Structural Concrete 01/2014 Free Sample Copy by Ernst & Sohn

1 Volume 15 March 2014 ISSN 1464-4177

- Long-term properties of recycled aggregate concrete - Resistance of hollow circular RC members under combined bending/shear â&#x20AC;&#x201C; 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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Contents

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

Structural Concrete Vol. 15 / 1

March 2014 ISSN 1464-4177 (print) ISSN 1751-7648 (online) Wilhelm Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG www.ernst-und-sohn.de

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

Journal of the fib

Peer reviewed journal Since 2009, Structural Concrete is indexed in Thomson Reuter’s Web of Knowledge (ISI Web of Science). Impact Factor 2012: 0.289

www.wileyonlinelibrary.com, the portal for Structural Concrete online subscriptions

Editorial 1

Xilin Lu Precast concrete structures in the future Technical Papers

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

István Völgyi, Andor Windisch, György Farkas Resistance of reinforced concrete members with hollow circular cross-sections under combined bending and shear – Part I: experimental investigation

István Völgyi, Andor Windisch Resistance of reinforced concrete members with hollow circular cross-sections under combined bending and shear – Part II: New calculation model

Jerzy Onysyk, Jan Biliszczuk, Przemysław Prabucki, Krzysztof Sadowski, Robert Toczkiewicz Strengthening the 100-year-old reinforced concrete dome of the Centennial Hall in Wrocław

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

John Cains Staggered lap joints for tension reinforcement

Johan Magnusson, Mikael Hallgren, Anders Ansell Shear in concrete structures subjected to dynamics loads

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

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

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

106 107 109 109 110 111 112 112 113

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Products and Projects Bautechnik 81 (2004), Heft 1

Imprint The journal “Structural Concrete”, the official journal of the International Federation for Structural Concrete (fib – fédération internationale du béton), provides conceptual and procedural guidance in the field of concrete construction, and features peerreviewed papers, keynote research and industry news covering all aspects of the design, construction, performance in service and demolition of concrete structures. “Structural Concrete” is published four times per year completely in English. Except for a manuscript, the publisher Ernst & Sohn purchases exclusive publishing rights. Only works are accepted for publication, whose content has never been published before. The publishing rights for the pictures and drawings made available are to be obtained from the author. The author undertakes not to reprint his article without the express permission of the publisher Ernst & Sohn. The “Notes for authors” regulate the relationship between author and editorial staff or publisher, and the composition of articles. These can be obtained from the publisher or in the Internet at www.ernstund-sohn.de/en/journals. The articles published in the journal are protected by copyright. All rights, particularly that of translation into foreign languages, are reserved. No part of this journal may be reproduced in any form without the written approval of the publisher. Names of brands or trade names published in the journal are not to be considered free under the terms of the law regarding the protection of trademarks, even if they are not individually marked as registered trademarks.

Editorial board Editor-in-Chief ß Luc Taerwe (Belgium), e-mail: Luc.Taerwe@UGent.be Deputy Editor ß Steinar Helland (Norway), e-mail: steinar.helland@skanska.no Members ß 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)

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Current prices The journal Structural Concrete has four issues per year. In addition to “Structural Concrete print”, the PDF version “Structural Concrete online” is available on subscription through the online service Wiley Online Library.

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Other currencies and bulk discounts are available on request. Members of the fib receive the journal Structural Concrete as part of their membership. Prices exclusive VAT and inclusive postage, errors and omissions excepted. Subject to change without notice. Prices are valid until 31 August 2014. A subscription lasts for one year. It can be terminated in writing at any time with a period of notice of three months to the end of the calendar year. Otherwise, the subscription extends for a further year without written notification. Bank details Commerzbank AG Mannheim account number 751118800 bank sort code 67080050 SWIFT: DRESDEFF670 Periodical postage paid at Jamaica NY 11431. Air freight and mailing in the USA by Publications Expediting Services Inc., 200 Meacham Ave., Elmont NY 11003. USA POSTMASTER: Send address changes to “Structural Concrete” c/o Wiley-VCH, 111 River Street, Hoboken, NJ 07030. Service for customers and readers Wiley-VCH Customer Service for Ernst & Sohn Boschstrasse 12, D-69469 Weinheim Tel.: +49 (0)800 1800 536 (within Germany) Tel.: +44 (0)1865476721 (outside Germany) Fax: +49 (0)6201 606184 cs-germany@wiley.com Quicklink: www.wileycustomerhelp.com © 2014 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin

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Structural Concrete 15 (2014), No. 1

Products & Projects

Indeed, it was the search for savings that prompted the development of the new scaffolding system. The Bilfinger company wanted to offer its customer an alternative to the free-standing scaffolding that was previously used for the most part. Until now, this was the only type of scaffolding which it was possible to use with structures such as tanks for which no anchoring is possible and any attempt to weld fittings to the side would damage the structure. The Bilfinger experts suggested a new approach involving the use of a magnet system. The magnetic scaffolding anchoring entails a permanent lifting magnet which can be switched on and off as required and produces a constant magnetic force. The necessary capacity is calculated for

each anchor by measuring the holding power and shear force. The results are reconciled with the static calculations and only when the measurements match the static calculations is the anchor approved for use. A specially developed testing device is utilised at the site to measure the capacity of the magnetic scaffolding anchoring to ensure the reliability of each individual anchor. Magnets which have proven themselves in a number of different industrial applications are used for this purpose. Thus, for example, the same types of magnets are utilised in rope and lifting systems for heavy loads. Explains Ruud van Doorn, Chief Executive Officer at Bilfinger Industrial Services Belgium/Netherlands: “We are observing mounting pressure on the part of our customers to have maintenance work performed safely and cost-efficiently. The use of magnetic anchoring in scaffolding is an excellent example which demonstrates the contribution which Bilfinger is making.”

The 3D Framework Program

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Cross-Sections

Bilfinger Industrial Services has entered new territory in scaffolding. Tall industrial scaffolding is normally affixed to the side of the building for which it is required. If this is not possible, freestanding, non-anchored scaffolding must be assembled. Working for one of its customers, Bilfinger Industrial Services Nederland has now assembled scaffolding affixed to a tank using magnetic anchoring. 35 m tall and 5 m wide, it is more compact than the free-standing scaffolding normally required for the tank. In this way it was possible to lower costs by some 30 %.

Structural Analysis and Design

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

Bridge Construction

Connections

3D Frameworks

Stability and Dynamics

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

Up-to-Date Information...

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)

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Products & Projects

Corridor Vc: High-performing wagon for high speed In the future, travelling between Budapest and Southern Dalmatia will take less time thanks to the Pan-European Corridor Vc. Numerous tunnels and bridges are erected along the 397 km route through Bosnia owing to the difficult topography. Doka’s contribution to the infrastructure initiative is a formwork solution including a total of ten Cantilever forming travellers for the Studenˇcica and Trebižat bridges crossing the valleys. Altogether the European route 73 is about 702 km long. A1 is an important section of this route in Bosnia-Herzegovina connecting the northern border to the Adriatic by way of Zenica – Sarajevo – Mostar. The two bridges, Studenˇcica and Trebižat, are intended to ˇ connect the valleys near the municipality of Capljina. Hering, subcontractor of OHL, the Spanish construction company, will benefit primarily from the extended pouring sections of the Doka-Cantilever forming traveller that will reduce construction time by about eight weeks. Decisive factors for awarding the contract to Doka Croatia were many joint projects, high-performing systems as well as the ability to rent the formwork materials. With a stretch of 555 m in length from one abutment to the other and maximum height of 81°m above the valley, Studenˇcica is the longer and higher of the two bridges. Four superstructures, each 12.4 m wide and placed at a distance of 120 m from the other, are established on a total of five piers. At a total length of 365 m and 59.5 m maximum height, Trebižat, the smaller pendant requires only three piers. Doka developed a safe and fast formwork solution consisting of Cantilever forming travellers. A total of ten

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

rentable Cantilever forming travellers, eight of them on the Studenˇcica Bridge and two on the Trebižat Bridge, are making for smooth and rapid progress at lofty heights.

First upward, then straight ahead High-performing Cantilever forming travellers allow for pouring of 5 m segments in a weekly cycle. In the Corridor Vc project, completely identical Forming wagons designed for 250 t carry maximum loads of 196.5 t. “These extended 5 m pouring segments reduce the number of segments and coupling joints and therefore save time and money”, says Project Manager Mario Jurisic. The suggestion by both, the Business Development and Bridge Competence Centers, to extend the pouring segment to 5 m facilitates completion with eight fewer segments thanks to the high-performing Cantilever forming travellers. In the case of a weekly cycle, this means the project is completed eight weeks ahead of time. By changing the cross slope and tapering the walls of the superstructures each segment was planned individually, thereby eliminating the need to adapt the formwork. Special installation of pieces made-to-measure and a custom solution with reusable removable elements in the interior formwork prevent loss of large quantities of materials. This system facilitates a height adjustment of the Cantilever forming traveller’s interior formwork especially for the cross slope change.

Tough as nails at the limit Fig. 1. High-performing at lofty heights: Ten Doka-Cantilever forming travellers allow for rapid and safe construction of both bridges along the Corridor 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 travellers that save time and resources thanks to extended pouring sections.

Structural Concrete 15 (2014), No. 1

Doka materials came into play for the piers as well. Columns were constructed with the help of the crane-lifted Climbing formwork MF240 and Framed formwork Framax Xlife. With hammerheads high-performing Supporting construction frames were used horizontally. Doka Croatia in cooperation with the Bridge Competence Center demonstrated planning precision as well as creativity in order to get the Forming wagons into position at a height of 81 m. Parts of a gantry crane placed on the formwork lifted the Cantilever forming traveller’s floor grate a bit at a time. The floor piece usually raised by its own winches at the Cantilever forming traveller can only be connected to the formwork once it is on the hammerhead. A Doka Formwork instructor on site ensures correct set-up and optimised use of the materials. Limited workspace on the hammerheads with dimensions of 8 m in length called for a special solution. Whereas the forming wagons weighing approximately 80 t start moving symmetrically in two directions with the cantilever forming principle, Doka’s structural engineers figured out a fine-grained custom solution for this project. Thanks to the exact calculations, one of the Cantilever forming travellers will first start off from the hammerhead. Then enough space is available for hitching the second traveller to it and offset the balancing act. In order to get around the lifting pro-

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Products & Projects cedure, the Cantilever forming travellers will return once the width of a span has been completed; they are then repositioned and used again for the next pier.

Cross-border cooperation The Forming wagon is fully equipped with secured platforms, safe Access systems and access to all places on the Forming wagon where work is done. This allows for safe progress even at lofty heights. In addition to fine-grained Formwork planning carried out by the teams at the Bridge and Business Development Competence Centers ahead of time, local engineers aid in smooth construction progress on site. Holedeck Rawconcrete (© Holdecek)

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

Probably the most sustainable concrete structure in the world The new concrete waffle slab HOLEDECK is a patented system of voided slabs that can be pierced all through its thickness by the building conductions and services. Using Holedeck means the reduction of total built volume, concrete consumption and Co2 footprint. Holedeck system is the answer to a wide problem in those buildings such as hospitals, offices or malls, which require both large spans and a high level of building services and installations. Holedeck avoids the necessity of a big edge with its waffle con-

crete slab solution, bidirectional perforated to imbibe all kinds of conductions and installations. This way, suspended ceilings and the extra height associated to them are not necessary anymore. Thanks to the integration of structure and installations, it is possible to get an extra storey per each five, reducing this way the total area of the exterior enclosure and the consequent energy losses. To all these advantages, the saving of materials and the simplification of the assembly of installations should be taken into account. The simplicity of the system allows service elements to be easily replaced and repositioned, with no need of hindrance to any other activity being carried on in the building. Holedeck standard module is 80 × 80 cm in horizontal layout so it can be easily adapted to accept installations and elements designed for standard modulated ceilings. Further Information: HOLEDECK S.L., Juan de Urbieta 10, Madrid 28007, Tel. +34 915021427, info@holedeck.com, www.holedeck.com

Multi-Storey Precast Concrete Framed Structures

Kim S. Elliott, Colin Jolly Multi-Storey Precast Concrete Framed Structures 2. Edition 2014. 760 pages. € 115,–* ISBN 978-1-4051-0614-6 Also available as

This book provides practicing engineers with detailed design procedures and reference material on what is now widely regarded as an economic, structurally sound and versatile form of construction for multi-storey buildings. This revised and updated 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.

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

Products & Projects

Reinforced Concrete Design According to EC 2 and Other International Standards With RSTAB and RFEM, Dlubal’s main programs for structural analysis, one can design reinforced concrete structures not only according to EC 2 but also three further international standards: ACI 318-11 (US Standard), SIA 262:2003 (Swiss Standard), GB 50010-2010 (Chinese Standard). 17 National Annexes are currently available for the design according to EC 2 (EN 1992-1-1:2004), among them the annexes of Germany, Austria, Italy, the Netherlands, France and Spain.

Functionality The designs for the ultimate and the serviceability limit state are performed for all standards in the corresponding CONCRETE add-on modules for surfaces (only in RFEM) and members. In addition, it is possible to consider cracked sections of the concrete (state II). Moreover, if rectangular or circular cross-sections are calculated according to EC 2, it is possible to perform the fire resistance design by applying the simplified approach (zone method) according to EN 1992-1-2.

Several design cases can be created. For example, one may perform all designs for particular structural components, and for some others one carries out only the ultimate limit state design. If desired, the concrete design modules can determine the minimum reinforcement according to the respective standard. Many detailed input options are provided so that one is very flexible with the creation of the corresponding designs for one’s concrete structure. Thus, one can for example specify a basic reinforcement to design available structures. It is also possible to insert the desired reinforcement, which the program completes, if necessary, by additional reinforcement. All intermediate values are shown after the calculation. In this way, one can retrace all performed designs. The determined reinforcement of members can be displayed by high quality visualization. At the same time, the calculation modules check automatically if the reinforcement fits in the structural component. All initial values, designs, tables, graphics etc. can be integrated in the printout report to create a structural analysis as a documentation 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, info@dlubal.com, www.dlubal.de

Twisted floors in weekly cycles – Evolution Tower, Moscow, Russia Every week, Moscow’s new landmark is gaining 4.30 m in height – with each completed floor twisted 3° in relation to the preceding one. For this, PERI engineers developed a crane-independent formwork concept on the basis of the RCS and ACS self-climbing technology.

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

The 249 m high Evolution Tower is part of Moscow’s international trade centre, “Moscow City”, which is currently the largest investment project in the Russian capital. Due to the fact that each of the 52 upper floors is constantly twisted by 3° whilst being arranged around the central core of the building, the skyscraper experiences an elegant rotational movement in a clockwise direction from the base to the top by more than 150°.

Corner column formwork with additional benefits The elegant rotation of the building is made even more striking through the spiral-shaped design of the distinctive rectangular columns on the building corners. The corner columns are thus not only inclined but also feature a twist. The project-specific PERI self-climbing formwork concept is based on ACS and RCS system components whilst a special gallows construction accelerates the shuttering and striking procedures. In addition, the climbing formwork for the rectangular columns fulfils two other tasks: in the area of the building corners, the external formwork serves as slab edge formwork when forming the floor slabs whilst the RCS formwork scaffold unit also acts as a climbing protection panel and thus part of the building enclosure.

Self-climbing core formwork

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

Structural Concrete 15 (2014), No. 1

Core walls and floor slabs are concreted in one pour, with each floor divided into three concreting sections. Up to the 26th floor, four ACS P climbing units have been used to form generously-sized working platforms whilst VARIO GT 24 wall form-

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Products & Projects

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

use of four ACS G brackets. As a result, the following storeys can also be efficiently climbed. For forming the floor slabs, customized UNIPORTAL slab tables keep pace with the fast rate of working. Fig. 1. With an elegant 150° rotation, the Evolution Tower spirals almost 250 m into the Moscow sky. Inclined and crane-independently climbed RCS protection panel units provide here a very high level of safety.

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

Rotating in safe conditions The top three floors under construction are tightly enclosed with the RCS climbing protection panel. The units climb the constant twist of the building in an inclined position – also crane-independent with the help of the mobile climbing hydraulics. The permanently installed rail-guided system ensures a fast and safe climbing procedure also in inclined positions. The

MC 2010 – the most comprehensive code on concrete structures

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The fib Model Code 2010 is now the most comprehensive code on concrete structures, including their complete life cycle: conceptual design, dimensioning, construction, conservation and dismantlement. It is expected to become an important document for both national and international code committees, practitioners and researchers. The fib Model Code 2010 was produced during the last ten years through an exceptional effort by Joost Walraven (Convener; Delft University of Technology, The Netherlands), Agnieszka Bigaj-van Vliet (Technical Secretary; TNO Built Environment and Geosciences, The Netherlands) as well as experts out of 44 countries from ﬁve continents.

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Products & Projects

Fig. 3. The inclined positioned climbing rails of the RCS climbing protection panel are permanently connected to the building by means of corresponding slab shoes.

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

Diagonally climbed and movable landing platforms Furthermore, on the sides of the building, RCS landing platforms are climbed for use as temporary storage areas and for moving of loads with the crane. The climbing procedure also takes place here without a crane, hydraulically with the help of the mobile climbing devices. On its inclined climbing path, the continuous vertically positioned circular columns present a permanent obstacle. Therefore, the RCS platforms were so designed so that they can be temporarily moved on varying positions – by means of flexibly adaptable forward and reverse inclinations without any time-consuming modification work.

Test set-up as part of the overall solution

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

climbing rails are connected to the building by means of corresponding slab shoes. In combination with the four climbing units of the rectangular columns, a gap-free enclosure is achieved – for safe and quick working operations particularly at great heights.

A10 Structural Concrete 15 (2014), No. 1

For PERI engineers, twisted high-rise buildings and inclined climbing procedures are nothing new: urban development highlights such as the Turning Torso in Sweden and the two Absolute World Towers in Canada likewise spiral upwards in a similar fashion – successfully realized with expert PERI support. The special feature of the Moscow EvolutionTower is the combined climbing formwork utilization for the vertical core walls and twisted corner supports in connection with the obliquely climbed protection panel and landing platform. In addition to the detailed formwork planning, a previously used test set-up was therefore an important part of the PERI overall solution. This meant that the applicability under construction site conditions could be demonstrated very early on, and the optimization potential for daily on-site working operations could be accelerated 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, Moscow@peri.ru, www.peri.ru

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Provider directory products & services

bridge accessories

Maurer Söhne GmbH & Co. KG Frankfurter Ring 193 D-80807 München Phone +49(0)89 32394-341 Fax +49(0)89 32394-306 Mail: ba@maurer-soehne.de Web: www.maurer-soehne.de Structural Protection Systems Expansion Joints Structural Bearings Seismic Devices Vibration Absorbers

literature

Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG Rotherstraße 21 10245 Berlin Phone +49 (0) 30 4 70 31-2 00 Fax +49 (0) 30 4 70 31-2 70 E-mail: info@ernst-und-sohn.de Web: www.ernst-und-sohn.de

fastening technology

HALFEN Vertriebsgesellschaft mbH Katzbergstraße 3 D-40764 Langenfeld Phone +49 (0) 21 73 9 70-0 Fax +49 (0) 21 73 9 70-2 25 Mail: info@halfen.de Web: www.halfen.de concrete: fixing systems facade: fastening technology framing systems: products and systems

post-tensioning

DYWIDAG-Systems International GmbH Max-Planck-Ring 1 40764 Langenfeld/Germany Phone +49 (0)21 73/7 90 20 Mail: dsihv@dywidag-systems.com Web: www.dywidag-systems.de

prestressed concrete

Max Frank GmbH & Co. KG Technologies for the construction industry Mitterweg 1 94339 Leiblfing Germany Phone +49 (0)94 27/1 89-0 Fax +49 (0)94 27/15 88 Mail: info@maxfrank.com Web: www.maxfrank.com

sealing technologies Paul Maschinenfabrik GmbH & Co. KG Max-Paul-Straße 1 88525 Dürmentingen/Germany Phone +49 (0)73 71/5 00-0 Fax +49 (0)73 71/5 00-1 11 Mail: stressing@paul.eu Web: www.paul.eu

software

reinforcement technologies

Max Frank GmbH & Co. KG Technologies for the construction industry Mitterweg 1 94339 Leiblfing Germany Phone +49 (0)94 27/1 89-0 Fax +49 (0)94 27/15 88 Mail: info@maxfrank.com Web: www.maxfrank.com

Dlubal Software GmbH Am Zellweg 2 93464 Tiefenbach Phone +49 (0) 96 73 92 03-0 Fax +49 (0) 96 73 92 03-51 Mail: info@dlubal.com Web: www.dlubal.de

stay cables

DYWIDAG-Systems International GmbH Max-Planck-Ring 1 40764 Langenfeld/Germany Phone +49 (0)21 73/7 90 20 Mail: dsihv@dywidag-systems.com Web: www.dywidag-systems.de

vibration isolation

BSW GmbH Am Hilgenacker 24 D-57319 Bad Berleburg Phone +49(0)2751 803-126 Mail: info@berleburger.de Web: www.bsw-vibration-technology.com under-screed impact sound insulation with European Technical Approval, PUR foam & PUR rubber materials for vibration isolation

Structural Concrete 15 (2014), No. 1

A11

Theory of Structures – Past and Present With short biographies of over 175 important engineers This book traces the evolution of theory of structures and strength of materials – the development of the geometrical thinking of the RenaisKarl-Eugen Kurrer The History of the Theory of Structures From Arch Analysis to Computational Mechanics 2008. 848 pages € 125,–* ISBN 978-3-433-01838-5 Also available as

sance to become the fundamental engineering science discipline rooted in classical mechanics. Starting with the strength experiments of Leonardo da Vinci and Galileo, the author examines the emergence of individual structural analysis methods and their formation into theory of structures in the 19th century.

A work of reference for a multitude This book provides the reader with a consistent approach to theory of structures on the basis of applied mechanics. It covers framed structures as well as plates and shells using elastic and plastic theory, and emphasizes the historical Peter Marti Theory of Structures Fundamentals, Framed Structures, Plates and Shells 2013. 680 pages € 98,–* ISBN 978-3-433-02991-6 Also available as

background and the relationship to practical engineering activities. This is the first comprehensive treatment of the school of structures that has evolved at the Swiss Federal Institute of Technology in Zurich over the last 50 years.

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Editorial

Precast concrete structures in the future Concrete is the most commonly used building material in the world, and precast concrete components and structures provide a creative way to extend the use of concrete. Facing the increasing challenges on the construction industry, including climate change, energy saving and environmental protection, structural engineers need a new vision for the potential of precast structures as well as for the sustainable use of concrete in general. In thinking about sustainable construction, we need to find innovative ways to reduce the impact of construction activity on our environment. Civil engineering provides human beings with essential support of their everyday life: housing, workplace, transport, communications and utility supplies (electricity, gas, water, etc.). Precast structures are wellrecognized as environmentally friendly structural systems, so there is no doubt that precast technology will play a very important role in future construction activities. In the 21st century, construction needs that will use precast concrete include: – tall residential buildings – tall office buildings – advanced modern factories – online shopping warehouses – large-scale infrastructure.

Xilin Lu

New residential and office buildings are widely required in the developing world for improving the living and working conditions of the local people. High quality – especially in terms of sustainability and durability – is a very critical aspect for construction, and precast technology can provide this. Advanced modern factories for IT-based manufacturing and online shopping warehouses currently provide many challenges for civil engineers. The high pressure on the construction period and the use of special facilities are common features, and precast technology usually provides the best solution. For large scale infrastructure, such as longspan bridges, high speed railway lines, subways, and stadiums, precast components and systems are already widely used and will find more applications in the future. Requirements for sustainability are being constantly updated, and innovation is the best driver to keep precast concrete structures moving on the right track. Concrete is easy to produce, cheap, robust, shapeable and suitable for almost all kinds of construction, and using precast technology is the best way to bring concrete into practical engineering. Further consideration of the sustainability aspects of precast concrete structures will always be necessary. For instance, life cycle energy saving strategy is essential for precast concrete structures, as with other materials, at both the component and the structure level. Use of lightweight concrete and embedding heatproof material may significantly reduce energy consumption in the everyday use of structures. Precast concrete structures, composed of prefabricated concrete members that are reinforced or prestressed are the best known form of

Editorial structural system. However, the main stream of precast concrete structures will soon include other hybrid materials and even more sustainable concrete members, such as steel-reinforced or fiber-reinforced concrete members and concrete members using recycled aggregate. Modular construction has always been seen as the highest application level of precast technology. A primary benefit of modular construction is its rapid delivery. The process of creating modules in a factory can take place even while the site work is continuing, so modular buildings can be constructed much faster than buildings constructed with a cast-insitu strategy. This allows the buildings to be occupied sooner and allows owners to see a faster return on investment. The expression “concrete forest” indicates that people are worried about the uncontrolled use of concrete. Therefore reducing the amount of concrete used is important from the public perspective. In this regard, recycled aggregate concrete should be used for future precast concrete structures by recycling prefabricated concrete members, components or whole subassemblies. We also realize that precast concrete structures reflect the local construction culture, so precast concrete structures in different countries and regions can show different cultural characteristics. The future development of structural systems will be colorful and will enrich the local cultural environment. In areas that are prone to seismic activity, the extensive use of precast concrete structures may be limited due to the lack of proper understanding of the complex seismic behavior. In order to extend the engineering application of this kind of structural system and to evaluate the seismic behavior of existing precast concrete structures in seismic zones, some research has been carried out around the world in the past few decades, such as the series of investigations in the 1990s in USA and Japan, and consideration of the seismic behavior of precast concrete structures with respect to Eurocode 8 in Europe. More efforts need to be focused on the seismic behavior of precast concrete structures worldwide in the future. Precast concrete is an important topic for “Structural Concrete”. In this issue, two papers introduce the experimental investigation and new developed calculation model for reinforced concrete members with hollow circular cross-section. One paper deals with shear failures of concrete structures under dynamic loads. Three papers look at steel fiber reinforced concrete columns, staggered lap joints, and reinforced concrete beams strengthened with carbon fiber composites. Another paper describes the renovation retrofitting work carried out on the 100-year-old reinforced concrete dome of the centennial hall in Wroclaw, which has been listed as a UNESCO world heritage site. One paper presents a stateof-the-art review of the long-term properties of recycled aggregate concrete, while another describes the application of a precast concrete immersed tunnel for the Hong Kong–Zhuhai–Macao Link project, mainly focusing on the early-age behavior of the tunnel. The final paper deals with the behavior of plain concrete ground supported slabs under step loading conditions. We can easily find the precast aspects in most of the papers. I believe, precast concrete structures, with constant innovation, are available and qualified for a better construction in the future.

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

Structural Concrete 15 (2014), No. 1

Technical Paper Jianzhuang Xiao* Long Li Vivian W.Y. Tam Hong Li

DOI: 10.1002/suco.201300024

The state of the art regarding the long-term properties of recycled aggregate concrete This paper reviews the long-term properties of recycled aggregate concrete (RAC), including long-term strength, shrinkage, creep, carbonation resistance, antifreeze resistance, impermeability, abrasion resistance, alkaline aggregate reactions, sulphate corrosion and fatigue behaviour. Most studies have shown that the long-term properties of RAC are inferior to those of natural aggregate concrete (NAC), and some researchers have observed that the long-term properties are better than those of NAC. RAC’s long-term properties are affected by many factors such as recycled coarse aggregate (RCA) replacement percentage, water-cement ratio, mineral admixtures and mix proportions. The long-term properties of RAC can be improved through better control of these factors. This paper will be helpful for a comprehensive understanding of and further research on RAC, and provides an important basis and references for the engineering applications of RAC. Keywords: recycled aggregate concrete, long-term properties, shrinkage and creep, carbonation resistance, impermeability, fatigue behaviour

Introduction

Huge amounts of solid waste are produced in the process of constructing new buildings and demolishing old ones all around the world. For example, approx. 1,350 million tons of construction waste are produced annually in China. Moreover, natural disasters such as the Wenchuan earthquake in 2008, the Yushu earthquake in 2010, the Yunnan earthquake in 2011 and the Ya’an earthquake in 2013 resulted in a great quantity of concrete waste. In 2008 the Wenchuan earthquake resulted in a total of 380 million tons of building waste [1]. With the rapid development of the construction industry and the excessive consumption of natural resources and deterioration of the environment in China, the conflict between sustainable development of the construction industry and shortage of resources is becoming serious. Therefore, the use of concrete containing demolished concrete is a very important issue in environmental sustainability [2]. The use of recycled coarse aggregate (RCA) as a partial replacement for natural aggregate, in what is called recycled aggregate concrete (RAC), has become a common method [3]. In recent

years, research into RAC has been carried out around the world and some successful applications of RAC in practical engineering have been seen. In the past, investigators have paid more attention to the mechanical behaviour of RAC and have conducted relatively limited research into its long-term properties. In order to understand the long-term properties of RAC better and prepare the ground for further research, this paper reviews related studies and past achievements, including long-term strength, shrinkage and creep, carbonation resistance, antifreeze resistance, impermeability, abrasion resistance, alkaline aggregate reactions, sulphate corrosion and fatigue behaviour. It will be helpful for the application and durability design of RAC.

