. Test specimens – dimensions and layout

62



318M-11, the required volumetric ratio of transverse steelρs is 0.0085. For all specimens, two metric No. 10 (nomi-nal diameter 9.5 mm) spirals or circular ties with a longitu-dinal spacing of 80 mm were used, as shown schematical-ly in Fig. 1, the total volumetric ratio of transverse steelprovided was nominally 0.0093.

Two classes of transverse reinforcement, class S andclass CT, were used; class S represents “spiral” and classCT represents “circular tie”. Five types of transverse rein-forcement splice were used, as shown in Fig. 2. For typeS1, lap splice length was 500 mm, ≈ 48db, where db is thenominal diameter of a metric No. 10 steel bar. For type S2,90° hooks at both ends bend directly into the concretecore. In addition, two 90° hooks for type S3 for all circularties engage with the same auxiliary longitudinal rebar. For

type S4, similar to rectilinear ties, two 90° hooks engagewith the same longitudinal rebar. For type S5, the circulartie overlaps with length �dh = 150 mm, where �dh is the required development length in tension with a standardhook.

The ends of the circular tie of type S5 terminate withhooks; one engages with a longitudinal steel bar and theother bends into the concrete core. For ease of construc-tion, type S5 does not require that both hooks engage witha longitudinal rebar like the newly proposed type in ACI318M-11. The nominal extension length of 90° hooks is120 mm or 12db for all types except type S1. The overlaplocations of adjacent circular ties except type S3 follow thesame rotation direction along the longitudinal reinforce-ment axis with designated staggered length. The nominalstaggered length is approx. �dh, 160 mm.

Table 2 lists set designations, class of transverse rein-forcement, type of transverse reinforcement splice, lengthof lap splice or overlap, extension length of 90° hook andstaggered length of each set of specimens. For set CT-S5-6db, the extension length of the 90° hook is 60 mm, 6db.For CT-S5-2L, the staggered length is 320 mm. In each setthere were two identical test specimens designated as “a”and “b” following the set designation.

The length of the columns (2550 mm) was threetimes the cross-sectional width. Each specimen was divid-ed into three segments, as shown in Figs. 1(a) and 1(b).The top and bottom segments were strengthened by providing higher concrete confinement achieved by re-ducing the longitudinal spacing of transverse reinforce-ment from 80 to 60 mm. As a result, the main failure ofthe column was then limited to the test segment. A 15 mmthick steel end plate capped each end of each column,and all the longitudinal steel bars were welded to theseend plates.

Three sets of steel forms were used for concreteplacement. The specimens were cast in an upright posi-tion and ready mixed concrete was used. The final levelof concrete placement was set to 20 mm below the topend plate. The remaining 20 mm gap was filled with non-shrink cement grout with a nominal compressive strengthof 56 MPa. The actual concrete compressive strength ofeach specimen can be found in Table 3. The actual yield and tensile strengths of the steel bars are listed inTable 4.

500 mm

120 mm

(a) Type S1 (b) Type S2

auxiliarylongitudinal rebar

main longitudinal rebar

(c) Type S3 (d) Type S4

120 mm

(e) Type S5

Fig. 2. Types of transverse reinforcement splice

Table 2. Test specimen specifications

Set designation Class of transverse Type of transverse Length of lap splice Extension length Staggered length reinforcement reinforcement or overlap [mm] of 90° hook [mm] of adjacent circular

splice ties [mm]

S-S1 S S1 500 – –

S-S4 S S4 – 120 –

CT-S2 CT S2 – 120 160

CT-S3 CT S3 – 120 –

CT-S4 CT S4 – 120 160

CT-S5-6db CT S5 150 60 160

CT-S5 CT S5 150 120 160

CT-S5-2L CT S5 150 120 320

63



2.2 Test setup and instrumentation

Specimens were tested using the 30 MN universal testingmachine housed in the large-scale structure testing labora-tory of the Architecture & Building Research Institute(ABRI) in Taiwan. The specimens were first centred andplumbed beneath the loading head. A monotonic com-pressive load was then applied using displacement controlat a strain rate of 0.0009/min. The loading test was termi-nated when the post-peak load dropped below 50 % of thepeak load.

The applied load was measured by the differentialpressure Δ-p cell built into the machine. Axial deformationof the test segment of the specimen was measured by fourdisplacement transducers (DT 1 to DT 4) installed uni-formly around the specimen, as shown in Fig. 3. The dis-placement measured by the LVDT built into the machinewas also recorded. Furthermore, transparent plastic sheetwas wrapped around the specimen to retain the spalledconcrete and thus protect the test segment deformationmeasuring system. Fig. 4 shows specimen CT-S5-2Lb dur-ing testing.

Table 3. Average strengths of reinforced concrete column specimens

Specimen Measured concrete compressive strength [MPa]

S-S1a 28.7

S-S1b 29.9

S-S4a 29.9

S-S4b 28.0

CT-S2a 29.2

CT-S2b 28.7

CT-S3a 31.4

CT-S3b 28.0

CT-S4a 28.7

CT-S4b 24.3

CT-S5-6dba 29.0

CT-S5-6dbb 26.8

CT-S5a 28.8

CT-S5b 29.0

CT-S5-2La 22.0

CT-S5-2Lb 22.0

Table 4. Mechanical properties of steel bars used

Specimen Steel bar Yield strength [MPa] Tensile strength [MPa]

S-S1(a,b), S-S4(a,b), CT-S3(a,b) No. 25 458 676

No. 10 445 631

CT-S2(a,b), CT-S4(a,b), CT-S5a, CT-S5-2L(a,b) No. 25 485 711

No. 10 456 729

CT-S5-6db(a,b), CT-S5b No. 25 447 658

No. 10 456 729

Unit mm

850

850

850

DT

Unit mm

Loading plate

850

850

850

Supporting thread

DT

DT gripper

Loading plate

Embedded threaded bar

Fig. 3. Displacement transducer installation scheme

CT-S5-2Lb

19 MN

Fig. 4. Transparent plastic sheet wrapped around specimen CT-S5-2Lb

64



3 Experimental results

Since the specimen was wrapped in plastic sheet, failure ofthe specimens during loading was difficult to identifyclearly by way of direct observation. However, the plasticsheet and the spalled concrete were removed after theloading test in order to inspect the specimen.

Fig. 5 shows specimen CT-S2a after removing theplastic sheet. Significant concrete spalling, longitudinalsteel bar buckling and core concrete crushing could beseen in the test segment for all test specimens. In the topand bottom segments of the specimens, significant con-crete spalling could be observed, but there were no signsof steel bar buckling. It was thus concluded that failure ofall specimens occurred in the desired manner in the topand bottom segments. For all specimens, the steel buck-

ling and core concrete crushing were observed at approxi-mately the same height around the circumference at theaverage column length location of 480 mm, as shown inFig. 6. Tensile fractures occurred in the spirals or circularties in all columns except specimens CT-S4b, CT-S5-6dbaand CT-S5-6dbb. This observation signifies that someperimeter hoops could reach their tensile strengths.

Figs. 7(a) and 7(b) show the measured load vs. axialdeformation curves of specimen S-S4a. The axial defor-mation data for curve A, designated δA, are the averagevalues of DT 1 to DT 4. The axial deformation data for

(a) Specimen S-S4b (b) Specimen CT-S4b (c) Specimen CT-S5-2Lb

S-S4b

CT-S5-2Lb

CT-S4b

Fig. 6. Typical test specimen failures

CT-S2a

Fig. 5. Failure of specimen CT-S2a

0

5

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Axial Displacement (mm)

Axi

al L

oad

(MN

)

A2

Axi

al l

oad

(M

N)

Axial Deformation A (mm)

Measured Axial Load-Deformation Curve

A1

Curve A

Spallδ

SpallPδ

0

5

10

15

20

25

0 5 10 15 20 25 30 35 40 45


Axi

al L

oad

(MN

)

A2

Axi

al l

oad

(M

N)

Axial Deformation A (mm)


A1

Curve A

Spallδ

SpallPδ

0

5

10

15

20

25

0 5 10 15 20 25 30 35 40 45


Axi

al L

oad

(MN

)A

xial

loa

d (

MN

)

Axial Deformation (mm)

Curve AShifted Curve B

Approximate Axial Load-Deformation Curve

’

Shifted & Corrected Curve B

C1

C2

C3 C3’

Spallδ

SpallPδ

Axi

al l

oad

(M

N)

0

5

10

15

20

25

0 5 10 15 20 25 30 35 40 45


Axi

al L

oad

(MN

)

Axial Deformation (mm)

Curve AShifted Curve B

Approximate Axial Load-Deformation Curve

’

Shifted & Corrected Curve B

C1

C2

C3 C3’

Spallδ

SpallPδ

Axi

al l

oad

(M

N)

0

5

10

15

20

25

0 5 10 15 20 25 30 35 40 45


Axi

al L

oad

(MN

)A

xial

loa

d (

MN

)

Axial Deformation B (mm)


B1

B2

B3

Curve B

SpallPδ

SpallB δδ )(0

5

10

15

20

25

0 5 10 15 20 25 30 35 40 45


Axi

al L

oad

(MN

)A

xial

loa

d (

MN

)

Axial Deformation B (mm)


B1

B2

B3

Curve B

SpallPδ

SpallB δδ )(

(a) Definitions of axial load-deformation curve in the elastic range

(b) Definitions of axial load-deformation curve in the plastic range

(c) Axial load-deformation curve, (a) and (b) combined

Fig. 7. Definitions of axial load-deformation curves

65



The C1-C2-C3′ curve in Fig. 7(c) is the P vs. δ curve ob-tained for specimen S-S4a. The C1-C2 segment is taken directly from the A1-A2 curve of Fig. 7(a). By shifting theB2-B3 curve of Fig. 7(b) horizontally and connecting B2 toC2, we obtain the C2-C3 curve. The horizontal differencebetween C2-C3 and C2-C3′ is the δ′ calculated according toEq. (3). The actual P vs. δ curve should be located some-where between C1-C2-C3 and C1-C2-C3′. Curve C1-C2-C3′ isused in the following discussion.

The P vs. δ curve for all the specimens was obtainedthrough the same procedure. Dividing δ by the length ofthe test segment (850 mm) enables the average strain inthe test segment ε to be obtained. Fig. 8 shows the P/P0 vs.ε curve for all specimens. Table 5 shows a summary of thetest results in which Ppeak is the maximum load reached,εpeak is the strain corresponding to Ppeak and εu is thestrain corresponding to 0.8P/P0 in the descending state ofthe P/P0 vs. ε curve. It was found that the two specimensin the same specimen set exhibited fairly similar behav-iour. Therefore, the average values of the two specimensin the same set, e.g. P–peak, ε–peak and ε–u, are used for the following discussion.

The maximum load P–peak is greater than P0 by5–15 % for all specimens, which indicates that the fullstrength of the specimens was achieved. The strain εpeak ismuch greater than 0.004 for 11 specimens, which showsthat these specimens regained strength after the concretecover had spalled. Although five specimens (S-S1a, S-S4a,CT-S3b, CT-S4a and CT-S5b) did not show clear signs of re-gaining strength, those specimens still possessed a certainamount of plastic deformation capacity, as can be seen inFig. 8. The significant difference in εpeak between twoidentical test specimens for all sets except CT-S5-6db andCT-S5-2L is also evident in Table 5. This indicates that thecorresponding strains at peak axial load vary considerablyin this research.

The transverse reinforcement used in this researchseems to work satisfactorily. This suggests that the trans-verse reinforcement schemes investigated here are all ac-ceptable for this specific column section. However, thereare some apparent differences in performance among thetransverse reinforcement schemes and they are discussedbelow.

The strain ε–u in CT-S5-6db is 48 % higher than that ofS-S1. Therefore, it can be concluded that a type S5 spliceis better than a type S1. The newly proposed type of circu-lar tie in ACI 318M-11 should be acceptable because CT-S5-6db matches the type proposed in ACI 318M-11 exceptthat the ends of the circular tie of type S5 terminate withhooks that engage with a longitudinal steel bar and bendinto the concrete core.

The difference in ε–u between S-S4 and CT-S5-6dbis about 5 %. This indicates that the performance of typeS4 for spirals could be as good as that of type 5. Hence,the improved ACI spiral splice type can provide a higher confining force than the traditional ACI spiral lap splice.

