Structural Concrete 01/2014 Free Sample Copy

1Volume 15March 2014ISSN 1464-4177

- Long-term properties of recycled aggregate concrete- Resistance of hollow circular RC members under combined

bending/shear – experiments, new model- Strengthening RC dome of century-old Centennial Hall- Reliability analysis of CFC-strengthened RC beams- Staggered lap joints for tension reinforcement- Shear in concrete structures subjected to dynamic loads- Degree of hydration concept for early-age behaviour of immersed tunnel- Behaviour and deformation of plain concrete ground slabs- Non-linear analysis of statically indeterminate SFRC columns

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March 2014ISSN 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. 15 / 1

Editorial

1 Xilin LuPrecast concrete structures in the future

Technical Papers

3 Jianzhuang Xiao, Long Li, Vivian W. Y. Tam, Hong LiThe state of the art regarding the long-term properties of recycled aggregate concrete

13 István Völgyi, Andor Windisch, György FarkasResistance of reinforced concrete members with hollow circular cross-sectionsunder combined bending and shear – Part I: experimental investigation

21 István Völgyi, Andor WindischResistance of reinforced concrete members with hollow circular cross-sectionsunder combined bending and shear – Part II: New calculation model

30 Jerzy Onysyk, Jan Biliszczuk, Przemysław Prabucki, Krzysztof Sadowski, Robert ToczkiewiczStrengthening the 100-year-old reinforced concrete dome of the Centennial Hallin Wrocław

38 Osvaldo Luiz de Carvalho Souza, Emil de Souza Sánchez Filho, Luiz Eloy Vaz, Júlio Jerônimo Holtz Silva FilhoReliability analysis of RC beams strengthened for torsion with carbon fibre composites

45 John CainsStaggered lap joints for tension reinforcement

55 Johan Magnusson, Mikael Hallgren, Anders AnsellShear in concrete structures subjected to dynamics loads

66 Xian Liu, Wei Jiang, Geert De Schutter, Yong Yuan, Quanke SuEarly-age behaviour of precast concrete immersed tunnel based on degree of hydration concept

81 Morteza Aboutalebi, Amir M. Alani, Joseph Rizzuto, Derrick BeckettStructural behaviour and deformation patterns in loaded plain concrete ground-supported slabs

94 Ali A. Abbas, Sharifah M. Syed Mohsin, Demetrios M. CotsovosNon-linear analysis of statically indeterminate SFRC columns

fib-news106 2014 fib Congress, Mumbai107 2014 Freyssinet Medals109 ConLife and 70th anniversary of NIISK109 fibUK seminar report110 20th anniversary of CBS111 Report from the Spanish NMG112 2015 fib Symposium112 fib Bulletins113 Congresses and symposia

A5 Products and Projects

The Bella Sky Hotel in Copenhagen is leaning at a gravity-defying 15 degree angle. The com-plexity of Bella Sky reflects not only great engineering and constructional achievements, butalso an architectural ambition to create a unique and personal hotel experience. Built enti-rely using precast concrete elements this unique structure has pushed the use of precastconcrete to a new level. The structure is among the winners of the 2014 fib Awards for Out-standing Structures (photo: Ramboll)

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

Journal of the fib

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

Impact Factor 2012: 0.289

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.

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If required, special prints can be produced of single articles. Requestsshould be sent to the publisher.

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

Current pricesThe journal Structural Concrete has four issues per year. In additionto “Structural Concrete print”, the PDF version “Structural Concreteonline” is available on subscription through the online service WileyOnline Library.

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Imprint

Structural Concrete 15 (2014), No. 1

Inserts in this issue: Fischerwerke GmbH & Co. KG, 72178 Waldachtal;Danish Concrete Society/fib annual conference 2015 – Copenhagen

Bilfinger Industrial Services has enterednew territory in scaffolding. Tall indus-trial scaffolding is normally affixed tothe side of the building for which it isrequired. If this is not possible, free-standing, non-anchored scaffoldingmust be assembled. Working for one ofits customers, Bilfinger Industrial Ser-vices Nederland has now assembledscaffolding affixed to a tank using mag-netic anchoring. 35 m tall and 5 m wide,it is more compact than the free-stand-ing scaffolding normally required forthe tank. In this way it was possible tolower costs by some 30 %.

Indeed, it was the search for savings thatprompted the development of the newscaffolding system. The Bilfinger compa-ny wanted to offer its customer an alter-native to the free-standing scaffoldingthat was previously used for the mostpart. Until now, this was the only type ofscaffolding which it was possible to usewith structures such as tanks for whichno anchoring is possible and any attemptto weld fittings to the side would damagethe structure. The Bilfinger experts sug-gested a new approach involving the useof a magnet system. The magnetic scaffolding anchoring en-tails a permanent lifting magnet whichcan be switched on and off as requiredand produces a constant magnetic force.The necessary capacity is calculated for

each anchor by measuring the holdingpower and shear force. The results arereconciled with the static calculationsand only when the measurements matchthe static calculations is the anchor ap-proved for use. A specially developed test-ing device is utilised at the site to mea-sure the capacity of the magnetic scaf-folding anchoring to ensure the reliabilityof each individual anchor. Magnetswhich have proven themselves in a num-ber of different industrial applications areused for this purpose. Thus, for example,the same types of magnets are utilised inrope and lifting systems for heavy loads.Explains Ruud van Doorn, Chief Execu-tive Officer at Bilfinger Industrial Ser-vices Belgium/Netherlands: “We are ob-serving mounting pressure on the part ofour customers to have maintenance workperformed safely and cost-efficiently. Theuse of magnetic anchoring in scaffoldingis an excellent example which demon-strates the contribution which Bilfinger ismaking.”

Further Information:Bilfinger Industrial Services GmbH, Gneisenaustr. 15, 80992 München, Tel. +49 (0)89 – 149 98 -0, Fax +49 (0)89 – 149 98-150, [email protected], www.industrial.bilfinger.com

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Scaffolding innovation: Bilfinger Industrial Services using magnetic scaffolding anchoring for the first time

The use of magnetic anchoring lowers the cost of scaffolding for tanks and other structures to which anchors cannot be welded or affixed by means of drilling. (© Bilfinger Industrial Services)

Corridor Vc: High-performing wagon for high speed In the future, travelling between Budapest and Southern Dal-matia will take less time thanks to the Pan-European CorridorVc. Numerous tunnels and bridges are erected along the 397km route through Bosnia owing to the difficult topography. Do-ka’s contribution to the infrastructure initiative is a formworksolution including a total of ten Cantilever forming travellersfor the Studencica and Trebižat bridges crossing the valleys.

Altogether the European route 73 is about 702 km long. A1 is animportant section of this route in Bosnia-Herzegovina connectingthe northern border to the Adriatic by way of Zenica – Sarajevo –Mostar. The two bridges, Studencica and Trebižat, are intended toconnect the valleys near the municipality of Capljina. Hering, sub-contractor of OHL, the Spanish construction company, will bene-fit primarily from the extended pouring sections of the Doka-Can-tilever forming traveller that will reduce construction time byabout eight weeks. Decisive factors for awarding the contract toDoka Croatia were many joint projects, high-performing systemsas well as the ability to rent the formwork materials. With a stretch of 555 m in length from one abutment to the otherand maximum height of 81°m above the valley, Studencica is thelonger and higher of the two bridges. Four superstructures, each12.4 m wide and placed at a distance of 120 m from the other, areestablished on a total of five piers. At a total length of 365 m and59.5 m maximum height, Trebižat, the smaller pendant requiresonly three piers. Doka developed a safe and fast formwork solu-tion consisting of Cantilever forming travellers. A total of ten

rentable Cantilever forming travellers, eight of them on the Stu-dencica Bridge and two on the Trebižat Bridge, are making forsmooth and rapid progress at lofty heights.

First upward, then straight aheadHigh-performing Cantilever forming travellers allow for pouring of5 m segments in a weekly cycle. In the Corridor Vc project, com-pletely identical Forming wagons designed for 250 t carry maxi-mum loads of 196.5 t. “These extended 5 m pouring segments re-duce the number of segments and coupling joints and thereforesave time and money”, says Project Manager Mario Jurisic. The suggestion by both, the Business Development and BridgeCompetence Centers, to extend the pouring segment to 5 m facili-tates completion with eight fewer segments thanks to the high-per-forming Cantilever forming travellers. In the case of a weekly cy-cle, this means the project is completed eight weeks ahead oftime. By changing the cross slope and tapering the walls of the super-structures each segment was planned individually, thereby elimi-nating the need to adapt the formwork. Special installation ofpieces made-to-measure and a custom solution with reusable re-movable elements in the interior formwork prevent loss of largequantities of materials. This system facilitates a height adjustmentof the Cantilever forming traveller’s interior formwork especiallyfor the cross slope change.

Tough as nails at the limitDoka materials came into play for the piers as well. Columns wereconstructed with the help of the crane-lifted Climbing formworkMF240 and Framed formwork Framax Xlife. With hammerheadshigh-performing Supporting construction frames were used hori-zontally. Doka Croatia in cooperation with the Bridge Compe-tence Center demonstrated planning precision as well as creativityin order to get the Forming wagons into position at a height of 81m. Parts of a gantry crane placed on the formwork lifted the Can-tilever forming traveller’s floor grate a bit at a time. The floorpiece usually raised by its own winches at the Cantilever formingtraveller can only be connected to the formwork once it is on thehammerhead. A Doka Formwork instructor on site ensures cor-rect set-up and optimised use of the materials.Limited workspace on the hammerheads with dimensions of 8 min length called for a special solution. Whereas the forming wag-ons weighing approximately 80 t start moving symmetrically intwo directions with the cantilever forming principle, Doka’s struc-tural engineers figured out a fine-grained custom solution for thisproject. Thanks to the exact calculations, one of the Cantileverforming travellers will first start off from the hammerhead. Thenenough space is available for hitching the second traveller to itand offset the balancing act. In order to get around the lifting pro-

A6 Structural Concrete 15 (2014), No. 1 Responsible for Products & Projects: Publishing House Ernst & Sohn

Products & Projects

Fig. 1. High-performing at lofty heights: Ten Doka-Cantilever forming travellers allow for rapid and safe construction of both bridges along theCorridor Vc.

Fig. 2. For construction of the bridges spanning 555 m and 365 m in length,Doka developed a formwork solution consisting of Cantilever forming trav-ellers that save time and resources thanks to extended pouring sections.

Fig. 3. The total number of ten Doka-Cantilever forming travellers wereplaced into their correct starting positions with the help of gantry craneparts. (© Doka)

cedure, the Cantilever forming travellers will return once thewidth of a span has been completed; they are then repositionedand used again for the next pier.

Cross-border cooperationThe Forming wagon is fully equipped with secured platforms, safeAccess systems and access to all places on the Forming wagonwhere work is done. This allows for safe progress even at loftyheights. In addition to fine-grained Formwork planning carriedout by the teams at the Bridge and Business Development Com-petence Centers ahead of time, local engineers aid in smooth con-struction progress on site.

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

crete slab solution, bidirectional perforated to imbibe all kindsof conductions and installations. This way, suspended ceilingsand the extra height associated to them are not necessary any-more.Thanks to the integration of structure and installations, it is pos-sible to get an extra storey per each five, reducing this way thetotal area of the exterior enclosure and the consequent energylosses. To all these advantages, the saving of materials and thesimplification of the assembly of installations should be takeninto account. The simplicity of the system allows service ele-ments to be easily replaced and repositioned, with no need ofhindrance to any other activity being carried on in the building.Holedeck standard module is 80 × 80 cm in horizontal layout soit can be easily adapted to accept installations and elements de-signed for standard modulated ceilings.

Further Information:HOLEDECK S.L., Juan de Urbieta 10, Madrid 28007, Tel. +34 915021427, [email protected], www.holedeck.com

Products & Projects

Probably the most sustainable concretestructure in the worldThe new concrete waffle slab HOLEDECK is a patented sys-tem of voided slabs that can be pierced all through its thick-ness by the building conductions and services. Using Hole-deck means the reduction of total built volume, concrete con-sumption and Co2 footprint.

Holedeck system is the answer to a wide problem in those build-ings such as hospitals, offices or malls, which require both largespans and a high level of building services and installations.Holedeck avoids the necessity of a big edge with its waffle con-

* € Prices are valid in Germany, exclusively, and subject to alterations. Prices incl. VAT. excl. shipping. 1064106_dp

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Ernst & SohnVerlag für Architektur und technischeWissenschaften GmbH & Co. KG

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This book provides practicing engineers with detailed design procedures and reference material on what is now widely re-garded as an economic, structurally sound and versatile form of construction for multi-storey buildings. This revised and up-dated edition features a new chapter on the design of Panel Structures, including the concepts of crosswall construction and volumetric construction. It also offers design examples to the new Eurocodes, using their British National Application Documents, along with numerous worked examples drawn from industry, as well as design charts, and tables.

Order online: www.ernst-und-sohn.de

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Reinforced Concrete Design According to EC 2 and Other International StandardsWith RSTAB and RFEM, Dlubal’s main programs for struc-tural analysis, one can design reinforced concrete structuresnot only according to EC 2 but also three further internation-al standards: ACI 318-11 (US Standard), SIA 262:2003 (SwissStandard), GB 50010-2010 (Chinese Standard).

17 National Annexes are currently available for the design ac-cording to EC 2 (EN 1992-1-1:2004), among them the annexes ofGermany, Austria, Italy, the Netherlands, France and Spain.

FunctionalityThe designs for the ultimate and the serviceability limit state areperformed for all standards in the corresponding CONCRETEadd-on modules for surfaces (only in RFEM) and members. Inaddition, it is possible to consider cracked sections of the con-crete (state II).Moreover, if rectangular or circular cross-sections are calculatedaccording to EC 2, it is possible to perform the fire resistancedesign by applying the simplified approach (zone method) ac-cording to EN 1992-1-2.

Several design cases can be created. For example, one may per-form all designs for particular structural components, and forsome others one carries out only the ultimate limit state design.If desired, the concrete design modules can determine the mini-mum reinforcement according to the respective standard. Manydetailed input options are provided so that one is very flexiblewith the creation of the corresponding designs for one’s con-crete structure. Thus, one can for example specify a basic rein-forcement to design available structures. It is also possible to in-sert the desired reinforcement, which the program completes, ifnecessary, by additional reinforcement.All intermediate values are shown after the calculation. In thisway, one can retrace all performed designs. The determined re-inforcement of members can be displayed by high quality visual-ization. At the same time, the calculation modules check auto-matically if the reinforcement fits in the structural component.All initial values, designs, tables, graphics etc. can be integratedin the printout report to create a structural analysis as a docu-mentation prepared for the test engineer.

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


Products & Projects

Fig 1. Required bottom reinforcement for a floor of an underground parkingdisplayed in RFEM

Fig. 2. T-beam with curtailed longitudinal reinforcement visualized in theRFEM add-on module RF-CONCRETE (© Dlubal)

Twisted floors in weekly cycles – Evolution Tower, Moscow, RussiaEvery week, Moscow’s new landmark is gaining 4.30 m inheight – with each completed floor twisted 3° in relation tothe preceding one. For this, PERI engineers developed a cra-ne-independent formwork concept on the basis of the RCSand ACS self-climbing technology.

The 249 m high Evolution Tower is part of Moscow’s interna-tional trade centre, “Moscow City”, which is currently the largestinvestment project in the Russian capital. Due to the fact thateach of the 52 upper floors is constantly twisted by 3° whilst being arranged around the central core of the building, the sky-scraper experiences an elegant rotational movement in a clock-wise direction from the base to the top by more than 150°.

Corner column formwork with additional benefitsThe elegant rotation of the building is made even more strikingthrough the spiral-shaped design of the distinctive rectangularcolumns on the building corners. The corner columns are thusnot only inclined but also feature a twist. The project-specificPERI self-climbing formwork concept is based on ACS and RCSsystem components whilst a special gallows construction accel-erates the shuttering and striking procedures. In addition, theclimbing formwork for the rectangular columns fulfils two othertasks: in the area of the building corners, the external formworkserves as slab edge formwork when forming the floor slabswhilst the RCS formwork scaffold unit also acts as a climbingprotection panel and thus part of the building enclosure.

Self-climbing core formworkCore walls and floor slabs are concreted in one pour, with eachfloor divided into three concreting sections. Up to the 26thfloor, four ACS P climbing units have been used to form gener-ously-sized working platforms whilst VARIO GT 24 wall form-

work elements serve as internal and external formwork. In addi-tion, the core floor plan changes and, for this, one of the ACSplatforms is quickly converted to a gallows variant through the

use of four ACS G brackets. As a result, the following storeys canalso be efficiently climbed. For forming the floor slabs, cus-tomized UNIPORTAL slab tables keep pace with the fast rate ofworking.

Rotating in safe conditionsThe top three floors under construction are tightly enclosedwith the RCS climbing protection panel. The units climb theconstant twist of the building in an inclined position – alsocrane-independent with the help of the mobile climbing hy-draulics. The permanently installed rail-guided system ensures afast and safe climbing procedure also in inclined positions. The

Products & Projects

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MC 2010 – the most comprehensivecode on concrete structures

The fi b Model Code 2010 is now the most comprehensive code on concrete structures, including their complete life cycle: con-ceptual design, dimensioning, construction, conservation and dismantlement. It is expected to become an important docu-ment for both national and international code committees, practitioners and researchers.

The fi b Model Code 2010 was produced during the last ten years through an exceptional effort by Joost Walraven (Conve-ner; Delft University of Technology, The Netherlands), Agniesz-ka Bigaj-van Vliet (Technical Secretary; TNO Built Environment and Geosciences, The Netherlands) as well as experts out of 44 countries from fi ve continents.


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Fig. 2. VARIO girder wall formwork for the core walls climbed with help ofthe ACS self-climbing system in regular weekly cycles with 4.30 m concret-ing cycle heights.

Fig. 1. With an elegant 150° rotation, the Evolution Tower spirals almost250 m into the Moscow sky. Inclined and crane-independently climbed RCSprotection panel units provide here a very high level of safety.

climbing rails are connected to the building by means of corre-sponding slab shoes. In combination with the four climbingunits of the rectangular columns, a gap-free enclosure isachieved – for safe and quick working operations particularly atgreat heights.

Diagonally climbed and movable landing platformsFurthermore, on the sides of the building, RCS landing plat-forms are climbed for use as temporary storage areas and formoving of loads with the crane. The climbing procedure alsotakes place here without a crane, hydraulically with the help ofthe mobile climbing devices. On its inclined climbing path, thecontinuous vertically positioned circular columns present a per-manent obstacle. Therefore, the RCS platforms were so designedso that they can be temporarily moved on varying positions – bymeans of flexibly adaptable forward and reverse inclinationswithout any time-consuming modification work.

Test set-up as part of the overall solutionFor PERI engineers, twisted high-rise buildings and inclinedclimbing procedures are nothing new: urban development high-lights such as the Turning Torso in Sweden and the two Ab-solute World Towers in Canada likewise spiral upwards in a sim-ilar fashion – successfully realized with expert PERI support.The special feature of the Moscow EvolutionTower is the com-bined climbing formwork utilization for the vertical core wallsand twisted corner supports in connection with the obliquelyclimbed protection panel and landing platform. In addition tothe detailed formwork planning, a previously used test set-upwas therefore an important part of the PERI overall solution.This meant that the applicability under construction site condi-tions could be demonstrated very early on, and the optimizationpotential for daily on-site working operations could be accelerat-ed through fine-tuning adjustments.

Further Information:OOO PERI, Territory “Noginsk-Tehnopark” 9, 142407, Noginsk District, Moscow Region, Russia, Tel. 007 – 4 95 – 6 42 81 13, Fax 007 – 4 95 – 6 42 64 44, [email protected], www.peri.ru


Products & Projects

Fig. 3. The inclined positioned climbing rails of the RCS climbing protectionpanel are permanently connected to the building by means of correspond-ing slab shoes.

Fig. 4. Even the landing platforms are rail-climbed – and without any cranesupport due to the use of the mobile RCS climbing hydraulics.

Fig. 5. The site management team from Renaissance Construction standingproudly in front of the elegantly twisting Evolution Tower. (© PERI)

Structural Concrete 15 (2014), No. 1 A11

software

Dlubal Software 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.comunder-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.deconcrete: 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

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.deStructural Protection Systems Expansion Joints Structural Bearings Seismic Devices Vibration Absorbers

literature

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fastening technology

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Concrete is the most commonly used building material in the world, andprecast concrete components and structures provide a creative way to ex-tend the use of concrete. Facing the increasing challenges on the construc-tion industry, including climate change, energy saving and environmentalprotection, structural engineers need a new vision for the potential of pre-cast structures as well as for the sustainable use of concrete in general. Inthinking about sustainable construction, we need to find innovative waysto reduce the impact of construction activity on our environment.

Civil engineering provides human beings with essential support oftheir everyday life: housing, workplace, transport, communications andutility supplies (electricity, gas, water, etc.). Precast structures are well-recognized as environmentally friendly structural systems, so there is nodoubt that precast technology will play a very important role in futureconstruction activities. In the 21st century, construction needs that willuse precast concrete include:– tall residential buildings– tall office buildings– advanced modern factories– online shopping warehouses– large-scale infrastructure.

New residential and office buildings are widely required in the develop-ing world for improving the living and working conditions of the localpeople. High quality – especially in terms of sustainability and durability– is a very critical aspect for construction, and precast technology canprovide this. Advanced modern factories for IT-based manufacturing andonline shopping warehouses currently provide many challenges for civilengineers. The high pressure on the construction period and the use ofspecial facilities are common features, and precast technology usuallyprovides the best solution. For large scale infrastructure, such as long-span bridges, high speed railway lines, subways, and stadiums, precastcomponents and systems are already widely used and will find more ap-plications in the future.

Requirements for sustainability are being constantly updated, andinnovation is the best driver to keep precast concrete structures movingon the right track. Concrete is easy to produce, cheap, robust, shapeableand suitable for almost all kinds of construction, and using precast tech-nology is the best way to bring concrete into practical engineering. Fur-ther consideration of the sustainability aspects of precast concrete struc-tures will always be necessary. For instance, life cycle energy saving strat-egy is essential for precast concrete structures, as with other materials, atboth the component and the structure level. Use of lightweight concreteand embedding heatproof material may significantly reduce energy con-sumption in the everyday use of structures.

Precast concrete structures, composed of prefabricated concretemembers that are reinforced or prestressed are the best known form of

Precast concrete structures in the future

Xilin Lu

Editorial

1© Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete 15 (2014), No. 1

structural system. However, the main stream of precast concrete struc-tures will soon include other hybrid materials and even more sustainableconcrete members, such as steel-reinforced or fiber-reinforced concretemembers and concrete members using recycled aggregate.

Modular construction has always been seen as the highest applica-tion level of precast technology. A primary benefit of modular construc-tion is its rapid delivery. The process of creating modules in a factory cantake place even while the site work is continuing, so modular buildingscan be constructed much faster than buildings constructed with a cast-in-situ strategy. This allows the buildings to be occupied sooner and allowsowners to see a faster return on investment.

The expression “concrete forest” indicates that people are worriedabout the uncontrolled use of concrete. Therefore reducing the amountof concrete used is important from the public perspective. In this regard,recycled aggregate concrete should be used for future precast concretestructures by recycling prefabricated concrete members, components orwhole subassemblies.

We also realize that precast concrete structures reflect the localconstruction culture, so precast concrete structures in different countriesand regions can show different cultural characteristics. The future devel-opment of structural systems will be colorful and will enrich the localcultural environment.

In areas that are prone to seismic activity, the extensive use of pre-cast concrete structures may be limited due to the lack of proper under-standing of the complex seismic behavior. In order to extend the engi-neering application of this kind of structural system and to evaluate theseismic behavior of existing precast concrete structures in seismic zones,some research has been carried out around the world in the past fewdecades, such as the series of investigations in the 1990s in USA andJapan, and consideration of the seismic behavior of precast concretestructures with respect to Eurocode 8 in Europe. More efforts need to befocused on the seismic behavior of precast concrete structures worldwidein the future.

Precast concrete is an important topic for “Structural Concrete”. Inthis issue, two papers introduce the experimental investigation and newdeveloped calculation model for reinforced concrete members with hol-low circular cross-section. One paper deals with shear failures of con-crete structures under dynamic loads. Three papers look at steel fiber re-inforced concrete columns, staggered lap joints, and reinforced concretebeams strengthened with carbon fiber composites. Another paper de-scribes the renovation retrofitting work carried out on the 100-year-oldreinforced concrete dome of the centennial hall in Wroclaw, which hasbeen listed as a UNESCO world heritage site. One paper presents a state-of-the-art review of the long-term properties of recycled aggregate con-crete, while another describes the application of a precast concrete im-mersed tunnel for the Hong Kong–Zhuhai–Macao Link project, mainlyfocusing on the early-age behavior of the tunnel. The final paper dealswith the behavior of plain concrete ground supported slabs under steploading conditions. We can easily find the precast aspects in most of thepapers.

I believe, precast concrete structures, with constant innovation, areavailable and qualified for a better construction in the future.

Xilin Lu, Professor and Vice-DirectorState Key Laboratory of Disaster Reduction for Civil Engineering, Tongji University, Shanghai, P. R. China

2 Structural Concrete 15 (2014), No. 1

Editorial

3© 2014 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete 15 (2014), No. 1

This paper reviews the long-term properties of recycled aggre-gate concrete (RAC), including long-term strength, shrinkage,creep, carbonation resistance, antifreeze resistance, imperme-ability, abrasion resistance, alkaline aggregate reactions, sul-phate corrosion and fatigue behaviour. Most studies have shownthat the long-term properties of RAC are inferior to those of natur-al aggregate concrete (NAC), and some researchers have ob-served that the long-term properties are better than those ofNAC. RAC’s long-term properties are affected by many factorssuch as recycled coarse aggregate (RCA) replacement percent-age, water-cement ratio, mineral admixtures and mix proportions.The long-term properties of RAC can be improved through bettercontrol of these factors. This paper will be helpful for a compre-hensive understanding of and further research on RAC, and pro-vides an important basis and references for the engineering ap-plications of RAC.

Keywords: recycled aggregate concrete, long-term properties, shrinkage andcreep, carbonation resistance, impermeability, fatigue behaviour

1 Introduction

Huge amounts of solid waste are produced in the processof constructing new buildings and demolishing old onesall around the world. For example, approx. 1,350 milliontons of construction waste are produced annually in Chi-na. Moreover, natural disasters such as the Wenchuanearthquake in 2008, the Yushu earthquake in 2010, theYunnan earthquake in 2011 and the Ya’an earthquake in2013 resulted in a great quantity of concrete waste. In2008 the Wenchuan earthquake resulted in a total of380 million tons of building waste [1]. With the rapid de-velopment of the construction industry and the excessiveconsumption of natural resources and deterioration of theenvironment in China, the conflict between sustainabledevelopment of the construction industry and shortage ofresources is becoming serious. Therefore, the use of con-crete containing demolished concrete is a very importantissue in environmental sustainability [2]. The use of recy-cled coarse aggregate (RCA) as a partial replacement fornatural aggregate, in what is called recycled aggregate con-crete (RAC), has become a common method [3]. In recent

years, research into RAC has been carried out around theworld and some successful applications of RAC in practi-cal engineering have been seen.

In the past, investigators have paid more attention tothe mechanical behaviour of RAC and have conducted rel-atively limited research into its long-term properties. In or-der to understand the long-term properties of RAC betterand prepare the ground for further research, this paper re-views related studies and past achievements, includinglong-term strength, shrinkage and creep, carbonation re-sistance, antifreeze resistance, impermeability, abrasion re-sistance, alkaline aggregate reactions, sulphate corrosionand fatigue behaviour. It will be helpful for the applicationand durability design of RAC.

2 Long-term strength of RAC

There is currently a lack of studies available concerningthe long-term strength of RAC and this subject requiresmore in-depth analysis by researchers.

Xiao et al. [4] studied the relationship between com-pressive strength and age of RAC experimentally, asshown in Fig. 1. It was shown that the compressivestrength of RAC increased over time, with an increase ofabout 60 % on the 360th day over that on the 28th day.Malhotra [5] obtained similar results. This is because thecompressive strength of RAC increases approximately lin-early with the increase in mass density [6], and the massdensity of RAC will increase with age and thus increasecarbonation inside the concrete.

Technical Paper

The state of the art regarding the long-termproperties of recycled aggregate concrete

Jianzhuang Xiao*Long LiVivian W.Y. TamHong Li

DOI: 10.1002/suco.201300024

* Corresponding author: [email protected]

Submitted for review: 23 April 2013Revised: 4 July 2013Accepted for publication: 10 July 2013 Fig. 1. Development of compressive strength of RAC over time

Numerous tests have been carried out to investigatethe influence of RCA content on the compressive strengthof RAC. It has been concluded that concrete strength de-creases with the increase in RCA replacement percentageand the strength reduction could be > 40 % [7]. Some re-searchers studied the differences in the long-term strengthof RAC and natural aggregate concrete (NAC). Kou et al.[8] studied the influence of RCA on the long-term me-chanical properties of concrete, and observed that RAChad a lower compressive strength and higher splitting ten-sile strength after 5 years of curing than the correspondingNAC, and the increase in compressive and splitting tensilestrengths from 28 days to 5 years was more significant inRAC than in NAC.

Khatib [9] studied the properties of concrete incor-porating recycled fine aggregate (RFA), including finecrushed concrete or brick. It was shown that a systematicreduction in the long-term strength occurs when class Msand is replaced with fine crushed concrete. This reduc-tion could reach about 30 % for 100 % RCA replacementbut be only 15 % for 25 % RCA replacement. However,when class M sand is replaced with fine crushed brick, itdoes not cause a substantial reduction in the long-termstrength, even at high replacement percentages. Kou et al.[10] carried out experimental studies of the properties ofNAC and RAC prepared with different mineral admixturesat different ages. It was shown that the compressivestrength and tensile splitting strength of NAC and RACmade with 10 % silica fumes and 15 % metakaolin werehigher than the other corresponding concrete mixtures(35 % fly ash and 55 % ground granulated blastfurnaceslag) both at early ages (4, 7 and 28 days) and at 90 days;the contributions of silica fumes and metakaolin to thecompressive strength of both NAC and RAC at early ageswere higher than at 90 days.

3 Shrinkage of RAC

The shrinkage mechanism of RAC should be almost thesame as NAC. In NAC, cement mortar causes the mainshrinkage deformation and coarse aggregate plays an in-hibitory role in the shrinkage deformation of cement mor-tar. In addition, old cement mortar adhering to the surfaceof RCA in RAC can also cause shrinkage deformation.RCA with a lower elastic modulus shows less inhibitionwhen it comes to reducing shrinkage deformation, andwater content will increase when using the prewettingmethod for improving working performance, and all ofthese factors lead to an increase in shrinkage deformation[11].

From the previous investigations [12–21] it has beenobserved that the shrinkage deformation of RAC is higherwith different degrees than that of NAC, and the increaseis in the range 0–100 %. A number of investigations [9, 12,19–25] have shown that RAC shrinkage increases with theincrease in RCA replacement percentage. Gomez-Soberon[19] concluded that this is due to a higher absorption ofRCA leading to the increase in shrinkage and creep ofRAC, and the higher the RCA replacement percentage, thegreater the increase in shrinkage and creep. The ratios(correction coefficients) of shrinkage deformation be-tween RAC with certain RCA replacement percentages

4

J. Xiao/L. Li/V. W.Y. Tam/H. Li · The state of the art regarding the long-term properties of recycled aggregate concrete


and NAC with the same strength provided by Belgium,The Netherlands and RILEM are shown in Table 1 [26].

The shrinkage deformation of RAC is affected bymany factors, and the basic rules are shown in the follow-ing. RAC shrinkage increases with the rise in RCA re-placement percentage, which has been discussed above.The drying shrinkage of RAC increases with age [16], in-creasing rapidly during the early period and slowly lateron [9, 12]. Sagoe-Crentsil et al. [16] found that the dryingshrinkage of RAC increases with age and stabilized atabout day 91, and is about 25 % greater than that of NAC.The shrinkage deformation of RAC increases with the in-crease in the water-binder ratio [23]. The test results ofRefs. [12, 22–25] showed that adding mineral admixturessuch as fly ash and slag can reduce the shrinkage defor-mation of RAC. The addition of a water-reducing agentwill increase the shrinkage of RAC with constant waterand cement contents [25]. Ravindrarajah [15] found thatthe shrinkage deformation of RAC increased with the risein strength and increase in shrinkage deformation of RAC,whose increase in strength is higher than that of NAC forthe same water-cement ratio.

In addition, Fathifazl et al. [27] studied the creep andshrinkage characteristics of RAC experimentally with anew method of mix proportioning, i.e. the equivalent mor-tar volume (EMV) method. The results showed that RACwith the EMV method experienced lower or comparablecreep and shrinkage than the reference NAC. By applyingthe residual mortar coefficients proposed in the study, inconjunction with the ACI and CEB creep and shrinkageprediction methods, a modified creep or shrinkage modelwas also proposed to calculate creep or shrinkage of RAC,and good agreement was observed between the predictedand measured creep and shrinkage strains for all testedspecimens.

4 Creep of RAC

The development trend of RAC creep is similar to NAC,and the creep of RAC is greater than that of NAC becausethe cement mortar content in RAC is greater than that inNAC, which could cause larger creep deformation [11].

In the previous investigations [19, 21, 28, 29] it wasobserved that creep deformation of RAC is 20–60 % high-er than that of NAC with the same mix proportions. Thetest results by Gomez-Soberon [19] showed that RACcreep deformation increases with the increase in RCA re-placement percentage. Domingo-Cabo et al. [21] observedthat creep of RAC with a 20 % RCA replacement percent-

Table 1. Shrinkage deformation correction coefficients for RAC with differ-ent RCA replacement percentages

Country/ Correction coefficientOrganization

100 % RCA 20 % RCA replacement replacement percentage percentage

Belgium 1.5 1.0

Netherlands 1.5 1.0

RILEM 1.35–1.55 1.0

5



age was found to be 35 % higher than that of NAC. For a50 % RCA replacement percentage, creep deformationwas about 42 % higher, whereas a 100 % replacement per-centage increases creep deformation by about 51 %. Theratios (correction coefficients) of creep deformation be-tween RAC with certain RCA replacement percentagesand NAC with the same strength provided by Belgium,The Netherlands and RILEM are shown in Table 2 [26].

Ravindrarajah et al. [15] observed that the creep de-formation of RAC increases with the strength class; it in-creases with the rise in cement content adhering to theRCA. Nishibayashi et al. [30] established that RAC creepdeformation increases rapidly with the increase in water-cement ratio, but the disparity of creep deformation be-tween RAC and NAC is almost stable at different water-ce-ment ratios and loadings. Zou et al. [31] studied the creepof RAC experimentally. The results indicate that RCAcould reduce the degree of creep in RAC, whereas the de-gree of creep in RAC increased with the increase in quan-tities of RFA; an increase in the stress level could be thereason for the increase in RAC creep deformation, where-as adding slag can reduce creep deformation. In theory,adding mineral admixtures such as fly ash and slag, steelfibres and bulking agent, which can reduce the shrinkagedeformation of RAC, can also reduce creep shrinkage.However, further studies are required to verify the results.

5 Carbonation of RAC

Xiao et al. [32] proposed that two effects should be inte-grated when comparing the carbonation resistance ofRAC and NAC:(1) As the porosity of RCA is greater than that of natural

aggregate, the porosity of RAC is much greater thanthat of NAC with the same water-cement ratio, andthis could definitely reduce the carbonation resistanceof RAC.

(2) As there is old cement attached in RCA, the total ce-ment content of RAC is greater than that of NAC,which means there are larger quantities of materialsavailable for carbonation, thus improving the carbona-tion resistance of RAC.

Most investigators have observed that the carbonation re-sistance of RAC is lower than that of NAC. The investiga-tions [33–35] revealed that the carbonation depth of RACis not significantly different from that of NAC. The BCSJ[36] concluded that carbonation rates were 1.2 to 2 timeshigher than those of controlled mixes when RAC was pro-

duced from RCA. Evangelista et al. [37] showed that car-bonation resistance is reduced by adding RFA to the con-crete; the CO2 penetration depth increased by about 40 %for concrete made with 30 % RFA and by about 110 % forconcrete made solely with RFA. However, Levy et al. [38]obtained contrary results that carbonation depth decreas-es when increasing the amount of RCA replacement per-centage, resulting in a better behaviour when this replace-ment was 20 or 50 %, mainly for recycled coarse and finemasonry aggregate. When using masonry or concrete re-cycled aggregate, even with a 100 % replacement percent-age, carbonation depth is still lower when compared witha reference concrete made with natural aggregates.

A number of researchers have studied variations thatinfluence the carbonation resistance of RAC. Many re-searchers [12, 39–42] thought that the carbonation resis-tance of RAC increases with the rise of RCA content. How-ever, Xiao et al. [32] and Zhang and Yan [43] found thatincreasing the RCA replacement percentage (< 70 %) in-creases the carbonation depth of RAC, but it decreaseswhen the RCA replacement percentage is 100 %, as shownin Fig. 2. Levy et al. [38] obtained contrary results, i.e. in-creasing the RCA replacement percentage decreases thecarbonation depth of RAC. It is generally considered thatcarbonation depth decreases with the increase in water-ce-ment ratio [32, 33, 35, 44]. Ryu [45] thought that the per-formance of RCA has a limited effect on carbonationdepth. Katz [7] concluded that RAC carbonation resistancewas not obvious when < 28 days old. However, Cui et al.[46] and Zhang and Yan [43] observed that using RCA fromhigh-strength concrete can reduce the carbonation depthof RAC. Shayan and Xu [47] established that the carbona-tion depth of both RAC and NAC are higher when aggre-gate was wetted through with sodium silicate solution. Asthis solution has a high CO2 absorption capacity, it will in-crease the carbonation rate of concrete. Sun [12] observedthat the carbonation resistance of RAC can be improved byadding slag or steel slag, but the quantity added should notbe too large or it will reduce carbonation resistance. Sun[12] and Kou et al. [41, 42] found that the addition of fly ashincreases the carbonation depth of RAC.

In addition, Xiao and Lei [48] established a calcula-tion model for recycled concrete carbonation depth basedon the investigation of the results available for carbona-tion of RAC and NAC carbonation test data. They pro-

Fig. 2. Effect of RCA percentage ratio on carbonation depth

Table 2. Creep deformation correction coefficients for RAC with differentRCA replacement percentages

Country/ Correction coefficientOrganization

100 % RCA 20 % RCA replacement replacement percentage percentage

Belgium 1.25 1.0

Netherlands 1.25 1.0

RILEM 1.25–1.45 1.0

posed the limit state method and the partial safety factormethod for RAC beams based on this model.

6 Freeze resistance of RAC

Many researchers [49–53] have conducted experiments onthe freeze-thaw durability of RAC. The results indicatethat RAC has good freeze-thaw resistance, even betterthan NAC with the same water-cement ratio. Richardsonet al. [52] compared the freeze-thaw durability of concretewith recycled demolition aggregate with that of NAC. Theresults showed that concrete cubes made with RCA wereabout 68 % more durable than plain cubes made with vir-gin aggregate and this may be caused by the variability ofgood quality RCA and curing procedures with soaked ag-gregate. However, concrete cubes made with RCA wereslightly more durable than those made with virgin aggre-gate when adding an air entrainer and polypropylene fi-bres. Medina et al. [53] researched the freeze-thaw durabil-ity of RAC containing ceramic aggregate, and the findingsshowed that concrete freeze-thaw resistance increasedwith rising RCA content and this may be due to the highmechanical quality of RAC plus the intrinsic properties ofnew aggregate. Hendriks [54] examined the difference be-tween the freeze-thaw durability of RAC and NAC andfound it to be insignificant. The reason is similar to light-weight aggregate concrete, which has a good freeze-thawresistance. Although RCA is no better at improving freeze-thaw resistance than lightweight aggregate, its largerporosity can play a micro-conservation role and reducethe water-cement ratio of cement mortar at the interface,thus improving the interface quality.

However, other investigators [13, 28, 55–65] conclud-ed that the freeze-thaw durability of RAC is lower and evensignificantly lower than that of NAC. As an example, the re-sults from Cao et al. [60], Dai et al. [63] and Zou et al. [65]are shown in Fig. 3. The main reason is fast absorption sat-uration in RCA (such as 10 min with up to 85 % saturationlevels and 30 min with up to 95 % saturation levels), butcritical saturation of freeze-thaw damage is about 92 %,thus freeze-thaw damage in RCA will appear earlier than ina new cement matrix. As a result, RCA becomes one of theweaknesses of RAC under freeze-thaw actions [11]. Some

6



investigators researched the freeze-thaw cycle of RAC ex-perimentally and conducted microstructural analyses onthe test results [13, 59, 66]. They pointed out that micro-cracks begin to concentrate at the old cement mortar ofRCA, then they are induced to occur around new mortarand, finally, cracks in new mortar will run through eachother only after several freeze-thaw cycles, resulting infreeze-thaw damage. Zou et al. [65] carried out experimentson the basic mechanical properties of RAC after freeze-thaw. The results showed that the freeze-thaw resistance ofRAC is worse than that of NAC and could reduce with theincrease in RCA replacement percentage and freeze-thawfrequency. Dai et al. [63] pointed out that the strength lossrate of RAC is higher than that of NAC, and the main rea-son is that RCA has lower freeze-thaw resistance because ofits high water absorption. Cui et al. [62] researched thefreeze-thaw cycle of RAC experimentally and found thatthe freeze-thaw resistance of RAC with 100 % RCA re-placement percentage is lower than that of NAC. The dura-bility factor of RAC with water-cement ratios of 0.45 and0.55 decreased by about 6 % and 10 % respectively whencompared with NAC. Cao et al. [60] indicated that thefreeze-thaw resistance of RAC is lower than that of NAC,but the freeze-thaw resistance of RAC with 50 % RCA re-placement percentage and natural sand fine aggregate isnot significantly different to that of NAC after 100 freeze-thaw cycles. So with a reasonable design approach, RACwith no more than 50 % RCA replacement percentage canbe used in building structures in cold regions.

Many methods can be employed to improve thefreeze-thaw durability of RAC. Test results indicate thatlowering the water-cement ratio can significantly improvethe freeze-thaw resistance of RAC [55, 56, 59, 61, 62, 64].Salem et al. [55, 56], Zhang et al. [64] and the BCSJ [36]showed that adding an air entrainer improve the freeze-thaw resistance of RAC quite distinctly. Salem et al. [55,56], Gokce et al. [59] and Zhang et al. [64] concluded thatsome mineral admixtures such as fly ash and kaolin canhelp to raise the freeze-thaw resistance of RAC. In addi-tion, decreasing RCA diameter and improving the qualityof RCA can also improve the freeze-thaw durability ofRAC.

7 Impermeability of RAC7.1 Water and air permeability

A number of investigators [18, 39, 67–71] have observedthat RAC’s resistance to water and air penetration is lowerthan that of NAC. The main reason is that initial cracks inRCA generated in the process of breaking, old cementmortar and old interfacial transition zones (ITZ) willchange the internal pore structure of RAC and increasethe porosity of RAC, and thus increase its permeability.Rasheeduzzafar and Khan [67] observed that the imper-meability of RAC will be equal to that of NAC when re-ducing RAC water-cement ratios by about 0.05–0.1. It wasobserved that the impermeability of RAC decreased withthe increase in RCA replacement percentage [39, 69, 71].Test results by Limbachiya et al. [39] indicate that the im-permeability of RAC is not significantly reduced with aRCA replacement percentage < 30 %. However, test resultsby Zhang et al. [72] showed that the impermeability of

Fig. 3. Effect of RCA replacement percentage on relative freeze-thaw para-meter

7



RAC with 50 % RCA replacement percentage was higherthan that of NAC. Olorunsogo and Padayachee [69] usedthe oxygen permeability index to describe RAC’s oxygenpermeability and observed that the index dropped withthe increase in RCA replacement percentage and in-creased with age. Zhang et al. [70] proposed that reducingthe water-cement ratio in a certain range, adding fly ashand confining crack expansion can enhance the imperme-ability of RAC. Tam et al. [73] proposed that RAC perme-ability can be enhanced when adopting a two-stage mixingapproach (TSMA). Somna et al. [74] observed that bothground fly ash and ground bagasse ash could reduce thewater permeability of RAC, although RAC compressivestrengths with both ash types were lower than those ofNAC.

7.2 Chloride permeability of RAC

A number of investigations [22, 33, 34, 37, 42, 69, 75–79]have indicated that RAC’s resistance to chloride penetra-tion is lower than that of NAC. Fig. 4 shows an examplefrom Kou et al. [80]. This is also due to the high porosityof RAC. Many investigators [22, 37, 39, 75, 76] observedthat increasing the RCA replacement percentage dimin-ished RAC’s resistance to chloride penetration, and it wasaffected significantly more by RFA than natural fine aggre-gate. Some researchers [10, 34, 79, 81] observed thatRAC’s resistance to chloride penetration can be enhancedby adding mineral admixtures such as fly ash. Hu et al.[78] established that reducing the water-cement ratio canalso improve chloride impermeability. Kou et al. [22] dis-covered that using steam curing while adding fly ash cansignificantly enhance the chloride impermeability of RAC.Otsuki et al. [33] observed that the chloride penetrationresistance of RAC can be improved by using the doublemixing method in the case of concrete with a high water-binder ratio.

Xiao et al. [82] proposed a model that consideredRAC as a five-phase composite material on the meso-scaleto describe the effect of RCA on chloride diffusion inRAC. The model is shown in Fig. 5. Theoretical equationswere also derived to calculate the effective chloride diffu-sivity Deff in the RAC modelled. The results showed thatvalues of Deff calculated from theoretical equations andfrom the finite element method (FEM) are in reasonableagreement. The simulation results show that Deff decreas-es with the rise in RCA volume fraction, but increases withthe adhesive rate of the old mortar adhering and the thick-ness of the ITZ. In addition, the RCA shape also influ-ences chloride concentration. Xiao et al. [83] simulatedchloride penetration characteristics numerically in mod-elled RAC (MRAC) to study RAC chloride penetrationcharacteristics. The results showed that chloride concen-tration distribution is not uniform within MRAC and chlo-ride concentration in RAC decreases wavelike over the dif-fusion depth, and the influence of RCA content, cementmortar and ITZ on the chloride concentration shows adistinct increase with diffusion depth. Ying et al. [84]found that the chloride diffusivity of RAC with Fuller gra-dation is smaller than that with an equal volume fractiongradation, and decreases with an increase in the minimumaggregate diameter.

8 Abrasion resistance of RAC

Abrasion resistance is an important indicator for evaluat-ing the performance of concrete pavements and it de-pends primarily on the strength and hardness of the sur-face layer of concrete. A number of investigations [16, 36,85] showed that the abrasion resistance of RAC is lowerthan NAC with the same mix proportions. Dhir et al. [85]observed that the wear depth of RAC increased with RCAreplacement percentages; wear depth of RAC exhibited nosignificant difference when RCA replacement percentagewas < 50 %, but was about 34 % higher than normal con-crete when the RCA replacement percentage was < 100 %.However, some researchers [86–88] observed that RACabrasion resistance is marginally higher than that of NAC.Test results showed that abrasion loss in RAC and NACfor strength class C30 was about 1544 and 1600 kg/m3 re-spectively, which indicates that the abrasion resistance ofRAC is higher than that of NAC [88]. In addition, Ying etal. [76] summarized that RAC abrasion resistance droppedwith the increase in RCA replacement percentage, yet in-creased with the RFA content. Test results in Yang et al.[89] showed that the abrasion resistance of RAC is highestwhen the RCA replacement percentage is about 40 %, andafter that it drops with the RCA replacement percentage.Sagoe et al. [16] and Yang et al. [89] discovered that RAC

Fig. 4. Relative chloride permeability with different water-cement ratios, flyash replacement percentages and age

Fig. 5. Five-phase composite sphere model of RAC

abrasion resistance diminished with the increase in water-binder ratio. Sagoe et al. [16] and Peng et al. [90] pointedout that adding slag and fly ash can improve the abrasionresistance of RAC. Concrete’s abrasion resistance is main-ly affected by concrete strength, aggregate properties andconcrete surface quality. Therefore, in theory, methodsthat can improve RAC strength, RCA properties and thequality of the RAC surface would increase the abrasion re-sistance of RAC. But additional studies in this area arestill necessary.

9 Alkaline aggregate reactions (AAR) of RAC

For investigations on how adherent mortar content influ-ences the properties of RAC, Marta et al. [91] observedthat the maximum alkali content in RAC, provided by ce-ment, will be about 0.12 % with respect to the concrete,namely 2.7 kg/m3, which is only just above the safe alkalicontent in concrete. Therefore, alkali content due to RCAcannot be ignored. Etxeberria et al. [92] found that adher-ent mortar on the surface of RCA exhibited alkaline activ-ity, and all recycled aggregates with adherent mortar werediscovered to have aureoles around them, which is thesign of AAR. It is indicated that expansion damage due toAAR can occur in RAC when aggregate in the originalconcrete exhibits alkaline activity. At present, there is nogenerally accepted method of measuring alkali activity inRCA, so the safest way is to avoid using RAC in whichAAR expansion damage has taken place and to controlthe total alkali content in RAC by using low-alkaline ce-ment or replacing some cement with a mineral admixture.For example, Shayan et al. [47] observed in experimentalstudies that using ganister sand to replace a certainamount of cement can reduce AAR dilatation of RAC.