Long-term strength of RAC

There is currently a lack of studies available concerning the long-term strength of RAC and this subject requires more in-depth analysis by researchers. Xiao et al. [4] studied the relationship between compressive strength and age of RAC experimentally, as shown in Fig. 1. It was shown that the compressive strength of RAC increased over time, with an increase of about 60 % on the 360th day over that on the 28th day. Malhotra [5] obtained similar results. This is because the compressive strength of RAC increases approximately linearly with the increase in mass density [6], and the mass density of RAC will increase with age and thus increase carbonation inside the concrete.

* Corresponding author: jzx@tongji.edu.cn Submitted for review: 23 April 2013 Revised: 4 July 2013 Accepted for publication: 10 July 2013

Fig. 1. Development of compressive strength of RAC over time

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

Numerous tests have been carried out to investigate the influence of RCA content on the compressive strength of RAC. It has been concluded that concrete strength decreases with the increase in RCA replacement percentage and the strength reduction could be > 40 % [7]. Some researchers studied the differences in the long-term strength of RAC and natural aggregate concrete (NAC). Kou et al. [8] studied the influence of RCA on the long-term mechanical properties of concrete, and observed that RAC had a lower compressive strength and higher splitting tensile strength after 5 years of curing than the corresponding NAC, and the increase in compressive and splitting tensile strengths from 28 days to 5 years was more significant in RAC than in NAC. Khatib [9] studied the properties of concrete incorporating recycled fine aggregate (RFA), including fine crushed concrete or brick. It was shown that a systematic reduction in the long-term strength occurs when class M sand is replaced with fine crushed concrete. This reduction could reach about 30 % for 100 % RCA replacement but be only 15 % for 25 % RCA replacement. However, when class M sand is replaced with fine crushed brick, it does not cause a substantial reduction in the long-term strength, even at high replacement percentages. Kou et al. [10] carried out experimental studies of the properties of NAC and RAC prepared with different mineral admixtures at different ages. It was shown that the compressive strength and tensile splitting strength of NAC and RAC made with 10 % silica fumes and 15 % metakaolin were higher than the other corresponding concrete mixtures (35 % fly ash and 55 % ground granulated blastfurnace slag) both at early ages (4, 7 and 28 days) and at 90 days; the contributions of silica fumes and metakaolin to the compressive strength of both NAC and RAC at early ages were higher than at 90 days.

Shrinkage of RAC

The shrinkage mechanism of RAC should be almost the same as NAC. In NAC, cement mortar causes the main shrinkage deformation and coarse aggregate plays an inhibitory role in the shrinkage deformation of cement mortar. In addition, old cement mortar adhering to the surface of RCA in RAC can also cause shrinkage deformation. RCA with a lower elastic modulus shows less inhibition when it comes to reducing shrinkage deformation, and water content will increase when using the prewetting method for improving working performance, and all of these factors lead to an increase in shrinkage deformation [11]. From the previous investigations [12–21] it has been observed that the shrinkage deformation of RAC is higher with different degrees than that of NAC, and the increase is in the range 0–100 %. A number of investigations [9, 12, 19–25] have shown that RAC shrinkage increases with the increase in RCA replacement percentage. Gomez-Soberon [19] concluded that this is due to a higher absorption of RCA leading to the increase in shrinkage and creep of RAC, and the higher the RCA replacement percentage, the greater the increase in shrinkage and creep. The ratios (correction coefficients) of shrinkage deformation between RAC with certain RCA replacement percentages

Structural Concrete 15 (2014), No. 1

Table 1. Shrinkage deformation correction coefficients for RAC with different RCA replacement percentages

Country/ Organization

Belgium Netherlands RILEM

Correction coefficient 100 % RCA replacement percentage

20 % RCA replacement percentage

1.5 1.5 1.35–1.55

1.0 1.0 1.0

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 by many factors, and the basic rules are shown in the following. RAC shrinkage increases with the rise in RCA replacement percentage, which has been discussed above. The drying shrinkage of RAC increases with age [16], increasing rapidly during the early period and slowly later on [9, 12]. Sagoe-Crentsil et al. [16] found that the drying shrinkage of RAC increases with age and stabilized at about day 91, and is about 25 % greater than that of NAC. The shrinkage deformation of RAC increases with the increase in the water-binder ratio [23]. The test results of Refs. [12, 22–25] showed that adding mineral admixtures such as fly ash and slag can reduce the shrinkage deformation of RAC. The addition of a water-reducing agent will increase the shrinkage of RAC with constant water and cement contents [25]. Ravindrarajah [15] found that the shrinkage deformation of RAC increased with the rise in strength and increase in shrinkage deformation of RAC, whose increase in strength is higher than that of NAC for the same water-cement ratio. In addition, Fathifazl et al. [27] studied the creep and shrinkage characteristics of RAC experimentally with a new method of mix proportioning, i.e. the equivalent mortar volume (EMV) method. The results showed that RAC with the EMV method experienced lower or comparable creep and shrinkage than the reference NAC. By applying the residual mortar coefficients proposed in the study, in conjunction with the ACI and CEB creep and shrinkage prediction methods, a modified creep or shrinkage model was also proposed to calculate creep or shrinkage of RAC, and good agreement was observed between the predicted and measured creep and shrinkage strains for all tested specimens.

Creep of RAC

The development trend of RAC creep is similar to NAC, and the creep of RAC is greater than that of NAC because the cement mortar content in RAC is greater than that in NAC, which could cause larger creep deformation [11]. In the previous investigations [19, 21, 28, 29] it was observed that creep deformation of RAC is 20–60 % higher than that of NAC with the same mix proportions. The test results by Gomez-Soberon [19] showed that RAC creep deformation increases with the increase in RCA replacement percentage. Domingo-Cabo et al. [21] observed that creep of RAC with a 20 % RCA replacement percent-

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

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

Country/ Organization

Belgium Netherlands RILEM

Correction coefficient 100 % RCA replacement percentage

20 % RCA replacement percentage

1.25 1.25 1.25–1.45

1.0 1.0 1.0

age was found to be 35 % higher than that of NAC. For a 50 % RCA replacement percentage, creep deformation was about 42 % higher, whereas a 100 % replacement percentage increases creep deformation by about 51 %. The ratios (correction coefficients) of creep deformation between RAC with certain RCA replacement percentages and 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 deformation of RAC increases with the strength class; it increases with the rise in cement content adhering to the RCA. Nishibayashi et al. [30] established that RAC creep deformation increases rapidly with the increase in watercement ratio, but the disparity of creep deformation between RAC and NAC is almost stable at different water-cement ratios and loadings. Zou et al. [31] studied the creep of RAC experimentally. The results indicate that RCA could reduce the degree of creep in RAC, whereas the degree of creep in RAC increased with the increase in quantities of RFA; an increase in the stress level could be the reason for the increase in RAC creep deformation, whereas adding slag can reduce creep deformation. In theory, adding mineral admixtures such as fly ash and slag, steel fibres and bulking agent, which can reduce the shrinkage deformation of RAC, can also reduce creep shrinkage. However, further studies are required to verify the results.

Carbonation of RAC

Xiao et al. [32] proposed that two effects should be integrated when comparing the carbonation resistance of RAC and NAC: (1) As the porosity of RCA is greater than that of natural aggregate, the porosity of RAC is much greater than that of NAC with the same water-cement ratio, and this could definitely reduce the carbonation resistance of RAC. (2) As there is old cement attached in RCA, the total cement content of RAC is greater than that of NAC, which means there are larger quantities of materials available for carbonation, thus improving the carbonation resistance of RAC. Most investigators have observed that the carbonation resistance of RAC is lower than that of NAC. The investigations [33–35] revealed that the carbonation depth of RAC is not significantly different from that of NAC. The BCSJ [36] concluded that carbonation rates were 1.2 to 2 times higher than those of controlled mixes when RAC was pro-

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

duced from RCA. Evangelista et al. [37] showed that carbonation resistance is reduced by adding RFA to the concrete; the CO2 penetration depth increased by about 40 % for concrete made with 30 % RFA and by about 110 % for concrete made solely with RFA. However, Levy et al. [38] obtained contrary results that carbonation depth decreases when increasing the amount of RCA replacement percentage, resulting in a better behaviour when this replacement was 20 or 50 %, mainly for recycled coarse and fine masonry aggregate. When using masonry or concrete recycled aggregate, even with a 100 % replacement percentage, carbonation depth is still lower when compared with a reference concrete made with natural aggregates. A number of researchers have studied variations that influence the carbonation resistance of RAC. Many researchers [12, 39–42] thought that the carbonation resistance of RAC increases with the rise of RCA content. However, Xiao et al. [32] and Zhang and Yan [43] found that increasing the RCA replacement percentage (< 70 %) increases the carbonation depth of RAC, but it decreases when the RCA replacement percentage is 100 %, as shown in Fig. 2. Levy et al. [38] obtained contrary results, i.e. increasing the RCA replacement percentage decreases the carbonation depth of RAC. It is generally considered that carbonation depth decreases with the increase in water-cement ratio [32, 33, 35, 44]. Ryu [45] thought that the performance of RCA has a limited effect on carbonation depth. Katz [7] concluded that RAC carbonation resistance was not obvious when < 28 days old. However, Cui et al. [46] and Zhang and Yan [43] observed that using RCA from high-strength concrete can reduce the carbonation depth of RAC. Shayan and Xu [47] established that the carbonation depth of both RAC and NAC are higher when aggregate was wetted through with sodium silicate solution. As this solution has a high CO2 absorption capacity, it will increase the carbonation rate of concrete. Sun [12] observed that the carbonation resistance of RAC can be improved by adding slag or steel slag, but the quantity added should not be too large or it will reduce carbonation resistance. Sun [12] and Kou et al. [41, 42] found that the addition of fly ash increases the carbonation depth of RAC. In addition, Xiao and Lei [48] established a calculation model for recycled concrete carbonation depth based on the investigation of the results available for carbonation of RAC and NAC carbonation test data. They pro-

Structural Concrete 15 (2014), No. 1

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

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

Freeze resistance of RAC

Many researchers [49–53] have conducted experiments on the freeze-thaw durability of RAC. The results indicate that RAC has good freeze-thaw resistance, even better than NAC with the same water-cement ratio. Richardson et al. [52] compared the freeze-thaw durability of concrete with recycled demolition aggregate with that of NAC. The results showed that concrete cubes made with RCA were about 68 % more durable than plain cubes made with virgin aggregate and this may be caused by the variability of good quality RCA and curing procedures with soaked aggregate. However, concrete cubes made with RCA were slightly more durable than those made with virgin aggregate when adding an air entrainer and polypropylene fibres. Medina et al. [53] researched the freeze-thaw durability of RAC containing ceramic aggregate, and the findings showed that concrete freeze-thaw resistance increased with rising RCA content and this may be due to the high mechanical quality of RAC plus the intrinsic properties of new aggregate. Hendriks [54] examined the difference between the freeze-thaw durability of RAC and NAC and found it to be insignificant. The reason is similar to lightweight aggregate concrete, which has a good freeze-thaw resistance. Although RCA is no better at improving freezethaw resistance than lightweight aggregate, its larger porosity can play a micro-conservation role and reduce the water-cement ratio of cement mortar at the interface, thus improving the interface quality. However, other investigators [13, 28, 55–65] concluded that the freeze-thaw durability of RAC is lower and even significantly lower than that of NAC. As an example, the results 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 saturation in RCA (such as 10 min with up to 85 % saturation levels and 30 min with up to 95 % saturation levels), but critical saturation of freeze-thaw damage is about 92 %, thus freeze-thaw damage in RCA will appear earlier than in a new cement matrix. As a result, RCA becomes one of the weaknesses of RAC under freeze-thaw actions [11]. Some

investigators researched the freeze-thaw cycle of RAC experimentally and conducted microstructural analyses on the test results [13, 59, 66]. They pointed out that microcracks begin to concentrate at the old cement mortar of RCA, then they are induced to occur around new mortar and, finally, cracks in new mortar will run through each other only after several freeze-thaw cycles, resulting in freeze-thaw damage. Zou et al. [65] carried out experiments on the basic mechanical properties of RAC after freezethaw. The results showed that the freeze-thaw resistance of RAC is worse than that of NAC and could reduce with the increase in RCA replacement percentage and freeze-thaw frequency. Dai et al. [63] pointed out that the strength loss rate of RAC is higher than that of NAC, and the main reason is that RCA has lower freeze-thaw resistance because of its high water absorption. Cui et al. [62] researched the freeze-thaw cycle of RAC experimentally and found that the freeze-thaw resistance of RAC with 100 % RCA replacement percentage is lower than that of NAC. The durability factor of RAC with water-cement ratios of 0.45 and 0.55 decreased by about 6 % and 10 % respectively when compared with NAC. Cao et al. [60] indicated that the freeze-thaw resistance of RAC is lower than that of NAC, but the freeze-thaw resistance of RAC with 50 % RCA replacement percentage and natural sand fine aggregate is not significantly different to that of NAC after 100 freezethaw cycles. So with a reasonable design approach, RAC with no more than 50 % RCA replacement percentage can be used in building structures in cold regions. Many methods can be employed to improve the freeze-thaw durability of RAC. Test results indicate that lowering the water-cement ratio can significantly improve the 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 freezethaw resistance of RAC quite distinctly. Salem et al. [55, 56], Gokce et al. [59] and Zhang et al. [64] concluded that some mineral admixtures such as fly ash and kaolin can help to raise the freeze-thaw resistance of RAC. In addition, decreasing RCA diameter and improving the quality of RCA can also improve the freeze-thaw durability of RAC.

7 7.1

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

Structural Concrete 15 (2014), No. 1

Impermeability of RAC Water and air permeability

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

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

RAC with 50 % RCA replacement percentage was higher than that of NAC. Olorunsogo and Padayachee [69] used the oxygen permeability index to describe RAC’s oxygen permeability and observed that the index dropped with the increase in RCA replacement percentage and increased with age. Zhang et al. [70] proposed that reducing the water-cement ratio in a certain range, adding fly ash and confining crack expansion can enhance the impermeability of RAC. Tam et al. [73] proposed that RAC permeability can be enhanced when adopting a two-stage mixing approach (TSMA). Somna et al. [74] observed that both ground fly ash and ground bagasse ash could reduce the water permeability of RAC, although RAC compressive strengths with both ash types were lower than those of NAC.

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 penetration is lower than that of NAC. Fig. 4 shows an example from Kou et al. [80]. This is also due to the high porosity of RAC. Many investigators [22, 37, 39, 75, 76] observed that increasing the RCA replacement percentage diminished RAC’s resistance to chloride penetration, and it was affected significantly more by RFA than natural fine aggregate. Some researchers [10, 34, 79, 81] observed that RAC’s resistance to chloride penetration can be enhanced by adding mineral admixtures such as fly ash. Hu et al. [78] established that reducing the water-cement ratio can also improve chloride impermeability. Kou et al. [22] discovered that using steam curing while adding fly ash can significantly enhance the chloride impermeability of RAC. Otsuki et al. [33] observed that the chloride penetration resistance of RAC can be improved by using the double mixing method in the case of concrete with a high waterbinder ratio. Xiao et al. [82] proposed a model that considered RAC as a five-phase composite material on the meso-scale to describe the effect of RCA on chloride diffusion in RAC. The model is shown in Fig. 5. Theoretical equations were also derived to calculate the effective chloride diffusivity Deff in the RAC modelled. The results showed that values of Deff calculated from theoretical equations and from the finite element method (FEM) are in reasonable agreement. The simulation results show that Deff decreases with the rise in RCA volume fraction, but increases with the adhesive rate of the old mortar adhering and the thickness of the ITZ. In addition, the RCA shape also influences chloride concentration. Xiao et al. [83] simulated chloride penetration characteristics numerically in modelled RAC (MRAC) to study RAC chloride penetration characteristics. The results showed that chloride concentration distribution is not uniform within MRAC and chloride concentration in RAC decreases wavelike over the diffusion depth, and the influence of RCA content, cement mortar and ITZ on the chloride concentration shows a distinct increase with diffusion depth. Ying et al. [84] found that the chloride diffusivity of RAC with Fuller gradation is smaller than that with an equal volume fraction gradation, and decreases with an increase in the minimum aggregate diameter.

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

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

Abrasion resistance of RAC

Abrasion resistance is an important indicator for evaluating the performance of concrete pavements and it depends primarily on the strength and hardness of the surface layer of concrete. A number of investigations [16, 36, 85] showed that the abrasion resistance of RAC is lower than NAC with the same mix proportions. Dhir et al. [85] observed that the wear depth of RAC increased with RCA replacement percentages; wear depth of RAC exhibited no significant difference when RCA replacement percentage was < 50 %, but was about 34 % higher than normal concrete when the RCA replacement percentage was < 100 %. However, some researchers [86–88] observed that RAC abrasion resistance is marginally higher than that of NAC. Test results showed that abrasion loss in RAC and NAC for strength class C30 was about 1544 and 1600 kg/m3 respectively, which indicates that the abrasion resistance of RAC is higher than that of NAC [88]. In addition, Ying et al. [76] summarized that RAC abrasion resistance dropped with the increase in RCA replacement percentage, yet increased with the RFA content. Test results in Yang et al. [89] showed that the abrasion resistance of RAC is highest when the RCA replacement percentage is about 40 %, and after that it drops with the RCA replacement percentage. Sagoe et al. [16] and Yang et al. [89] discovered that RAC

Structural Concrete 15 (2014), No. 1

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

abrasion resistance diminished with the increase in waterbinder ratio. Sagoe et al. [16] and Peng et al. [90] pointed out that adding slag and fly ash can improve the abrasion resistance of RAC. Concrete’s abrasion resistance is mainly affected by concrete strength, aggregate properties and concrete surface quality. Therefore, in theory, methods that can improve RAC strength, RCA properties and the quality of the RAC surface would increase the abrasion resistance of RAC. But additional studies in this area are still necessary.

Alkaline aggregate reactions (AAR) of RAC

For investigations on how adherent mortar content influences the properties of RAC, Marta et al. [91] observed that the maximum alkali content in RAC, provided by cement, will be about 0.12 % with respect to the concrete, namely 2.7 kg/m3, which is only just above the safe alkali content in concrete. Therefore, alkali content due to RCA cannot be ignored. Etxeberria et al. [92] found that adherent mortar on the surface of RCA exhibited alkaline activity, and all recycled aggregates with adherent mortar were discovered to have aureoles around them, which is the sign of AAR. It is indicated that expansion damage due to AAR can occur in RAC when aggregate in the original concrete exhibits alkaline activity. At present, there is no generally accepted method of measuring alkali activity in RCA, so the safest way is to avoid using RAC in which AAR expansion damage has taken place and to control the total alkali content in RAC by using low-alkaline cement or replacing some cement with a mineral admixture. For example, Shayan et al. [47] observed in experimental studies that using ganister sand to replace a certain amount of cement can reduce AAR dilatation of RAC.

Sulphate corrosion of RAC

Sulphate solution can develop a chemical reaction with hydration products in concrete, which will cause volume expansion in concrete and may cause damage. A number of investigations [17, 18, 30, 85] indicated that the sulphate resistance of RAC is slightly lower than that of NAC with the same water-cement ratio. The test results of Dhir et al. [85] showed that RAC’s sulphate resistance was very close to that of NAC when the RCA replacement percentage is < 30 %; the sulphate resistance of RAC decreased with the rise in RCA replacement percentage, but at a modest rate. Xiao [75] observed that RAC’s sulphate resistance decreased with the increase in RCA replacement percentage; the decrease was not obvious with an RCA replacement percentage < 50 %, but there was a significant decrease with RCA replacement percentages > 50 %, and the reduction was about 18.5 % with 100 % RCA replacement. Marta and Pilar [91] estimated that the sulphate content in RAC due to RCA was about 4 % when considering the sulphate content of cements, and the results showed that the maximum sulphate content in RAC would be up to 0.5 %, namely 11.2 kg/m3. Therefore, sulphate content in RAC provided by RCA cannot be ignored. The sulphate resistance of RAC can be improved by adding fly ash, highrange water-reducing agents and mineral admixtures or by modifying the properties of RCA [75].

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Fatigue behaviour of RAC

Fatigue behaviour of concrete materials is very important for structures under repeated loadings, such as floors subject to crowd vibration, road pavements and girders supporting highway bridges carrying traffic and offshore structures battered by wind and waves. In order to utilize RAC for practical engineering, it is significant and necessary to study the fatigue behaviour of RAC and compare the difference between RAC and NAC. However, only a few investigations into the fatigue behaviour of RAC have been carried out. Xiao et al. [93] proposed expressing the compressive fatigue strength of RAC based on its static strength distribution and analysed the effects of stressstrain ratio and RCA replacement percentage on the fatigue strength of RAC. The results showed that RAC’s fatigue strength increased with the RCA replacement percentage. According to the proposed formula, axial compression fatigue strength with different fatigue lives and guaranteed rates can be estimated, providing the basis for RAC pavement design. Li and Xiao [94] established the relationship between the elastic modulus and fatigue strength of RAC through experimental results and theoretical analysis. The results showed that the fatigue strength of RAC calculated with the proposed formula was close to the experimental results. It is indicated that the formula can provide a reliable prediction of the fatigue strength of RAC and can be used to guide engineering practice. Xiao et al. [95] analysed the fatigue damage evolution of RAC quantitatively with different damage variations and found three obvious phases as for the fatigue damage evolution of NAC. They also proposed an inverted-S, non-linear fatigue damage cumulative model for studying the damage evolution and fatigue life of RAC. The results showed that the damage evolution equation and fatigue life of RAC were highly relevant in experimental results. Ji et al. [96] studied the fatigue behaviour of RAC with fly ash by conducting flexural fatigue tests on RAC beams, and the results showed that the flexural fatigue behaviour of RAC with fly ash is similar to that of Portland cement concrete, especially at low stresses. Zhu and Li [97] proposed empirical expressions for residual strength corresponding to the number of cycles that can be used to predict residual strength with reliability. Yan et al. [98, 99] studied the fatigue behaviour of recycled aggregate reinforced concrete experimentally with different RCA replacement percentages under axial and eccentric compression. On the whole there were some differences between the compressive fatigue behaviour of RAC and NAC, but it is feasible to use RAC in practical engineering. Xiao et al. [100] carried out experiments on the fatigue behaviour of RAC with 100 % RCA replacement percentage under uniaxial compression and bending cyclic loadings. The S-N curves of RAC and NAC under uniaxial compression and bending cyclic loading are shown in Figs. 6 and 7. These are based on the test results and some other research on the fatigue behaviour of NAC. It was shown that there were some differences between the compressive fatigue behaviour of RAC and NAC, and the fatigue life of RAC is lower than that of NAC for the same stress level under cyclic bending. A fatigue model for RAC under uniaxial compression with a constant stress range,

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

Fig. 6. S-N curves of RAC and NAC under uniaxial compression cyclic loading (Xiao et al. [100])

(3) The creep deformation of RAC is about 20–60 % higher than that of NAC and increases with the increase in the RCA replacement percentage. (4) There is still no generally accepted conclusion regarding the difference in carbonation resistance between RAC and NAC; adding slag, steel slag, reasonable control of water-cement ratio, etc. can improve carbonation resistance. (5) There are also contradictory conclusions regarding the freeze resistance of RAC from different researchers; lowering the water-cement ratio, adding airentraining agent, mineral admixtures such as fly ash and kaolin and improving the quality of RCA can enhance the freeze resistance of RAC. (6) The impermeability of RAC is lower than that of NAC and decreases with the increase in RCA replacement percentage; reducing the water-cement ratio in a certain range, adding admixtures such as fly ash or using TSMA can improve impermeability. (7) The abrasion resistance and sulphate resistance of RAC are lower than those of NAC. (8) There is some difference between the fatigue behaviour of RAC and NAC, but it is feasible to apply RAC to practical engineering. On the whole the study of the long-term properties of RAC is still at an early stage. It requires more in-depth analysis by researchers looking into mechanisms, physical models and measures to improve the long-term properties of RAC.

Acknowledgments

Fig. 7. S-N curves of RAC and NAC under bending cyclic loading (Xiao et al. [100])

The authors wish to acknowledge the financial support of the National Natural Science Foundation of China (NSFC) (project No: 51178340) and NSFC Research Fund for International Young Scientists (project No: 51250110074). References

which relates fatigue strain variation and fatigue modulus degradation to fatigue damage evolution, was also proposed, and the results calculated with this model agreed well with the fatigue tests results.

Conclusion

This paper has presented a state-of-the-art report on the relevant research work and findings concerning the longterm properties of RAC. The main conclusions can be summarized as follows: (1) The compressive strength of RAC increases with age; the long-term compressive strength of RAC is lower than that of NAC, but the extent of the disparity between RAC and NC decreases with age. (2) The shrinkage and deformation of RAC is higher than that of NAC and increases with the increase in RCA replacement percentage; the drying shrinkage of RAC increases rapidly during the early period and slowly during the later period; adding mineral admixtures, water-reducing agents, bulking agents, etc. can reduce shrinkage deformation.

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Jianzhuang Xiao Department of Building Engineering Tongji University Shanghai, 200092, P.R. China

Long Li Department of Building Engineering Tongji University Shanghai, 200092, P.R. China Vivian W.Y. Tam School of Computing, Engineering & Mathematics University of Western Sydney Locked Bag 1797, Penrith, NSW 2751 Australia also: Department of Building Engineering Tongji University Shanghai, 200092, P.R. China

Hong Li Department of Building Engineering Tongji University Shanghai, 200092, P.R. China

Technical Paper István Völgyi* Andor Windisch György Farkas

DOI: 10.1002/suco.201200035

Resistance of reinforced concrete members with hollow circular cross-sections under combined bending and shear – Part I: experimental investigation Part I of this paper introduces an experimental programme carried out on RC members with thick-walled hollow circular crosssections to study their behaviour under combined bending and shear. The study looked at ultimate resistance and propagation of characteristic crack pattern as well as the shape and behaviour of the failure sections as a function of wall thickness, amount of longitudinal and transverse reinforcement, shear span and axial force. Test results were used to verify a newly developed calculation model describing the behaviour of the members investigated at failure under combined bending and shear. This model will be presented in Part II. Keywords: combined bending and shear behaviour, parametric experimental study, hollow circular cross-section, failure section, sliding surface

Introduction

Piles, poles, towers supporting wind turbines and many other RC members are frequently built with a hollow circular cross-section. Despite the extensive use of this crosssectional shape, no widely accepted method exists for assessing the shear resistance of these members. Several shear design methods used in the recent past are based on strut-and-tie models and modified compression field theory [1]. Traditionally, the methods express the shear resistance of an RC member with shear reinforcement as a function of the effective depth and amount of transverse reinforcement. Formulae have been verified for plane webs, but webs with a curvature in the direction of shear, as in hollow circular cross-sections, have not been considered. The applicability of these formulae for members with hollow circular cross-sections is also questionable. The following two experimental research projects investigating the shear resistance of RC members with hollow circular cross-sections and transverse reinforcement on the outside of the wall only (single-hooped) are available in the literature. A test programme carried out on four RC members with a thick-walled hollow circular cross-section plus diaphragms at the ends and the load application point was

* Corresponding author: volgyi@vbt.bme.hu Submitted for review: 24 September 2012 Revised: 18 July 2013 Accepted for publication: 18 July 2013

published by Turmo et al. [2]. Two different concrete mixes were investigated and the specimens were loaded at a low shear span ratio. Uehara [3] carried out a test programme involving 42 specimens. The research dealt with the influence of the axial force on the ultimate resistance of hollow circular specimens under combined shear and bending (bendingshear resistance). Shear failure mode was observed on four specimens. Jensen and Hoang [4] developed an empirical calculation method based on the experimental results of Turmo and Uehara. An experimental programme was needed because few experimental data and no extensive parametric studies were available on this topic. The aim of this experimental research was to establish a basis for the calculation of shear resistance for members with hollow circular crosssections. The model developed will be shown in Part II of this paper. The basic idea of this model is to improve the classic Mörsch-type strut-and-tie model by considering the contribution of the flexural compression zone in the bending-shear resistance of the members. Part I presents the experimental results of the 45 specimens loaded under combined bending and shear up to failure.