The difference in ε–u between CT-S5 and CT-S5-6db isabout 3 %. It is apparent that the short extension length ofthe 90° hook did not lead to unfavourable results. Conse-quently, the extension length of six times the transverse re-inforcement diameter for a 90° hook on a circular tie, in

curve B, designated δB, are from the built-in LVDT of thetesting machine. The axial deformation of the test seg-ment, designated δ hereinafter, was expected to be equalto δA. Although the cracked concrete cover was retainedby the plastic sheet to avoid damaging the displacementmeasuring system, δA started to become unreliable as theaxial deformation of the test segment exceeded valuesranging from 1.275 to 1.7 mm, expressed as δSpall, which isequivalent to an axial compressive strain of between0.0015 and 0.002. This is mainly because the embeddedthreaded bars for mounting the DTs were distorted by thecracked concrete cover. Therefore, the axial deformationdata had to be corrected to δB once axial deformations ex-ceeded δSpall.

The measured δB included the deformation of thewhole system, which included the three segments of thespecimen and the loading system. The axial elastic stiff-ness of the column is designated KA and was obtained bylinear regression of the P vs. δA data points within 20 to70 % of P0 as calculated according to Eq. (1) with actualmaterial strengths:

(1)

wherefc′ measured compressive strength of concrete in Table 3Ast total area of longitudinal reinforcementfy yield strength of reinforcement

The elastic stiffness of the whole system, designated KB,was obtained by linear regression of the P vs. δB datapoints in the range from 20 to 70 % of P0. Further, theelastic stiffness of the loading system KLS can be obtainedfrom Eq. (2) by using the equivalent spring concept for

multiple springs in series :

(2)

Once the axial deformation reaches δSpall, it is assumedthat the top specimen segment, the bottom specimen seg-ment and the loading system all remain in the elasticrange with stiffnesses of KA, KA and KLS respectively. Asthe axial deformation increased, the load varied. Further,the differential axial deformation δ′ of the top specimensegment, the bottom specimen segment and the loadingsystem can be calculated according to Eq. (3):

(3)

where PδSpall is the load reading at axial deformationequal to δSpall.

Consequently, δ beyond δSpall can be obtained by usingEq. (4):

(4)

where (δB)δSpall is δB corresponding to PδSpall.

δ ′ = ×−

+−δ δP P

K

P P

KA LS

Spall Spall2( ) ( )

=−

KK K

K KLSA B

A B3

= +K K KB A LS

1 3 1

= ′ − +P f A A f Ac g st y st0.850 ( )

δ δ δ δ δ= + − + ′δSpall B B Spall[ ( ) ]

66



accordance with stirrup and tie hooks in ACI, is appro -priate.

The strain ε–u of CT-S5-2L is 16 % higher than that ofCT-S5. Accordingly, it can be concluded that the largeroverlap staggered length for type S5 can provide a higherconfining force. At the same time, the ACI 318M-11 recom-mendation that overlaps at ends of adjacent circular tiesshould be staggered around the circumference enclosingthe longitudinal bars is reasonable.

The difference in ε–u between CT-S2 and CT-S3 isabout 5 %. But it is obvious that CT-S2 and CT-S3 are bet-ter than S-S1 and close to S-S4.

The strain ε–u of CT-S4 is 10 % higher than that of CT-S5-6db and 16 % higher than that of S-S4. Therefore, itcan be concluded that a type CT-S4 splice is better thanCT-S5-6db and S-S4.

The performance of CT-S5-6db, CT-S5 and CT-S5-2Lis in each case better than that of S-S1. Therefore, a typeS5 splice layout is acceptable for performance and ease ofconstruction.

In this paper, S-S1 is the only set that used the lapsplice type for the spiral, whereas the other sets used 90°hooks at both ends. Both spiral and circular ties were bentinto the concrete core. According to the results shown in

0.01 0.02 0.03 0.04 0.05 0.06Axial Strain (mm/mm)

0

0.2

0.4

0.6

0.8

1

1.2

P/P 0

0 0.01 0.02 0.03 0.04 0.05 0.06Axial Strain (mm/mm)

0.2

0.4

0.6

0.8

1

1.2

P/P 0

0.2

0.4

0.6

0.8

1

1.2

P/P 0

0.2

0.4

0.6

0.8

1

1.2

P/P 0

0 0.01 0.02 0.03 0.04 0.05 0.06Axial Strain (mm/mm)

0.01 0.02 0.03 0.04 0.05 0.06Axial Strain (mm/mm)

0

0.2

0.4

0.6

0.8

1

1.2

P/P 0

0.2

0.4

0.6

0.8

1

1.2

P/P 0

0.2

0.4

0.6

0.8

1

1.2

P/P 0

0.2

0.4

0.6

0.8

1

1.2

P/P 0

S-S1aS-S1b

S-S4aS-S4b

CT-S2aCT-S2b

CT-S3aCT-S3b

CT-S4aCT-S4b

CT-S5-6dbaCT-S5-6dbb

CT-S5aCT-S5b

CT-S5-2LaCT-S5-2Lb

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Axial Load-Deformation Curves

Fig. 8. Axial load-displacement curves for all specimens

67



Table 5, the performance of 90° hooks at both ends is sig-nificantly better than that of the lap splice. It can be rea-soned that the 90° hooks bent into the concrete core arehelped by the better confinement of the core after the con-crete cover has spalled. Some evidence of this mechanicalphenomenon is provided by the fact that even the 90°hooks bent directly into the concrete core without engag-ing any longitudinal rebar (CT-S2) also exhibited accept-able performance.

4 Conclusions and recommendations

The effectiveness of several transverse reinforcementschemes for columns was investigated by axial load testson 16 large circular column specimens. Based on the testresults reported here, the following conclusions can bedrawn:(1) The circular tie newly proposed in ACI 318M-11,

where the ends overlap by 150 mm and terminate withtie hooks that engage with a longitudinal column bar,exhibits acceptable performance.

(2) The improved ACI spiral splice type with two 90°hooks and an extension length of 12 times the trans-verse reinforcement diameter engaging with the samelongitudinal rebar can provide a higher confiningforce than the traditional ACI spiral lap splice.

(3) The extension length of six times the transverse rein-forcement diameter for a 90° hook on a circular tie, inaccordance with tie hooks in ACI, is appropriate.

(4) The larger overlap staggered length of adjacent circu-lar ties can provide a higher confining force. The ACI318M-11 recommendation that overlaps at ends of

adjacent circular ties should be staggered around thecircumference enclosing the longitudinal bars is rea-sonable.

(5) The performance figures of circular ties with twohooks bending into the concrete core and engagingwith the same auxiliary longitudinal rebar are veryclose, better than the traditional ACI spiral lap spliceand close to the improved ACI spiral splice type.

(6) Circular ties with two 90° hooks and an extensionlength of 12 times the transverse reinforcement diam-eter engaging with the same longitudinal rebar spliceare better than the improved ACI spiral splice.

(7) The circular tie scheme in which the ends terminatewith hooks that engage with a longitudinal steel barand bend into the concrete core, similar to the newlyproposed type in ACI 318M-11, is acceptable for per-formance and ease of construction. It is recommend-ed for practical design. However, the effectiveness under cyclic loading needs further study.

Acknowledgements

The writers gratefully acknowledge the support of andcontributions to this project from the Architecture &Building Research Institute.

Notation

Ag gross area of sectionAst longitudinal reinforcement areadb nominal diameter of spiral or circular hoop rein-

forcement

Table 5. Summary of test results

Specimen set Specimen Ppeak/P0 εpeak εu P–peak/P0 ε–peak ε–u ε–u/(ε

–u)S–S1

S-S1 S-S1a 1.07 0.0027 0.0281.07 0.0056 0.027 1.00

S-S1b 1.07 0.0084 0.026

S-S4 S-S4a 1.17 0.0021 0.0331.15 0.0049 0.038 1.41

S-S4b 1.12 0.0077 0.043

CT-S2 CT-S2a 1.14 0.0080 0.0341.12 0.0092 0.037 1.37

CT-S2b 1.10 0.0103 0.040

CT-S3 CT-S3a 1.06 0.0083 0.0281.07 0.0053 0.035 1.30

CT-S3b 1.07 0.0022 0.041

CT-S4 CT-S4a 1.06 0.0037 0.0431.08 0.0113 0.044 1.63

CT-S4b 1.10 0.0189 0.044

CT-S5-6db CT-S5-6dba 1.05 0.0155 0.0381.05 0.0156 0.040 1.48

CT-S5-6dbb 1.04 0.0157 0.042

CT-S5 CT-S5a 1.10 0.0095 0.0421.12 0.0072 0.039 1.44

CT-S5b 1.14 0.0048 0.036

CT-S5-2L CT-S5-2La 1.13 0.0154 0.0401.15 0.0164 0.045 1.67

CT-S5-2Lb 1.17 0.0174 0.049

68



fc′ specified or measured compressive strength ofconcrete

fy specified yield strength of longitudinal reinforce-ment

KA elastic stiffness of three segments of specimenKB elastic stiffness of whole systemKLS elastic stiffness of loading system�dh development length in tension of deformed bar

with standard hookP axial loadP0 axial maximum nominal strengthPδSpall load reading at axial deformation equal to

δSpallPpeak maximum loadP–peak average value of Ppeakδ axial deformation of test segment of specimensδA axial deformation of test segment of specimens

(average values of four DTs)δB axial deformation of whole system (measured by

LVDT built into 30 MN universal testing ma-chine)

δSpall axial compressive strain between 0.0015 and0.002

(δB)δSpall δB corresponding to PδSpallδ′ axial deformation difference considering elastic

effect of top specimen segment, bottom speci-men segment and loading system

ε strain in test segment of specimensεpeak strain corresponding to Ppeakεu strain corresponding to 0.8P/P0 in descending

state of P/P0 vs. ε curveε–peak average value of εpeakε–u average value of εuρs ratio of volume of spiral reinforcement to total

volume of core confined by the spiral (measuredoutside-to-outside of spirals)

References

1. AASHTO: AASHTO LRFD bridge design specifications.American Association of State Highway & TransportationOfficials, SI Units, 3rd ed., Washington, D.C., USA, 2005.

2. ABRI, Ministry of the Interior: Axial ductile performance oflarge-scale circular reinforced concrete columns with differ-ent design details. ABRI report 098301070000G2026, Taipei,Taiwan, 2009 (in Chinese).

3. ABRI, Ministry of the Interior: Axial ductile performance oflarge-scale circular reinforced concrete columns with circu-lar ties. ABRI report 099301070000G2020, Taipei, Taiwan,2010 (in Chinese).

4. ACI Committee 318: Building code requirements for struc-tural concrete (ACI 318M-08) and commentary. FarmingtonHills, Michigan: American Concrete Institute, 2008.

5. ACI Committee 318: Building code requirements for struc-tural concrete (ACI 318M-11) and commentary. FarmingtonHills, Michigan: American Concrete Institute, 2011.

6. Chang, K. C., Yin, Y. L., Wang, J. C., Wang, B. S.: Experimen-tal study of spiral application to rectangular columns. Engi-neering 2005: 78 (3), pp. 101–124, Chinese Institute of Engi-neers, Taipei, Taiwan (in Chinese).

7. Japan Road Association: Seismic design specifications ofhighway bridges. Maruzen, Tokyo, Japan, 1996.

8. Japan Road Association: Seismic design specifications ofhighway bridges. Maruzen, Tokyo, Japan, 2002.

9. Korean Ministry of Construction & Transportation/KoreanSociety of Civil Engineers: Design specifications for highwaybridges, Korea, 2000.

10. Weng, C. C., Yin, Y. L., Wang, J. C., Liang, C. Y.: Seismiccyclic loading test of SRC columns confined with 5-spirals.Science in China Series E: Technological Sciences 2008: 51(5), pp. 529–555, Chinese Academy of Sciences, Beijing, China.

11. Weng, C. C., Yin, Y. L., Wang, J. C., Liang, C. Y., Lin, K. Y.:Seismic cyclic loading test of RC columns confined with 5-spirals. Structural Engineering 2011: 26 (1), pp. 57–91, Chinese Society of Structural Engineering, Taipei, Taiwan(in Chinese).