10 Sulphate corrosion of RAC

Sulphate solution can develop a chemical reaction withhydration products in concrete, which will cause volumeexpansion in concrete and may cause damage. A numberof investigations [17, 18, 30, 85] indicated that the sulphateresistance of RAC is slightly lower than that of NAC withthe same water-cement ratio. The test results of Dhir et al.[85] showed that RAC’s sulphate resistance was very closeto that of NAC when the RCA replacement percentage is< 30 %; the sulphate resistance of RAC decreased with therise in RCA replacement percentage, but at a modest rate.Xiao [75] observed that RAC’s sulphate resistance de-creased with the increase in RCA replacement percentage;the decrease was not obvious with an RCA replacementpercentage < 50 %, but there was a significant decreasewith RCA replacement percentages > 50 %, and the reduc-tion was about 18.5 % with 100 % RCA replacement. Mar-ta and Pilar [91] estimated that the sulphate content inRAC due to RCA was about 4 % when considering the sul-phate content of cements, and the results showed that themaximum sulphate content in RAC would be up to 0.5 %,namely 11.2 kg/m3. Therefore, sulphate content in RACprovided by RCA cannot be ignored. The sulphate resis-tance of RAC can be improved by adding fly ash, high-range water-reducing agents and mineral admixtures or bymodifying the properties of RCA [75].

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11 Fatigue behaviour of RAC

Fatigue behaviour of concrete materials is very importantfor structures under repeated loadings, such as floors sub-ject to crowd vibration, road pavements and girders sup-porting highway bridges carrying traffic and offshorestructures battered by wind and waves. In order to utilizeRAC for practical engineering, it is significant and neces-sary to study the fatigue behaviour of RAC and comparethe difference between RAC and NAC. However, only afew investigations into the fatigue behaviour of RAC havebeen carried out. Xiao et al. [93] proposed expressing thecompressive fatigue strength of RAC based on its staticstrength distribution and analysed the effects of stress-strain ratio and RCA replacement percentage on the fatigue strength of RAC. The results showed that RAC’s fatigue strength increased with the RCA replacement per-centage. According to the proposed formula, axial com-pression fatigue strength with different fatigue lives andguaranteed rates can be estimated, providing the basis forRAC pavement design. Li and Xiao [94] established the relationship between the elastic modulus and fatiguestrength of RAC through experimental results and theoret-ical analysis. The results showed that the fatigue strengthof RAC calculated with the proposed formula was close tothe experimental results. It is indicated that the formulacan provide a reliable prediction of the fatigue strength ofRAC and can be used to guide engineering practice. Xiaoet al. [95] analysed the fatigue damage evolution of RACquantitatively with different damage variations and foundthree obvious phases as for the fatigue damage evolutionof NAC. They also proposed an inverted-S, non-linear fa-tigue damage cumulative model for studying the damageevolution and fatigue life of RAC. The results showed thatthe damage evolution equation and fatigue life of RACwere highly relevant in experimental results. Ji et al. [96]studied the fatigue behaviour of RAC with fly ash by con-ducting flexural fatigue tests on RAC beams, and the re-sults showed that the flexural fatigue behaviour of RACwith fly ash is similar to that of Portland cement concrete,especially at low stresses. Zhu and Li [97] proposed empir-ical expressions for residual strength corresponding to thenumber of cycles that can be used to predict residualstrength with reliability. Yan et al. [98, 99] studied the fa-tigue behaviour of recycled aggregate reinforced concreteexperimentally with different RCA replacement percent-ages under axial and eccentric compression. On the wholethere were some differences between the compressive fa-tigue behaviour of RAC and NAC, but it is feasible to useRAC in practical engineering. Xiao et al. [100] carried outexperiments on the fatigue behaviour of RAC with 100 %RCA replacement percentage under uniaxial compressionand bending cyclic loadings.

The S-N curves of RAC and NAC under uniaxialcompression and bending cyclic loading are shown inFigs. 6 and 7. These are based on the test results and someother research on the fatigue behaviour of NAC. It wasshown that there were some differences between the com-pressive fatigue behaviour of RAC and NAC, and the fa-tigue life of RAC is lower than that of NAC for the samestress level under cyclic bending. A fatigue model for RACunder uniaxial compression with a constant stress range,

9



which relates fatigue strain variation and fatigue modulusdegradation to fatigue damage evolution, was also pro-posed, and the results calculated with this model agreedwell with the fatigue tests results.

12 Conclusion

This paper has presented a state-of-the-art report on therelevant research work and findings concerning the long-term properties of RAC. The main conclusions can besummarized as follows:(1) The compressive strength of RAC increases with age;

the long-term compressive strength of RAC is lowerthan that of NAC, but the extent of the disparity be-tween RAC and NC decreases with age.

(2) The shrinkage and deformation of RAC is higher thanthat of NAC and increases with the increase in RCAreplacement percentage; the drying shrinkage of RACincreases rapidly during the early period and slowlyduring the later period; adding mineral admixtures,water-reducing agents, bulking agents, etc. can reduceshrinkage deformation.

(3) The creep deformation of RAC is about 20–60 % high-er than that of NAC and increases with the increase inthe RCA replacement percentage.

(4) There is still no generally accepted conclusion regard-ing the difference in carbonation resistance betweenRAC and NAC; adding slag, steel slag, reasonable con-trol of water-cement ratio, etc. can improve carbona-tion resistance.

(5) There are also contradictory conclusions regardingthe freeze resistance of RAC from different re-searchers; lowering the water-cement ratio, adding air-entraining agent, mineral admixtures such as fly ashand kaolin and improving the quality of RCA can en-hance the freeze resistance of RAC.

(6) The impermeability of RAC is lower than that of NACand decreases with the increase in RCA replacementpercentage; reducing the water-cement ratio in a cer-tain range, adding admixtures such as fly ash or usingTSMA can improve impermeability.

(7) The abrasion resistance and sulphate resistance ofRAC are lower than those of NAC.

(8) There is some difference between the fatigue behav-iour of RAC and NAC, but it is feasible to apply RACto practical engineering.

On the whole the study of the long-term properties ofRAC is still at an early stage. It requires more in-depthanalysis by researchers looking into mechanisms, physicalmodels and measures to improve the long-term propertiesof RAC.

Acknowledgments

The authors wish to acknowledge the financial support ofthe National Natural Science Foundation of China (NS-FC) (project No: 51178340) and NSFC Research Fund forInternational Young Scientists (project No: 51250110074).

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94. Li, H., Xiao, J. Z.: On fatigue strength of recycled aggregateconcrete based on its elastic modulus. Journal of BuildingMaterials, 15 (2), 2012, pp. 260–263 (in Chinese).

95. Xiao, J. Q., Ding, D. X., Luo, X. W., Xu, G.: Quantitativeanalysis of damage evolution as recycled concrete approach-es fatigue failure. Journal of Central South University (Sci-ence & Technology), 42 (1), 2011, pp. 170–176 (in Chinese).

96. Ji, T. P., Xiao, P., Gao, Y. F.: Fatigue performance of recyclingconcrete with fly ash. Journal of Hohai University (NaturalSciences), 38 (3), 2010, pp. 274–277 (in Chinese).

97. Zhu, H. B., Li, X.: Experimental research on residualstrength of recycled aggregate concrete under compressive

12



fatigue loading. Advances in Composites, pp. 150–151, 2011.pp. 1379–1382.

98. Yan, H. Q., Wang, Q. Y., Ning, Y.: Experimental research onfatigue behavior of recycled aggregate reinforcement con-crete made from building scrap. Advanced ManufacturingSystems, 339, 2011, pp. 448–451.

99. Yan, H. Q., Wang, Q. Y.: Experimental research on fatigue be-havior of recycled aggregate reinforcement concrete fromearthquake-stricken area. Materials Science and EngineeringApplications, 160–162, 2011, pp. 906–909.

100. Xiao, J. Z., Li, H., Yang, Z. J.: Fatigue behavior of recycled ag-gregate concrete under compression and bending cyclicloadings. Construction and Building Materials, 38, 2013, pp.681–688.

Long LiDepartment of Building EngineeringTongji UniversityShanghai, 200092, P.R. China

Vivian W.Y. TamSchool of Computing, Engineering & MathematicsUniversity of Western SydneyLocked Bag 1797, Penrith, NSW 2751Australia also: Department of Building EngineeringTongji UniversityShanghai, 200092, P.R. China

Hong LiDepartment of Building EngineeringTongji UniversityShanghai, 200092, P.R. China

Jianzhuang XiaoDepartment of Building EngineeringTongji UniversityShanghai, 200092, P.R. China


Part I of this paper introduces an experimental programme car-ried out on RC members with thick-walled hollow circular cross-sections to study their behaviour under combined bending andshear. The study looked at ultimate resistance and propagation ofcharacteristic crack pattern as well as the shape and behaviourof the failure sections as a function of wall thickness, amount oflongitudinal and transverse reinforcement, shear span and axialforce. Test results were used to verify a newly developed calcu-lation model describing the behaviour of the members investigat-ed at failure under combined bending and shear. This model willbe presented in Part II.

Keywords: combined bending and shear behaviour, parametric experimentalstudy, hollow circular cross-section, failure section, sliding surface

1 Introduction

Piles, poles, towers supporting wind turbines and manyother RC members are frequently built with a hollow cir-cular cross-section. Despite the extensive use of this cross-sectional shape, no widely accepted method exists for as-sessing the shear resistance of these members.

Several shear design methods used in the recent pastare based on strut-and-tie models and modified compres-sion field theory [1]. Traditionally, the methods expressthe shear resistance of an RC member with shear rein-forcement as a function of the effective depth and amountof transverse reinforcement. Formulae have been verifiedfor plane webs, but webs with a curvature in the directionof shear, as in hollow circular cross-sections, have notbeen considered. The applicability of these formulae formembers with hollow circular cross-sections is also ques-tionable.

The following two experimental research projects in-vestigating the shear resistance of RC members with hol-low circular cross-sections and transverse reinforcementon the outside of the wall only (single-hooped) are avail-able in the literature.

A test programme carried out on four RC memberswith a thick-walled hollow circular cross-section plus di-aphragms at the ends and the load application point was

published by Turmo et al. [2]. Two different concrete mix-es were investigated and the specimens were loaded at alow shear span ratio.

Uehara [3] carried out a test programme involving42 specimens. The research dealt with the influence of theaxial force on the ultimate resistance of hollow circularspecimens under combined shear and bending (bending-shear resistance). Shear failure mode was observed onfour specimens.

Jensen and Hoang [4] developed an empirical calcu-lation method based on the experimental results of Turmoand Uehara.

An experimental programme was needed becausefew experimental data and no extensive parametric stud-ies were available on this topic. The aim of this experi-mental research was to establish a basis for the calculationof shear resistance for members with hollow circular cross-sections. The model developed will be shown in Part II ofthis paper. The basic idea of this model is to improve theclassic Mörsch-type strut-and-tie model by considering thecontribution of the flexural compression zone in the bend-ing-shear resistance of the members. Part I presents the ex-perimental results of the 45 specimens loaded under com-bined bending and shear up to failure.

2 Test variables

The experimental programme presented here looked atthe influence of wall thickness, amount of longitudinaland transverse reinforcement, load-to-support distanceand axial force on the bending-shear behaviour of single-hooped RC members with a hollow circular cross-section.

3 Experimental investigations3.1 Test setup

The test setup is shown in Fig. 1. Bearings under the spec-imens were composed of rigid steel blocks and allowedlongitudinal displacement and rotation. Plastic sheetswere placed between the specimen and the steel blocks.One concentrated load was applied in 20–30 kN steps bymeans of the hydraulic jack of a WPM ZD600 test ma-chine. The load and the displacement of sections shownin Fig. 1 were measured electronically. The applied loadwas positioned asymmetrically to produce shear failure inthe shorter shear span.

Technical Paper

Resistance of reinforced concrete memberswith hollow circular cross-sections under combined bending and shear – Part I: experimental investigation

István Völgyi*Andor WindischGyörgy Farkas

DOI: 10.1002/suco.201200035


Submitted for review: 24 September 2012Revised: 18 July 2013Accepted for publication: 18 July 2013

The crack pattern was recorded manually in the fail-ure zone at each loading step. The width of the criticalshear crack was measured by LEDTs at mid-depth of thespecimens in two orthogonal (vertical and longitudinal)directions. The specimens were loaded unilaterally to fail-ure (deflection rate at section C was set to ∼0.1–0.5 mm/s).

3.2 Specimens, parameters

The test specimens had a constant hollow circular cross-section of 300 mm outside diameter and a nominal wallthickness of 55 or 90 mm. For most specimens, the gradeB500B longitudinal reinforcement consisted of 12 de-formed (ribbed) bars with a diameter of 12, 14 or 16 mm.A few specimens were cast without transverse reinforce-ment. As transverse reinforcement, a grade B500B ribbedbar with a diameter of 5 mm was provided at a pitch of150, 110 or 75 mm for specimens with transverse rein-forcement. The transverse reinforcement was positionedon the outer side of the wall of the specimens. The con-crete cover to the longitudinal reinforcement was 20 mm.The longitudinal bars were fully anchored at the end sec-tions by welding them to the end stirrups according toFig. 1.

Eighteen specimens were centrically pretensioned.Two specimens were cast with 12 strands in the longitudi-nal direction. In these cases the diameter of the flexuralreinforcing bars is denoted with “0”. At the other 16 pre-stressed specimens, four of the 12 longitudinal bars werechanged to strands. Effective prestressing forces at thetime of the tests are given in Table 1.

The specimen information in Table 1 includes thenominal wall thickness [mm], the diameter of the longitu-dinal reinforcement [mm], the pitch of the spiral (helicaltransverse reinforcement) [mm], the prestressing level (if

14

I. Völgyi/A. Windisch/G. Farkas · Resistance of reinforced concrete members with hollow circular cross-sections under combined bending and shear – Part I: experimental investigation


applicable) [kN], and the load-to-support distance [mm].Specimens with a lower prestressing level are denotedwith F1.

To study the influence of the bending-to-shear ratioon the resistance of the member, different shear span ra-tios were applied, according to Fig. 1. The parameters ofthe specimens and the loading setup are summarized inTable 1.

The most important material properties of the rein-forcing and prestressing steel used in the specimens aregiven in Table 2. See [5], [6], [7] for more detailed informa-tion on the materials and the specimens.

4 Test results4.1 Failure mode

A complex failure mode associated with combined bend-ing and shear was observed for all of the specimensanalysed in this paper. The typical inclined crack of thelater failure section opened and caused yielding in thetransverse reinforcement, and the concrete zone subjectedto compression and shear started to fail along a slidingsurface [8]. This sliding surface, like a slope (as knownfrom geotechnics), develops as an extension of the criticalshear crack. For more details see Part II.

Fig. 2 shows a typical crack pattern in the failurezone just before failure. The first bending-dominantcracks (crack No. 1) appeared at the lower fibre of thecross-section under the loading block. The cracked zoneexpanded as the load intensity increased. The inclinationof cracks further away from the loading block graduallydecreased because of the increment in the shear-to-bend-ing moment ratio (crack No. 2 – No. 4).

Assuming a perfect bond between concrete and steeland that “plane section remains plane after deformation”

Fig. 1. Testing and loading setup

15



(general assumptions), the calculated depth of the com-pression zone under the loading block (pure bending) isindicated by the red line in Fig. 2. Although the bendingmoment along the shear span decreased from the loadingblock to the support, the top ends of the bending-shearcrack part of the polyline-shaped discontinuity lines (in-

clined bending-shear crack and expanding sliding surface)were closer to the top extreme fibre than the top ends ofthe cracks caused by (almost) pure but greater bending un-der the loading block. The effective depth of the compres-sion zone of sections under combined bending and shearwas also smaller than the calculated compression zonedepth of a cross-section under pure but greater bending ac-cording to the general assumptions. This phenomenon iscaused by the influence of the combined shear force; thus,the depth of the compression zone of a cross-section un-der pure bending is inversely proportional to the intensityof the bending moment.

In Fig. 2 the failure section is marked with a thickblack line. Prior to failure, a change in direction of the fail-ure section appeared at both ends. The inclination of thelower branch of the crack decreased compared with thatof the intermediate branch. At the same time, relativelyhorizontal cracks appeared along the longitudinal rebarsin the tension zone, which resulted in the degradation inbond beyond both faces of the critical crack. This degra-dation was caused by the combination of axial pull-outand transverse displacement (shear slip) of the tensile lon-gitudinal rebars. This phenomenon has been analysed ear-lier by Maekawa et al. [9]. This degradation in bond stiff-ness for the tensile bars also resulted in the growth of thecrack width and, as a consequence, the extension of

Table 1. Specimen data and experimental results Table 2. Average values of measured steel properties

Reinforcing 0.2 % proof stress Tensile strength bars (f0.2) [MPa] (ft) [MPa]

∅5 581 609

Reinforcing bars Yield strength Tensile strength (fy) [MPa] (ft) [MPa]

∅12 589 639

∅14 593 644

∅16 626 709

Prestressing strands 0.1 % proof stress Tensile strength (fp0.1) [MPa] (fp) [MPa]

T93 1557 1753

2

5

4 1

3

Fig. 2. Crack pattern of specimen 90-16-150-825: Nos. 1–5: cracks analysed;red line: depth of compression zone calculated by assuming a perfect bondbetween steel and concrete; black line: parts of failure section, criticalcrack and sliding surface (dashed); blue line: zone of maximum shear force.

cracks into the compression zone (calculated assumingperfect bond). A further consequence was that the resis-tance of the failure section dropped below that of the sec-tion including crack No. 4, in which the amount of trans-verse reinforcement crossing the cracked section was lower.

Considering the actual internal force distribution inthe member, the intensity of the shear force along theshear span was not constant (see Fig. 1). The part of theshear span with the highest transverse loading is markedwith a blue line in Fig. 2. The appearance of a couple ofshear cracks in the marked zone was expected. The shapeof the section including crack No. 5 was very similar tothat of the failure section. However, its higher resistancewas explained by the lower compressive stress caused by asmaller bending moment.

The failure section developed from one of the char-acteristic cracks, which appeared during an earlier loadingphase. A more detailed definition of a characteristic crackcan be found in [8]. The position of the early cracks andthat of the failure section varies depending on the actuallocal concrete tensile strength distribution along the spec-imens. The variable position of the tip of the characteris-tic crack is the main reason for the usual variation in thebending-shear failure loads amounting to about 10 %, evenfor precisely repeated tests in the literature.

4.2 Influence of shear span ratio on resistance of failure section

The influence of load-to-support distance (shear span) onthe shear resistance of RC beams has been studied by sev-eral researchers in the past. It is well known that if theshear span is less than a certain limit value, then the shearresistance of a beam increases as shear span decreases. Itis important to note that in the case of three-point loading,the full length of the failure section must fit between theinner edges of the support and the loading block, and thelength of the failure section must be less than or equal tothe distance between the inner edges. Therefore, internalforces developing along each potential failure sectionhave to balance the actual bending moment and the totalshear force resulting from the reaction force. For the spec-imens tested with their different shear spans, the bending-to-shear ratio and the geometry of the failure section dif-fered. The failure section of specimens with a longload-to-support distance was longer than the total load-to-support distance of specimens with a short shear span (seeFig. 3). The resistance of specimens with a short load-to-support distance was higher than that for specimens witha longer load-to-support distance, although the amount oftransverse reinforcement crossing the shorter failure sec-tion was lower. The additional resistance for specimenswith a short load-to-support distance originated from thedifferent shape of the failure section across the compres-sion zone. Prior to failure, the longitudinal distance of theupper end of the critical crack from the loading block wassmaller than that for the case of a specimen with a largerload-to-support distance, see Fig. 3e (failure shear force:228 kN) and Fig. 3a (177 kN). The justification based onthe shorter sliding surface is presented in Part II of this paper.

16



4.3 Influence of transverse reinforcement on resistance of failure section

It is well known that the amount of transverse reinforce-ment influences the shear resistance of a beam. Note thatthe shear resistance of an RC member is a quasi-linearfunction of the amount of transverse reinforcement (see

Fig. 3. Crack pattern and failure section of specimens prior to or after fail-ure. Cracks were marked by black or blue colours during the test. Numbersshown near cracks indicate total active load [kN] acting at mid-span whenthe cracks appeared. Cracks marked with red appeared during the finalload step, prior to failure. Thick lines show the failure section of each specimen.

17



Fig. 4). Furthermore, the shear resistance of specimenswithout transverse reinforcement is higher than the shearforce at the appearance of the first shear crack (see Fig. 4).The remaining shear resistance depends very much on theamount of longitudinal reinforcement, the wall thicknessof the specimen and on the load-to-support distance. Inthe absence of nearly orthogonal reinforcement crossingthe shear crack, the crack width growth is not restrainedefficiently. Consequently, intensive shear crack propaga-tion is expected. During this test, each specimen exhibitedconsiderable ductile behaviour as shown in Fig 5. The remaining shear resistance is the consequence of the sig-

nificant shear contribution of the flexural compressionzone.

4.4 Influence of concrete compression zone on resistanceof failure section

The influence of the concrete compression zone on theshear resistance of RC members has been demonstratedpreviously by Walther [10] and Juhász [11]. It has nowbeen shown that the resistance of the concrete compres-sion zone is influenced by the horizontal and vertical di-mensions of this zone between the top end of the bending-shear crack and the edge of the loading block. Thedimensions are determined by the loading and geometryparameters of the specimen.

4.5 Influence of flexural reinforcement on resistance of failure section

Shear failure develops in members independently of thefact of whether the longitudinal reinforcement yields. Theopening and propagation of a critical crack under monot-onic loading limits the depth and shear capacity of thecompression zone. The depth of the compression zone de-pends on the amount and bond characteristics of the lon-gitudinal reinforcement, i.e. on crack width and shear slip,too. The shear resistance of RC members with both longi-tudinal and shear reinforcement which influences by theamount of longitudinal reinforcement which influencesthe depth of the effective compression zone (see Fig. 4).

4.6 Influence of axial force due to prestressing on resistance of failure section

The initial increase in the shear resistance of a beam dueto prestressing is well known. However, specimens testedin this research also showed that replacing rebars with

60

80

100

120

140

160

180

200

220

-0,2 0 0,2 0,4 0,6 0,8 1 1,2 1,4

1/s [1/dm]

Sh

ear

forc

e at

fai

lure

[kN

]

55-12

55-14

55-16

90-16

55-16

55-14

black: L=625 mmred: L=825 mm

Fig. 4. Failure load as a function of pitch of spiral reinforcement (s)

Fig. 5. Shear force plotted against mid-span deflection – typical diagrams (unloading branches removed)

prestressing strands might even be disadvantageous due tothe less efficient bond properties of strands comparedwith ribbed reinforcing bars. Furthermore, strands have anegligible dowel effect. These circumstances may result ina prestressed member having a lower resistance comparedwith one having reinforcing bars only. The loadbearing ca-pacity of specimens with the F1 prestressing level was of-ten lower than that of specimens without prestressing.Nevertheless, the failure load of each specimen with theF2 prestressing level was always higher than that for spec-imens with identical parameters and the F1 prestressinglevel. These pairs of specimens demonstrated the advanta-geous effect of prestressing (see Table 1).

4.7 Influence of wall thickness on resistance of failure section

The contribution of the concrete compression zone to theshear resistance of a member is reduced by the degrada-tion of the bond stiffness of longitudinal bars in tension.The ductility and the strength of the bond around the em-bedded surface of the bars depend on the thickness of theconcrete cover and the wall thickness of the member. Fig.3 shows that horizontal cracking along longitudinal barswas more intensive for specimens with a small wall thick-ness. The effective depth of the compression zone was al-so lower for those specimens. This resulted in a lowerloadbearing capacity for these specimens compared withothers with thicker walls.

The local behaviour of the specimens was analysedin [7]. The deformation of the annular cross-section underloading results in additional transverse tensile stresses inthe outer fibres of the wall, which intensifies the crackpropagation along the longitudinal bars [7]. Bond degra-dation and, as a consequence, a decrease in the efficiencyof the dowel effect of longitudinal bars for specimens withthin walls was more intensive (see Figs. 3a and 3c).

4.8 Effect of aggregate interlock on resistance of failure section

It has been demonstrated by several researchers that ag-gregate interlock is one component in the shear resistanceof RC members. However, aggregate interlock is activatedonly if crack faces move essentially parallel to each otherand the crack width is relatively small. A typical relativedisplacement between the crack faces in the web is shownin Fig. 6. When the crack occurred, the relative displace-ment between its faces was approximately orthogonal tothe crack. The trend of the subsequent relative displace-ments recorded reveals that the instantaneous relative dis-placements of crack faces had dominant rotational com-ponents and that the centre of rotation was located closeto the current tip of the crack. The relative movement wasalways close to perpendicular to the radius drawn fromthe current tip of the crack to the point observed. Prior tofailure, the width of the critical crack was 1–3 mm. An ex-cerpt from the crack width measurements can be seen inFig. 7, which shows the real relative displacement betweenthe real crack faces. The figure reveals that aggregate in-terlock in the tensile zone cannot be effective. Furtheranalysis of relative displacements between the crack faces

18



is given in [7]. Detailed research into the relative displace-ments between the crack faces was published by Muttoniet al [12]. Fig. 8, which is taken from [12], also leads to thesame conclusion: aggregate interlock along a shear crackcannot contribute significantly to the shear resistance ofthe section.

Widening of the crack width in the longitudinal di-rection usually stops when the ultimate moment occurs(top point of load–displacement curve). When the com-pression zone fails along a sliding surface and equilibriumat the crack in the longitudinal direction is no longer en-sured, then the two parts of the specimen move towardseach other. Hence, the longitudinal component of thecrack width disappears or is reduced to a minimum,whereas vertical components begin to increase at a highrate. That is the reason why photos taken after failure maylead to the phenomenon being misinterpreted.

Aggregate interlock in the compression zone is acompletely different issue. The failure process in the com-pression zone takes place along a sliding surface (see thedashed lines in Figs. 2 and 3). The faces of the developingsliding surface are pushed together by normal compres-

Fig. 6. Schematic crack pattern and relative displacement between crackfaces at mid-depth of the specimen for different load steps; colours showdifferent load levels.

Fig. 7. Relative displacements between crack faces of critical crack in tension zone

19



sion. Prior to failure, these faces slide infinitesimally alongeach other. Consequently, crack width remains very low,ensuring that the favourable effect of aggregate interlockalso remains active. Longitudinal components of aggre-gate interlock forces increase the axial compression andthe transverse components contribute to the shear resis-tance of the compression zone. Further analysis of thecompression zone as well as the sliding surface is given inPart II of this paper.

4.9 Effect of dowel action on resistance of failure section

Dowel action of longitudinal rebars is a potential compo-nent in the shear resistance of an RC member. This effectis activated when transverse displacement between thecrack faces occurs. The stiffness of rebars and their resis-tance to transverse displacement depend on their stressstate and bond properties [9]. Stiffness is high immediatelyafter the appearance of a crack. It was shown by Muttoni[12] that transverse displacement between the crack facesis very low at the beginning of crack opening. Rebar dow-el action activates transverse tensile stresses in the wall ofthe specimens, especially in the bottom one-third of thecircular cross-section. Transverse tensile stresses aroundthe rebars are also caused by the mechanical bond be-tween the bars and the concrete. These effects degrade thebond around the longitudinal reinforcement and result inlongitudinal cracking (see Fig. 3). The stiffness of dowelaction in the tensile zone decreases radically, whereascrack width increases and longitudinal cracks propagate.This stiffness degradation was much more intensive formembers with a hollow circular cross-section with spiral

reinforcement on the outer side of the wall only than formembers with a solid cross-section.

Axial stress in the tensile reinforcement at failurewas usually close or equal to its yield strength. If a baryields, then its resistance to transverse forces is practicallyzero, which results in a negligible dowel effect.

5 Conclusions

A test programme involving 45 specimens was carried outto analyse the resistance of thick-walled hollow circularspecimens subjected to combined bending and shear.

The crack pattern and the effect of test parameterson the resistance of the members were analysed. It wasconcluded that the shape of the failure section under com-bined bending and shear depends on the geometrical con-ditions.

A failure section consisted of a crack developed inthe tensile zone under combined bending and shear and asliding surface across the compression zone. The depth ofthe compression zone in a particular cross-section subject-ed to combined bending and shear was found to be small-er than that in a section subjected to pure bending only.The reason for this was the degradation in the bond stiff-ness of the longitudinal reinforcement.

The resistance of the hollow circular RC memberstested (with spiral reinforcement on the outer side of thewall only) increases with greater wall thickness, with theamount of longitudinal and transverse reinforcement, withthe degree of prestress and with a reduction in the shearspan (a/d < ∼3.25).

The influence of transverse reinforcement on the re-sistance was quasi-linear. The resistance of specimenswithout transverse reinforcement was greater than that atthe appearance of the first shear crack.

Based on the results shown in this Part I, a new me-chanical model for the bending-shear resistance of hollowcircular RC members will be proposed in Part II.

Acknowledgements

The authors wish to express their gratitude to LábatlaniVasbetonipari Zrt. for supplying the materials and spon-soring the research. Thanks also go to the colleagues ofthe Structural Laboratory of TU Budapest (BMGE) fortheir assistance in the laboratory work.

This work is connected with the scientific pro-gramme of the “Development of quality-oriented and har-monized R+D+I strategy and functional model at BMGE”project. This project is supported by the New HungaryDevelopment Plan (project ID: TÁMOP-4.2.1/B-09/1/KMR-2010-0002).

References

1. Balázs, L. G.: A historical review of shear. fib Bulletin 57,Shear and punching shear in RC and FRC elements, 2010,pp. 1–13.

2. Turmo, J., Ramos, G., Aparacio, A. C.: Shear truss analogyfor concrete members of solid and hollow circular cross-sec-tion. Engineering Structures, 2008.

3. Uehara, S., Sakino, K., Esaki F.: Limit Analysis of ReinforcedConcrete Columns by Yield Line Theory Considering Inter-

P1

0.4 mm(0.016 in)

Fig. 8. Propagation of critical crack and relative displacements betweencrack faces (Muttoni [12])

Yielding1.0(0.039)

V = 0.93 Vmax

V = 0.65 Vmax

V = 0.85 Vmax

V = 0.86 Vmax

2.2(0.087)

∆ [mm (in)]u

∆ [mm (in)]ν

action of Combined Forces. Transactions of Japan ConcreteInstitute, vol. 22 (2000), pp. 413–426.

4. Jensen, U. G., Hoang, L. C.: Shear Strength of ReinforcedConcrete Piers and Piles with Hollow Circular Cross Section.Structural Engineering International, 3/2010, pp. 260–267.

5. Völgyi, I., Farkas, G., Nehme, S. G.: Concrete Strength Ten-dency in the Wall of Cylindrical Spun-Cast Concrete Ele-ments. Periodica Polytechnica Civil Engineering 54/1(2010), pp. 23–30.

6. Völgyi, I., Farkas, G.: Rebound Testing of Cylindrical Spun-Cast Concrete Elements. Periodica Polytechnica Civil Engi-neering 56 (2011), pp. 129–135.

7. Völgyi, I.: Shear-bending behaviour of prismatic, singlehooped, ring shaped, spun-cast concrete members. PhD the-sis (in Hungarian), 2011.

8. Windisch, A.: Das Modell der charakteristischen Bruchquer-schnitte – Ein Beitrag zur Bemessung der Sonderbereichevon Stahlbetontragwerken. Beton- und Stahlbetonbau 83(1988), No. 10, pp. 271–274.

9. Maekawa, K., Qureshi, J.: Embedded bar behavior in con-crete under combined axial pullout and transverse displace-ment. J Materials, Concrete Structures, No. 532, vol. 30,1996, pp. 183–195.

10. Walther, R.: Über die Berechnung der Schubtragfähigkeitvon Stahl- und Spannbetonbalken – Schubbruchtheorie. Be-ton und Stahlbetonbau, 11/1962, pp. 261–271.

11. Juhász, B.: Problems of shear resistance of RC members un-der bending. Thesis (in Hungarian), Budapest, 1968.

12. Muttoni, R. V., Ruiz, M. F.: Influence of Capacity of Rein-forced Concrete Members without Shear Reinforcement.ACI Structural Journal, Sept-Oct 2010, pp. 516–525.

20



Dr. István Völgyi Assistant ProfessorDept. of Structural EngineeringTechnical University of Budapest (BME)3. Muegyetem rkp.H-1111 Budapest, HungaryTel: +36 1 4631968E-mail: [email protected]

Dr. Andor WindischHonorary ProfessorDept. of Structural EngineeringTechnical University of Budapest (BME)3. Muegyetem rkp.H-1111 Budapest, HungaryE-mail: [email protected]

Dr. György Farkas ProfessorDept. of Structural EngineeringTechnical University of Budapest (BME)3. Muegyetem rkp.H-1111 Budapest, HungaryTel: +36 1 4631718E-mail: [email protected]


Part II analyses the applicability of current shear design modelsfor RC members with a hollow circular cross-section on the basisof experimental results introduced in Part I of this paper. A newcalculation model is proposed which assigns the contribution ofthe concrete zone in compression to shear resistance. The pro-posed model takes into account how the flexural and shear rein-forcement, the load-to-support distance and the shape of thecross-section affect the shear resistance.The model is based on the analysis of potential failure sectionssubjected to bending and shear, and applies a compatibility crite-rion that considers how the member carries the load. The analo-gy between the failure of the concrete compression zone and thefailure of the soil along a sliding surface are presented as well asthe conditions for the development of the failure section.

Keywords: behaviour under combined bending and shear, hollow circularcross-section, contribution of compressed concrete to shear resistance,sliding surface

1 Introduction

This paper presents a new calculation model for the resis-tance of RC and PC members under combined bendingand shear (bending-shear resistance). Bending-shear resis-tance emphasizes the fact that shear resistance dependson the intensity of simultaneous bending moment com-bined with shear force. In contrast to conventional designmethods, shear and bending resistances are interrelated.The proposed calculation method is based on the resultsof a parametric experimental programme carried out onhollow circular RC members. The details of the test pro-gramme have been published in [1], [2], [3], [4] and [5].

Current shear design models can be divided intothree main groups:a) Cross-section designb) Strut-and-tie modelsc) Models based on presumed stress fields.

These models apply independent bending and shear de-sign procedures. Shear resistance is interpreted for mem-

bers with solid, plane webs and with two separate groupsof flexural reinforcement (one in tension and one in com-pression). In usual cases these assumptions are satisfied.However, their validity comes under question when apply-ing them to the analysis of members with hollow cross-sec-tions and curved webs.

In the case of members with a hollow circular cross-section, the “struts” of an assumed strut-and-tie model orthe compressed arch in the vicinity of the supports be-come three-dimensional. According to shear model typesa) and b), these “struts” and “arches” require additional in-ternal deviation forces, which should reduce the shear re-sistance of members with a hollow circular cross-sectioncompared with that of members with plane webs. There-fore, these deviation forces should also reduce the tying ef-fect of transverse reinforcement in a strut-and-tie model,see Fig. 1. The performed tests revealed that the actualshear behaviour of members with a hollow circular cross-section is different and the above interpretations of shearbehaviour on the basis of design model types a) and b)cannot be applied.

The problems of models based on presumed stressfields are similar. High additional stresses should developas a consequence of the “curved webs”. Applying thesemodels to hollow circular member without modificationsis theoretically incorrect.

The model proposed in this paper calculates theshear resistance of a hollow circular member under com-bined bending and shear on the basis of an equivalent I-shaped cross-section (as shown in Fig. 2), which hasvarying “web thickness” over its depth and a cross-section-al area and moment of inertia identical with that of thehollow circular cross-section.

Technical Paper

Resistance of reinforced concrete memberswith hollow circular cross-section under combined bending and shear – Part II: New calculation model

István Völgyi*Andor Windisch

DOI: 10.1002/suco.201200036


Submitted for review: 25 September 2012Revised: 18 July 2013Accepted for publication: 18 July 2013

Fig. 1. The assumed three-dimensional inclined compression strut of astrut-and-tie model

θ

2 Excerpt from experimental results – basis of proposed calculation model

A more detailed introduction to the test results dealt within this section is given in Part I of this paper [5].

The failure of a hollow circular RC member undercombined bending and shear occurs along a failure sec-tion, which consists of a critical bending-shear crack in thetension zone and its extension as a sliding surface acrossthe concrete compression zone. The polyline shape of thepotential failure sections depends on the bending-to-shearratio as well as on the geometrical and boundary condi-tions [6].

A similar phenomenon can be observed for the bend-ing failure members with a rectangular cross-section underpure bending. Prior to failure, a sliding surface starts to de-velop on one or both sides of the tip of the critical bendingcrack, which first runs roughly parallel to the longitudinalaxis, later across the compression zone of the member [7].This failure of the compression zone along a sliding sur-face is similar to that of soils.

When assuming combined bending and shear, theposition of the first crack depends on the stress patternand the actual concrete tensile strength distribution. Theoccurrence of further cracks depends not only on thestress pattern but on the amount, the arrangement and thebond properties of the reinforcement, too. At load levelsclose to failure, large relative displacements with a signifi-cant component normal to the longitudinal axis of themember occur along the critical crack in the tension zone.Parallel to that, flat or longitudinal cracks develop alongthe longitudinal bars (see Fig. 4). A consequence of the lat-eral deflection of tensile flexural bars is the degradation inthe bond stiffness of these rebars due to dowel action andthe splitting stresses caused by the bond of the rebars aftercracking [8]. This degradation results in increased slip andelongation along the transmission lengths, which also al-low the crack width to increase. Consequently, comparedwith the case of perfect bond, wider and longer cracks oc-cur, which result in additional compressive stresses in thecompression zone. Furthermore, kinked tension barscrossing these longitudinal cracks become eccentricallytensioned, which lowers their effective yield strength. Thisis the reason why the depth of the compression zone atthe end of a crack caused predominantly by shear is small-er than that calculated with when assuming a perfect bond

22

I. Völgyi/A. Windisch · Resistance of reinforced concrete members with hollow circular cross-section under combined bending and shear – Part II: New calculation model


between rebars and concrete. Close to ultimate load lev-els, the tensile stress in tension rebars is usually close totheir yield strength, hence, rebar resistance to lateral de-formation in this state is very low. Consequently, dowel ac-tion at lower load levels might be relevant but is usuallynegligible prior to failure.

The size and direction of relative displacements be-tween the faces of the critical crack has been analysed fur-ther. It was demonstrated that aggregate interlock in thetension zone was not effective [4], [5]. At failure, a slidingsurface develops from the top end of the critical bending-shear crack across the compression zone. Its shape andshear resistance depend on the depth of the compressionzone, the actual concrete strength, the amount andstrength of longitudinal rebars in the compression zoneand the compression force due to bending moment and, ifany, the axial force. Another influencing factor is the dis-tance lc of the tip of the crack from the next significantgeometrical boundary condition (position of loadingblock, support, hoops, etc.).

3 Most important shear strength models from the point of view of European standardization

Calculation methods for the shear strength of memberswith shear reinforcement are discussed below. After sum-marizing their theoretical background, their applicabilityis analysed from the point of view of the experimental re-sults.

Calculation formulae for the failure of inclined com-pression struts are outside the focus of this discussion be-cause this failure mode was not investigated in the actualresearch. However, crushing of inclined struts cannot beexcluded for very high ratios of transverse reinforcement.

3.1 Methods implemented in ENV 1992 and EN 1992

Two methods were proposed in ENV 1992-1-1 [9]. Accord-ing to the standard method (ENV 1992 I), the shear resis-tance of a cross-section is the sum of the contribution ofshear reinforcement crossing the shear crack, whose angleto the longitudinal axis is assumed to be 45°, and the con-tribution of concrete, being a function of the width anddepth of the web and the concrete’s “shear strength”.

The second method (ENV 1992 II) is based on thevariable strut inclination method. The possibility ofchoosing the strut inclination over a wide range is doubt-ful. The reason for the difference between the actual incli-nation of the shear crack and the assumed angle of the in-clined compression strut with respect to the longitudinalaxis of the member is the hypothetical aggregate interlock.

Our experimental results question the existence ofaggregate interlock in the tension zone of the member. In-stead, they indicate a significant contribution of the com-pression zone to shear resistance and also that shear resis-tance is a function of the amount of longitudinal andshear reinforcement and the load-to-support distance. Themodel of the variable angle of strut inclination is not ableto consider some of these effects.

ENV 1992 has been superseded by EN 1992-1-1 [10],which contains solely the variable strut inclinationmethod to calculate shear resistance.

Fig. 2. Hollow circular and I-shaped solid cross-sections with same areaand moment of inertia

23



3.2 Methods implemented in the final draft (2012) of fib Model Code 2010

Three methods denoted as Approximation Levels I, II andIII are implemented in the final draft of the fib ModelCode for Concrete Structures [11], to calculate the shearresistance of members with shear reinforcement. Thecomplexity of the model and the expected accuracy in-crease with the approximation level.

Shear resistance at Approximation Level I is ensuredsolely by the contribution of shear reinforcement. The for-mulae are similar to those in EN 1992. Different minimumcompressive stress field inclinations are defined for RCmembers with or without axial force. The effects of bend-ing moment and amount of tension reinforcement onshear resistance are not integrated into the model.

Shear resistance attributed to concrete is also ne-glected in Approximation Level II. The main differencebetween this and Approximation Level I is a formula thatis proposed for calculating the minimum angle of inclina-tion as a function of the longitudinal strain at mid-depthof the effective shear depth. This empirical formula is a bighelp compared with the “free choice” allowed by EN 1992.By calculating the longitudinal strain, the effect of thedepth of the compression zone and the presence of thecompression force on the shear resistance are allowed for.Less elongation at mid-depth results in a higher shear re-sistance. This is supported by our own experimental re-sults.

Approximation Level III is based on simplified mod-ified compression field theory (MCFT) [11]. The calculat-ed shear resistance of the concrete is a function of the ef-fective cross-sectional area of the web, the longitudinalreinforcement and the ratio of the combined externalforces (axial force, bending moment) in the cross-sectionanalysed, which is assumed to be plane and perpendicularto the longitudinal axis of the member.

It should be noted that applying fib Model Code2010 provisions to the recalculation of experimental datarequires an iterative procedure, since the strength predic-tions depend on the predicted results.

3.3 Walther ‘s theory

According to Walther [14], the contribution of concrete toshear resistance is attributed to the compression zone.

This contribution is calculated on the basis of a Mohr-Coulomb failure criterion, which is described by a para-bolic-elliptic σ-τ curve. The ratio of tensile to compressivestrength is set to 1/8.

Walther’s theory does not take into account that thegeometry of the sliding surface may change and that thecompression zone is reduced during the failure processdue to the degradation of the bond stiffness of the longitu-dinal reinforcement.

3.4 Definition of model parameters and their interpretationfor hollow circular cross-sections

The models discussed were developed in the first place forangular cross-sections, and therefore the parameters in-cluded need to be interpreted for hollow circular cross-sec-tions. None of the documents analysed state that the re-spective method applies to angular cross-sections only.

As longitudinal reinforcement is uniformly distrib-uted around the perimeter for hollow circular sections, theseparation of tension and compression reinforcement aswell as the definition of effective depth are therefore notobvious.

In the shear design models, effective depth is used tocalculate the number of stirrups contributing to the shearstrength of the section analysed. Accordingly, effectivedepth for hollow circular cross-sections is defined as thedistance between the extreme compressed fibre and theextreme rebar in tension.

The double wall thickness is used as the minimumwidth of the hollow circular cross-section. Tension rein-forcement is taken as the area of rebars falling within thetension part of the cross-section irrespective of their stress.Efficiency of helical bars in shear resistance is measuredby that component of the tangent unit vector drawn to theintersection point of the crack and the side view of the he-lical bar parallel to the load.

3.5 Conclusions for the models analysed

Table 1 contains a statistical analysis of numerical resultscalculated from the algorithms discussed in section 3.Mean values of material strengths and geometrical prop-erties were used for calculation purposes. Maximum resis-tance was aimed for in the analysis when setting the para-meters to be chosen between defined limits.

Table 1. Summary of statistical analysis of calculated shear resistance to measured shear resistance ratios calculated using the mean value of the materi-al properties (VR/Vu)

ENV 1992 I EN 1992 fib fib fib Walther* ProposedMC 2010 I MC 2010 II MC 2010 III

Average: 0.74 0.71 0.47 0.55 0.67 1.66 0.95

Standard deviation: 0.13 0.20 0.14 0.16 0.17 0.34 0.11

Variation coefficient: 18% 29% 29% 30% 25% 21% 12%

Minimum: 0.51 0.40 0.28 0.29 0.27 0.97 0.68

Maximum: 1.07 1.30 0.86 0.90 1.02 2.59 1.11

* The fct/fc ratio is 1/8 in Walther’s original publication; 1/12 is used in this analysis, which is a better estimation for the concrete materialsof higher compressive strength used in the actual research.

Comparing the results based on the methods of EN1992 and ENV 1992 I is interesting; for angular cross-sec-tions it was discussed earlier [15][16]. Shear resistance ac-cording to ENV 1992 I is calculated as the sum of the re-sistance of the contribution of concrete and shearreinforcement. This method is called “simplified”, al-though its theoretical base is more realistic than that ofthe EN 1992 method. Results of the ENV 1992 I methodare more reliable for all aspects analysed.

The theory of the variable strut inclination method(EN 1992) considerably overestimates the shear resistancefor specimens with a high amount of shear reinforcementwhen using the minimum proposed angle of inclination.

Best agreement between test results and calculationwas found in the case of the ENV 1992 I model for mem-bers with a hollow circular cross-section under bendingand shear. The applicability of the fib Model Code 2010methods was limited for the test results. ApproximationLevel III was most efficient, despite an observed systemat-ic error. The VR/Vu ratio was close to unity for specimenswith a high amount of transverse reinforcement and smallwall thickness; however, the resistance was massively un-derestimated for specimens with a low amount of trans-verse reinforcement, large wall thickness and short load-to-support distance.

Walther’s method was applied to the calculation ofshear resistance for the cross-section next to the loadingblock. The method overestimated the shear resistance ofthe concrete compression zone. Results clearly showedthat it is necessary to consider a reduction in the depth ofthe compression zone due to the opening of the criticalcrack.

The standard deviation and the variation coefficientof results for each method are relatively high. The system-atic errors in the calculated results are caused by the theo-retical deficiencies discussed above. Moreover, the as-sumptions of the methods do not coincide with ourobservations during the tests [4], [5]. To overcome this, anew bending-shear resistance calculation model for mem-bers with a hollow circular cross-section will be shown insection 4. The proposed model is based on the actual fail-ure mechanism.

4 The proposed mechanical model4.1 Basic equation

For cross-sections under pure bending, plane cross-sec-tions and a perfect bond between steel and concrete areusually assumed and result in an acceptably low differencebetween calculations and actual load-carrying capacity.However, the increase in bond slip of longitudinal rebarsat sections under simultaneous significant shear and bend-ing has a large effect on the resistance of RC memberswith a hollow circular cross-section and with transverse re-inforcement on the outer side of the wall only. This degra-dation in bond stiffness is caused by the transverse forcesand deformations acting on the reinforcing bars aroundthe shear crack. That also leads to a reduction in thedepth of the compression zone.

Theoretically, there is no limit to the shape and posi-tion of the potential failure sections. Nevertheless, detail-ing rules regarding the position and amount of reinforce-

24



ment assure that the angle of inclination of the failure sec-tion in members designed according to the existing stan-dards is 45° or lower.

The shear resistance of an RC element can be calcu-lated as the sum of the contribution of the concrete com-pression zone (including longitudinal reinforcement) Vc

*

and the contribution of the transverse reinforcementcrossing the real shear crack part of the polyline-shapedfailure section Vw (Eq. (1)):

(1)

This proposed method is based on the equilibrium of in-ternal forces along a polyline-shaped section, and so theshift between the matching compressive and tensile forcesin the longitudinal direction is considered geometrically.Therefore, it is not necessary to modify the tensile force inthe longitudinal tensile reinforcement due to shear.

4.2 Contribution of transverse reinforcement

Transverse reinforcement does not take part efficiently inshear resistance before cracking. Crack development isthe condition for the stress increase in the tension rein-forcement as well as in the transverse reinforcement cross-ing the polyline-shaped section in the tension zone (activeshear reinforcement). In addition, the contribution oftransverse reinforcement, which intersects the failure sec-tion in the compression zone, remains low. The verticalcomponent of the tensile force carried by the active heli-cal bars is calculated using Eq. (2):

(2)

The vertical component of the tangent unit vector varies along the helical bars. The number and position ofintersection points of any potential failure section and thehelical reinforcement have a stochastic character. There-fore, the average of the calculated resistances associatedwith different longitudinal positions of helical reinforce-ment relative to the failure section is taken into account inthe proposed model.