Test variables

The experimental programme presented here looked at the influence of wall thickness, amount of longitudinal and transverse reinforcement, load-to-support distance and axial force on the bending-shear behaviour of singlehooped RC members with a hollow circular cross-section.

3 3.1

Experimental investigations Test setup

The test setup is shown in Fig. 1. Bearings under the specimens were composed of rigid steel blocks and allowed longitudinal displacement and rotation. Plastic sheets were placed between the specimen and the steel blocks. One concentrated load was applied in 20–30 kN steps by means of the hydraulic jack of a WPM ZD600 test machine. The load and the displacement of sections shown in Fig. 1 were measured electronically. The applied load was positioned asymmetrically to produce shear failure in the shorter shear span.

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

Fig. 1. Testing and loading setup

The crack pattern was recorded manually in the failure zone at each loading step. The width of the critical shear crack was measured by LEDTs at mid-depth of the specimens in two orthogonal (vertical and longitudinal) directions. The specimens were loaded unilaterally to failure (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 crosssection of 300 mm outside diameter and a nominal wall thickness of 55 or 90 mm. For most specimens, the grade B500B longitudinal reinforcement consisted of 12 deformed (ribbed) bars with a diameter of 12, 14 or 16 mm. A few specimens were cast without transverse reinforcement. As transverse reinforcement, a grade B500B ribbed bar with a diameter of 5 mm was provided at a pitch of 150, 110 or 75 mm for specimens with transverse reinforcement. The transverse reinforcement was positioned on the outer side of the wall of the specimens. The concrete cover to the longitudinal reinforcement was 20 mm. The longitudinal bars were fully anchored at the end sections by welding them to the end stirrups according to Fig. 1. Eighteen specimens were centrically pretensioned. Two specimens were cast with 12 strands in the longitudinal direction. In these cases the diameter of the flexural reinforcing bars is denoted with “0”. At the other 16 prestressed specimens, four of the 12 longitudinal bars were changed to strands. Effective prestressing forces at the time of the tests are given in Table 1. The specimen information in Table 1 includes the nominal wall thickness [mm], the diameter of the longitudinal reinforcement [mm], the pitch of the spiral (helical transverse reinforcement) [mm], the prestressing level (if

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applicable) [kN], and the load-to-support distance [mm]. Specimens with a lower prestressing level are denoted with F1. To study the influence of the bending-to-shear ratio on the resistance of the member, different shear span ratios were applied, according to Fig. 1. The parameters of the specimens and the loading setup are summarized in Table 1. The most important material properties of the reinforcing and prestressing steel used in the specimens are given in Table 2. See [5], [6], [7] for more detailed information on the materials and the specimens.

4 4.1

Test results Failure mode

A complex failure mode associated with combined bending and shear was observed for all of the specimens analysed in this paper. The typical inclined crack of the later failure section opened and caused yielding in the transverse reinforcement, and the concrete zone subjected to compression and shear started to fail along a sliding surface [8]. This sliding surface, like a slope (as known from geotechnics), develops as an extension of the critical shear crack. For more details see Part II. Fig. 2 shows a typical crack pattern in the failure zone just before failure. The first bending-dominant cracks (crack No. 1) appeared at the lower fibre of the cross-section under the loading block. The cracked zone expanded as the load intensity increased. The inclination of cracks further away from the loading block gradually decreased because of the increment in the shear-to-bending moment ratio (crack No. 2 – No. 4). Assuming a perfect bond between concrete and steel and that “plane section remains plane after deformation”

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

Table 1. Specimen data and experimental results

Table 2. Average values of measured steel properties

Reinforcing bars

0.2 % proof stress (f0.2) [MPa]

Tensile strength (ft) [MPa]

∅5

581

609

Reinforcing bars

Yield strength (fy) [MPa]

Tensile strength (ft) [MPa]

∅12

589

639

∅14

593

644

∅16

626

709

Prestressing strands

0.1 % proof stress (fp0.1) [MPa]

Tensile strength (fp) [MPa]

T93

1557

1753

3 4

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 bond between steel and concrete; black line: parts of failure section, critical crack and sliding surface (dashed); blue line: zone of maximum shear force.

(general assumptions), the calculated depth of the compression zone under the loading block (pure bending) is indicated by the red line in Fig. 2. Although the bending moment along the shear span decreased from the loading block to the support, the top ends of the bending-shear crack 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 of the cracks caused by (almost) pure but greater bending under the loading block. The effective depth of the compression zone of sections under combined bending and shear was also smaller than the calculated compression zone depth of a cross-section under pure but greater bending according to the general assumptions. This phenomenon is caused by the influence of the combined shear force; thus, the depth of the compression zone of a cross-section under pure bending is inversely proportional to the intensity of the bending moment. In Fig. 2 the failure section is marked with a thick black line. Prior to failure, a change in direction of the failure section appeared at both ends. The inclination of the lower branch of the crack decreased compared with that of the intermediate branch. At the same time, relatively horizontal cracks appeared along the longitudinal rebars in the tension zone, which resulted in the degradation in bond beyond both faces of the critical crack. This degradation was caused by the combination of axial pull-out and transverse displacement (shear slip) of the tensile longitudinal rebars. This phenomenon has been analysed earlier by Maekawa et al. [9]. This degradation in bond stiffness for the tensile bars also resulted in the growth of the crack width and, as a consequence, the extension of

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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

cracks into the compression zone (calculated assuming perfect bond). A further consequence was that the resistance of the failure section dropped below that of the section including crack No. 4, in which the amount of transverse reinforcement crossing the cracked section was lower. Considering the actual internal force distribution in the member, the intensity of the shear force along the shear span was not constant (see Fig. 1). The part of the shear span with the highest transverse loading is marked with a blue line in Fig. 2. The appearance of a couple of shear cracks in the marked zone was expected. The shape of the section including crack No. 5 was very similar to that of the failure section. However, its higher resistance was explained by the lower compressive stress caused by a smaller bending moment. The failure section developed from one of the characteristic cracks, which appeared during an earlier loading phase. A more detailed definition of a characteristic crack can be found in [8]. The position of the early cracks and that of the failure section varies depending on the actual local concrete tensile strength distribution along the specimens. The variable position of the tip of the characteristic crack is the main reason for the usual variation in the bending-shear failure loads amounting to about 10 %, even for 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) on the shear resistance of RC beams has been studied by several researchers in the past. It is well known that if the shear span is less than a certain limit value, then the shear resistance of a beam increases as shear span decreases. It is important to note that in the case of three-point loading, the full length of the failure section must fit between the inner edges of the support and the loading block, and the length of the failure section must be less than or equal to the distance between the inner edges. Therefore, internal forces developing along each potential failure section have to balance the actual bending moment and the total shear force resulting from the reaction force. For the specimens tested with their different shear spans, the bendingto-shear ratio and the geometry of the failure section differed. The failure section of specimens with a long load-to-support distance was longer than the total load-tosupport distance of specimens with a short shear span (see Fig. 3). The resistance of specimens with a short load-tosupport distance was higher than that for specimens with a longer load-to-support distance, although the amount of transverse reinforcement crossing the shorter failure section was lower. The additional resistance for specimens with a short load-to-support distance originated from the different shape of the failure section across the compression zone. Prior to failure, the longitudinal distance of the upper end of the critical crack from the loading block was smaller than that for the case of a specimen with a larger load-to-support distance, see Fig. 3e (failure shear force: 228 kN) and Fig. 3a (177 kN). The justification based on the shorter sliding surface is presented in Part II of this paper.

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

4.3

Influence of transverse reinforcement on resistance of failure section

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

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 220

nificant shear contribution of the flexural compression zone.

55-12 55-14 55-16

200

4.4

90-16 55-16 180

140

120

55-14 Shear force at failure [kN]

160

The influence of the concrete compression zone on the shear resistance of RC members has been demonstrated previously by Walther [10] and Juhász [11]. It has now been shown that the resistance of the concrete compression zone is influenced by the horizontal and vertical dimensions of this zone between the top end of the bendingshear crack and the edge of the loading block. The dimensions are determined by the loading and geometry parameters of the specimen.

black: L=625 mm red: L=825 mm 100

4.5 80 1/s [1/dm] 60 -0,2

Influence of concrete compression zone on resistance of failure section

0,2

0,4

0,6

0,8

1,2

1,4

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

Fig. 4). Furthermore, the shear resistance of specimens without transverse reinforcement is higher than the shear force at the appearance of the first shear crack (see Fig. 4). The remaining shear resistance depends very much on the amount of longitudinal reinforcement, the wall thickness of the specimen and on the load-to-support distance. In the absence of nearly orthogonal reinforcement crossing the shear crack, the crack width growth is not restrained efficiently. Consequently, intensive shear crack propagation is expected. During this test, each specimen exhibited considerable ductile behaviour as shown in Fig 5. The remaining shear resistance is the consequence of the sig-

Influence of flexural reinforcement on resistance of failure section

Shear failure develops in members independently of the fact of whether the longitudinal reinforcement yields. The opening and propagation of a critical crack under monotonic loading limits the depth and shear capacity of the compression zone. The depth of the compression zone depends on the amount and bond characteristics of the longitudinal reinforcement, i.e. on crack width and shear slip, too. The shear resistance of RC members with both longitudinal and shear reinforcement which influences by the amount of longitudinal reinforcement which influences the 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 due to prestressing is well known. However, specimens tested in this research also showed that replacing rebars with

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

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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

prestressing strands might even be disadvantageous due to the less efficient bond properties of strands compared with ribbed reinforcing bars. Furthermore, strands have a negligible dowel effect. These circumstances may result in a prestressed member having a lower resistance compared with one having reinforcing bars only. The loadbearing capacity of specimens with the F1 prestressing level was often lower than that of specimens without prestressing. Nevertheless, the failure load of each specimen with the F2 prestressing level was always higher than that for specimens with identical parameters and the F1 prestressing level. These pairs of specimens demonstrated the advantageous 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 the shear resistance of a member is reduced by the degradation of the bond stiffness of longitudinal bars in tension. The ductility and the strength of the bond around the embedded surface of the bars depend on the thickness of the concrete cover and the wall thickness of the member. Fig. 3 shows that horizontal cracking along longitudinal bars was more intensive for specimens with a small wall thickness. The effective depth of the compression zone was also lower for those specimens. This resulted in a lower loadbearing capacity for these specimens compared with others with thicker walls. The local behaviour of the specimens was analysed in [7]. The deformation of the annular cross-section under loading results in additional transverse tensile stresses in the outer fibres of the wall, which intensifies the crack propagation along the longitudinal bars [7]. Bond degradation and, as a consequence, a decrease in the efficiency of the dowel effect of longitudinal bars for specimens with thin walls was more intensive (see Figs. 3a and 3c).

4.8

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

Effect of aggregate interlock on resistance of failure section

It has been demonstrated by several researchers that aggregate interlock is one component in the shear resistance of RC members. However, aggregate interlock is activated only if crack faces move essentially parallel to each other and the crack width is relatively small. A typical relative displacement between the crack faces in the web is shown in Fig. 6. When the crack occurred, the relative displacement between its faces was approximately orthogonal to the crack. The trend of the subsequent relative displacements recorded reveals that the instantaneous relative displacements of crack faces had dominant rotational components and that the centre of rotation was located close to the current tip of the crack. The relative movement was always close to perpendicular to the radius drawn from the current tip of the crack to the point observed. Prior to failure, the width of the critical crack was 1–3 mm. An excerpt from the crack width measurements can be seen in Fig. 7, which shows the real relative displacement between the real crack faces. The figure reveals that aggregate interlock in the tensile zone cannot be effective. Further analysis of relative displacements between the crack faces

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

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is given in [7]. Detailed research into the relative displacements between the crack faces was published by Muttoni et al [12]. Fig. 8, which is taken from [12], also leads to the same conclusion: aggregate interlock along a shear crack cannot contribute significantly to the shear resistance of the section. Widening of the crack width in the longitudinal direction usually stops when the ultimate moment occurs (top point of load–displacement curve). When the compression zone fails along a sliding surface and equilibrium at the crack in the longitudinal direction is no longer ensured, then the two parts of the specimen move towards each other. Hence, the longitudinal component of the crack width disappears or is reduced to a minimum, whereas vertical components begin to increase at a high rate. That is the reason why photos taken after failure may lead to the phenomenon being misinterpreted. Aggregate interlock in the compression zone is a completely different issue. The failure process in the compression zone takes place along a sliding surface (see the dashed lines in Figs. 2 and 3). The faces of the developing sliding surface are pushed together by normal compres-

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

0.4 mm (0.016 in)

reinforcement on the outer side of the wall only than for members with a solid cross-section. Axial stress in the tensile reinforcement at failure was usually close or equal to its yield strength. If a bar yields, then its resistance to transverse forces is practically zero, which results in a negligible dowel effect.

V = 0.93 Vmax

∆ν [mm (in)]

1.0 (0.039)

∆u [mm (in)] Yielding 2.2 (0.087) V = 0.86 Vmax V = 0.85 Vmax V = 0.65 Vmax

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

sion. Prior to failure, these faces slide infinitesimally along each other. Consequently, crack width remains very low, ensuring that the favourable effect of aggregate interlock also remains active. Longitudinal components of aggregate interlock forces increase the axial compression and the transverse components contribute to the shear resistance of the compression zone. Further analysis of the compression zone as well as the sliding surface is given in Part II of this paper.

Conclusions

A test programme involving 45 specimens was carried out to analyse the resistance of thick-walled hollow circular specimens subjected to combined bending and shear. The crack pattern and the effect of test parameters on the resistance of the members were analysed. It was concluded that the shape of the failure section under combined bending and shear depends on the geometrical conditions. A failure section consisted of a crack developed in the tensile zone under combined bending and shear and a sliding surface across the compression zone. The depth of the compression zone in a particular cross-section subjected to combined bending and shear was found to be smaller than that in a section subjected to pure bending only. The reason for this was the degradation in the bond stiffness of the longitudinal reinforcement. The resistance of the hollow circular RC members tested (with spiral reinforcement on the outer side of the wall only) increases with greater wall thickness, with the amount of longitudinal and transverse reinforcement, with the degree of prestress and with a reduction in the shear span (a/d < ∼3.25). The influence of transverse reinforcement on the resistance was quasi-linear. The resistance of specimens without transverse reinforcement was greater than that at the appearance of the first shear crack. Based on the results shown in this Part I, a new mechanical model for the bending-shear resistance of hollow circular RC members will be proposed in Part II.

Acknowledgements 4.9

Effect of dowel action on resistance of failure section

Dowel action of longitudinal rebars is a potential component in the shear resistance of an RC member. This effect is activated when transverse displacement between the crack faces occurs. The stiffness of rebars and their resistance to transverse displacement depend on their stress state and bond properties [9]. Stiffness is high immediately after the appearance of a crack. It was shown by Muttoni [12] that transverse displacement between the crack faces is very low at the beginning of crack opening. Rebar dowel action activates transverse tensile stresses in the wall of the specimens, especially in the bottom one-third of the circular cross-section. Transverse tensile stresses around the rebars are also caused by the mechanical bond between the bars and the concrete. These effects degrade the bond around the longitudinal reinforcement and result in longitudinal cracking (see Fig. 3). The stiffness of dowel action in the tensile zone decreases radically, whereas crack width increases and longitudinal cracks propagate. This stiffness degradation was much more intensive for members with a hollow circular cross-section with spiral

The authors wish to express their gratitude to Lábatlani Vasbetonipari Zrt. for supplying the materials and sponsoring the research. Thanks also go to the colleagues of the Structural Laboratory of TU Budapest (BMGE) for their assistance in the laboratory work. This work is connected with the scientific programme of the “Development of quality-oriented and harmonized R+D+I strategy and functional model at BMGE” project. This project is supported by the New Hungary Development 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 analogy for concrete members of solid and hollow circular cross-section. Engineering Structures, 2008. 3. Uehara, S., Sakino, K., Esaki F.: Limit Analysis of Reinforced Concrete Columns by Yield Line Theory Considering Inter-

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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

10.

11. 12.

action of Combined Forces. Transactions of Japan Concrete Institute, vol. 22 (2000), pp. 413–426. Jensen, U. G., Hoang, L. C.: Shear Strength of Reinforced Concrete Piers and Piles with Hollow Circular Cross Section. Structural Engineering International, 3/2010, pp. 260–267. Völgyi, I., Farkas, G., Nehme, S. G.: Concrete Strength Tendency in the Wall of Cylindrical Spun-Cast Concrete Elements. Periodica Polytechnica Civil Engineering 54/1 (2010), pp. 23–30. Völgyi, I., Farkas, G.: Rebound Testing of Cylindrical SpunCast Concrete Elements. Periodica Polytechnica Civil Engineering 56 (2011), pp. 129–135. Völgyi, I.: Shear-bending behaviour of prismatic, single hooped, ring shaped, spun-cast concrete members. PhD thesis (in Hungarian), 2011. Windisch, A.: Das Modell der charakteristischen Bruchquerschnitte – Ein Beitrag zur Bemessung der Sonderbereiche von Stahlbetontragwerken. Beton- und Stahlbetonbau 83 (1988), No. 10, pp. 271–274. Maekawa, K., Qureshi, J.: Embedded bar behavior in concrete under combined axial pullout and transverse displacement. J Materials, Concrete Structures, No. 532, vol. 30, 1996, pp. 183–195. Walther, R.: Über die Berechnung der Schubtragfähigkeit von Stahl- und Spannbetonbalken – Schubbruchtheorie. Beton und Stahlbetonbau, 11/1962, pp. 261–271. Juhász, B.: Problems of shear resistance of RC members under bending. Thesis (in Hungarian), Budapest, 1968. Muttoni, R. V., Ruiz, M. F.: Influence of Capacity of Reinforced Concrete Members without Shear Reinforcement. ACI Structural Journal, Sept-Oct 2010, pp. 516–525.

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Dr. István Völgyi Assistant Professor Dept. of Structural Engineering Technical University of Budapest (BME) 3. Muegyetem rkp. H-1111 Budapest, Hungary Tel: +36 1 4631968 E-mail: volgyi@vbt.bme.hu

Dr. Andor Windisch Honorary Professor Dept. of Structural Engineering Technical University of Budapest (BME) 3. Muegyetem rkp. H-1111 Budapest, Hungary E-mail: Andor.Windisch@web.de

Dr. György Farkas Professor Dept. of Structural Engineering Technical University of Budapest (BME) 3. Muegyetem rkp. H-1111 Budapest, Hungary Tel: +36 1 4631718 E-mail: farkas@vbt.bme.hu

Technical Paper István Völgyi* Andor Windisch

DOI: 10.1002/suco.201200036

Resistance of reinforced concrete members with hollow circular cross-section under combined bending and shear – Part II: New calculation model Part II analyses the applicability of current shear design models for RC members with a hollow circular cross-section on the basis of experimental results introduced in Part I of this paper. A new calculation model is proposed which assigns the contribution of the concrete zone in compression to shear resistance. The proposed model takes into account how the flexural and shear reinforcement, the load-to-support distance and the shape of the cross-section affect the shear resistance. The model is based on the analysis of potential failure sections subjected to bending and shear, and applies a compatibility criterion that considers how the member carries the load. The analogy between the failure of the concrete compression zone and the failure of the soil along a sliding surface are presented as well as the conditions for the development of the failure section. Keywords: behaviour under combined bending and shear, hollow circular cross-section, contribution of compressed concrete to shear resistance, sliding surface

Introduction

This paper presents a new calculation model for the resistance of RC and PC members under combined bending and shear (bending-shear resistance). Bending-shear resistance emphasizes the fact that shear resistance depends on the intensity of simultaneous bending moment combined with shear force. In contrast to conventional design methods, shear and bending resistances are interrelated. The proposed calculation method is based on the results of a parametric experimental programme carried out on hollow circular RC members. The details of the test programme have been published in [1], [2], [3], [4] and [5]. Current shear design models can be divided into three main groups: a) Cross-section design b) Strut-and-tie models c) Models based on presumed stress fields. These models apply independent bending and shear design procedures. Shear resistance is interpreted for mem-

* Corresponding author: Volgyi@vbt.bme.hu Submitted for review: 25 September 2012 Revised: 18 July 2013 Accepted for publication: 18 July 2013

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

bers with solid, plane webs and with two separate groups of flexural reinforcement (one in tension and one in compression). In usual cases these assumptions are satisfied. However, their validity comes under question when applying them to the analysis of members with hollow cross-sections and curved webs. In the case of members with a hollow circular crosssection, the “struts” of an assumed strut-and-tie model or the compressed arch in the vicinity of the supports become three-dimensional. According to shear model types a) and b), these “struts” and “arches” require additional internal deviation forces, which should reduce the shear resistance of members with a hollow circular cross-section compared with that of members with plane webs. Therefore, these deviation forces should also reduce the tying effect of transverse reinforcement in a strut-and-tie model, see Fig. 1. The performed tests revealed that the actual shear behaviour of members with a hollow circular crosssection is different and the above interpretations of shear behaviour on the basis of design model types a) and b) cannot be applied. The problems of models based on presumed stress fields are similar. High additional stresses should develop as a consequence of the “curved webs”. Applying these models to hollow circular member without modifications is theoretically incorrect. The model proposed in this paper calculates the shear resistance of a hollow circular member under combined bending and shear on the basis of an equivalent I-shaped cross-section (as shown in Fig. 2), which has varying “web thickness” over its depth and a cross-sectional area and moment of inertia identical with that of the hollow circular cross-section.

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

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

Excerpt from experimental results – basis of proposed calculation model

A more detailed introduction to the test results dealt with in this section is given in Part I of this paper [5]. The failure of a hollow circular RC member under combined bending and shear occurs along a failure section, which consists of a critical bending-shear crack in the tension zone and its extension as a sliding surface across the concrete compression zone. The polyline shape of the potential failure sections depends on the bending-to-shear ratio as well as on the geometrical and boundary conditions [6]. A similar phenomenon can be observed for the bending failure members with a rectangular cross-section under pure bending. Prior to failure, a sliding surface starts to develop on one or both sides of the tip of the critical bending crack, which first runs roughly parallel to the longitudinal axis, later across the compression zone of the member [7]. This failure of the compression zone along a sliding surface is similar to that of soils. When assuming combined bending and shear, the position of the first crack depends on the stress pattern and the actual concrete tensile strength distribution. The occurrence of further cracks depends not only on the stress pattern but on the amount, the arrangement and the bond properties of the reinforcement, too. At load levels close to failure, large relative displacements with a significant component normal to the longitudinal axis of the member occur along the critical crack in the tension zone. Parallel to that, flat or longitudinal cracks develop along the longitudinal bars (see Fig. 4). A consequence of the lateral deflection of tensile flexural bars is the degradation in the bond stiffness of these rebars due to dowel action and the splitting stresses caused by the bond of the rebars after cracking [8]. This degradation results in increased slip and elongation along the transmission lengths, which also allow the crack width to increase. Consequently, compared with the case of perfect bond, wider and longer cracks occur, which result in additional compressive stresses in the compression zone. Furthermore, kinked tension bars crossing these longitudinal cracks become eccentrically tensioned, which lowers their effective yield strength. This is the reason why the depth of the compression zone at the end of a crack caused predominantly by shear is smaller than that calculated with when assuming a perfect bond

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between rebars and concrete. Close to ultimate load levels, the tensile stress in tension rebars is usually close to their yield strength, hence, rebar resistance to lateral deformation in this state is very low. Consequently, dowel action at lower load levels might be relevant but is usually negligible prior to failure. The size and direction of relative displacements between the faces of the critical crack has been analysed further. It was demonstrated that aggregate interlock in the tension zone was not effective [4], [5]. At failure, a sliding surface develops from the top end of the critical bendingshear crack across the compression zone. Its shape and shear resistance depend on the depth of the compression zone, the actual concrete strength, the amount and strength of longitudinal rebars in the compression zone and the compression force due to bending moment and, if any, the axial force. Another influencing factor is the distance lc of the tip of the crack from the next significant geometrical boundary condition (position of loading block, support, hoops, etc.).

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

Calculation methods for the shear strength of members with shear reinforcement are discussed below. After summarizing their theoretical background, their applicability is analysed from the point of view of the experimental results. Calculation formulae for the failure of inclined compression struts are outside the focus of this discussion because this failure mode was not investigated in the actual research. However, crushing of inclined struts cannot be excluded 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]. According to the standard method (ENV 1992 I), the shear resistance of a cross-section is the sum of the contribution of shear reinforcement crossing the shear crack, whose angle to the longitudinal axis is assumed to be 45°, and the contribution of concrete, being a function of the width and depth of the web and the concrete’s “shear strength”. The second method (ENV 1992 II) is based on the variable strut inclination method. The possibility of choosing the strut inclination over a wide range is doubtful. The reason for the difference between the actual inclination of the shear crack and the assumed angle of the inclined compression strut with respect to the longitudinal axis of the member is the hypothetical aggregate interlock. Our experimental results question the existence of aggregate interlock in the tension zone of the member. Instead, they indicate a significant contribution of the compression zone to shear resistance and also that shear resistance is a function of the amount of longitudinal and shear reinforcement and the load-to-support distance. The model of the variable angle of strut inclination is not able to consider some of these effects. ENV 1992 has been superseded by EN 1992-1-1 [10], which contains solely the variable strut inclination method to calculate shear resistance.

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

3.2

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

Three methods denoted as Approximation Levels I, II and III are implemented in the final draft of the fib Model Code for Concrete Structures [11], to calculate the shear resistance of members with shear reinforcement. The complexity of the model and the expected accuracy increase with the approximation level. Shear resistance at Approximation Level I is ensured solely by the contribution of shear reinforcement. The formulae are similar to those in EN 1992. Different minimum compressive stress field inclinations are defined for RC members with or without axial force. The effects of bending moment and amount of tension reinforcement on shear resistance are not integrated into the model. Shear resistance attributed to concrete is also neglected in Approximation Level II. The main difference between this and Approximation Level I is a formula that is proposed for calculating the minimum angle of inclination as a function of the longitudinal strain at mid-depth of the effective shear depth. This empirical formula is a big help compared with the “free choice” allowed by EN 1992. By calculating the longitudinal strain, the effect of the depth of the compression zone and the presence of the compression force on the shear resistance are allowed for. Less elongation at mid-depth results in a higher shear resistance. This is supported by our own experimental results. Approximation Level III is based on simplified modified compression field theory (MCFT) [11]. The calculated shear resistance of the concrete is a function of the effective cross-sectional area of the web, the longitudinal reinforcement and the ratio of the combined external forces (axial force, bending moment) in the cross-section analysed, which is assumed to be plane and perpendicular to the longitudinal axis of the member. It should be noted that applying fib Model Code 2010 provisions to the recalculation of experimental data requires an iterative procedure, since the strength predictions depend on the predicted results.