Cheng-Cheng ChenProfessor, Department of Construc-tion Engineering, National TaiwanUniversity of Science & Technology,No. 43, Keelung Rd., Sect. 4, Taipei,Taiwan

Tai-Kuang LeeResearcher, Architecture & BuildingResearch Institute, Ministry of the Interior, 13F, No. 200, Beisin Rd., Sect. 3, Sindian, New Taipei City, Taiwan

Kai-Yuan HsiueFormerly Research & DevelopmentSubstitute Services (RDSS), Architecture & Building ResearchInstitute, Ministry of the Interior, 13F, No. 200, Beisin Rd., Sect. 3, Sindian,New Taipei City, Taiwan

Austin D.E. PanTechnical Services Division Manager,Western Region Infrastructure Sector, P.O. Box 50012,Madinat Zayed,Abu Dhabi, United Arab Emirates

Ken HwaAssociate Professor, Department of Architecture, Taoyuan InnovationInstitute of Technology, No. 414,Sect. 3, Chung-Shang E. Rd.,Chungli, Taoyuan, Taiwan

Wei-Ming TsaiFormerly Research & Development Substitute Services (RDSS), Architecture & Building Research Institute, Ministry of the Interior, 13F,No. 200, Beisin Rd., Sect. 3, Sindian,New Taipei City, Taiwan


This article describes an experimental programme aimed atstudying the effect of cover, ratio between diameter and effectivereinforcement ratio (φ/ρs,ef) and the influence of stirrup spacingon the cracking behaviour of reinforced concrete elements. Theexperimental programme was conceived in order to contribute tothe debate – fuelled by the publication in recent years of Euro -code 2 EN1992-1-1 and the revision of the Model Code under waywhen the tests were carried out (and now published as a final-ized document) – regarding the influence of these parameters oncracking. Important theoretical aspects are discussed, includingwhere the crack width is estimated by current code formulationsand what relevance this may have on the correlation betweencrack opening and durability of RC structures, especially with regard to structures with large covers. The effect of stirrup spac-ing, a variable absent from current codes, is also discussed.

Keywords: cracking, φ/ρs,ef, cover, influence of stirrups

1 Introduction

There has been a long-lasting debate regarding models forthe calculation of crack width design. Borosnyói andBalázs [1] compiled a total of 23 different mathematicalformulations for the calculation of crack spacing and 33different formulae for the calculation of crack width.These figures provide an idea of how far consensus goes inthe modelling of cracking of concrete structures. Further-more, in 2004 Beeby [2] agitated the debate by publishingan article heavily defending the thesis that crack spacing isindependent of parameter φ/ρs,ef and depends only on thedistance from the nearest reinforcing bar. This was a verycontroversial statement, since the dependence of crackspacing on φ/ρs,ef is a direct consequence of theory, where-as dependence of crack spacing on cover and bar distanceis more empirical. Despite a database with more than 300tests from various researchers [3–10], it was not possible toobtain conclusive evidence that could settle this question.For this reason, with a view to proposing a cracking formulation for Model Code 2010 [11], and working fromthe joint effort of fib Task Group 4.1, an experimentalstudy was undertaken with the financial support of

COMSAEMTE. The aim of this was to distinguish the ef-fect on cracking of cover, φ/ρs,ef and stirrup spacing. Theresults of this experimental programme are presented forthe first time in this paper.

Another very important issue addressed in this pa-per, and which has been the subject of much confusion, is:Where do cracking models provide crack width? At thesurface of the reinforcement or at the surface of the con-crete?

2 Experimental programme2.1 Description of tests

An experimental programme involving 12 beam speci-mens was carried out at the Structures Laboratory of theCivil Engineering School of the Polytechnic University ofMadrid from May to October 2009. The tests featuredpoint loading with a constant moment span of 3.42 m.Fig. 1 shows the test setup. All beams had a rectangularcross-section 0.35 m wide and 0.45 m deep. All specimenswere concreted at the same time using the same concreteof strength class C25/33. Table 1 shows the results of thecompression tests carried out at seven and 28 days.

The parameters studied were cover (20 and 70 mm),φ/ρs,ef ratio (diameter / amount of reinforcement per effec-tive area of concrete), for which bar diameters of 12 mmand 25 mm (four bars in tension) were considered, andstirrup spacing sw. To do this, three configurations wereconsidered: no stirrups in the constant bending momentspan, stirrups spaced at 10 cm and stirrups spaced at 30cm. Stirrup diameter was 8 mm. The specimens were cod-ed XX-YY-ZZ, with XX referring to bar diameter (12 or 25),YY referring to cover (20 or 70) and ZZ referring to stirrupspacing (00 for no stirrups, 10 and 30, for 10 cm and 30 cmspacing respectively). The cross-sections of the specimensare shown in Fig. 2.

Table 2 shows the cover c, φ/ρs,ef ratio and stirrupspacing sw of each specimen. The effective area is calcu-lated according to the definitions of EN 1992-1-1 (or MC2010, which are the same), according to which the effec-tive depth of the effective concrete tensile zone is the less-er of 2.5(h-d), h/2 and (h-x)/3, where h is the total depthof the cross section, d the effective depth and x the depthof the neutral axis for the cracked cross-section. In speci-mens 25-70-ZZ, the depth of the effective zone hef is limit-ed by the third condition, i.e. that it be smaller than one-

Articles

Cracking of RC members revisited: influence of cover, φ/ρs,ef and stirrup spacing – an experimental and theoretical study

Alejandro Pérez Caldentey*

Hugo Corres PeirettiJoan Peset IribarrenAlejandro Giraldo Soto

DOI: 10.1002/suco.201200016


Submitted for review: 26 June 2012Revised: 2 October 2012Accepted for publication: 10 December 2012

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A. Pérez Caldentey/H. Corres Peiretti/J. Peset Iribarren/A. Giraldo Soto · Cracking of RC members revisited: influence of cover, φ/ρs,ef and stirrup spacing – an experimental and theoretical study


Fig. 1. Test setup

Table 1. Compressive strength of concrete at seven and 28 days; specimens concreted on 26 March 2009

Specimen Date of Test Age of concrete Density [t/m3] Measured compressive Mean Value [fcm][days] stress fc [MPa]

1 04/02/2009 7 2.29 21.32 04/02/2009 7 2.28 22.3 21.93 04/02/2009 7 2.27 22.0

4 04/23/2009 28 2.29 26.25 04/23/2009 28 2.28 27.1 26.96 04/23/2009 28 2.29 27.4

12–20–00 25–20–00 25–70–0012–70–00

12–20–10/30 25–20–10/30 12–70–10/30 25–70–10/30

0.35 0.35 0.35 0.35

0.45

0.45

0.45

0.45

0.45

0.45

0.45

0.45

0.02

+0.0

12

0.02

+0.0

12

0.07

0+0.

012

0.07

0+0.

012

0.35 0.35 0.35 0.35

0.02

0.02

0.07

0.07

Fig. 2. Beam cross-sections

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third of the depth h of the member minus the depth of theneutral axis x.

All beams were loaded until failure so that the ser-viceability working area could be fully explored. More de-tails can be found in [12], corresponding to the researchproject report.

2.2 Measurements

The following data were measured for each beam:– Applied load– Support reactions– Deflections at cantilever ends, mid-span and quarter-

span points– Strain along the compression face in correspondence

with the location of longitudinal reinforcement in theside of the beam, using a digital extensometer with abase of 20 cm

– Strain along the tension face in correspondence withthe location of longitudinal reinforcement in the side of

the beam, using a digital extensometer with a base of20 cm

– Strain along the tension face in correspondence withthe location of longitudinal reinforcement in the top ofthe beam, using a digital extensometer with a base of20 cm

2.3 Test results

A summary of test results in terms of mean sr,m and maxi-mum sr,max crack spacing is given in Table 3. Fig. 3 showsthe crack patterns of the 12 beams tested. The observed ef-fects of cover c, φ/ρs,ef ratio and stirrup spacing on crackspacing are presented in the following paragraphs.

2.3.1 Measuring crack width

The conceptual equation for the calculation of crackwidth can be written as

(1)

wherewm mean crack widthsr,m mean crack spacingσs theoretical stress in reinforcing steel at crackEs longitudinal elastic modulus of steelTS effect of tension stiffening

The tension stiffening effect takes into account the factthat in between cracks, part of the tensile force carried bythe steel at the crack is taken by the concrete, thus reduc-ing the stress in the concrete and increasing the strain inthe concrete. This effect reduces the crack width by reduc-ing the mean difference in strain between steel and con-crete. This equation allows an experimental value for thecrack spacing to be derived, based on the measured valueof wm:

(2)

σ=w

Es TSm

s

sr m,

σ=s

w ETSr m

m s

s,

Table 2. Main characteristics of the tested beams

Beam ID φ [mm] c [mm] φ/ρs,ef [mm] sw [mm]

25-20-00 25 20 460 –25-20-10 25 20 460 10025-20-30 25 20 460 300

12-20-00 12 20 882 –12-20-10 12 20 882 10012-20-30 12 20 882 300

25-70-00 25 70 473 (*) –25-70-10 25 70 473 (*) 10025-70-30 25 70 473 (*) 300

12-70-00 12 70 1172 –12-70-10 12 70 1172 10012-70-30 12 70 1172 300

* hef = (h-x)/3

Table 3. Measured mean and maximum crack spacing

Beam ID φ [mm] c [mm] φ/ρs,ef [mm] sw [mm] sr,m [mm] sr,max [mm]

25-20-00 25 20 460 – 131 234

25-20-10 25 20 460 100 114 230

25-20-30 25 20 460 300 152 258

12-20-00 12 20 882 – 173 269

12-20-10 12 20 882 100 182 320

12-20-30 12 20 882 300 274 358

25-70-00 25 70 473 – 227 423

25-70-10 25 70 473 100 189 460

25-70-30 25 70 473 300 200 442

12-70-00 12 70 1172 – 236 412

12-70-10 12 70 1172 100 260 381

12-70-30 12 70 1172 300 281 383

It has been argued, most notably by Beeby [13], that this isa better estimate of the crack spacing than the actual spac-ing, which can be obtained from counting the number ofcracks and dividing the length of the constant bending

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moment span by this number, due to the fact that it cannever be stated that cracking is stabilized. However, it isthe authors’ experience that these values indeed differ inmany tests reported in the literature, but it seems that this

Fig. 3a. Effect of stirrup spacing on crack spacing in specimens with 12 mm dia. rebar

Fig. 3b. Effect of stirrup spacing on crack spacing in specimens with 25 mm dia. rebar

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discrepancy can also be attributed to errors in measuringthe crack width, and not only to non-stabilized cracking. Itis well known that direct crack measurement by visualmeans carries with it a strong subjective component re-garding the exact position in which the measurement istaken. Cracks open and close during a test, their widthvaries along their length, they divide and converge at dif-ferent load steps and in many cases do not form perpen-dicularly to the reinforcement. Further, direct visual mea-surement of the crack width is very difficult due to thestrain it puts on the eyes of the person reading the instru-ment. For this reason, the crack width was estimated inthis study by measuring the mean strain along the tensilechord in correspondence with the reinforcement both inthe side of the beam and in the top of the beam. The meancrack width was determined by dividing the mean strainby the number of cracks. This measurement already in-cludes the effect of tension stiffening. Crack spacing wasdetermined by direct observation. It was also observedthat the crack pattern became fairly stable after a certainpoint in the test, so that it can be said that a stabilizedcrack pattern was reached in all tests.

Eq. (3) shows the expressions used to estimate themean and maximum crack widths.

(3)

whereεtension mean strain in tension chordL length of constant moment zoneεmax maximum measured strain in tension chord

∑ ∑ε ε

ε ε ε

ε

( )× = + × → = =

= − ≈

≈ ×

L w L ww

nL

nL

nw l

tension c mcracks

tension ccracks

tensioncracks

max max

l measurement length of extensometer (20 cm)Σw sum of crack openings within constant moment

spanncracks number of cracks located within L

The above expressions take into account the fact that thestress in the reinforcement is reduced between cracks dueto the contribution of the concrete, but ignore the effect ofthe tensile strain in the concrete and therefore slightlyoverestimate the crack width. However, this error is small.An example can be considered to support this statement.Assuming a relatively large 30 cm crack spacing, a tensilestrength of 3.2 MPa, a modulus of elasticity of concrete of30 000 MPa and a parabolic law for the tensile strain vari-ation in the concrete, the tensile elongation of the con-crete would result in a reduction in the crack width of on-ly 2/3 × 0.3 × 3.2/30 000 = 0.02 mm.