4.3 Contribution of concrete compression zone

It was demonstrated in previous studies [14], [17] that theconcrete’s contribution to the shear resistance of a mem-ber is attributed to the compression zone. The depth ofthe compression zone is a function of the amount and thebond properties of longitudinal reinforcement as well asthe intensity of simultaneous bending moment and axialforce acting on the section. The depth of the compressionzone can be calculated similarly to that for a cross-sectionsubjected to pure bending and assuming a plane cross-sec-tion. Nevertheless, test results show that the depth of thecompression zone of a section under combined bendingand shear is lower than that of a cross-section under thesame bending moment without shear. The difference iscaused by the more intensive bond slip of the longitudinaltensile rebars along the longer transmission lengths, whichalso results in wider and longer cracks. To consider this,

V A f ew sw ywlt

�

e�

*V V VR c w

25



an idealized, fictitious material law for longitudinal, tensilereinforcing steel according to Fig. 3 has been introducedin the proposed mechanical model. Immediately aftercracking, an apparent reduced axial stiffness for the ten-sion reinforcement – due to the bond slip – is mobilized.The increased elongation of bars along the transmissionlength beyond crack faces is considered through a ficti-tious ultimate steel strain. A composite action factor ηs,which characterizes the composite action between steelbars and concrete along the transmission length beyondcracks, is defined for the reinforcing bars. The experimen-tal results [4], [5] show that this composite action factor isa function of the wall thickness. The thinner the wall ofthe specimen, the smaller the composite action observed.The proposed function for the composite action factor iscalculated using Eq. (3). Owing to the relatively smoothsurface of prestressing wires, the bond properties ofstrands are even poorer than those of rebars. Therefore, areduced composite action factor for strands ηp is pro-

posed, see Eq. (4). The validity of the proposed compositeaction factors is the range D/6 < v < D/3.

(3)

(4)

Owing to crack propagation, the effective depth of thecompression zone decreases if the intensity of load in-creases. In addition, the compressive force in the com-pression zone due to the bending moment also increases.Following yielding of the transverse reinforcement, thefurther increase in shear force is also carried by the con-crete compression zone. Due to this combined state ofstress, starting from the tip of the crack, a sliding surfacedevelops across the concrete compression zone [14]. Inthe experimental setup, the length of the sliding surfacedepends on the distance between crack tip and loading

1 0.3 R vRs

0.8p s

Fig. 3. Applied σ-ε model of flexural reinforcement under longitudinal pull-out and transverse displacement vs. σ-ε diagram of reinforcing bar withperfect bond under pure tension

Fig. 4. Crack pattern and shape of failure section of specimens 9-16-150-825 and 9-16-150-625

Fig. 5. Scheme of FE model of compression zone

block. Usually, the failure section does not enter the zoneunder the loading block because of the higher effectivestrength of confined concrete there. For long support-to-load distances, the sliding surface through the compres-sion zone becomes very flat, see Fig. 4 and [5]. It will beshown in the following that in addition to the decrease inthe length of the sliding surface, its shear resistance in-creases significantly.

The shear resistance of the compression zone wasanalysed as a function of the distance between the tip ofthe crack and the distance to the loading block lc. Thedepth of the compression zone x for a given compressionforce due to bending moment was calculated according tothe following procedure.

A non-linear 2D FE shell model of the individualcompression zone was developed (Fig. 5). The inclinationof the shear-influenced middle part of the failure sectionwas taken as 45°. The variable parameters of the shellmodel were the depth of the effective compression zone xand the horizontal distance between the top end of thebending-shear crack and the face of the loading block lc.The width of the shell elements and the supposed distribu-tion of the axial and shear stresses at the “loaded edge” areshown in Fig. 5. The resultant force of the applied axialstresses was equal to the sum of the compressive resultantforce due to bending moment and axial load including, ifany, prestressing.

A special Mohr-Coulomb-type failure criterion wasapplied to the concrete in the compression zone analysed.Katzenbach et al. showed the gradual development of the

26



sliding surface in soils [7]. The stress distribution along thedeveloping sliding surface is shown in Fig. 6. In the firstphase, a peak stress close to the loaded end of the slidingsurface can be observed, which further develops intodegradation of this zone, resulting in relative displacement(sliding) between the faces of the discontinuity line. Afterthis sliding, a new failure criterion with no cohesion andreduced angle of internal friction applies (Fig. 7.). The de-velopment of the sliding surface across the concrete com-pression zone is similar.

The initial cohesion and angle of internal friction ofthe concrete were calculated on the basis of its compres-sive and tensile strengths. After cracking, cohesion wastaken as zero and 37° (gravel) as the angle of internal fric-tion ϕ2.

The results of the associated parametric study can beseen in Fig. 8, representing the relationship between theshear resistance of the compression zone Vc and thelength of the sliding surface lc. As shown, Vc is sensitive tolc for high compression and is not sensitive when shear iscombined with low compression. The influence of axialstress on Vc is different for short and long sliding surfaces.Normal (σ) and shear (τ) components of the compressionforce Fc are shown in Fig. 9 for the sliding surfaces withdifferent inclination caused by a simultaneous bendingmoment. A compression force results in normal stressesdominating for sliding surfaces with high inclination andshear stresses for sliding surfaces with low inclination.Shear stresses consume frictional resistance along the slid-ing surface, whereas axial stresses increase it. That is why

Fig. 6. Stress distribution along a sliding surface (after Katzenbach et al. [7])

Fig. 7. Applied Mohr-Coulomb failure criterion of concrete material beforeand after sliding

40

80

120

160

200

0 1 2 3 4

lc/xc

Vc

[kN

]

.

.

.

.

.

σmax = 1/6∙fcσmax = 2/6∙fcσmax = 3/6∙fcσmax = 4/6∙fcσmax = 5/6∙fc

Fig. 8. Shear resistance of concrete compression zone vs. length of slidingsurface in the case of different axial stress levels (x = 80 mm, fc = 70 MPa)

Fig. 9. Axial and shear stress components of compression force for slidingsurfaces with different lengths

27



high axial stress is advantageous for sliding surfaces withhigh inclination and disadvantageous for those with lowinclination.

For a long support-to-load distance of the member,the formation of a long sliding surface with low inclinationand low shear resistance is geometrically possible, but im-possible for a short support-to-load distance due to the geo-metrical constraints. This results in concrete contributingmore to the shear resistance of the member. Consequently,solely for geometrical reasons, the load-carrying capacity ofa member with small support-to-load distance is higherthan that with long support-to-load distance despite thefewer transverse bars crossing the shorter failure section. Itis important to note that the failure section is situatedwholly between the inner faces of the support and the load-ing block. This means that it is necessary to analyse theequilibrium of simultaneous shear force and bending mo-ment with internal forces along the failure section.

Dowel action of longitudinal bars in the tension zoneis neglected because of the softened bond zone and thehigh-intensity tensile stresses equal or close to yield strength.

The vertical component of the relative displacementin the compression zone remains very low until full devel-opment of the sliding surface. It is also assumed that thedistribution of shear force attributed to the compressionzone between concrete and longitudinal rebar is propor-tional to the latter’s modulus of elasticity. Dowel action oflongitudinal bars in the compression zone is taken into ac-count according to Eq. (5):

(5)

It is interesting to note the difference in behaviour be-tween members with hollow circular and I-shaped cross-sections. The compression zone of a hollow circular cross-section is completely effective because the sliding surfacemust cross the whole zone right to the top of the cross-sec-tion to induce failure, whereas for T- and I-shaped cross-sections the failure section often runs under the top flangeas a result of an insufficient web-to-flange connection. Theeffectiveness of very wide flanges for T- and I-shapedmembers is limited because the sliding surface does notrun through the whole flange width. The sliding surface ofthese types of members can be analysed using 3D FE mod-els. Thin webs of members with I, T and hollow circularcross-sections allow shear cracks to appear first indepen-dently of bending cracks.

5 Verification of proposed model

The proposed model was used for calculating the shear re-sistance of the 45 test specimens. The mean values of re-sistance were calculated using Eq. (1). The results can befound in Table 2. The notation of specimens contains thenominal wall thickness [mm], the diameter of the longitu-dinal reinforcing bars [mm], the pitch of the transverse reinforcement [mm], indication of prestressing level (F1 <F2, if applicable) and the support-to-load distance [mm].Two specimens were manufactured with 12 strands as lon-gitudinal reinforcement; in these cases the diameter oflongitudinal reinforcing bars was denoted by 0.

(1 )*V VEEc c l s

s

c

The reliability of the results of the proposed model isexcellent. The average of the ratio of calculated to mea-sured resistance is 95 % and the associated standard devi-ation remains below 11 %. The proposed model showsvery good agreement with the test results, without any no-ticeable systematic error. As a conclusion, the applicabilityof the proposed model for determining the mean bending-shear resistance of RC and PC members with hollow cir-cular cross section is demonstrated.

6 Practical applications

If the proposed model is to be used for design purposes,the following procedure with the design values of materialstrengths is necessary:– Set the reference cross-section to be checked (see

Fig. 10).– Calculate the internal forces of the reference cross-sec-

tion (shear force, axial force, bending moment) usingcustomary beam theory.

– Calculate the depth of the compression zone taking intoaccount Eqs. (3) and (4).

– Define the polyline-shaped potential failure section.Take the inclination in the mid-zone as 45° and 15° forboth the top and the bottom part of the section if possi-ble; otherwise, fit the section between the inner faces ofthe loading block and the support by approximating theabove inclination as far as possible.

– Calculate the resistance of the compression zone ac-cording to section 4.

– Calculate the resistance of the transverse reinforcementusing Eq. (2).

– Summarize the contribution of concrete and steel usingEq. (1).

The extension of the proposed method to other types ofcross-section and more complex stress states is inprogress. In the next step the resistance of the concretecompression zone Vc will be formulated to support practi-cal design. At the moment Vc can be calculated with FEprograms.

7 Conclusions

A test programme was carried out on 45 specimens toanalyse the resistance of RC and PC members with a hol-low circular cross-section under combined bending andshear. Crack patterns and the influence of test parameterson resistance were analysed. The experimental resultswere presented in Part I of this paper.

Fig. 10. Position of analysed section with respect to reference section

There was a discussion on how the application of re-cent calculation models of standards and accepted publi-cations is problematic. Furthermore, their applicability forcalculating the shear resistance of members with a hollowcircular cross-section is limited. These models are usually(sometimes extremely) conservative, but on the otherhand sometimes overestimate the shear strength. More-over, their results scatter over an unacceptably wide range.

A new model was proposed for calculating the shearresistance of RC and PC members with a hollow circular

28



cross-section. This model defines the contribution of theconcrete compression zone to shear resistance and alsotakes into account how the amount of longitudinal andtransverse reinforcement, the wall thickness of the cross-section, the strengths of concrete and reinforcing bars, theload-to-support distance and the simultaneity of bendingmoment and axial force with shear force influence the re-sistance of the member. The proposed model is able toconsider several potential failure sections with differentposition and shape.

Table 2. Data of specimens and results of proposed model

Specimen Wal

l thi

ckne

ss [m

m]

Con

cret

e co

mpr

essi

ve s

treng

th

[N/m

m2]

Effe

ctiv

e pr

estre

ssin

g fo

rce

[kN

]

Exp

erim

enta

l she

ar re

sist

ance

of

the

spec

imen

[kN

]

Cal

cula

ted

dept

h of

co

mpr

essi

on z

one

[mm

]

Com

pres

sion

forc

e in

co

mpr

essi

on z

one

[kN

]

Con

tribu

tion

of th

e co

mpr

essi

on

zone

[kN

]

Con

tribu

tion

of th

e tra

nsve

rsal

re

info

rcem

ent [

kN]

Cal

cula

ted

resi

stan

ce o

f the

sp

ecim

en [k

N]

Cal

cula

ted

/ mea

sure

d re

sist

ance

ratio

(VR/V

u)

55-12-0-975 57 73 0 69 69 273 63 0 63 0.9255-12-0-625 58 73 0 105 69 250 94 0 94 0.8955-12-150-825 57 67 0 105 65 370 65 47 111 1.0655-12-150-625 55 67 0 135 69 332 88 37 125 0.9355-14-0-825 59 66 0 72 78 225 75 0 75 1.0455-14-0-625 60 66 0 83 78 182 92 0 92 1.1155-14-150-825 54 67 0 133 70 459 70 43 113 0.8555-14-150-625 60 67 0 162 76 386 114 35 149 0.9255-14-75-825 56 66 0 143 61 506 55 96 151 1.0655-14-75-789 59 66 0 154 61 518 63 96 159 1.0455-16-0-975 64 67 0 78 84 291 80 0 80 1.03 average 0.9855-16-0-825 57 67 0 85 84 261 74 0 74 0.87 st. deviation 0.0955-16-150-975 55 73 0 115 84 437 87 39 126 1.10 minimum: 0.8555-16-150-825 59 73 0 140 83 445 94 37 131 0.93 maximum: 1.1190-12-0-825 96 70 0 95 71 310 105 0 105 1.1090-12-0-625 92 70 0 158 64 403 107 0 107 0.6890-16-0-825 96 67 0 134 85 420 136 0 136 1.0190-16-0-825 99 67 0 135 85 423 136 0 136 1.0190-16-150-975 93 70 0 158 77 634 120 42 162 1.0390-16-150-825 96 67 0 177 83 571 139 37 176 0.9990-16-150-825 94 67 0 169 83 545 138 37 174 1.0390-16-150-825 93 70 0 178 80 586 135 37 172 0.9790-16-150-625 96 70 0 218 84 502 162 30 193 0.8890-16-150-625 94 70 0 228 83 531 162 31 192 0.84 average 0.9490-16-110-825 91 67 0 187 78 617 129 53 182 0.98 st. deviation 0.1190-16-110-625 92 67 0 210 85 481 156 40 196 0.93 minimum: 0.6890-16-75-635 99 67 0 258 79 625 142 66 208 0.81 maximum: 1.1055-16-150-F1-825 58 63 148 140 91 502 75 35 110 0.7855-16-150-F1-625 60 63 148 147 92 393 110 28 138 0.9455-16-75-F1-825 61 63 148 170 87 599 81 74 155 0.9155-16-75-F1-625 58 63 148 180 92 469 113 59 172 0.9690-16-150-F1-975 92 65 88 141 83 590 114 39 153 1.0990-16-150-F1-975 93 70 106 146 81 620 115 41 156 1.0790-16-150-F1-825 96 65 116 165 86 581 132 36 168 1.0290-16-150-F1-825 92 70 128 167 84 597 137 37 173 1.0490-16-150-F1-625 95 65 118 229 86 585 144 30 174 0.7690-16-150-F1-625 95 65 108 234 85 597 143 30 174 0.7490-16-150-F2-975 93 63 228 163 82 721 99 39 139 0.8590-16-150-F2-975 95 70 238 162 84 731 126 39 165 1.0290-16-150-F2-825 97 63 286 186 94 714 140 35 174 0.9490-16-150-F2-825 95 70 255 179 90 685 150 36 186 1.0490-16-150-F2-625 99 63 273 233 96 652 157 28 185 0.79 average 0.9290-16-150-F2-625 96 63 306 216 98 627 159 27 186 0.86 st. deviation 0.1190-0-150-F2-825 92 72 237 174 80 689 113 37 151 0.87 minimum: 0.7490-0-150-F2-975 90 72 180 145 78 683 99 42 140 0.97 maximum: 1.09

average 0.95st. deviation 0.11minimum: 0.68maximum: 1.11

Stat

istic

s of

pre

stes

sed

spec

imen

s

Statistics of all specimens:

Measured test results Results from the proposed model

Statistics of (VR/Vu)

.

Stat

istic

s of

spe

cim

ens

with

sm

all w

all t

hick

ness

Sta

tistic

s of

spe

cim

ens

w

ith la

rge

wal

l thi

ckne

ss

29



A new idealized material law for reinforcing steel andprestressing strands was defined to determine the depth ofthe concrete compression zone for sections under com-bined shear and bending.

The calculation of the shear resistance of the con-crete compression zone was similar to that of sliding sur-faces well known from soil mechanics. This can be con-sidered as a new interpretation of the contribution of theconcrete compression zone to the shear resistance of RCor PC members under combined bending and shear. Thecalculated ultimate loads agreed very well with the test re-sults. No systematic deviation was detected.

In order to extend the proposed method to othercross-section types and more complex stress states, the re-search programme is to be continued.

Notation

As cross-sectional area of longitudinal reinforcementAsw cross-sectional area of transverse reinforcement

vertical component of the tangent unit vectordrawn to the intersection point of the crackanalysed and the helical transverse bar

Ec secant modulus of elasticity of concreteEs modulus of elasticity of reinforcing steelfc compressive cylinder strength of concrete fct tensile strength of concretefyw yield strength of transverse reinforcementlc length of sliding surface lt length of (bending-)shear crack in tension zones pitch of helical reinforcementD/R outer diameter/radius of hollow circular cross-sec-

tionv wall thickness of specimenVc shear resistance component provided by concrete

compression zoneVc

* shear resistance of concrete compression zone tak-ing into account the effect of reinforcement in thecompression zone

VR calculated shear capacity of RC member undercombined bending and shear

Vu shear failure capacity of specimen under combinedbending and shear (experimental)

Vw shear resistance component provided by transversereinforcement

ρl longitudinal reinforcement ratio (based on totallongitudinal reinforcement)

ηs, ηp factor taking into account composite action be-tween reinforcing bar (s) or strand (p) and concrete

References

[1] Völgyi, I., Farkas, G., Nehme, S. G.: Concrete Strength Ten-dency in the Wall of Cylindrical Spun-Cast Concrete Ele-ments. Periodica Polytechnica Civil Engineering 54/1(2010),pp. 23–30.

[2] Völgyi, I., Farkas, G.: Rebound testing of cylindrical spuncast concrete elements. Periodica Polytechnica Civil Engi-neering 55/2(2011), pp. 129–135.

[3] Völgyi, I., Farkas, G.: Experimental study on shear strengthof hollow cylindrical spun cast concrete elements – Local be-haviour. Asian Journal of Civil Engineering; 13/1 (2012), pp.113–126.

e�

[4] Völgyi, I.: Shear-bending behaviour of prismatic, singlehooped, ring shaped, spun-cast concrete memebers. PhDthesis, 2011 (in Hungarian).

[5] Völgyi, I., Windisch, A., Farkas G.: Resistance of reinforcedconcrete members with hollow circular cross-section undercombined bending and shear – Part I: Experimental Inves -tigation. Structural Concrete, 15: 13–20. doi: 10.1002/suco.201200035.

[6] Windisch, A.: Das Modell der charakteristischen Bruchquer-schnitte – Ein Beitrag zur Bemessung der Sonderbereichevon Stahlbetontragwerken. Beton- und Stahlbetonbau 83(1988), No. 10, pp. 271–274.

[7] Zilch, K., Zehetmaier, G.: Bemessung im konstruktiven Be-tonbau. Nach DIN 1045-1 und DIN EN1992-1-1. Springer,2006.

[8] Maekawa, K., Qureshi, J.: Embedded bar behavior in con-crete under combined axial pullout and transverse displace-ment. J Materials, Concrete Structures; No. 532, vol. 30(1996), pp. 183–195.

[9] ENV1992-1-1:1999 Design of concrete structures, Generalrules and rules for buildings.

[10] EN1992-1-1:2010 Design of concrete structures, Generalrules and rules for buildings.

[11] fib Model Code for Concrete Structures 2010 (final draft),2012.

[12] Sigrist, V., Bentz, E., Ruiz, M. F., Foster, S. and Muttoni, A.(2013), Background to the fib Model Code 2010 shear provi-sions – part I: beams and slabs. Structural Concrete, 14:195–203. doi: 10.1002/suco.201200066.

[13] Collins, M. P.: Improving analytical models for shear designand evaluation of reinforced concrete structures. fib bulletin57, Shear and punching shear in RC and FRC elements, Salo,2010, pp. 77–92.

[14] Walther, R.: Über die Berechnung der Schubtragfähigkeitvon Stahl- und Spannbetonbalken – Schubbruchtheorie. Be-ton und Stahlbetonbau, 11/1962, pp. 261–271.

[15] Gulvanessian, H., Farkas, G., Kovács, T.: Comparativeanalysis on using Eurocode and two national codes in con-crete bridge design. Revue française de génie civil; 5/4(2001), pp. 435–467.

[16] Farkas, G., Kovács, T., Szalai, K.: Comparison of the Hun-garian concrete highway bridge codes with the Eurocode.Concrete Structures, I/3 (1999), pp. 73–80 (in Hungarian).

[17] Juhász, B.: Some questions of the shear resistance of RCmembers under bending. Candidate dissertation, Budapest,1968 (in Hungarian).

[18] Katzenbach, R., Bachmann, G.: Scherbandentwicklung imBoden. Bauingenieur, vol. 83 (2008), pp. 351–356.

Dr. István VÖLGYIAssistant ProfessorDept. of Structural EngineeringTechnical University of Budapest (BME)3. Muegyetem rkp.H-1111 Budapest, HungaryTel: 00364631968E-mail: [email protected]

Dr. Andor WINDISCHDept. of Structural EngineeringTechnical University of Budapest (BME)3. Muegyetem rkp.H-1111 Budapest, HungaryE-mail: [email protected]

30 © 2014 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete 15 (2014), No. 1

Technical Paper

DOI: 10.1002/suco.201300007

The Centennial Hall, a reinforced concrete structure with an auditorium for 10 000 people, was opened in Wrocław, Poland(then Breslau, Germany), in 1913 after two years of construction.Its dome, covering the whole building, has a diameter of 65.0 mand in the year it was completed was the largest reinforced con-crete dome in the world. This broke the previous record, held bythe dome of the Pantheon in Rome (43.3 m), which had lasted for1787 years. This paper describes the structure of the building, itscondition after 100 years of use and the renovation works carriedout in 2009–2011. An important part of the renovation wasstrengthening the lower (tension) ring of the ribbed dome by wayof external prestressing. Details concerning the assessment ofthe technical condition of the hall, numerical calculations and theproposed system of strengthening are presented. In 2006 themonumental Centennial Hall was listed as a UNESCO World Heritage Site for its pioneering reinforced concrete structure, designed in the style of modernism.

Keywords: pioneering concrete structure, renovation, FEM analysis,strengthening

1 Short historical outline of massive domes

The most famous building with a roof constructed as acoffered concrete dome is the 2000-year-old Pantheon inRome, commissioned by Marcus Agrippa in 27 BC and re-built by Emperor Hadrian in about 126 AD [1]. During itshistory, the building had various functions and was even-tually turned into a church. It is a great structure with acentral opening (oculus) at the crown and a lower ring43.3 m in diameter. The thickness of the dome varies from6.4 m at its base to 1.2 m at the level of the oculus [2]. Thestresses in the dome were reduced by using lightweight ag-gregate, e.g. pieces of pumice in higher layers, which de-creased the density [3]. This reduced the weight of theroof, as did the coffered structure of the dome (Fig. 1) andeliminating the crown of the dome by including the ocu-lus. The height of the Pantheon up to the oculus and theinside diameter are the same. The drum supporting struc-ture is enclosed with façade walls, making the buildinglook like a temple. With an inside diameter of 43.3 m, the

Pantheon remains today the largest dome constructed ofunreinforced concrete.

Examples of the next largest domes are the Baths ofCaracalla, built in Rome between AD 212 and 216, with adiameter of 35.1 m [4], and the ashlar masonry dome ofConstantinople’s Hagia Sophia, with a diameter of 31 m[5]. This latter building (Fig. 2), erected under Justinian be-tween AD 532 and 537, is one of the greatest achievementsof Byzantine culture and has undergone a turbulent histo-ry, also during its construction. In May 558, following theearthquakes of August 553 and December 557, parts of thecentral dome and its supporting structure collapsed [5].Between 558 and 562 a new modified design was intro-duced, resulting in the dome we see today.

The next large dome structures were built in Europeduring the Renaissance [7]; Florence Cathedral (thelargest dome since antiquity, with a diameter of 44 m) andSt. Peter’s Basilica in Rome (on the left in Fig. 3), whichhas a dome with an inside diameter of 42.7 m [8]. This is adouble shell structure made of bricks and travertineblocks held together with lime mortar, stiffened by 16 ribsand supported by a cylindrical structure stabilized by 16buttresses [8]. During the construction of the dome, car-ried out in 1589–1592 by Giacomo della Porta, three ironchains were built into the internal shell, and in 1590 twoadditional hoops were added at the base of the lantern [9].

Strengthening the 100-year-old reinforcedconcrete dome of the Centennial Hall in Wrocław

Jerzy OnysykJan Biliszczuk*Przemysław PrabuckiKrzysztof SadowskiRobert Toczkiewicz


Submitted for review: 6 February 2013Revised: 17 May 2013Accepted for publication: 24 July 2013

Fig. 1. Roman Pantheon with coffered concrete dome measuring 43.3 m indiameter

31

J. Onysyk/J. Biliszczuk/P. Prabucki/K. Sadowski/R. Toczkiewicz · Strengthening the 100-year-old reinforced concrete dome of the Centennial Hall in Wrocław


After the dome’s completion, cracks began to devel-op and in the middle of the 18th century serious damagewas noticed [8]. Pope Benedict XIV decided to consult afamous Italian scholar, Giovanni Poleni. Following an in-spection, Poleni proposed strengthening the dome byplacing five iron rings around it [10]. A sixth hoop wasadded while work was in progress when it turned out thatone of the original rings had broken. To determine the sec-tion for the hoops, Poleni conducted experiments using amodel (on the right in Fig. 3), which allowed an evaluationof the relationship between the section of an iron rod andits strength [11]. A special system consisting of two lockingwedges, which prevent the rings from losing their tension,was introduced to join elements of the chains [10].

The analyses performed by Poleni, concluding with aproposal for the strengthening method, can be consideredas one of the first expert reports concerning a structure inour modern understanding of such a study.

The next monumental building with a roof in theform of a massive structure (reinforced concrete dome)

was the Centennial Hall (Fig. 4), built in Wrocław, in1911–1913 [12, 13]. This is a unique structure in terms ofits architectural and structural solutions, and took advan-tage of the potential of a new material (reinforced con-crete), new computational methods based on the mechan-

Fig. 2. Longitudinal section through Hagia Sophia in Constantinople [6]

Fig. 3. The dome of St. Peter’s Basilica (left); the idea of strengthening and model load testing (right) [10]

Fig. 4. View of Centennial Hall after its opening in 1913 [12]

32



ics of structures and new construction technologies. Ini-tially called “Festhalle” (Celebrational Hall) [13], it was lat-er given the name “Die Jahrhunderthalle” (CentennialHall) to commemorate the 100th anniversary of KingFrederick William III of Prussia’s proclamation calling up-on the people to rise up against Napoleon (17 March 1813)[14].

The designer of the Centennial Hall was a Germanarchitect, Max Berg (Fig. 5). Structural calculations wereperformed by G. Trauer and W. Gehler [13]. The hall wasconstructed by Dyckerhoff & Widmann from Dresden(now DYWIDAG). The period of design and constructionof the hall coincided with the beginning of the widespread

use of reinforced concrete in the construction industry.Impressive reinforced concrete structures such as the mar-ket halls in Wrocław and Gdansk and the main hall of therailway station in Leipzig [14] were built around the sametime.

The hall has been used for nearly 100 years withoutany major repairs, especially since it was not significantlydamaged during the Second World War (other than re-moving the great organs). In 2006 the monumental Cen-tennial Hall (known for 55 years as the People’s Hall) waslisted as a UNESCO World Heritage Site for its pioneeringreinforced concrete structure designed in the style of mod-ernism.

The dome of the hall with a diameter of 65.0 m wasthe first massive dome larger than the Pantheon’s dome.This structure is often referred to in writings. At the IABSE-IASS (International Association for Shell and Spatial Structures) Symposium in September 2011, theCentennial Hall was mentioned in one of the keynotespeeches concerning roof milestones in history [15].

2 Structure of the Centennial Hall’s dome

At the time of its construction the Centennial Hall was anexceptional and outstanding structure with the largestconcrete dome in the world. The plan of the building waslaid out on a symmetrical quatrefoil (tetrakonchos)around the central circular main hall (Fig. 6), whose struc-ture consists of two separate main parts. The upper struc-ture is a ribbed dome formed by 32 reinforced concreteribs supported by a lower tension ring with an inside di-ameter of 65.0 m and connected by an upper compressionring with an inside diameter of 14.4 m. The ribs are stabi-lized at three levels by stiffening rings on the circumfer-

Fig. 5. Max Berg (1870–1947) – designer of the Centennial Hall [12]

Fig. 6. Section through and plan on Centennial Hall [14]; view of the interior of the hall today (photo: M. Golen/Hala Stulecia).

33



therefore separated from the bottom cylindrical structure,which is imperceptible in the façade.

Prefabricated reinforced concrete elements weighingabout 2.5 t were used in the construction of the dome –probably for the first time in Europe [16].

The window frames made of iron mahogany are in-teresting; they were imported all the way from Australiaduring the construction of the hall [16]. This wood has avery high density and hardness, and therefore is weather-resistant. Most of the elements of the original woodworkhave been preserved to this day, renovated and rebuilt.The wood was too good a building material in those timesto have let these trees survive to the present day!

3 Technical condition of the hall

Since the Second World War, the hall has been used in ac-cordance with its intended purpose as a multi-functionalmeeting facility for exhibitions, celebrations and sportsevents. No major renovation works have been carried out– other than changing linings, rearranging the interior ofthe hall and other minor repairs – since 1945. Almost acentury of intensive use has resulted in deterioration ofthe hall and without remedial action, rapidly advancingdegradations would have been the outcome [16]. Also, theinterior of the hall no longer met modern requirements. In2006 the Centennial Hall was listed as a UNESCO WorldHeritage Site, which imposed a responsibility for the strictprotection and maintenance of the hall. These facts led tothe decision to implement an extensive plan of restora-tion, including renovation of the hall and modernizationof the interior.

The renovation was carried out in 2009–2011 in twophases: the first phase included renovation of the façadeand the second the renovation of the building’s interior.Before proceeding with the first phase, a complex expertreport on the technical condition of all structural ele-ments, walls, ceilings, etc. was prepared [16, 17]. This re-port revealed a wide variety of defects, mainly cracks, cav-ities, thin concrete cover zones and other material andstructural deficiencies. The defects resulted partly fromthe fact that the hall was erected in the pioneering years ofreinforced concrete, which was then regarded as a verydurable, almost indestructible material.

The most significant defects were noticed in the low-er ring, an important structural element of the dome, car-rying forces induced by the thrust of the dome’s curvedribs. Vertical cracks were found in the surface of the ringover its entire height, at intervals of several metres, andaround the whole perimeter of the ring (Fig. 8). Consider-ing the structural purpose of this element and the condi-tion of the steel trusses in tension, it was decided that thering needed to be strengthened [16, 17]. The design basiswas the assumption that the reinforcing elements shouldbe able to carry the whole tensile force in the ring in thecase of failure of the steel trusses. Obviously, the strength-ening system must not interfere with the elevation of thehall. Finally, the project of renovating the hall’s façade andstrengthening the ring using multi-layered CFRP plates onthe ring’s circumference was prepared. During façade re-pairs, the contractor, after consultation with the designerof the renovation works (architect L. Konarzewski, PhD),

ence of the dome. The roofing system in the form of ter-races enabled four circumferential rows of windows, illu-minating the interior of the hall (Fig. 6).

The dome is supported by movable steel bearingsplaced on the lower structure, which consists of four arch-es curved on plan, forming a cylindrical base to the hall.The arches are supported by buttresses (concrete ribs)forming four open semicircular side apses, where the audi-torium is situated. Inside the hall, the structural concreteelements were left exposed (Fig. 6).

An important structural part of the dome is the low-er tension ring, carrying forces induced by the thrust ofthe arched ribs. Tensile axial forces are carried by thechords of two trusses embedded horizontally in concreteon the circumference of the ring (Fig. 7). Each of thechords consists of two plates, 13 × 365 mm, and two anglebars, 120 × 120 × 13 mm, (Fig. 10) giving a total cross-sec-tional area of steel of 615.7 cm2. Elements of the trussesare connected by rivets and bolts.

An interesting structural solution is the dome sup-port on pinned bearings, placed between the lower ringand the upper surface of the base drum structure (at a lev-el of about +19.0 m), shown in Fig. 7. The bearings are lo-cated on the circumference of the dome in the placeswhere the 32 ribs are fixed. There is freedom of movementin the direction of the radius of the dome. The dome is

Fig. 7. Reinforcement of the lower ring consisting of two trusses (photo tak-en during construction) [12]; bearings under ring (for section through ringsee Fig. 10)

34



proposed to change the method of strengthening and toprepare a new project.

The basis for the change to the strengthening methodwas the research conducted during the repair works. Itwas possible to carry out a thorough assessment of thecondition and properties of the steel trusses once theywere partially uncovered. It turned out that they were in asatisfactory condition; no major corrosion damage was ev-ident. The only corrosion products found dated back tothe construction period. Some adverse characteristics ofthe steel microstructure were assessed as not resultingfrom the use of the hall. Steel aging and some observedchanges were assessed as normal phenomena.

Refurbishment of the hall included [17, 18]:– renovation of the façade and fitting-out elements (e.g.

window frames)– replacement of the roof covering to the dome– filling of concrete cavities in the structural elements of

the hall– injection of cracks observed in concrete (Fig. 8)– strengthening of the lower ring of the dome– reconstruction of the auditorium

The most interesting problem from the point of view of anengineer was strengthening the lower (tension) ring of thedome, which is discussed below.

4 Strengthening of the lower ring of the dome4.1 Assumptions and structural analysis

The revised version of the project also included the as-sumptions that the strengthening system should be able tocarry the whole tensile force and that it should not changethe elevation.

The strengthening of the ring was inspired by the so-lution proposed for the dome of St. Peter’s Basilica, pre-

sented in Fig. 3. Since that time, new possibilities for im-plementing such a concept, using concrete prestressingtechnology, have been developed. Therefore, it was decid-ed to design the strengthening system using the tendonsand anchorages common in bridges, silos, etc. [19].

A 3D FEM model of the dome was used in the struc-tural analysis (Fig. 9). The ribs of the dome, rings andcolumns between sets of windows were discretized as barelements, the ribbed plates of the ceilings as shell ele-ments. The following materials were assumed: concreteclass C12/15, steel grade St3SX, reinforcing steel gradeSt0S [16]. The permissible tensile stress in the steel in theoriginal calculations [13] was limited to 1100 kG/cm2

(∼ 110 MPa).Dead loads, live loads (wind and snow) and service

loads (e.g. screens, loudspeakers, etc.) acting at differentpoints of the dome (upper ring, ribs) with a total weight of 30–40 t were considered in the analysis. Load combi -nations including dead, live and service loads give the following extreme internal forces in the ring: axial force N = 6012 kN (tension), bending moments My = 483.0 kNm and Mz = 22.5 kNm. Taking into con -sideration dead loads only, we get N = 5444 kN, My = 413.0 kNm and Mz = 7.8 kNm [19]. Comparison ofthese values proves that the dead loads are dominant in-fluence for the tensile force in the ring. Structural calcula-tions using modern software increased the tensile forcesin the ring by about 10 % in relation to the design value ofthis force [13]. Part of this difference might be caused bysnow and wind loads different from those assumed in [13].

4.2 Strengthening method

According to the assumptions, it was decided to design apassive strengthening system around the ring, consistingof unbonded strands used for prestressing (type T15S pro-

Fig. 8. Injected vertical cracks in lower ring and view of surface after repair works; uncovered truss element near node – bolt heads visible

35



duced by Freyssinet) [20]. The number of cables was cal-culated assuming their load-carrying capacity to be equalto the maximum tensile force value N = 6012 kN. Thecharacteristic stress value was limited to 80 % of the pre-

stressing steel strength (0.80 · 1860 MPa). This high stresslevel was allowed due to the exceptional character of suchan occurrence. The permanent force in the cables is inthis case not important because they are tensioned with a

Fig. 9. Finite element model of structure (bar elements only shown) and diagrams of internal forces (combination of load cases)

Fig. 10. Strengthening system for ring consisting of prestressing tendons (type 3C15) and X-type anchorages; 6021 m of ∅15.7 mm tendons, 1956 m ofsheath ducts and nine anchorage units were used [19, 20]

36



force equal to only 15 % of their ultimate strength, whichguarantees proper anchorage.

Eventually, 27 strands (galvanized, grease-protected,covered with individual HDPE sheaths) with a diameter of15.7 mm were used, grouped in nine cables. The strandsare conducted in plastic sheath ducts with a diameter of50 mm, filled with cement grout. Fig. 10 shows the schemeof the strengthening system and Fig. 11 shows the cablesduring installation.

The maximum internal forces in the elements of thedome resulting from cable tensioning are: N = –928.6 kN(compression), My = 35.6 kNm, Mz = 102.2 kNm. Ten-sioned circumferential cables reduced the axial force inthe lower ring. The analysis showed no significant adverseinfluence of tensioned cables on the ring and other ele-ments of the dome. Designed strengthening, apart frompassive action, reduces the radial and circumferential de-formability of the ring, which should be considered to be apositive effect on the structure of the dome.

A crucial assumption in the design was the require-ment that the strengthening elements (including anchor-ages) should not extend beyond the outline of the dome,and should not be visible on the façade. This made it im-possible to tension cables section by section around thecircumference of the ring. Eventually, the cables anchor-ages were hidden in the service staircase added to the halland separated from the ring. It was necessary to createholes to install the anchorages and tension the cables. Fig.10 shows the arrangement of the anchorages on the sur-face of the ring in the staircase. Sheath ducts were coveredwith a layer of mortar. The surface was textured andglazed (a painting technique known since the Renais-sance). The reinforcement is not visible on the perimeterof the ring, and the resulting two new edges do not lead toany disharmony in the hall’s façade (Fig. 12).

The strengthening method described here is compa-rable to the one implemented in the dome of the Sanctu-ary of Vicoforte (Italy) [21]. That is a building of great architectural and structural significance with a huge ellip-tical masonry dome, the biggest in the world with thisshape in terms of dimensions (internal axes 37.2 ×24.9 m).The structure has suffered over the years from significantstructural problems resulting in cracking and thereforeneeded to be strengthened. The strengthening system, in-stalled in 1985–1987, consists of 56 high-strength steel tie

bars with a diameter of 32 mm, placed within holes drilledin the masonry at the top of the drum, along 14 tangentsaround the perimeter. The heads of adjacent bars are in-terconnected by steel frames. The bars were minimallytensioned at the time of their installation and retensionedin 1997 [21].

5 Conclusions

The Centennial Hall built in 1911–1913 is a milestone inmodern concrete architecture. Its historical significancehas been acknowledged through its inclusion in the UNESCO World Heritage List since 2006. It owes itsunique character to the reinforced concrete ribbed domewith a span of 65 m, the largest since the time when theRoman Pantheon was built.

Almost a century of intensive use of the facility andlack of proper conservation resulted in deterioration ofthe building. The most significant structural defects (verti-cal cracks) were noticed in the lower ring of the dome. Itsstrengthening was included in the extensive renovationplan for the hall. The passive strengthening proposed didnot introduce large additional forces into the structure,but reduced the radial and circumferential deformabilityof the ring. The system installed allows for retensioningthe cables if there is a need to in the future. What is im-portant is that the strengthening does not interfere withthe appearance of the historic façade of the building. The

Fig. 11. Hall façade renovation work and strengthening the lower ring of the dome

Fig. 12. Final effect – hall’s façade after renovation

37



cable anchorages have been hidden inside the servicestaircase and are not visible from the outside. Althoughthe strengthening uses modern concrete prestressing tech-nology, the idea is similar to the one proposed more than250 years ago by Poleni in the case of St Peter’s Basilica inRome.

It seems that after refurbishment, the CentennialHall will be in use for at least another few decades. In thehall a museum has been set up with interactive multime-dia presentations on the construction and history of thisoutstanding building.

References

1. MacDonald, W. L.: The Pantheon: Design, Meaning andProgeny. Harvard University Press, Cambridge, 1976.

2. Cowan, H.: The Master Builders: A History of Structural andEnvironmental Design From Ancient Egypt to the Nine-teenth Century. John Wiley & Sons, New York, 1977.

3. Mark, R., Hutchinson, P.: On the structure of the RomanPantheon. Art Bulletin, vol. 68, No. 1, 1986, pp. 24–34.

4. Heinle, E., Schlaich, J.: Kuppeln aller Zeiten, aller Kulturen.Deutsche Verlags-Anstalt, Stuttgart, 1996.

5. Çakmaka, A. S, Taylor, R. M., Durukalc E.: The structuralconfiguration of the first dome of Justinian’s Hagia Sophia(A.D. 537–558): An investigation based on structural and lit-erary analysis. Soil Dynamics and Earthquake Engineering,vol. 29, No. 4, 2009, pp. 693–698.

6. Lübke, W., Semrau M.: Grundriß der Kunstgeschichte (14thed.,) Paul Neff Verlag, Esslingen, 1908.

7. Hartt, F.: History of Italian Renaissance Art (6th ed.). Pren-tice Hall, Englewood Cliffs, 2006.

8. Como, M.: Statics of Historic Masonry Constructions.Springer-Verlag, Berlin/Heidelberg, 2012.

9. Bellini, F.: St. Peter in Rom 1506–2006. In: Satzinger, G.,Schütze, S. (eds.): Sankt Peter in Rom 1506–2006. Hirmer,Munich, 2007, pp. 175–194.

10. Poleni, G.: Memorie istoriche della Gran Cupola del TempioVaticano e de’ danni di essa, e de’ ristoramenti loro, divise inlibri cinque. Stamperia del Seminario, Padova, 1748.

11. Gargiani, R.: Vers une construction parfaite. Machines etcalcul de résistance des matériaux. Matières, vol. 6, 2003, pp.99–115.

12. Trauer, G., Gehler, W.: Die Jahrhunderthalle in Breslau. JuliusSpringer, Berlin, 1914.

13. Trauer, G., Gehler, W.: Festhalle in Breslau. Berechnung derKuppel, 1911 (typescript).

14. Ramm, W.: Über die faszinierende Geschichte des Beton-baus vom Beginn bis zur Zeit nach dem 2. Weltkrieg. In:Curbach, M. et al.: Gebaute Visionen: 100 Jahre DeutscherAusschuss für Stahlbeton 1907–2007. Beuth-Verlag, Berlin/Vienna/Zurich, 2007, pp. 27–130.

15. Kawaguchi, M.: The Lighter, the Better. IABSE-IASS Sym-posium 2011 Report, Taller, Longer, Lighter, pp. 18–25.

16. Persona, M.: Ekspertyza stanu technicznego konstrukcji budynku Hali Ludowej we Wrocławiu (Expert report on thetechnical condition of the Centennial Hall’s structure inWrocław – in Polish). MBM Sp. z o.o., Wrocław, 2008.

17. Huber, H. S., Mikolajonek, M., Filipczak, P.: Die Jahrhun-derthalle in Breslau. Sanierung eines Weltkulturerbes. Be-ton- und Stahlbetonbau, vol. 105, No. 11, 2010, pp. 729–736.

18. Hildebrand, M.: Remont Hali Stulecia we Wrocławiu (Reno-vation of the Centennial Hall in Wrocław – in Polish). Mate-riały Budowlane, vol. 2/2011, pp. 34–35.

19. Projekt wykonawczy w zakresie zmiany sposobu wzmocnie-nia głównego pierscienia rozcia ganego kopuły zebrowej Ha-li Stulecia (Detailed design of change of strengthening of the

main tensiled ring of the Centennial Hall’s ribbed dome – inPolish). Zespół Badawczo-Projektowy MOSTY-WROCŁAW(Research & Design Office MOSTY-WROCŁAW), 2009.

20. Onysyk, J., Prabucki, P., Sadowski, K., Biliszczuk, J.:Strengthening of the lower ring of the ribbed reinforced con-crete dome of the Centennial Hall in Wrocław. Proc. of 7thCentral European Congress on Concrete Engineering, Bala-tonfüred, 22–23 Sept 2011, pp. 283–287.

21. Chiorinoa, M. A., Ceravolo, R., Lai, C. G., Casalegno, C.: Sur-vey, seismic input and structural modeling of the “ReginaMontis Regalis” Basilica and large elliptical dome at Vico-forte, northern Italy. Proc. of 8th International Conferenceon Structural Analysis of Historical Constructions SAHC2012, Wrocław, 15–17 Oct 2012, pp. 1432–1440.

Contact address:Jan BiliszczukWrocław University of TechnologyWybrzeze Wyspianskiego 2750-370 Wrocław, Polande-mail: [email protected]

Robert Toczkiewicz, PhD, Civ. Eng.Research & Design Office MOSTY-WROCŁAW

Jan Biliszczuk, Prof., PhD, Civ. Eng.Wrocław University of TechnologyResearch & Design Office MOSTY-WROCŁAW

Przemyslaw Prabucki, M.Sc., Civ. Eng.Research & Design Office MOSTY-WROCŁAW

Krzysztof Sadowski, PhD, Civ. Eng.Wrocław University of Technology

Jerzy Onysyk, PhD, Civ. Eng.Wrocław University of TechnologyResearch & Design Office MOSTY-WROCŁAW


Technical Paper

DOI: 10.1002/suco.201300013

Two sets of reliability analyses for two beam series strengthenedwith carbon fibre composites (CFC) in different ways and subject-ed to torsional moments are described in this paper. The analy-ses consider three failure functions and the system is regardedas a series system formed by these three limit state modes.Five random variables are taken into account in the first set ofanalyses. The analyses are performed for different torsional mo-ment ratios, defined as the ratio of the torsional moment due tolive loads to the total torsional moment. The system reliability in-dexes and the factors of importance associated with each ran-dom variable are obtained. In the second set of reliability analy-ses, only the two most relevant random variables selected in thefirst set of analyses according to the values of their factors of im-portance are considered, and new reliability indexes are deter-mined. The examples show that despite the constant value of thetotal torsional moment, the increase in the torsional moment ratioleads to a decrease in the system reliability levels. The fact thatthe values of the reliability indexes obtained in both sets of relia-bility analyses are very similar validates the efficiency of the sen-sitivity analyses.

Keywords: reliability index, torsion in RC beams, carbon fibre composites

1 Introduction

Structural projects are designed so that they can satisfy re-quirements regarding safety, serviceability and durability.In such projects there are several random variables thatintroduce uncertainties which remain throughout the life-time of the structure.

The Brazilian code NBR 6118 [1] contemplates theseuncertainties (resistances and loads) by using the ultimatelimit state (ULS).

ULS expressions for the design of reinforced con-crete structures are written in terms of the design valuesfor the random variables. These values are obtained fromthe characteristic values of the random variables by divid-ing or multiplying them (always on the safe side) by partialsafety factors > 1. The characteristic value of the randomvariable is defined as a value of low probability that has tobe less (for resistances) or greater than (for loads) a pre-scribed value for the cumulative probability. The design

values are used to define the design resistances Rd and de-sign actions Sd at the level of the cross-sectional forces inthe structural elements. The ULS expressions in NBR6118 [1] have the general form Rd ≤ Sd. This methodologyis called semi-probabilistic. The partial safety factors con-fer safety on the structure and reliability indexes intrinsicto it.

Silva Filho [2] tested two sets of three reinforcedconcrete beams strengthened with carbon fibre compos-ites (CFC). One series was denoted VT beams (with trans-verse CFC reinforcement) and the other VTL beams (withtransverse and longitudinal CFC reinforcement). Thebeams tested were subjected to torsion, and had been de-signed to resist torsion according to a design methodbased on NBR 6118 [1] and proposed in his work.

This paper focuses on the reliability analysis of thesetwo beam series. For the reliability analyses, the mean val-ues of the resistant torsional moments of the beams areevaluated using the mean values of the random variablesin the design expressions. In the two sets of reliabilityanalyses, the mean values of the resistant and the appliedtorsional moments are then considered to be equal tothose of the concrete strut. The torsional moments ap-plied are supposed to be formed by two components – onerelated to permanent loads, the other associated with liveloads. The mean values of the components may vary, al-though their sum remains constant.

2 Description of the beams analysed

In his theoretical and experimental study, Silva Filho [2]evaluates the behaviour and the increasing strength of RCbeams (VT and VTL) strengthened with CFC and subject-ed to pure torsion. In his study Silva Filho [2] adopted thegeneralized spatial truss model and the methodology ofEN 1990 [3], which concerns the resistance of concretestrut, longitudinal reinforcement and steel stirrups.

The effective bond stress between CFC and concretewas considered by means of the Chen and Teng [4] model,and the concrete strut angle by the Aprile et al. [5] formu-lation. The mean values of the concrete compressivestrength, the steel yield stress and the CFC elastic modulusare obtained by Silva Filho [2] from laboratory tests; theyare 36.7 MPa, 565.3 MPa and 256.7 GPa respectively.

The two sets of reinforced concrete beams (VT andVTL) have equal amounts of steel reinforcement (cross-

Reliability analysis of RC beams strengthenedfor torsion with carbon fibre composites

Osvaldo Luiz de Carvalho SouzaEmil de Souza Sánchez Filho*Luiz Eloy VazJúlio Jerônimo Holtz Silva Filho


Submitted for review: 14 March 2013Revised: 17 June 2013Accepted for publication: 24 July 2013

39

O. L. de Carvalho Souza/E. de Souza Sánchez Filho/L. E. Vaz/J. J. Holtz Silva Filho · Reliability analysis of RC beams strengthened for torsion with carbon fibre composites


sectional area of longitudinal bars = 7.36 cm2, cross-sec-tional area of stirrups = 0.79 cm2 spaced every 15 cm) anddifferent CFC reinforcement configurations: VT seriestransverse reinforcement = 0.18 cm2 spaced every 30 cm;VTL series longitudinal reinforcement = 0.73 cm2 andtransverse reinforcement = 0.18 cm2 spaced every 30 cm.These configurations were adopted in this paper. Fig. 1shows the CFC reinforcement configurations of the VTand VTL series.