3.3

Walther ‘s theory

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

This contribution is calculated on the basis of a MohrCoulomb failure criterion, which is described by a parabolic-elliptic σ-τ curve. The ratio of tensile to compressive strength is set to 1/8. Walther’s theory does not take into account that the geometry of the sliding surface may change and that the compression zone is reduced during the failure process due to the degradation of the bond stiffness of the longitudinal reinforcement.

3.4

Definition of model parameters and their interpretation for hollow circular cross-sections

The models discussed were developed in the first place for angular cross-sections, and therefore the parameters included need to be interpreted for hollow circular cross-sections. None of the documents analysed state that the respective method applies to angular cross-sections only. As longitudinal reinforcement is uniformly distributed around the perimeter for hollow circular sections, the separation of tension and compression reinforcement as well as the definition of effective depth are therefore not obvious. In the shear design models, effective depth is used to calculate the number of stirrups contributing to the shear strength of the section analysed. Accordingly, effective depth for hollow circular cross-sections is defined as the distance between the extreme compressed fibre and the extreme rebar in tension. The double wall thickness is used as the minimum width of the hollow circular cross-section. Tension reinforcement is taken as the area of rebars falling within the tension part of the cross-section irrespective of their stress. Efficiency of helical bars in shear resistance is measured by that component of the tangent unit vector drawn to the intersection point of the crack and the side view of the helical bar parallel to the load.

3.5

Conclusions for the models analysed

Table 1 contains a statistical analysis of numerical results calculated from the algorithms discussed in section 3. Mean values of material strengths and geometrical properties were used for calculation purposes. Maximum resistance was aimed for in the analysis when setting the parameters 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 material properties (VR /Vu)

ENV 1992 I

EN 1992

fib MC 2010 I

fib MC 2010 II

fib MC 2010 III

Walther*

Proposed

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%

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 materials of higher compressive strength used in the actual research.

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

Comparing the results based on the methods of EN 1992 and ENV 1992 I is interesting; for angular cross-sections it was discussed earlier [15][16]. Shear resistance according to ENV 1992 I is calculated as the sum of the resistance of the contribution of concrete and shear reinforcement. This method is called “simplified”, although its theoretical base is more realistic than that of the EN 1992 method. Results of the ENV 1992 I method are more reliable for all aspects analysed. The theory of the variable strut inclination method (EN 1992) considerably overestimates the shear resistance for specimens with a high amount of shear reinforcement when using the minimum proposed angle of inclination. Best agreement between test results and calculation was found in the case of the ENV 1992 I model for members with a hollow circular cross-section under bending and shear. The applicability of the fib Model Code 2010 methods was limited for the test results. Approximation Level III was most efficient, despite an observed systematic error. The VR/Vu ratio was close to unity for specimens with a high amount of transverse reinforcement and small wall thickness; however, the resistance was massively underestimated for specimens with a low amount of transverse reinforcement, large wall thickness and short loadto-support distance. Walther’s method was applied to the calculation of shear resistance for the cross-section next to the loading block. The method overestimated the shear resistance of the concrete compression zone. Results clearly showed that it is necessary to consider a reduction in the depth of the compression zone due to the opening of the critical crack. The standard deviation and the variation coefficient of results for each method are relatively high. The systematic errors in the calculated results are caused by the theoretical deficiencies discussed above. Moreover, the assumptions of the methods do not coincide with our observations during the tests [4], [5]. To overcome this, a new bending-shear resistance calculation model for members with a hollow circular cross-section will be shown in section 4. The proposed model is based on the actual failure mechanism.

4 4.1

The proposed mechanical model Basic equation

For cross-sections under pure bending, plane cross-sections and a perfect bond between steel and concrete are usually assumed and result in an acceptably low difference between calculations and actual load-carrying capacity. However, the increase in bond slip of longitudinal rebars at sections under simultaneous significant shear and bending has a large effect on the resistance of RC members with a hollow circular cross-section and with transverse reinforcement on the outer side of the wall only. This degradation in bond stiffness is caused by the transverse forces and deformations acting on the reinforcing bars around the shear crack. That also leads to a reduction in the depth of the compression zone. Theoretically, there is no limit to the shape and position of the potential failure sections. Nevertheless, detailing rules regarding the position and amount of reinforce-

Structural Concrete 15 (2014), No. 1

ment assure that the angle of inclination of the failure section in members designed according to the existing standards is 45° or lower. The shear resistance of an RC element can be calculated as the sum of the contribution of the concrete compression zone (including longitudinal reinforcement) Vc* and the contribution of the transverse reinforcement crossing the real shear crack part of the polyline-shaped failure section Vw (Eq. (1)): VR  Vc*  Vw

(1)

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

4.2

Contribution of transverse reinforcement

Transverse reinforcement does not take part efficiently in shear resistance before cracking. Crack development is the condition for the stress increase in the tension reinforcement as well as in the transverse reinforcement crossing the polyline-shaped section in the tension zone (active shear reinforcement). In addition, the contribution of transverse reinforcement, which intersects the failure section in the compression zone, remains low. The vertical component of the tensile force carried by the active helical bars is calculated using Eq. (2): Vw 

 Asw  fyw  e

(2)

The vertical component of the tangent unit vector e varies along the helical bars. The number and position of intersection points of any potential failure section and the helical reinforcement have a stochastic character. Therefore, the average of the calculated resistances associated with different longitudinal positions of helical reinforcement relative to the failure section is taken into account in the proposed model.

4.3

Contribution of concrete compression zone

It was demonstrated in previous studies [14], [17] that the concrete’s contribution to the shear resistance of a member is attributed to the compression zone. The depth of the compression zone is a function of the amount and the bond properties of longitudinal reinforcement as well as the intensity of simultaneous bending moment and axial force acting on the section. The depth of the compression zone can be calculated similarly to that for a cross-section subjected to pure bending and assuming a plane cross-section. Nevertheless, test results show that the depth of the compression zone of a section under combined bending and shear is lower than that of a cross-section under the same bending moment without shear. The difference is caused by the more intensive bond slip of the longitudinal tensile rebars along the longer transmission lengths, which also results in wider and longer cracks. To consider this,

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

Fig. 3. Applied σ-ε model of flexural reinforcement under longitudinal pullout and transverse displacement vs. σ-ε diagram of reinforcing bar with perfect bond under pure tension

an idealized, fictitious material law for longitudinal, tensile reinforcing steel according to Fig. 3 has been introduced in the proposed mechanical model. Immediately after cracking, an apparent reduced axial stiffness for the tension reinforcement – due to the bond slip – is mobilized. The increased elongation of bars along the transmission length beyond crack faces is considered through a fictitious ultimate steel strain. A composite action factor ηs, which characterizes the composite action between steel bars and concrete along the transmission length beyond cracks, is defined for the reinforcing bars. The experimental results [4], [5] show that this composite action factor is a function of the wall thickness. The thinner the wall of the specimen, the smaller the composite action observed. The proposed function for the composite action factor is calculated using Eq. (3). Owing to the relatively smooth surface of prestressing wires, the bond properties of strands are even poorer than those of rebars. Therefore, a reduced composite action factor for strands ηp is pro-

Fig. 4. Crack pattern and shape of failure section of specimens 9-16-150825 and 9-16-150-625

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

s  1  0.3 

Rv R

(3)

 p  0.8  s

(4)

Owing to crack propagation, the effective depth of the compression zone decreases if the intensity of load increases. In addition, the compressive force in the compression zone due to the bending moment also increases. Following yielding of the transverse reinforcement, the further increase in shear force is also carried by the concrete compression zone. Due to this combined state of stress, starting from the tip of the crack, a sliding surface develops across the concrete compression zone [14]. In the experimental setup, the length of the sliding surface depends on the distance between crack tip and loading

Fig. 5. Scheme of FE model of compression zone

Structural Concrete 15 (2014), No. 1

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

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

Vc [kN]

200

. .

160

120

80 lc/xc 40 0

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

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

block. Usually, the failure section does not enter the zone under the loading block because of the higher effective strength of confined concrete there. For long support-toload distances, the sliding surface through the compression zone becomes very flat, see Fig. 4 and [5]. It will be shown in the following that in addition to the decrease in the length of the sliding surface, its shear resistance increases significantly. The shear resistance of the compression zone was analysed as a function of the distance between the tip of the crack and the distance to the loading block lc. The depth of the compression zone x for a given compression force due to bending moment was calculated according to the following procedure. A non-linear 2D FE shell model of the individual compression zone was developed (Fig. 5). The inclination of the shear-influenced middle part of the failure section was taken as 45°. The variable parameters of the shell model were the depth of the effective compression zone x and the horizontal distance between the top end of the bending-shear crack and the face of the loading block lc. The width of the shell elements and the supposed distribution of the axial and shear stresses at the “loaded edge” are shown in Fig. 5. The resultant force of the applied axial stresses was equal to the sum of the compressive resultant force due to bending moment and axial load including, if any, prestressing. A special Mohr-Coulomb-type failure criterion was applied to the concrete in the compression zone analysed. Katzenbach et al. showed the gradual development of the

sliding surface in soils [7]. The stress distribution along the developing sliding surface is shown in Fig. 6. In the first phase, a peak stress close to the loaded end of the sliding surface can be observed, which further develops into degradation of this zone, resulting in relative displacement (sliding) between the faces of the discontinuity line. After this sliding, a new failure criterion with no cohesion and reduced angle of internal friction applies (Fig. 7.). The development of the sliding surface across the concrete compression zone is similar. The initial cohesion and angle of internal friction of the concrete were calculated on the basis of its compressive and tensile strengths. After cracking, cohesion was taken as zero and 37° (gravel) as the angle of internal friction ϕ2. The results of the associated parametric study can be seen in Fig. 8, representing the relationship between the shear resistance of the compression zone Vc and the length of the sliding surface lc. As shown, Vc is sensitive to lc for high compression and is not sensitive when shear is combined with low compression. The influence of axial stress on Vc is different for short and long sliding surfaces. Normal (σ) and shear (τ) components of the compression force Fc are shown in Fig. 9 for the sliding surfaces with different inclination caused by a simultaneous bending moment. A compression force results in normal stresses dominating for sliding surfaces with high inclination and shear stresses for sliding surfaces with low inclination. Shear stresses consume frictional resistance along the sliding surface, whereas axial stresses increase it. That is why

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

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

Structural Concrete 15 (2014), No. 1

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

high axial stress is advantageous for sliding surfaces with high inclination and disadvantageous for those with low inclination. For a long support-to-load distance of the member, the formation of a long sliding surface with low inclination and low shear resistance is geometrically possible, but impossible for a short support-to-load distance due to the geometrical constraints. This results in concrete contributing more to the shear resistance of the member. Consequently, solely for geometrical reasons, the load-carrying capacity of a member with small support-to-load distance is higher than that with long support-to-load distance despite the fewer transverse bars crossing the shorter failure section. It is important to note that the failure section is situated wholly between the inner faces of the support and the loading block. This means that it is necessary to analyse the equilibrium of simultaneous shear force and bending moment with internal forces along the failure section. Dowel action of longitudinal bars in the tension zone is neglected because of the softened bond zone and the high-intensity tensile stresses equal or close to yield strength. The vertical component of the relative displacement in the compression zone remains very low until full development of the sliding surface. It is also assumed that the distribution of shear force attributed to the compression zone between concrete and longitudinal rebar is proportional to the latter’s modulus of elasticity. Dowel action of longitudinal bars in the compression zone is taken into account according to Eq. (5): Vc*  Vc  (1  l  s ) 

Es Ec

(5)

It is interesting to note the difference in behaviour between members with hollow circular and I-shaped crosssections. The compression zone of a hollow circular crosssection is completely effective because the sliding surface must cross the whole zone right to the top of the cross-section to induce failure, whereas for T- and I-shaped crosssections the failure section often runs under the top flange as a result of an insufficient web-to-flange connection. The effectiveness of very wide flanges for T- and I-shaped members is limited because the sliding surface does not run through the whole flange width. The sliding surface of these types of members can be analysed using 3D FE models. Thin webs of members with I, T and hollow circular cross-sections allow shear cracks to appear first independently of bending cracks.

Verification of proposed model

The proposed model was used for calculating the shear resistance of the 45 test specimens. The mean values of resistance were calculated using Eq. (1). The results can be found in Table 2. The notation of specimens contains the nominal wall thickness [mm], the diameter of the longitudinal 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 longitudinal reinforcement; in these cases the diameter of longitudinal reinforcing bars was denoted by 0.

The reliability of the results of the proposed model is excellent. The average of the ratio of calculated to measured resistance is 95 % and the associated standard deviation remains below 11 %. The proposed model shows very good agreement with the test results, without any noticeable systematic error. As a conclusion, the applicability of the proposed model for determining the mean bendingshear resistance of RC and PC members with hollow circular cross section is demonstrated.

Practical applications

If the proposed model is to be used for design purposes, the following procedure with the design values of material strengths is necessary: – Set the reference cross-section to be checked (see Fig. 10). – Calculate the internal forces of the reference cross-section (shear force, axial force, bending moment) using customary beam theory. – Calculate the depth of the compression zone taking into account Eqs. (3) and (4). – Define the polyline-shaped potential failure section. Take the inclination in the mid-zone as 45° and 15° for both the top and the bottom part of the section if possible; otherwise, fit the section between the inner faces of the loading block and the support by approximating the above inclination as far as possible. – Calculate the resistance of the compression zone according to section 4. – Calculate the resistance of the transverse reinforcement using Eq. (2). – Summarize the contribution of concrete and steel using Eq. (1). The extension of the proposed method to other types of cross-section and more complex stress states is in progress. In the next step the resistance of the concrete compression zone Vc will be formulated to support practical design. At the moment Vc can be calculated with FE programs.

Conclusions

A test programme was carried out on 45 specimens to analyse the resistance of RC and PC members with a hollow circular cross-section under combined bending and shear. Crack patterns and the influence of test parameters on resistance were analysed. The experimental results were presented in Part I of this paper.

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

Structural Concrete 15 (2014), No. 1

I. VĂślgyi/A. Windisch Âˇ Resistance of reinforced concrete members with hollow circular cross-section under combined bending and shear â&#x20AC;&#x201C; Part II: New calculation model

Table 2. Data of specimens and results of proposed model

Calculated resistance of the specimen [kN]

Calculated / measured resistance ratio (VR/Vu)

273 250 370 332 225 182 459 386 506 518 291 261 437 445 310 403 420 423 634 571 545 586 502 531 617 481 625 502 393 599 469 590 620 581 597 585 597 721 731 714 685 652 627 689 683

63 94 65 88 75 92 70 114 55 63 80 74 87 94 105 107 136 136 120 139 138 135 162 162 129 156 142 75 110 81 113 114 115 132 137 144 143 99 126 140 150 157 159 113 99

0 0 47 37 0 0 43 35 96 96 0 0 39 37 0 0 0 0 42 37 37 37 30 31 53 40 66 35 28 74 59 39 41 36 37 30 30 39 39 35 36 28 27 37 42

63 94 111 125 75 92 113 149 151 159 80 74 126 131 105 107 136 136 162 176 174 172 193 192 182 196 208 110 138 155 172 153 156 168 173 174 174 139 165 174 186 185 186 151 140

0.92 0.89 1.06 0.93 1.04 1.11 0.85 0.92 1.06 1.04 1.03 0.87 1.10 0.93 1.10 0.68 1.01 1.01 1.03 0.99 1.03 0.97 0.88 0.84 0.98 0.93 0.81 0.78 0.94 0.91 0.96 1.09 1.07 1.02 1.04 0.76 0.74 0.85 1.02 0.94 1.04 0.79 0.86 0.87 0.97

Statistics of all specimens:

There was a discussion on how the application of recent calculation models of standards and accepted publications is problematic. Furthermore, their applicability for calculating the shear resistance of members with a hollow circular cross-section is limited. These models are usually (sometimes extremely) conservative, but on the other hand sometimes overestimate the shear strength. Moreover, their results scatter over an unacceptably wide range. A new model was proposed for calculating the shear resistance of RC and PC members with a hollow circular

Structural Concrete 15 (2014), No. 1

Statistics of specimens with small wall thickness

Contribution of the transversal reinforcement [kN]

69 69 65 69 78 78 70 76 61 61 84 84 84 83 71 64 85 85 77 83 83 80 84 83 78 85 79 91 92 87 92 83 81 86 84 86 85 82 84 94 90 96 98 80 78

average st. deviation minimum: maximum:

0.98 0.09 0.85 1.11

Statistics of specimens with large wall thickness

Contribution of the compression zone [kN]

69 105 105 135 72 83 133 162 143 154 78 85 115 140 95 158 134 135 158 177 169 178 218 228 187 210 258 140 147 170 180 141 146 165 167 229 234 163 162 186 179 233 216 174 145

Statistics of (VR/Vu) .

average st. deviation minimum: maximum:

0.94 0.11 0.68 1.10

Statistics of prestessed specimens

Compression force in compression zone [kN]

Effective prestressing force [kN] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 148 148 148 148 88 106 116 128 118 108 228 238 286 255 273 306 237 180

Calculated depth of compression zone [mm]

73 73 67 67 66 66 67 67 66 66 67 67 73 73 70 70 67 67 70 67 67 70 70 70 67 67 67 63 63 63 63 65 70 65 70 65 65 63 70 63 70 63 63 72 72

Results from the proposed model

Experimental shear resistance of the specimen [kN]

57 58 57 55 59 60 54 60 56 59 64 57 55 59 96 92 96 99 93 96 94 93 96 94 91 92 99 58 60 61 58 92 93 96 92 95 95 93 95 97 95 99 96 92 90

Concrete compressive strength [N/mm2]

Specimen 55-12-0-975 55-12-0-625 55-12-150-825 55-12-150-625 55-14-0-825 55-14-0-625 55-14-150-825 55-14-150-625 55-14-75-825 55-14-75-789 55-16-0-975 55-16-0-825 55-16-150-975 55-16-150-825 90-12-0-825 90-12-0-625 90-16-0-825 90-16-0-825 90-16-150-975 90-16-150-825 90-16-150-825 90-16-150-825 90-16-150-625 90-16-150-625 90-16-110-825 90-16-110-625 90-16-75-635 55-16-150-F1-825 55-16-150-F1-625 55-16-75-F1-825 55-16-75-F1-625 90-16-150-F1-975 90-16-150-F1-975 90-16-150-F1-825 90-16-150-F1-825 90-16-150-F1-625 90-16-150-F1-625 90-16-150-F2-975 90-16-150-F2-975 90-16-150-F2-825 90-16-150-F2-825 90-16-150-F2-625 90-16-150-F2-625 90-0-150-F2-825 90-0-150-F2-975

Wall thickness [mm]

Measured test results

average st. deviation minimum: maximum: average st. deviation minimum: maximum:

0.92 0.11 0.74 1.09 0.95 0.11 0.68 1.11

cross-section. This model defines the contribution of the concrete compression zone to shear resistance and also takes into account how the amount of longitudinal and transverse reinforcement, the wall thickness of the crosssection, the strengths of concrete and reinforcing bars, the load-to-support distance and the simultaneity of bending moment and axial force with shear force influence the resistance of the member. The proposed model is able to consider several potential failure sections with different position and shape.

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

A new idealized material law for reinforcing steel and prestressing strands was defined to determine the depth of the concrete compression zone for sections under combined shear and bending. The calculation of the shear resistance of the concrete compression zone was similar to that of sliding surfaces well known from soil mechanics. This can be considered as a new interpretation of the contribution of the concrete compression zone to the shear resistance of RC or PC members under combined bending and shear. The calculated ultimate loads agreed very well with the test results. No systematic deviation was detected. In order to extend the proposed method to other cross-section types and more complex stress states, the research programme is to be continued.

Notation cross-sectional area of longitudinal reinforcement cross-sectional area of transverse reinforcement vertical component of the tangent unit vector drawn to the intersection point of the crack analysed and the helical transverse bar Ec secant modulus of elasticity of concrete Es modulus of elasticity of reinforcing steel fc compressive cylinder strength of concrete fct tensile strength of concrete fyw yield strength of transverse reinforcement lc length of sliding surface lt length of (bending-)shear crack in tension zone s pitch of helical reinforcement D/R outer diameter/radius of hollow circular cross-section v wall thickness of specimen Vc shear resistance component provided by concrete compression zone Vc* shear resistance of concrete compression zone taking into account the effect of reinforcement in the compression zone VR calculated shear capacity of RC member under combined bending and shear Vu shear failure capacity of specimen under combined bending and shear (experimental) Vw shear resistance component provided by transverse reinforcement ρl longitudinal reinforcement ratio (based on total longitudinal reinforcement) ηs, ηp factor taking into account composite action between reinforcing bar (s) or strand (p) and concrete As Asw e

References [1] Völgyi, I., Farkas, G., Nehme, S. G.: Concrete Strength Tendency in the Wall of Cylindrical Spun-Cast Concrete Elements. Periodica Polytechnica Civil Engineering 54/1(2010), pp. 23–30. [2] Völgyi, I., Farkas, G.: Rebound testing of cylindrical spun cast concrete elements. Periodica Polytechnica Civil Engineering 55/2(2011), pp. 129–135. [3] Völgyi, I., Farkas, G.: Experimental study on shear strength of hollow cylindrical spun cast concrete elements – Local behaviour. Asian Journal of Civil Engineering; 13/1 (2012), pp. 113–126.

[4] Völgyi, I.: Shear-bending behaviour of prismatic, single hooped, ring shaped, spun-cast concrete memebers. PhD thesis, 2011 (in Hungarian). [5] Völgyi, I., Windisch, A., Farkas G.: Resistance of reinforced concrete members with hollow circular cross-section under combined bending and shear – Part I: Experimental Investigation. Structural Concrete, 15: 13–20. doi: 10.1002/ suco.201200035. [6] Windisch, A.: Das Modell der charakteristischen Bruchquerschnitte – Ein Beitrag zur Bemessung der Sonderbereiche von Stahlbetontragwerken. Beton- und Stahlbetonbau 83 (1988), No. 10, pp. 271–274. [7] Zilch, K., Zehetmaier, G.: Bemessung im konstruktiven Betonbau. Nach DIN 1045-1 und DIN EN1992-1-1. Springer, 2006. [8] Maekawa, K., Qureshi, J.: Embedded bar behavior in concrete under combined axial pullout and transverse displacement. J Materials, Concrete Structures; No. 532, vol. 30 (1996), pp. 183–195. [9] ENV1992-1-1:1999 Design of concrete structures, General rules and rules for buildings. [10] EN1992-1-1:2010 Design of concrete structures, General rules 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 provisions – part I: beams and slabs. Structural Concrete, 14: 195–203. doi: 10.1002/suco.201200066. [13] Collins, M. P.: Improving analytical models for shear design and evaluation of reinforced concrete structures. fib bulletin 57, Shear and punching shear in RC and FRC elements, Salo, 2010, pp. 77–92. [14] Walther, R.: Über die Berechnung der Schubtragfähigkeit von Stahl- und Spannbetonbalken – Schubbruchtheorie. Beton und Stahlbetonbau, 11/1962, pp. 261–271. [15] Gulvanessian, H., Farkas, G., Kovács, T.: Comparative analysis on using Eurocode and two national codes in concrete bridge design. Revue française de génie civil; 5/4 (2001), pp. 435–467. [16] Farkas, G., Kovács, T., Szalai, K.: Comparison of the Hungarian 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 RC members under bending. Candidate dissertation, Budapest, 1968 (in Hungarian). [18] Katzenbach, R., Bachmann, G.: Scherbandentwicklung im Boden. Bauingenieur, vol. 83 (2008), pp. 351–356.

Dr. István VÖLGYI Assistant Professor Dept. of Structural Engineering Technical University of Budapest (BME) 3. Muegyetem rkp. H-1111 Budapest, Hungary Tel: 00364631968 E-mail: Volgyi@vbt.bme.hu

Dr. Andor WINDISCH Dept. of Structural Engineering Technical University of Budapest (BME) 3. Muegyetem rkp. H-1111 Budapest, Hungary E-mail: Andor.Windisch@web.de

Structural Concrete 15 (2014), No. 1

Technical Paper Jerzy Onysyk Jan Biliszczuk* Przemysław Prabucki Krzysztof Sadowski Robert Toczkiewicz

DOI: 10.1002/suco.201300007

Strengthening the 100-year-old reinforced concrete dome of the Centennial Hall in Wrocław 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 m and in the year it was completed was the largest reinforced concrete dome in the world. This broke the previous record, held by the dome of the Pantheon in Rome (43.3 m), which had lasted for 1787 years. This paper describes the structure of the building, its condition after 100 years of use and the renovation works carried out in 2009–2011. An important part of the renovation was strengthening the lower (tension) ring of the ribbed dome by way of external prestressing. Details concerning the assessment of the technical condition of the hall, numerical calculations and the proposed system of strengthening are presented. In 2006 the monumental Centennial Hall was listed as a UNESCO World Heritage Site for its pioneering reinforced concrete structure, designed in the style of modernism.

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

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

Short historical outline of massive domes

The most famous building with a roof constructed as a coffered concrete dome is the 2000-year-old Pantheon in Rome, commissioned by Marcus Agrippa in 27 BC and rebuilt by Emperor Hadrian in about 126 AD [1]. During its history, the building had various functions and was eventually turned into a church. It is a great structure with a central opening (oculus) at the crown and a lower ring 43.3 m in diameter. The thickness of the dome varies from 6.4 m at its base to 1.2 m at the level of the oculus [2]. The stresses in the dome were reduced by using lightweight aggregate, e.g. pieces of pumice in higher layers, which decreased the density [3]. This reduced the weight of the roof, as did the coffered structure of the dome (Fig. 1) and eliminating the crown of the dome by including the oculus. The height of the Pantheon up to the oculus and the inside diameter are the same. The drum supporting structure is enclosed with façade walls, making the building look like a temple. With an inside diameter of 43.3 m, the

* Corresponding author: jan.biliszczuk@pwr.wroc.pl Submitted for review: 6 February 2013 Revised: 17 May 2013 Accepted for publication: 24 July 2013

Pantheon remains today the largest dome constructed of unreinforced concrete. Examples of the next largest domes are the Baths of Caracalla, built in Rome between AD 212 and 216, with a diameter of 35.1 m [4], and the ashlar masonry dome of Constantinople’s Hagia Sophia, with a diameter of 31 m [5]. This latter building (Fig. 2), erected under Justinian between AD 532 and 537, is one of the greatest achievements of Byzantine culture and has undergone a turbulent history, also during its construction. In May 558, following the earthquakes of August 553 and December 557, parts of the central dome and its supporting structure collapsed [5]. Between 558 and 562 a new modified design was introduced, resulting in the dome we see today. The next large dome structures were built in Europe during the Renaissance [7]; Florence Cathedral (the largest dome since antiquity, with a diameter of 44 m) and St. Peter’s Basilica in Rome (on the left in Fig. 3), which has a dome with an inside diameter of 42.7 m [8]. This is a double shell structure made of bricks and travertine blocks held together with lime mortar, stiffened by 16 ribs and supported by a cylindrical structure stabilized by 16 buttresses [8]. During the construction of the dome, carried out in 1589–1592 by Giacomo della Porta, three iron chains were built into the internal shell, and in 1590 two additional hoops were added at the base of the lantern [9].