2.3.2 Influence of cover

The influence of cover, irrespective of the value of φ/ρs,ef,can be best appreciated by comparing the results fromtests 25-20-XX and 25-70-XX. This is because these testshave almost the same φ/ρs,ef ratio due to the fact that thedepth of the effective concrete area is limited, as shown intable 2 (both in EN 1992-1-1[14] and MC90 [15]), by thevalue of (h-x)/3.

Fig. 4 shows very clearly how cover increases crackwidth. This increase is clearly related to an increase incrack spacing (and therefore crack width), as can be seenin Fig. 5. The mean crack spacing increased from 13.1 cmin beam 25-20-00 (28 cracks) to 22.7 cm in beam 25-70-00(16 cracks). These results confirm that cover is an impor-tant factor in the development of the cracking pattern andthat models that do not consider this variable, such as

Fig. 4. The effect of cover on crack width: a very clear influence is observed in specimens having nearly the same effective concrete area

Model Code 90 [15], are incomplete. From a theoreticalpoint of view, the effect of cover on crack spacing can beunderstood by the need to transmit tension stresses gener-ated at the bar-concrete interface to the effective concretearea surrounding the bar in order to generate actual crack-ing. However, this is only part of the explanation of howcover affects crack spacing. Another aspect of the influ-ence of cover on crack spacing has to do with secondarycracks and whether or not these cracks eventually becomepassing cracks. This topic is addressed in more detail insection 3.2.

2.3.3 Influence of φ/ρs,ef

The influence of the φ/ρs,ef ratio on crack spacing is a di-rect consequence of the definition of the transfer lengthand can be easily derived from the equilibrium of the barbetween a crack and the zero slip section and from theequilibrium of the two sections. The influence of this fac-tor on crack spacing can easily be compared by countingthe number of cracks in specimens having the same cover.Fig. 6 shows this comparison. A clear influence can be

74



seen as the crack spacing increases with the value ofφ/ρs,ef. These results seem to show a larger influence ofthis parameter for a smaller cover. This seems logical sincecrack spacing can be modelled as the sum of the effect ofcover and the effect of φ/ρs,ef, as shown in Eq. (4):

(4)

As the cover c increases, so the relative importance of thesecond term in φ/ρs,ef becomes smaller. In Eq. (4), k1 andk2 are constants.

2.3.4 Influence of stirrup spacing

Most cracking tests carried out avoid the presence of stir-rups, because they influence the cracking pattern. A goodexample of this can be seen in the tie cracking tests car-ried out by Gómez Navarro [16] in Lausanne, shown inFig. 7. It can be very clearly seen in these tests that cracksform every 10 cm on the sides where stirrups are placed atthis distance and at 20 cm in the central part of the tie,

φρ

= +s k c kr ms ef

, 1 2,

Fig. 5. The effect of cover on crack spacing: beam 25-20-00 has a mean crack spacing of 13.1 cm, whereas beam 25-70-00 has a crack spacing of 22.7 cm

Fig. 6. Influence of φ/ρs,ef on mean crack spacing

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which also coincides with stirrup spacing and location.This type of result has made the fact that cracking modelsincluded in codes do not consider the presence of stirrupsrather puzzling for some. For this reason, in the test seriesof the Polytechnic University of Madrid (UPM) it was de-cided to include stirrup spacing as a variable to be studiedin cracking.

From the results in Table 4, which shows the meanand maximum crack spacing in each of the beams tested,it is difficult to make a clear-cut statement regarding howstirrups influence the formation of cracks. Despite the factthat cracks tend to develop at the stirrup positions, asshown by the experimental results of Gómez Navarro [16],it cannot be ruled out that cracks develop between stir-rups, or sometimes fail to develop at stirrup locations. Fora better understanding, in addition to the mean and maxi-mum crack spacing, it is necessary to examine the surfaceof the beams in order to achieve a better interpretation ofthe results (Figs. 3a and 3b).

Figs. 3a and 3b show the cracks in each of the beamstested and the stirrup positions (black lines along the topof each beam).

It can be seen that the beams with 20 mm cover arethe ones that have a better correlation between the posi-tions of the cracks and the stirrups. Focusing on beam 12-20-10, it can seen that the cracks have developed, in gen-eral, every two stirrups, approximately every 200 mm, andthat they also correlate rather well with the observedmean crack spacing of 182 mm. In beam 12-20-30 it can beseen that each crack systematically coincides with a stir-rup position. In this case the measured mean spacing of274 mm is very close to the stirrup spacing of 300 mm.

Similarly, in beam 25-20-10 the cracks coincide withthe stirrup positions (100 mm) and the mean separationobtained is 114 mm. In beam 25-20-30, cracks develop atthe location of each stirrup and other cracks develop mid-way between stirrups, resulting in a mean crack spacing of152 mm.

The beams with 70 mm cover also show, in a generalmanner, a tendency for cracks to coincide with the posi-tions of stirrups, but in a less homogeneous way than inbeams with 20 mm cover. The exception is beam 12-70-30,where cracks develop systematically at the positions of thestirrups (300 mm), resulting in a mean experimental sepa-ration of 281 mm.

From the above observations with respect to the ef-fect of stirrups on crack spacing it can be stated that:– Stirrups induce the formation of cracks. This effect is

stronger with smaller covers.– It is not, however, correct to assimilate crack spacing

and stirrup spacing. Cracks sometimes develop betweenstirrups and sometimes they do not develop at stirrup lo-cations. Transfer length clearly still plays a role in crackformation.

– Although stirrup spacing has a significant effect on themean crack spacing, the test results show that their in-fluence on the maximum crack spacing is much less.This is very clear in specimens with a 70 mm cover,

Table 4. Summary of results regarding separation between cracks

Beam ID sr,m [mm] sr,max [mm]

25-20-00 131 234

25-20-10 114 230

25-20-30 152 258

12-20-00 173 269

12-20-10 182 320

12-20-30 274 358

25-70-00 227 423

25-70-10 189 460

25-70-30 200 442

12-70-00 236 412

12-70-10 260 381

12-70-30 281 383

5 4 3 1 2

1

3

A

A–AØ 22 Ø 10 Ø 14 Ø 14Ø 8@ 100 @ 200

A

50

50

1507575

7575

150

150

150

45 45130

Fig. 7. Crack pattern governed by stirrup spacing in a test carried out by Gómez Navarro

where crack spacing is very similar in specimens withand without stirrups, and can also be observed in beamswith 20 mm cover.

– Since what matters for crack control is maximum crackspacing and not mean crack spacing, excluding stirrupspacing from the cracking models of current and futurestandards seems justified.

3 Some theoretical observations3.1 Basic variables

As shown by the results of the experimental programmeand some of the existing cracking models, crack spacingcan be determined as a linear sum of two terms as ex-pressed in Eq. (4). The second term corresponds to bondtheory and, as stated above, can be derived from equilibri-um of the bar and cross-sections located between thecrack and the section of zero slip by applying the conceptof transfer length, i.e. the length needed to transmit a ten-sion force able to crack the concrete from the bar to the ef-fective concrete area. The first term, dependent upon cov-er, can be explained by the need to transmit these tensilestresses from the bar surface to the centre of the effectivearea located on either side of the bar as shown in Fig. 8.

3.2 Differences between crack spacing at bar level and on the concrete surface

Experimental evidence supports the fact that a large in-crease in the crack width happens as the crack is mea-sured further away from the bar. The work of Husain andFerguson [17] (see Fig. 9) or, more recently, the work ofBorosnyói and Snóbli [18] (see Fig. 10) can be cited as ex-amples of such results. One possible explanation for thislarge increase would be that it is due to shear lag strain inthe cover, since the concrete cover deformation is more re-stricted by reinforcement close to the bar than remotefrom it. However, a simple house number is enough to ruleout shear lag as the reason behind crack width increase.Indeed, the strain in free concrete after cracking can be es-timated as fctm/Es∼10–4, so the crack opening due to shearlag would be equal to this value multiplied by crack spac-ing (which could be 30 cm as a generous estimate) minusslip occurring at bar level. This means that shear lag couldbe responsible for a crack width increase of much lessthan 0.03 mm, since slip will occur at the bar-concrete in-

76



terface. It is therefore clear that shear lag has a negligibleeffect. So why does the width of the crack increase?

An interesting observation taken from the experi-mental results mentioned above is that the crack openingat bar level is truly very small (approx. 0.05 mm). This pro-vides the key to interpreting the phenomenon. It is wellknown, from the work of Goto [19], that secondary, non-passing cracks occur near the bar surface. These sec-ondary cracks help to distribute the slip and reduce theopening of the passing crack at bar level. As these internalcracks close, strain is concentrated in the passing crack,thus explaining the increase. This effect is similar to thatobserved in beam webs and is the origin for the need toprovide web reinforcement, as has been incorporated incodes of practice for many years (see Fig. 11).

Fig. 8. Diffusion of tensile forces is needed to crack concrete, thus explain-ing the dependence of crack spacing on cover from a theoretical point ofview

Fig. 9. Tests of Husain and Ferguson, showing how crack width increasesaway from the bar surface (note the very small crack width at the bar sur-face)

Fig. 10. Tests of Borosnyói and Snóbli, again showing how crack width increases away from the bar surface (again note the very small crack width at thebar surface)

77



The consequence of this interpretation is that crackmodels provide the crack width at the surface of the con-crete elements. The crack at the reinforcement level ismuch smaller.

With regard to this topic, if it is agreed that the in-crease in crack width as the distance from the bar increas-es is mainly due to the closing of secondary cracks, whichseems reasonable, a strong case can be made against thecurrent practice of demanding the same crack width limitsfor elements with large covers as for elements with smallercovers for durability reasons. This argument can be betterunderstood by considering Fig. 12, which shows two ele-ments with different covers: one with a large cover (top)and one with a smaller cover (bottom). It can be seen thatin the one with a large cover, secondary cracks close be-fore reaching the surface. Therefore, on the surface, crackwidth and crack spacing in the specimen with large coverare doubled with respect to the one with the smaller cover.In the specimen with smaller cover, the secondary cracksin the beam with large cover actually become primarycracks and cracking would seem to be better controlled.This is certainly the case if crack width is being limited foraesthetic reasons. However, from a durability point ofview, the crack opening at the level of the reinforcementwould be exactly the same and, if anything, the elementwith a large cover would be better protected.

This argument allows a proposal to be made regard-ing crack width verification when durability is a concern.Assuming crack width limits for durability reasons havebeen specified for a certain reference cover c0 (if the ENV1992-1-1 [20] model is taken as a reference, then as in thecracking equation where the term 2c is given as 50 mm, c0might be taken as 25 mm), if the crack opening is being lim-ited for durability reasons, crack openings to be comparedwith admissible limits should be computed using this refer-ence value c0. However, the client should be advised thatthe cracks actually appearing on the surface will be larger.

4 Conclusions

From the above considerations, it is possible to draw thefollowing conclusions:– The tests carried out at the Structures Laboratory of the

Civil Engineering school of Madrid, designed to con-firm, or discard, the effect of cover and parameter φ/ρs,efon crack spacing, in the light of current controversy,have confirmed that both of these are important para-meters affecting crack spacing.

– The tests have also confirmed that stirrup spacing hasan influence on crack spacing. However, this influenceis mainly relevant for mean crack spacing. Its influenceon maximum crack spacing, which is the value relevantfor the verification of the serviceability limit state ofcracking, is much smaller. This fact would justify exclud-ing this from the relevant parameters in current and fu-ture codes of practice.

– The large difference between crack spacing at the rein-forcement surface and crack spacing at the concrete sur-face observed in tests can be attributed to internalcracking (or Goto cracks). At the bar surface, the differ-ential strain between steel and concrete is distributedamong the passing crack and the internal non-passingcracks. The increase in the width of the passing crack isonly a reflection of the closing of the internal cracks.

– The effects of shear lag in the effective concrete area arenegligible. For this reason it can be said that currentcrack models are actually providing an estimate of thecrack width at the concrete surface.

– If it is agreed that the increase in the opening of cracksincreasing with the distance from the bar is due to theclosing of secondary cracks, it does not make sense topenalize cross-sections with large covers when crackwidth is being limited for durability considerations.Large covers will result in larger superficial cracks dueto the fact that a fewer internal cracks will make theirway to the surface. However, at the bar level, the crackopening for small and large covers would be expected tobe the same.