3 Design torsional moments

The design torsional moments TRd of the VT and VTLbeams are obtained by means of the semi-probabilisticmethod according to Brazilian code NBR 6118 [1] and themethodology developed by Silva Filho [2] and Silva Filhoet al. [6].

Table 1 shows the apportioned values of the designtorsional moments resisted by the concrete strut TRd-Strut,by the longitudinal steel and CFC reinforcement TRd-Long,and by the steel and CFC stirrups TRd-Trans of the VT andVTL beams.

The beam strength is determined by the design tor-sional moment of the concrete strut.

The design torsional moments of the concrete strutTRd-strut of the VT and VTL beams are transformed fromEq. (1) into characteristic strength values of 18.81 and18.75 kNm. A partial safety factor of 1.4 is applied as rec-ommended by NBR 6118 [1]:

(1)

where TRk-strut is the characteristic value of the torsionalmoment resisted by the concrete strut.

For the purposes of the reliability analysis, the char-acteristic values of the torsional moments TRk-strut are

1.4T TRd strut Rk strut

Fig. 1. Steel and CFC reinforcement configurations for VT and VTL series [2]

Table 1. Design torsion moments of VT and VTL beams (kNm)

Beam TRd-Strut TRd-Long TRd-Trans

VT 26.34 29.46 30.26

VTL 26.26 32.14 26.93

40



considered to be formed by two components: torsionalmoment Tq for live load and torsional moment Tg for deadload, whose values vary according to the live load ratio0.3 ≤ rq ≤ 0.8 thus:

(2)

4 Reliability analysis

The reliability analyses are performed using the first-orderreliability method as described by Melchers [7].

4.1 Target reliability index

The target reliability index βt may be defined as the mini-mum value of the reliability index of a structure such thatit presents an adequate level of performance and probabil-ity of failure below a prescribed value.

EN 1990 [3] stipulates the target reliability indexesfrom the determination of the consequences of failure, thereliability classes and the return period. The classes of fail-ure consequences are established according to the impactcaused by the occurrence of a failure, i.e. loss of humanlife and environmental, social or economic consequences:CC1 – small impact, CC2 – moderate impact, CC3 – highimpact.

Table 2 shows the reliability indexes βt obtained re-garding the return period and the reliability classes RC1,RC2 and RC3, which are associated with the consequenceclasses CC1, CC2 and CC3 respectively.

4.2 Failure functions for the problem

The failure functions or limit state functions associatedwith the ULS expressions defined by Silva Filho [2] arepresented in the following.

The equation of failure regarding crushing of theconcrete strut in a reinforced concrete beam is

(3)

The equation of failure associated with the longitudinalsteel and CFC reinforcement is

(4)

T T TRk strut g q

2 0,7 0,7200 1

( )1gf

ftA

T Tcc

kg q

tgtg

2 2 0,192 ( )2g A tgA fu

A

ubh

E

tf tg T Tk

sl s

k

fl f

fc g q

The equation of failure related to the transverse steel andCFC reinforcement is

(5)

The tangent of the concrete strut angle used in Eqs. (3),(4) and (5) is given by

(6)

where:Afl cross-sectional area of longitudinal CFC reinforce-

mentAft cross-sectional area of transverse CFC reinforcementAk area enclosed by centre-line of shear flowAst cross-sectional area of transverse steel reinforcementAsl cross-sectional area of longitudinal steel reinforce-

mentb width of beamEf CFC elastic modulusEs steel elastic modulusEc concrete elastic modulusfc concrete compressive strengthfs steel yield stressh depth of beams spacing of transverse reinforcementsf spacing of CFC stirrupst thickness of effective walltf thickness of CFC reinforcementu perimeter of cross-sectionuk perimeter of area Ak

4.3 Random variables data

Among the variables present in the three failure modesdefined in section 4.2, the following ones are consideredto be random: concrete compressive strength fc, steel yieldstress fs, CFC elastic modulus Ef, torsional moment due todead load Tg and torsional moment due to live load Tq.The other variables are considered to be deterministic.

The random variables considered in the first set ofreliability analyses are: compressive strength of concretefc, yield stress of steel fy, elastic modulus of composite material Ef, applied torsional moment Tg (related to per-manent loads) and applied torsional moment Tq (relatedto live loads). As a result of these analyses we obtain thevariation in the reliability index β5i associated with thefailure mode i, the variation in the reliability index of theseries system β5s (considered as the upper bound based onfirst-order approximation of the three limit state functions)and their corresponding failure probabilities Pf5i and Pf5s with respect to different load ratios rq in the range0.3 ≤ rq ≤ 0.8.

1 1

1 14tg

E AE tu

E A

E tu

E AE ts

E A

E ts

s sl

c

f fl

c k

s st

c

f ft

c f

2 12 0,192

( )3g Atg

A fs

A

sbh

E

tf

tgT Tk

st s

ft

f

f

fc

g q

Table 2. Values of β t, EN 1990 [3]

Consequences Reliability βtclass class

ULS

1 year 50 years

CC3 RC3 5.2 4.3

CC2 RC2 4.7 3.8

CC1 RC1 4.2 3.3

41



The values of the factors of relative importance, orsensitivity factors alpha, Ifc, Ifs, IEf, ITg and ITq, are also cal-culated, making it possible to determine which randomvariables may be neglected in the second set of reliabilityanalyses. The results of sensitivity studies highlight thatthe compressive concrete strength fc and, especially, theapplied torsional moment due to live loads Tq are by farthe most deterministic random variables.

The beams are then reanalysed considering only therandomness of the two more relevant variables. The otherthree random variables from the first reliability analysisare now treated as deterministic. As in the first set ofanalyses we obtain the reliability index β2i of the failuremodes i and the reliability index β2s of the series system aswell as their respective failure probabilities Pf2i and Pf2s,but now only with respect to the load ratio rq = 0.5. Thisratio was chosen to represent best the load of a regularstructure.

Brazilian code NBR 8681 [8] considers the mean val-ue of the torsional moments for dead load μTg, equal to itscharacteristic value, and the mean value of the torsionalmoments for live load μTq, equal to the one whose proba-bility of being exceeded is between 25 and 35 %; this pa-per considers 35 %. Table 3 shows the mean values of thetorsional moments for live and dead loads with regard toeach live load ratio rq used in this paper, obtained accord-ing to NBR 8681 [8]. The characteristic values of the tor-sional moments listed in the table vary, although theirsums are constant as a consequence of the variation in theload ratios in the range 0.3 ≤ rq ≤ 0.8.

The statistical parameters and the associated distrib-ution function for the random variables are given inTable 4, in accordance with JCSS [9] and Lopes [10].

4.4 Result of the analyses

Tables 5 and 6 show the results of the reliability analysesperformed with the five random variables for VT and VTL

beams respectively for all the variable load ratios adopted.The results of each beam differ because of their differentstrengthening configurations. The tables show the reliabil-ity indexes of each failure mode, β5,1, β5,2 and β5,3, plustheir respective probabilities of failure, Pf5,1, Pf5,2 andPf5,3, and the series system reliability index β5s and its re-spective probability of failure Pf5s.

Figs. 2 and 3 show, for beams VT and VTL respec-tively, the variation in the reliability index for the failuremodes β5i, and the series system reliability index β5s plot-ted against the variation in the live load ratio rq. The relia-bility index βt = 3.8 adopted by EN 1990 [3] is taken as areference for buildings with moderate consequence of fail-ure (CC2) and a design lifetime of 50 years for the struc-ture.

Observing the curves for the reliability indexes inFigs. 2 and 3, an important conclusion can be drawn: thestructure is not reliable enough for load ratio values > 0.5(they are lower than the target value recommended by theEuropean code). This means that the partial factors ofsafety of the Brazilian code are not precisely calibrated.

From the reliability analyses performed using theFORM, it is possible to quantify the factors of importanceIfc, Ifs, IEf, ITg and ITq of the variables for each failure modeanalysed.

Figs. 4 and 5 show, for the VT and VTL beams re-spectively, the factors of relative importance, presented aspercentages, for the three variables whose values are moresignificant for the three failure modes. These values referto tests with the load ratio rq = 0.50.

Fig. 4, for the VT beam, shows that the most signi -ficant factors of importance for the failure function g1 re-lated to the rupture of the concrete strut are Ifc, ITg andITq. For the failure function g2 associated with yield of thelongitudinal steel and CFC reinforcement they are Ifs, ITgand ITq, and for the failure function g3 linked with yield ofthe transverse and CFC reinforcement, again Ifs, ITg andITq. Fig. 5, for the VTL beam, depicts a similar behaviour of

Table 3. Mean values of torsional moments for live and dead loads (kNm)

VT VTL

rq TRkg μTg TRkq μTq rq TRkg μTg TRkq μTq

0.3 13.17 13.17 5.64 5.34 0.3 13.12 13.12 5.63 5.32

0.4 11.28 11.28 7.53 7.11 0.4 11.25 11.25 7.50 7.09

0.5 9.41 9.41 9.41 8.89 0.5 9.38 9.38 9.38 8.87

0.6 7.53 7.53 11.28 10.67 0.6 7.50 7.50 11.25 10.64

0.7 5.64 5.64 13.17 12.45 0.7 5.63 5.63 13.12 12.41

0.8 3.76 3.76 15.05 14.23 0.8 3.75 3.75 15.01 14.19

Table 4. Statistical parameters and distribution functions of the random variables

Basic variable Char. Mean Standard Coef. Distributionvalue deviation of var.

Concrete compressive strength (MPa) 30 36.7 4 0.11 lognormal JCSS [9]

Steel yield stress (MPa) 500 565,3 39,6 0.07 lognormal JCSS [9]

CFC elastic modulus (GPa) – 256.7 10.21 0.04 Weibull Lopes [10]

Torsional moment – Tg (kNm) var. var. – 0.05 normal Lopes [10]

Torsional moment – Tq (kNm) var. var. – 0.28 Gumbel JCSS [9]

42



Table 5. Results of reliability analysis for five variables: VT beam series

Functions of failure gi rq = q/(g + q) β5i Pf5i β5s Pf5s

Strut g1 5.07 1.99 ×10–7

Long. reinft. g2 0.30 5.00 2.88 ×10–7 4.91 4.55 ×10–7

Trans. reinft. g3 5.64 8.45 ×10–9

Strut g1 4.45 4.27 ×10–6

Long. reinft. g2 0.40 4.37 6.36 ×10–6 4.29 9.09 ×10–6

Trans. reinft. g3 4.88 5.28 ×10–7

Strut g1 3.99 3.30 ×10–5

Long. reinft. g2 0.50 3.90 4.77 ×10–5 3.84 6.22 ×10–5

Trans. reinft. g3 4.34 7.09 ×10–6

Strut g1 3.64 1.38 ×10–4 3.50 2.31 ×10–4

Long. reinft. g2 0.60 3.55 1.93 ×10–4

Trans. reinf. g3 3.94 4.14 ×10–4

Strut g1 3.36 3.97 ×10–4

Long. reinft. g2 0.70 3.27 5.38 ×10–4 3.24 5.91 ×10–4

Trans. reinft. g3 3.62 1.48 ×10–4

Strut g1 3.12 8.98 ×10–4

Long. reinft. g2 0.80 3.04 1.18 ×10–3 3.03 1.20 ×10–3

Trans. reinft. g3 3.36 3.90 ×10–3

Table 6. Results of reliability analysis for five variables: VTL beam series

Functions of failure gi rq = q/(g + q) β5i Pf5i β5s Pf5s

Strut g1 5.07 1.97 ×10–7

Long. reinft. g2 0.30 5.69 6.28 ×10–9 4.81 7.56 ×10–7

Trans. reinft.g3 4.85 6.20 ×10–7

Strut g1 4.45 4.33 ×10–6

Long. reinft. g2 0.40 4.95 3.79 ×10–7 4.17 1.54 ×10–5

Trans. reinft. g3 4.20 1.34 ×10–5

Strut g1 3.99 3.36 ×10–5

Long. reinft. g2 0.50 4.41 5.12 ×10–6 3.71 1.03 ×10–5

Trans. reinft. g3 3.74 9.39 ×10–5

Strut g1 3.64 1.39 ×10–4

Long. reinft. g2 0.60 4.01 3.01 ×10–5 3.39 3.52 ×10–4

Trans. reinft. g3 3.39 3.52 ×10–4

Strut g1 3.35 3.99 ×10–4

Long. reinft. g2 0.70 3.70 1.10 ×10–4 3.11 9.26 ×10–4

Trans. reinft. g3 3.11 9.26 ×10–4

Strut g1 3.12 8.98 ×10–4

Long. reinft. g2 0.80 3.44 2.96 ×10–4 2.89 1.94 ×10–3

Trans. reinft. g3 2.89 1.94 ×10–3

43



the factors of importance for the different failure func-tions.

The results of the sensitivity studies highlight the im-portance of the compressive concrete strength fc and, es-pecially, the torsional moment due to live load Tq com-pared with the other random variables involved in theanalysis.

The low values of the relative factors of importanceof the other variables enable a deterministic treatment forthose variables. Therefore, to emphasize the efficiency ofthe sensitivity analyses, the VT and VTL beams are re-

analysed considering only fc and Tq as random variables.Load ratio rq = 0.50 is used in this analyses.

Table 7 shows the values of the reliability indexesand their respective failure probabilities β2i and Pf2i aswell as β5i and Pf5i obtained in the reliability analysis ofthe VT and VTL beams respectively using the FORM, withtwo random variables, namely fc and Tq, and five randomvariables, namely, fc, Ef, Tq, Tg and fs.

The values of the reliability indexes β2i and β5i, con-cerning each failure mode, and the values of the reliabilityindexes of the series system β2s and β5s and their respec-tive failure probabilities Pf2s and Pf5s, presented inTable 7, differ little from each other. This fact validates thestudy of the sensitivity measure that evaluates the factorsof importance of the variables in this reliability analysis.

The decrease in the system reliability index with theincrease in the load ratio is very probably a consequenceof the type of probability density function for extreme val-ues which represents the live load (Gumbel), and of thehigh value of its coefficient of variation δq. This aspectand the high values obtained for the factor of importanceof the live load ITq compared with the other factors of im-

Fig. 2. Reliability index vs. live load ratio , VT beam

Fig. 3. Reliability index vs. live load ratio , VTL beam

Fig. 4. Factors of importance (sensitivity factors alpha) for rq = 0.50, VT beam

Fig. 5. Factors of importance (sensitivity factors alpha) for rq = 0.50, VTL beam

Table 7. Results of reliability analysis for two and five random variables

Beam Functions of failure gi β2i β5i β2s Pf2i β5s Pf5s

Strut g1 4.00 3.99

VT Long. reinft. g2 4.11 3.90 3.96 3.65 ×10–5 3.84 6.22 ×10–5

Trans. reinft.g3 4.44 4.34

Strut g1 3.98 3.99

VTL Long. reinft. g2 4.57 4.41 3.82 6.79 ×10–5 3.71 1.03 ×10–5

Trans. reinft.g3 3.85 3.74

44



portance highlight the need for a different treatment of thedead and live load partial safety factors in NBR 6118 [1].For the semi-probabilistic methodology, this code adoptsthe partial safety factors γg = 1.4 and γq = 1.4 for dead andlive loads respectively, neglecting the difference betweentheir probabilistic characteristics.

The values of the reliability index in the reliabilityanalyses with two basic variables are higher than the onesobtained in the reliability analyses with five basic vari-ables because of the existence of less uncertainty. In those,two and five random variables are considered respectively.

5 Conclusions

Despite the constant value of the total torsional moment,the relative increase in the mean of the applied torsionalmoment due to the live load leads to a decrease in the re-liability levels of the failure modes and the series system,allowing an increase in the probability failure of the struc-tural element.

The reliability index β5s of the VT and VTL beamstakes values below the target index βt for rq > 0.50, indi-cating that the semi-probabilistic treatment given by theBrazilian code NBR 6118 [1] applied to the methodologydeveloped by Silva Filho [2] is inconsistent for this range(rq ≥ 0.5).

The deterministic treatment applied to the randomvariables with low factors of relative importance led tonew reliability index values that differ little from the previ-ous values obtained in the studies where their randomnessis considered. This fact stresses the efficiency of the sensi-tivity studies.

References

1. Associação Brasileira de Normas Técnicas: Design of Rein-forced Concrete Structures – Proc., NBR 6118. Rio deJaneiro, Brazil. 2007.

2. Silva Filho, J. J. H.: Carbon Fiber Reinforced Polymer Tor-sion Strengthening of Reinforced Concrete Beams. Doctoralthesis, PUC-Rio, Brazil. 2007.

3. European Committee for Standardization (CEN): Eurocode:Basis of structural Design – EN 1990, Brussels. 2001.

4. Chen, J. F., Teng, J. G.: Shear Capacity of FRP-strengthenedRC beams: FRP debonding. Construction and Building Ma-terials, vol. 17, 2003, pp. 27–41.

5. Aprile, A., Benedetti, A.: Coupled Flexural-Shear Design ofR/C Beams Strengthened with FRP. Composites: Part B, No.35, 2004, pp. 1–25.

6. Silva Filho, J. J. H, Sánchez Filho, E. S., Velasco, M. de S. L.:Torsion Strengthening of RC Beams with Carbon Fibre Com-posites. Structural Concrete, (London, 1999), vol. 11, 2010,pp. 181–190, ISSN: 1464-4177, E-ISSN: 1751-7648.

7. Melchers, R. E.: Structural Reliability Analysis and Predic-tion. John Wiley & Sons, New York, 2002.

8. Associação Brasileira de Normas Técnicas: Loads and safetyof the structures – Proc., NBR 8681. Rio de Janeiro, Brazil.2003.

9. Joint Committee on Structural Safety: JCSS: ProbabilisticModel Code, 2001.

10. Lopes, M. T. A.: Structural Reliability Analysis Application tothe Design of Carbon Fibres Reinforced Polymer ShearStrengthening of Reinforced Concrete Beams. Doctoral the-sis, PUC-Rio, Brazil. 2007.

Júlio Jerônimo Holtz Silva Filho, D. Sc.PUC-RioCivil Engineering DepartmentRua Pinheiro Guimarães,145/ 40422281-080, Botafogo, Rio de Janeiro, RJ, Brasil

Luiz Eloy Vaz, Dr.-Ing.Fluminense Federal UniversityCivil Engineering DepartmentRua Álvaro Americano, 822451-200, Gávea, Rio de Janeiro, RJ, Brasil

Emil de Souza Sánchez Filho, D. Sc.Fluminense Federal UniversityCivil Engineering DepartmentRua Prof. Gastão Bahiana, 155/70122071-030, Copacabana, Rio de Janeiro, RJ, Brasil

Osvaldo Luiz de Carvalho Souza, D. Sc.Rural Federal University of the Rio de JaneiroEngineering DepartmentAv. Comandante Ary Parreiras 60/ 130124230-322, Icaraí, Niterói, RJ, Brasil


Staggering lapped joints increases the complexity of detailingand steel fixing, and may require additional resources and slowconstruction on site. Major design codes encourage staggeringlapped joints in tension by imposing a penalty on lap length de-pending on the proportion of bars lapped at the same section.There are, however, inconsistencies in the value of the coeffi-cients to be applied, and little evidence is available for validation.A programme of 17 physical tests found no evidence of an in-crease in strength when laps were staggered, and when al-lowance is made for increases in transverse spacing, staggeringwas found to reduce lap strength. Differences in the distributionof bond stress through a lap joint and in the share of the tensionforce taken by continuous and lapped bars are demonstrated tobe responsible for the reduction.

Keywords: lapped joints, bond, detailing

1 Introduction

Lapped joints serve to provide continuity of reinforce-ment in concrete structures. The force in one bar is trans-ferred to the surrounding concrete through bond stressover the bar surface, then from the concrete to the otherlapped bar. It is widely considered as good practice toavoid lapping all reinforcing bars at the same section. If allbars in the section need to be lapped, then laps should ei-ther be staggered in the longitudinal direction so that atany section only some of the bars are lapped, or the lengthof the lap increased. The penalty imposed by codes forlapping all bars at a section is substantial. Eurocode 2 [1],fib Model Code 90 [2] and ACI 318 [3] require lap lengthsto be increased by, respectively, up to 1.5, 2.0 and 1.3 timesthe corresponding anchorage or development length, andthe coefficient to be applied therefore differs significantlybetween codes.

The overall length of a lap zone is obviously muchgreater if laps are staggered than if all bars are lapped atthe same section, even allowing for an increased laplength. This may impede construction work as the greaterlength of a staggered lap zone reduces flexibility when lo-cating construction joints and will often require addition-al formwork.

Although many studies – together detailing well over1000 tests – have been conducted to evaluate how con-crete strength and confinement provided by cover andtransverse reinforcement influence the strength of lappedjoints, the test data is almost exclusively confined to speci-mens in which all bars are lapped at the same section.Considering that the factor for the proportion of barslapped can be as influential as that for confinement, sur-prisingly little research has been undertaken to assess theperformance of staggered laps.

Although the content of EC2 draws heavily on fibModel Code 90, the coefficients α6 for proportion lappedare somewhat lower, and attempts to discover the basis foreither the original coefficients or the change were fruitless.This investigation was therefore undertaken with the aimof assessing whether current design provisions for stag-gered laps are soundly based.

2 Strength of lapped joints: general background

Lapped joints rely on the bond between reinforcementand concrete to transfer forces. Bond is conventionally re-garded as a shear stress on the surface of the bar, and de-fined as the change in force along the bar divided by the(nominal) bar surface area over which this change takesplace, Eq. (1). However, Eq. (1) represents a major simplifi-cation of the real behaviour as most bars produced todayrely on the bearing of ribs rolled onto the surface of thebar during manufacture to transfer force. The definition ofEq. (1) is, nonetheless, a convenient one and will be usedhere.

fb = Δfs · As/πφ lb (1)

There are two broad modes of bond failure, the distinctionbetween the two being dependent on whether or not theconcrete cover splits. Lapped joints for larger diameterbars typically have a minimum concrete cover of threetimes the bar diameter or less, and fail in a splitting modewith a longitudinal crack forming in the concrete coverunless the lap is long enough for the reinforcement toreach yield. Splitting mode failures tend to be brittle evenif confining reinforcement in the form of links is providedto maintain splitting resistance once the cover cracks, andthe potential for failures by this mode should therefore beavoided. Where cover exceeds five times the bar diameter,

Technical Paper

Staggered lap joints for tension reinforcement

John Cairns DOI: 10.1002/suco.201300041

Corresponding author: [email protected]

Submitted for review: 11 June 2013Revised: 31 July 2013Accepted for publication: 4 August 2013

bond failure occurs by shearing of the concrete along asurface over the tops of the ribs and the bar pulls out ofthe concrete, leaving a relatively smooth bore. The split-ting mode is the weaker type and is generally of greaterconcern for laps.

The evaluation of bond resistance is more complexthan implied by Eq. (1), and EC2 includes no less than 10parameters for calculating anchorage and lap lengths. Theexpression presented in the fib Model Code for ConcreteStructures 2010 [4] and reproduced here as Eq. (2) may beused to estimate the stress developed by a lapped joint be-tween ribbed bars in “good” conditions. Eq. (2) has beencalibrated from tests in which all bars were lapped at thesame section, and has a coefficient of variation of 14 %when calibrated against an extensive database. The coeffi-cient of 54 in Eq. (2) has units of MPa.

(2)

EC2 states that laps should normally be staggered. Forlaps to be classified as staggered, the longitudinal distancebetween two adjacent laps should not be less than 0.3times the lap length l0, Fig. 2. Where laps are staggered,the clear spacing between laps cs is taken as shown inFig. 2. The notation “a” is used for cs in EC2.

Lap lengths for tension reinforcement depend on theproportion of bars lapped at a section, Fig. 3. Lap lengthfactors in EC2 and MC90 are the factors by which theequivalent anchorage length is to be multiplied to obtainthe lap length. The factor in ACI 318 applies to the devel-

5425

25

, 10

0.25 0.2 0.55

min0.25

max

min

0.1

f

f l c cc

k K

f fl

stm

cm om tr

y co

46

J. Cairns · Staggered lap joints for tension reinforcement


opment length. Fig. 3 compares the proportion lapped co-efficients given in each code, and shows the marked differ-ences between these codes.

3 Review of previous work

Magnusson [5] reported on four tests in which only a por-tion of the reinforcement was lapped at a section. Threepairs of specimens, each reinforced with three longitudi-nal bars, were tested. In one pair all longitudinal bars werelapped, with either two of three or one of three bars beinglapped in the other two pairs. The bond length used was,at 7.5φ, relatively short and sufficient only to developabout 35–55 % of the yield strength of the bars. Conse-quently, significant increases in strength were recorded inspecimens with greater proportions of continuous rein-forcement. Tests in which only one-third or one-half of thebars were lapped were on average 50 and 110 % strongerrespectively than the reference specimens in which allbars were lapped.

A few tests have been conducted with longer laplengths. Ferguson and Briceno [6] tested four beams with50 % of the bars continuous through the lap zone alongwith three similar specimens in which all bars were lappedat the same section. The 50 % lapped specimens were onaverage 10–15 % stronger, but if allowance is made for thegreater spacing between lapped pairs, the difference be-comes insignificant and they may even be interpreted asbeing weaker depending on the model used to make al-lowance for clear spacing. A broadly similar conclusioncan be reached from tests on wide beam splices byThompson et al. [7] in which edge bars were continuous insome specimens and lapped in others.

Metelli et al. [8] report on 24 tests in which a propor-tion of between 25 and 100 % of the longitudinal rein-forcement was lapped, the remaining bars being continu-ous throughout the span. Lap length was designed toensure a bar stress approaching yield in these tests. Fourtest series were conducted, covering two grades of con-crete, two bar diameters (16 and 20 mm) and a variety ofdetails, with laps confined by links. Results tend to indi-cate that lapping only some bars at a section weakens lapstrength if allowance is made for the difference in spacing.Bond strength ratio appears to dip from a maximum at100 % lapped to a minimum at 50 % lapped before par-tially recovering as the proportion lapped drops further.Cairns [9] has reported a similar trend in an investigation

Fig. 1. Concrete covers, Eq. (2)

Fig. 2. Staggered lapped joints, adapted from EC2

47



of the lapped joints of bundled bars. Failure of laps inwhich only a portion of bars was lapped at a section wasobserved to be less brittle.

4 Analysis of influence of proportion of bars lapped

Three factors will affect the performance of a lapped jointwith a portion of the bars lapped compared with an equiv-alent detail in which all bars in the section are lapped:1. Increased resistance to cover splitting as a consequence

of wider spacing cs between laps.2. Changes in the distribution of bond stress within a lap.3. Redistribution of the share of tension force taken by

continuous and lapped bars.

Factors 2 and 3 in the above list are closely inter-related,but will be treated as separate effects for exploration here.

4.1 Spacing between bars

Assuming overall section breadth is unchanged, the clearspacing between lapped bars is greater where only some ofthe bars are lapped at a section. Resistance to the burstingforces generated by bond action therefore increases. Mostmodern codes recognize the beneficial influence of mini-mum cover on bond resistance, and several semi-empiricalanalyses also present the increase in bond resistance withclear spacing: Zuo and Darwin [10], Canbay and Frosch[11], fib Model Code 2010.

Eq. (2) may be used to estimate the influence of clearspacing. Fig. 4 shows sections through laps with variousproportions of bars lapped. Where all bars are lapped atthe same section, Fig. 4a, clear spacing cs is taken as 2φ,the minimum permitted by EC2. Based on the samebreadth of section, clear spacing between pairs of laps csincreases to 6φ and 10φ where 50 % and 33 % respectivelyof the bars are lapped, Figs. 4b and 4c. The increase inbond resistance estimated by Eq. (2) as a result of stagger-ing laps is presented in Fig. 5 for three values of bottomcover cy: φ, 2φ and 3φ. The estimated increase in lapstrength tends to be less than that implied by the designcode coefficients in Fig. 3, particularly at higher cy values.Proportionally lower increases would be predicted if Ktr > 0 or for a wider initial spacing.

4.2 Distribution of bond stress along lap

The distribution of bond stress along a lap length is affect-ed by the proportion of bars lapped. Considering a lappedjoint that lies within a constant moment zone, the totaltension in the reinforcement must remain constantthroughout the lap length. (Tension stiffening effects andminor changes in neutral axis depth are neglected here forsimplicity.) Thus, where all bars are lapped, one bar of thelapped pair must shed load at the same rate as the otherpicks it up. It follows by symmetry that if lapped bars areof the same diameter, the force in the two bars at the mid-point of the lap must be equal, and half the bar force mustbe transferred within each half of the lap length. If, how-ever, only some of the bars are lapped at the section, and ifit is further assumed that there is no bond slip near thecentre of the lap, then for compatibility of bar strains, con-tinuous and lapped bars each carry a stress given by Eq.(3) at the middle of the lap. A schematic plot of stress dis-tributions for laps with varying proportions of bars lappedat a section, based on the assumption that all bars take anequal share of the load, is shown in Fig. 6. The force to betransferred over the end half lap length increases when on-ly some of the bars are lapped, and peak bond stresseswould be correspondingly higher and therefore potentially

Fig. 3. Lap length factors for proportion of bars lapped at a sectionFig. 4. Spacing between lapped bars: a) 100 % lapped, b) 50 % lapped, c) 33 % lapped

0,90

0,95

1,00

1,05

1,10

1,15

1,20

100% 50% 33% 25% 20%

Cove

r co

effici

ent

(cm

ax/c

min

)0.1

Propor�on lapped cx=cy=φ cx=cy=2φ cx=cy=3φ

Fig. 5. Influence of increased spacing between laps

lead to an earlier failure. In reality, tension stiffening andbond slip would mitigate the differences shown in Fig. 6.

fs,m = fs(1 + ρlap)–1 (3)

4.3 Sharing tension force between lapped and continuous bars

The share of the tension force taken by lapped bars willdepend on their stiffness relative to that of continuousbars. The elongation of a continuous bar over the laplength is given by Eq. (4). For simplicity, the effects of ten-sion stiffening are again neglected.

(4)

Bar displacement at the loaded end of the lap is the sum oftwo components: the elongation of a lapped bar over thelap length plus the unloaded end slip sfe of a lapped bar,Eq. (5).

(5)

Cairns and Jones [12] reported that laps failed at a freeend slip of 0.01–0.04 mm, which is small relative to the de-formation represented by the integral in Eqs. (4) and (5)when the stress developed by the lapped bars is near yield.Strain εs,l in lapped bars varies from zero at the end of the bar to a maximum at the opposite end of the lap,whereas strain εs,c in a continuous bar will be relativelyuniform throughout the lap length. It follows that for com-patibility of deformations of lapped and continuous bars,δcont = δlap, strains at the ends of the lapped bars must begreater than those in continuous bars. In other words, thetension force in the reinforcement is not shared betweenlapped and continuous bars in equal proportions.

An exploratory finite element analysis (FEA) was un-dertaken to investigate sharing of force between lappedand continuous bars. Three lap configurations wereanalysed, one with all bars lapped simultaneously (100 %lapped), one containing a single continuous bar and alapped pair (50 % lapped), and one containing two contin-uous bars and a lapped pair (33 % lapped). The model rep-resents a lap length of 20 times the bar diameter, as in theexperimental investigation, plus a distance equal to half alap length to either side. Half the breadth of the section ismodelled, Fig. 7, with deformations restrained along the

·,0dx slap s l fe

lo

·,0dxcont s c

lo

48



axis of symmetry in the perpendicular direction. Thebreadth of each section was varied so that the effectivegeometric ratio of reinforcement outside the lap was 2.6 %in all analyses.

The FEA was conducted using the LUSAS softwaresuite [13]. Steel reinforcement was represented by elasticbar elements, and concrete represented using 8-nodedisoparametric elements and the inbuilt non-linear massconcrete material model. The applied loading was im-posed by displacements of equal magnitude and oppositedirection along opposite ends of the model. Bond slip be-haviour is not included in the results reported here. TheLUSAS modeller was found to have some limitations thatdistort bond stiffness at changes in the FE mesh. Thebar/bar slip at the ends of the lap at convergence failurewas around 0.2 mm, similar to that reported by Cairns andJones in their physical tests on lap joint specimens. It wastherefore decided to neglect bond slip behaviour to avoidthe difficulties that were experienced in iterating to the in-tended level of bar stress.

Plots of the variation in bar force are shown in Fig. 8.The origin of the plots lies at the centre of the lap length,and the lap extends from –0.5 to +0.5 on the horizontal ax-is. Results are scaled with the vertical axis representingthe share of the total force taken by each bar. Bar force istherefore 100 % of the total at the ends of the lap in whichall bars are lapped, Fig. 8a. Elsewhere, the total is some-what less than 100 % due to the stiffening contribution ofconcrete in tension.

With 50 % of bars lapped, the force in the continu-ous bar at the end of the lap is slightly less than half the to-tal, 45.5 %, Fig. 8b, while the lapped bar is responsible forthe balance of 54.5 %, equivalent to a stress 20 % greaterthan that in the continuous bar and 9 % higher than thatwhich would be obtained by averaging tension across con-tinuous and lapped bars. Where one-third of the bars islapped, Fig. 8c, the lapped bar develops 38.6 % of the to-tal, equivalent to a stress 26 % greater than the average forthe two continuous bars and 16 % higher than the averageacross all bars. The greater stiffness of the lapped pairtherefore results in their having to develop a greater shareof the total force. The ratio of stresses at mid-length of alapped bar to that at the ends increases from 0.42 when

Fig. 6. Distribution of bond stress through lapped joint, schematic

Fig. 7. FE meshes: a) 100 % lapped, b) 50 % lapped, c) 33 % lapped

49



100 % of bars is lapped to 0.48 when 33 % is lapped. Theresults therefore follow the trend illustrated in Fig. 6, al-though the ratios are lower than estimated by Eq. (3) dueto tension stiffening effects.

In summary, this section has identified three differ-ences – one beneficial, the other two adverse – betweenlaps in which all bars are lapped at the same section andthose in which only some bars are lapped at a section. Onthe basis of these analyses it can be speculated that an in-crease in bond resistance from confinement from in-creased spacing between lapped bars would readily be off-set by changes in demand due to differences in thedistribution of bond stress, and hence that the lower laplength permitted when only some bars are lapped, Fig. 3,might not reflect the performance of staggered laps. This

admittedly simplified analysis therefore raises doubts as towhether current guidance on staggering of lapped joints issoundly based.

5 Experimental programme5.1 Design

The test programme comprised four groups of specimenscontaining a total of 17 beams, with variations in the pro-portion of bars lapped at a section and the longitudinalstagger of individual lapped joints within each group. Thestagger dimension as is defined in Fig. 2. For the detail il-lustrated in Fig. 2, for example, the proportion of barslapped is 50 % and the stagger distance equals 130 % ofthe lap length. The parameter for proportion lapped usedhere denotes the proportion of bars lapped at the samesection, neglecting the requirements of EC2 for a gap be-tween lap zones, i.e. laps are considered staggered whenas ≥ lo.

Groups B and G were reinforced with three pairs of16 mm diameter bars, and the proportion lapped at a sec-tion was either 100 % or 33 %, whereas groups C and Dwere reinforced with two pairs of 20 mm diameter bars,and the proportion lapped was either 100 % or 50 %. Eachgroup contained one or more specimens with all barsspliced at the same section to serve as a benchmark for thewider data population. Reinforcement layouts for all spec-imens are shown schematically in Fig. 9, with details of di-mensions in Table 1. Lap length was set at 20 times the

0,0%

5,0%

10,0%

15,0%

20,0%

25,0%

30,0%

35,0%

40,0%

45,0%

-0,8 -0,6 -0,4 -0,2 0 0,2 0,4 0,6 0,8

Shar

e of

forc

e

Distance from centre of lap (as propor�on of lap length)

Con�nuous 1 Con�nuous 2 Lap le� Lap right

Fig. 8. Variation in bar stress through lap FE meshs (a) 100 % lapped (b) 50 % lapped (c) 33 % lapped

Fig. 9. Reinforcement details

0,0%

20,0%

40,0%

60,0%

80,0%

100,0%

120,0%

-0,8 -0,6 -0,4 -0,2 0 0,2 0,4 0,6 0,8

Shar

e of

load

Distance from centre of lap (as propor�on of lap length)

Lap le� Lap right

0,0%

10,0%

20,0%

30,0%

40,0%

50,0%

60,0%

-0,8 -0,6 -0,4 -0,2 0 0,2 0,4 0,6 0,8

Shar

e of

load

Distance from centre of lap (as propor�on of lap length) Con�nuous Lap le� Lap right

bar diameter to ensure bond failure would precede yield ofreinforcement in all but two beams. Specimen G1.5S useda shorter lap length of 15.3 bar diameters, reflecting thedifference in the α6 coefficient in EC2 for laps with 100and 33 % of bars lapped at a section relative to G0, where-as C0a used a longer lap length of 24 bar diameters, re-flecting the corresponding difference in α6 relative toC1.5a and C1.5b.

Beams contained between 0.8 and 1.2 % longitudinalreinforcement, and minimum covers were between 20 and25 mm, giving a minimum cover to bar diameter ratio ofbetween 1.0 and 1.56. A modest quantity of secondary re-inforcement in the form of closed links was provided inthe lap zones of series B, C and D. The quantity was keptclose to the permitted minimum to reduce uncertainties inthe interpretation of how links contribute to the strengthof laps in which only a portion of the bars is spliced at asection. Series G did not contain links within the lapzones. The number of 8 mm mild steel links provided foreach lap zone is given in Table 1. Links were provided at300 mm centres within the shear span in all cases.

5.2 Materials

Longitudinal reinforcement was of grade 500B to BS 4449[14] (characteristic 0.2 % proof strength 500 MPa). Barshad pairs of crescent-shaped ribs on opposite sides whichmerge into the core. Relative rib area was not measuredon these particular bars, but from similar production hasbeen found to lie typically in the range 0.055–0.065. Con-crete cover to longitudinal bars was provided by propri-etary spacers. Concrete was of medium workability (classS2 to BS EN 206 [15], slump typically 60 mm), maximum

50



aggregate size 20 mm, containing a water-reducing admix-ture and supplied by a local ready-mix company. Series B,D and G were each cast from a single batch; series C wascast from three different batches. Concrete was compact-ed by internal vibration and subsequently cured underdamp hessian and polythene for at least three days beforestripping and storage in the laboratory until being tested.Standard cube control specimens were taken from eachbatch and tested at the same age as the lap specimens.The results are reported in Table 1.

5.3 Test procedure

The beams were tested in four-point bending with lapzones positioned within the constant moment zone. Theload was monotonically increased to failure over a periodof approx. 30 min, applied in increments of either 10 or25 kN, with crack development marked at each stage.Loading was continued until residual strength dropped byat least 25 % after peak load had been passed. The rate ofdisplacement was increased during this stage. Load andmid-span deflection were logged at 2 s intervals through-out the loading sequence.

6 Test results

The load/deflection response of all beams was close to lin-ear up to peak load. Minor departures were evident at lowloads prior to initiation of flexural cracking, where stiff-ness was slightly greater, and close to failure, where the re-sponse softened slightly. Vertical flexural cracks formedwithin the constant moment zone first, followed by slight-ly inclined flexural cracks within the shear spans. Failure

Table 1. Details of test specimens

Test ref. Concrete Longitudinal Lap % Stagger Section Section Cover and No. of cube reinforcement length lapped breadth depth spacing linksstrength at each lapfcu dia. No. lb b h cx, cy cs[MPa] [mm] [mm] [%] [mm] [mm] [mm] [mm] [mm]

B0 43.1 16 3 320 100 0 226 254 20 39 3

B1.1 43.1 16 3 320 33 360 228 255 20 98 2

C0a 43.1 20 2 480 100 0 226 270 20 94 3

C0b 38.0 20 2 400 100 0 225 280 23 93 3

C0.5 42.0 20 2 400 100 200 226 270 20 94 3

C1.1a 42.0 20 2 400 50 440 224 303 23 161 2

C1.1b 38.0 20 2 400 50 440 225 290 23 162 2

C1.5a 42.0 20 2 400 50 600 226 270 20 160 2

C1.5b 38.0 20 2 400 50 595 225 274 20 159 2

D0 37.7 20 2 400 100 0 250 285 22 94 3

D0.5 37.7 20 2 400 100 200 250 285 22 94 3

D1 37.7 20 2 400 50 400 250 285 22 94 3

D1.25 37.7 20 2 400 50 500 250 285 22 172 3

G0 32.1 16 3 320 100 0 260 320 25 57 0

G0.5 32.1 16 3 320 100 160 250 310 25 52 0

G1.3 32.1 16 3 320 33 420 250 310 25 193 0

G1.3S 32.1 16 3 245 33 320 250 310 25 193 0

Notes for link detail: 2–40 mm from both ends of each lap3–40 mm from both ends and centre of each lap

51



spectively given in EC2. If the α6 coefficients in EC2 arean accurate reflection of behaviour, these two specimenswould be expected to develop the same strength. Test re-sults show the staggered lap detail of G1.3S to be 16 %weaker.

Fig. 11 plots lap strength for specimens with a laplength of 20φ classified according to the proportion ofbars lapped at the section. Bond strength is not affected bythe proportion of bars lapped. Fig. 12 shows a similar plotwith specimens classified according to stagger distance.The strength dropped by about 10 % where bars were stag-gered by one lap length or more, in contradiction to ex-pectations on the basis of Fig. 3.

Spacing between laps is increased where only someof the bars are lapped at a section. To allow for differences

occurred suddenly as a widening flexural crack formednear one end of a lap zone and longitudinal cracks propa-gated along longitudinal tension bars over the lap length.The load dropped under increasing deflection immediate-ly after the peak was reached in all tests.

Table 2 lists mid-span bending moments at peak loadand the corresponding lap strength for all specimens. Theaverage stress in the reinforcement at peak load fs,test iscalculated using the rectangular stress block for concretein EC2 with safety factors taken as 1.0. An indication ofthe brittleness of failure is given by the parameter Dres, cal-culated as the ratio of residual load at a deflection of 1.5times the peak load deflection to the peak load itself,Fig. 10.

The strength of specimens where all bars werelapped simultaneously has been compared with strengthsestimated by Eq. (2). The cylinder compressive strengthfor use in Eq. (2) is taken as 0.8 times the cube strength inTable 1. The ratio of measured to estimated lap strengthfor 100 % lapped specimens averages 0.99 with a coeffi-cient of variation of 0.14, almost identical to the scatter re-ported for Eq. (2) against a database of over 800 lap jointtests [16] and by Canby and Frosch and Zuo and Darwinfor their best fit expressions. The results presented heremay therefore be considered as representative of the larg-er body of test data, and hence constitute a valid bench-mark against which strength of staggered laps may becompared.

A direct comparison of equivalent laps for staggeredand non-staggered laps is possible for only one pair ofspecimens. Lap lengths for G0 and G1.3S were 320 and245 mm respectively, reflecting the corresponding α6 coef-ficient values of 1.5 and 1.15 for 100 and 33 % lapped re-

Table 2. Test results

Beam Max. Lap strength Bond Ductilityref. moment strength

ratioTest Calculated, fb,test/

Eq. (2) fb,calcfs,test fstm Dres

[kN · m] [MPa] [MPa]

B0 47.3 388 352 1.10 0.75

B1.1 48.8 373 479 0.78 0.30

C0a 51.0 430 382 1.13 0.23

C0b 45.1 304 361 0.84 0.51

C0.5 59.9 359 357 1.01 0.42

C1.1a 45.0 312 407 0.77 0.55

C1.1b 44.4 291 405 0.72 0.48

C1.5a 43.0 312 401 0.78 0.62

C1.5b 50.7 298 394 0.76 0.92

D0 53.6 331 359 0.92 0.52

D0.5 56.4 373 359 1.04 0.28

D1 51.7 358 428 0.83 0.57

D1.25 48.1 394 452 0.87 0.48

G0 52.6 313 294 1.07 –

G0.5 52.8 328 291 1.13 –

G1.3 49.7 307 336 0.91 –

G1.3S 43.7 263 290 0.91 –

100

80

60

40

20

00 10 20 30 40 50 60

Residualload at 1.5�mes peakload defln.

Peak

load

Midspan deflec�on (mm)

App

lied

load

(kN

) Dres=Residual loard Peakloard

Fig. 10. Typical load vs. mid-span deflection, B1.1

0

50

100

150

200

250

300

350

400

450

0% 20% 40% 60% 80% 100% 120%

Lap

Str

engt

h (M

Pa)

Propor�on lapped

Fig. 11. Influence of proportion of bars lapped on measured lap strength

0

50

100

150

200

250

300

350

400

450

0,00 0,50 1,00 1,50 2,00

Lap

Str

engt

h (M

Pa)

Stagger/lap length

Fig. 12. Influence of stagger distance on measured lap strength

in confinement between staggered and non-staggered laps,and also for minor variations in concrete strength and laplength, further analysis of the results is based on “lapstrength ratio”, i.e. the ratio of measured lap strength tothat estimated by Eq. (2), as listed in the penultimate col-umn of Table 2. Where laps do not overlap, i.e. where thestagger distance as is at least one lap length, details (c) and(f) in Fig. 9, the transverse spacing between lapped bars iscalculated as if the transverse section were repeated later-ally, i.e. clear spacing cs = b – 2φ. Where laps do overlap,details (a), (b), (d) and (e) in Fig. 9, the clear spacing is calculated on a section within the overlap length, cs =(b – 2cx – 2.nb.φ)/(nb – 1), where nb is the number oflapped pairs.

Fig. 13 plots the variation in lap strength ratio withstagger distance as for all specimens. There is no signifi-cant difference between laps with no stagger and laps stag-gered by half a lap length, nor between laps staggered byone and one-and-a-half lap lengths. Taking account of dif-ferences in confinement, staggering laps by one lap lengthor more reduces lap strength by about 20 %. Note that on-ly those specimens listed as having a stagger distance inexcess of 1.3 would be considered to qualify for a reducedα6 coefficient according to EC2.

None of the failures were ductile, although failurewas less brittle where fewer bars were lapped at a section.The deformability index Dres increased from an average of

52



0.4 where laps were not staggered or partially staggered to0.6 when laps were staggered, Fig. 14. However, the exper-imental design resulted in an inverse correlation betweendensity of transverse reinforcement and proportion ofbars lapped at a section. Confining reinforcement is wide-ly recognized to restrain the brittleness of lapped joints,and hence the parameter responsible for the improvementin ductility cannot be ascertained with confidence fromthese tests.

7 Discussion of results

This investigation raises doubts regarding the perceivedadvantages of lapping only a portion of bars at a section.The results presented here suggest that differences in thedistribution of bond stress and the share of load taken bylapped and continuous bars result in either no gain instrength or a reduction of up to 20 % when laps are stag-gered, depending on the basis for the comparison. The ap-parent reduction is based on the assumption that all barsare stressed equally, which the analyses shown in Fig. 8demonstrate to be incorrect. The brittle nature of the split-ting mode of bond failure means that, as a lap fails, stress-es in lapped bars drop before continuous bars reach yield.However, it is not possible to determine the stresses thatactually develop in lapped bars without strain measure-ments on individual bars.

Although failures were less brittle when laps werestaggered, it is not clear whether this can be attributed tothe staggering of the laps or to differences in the density oftransverse reinforcement, and lap failure remained non-ductile in all cases.

The lap lengths tested here were less than those re-quired to develop the design strength of the reinforce-ment, far less the actual yield strength. As lapped bars aremore highly strained than continuous bars at the ends ofthe lap, Fig. 8, they would have to achieve strains in excessof yield before continuous bars can reach yield. Bond re-duces where bars are strained above yield. Differences be-tween staggered and non-staggered laps might thus be ac-centuated in full-strength laps.

The fib Model Code 2010 introduced clear spacingbetween bars as an additional parameter in the design oflaps and anchorages, Eq. (2). This permits shorter laps inslabs and walls where bars are widely spaced. Clear spac-ing between lapped pairs is increased where only a pro-portion of bars is lapped at a section, and increases con-finement to lapped bars and hence their bond resistance.It is not known whether this was recognized and utilizedwhen the proportion lapped rules in MC90 and EC2 wereformulated, but there remains a possibility that the “pro-portion lapped” provisions are implicitly linked to clearspacing. Permitting lap length to be reduced for both in-creased spacing and for proportion lapped would doublecount the spacing effect. The proportion lapped coeffi-cient should therefore be discontinued as a consequenceof introducing the cmax/cmin parameter in Eq. (2).

Ends of lapped bars act as stress concentrators andthere are concerns that larger crack widths form when allbars are lapped at the same location. Flexural crack widthis related to the stresses in the bars. As discussed above,staggering of laps results in lapped bars carrying a dispro-

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

Duc

�lit

y In

dex

Dre

s

Stagger distance as/lo

Fig. 13. Influence of stagger distance on lap strength ratio

Fig. 14. Influence of stagger distance on ratio of measured lap strength tothat estimated from EC2

53



portionate share of tension at the ends of laps, hence stag-gering could lead to increases in the widths of transversecracks at the ends of laps. Although this has not been in-vestigated experimentally here, it is thought likely thatstaggering of laps according to EC2 provisions would re-sult in wider cracks. If laps were partially staggered, how-ever, i.e. if as < lo, strains in continuous bars at ends of lapswould be lower, probably resulting in lower crack widths.