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

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]

After the dome’s completion, cracks began to develop and in the middle of the 18th century serious damage was noticed [8]. Pope Benedict XIV decided to consult a famous Italian scholar, Giovanni Poleni. Following an inspection, Poleni proposed strengthening the dome by placing five iron rings around it [10]. A sixth hoop was added while work was in progress when it turned out that one of the original rings had broken. To determine the section for the hoops, Poleni conducted experiments using a model (on the right in Fig. 3), which allowed an evaluation of the relationship between the section of an iron rod and its strength [11]. A special system consisting of two locking wedges, which prevent the rings from losing their tension, was introduced to join elements of the chains [10]. The analyses performed by Poleni, concluding with a proposal for the strengthening method, can be considered as one of the first expert reports concerning a structure in our modern understanding of such a study. The next monumental building with a roof in the form of a massive structure (reinforced concrete dome)

was the Centennial Hall (Fig. 4), built in Wrocław, in 1911–1913 [12, 13]. This is a unique structure in terms of its architectural and structural solutions, and took advantage of the potential of a new material (reinforced concrete), new computational methods based on the mechan-

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

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

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

ics of structures and new construction technologies. Initially called “Festhalle” (Celebrational Hall) [13], it was later given the name “Die Jahrhunderthalle” (Centennial Hall) to commemorate the 100th anniversary of King Frederick William III of Prussia’s proclamation calling upon the people to rise up against Napoleon (17 March 1813) [14]. The designer of the Centennial Hall was a German architect, Max Berg (Fig. 5). Structural calculations were performed by G. Trauer and W. Gehler [13]. The hall was constructed by Dyckerhoff & Widmann from Dresden (now DYWIDAG). The period of design and construction of the hall coincided with the beginning of the widespread

use of reinforced concrete in the construction industry. Impressive reinforced concrete structures such as the market halls in Wrocław and Gdan´sk and the main hall of the railway station in Leipzig [14] were built around the same time. The hall has been used for nearly 100 years without any major repairs, especially since it was not significantly damaged during the Second World War (other than removing the great organs). In 2006 the monumental Centennial Hall (known for 55 years as the People’s Hall) was listed as a UNESCO World Heritage Site for its pioneering reinforced concrete structure designed in the style of modernism. The dome of the hall with a diameter of 65.0 m was the 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, the Centennial Hall was mentioned in one of the keynote speeches concerning roof milestones in history [15].

Structure of the Centennial Hall’s dome

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

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

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

ence of the dome. The roofing system in the form of terraces enabled four circumferential rows of windows, illuminating the interior of the hall (Fig. 6). The dome is supported by movable steel bearings placed on the lower structure, which consists of four arches 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 auditorium is situated. Inside the hall, the structural concrete elements were left exposed (Fig. 6). An important structural part of the dome is the lower tension ring, carrying forces induced by the thrust of the arched ribs. Tensile axial forces are carried by the chords of two trusses embedded horizontally in concrete on the circumference of the ring (Fig. 7). Each of the chords consists of two plates, 13 × 365 mm, and two angle bars, 120 × 120 × 13 mm, (Fig. 10) giving a total cross-sectional area of steel of 615.7 cm2. Elements of the trusses are connected by rivets and bolts. An interesting structural solution is the dome support on pinned bearings, placed between the lower ring and the upper surface of the base drum structure (at a level of about +19.0 m), shown in Fig. 7. The bearings are located on the circumference of the dome in the places where the 32 ribs are fixed. There is freedom of movement in the direction of the radius of the dome. The dome is

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

therefore separated from the bottom cylindrical structure, which is imperceptible in the façade. Prefabricated reinforced concrete elements weighing about 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 interesting; they were imported all the way from Australia during the construction of the hall [16]. This wood has a very high density and hardness, and therefore is weatherresistant. Most of the elements of the original woodwork have been preserved to this day, renovated and rebuilt. The wood was too good a building material in those times to have let these trees survive to the present day!

Technical condition of the hall

Since the Second World War, the hall has been used in accordance with its intended purpose as a multi-functional meeting facility for exhibitions, celebrations and sports events. No major renovation works have been carried out – other than changing linings, rearranging the interior of the hall and other minor repairs – since 1945. Almost a century of intensive use has resulted in deterioration of the hall and without remedial action, rapidly advancing degradations would have been the outcome [16]. Also, the interior of the hall no longer met modern requirements. In 2006 the Centennial Hall was listed as a UNESCO World Heritage Site, which imposed a responsibility for the strict protection and maintenance of the hall. These facts led to the decision to implement an extensive plan of restoration, including renovation of the hall and modernization of the interior. The renovation was carried out in 2009–2011 in two phases: the first phase included renovation of the façade and the second the renovation of the building’s interior. Before proceeding with the first phase, a complex expert report on the technical condition of all structural elements, walls, ceilings, etc. was prepared [16, 17]. This report revealed a wide variety of defects, mainly cracks, cavities, thin concrete cover zones and other material and structural deficiencies. The defects resulted partly from the fact that the hall was erected in the pioneering years of reinforced concrete, which was then regarded as a very durable, almost indestructible material. The most significant defects were noticed in the lower ring, an important structural element of the dome, carrying forces induced by the thrust of the dome’s curved ribs. Vertical cracks were found in the surface of the ring over its entire height, at intervals of several metres, and around the whole perimeter of the ring (Fig. 8). Considering the structural purpose of this element and the condition of the steel trusses in tension, it was decided that the ring needed to be strengthened [16, 17]. The design basis was the assumption that the reinforcing elements should be able to carry the whole tensile force in the ring in the case of failure of the steel trusses. Obviously, the strengthening system must not interfere with the elevation of the hall. Finally, the project of renovating the hall’s façade and strengthening the ring using multi-layered CFRP plates on the ring’s circumference was prepared. During façade repairs, the contractor, after consultation with the designer of the renovation works (architect L. Konarzewski, PhD),

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

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

proposed to change the method of strengthening and to prepare a new project. The basis for the change to the strengthening method was the research conducted during the repair works. It was possible to carry out a thorough assessment of the condition and properties of the steel trusses once they were partially uncovered. It turned out that they were in a satisfactory condition; no major corrosion damage was evident. The only corrosion products found dated back to the construction period. Some adverse characteristics of the steel microstructure were assessed as not resulting from the use of the hall. Steel aging and some observed changes 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 an engineer was strengthening the lower (tension) ring of the dome, which is discussed below.

4 4.1

Strengthening of the lower ring of the dome Assumptions and structural analysis

The revised version of the project also included the assumptions that the strengthening system should be able to carry the whole tensile force and that it should not change the elevation. The strengthening of the ring was inspired by the solution proposed for the dome of St. Peter’s Basilica, pre-

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sented in Fig. 3. Since that time, new possibilities for implementing such a concept, using concrete prestressing technology, have been developed. Therefore, it was decided to design the strengthening system using the tendons and anchorages common in bridges, silos, etc. [19]. A 3D FEM model of the dome was used in the structural analysis (Fig. 9). The ribs of the dome, rings and columns between sets of windows were discretized as bar elements, the ribbed plates of the ceilings as shell elements. The following materials were assumed: concrete class C12/15, steel grade St3SX, reinforcing steel grade St0S [16]. The permissible tensile stress in the steel in the original 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 different points of the dome (upper ring, ribs) with a total weight of 30–40 t were considered in the analysis. Load combinations 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 consideration dead loads only, we get N = 5444 kN, My = 413.0 kNm and Mz = 7.8 kNm [19]. Comparison of these values proves that the dead loads are dominant influence for the tensile force in the ring. Structural calculations using modern software increased the tensile forces in the ring by about 10 % in relation to the design value of this force [13]. Part of this difference might be caused by snow and wind loads different from those assumed in [13].

4.2

Strengthening method

According to the assumptions, it was decided to design a passive strengthening system around the ring, consisting of unbonded strands used for prestressing (type T15S pro-

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

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 of sheath ducts and nine anchorage units were used [19, 20]

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

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

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

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

force equal to only 15 % of their ultimate strength, which guarantees proper anchorage. Eventually, 27 strands (galvanized, grease-protected, covered with individual HDPE sheaths) with a diameter of 15.7 mm were used, grouped in nine cables. The strands are conducted in plastic sheath ducts with a diameter of 50 mm, filled with cement grout. Fig. 10 shows the scheme of the strengthening system and Fig. 11 shows the cables during installation. The maximum internal forces in the elements of the dome resulting from cable tensioning are: N = –928.6 kN (compression), My = 35.6 kNm, Mz = 102.2 kNm. Tensioned circumferential cables reduced the axial force in the lower ring. The analysis showed no significant adverse influence of tensioned cables on the ring and other elements of the dome. Designed strengthening, apart from passive action, reduces the radial and circumferential deformability of the ring, which should be considered to be a positive effect on the structure of the dome. A crucial assumption in the design was the requirement that the strengthening elements (including anchorages) should not extend beyond the outline of the dome, and should not be visible on the façade. This made it impossible to tension cables section by section around the circumference of the ring. Eventually, the cables anchorages were hidden in the service staircase added to the hall and separated from the ring. It was necessary to create holes to install the anchorages and tension the cables. Fig. 10 shows the arrangement of the anchorages on the surface of the ring in the staircase. Sheath ducts were covered with a layer of mortar. The surface was textured and glazed (a painting technique known since the Renaissance). The reinforcement is not visible on the perimeter of the ring, and the resulting two new edges do not lead to any disharmony in the hall’s façade (Fig. 12). The strengthening method described here is comparable to the one implemented in the dome of the Sanctuary of Vicoforte (Italy) [21]. That is a building of great architectural and structural significance with a huge elliptical masonry dome, the biggest in the world with this shape in terms of dimensions (internal axes 37.2 × 24.9 m). The structure has suffered over the years from significant structural problems resulting in cracking and therefore needed to be strengthened. The strengthening system, installed in 1985–1987, consists of 56 high-strength steel tie

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

bars with a diameter of 32 mm, placed within holes drilled in the masonry at the top of the drum, along 14 tangents around the perimeter. The heads of adjacent bars are interconnected by steel frames. The bars were minimally tensioned at the time of their installation and retensioned in 1997 [21].

Conclusions

The Centennial Hall built in 1911–1913 is a milestone in modern concrete architecture. Its historical significance has been acknowledged through its inclusion in the UNESCO World Heritage List since 2006. It owes its unique character to the reinforced concrete ribbed dome with a span of 65 m, the largest since the time when the Roman Pantheon was built. Almost a century of intensive use of the facility and lack of proper conservation resulted in deterioration of the building. The most significant structural defects (vertical cracks) were noticed in the lower ring of the dome. Its strengthening was included in the extensive renovation plan for the hall. The passive strengthening proposed did not introduce large additional forces into the structure, but reduced the radial and circumferential deformability of the ring. The system installed allows for retensioning the cables if there is a need to in the future. What is important is that the strengthening does not interfere with the appearance of the historic façade of the building. The

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

cable anchorages have been hidden inside the service staircase and are not visible from the outside. Although the strengthening uses modern concrete prestressing technology, the idea is similar to the one proposed more than 250 years ago by Poleni in the case of St Peter’s Basilica in Rome. It seems that after refurbishment, the Centennial Hall will be in use for at least another few decades. In the hall a museum has been set up with interactive multimedia presentations on the construction and history of this outstanding building. References 1. MacDonald, W. L.: The Pantheon: Design, Meaning and Progeny. Harvard University Press, Cambridge, 1976. 2. Cowan, H.: The Master Builders: A History of Structural and Environmental Design From Ancient Egypt to the Nineteenth Century. John Wiley & Sons, New York, 1977. 3. Mark, R., Hutchinson, P.: On the structure of the Roman Pantheon. 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 structural configuration of the first dome of Justinian’s Hagia Sophia (A.D. 537–558): An investigation based on structural and literary analysis. Soil Dynamics and Earthquake Engineering, vol. 29, No. 4, 2009, pp. 693–698. 6. Lübke, W., Semrau M.: Grundriß der Kunstgeschichte (14th ed.,) Paul Neff Verlag, Esslingen, 1908. 7. Hartt, F.: History of Italian Renaissance Art (6th ed.). Prentice 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 Tempio Vaticano e de’ danni di essa, e de’ ristoramenti loro, divise in libri cinque. Stamperia del Seminario, Padova, 1748. 11. Gargiani, R.: Vers une construction parfaite. Machines et calcul de résistance des matériaux. Matières, vol. 6, 2003, pp. 99–115. 12. Trauer, G., Gehler, W.: Die Jahrhunderthalle in Breslau. Julius Springer, Berlin, 1914. 13. Trauer, G., Gehler, W.: Festhalle in Breslau. Berechnung der Kuppel, 1911 (typescript). 14. Ramm, W.: Über die faszinierende Geschichte des Betonbaus vom Beginn bis zur Zeit nach dem 2. Weltkrieg. In: Curbach, M. et al.: Gebaute Visionen: 100 Jahre Deutscher Ausschuss für Stahlbeton 1907–2007. Beuth-Verlag, Berlin/ Vienna/Zurich, 2007, pp. 27–130. 15. Kawaguchi, M.: The Lighter, the Better. IABSE-IASS Symposium 2011 Report, Taller, Longer, Lighter, pp. 18–25. 16. Persona, M.: Ekspertyza stanu technicznego konstrukcji budynku Hali Ludowej we Wrocławiu (Expert report on the technical condition of the Centennial Hall’s structure in Wrocław – in Polish). MBM Sp. z o.o., Wrocław, 2008. 17. Huber, H. S., Mikolajonek, M., Filipczak, P.: Die Jahrhunderthalle in Breslau. Sanierung eines Weltkulturerbes. Beton- und Stahlbetonbau, vol. 105, No. 11, 2010, pp. 729–736. 18. Hildebrand, M.: Remont Hali Stulecia we Wrocławiu (Renovation of the Centennial Hall in Wrocław – in Polish). Materiały Budowlane, vol. 2/2011, pp. 34–35. 19. Projekt wykonawczy w zakresie zmiany sposobu wzmocnienia głównego piers´cienia rozcia ganego kopuły z˙ebrowej Hali Stulecia (Detailed design of change of strengthening of the

main tensiled ring of the Centennial Hall’s ribbed dome – in Polish). 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 concrete dome of the Centennial Hall in Wrocław. Proc. of 7th Central European Congress on Concrete Engineering, Balatonfüred, 22–23 Sept 2011, pp. 283–287. 21. Chiorinoa, M. A., Ceravolo, R., Lai, C. G., Casalegno, C.: Survey, seismic input and structural modeling of the “Regina Montis Regalis” Basilica and large elliptical dome at Vicoforte, northern Italy. Proc. of 8th International Conference on Structural Analysis of Historical Constructions SAHC 2012, Wrocław, 15–17 Oct 2012, pp. 1432–1440.

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

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

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

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

Robert Toczkiewicz, PhD, Civ. Eng. Research & Design Office MOSTY-WROCŁAW Contact address: Jan Biliszczuk Wrocław University of Technology Wybrzez˙e Wyspian´skiego 27 50-370 Wrocław, Poland e-mail: jan.biliszczuk@pwr.wroc.pl

Structural Concrete 15 (2014), No. 1

Technical Paper Osvaldo Luiz de Carvalho Souza Emil de Souza Sánchez Filho* Luiz Eloy Vaz Júlio Jerônimo Holtz Silva Filho

DOI: 10.1002/suco.201300013

Reliability analysis of RC beams strengthened for torsion with carbon fibre composites Two sets of reliability analyses for two beam series strengthened with carbon fibre composites (CFC) in different ways and subjected to torsional moments are described in this paper. The analyses consider three failure functions and the system is regarded as a series system formed by these three limit state modes. Five random variables are taken into account in the first set of analyses. The analyses are performed for different torsional moment ratios, defined as the ratio of the torsional moment due to live loads to the total torsional moment. The system reliability indexes and the factors of importance associated with each random variable are obtained. In the second set of reliability analyses, only the two most relevant random variables selected in the first set of analyses according to the values of their factors of importance are considered, and new reliability indexes are determined. The examples show that despite the constant value of the total torsional moment, the increase in the torsional moment ratio leads to a decrease in the system reliability levels. The fact that the values of the reliability indexes obtained in both sets of reliability analyses are very similar validates the efficiency of the sensitivity analyses. Keywords: reliability index, torsion in RC beams, carbon fibre composites

Introduction

Structural projects are designed so that they can satisfy requirements regarding safety, serviceability and durability. In such projects there are several random variables that introduce uncertainties which remain throughout the lifetime of the structure. The Brazilian code NBR 6118 [1] contemplates these uncertainties (resistances and loads) by using the ultimate limit state (ULS). ULS expressions for the design of reinforced concrete structures are written in terms of the design values for the random variables. These values are obtained from the characteristic values of the random variables by dividing or multiplying them (always on the safe side) by partial safety factors > 1. The characteristic value of the random variable is defined as a value of low probability that has to be less (for resistances) or greater than (for loads) a prescribed value for the cumulative probability. The design * Corresponding author: emilsanchez@uol.com.br Submitted for review: 14 March 2013 Revised: 17 June 2013 Accepted for publication: 24 July 2013

values are used to define the design resistances Rd and design actions Sd at the level of the cross-sectional forces in the structural elements. The ULS expressions in NBR 6118 [1] have the general form Rd ≤ Sd. This methodology is called semi-probabilistic. The partial safety factors confer safety on the structure and reliability indexes intrinsic to it. Silva Filho [2] tested two sets of three reinforced concrete beams strengthened with carbon fibre composites (CFC). One series was denoted VT beams (with transverse CFC reinforcement) and the other VTL beams (with transverse and longitudinal CFC reinforcement). The beams tested were subjected to torsion, and had been designed to resist torsion according to a design method based on NBR 6118 [1] and proposed in his work. This paper focuses on the reliability analysis of these two beam series. For the reliability analyses, the mean values of the resistant torsional moments of the beams are evaluated using the mean values of the random variables in the design expressions. In the two sets of reliability analyses, the mean values of the resistant and the applied torsional moments are then considered to be equal to those of the concrete strut. The torsional moments applied are supposed to be formed by two components – one related to permanent loads, the other associated with live loads. The mean values of the components may vary, although their sum remains constant.

Description of the beams analysed

In his theoretical and experimental study, Silva Filho [2] evaluates the behaviour and the increasing strength of RC beams (VT and VTL) strengthened with CFC and subjected to pure torsion. In his study Silva Filho [2] adopted the generalized spatial truss model and the methodology of EN 1990 [3], which concerns the resistance of concrete strut, longitudinal reinforcement and steel stirrups. The effective bond stress between CFC and concrete was considered by means of the Chen and Teng [4] model, and the concrete strut angle by the Aprile et al. [5] formulation. The mean values of the concrete compressive strength, the steel yield stress and the CFC elastic modulus are obtained by Silva Filho [2] from laboratory tests; they are 36.7 MPa, 565.3 MPa and 256.7 GPa respectively. The two sets of reinforced concrete beams (VT and VTL) have equal amounts of steel reinforcement (cross-

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

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

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

Design torsional moments

The design torsional moments TRd of the VT and VTL beams are obtained by means of the semi-probabilistic method according to Brazilian code NBR 6118 [1] and the methodology developed by Silva Filho [2] and Silva Filho et al. [6]. Table 1 shows the apportioned values of the design torsional 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 and VTL beams.

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

Beam

TRd-Strut

TRd-Long

TRd-Trans

VT VTL

26.34 26.26

29.46 32.14

30.26 26.93

The beam strength is determined by the design torsional moment of the concrete strut. The design torsional moments of the concrete strut TRd-strut of the VT and VTL beams are transformed from Eq. (1) into characteristic strength values of 18.81 and 18.75 kNm. A partial safety factor of 1.4 is applied as recommended by NBR 6118 [1]: TRd  strut  1.4  TRk  strut

(1)

where TRk-strut is the characteristic value of the torsional moment resisted by the concrete strut. For the purposes of the reliability analysis, the characteristic values of the torsional moments TRk-strut are

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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

considered to be formed by two components: torsional moment Tq for live load and torsional moment Tg for dead load, whose values vary according to the live load ratio 0.3 ≤ rq ≤ 0.8 thus: TRk  strut  Tg  Tq

(2)

Failure functions for the problem

The failure functions or limit state functions associated with the ULS expressions defined by Silva Filho [2] are presented in the following. The equation of failure regarding crushing of the concrete strut in a reinforced concrete beam is     fc    tAk    (Tg  Tq ) g1  2 0,7  0,7  f  200   c  1    tg   tg 

(3)

The equation of failure associated with the longitudinal steel and CFC reinforcement is g2  2 Aktg

  E Asl fs Afl  2bh 0,192 f fc  tg  (Tg  Tq ) (4) uk u tf    

Table 2. Values of β t, EN 1990 [3]

Consequences class

CC3 CC2 CC1

(5)

Reliability class

RC3 RC2 RC1

Structural Concrete 15 (2014), No. 1

The tangent of the concrete strut angle used in Eqs. (3), (4) and (5) is given by 1 Es Asl Ef Afl  Ectu Ectuk tg  4 1 1 Es Ast Ef Aft  Ects Ects f 1

Target reliability index

The target reliability index β t may be defined as the minimum value of the reliability index of a structure such that it presents an adequate level of performance and probability of failure below a prescribed value. EN 1990 [3] stipulates the target reliability indexes from the determination of the consequences of failure, the reliability classes and the return period. The classes of failure consequences are established according to the impact caused by the occurrence of a failure, i.e. loss of human life and environmental, social or economic consequences: CC1 – small impact, CC2 – moderate impact, CC3 – high impact. Table 2 shows the reliability indexes β t obtained regarding the return period and the reliability classes RC1, RC2 and RC3, which are associated with the consequence classes CC1, CC2 and CC3 respectively.

4.2

  E 2bh 0,192 f fc  sf tf   1 Ast fs    (T  T ) g3  2 Ak  g q tg s tg Aft

Reliability analysis

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

4.1

The equation of failure related to the transverse steel and CFC reinforcement is

βt ULS 1 year

50 years

5.2 4.7 4.2

4.3 3.8 3.3

(6)

where: Afl cross-sectional area of longitudinal CFC reinforcement Aft cross-sectional area of transverse CFC reinforcement Ak area enclosed by centre-line of shear flow Ast cross-sectional area of transverse steel reinforcement Asl cross-sectional area of longitudinal steel reinforcement b width of beam Ef CFC elastic modulus Es steel elastic modulus Ec concrete elastic modulus fc concrete compressive strength fs steel yield stress h depth of beam s spacing of transverse reinforcement sf spacing of CFC stirrups t thickness of effective wall tf thickness of CFC reinforcement u perimeter of cross-section uk perimeter of area Ak

4.3

Random variables data

Among the variables present in the three failure modes defined in section 4.2, the following ones are considered to be random: concrete compressive strength fc, steel yield stress fs, CFC elastic modulus Ef, torsional moment due to dead 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 of reliability analyses are: compressive strength of concrete fc, yield stress of steel fy, elastic modulus of composite material Ef, applied torsional moment Tg (related to permanent loads) and applied torsional moment Tq (related to live loads). As a result of these analyses we obtain the variation in the reliability index β 5i associated with the failure mode i, the variation in the reliability index of the series system β 5s (considered as the upper bound based on first-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 range 0.3 ≤ rq ≤ 0.8.

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

The values of the factors of relative importance, or sensitivity factors alpha, Ifc, Ifs, IEf, ITg and ITq, are also calculated, making it possible to determine which random variables may be neglected in the second set of reliability analyses. The results of sensitivity studies highlight that the compressive concrete strength fc and, especially, the applied torsional moment due to live loads Tq are by far the most deterministic random variables. The beams are then reanalysed considering only the randomness of the two more relevant variables. The other three random variables from the first reliability analysis are now treated as deterministic. As in the first set of analyses we obtain the reliability index β 2i of the failure modes i and the reliability index β 2s of the series system as well as their respective failure probabilities Pf2i and Pf2s, but now only with respect to the load ratio rq = 0.5. This ratio was chosen to represent best the load of a regular structure. Brazilian code NBR 8681 [8] considers the mean value of the torsional moments for dead load μTg, equal to its characteristic value, and the mean value of the torsional moments for live load μTq, equal to the one whose probability of being exceeded is between 25 and 35 %; this paper considers 35 %. Table 3 shows the mean values of the torsional moments for live and dead loads with regard to each live load ratio rq used in this paper, obtained according to NBR 8681 [8]. The characteristic values of the torsional moments listed in the table vary, although their sums are constant as a consequence of the variation in the load ratios in the range 0.3 ≤ rq ≤ 0.8. The statistical parameters and the associated distribution function for the random variables are given in Table 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 analyses performed 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 different strengthening configurations. The tables show the reliability indexes of each failure mode, β5,1, β5,2 and β5,3, plus their respective probabilities of failure, Pf5,1, Pf5,2 and Pf5,3, and the series system reliability index β5s and its respective probability of failure Pf5s. Figs. 2 and 3 show, for beams VT and VTL respectively, the variation in the reliability index for the failure modes β5i, and the series system reliability index β5s plotted against the variation in the live load ratio rq. The reliability index β t = 3.8 adopted by EN 1990 [3] is taken as a reference for buildings with moderate consequence of failure (CC2) and a design lifetime of 50 years for the structure. Observing the curves for the reliability indexes in Figs. 2 and 3, an important conclusion can be drawn: the structure is not reliable enough for load ratio values > 0.5 (they are lower than the target value recommended by the European code). This means that the partial factors of safety of the Brazilian code are not precisely calibrated. From the reliability analyses performed using the FORM, it is possible to quantify the factors of importance Ifc, Ifs, IEf, ITg and ITq of the variables for each failure mode analysed. Figs. 4 and 5 show, for the VT and VTL beams respectively, the factors of relative importance, presented as percentages, for the three variables whose values are more significant for the three failure modes. These values refer to tests with the load ratio rq = 0.50. Fig. 4, for the VT beam, shows that the most significant factors of importance for the failure function g1 related to the rupture of the concrete strut are Ifc, ITg and ITq. For the failure function g2 associated with yield of the longitudinal steel and CFC reinforcement they are Ifs, ITg and ITq, and for the failure function g3 linked with yield of the transverse and CFC reinforcement, again Ifs, ITg and ITq. 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 rq 0.3 0.4 0.5 0.6 0.7 0.8

VTL TRkg 13.17 11.28 9.41 7.53 5.64 3.76

μTg 13.17 11.28 9.41 7.53 5.64 3.76

TRkq 5.64 7.53 9.41 11.28 13.17 15.05

μTq 5.34 7.11 8.89 10.67 12.45 14.23

rq 0.3 0.4 0.5 0.6 0.7 0.8

μTg 13.12 11.25 9.38 7.50 5.63 3.75

TRkg 13.12 11.25 9.38 7.50 5.63 3.75

TRkq 5.63 7.50 9.38 11.25 13.12 15.01

μTq 5.32 7.09 8.87 10.64 12.41 14.19

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

Basic variable

Char. value

Mean

Standard deviation

Coef. of var.

Distribution

Concrete compressive strength (MPa) Steel yield stress (MPa) CFC elastic modulus (GPa) Torsional moment – Tg (kNm) Torsional moment – Tq (kNm)

30 500 – var. var.

36.7 565,3 256.7 var. var.