Notation

εc tensile strain in concrete between cracksεs tensile strain in steelεtension mean measured tensile strain along constant mo-

ment span at level of reinforcementφ bar diameterρs,ef effective reinforcement ratioσs stress in reinforcement at crack

Fig. 11. Cracking in beam webs: need for web reinforcement to controlcracking due to merging of smaller cracks (analogy with secondary crack-ing or Goto cracks)

Fig. 12. Relationship between increase in surface crack width and coverbearing on to the closure of secondary cracks

c clear cover to longitudinal reinforcementd effective depth of reinforcementEs modulus of elasticity of steelfctm mean tensile strength of concreteh depth of cross-sectionhef depth of effective concrete areak1,k2 model constantsl length used for strain measurement (l = 20 cm)L span of constant bending moment zonencracks number of cracks in constant moment span after

stabilization of crack patternsr,m mean crack spacingsr,max maximum crack spacingsw stirrup spacingTS factor (< 1) accounting for tension stiffeningw crack openingwm mean crack openingwmax maximum crack openingx depth of neutral axis assuming fully cracked section

Acknowledgements

The tests carried out at the Structures Laboratory of theCivil Engineering School of UPM were performed withinthe framework of the Estudio de fisuración en muros pan-talla research programme led by COMSAEMTE, S.A., withthe participation of FHECOR Consulting Engineers. Thetests were partly funded by Centro de Desarrollo Tecnoló -gico Industrial (CDTI), a body of the Spanish Ministry ofScience & Technology, under project No. IDI-20080937.

The authors also wish to thank the head of the labo-ratory, José Torrico, and visiting students from Politecnicodi Milano as well as Francesco dal Pont and Andrea Facchini for their help in carrying out the tests.

References

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11. fib: Model Code 2010, final draft. Bulletin Nos. 65 & 66.12. Pérez Caldentey, A., Corres Peiretti, H., Peset, J.: Estudio de

fisuración en muros pantallas. Final report, research projectNo. IDI-20080937, funded by CDTI. Ministry of Science &Technology. Spain, 2010.

13. Beeby, A., Base, G. D., Read, J. B., Taylor, H. P.: An Investi-gation of the crack control characteristics of various types ofbar in reinforced concrete beams. Cement & Concrete Asso-ciation. Research report No. 18, pt. 1. Dec 1966.

14. CEN: EN-1992-1-1. Eurocode 2. Design of concrete struc-tures – Part 1-1. General rules and rules for buildings, 2004.

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Concrete Composite Bridges. PhD Thesis No. 2268, Lau-sanne, 2000.

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19. Goto, Y.: Cracks Formed in Concrete Around Deformed Ten-sion Bars. ACI Journal. vol. 68, No. 4. Apr 1971.

Alejandro Giraldo SotoPolytechnic University of Madrid – Mecánicade Medios Continuos y Teoría de Estructuras, Madrid, [email protected]

Hugo Corres PeirettiPolytechnic University of Madrid – Mecánicade Medios Continuos y Teoría de Estructuras, Madrid, SpainFhecor Consulting Engineers, Calle de Barquillo, 23, 2, 28004 Madrid, [email protected]

Alejandro Pérez CaldenteyPolytechnic University of Madrid – Mecánicade Medios Continuos y Teoría de EstructurasCalle Profesor de Arenguren, s/n Escuela Superior de Ingenieros de Caminos, Canales y Puertos MadridMadrid 28040, SpainFhecor Consulting Engineers, Calle de Barquillo, 23, 2, 28004 Madrid, [email protected]

Joan Peset IribarrenComsaemte – Gestión del Conocimiento e Innovación Tecnológica, S.A., Edificio Numancia 1. Viriato, 47, 08014 Barcelona, Spain

Structural Concrete 14 (2013), No. 1 79

fib-news

In preparation for the 2014 fib Con-gress in Mumbai the Indian Nation-al Member Group of fib organised aseries of “fib-days” over the past fewyears in major cities across India toassist in raising awareness of fib andto publicise the forthcoming Con-gress. The latest of these was held inChennai, Tamil Nadu, on 10th and11th January 2013 and was attendedby about 350 engineers and stu-dents. It was hosted at the head-quarters of Larsen & Toubro, one ofIndia’s largest contractors and or-ganised for the Institution of Engi-neers (India). L&T’s EngineeringDesign and Research Centre was therecipient of a Special Mention in thefib Awards for Outstanding Struc-tures in 2002 and is a remarkableiconic concrete structure.

fib President Gordon Clark and Im-mediate Past President György L.Balázs attended and presentedkeynote papers on “Recent Inspec-tions of Post-Tensioned Bridges andlessons learnt” and “Fibres in Con-crete”. Milan Kalny, Head of the

Czech National Delegation in fiband Frank Dehn, Chairman of Com-mission 8, also attended by invita-tion and presented keynote paperson “Rehabilitation of ConcreteBridges” and “Multifunctional Con-struction Materials”. The invitedkeynote speakers were given a verywarm welcome by the audience andthe organisers.

There were also several invited papers from experts from around India including: “Geopolymer con-crete for sustainable development”

(Dr Nagesh R. Iyer, CSIR-StructuralEngineering Research Centre, Chen-nai), “Special concretes used in In-dia – its future and way forward”(Dr Ravindra Gettu, Indian Instituteof Technology, Madras), “U.S. expe-rience with seismic design and con-struction of precast concrete xtruc-tures” (S.K. Ghosh, California,USA), “Use of concrete in hydro-electric/irrigation projects” (S.K.Dharmadhikari, Chief Technical Of-ficer, HCC Group), “Elevated corri-dors for road connectivity” (VinayGupta, CEO, Tandon Consultants,New Delhi), “Materials for sustain-able concretes in India” (Dr M.R.

fib-days in Chennai, India

fib-news is produced as an integral partof the fib Journal Structural Concrete.

Contents Issue 1 (2013)

fib-days in Chennai, India 79

fibUK Technical Meeting 80

Design of concrete bridges:fib short course in Turkey 81

New fib officers 81

Gordon Clark visits Japan 81

Short notes 82

Congresses and symposia 83

fib membership benefits 84

Acknowledgement 85

fib President Gordon Clark and Immediate Past President György L. Balázs with students whoattended the conference, in front of the Larsen & Toubro Engineering Design and Research Center.

From left to right: Milan Kalny, RavindraGettu, HarshavardhanSubbarao (ChairmanConstruma Consultancy,Mumbai), Frank Dehn, V.N.Heggade (Head ofTechnical ManagementGammon India, Mumbai),György L. Balázs


fib-news

Kalgal, UltraTech Cement), “Precastconcrete construction” (Dr A. Ra-makrishna, formerly of L&T), “Con-crete construction for metros” (V.BGadgil, L&T Metro Rail Hyder-abad).

Additionally there were summariespresented of several noteworthy pa-pers from the past two fib Symposiaheld in Prague in 2011 and in Stock-holm in 2012.

On the evening of the first day therewas a delightful cultural event forparticipants by two dancers whoportrayed some traditional dancingof the region.

Following the event Gordon Clark,György Balázs and Milan Kalny trav-elled to Mumbai, where they hadeach been invited to present to theconference “Concrete Futures” on12th January organised by the Foun-dations Knowledge Initiative of Am-buja Cement, with an invited audi-ence of about 200 engineers,architects and clients and wheretheir presentations attracted livelydebate during a closing panel discus-sion session.

It is anticipated that this sixth fib-days Conference in the importantand successful series will strengtheninterest in the Mumbai Congress(10-14 February 2014; see www.fib-congress2014 mumbai.com).

Gordon Clark

A hundred engineers gath-ered at theHeadquartersof The Institu-tion of Struc-tural Engineerson the eveningof 29th No-vember to hearabout Deflec-

tions in Concrete. This inauguraljoint meeting of fibUK and The In-stitution of Structural Engineers washeld to recognise the contributionsof Professor Andrew Beeby to bothorganisations and to concrete engi-neering in general.

Prof Steve Denton (Chairman,fibUK) spoke for many by alludingto Prof Beeby’s mythical status toconcrete designers. The three speak-ers were delighted to explain someof Prof Beeby’s contributions in thefield of deflection.

Robin Whittle spoke about tensionstiffening and the problems of deter-mining deflections in the reality be-tween uncracked and fully crackedbehaviour. Prof Beeby’s early tension stiffening model had beenincorporated into BS8110 Structuraluse of concrete and Robin had usedthis to predict deflections on a testslab – predictions that proved horri-bly wrong! It was only through asuggestion by Prof Beeby some yearslater that research was undertakenon the rate of decay of tension stiff-ening. This research showed thattension stiffening dropped 50% in19 days – just as Prof Beeby had pre-dicted – and much to the relief ofthe speaker.

Dr Richard Scott bumped into hisfriend Prof Beeby on a train: “Whydon’t you do some work on serviceloads at Cardington?” Cardingtonwas the full scale in-situ test buildingbeing built inside an airship hanger.Funding was quickly arranged to en-able measurement of in-situ strainsin the 6th of 7 flat slabs. With the

help of Arup, different tension stiff-ening models were investigated andfound to give very different answers.With the caveats that only transientloads and one highly reinforced slab(1.7%) were investigated, Richardconcluded that ICE Technical Note372 appeared most appropriate – atleast for slabs on the cusp of beingcracked.

Dr Robert Vollum talked aboutspan: effective depth (L/d) ratios,where Prof Beeby was a pioneer, de-veloping rules for BS8110. Overtime these rules proved to work verywell. It became increasingly clearthat tension stiffening has most in-fluence on uncracked sections.Therefore load history and crackingbecome very important in determin-ing deflection. This was recognisedin the background to the Eurocode2 L/d rules. Unfortunately some ofthe assumptions made have nowproved to be unconservative forlightly loaded slabs in multi-storeyconstruction. Dr Vollum explainedhow improvements could be madeand would be proposed.

Questions and discussion followed.The chairman closed proceedings byleading a warm round of applause.

A recording of this lecture is avail-able as a freely accessible webinarfrom the website of the Institutionof Structural Engineers:www.istructe.org/resources-centre/webinars

Charles Goodchild

Editor’s note:Andrew Beeby, long-time member ofCEB and fib, Model Code and Struc-tural Concrete Textbook author, andfirst Editor in chief of fib’s Structur-al Concrete Journal, passed away on28 October 2011.

fibUK Technical Meeting inrecognition of Andrew Beeby

Andrew Beeby


fib-news

fib is pleased toannounce thatGordon Clark(Ramboll, UK) hastaken office since1st January asPresident of fib forthe term 2013-2014. The newDeputy Presidentis Harald Müller(Karlsruhe Insti-tute of Technolo-gy, Germany). Wewish them both asuccessful and re-warding time intheir new roles.

For the full list of fib Presidium members, visit www.fib-international.org/presidium.

fib, the Chamber of Civil Engineersof Turkey and Middle East Techni-cal University (METU), organized ashort course/workshop on design ofconcrete bridges, on October 15 and16, 2012. The event took place atthe Cultural and Convention Centreof METU, in conjunction with theConference ACE2012 (Advances inCivil Engineering, 2012) organizedby METU at the same venue, fromOctober 17 to 20. The local organiz-ers were Prof. Alp Caner, AssociateProfessor at the Civil EngineeringDepartment, METU, and Prof.Guney Özcebe, Professor and Chair-man of the Civil Engineering De-partment, METU.

The technical programme includedthe following presentations:

– Conceptual design of bridges(Hugo Corres-Peiretti, fib)

– General design concepts of con-crete integral bridges (Murat Di-cleli, METU)

– Pinerolo bridge: Cast in situ bridgebuilt on classical scaffolding(Giuseppe Mancini, fib)

– Roccaprebalza bridge: Compositebox girder bridge built by can-tilevering (Giuseppe Mancini, fib)

– Seismic design of concrete bridgesaccording to Eurocode 8 (MichaelFardis, fib)

– Bridges built with free cantilevermethod: Tajuña and ManzanalBridge (Hugo Corres-Peiretti, fib)

– Secondino Ventura bridge: Cast insitu launched bridge (GiuseppeMancini, fib)

– Precast concrete bridges. (HugoCorres-Peiretti, fib)

– Verolengo bridge: precast on siteassembled bridge (GiuseppeMancini, fib)

– Concrete viaducts for high speedrailway lines: General conceptsand examples using different con-struction methods. (Hugo Corres-Peiretti, fib)

– Ortakoy bridge, Artvin: LRFD-based design of segmental con-crete bridge utilizing balancedcantilever construction (AlpCaner, METU)

There were 45 registered partici-pants, from Ankara and other citiesin Turkey, as well as from neigh-bouring countries. They receivedcopies of the presentations and cer-tificates of attendance signed by AlpCaner, as main organizer of thecourse, M.N. Fardis on behalf of fiband Mr Taner Yüzgeç, President ofthe Chamber of Civil Engineers ofTurkey.