It was mentioned in the introduction that the greaterlength of staggered lap zones may impede construction.There would be advantages for construction if currentrules for staggered laps in EC2 were modified to permitstagger distances to be reduced below 1.3 times the laplength. Results from this study suggest that stagger dis-tances of half a lap length where 50 % of bars are lapped(and by implication, stagger distances of one-third of a laplength where 33 % of bars are lapped) would result in lapsas strong as those designed to current requirements with astagger of 1.3lo, but with smaller flexural crack widths atends of laps. The results here suggest that a reduction inlap strength due to a smaller clear spacing between lappedpairs when laps are partially staggered or not staggeredwould be offset by increases associated with changes inthe distribution of bond stresses. Further research into al-ternatives to current rules for staggered laps would there-fore be worthwhile.

8 Summary and conclusions

Design codes, including EC2 and ACI 318, encourage stag-gering of lapped joints. The requirements to staggerlapped joints increase the complexity of detailing and steelfixing, may consume additional resources and slow downconstruction on site. Although coefficients for proportionlapped are at least as influential as those for any other pa-rameter, minimal research has been carried out on stag-gered laps and the origin of current rules is obscure.1. Staggering of laps does not increase lap strength de-

spite an increase in clear spacing between pairs oflapped bars.

2. When allowance is made for the difference in clearspacing between staggered and non-staggered laps,staggering was found to reduce lap strength.

3. Differences in the share of tension force taken by con-tinuous and lapped bars is thought to be responsiblefor the difference in strength observed experimentally.

4. Although brittleness was reduced when laps were stag-gered, it is unclear whether this is due to staggering orto transverse reinforcement.

5. Further work on staggered laps capable of developingstresses exceeding the design strength of the reinforce-ment is recommended.

The conclusions here are limited to the relationship be-tween lap lengths for staggered and non-staggered lapsand not to bond strengths for design purposes. Specifical-ly, the conclusions presented here must not be regarded asjustification for omitting the proportion lapped coefficientα6 from design calculations to EC2 or setting it at a value< 1.5 where all bars are lapped at the same section. A fur-ther paper to review the overall safety level of EC2 rulesfor design of lap length is in preparation.

ACI 318 also allows shorter lap (splice) lengthswhere laps are staggered. Unlike EC2, a further conditionis applied which limits the design stress in the bars to amaximum of 50 % of their design strength. These ruleswould appear to be justifiable on the basis that lightlystressed laps would only be required to develop the fullstrength of a bar under accidental loading conditions, inwhich case a lower factor of safety would be acceptable.

Acknowledgements

The author wishes to acknowledge the contribution of A.Hutt, M. Angelov, L. Gillon and G. Sorley to the experi-mental work reported here.

Notation

As cross-sectional area of main barAsv area of each leg of a linkcmax, cmin minimum and maximum concrete dimensions

as defined in Fig. 1fb average bond stress over bond length lbΔfs change in bar stress over bond length lbfcm mean concrete cylinder compressive strengthfcu measured concrete cube compressive

strengthfs,m, fs bar stresses at centre and ends of lap respec-

tively.fstm, fy stress developed in bar (mean value) and yield

strength respectivelyKtr density of confining reinforcement,

Ktr = nl · ng · Asv/(lb · φ · nb) ≤ 0.05lo lap lengthng number of groups of links within lap lengthnl number of legs of a link in each groupnb number of pairs of lapped barskm “effectiveness factor” for link confinement,

km = 12 for bars confined by a link passingthrough an angle of 90o

εs,c, εs,l axial strains in continuous and lapped bars respectively

φ nominal bar diameterρlap proportion of bars lapped at a section

References

1. BS EN 1992-1-1:2004: Eurocode 2: Design of concrete struc-tures – Part 1-1: General rules and rules for buildings. BritishStandards Institution, London.

2. CEB-FIP Model Code 90. CEB, Lausanne, 1993.3. ACI 318-11: Building Code Requirements for Structural Con-

crete and Commentary. American Concrete Institute, Michi-gan, USA, 2011.

4. fib Model Code 2010 – Final draft, vol. 1. Model Code, ISBN978-2-88394-105-2, Mar 2012.

5. Magnusson, J.: Bond and anchorage of ribbed bars in high-strength concrete. PhD thesis, Division of Concrete Struc-tures, Chalmers University of Technology, Gothenburg, Swe-den, 2000.

6. Ferguson, P. M., Briceno, E. A.: Tensile lap splices part 1: Re-taining wall type varying moment zone. Research Report113-2. Centre for Highway Research, University of Texas atAustin, Jul 1969.

7. Thompson, M. A., Jirsa, J. O., Breen, J. E., Meinheit, D. F.:The behaviour of multiple lap splices in wide sections. Re-search Report 154-1, Centre for Highway Research, Univer -sity of Texas at Austin. Jan 1975.

8. Metelli, G., Cairns, J., Plizzari, G.: Influence of bar continuityon behaviour of lapped splices. Precast Concrete Institute,Chicago: No. 102, Proc. of 3rd International fib Congress &Exhibition: Think Globally, build locally. 29 May–2 Jun2010, Washington, USA.

9. Cairns, J.: Lap splices of bars in bundles. ACI Structural Jour-nal, vol. 110, No. 2, Mar 2013, pp. 183–192.

10. Zuo, J., Darwin, D.: Splice Strength of Conventional andHigh Relative Rib Area Bars in Normal and High-StrengthConcrete. ACI Structural Journal, vol. 97 No. 4, Jul 2000, pp.630–641.

11. Canbay, E., Frosch, R. J.: Bond Strength of Lap-Spliced Bars.ACI Structural Journal, vol. 102, No. 4, Jul 2005.

12. Cairns, J., Jones, K.: The splitting forces generated by bond.Magazine of Concrete Research, vol. 47, No. 171, Jun 1995,pp. 153–165.

13. http://www.lusas.com/products/civil_tour_overview.html.

54



14. BS 4449:2005+A2:2009: Steel for the reinforcement of con-crete. Weldable reinforcing steel. Bar, coil and decoiledproduct. Specification. British Standards Institution, Lon-don.

15. BS EN 206-1:2000: Concrete. Specification, performance,production and conformity. British Standards Institution,London.

16. fib Bulletin: Background to provisions for laps and anchor-ages in the fib Model Code 2010 (in preparation).

John CairnsHeriot-Watt UniversityEdinburgh EH14 4AS, [email protected]


Shear failures in reinforced concrete structures under intensedynamic loads are brittle and limit the structure’s energy-absorb-ing capabilities. This paper comprises a review of the literaturedealing with the problem of dynamic shear of reinforced concreteelements, with a focus on parameters that control flexural shearand direct shear. In this context, dynamic loads refer to intenseevents due to explosions and impacts. For this reason, the initialresponse is also highlighted. Experimental investigations and cal-culations show that shear force and bending moment distribu-tions in dynamic events are initially significantly different from thedistributions under slowly applied loads. Therefore, structuralwave propagation, geometrical properties of elements, strain rateeffects and dynamic load characteristics need to be consideredwhen analysing shear. The review also indicates that arch actionin the shear span soon after the load has been applied has alarge influence on the shear capacity of an element. This actionis of particular importance in intense loading events. Finally, suggestions for further research are identified.

Keywords: dynamic loads, impulsive loads, rise time, shear, initial response,support reactions, arch action

1 Introduction

Dynamic loads such as explosions can cause severe dam-age to concrete structures. An explosion in air is the resultof detonating explosive charges, the rapid combustion of afuel-air mixture or bursting pressure vessels. The explo-sion generates a blast wave that propagates through the airat supersonic velocity in all directions. As the blast wavestrikes an object such as the wall of a building, the pres-sures are reinforced due to reflections. In a case where thereflected pressures are sufficiently high, local failures ofstructural elements such as loadbearing walls or columnscan occur.

In the design of concrete structures to resist the ef-fects of blast loads, impacts or other severe dynamic loads,it is not practical to consider a structural response in theelastic range only. The structural elements should there-fore be allowed to deform plastically, which better utilizestheir energy-absorbing capabilities. A certain amount of

damage, i.e. concrete cracking and yielding of the rein-forcement due to flexure, is therefore usually accepted inthe design of structures to resist blast loads. Structural ele-ments should generally be designed for a flexural re-sponse. However, real events [1] have shown that highlyintense loads from blasts at close range can cause localshear failures in concrete structures, which is a brittlemode of failure. In the Oklahoma City bombing, two con-crete columns were reported to have failed in shear. Apartfrom real events, shear failures in concrete elements havealso been observed experimentally in several investiga-tions involving blast and impact loads [2–7]. In several cas-es these tests confirm that elements that fail in flexure un-der a slowly applied (quasi-static) load may fail in shearunder dynamic loads.

The purpose of the present paper is to conduct a re-view of the literature on the shear problem of reinforcedconcrete structures subjected to intense dynamic loadsand to identify areas for further research. In this context,dynamic loads refer to intense events due to explosionsand impacts. The review focuses on behavioural aspects ofdynamic shear and on the parameters that control themode of failure. Highlighting the initial response of con-crete elements under dynamic loads represents another fo-cus. The modes discussed here are flexural shear and di-rect shear. A third mode of shear failure is punching shear.This type of failure can occur as an object impacts on aconcrete surface with inclined shear cracks and the forma-tion of a conical shear plug through the thickness of theconcrete element [8]. However, dynamic punching shear isoutside the scope of this paper.

2 Quasi-static shear

Shear failure in reinforced concrete elements can general-ly be related to flexural shear and direct shear. In princi-ple, flexural shear and direct shear exhibit similar funda-mental behaviour since they share many features such asthe mechanisms that transfer shear across a crack. Thesemechanisms are friction, aggregate interlock and the dow-el action of the longitudinal reinforcement. Flexural shearoccurs at locations where both shear and flexural stressesexist. This failure mode is characterized by an initial flex-ural crack that, under the action of an increasing load, de-velops into a crack inclined with respect to the longitudi-nal axis of the element, see Fig. 1a. These inclined cracks

Technical Paper

Shear in concrete structures subjectedto dynamic loads

Johan Magnusson*Mikael HallgrenAnders Ansell

DOI: 10.1002/suco.201300040


Submitted for review: 11 June 2013Revised: 7 August 2013Accepted for publication: 7 September 2013

appear in regions of high shear forces and are due to theprincipal tensile stresses that occur in the element. Flexur-al shear typically occurs in beams carrying point loadswith a shear span to effective depth ratio a/d = 3–7 [9]. Incases where the load is located closer to the support, thediagonal crack can be initiated in the region of the neutralaxis of the element, such as in the webs of flanged beams,or in cases with a/d < 2.5 for rectangular cross-sections [9],see Fig. 1b. In this case failure is due to crushing or split-ting of the compressive strut that develops between theload and the support.

Direct shear failure is characterized by a sliding typeof failure along a well-defined plane (the shear plane)through the depth of the element. This type of shear fail-ure typically occurs at concentrated loads close to the sup-ports. In the case of elements subjected to quasi-staticloads, direct shear can only be critical for a/d = approx.0.5 or less under a concentrated load condition [9], see Fig.1c. The failure mechanism of direct shear is different ininitially uncracked and cracked concrete. In the latter casethe shear transfer mechanism will be due to aggregate in-terlock and the dowel action of the longitudinal reinforce-ment. Shear transfer for initially uncracked concrete willcause several short diagonal tension cracks to developalong the shear plane [10]. Shear failure will occur whenthe concrete struts fail under the combined action of com-pression and shear, or when the local shear stresses at theends of the struts reach a critical value.

3 Dynamic shear3.1 Characteristics of dynamic loads

Shear failure of concrete elements may occur due to theintensity of the dynamic load. The intensity of a load gen-erally refers to its rise time and its peak value. It is wellknown that the flexural response of elements to dynamicloads depends on the rise time and the applied peak withrespect to the natural period of vibration and the resis-tance of the element [12, 13]. Fig. 2 shows an idealizedrepresentation of a blast wave profile, illustrated with thetime axis at ambient pressure, at a given distance from thecentre of an explosion in air. The arrival of the blast wavecreates an almost instantaneous increase from ambientpressure to the peak overpressure and is immediately fol-lowed by an exponential decay to ambient pressure. Thisfirst part of the blast wave is termed the positive phase,which is normally the only phase of interest whenanalysing blast-loaded structures. The second part of the

56

J. Magnusson/M. Hallgren/A. Ansell · Shear in concrete structures subjected to dynamic loads


blast wave, termed the negative phase, may be of impor-tance for windows and for the flexural behaviour of wallsexposed to explosions at close range. However, for the pur-pose of the present paper, any influences of the negativephase on shear are not included. Blast waves have an al-most indefinitely small rise time, e.g. a fraction of a mil-lisecond [14], whereas loads from objects impacting on aconcrete element typically have rise times of about onemillisecond [4, 15]. This applies to impact velocities ofabout a few metres per second. Another way of describingthe load variations over time is to refer to their frequencycontent. Accordingly, a short rise time can be regarded asa load containing a large number of frequencies as op-posed to a load with a longer rise time.

When considering intense dynamic loads such asblast loads, it is convenient to relate their duration to thenatural period of vibration T of the element in question.Impulsive loads are typically of short duration in relationto the natural period of vibration of the loaded elementand have high amplitudes. It is suggested in [13] that aload can be regarded as impulsive if the duration is < 0.1times the natural period of the system. Due to this shortduration, no significant deflections take place during thisperiod of time. Explosions close to a wall and impacts aretypically regarded as impulsive loads.

3.2 Dynamic flexural shear

Several studies have shown that concrete elements thatfailed in flexure under a slowly applied load could fail inshear under a dynamic load. Flexural shear failures have

Fig. 1. Schematic views of flexural shear (a), web shear (b) and direct shear (c)

Fig. 2. Idealized blast wave profile at a given distance from centre of explo-sion with overpressures on vertical axis (time axis at ambient pressure)

57



been observed in investigations involving blast waves [5,7]. Fig. 3 shows one of the beams that failed in flexuralshear. In this case the beam was subjected to an evenlydistributed blast load over its top surface [5]. The first au-thor of the present paper performed numerical simula-tions of several of the tests in [5] using the Ansys-Autodynsoftware [16]. A sequence was extracted from these simula-tions to show the development of the diagonal shearcrack, see Fig. 4. This figure shows that flexural shear fail-ures in dynamic events follow the same series of events asin the case of quasi-static loads. Thus, a certain amount offlexure occurs prior to the development of inclined shearcracks. Blast tests on concrete beams have shown that rel-atively large reactions were registered before any notice-able deflections were measured, suggesting that the beamwas initially subjected to large shear forces [17].

Flexural shear has also been observed in investiga-tions involving impact loads on concrete beams [3, 4, 6].The tests performed in [4] involved impact tests on simplysupported reinforced concrete beams. In these tests therise time and amplitude of the load were controlled byplacing rubber pads between the striking mass and thebeam in the impact zone. Thus, for the same applied ener-gy level, the magnitude of the applied load could be re-duced and the rise time increased to create a softer im-pact. The tests showed that flexural failure occurred whena beam was subjected to a soft impact, whereas beams sub-jected to harder impacts failed in flexural shear. These

tests were performed with the same impacting speed andmass. A similar observation was made in [15] (see also [3]),where the harder impact resulted in flexural shear failure.Thus, these findings show that the failure mode of a con-crete beam may depend on the frequency content of theapplied load.

According to [3, 4], a dynamic load with high fre-quency content excites higher vibration modes in an ele-ment compared with the case with a slowly applied load.Thus, as higher modes are excited, a larger portion of thestrain energy is due to shear rather than flexure. The firstfree vibration modes of a simply supported beam areshown in Fig. 5. A quasi-static load cannot affect the ele-

Fig. 3. Test on reinforced concrete beam resulting in flexural shear failure [5]

Fig. 4. Simulation sequence of propagation of diagonal cracks at 2.0, 2.5 and 4.0 ms after blast load was applied (sequence extracted from simulation S40d in [16])

Fig. 5. First free vibration modes of pin-ended simply supported beam

ment any more than in its fundamental mode and theshear forces in the element are therefore limited. Besidesthe rise time, the magnitude of the load is also important,i.e. high shear forces occur for loads with high magnitudes.

Several investigations have also shown that the beamstiffness plays an important role in the failure mode. A pre-vious literature review [19] showed that a majority of thetests on concrete beams with a relatively high reinforce-ment content and subjected to dynamic loading exhibitedshear failures, whereas beams with lower reinforcementcontents failed in flexure. The results in [4–6, 20] supportthese findings. The shear forces occurring in a stiff ele-ment are higher than those in a softer element under dy-namic loading. Furthermore, concrete and steel reinforc-ing bars exhibit increased strength in tension andcompression when subjected to dynamic loads – common-ly known as strain rate effects [21–23]. Owing to these ef-fects, a concrete element will become stiffer under dynam-ic loading and may therefore become more susceptible toshear failures.

3.3 Dynamic direct shear

As previously mentioned, direct shear failures can occur inuncracked elements at locations near a support when astatic load is applied in its proximity. However, tests haveshown that concrete elements can also fail in a directshear mode under the action of an intense dynamic loaddistributed along the length of the element [2]. In thesetests the roofs of reinforced concrete box structures weresubjected to loads from detonating explosive charges. Thebox structures were cast monolithically with two openends and, for one series of tests, with dimensions and rein-forcement as shown in Fig. 6. The roof slab did not haveany prior crack planes through its thickness. The test re-sults show that the slabs failed in direct shear in severalcases and that the slabs were completely severed from thewalls along vertical failure planes. Most of the slab rein-forcing bars were pulled out of the wall, with a few brokenbars exhibiting minor necking. It was further observed inseveral tests that the central portion of the roof slab re-mained relatively flat, as though no flexural deformationshad taken place (shown schematically in Fig. 7).

58



Little is known about the actual fracturing and directshearing process in dynamic events and therefore it wasassumed in [14] that the direct shear failure in the dynam-ic case behaves in accordance with the shear transfermechanism under quasi-static loading conditions. It wasstated in [14] that the direct shear failure of the roof slabsis characterized by the rapid propagation of a verticalcrack through the element depth. Since direct shear is as-sociated with crack planes perpendicular to the longitudi-nal axis of the element, such failures are also possible inelements designed for flexural shear. Failure curves for re-inforced concrete elements were developed in [14] andused in a parametric study of direct shear failures, seeFig. 8. The failure curve is unique for the specific elementin question such that a family of curves could be generat-ed for elements with different properties. A failure curve isconstructed such that the combined values of pressureand rise time below the curve relate to no failure, and val-ues above the curve relate to direct shear failure. The in-crease in pressure for an increasing rise time implies thatthe element is able to resist direct shear at higher pressurelevels if the load is applied more slowly. The shape of thefailure curve also indicates that for very small rise times,in this case < 0.1 ms, the maximum pressure appears to beapproximately constant.

The analyses in [14] indicate that the resistance to di-rect shear increases as the element span to effective depthratio L/d for uniformly distributed loads increases. How-ever, the influence of L/d diminishes for small rise timesand disappears at rise times close to zero. Another case isthe comparison between elements with fixed support con-ditions and reduced end restraints. Two failure curves

Fig. 6. Concrete box structure used in direct shear tests [2] (courtesy of U.S. Army Engineer Research Development Center)

Fig. 7. Illustration of a post-test view of a slab (based on test DS2-3 in [2])

59



were generated and the difference between these curvesdiminishes for small rise times. Further results in [14] sug-gest that strength enhancement due to strain rate effectsincreases the shear resistance such that the entire failurecurve is shifted upwards. Thus, even for the case with zerorise time, the failure curves do not coincide. It was alsomentioned in [14] that the load duration does not affectthe direct shear failure curve significantly. Other investiga-tions have involved theoretical analyses of the direct shearmode of concrete elements [24–26]. However, this work isnot the focus of the present paper.

4 Initial response of concrete elements subjected to dynamic loads

4.1 Initial response

Under quasi-static loads, material fractures such as cracksin concrete are initiated and propagate according to thestress and strain fields existing throughout the concrete el-ement. The weakest elements will thus govern the loca-tions and levels of cracking in these strain fields. However,under dynamic conditions, local regions with high stressesand strains can develop and their location may change be-fore an initiated crack has time to propagate. Owing tosuch conditions, wave propagation effects become increas-ingly important in the analyses of dynamically loadedstructures. Shear failures typically occur at an early stage,before any appreciable deformations have taken place. Itis therefore of interest to analyse the initial structural re-sponse soon after the load has been applied, with its dis-tribution of displacements, shear forces and bending mo-ments. In this context, a simply supported beam isconsidered subjected to a uniformly distributed blast load.Other researchers have analysed elastic beams using theBernoulli-Euler and Timoshenko beam theories [3, 14, 18]and finite element analysis [27, 28]. Initial response has al-so been observed experimentally in [2, 29].

The Bernoulli-Euler equation for the forced vibra-tions of a linear elastic beam only allows for flexure andtranslatory inertia, i.e. the transverse vibrations of a beam.However, the effects of shear deformations and rotary in-ertia, which are included in the Timoshenko theory, be-come more significant as the number of modes excited in-creases. The work in [30] shows that the Bernoulli-Euler

theory results in an increasing overestimation of the nat-ural frequency for modes higher than the fundamentalmode, whereas results with the Timoshenko theory arewithin 3 % for the first 11 modes. However, for the purposeof analysing the early response qualitatively and for para-metric studies, the Bernoulli-Euler theory can be used,which also comprised the work in [18]. The Bernoulli-Euler beam equation for a dynamic distributed load q isexpressed as

(1)

where:EI flexural stiffness ρA mass per unit length

When considering a simply supported beam subjected to auniformly distributed load over the beam span and a loadfunction according to Fig. 9, the solution to the beam de-formations becomes [18]

(2)

where:q0 maximum distributed loadκ shape constant for dynamic load L beam span

The time function gn (t) is calculated according to [18]:

(3)

It should be noted that Eq. 2 is valid for the initial condi-tions y(x, 0) = y·(x, 0) = 0. The natural frequencies of thebeam are given by

(4)

Note that with a uniform symmetric load, only the oddmodes contribute to the response [13, 18]. The same loadfunction as in [18] was used and is a suitable approxima-tion of a blast load, see Fig. 9:

(5)

Derivation of Eq. (2) yields the solutions for the bendingmoment and shear force distributions along the beam asin [18]:

(6)

q t q e t0

n

LEIA

2 1n

2 2

2

g t e sin t cos tnt

nn n

�

y x tq LEI

sin n xL

n

g t, · 42 1

2 1 · 1

· ( )n

n

n0

4

51 5

2

EI yx

A yt

q x t( , )4

4

2

2

M x t q Lsin n x

L

n

g t, · 42 1

2 1 1

· ( )n

n

n02

31 3

2

�

Fig. 8. Failure curve for direct shear of a concrete element with fixed support conditions (diagram based on analyses in [14])

60



(7)

The calculations were performed for a concrete beam withthe same dimensions as in tests performed previously [5],i.e. with a depth of 160 mm, a width of 300 mm and a spanof 1.5 m. Using a value of 30 GPa for the elastic modulusof concrete results in EI = 3.07 MNm2. The ratio κ/ω1 wasset to 4.0, which results in a load duration of approx. 0.25times the natural period of vibration of the beam. Plottingthe solutions for deflections, moments and shear forces at different times after the load has been applied and for

V x t q L ·cos n x

L

n

g t, 42 1

2 1 1

· ( )n

n

n0 21 2

2

�

Fig. 9. Load function used in the calculations

Fig. 10. Calculated deflected shapes at different times for a simply supported beam subjected to a uniformly distributed blast load

Fig. 11. Calculated distribution of bending moments at different times for a simply supported beam subjected to a uniformly distributed blast load

61



the first 15 odd modes yields diagrams as shown inFigs. 10–12. Note that the vertical axes of these figures arenormalized to the corresponding static quantities suchthat ystat, Vstat and Mstat are calculated as

(8)

(9)

(10)

The signs for the deflections, moments and shear forces inFigs. 10–12 correspond to the case with a horizontal beam

Mq L

8stat0

2

yq L

EI5385stat

04

Vq L2stat0

subjected to a vertical downward dynamic load. It was ob-served that the y/ystat, V/Vstat and M/Mstat ratios becomerather small. The reason is the rapid decay in the dynamicload compared with a static load having the same amplitude,which is constant over time. In a case with a more gradualdecay, i.e. small κ values, the duration of the applied load in-creases and the corresponding deflections, shear forces andbending moments also increase. For a suddenly applied con-stant load with an instantaneous increase to peak pressure,typically a rectangular-pulse load of infinite duration, the ra-tios in question eventually become equal to 2 after a certaintime. This is a well-known feature for linear elastic systemssubjected to these types of load and can be shown using en-ergy relations [13, 18]. Furthermore, even though the calcu-lated ratios are small, the shear forces and moments may ex-ceed the corresponding capacities of the beam.

Fig. 12. Calculated distribution of shear forces at different times for a simply supported beam subjected to a uniformly distributed blast load

Fig. 13. Calculated shear distribution over half the beam span for vibration modes 1, 3, 5 and 7 at ω1t = 0.025

A concrete beam subjected to dynamic loads will ini-tially exhibit deformations, shear forces and bending mo-ments with significantly different distributions comparedwith the corresponding distributions under slowly appliedloads. Soon after the dynamic load has been applied tothe beam surface, the entire beam – except for the partsadjacent to the supports – will be accelerated in the direc-tion of the load. At this point in time, the remaining partsof the beam will be subjected to a rigid body motion with-out any deformations, see Fig. 10. As time progresses, thestrains and stresses in terms of flexure and shear in thevicinity of the supports will be distributed to the remain-ing parts of the beam through structural wave motionsand the beam will gradually acquire a deflected shape thatcorresponds to the first mode of vibration. Shear forcesand bending moments will also initially occur locally atthe supports and their distributions will also change overtime through the propagation of flexural and shear wavestowards mid-span, see Figs. 11–12. Owing to this wavepropagation, the shear and moment distributions willeventually become similar to those of a quasi-static mode.Fig. 12 shows that relatively large shear forces also occurat approximately points L/3 and 2L/3 at an early time.This figure also shows that the shear force changes sign ata later time and that the shear distribution gradually ap-proaches the distribution for static loads. This occurs atapprox. ω1t = 1. The calculated initial moment distribu-tion in Fig. 11 indicates that yielding of the tension rein-forcement in regions close to the supports can occur un-der a sufficiently intense load.

Fig. 13 shows how the calculated first four oddmodes contribute to the shear forces at an early time(ω1t = 0.025). It is clear from the figure that the highermodes significantly contribute to the build-up of shear atthe supports compared with that of the fundamentalmode. At this early time, the contribution of the first modeis close to zero because both deflected shape and momentdistribution are different from the corresponding staticdistribution. However, as time progresses, the contributionof this mode increases and eventually becomes the domi-nant mode of response.

4.2 Arch action in the shear span

For concrete beams, it is well known that a part of the ap-plied load is carried through arch action between the ap-plied load and the support [11]. This action becomes in-creasingly pronounced as the distance between the loadand the support decreases, i.e. with reducing shear slen-derness, defined as shear span to depth ratio. Arch actionalso develops for beams under uniform loads, only in thiscase the shear slenderness is defined as the beam span todepth ratio. It has been observed that the shear force atfailure increases at a/d = approx. 2.5 for beams subjectedto point loads and at L/d = 10 for uniform loads [31]. Theeffect of this arch action was originally included in theguidelines [32] and has also been incorporated in [33] inthe design of concrete structures subjected to blast loadsfor a/d ≤ 1.5. This method makes use of the initial re-sponse of elements with shear forces concentrated in thevicinity of the supports, and the fact that large portions ofthe element are initially displaced as a rigid body. The

62



shear span ατ for a simply supported element is calculatedin [33] as

(11)

where:L beam spanqd element static resistance without strain rate effectsp peak overpressure

Using the calculated shear slenderness it is possible to de-termine a certain enhancement of the shear capacity of anelement. This method accounts for the positive effect ofthe arch action and that a certain amount of the load istransferred directly to the supports.

4.3 Dynamic support reactions

Knowledge of the dynamic support reactions is of impor-tance because these can be related to the shear forces thatoccur in the element near the supports during the loadingand deflection event. The most common way of determin-ing the reactions is by considering the dynamic equilibri-um of the element, see Fig. 14 [13]. For a beam with a con-stant cross-section, the inertia has the same distribution asthe assumed deflected shape. The expression for the reac-tion V(t) becomes

(12)

where:R dynamic resistance (includes strain rate effects of

reinforcement and concrete)F total applied loadχR constant for resistanceχp constant for applied load

Thus, the dynamic reaction is a function of both the dy-namic resistance and the total applied load. The dynamicresistance R is defined as

(13)

where:M dynamic bending moment capacity

aL

qp

0.025 0.25 · d

V t R t F t· ( ) · ( )R p

R ML

8

Fig. 14. Distribution of inertia force for a simply supported beam subjectedto a uniform dynamic load (based on [16])

63



The constants χR and χp depend on the assumed deflectedshape of the beam. For the elastic response of a simplysupported beam, the values of these constants are 0.39and 0.11 respectively. During a pure plastic responsewhere the beam is assumed to deform as two rigid bodieswith a plastic hinge at mid-span, the corresponding valueschange to 0.38 and 0.12. Values for the constants are list-ed in [13] for beams and slabs with other load distributionsand support conditions. If the element survives the initialshear and continues to deflect, the response will eventual-ly become plastic, with cracking of the concrete and theformation of a plastic hinge around mid-span. Once theplastic hinge has formed, the maximum element resistancewill soon develop and the reactions are therefore limited.Furthermore, since R in Eqs. (12) and (13) refers to the dy-namic resistance, it is evident that this contributes to larg-er shear forces in the element, as discussed in section 3.2.

Eq. (12) indicates that the applied load is the domi-nant contributor to the reactions at an early time since theelement resistance has had no time to develop. Thus, inthe case of impulsive loads with comparatively high ampli-tudes, the reactions may exceed the shear resistance of theelement with shear failure being the consequence. At theseearly times of the response, the deflected shape is dramat-ically different from that of the fundamental mode as dis-cussed in section 4.1. As the deflected shape changes withtime during the initial phase, the distribution of inertiaforces must also change with time. Thus, it may be appro-priate to introduce functions that allow variations of χRandχp over time during the initial phase. This method wasadapted in [27, 28]. Other ways of calculating supportshear use numerical simulations, used in the work of [27,34], for instance.

5 Conclusions5.1 Summary and discussion

The present paper comprises a review of the literaturedealing with the problem of the dynamic shear of rein-forced concrete elements, with a focus on parameters thatcontrol shear. For this reason, the initial response was alsohighlighted. In dynamic events, high stresses and strainscan occur locally in the structure for short periods of time.The effects of structural wave propagation and strain rateas well as dynamic load characteristics therefore need tobe considered in shear analyses. From the present reviewit can be generally concluded that shear in concrete ele-ments depends on load characteristics, element parame-ters and support conditions. These three areas will bebriefly summarized and discussed below.

Load characteristics that were found typically tocontribute to shear are peak load and rise time. These pa-rameters are important in both flexural and direct shear.The typical characteristics of impulsive loads are highpressures, small rise times and short durations, which iswhy such loads contribute to large shear forces in thestructure. The load duration was reported in [14] as nothaving a significant influence on direct shear, which is areasonable statement since direct shear occurs at an earlytime. However, the load duration may have some influ-ence on flexural shear since this mode occurs at a muchlater time. Another aspect of interest may be the load dis-

tribution. Explosions on the ground close to an exteriorwall of a building will subject the wall to unevenly distrib-uted overpressures such that high pressures will occur atground level with diminishing pressures in the horizontaland vertical directions. The lower supports will thereforebe exposed to larger shear forces compared with those further up. Further analysis of this loading scenario and its influence on shear would therefore be of interest. Inthis context, also interesting would be to include the dynamic support reactions that occur for impulsive typesof loads.

It was also concluded that structural parameters im-portant to shear were element resistance and stiffness, L/dratio and strain rate effects. Higher stiffness and resistancecontribute to larger shear forces in the element comparedwith a softer element with a lower resistance. The L/d ra-tio has the same influence on shear such that low ratiosgive rise to larger shear forces compared with larger L/dratios. Strain rate effects in the concrete and reinforcingsteel also contribute to stiffer elements. The support con-ditions influence the element stiffness such that fixed-endbeams will subject the element to larger shear forces com-pared with simply supported beams. These findings re-garding stiffness can also be related to the fact that a stiffelement exhibits higher natural frequencies comparedwith softer elements, which leads to larger shear forces.

The results shown in Figs. 10–13 are for a purely elas-tic response, and as soon as cracks are initiated and startto propagate in the concrete the response will change dueto the reduced flexural stiffness. This makes the use ofnon-linear finite element analysis a suitable tool foranalysing the influence of cracks on the initial response. Itwould also be of interest to investigate the influence oflarge moments that initially appear close to the supports.A layered beam model and modified compression fieldtheory were used in [35] to predict the interaction betweenmoment and shear that occur simultaneously in a section.These analyses indicate that at locations where a momentexceeded half the ultimate moment, the section was un-able to develop its ultimate shear capacity. This impliesthat at locations where both high moment and shear occursimultaneously, shear failure can occur at values lowerthan the ultimate shear resistance. For a simply supportedbeam this combination of high shear and moment maynever occur, see Figs. 11–12, but could, on the contrary, bethe case for a beam with fixed support conditions. It wouldtherefore be interesting to include this moment-shear in-teraction in further research.

Arch action in the shear span will always be presentto a certain degree when a concrete element is subjectedto out-of-plane loads. In dynamic events this arch actiondistributes a portion of the large initial loads directly tothe supports, especially during the initial response. The el-ement may therefore be regarded as temporarily respond-ing with an apparently low shear slenderness (L/d for dis-tributed loads). Wave propagation effects over time willchange the shear distribution, eventually becoming similarto that of quasi-static loading, and the apparent shear slen-derness will increase. Thus, the initial positive effects onthe flexural shear capacity of a small shear slendernesswill gradually diminish over time. Since the shear slender-ness is regarded as constant in [33], it would be of interest

to analyse further its gradual change during the initial re-sponse phase.

5.2 Suggestions for further research

Due to the complexity of initial shear in concrete struc-tures subjected to suddenly applied loads, further researchto gain a better understanding of this area would be worth-while. Such research may serve as a basis for the develop-ment of design recommendations or for providing guid-ance for upgrades to existing structures.

The origin of initial arch action in the shear spanshould be included in further research. The use of non-lin-ear simulation is a useful tool when analysing the develop-ment of the arch mechanism and the gradual change inthe apparent shear slenderness over time. Such workshould also include the influence of support conditions,element stiffness and load distributions. Furthermore,large moments and shear forces that occur simultaneouslyin a section may limit the shear capacity of an element. Itwould therefore be of interest to include the moment-shear interaction for different support conditions in futureresearch. Another area of interest is further analysis of themagnitude of the dynamic reactions for impulse-typeloads. Since such loads typically have a short duration inrelation to the fundamental mode of vibration, such analy-ses are strongly linked with the initial response of con-crete elements.

Acknowledgements

The work on this paper was carried out at the Division ofConcrete Structures at the KTH Royal Institute of Tech-nology, and was supported financially by Grontmij AB.Their support is gratefully acknowledged by the authors.

References

1. Federal Emergency Management Agency: The OklahomaCity Bombing: Improving Building Performance throughMulti-Hazard Mitigation. FEMA 277, 1996.

2. Slawson, T. R.: Dynamic Shear Failure of Shallow-BuriedFlat-Roofed Reinforced Concrete Structures Subjected toBlast Loading. U.S. Army Engineer Waterways ExperimentStation, Technical Report SL-84-7, Vicksburg, 1984.

3. Hughes, G., Beeby, A. W.: Investigation of the effect of im-pact loading on concrete beams. The Structural Engineer,vol. 60B, No. 3, 1982, pp. 45–52.

4. Niklasson, G.: (Skjuvbrott i armerade betongbalkar –utvärdering av försöksserie) Shear Failure in ReinforcedConcrete Beams – An experimental investigation. SwedishDefence Research Agency (FOI), report D 20241-2.6, Sund-byberg, 1994 (in Swedish).

5. Magnusson, J., Hallgren, M., Ansell, A.: Air-blast-loaded,high-strength concrete beams. Part I: Experimental investi-gation. Magazine of Concrete Research, vol. 62, No. 2, 2010,pp. 127–136.

6. Kishi, N., Mikami, H., Matsuoka, K. G., Ando, T.: Impact be-haviour of shear-failure type RC beams without shear rebar.Int. Journal of Impact Engineering, vol. 27, 2002, pp.955–968.

7. Morales-Alonso, G., Cendón, D. A., Gálvez, F., Erice, B.,Sánchez-Gálvez, V.: Blast Response Analysis of ReinforcedConcrete Slabs. Experimental Procedure and NumericalSimulation. Journal of Applied Mechanics, vol. 78, 2011.

64



8. Zielinski, A. J.: Concrete Structures under Impact Loading –Rate Effects. Delft University of Technology, report 5-18-14,Delft, 1984.

9. Park, R., Paulay, T.: Reinforced Concrete Structures, JohnWiley & Sons, New York, 1974.

10. Mattock, A. H., Hawkins, N. M.: Shear Transfer in Rein-forced Concrete – Recent Research. Journal of the Pre-stressed Concrete Institute, vol. 17, No. 2, 1972, pp. 55–75.

11. Ansell, A., Hallgren, H., Holmgren, J., Lagerblad, B., Wester-berg, B.: Concrete Structures. KTH Royal Institute of Tech-nology, report 143, 2012.

12. Granström, S. A.: Analysis of Structures Subjected to AirBlast. Swedish Fortifications Agency, Report 103:18, Stock-holm, 1958 (in Swedish).

13. Biggs, J. M.: Introduction to Structural Dynamics, McGraw-Hill, New York, 1964.

14. Ross, T. J.: Direct Shear Failure in Reinforced ConcreteBeams under Impulsive Loading. Air Force Weapons Labo-ratory, AFWL-TR-83-84, Kirtland, 1983.

15. Hughes, G., Speirs, D. M.: An investigation of the beam im-pact problem. Cement and Concrete Association, TechnicalReport 546, London, 1982.

16. Magnusson, J., Ansell, A., Hansson, H.: Air-blast-loaded,high-strength concrete beams. Part II: Numerical non-linearanalysis. Magazine of Concrete Research, vol. 62, No. 4,2010, pp. 235–242.

17. Magnusson, J.: Structural Concrete Elements Subjected toAir Blast Loading. KTH Royal Institute of Technology, licen-tiate thesis, Bulletin 92, Stockholm, 2007.

18. Svedbjörk, G.: Elastic beam subjected to transient load. Mo-ment and shear distributions in time and space. Swedish For-tifications Agency, pub. 42, Eskilstuna, 1975.

19. Palm, J.: On Concrete Structures Subjected to DynamicLoading. Swedish Fortifications Agency, Report A4:89, Eskil-stuna, 1989 (in Swedish).

20. Kamali, A. Z.: Shear Strength of Reinforced Concrete BeamsSubjected to Blast Loading. Non-Linear Dynamic Analysis.KTH Royal Institute of Technology, master’s thesis 368,Stockholm, 2012.

21. Bishoff, P. H., Perry, S. H.: Compressive behaviour of con-crete at high strain rates. Materials and Structures, vol. 24,1991, pp. 425–450.

22. Malvar, L. J., Crawford, J. E.: Dynamic increase factors forconcrete. 28th Department of Defence Explosives SafetySeminar (DDESB), Orlando, FL, 1998.

23. Malvar, L. J., Crawford, J. E.: Dynamic increase factors forsteel reinforcing bars. 28th Department of Defence Explo-sives Safety Seminar (DDESB), Orlando, FL, 1998.

24. Krauthammer, T., Bazeos, N., Holmquist, T. J.: Modified SD-OF Analysis of RC Box-Type Structures. Journal of StructuralEngineering, vol. 112, No. 4, 1986, pp. 726–744.

25. Krauthammer, T., Shahriar, S., Shanaa, H. M.: Response ofReinforced Concrete Elements to Severe Impulsive Loads.Journal of Structural Engineering, vol. 116, No. 4, 1990, pp.1061–1079.

26. Chee, K. H.: Analysis of Shallow Buried Reinforced ConcreteBox Structures Subjected to Airblast Loads. University ofFlorida, master’s thesis, 2008.

27. Ardila-Giraldo, O. A.: Investigation on the Initial Responseof Beams to Blast and Fluid Impact. Purdue University, PhDthesis , West Lafayette, 2010.

28. Andersson, S., Karlsson, H.: Structural Response of Rein-forced Concrete Beams Subjected to Explosions. Time De-pendent Transformation factors, Support Reactions and Dis-tribution of Section Forces. Chalmers University ofTechnology, master’s thesis, 2012:103, Gothenburg, 2012.

29. Menkes, S. B., Opat, H. J.: Broken Beams. Experimental Me-chanics, vol. 13, No. 11, 1973, pp. 481–486.

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30. Adamson, B.: Behaviour of Elastic Beams under Action ofDetonating Charges with Special Reference to Rotary Inertiaand Shearing Forces. Swedish Fortifications Agency, report109:10, Stockholm, 1955 (in Swedish).

31. Leonhardt, F., Walther, R.: Schubversuche an einfeldrigenStahlbetonbalken mit und ohne Schubbewehrung. Deut-scher Ausschuss für Stahlbeton, pub. 151, Berlin, 1962.

32. Swedish Fortifications Agency: Design of protective struc-tures in reinforced concrete against conventional weaponseffects at close range. Pub. 25, Stockholm, 1973.

33. Swedish Fortifications Agency: Design Manual for ProtectiveConstruction. Dnr 4535/2011, Eskilstuna, 2011.

34. Magnusson, J., Hansson, H.: Simulations of Air Blast LoadedStructural Reinforced Concrete Elements. Swedish Fortifica-tions Agency, Report FOI-R—1764—SE, Tumba, 2005.

35. Vecchio, F. J., Collins, M. P.: Predicting the Response of Re-inforced Concrete Beams Subjected to Shear Using ModifiedCompression Field Theory. ACI Structural Journal, vol. 85,No. 3, 1988, pp. 258–268.

Anders AnsellProfessorKTH Royal Institute of TechnologyDepartment of Civil & Architectural EngineeringDivision of Concrete StructuresSE-100 44 Stockholm, Sweden

Johan MagnussonPhD student Grontmij AB, Box 332SE-631 05 Eskilstuna, SwedenE-mail: [email protected]: +46 10 480 2955Fax: +46 10 480 2999

Mikael HallgrenAdjunct ProfessorKTH Royal Institute of TechnologyDepartment of Civil & Architectural EngineeringDivision of Concrete StructuresSE-100 44 Stockholm, Sweden


Technical Paper

DOI: 10.1002/suco.201300027

Using the Hong Kong–Zhuhai–Macao Link project as an example,the focus of this research is to describe the early-age behaviourof a precast immersed tunnel using a constitutive model based onthe degree of hydration concept. In this way, the effect of bothage and temperature on the early-age behaviour can be taken in-to account simultaneously. Special attention is also paid to early-age creep under varying stress levels combined with the degreeof hydration concept. Numerical procedures are proposed to pre-dict the early-age behaviour of immersed tunnel segments duringthe entire fabrication process. The engineering factors related toearly-age cracking are analysed and discussed. This in-depthstudy results in a better understanding, and further appropriatepractical measures can be employed to control early-age crack-ing in the actual project.

Keywords: precast immersed tunnel, early-age cracking, degree of hydration,creep under varying stress levels

1 Introduction

Although the control of early-age cracking in concretestructures is not a new subject, it is still a hot engineeringtopic concerning the growing demand for durable and sus-tainable structures. As far as precast concrete immersedtunnels are concerned, the control of early-age crackingseems to be complex in practice and there are always de-bates when designing or concreting the structures. Engi-neering practice shows that both the material propertiesand construction technology are of prime importance forthis early-age deterioration. For example, immersed tun-nels are normally located in a severe service environmentsuch as exposure to chloride; however, a long service lifeis still required, normally 100 years. Accordingly, this dura-bility requirement leads to a series of countermeasures re-lated to material properties, which normally include theaddition of reactive fillers or the use of a lower water/ce-ment ratio to decrease permeability [1–3]. However, thesemeasures could bring the additional risk of early-agecracking caused by higher heat generation during hydra-tion or larger autogenous shrinkage. Meanwhile, the con-struction scheme has become one of the most influential

factors for early-age cracking; in this respect, casting andcuring temperatures are normally very important forcracking control. For example, in the Øresund Tunnellinking Denmark and Sweden, maximum allowable tem-perature differences of 15 °C were required to prevent ear-ly-age cracking during construction [4]. A requirement of20 °C was specified for the Busan-Geoje Tunnel in SouthKorea [5]. Contrasting with the factory fabricationmethod, the Istanbul Strait immersed tunnel was cast on afloating vessel, and two limiting temperature differenceswere applied, i.e. 8 °C as an allowable difference and 15 °Cas an additional allowance between restrained neighbour-ing parts [6]. Beyond these construction schemes, a debateconcerning the pouring of the concrete is normal whendrawing up the construction plan. Which approach is bet-ter for early-age cracking control: continuous concretingor block concreting? [7]

The above engineering experiences provide insightsinto the early-age behaviour of precast immersed tunnels.In this respect, numerical models are of great use and nor-mally employed to describe the structural behaviour. Forexample, heat-development stress calculations were per-formed for the Øresund Tunnel [4]. An assessment strategywas proposed to reduce the temperature difference duringthe control of early-age cracking in the Busan-Geoje Tun-nel [5]. In the Istanbul Strait immersed tunnel, numericalsimulation was conducted prior to commencement of ac-tual concreting works [3]. In similar research studies,Cervera et al. proposed a numerical model concerningconcrete curing and applied it to the curing on a viaductdeck of the Øresund Link [8]. Lackner et al. developed achemoplastic material model for simulating early-agecracking in a roller-compacted concrete dam [9]. Azenhaet al. predicted the temperature and stress developmentduring construction of the RC foundation to a wind tur-bine tower [10]. Benboudjema et al. also developed a nu-merical model to predict early-age cracking for concretefor nuclear containments [11]. Similar studies have beencarried out by Craeye et al. for the case of concrete super-containers for radioactive waste disposal [12].

The time-dependency of hydration and mechanicalproperties has to be considered for the above analysis.However, the development of the early-age properties ofmaterials also significantly depends on the temperature[13]. Higher temperatures during early age will lead tofaster heat generation, earlier strength, or a higher elastic

Early-age behaviour of precast concrete immersedtunnel based on degree of hydration concept

Xian Liu*Wei JiangGeert De SchutterYong YuanQuanke Su


Submitted for review: 3 May 2013Revised: 25 June 2013Accepted for publication: 9 July 2013

67

X. Liu/W. Jiang/G. De Schutter/Y. Yuan/Q. Su · Early-age behaviour of precast concrete immersed tunnel based on degree of hydration concept


modulus [14]. Therefore, in massive concrete structuressuch as immersed tunnels, different parts with the sameage may have different early-age properties when takingheat transfer and the resulting internal temperature distri-bution into account. Moreover, when it comes to the de-bate about continuous or block concreting, the age-depen-dent model brings difficulties into the correspondingnumerical treatment because different parts will have dif-ferent ages in continuous concreting. In order to modelthe fabrication of precast immersed tunnels accurately,the concept of degree of hydration is adopted in this re-search to ascertain the early-age behaviour of precast im-mersed tunnels.

Based on the thermodynamics of chemically reactiveporous media, the degree of hydration concept was devel-oped to describe the performance of early-age concretemacroscopically [15]. It has been proved to be equivalentto the maturity method [16] and has been verified on themicroscopic scale [17]. As it integrates age and tempera-ture effects, the degree of hydration concept is further in-troduced to analyse the behaviour of concrete structures,with attention given to production processes or environ-mental conditions during early age [18]. So far, most of themechanical properties of early-age concrete and the basiccreep can be successfully described through the degree ofhydration [15, 19, 20], where the basic creep normally fo-cuses on the time-dependent increase in strain in hard-ened concrete subjected to constant stress [21]. However,for massive structures like immersed tunnels, the internalstress is normally caused by temperature-dependent re-strained deformation. Or in other words, the stress insidevaries over the whole construction procedure, and is alsodependent on the concrete creep behaviour under varyingstress levels.

Using the Hong Kong–Zhuhai–Macao Link projectas an example, the focus of this research is to describe theearly-age behaviour of a precast immersed tunnel using aconstitutive model based on the degree of hydration con-cept. This will lead to a better understanding of engineer-ing practice, and appropriate measures can be taken tocontrol the early-age cracking during the fabrication of theimmersed tunnel.

The study is organized as follows: after a general de-scription of the background to the project, the constitutive

model based on degree of hydration is introduced, withspecial attention given to early-age creep under varyingstress levels. The corresponding material parameters arealso estimated by way of specific experiments. Afterwards,the early-age behaviour of the immersed tunnel is simulat-ed with respect to its fabrication process. Finally, the engi-neering factors related to early-age cracking are analysedand discussed.