4 39,6 10.21 – –

0.11 0.07 0.04 0.05 0.28

lognormal lognormal Weibull normal Gumbel

JCSS [9] JCSS [9] Lopes [10] Lopes [10] JCSS [9]

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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

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

β5i

Pf5i

5.07

1.99 × 10–7

5.00

2.88 × 10–7

Trans. reinft. g3

5.64

8.45 × 10–9

Strut g1

4.45

4.27 × 10–6

4.37

6.36 × 10–6

Trans. reinft. g3

4.88

5.28 × 10–7

Strut g1

3.99

3.30 × 10–5

3.90

4.77 × 10–5

Trans. reinft. g3

4.34

7.09 × 10–6

Strut g1

3.64

1.38 × 10–4

3.55

1.93 × 10–4

Trans. reinf. g3

3.94

4.14 × 10–4

Strut g1

3.36

3.97 × 10–4

3.27

5.38 × 10–4

Trans. reinft. g3

3.62

1.48 × 10–4

Strut g1

3.12

8.98 × 10–4

3.04

1.18 × 10–3

3.36

3.90 × 10–3

Functions of failure gi

rq = q/(g + q)

Strut g1 Long. reinft. g2

Long. reinft. g2

0.30

0.40

0.50

0.60

0.70

0.80

Trans. reinft. g3

β5s

Pf5s

4.91

4.55 × 10–7

4.29

9.09 × 10–6

3.84

6.22 × 10–5

3.50

2.31 × 10–4

3.24

5.91 × 10–4

3.03

1.20 × 10–3

β5s

Pf5s

4.81

7.56 × 10–7

4.17

1.54 × 10–5

3.71

1.03 × 10–5

3.39

3.52 × 10–4

3.11

9.26 × 10–4

2.89

1.94 × 10–3

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

β5i

Pf5i

5.07

1.97 × 10–7

5.69

6.28 × 10–9

Trans. reinft.g3

4.85

6.20 × 10–7

Strut g1

4.45

4.33 × 10–6

4.95

3.79 × 10–7

Trans. reinft. g3

4.20

1.34 × 10–5

Strut g1

3.99

3.36 × 10–5

4.41

5.12 × 10–6

Trans. reinft. g3

3.74

9.39 × 10–5

Strut g1

3.64

1.39 × 10–4

4.01

3.01 × 10–5

Trans. reinft. g3

3.39

3.52 × 10–4

Strut g1

3.35

3.99 × 10–4

3.70

1.10 × 10–4

Trans. reinft. g3

3.11

9.26 × 10–4

Strut g1

3.12

8.98 × 10–4

3.44

2.96 × 10–4

2.89

1.94 × 10–3

Functions of failure gi

rq = q/(g + q)

Strut g1 Long. reinft. g2

Long. reinft. g2

Long. reinft. g2 Trans. reinft. g3

Structural Concrete 15 (2014), No. 1

0.30

0.40

0.50

0.60

0.70

0.80

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

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

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

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

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

the factors of importance for the different failure functions. The results of the sensitivity studies highlight the importance of the compressive concrete strength fc and, especially, the torsional moment due to live load Tq compared with the other random variables involved in the analysis. The low values of the relative factors of importance of the other variables enable a deterministic treatment for those variables. Therefore, to emphasize the efficiency of the 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 indexes and their respective failure probabilities β2i and Pf2i as well as β5i and Pf5i obtained in the reliability analysis of the VT and VTL beams respectively using the FORM, with two random variables, namely fc and Tq, and five random variables, namely, fc, Ef, Tq, Tg and fs. The values of the reliability indexes β2i and β5i, concerning each failure mode, and the values of the reliability indexes of the series system β2s and β5s and their respective failure probabilities Pf2s and Pf5s, presented in Table 7, differ little from each other. This fact validates the study of the sensitivity measure that evaluates the factors of importance of the variables in this reliability analysis. The decrease in the system reliability index with the increase in the load ratio is very probably a consequence of the type of probability density function for extreme values which represents the live load (Gumbel), and of the high value of its coefficient of variation δq. This aspect and the high values obtained for the factor of importance of the live load ITq compared with the other factors of im-

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

Beam

VTL

Functions of failure gi

β2i

β5i

Strut g1

4.00

3.99

Long. reinft. g2

4.11

3.90

Trans. reinft.g3

4.44

4.34

Strut g1

3.98

3.99

Long. reinft. g2

4.57

4.41

Trans. reinft.g3

3.85

3.74

β2s

Pf2i

β5s

Pf5s

3.96

3.65 × 10–5

3.84

6.22 × 10–5

3.82

6.79 × 10–5

3.71

1.03 × 10–5

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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

portance highlight the need for a different treatment of the dead and live load partial safety factors in NBR 6118 [1]. For the semi-probabilistic methodology, this code adopts the partial safety factors γ g = 1.4 and γ q = 1.4 for dead and live loads respectively, neglecting the difference between their probabilistic characteristics. The values of the reliability index in the reliability analyses with two basic variables are higher than the ones obtained in the reliability analyses with five basic variables because of the existence of less uncertainty. In those, two and five random variables are considered respectively.

Conclusions

Despite the constant value of the total torsional moment, the relative increase in the mean of the applied torsional moment due to the live load leads to a decrease in the reliability levels of the failure modes and the series system, allowing an increase in the probability failure of the structural element. The reliability index β5s of the VT and VTL beams takes values below the target index β t for rq > 0.50, indicating that the semi-probabilistic treatment given by the Brazilian code NBR 6118 [1] applied to the methodology developed by Silva Filho [2] is inconsistent for this range (rq ≥ 0.5). The deterministic treatment applied to the random variables with low factors of relative importance led to new reliability index values that differ little from the previous values obtained in the studies where their randomness is considered. This fact stresses the efficiency of the sensitivity studies.

6. Silva Filho, J. J. H, Sánchez Filho, E. S., Velasco, M. de S. L.: Torsion Strengthening of RC Beams with Carbon Fibre Composites. 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 Prediction. John Wiley & Sons, New York, 2002. 8. Associação Brasileira de Normas Técnicas: Loads and safety of the structures – Proc., NBR 8681. Rio de Janeiro, Brazil. 2003. 9. Joint Committee on Structural Safety: JCSS: Probabilistic Model Code, 2001. 10. Lopes, M. T. A.: Structural Reliability Analysis Application to the Design of Carbon Fibres Reinforced Polymer Shear Strengthening of Reinforced Concrete Beams. Doctoral thesis, PUC-Rio, Brazil. 2007.

Osvaldo Luiz de Carvalho Souza, D. Sc. Rural Federal University of the Rio de Janeiro Engineering Department Av. Comandante Ary Parreiras 60/ 1301 24230-322, Icaraí, Niterói, RJ, Brasil

Emil de Souza Sánchez Filho, D. Sc. Fluminense Federal University Civil Engineering Department Rua Prof. Gastão Bahiana, 155/701 22071-030, Copacabana, Rio de Janeiro, RJ, Brasil

References 1. Associação Brasileira de Normas Técnicas: Design of Reinforced Concrete Structures – Proc., NBR 6118. Rio de Janeiro, Brazil. 2007. 2. Silva Filho, J. J. H.: Carbon Fiber Reinforced Polymer Torsion Strengthening of Reinforced Concrete Beams. Doctoral thesis, 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-strengthened RC beams: FRP debonding. Construction and Building Materials, vol. 17, 2003, pp. 27–41. 5. Aprile, A., Benedetti, A.: Coupled Flexural-Shear Design of R/C Beams Strengthened with FRP. Composites: Part B, No. 35, 2004, pp. 1–25.

Structural Concrete 15 (2014), No. 1

Luiz Eloy Vaz, Dr.-Ing. Fluminense Federal University Civil Engineering Department Rua Álvaro Americano, 822451-200, Gávea, Rio de Janeiro, RJ, Brasil

Júlio Jerônimo Holtz Silva Filho, D. Sc. PUC-Rio Civil Engineering Department Rua Pinheiro Guimarães,145/ 404 22281-080, Botafogo, Rio de Janeiro, RJ, Brasil

Technical Paper John Cairns

DOI: 10.1002/suco.201300041

Staggered lap joints for tension reinforcement Staggering lapped joints increases the complexity of detailing and steel fixing, and may require additional resources and slow construction on site. Major design codes encourage staggering lapped joints in tension by imposing a penalty on lap length depending on the proportion of bars lapped at the same section. There are, however, inconsistencies in the value of the coefficients to be applied, and little evidence is available for validation. A programme of 17 physical tests found no evidence of an increase in strength when laps were staggered, and when allowance is made for increases in transverse spacing, staggering was found to reduce lap strength. Differences in the distribution of bond stress through a lap joint and in the share of the tension force taken by continuous and lapped bars are demonstrated to be responsible for the reduction. Keywords: lapped joints, bond, detailing

Introduction

Lapped joints serve to provide continuity of reinforcement in concrete structures. The force in one bar is transferred to the surrounding concrete through bond stress over the bar surface, then from the concrete to the other lapped bar. It is widely considered as good practice to avoid lapping all reinforcing bars at the same section. If all bars in the section need to be lapped, then laps should either be staggered in the longitudinal direction so that at any section only some of the bars are lapped, or the length of the lap increased. The penalty imposed by codes for lapping all bars at a section is substantial. Eurocode 2 [1], fib Model Code 90 [2] and ACI 318 [3] require lap lengths to be increased by, respectively, up to 1.5, 2.0 and 1.3 times the corresponding anchorage or development length, and the coefficient to be applied therefore differs significantly between codes. The overall length of a lap zone is obviously much greater if laps are staggered than if all bars are lapped at the same section, even allowing for an increased lap length. This may impede construction work as the greater length of a staggered lap zone reduces flexibility when locating construction joints and will often require additional formwork. Corresponding author: j.j.cairns@hw.ac.uk Submitted for review: 11 June 2013 Revised: 31 July 2013 Accepted for publication: 4 August 2013

Although many studies – together detailing well over 1000 tests – have been conducted to evaluate how concrete strength and confinement provided by cover and transverse reinforcement influence the strength of lapped joints, the test data is almost exclusively confined to specimens in which all bars are lapped at the same section. Considering that the factor for the proportion of bars lapped can be as influential as that for confinement, surprisingly little research has been undertaken to assess the performance of staggered laps. Although the content of EC2 draws heavily on fib Model Code 90, the coefficients α6 for proportion lapped are somewhat lower, and attempts to discover the basis for either the original coefficients or the change were fruitless. This investigation was therefore undertaken with the aim of assessing whether current design provisions for staggered laps are soundly based.

Strength of lapped joints: general background

Lapped joints rely on the bond between reinforcement and concrete to transfer forces. Bond is conventionally regarded as a shear stress on the surface of the bar, and defined as the change in force along the bar divided by the (nominal) bar surface area over which this change takes place, Eq. (1). However, Eq. (1) represents a major simplification of the real behaviour as most bars produced today rely on the bearing of ribs rolled onto the surface of the bar during manufacture to transfer force. The definition of Eq. (1) is, nonetheless, a convenient one and will be used here. fb = Δfs · As/πφ lb

(1)

There are two broad modes of bond failure, the distinction between the two being dependent on whether or not the concrete cover splits. Lapped joints for larger diameter bars typically have a minimum concrete cover of three times the bar diameter or less, and fail in a splitting mode with a longitudinal crack forming in the concrete cover unless the lap is long enough for the reinforcement to reach yield. Splitting mode failures tend to be brittle even if confining reinforcement in the form of links is provided to maintain splitting resistance once the cover cracks, and the potential for failures by this mode should therefore be avoided. Where cover exceeds five times the bar diameter,

J. Cairns · Staggered lap joints for tension reinforcement

opment length. Fig. 3 compares the proportion lapped coefficients given in each code, and shows the marked differences between these codes.

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

bond failure occurs by shearing of the concrete along a surface over the tops of the ribs and the bar pulls out of the concrete, leaving a relatively smooth bore. The splitting mode is the weaker type and is generally of greater concern for laps. The evaluation of bond resistance is more complex than implied by Eq. (1), and EC2 includes no less than 10 parameters for calculating anchorage and lap lengths. The expression presented in the fib Model Code for Concrete Structures 2010 [4] and reproduced here as Eq. (2) may be used to estimate the stress developed by a lapped joint between ribbed bars in “good” conditions. Eq. (2) has been calibrated from tests in which all bars were lapped at the same section, and has a coefficient of variation of 14 % when calibrated against an extensive database. The coefficient of 54 in Eq. (2) has units of MPa. fstm  f  54  cm   25 

0.25

 fy ,  10 fc

 25   

0.2

 lo    

0.55 

 cmin     

0.25

 cmax  c   min 



0.1

  kmKtr    (2)

EC2 states that laps should normally be staggered. For laps to be classified as staggered, the longitudinal distance between two adjacent laps should not be less than 0.3 times the lap length l0, Fig. 2. Where laps are staggered, the clear spacing between laps cs is taken as shown in Fig. 2. The notation “a” is used for cs in EC2. Lap lengths for tension reinforcement depend on the proportion of bars lapped at a section, Fig. 3. Lap length factors in EC2 and MC90 are the factors by which the equivalent anchorage length is to be multiplied to obtain the lap length. The factor in ACI 318 applies to the devel-

Fig. 2. Staggered lapped joints, adapted from EC2

Structural Concrete 15 (2014), No. 1

Review of previous work

Magnusson [5] reported on four tests in which only a portion of the reinforcement was lapped at a section. Three pairs of specimens, each reinforced with three longitudinal bars, were tested. In one pair all longitudinal bars were lapped, with either two of three or one of three bars being lapped in the other two pairs. The bond length used was, at 7.5φ, relatively short and sufficient only to develop about 35–55 % of the yield strength of the bars. Consequently, significant increases in strength were recorded in specimens with greater proportions of continuous reinforcement. Tests in which only one-third or one-half of the bars were lapped were on average 50 and 110 % stronger respectively than the reference specimens in which all bars were lapped. A few tests have been conducted with longer lap lengths. Ferguson and Briceno [6] tested four beams with 50 % of the bars continuous through the lap zone along with three similar specimens in which all bars were lapped at the same section. The 50 % lapped specimens were on average 10–15 % stronger, but if allowance is made for the greater spacing between lapped pairs, the difference becomes insignificant and they may even be interpreted as being weaker depending on the model used to make allowance for clear spacing. A broadly similar conclusion can be reached from tests on wide beam splices by Thompson et al. [7] in which edge bars were continuous in some specimens and lapped in others. Metelli et al. [8] report on 24 tests in which a proportion of between 25 and 100 % of the longitudinal reinforcement was lapped, the remaining bars being continuous throughout the span. Lap length was designed to ensure a bar stress approaching yield in these tests. Four test series were conducted, covering two grades of concrete, two bar diameters (16 and 20 mm) and a variety of details, with laps confined by links. Results tend to indicate that lapping only some bars at a section weakens lap strength if allowance is made for the difference in spacing. Bond strength ratio appears to dip from a maximum at 100 % lapped to a minimum at 50 % lapped before partially recovering as the proportion lapped drops further. Cairns [9] has reported a similar trend in an investigation

J. Cairns · Staggered lap joints for tension reinforcement

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

Analysis of influence of proportion of bars lapped

Three factors will affect the performance of a lapped joint with a portion of the bars lapped compared with an equivalent 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

1,20 Cover coeﬃcient (c max/cmin)0.1

of the lapped joints of bundled bars. Failure of laps in which only a portion of bars was lapped at a section was observed to be less brittle.

1,15 1,10

1,05 1,00

0,95 0,90 100%

50%

cx=cy=φ

33% Propor on lapped cx=cy=2φ

25%

20% cx=cy=3φ

Fig. 5. Influence of increased spacing between laps

Spacing between bars 4.2

Assuming overall section breadth is unchanged, the clear spacing between lapped bars is greater where only some of the bars are lapped at a section. Resistance to the bursting forces generated by bond action therefore increases. Most modern codes recognize the beneficial influence of minimum cover on bond resistance, and several semi-empirical analyses also present the increase in bond resistance with clear spacing: Zuo and Darwin [10], Canbay and Frosch [11], fib Model Code 2010. Eq. (2) may be used to estimate the influence of clear spacing. Fig. 4 shows sections through laps with various proportions of bars lapped. Where all bars are lapped at the same section, Fig. 4a, clear spacing cs is taken as 2φ, the minimum permitted by EC2. Based on the same breadth of section, clear spacing between pairs of laps cs increases to 6φ and 10φ where 50 % and 33 % respectively of the bars are lapped, Figs. 4b and 4c. The increase in bond resistance estimated by Eq. (2) as a result of staggering laps is presented in Fig. 5 for three values of bottom cover cy: φ, 2φ and 3φ. The estimated increase in lap strength tends to be less than that implied by the design code coefficients in Fig. 3, particularly at higher cy values. Proportionally lower increases would be predicted if Ktr > 0 or for a wider initial spacing.

Distribution of bond stress along lap

The distribution of bond stress along a lap length is affected by the proportion of bars lapped. Considering a lapped joint that lies within a constant moment zone, the total tension in the reinforcement must remain constant throughout the lap length. (Tension stiffening effects and minor changes in neutral axis depth are neglected here for simplicity.) Thus, where all bars are lapped, one bar of the lapped pair must shed load at the same rate as the other picks it up. It follows by symmetry that if lapped bars are of the same diameter, the force in the two bars at the midpoint of the lap must be equal, and half the bar force must be transferred within each half of the lap length. If, however, only some of the bars are lapped at the section, and if it is further assumed that there is no bond slip near the centre of the lap, then for compatibility of bar strains, continuous and lapped bars each carry a stress given by Eq. (3) at the middle of the lap. A schematic plot of stress distributions for laps with varying proportions of bars lapped at a section, based on the assumption that all bars take an equal share of the load, is shown in Fig. 6. The force to be transferred over the end half lap length increases when only some of the bars are lapped, and peak bond stresses would be correspondingly higher and therefore potentially

Structural Concrete 15 (2014), No. 1

J. Cairns · Staggered lap joints for tension reinforcement

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

lead to an earlier failure. In reality, tension stiffening and bond slip would mitigate the differences shown in Fig. 6. fs,m = fs(1 + ρlap)–1

4.3

(3)

Sharing tension force between lapped and continuous bars

The share of the tension force taken by lapped bars will depend on their stiffness relative to that of continuous bars. The elongation of a continuous bar over the lap length is given by Eq. (4). For simplicity, the effects of tension stiffening are again neglected.  cont 

0

 s,c · dx

(4)

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

0

 s,l · dx  s fe

(5)

Cairns and Jones [12] reported that laps failed at a free end slip of 0.01–0.04 mm, which is small relative to the deformation 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 relatively uniform throughout the lap length. It follows that for compatibility of deformations of lapped and continuous bars, δcont = δlap, strains at the ends of the lapped bars must be greater than those in continuous bars. In other words, the tension force in the reinforcement is not shared between lapped and continuous bars in equal proportions. An exploratory finite element analysis (FEA) was undertaken to investigate sharing of force between lapped and continuous bars. Three lap configurations were analysed, one with all bars lapped simultaneously (100 % lapped), one containing a single continuous bar and a lapped pair (50 % lapped), and one containing two continuous bars and a lapped pair (33 % lapped). The model represents a lap length of 20 times the bar diameter, as in the experimental investigation, plus a distance equal to half a lap length to either side. Half the breadth of the section is modelled, Fig. 7, with deformations restrained along the

Structural Concrete 15 (2014), No. 1

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

axis of symmetry in the perpendicular direction. The breadth of each section was varied so that the effective geometric ratio of reinforcement outside the lap was 2.6 % in all analyses. The FEA was conducted using the LUSAS software suite [13]. Steel reinforcement was represented by elastic bar elements, and concrete represented using 8-noded isoparametric elements and the inbuilt non-linear mass concrete material model. The applied loading was imposed by displacements of equal magnitude and opposite direction along opposite ends of the model. Bond slip behaviour is not included in the results reported here. The LUSAS modeller was found to have some limitations that distort bond stiffness at changes in the FE mesh. The bar/bar slip at the ends of the lap at convergence failure was around 0.2 mm, similar to that reported by Cairns and Jones in their physical tests on lap joint specimens. It was therefore decided to neglect bond slip behaviour to avoid the difficulties that were experienced in iterating to the intended 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 axis. Results are scaled with the vertical axis representing the share of the total force taken by each bar. Bar force is therefore 100 % of the total at the ends of the lap in which all bars are lapped, Fig. 8a. Elsewhere, the total is somewhat less than 100 % due to the stiffening contribution of concrete in tension. With 50 % of bars lapped, the force in the continuous bar at the end of the lap is slightly less than half the total, 45.5 %, Fig. 8b, while the lapped bar is responsible for the balance of 54.5 %, equivalent to a stress 20 % greater than that in the continuous bar and 9 % higher than that which would be obtained by averaging tension across continuous and lapped bars. Where one-third of the bars is lapped, Fig. 8c, the lapped bar develops 38.6 % of the total, equivalent to a stress 26 % greater than the average for the two continuous bars and 16 % higher than the average across all bars. The greater stiffness of the lapped pair therefore results in their having to develop a greater share of the total force. The ratio of stresses at mid-length of a lapped bar to that at the ends increases from 0.42 when

J. Cairns · Staggered lap joints for tension reinforcement 120,0% 100,0% Share of load

80,0% 60,0% 40,0% 20,0% 0,0%

-0,8

-0,6

-0,4

-0,2

0,2

0,4

0,6

0,8

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

60,0% 50,0% Share of load

40,0% 30,0% 20,0% 10,0% 0,0%

-0,8

-0,6

-0,4

-0,2

0,2

0,4

0,6

0,8

Distance from centre of lap (as propor on of lap length) Con nuous Lap le Lap right 45,0%

Fig. 9. Reinforcement details

40,0% 35,0% Share of force

30,0%

admittedly simplified analysis therefore raises doubts as to whether current guidance on staggering of lapped joints is soundly based.

25,0% 20,0% 15,0% 10,0%

5 5.1

5,0%

0,0% -0,8

-0,6

-0,4

-0,2

0,2

0,4

Distance from centre of lap (as propor on of lap length) Lap le Con nuous 2 Con nuous 1

0,6

0,8 Lap right

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

100 % of bars is lapped to 0.48 when 33 % is lapped. The results therefore follow the trend illustrated in Fig. 6, although the ratios are lower than estimated by Eq. (3) due to tension stiffening effects. In summary, this section has identified three differences – one beneficial, the other two adverse – between laps in which all bars are lapped at the same section and those in which only some bars are lapped at a section. On the basis of these analyses it can be speculated that an increase in bond resistance from confinement from increased spacing between lapped bars would readily be offset by changes in demand due to differences in the distribution of bond stress, and hence that the lower lap length permitted when only some bars are lapped, Fig. 3, might not reflect the performance of staggered laps. This

Experimental programme Design

The test programme comprised four groups of specimens containing a total of 17 beams, with variations in the proportion of bars lapped at a section and the longitudinal stagger of individual lapped joints within each group. The stagger dimension as is defined in Fig. 2. For the detail illustrated in Fig. 2, for example, the proportion of bars lapped is 50 % and the stagger distance equals 130 % of the lap length. The parameter for proportion lapped used here denotes the proportion of bars lapped at the same section, neglecting the requirements of EC2 for a gap between lap zones, i.e. laps are considered staggered when as ≥ lo. Groups B and G were reinforced with three pairs of 16 mm diameter bars, and the proportion lapped at a section was either 100 % or 33 %, whereas groups C and D were reinforced with two pairs of 20 mm diameter bars, and the proportion lapped was either 100 % or 50 %. Each group contained one or more specimens with all bars spliced at the same section to serve as a benchmark for the wider data population. Reinforcement layouts for all specimens are shown schematically in Fig. 9, with details of dimensions in Table 1. Lap length was set at 20 times the

Structural Concrete 15 (2014), No. 1

J. Cairns · Staggered lap joints for tension reinforcement

Table 1. Details of test specimens

Test ref.

B0 B1.1 C0a C0b C0.5 C1.1a C1.1b C1.5a C1.5b D0 D0.5 D1 D1.25 G0 G0.5 G1.3 G1.3S

Concrete cube strength fcu [MPa]

Longitudinal reinforcement

Lap length

% lapped

Stagger

Section breadth

Section depth

Cover and spacing

dia. [mm]

No.

lb [mm]

[%]

[mm]

b [mm]

h [mm]

cx, cy [mm]

cs [mm]

43.1 43.1 43.1 38.0 42.0 42.0 38.0 42.0 38.0 37.7 37.7 37.7 37.7 32.1 32.1 32.1 32.1

16 16 20 20 20 20 20 20 20 20 20 20 20 16 16 16 16

3 3 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3

320 320 480 400 400 400 400 400 400 400 400 400 400 320 320 320 245

100 33 100 100 100 50 50 50 50 100 100 50 50 100 100 33 33

0 360 0 0 200 440 440 600 595 0 200 400 500 0 160 420 320

226 228 226 225 226 224 225 226 225 250 250 250 250 260 250 250 250

254 255 270 280 270 303 290 270 274 285 285 285 285 320 310 310 310

20 20 20 23 20 23 23 20 20 22 22 22 22 25 25 25 25

39 98 94 93 94 161 162 160 159 94 94 94 172 57 52 193 193

No. of links at each lap

3 2 3 3 3 2 2 2 2 3 3 3 3 0 0 0 0

Notes for link detail: 2–40 mm from both ends of each lap 3–40 mm from both ends and centre of each lap

bar diameter to ensure bond failure would precede yield of reinforcement in all but two beams. Specimen G1.5S used a shorter lap length of 15.3 bar diameters, reflecting the difference in the α6 coefficient in EC2 for laps with 100 and 33 % of bars lapped at a section relative to G0, whereas C0a used a longer lap length of 24 bar diameters, reflecting the corresponding difference in α6 relative to C1.5a and C1.5b. Beams contained between 0.8 and 1.2 % longitudinal reinforcement, and minimum covers were between 20 and 25 mm, giving a minimum cover to bar diameter ratio of between 1.0 and 1.56. A modest quantity of secondary reinforcement in the form of closed links was provided in the lap zones of series B, C and D. The quantity was kept close to the permitted minimum to reduce uncertainties in the interpretation of how links contribute to the strength of laps in which only a portion of the bars is spliced at a section. Series G did not contain links within the lap zones. The number of 8 mm mild steel links provided for each lap zone is given in Table 1. Links were provided at 300 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). Bars had pairs of crescent-shaped ribs on opposite sides which merge into the core. Relative rib area was not measured on these particular bars, but from similar production has been found to lie typically in the range 0.055–0.065. Concrete cover to longitudinal bars was provided by proprietary spacers. Concrete was of medium workability (class S2 to BS EN 206 [15], slump typically 60 mm), maximum

Structural Concrete 15 (2014), No. 1

aggregate size 20 mm, containing a water-reducing admixture and supplied by a local ready-mix company. Series B, D and G were each cast from a single batch; series C was cast from three different batches. Concrete was compacted by internal vibration and subsequently cured under damp hessian and polythene for at least three days before stripping and storage in the laboratory until being tested. Standard cube control specimens were taken from each batch 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 lap zones positioned within the constant moment zone. The load was monotonically increased to failure over a period of approx. 30 min, applied in increments of either 10 or 25 kN, with crack development marked at each stage. Loading was continued until residual strength dropped by at least 25 % after peak load had been passed. The rate of displacement was increased during this stage. Load and mid-span deflection were logged at 2 s intervals throughout the loading sequence.

Test results

The load/deflection response of all beams was close to linear up to peak load. Minor departures were evident at low loads prior to initiation of flexural cracking, where stiffness was slightly greater, and close to failure, where the response softened slightly. Vertical flexural cracks formed within the constant moment zone first, followed by slightly inclined flexural cracks within the shear spans. Failure

J. Cairns · Staggered lap joints for tension reinforcement 100

Lap strength

Test

B0 B1.1 C0a C0b C0.5 C1.1a C1.1b C1.5a C1.5b D0 D0.5 D1 D1.25 G0 G0.5 G1.3 G1.3S

[kN · m]

fs,test [MPa]

Calculated, Eq. (2) fstm [MPa]

47.3 48.8 51.0 45.1 59.9 45.0 44.4 43.0 50.7 53.6 56.4 51.7 48.1 52.6 52.8 49.7 43.7

388 373 430 304 359 312 291 312 298 331 373 358 394 313 328 307 263

352 479 382 361 357 407 405 401 394 359 359 428 452 294 291 336 290

Bond Ductility strength ratio fb,test/ fb,calc Dres

Dres=Residual loard Peakloard

Peakload

Max. moment

40 20

Residualload at 1.5 mes peakload deﬂn.

1.10 0.78 1.13 0.84 1.01 0.77 0.72 0.78 0.76 0.92 1.04 0.83 0.87 1.07 1.13 0.91 0.91

0.75 0.30 0.23 0.51 0.42 0.55 0.48 0.62 0.92 0.52 0.28 0.57 0.48 – – – –

100%

120%

Midspan deﬂec on (mm)

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

450 400

Lap Strength (MPa)

Beam ref.