On the occasion of the fib event, theco-sponsor, Turkish IABSE group,organized a dinner honoring Emeri-tus Professor Erhan Karaesmen,who had started his engineering ca-reer working at the CEB Secretariatin Paris, from 1962 to 1965.

For further information about fibShort Courses, visit: www.fib-inter-national.org/courses.

Michael N. Fardis

Design of Concrete Bridges: fib short course in Ankara, Turkey

Gordon Clark

Harald Müller

New fib officers

Gordon Clarkvisits Japanfib President Gordon Clark was in-vited by NEXCO-RI (Nippon Ex-pressway Company Research Insti-tute, part of the former JapanHighways Authority, now privatisedsince 2005) to travel to Japan from17 to 24 November 2012 to givetwo lectures and to visit some oftheir new post-tensioned bridges un-

Lecture to JPCI

The Takubogawa bridge has precastfibre-reinforced pretensioned webpanels and a combination of inter-nal and external prestressing usingepoxy coated strand. The featuresare described in the paper “Con-struction of a Butterfly Web Bridge”by Kenichiro Ashizuka et al., pub-lished in the 2012 fib Stockholmsymposium proceedings (www.fib-stockholm2012.se).

He also visited the Toyota Arrowsbridge – the world’s longest pre-stressed concrete bridge with corru-gated webs.

While in Japan Gordon met severalmembers of the Japanese fib groupincluding Akio Kasuga, who organ-ised the site visits, Presidium mem-ber Jun Yamazaki, and Shoji Ikeda,former member of the Japanese del-egation and former Presidium mem-ber. Professor Hiroshi Mutsuyoshiof fib Commission 9 had arrangedthe presentation to JPCI at whichGordon met with the President ofJPCI Professor Toyo Miyagawa.

Gordon Clark commented on hisvisit: “Exchange of knowledge inthe area of post-tensioned concretebridges is very important as allcountries of the world are facedwith some repairs. It was impressiveto see how Japan has embraced newtechnologies in construction of theirnew post-tensioned bridges.”

Birthdays of note

Congratulations to Jacques Com-bault, who was awarded the fibMedal of Merit in 2004, on the occasion of his 70th birthday inFebruary.

Congratulations also go RüdigerTewes, former CEB and fib Secre-tary General, who will celebrate his70 years in March.

Honorary doctorate to Konrad Bergmeister

Congratulations go to KonradBergmeister (deputy chair of fibCommission 2, Head of Delegationfor Austria) who was presented withan honorary doctorate by the Uni-versität der Bundeswehr Münchenon 1st February 2013, in recognitionof his outstanding technical andpersonal achievements. The ceremo-ny took place at the Faculty of CivilEngineering and Environmental Sciences and was presented by thefaculty Dean Prof Jürgen Schwarzand university President ProfMerith Niehuss, with a laudatoryspeech given by Prof ManfredKeuser.

Short notes


fib-news

der construction using new tech-nologies. The topics were “Groutingand durability of post-tensionedconcrete bridges”, delivered to theJapan Prestressed Concrete Associa-tion which attracted an audience ofabout 120 from across Japan, and“Inspection and repair of post-ten-sioned concrete bridges”, deliveredto NEXCO-RI with an audience ofabout 50 NEXCO staff from variousbridge departments. Both lectureswere interpreted into Japanese.

The various parts of NEXCO are re-sponsible for management of about9000 km of expressways acrossJapan and 20,000 bridges of whichabout 8,000 are post-tensioned,some dating back to the 1960’s.Management and maintenance ofthese bridges is a specialist areawhere international expertise is de-veloping and Gordon’s involvementin fib’s technical work on the stateof the art of post-tensioning and in-ternational standards for groutingfor over 20 years, together withRamboll’s depth of experience, hasgiven him significant knowledgeand standing in this field.

During his visit Gordon visited theTakubogawa bridge constructionsite with representatives of NEXCOand Sumitomo Mitsui Construction.The contractor got the whole siteworking for the occasion, eventhough it was a public holiday.

Representatives of NEXCOplus Gordon Clark and Akio Kasuga (second fromright) at the constructionsite of the Takubogawabridge. On the far right isKeiichi Aoki, Head of BridgeDivision, NEXCO-RI.

Dean Prof Jürgen Schwarz, Prof KonradBergmeister and President Prof Merith Niehuss(from left)


fib-news

Date and location Event Main organiser Contact

4–5 April 2013 Development of large-panel PATRIOT Engineering [email protected], Russia housing construction in Russia [email protected]

11–12 April 2013 Deutscher Bautechnik-Tag Deutscher Beton- und. www.betonverein.de/Hamburg, Germany Bautechnik- Verein E.V bautechniktag2013.php

22–24 April 2013 fib Symposium: Engineering fib group Israel www.fib2013tel-aviv.co.ilTel-Aviv, Israel a Concrete Future: Technology,

Modeling and Construction

27–29 May 2013 1st International Conference JCI www.jci-iccs13.jpTokyo, Japan on Concrete Sustainability

16–19 June 2013 Sixth Symposium on Strait Norwegian Public Roads www.sc2013.noBergen, Norway Crossings Administration (NPRA)

26–28 June 2013 11th Int. Symposium on Fibre University of Minho, www.frprcs11.uminho.ptGuimaraes, Portugal Reinforced Polymers for ISISE

Reinforced Concrete Structures

23–25 September 2013 7th International Conference Hong Kong University of www.consec13.comNanjing, China on Concrete under Severe – Science and Technology

Conditions (CONSEC13)

25–27 September 2013 Third International Workshop CSTB Paris, TU Delft, website to be announcedParis, France on Concrete Spalling due to MFPA Leipzig

Fire Exposure (IWCS 2013)

1–3 October 2013 2nd International Symposium AFGC www.afgc.asso.frMarseilles, France on UHPFRC

10–14 February 2014 4th International fib Congress fib group India www.fibcongress2014mumbai.comMumbai, India and Exhibition

18–20 February 2014 58th BetonTage FBF Betondienst GmbH www.betontage.comNeu-Ulm, Germany

11–13 June 2014 Concrete Innovation Norwegian Concrete www.cic2014.comOslo, Norway Conference (CIC2014) Assocation

21–23 July 2014 10th fib International Ph.D. Université Laval www.fib-phd.ulaval.caQuebec, Canada Symposium in Civil Engineering

10–18 September 2014 10th International symposium Beijing Jiaotong www.hpc-2014.comBeijing, China on Utilization of HS/HP University

Concretes

Congresses and symposia

The calendar lists fib congresses and symposia, co-sponsored events and, if space permits, eventssupported by fib or organised by one of its National Groups. It reflects the state of information available tothe Secretariat at the time of printing; the information given may be subject to change.Visit www.fib-international.org/events for a continuously updated online version of the events calendar anda link to the calendar of events of the Liaison Committee of International Associations of Civil Engineering.


fib-news

fib membership benefits

fib has 41 National Member Groups as statutory members, and about 1000 individual or corporate members in about60 countries. The objectives of fib are to develop at an international level the study of scientific and practical matters capableof advancing the technical, economic, aesthetic and environmental performance of concrete construction. These objectivesshall be achieved by the stimulation of research, the synthesis of findings from research and practice, and the dissemination ofthe results by way of publications, guidance documents and the organisation of international congresses and symposia. Theproduction of recommendations for the design and construction of concrete structures, and the information of members on thelatest developments also belong to these objectives.Individual membership is offered in two categories with the following benefits: Ordinary members receive the quarterly journal

Structural Concrete and one technical publication (‘Bulletin’) of their choice per year at a discount rate. Students (personsunder 30 years of age) receive the same benefits as ordinary members for the reduced fee of 90 CHF/year instead of190 CHF/year. Subscribing members receive one copy of all technical publications (on average six Bulletins/year, plus thejournal) and may order any quantity of publications at a discount rate (including former CEB or FIP publications). Furthermore,individual members receive discounts when attending official fib congresses or symposia.

Corporate membership is available in three categories with the following benefits: Associate members (libraries, companies,engineering offices, etc.) may nominate one representative to be registered as individual member of fib, and, in addition to thebenefits described above for subscribing members, may request two copies of all technical publications at no extra charge. Inaddition to this, supporting members are entitled to nominate two representatives to be registered as individual members. Theyare also entitled to a special mention in the Directory and receive discount rates when advertising in the journal StructuralConcrete. In addition to this, sponsoring members receive special mention on the fib website, including a link to theirhomepage. They may use fib's logo by stating ‘Sponsoring member of fib’ in their letterhead, and may nominate threerepresentatives to be registered as individual members. They are entitled to nominate a member of a task group in oneparticular field or interest and may send a representative to the General Assembly.

In addition, all members receive the fib Directory free of charge and free access to the onlines services on fib's website.

Application Form

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remittance, free of charge for the receiver, to: fib—fédération sending to the fib secretariat a cheque international du béton, 1015 Lausanne, Switzerland, account made out in CHF, drawn on a Swiss No. 710.250.00 V, at the Union Bank of Switzerland (UBS), clearing bankCase Postale 2950, CH-1211 Geneva 2, Dépôt(Swiftcode UBSWCHZH12A, IBAN: CH19 0024 0240 7102 5000 V,BIC: UBSWCHZH80A)

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National Member Groups

AAHES – Asociación Argentina delHormigón Estructural

CIA – Concrete Institute ofAustralia

ÖBV – Österreichische BautechnikVereinigung, Austria

GBB – Groupement Belge du Béton,Belgium

ABCIC – Associação Brasileira daConstrução Industrializada deConcreto, Brazil

ABECE – Associação Brasileira deEngenharia e ConsultoriaEstrutural, Brazil

fib Group of CanadaCCES – China Civil Engineering

SocietyHrvatska Ogranak fib-a (HOFIB)

Croatian Group of fibCyprus University of TechnologyCeska betonarska spolecnost, Czech

RepublicDBF – Dansk Betonforening,

DenmarkSuomen Betoniyhdistys r.y, FinlandAFGC – Association Française de

Génie Civil, FranceDeutscher Ausschuss fürStahlbeton

e.V., GermanyDBV – Deutscher Beton- und

Bautechnik- Verein e.V., GermanyFDB – Fachvereinigung Deutscher

Betonfertigteilbau e.V., GermanyTechnical Chamber of GreeceHungarian Group of fibThe Institution of Engineers

(India)Technical executive bureau, IranIACIE – Israeli Association of

Construction and InfrastructureEngineers

Consiglio Nazionale delle Ricerche,Italy

JCI – Japan Concrete Institute JPCI – Japan Prestressed Concrete

Institute Admin. des Ponts et Chaussées,

Luxembourgfib NetherlandsNew Zealand Concrete SocietyNorsk Betongforening, NorwayCommittee of Civil Engineering,

PolandPolish Academy of SciencesGPBE – Grupo Portugês de Betão

Estrutural Society for Concrete and Prefab

Units of RomaniaTechnical University of Civil

EngineeringUniversity of Transylvania Brasov,

RomaniaASC – Association for Structural

Concrete, RussiaAssociation of Structural Engineers,

SerbiaSlovak Union of Civil EngineersSlovenian Society of Structural

EngineersConcrete Society of Southern AfricaKCI – Korean Concrete InstituteACHE – Asociacion Cientifico-

Técnica del Hormigon EstructuralSvenska Betongföreningen, SwedenDélégation nationale suisse de la fib,

Switzerland ITU – Istanbul Technical University,

TurkeyResearch Institute of Building

Constructions, Ukraine fib UK GroupASBI – American Segmental Bridge

InstitutePCI – Precast/Prestressed Concrete

InstitutePTI – Post Tensioning Institute

Sponsoring Members

Preconco Limited, BarbadosLiuzhou OVM Machinery Co.,

ChinaCONSOLIS Technology, FinlandFBF Betondienst GmbH, GermanyFIREP Rebar Technology GmbH,

GermanyMKT Metall-Kunststoff-Technik

GmbH, GermanyVBBF – Verein zur Förderung und

Entwicklung der Befestigungs-,Bewehrungs- undFassadentechnik e.V., Germany

Larsen & Toubro ECC Division,India

ATP, ItalySireg, ItalyFuji P. S. Corporation, JapanIHI Construction Service Co., JapanObyashi Corporation, JapanOriental Shiraishi Corporation,

JapanP.S. Mitsubishi Construction Co.,

JapanSE Corporation, JapanSumitomo Mitsui Construct. Co.,

JapanPatriot Engineering, RussiaBBR VT International,SwitzerlandSIKA Services, SwitzerlandSwiss Macro Polymers, SwitzerlandVSL International, SwitzerlandChina Engineering Consultants,

Taiwan (China)PBL Group, ThailandCCL Stressing Systems, United

KingdomStrongforce, United Kingdom

Acknowledgement

fib – fédération internationale du béton – the International Federation for Structural Concrete – is grateful for theinvaluable support of the following National Member Groups and Sponsoring Members, which contributes to thepublication of fib technical bulletins, the Structural Concrete Journal, and fib-news.