2 Project description

The background to this study is provided by the HongKong–Zhuhai–Macao Link, a major infrastructure projectcurrently under construction in China. The project linksthree regions, including Hong Kong, Zhuhai and Macao,and is scheduled to open in 2017. The main structures ofthe project consist of one cable-stayed bridge, two artifi-cial islands and an immersed tunnel, and the link is one ofthe longest of its kind in the world, with a total length of49.968 km.

The GZM (Hong Kong–Zhuhai–Macao Link) im-mersed tunnel consists of 33 elements, varying from 112.5to 180 m in length and resulting in a total immersed tun-nel length of 5664 m. Each standard element consists ofeight segments each 22.5 m long joined together by tem-porary prestressing. The outer cross-section of the seg-ments is 37.96 m wide by 11.4 m high, which is capable ofenclosing four lanes and a central escape and servicesgallery. Fig. 1 shows the basic rectangular cross-section ofthe immersed tunnel segment. The thickness of the majorreinforced concrete sections of the tunnel segment are asfollows: 1) base slab 1500 mm, 2) side walls 1500 mm, 3)inner wall 800 mm, and 4) top slab 1500 mm.

The GZM project is designed to achieve a service lifeof 120 years in environmental conditions that are aggres-sive to concrete, such as marine environment and high wa-ter pressure. As to the GZM immersed tunnel, it is de-signed to be watertight without external waterproofingmeasures such that the water intake of external tunnel ele-ments is strictly prohibited. As a result, in order to protectthe reinforced concrete tunnel structure from all aggres-sive attacks during the specified service life of 120 years,early-age cracking is not permitted. These design require-ments in turn result in great challenges related to the fab-

Fig. 1. Basic cross-section of immersed tunnel (unit: cm)

68



rication of the immersed tube, some of which are listed be-low.(1) How do the concrete compositions influence the ear-

ly-age behaviour when considering a service-life re-quirement of 120 years?The requirement for a service life of 120 years in theGZM tubes means blastfurnace slag must be added asreactive filler and the water/cement ratio reduced fordurability. As mentioned, these countermeasurescould lead to a higher heat generation during hydra-tion or greater autogenous shrinkage [22, 23], whichwill introduce uncertainty into the cracking control. Itis therefore important to understand their influenceon the early-age performance of the immersed tubes.

(2) Which kind of casting scheme should be adoptedwhen concreting the precast tubes in the factory?The concrete pouring programme is one of the keystrategic decisions before concreting the tubes. Thecontinuous concreting method divides the tubes intoseveral parts and concretes them separately with atime delay, which is a traditional casting method andwas employed during the construction of the tunnel[3]. This approach allowed the heat accumulationcaused by hydration to be relieved, and the deforma-tion caused by temperature difference thus decreased.The block concreting method involves casting thetubes in a single pour. This approach reduces the fab-rication time. Both the Øresund Tunnel [1] and theBusan-Geoje Tunnel [2] have successful experience ofthis. So, which method is more beneficial for early-agecracking control? Or in other words, does a balanceexist between relieving thermal deformation andshortening overall construction time? It is necessaryto perform a comparative study before making the fi-nal decision.

(3) How do the curing conditions influence the early-agebehaviour during the fabrication of the immersedtubes?Besides the casting scheme mentioned above, the cur-ing scheme is also one of the widely used practicalmethods for controlling early-age cracking. The relat-ed control conditions normally include the fresh con-crete temperature, the conductivity of formwork andthe curing temperature, etc. However, how sensitive iscrack formation to these control parameters? Or inother words, which condition is more efficient for con-trolling early-age cracking? In this respect, a sensitivi-ty study is a great help.

To answer the above questions, the early-age behaviour ofthe precast concrete immersed tunnel should be under-stood in depth and the numerical model employed shouldbe capable of taking the above considerations into ac-count.

3 Early-age constitutive model based on degree of hydration

3.1 Degree of hydration concept

The concept of the degree of hydration is adopted to mon-itor the degree of completion of cement hydration, whichcan be normalized through the rate of heat production

during hydration. Normally, the kinetics of hydration canbe represented by an Arrhenius law with the form [24]

(1)

where:Ea activation energy (J/mol)R universal gas constant (8.314 J/mol K–1)qmax maximum value of heat production rate (J/s) at 20 °Cf(α) evolution of normalized heat production rate as a

function of hydration degree α

Eq. (1) can be accurately estimated based on hydrationtests on the concrete mix.

For civil engineering applications, the hydration de-gree α can be further computed as the ratio between theheat released up to a certain time t and the total heat ex-pected upon completion of the hydration reaction:

(2)

where α(t) is the degree of hydration at time t.The total heat of hydration Qtot liberated after com-

plete hydration is determined by the cement composition.A practical method to estimate the total cumulated heatfor these complex binder systems is to determine experi-mentally the total heat development Qmax correspondingto the end of the hydration test. So, given the heat genera-tion during hydration for any cementitious material, thecorresponding degree of hydration at any time can be ap-proximated by the degree of reaction based on Eq. (3):

(3)

where r(t) is the degree of reaction at time t.The maximum heat of hydration Qmax liberated,

which is the total cumulated heat corresponding to theend of hydration test, can then be estimated practically byexperiment. During this work, different hydration testswere conducted first to determine the adequate time peri-od to obtain Qmax. It is shown that the rate of heat libera-tion for the binding material tested is < 0.2 J/gh at 14 days.Thus, the test time period of 14 days is employed in Eq. (3)for the complex binder systems in this work.

After specifying the above test time period, the de-gree of reaction r could thus be related to the degree of hy-dration α via the following equation:

(4)

Through the definition given in Eq. (2) or (3), the absolutetime, which is normally used to measure the hydrationprocess, can be linked to the concept of hydration or reac-tion degree. From the normalization, the concept of hy-dration (reaction) degree reflects the state of the chemicalreaction between hydraulic binders and water in macro-scopic conditions. In this respect, the concept of hydra-tion degree could be further combined to describe the ear-

( ) ( ) 1 ( )max max 0

r t Q tQ Q

q t dtt

( ) ( ) · maxt r tQQtot

( )maxQ q f eERT

a�

( ) ( ) 1 ( )0

t Q tQ Q

q t dttot tot

t

69



ly-age properties of cementitious materials such as shrink-age, creep and tensile strength, which will be addressed be-low.

3.2 Early-age constitutive model based on degree of hydration

Many researchers have proposed different approaches todescribe early-age concrete properties [16, 25, 26]. As theearly-age volume changes are caused by several differentmechanisms, an incremental stress-strain law is normallyadopted to describe the early-age behaviour of materials,which can be represented as follows:

(5)

where:D material stiffnessΔεe incremental elastic strainΔεT

n+1, Δε shn+1, Δε cr

n+1 thermal, shrinkage and creep strain in-crement respectively

These mechanical properties can be related to the degreeof hydration as explained below.

3.2.1 Modulus of elasticity and Poisson’s ratio

The development of modulus of elasticity is relatedto the strength. The modulus of elasticity is modelled bythe degree of reaction as follows [15]:

(6)

where:E(r) modulus of elasticity at degree of reaction rE(r = 1) modulus of elasticity at degree of reaction r = 1r0 percolation threshold for degree of reactionb parametersr0 = 0.25, b = 0.5 for the type of concrete

Poisson’s ratio is not constant during hardening. Based onthe experimental results and the findings mentioned in theliterature, a degree of hydration-based model for Poisson’sratio can be deduced [20].

(7)

where:v(r) Poisson’s ratio at degree of reaction rr degree of reaction

The Poisson’s ratio model is shown in Fig. 2.

3.2.2 Thermal expansion

It is known that the coefficient of thermal expansion(CTE) evolves during hydration, especially at an early age.The CTE varies rapidly at a very early age, normally15–30 h after casting [27], which has a minor influence onthe thermal stresses within the concrete structure. There-

( ) 0.18sin2

0.5 10v r r e r

( )( 1)

(1

)0

0

E rE r

r rr

b

[ ]1 1 1 1 1D Dn e n nT

nsh

ncr

fore, a constant value equal to 10 με/°C is considered forCTE within the further simulation program.

3.2.3 Shrinkage

Autogenous shrinkage strain is obtained in line with Eurocode 2 EN 1992-1-1 [28]. The autogenous shrinkagestrain follows from

(8)

where

(9)

and

(10)

where fck is the cylinder strength of the concrete at 28days and t is given in days.

The curve is shown in Fig. 3 as a function of the degree of reaction.

( ) ( ) ( )�t tca as ca

( ) 2.5( 10)10 6� fca ck

( ) 1 exp( 0.2 )0.5t tas

Degree of reaction

Poi

sson

's ra

tio

0.5

0.4

0.3

0.2

0.1

0.00.0 0.2 0.4 0.6 0.8 1.0

Fig. 2. Development of Poisson’s ratio

100

90

80

70

60

50

40

30

20

10

00.0 0.2 0.4 0.6 0.8 1.0

Degree of reaction

Aut

ogen

ous

shrin

kage

(µm

/m)

Fig. 3. Development of autogenous shrinkage over 28 days

70



3.2.4 Creep

Some formulas have been developed for basic creep basedon the degree of hydration (degree of reaction). A goodsimulation model for the basic creep of early-age concretehas been investigated by Guenot el al. [29]. The expressionfor the specific basic creep can be written as follows:

(11)

where

(12)

(13)

Parameter μ1 depends on the degree of hydration rt0 at themoment of loading t0, whereas parameter μ0 also dependson the stress level α at the moment of loading. The creepdevelopment is thus influenced by both rt0 and the stresslevel α.

Parameters P1(rt0) and P2(rt0) for the concrete used inthe GZM project have been obtained in a creep test:

(14)

(15)

Creep models for concrete typically predict the evolutionof the deformation for a constant stress. However, in reali-ty, stress levels do not remain constant [30], especially dur-ing the early-age stage. Accordingly, an incremental calcu-lation model for creep is developed here, which gives adirect relation between stress and strain increment. Thefictitious degree of hydration method and principle of su-perposition have been applied to take into account boththe build-up and relieving of stress during the stress devel-opment in the tube. More details can be found in [31].

3.2.5 Tensile strength

The splitting tensile strength of the concrete used in theproject is modelled as follows:

(16)

where:fc(r) tensile strength at degree of reaction r

( , , ) ( , )(( )

)0 00

1 0

0.350 0

0

C t t r rt t

r t tt tt

( ) 60013

0 0r rt t

( , ) 1 ( )(1 ( ) )028

1 22

0 0 0r

EP r P rt t t

( ) 9.2 10 0.857 0.38119 17.87

0 0 0P r r rt t t

P rt ( ) 02 0

( )( 1)

(1

)0

0

f rf r

r rr

ct

ct

c

fc(r = 1) tensile strength at degree of reaction r = 1r0 percolation threshold for degree of reactionb parametersr0 = 0.25, b = 0.5 for the type of concrete

Therefore, the age-dependent behaviour of early-age con-crete, such as modulus of elasticity, autogenous shrinkage,creep under varying stress levels and splitting tensile andfracture energy can be modelled as outlined above. Soonce the age-dependent behaviour of materials at a stan-dard condition is known, the corresponding properties atthe real condition can be extrapolated via the link of de-gree of hydration. In this way, the effects of age and curingtemperature can be considered simultaneously.

3.3 Model parameter estimation

According to the degree of hydration-based descriptionfor the constitutive model, the related model parametersneed to be tested to estimate the input parameters.

3.3.1 Materials

High-strength concrete (HSC) is used for the tube. Anoverview of the HSC, to which fly ash and ground slag areadded, is given in Table 1.

3.3.2 Determining the heat of hydration

Isothermal hydration tests were performed on cementpaste according to the given mix. The tests were carriedout at 20 °C and lasted for 14 days. Measurement of theheat production rate q (J/(g · h) proceeds continuously,starting immediately after adding the water. The heat pro-duction rates are calculated per unit weight of binder. Thefirst (wetting) peak of the heat production is not consid-ered here. The degree of hydration (degree of reaction) ofthe mix proportion can be thus obtained (shown in Figs. 4and 5).

3.3.3 Early-age creep measured on laboratory specimens

Concrete specimens used for the creep tests are prismsmeasuring 100 × 100 × 515 mm. All specimens were castand stored in a curing chamber at 20 ± 2 °C and> 90 % R.H. for one day. Afterwards, they were removedfrom their moulds and sealed by means of self-adhesivealuminium sheets in order to prevent moisture exchangewith the environment. After being equipped with the mea-suring devices, each specimen is placed in the creep appa-ratus immediately, in a controlled atmosphere at 20 ± 2 °C

Table 1. High-strength concrete composition in kg/m3

W/B Binding Water Cement Fly ash Slag Gravel Sandmaterial kg/m3

5∼10 mm 10∼20 mmkg/m3

% % % kg/m3 kg/m3 kg/m3

0.34 400 136 45 20 35 497.3 607.9 739.6

* Qualification of superplasticizer: water-reducing ratio of cement mortar = 29.2 %

71



and 60 ± 5 % R.H. A sealed dummy specimen is used tomonitor the deformations due to temperature changes andautogenous shrinkage (shown in Fig. 6).

In order to study the basic creep behaviour at earlyage, creep tests at constant stress level were carried out fora loading age varying from 12 hours to 14 days. Fourgroups of concrete compressive creep tests were conduct-ed at different ages of loading (1 d, 2 d, 3 d and 7 d) andlasted for 28 days. The stress/strength ratio at the age ofloading is 40 %.

4 Application to precast immersed tunnel4.1 Early-age behaviour within the tubes

After defining the early-age behaviour of the materials, thebehaviour of the structure could be modelled through theprocess of heat transfer and the stress increase caused bydifferent volume changes, which is a typical coupled-fieldproblem.

As the evolution of the hydration reaction is practi-cally independent of the strains and stresses that developin concrete, it is usual to consider a unidirectional cou-pling in which the mechanical analyses are performed af-ter the thermal computations. With such an option, the

thermal problem is assumed to be independent of the me-chanical one. And the corresponding thermal analysis canbe described as follows.

At an early age, a great deal of heat will be generatedas the cement hydrates, and the temperature inside thetubes would vary over time. With the help of heat conduc-tion theory [32], the transient heat conduction within thetubes can be expressed by the following heat diffusionequation:

(17)

where:T temperature of concrete within structure [K]k thermal conductivity [W/m°C]ρ density [kg/m3]c specific heat ratio of concrete [J/kgK]Q·

rate of heat generated from hydration, which can berepresented according to Eq. (1)

The sequentially coupled thermal stress analysis is carriedout after the heat transfer analysis. As far as the mechani-cal analysis is concerned, it can only be activated after thethermal model, from which it receives the local tempera-tures indispensable for computing the thermal strainbased on Eq. (3) together with autogenous shrinkage andcreep strain.

The basic procedure described above for modellingthe early-age behaviour of concrete structures will be ap-plied to all the fabrication procedures for the immersedtunnel. The strain and stress that develop in the segmentsduring the first 30 days after the setting phases can thus bepredicted.

During the numerical simulation, the hydrationprocess is separated by several calculation steps (1…n…).The stress at step n + 1 can be expressed by subtracting thestrains due to temperature, shrinkage and creep from thetotal strain:

(18)

where:D stiffness matrix of materialΔεT

n+1 thermal stain incrementΔε sh

n+1, Δε crn+1 shrinkage and creep strain increment during

step respectively

( )k T Q cT� �

[ ]1 1 1 1 1Dn n nT

nsh

ncr

Time (h)

Hea

t pro

duct

ion

rate

(J/g

h)7

6

5

4

3

2

1

00 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360

Fig. 4. Heat production rate q(t) as a function of time

Hea

t pro

duct

ion

rate

q (J

/gh)

Degree of reaction

5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.00.0 0.2 0.4 0.6 0.8 1.0

Fig. 5. Heat production rate q(t) as a function of degree of reaction

Fig. 6. Shrinkage (left) and creep (right) test setups

72



As the degree of hydration is used as a measure of timeduring the simulation, the behaviour of early-age concreteis modelled as a function of the degree of hydration.

The analyses were carried out using a three-dimen-sional model of the segment, with discretization using 8-noded elements. Appropriate attention was paid to ensur-ing that the thermal and mechanical meshes overlapperfectly, see Fig. 7. The mesh fineness, with respect tomesh sensitivity and accuracy of the simulation results, ischecked in a separate numerical study. The details of thestudy are beyond the scope of this contribution.

4.2 Boundaries

The fabrication of the immersed tunnel can be separatedinto several stages, each of which can have some kind ofinfluence on the occurrence of early-age cracking. In theproposed numerical model, besides the difference in thedegree of hydration at each stage, the boundary condi-tions should also be changed with different stages.

For the GZM Link, the fabrication stages connectedto the early-age behaviour can be described as follows.(The other stages, including reinforcing steel cage prepara-tion and formwork manoeuvre, are skipped for simplicity.)(1) Casting stage: after the reinforcing steel and formwork

are in position, 3400 m3 of concrete are placed in acontinuous or discontinuous process.

(2) Indoor curing stage: after several days, the specifiedformwork striking time, the formwork is struck andthe completed segment is ready to be jacked out of thecasting pit. During jacking, the segments are support-ed on 36 active hydraulic jacks connected together inthree groups of 12. After jacking, the completed seg-ment is still in the factory building.

(3) Outdoor curing stage: after jacking the completed seg-ment through 22.5 m, the following segment can bemade. The above process is repeated. When the grow-ing tunnel element is jacked for the third time, the firstsegment begins to leave the casting hall for further cur-ing outside the factory building.

Once eight segments have been cast, they are held togeth-er with temporary prestressing cables. The whole elementis then pushed further to the dock area in preparation forflotation of the elements inside the basin.

According to the above description, the correspond-ing boundary conditions can be defined below.

4.2.1 Thermal analysis

Concerning the thermal analysis, different boundarieswere considered depending on the fabrication stages:(1) Casting stage: concerning the formwork adopted for

the outer and inner surfaces, which are used as curingmeasures. Thus the ‘equivalent boundary coefficient’heq can be modified according to the formwork con-ductivity properties. For practical use, the formworklayers existing between the tunnel surface and the airmay be viewed as associated in series, and the equiva-lent boundary coefficient can be computed according-ly as

(19)

where:h heat exchange coefficient between concrete sur-

face and environment (9.9∼17.9 W/m2K)A unit area through which heat transfer occursLi thickness of each ith layerki conduction coefficient for each ith layer

In the case of steel formwork with a thickness of onlymillimetres, the equivalent boundary coefficient iscomputed as 9.9 W/m2K, and 2.6 W/m2K for timberformwork according to Eq. (18).

(2) Indoor curing stage: where the formwork is strippedand all the surfaces of segments are assumed to be indirect contact with the air. As the segment is still in-side the factory, a heat exchange coefficientheq = W/(m2 · K) and indoor temperature Tin wereadopted.

(3) Outdoor curing stage: where the segment is pushedoutside of the casting hall, a heat exchange coefficientheq = W/(m2 · K) and outdoor temperature Tout wereused, which also considers the possible wet burlap/plastic membrane which covered the outer surfaceduring the processes.

4.2.2 Mechanical analysis

With regard to the mechanical boundary conditions,these also vary up to the fabrication stages.(1) Casting stage: while the formwork is in position at the

casting pit, the descending vertical displacementswere restrained at all points on the outline of the baseslab. Besides, between the base slab and the bottomformwork, special contact elements were adopted thatallow limited sliding at this stage.

(2) Indoor and outdoor curing stages: during these laterfabrication stages, the base formwork is released, andthe segment then rests on six skidding beams posi-tioned underneath the tunnel walls. These supportingconcrete beams are continuous over a certain lengthand are provided with stainless steel plates on top. Sixbearing pads per section are placed on each beam sothat a total of 36 pads carry one segment. Jacking for-wards is performed by pressing against the segmentjoint, moving the pads along the steel plate. Thus, thepoints supported by the pads at the base slab are re-

( 1 )1

1hhA

Lk Aeq

i

ii

n

Fig. 7. Finite element mesh for segment

73



strained vertically and the other constraints are re-leased.

When applying the above restraint condition to the FEMmodelling, different springs are employed to simulate therestraint effect at the corresponding stages. For example,the stiffness coefficient for the springs restraining the ver-tical displacements is set to be large enough such that novertical displacement is allowed at the bottom of the baseslab. The stiffness coefficient for the springs restrainingthe horizontal displacements can be calculated as follows:

(20)

where:μ friction factorN weight of tubeA base area of tube tunnel

A stiffness coefficient of 3.8 × 105 N/m2 is set during themodelling.

5 Results and discussion5.1 Simulation results

To perform the proposed numerical procedure, a generalcase was set as the reference one with the fabrication pa-rameters as follows: fresh concrete temperature 20 °C,formwork conductivity 9.9 W/m2K; indoor curing temper-ature 20 °C, ambient temperature 30 °C. A whole pictureof behaviour development during the fabrication stagescan thus be plotted in the following.

5.1.1 Temperature field

As the length of segment (22.5 m) is larger than the thick-ness of slabs and walls (1.5 m), it can be expected that theheat transfer essentially occurs in directions X and Y, i.e.the direction of thickness. The evolution of early-age tem-peratures is predicted numerically on the segment at the

k NA

cross-section, as shown in Fig. 8, in which the results at 1,2.4, 5, 7, 14 and 28 days after pouring are plotted togetherfor comparison.

It can be seen from Fig. 8 that the temperature distri-butions along the base slab, side walls and top slab aresymmetrical, with the middle parts having a higher tem-perature, because the curing conditions both inside andoutside the elements are the same during fabrication. Itshould be pointed out that in Fig. 8 the inner wall temper-atures are observed to be lower than those of the othersegment elements. This is because the inner wall thicknessis less than the other segmental elements, thus less heatcumulates during hydration.

As the fabrication stages progress, so the tempera-ture increases at first because of the release of hydrationheat. A peak value of 65 °C is reached at the centre of thebase slab, side walls and top slab simultaneously at an ageof 2.4 days. After demoulding, the temperature at the sur-face of the segment decreases to the curing temperatureuntil the centre and the surface have the same tempera-ture in the later fabrication stages.

To ascertain the influence of the fabrication moreclearly, the temperature distribution and variation ob-tained at the core and near the surface of the side wall arepresented in Fig. 9.

It can be seen that owing to its large dimensions, thestructure undergoes a large increase in temperature, main-ly in the core. A maximum temperature of 51.5 °C isreached at an age of 2.4 days. The surfaces experiencethermal transfer by convection with the environment andhave a lower temperature than the core. A sudden temper-ature increase is found at an age of 7 days. The reason forthis lies in the fact that at this stage the segment is jackedout of the casting hall and the ambient temperature is sethigher than that of the indoor curing temperature in thereference case.

5.1.2 Stress field

The discussion on the numerical results from the me-chanical model is carried out by analysing the normal

1 day

5 days

14 days

2.4 days

7 days

28 days

+ 54.3+ 51.4+ 48.6+ 45.7+ 42.9+ 40.0+ 37.2+ 34.3+ 31.4+ 28.5+ 25.7+ 22.9+ 20.0

Temperature

Fig. 8. Temperature development at different fabrication stages (1, 2.4, 5, 7, 14 and 28 days)

74



stresses that develop over time in the three directions ofthe finite element mesh: X (horizontal), Y (vertical) and Z(longitudinal). It should be noted that due to the geometrydifference of the segment, the stresses σx and σz are of ut-most relevance, with greater values (both in tension andcompression) than σy.

The evolution of stress σx can be observed in Fig. 10.During the heating phase (between pouring and an age of3 days), and due to the fact that the thermal volumetric ex-pansion of the core is significantly larger than that of thesurface areas, tensile stresses arise near the segment sur-faces.

After 3 days (onset of cooling phase) this process isreversed: the volumetric contraction of the slab core be-comes larger than that of the surface areas (due to thehigher temperatures in the core); accordingly, compressivestresses develop in the surface and tensile stresses in thecore.

A detailed analysis of the stress sign inversions is pos-sible by observing Fig. 11, which reproduces the calculatedevolution of the horizontal stress for a specific point onthe side wall.

The difference between the surface and core temper-atures observed in Fig. 9 generates a system of self-balanc-ing stresses, with tension at the surface and compressionat the core. An abrupt change in stress can be found,which is caused by the sudden temperature difference af-ter the segment is jacked outside of the casting hall. How-ever, even in the most unfavourable instance of analysis,compressive stresses σx do not reach 2 MPa.

The interpretation of the normal stress σz that devel-ops can be carried out analogously to that for stress σx be-cause the respective volumetric restraints to deformationare quite similar. This resemblance is reflected in the verysimilar distribution of σx and σz, depicted in Figs. 12 and13. Nevertheless, as the volumetric restraints in directionX are larger than those in direction Z (see Fig. 11), and soon, normal stress σz is less than σx.

In terms of results, attention is drawn to the stressesin the X and Z directions, depicted in Figs. 10 and 12 for2.4 days when maximum tensile stresses are observed inFigs. 11 and 13. The simulated stress is up to 2.5 MPa atthe surface. These larger tensile stresses are the conse-quence of the higher thermal gradient resulting from thelower thermal insulation value of the formwork.

5.2 Discussion

The questions raised relating to the early-age crackingcontrol in section 2 can be answered based on the numer-ical analysis performed. An index Icr, called the crackingrisk index, is defined as the ratio of the principal tensilestress (which is obtained from the numerical modelling) tothe splitting tensile strength for comparative study later.

(21)

where σ1(r) and f1(r) are the first principal tensile stressand tensile strength at reaction degree r respectively.

How several factors influence the structural perfor-mance of concrete at an early age is discussed below, con-sidering three types of parameter.

( )( )1I

rf rcrt

0 7 14 21 28

20

25

30

35

40

45

50

55Te

mpe

ratu

re /o C

time /d

middle surface

Fig. 9. Temperature distribution and variation along the side wall

1 day

5 days

14 days

2.4 days

7 days

28 days

+2.100e+06+1.820e+06+1.539e+06+1.259e+06+9.780e+05+6.974e+05+4.169e+05+1.363e+05–1.442e+05–4.248e+05–7.053e+05–9.859e+05–1.266e+05

S, S33(Avg: 75%)

Fig. 10. Horizontal stress sx development at different fabrication stages (1, 2.4, 5, 7, 14 and 28 days)

75



5.2.1 Influence of mix design

Concrete mix design depends not only on durability re-quirements, but also refers to the performance of early-ageconcrete.

As the heat of hydration is the main origin of early-age cracking, the rate of releasing this heat and the maxi-mum heat of hydration, depending on the mix design, havean obvious influence on the performance of early-age con-crete. Two kinds of concrete with different cement typesand content are compared here (see Table 2); these arecommon mix proportions for massive concrete structuresin China.

Although there is a minor difference in the W/B be-tween these two mixes, the release of heat of hydration isquite different. Based on the hydration tests, the adiabatictemperature rise of groups I and II is 41.4 and 60.0 °C re-spectively. More heat and a faster rate of heat release have

been noticed in group II, which is mainly caused by thedifferent types and various components of cementitiousmaterials. Therefore, the influence of concrete mixes isstudied based on these two groups.

From the simulation of the thermal fields, the tem-perature development at the corner of a segment for bothgroups is shown in Fig. 14. It can be seen that the maxi-mum temperature rise is 52.3 °C at 2.7 days and 67.8 °C at2.47 days for groups I and II respectively. The difference inmaximum temperature is nearly 15.5 °C, which is causedby more hydration heat and a much faster rate of heat re-lease in group II.

According to the analysis given in section 5.1, dan-gerous tensile stresses occur on the surface at the corner(shown in Fig. 15). Therefore, the development of thecracking risk index for groups I and II on the surface atthe corner are selected to compare the influence of con-

0 7 14 21 28

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5H

oriz

onta

l stre

ss /M

pa

time /d

surface point at roof

Fig. 11. Horizontal stress development at specific point

S, S11(Avg: 75%)

+2.245e+06+1.970e+06+1.695e+06+1.420e+06+1.145e+06+8.697e+05+5.947e+05+3.197e+05+4.465e+04–2.304e+05–5.054e+05–7.804e+05–1.055e+06

1 day

5 days

14 days

2.4 days

7 days

28 days

Fig. 12. Longitudinal stress σz development at different fabrication stages (1, 2.4, 5, 7, 14 and 28 days)

0 7 14 21 28-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

long

itudi

nal s

tress

/Mpa

time /d

surface point at side wall

Fig. 13. Longitudinal stress development at specific point

76



crete mixes, (shown in Fig. 16). This is obtained from thesimulation results of the precast immersed tunnel basedon two mix design groups.

It is shown that a higher risk is noted for group IIduring hydration, which is 1.13 at degree of reaction 0.55compared with 1.04 at degree of reaction 0.42 for group I.The reason is that a higher thermal gradient between thesurface and the core have been reached in the case ofgroup II, which leads to a higher cracking risk index.

5.2.2 Influence of casting scheme

Block and continuous concreting methods are two com-mon casting methods for massive concrete structures.

For the continuous concreting method, the simulat-ed segment was divided into three parts, as shown inFig. 17. The base slab is cast first, followed by the sidewalls and then the top slab. Intervals of 3 or 7 days are cal-culated.

The block concreting method is simulated for thecase where the segments are cast without intervals. Theambient temperature is set equal to 20 °C during fabrica-tion. As mentioned before, the development of the crack-ing risk index at the surface of a corner, which is the mostdangerous point, has been picked up to compare the twocasting schemes.

As can be seen in Fig. 18, all the cracking risk index-es are < 1.0 for the three cases. The peak values are 0.6 for

Table 2. Concrete composition in kg/m3

Group W/B Binding Water Cement Fly ash Slag 8 Gravel Sand Super-material kg/m3

5∼10 mm 10∼20 mmplasticizer

kg/m3

% % % kg/m3 kg/m3 kg/m3 kg/m3

I 0.34 400 136 45 20 35 497.3 607.9 739.6 3.08

II 0.37 430 160 51 30 19 480 550 760 4.73

70

60

50

40

30

200 7 14 21 28

Group IGroup II

Time (Day)

Tem

pera

ture

(°C

)

Fig. 14. Temperature development on surface of corner

Point selected foranalysing surface ofcorner

Fig. 15. Specific point selected for analysing surface of corner

1.2

1.0

0.8

0.6

0.4

0.2

0.00.0 0.2 0.4 0.6 0.8 1.0

Group IGroup II

Degree of reaction

Cra

ckin

g ris

k in

dex

Fig. 16. Development of cracking risk index at surface of corner

Y

Z X First Placement

Second Placement

Third Placement

Fig. 17. Casting the segment in three parts

77



block concreting and 0.51 and 0.37 for continuous con-creting for 3 and 7 days respectively. The difference can beexplained by the development of the temperature, which isshown in Figs. 19 to 21 for the middle part of the base slab,side wall and top slab.

It can be found that the highest temperature in thebase slab decreases for the three cases, being 58.1 °C forblock concreting and 46.8 and 43.5 °C for continuous con-creting for 3 and 7 days respectively. The reason lies in thesuperimposed effect of the heat of hydration of the baseslab and the side wall. The influence is lower when the in-terval between base slab and side wall is increased. Theconduction of hydration heat in the subsequent part couldheat up the prior part, which is advantageous for crackingcontrol due to the reduced temperature difference be-tween surfaces and core.

On the other hand, the shrinkage stress has obvious-ly increased because the base concrete cast first restrainsthe wall concrete cast later, resulting in tension stresses inthe side walls. The longitudinal stress development –mainly caused by shrinkage of materials – was obtainedfrom the simulation results in Fig. 22.

As shown in Fig. 22, the highest stress is 0.26 MPafor continuous concreting with a 3-day interval, comparedwith 0.18 MPa for a 7-day interval. Therefore, comparedwith the block concreting method, continuous concretinghas both advantages and disadvantages. The shrinkagestress in the continuous concreting method will increasewith the length of segment and roughness of the interface.Meanwhile, the thermal stress is closely related to the bulkand the hydration heat of parts. It is better to take thesefactors into account when determining the castingscheme.

5.2.3 Influence of curing conditions

(1) Fresh concrete temperatureFour groups of calculations have been carried out withfresh concrete temperatures of 20, 22, 25 and 28 °C. As be-fore, the development of the cracking risk index at the sur-face of a corner was picked up for comparison in Fig. 23.

The maximum cracking risk index decreased from1.35 to 1.32, 1.23 and 1.04 when the fresh concrete tem-perature was decreased from 28 to 20 °C. The reason is

Cra

ckin

g ris

k in

dex

Time (Day)

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.00 1 2 3 4 5 6 7

Block concretingContinuous concreting at3-day intervalsContinuous concreting at7-day intervals

Fig. 18. Development of cracking risk index at surface of corner in baseslab

Base slabSide wallTop slab

Tem

pera

ture

(°C

)

Time (Day)

70

60

50

40

30

20

10

00 7 14 21 28

Fig. 19. Temperature development without casting interval


60

50

40

30

20

10

00 7 14 21 28

Time (Day)

Tem

pera

ture

(°C

)

Fig. 20. Temperature development with 3-day intervals


Time (Day)

Tem

pera

ture

(°C

)

60

50

40

30

20

10

00 7 14 21 28

Fig. 21. Temperature development with 7-day intervals

78



that the maximum thermal stress decreases with the dropin the fresh concrete temperature. When lowering thefresh concrete temperature, the temperature difference in-side a segment will decrease for the same adiabatic tem-perature, and thus the thermal stress can decrease. It isthus shown that controlling the fresh concrete tempera-ture could be an effective way of controlling early-agecracking.

(2) Curing temperatureThe curing temperature is closely related to the thermalfields in the structure during hydration. A proper curingtemperature will maintain the temperature difference be-tween internal and external structure at a lower level,which is significant for the thermal stresses within the con-crete. The influence of ambient temperature is obtainedfrom five groups of calculations for which the ambienttemperatures are 20, 25, 30 and 35 °C.

The development of the cracking risk index at thesurface of a corner has been selected for comparison inFig. 24. An obvious drop in the cracking risk index from

1.23 to 0.51 has been noticed when the curing temperatureincreased from 15 to 35 °C. It is shown that the segment ismuch safer when curing at a higher ambient temperature –due to the minor temperature difference between externalsurface and core. Therefore, it is necessary to maintain thecuring temperature as a higher temperature to lower thetemperature difference of the concrete structure.

(3) Conductivity of formworkThe conductivity of the formwork has a distinct influenceon the thermal exchange during hydration. It is noticedthat a lower formwork conductivity is necessary for con-trolling early-age cracking of concrete structures. Twogroups of calculations have been carried out, for which theequivalent boundary coefficients of the internal surfaceare 8.8 and 2.6 W/m2K respectively.

The development of the cracking risk index at thesurface of a corner has been selected for comparison inFig. 25. It is found that the cracking risk index has beensignificantly reduced from 1.04 to 0.49 when the form-work conductivity is changed from 8.8 to 2.6 W/m2K.

Time (Day)

Stre

ss (M

Pa)

0.30

0.25

0.20

0.15

0.10

0.05

0.000 7 14 21 28

3-day intervals7-day intervals

Fig. 22. Longitudinal stress development in side wall

Degree of reaction

Cra

ckin

g ris

k in

dex

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.00.0 0.2 0.4 0.6 0.8 1.0

20°C22°C25°C28°C


Degree of reaction

Cra

ckin

g ris

k in

dex

1.2

1.0

0.8

0.6

0.4

0.2

0.00.0 0.2 0.4 0.6 0.8 1.0

8.8W(m2K)2.6W(m2K)


Degree of reaction

Cra

ckin

g ris

k in

dex

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.00.0 0.2 0.4 0.6 0.8 1.0

15°C20°C25°C30°C35°C


79



A major temperature difference between core and surfaceof concrete is avoided when the heat insulation is effec-tive, which leads to only minor thermal stresses at an earlyage.

6 Conclusion

The early-age behaviour of precast concrete immersed tun-nels during fabrication is influenced by the concrete mixdesign and also by the construction technology. Early-agecracking control represents a great challenge for engineer-ing practice. Numerical analysis is normally employed toinvestigate the age-dependent behaviour in structures.

In this contribution, the degree of hydration conceptis considered for the constitutive model of the hardeningconcrete. This approach allows the effects of both age andtemperature on hydration to be taken into account simul-taneously. The numerical procedure is described to simu-late the early-age behaviour of the precast immersed tubesillustrated.

Based on the proposed numerical model, the influ-ences of mix design, casting scheme and curing conditionson the early-age behaviour of the immersed tubes are in-vestigated. It is found that:(1) Mixes with a higher heat of hydration cause a higher

maximum temperature and higher cracking risk indexin the immersed tube simulated, which means greaterdifficulty in controlling early-age cracking. And evenminor adjustment of the filler content in mix designcan be found to influence the tube’s early-age perfor-mance via simulation. Thus, when designing mixes, inpractice it is necessary to investigate experimentallythe influence of mix compositions on the heat re-leased during hydration.

(2) Comparing the results of different casting schemes, itcan be found that the segmental concreting methodwill bring about a lower cracking risk index by de-creasing the heat accumulation in the immersed seg-ment simulated, which is more noteworthy with alonger time interval between the casting of the differ-ent segments. However, the cracking risk in the longi-tudinal direction will increase as the deformation inthe newly cast segment will be restrained by the seg-ment cast previously. The decision concerning thecasting scheme normally depends on several factors,however. Therefore, if the block concreting method isemployed in practice, more attention – with emphasison the curing condition – should be paid to control-ling early-age cracking.

(3) Controlling the fresh concrete temperature, propercuring temperatures and using formwork with a lowerconductivity are all factors that could be employed tocontrol early-age cracking. And their specific determi-nation could be analysed using the method describedin this work after setting the control criterion referringto the cracking risk index. Moreover, a sensitivityanalysis could be conducted to identify their level ofinfluence.

To validate the numerical procedure developed in thiscontribution, full-scale trial casting is now being conduct-ed. After that, the proposed procedure can be further used

for early-age cracking control in engineering practice byproviding recommendations on the pertinent curing strat-egy to minimize the cracking risk.

Acknowledgements

The research was financially supported by the NationalNatural Science Foundation of China, Ref. Nos. 50908167and 50838004, the National Science and Technology Sup-port Programme, Ref No. 2011BAG07B04, and the Funda-mental Research Funds for the Central Universities of Chi-na, all of which is gratefully acknowledged.

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4. Lykke, S., Skotting, E., Kjaer, U.: Prediction and control ofearly-age cracking: experiences from the Øresund Tunnel.Concrete International, 2000, 22(9), pp. 61–65.

5. Jeon, S.-J.: Advanced Assessment of Cracking due to Heat ofHydration and Internal Restraint. ACI Materials Journal,2008, 105(4), pp. 325–333.

6. Tasdemir, M. A., Akkaya, Y., Erdogdu, S., Öztürk, M.: Qualityassurance for the deepest immersed tube tunnel: Marmarayproject 12/2009, 3rd Asian Conference on Ecstacy in Con-crete, ACECON, Chennai, 12/1/2010–12/1/2010.

7. De Schutter, G., Vuylsteke, M.: Minimisation of early agethermal cracking in a J-shaped non-reinforced massive con-crete quay wall. Engineering Structures, 2006, 26, pp.801–808.

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9. Lackner, R., Mang, H. A.: Chemoplastic material model forthe simulation of early-age cracking: from the constitutivelaw to numerical analyses of massive concrete structures. Cement Concrete Composites, 2004, 26, pp. 551–562.

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11. Benboudjema, F., Torrenti, J. M.: Early-age behaviour of concrete nuclear containments. Nuclear Engineering andDesign, 2008, 238, pp. 2495–2506.

12. Craeye, B., De Schutter, G., Van Humbeeck, H., et al.: Early-age behaviour of concrete supercontainers for radioactivewaste disposal. Nuclear Engineering and Design, 2009, 239(1), pp. 23–35.

13. Schindler, A. K.: Effect of temperature on hydration of ce-mentitious materials. ACI Materials Journal, 2004, 101, pp.72–81.

14. Wang, X. Y., Lee, H. S.: Evaluation of the mechanical proper-ties of concrete considering the effects of temperature andaging. Construction and Building Materials, 2012, 29, pp.581–590.

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15. De Schutter, G., Taerwe, L.: Degree of hydration-based de-scription of mechanical properties of early age concrete. Ma-terial Structure, 1996, 29, pp. 335–344.

16. De Schutter, G.: Applicability of degree of hydration conceptand maturity method for thermo-visco-elastic behaviour ofearly-age concrete. Cement and Concrete Composites, 2004,26, pp. 437–443.

17. Bernard, O., Ulm, F. J., Lemarchand, E.: A multiscale micro-mechanics-hydration model for the early-age elastic proper-ties of cement-based materials. Cement and Concrete Re-search, 2003, 33, pp. 1293–1309.

18. De Schutter, G.: Finite element simulation of thermal crack-ing in massive hardening concrete elements using degree ofhydration-based material laws. Computation & Structures,2002, 80, pp. 2035–2042.

19. De Schutter, G.: Degree of hydration based Kelvin model forthe basic creep of early-age concrete. Material Structure,1999, 32, pp. 260–265.

20. De Schutter, G., Taerwe, L.: Fictitious degree of hydrationmethod for the basic creep of early-age concrete. MaterialStructure, 2000, 33, pp. 370–380.

21. Tailhan, J. L., Boulay, C., Rossi, P., Maou, F. L., Martin, E.:Compressive, tensile and bending basic creep behaviors re-lated to the same concrete. Structural Concrete, 2013, 14 (2),pp. 124–130.

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23. Antonio, A. M. N., Maria, A. C., Wellington, R.: Drying andautogenous shrinkage of pastes and mortars with activatedslag cement. Cement and Concrete Research, 2008, 38 (4),pp. 565–574.

24. Brown, T. L., Lemay, H. E.: Chemistry: The Central Science,4th ed. Prentice Hall, Englewood Cliffs, NJ, 1988.

25. Gawin, D., Pesavento, F., Schrefler, B. A.: Hygro-thermo-chemo-mechanical modelling of concrete at early ages andbeyond. Part II: shrinkage and creep of concrete. Journal forNumerical Methods in Engineering, 2006, 67 (3), pp.332–363.

26. Waller, V., D’Aloia, L., Cussigh, F., Lecrux, S.: Using the ma-turity method in concrete cracking control at early ages. Ce-ment and Concrete Composites, 2004, 26 (5), pp. 589–599.

27. Loser, R., Münch, B., Lura, B. P.: A volumetric technique formeasuring the coefficient of thermal expansion of hardeningcement paste and mortar. Cement and Concrete Research,2010, 40 (7), pp. 1138–1147.

28. EN 1992-1-1:2004: Eurocode 2: Design of concrete struc-tures.

29. Guenot, L., Torrenti, J. M.: Stresses in concrete at early ages:comparison of different creep models. Proc. of internationalRILEM symposium on thermal cracking in concrete at earlyages, pp. 103–110, Spon, London, 1994.

30. Bazant, Z. P.: Mathematical modeling of creep and shrink-age of concrete. John Wiley & Sons Ltd., New York, 1988.

31. Jiang, W.: Constitutive model of early age concrete and itsstructural performance. Ghent University, 2012.

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Wei JiangSchool of Materials Science and EngineeringTongji UniversityShanghai 201804, P.R. China

Geert De SchutterMagnel Laboratory for Concrete ResearchDepartment of Structural EngineeringGhent UniversityGhent B-9052, Belgium

Yong YuanDepartment of Geotechnical EngineeringTongji UniversityShanghai 200092, P.R. China

Quanke SuHong Kong-Zhuhai-Macao Bridge AuthorityZhuhai 519000, P.R. China

Xian LiuDepartment of Geotechnical EngineeringTongji UniversityShanghai 200092, P.R. ChinaE-mail: [email protected]: +86-(0)21 6598 0234Fax: +86-(0)21 6598 0234


The work presented in this paper is considered to be an attemptto contribute towards a better understanding of the structural be-haviour of plain concrete slabs under step loading conditions.The Concrete Society Technical Report TR34 “Concrete IndustrialGround Floors” is in its 3rd edition (2003) and is currently underreview. TR34 covers the design of concrete ground-supportedslabs containing fibres, both steel and synthetic, as an alternativeto mesh reinforcement. This work reports on tests carried out atdifferent critical loading locations, including the centre, edgesand corners of a 6.0 × 6.0 × 0.15 m deep plain concrete slab. Thetest results are compared with theoretical values derived usingavailable design codes and other information sources. The re-sults show a notable difference between the test results and thetheoretical values.

Keywords: ground-supported slab, displacement, crack propagation,bending, punching

1 Introduction

More than 30 tests on ground-supported slabs were under-taken at the University of Greenwich between 1989 and1999 using a test rig capable of applying a concentratedload of up to 600 kN (60 t) at any location within an areahaving maximum dimensions of 11 m long and 3 m wide.The results of these tests were summarized in the proceed-ings of the 4th and 5th International Colloquiums on In-dustrial Floors [1], [2]. Further tests using an upgradedground slab test rig with similar loading capabilities butsignificantly larger maximum dimensions, 12 m long and6 m wide, were published in the proceedings of the 2007Industrial Floors Colloquium [3]. The majority of the testslabs had dimensions of 3 × 3 × 0.15 m deep and were sub-ject to internal, edge and corner loading. In all cases, theloading plates were 100 × 100 mm, which was intended tosimulate single- or double-racking leg loads. The loadingtests included plain concrete, fabric (mesh), steel and syn-thetic fibre reinforcement. The majority of tests were onslabs containing steel fibres of variable geometry, includ-ing plain, undulating and hook-ended, with fibre contentsranging between 20 and 40 kg/m3.

These tests and others [4] formed the basis for an ap-pendix in the 2nd edition of TR34 (1994) [5], which intro-duced a plastic approach to the thickness design of concreteground slabs based on the work of Meyerhof [6]. The 1st edi-tion of TR34 (1988) [7] used an elastic analysis approach forslab thickness design based on the pioneering work of H. M.Westergaard (1926) [8]. The 3rd edition of TR34 was pub-lished in March 2003 and the sections on thickness designand the worked examples were undertaken by Beckett andClarke [9]. These were in an ultimate limit state format andin line with the draft version of Eurocode 2 [10]. The 3rdedition of TR34 pays greater attention to crack control, de-flections and load transfer across joints. In addition, signifi-cant emphasis is paid to the use of fibres, steel and synthet-ic, as an alternative to fabric (mesh) reinforcement. Thefinal version of Eurocode 2 [11] was published in 2004 andnow incorporates the Jan 2008 corrigendum. The 2003 edi-tion of TR34 is currently being revised and there are severalissues that need resolving. These include the fact that theequation for the characteristic flexural strength of plain con-crete in the 2004 edition of EC2 gives significantly lower val-ues than those given in TR34 (2003), which uses the draftEC2 formula. TR34 (2003) recommends that the character-istic flexural strength of plain concrete should be taken as

fctk.fl = [1 + (200/h)0.5] fctk(0.05) ≤ 2 fctk(0.05)Eq. 9.1 TR34 (2003)

where:h total slab thickness in mm (h > 100 mm)fctk.fl characteristic flexural strength of plain concretefctk (0.05) characteristic axial tensile strength of plain con-

crete (5 % fractile)

EC2 (2004) recommends that the following relationshipmay be used for calculating the mean axial tensile strengthof reinforced concrete:

fctm(fl) = max [(1.6 – h/1000) fctm] Eq. 3.23 EC2 (2004)

where:h total member depth in mm fctm mean axial tensile strength (TR34, Table 3.1)

The relation given in Eq, (3.23) also applies for the char-acteristic tensile strength values. Other issues include the

Technical Paper

Structural behaviour and deformationpatterns in loaded plain concreteground-supported slabs

Morteza Aboutalebi*Amir M. AlaniJoseph RizzutoDerrick Beckett

DOI: 10.1002/suco.201300043


Submitted for review: 12 June 2013Revised: 12 June 2013Accepted for publication: 6 July 2013

influence of ground support on punching failure, design ofpiled ground slabs and the effect of creep on the long-termflexural strength of concrete, which is not addressed inTR34 (2003). In addition to the above, no reported workhas been identified concerning the punching shear failureof steel and synthetic fibre-reinforced slabs larger than3.0 × 3.0 m. The limitations of a 3.0 × 3.0 m slab with re-gard to lifting of the corners and edges were observed dur-ing the earlier tests. Therefore, by increasing the plan area,this effect may be significantly reduced.

The construction of a new test rig at the University ofGreenwich provided the opportunity to cast test slabswith a much larger plan area and more in line with indus-try practice. Similar to the previous rig, the new facility iscapable of applying a load of up to 600 kN (60 t) at anyposition and the plan dimensions of the test slabs can beincreased to up to 6 m wide and 12 m long (72 m2).

The first phase of new set of 6.0 × 6.0 × 0.15 m deepslab tests started in March 2010. One of the main reasonsfor constructing ground slabs on this scale was to investi-gate the limitations of the smaller slabs referred to above[12]. In February 2011 the second phase of testing was re-alized with synthetic fibres [13]. The plain concrete slabwas subjected to central, edge and corner loading duringthe testing. Further tests are planned, including mesh-rein-forced concrete.

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M. Aboutalebi/A. M. Alani/J. Rizzuto/D. Beckett · Structural behaviour and deformation patterns in loaded plain concrete ground-supported slabs


2 Test facility apparatus

The ground slab testing facility is comprised of a flat bedover which a slab can be cast. A single point load can beapplied to the test slab via a compressor attached to atransverse plate girder spanning over the slab. The trans-verse girder can be moved back and forth two steel-platedground beams, spaced at 8.5 m centres. These ground

Fig. 1. CBR-equivalent plate testing of re-engineered soil

Fig. 2. (a) to (d): concrete placement and cast slab

(a) (b)

(d)(c)

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beams run either side of the test rig and are restrainedagainst uplift by tension piles. The ground beams are 16 mlong and so the point load can be located anywhere with-in a 6 × 12 m surface area of a slab.