Applied load (kN)

Table 2. Test results

350 300 250 200 150 100 50

0 0%

20%

40%

60%

80%

Propor on lapped

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

450 400 Lap Strength (MPa)

occurred suddenly as a widening flexural crack formed near one end of a lap zone and longitudinal cracks propagated along longitudinal tension bars over the lap length. The load dropped under increasing deflection immediately after the peak was reached in all tests. Table 2 lists mid-span bending moments at peak load and the corresponding lap strength for all specimens. The average stress in the reinforcement at peak load fs,test is calculated using the rectangular stress block for concrete in EC2 with safety factors taken as 1.0. An indication of the brittleness of failure is given by the parameter Dres, calculated as the ratio of residual load at a deflection of 1.5 times the peak load deflection to the peak load itself, Fig. 10. The strength of specimens where all bars were lapped simultaneously has been compared with strengths estimated by Eq. (2). The cylinder compressive strength for use in Eq. (2) is taken as 0.8 times the cube strength in Table 1. The ratio of measured to estimated lap strength for 100 % lapped specimens averages 0.99 with a coefficient of variation of 0.14, almost identical to the scatter reported for Eq. (2) against a database of over 800 lap joint tests [16] and by Canby and Frosch and Zuo and Darwin for their best fit expressions. The results presented here may therefore be considered as representative of the larger body of test data, and hence constitute a valid benchmark against which strength of staggered laps may be compared. A direct comparison of equivalent laps for staggered and non-staggered laps is possible for only one pair of specimens. Lap lengths for G0 and G1.3S were 320 and 245 mm respectively, reflecting the corresponding α6 coefficient values of 1.5 and 1.15 for 100 and 33 % lapped re-

350 300 250 200

150 100 50

0 0,00

0,50

1,00

1,50

2,00

Stagger/lap length

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

spectively given in EC2. If the α6 coefficients in EC2 are an accurate reflection of behaviour, these two specimens would be expected to develop the same strength. Test results show the staggered lap detail of G1.3S to be 16 % weaker. Fig. 11 plots lap strength for specimens with a lap length of 20φ classified according to the proportion of bars lapped at the section. Bond strength is not affected by the proportion of bars lapped. Fig. 12 shows a similar plot with specimens classified according to stagger distance. The strength dropped by about 10 % where bars were staggered by one lap length or more, in contradiction to expectations on the basis of Fig. 3. Spacing between laps is increased where only some of the bars are lapped at a section. To allow for differences

Structural Concrete 15 (2014), No. 1

J. Cairns · Staggered lap joints for tension reinforcement 0,80

0.4 where laps were not staggered or partially staggered to 0.6 when laps were staggered, Fig. 14. However, the experimental design resulted in an inverse correlation between density of transverse reinforcement and proportion of bars lapped at a section. Confining reinforcement is widely recognized to restrain the brittleness of lapped joints, and hence the parameter responsible for the improvement in ductility cannot be ascertained with confidence from these tests.

Duc lity Index Dres

0,70 0,60 0,50 0,40 0,30 0,20 0,10 0,00 0

0,2

0,4

0,6

0,8

1,2

1,4

1,6

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 to that estimated from EC2

in confinement between staggered and non-staggered laps, and also for minor variations in concrete strength and lap length, further analysis of the results is based on “lap strength ratio”, i.e. the ratio of measured lap strength to that estimated by Eq. (2), as listed in the penultimate column of Table 2. Where laps do not overlap, i.e. where the stagger distance as is at least one lap length, details (c) and (f) in Fig. 9, the transverse spacing between lapped bars is calculated as if the transverse section were repeated laterally, 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 of lapped pairs. Fig. 13 plots the variation in lap strength ratio with stagger distance as for all specimens. There is no significant difference between laps with no stagger and laps staggered by half a lap length, nor between laps staggered by one and one-and-a-half lap lengths. Taking account of differences in confinement, staggering laps by one lap length or more reduces lap strength by about 20 %. Note that only those specimens listed as having a stagger distance in excess of 1.3 would be considered to qualify for a reduced α6 coefficient according to EC2. None of the failures were ductile, although failure was less brittle where fewer bars were lapped at a section. The deformability index Dres increased from an average of

Structural Concrete 15 (2014), No. 1

Discussion of results

This investigation raises doubts regarding the perceived advantages of lapping only a portion of bars at a section. The results presented here suggest that differences in the distribution of bond stress and the share of load taken by lapped and continuous bars result in either no gain in strength or a reduction of up to 20 % when laps are staggered, depending on the basis for the comparison. The apparent reduction is based on the assumption that all bars are stressed equally, which the analyses shown in Fig. 8 demonstrate to be incorrect. The brittle nature of the splitting mode of bond failure means that, as a lap fails, stresses in lapped bars drop before continuous bars reach yield. However, it is not possible to determine the stresses that actually develop in lapped bars without strain measurements on individual bars. Although failures were less brittle when laps were staggered, it is not clear whether this can be attributed to the staggering of the laps or to differences in the density of transverse reinforcement, and lap failure remained nonductile in all cases. The lap lengths tested here were less than those required to develop the design strength of the reinforcement, far less the actual yield strength. As lapped bars are more highly strained than continuous bars at the ends of the lap, Fig. 8, they would have to achieve strains in excess of yield before continuous bars can reach yield. Bond reduces where bars are strained above yield. Differences between staggered and non-staggered laps might thus be accentuated in full-strength laps. The fib Model Code 2010 introduced clear spacing between bars as an additional parameter in the design of laps and anchorages, Eq. (2). This permits shorter laps in slabs and walls where bars are widely spaced. Clear spacing between lapped pairs is increased where only a proportion of bars is lapped at a section, and increases confinement to lapped bars and hence their bond resistance. It is not known whether this was recognized and utilized when the proportion lapped rules in MC90 and EC2 were formulated, but there remains a possibility that the “proportion lapped” provisions are implicitly linked to clear spacing. Permitting lap length to be reduced for both increased spacing and for proportion lapped would double count the spacing effect. The proportion lapped coefficient should therefore be discontinued as a consequence of introducing the cmax/cmin parameter in Eq. (2). Ends of lapped bars act as stress concentrators and there are concerns that larger crack widths form when all bars are lapped at the same location. Flexural crack width is related to the stresses in the bars. As discussed above, staggering of laps results in lapped bars carrying a dispro-

J. Cairns · Staggered lap joints for tension reinforcement

portionate share of tension at the ends of laps, hence staggering could lead to increases in the widths of transverse cracks at the ends of laps. Although this has not been investigated experimentally here, it is thought likely that staggering of laps according to EC2 provisions would result in wider cracks. If laps were partially staggered, however, i.e. if as < lo, strains in continuous bars at ends of laps would be lower, probably resulting in lower crack widths. It was mentioned in the introduction that the greater length of staggered lap zones may impede construction. There would be advantages for construction if current rules for staggered laps in EC2 were modified to permit stagger distances to be reduced below 1.3 times the lap length. Results from this study suggest that stagger distances of half a lap length where 50 % of bars are lapped (and by implication, stagger distances of one-third of a lap length where 33 % of bars are lapped) would result in laps as strong as those designed to current requirements with a stagger of 1.3lo, but with smaller flexural crack widths at ends of laps. The results here suggest that a reduction in lap strength due to a smaller clear spacing between lapped pairs when laps are partially staggered or not staggered would be offset by increases associated with changes in the distribution of bond stresses. Further research into alternatives to current rules for staggered laps would therefore be worthwhile.

Summary and conclusions

Design codes, including EC2 and ACI 318, encourage staggering of lapped joints. The requirements to stagger lapped joints increase the complexity of detailing and steel fixing, may consume additional resources and slow down construction on site. Although coefficients for proportion lapped are at least as influential as those for any other parameter, minimal research has been carried out on staggered laps and the origin of current rules is obscure. 1. Staggering of laps does not increase lap strength despite an increase in clear spacing between pairs of lapped bars. 2. When allowance is made for the difference in clear spacing between staggered and non-staggered laps, staggering was found to reduce lap strength. 3. Differences in the share of tension force taken by continuous and lapped bars is thought to be responsible for the difference in strength observed experimentally. 4. Although brittleness was reduced when laps were staggered, it is unclear whether this is due to staggering or to transverse reinforcement. 5. Further work on staggered laps capable of developing stresses exceeding the design strength of the reinforcement is recommended. The conclusions here are limited to the relationship between lap lengths for staggered and non-staggered laps and not to bond strengths for design purposes. Specifically, the conclusions presented here must not be regarded as justification for omitting the proportion lapped coefficient α6 from design calculations to EC2 or setting it at a value < 1.5 where all bars are lapped at the same section. A further paper to review the overall safety level of EC2 rules for design of lap length is in preparation.

ACI 318 also allows shorter lap (splice) lengths where laps are staggered. Unlike EC2, a further condition is applied which limits the design stress in the bars to a maximum of 50 % of their design strength. These rules would appear to be justifiable on the basis that lightly stressed laps would only be required to develop the full strength of a bar under accidental loading conditions, in which 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 experimental work reported here.

Notation As cross-sectional area of main bar Asv area of each leg of a link cmax, cmin minimum and maximum concrete dimensions as defined in Fig. 1 fb average bond stress over bond length lb Δ fs change in bar stress over bond length lb fcm mean concrete cylinder compressive strength fcu measured concrete cube compressive strength fs,m, fs bar stresses at centre and ends of lap respectively. fstm, fy stress developed in bar (mean value) and yield strength respectively Ktr density of confining reinforcement, Ktr = nl · ng · Asv/(lb · φ · nb) ≤ 0.05 lo lap length ng number of groups of links within lap length nl number of legs of a link in each group nb number of pairs of lapped bars km “effectiveness factor” for link confinement, km = 12 for bars confined by a link passing through an angle of 90o εs,c, εs,l axial strains in continuous and lapped bars respectively φ nominal bar diameter proportion of bars lapped at a section ρlap References 1. BS EN 1992-1-1:2004: Eurocode 2: Design of concrete structures – Part 1-1: General rules and rules for buildings. British Standards Institution, London. 2. CEB-FIP Model Code 90. CEB, Lausanne, 1993. 3. ACI 318-11: Building Code Requirements for Structural Concrete and Commentary. American Concrete Institute, Michigan, USA, 2011. 4. fib Model Code 2010 – Final draft, vol. 1. Model Code, ISBN 978-2-88394-105-2, Mar 2012. 5. Magnusson, J.: Bond and anchorage of ribbed bars in highstrength concrete. PhD thesis, Division of Concrete Structures, Chalmers University of Technology, Gothenburg, Sweden, 2000. 6. Ferguson, P. M., Briceno, E. A.: Tensile lap splices part 1: Retaining wall type varying moment zone. Research Report 113-2. Centre for Highway Research, University of Texas at Austin, Jul 1969.

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J. Cairns · Staggered lap joints for tension reinforcement

7. Thompson, M. A., Jirsa, J. O., Breen, J. E., Meinheit, D. F.: The behaviour of multiple lap splices in wide sections. Research Report 154-1, Centre for Highway Research, University of Texas at Austin. Jan 1975. 8. Metelli, G., Cairns, J., Plizzari, G.: Influence of bar continuity on behaviour of lapped splices. Precast Concrete Institute, Chicago: No. 102, Proc. of 3rd International fib Congress & Exhibition: Think Globally, build locally. 29 May–2 Jun 2010, Washington, USA. 9. Cairns, J.: Lap splices of bars in bundles. ACI Structural Journal, vol. 110, No. 2, Mar 2013, pp. 183–192. 10. Zuo, J., Darwin, D.: Splice Strength of Conventional and High Relative Rib Area Bars in Normal and High-Strength Concrete. 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.

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14. BS 4449:2005+A2:2009: Steel for the reinforcement of concrete. Weldable reinforcing steel. Bar, coil and decoiled product. Specification. British Standards Institution, London. 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 anchorages in the fib Model Code 2010 (in preparation).

John Cairns Heriot-Watt University Edinburgh EH14 4AS, UK j.j.cairns@hw.ac.uk

Technical Paper Johan Magnusson* Mikael Hallgren Anders Ansell

DOI: 10.1002/suco.201300040

Shear in concrete structures subjected to dynamic loads Shear failures in reinforced concrete structures under intense dynamic loads are brittle and limit the structure’s energy-absorbing capabilities. This paper comprises a review of the literature dealing with the problem of dynamic shear of reinforced concrete elements, with a focus on parameters that control flexural shear and direct shear. In this context, dynamic loads refer to intense events due to explosions and impacts. For this reason, the initial response is also highlighted. Experimental investigations and calculations show that shear force and bending moment distributions in dynamic events are initially significantly different from the distributions under slowly applied loads. Therefore, structural wave propagation, geometrical properties of elements, strain rate effects and dynamic load characteristics need to be considered when analysing shear. The review also indicates that arch action in the shear span soon after the load has been applied has a large influence on the shear capacity of an element. This action is 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

Introduction

Dynamic loads such as explosions can cause severe damage to concrete structures. An explosion in air is the result of detonating explosive charges, the rapid combustion of a fuel-air mixture or bursting pressure vessels. The explosion generates a blast wave that propagates through the air at supersonic velocity in all directions. As the blast wave strikes an object such as the wall of a building, the pressures are reinforced due to reflections. In a case where the reflected pressures are sufficiently high, local failures of structural elements such as loadbearing walls or columns can occur. In the design of concrete structures to resist the effects of blast loads, impacts or other severe dynamic loads, it is not practical to consider a structural response in the elastic range only. The structural elements should therefore be allowed to deform plastically, which better utilizes their energy-absorbing capabilities. A certain amount of

* Corresponding author: johan.magnusson@grontmij.com Submitted for review: 11 June 2013 Revised: 7 August 2013 Accepted for publication: 7 September 2013

damage, i.e. concrete cracking and yielding of the reinforcement due to flexure, is therefore usually accepted in the design of structures to resist blast loads. Structural elements should generally be designed for a flexural response. However, real events [1] have shown that highly intense loads from blasts at close range can cause local shear failures in concrete structures, which is a brittle mode of failure. In the Oklahoma City bombing, two concrete columns were reported to have failed in shear. Apart from real events, shear failures in concrete elements have also been observed experimentally in several investigations involving blast and impact loads [2–7]. In several cases these tests confirm that elements that fail in flexure under a slowly applied (quasi-static) load may fail in shear under dynamic loads. The purpose of the present paper is to conduct a review of the literature on the shear problem of reinforced concrete structures subjected to intense dynamic loads and to identify areas for further research. In this context, dynamic loads refer to intense events due to explosions and impacts. The review focuses on behavioural aspects of dynamic shear and on the parameters that control the mode of failure. Highlighting the initial response of concrete elements under dynamic loads represents another focus. The modes discussed here are flexural shear and direct shear. A third mode of shear failure is punching shear. This type of failure can occur as an object impacts on a concrete surface with inclined shear cracks and the formation of a conical shear plug through the thickness of the concrete element [8]. However, dynamic punching shear is outside the scope of this paper.

Quasi-static shear

Shear failure in reinforced concrete elements can generally be related to flexural shear and direct shear. In principle, flexural shear and direct shear exhibit similar fundamental behaviour since they share many features such as the mechanisms that transfer shear across a crack. These mechanisms are friction, aggregate interlock and the dowel action of the longitudinal reinforcement. Flexural shear occurs at locations where both shear and flexural stresses exist. This failure mode is characterized by an initial flexural crack that, under the action of an increasing load, develops into a crack inclined with respect to the longitudinal axis of the element, see Fig. 1a. These inclined cracks

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

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

appear in regions of high shear forces and are due to the principal tensile stresses that occur in the element. Flexural shear typically occurs in beams carrying point loads with a shear span to effective depth ratio a/d = 3â&#x20AC;&#x201C;7 [9]. In cases where the load is located closer to the support, the diagonal crack can be initiated in the region of the neutral axis 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 splitting of the compressive strut that develops between the load and the support. Direct shear failure is characterized by a sliding type of failure along a well-defined plane (the shear plane) through the depth of the element. This type of shear failure typically occurs at concentrated loads close to the supports. In the case of elements subjected to quasi-static loads, 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 in initially uncracked and cracked concrete. In the latter case the shear transfer mechanism will be due to aggregate interlock and the dowel action of the longitudinal reinforcement. Shear transfer for initially uncracked concrete will cause several short diagonal tension cracks to develop along the shear plane [10]. Shear failure will occur when the concrete struts fail under the combined action of compression and shear, or when the local shear stresses at the ends of the struts reach a critical value.

3 3.1

Dynamic shear Characteristics of dynamic loads

Shear failure of concrete elements may occur due to the intensity of the dynamic load. The intensity of a load generally refers to its rise time and its peak value. It is well known that the flexural response of elements to dynamic loads depends on the rise time and the applied peak with respect to the natural period of vibration and the resistance of the element [12, 13]. Fig. 2 shows an idealized representation of a blast wave profile, illustrated with the time axis at ambient pressure, at a given distance from the centre of an explosion in air. The arrival of the blast wave creates an almost instantaneous increase from ambient pressure to the peak overpressure and is immediately followed by an exponential decay to ambient pressure. This first part of the blast wave is termed the positive phase, which is normally the only phase of interest when analysing blast-loaded structures. The second part of the

Structural Concrete 15 (2014), No. 1

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

blast wave, termed the negative phase, may be of importance for windows and for the flexural behaviour of walls exposed to explosions at close range. However, for the purpose of the present paper, any influences of the negative phase on shear are not included. Blast waves have an almost indefinitely small rise time, e.g. a fraction of a millisecond [14], whereas loads from objects impacting on a concrete element typically have rise times of about one millisecond [4, 15]. This applies to impact velocities of about a few metres per second. Another way of describing the load variations over time is to refer to their frequency content. Accordingly, a short rise time can be regarded as a load containing a large number of frequencies as opposed to a load with a longer rise time. When considering intense dynamic loads such as blast loads, it is convenient to relate their duration to the natural period of vibration T of the element in question. Impulsive loads are typically of short duration in relation to the natural period of vibration of the loaded element and have high amplitudes. It is suggested in [13] that a load can be regarded as impulsive if the duration is < 0.1 times the natural period of the system. Due to this short duration, no significant deflections take place during this period of time. Explosions close to a wall and impacts are typically regarded as impulsive loads.

3.2

Dynamic flexural shear

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

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

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])

been observed in investigations involving blast waves [5, 7]. Fig. 3 shows one of the beams that failed in flexural shear. In this case the beam was subjected to an evenly distributed blast load over its top surface [5]. The first author of the present paper performed numerical simulations of several of the tests in [5] using the Ansys-Autodyn software [16]. A sequence was extracted from these simulations to show the development of the diagonal shear crack, see Fig. 4. This figure shows that flexural shear failures in dynamic events follow the same series of events as in the case of quasi-static loads. Thus, a certain amount of flexure occurs prior to the development of inclined shear cracks. Blast tests on concrete beams have shown that relatively large reactions were registered before any noticeable deflections were measured, suggesting that the beam was initially subjected to large shear forces [17]. Flexural shear has also been observed in investigations involving impact loads on concrete beams [3, 4, 6]. The tests performed in [4] involved impact tests on simply supported reinforced concrete beams. In these tests the rise time and amplitude of the load were controlled by placing rubber pads between the striking mass and the beam in the impact zone. Thus, for the same applied energy level, the magnitude of the applied load could be reduced and the rise time increased to create a softer impact. The tests showed that flexural failure occurred when a beam was subjected to a soft impact, whereas beams subjected to harder impacts failed in flexural shear. These

tests were performed with the same impacting speed and mass. 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 concrete beam may depend on the frequency content of the applied load. According to [3, 4], a dynamic load with high frequency content excites higher vibration modes in an element compared with the case with a slowly applied load. Thus, as higher modes are excited, a larger portion of the strain energy is due to shear rather than flexure. The first free vibration modes of a simply supported beam are shown in Fig. 5. A quasi-static load cannot affect the ele-

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

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

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

ment any more than in its fundamental mode and the shear forces in the element are therefore limited. Besides the 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 beam stiffness plays an important role in the failure mode. A previous literature review [19] showed that a majority of the tests on concrete beams with a relatively high reinforcement content and subjected to dynamic loading exhibited shear failures, whereas beams with lower reinforcement contents failed in flexure. The results in [4–6, 20] support these findings. The shear forces occurring in a stiff element are higher than those in a softer element under dynamic loading. Furthermore, concrete and steel reinforcing bars exhibit increased strength in tension and compression when subjected to dynamic loads – commonly known as strain rate effects [21–23]. Owing to these effects, a concrete element will become stiffer under dynamic loading and may therefore become more susceptible to shear failures.

3.3

Dynamic direct shear

As previously mentioned, direct shear failures can occur in uncracked elements at locations near a support when a static load is applied in its proximity. However, tests have shown that concrete elements can also fail in a direct shear mode under the action of an intense dynamic load distributed along the length of the element [2]. In these tests the roofs of reinforced concrete box structures were subjected to loads from detonating explosive charges. The box structures were cast monolithically with two open ends and, for one series of tests, with dimensions and reinforcement as shown in Fig. 6. The roof slab did not have any prior crack planes through its thickness. The test results show that the slabs failed in direct shear in several cases and that the slabs were completely severed from the walls along vertical failure planes. Most of the slab reinforcing bars were pulled out of the wall, with a few broken bars exhibiting minor necking. It was further observed in several tests that the central portion of the roof slab remained relatively flat, as though no flexural deformations had taken place (shown schematically in Fig. 7).

Structural Concrete 15 (2014), No. 1

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

Little is known about the actual fracturing and direct shearing process in dynamic events and therefore it was assumed in [14] that the direct shear failure in the dynamic case behaves in accordance with the shear transfer mechanism under quasi-static loading conditions. It was stated in [14] that the direct shear failure of the roof slabs is characterized by the rapid propagation of a vertical crack through the element depth. Since direct shear is associated with crack planes perpendicular to the longitudinal axis of the element, such failures are also possible in elements designed for flexural shear. Failure curves for reinforced concrete elements were developed in [14] and used in a parametric study of direct shear failures, see Fig. 8. The failure curve is unique for the specific element in question such that a family of curves could be generated for elements with different properties. A failure curve is constructed such that the combined values of pressure and rise time below the curve relate to no failure, and values above the curve relate to direct shear failure. The increase in pressure for an increasing rise time implies that the element is able to resist direct shear at higher pressure levels if the load is applied more slowly. The shape of the failure curve also indicates that for very small rise times, in this case < 0.1 ms, the maximum pressure appears to be approximately constant. The analyses in [14] indicate that the resistance to direct shear increases as the element span to effective depth ratio L/d for uniformly distributed loads increases. However, the influence of L/d diminishes for small rise times and disappears at rise times close to zero. Another case is the comparison between elements with fixed support conditions and reduced end restraints. Two failure curves

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

theory results in an increasing overestimation of the natural frequency for modes higher than the fundamental mode, whereas results with the Timoshenko theory are within 3 % for the first 11 modes. However, for the purpose of analysing the early response qualitatively and for parametric studies, the Bernoulli-Euler theory can be used, which also comprised the work in [18]. The BernoulliEuler beam equation for a dynamic distributed load q is expressed as EI

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

were generated and the difference between these curves diminishes for small rise times. Further results in [14] suggest that strength enhancement due to strain rate effects increases the shear resistance such that the entire failure curve is shifted upwards. Thus, even for the case with zero rise time, the failure curves do not coincide. It was also mentioned in [14] that the load duration does not affect the direct shear failure curve significantly. Other investigations have involved theoretical analyses of the direct shear mode of concrete elements [24–26]. However, this work is not the focus of the present paper.

4 4.1

Initial response of concrete elements subjected to dynamic loads Initial response

2 y 4 y   A 2  q (x, t) 4 t x

(1)

where: EI flexural stiffness ρA mass per unit length When considering a simply supported beam subjected to a uniformly distributed load over the beam span and a load function according to Fig. 9, the solution to the beam deformations becomes [18]

 

y x, t 

q0 4 · EI  5



n1

  x sin  2n  1 L   · gn(t) 2     5 2n  1 · 1        n   



⬁





(2)



where: q0 maximum distributed load κ shape constant for dynamic load L beam span The time function gn (t) is calculated according to [18]:

Under quasi-static loads, material fractures such as cracks in concrete are initiated and propagate according to the stress and strain fields existing throughout the concrete element. The weakest elements will thus govern the locations and levels of cracking in these strain fields. However, under dynamic conditions, local regions with high stresses and strains can develop and their location may change before an initiated crack has time to propagate. Owing to such conditions, wave propagation effects become increasingly important in the analyses of dynamically loaded structures. Shear failures typically occur at an early stage, before any appreciable deformations have taken place. It is therefore of interest to analyse the initial structural response soon after the load has been applied, with its distribution of displacements, shear forces and bending moments. In this context, a simply supported beam is considered subjected to a uniformly distributed blast load. Other researchers have analysed elastic beams using the Bernoulli-Euler and Timoshenko beam theories [3, 14, 18] and finite element analysis [27, 28]. Initial response has also been observed experimentally in [2, 29]. The Bernoulli-Euler equation for the forced vibrations of a linear elastic beam only allows for flexure and translatory inertia, i.e. the transverse vibrations of a beam. However, the effects of shear deformations and rotary inertia, which are included in the Timoshenko theory, become more significant as the number of modes excited increases. The work in [30] shows that the Bernoulli-Euler



gn t  e  t 

 

 sin  nt  cos  nt n

(3)

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

n 

2n  1

2

EI A

(4)

Note that with a uniform symmetric load, only the odd modes contribute to the response [13, 18]. The same load function as in [18] was used and is a suitable approximation of a blast load, see Fig. 9:



q t  q0e  t

(5)

Derivation of Eq. (2) yields the solutions for the bending moment and shear force distributions along the beam as in [18]:

 

M x, t  q0L2 ·

4 3

⬁



n1

  x sin  2n  1 L   · gn(t) 2     3 2n  1 1        n   





(6)



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

 

V x, t  q0L ·

Fig. 9. Load function used in the calculations

4 2

⬁



n1

  x cos  2n  1 L   · gn(t) 2     2 2n  1 1        n   





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

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

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(7)

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

the first 15 odd modes yields diagrams as shown in Figs. 10–12. Note that the vertical axes of these figures are normalized to the corresponding static quantities such that ystat, Vstat and Mstat are calculated as ystat 

5q0L4 385EI

(8)

Vstat 

q0L 2

(9)

Mstat 

q0L2 8

(10)

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

subjected to a vertical downward dynamic load. It was observed that the y/ystat, V/Vstat and M/Mstat ratios become rather small. The reason is the rapid decay in the dynamic load compared with a static load having the same amplitude, which is constant over time. In a case with a more gradual decay, i.e. small κ values, the duration of the applied load increases and the corresponding deflections, shear forces and bending moments also increase. For a suddenly applied constant load with an instantaneous increase to peak pressure, typically a rectangular-pulse load of infinite duration, the ratios in question eventually become equal to 2 after a certain time. This is a well-known feature for linear elastic systems subjected to these types of load and can be shown using energy relations [13, 18]. Furthermore, even though the calculated ratios are small, the shear forces and moments may exceed 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

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

A concrete beam subjected to dynamic loads will initially exhibit deformations, shear forces and bending moments with significantly different distributions compared with the corresponding distributions under slowly applied loads. Soon after the dynamic load has been applied to the beam surface, the entire beam – except for the parts adjacent to the supports – will be accelerated in the direction of the load. At this point in time, the remaining parts of the beam will be subjected to a rigid body motion without any deformations, see Fig. 10. As time progresses, the strains and stresses in terms of flexure and shear in the vicinity of the supports will be distributed to the remaining parts of the beam through structural wave motions and the beam will gradually acquire a deflected shape that corresponds to the first mode of vibration. Shear forces and bending moments will also initially occur locally at the supports and their distributions will also change over time through the propagation of flexural and shear waves towards mid-span, see Figs. 11–12. Owing to this wave propagation, the shear and moment distributions will eventually become similar to those of a quasi-static mode. Fig. 12 shows that relatively large shear forces also occur at approximately points L/3 and 2L/3 at an early time. This figure also shows that the shear force changes sign at a later time and that the shear distribution gradually approaches the distribution for static loads. This occurs at approx. ω1t = 1. The calculated initial moment distribution in Fig. 11 indicates that yielding of the tension reinforcement in regions close to the supports can occur under a sufficiently intense load. Fig. 13 shows how the calculated first four odd modes contribute to the shear forces at an early time (ω1t = 0.025). It is clear from the figure that the higher modes significantly contribute to the build-up of shear at the supports compared with that of the fundamental mode. At this early time, the contribution of the first mode is close to zero because both deflected shape and moment distribution are different from the corresponding static distribution. However, as time progresses, the contribution of this mode increases and eventually becomes the dominant mode of response.