Hugo Corres PeirettiConceptual design, the only procedurefor achieving sound engineering proposals according to fib Model Code 2010

György L. Balázs et al.Design for SLS according to fib ModelCode 2010

Raphael Breiner, Harald Müller, IsabelAnders (nee Burkart), Michael Vogel Concrete: treatment of types and properties in fib Model Code 2010

Pierre Rossi, Jean-Louis Tailhan, Claude Boulay, Fabrice Le Maou, Eric MartinCompressive, tensile and flexural basic creep behaviours of a same concrete

Jung-Chul Kim, Taeseok SeoBehaviour of concrete in a stress continuity region after cracking underrestrained drying shrinkage

Robert Lark, Ben Isaacs, Tony Jefferson,Robert Davies, Simon DunnCrack healing of cementitious materalusing shrinkable polymer tendons

Tian Sing Ng, Stephen J. FosterDevelopment of a mix design method-ology for high performance geopoly-mer mortars

Miguel Fernández Ruiz, Thibault Clément, António Pinho Ramos, Aurelio Muttoni Design for punching of prestressedconcrete slabs

Conceptual design is the approach that creates an idea in order to find a solution to a new proposalfor a structure or solve a detail in a specific structure. It is a personal approach that is learned overtime and with experience. It is not normally dealt with at university, but is vitally important for produc-ing sound structures. The fib Model Code 2010 introduced this concept in the first section of chapter 7“Design”. The content of that section explains the general approach to developing conceptual design.The picture shows the final proposal for a footbridge competition (Dr. Techn. Olav Olsen + FHECOR Ingenieros Consultores + OKAW + Gullik Gulliksen)

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Structural Concrete 2/2013

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Annual table of contentsEditor-in-Chief:Luc Taerwe

Deputy Editor:Steinar Helland

Members:György L. BalázsJosée Bastien Mikael Braestrup Tom d’ Arcy

Michael Fardis Stephen Foster Tim Ibell S.G. Joglekar Akio Kasuga Gaetano Manfredi Pierre Rossi Guilhemo Sales Melo Petra Schumacher Tamon Ueda Yong Yuan

2012Volume 13No. 1–4ISSN 1464-4177

Annual table of contents 2012

2 Structural Concrete 13 www.ernst-und-sohn.de

Aboutalebi, Morteza; see Alani,Amir M.

Aguiar, Eduardo Aurélio Barros;Bellucio, Ellen Kellen; El Debs,Mounir Khalil: Behaviour ofgrouted dowels used in precastconcrete connections Issue 2 84–94 A

Al-Akhras, Nabil M.: Performanceof olive waste ash concreteexposed to alkali-silica reaction Issue 4 221–226 A

Alani, Amir M.; Aboutalebi,Morteza: Analysis of the sub-grade stiffness effect on thebehaviour of ground-supportedconcrete slabs Issue 2 102–108 A

Ayoub, Essam; Malek, Charles;Helmy, Gamal: Considerationsfor the design of doubly unsym-metrical precast pretensionedbeams used for box girder con-struction Issue 3 193–199 A

Baird, Andrew; Palermo, Alessan-dro; Pampanin, Stefano: Façadedamage assessment of concretebuildings in the 2011Christchurch earthquake Issue 1 3–13 A

Beck, Matthias; Burkert, Andreas;Harnisch, Jörg; Isecke, Bernd;Osterminski, Kai; Raupach,Michael; Schießl, Peter; Tian,Wei; Warkus, Jürgen: Deteriora-tion model and input parametersfor reinforcement corrosion Issue 3 145–155 A

Beckmann, Birgit; Schicktanz,Kai; Reischl, Dirk; Curbach,Manfred: DEM simulation ofconcrete fracture and crack evo-lution Issue 4 213–220 A

Bellucio, Ellen Kellen; see Aguiar,Eduardo Aurélio Barros

Bertagnoli, Gabriele; Giordano,Luca; Mancini, Simona: Designand optimization of skew rein-forcement in concrete shells Issue 4 248–258 A

Boska, Erik; see Graubner, Carl-Alexander

Burkert, Andreas; see Beck,Matthias

Camnasio, Elena; see Palermo,Alessandro

Caratelli, Angelo; Meda, Alberto;Rinaldi, Zila: Design accordingto MC2010 of a fibre-reinforcedconcrete tunnel in Monte Lirio,Panama Issue 3 166–173 A

Chateauneuf, Alaa; see Raphael,Wassim

Clark, Gordon: Concrete, Cars,Computers and Climate Change Issue 4 211–212 E

Colombo, Antonella; see Toniolo,Giandomenico

Curbach, Manfred; see Beck-mann, Birgit

Dancygier, Avraham N.: Engineer-ing a concrete future Issue 2 71–72 E

De Schutter, Geert; see Desnerck,Pieter

De Schutter, Geert; see Jiang, WeiDehn, Frank; see Graubner, Carl-

AlexanderDesnerck, Pieter; De Schutter,

Geert; Taerwe, Luc: Stress-strain behaviour of self-compact-ing concretes containing lime-stone fillers Issue 2 95–101 A

El Debs, Mounir Khalil; seeAguiar, Eduardo Aurélio Bar-ros

Faddoul, Rafic; see Raphael, Was-sim

Geara, Fadi; see Raphael, WassimGiordano, Luca; see Bertagnoli,

GabrieleGmainer, Susanne; see Kollegger,

JohannGong, Jian; see Jiang, WeiGraubner, Carl-Alexander; Boska,

Erik; Motzko, Christoph;Proske, Tilo; Dehn, Frank:Formwork pressure induced byhighly flowable concretes –design approach and transferinto practice Issue 1 51–60 A

Harnisch, Jörg; see Beck, MatthiasHelland, Steinar; see Taerwe, LucHelmy, Gamal; see Ayoub, EssamHogan, Lucas; see Palermo,

AlessandroHuang, Yulin; see Jiang, WeiIsecke, Bernd; see Beck, MatthiasJiang, Wei; Gong, Jian; De Schut-

ter, Geert; Huang, Yulin; Yuan,Yong: Time-dependent analysisduring construction of concretetube for tower high-rise building Issue 4 236–247 A

Kollegger, Johann; Gmainer,Susanne; Lehner, Klaus;Simader, Josef: Ultimatestrength of curved strand ten-dons Issue 1 42–50 A

Kolácek, Jan; see Stráský, JiríLarsson, Oskar; Thelandersson,

Sven: Transverse thermal stress-es in concrete box cross-sectionsdue to climatic exposure Issue 4 227–235 A

Le Heux, Mitchel; see Palermo,Alessandro

Lehner, Klaus; see Kollegger,Johann

Structural Concrete: Table of contents Volume 13 (2012)

List of authors(A = Article, E = Editorial)

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www.ernst-und-sohn.de Structural Concrete 13

Lohaus, Ludger; Oneschkow,Nadja; Wefer, Maik: Designmodel for the fatigue behaviourof normal-strength, high-strengthand ultra-high-strength concrete Issue 3 182–192 A

Malek, Charles; see Ayoub, EssamMancini, Simona; see Bertagnoli,

GabrieleMeda, Alberto; see Caratelli,

AngeloMotzko, Christoph; see Graubner,

Carl-AlexanderMuttoni, Aurelio; Ruiz, Miguel

Fernández: The levels-of-approx-imation approach in MC 2010:application to punching shearprovisions Issue 1 32–41 A

Necas, Radim; see Stráský, JiríNeocleous, Kyriacos; see Torres,

LluisOneschkow, Nadja; see Lohaus,

LudgerOsterminski, Kai; Schießl, Peter:

Design model for reinforcementcorrosion Issue 3 156–165 A

Osterminski, Kai; see Beck,Matthias

Palermo, Alessandro; Wother-spoon, Liam; Hogan, Lucas;Le Heux, Mitchel; Camnasio,Elena: Seismic performance ofconcrete bridges during Canter-bury earthquakes Issue 1 14–26 A

Palermo, Alessandro; see Baird,Andrew

Pampanin, Stefano; see Baird,Andrew

Pilakoutas, Kypros; see Torres,Lluis

Proske, Tilo; see Graubner, Carl-Alexander

Raphael, Wassim; Faddoul, Rafic;Geara, Fadi; Chateauneuf,Alaa: Improvements to theEurocode 2 shrinkage model forconcrete using a large experi-mental database Issue 3 174–181 A

Raupach, Michael; see Beck,Matthias

Reischl, Dirk; see Beckmann, Bir-git

Rinaldi, Zila; see Caratelli, AngeloRuiz, Miguel Fernández; see Mut-

toni, AurelioSchicktanz, Kai; see Beckmann,

BirgitSchießl, Peter; see Beck, MatthiasSchießl, Peter; see Osterminski,

KaiSilfwerbrand, Johan: Sustainable

concrete is more than justdurable concrete Issue 1 1–2 E

Simader, Josef; see Kollegger,Johann

Steenbergen, R.D.J.M.; Vervuurt,A.H.J.M.: Determining the insitu concrete strength of existingstructures for assessing theirstructural safety Issue 1 27–31 A

Stráský, Jirí; Necas, Radim;Kolácek, Jan: Dynamic responseof concrete footbridges Issue 2 109–118 A

Stucchi, Fernando: The challengeof structural design Issue 3 143–144 E

Taerwe, Luc; Helland, Steinar:Recent developments Issue 3 141–142 E

Taerwe, Luc; see Desnerck, PieterThelandersson, Sven; see Larsson,

OskarTian, Wei; see Beck, MatthiasToniolo, Giandomenico; Colom-

bo, Antonella: Precast concretestructures: the lessons learnedfrom the L’Aquila earthquake Issue 2 73–83 A

Torres, Lluis; Neocleous, Kyria-cos; Pilakoutas, Kypros: Designprocedure and simplified equa-tions for the flexural capacity ofconcrete members reinforcedwith fibre-reinforced polymerbars Issue 2 119–129 A

Vervuurt, A.H.J.M.; see Steenber-gen, R.D.J.M.