2.1 Ground conditions

The soil type within the test rig can be readily modified byexcavation and reinstatement. This exercise can modifythe soil compaction level to give any desired compressibleconditions. In April 2010 the ground conditions were mod-ified and subsequently re-evaluated using a plate-equiva-lent CBR test in line with BS 1377, Part 9, 4.1 [14]. Themodulus of subgrade reaction k, modified for plate diame-ter, was found to vary from 44 to 55 MPa/m. Figs. 1 and 2depict the process of the ground improvement work car-ried out for the investigation together with the concreteplacement and casting of the plain concrete slab.

2.2 Slab loading procedure

The load was applied to the ground-supported slab at aconstant rate by the electronic control of the hydrauliccompressor. As the load was applied, a load pressure cell,located between hydraulic jack and load plate, recordedthe load to which the slab was being subjected. The de-flection of the slab was recorded with linear variable dif-ferential transducers (LVDTs) at the load point and at var-ious other locations across the slab surface. Figs. 3, 4 and5 show detailed views of the regions where the load wasapplied. The precise location of the deflection monitorsand the load point was varied in each test (see Fig. 6 andspecific load tests for details).

3 Tests

The slab was cast on 11 January 2012. The following con-crete specification was used:– Strength class of concrete C32/40 in accordance with

Table 9.1 of TR34 (2003) with a maximum water/cementratio of 0.55

CBR tests on the subsoil supporting the slab area gave anaverage modulus of subgrade reaction k = 0.05 N/mm3.

3.1 Slab loading tests

Loading on the slab commenced after a minimum curingperiod of 28 days and five tests were undertaken with oneinternal, two edge and two corner loading locations. Theload locations were as shown in Fig. 4. The positions ofdisplacement transducers and acoustic sensors are depict-ed later in the text under the discussion of results asshown in Fig. 5. The 100 × 100 mm steel loading plate wassandwiched between a similar-sized plywood spreaderplate to counteract any unevenness on the concrete sur-face and the 200 × 200 mm steel plate on which four trans-ducers were placed (1–4). The load control was automatedand the loading jack was connected via a top plate to thereaction beams. A general view of the test area includingthe cover, the 6.0 × 6.0 × 0.15 m concrete slab and reactionbeams can be seen in Figs. 2 and 3.

Fig. 3. Overview of testing facility together with test in progress, centrepunch load application point on slab

Fig. 4. Test in progress, 150 mm edge load application point on slab

Fig. 5. Test in progress, 300 mm edge load application point on slab

3.2 Compressive strength tests

A total of nine 150 × 150 × 150 mm cubes were tested. The28-day average compressive strength results are shown inTable 1.

The concrete cubes and cylinders were tested at thetime the particular slab tests were carried out in order toenable accurate comparison of the experimental and theo-retical outputs. The following ages of concrete were usedin this work:

Ground slab cast on 11 January 2012, test 1, centreloading, test 2, 150 mm edge loading, test 3, 300 mm edgeloading, all carried out at 28 days; test 4, 300 mm corner

84



loading carried out at 49 day; test 5, 150 mm corner load-ing carried out at 70 days.

Table 2 gives a summary of the results of the five tests on the 6.0 × 6.0 × 0.15 m deep slab (different loadinglocations) with comments on the modes of failure de -picted.

4 Test results

Test No. 1 – central loading (refer to Table 1)Fig. 7 illustrates the loading position together with the locations of the displacement transducers and theacoustic sensors utilized during the test. The failure loadwas 479 kN and no cracks were visible on the top surfaceof the slab at failure. Deflections due to step loading conditions at the punching shear failure mode are shownin Figs. 8 and 9. Fig. 10 depicts the crack propagation profiles at 300 kN load and 479 kN at failure. Fig. 11shows surface deformation profiles achieved under300 kN load and 479 kN at failure. The Meyerhof valuefor bending is 232.1 kN and for punching shear 290.3 kN.Membrane action influences the failure load for centralloading and, further, the use of d = 0.75 h = 112.5 mm for

Fig. 6. Loading locations on 6.0 × 6.0 × 0.15 m deep slab

Table 1. Compressive strength test results

150 × 150 × 150 mm cubes 28 days 49 days 70 days

Average compressive strength (MPa), fcu 47.6 46.8 51.7

Average density (kg/m3) 2338.5 2353.3 2342.9

Averaged measured and EC2, Table 3.1, cylinder compressive strength (MPa), fck 38.0 37.8 41.3

Table 2. Summary of results for slab tests 1–5 with comments on crack formation

Test Load at Load at Average deflection Commentsfirst crack (kN) failure (kN) (mm), transducers 1–4

at first crack at failure

Test No. 1 No cracks visible on surface of slab at failure – Internal centre

– 479.0 – –5.54punching shear mode.

punch load (28 days)

Test No. 2 Vertical cracks on side of slab gradually Edge 1 – 150 mm 12.6 407.0 0.5 –18.75 widening with increase in load followed by (28 days) circumferential & radial cracks up to failure.

Test No. 3 Vertical cracks followed by circumferential Edge 2 – 300 mm 10.9 443.0 0.5 –18.82 cracks with punching-type failure at 443 kN.(28 days)

Test No. 4 Circumferential cracks apparent.Corner 1 – 300 mm 10.5 262.3.0 0.7 –16.85(49 days)

Test No. 5 At failure circumferential, radial & vertical Corner 2 – 150 mm 20.0 192.0 1.4 –12.25 cracks (sides) & punching.(70 days)

85



the effective depth of the slab is conservative (TR34,2003). See Table 3 below for all theoretical and test re-sults.

Test No. 2 – edge loading (150 mm)Fig. 12 depicts the loading position together with the loca-tions of the displacement transducers and the acousticsensors utilized during the test.

For test No. 2, the loading plate was centred 150 mmfrom the slab edge. Vertical cracks appeared on the side ofthe slab, which gradually widened as the load increased,followed by circumferential and radial cracks leading topunching failure at 407.0 kN. Figs. 13 and 14 show the de-flections recorded as a result of step loading applied at theedge of the slab.

Test No. 3 – edge loading (300 mm)Fig. 6 depicts the loading position together with the loca-tions of the displacement transducers and the acousticsensors utilized during the test.

For test No. 3, the loading plate was centred 300 mmfrom the slab edge. Vertical cracks appeared on the side ofthe slab, which gradually widened as the load increased,followed by circumferential and radial cracks leading topunching failure at 443.3 kN. Figs. 15 and 16 show the de-flections recorded as a result of step loading applied at theedge of the slab.

Test No. 4 – corner loading (300 mm)Fig. 6 depicts the loading position together with the locationsof the displacement transducers utilized during the test.

Fig. 7. Central loading location and positions of sensors

-6

-5

-4

-3

-2

-1

0

1

-3000 -2000 -1000 0 1000 2000 3000

Dep

th (m

m)

Sensor Posi�on (mm)

Centre Punch Test W-E Axis

100kN

200kN

300kN

400kN

478kN

08/02/2012

Fig. 8. Displacement plotted against position along axis 1 (W-E) caused by incremental step loading

For test No. 4, the loading plate was centred 300 mmfrom the slab corner and circumferential cracks first ap-peared at 10.5 kN. As the load increased, so circumferen-tial and radial cracks appeared, followed by vertical

86



cracks on the side of the slabs, with punching failure at262.3 kN. Figs. 17 and 18 illustrate the displacementsrecorded with respect to step loading conditions appliedin both axes.

-6

-5

-4

-3

-2

-1

0

1

-3000 -2000 -1000 0 1000 2000 3000

Dep

th (m

m)


Centre Punch Test N-S Axis

100kN

200kN

300kN

400kN

478kN

08/02/2012

Fig. 9. Displacement plotted against position along axis 2 (N-S) caused by incremental step loading

Fig. 10. Crack propagation profiles at 300 kN load and 479 kN at failure

-3000-2250 -1500 -750

-145 0145 750

15002250 300000

-2250-1500

-750-145

0145

7501500

22503000

-1

0

1

2

3

4

5

6

-1-00-11-22-33-44-55-6

-1-00-11-22-33-44-55-6

-3000 -2250 -1500 -750 -145 0 145 750 1500 2250 -2250-1500

-750-145

0145

7501500

22503000

-1

0

1

2

3

4

5

6

300000

Displacement (mm) Displacement (mm)

Fig. 11. Surface deformation profiles achieved under 300 kN load and 479 kN at failure

87



Test No. 5 – corner loading (150 mm)Fig. 19 depicts the loading position together with the loca-tions of the displacement transducers utilized during thetest.

For test No. 5, the loading plate was centred 150 mmfrom the slab corner and circumferential cracks first ap-peared at 20.0 kN. As the load increased, so circumferen-tial and radial cracks appeared, followed by verticalcracks on the side of the slabs, with punching failure at192.0 kN. Figs. 20 and 21 illustrate the displacementsrecorded with respect to step loading conditions appliedin both axes.

5 Theoretical calculations

Theoretical calculations for the five tests were undertakenin accordance with Chapter 9 of TR34, 2003 (see below),using Meyerhof Eqs. 9.10 (a & b), 9.11 (a & b) and 9.12(a & b) for bending.

For an internal load with

a/l = 0:Pu = 2π (Mp + Mn) Eq. 9.10a

a/l > 0.2:Pu = 4π (Mp + Mn)/[1 – 2α/3l] Eq. 9.10b

Fig. 12. Edge loading position 300 mm from edge of slab

-20

-15

-10

-5

0

5

-3000 -2000 -1000 0 1000 2000 3000

Dep

th (m

m)


Edge 150 Test N-S Axis

100kN

200kN

300kN

400kN

407kN

Fig. 13. Displacement plotted against position along axis 1 (N-S) caused by incremental step loading

88



-20

-15

-10

-5

0

5

0 500 1000 1500 2000 2500 3000 3500

Dep

th (m

m)


Edge 150 Test W-E Axis

100kN

200kN

300kN

400kN

407kN

08/02/2012

Fig. 14. Displacement plotted against position along axis 2 (W-E) caused by incremental step loading

-20

-15

-10

-5

0

5

-500 0 500 1000 1500 2000 2500 3000 3500

Dep

th (m

m)


Edge 300 Test N-S Axis

100kN

200kN

300kN

400kN

443kN

08/02/2012

Fig. 15. Displacements recorded as a result of step loading at the 300 mm loading position at the corner of the slab axis 1 (N-S)

-20

-15

-10

-5

0

5

-3000 -2000 -1000 0 1000 2000 3000

Dep

th (m

m)


Edge 300 Test W-E Axis

100kN

200kN

300kN

400kN

443kN

Fig. 16. Displacements recorded as a result of step loading at the 300 mm loading position at the corner of the slab axis 2 (W-E)

89



For an edge load with

a/l = 0:Pu = [π (Mp + Mn)/2] + 2 Mn Eq. 9.11a

a/l > 0.2:Pu = [π (Mp + Mn ) + 4Mn ]/[1 – 2α/3l] Eq. 9.11b

For a true free corner load with

a/l = 0:Pu = 2 Mn Eq. 9.12a

a/l > 0.2:Pu = 4.0 Mn/[1 – (a/l)]

For punching shear, section 9.11 of TR34 (2003) wasadopted using Eqs. 9.28 to 9.33 and Fig. 9.11.

In accordance with the draft of Eurocode 2, irrespec-tive of the amount of any reinforcement in the slab, theshear stress at the face of the contact area should not ex-ceed a value νmax given by

νmax = 0.5 k2 ƒcd Eq. 9.28

where:ƒcd design concrete compressive strength (cylinder) =

ƒck/γc

k2 = 0.6 (1 – ƒck/250)

where: ƒck characteristic concrete compressive strength (cylinder)

Hence, the maximum load capacity in punching Pp,max isgiven by

-20

-15

-10

-5

0

5

10

0 200 400 600 800 1000 1200 1400 1600

Dep

th (m

m)


Corner 300 Test North Face

50kN

100kN

150kN

200kN

250kN

29/02/2012

Fig. 17. Displacements recorded as a result of step loading at the loading position 300 mm from the edge

-20

-15

-10

-5

0

5

10

0 200 400 600 800 1000 1200 1400 1600

Dep

th (m

m)


Corner 300 Test West Face

50kN

100kN

150kN

200kN

250kN

29/02/2012

Fig. 18. Displacements recorded as a result of step loading at the loading position 300 mm from the edge.

Pp,max = Vmax uod Eq. 9.29

where:uo length of perimeter at face of load area

5.1 Summary of input data

Slab depth h = 150 mmModulus of subgrade reaction k = 0.05 N/mm3 – average

CBR = 8.325, seeTR34 (2003), Fig. 6.2– ‘CBR percentage’ vs.‘k’ N/mm3

For all five tests, ν = 0.2 – Poisson’s ratio,see TR34 (2003)

90



For tests 1–3 (28 days)fcu = 47.6 N/mm2 – (average)fck = 38.0 N/mm2 – see Table 3.1, EC2 (2004)fctk (0.05) = 2.37 N/mm2

Ecm = 34.8 kN/mm2

For test 4 (49 days)fcu = 46.8 N/mm2 (average)fck = 37.6 N/mm2 – see Table 3.1, EC2 (2004)fctk (0.05) = 2.36 N/mm2

Ecm = 34.7 kN/mm2

For test 5 (70 days)fcu = 51.7 N/mm2 (average)fck = 40.1 N/mm2 – see Table 3.1, EC2 (2004)

Fig. 19. Corner loading position at 150mm from edge of slab

-14

-12

-10

-8

-6

-4

-2

0

2

4

0 200 400 600 800 1000 1200 1400 1600

Dep

th (m

m)


Corner 150 Test West Face

50kN

100kN

150kN

192kN

21/03/2012

Fig. 20. Displacement plotted against position along axis 1 west face due to different loading conditions

91



fctk (0.05) = 2.46 N/mm2

Ecm = 35.2 kN/mm2

The summary of calculations tabulated in Table 3 is basedon TR34 (2003). However, the characteristic strength ofplain concrete was calculated using EC2 (2004) for com-parison purposes.

From TR34 (2003), the characteristic flexuralstrength of plain concrete is given by

fctk.fl = 5.12 N/mm2 – tests 1–3= 5.08 N/mm2 – test 4= 5.30 N/mm2 – test 5

From EC2 (2004), Eq. 3.25:

fctk.fl = 4.92 N/mm2 – tests 1–3= 4.88 N/mm2 – test 4= 5.10 N/mm2 – test 5

For all five tests, the equivalent radius of the 100 ×100 mmsquare loading plate is given by

a = (100/p2)0.5

= 56.4 mm

The radius of relative stiffness l = [Ecm h3/12 (1 – ν2)k]0.25 – Eq. 9.4, TR34(2003)

= 671.9 mm – tests 1–3= 671.4 mm – test 4= 674.1 mm – test 5

a/l = 0.0840 – tests 1–3= 0.0840 – test 4= 0.0837 – test 5

The load/deflection relationship was recorded automati-cally. As there was no reinforcement present, using Eq. 9.6(TR34, 2003), the positive and negative moments (Mp andMn) are taken as equal and are as follows:

For tests 1–3:Mn = 12.79 kNm/mMp = 12.79 kNm/mMp + Mn = 25.58 kNm/m

For test 4:Mn = 12.70 kNm/mMp = 12.70 kNm/mMp + Mn = 25.40 kNm/m

For test 5:Mn = 13.25 kNm/mMp = 13.25 kNm/mMp + Mn = 26.50 kNm/m

Table 3 depicts the theoretical values for bending usingthe Meyerhof equations together with the punching shearvalues in comparison with the test results.

By reference to Tables 2 and 3, the disparity betweenthe test results and those obtained from TR34 (2003) forpunching are apparent. In 1997 Shentu et al. [15] used a fi-nite element model, assuming a Winkler slab, to develop asimple formula to determine the load-carrying capacity ofa plain concrete slab on grade subjected to an interiorconcentrated load. The load capacity P can be expressedas

P = 1.72 [(k · r/Ec) × 104 + 3.6] f1t · h2

where:k modulus of subgrade reactionr radius of loaded areaEc modulus of elasticity of concretef1t uniaxial tensile strength of concreteh depth of slab

Using the data for test No. 1, assuming PLAIN concrete,with h = 150 mm, k = 0.05 N/mm3, r = 56.4 mm, Ec =34.8 kN/mm2, f1t = 2.37 N/mm2 [fctk . fl (0.05)], then

-14

-12

-10

-8

-6

-4

-2

0

2

4

0 200 400 600 800 1000 1200 1400 1600

Dep

th (m

m)


Corner 150 Test North Face

50kN

100kN

150kN

192kN

21/03/2012

Fig. 21. Displacement plotted against position along axis 2 north face due to different loading conditions

P = 1.72 [(0.05 × 56.4/34.8 × 103) × 104 + 3.6] 2.37 × 1502

= 404.5 kN

Using the mean value fct of 3.4 N/mm2 (from EC2, 2004),then the value P = 577.9 kN is 20.7 % greater than the testvalue of 479.0 kN. The work of Shentu et al. did not in-clude edge or corner loading and the slab tested was cir -cular.

6 Discussion of results

With the load centred at 300 mm from the edge of theslab, the failure load of 443 kN was 92 % of the internalload condition (479.0 kN), whereas the failure load for150 mm from the edge of the slab was 407.0 kN, i.e. 85 %of the internal load. For test No. 2, the load at first crackwas 84 % of that for test No. 3. A similar pattern emergedfor test Nos. 4 and 5. The load at first crack for test No. 4was 47.5 % of that for test No. 5, and the failure load per-centage was 63 %. This demonstrates that, in practice,placing racking legs closer than 300 mm from the edges orcorners of a ground slab should be avoided if there is noload transfer to adjacent slabs or beams.

7 Conclusions

The calculations are summarized and it is apparent thatthe theoretical failure loads are significantly lower thanthe test values.

The results of this research clearly demonstrate thesignificance of tests at similar scales to those used in prac-tice. The results were conclusive in overcoming the limita-tions of a 3.0 × 3.0 m slab with regard to lifting of the cor-ners and edges as observed and reported in the earlierworks.

The significance of loading positions on the edgesand corners of slabs in terms of ultimate shear failureachieved has been clearly demonstrated.

92



Acknowledgements

The authors would like to express their thanks to IanCakebread, Tony Stevens, Bruce Hassan and Marc Van DePeer for setting up the test rig, installing instrumentation,carrying out the loadings and recording the results for thetests.

References

1. Beckett, D.: A comparison of thickness design methods forconcrete industrial ground floors. Technische AkademieEsslingen, 4th International Colloquium, 12–14 Jan 1999, In-dustrial Floors 99, vol. 2, p. 159.

2. Beckett, D.: Strength & serviceability design of concrete in-dustrial ground floors. Teknische Akadamie Esslingen, 5thInternational Colloquium, 21–23 Jan 2003, Industrial Floors03, vol. 2, p. 601.

3. Beckett, D.: Concrete ground slab test facilities at the Uni-versity of Greenwich: an update. Technische AkademieEsslingen, 6th International Colloquium, 16–18 Jan 2007, In-dustrial Floors 07, vol. 2, p. 707.

4. Falkner, H., Teusch, M.: Comparative investigations of plainand steel fibre reinforced industrial ground slabs. TU Braun-schweig, 1993.

5. The Concrete Society, Technical Report 34, Concrete indus-trial ground floor slabs – a guide to their design and con-struction, 2nd ed., 1994.

6. Meyerhof, G. G. W.: Load-carrying capacity of concrete pave-ments. Journal of the Soil Mechanics & Foundations Divi-sion. Proc. of American Society of Civil Engineers (ASCE),vol. 88, Jun 1962, pp. 89–166.

7. The Concrete Society, Technical Report 34, Concrete indus-trial ground floor slabs – a guide to their design and con-struction, 1st ed., 1988.

8. Westergaard, H. M.: Stresses in concrete pavements comput-ed by theoretical analysis. Public Roads, vol. 7, No. 2, Apr1926.

9. The Concrete Society, Technical Report 34, Concrete indus-trial ground floor slabs – a guide to their design and con-struction, 3rd ed., 2003.

Table 3. Theoretical values obtained using TR34 (2003) and test results from Table 1

Location Theoretical values Test values

Bending (kN) Punching (kN) Bending (kN) Punching (kN)

Test No. 1Internal centre punch 232.1 290.3 (face) – 479.0load (28 days) 124.5 (critical section)

Test No. 2Edge 1 (150 mm) 72.6 217.7 (face) – 407.0(28 days) 77.4 (critical section)

Test No. 3Edge 2 (300 mm) 79.6 217.7 (face) – 443.0(28 days) 89.7 (critical section)

Test No. 4Corner 1 (300 mm) 45.8 143.8 (face) – 262.3(49 days) 76.3 (critical section)

Test No. 5Corner 2 (150 mm) 43.7 151.7 (face) – 192.0(70 days) 58.8 (critical section)

93



10. British Standards Institution, BS EN 1992-1, Draft Eurocode2, Design of concrete structures – Part 1: General rules andrules for buildings.

11. British Standards Institution, BS EN 1992-1-1: 2004 (incor-porating corrigendum Janu 2008), Eurocode 2: Design ofconcrete structures – Part 1-1: General rules and rules forbuildings.

12. Alani, A. M., Beckett, D., Khosrowshahi, F.: Mechanical be-haviour of a steel fibre reinforced concrete ground slab. Mag-azine of Concrete Research, ICE, 2012, pp. 1–12.

13. Alani, A. M., Beckett, D.: Mechanical Properties of a largeScale Synthetic Fibre Reinforced Concrete Ground Slab.Journal of Construction and Building Materials, vol. 41, Apr2013, pp. 335–344.

14. BS 1377, Part 9: Methods for test for soils for civil engineer-ing purposes – in situ tests; 1990.

15. Shentu, L., Jiang, D., Hsu, C. T. T.: Load-carrying capacityfor slabs on grade. ASCE Journal of Structural Engineering,Jan 1997.

Dr. Morteza AboutalebiB.Sc. (Hons), M.Sc. (Distinction), Ph.DSenior Lecturer,Department of Civil EngineeringSchool of EngineeringUniversity of GreenwichCentral Avenue, Chatham MaritimeKent. ME4 4TB, UKTel: +44(0)1634883019Email: [email protected]

Dr Joseph RizzutoBSc, MSc, PhD, CertEd, CEng, MICE, MIStructE, MCIHT Deputy Head Department of Civil Engineering University of Greenwich Department of Civil Engineering Faculty of Engineering & ScienceCentral Avenue, Chatham Maritime Kent ME4 4TB, UKEmail: [email protected]. +44(0) 1634 883584Fax. +44(0) 1634 883153

Derrick Beckett BSc Eng, MPhil, PhD, CEng, MICE, MCIOBVisiting Professor, Department of Civil EngineeringSchool of EngineeringUniversity of GreenwichCentral Avenue, Chatham MaritimeKent. ME4 4TB, UK

Professor Amir Alani BSc (Hons), MSc, PhD, CEng, FIMechE, FHEA, MCIHTHead of Department of Civil EngineeringThe Bridge Wardens’ Chair in Bridge and Tunnel EngineeringSchool of EngineeringUniversity of GreenwichCentral Avenue, Chatham MaritimeKent. ME4 4TB, UKTel: +44(0)1634 883293Email: [email protected]


Technical Paper

DOI: 10.1002/suco.201300004

The structural behaviour of steel fibre-reinforced concrete(SFRC) has been studied using non-linear finite element analysis(NLFEA) and ABAQUS software. An interesting feature of thiswork is the consideration of statically indeterminate SFRCcolumns. Most of the SFRC specimens studied in the literatureare simply supported beams, and information on statically inde-terminate columns is sparse. In addition, both axial and lateralloads were considered in order to allow for compression andflexural effects on the columns. The aim of the work was to ex-amine the potential for using steel fibres to reduce the amount ofconventional transverse steel reinforcement without compromis-ing ductility and strength requirements. To achieve this, the spac-ing between shear links was increased while steel fibres wereadded as a substitute (spacing between shear links increased by50 and 100 % with fibre volume fraction Vf increased to Vf = 1, 1.5,2 and 2.5 %). The numerical model was carefully calibratedagainst existing experimental data to ensure the reliability of itspredictions. Parametric studies were subsequently carried out,which provided insight into how the steel fibres can help reducethe number of conventional shear links.

Keywords: fibre-reinforced concrete, finite element methods, structuralanalysis

1 Introduction

Due to the inherent brittle nature of plain concrete, steelfibres are usually provided as a means of enhancing duc-tility. This paper presents the results of numerical inves -tigations of steel fibre-reinforced concrete (SFRC) two-span columns using non-linear finite element analysis(NLFEA). This arrangement was chosen to allow for astudy of statically indeterminate SFRC columns, whichhas been addressed only occasionally as most of the re-search work reported in the literature focuses on simplysupported beams [1–4]. Axial loads have also been consid-ered (in addition to lateral loads as depicted schematicallyin Fig. 1), so both compression and bending responses canbe modelled (again, previous work predominantly focusedon lateral loads on beams).

A key issue assessed is the potential for steel fibres tocontribute to a reduction in conventional transverse rein-

forcement without compromising ductility and strengthrequirements. In this respect, the spacing between shearlinks was increased while steel fibres were added to seewhether or not the loss of strength can be compensatedfor in this way. This is particularly useful in situationswhere the conventional transverse reinforcement requiredcan lead to congestion of shear links, e.g. in seismic design[5]. The NLFEA investigations provided insights into howthe steel fibres can help reduce the number of convention-al shear links. The effect of the steel fibres was directlymodelled into an existing concrete material model em-ployed in the ABAQUS [6] software package to describeits non-linear behaviour. This is achieved through appro-priate modification of the stress-strain relationship of con-crete in uniaxial tension. Initially, column specimens in-vestigated experimentally by Kotsovos et al. [7] wereselected to calibrate the numerical model and thus ensurethe reliability of its predictions. The experimental datawas useful in providing a benchmark to validate the FE re-sults; however, the range of fibre content considered waslimited. The present research work, on the other hand,covers the full practical range of fibre contents and reduc-tion in the number of stirrups. Therefore, once the calibra-tion work was concluded, full NLFEA-based parametricstudies were subsequently carried out with the spacing be-tween shear stirrups increased by 50 and 100 %, whereasthe fibre volume fraction Vf was increased to Vf = 1, 1.5, 2and 2.5 % to see whether or not fibres can compensate forthe reduction in transverse reinforcement. The originalstirrup spacing was 40 and 140 mm at support and mid-span regions respectively, as depicted in Fig. 1. Thus, theadditional spacings adopted were 60 and 210 mm and 80and 280 mm, corresponding to 50 and 100 % increases re-spectively. Similarly, the fibre contents used were 80, 120,160 and 200 kg/m3, corresponding to Vf = 1, 1.5, 2 and2.5 % respectively. Columns with no fibres (i.e. Vf = 0 %)were also considered in the parametric studies. However,any potential improvements due to fibres provided in highamounts (i.e. Vf > 2%) must be tempered by practical con-siderations such as workability issues, which are usuallyaddressed by adding water-reducing admixtures. It is alsocommon to use fly ash, slag or silica fume to facilitate theinclusion of fibres and improve workability. Adjustmentsto the mix design is often needed as well to accommodatehigh fibre contents, and the mixing method should consid-er the type and content of fibres used in order to ensure

Non-linear analysis of staticallyindeterminate SFRC columns

Ali A. Abbas*Sharifah M. Syed MohsinDemetrios M. Cotsovos


Submitted for review: 18 January 2013Revised: 22 August 2013Accepted for publication: 22 August 2013

95

A. A. Abbas/S. M. Syed Mohsin/D. M. Cotsovos · Non-linear analysis of statically indeterminate SFRC columns


uniform distribution (however, this is beyond the scope ofthis paper).

2 Constitutive models for SFRC and numerical modelling strategy

The failure of plain concrete is governed by crack forma-tion (when the maximum principal tensile stress exceedsthe tensile strength of the concrete), which continue to ex-tend as the load is increased. In SFRC, after the onset ofcracking, the fibres provide a crack-bridging effect to resistfurther crack opening. There are different potential failuremodes depending on the effectiveness of the fibres inbridging the cracks. In order to model the structural re-sponse of SFRC structural members, key characteristicswere studied and corresponding constitutive models wereexamined. The effects of fibres were modelled by modify-ing existing models for plain concrete already available inthe ABAQUS software package. In this respect, the “brittlecracking model” in ABAQUS [6] is currently adopted todescribe brittle material behaviour dominated by tensilecracking, as is the case for structural concrete. A summaryof the constitutive models and the FE modelling strategyis provided next.

2.1 Tensile behaviour

The structural response of SFRC elements is character-ized by their tensile post-cracking behaviour. A number ofconstitutive models available for SFRC have been identi-fied, such as those proposed by RILEM [8, 9], Barros [10,11], Tlemat et al. [12], Lok and Pei [13] and Lok and Xiao[14]. The constitutive relations have been developed to de-scribe the uniaxial tensile stress-strain relationship ofSFRC. In particular, they depict the effect of SFRC on thepost-cracking behaviour of concrete from the brittle sharpdrop associated with plain concrete to either a tensionsoftening or hardening response depending on fibre con-tent, fibre geometry and shape and bond stress. In thesemodels the residual strength beyond the cracking point ofthe concrete is made up of two components: the steel fi-bres bridging the crack and the concrete matrix followedby the pull-out phase (i.e. bond failure). The main charac-teristics of the models were closely studied and a calibra-tion study was undertaken by Syed Mohsin [15] and Abbaset al. [16, 17] using NLFEA to examine these models and,consequently, the one proposed by Lok and Xiao [14] wasselected for the subsequent parametric studies. The uniax-

ial tension stress-strain relationships proposed in the mod-el are

(1)

where:ft and εto ultimate tensile strength and strain (i.e. at onset

of cracking) respectivelyftu and εt1 residual strength and corresponding strain of

SFRC, defined as [13]

(2)

where:η fibre orientation factor that takes account of the

three-dimensional (3D) random distribution of thefibres, which takes values between 0.405 and 0.5 [14]

Vf fibre volume fractionτd bond stress between concrete and steel fibresL/d aspect ratio of steel fibresEs modulus of elasticity of steel fibres.

2.2 Compression behaviour

Previous work on SFRC [8, 9, 12, 14] suggests that thecompression behaviour of SFRC can be conveniently as-sumed to be similar to that of plain concrete. Investiga-tions carried out by Bencardino et al. [18] support thisconclusion, as the observed results show that the additionof steel fibres does not significantly affect the compressivestrength of the concrete (with the potentially improved ul-timate strain safely ignored). However, it should be bornein mind that there are several other studies in which an in-crease in the compressive strength was attained by addingfibres, plus enhanced ductility in compression [19]. There-fore, in the present work, the steel fibres are conservative-ly considered to have no effect on the compression behav-iour of plain concrete.

2.3 Shear behaviour

In the NLFEA of reinforced concrete (RC) structures,“shear retention” is often used to allow for the effect of ag-gregate interlock and dowel action. Fibres have a similar

f V L d L d · E· · · / and · / 1/tu f d t d s1

f

f f f

f

2 / / for(0 )

1 1 / / for( )

for( )

t to to to

t tu t to t to to t

tu t tu

2

1 1

1

N = constant axial loadP = monotonic lateral load

NP

N

Inflexion point

Fig. 1. Idealization of SFRC continuous column under gravity and lateral loads

96



effect on shear response (i.e. in a direction parallel to thecrack) and therefore it was modelled using the “shear re-tention” part of the ABAQUS (2007) concrete model [9,15, 17]. The shear stiffness of concrete decreases as crackspropagate. Therefore, in order to allow for a degradationin shear stiffness due to crack propagation, the shear mod-ulus was reduced in a linear fashion from full shear reten-tion (i.e. no degradation) at the cracking strain to 50 % atthe ultimate tensile strain.

2.4 FE modelling strategy

The ABAQUS software package offers a few materialmodels for the non-linear analysis of plain concrete andassociated cracking processes. The models also allow forthe effect of “tension stiffening” to be included (an effectrelated to the stiffness provided by concrete betweencracks or interaction between concrete and reinforce-ment). This is effectively achieved by modifying the post-cracking tensile stress-strain diagram. Therefore, this wasconveniently used to input the tensile constitutive modelsfor SFRC. The shear retention values were also adjusted asexplained above. The concrete medium was modelled by amesh of 8-node 3D brick elements, whereas 2-node 1D barelements representing conventional steel reinforcing barsand shear links were included to mimic the actual arrange-ment in the specimens modelled (e.g. cover allowed for).The steel properties were modelled using the stress-strainrelation recommended in Eurocode 2 [20]. An ultimatetensile strain was also defined to detect any failure of thesteel main bars or stirrups.

The cracking process that concrete undergoes ismodelled by the smeared crack approach. A crack formswhen the predicted value of stress developing in a givenpart of the structure corresponds to a point in the princi-pal stress space that lies outside the surface defining thefailure criterion for concrete, thus resulting in localizedmaterial failure. The plane of the crack is normal to the di-rection in which the largest principal tensile stress acts.For the purposes of crack detection, a simple Rankine fail-ure criterion is used to detect crack initiation (i.e. a crackforms when the maximum principal tensile stress attainsthe specified tensile strength of the concrete). The con-crete medium is modelled by a dense mesh of 8-node brickelements, and the element formulation adopts a reducedintegration scheme. The concrete model adopts fixed, or-thogonal cracks, with the maximum number of cracks at amaterial point limited by the number of direct stress com-ponents present at that material (Gauss) point of the finiteelement model (a maximum of three cracks in 3D). An it-erative procedure based on the well-established Newton-Raphson method is used in order to account for the stressredistributions during which the crack formation and clo-sure checks as well as convergence are carried out.

The “brittle cracking model” available in ABAQUS[6] was adopted in the present work as it is designed formaterials that are dominated by tensile cracking, such asconcrete. Since the focus is on the all-important brittletensile aspect of concrete behaviour, a simplification em-ployed in the model is that the behaviour in compressionis assumed to be linear elastic. This is justified, particular-ly for 3D modelling, because at least one of the three pre-

dicted values of the principal stresses needs to be tensileand greater than the tensile strength required to initiatecracking (whereas the other two principal stresses couldbe compressive). The main attractive feature of the modelis that it focuses on the main mechanisms for failure inconcrete, namely its brittleness and cracking (predomi-nantly in tension). Thus, the simplification made with re-gard to compressive behaviour is intended to make the so-lution process more efficient without compromising itsability to mimic the non-linear response of concrete struc-tural elements. As a further precaution, the strain resultswere checked to ensure that the values of ultimate com-pressive strain did not exceed 0.0035 before failure [20].

In order to improve the efficiency of the numericalsolution and to enhance numerical stability (which is ad-versely affected by cracking), the analysis was carried outusing the dynamic solver as a quasi-static one (i.e. at a lowrate of loading). This was used in conjunction with the ex-plicit dynamic procedure available in ABAQUS/Explicit[6]. The ratio between kinetic and strain energies waschecked to ensure that it remains below ∼5 %, indicatingthat the analysis remains quasi-static. A similar approachis commonly used in the modelling of RC structures [21].This was also confirmed by examining both the deformedshape and cracking pattern of the structure. In addition,the load was applied using a displacement-based methodto minimize convergence problems.

3 Calibration with experimental work

A series of statically indeterminate SFRC columns wastested under monotonic loading by Kotsovos et al. [7] tostudy their structural behaviour. The results of some ofthese specimens were used to calibrate the present numer-ical work as discussed next.

3.1 Experimental cases considered

Several two-span continuous columns were tested byKotsovos et al. [7]. The parameters considered were: con-crete strength, longitudinal and shear reinforcement prop-erties and a specimen with fibre-reinforced concrete. Thecolumns were cast and tested as horizontal members.Therefore, the axial force was applied horizontally and lat-eral loading P was applied vertically as shown in Fig. 2(thus representing the column idealized in Fig. 1). In thepresent NLFEA work, one of these columns was selectedfor the calibration (referred to in the experimental work asD16-FC30-M with the key features depicted in Fig. 2). Thesteel fibres used were DRAMIX RC80/60BN, which arehooked-end cold-drawn wire fibres with a diameter of0.75 mm, length of 60 mm and strength of 1050 MPa. Theconcrete compressive strength for the specimen was ap-prox. 37 MPa. The longitudinal reinforcement has a yieldstress fy = 555 MPa, the transverse reinforcement a yieldstress fy = 470 MPa. The modulus of elasticity for steel Esis 200 GPa. The axial force N applied at the column endswas taken to be 20 % of the compressive resistance of thecolumn provided by the concrete Nu. The latter can be ex-pressed as Nu = fc bh, where fc is the uniaxial cylinder com-pressive strength of concrete, and b and h are the cross-sectional dimensions of the column. Once the axial force

97



was introduced, the lateral monotonic loading was ap-plied (using a displacement-based method) at point C inFig. 2. Consequently, the load and deflection values mea-sured to plot the ensuing load-deflection curves were alsotaken at point C.

3.2 Results of calibration work

A comparison between the load-deflection curves basedon the experimental and numerical results are depictedFig. 3, which shows good agreement between the two setsof data (with the curves almost identical up to a deflectionof about 40 mm, whereas the slight discrepancy after-wards, i.e. ∼5 %, is negligible). A summary of the key loadand deflection values is provided in Table 1, with Py rep-resenting the load at yield, Pmax the maximum load (i.e.strength), Pu the ultimate load of the column at failure (i.e.residual strength), δy the deflection at yield, δu the ulti-mate deflection and μ the ductility (defined as μ = δu/δy).The table confirms the good agreement between the ex-

perimental and numerical data. In order to confirm thefailure point, the kinetic energy of the column is plottedagainst the deflection in Fig. 4. A clear, abrupt rise can beobserved, indicating failure (i.e. the presence of exten-sive/wide cracks that impair structural integrity) at∼60 mm, which is close to the experimental value of∼65 mm.

The calibration study was an important initial step inthe present research work as it allowed the determinationof some parameters needed for the numerical simulations.For instance, the FE mesh adopted (with an element sizeof 30 mm) was determined based on a sensitivity analysiscarried out in order to assess the effect of the mesh size onthe accuracy of the numerical predictions. Thus, the cali-bration work carried out against experimental data wascrucial in selecting the best mesh size that represents ac-curately the true structural response (i.e. the mesh thatbest replicates experimental results). Similarly, the calibra-tion data was useful in determining a reliable loading rateto be used in the numerical model. The comparison with

975 mm

200 mm

200 mm

P975 mm

1950 mm1200 mm 2 T16

2 T16

R8 NN

R8/40 R8/40R8/140R8/140 R8/40 R8/140 R8/40

300 mm 720 mm 560 mm 560 mm415 mm 300 mm495 mm

C

Fig. 2. Loading arrangement and reinforcement details of column

020406080

100120140160180200

0 10 20 30 40 50 60 70

Load

(kN

)

Deflection (mm)

Experimental(Vf=0.4%)

FE model(Vf=0.4%)

Fig. 3. A comparison between experimental and numerical load-deflection curves

Table 1. Summary of load-deflection curves, calibration work

Column Py (kN) δy (mm) Pu (kN) δu (mm) Pmax (kN) μ = δu/δy Pmax/Py

Experimental 155.0 11 158 65.5 187 6.0 1.21

FE model 144.3 9.7 174.1 60.3 182.9 6.2 1.33

98



experimental data also helped ascertain the reliability ofboth the constitutive relationships adopted for SFRC andthe brittle cracking model used to implement them inABAQUS (no alterations to the parameters of the consti-tutive model summarized in Eqs. (1) and (2) were neededand the values of the parameters were kept the same asthe input values used in the experiments).

4 Parametric studies of statically indeterminate SFRC columns

Following the calibration work, parametric studies werecarried out (by means of NLFEA) incorporating two keyparameters: increase in spacing SI between shear stirrupsand steel fibres volume fraction Vf. The spacing between

the stirrups was increased with SI = 0, 50 and 100 %. Atthe same time, the fibre volume fraction was increasedwith Vf = 0, 1, 1.5, 2 and 2.5 % to see whether or not fibrescan compensate for the reduction in shear reinforcement.The tensile stress-strain relations for each fibre volumefraction are depicted in Fig. 5, with the key values of stressand strain summarized in Table 2. The results obtainedare discussed next.

4.1 Load-deflection curves

The load-deflection curves for specimens with increasedstirrup spacing SI = 0 %, SI = 50 % and SI = 100 % arepresented in Figs. 6(a) to (c) respectively. The control col-umn specimen (i.e. the one with no reduction in shear re-inforcement and no fibres) is also included in the figuresto illustrate whether the addition of fibres can restore theoriginal response. Additionally, a summary of the keyload and deflection results is provided in Tables 3(a) to(c). The ratio between the ultimate load (i.e. residualstrength) Pu and the maximum load (i.e. strength) Pmaxwas added to the tables. This is to ensure that the slightsoftening trend in the load-deflection curves beyond peak(i.e. maximum) load is not significant, so the residualstrength and corresponding ductility levels remain ofpractical value. From the tables it is clear that the resid-ual strength is at least ∼90 % of the peak value, confirm-ing that the softening is negligible. The load-deflectioncurves show that there is a gradual increase in strength,stiffness and ductility as the fibres content is increased.This will be discussed next.

0100020003000400050006000700080009000

10000

0 10 20 30 40 50 60 70

Kin

etic

ene

rgy

(J)

Deflection (mm)

Fig. 4. Kinetic energy plots to determine failure of column

Table 2. Tensile stress-strain key values adopted

Point Strain (‰) Stress (MPa)

Vf = 0.0 % Vf = 1.0 % Vf = 1.5 % Vf = 2.0 % Vf = 2.5 %

Origin 0 0 0 0 0 0

Ultimate tensile strength – Plain (A) 0.215 3.70 3.70 3.70 3.7 3.70

Ultimate tensile strain – Plain (B0) 2.0 0 – – – –

Beginning of plateau – SFRC (B) 2.12 – 2.12 3.18 4.24 5.30

End of plateau – SFRC (C) 18 – 2.12 3.18 4.24 5.30

Ultimate tensile strain – SFRC (D) 20 – 0 0 0 0

0

1

2

3

4

5

6

0 0.005 0.01 0.015 0.02 0.025

Stre

ss (M

Pa)

Strain (-)

Vf = 0%

Vf = 1%

Vf = 1.5%

Vf = 2%

Vf = 2.5%

A

B C

DB0

Fig. 5. Stress–strain relations in tension adopted for parametric studies of statically indeterminate SFRC columns

99



0

50

100

150

200

250

0 10 20 30 40 50 60 70

Loa

d (k

N)

Def lection (mm)

Controlcolumn

Vf = 0%

Vf = 1%

Vf = 1.5%

Vf = 2%

Vf = 2.5%

Fig. 6(b). Load-deflection curves for columns with SI = 50 %

0

50

100

150

200

250

0 10 20 30 40 50 60 70

Load

(kN

)

Deflection (mm)

Controlcolumn

Vf = 0%

Vf = 1%

Vf = 1.5%

Vf = 2%

Vf = 2.5%

Fig. 6(c). Load-deflection curves for columns with SI = 100 %

0

50

100

150

200

250

0 10 20 30 40 50 60 70

Load

(kN

)

Def lection (mm)

Vf = 0%

Vf = 1%

Vf = 1.5%

Vf = 2%

Vf = 2.5%

Fig. 6(a). Load-deflection curves for columns with SI = 0 %

100



4.2 Strength

The load-deflection curves show that the increase in theamount of fibres provided led to an increase in load-carry-ing capacity Pmax. Comparing the strength of each SFRCcolumn with the strength of the column with no fibresshows that the load-carrying capacity increased by up to14 %. In addition, the value of the load at yield Py for theSFRC columns increased gradually up to an average of23.5 % in comparison to the yield load of columns with nofibres. This shows the effectiveness of fibres in bridgingthe crack opening, thus enhancing the load at yield of thecolumns, which leads to enhanced stiffness.

Taking the column with conventional reinforcementand no fibres (Vf = 0 %) with a stirrup spacing increaseSI = 0 % as the reference or control column specimen(CC), further comparisons were made with columns hav-ing varying fibre content and stirrup spacing. FromFigs. 6(a) to (c) and Tables 3(a) to (c) it can be seen thatthe strength properties of the SFRC columns withSI = 50 % and SI = 100 % exhibit a better performancethan the control column specimen. The values of Py andPmax obtained are also higher than the corresponding val-ues for the control column, even at a fibre volume fractionas low as 1 %.

4.3 Ductility

The ductility of the columns can be analysed by examin-ing the ultimate deflection δu and the ductility ratio μ. Anupward trend in both parameters is observed with the in-crease in fibre volume fraction. However, this pattern isonly true up to a certain critical fibre volume ratio; thehigher the spacing between the stirrups, the higher thecritical fibre volume ratio. In this parametric study thehighest ductility ratio is obtained for the column withVf = 1 % for SI = 0 %, Vf = 1.5 % for SI = 50 %, and Vf = 2 %for SI = 100 %. It is interesting to note that increasing thefibre content beyond 1.5∼2 % has actually led to a reduc-tion (rather than an increase) in ductility. The reduction inductility is more pronounced in the case of specimenswhere fibres were added in addition to full conventionalshear reinforcement, i.e. SI = 0 % (the response becameless ductile even when fibre provision exceeded Vf = 1 %).This suggests that a situation similar to the one experi-enced when main flexural reinforcement is increased be-yond a certain threshold (i.e. over-reinforced), which leadsto an increase in strength but reduction in ductility.

Furthermore, for every SI value there is a certain fi-bre volume fraction for which the ductility of the SFRCcolumn is comparable with that associated with the origi-

Table 3(c). Summary of load-deflection curves for columns with SI = 100 % (* CC is the control column specimen with Vf = 0 % and SI = 0 %)

Vf (%) Py (kN) δ y (mm) Pu (kN) δu (mm) Pmax (kN) Pu/Pmax μ = δu /δy

CC* 136.3 9.36 170.6 56.4 179.9 95 % 6.03

0 137.9 9.12 170.8 33.4 170.8 100 % 3.66

1 155.4 9.04 180.3 48.1 181.6 99 % 5.32

1.5 161.6 9.02 169.4 47.7 183.1 93 % 5.29

2 167.6 9.01 179.4 47.8 188.7 95 % 5.31

2.5 173.1 9.00 185.4 42.8 193.6 96 % 4.76

Table 3(b). Summary of load-deflection curves for columns with SI = 50 % (* CC is the control column with Vf = 0 % and SI = 0 %)


CC* 136.3 9.36 170.6 56.4 179.9 95 % 6.03

0 139.4 9.4 173.0 44.4 176.1 98 % 4.72

1 152.62 9.33 182.5 53.7 182.5 100 % 5.76

1.5 162.85 9.32 177.7 62.5 183.7 97 % 6.71

2 168.4 9.32 175.8 48.2 192.3 100 % 5.17

2.5 174.3 9.31 189.2 43.4 200.6 94 % 4.66

Table 3(a). Summary of load-deflection curves for columns with SI = 0 %


0 136.3 9.36 170.6 56.4 179.9 95 % 6.03

1 147.6 9.34 180.1 60.9 183.2 98 % 6.52

1.5 155.9 9.32 180.7 59.3 184.6 98 % 6.36

2 162.1 9.3 190.0 44.1 192.0 99 % 4.74

2.5 167.3 9.3 195.5 39.4 200.7 97 % 4.24

101



nal control specimen (i.e. with no fibres and full conven-tional shear reinforcement). This is significant from apractical viewpoint as it indicates that fibres provided incertain amounts can compensate for the decrease in duc-tility due to a reduction in shear reinforcement. These fi-bre volume fractions are 1.5 % for SI = 50 % and between1.5 and 2 % for SI = 100 %.

4.4 Principal strain vectors and crack patterns

The principal strain vectors at failure were studied and thedata provided an insight into the failure mechanism aswell as cracking formation and patterns. The principalstrain vectors for columns with SI = 0 %, SI = 50 % andSI = 100 % are presented in Figs. 7, 8 and 9 respectively.From these figures it can be seen that the failure of thecolumns is characterized by tensile cracking in two re-gions: (i) the top of the section at the intermediate supportand (ii) the bottom of the section where the lateral load Pis applied. The principal strain vectors are also highlight-ed in the column’s span between these two regions for thecolumn with no fibres, indicating some cracks propagatedin this span, especially in the column with SI = 100 %. Thestrain vectors depict the cracks that developed in the spanbetween the intermediate support and the point where lat-eral load is applied. Thus, it can be concluded that in thisparticular column with no fibres for the column withSI = 100 %, the cracking pattern suggested a bending-shear failure. However, the inclusion of steel fibres, even afibre volume ratio of just 1 %, improves the crack propa-gation and changes the mode of failure of the SFRCcolumns from shear to bending. Based on the crackingpattern observed in these figures it can be concluded thatall columns show a bending failure mode, except the col-umn with no fibres and the most critical stirrups spacing(i.e. SI = 100 %). Thus, it can be concluded that the addi-tion of fibres reduces the crack propagation and limits itto regions local to the intermediate support and the later-al loading point.

4.5 Comparative study with control specimen using non-dimensional ratios

In this section, an overall comparison is made between thecontrol column specimen (i.e. the one with no fibres andfull conventional shear reinforcement) and the columnswith various fibre dosages and increased stirrup spacing.The strength, ductility and energy absorption values werenormalized by dividing them by the corresponding controlspecimen values. This allowed overall conclusions to bereached regarding the potential of fibres to compensatefor a reduction in conventional transverse reinforcement.

(a)

(b)

(c)

(d)

(e)

Fig. 7. Principal strain vectors for case study 2(a) column with SI = 0 % for(a) Vf = 0 %, (b) Vf = 1 %, (c) Vf = 1.5 %, (d) Vf = 2 % and (e) Vf = 2.5 %

(a)

(b)

(c)

(d)

(e)

Fig. 8. Principal strain vectors for case study 2(a) column with SI = 50 % for(a) Vf = 0 %, (b) Vf = 1 %, (c) Vf = 1.5 %, (d) Vf = 2 % and (e) Vf = 2.5 %

(a)

(b)

(c)

(d)

(e)

Fig. 9. Principal strain vectors for case study 2(a) column with SI = 100 %for (a) Vf = 0 %, (b) Vf = 1 %, (c) Vf = 1.5 %, (d) Vf = 2 % and (e) Vf = 2.5 %

102



4.5.1 Strength ratio

The ratio between the maximum load Pmax of each col-umn and that of the control column specimen Pmax,o is de-picted in Fig. 10, which shows that there is an upwardtrend in the Pmax/Pmax,o ratio for all columns as the fibrepercentages are increased. It can also be seen that thecolumns with SI = 100 % result in lower strength increasesthan the other columns. From Fig. 10 it can be concludedthat the Pmax/Pmax,o ratio for all SFRC columns is higherthan the corresponding ratio for the control specimen (i.e.Pmax/Pmax,o = 1.0) when fibres are provided with a mini-mum value Vf = ∼0.8 %. This indicates that the fibres atthis dosage compensate for the loss of strength due to thereduction in conventional shear reinforcement for thespecimens considered in the present parametric studies.

4.5.2 Ductility ratio

The ductility ratios of all the columns were normalized bydividing them by the ductility ratio of the control speci-men, i.e. μ/μo, and the results were plotted against thechange in fibre volume fraction as depicted in Fig. 11. The

values of the ductility ratios for all columns considered arealso included in Fig. 11, which were all > 3 and thus thevertical axis was truncated to aid clarity. It can be con-cluded that the addition of fibres improved the ductility ofthe specimens provided the fibre amount does not exceeda certain threshold. Therefore, an optimum ratio of fibreswas determined in all specimens (i.e. for columns withSI = 0, 50 and 100 %, the optimum fibre volume fractionsare 1, 1.5 and 2 % respectively). The addition of steel fi-bres above these fibre dosages led to a reduction in theductility ratio, with the worst decease in SFRC columnswith Vf = 2.5 %, as can be seen in Fig. 11. This can be ex-plained by recalling that a higher fibre ratio leads to amuch stiffer response, causing the column to deflect less.This is similar to the brittle “over-reinforced” response ex-perienced in RC design when main flexural reinforcementis increased beyond a certain threshold, leading to a re-duction in ductility.

Moreover, it is interesting to note that columns withSI = 50 % strengthened with fibres with a Vf = 1.5 %dosage show better performance in term of ductility thanthe control specimen (i.e. the one with no spacing in-crease and no fibres). Additionally, in the columns with a

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

1.1

1.12

1.14

0 0.5 1 1.5 2 2.5 3

Pmax

/ Pm

ax,o

Vf (%)

SI=0%

SI=50%

SI=100%

Fig. 10. Ratio between the maximum load and that in the control column (SI = 0 %, Vf = 0 %) plotted against fibre volume fraction

0.50

0.67

0.83

1.00

1.17

0 0.5 1 1.5 2 2.5 3

µ/ µ

,o

SI=0%

SI=50%

SI=100%

3

4

6

7

µ

5

Vf (%)

Fig. 11. Ratio between the ductility ratio in each column and that in the control column (SI = 0 %, Vf = 0 %) plotted against fibre volume fraction (ductility ratios are also shown)

103



considerable spacing increase (i.e. SI = 100 %), the provi-sion of fibres has led to ductility levels that are close(∼85 %) to the initial ductility level associated with thecontrol specimen. It is also interesting to note that theductility levels associated with the columns with no spac-ing increase (i.e. SI = 0 %) are worse than those related tocolumns with SI = 50 % if fibre dosage is Vf = 1.5 % ormore (similarly, they are worse than columns withSI = 100 % if fibre dosage is Vf = 2 % or more). This indi-cates that, in terms of ductility, the combination of fullconventional transverse reinforcement and fibres at highdosages will lead to reduced – rather than increased – duc-tility. Thus, it can be concluded that fibres have the poten-tial to replace conventional reinforcement if excessivecombinations of the two types of reinforcement are avoid-ed (i.e. fibres should be provided to replace a reducedamount of conventional reinforcement but not in additionto full amounts of the latter). Notwithstanding the aboveobservations, adding fibres will lead to ductility ratiosμ > 4, as presented in Tables 3(a) to (c) and Fig. 11, whichwill be useful in practice. This is true even for highdosages such as Vf = 2.5 %, which could be used forstrength enhancement purposes.

4.5.3 Energy absorption

The ratio between the energy absorption Ea in each col-umn and that in the control column Ea,o is depicted inFig. 12. In columns with SI = 0 %, the energy absorptionratio increases by up to 15 %, but decreased by 25 % whenthe fibre volume fractions exceeded 1.5 %. In columnswith SI = 50 %, a fibre dosage Vf = 1.5 % led to a ratio larg-er than the one associated with the control specimen,whereas for columns with SI = 100 %, a fibre dosageVf = 2 % led to a ratio close to that of the control speci-men. The trend in the energy absorption data is similar tothe one for ductility discussed in the previous section.

To investigate the energy absorption response fur-ther, another comparison was made, but now the energyabsorption ratio for every SFRC column is normalized bythat for its counterpart column with the same SI value butwithout fibres (i.e. Vf = 0 %) as shown in Fig. 13. It is clearthat the energy absorption for SFRC columns increasedsignificantly, up to 61 and 77 % for SI = 50 % andSI = 100 % respectively. It is interesting to note that theenergy absorption ratio for the columns with SI = 100 %provides the greatest enhancement. This demonstrates

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0 0.5 1 1.5 2 2.5 3

E a/ E

a,o

Vf (%)

SI=0%

SI=50%

SI=100%

Fig. 12. Ratio between the energy absorption in each column and that in the control column (SI = 0 %, Vf = 0 %) plotted against fibre volume fraction

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 0.5 1 1.5 2 2.5 3

Ea

/ Ea,

Vf=

0%

Vf (%)

SI=0%

SI=50%

SI=100%

Fig. 13. Ratio between the energy absorption in each column and its counterpart with the same SI value but without fibres plotted against fibre volume fraction

104



that there is more room for enhancement by fibres as con-ventional reinforcement is reduced. This confirms thefinding that fibres will absorb more energy and improveductility as conventional reinforcement is reduced. Con-versely, the response becomes less ductile if the fibres areprovided in addition to full conventional reinforcement.Additionally, Fig. 13 also confirms that there is an opti-mum fibre content that can help provide the best strength,ductility and energy absorption levels.

4.6 Conclusions

Fibres were utilized in order to enhance the properties ofan inherently brittle and crack-prone cement-based ma-trix. Parametric studies of two-span continuous (i.e. stati-cally indeterminate) SFRC columns were carried out bymeans of NLFEA, which were initially calibrated and ver-ified against existing experimental data. Despite the sim-plicity of the constitutive model used for the concrete, theproposed NLFEA model employed was capable of yield-ing realistic predictions of the responses of several SFRCcolumns. A key aim of the research work was to examinethe effect of fibres on the structural response and, in par-ticular, their potential to compensate for a reduction inconventional transverse reinforcement without compro-mising ductility and strength requirements. This was in-vestigated by increasing the spacing between shear linkswhile adding steel fibres to see whether or not the loss instrength and ductility can be compensated for in this way.

Based on the results obtained, it can be concludedthat the strength of the columns is consistently enhancedas the amount of fibres is increased. It was also found thatthe original strength level associated with the controlspecimen (with no spacing increase and no fibres) can berestored when the spacing is increased by 50∼100 % byadding fibres at a volume fraction of ∼0.8 % for the pre-sent study. Moreover, it was found that the stiffness andductility of the columns improved with the addition of fi-bres. This indicates that the addition of fibres has led toimprovements at both the serviceability and ultimate limitstates. Interestingly, however, it was found that the in-crease in ductility seems to drop if excessive amounts of fi-bres are provided (so excessive amounts of fibres result inthe columns becoming much stiffer and deflecting less).This suggests that there is an optimum amount of fibresthat can be added to enhance ductility, but adding fibresbeyond this threshold should be avoided. This is similar tothe situation experienced in RC design when reinforce-ment is increased beyond a certain threshold (i.e. “over-re-inforced”), which leads to an increase in strength but re-duction in ductility. For the columns with SI = 0, 50 and100 %, the optimum fibre volume fraction values obtainedwere Vf = 1 %, Vf = 1.5 % and Vf = 2 % respectively. Never-theless, adding fibres resulted in ductility ratios μ > 4 inthe present study, which is substantial and will be useful inpractice. This is even true for dosages as high asVf = 2.5 %, which could be used for strength enhancementpurposes. However, it must be pointed out that the provi-sion of high fibre dosages (in excess of Vf = 2∼2.5 %) in theconcrete mix can lead to practical mixing difficulties. Soto improve the workability of mixes with such high fibrevolumes, water-reducing admixtures are often used. Care

is also needed to ensure that the mix composition is ad-justed taking into account the natural disturbing effectthat fibres have on the arrangement of the granular mater-ial. In general, the mixing method should consider thetype and content of fibres used in order to ensure uniformdistribution and bonding within the concrete paste. Basedon the above analysis of the numerical predictions, it is in-teresting to point out that apart from mixing difficulties,the use of excessive fibre contents can also result in a re-duction in the ductility of the structural elements present-ly considered once an optimum fibre content value ispassed. A similar pattern was observed for energy absorp-tion, which, alongside ductility, is an important indicatorof structural performance. Additionally, it was found thatthe energy absorption ratio for the columns withSI = 100 % provided the greatest enhancement. Thisdemonstrates that there is more room for enhancement byfibres as conventional reinforcement is reduced, and indi-cates that fibres will provide higher energy absorption andductility improvement as the conventional reinforcementis reduced. Conversely, the response becomes less ductileif excessive fibres are provided in addition to full conven-tional reinforcement as discussed earlier. Furthermore, itwas observed that fibres help control the cracking andminimize crack opening especially in the section betweenthe intermediate support and the point where the lateralload is applied. Most of the cracking develops in two mainregions, which are the intermediate support and the pointwhere the lateral load is applied. In the column withSI = 100 % it was clear that the inclusion of fibres im-proved the cracking pattern of the column, even at a lowfibre volume fraction of 1 %.

Summing up, it can be concluded that the additionof steel fibres improves the strength of the columns con-sistently. A similar trend is observed with regard to thestiffness and ductility of the SFRC columns. A criticalthreshold was found, however, beyond which the additionof more fibres led to a less ductile response. Interestingly,the threshold seems to be of the same order of magnitudeas that associated with practical mixing difficulties (thus,providing fibres at Vf > 2∼2.5 % can be regarded as bothimpractical and counterproductive from a ductility view-point). Nevertheless, the study has also confirmed the po-tential for fibres to compensate for a reduction in conven-tional transverse reinforcement. This can be useful insituations where the number of stirrups required can leadto congestion, whereas the use of fibres can resolve thisand also simplify complex construction arrangements (e.g.beam-column joints).

Notation

Ea energy absorptionEa,0 energy absorption of control specimenEs Young’s modulus for steelL/d aspect ratio of steel fibreN axial force applied to columnNu compression resistance of column provided by

concrete P lateral monotonic loadSI increase in stirrup spacingPy load at yield

105



Pmax load-carrying capacityPmax,0 load-carrying capacity of control specimenPu ultimate loadVf volume fraction of fibresb and h cross-sectional dimensions of columnfc uniaxial cylinder compressive strength of con-

creteft ultimate tensile strength of SFRCftu residual tensile strength of SFRCfy steel yield stressδy deflection at yieldδu ultimate deflectionεto ultimate tensile strain in SFRCεt1 residual tensile strain in SFRCη fibre orientation factorμ ductility ratioμ,o ductility ratio of control specimenτd bond stress between concrete and steel fibres CC control column specimenFEA finite element analysisSFRC steel fibre-reinforced concreteNLFEA non-linear finite element analysisRC reinforced concrete

References

1. Campione, G., Mangiavillano, M.: Fibrous reinforced con-crete beams in flexure: Experimental investigation, analyti-cal modelling and design considerations. Engineering Struc-tures, 2008, 30, pp. 2970–2980.

2. Cho, S. H., Kim, Y. I.: Effect of steel fibres on short beamsloaded in shear. ACI Structural Journal, 2003, 100, pp.765–774.

3. Trottier, J. F., Banthia, N.: Toughness Characterization ofSteel Fiber-Reinforced Concrete. Journal of Materials in Civil Engineering, ASCE, 1994, 6, No. 2, pp. 264–289.

4. Sharma, A. K.: Shear Strength of Steel Fibre ReinforcedConcrete Beams. ACI Journal, 1986, 83, pp. 624–628.

5. BS EN 1998-1: Eurocode 8: Design of structures for earth-quake resistance – Part 1: General rules, seismic actions andrules for buildings. BSI, London, 2004.

6. ABAQUS Version 6.7 Documentation, 2007. Available atwww.engine.brown.edu:2080/v6.7/index.html.

7. Kotsovos, G., Zeris, C., Kotsovos, M.: The effect of steel fibreson the earthquake-resistant design of reinforced concretestructures. Materials and Structures, RILEM, 2007, 40, pp.175–188.

8. RILEM Technical Committees, RILEM TC 162-TDF: Testand Design Methods for Steel Fibre-Reinforced Concrete,Recommendation: s-e Design Method. Materials and Struc-tures, RILEM, 2000, 33, pp. 75–81.

9. RILEM Technical Committees, RILEM TC 162-TDF: Testand Design Methods for Steel Fibre-Reinforced Concrete, Final Recommendation: s-e Design Method. Materials andStructures, RILEM, 2003, 36, pp. 560–567.

10. Barros, J. A., Figueiras, J. A.: Flexural behavior of SFRC: Test-ing and modelling. Journal of Materials in Civil EngineeringASCE, 1999, 11, No. 4, pp. 331–339.

11. Barros, J. A., Figueiras, J. A.: Model for the Analysis of SteelFibre Reinforced Concrete Slabs on Grade. Computers andStructures, 2001, 79, No. 1, pp. 97–106.

12. Tlemat, H., Pilakoutas, K., Neocleous, K.: Modelling ofSFRC using Inverse Finite Element Analysis. Materials andStructures, RILEM, 2006, 39, pp. 221–233.

13. Lok, T. S., Pei, J. S.: Flexural Behavior of Steel Fiber-Rein-forced Concrete. Journal of Materials in Civil EngineeringASCE, 1998, 10, No. 2, pp. 86–97.

14. Lok, T. S., Xiao, J. R.: Flexural Strength Assessment of SteelFiber-Reinforced Concrete. Journal of Materials in Civil En-gineering ASCE, 1999, 11, No. 3, pp. 188–196.

15. Syed Mohsin, S. M.: Behaviour of fibre-reinforced concretestructures under seismic loading. PhD thesis, Imperial Col-lege London, 2012.

16. Abbas, A. A., Syed Mohsin, S. M., Cotsovos, D. M.: Numeri-cal modelling of fibre-reinforced concrete. Proc. of Inter -national Conference on Computing in Civil & Building Engineering icccbe 2010, (ed W. Tizani), University of Not-tingham Press, Nottingham, UK, 2010, paper 237, p. 473, ISBN 978-1-907284-60-1.

17. Abbas, A. A., Syed Mohsin, S. M., Cotsovos, D. M.: A com-parative study on modelling approaches for fibre-reinforcedconcrete. Proc. of 9th HSTAM International Congress onMechanics, Limassol, Cyprus, 12–14 July 2010.

18. Bencardino, F., Rizzuti, L., Spadea, G., Ramnath, N.: Stress-Strain Behavior of Steel Fiber-Reinforced Concrete in Com-pression. Journal of Materials in Civil Engineering ASCE,2008, 20, No. 3, pp. 255–262.

19. Ghosh, S., Bhattacharjya, S., Chakraborty, S.: Compressivebehaviour of short-fibre-reinforced concrete. Magazine ofConcrete Research, 2007, 59, No. 8, pp. 567–574

20. BS EN 1992-1-1: Eurocode 2: Design of Concrete Structures– Part 1-1: General Rules and Rules for Buildings. BSI, Lon-don, 2004.

21. Zheng, Y., Robinson, D., Taylor, S., Cleland, D.: Non-linear fi-nite-element analysis of punching capacities of steel-con-crete bridge deck slabs. Structures and Buildings, ICE Proc.,2012, 165, No. 5, pp. 255–259.

Sharifah M. Syed Mohsin BSc(Eng.), DIC, PhDSenior LecturerFaculty of Civil & Earth ResourcesUniversiti Malaysia PahangLebuhraya Tun Razak, 26300 GambangKuantang, Pahang, MalaysiaE-mail: [email protected]

Ali A. Abbas BSc(Eng.), DIC, PhD, FHEASenior Lecturer in Structural EngineeringSchool of Architecture, Computing & EngineeringUniversity of East LondonLondon E16 2RD, UKTel.: 020 8223 6279Fax: 020 8223 2963E-mail: [email protected]

Demetrios M. Cotsovos Dipl Ing, MSc, DIC, PhD, CEngLecturer in Structural EngineeringInstitute of Infrastructure & EnvironmentSchool of the Built EnvironmentHeriot-Watt UniversityEdinburgh, EH14 4AS, UKE-mail: [email protected]

Held from 10 to 13 February 2014in Mumbai, India, the fourth fib In-ternational Congress and Exhibitionwas a memorable event from start tofinish, with high level technical pre-sentations, special invited lectures,valuable opportunities for network-ing and exchanges, as well as a richoffering of cultural activities, culi-nary delights and a picturesque lake-side venue.

Organised around the theme, “Im-proving performance of concretestructures”, the Congress focused on the needs of today’s changing society. Topics covered during thefour- day event included, amongothers:

– Existing concrete structures: re-pair, rehabilitation, retrofitting,

– Model Codes and their influenceon national codes,

– Design, construction and mainte-nance of large and/or innovativestructures precast concrete struc-tures,

– Steel-concrete hybrid structures,

– Improvements in prestressing systems,

– Improved understanding of newmaterials,

– High Performance and Ultra HighPerformance Concretes.

The Congress commenced on Mon-day 10 February with the ceremoni-al lighting of the Lamps of Knowl-edge. C.R. Alimchandani (Chairmanof the Organising Committee and ofIMC-fib), Ashok Basa (President ofIE(I)), and Gordon Clark (Presidentof fib) conveyed their warm wel-comes to the delegates, noting thewelcome return of fib to India fol-lowing the 1986 FIP Congress and2004 Symposium in New Delhi.Gordon Clark also drew attention tothe combined 60-year anniversary offib-CEB-FIP with a presentation onthe history and highlights of the as-sociation.

Also present to offer their welcomewishes to the delegates were Imme-diate Past President of IE(I) S.S.Rathore and the Director General of

IE(I) Major General (Retired) R. K.Sanan.

After the break, Gordon Clark pre-sented the 2014 Freyssinet Medals toJoost Walraven and Armando Ritoand Honorary Memberships toArnold van Acker (in absentia), Fernando Stucchi and C.R. Alim-chandani (see report on pp107–109). One of the highlights ofthe inaugural session was the presen-tation of the 2014 fib Awards forOutstanding Concrete Structures bythe jury chairman and ImmediatePast President of fib, György L.Balázs. This edition of the presti-gious award recognised five winningstructures and six special mention re-cipients; see the December 2013 is-sue of fib-news (http://www.fib-inter-national.org/fib_news_Dec2013.pdf)for the full results of the competition.

The afternoon sessions were devot-ed to plenary lectures by GiuseppeMancini (A sustainable approach toexisting structures), Hideki Kimura(Large scale application of HS-HP


2014 fib Congress, Mumbai: Improving performance of concrete structures

fib-news is produced as an integral partof the fib Journal Structural Concrete.

Contents Issue 1 (2014)

2014 fib Congress, Mumbai 106

2014 Freyssinet Medals 107

ConLife and 70thanniversary of NIISK 109

fibUK seminar report 109

20th anniversary of CBS 110

Report from the Spanish NMG 111

2015 fib Symposium 112

fib Bulletins 112

Congresses and symposia 113

Diginitaries with the traditional Lamps of Knowledge: R.K. Sanan, S.S. Rathore, C.R. Alimchandani, V.N. Heggade, S.G. Joglekar, Harald S. Müller, Ashok Basa, György L. Balázs, Gordon Clark

of the 2018 congress in Melbourne,Australia. Upcoming fib events wereannounced and previewed, the nextof which will be the 2015 sympo-sium in Copenhagen (see call for papers announcement on page 112),to be followed by symposia in CapeTown (2016) and Maastricht (2017).

Events continued even after the endof the Congress: three successfulworkshops on highly relevant topicswere held on 13 and 14 February:- fib Model Code for Concrete

Structures 2010 short course,- Workshop on durability,- Workshop on High Performance

Fiber Reinforced CementitiousComposites.

Technical Council, General Assemblyand Elections

In conjunction with the Congress,meetings were held by fib Commis-sions and Task Groups, as well asthe Technical Council and GeneralAssembly.

The Technical Council approved amajor initiative of the Presidium torestructure fib‘s Commissions andTask Groups. The details of the newstructure will be given in an upcom-ing issue of fib-news. The TechnicalCouncil appointed new Chairs andDeputy Chairs for 2015–2018 aswell as electing their two newDeputy-Chairs, Stephen Foster andFrank Dehn to represent the Techni-cal Council on the Presidium for thesame term.

FRC in Japan) and Joost Walraven(Dealing with the service life of con-crete structures – a continuous ad-venture).

The cultural programme includedperformances of Indian dance, dra-ma and music held on the Mondayand Tuesday evenings, providing fes-tive conclusions to the events of theday. The Gala dinner on Wednesdayevening was a sumptuous offering ofIndian specialities in the multi-course meal.

From Tuesday to Thursday, over250 papers were presented in about50 parallel sessions, in addition tospecial invited “on forefront of tech-nology” lectures that included re-ports from selected fib Commis-sions, Special Activity Groups andTask Groups. National reports werealso presented by fib National Mem-ber Groups: Brazil, Czech Republic,Denmark, France, Hungary, India,Japan, Norway, Portugal, Slovakia,Switzerland and the UK.

The valedictory session gave the opportunity for fib PresidentGordon Clark, fib President-electHarald S. Müller, Organising Com-mittee chairman C.R. Alimchandaniand selected delegates to give theirimpressions of this milestone eventand congratulate the organisers.

Following a vote of thanks, the tra-ditional fib Congress bell was hand-ed over to Stephen Foster and DavidMillar, representing the organisers

Structural Concrete 15 (2014), No. 1 107

fib-news

In additional to the usual businessof budget and balance approvals,the General Assembly approvedthree Honorary Memberships (seenext article).

Elections for the next terms wereheld by secret ballot and the follow-ing officers were elected:

– President, 1st January 2015 – 31December 2016: Harald S. Müller;

– Deputy-President, 1st January2015 – 31 December 2016: HugoCorres Peiretti (Spain);

– Four elected Presidium Members,1st January 2015 – 31 December2018: Josée Bastien (Canada),Akio Kasuga (Japan), AurelioMuttoni (Switzerland), Tor OleOlsen (Norway);

– Honorary treasurer 1st January2015 – 31 December 2018: HansRudolf Ganz (Switzerland).

Awardedevery fouryears at theoccasion of anfib Congress,the FreyssinetMedal is thehighest dis-

tinction awarded by fib. It is given“in recognition of outstanding tech-nical contributions in the field ofstructural concrete”, and is a contin-uation of the Freyssinet Medalsawarded by fib’s predecessor FIP(Fédération Internationale de la Précontrainte), since 1970.

The two 2014 Freyssinet Medalswere awarded by fib President Gor-don Clark to Joost Walraven (theNetherlands) and Armando Rito(Portugal) during the inaugural ses-sion of the recent 2014 Congress inMumbai.

2014 FreyssinetMedals

Handover of theCongress bell (fromleft to right: StephenFoster, C.R.Alimchandani, S.G.Joglekar)


fib-news

Joost Walraven received his PhDfrom the Technical University ofDelft, the Netherlands, in 1980. Af-ter several years as a design engi-neer for Corsmit Consulting Engi-neers, he began his academic careerin 1985 as a professor at the Techni-cal University of Darmstadt, Ger-many. In 1989 he returned to Delftas professor of concrete structures,where he was selected for the “Dis-tinguished Teacher Award” in 2005.He held this professorship until hisretirement in 2012, when he becameEmeritus Professor.

He is the author or co-author of 400publications in scientific and profes-sional journals and conference pro-ceedings, and advisor or co-advisorfor over 50 PhDs in the Nether-lands, Germany, Belgium, Swedenand Norway.

He has been prominently involvedin the work of CEB and fib for wellover two decades as Head of theDutch National Member groupsince 1991, member of the CEB andthen fib Presidium from 1992 to2006, and President of fib from 2000to 2002. He has been and continuesto be a member of numerous fibTask Groups and Special ActivityGroups in fib, contributing to bul-letins on service life design, retro-fitting of concrete structures, consti-tutive modeling of HS/HPC, shearand punching shear, and the twoedition of the fib Structural Con-crete textbook.

His most notable contribution in re-cent years has been as the convenerof Special Activity Group 5, NewModel Code. In this role he headed,during a period of nearly ten years,the development and drafting of the2010 fib Model Code for ConcreteStructures which was approved bythe fib General Assembly in 2011and published in hardcover andebook editions in 2013.

Joost Walraven has been awardednumerous honours and distinctionsaround the world, including the FIPMedal in 1998.

Armando Rito received his civil en-gineering degree in 1969 at theTechnical University of Lisbon. Hefounded his design office soon after,in 1971, and devoted his work main-ly to bridge design with a focus onsimplicity of design and construc-tion, feasibility, functionality, dura-bility, economy and aesthetical val-ue. To date, several hundred of hisbridge and viaduct designs havebeen built, including the Miguel Tor-ga bridge, the Arade River bridge,the Vila Pouca de Aguiar viaductand the 4th April bridge over theCatumbel river in Angola.

He has introduced and developedseveral new bridge design conceptsthat were adopted as standards byPortuguese bridge designers, for ex-ample two-beam (Π) decks, thepile/pier where the pier is the natur-al extension of the pile, the structur-al and visual continuity between Π

Left: Gordon Clark with Joost and Rose Walraven; right: with Isabel and Armando Rito

decks in span-by-span constructionand box girders of balanced can-tilever construction, new cross sec-tions on the designs of high-risepiers, refinements on box girders forthe arrangement of prestressing ca-bles.

In addition to his design work, hewas an invited professor of bridgedesign at ISEL – Lisbon PolytechnicInstitute and at the PortugueseCatholic University, retired since2008.

He was an expert member of the“Project Team 2”, EC2 – Part 2:Concrete bridges, member of fibTask Group 1.2 “Bridges”, and haspublished over 70 papers andkeynote lectures on the subject ofbridge design and construction.

Armando Rito has been laudedthrough a number of internationalprizes and honours; he was alsoawarded the FIP Medal in 1998.

Honorary Memberships

Honorary life memberships are giv-en by the fib General Assembly inrecognition of significant personalcontributions to the work of fib. Atthe 2014 General Assembly, hon-orary memberships were bestowedon C.R. Alimchandani (India), Fer-nando Stucchi (Brazil) and Arnoldvan Acker (Belgium).

C.R. Alimchandaniwas awarded Hon-orary Membershipin recognition ofhis invaluable rolesas FIP Vice Presi-dent, Head of the

Indian National Member Group, or-ganiser of the 1986 FIP Congress inNew Delhi and of the 2014 fib Con-gress in Mumbai, and member of fibCommission 1.

Fernando Stucchi was awardedHonorary Membership in recogni-tion of his invaluable roles as Head


fib-news

fibUK held its first half-day seminar“DISC2013 – Developments inStructural Concrete” on 6th Nov2013. Such was its success that itwill become an annual event, sched-uled on the day of the group’s Annu-al General Meeting.

DISC2013 covered off-site manufac-ture, service life design, shear inbeams and concrete cable stayedbridges. The structure of the after-noon worked well with each of thetwo sessions consisting of two 30-minute technical presentations andone 15-minute presentation on anaspect of fib, followed by time forquestions.

Presentations and other useful docu-ments were made available to fee-paying delegates on a fibUK brand-ed flashdrive. Members of the UKGroup can view videos of the pre-sentations on the group’s website

(www.fibuk.org). An outline of theseminar presentations is given be-low.

Session 1

Laing O’Rourke’s Dr. John Stehlediscussed the off-site manufacturingprocesses at its UK factories andpresented two case studies highlight-ing how complex design and con-struction issues were overcome by aone team approach.

Prof. Tom Harrison, visiting profes-sor at Dundee University, describedthe challenges and limitations onserviceability design by carbonation,corrosion (chloride induced or oth-erwise) and chemical attacks. Heshowed the differences in current re-quirements in the fib model code,ISO16204 & Eurocodes.

fib President Gordon Clark briefedthe audience on the wide range offib activities, the history of the fib’sformation and its achievements.

Session 2

Prof. Steve Denton explained howthe new CEN/TC250 commissionwas focussing on ease of use of theEurocodes for the second genera-tion of Eurocodes.

Dr. Tony Jones of Arup presentedon shear. He illustrated the shear re-inforcement against shear stress forvariable strut inclinations and com-pared this against traditional Vc+Vs.He discussed the effect of pre-stresson shear (benefit/loss) comparingEN1991-1-1 to the model code andidentified this as one of the areas forimprovement along with shear forcircular sections.

David MacKenzie from Flint &Neill argued that the recent develop-ments in concrete cable stayedbridges made them an economic al-ternative to other materials. He alsoexplained the contribution made bythe Model Code in bridge designs.

fibUK seminarhailed a success

fib President Gordon Clark travelledto give presentations in Moscowand Kiev during November and De-cember. He was invited as a keynotespeaker at the opening of the confer-ence “ConLife” in Moscow on 27November, which is an annual 4-dayconference and exhibition for theConcrete Industry. After the wel-come by an official from the organi-sation responsible for Russian Build-ing Standards, during which it wasannounced that Russia have signedan agreement with CENELEC toadapt Eurocodes for use in Russia,he spoke about fib, its organisationand activities, and the new ModelCode 2010, explaining that it is ex-pected to form the basis for the nextrevision of the Concrete Eurocode.

ConLife and 70th anniversaryof NIISK

of the BrazilianNational MemberGroup and jurychairman for the2013 and 2015 editions of the fibAchievementAwards for Young

Engineers, as well as his contribu-tions to the fib Model Code for Con-crete Structures 2010.

Arnold van Ackerwas awarded Hon-orary Membership(in absentia) inrecognition of hisinvaluable chair-manship of the Pre-fabrication Com-

mission for many years, his role asex-officio member of the fib SteeringCommittee and his authorship ofseveral important fib bulletins onprefabrication.

In Kiev, Gordon was invited by theUkraine Research Institute forBuilding Construction “NIISK” togive a welcome and congratulatoryspeech on the occasion of the 70thAnniversary of their foundation in1943. The Institute was foundedduring the Second World War witha remit to set standards and assist inreconstruction of the damaged Infra-structure in the country. Since thenit has now taken responsibility inthe post-Soviet era for the UkraineBuilding Standards and holds the fibNational Membership. He speciallywelcomed the long-standing supportby the Institute for fib and formerlyfor FIP since the 1960’s. About 200invited guests were present at theevent from across the Ukraine andRussia, as well as other Europeanguests.


fib-news

In November2013 the CzechConcrete Society(CBS), in con-junction withmany Czechtechnical experts,

local collaborators and internationalpartners, commemorated the 20thanniversary of its founding. The oc-casion was an opportunity to recalland pay tribute to twenty years of ef-forts by CBS to maintain the excel-lent level of Czech concrete struc-tures within the local constructionmarket.

CBS was founded on 8th December2002, under umbrella of the CSSI(Czech Society of Civil Engineers),by several professionals includingboth academics and engineers fromthe Czech construction industry.They formulated three principalgoals for CBS that have determinedthe character of the Society up tothe present: (1) to maintain the tra-ditionally high level of Czech con-crete structures; (2) to promote con-crete as an efficient buildingmaterial; (3) to create a social andcommunication platform for allCzech professionals involved in con-crete construction. There were twomore key features of CBS inscribedinto its statutes at that time: (a) in-dependence from any commercial

groups on the market, (b) focus ontechnical matters only.

The first 5-6 years of CBS’ existencewas marked by a quest for a stableposition, both in terms of financingand production of viable projects.Other significant factors for the peri-od of 1994–1999 were the search fora sound status and significant andsharp changes in CBS membership.Soon it became obvious that in-creasing CBS aspirations and the ex-pectations of its members surpassedthe possibilities of its representa-tives, who were still just volunteers.Despite its non-professional admin-istrative base, CBS founded andmaintained several successful andappreciated projects, namely its an-nual (Czech) Concrete Day confer-ence, the “Beton a zdivo” (Concreteand Masonry) journal and an Out-standing Concrete Structure Award.Also, multiple contacts and partici-pation in the international activitiesof IABSE, CEB and especially ofFIP/fib were kept and enhanced.

Since 2000 CBS developed steadilyand rapidly, primarily thanks to ofincreasing Czech construction mar-ket and growing economy. A boom-ing government investment into in-frastructure at that time generatedan abundance of both technicalknowledge and business informa-

20th Anniversary of the Czech Concrete Societytion, attracting a huge attendance atCBS events. But also a brand newCBS organization and internal regu-lations focused on financing, divi-sion of responsibility, etc., led toquite long period of expansion andgrowth. A new, professional CBS office was opened in Prague, and itsfull-time staff, under the guidance ofDr. Vlastimil Šruma, Managing Di-rector of CBS, succeeded in manag-ing the expanding portfolio of CBSprojects and events. Consequentlyboth the numbers of CBS membersand participants in CBS activitiesexpanded substantially between2000 and 2008.

For the last five years CBS has beenfacing bitter impacts of the consider-able depression of the Czech con-struction market. There are also,partly as a consequence of thebroader European financial crisis,more general changes in companies’and individuals’ behaviour in theconstruction market and in thespreading of information. As a resultof all these impacts, it seems to bealmost necessary at least to rethink,and maybe also to redefine, thetwenty-year old key principles of thecurrent CBS. Thus also the CzechConcrete Society is searching againfor long-term stability and efficiencyfor the demanding years to come.

The main celebration of the 20thCBS anniversary took place inHradec Kralove on 27–28 Novem-ber 2013. Among CBS representa-tives, CBS honorary members andnumerous leading personalities fromthe Czech construction industry andtechnical universities, there were al-so some close friends and partnersof CBS present from abroad: Mr.Gordon Clark, President of fib, Prof.György L. Balázs, Past-president offib, Dr. Lars Mayer and Ing. Michael Pauser, directors of concrete/construction societies ofGermany and Austria.

Dr. Vlastimil Šruma, CBS ManagingDirector

Shortly before the cutting of the 20th CBS anniversary cake: (from the left) Jirí Kolísko (CBS President),György L. Balázs (fib Immediate Past President), Gordon Clark (fib President), Milan Kalný (CBS PastPresident), Jan L. Vítek (CBS Past President), Pavel Cížek (first CBS President), Michael Pauser(Austrian Concrete Society), Vlastimil Šruma (Director CBS) and Lars Meyer (DBV Germany)


fib-news

This report describes the activities ofACHE (Spanish abbreviation forScientific and Technical Associationfor Structural Concrete, www.e-ache.com). This association is the re-sult of merging the two parent asso-ciations: GEHO (the Spanishsubsidiary of CEB) and ATEP (theSpanish subsidiary of FIP). It hasover 900 members; most of them areindividuals but there is also an im-portant participation of institutions:consulting companies, contractors,fabricators, suppliers, software com-panies, etc. ACHE’s income mainlycomes from the member fees andconferences.

Its activities are organized on the ba-sis of three-year terms. At the end ofeach term a congress is organized(the next is 17–19 June 2014) andhalf of the Council of the association,including the President, is renovated.The congress is a big event with over400 participants and about the samenumber of papers being presented.Every year ACHE also organizes atleast one symposium on a specifictopic, generally related to the activi-ties of one of its work groups. Finally,ACHE also organizes courses, gener-ally related to the publication of newconcrete codes.

The secretariat of ACHE includesone full-time and two part-time posi-tions, but most of its activities arebased on voluntary work. The mostimportant results come from thework groups. They are organized infive commissions: design, materials,execution, maintenance and structur-al elements. Each of these commis-sions monitors a number of workinggroups and reports on progress everytwo months. The total number ofworking groups which are active atthis moment is 26. The activities ofeach working group end when amonograph is published and distrib-uted among the members of the Asso-ciation. These activities are the basefor interchanging new developmentsand for including them in future stan-dards. These documents are an im-

portant reference in Spain for thewhole concrete related industry.

Among the last monographs whichhave been published we might men-tion a compilation of all topics relat-ed to the design and construction ofhigh rise buildings (two books ofabout 500 pages each) which wasthe result of efforts by many differ-ent professionals, as is the casewhen such a building has to beplanned, designed and built. Thesemonographs may also consist of atheoretical development related toconcrete such as a recent one onstatistical methods or they also mayinclude some contributions to con-troversial topics which may be de-bated in international groups suchas two recently published mono-graphs on imposed deformations inconcrete structures or on shearstrength of elements without trans-verse reinforcement.

A reduced list of active workinggroups which should end their workin a short delay would include:Graphic representation of concretestructures, Design of concrete struc-tures in seismic areas, Aggregates forstructural concrete, Movement ofgreat weights, External aspect ofconcrete, Systems for increasing thedurability of existing structures,Maintenance manuals, Retrofittingof columns, Examples of applicationof Eurocode 2. Newly formed work-ing groups include the followingtopics: Nanotechnology, Fibre-rein-forced concrete, Materials for ther-mal insulation, Execution of incre-mentally launched decks, Selflaunching gantries and travellers, In-spection and monitoring techniques.

The most significant product ofACHE is the quarterly Journal“Hormigón y Acero” (Concrete andSteel in Spanish) which was foundedin 1950. This journal accepts contri-butions from the industry as well asfrom the universities and research in-stitutes. Consequently it is usual tosee papers on the design and con-

struction of structures along with re-search papers. This possibility ofcommunication between all the dif-ferent participants in the construc-tion industry and the researchers ofUniversities and Institutes is veryprofitable for all of them and is oneof the main assets of the Associationand of the “Hormigón y Acero”. Thejournal is published in Spanish al-though each paper includes an ab-stract in English. Every issue of thejournal includes a first principal pa-per, which is published in Spanishand in English; this paper generallyconsists in the presentation of a veryrelevant project and, as it is only lim-ited to 10000 words, it usually pre-sents many interesting details of thecorresponding project. These princi-pal papers are freely accessiblethrough the web (http://e-ache.com/mod-ules/pd-downloads/viewcat. php?cid=1). Allthe details of the journal may befound in http://e-ache.com/mod-ules/smartsection/item.php?itemid=99. Beginning in 2014, “Hormigón yAcero” will be edited by Elsevier.

Like other fibNational MemberGroups, ACHE oc-casionally publish-es a national reporton the most inter-esting project thatwere completed inthe correspondingtime period. The

last one covers the period between1998 and 2008; it includes 140works and was presented at the2010 fib Congress. The projects in-cluded show the extraordinary de-velopment experienced by Spanishstructural engineering in recentyears. We wish to spread and shareour experience with our colleaguesaround the world which is why wehave provided a bilingual Spanish-English publication. Details on thisbook may be found at http://e-ache.com/modules/smart-section/item.php?itemid=119ACHE is currently making an effort

Report from the Spanish fib Member Group


fib-news

fib Bulletin 70:Code-type modelsfor structural be-haviour of concrete– Background ofthe constitutive re-lations and materialmodels in MC2010.State-of-art re-

port, November 2013. 196 pages, ISBN 978-2-88394-110-6, Non-mem-ber price: 120 CHF.

The fib Model Code for ConcreteStructures 2010 (MC2010) repre-sents the state-of-the-art of code-typemodels for structural behaviour ofconcrete, providing constitutive rela-tions and material models togetherwith the most important explanatorynotes. However the underlying nor-mative work, i.e. the fundamentaldata as well as the considerationsand discussions behind the formu-las, could not be given within theModel Code text. Based on experi-ence gained after the publication ofModel Code 1990, this will lead tonumerous questions arising fromModel Code users.

fib Bulletin 70 aims to conquer thisgeneral weakness of codes in a wayto guard against future misunder-standings of MC2010 chapter 5.1(Concrete). It discusses the givenformulas in connection with experi-mental data and the most importantinternational literature. The consti-tutive relations or material models,being included in MC1990 andforming the basis and point of originof the Task Group’s work, were crit-ically evaluated, if necessary andpossible adjusted, or replaced bycompletely new approaches. Majorcriteria were physical and thermody-namical soundness and practicalconsiderations like simplicity andoperationality.

Besides being a background docu-ment for Chapter 5.1 of MC2010,Buletin 70 will provide an importantfoundation for the development offuture generations of code-type mod-

els related to the characteristics andthe behaviour of structural concrete.

fib Bulletin 71:Integrated Life Cycle Assessmentof concrete struc-tures. State-of-artreport, December2013. 64 pages,ISBN 978-2-88394-111-3,

Non-member price: 80 CHF.

Concrete is after water the secondmost used material. The productionof concrete in the industrializedcountries annually amounts to 1.5-3tonne per capita and is still increas-ing. This has significant impact onthe environment. Thus there is anurgent need for more effective use ofconcrete in structures and their as-sessment.

The scope of fib Task Group 3.7’swork was to define the methodologyfor integrated life-cycle assessmentof concrete structures and to set upbasic methodology to be helpful indevelopment of design and assess-ment tools focused on sustainabilityof concrete structure within thewhole life cycle. Integrated Life Cy-cle Assessment (ILCA) represents anadvanced approach integrating dif-ferent aspects of sustainability inone complex assessment procedure.The integrated approach is neces-sary to insure that the structure willserve during the whole expected ser-vice life with a maximum functionalquality and safety, while environ-mental and economic loads will bekept at a low level. The effective ap-plication and quality of results aredependent on the availability of rele-vant input data obtained using a de-tailed inventory analysis, based onspecific regional conditions. Theevaluation of the real level of totalquality of concrete structure shouldbe based on a detailed ILCA analy-sis using regionally or locally rele-vant data sets.

fib Bulletinsto promote its activities through theweb to make all its publicationsmore accessible to foreign individu-als and institutions and it also actsas the distribution node for the pub-lications and activities of fib to pro-mote the progress of structural con-crete in Spain. Foreign engineersand architects are invited to partici-pate in our activities and to publishtheir work in our Journal or to pre-sent it in our Congresses.

Miguel A. Astiz, President of ACHE

Abstracts are now being acceptedfor the 2015 fib Symposium, takingplace in Copenhagen, Denmark,from 18 to 20 May 2015. The ab-stract text must be max. 500 wordswith no tables or pictures; the dead-line for submission is 1st May 2014.

The symposium theme is “Concrete:Innovation and Design”, with thefollowing sub-topics:– Civil works– Conservation of structures– Innovation in buildings– New materials and structures– Analysis and design– Modeling of concrete– Numerical modeling– Life cycle design– Safety and reliability

A “case studies” format will be of-fered for oral presentations of struc-tural concrete projects, under execu-tion or recently completed, withouta submitted paper. The PowerPointpresentation is subject to review bythe Scientific Committee.

To submit an abstract and for fur-ther information about the event,visit www.fibcopenhagen2015.dk.

2015 symposium: call for papers


fib-news

Congresses and symposia

The calendar lists fib congresses and symposia, co-sponsored events and, if space permits, events supported by fib or organised by one of its NationalMember Groups. It reflects the state of information available to the Secretariat at the time of printing; the information given may be subject to change. Thecalendar of events on the fib website (www.fib-international.org/upcoming-event) is updated continuously.

Date and location Event Main organiser Contact

12–16 May 2014 3nd All-Russia (International) Russian Academy of http://concrete2014.mgsu.ruMoscow, Russia Conference on Concrete and Science and others

Reinforced Concrete

11–13 June 2014 Concrete Innovation Norwegian Concrete www.cic2014.comOslo, Norway Conference (CIC2014) Assocation

16–18 June 2014 AMCM 2014: Analytical Models fib Group Poland www.amcm2014.pwr.wroc.plWroclaw, Poland and New Concepts in Concrete

and Masonry Structures

21–23 July 2014 10th fib International Ph.D. Université Laval www.fib-phd.ulaval.caQuebec, Canada Symposium in Civil Engineering

24–25 July 2014 2nd FRC Int. Workshop ACI-fib www.polymtl.ca/frc2014Montreal, Canada (1st ACI–fib Joint Workshop)

on Fibre Reinforced Concrete

14–17 September 2014 Int. Conf. on Application of TU Dresden [email protected], Germany superabsorbent polymers

and other new admixtures in concrete construction

15–18 September 2014 10th International symposium Beijing Jiaotong University www.hpc-2014.comBeijing, China on Utilization of HS/HPC

21–24 September 2014 6th International Conference Asian Concrete Federation www.acf2014.krSeoul, Korea of Asis Concrete Federation Korea Concrete Institute

18–20 May 2015 fib Symposium: Concrete Danish Concrete Society www.fibcopenhagen2015.dkCopenhagen, Denmark – innovation and design

24–26 May 2015 5th Int. Symposium on www.nicom5.orgChicago, USA Nanotechnology in

Construction – NICOM5

5–7 October 2015 4th Int. Conf. on Concrete MFPA Leipzig GmbH [email protected], Germany Repair, Rehabilitation and University of Cape Town

Retrofitting (ICCRRR 2015)

8–9 October 2015 4th International Workshop MFPA Leipzig GmbH [email protected], Germany on Concrete Spalling due to TU Delft

Fire Exposure

21–23 November 2016 fib Symposium fib Group South Africa To be announcedCape Town, South Africa

13–17 June 2017 fib Symposium fib Group Netherlands To be announcedMaastricht, Netherlands

6–12 October 2018 5th fib Congress and fib Group Australia www.fibcongress2018.comMelbourne, Australia Exhibition

Giancarlo Groli, Caldentey Pérez,Giraldo Alejandro, Alejandro Soto Cracking Performance of SCCreinforced with recycled fibres: an experimental study

Xian Liu, Yong Yuan, Ke SuSensitivity analysis of the early-agecracking risk in immersed tunnel

Günther Meschke, Rolf Breitenbücher,Fanbing Song, Yjian ZhanExperimental, analytical andnumerical analysis of the pulloutbehavior of steel fibers consideringdifferent fiber types, inclinations andconcrete strengths

Sevket Ozden, Hilal M. Atalay, Erkan Akpinar, Hakan Erdogan, Yilmaz Zafer VulasShear Strengthening of RC T-Beamswith Fully or Partially Bonded FRPComposites

Alfred Strauss, Jan Podrouzek, Konrad BergmeisterRobustness based performanceassessment of concrete bridges

Bhupinder Singh, M. John Robert PrinceInvestigation of bond behaviourbetween recycled aggregate concreteand deformed steel bars

Jianzhuang Xiao, Yuhui Fan, Vivian Tam Effect of old attached mortar on thecreep of recycled aggregate concrete

Vladimir Cervenka, Hans GanzValidation of post-tensioninganchorage zones by laboratory testingand numerical simulation

Yong Yuan, Yang ChiWater permeability of concrete underuniaxial tension

Morteza Aboutalebi, Amir Alani,Gokhan KilicApplications of non-contact senor(IBIS-S) and finite element method inassessment of bridge deck structures

Preview

Structural Concrete 2/2014

The paper by Alfred Strauss, Jan Podrouzek and Konrad Bergmeister presents strategies for robust-ness based performance assessment using nonlinear modeling. It also discusses relevant reliability-based quantities and performance indicators in relation to structural damage, at the example of specific degradation events in an existing prestressed box-girder bridge. The paper also describesstrategies on the basis of the novel approach for general complex engineering structures.

The potential and the limitations of numerical methods

The book gives a compact review of fi nite element and other nu-merical methods. The key to these methods is through a proper description of material behavior. Thus, the book summarizes the essential material properties of concrete and reinforcement and their interaction through bond.

Most problems are illustrated by examples which are solved by the program package ConFem, based on the freely available Py-thon programming language. The ConFem source code together with the problem data is available under open source rules in combination with this book.

Table of content:

fi nite element in a nutschell uniaxial structural concrete behavior 2D structural beams and frames strut-and-tie models multiaxial concrete material behavior deep beams slabs appendix

*€ Prices are valid in Germany, exclusively, and subject to alterations. Prices incl. VAT. excl. shipping. 1044106_dp


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