Warkus, Jürgen; see Beck,Matthias

Wefer, Maik; see Lohaus, LudgerWotherspoon, Liam; see Palermo,

AlessandroYuan, Yong; see Jiang, Wei

Analysis and design methods – Berechnungs- undBemessungsverfahren

Aguiar, Eduardo Aurélio Barros;Bellucio, Ellen Kellen; El Debs,Mounir Khalil: Behaviour ofgrouted dowels used in precastconcrete connections [beam- column connection; grouteddowels; semi-rigid connection;precast concrete] Issue 2 84–94

Al-Akhras, Nabil M.: Performanceof olive waste ash concreteexposed to alkali-silica reaction[alkali-silica reaction; air-entrained; expansion; concrete;olive waste ash] Issue 4 221–226

Alani, Amir M.; Aboutalebi,Morteza: Analysis of the sub-grade stiffness effect on thebehaviour of ground-supportedconcrete slabs [stiffness; groundslab; failure; ductility; behaviour] Issue 2 102–108

Ayoub, Essam; Malek, Charles;Helmy, Gamal: Considerationsfor the design of doublyunsymmetrical precast preten-sioned beams used for boxgirder construction [bridge; precast beam; unsymmetricalsection; prestressing; distortion;finite element; stress analysis] Issue 3 193–199

Beckmann, Birgit; Schicktanz, Kai;Reischl, Dirk; Curbach, Man-fred: DEM simulation of concrete fracture and crackevolution [discrete elementmethod; crack pattern; concretecomponent structure; ratio oflateral to longitudinal strain] Issue 4 213–220

Bertagnoli, Gabriele; Giordano,Luca; Mancini, Simona: Designand optimization of skew rein-forcement in concrete shells[concrete; shell; skew; reinforce-ment; genetic algorithm] Issue 4 248–258

Caratelli, Angelo; Meda, Alberto;Rinaldi, Zila: Design accordingto MC2010 of a fibre-rein-forced concrete tunnel inMonte Lirio, Panama [precasttunnel segment; fibre-reinforcedconcrete; full-scale test] Issue 3 166–173

Desnerck, Pieter; De Schutter,Geert; Taerwe, Luc: Stress-strain behaviour of self-com-pacting concretes containinglimestone fillers [self-compact-ing concrete; stress-strain relationship; strain-softening;peak strain; toughness; lime-stone filler] Issue 2 95–101

Graubner, Carl-Alexander; Boska,Erik; Motzko, Christoph;Proske, Tilo; Dehn, Frank:Formwork pressure induced byhighly flowable concretes –design approach and transferinto practice [formwork pres-sure; friction; fresh concreteproperties; setting] Issue 1 51–60

Larsson, Oskar; Thelandersson,Sven: Transverse thermalstresses in concrete box cross-sections due to climatic expo-sure [concrete; box cross-sec-tion; thermal stress; finite ele-ment method; thermal factors;climate data] Issue 4 227–235

Lohaus, Ludger; Oneschkow,Nadja; Wefer, Maik: Designmodel for the fatigue behaviourof normal-strength, high-strength and ultra-high-strength concrete [fatigue;design model; high-performanceconcrete; Model Code 2010] Issue 3 182–192

Muttoni, Aurelio; Ruiz, Miguel Fernández: The levels-of-approximation approach in MC2010: application to punchingshear provisions [levels-of-approximation approach; designcodes; Model Code 2010; assess-ment of structural safety; criticalshear crack theory] Issue 1 32–41

Raphael, Wassim; Faddoul, Rafic;Geara, Fadi; Chateauneuf, Alaa:Improvements to the Eurocode2 shrinkage model for concreteusing a large experimentaldatabase [shrinkage strain; con-crete; correction factor; experi-mental tests; Eurocode 2] Issue 3 174–181

Toniolo, Giandomenico; Colombo,Antonella: Precast concretestructures: the lessons learnedfrom the L’Aquila earthquake[precast structures; seismicbehaviour; structural connec-tions] Issue 2 73–83

Torres, Lluis; Neocleous, Kyriacos;Pilakoutas, Kypros: Design pro-cedure and simplified equa-tions for the flexural capacityof concrete members reinforcedwith fibre-reinforced polymerbars [design; reinforced con-crete; FRP bars; flexural capaci-ty; FRP rupture; concrete crush-ing] Issue 2 119–129



Subject codes and keywords

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Bridge construction – Brückenbau

Ayoub, Essam; Malek, Charles;Helmy, Gamal: Considerationsfor the design of doublyunsymmetrical precast preten-sioned beams used for boxgirder construction [bridge; precast beam; unsymmetricalsection; prestressing; distortion;finite element; stress analysis] Issue 3 193–199


Palermo, Alessandro; Wother-spoon, Liam; Hogan, Lucas;Le Heux, Mitchel; Camnasio,Elena: Seismic performance ofconcrete bridges during Canterbury earthquakes [earth-quake damage; Christchurchearthquake] Issue 1 14–26

Stráský, Jirí; Necas, Radim;Kolácek, Jan: Dynamic responseof concrete footbridges [foot-bridge; dynamic response; stressribbon; slender deck; arch struc-ture] Issue 2 109–118

Building maintenance/refurbishment –Bauwerkserhaltung/Sanierung

Baird, Andrew; Palermo, Alessan-dro; Pampanin, Stefano: Façadedamage assessment of concretebuildings in the 2011Christchurch earthquake[facade; concrete panels; earth-quake damage; performance levels; Christchurch earthquake] Issue 1 3–13

Steenbergen, R.D.J.M.; Vervuurt,A.H.J.M.: Determining the insitu concrete strength of exist-ing structures for assessingtheir structural safety [concretestrength; structural safety; codes] Issue 1 27–31

Building materials – Baustoffe


Beck, Matthias; Burkert, Andreas;Harnisch, Jörg; Isecke, Bernd;Osterminski, Kai; Raupach,Michael; Schießl, Peter; Tian,Wei; Warkus, Jürgen: Deteriora-tion model and input parame-

ters for reinforcement corro-sion [reinforcement corrosion;macrocell corrosion model;design for durability] Issue 3 145–155

Beckmann, Birgit; Schicktanz, Kai;Reischl, Dirk; Curbach, Man-fred: DEM simulation of con-crete fracture and crack evolu-tion [discrete element method;crack pattern; concrete compo-nent structure; ratio of lateral tolongitudinal strain] Issue 4 213–220

Desnerck, Pieter; De Schutter,Geert; Taerwe, Luc: Stress-strain behaviour of self-com-pacting concretes containinglimestone fillers [self-compact-ing concrete; stress-strain rela-tionship; strain-softening; peakstrain; toughness; limestonefiller] Issue 2 95–101

Graubner, Carl-Alexander; Boska,Erik; Motzko, Christoph;Proske, Tilo; Dehn, Frank:Formwork pressure induced byhighly flowable concretes –design approach and transferinto practice [formwork pres-sure; friction; fresh concreteproperties; setting] Issue 1 51–60

Jiang, Wei; Gong, Jian; De Schut-ter, Geert; Huang, Yulin; Yuan,Yong: Time-dependent analysisduring construction of concretetube for tower high-rise build-ing [high-rise building; time-dependent; vertical deformation] Issue 4 236–247

Kollegger, Johann; Gmainer,Susanne; Lehner, Klaus; Simader, Josef: Ultimatestrength of curved strand ten-dons [heavy lifting; balanced liftmethod; strand tendons; post-tensioning; radius of curvature;full scale tests] Issue 1 42–50


Osterminski, Kai; Schießl, Peter:Design model for reinforce-ment corrosion [reinforcementcorrosion; full-probabilistic modelling; durability design] Issue 3 156–165


Steenbergen, R.D.J.M.; Vervuurt,A.H.J.M.: Determining the insitu concrete strength of exist-



ing structures for assessingtheir structural safety [concretestrength; structural safety; codes] Issue 1 27–31

Corrosion – Korrosion

Beck, Matthias; Burkert, Andreas;Harnisch, Jörg; Isecke, Bernd;Osterminski, Kai; Raupach,Michael; Schießl, Peter; Tian,Wei; Warkus, Jürgen: Deteriora-tion model and input parame-ters for reinforcement corro-sion [reinforcement corrosion;macrocell corrosion model;design for durability] Issue 3 145–155

Osterminski, Kai; Schießl, Peter:Design model for reinforce-ment corrosion [reinforcementcorrosion; full-probabilistic mod-elling; durability design] Issue 3 156–165

Design and construction – Entwurf und Konstruktion

Aguiar, Eduardo Aurélio Barros;Bellucio, Ellen Kellen; El Debs,Mounir Khalil: Behaviour ofgrouted dowels used in precastconcrete connections [beam- column connection; grouteddowels; semi-rigid connection;precast concrete] Issue 2 84–94



Ayoub, Essam; Malek, Charles;Helmy, Gamal: Considerationsfor the design of doublyunsymmetrical precast preten-sioned beams used for boxgirder construction [bridge; pre-cast beam; unsymmetrical sec-tion; prestressing; distortion;finite element; stress analysis] Issue 3 193–199


Bertagnoli, Gabriele; Giordano,Luca; Mancini, Simona: Designand optimization of skew rein-

forcement in concrete shells[concrete; shell; skew; reinforce-ment; genetic algorithm] Issue 4 248–258

Jiang, Wei; Gong, Jian; De Schutter, Geert; Huang, Yulin;Yuan, Yong: Time-dependentanalysis during constructionof concrete tube for towerhigh-rise building [high-risebuilding; time-dependent; vertical deformation] Issue 4 236–247



Toniolo, Giandomenico; Colombo,Antonella: Precast concretestructures: the lessons learnedfrom the L’Aquila earthquake[precast structures; seismicbehaviour; structural connec-tions] Issue 2 73–83

Dynamic actions/earthquakes – DynamischeEinwirkungen/Erdbeben

Baird, Andrew; Palermo, Alessan-dro; Pampanin, Stefano: Façadedamage assessment of concretebuildings in the 2011Christchurch earthquake[facade; concrete panels; earth-quake damage; performance lev-els; Christchurch earthquake] Issue 1 3–13

Kollegger, Johann; Gmainer,Susanne; Lehner, Klaus; Simader, Josef: Ultimatestrength of curved strand ten-dons [heavy lifting; balanced liftmethod; strand tendons; post-tensioning; radius of curvature;full scale tests] Issue 1 42–50

Palermo, Alessandro; Wother-spoon, Liam; Hogan, Lucas;Le Heux, Mitchel; Camnasio,Elena: Seismic performance ofconcrete bridges during Can-terbury earthquakes [earth-quake damage; Christchurchearthquake] Issue 1 14–26


Toniolo, Giandomenico; Colombo,Antonella: Precast concretestructures: the lessons learnedfrom the L’Aquila earthquake[precast structures; seismic

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behaviour; structural connec-tions] Issue 2 73–83

Eurocode



Torres, Lluis; Neocleous, Kyriacos;Pilakoutas, Kypros: Design pro-cedure and simplified equa-tions for the flexural capacityof concrete members reinforcedwith fibre-reinforced polymerbars [design; reinforced con-crete; FRP bars; flexural capaci-ty; FRP rupture; concrete crushing] Issue 2 119–129

Execution of construction works – Bauausführung

Jiang, Wei; Gong, Jian; De Schut-ter, Geert; Huang, Yulin; Yuan,Yong: Time-dependent analysisduring construction of concretetube for tower high-rise build-ing [high-rise building; time-dependent; vertical deformation] Issue 4 236–247

General – Allgemeines

Beckmann, Birgit; Schicktanz, Kai;Reischl, Dirk; Curbach, Man-fred: DEM simulation of con-crete fracture and crack evolu-tion [discrete element method;crack pattern; concrete compo-nent structure; ratio of lateral tolongitudinal strain] Issue 4 213–220

Bertagnoli, Gabriele; Giordano,Luca; Mancini, Simona: Designand optimization of skew rein-forcement in concrete shells[concrete; shell; skew; reinforce-ment; genetic algorithm] Issue 4 248–258

Prestressed concrete – Spannbeton

Stráský, Jirí; Necas, Radim;Kolácek, Jan: Dynamic responseof concrete footbridges [foot-

bridge; dynamic response; stressribbon; slender deck; arch struc-ture] Issue 2 109–118

Reinforcement – Bewehrung



Torres, Lluis; Neocleous, Kyriacos;Pilakoutas, Kypros: Design pro-cedure and simplified equa-tions for the flexural capacityof concrete members reinforcedwith fibre-reinforced polymerbars [design; reinforced con-crete; FRP bars; flexural capaci-ty; FRP rupture; concrete crushing] Issue 2 119–129

Standards, regulations, guidelines, directives – Normen,Vorschriften, Richtlinien



Muttoni, Aurelio; Ruiz, Miguel Fer-nández: The levels-of-approxi-mation approach in MC 2010:application to punching shearprovisions [levels-of-approxima-tion approach; design codes;Model Code 2010; assessment ofstructural safety; critical shearcrack theory] Issue 1 32–41

Testing/experiments – Versuche

Aguiar, Eduardo Aurélio Barros;Bellucio, Ellen Kellen; El Debs,Mounir Khalil: Behaviour of



grouted dowels used in precastconcrete connections [beam- column connection; grouteddowels; semi-rigid connection;precast concrete] Issue 2 84–94


Desnerck, Pieter; De Schutter,Geert; Taerwe, Luc: Stress-strain behaviour of self-com-pacting concretes containinglimestone fillers [self-compact-ing concrete; stress-strain rela-tionship; strain-softening; peakstrain; toughness; limestonefiller] Issue 2 95–101


Tunnelling – Tunnelbau


Documents

Structural Concrete 01/2013