4.2

Arch action in the shear span

For concrete beams, it is well known that a part of the applied load is carried through arch action between the applied load and the support [11]. This action becomes increasingly pronounced as the distance between the load and the support decreases, i.e. with reducing shear slenderness, defined as shear span to depth ratio. Arch action also develops for beams under uniform loads, only in this case the shear slenderness is defined as the beam span to depth ratio. It has been observed that the shear force at failure increases at a/d = approx. 2.5 for beams subjected to point loads and at L/d = 10 for uniform loads [31]. The effect of this arch action was originally included in the guidelines [32] and has also been incorporated in [33] in the design of concrete structures subjected to blast loads for a/d ≤ 1.5. This method makes use of the initial response of elements with shear forces concentrated in the vicinity of the supports, and the fact that large portions of the element are initially displaced as a rigid body. The

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shear span ατ for a simply supported element is calculated in [33] as a  0.025  0.25 · L

qd p

(11)

where: L beam span qd element static resistance without strain rate effects p peak overpressure Using the calculated shear slenderness it is possible to determine a certain enhancement of the shear capacity of an element. This method accounts for the positive effect of the arch action and that a certain amount of the load is transferred directly to the supports.

4.3

Dynamic support reactions

Knowledge of the dynamic support reactions is of importance because these can be related to the shear forces that occur in the element near the supports during the loading and deflection event. The most common way of determining the reactions is by considering the dynamic equilibrium of the element, see Fig. 14 [13]. For a beam with a constant cross-section, the inertia has the same distribution as the assumed deflected shape. The expression for the reaction V(t) becomes



V t   R · R(t)   p · F(t)

(12)

where: R dynamic resistance (includes strain rate effects of reinforcement and concrete) F total applied load χR constant for resistance χp constant for applied load Thus, the dynamic reaction is a function of both the dynamic resistance and the total applied load. The dynamic resistance R is defined as R

8M L

(13)

where: M dynamic bending moment capacity

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

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

The constants χR and χp depend on the assumed deflected shape of the beam. For the elastic response of a simply supported beam, the values of these constants are 0.39 and 0.11 respectively. During a pure plastic response where the beam is assumed to deform as two rigid bodies with a plastic hinge at mid-span, the corresponding values change to 0.38 and 0.12. Values for the constants are listed in [13] for beams and slabs with other load distributions and support conditions. If the element survives the initial shear and continues to deflect, the response will eventually become plastic, with cracking of the concrete and the formation of a plastic hinge around mid-span. Once the plastic hinge has formed, the maximum element resistance will soon develop and the reactions are therefore limited. Furthermore, since R in Eqs. (12) and (13) refers to the dynamic resistance, it is evident that this contributes to larger shear forces in the element, as discussed in section 3.2. Eq. (12) indicates that the applied load is the dominant contributor to the reactions at an early time since the element resistance has had no time to develop. Thus, in the case of impulsive loads with comparatively high amplitudes, the reactions may exceed the shear resistance of the element with shear failure being the consequence. At these early times of the response, the deflected shape is dramatically different from that of the fundamental mode as discussed in section 4.1. As the deflected shape changes with time during the initial phase, the distribution of inertia forces must also change with time. Thus, it may be appropriate to introduce functions that allow variations of χR andχp over time during the initial phase. This method was adapted in [27, 28]. Other ways of calculating support shear use numerical simulations, used in the work of [27, 34], for instance.

5 5.1

Conclusions Summary and discussion

The present paper comprises a review of the literature dealing with the problem of the dynamic shear of reinforced concrete elements, with a focus on parameters that control shear. For this reason, the initial response was also highlighted. In dynamic events, high stresses and strains can occur locally in the structure for short periods of time. The effects of structural wave propagation and strain rate as well as dynamic load characteristics therefore need to be considered in shear analyses. From the present review it can be generally concluded that shear in concrete elements depends on load characteristics, element parameters and support conditions. These three areas will be briefly summarized and discussed below. Load characteristics that were found typically to contribute to shear are peak load and rise time. These parameters are important in both flexural and direct shear. The typical characteristics of impulsive loads are high pressures, small rise times and short durations, which is why such loads contribute to large shear forces in the structure. The load duration was reported in [14] as not having a significant influence on direct shear, which is a reasonable statement since direct shear occurs at an early time. However, the load duration may have some influence on flexural shear since this mode occurs at a much later time. Another aspect of interest may be the load dis-

tribution. Explosions on the ground close to an exterior wall of a building will subject the wall to unevenly distributed overpressures such that high pressures will occur at ground level with diminishing pressures in the horizontal and vertical directions. The lower supports will therefore be 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. In this context, also interesting would be to include the dynamic support reactions that occur for impulsive types of loads. It was also concluded that structural parameters important to shear were element resistance and stiffness, L/d ratio and strain rate effects. Higher stiffness and resistance contribute to larger shear forces in the element compared with a softer element with a lower resistance. The L/d ratio has the same influence on shear such that low ratios give rise to larger shear forces compared with larger L/d ratios. Strain rate effects in the concrete and reinforcing steel also contribute to stiffer elements. The support conditions influence the element stiffness such that fixed-end beams will subject the element to larger shear forces compared with simply supported beams. These findings regarding stiffness can also be related to the fact that a stiff element exhibits higher natural frequencies compared with softer elements, which leads to larger shear forces. The results shown in Figs. 10–13 are for a purely elastic response, and as soon as cracks are initiated and start to propagate in the concrete the response will change due to the reduced flexural stiffness. This makes the use of non-linear finite element analysis a suitable tool for analysing the influence of cracks on the initial response. It would also be of interest to investigate the influence of large moments that initially appear close to the supports. A layered beam model and modified compression field theory were used in [35] to predict the interaction between moment and shear that occur simultaneously in a section. These analyses indicate that at locations where a moment exceeded half the ultimate moment, the section was unable to develop its ultimate shear capacity. This implies that at locations where both high moment and shear occur simultaneously, shear failure can occur at values lower than the ultimate shear resistance. For a simply supported beam this combination of high shear and moment may never occur, see Figs. 11–12, but could, on the contrary, be the case for a beam with fixed support conditions. It would therefore be interesting to include this moment-shear interaction in further research. Arch action in the shear span will always be present to a certain degree when a concrete element is subjected to out-of-plane loads. In dynamic events this arch action distributes a portion of the large initial loads directly to the supports, especially during the initial response. The element may therefore be regarded as temporarily responding with an apparently low shear slenderness (L/d for distributed loads). Wave propagation effects over time will change the shear distribution, eventually becoming similar to that of quasi-static loading, and the apparent shear slenderness will increase. Thus, the initial positive effects on the flexural shear capacity of a small shear slenderness will gradually diminish over time. Since the shear slenderness is regarded as constant in [33], it would be of interest

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

to analyse further its gradual change during the initial response phase.

5.2

Suggestions for further research

Due to the complexity of initial shear in concrete structures subjected to suddenly applied loads, further research to gain a better understanding of this area would be worthwhile. Such research may serve as a basis for the development of design recommendations or for providing guidance for upgrades to existing structures. The origin of initial arch action in the shear span should be included in further research. The use of non-linear simulation is a useful tool when analysing the development of the arch mechanism and the gradual change in the apparent shear slenderness over time. Such work should also include the influence of support conditions, element stiffness and load distributions. Furthermore, large moments and shear forces that occur simultaneously in a section may limit the shear capacity of an element. It would therefore be of interest to include the momentshear interaction for different support conditions in future research. Another area of interest is further analysis of the magnitude of the dynamic reactions for impulse-type loads. Since such loads typically have a short duration in relation to the fundamental mode of vibration, such analyses are strongly linked with the initial response of concrete elements.

Acknowledgements The work on this paper was carried out at the Division of Concrete Structures at the KTH Royal Institute of Technology, and was supported financially by Grontmij AB. Their support is gratefully acknowledged by the authors. References 1. Federal Emergency Management Agency: The Oklahoma City Bombing: Improving Building Performance through Multi-Hazard Mitigation. FEMA 277, 1996. 2. Slawson, T. R.: Dynamic Shear Failure of Shallow-Buried Flat-Roofed Reinforced Concrete Structures Subjected to Blast Loading. U.S. Army Engineer Waterways Experiment Station, Technical Report SL-84-7, Vicksburg, 1984. 3. Hughes, G., Beeby, A. W.: Investigation of the effect of impact 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 Reinforced Concrete Beams – An experimental investigation. Swedish Defence Research Agency (FOI), report D 20241-2.6, Sundbyberg, 1994 (in Swedish). 5. Magnusson, J., Hallgren, M., Ansell, A.: Air-blast-loaded, high-strength concrete beams. Part I: Experimental investigation. Magazine of Concrete Research, vol. 62, No. 2, 2010, pp. 127–136. 6. Kishi, N., Mikami, H., Matsuoka, K. G., Ando, T.: Impact behaviour 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 Reinforced Concrete Slabs. Experimental Procedure and Numerical Simulation. Journal of Applied Mechanics, vol. 78, 2011.

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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, John Wiley & Sons, New York, 1974. 10. Mattock, A. H., Hawkins, N. M.: Shear Transfer in Reinforced Concrete – Recent Research. Journal of the Prestressed Concrete Institute, vol. 17, No. 2, 1972, pp. 55–75. 11. Ansell, A., Hallgren, H., Holmgren, J., Lagerblad, B., Westerberg, B.: Concrete Structures. KTH Royal Institute of Technology, report 143, 2012. 12. Granström, S. A.: Analysis of Structures Subjected to Air Blast. Swedish Fortifications Agency, Report 103:18, Stockholm, 1958 (in Swedish). 13. Biggs, J. M.: Introduction to Structural Dynamics, McGrawHill, New York, 1964. 14. Ross, T. J.: Direct Shear Failure in Reinforced Concrete Beams under Impulsive Loading. Air Force Weapons Laboratory, AFWL-TR-83-84, Kirtland, 1983. 15. Hughes, G., Speirs, D. M.: An investigation of the beam impact problem. Cement and Concrete Association, Technical Report 546, London, 1982. 16. Magnusson, J., Ansell, A., Hansson, H.: Air-blast-loaded, high-strength concrete beams. Part II: Numerical non-linear analysis. Magazine of Concrete Research, vol. 62, No. 4, 2010, pp. 235–242. 17. Magnusson, J.: Structural Concrete Elements Subjected to Air Blast Loading. KTH Royal Institute of Technology, licentiate thesis, Bulletin 92, Stockholm, 2007. 18. Svedbjörk, G.: Elastic beam subjected to transient load. Moment and shear distributions in time and space. Swedish Fortifications Agency, pub. 42, Eskilstuna, 1975. 19. Palm, J.: On Concrete Structures Subjected to Dynamic Loading. Swedish Fortifications Agency, Report A4:89, Eskilstuna, 1989 (in Swedish). 20. Kamali, A. Z.: Shear Strength of Reinforced Concrete Beams Subjected 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 concrete at high strain rates. Materials and Structures, vol. 24, 1991, pp. 425–450. 22. Malvar, L. J., Crawford, J. E.: Dynamic increase factors for concrete. 28th Department of Defence Explosives Safety Seminar (DDESB), Orlando, FL, 1998. 23. Malvar, L. J., Crawford, J. E.: Dynamic increase factors for steel reinforcing bars. 28th Department of Defence Explosives Safety Seminar (DDESB), Orlando, FL, 1998. 24. Krauthammer, T., Bazeos, N., Holmquist, T. J.: Modified SDOF Analysis of RC Box-Type Structures. Journal of Structural Engineering, vol. 112, No. 4, 1986, pp. 726–744. 25. Krauthammer, T., Shahriar, S., Shanaa, H. M.: Response of Reinforced 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 Concrete Box Structures Subjected to Airblast Loads. University of Florida, master’s thesis, 2008. 27. Ardila-Giraldo, O. A.: Investigation on the Initial Response of Beams to Blast and Fluid Impact. Purdue University, PhD thesis , West Lafayette, 2010. 28. Andersson, S., Karlsson, H.: Structural Response of Reinforced Concrete Beams Subjected to Explosions. Time Dependent Transformation factors, Support Reactions and Distribution of Section Forces. Chalmers University of Technology, master’s thesis, 2012:103, Gothenburg, 2012. 29. Menkes, S. B., Opat, H. J.: Broken Beams. Experimental Mechanics, vol. 13, No. 11, 1973, pp. 481–486.

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

30. Adamson, B.: Behaviour of Elastic Beams under Action of Detonating Charges with Special Reference to Rotary Inertia and Shearing Forces. Swedish Fortifications Agency, report 109:10, Stockholm, 1955 (in Swedish). 31. Leonhardt, F., Walther, R.: Schubversuche an einfeldrigen Stahlbetonbalken mit und ohne Schubbewehrung. Deutscher Ausschuss für Stahlbeton, pub. 151, Berlin, 1962. 32. Swedish Fortifications Agency: Design of protective structures in reinforced concrete against conventional weapons effects at close range. Pub. 25, Stockholm, 1973. 33. Swedish Fortifications Agency: Design Manual for Protective Construction. Dnr 4535/2011, Eskilstuna, 2011. 34. Magnusson, J., Hansson, H.: Simulations of Air Blast Loaded Structural Reinforced Concrete Elements. Swedish Fortifications Agency, Report FOI-R—1764—SE, Tumba, 2005. 35. Vecchio, F. J., Collins, M. P.: Predicting the Response of Reinforced Concrete Beams Subjected to Shear Using Modified Compression Field Theory. ACI Structural Journal, vol. 85, No. 3, 1988, pp. 258–268.

Johan Magnusson PhD student Grontmij AB, Box 332 SE-631 05 Eskilstuna, Sweden E-mail: johan.magnusson@grontmij.com Tel: +46 10 480 2955 Fax: +46 10 480 2999

Mikael Hallgren Adjunct Professor KTH Royal Institute of Technology Department of Civil & Architectural Engineering Division of Concrete Structures SE-100 44 Stockholm, Sweden

Anders Ansell Professor KTH Royal Institute of Technology Department of Civil & Architectural Engineering Division of Concrete Structures SE-100 44 Stockholm, Sweden

Structural Concrete 15 (2014), No. 1

Technical Paper Xian Liu* Wei Jiang Geert De Schutter Yong Yuan Quanke Su

DOI: 10.1002/suco.201300027

Early-age behaviour of precast concrete immersed tunnel based on degree of hydration concept Using the Hong Kong–Zhuhai–Macao Link project as an example, the focus of this research is to describe the early-age behaviour of a precast immersed tunnel using a constitutive model based on the degree of hydration concept. In this way, the effect of both age and temperature on the early-age behaviour can be taken into account simultaneously. Special attention is also paid to earlyage creep under varying stress levels combined with the degree of hydration concept. Numerical procedures are proposed to predict the early-age behaviour of immersed tunnel segments during the entire fabrication process. The engineering factors related to early-age cracking are analysed and discussed. This in-depth study results in a better understanding, and further appropriate practical measures can be employed to control early-age cracking in the actual project. Keywords: precast immersed tunnel, early-age cracking, degree of hydration, creep under varying stress levels

Introduction

Although the control of early-age cracking in concrete structures is not a new subject, it is still a hot engineering topic concerning the growing demand for durable and sustainable structures. As far as precast concrete immersed tunnels are concerned, the control of early-age cracking seems to be complex in practice and there are always debates when designing or concreting the structures. Engineering practice shows that both the material properties and construction technology are of prime importance for this early-age deterioration. For example, immersed tunnels are normally located in a severe service environment such as exposure to chloride; however, a long service life is still required, normally 100 years. Accordingly, this durability requirement leads to a series of countermeasures related to material properties, which normally include the addition of reactive fillers or the use of a lower water/cement ratio to decrease permeability [1–3]. However, these measures could bring the additional risk of early-age cracking caused by higher heat generation during hydration or larger autogenous shrinkage. Meanwhile, the construction scheme has become one of the most influential

* Corresponding author: xian.liu@tongji.edu.cn Submitted for review: 3 May 2013 Revised: 25 June 2013 Accepted for publication: 9 July 2013

factors for early-age cracking; in this respect, casting and curing temperatures are normally very important for cracking control. For example, in the Øresund Tunnel linking Denmark and Sweden, maximum allowable temperature differences of 15 °C were required to prevent early-age cracking during construction [4]. A requirement of 20 °C was specified for the Busan-Geoje Tunnel in South Korea [5]. Contrasting with the factory fabrication method, the Istanbul Strait immersed tunnel was cast on a floating vessel, and two limiting temperature differences were applied, i.e. 8 °C as an allowable difference and 15 °C as an additional allowance between restrained neighbouring parts [6]. Beyond these construction schemes, a debate concerning the pouring of the concrete is normal when drawing up the construction plan. Which approach is better for early-age cracking control: continuous concreting or block concreting? [7] The above engineering experiences provide insights into the early-age behaviour of precast immersed tunnels. In this respect, numerical models are of great use and normally employed to describe the structural behaviour. For example, heat-development stress calculations were performed for the Øresund Tunnel [4]. An assessment strategy was proposed to reduce the temperature difference during the control of early-age cracking in the Busan-Geoje Tunnel [5]. In the Istanbul Strait immersed tunnel, numerical simulation was conducted prior to commencement of actual concreting works [3]. In similar research studies, Cervera et al. proposed a numerical model concerning concrete curing and applied it to the curing on a viaduct deck of the Øresund Link [8]. Lackner et al. developed a chemoplastic material model for simulating early-age cracking in a roller-compacted concrete dam [9]. Azenha et al. predicted the temperature and stress development during construction of the RC foundation to a wind turbine tower [10]. Benboudjema et al. also developed a numerical model to predict early-age cracking for concrete for nuclear containments [11]. Similar studies have been carried out by Craeye et al. for the case of concrete supercontainers for radioactive waste disposal [12]. The time-dependency of hydration and mechanical properties has to be considered for the above analysis. However, the development of the early-age properties of materials also significantly depends on the temperature [13]. Higher temperatures during early age will lead to faster heat generation, earlier strength, or a higher elastic

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 structures such as immersed tunnels, different parts with the same age may have different early-age properties when taking heat transfer and the resulting internal temperature distribution into account. Moreover, when it comes to the debate about continuous or block concreting, the age-dependent model brings difficulties into the corresponding numerical treatment because different parts will have different ages in continuous concreting. In order to model the fabrication of precast immersed tunnels accurately, the concept of degree of hydration is adopted in this research to ascertain the early-age behaviour of precast immersed tunnels. Based on the thermodynamics of chemically reactive porous media, the degree of hydration concept was developed to describe the performance of early-age concrete macroscopically [15]. It has been proved to be equivalent to the maturity method [16] and has been verified on the microscopic scale [17]. As it integrates age and temperature effects, the degree of hydration concept is further introduced to analyse the behaviour of concrete structures, with attention given to production processes or environmental conditions during early age [18]. So far, most of the mechanical properties of early-age concrete and the basic creep can be successfully described through the degree of hydration [15, 19, 20], where the basic creep normally focuses on the time-dependent increase in strain in hardened concrete subjected to constant stress [21]. However, for massive structures like immersed tunnels, the internal stress is normally caused by temperature-dependent restrained deformation. Or in other words, the stress inside varies over the whole construction procedure, and is also dependent on the concrete creep behaviour under varying stress levels. Using the Hong Kong–Zhuhai–Macao Link project as an example, the focus of this research is to describe the early-age behaviour of a precast immersed tunnel using a constitutive model based on the degree of hydration concept. This will lead to a better understanding of engineering practice, and appropriate measures can be taken to control the early-age cracking during the fabrication of the immersed tunnel. The study is organized as follows: after a general description of the background to the project, the constitutive

model based on degree of hydration is introduced, with special attention given to early-age creep under varying stress levels. The corresponding material parameters are also estimated by way of specific experiments. Afterwards, the early-age behaviour of the immersed tunnel is simulated with respect to its fabrication process. Finally, the engineering factors related to early-age cracking are analysed and discussed.

Project description

The background to this study is provided by the Hong Kong–Zhuhai–Macao Link, a major infrastructure project currently under construction in China. The project links three regions, including Hong Kong, Zhuhai and Macao, and is scheduled to open in 2017. The main structures of the project consist of one cable-stayed bridge, two artificial islands and an immersed tunnel, and the link is one of the longest of its kind in the world, with a total length of 49.968 km. The GZM (Hong Kong–Zhuhai–Macao Link) immersed tunnel consists of 33 elements, varying from 112.5 to 180 m in length and resulting in a total immersed tunnel length of 5664 m. Each standard element consists of eight segments each 22.5 m long joined together by temporary prestressing. The outer cross-section of the segments is 37.96 m wide by 11.4 m high, which is capable of enclosing four lanes and a central escape and services gallery. Fig. 1 shows the basic rectangular cross-section of the immersed tunnel segment. The thickness of the major reinforced concrete sections of the tunnel segment are as follows: 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 life of 120 years in environmental conditions that are aggressive to concrete, such as marine environment and high water pressure. As to the GZM immersed tunnel, it is designed to be watertight without external waterproofing measures such that the water intake of external tunnel elements is strictly prohibited. As a result, in order to protect the reinforced concrete tunnel structure from all aggressive attacks during the specified service life of 120 years, early-age cracking is not permitted. These design requirements in turn result in great challenges related to the fab-

Fig. 1. Basic cross-section of immersed tunnel (unit: cm)

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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

rication of the immersed tube, some of which are listed below. (1) How do the concrete compositions influence the early-age behaviour when considering a service-life requirement of 120 years? The requirement for a service life of 120 years in the GZM tubes means blastfurnace slag must be added as reactive filler and the water/cement ratio reduced for durability. As mentioned, these countermeasures could lead to a higher heat generation during hydration or greater autogenous shrinkage [22, 23], which will introduce uncertainty into the cracking control. It is therefore important to understand their influence on the early-age performance of the immersed tubes. (2) Which kind of casting scheme should be adopted when concreting the precast tubes in the factory? The concrete pouring programme is one of the key strategic decisions before concreting the tubes. The continuous concreting method divides the tubes into several parts and concretes them separately with a time delay, which is a traditional casting method and was employed during the construction of the tunnel [3]. This approach allowed the heat accumulation caused by hydration to be relieved, and the deformation caused by temperature difference thus decreased. The block concreting method involves casting the tubes in a single pour. This approach reduces the fabrication time. Both the Øresund Tunnel [1] and the Busan-Geoje Tunnel [2] have successful experience of this. So, which method is more beneficial for early-age cracking control? Or in other words, does a balance exist between relieving thermal deformation and shortening overall construction time? It is necessary to perform a comparative study before making the final decision. (3) How do the curing conditions influence the early-age behaviour during the fabrication of the immersed tubes? Besides the casting scheme mentioned above, the curing scheme is also one of the widely used practical methods for controlling early-age cracking. The related control conditions normally include the fresh concrete temperature, the conductivity of formwork and the curing temperature, etc. However, how sensitive is crack formation to these control parameters? Or in other words, which condition is more efficient for controlling early-age cracking? In this respect, a sensitivity study is a great help. To answer the above questions, the early-age behaviour of the precast concrete immersed tunnel should be understood in depth and the numerical model employed should be capable of taking the above considerations into account.

3 3.1

Early-age constitutive model based on degree of hydration Degree of hydration concept

The concept of the degree of hydration is adopted to monitor the degree of completion of cement hydration, which can be normalized through the rate of heat production

Structural Concrete 15 (2014), No. 1

during hydration. Normally, the kinetics of hydration can be represented by an Arrhenius law with the form [24] Ea

 Q  qmax f( )e RT

(1)

where: activation energy (J/mol) Ea R universal gas constant (8.314 J/mol K–1) qmax maximum value of heat production rate (J/s) at 20 °C f(α ) evolution of normalized heat production rate as a function of hydration degree α Eq. (1) can be accurately estimated based on hydration tests on the concrete mix. For civil engineering applications, the hydration degree α can be further computed as the ratio between the heat released up to a certain time t and the total heat expected upon completion of the hydration reaction:

(t) 

Q(t) 1  Qtot Qtot

0 q(t) dt

(2)

where α (t) is the degree of hydration at time t. The total heat of hydration Qtot liberated after complete hydration is determined by the cement composition. A practical method to estimate the total cumulated heat for these complex binder systems is to determine experimentally the total heat development Qmax corresponding to the end of the hydration test. So, given the heat generation during hydration for any cementitious material, the corresponding degree of hydration at any time can be approximated by the degree of reaction based on Eq. (3): r(t) 

Q(t) 1  Qmax Qmax

0 q(t) dt

(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 the end of hydration test, can then be estimated practically by experiment. During this work, different hydration tests were conducted first to determine the adequate time period to obtain Qmax. It is shown that the rate of heat liberation 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 degree of reaction r could thus be related to the degree of hydration α via the following equation:

(t)  r(t) ·

Qmax Qtot

(4)

Through the definition given in Eq. (2) or (3), the absolute time, which is normally used to measure the hydration process, can be linked to the concept of hydration or reaction degree. From the normalization, the concept of hydration (reaction) degree reflects the state of the chemical reaction between hydraulic binders and water in macroscopic conditions. In this respect, the concept of hydration degree could be further combined to describe the ear-

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

ly-age properties of cementitious materials such as shrinkage, creep and tensile strength, which will be addressed below.

Early-age constitutive model based on degree of hydration

Many researchers have proposed different approaches to describe early-age concrete properties [16, 25, 26]. As the early-age volume changes are caused by several different mechanisms, an incremental stress-strain law is normally adopted to describe the early-age behaviour of materials, which can be represented as follows:

 n1  D   e  D [  n1   nT1   nsh1   ncr1]

0.4

Poisson's ratio

3.2

0.5

0.3

0.2

0.1

0.0 0.0

(5)

0.2

0.4

0.6

0.8

1.0

Degree of reaction

where: D material stiffness Δεe incremental elastic strain sh , Δε cr Δε Tn+1, Δε n+1 n+1 thermal, shrinkage and creep strain increment respectively These mechanical properties can be related to the degree of hydration as explained below.

3.2.1 Modulus of elasticity and Poisson’s ratio The development of modulus of elasticity is related to the strength. The modulus of elasticity is modelled by the degree of reaction as follows [15]: (6)

Poisson’s ratio is not constant during hardening. Based on the experimental results and the findings mentioned in the literature, a degree of hydration-based model for Poisson’s ratio can be deduced [20].

r  0.5e 10r 2

3.2.3 Shrinkage Autogenous shrinkage strain is obtained in line with Eurocode 2 EN 1992-1-1 [28]. The autogenous shrinkage strain follows from

 ca(t)   as(t) ca(⬁)

(8)

where

 ca(⬁)  2.5( fck  10)106

where: E(r) modulus of elasticity at degree of reaction r E(r = 1) modulus of elasticity at degree of reaction r = 1 r0 percolation threshold for degree of reaction b parameters r0 = 0.25, b = 0.5 for the type of concrete

v(r)  0.18 sin

fore, a constant value equal to 10 με/°C is considered for CTE within the further simulation program.

(9)

and

 as(t)  1  exp(0.2t 0.5)

(10)

where fck is the cylinder strength of the concrete at 28 days and t is given in days. The curve is shown in Fig. 3 as a function of the degree of reaction. 100 90

(7)

where: v(r) Poisson’s ratio at degree of reaction r r 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, normally 15–30 h after casting [27], which has a minor influence on the thermal stresses within the concrete structure. There-

Autogenous shrinkage (µm/m)

r  r0 b E(r) ) ( E(r  1) 1  r0

Fig. 2. Development of Poisson’s ratio

80 70 60 50 40 30 20 10 0 0.0

0.2

0.4

0.6

0.8

1.0

Degree of reaction Fig. 3. Development of autogenous shrinkage over 28 days

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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

Table 1. High-strength concrete composition in kg/m3

W/B

Binding material kg/m3

0.34

Water kg/m3

400

Cement

136

Fly ash

Slag

Gravel

Sand

5∼10 mm

10∼20 mm

kg/m3

497.3

607.9

739.6

* Qualification of superplasticizer: water-reducing ratio of cement mortar = 29.2 %

3.2.4 Creep Some formulas have been developed for basic creep based on the degree of hydration (degree of reaction). A good simulation model for the basic creep of early-age concrete has been investigated by Guenot el al. [29]. The expression for the specific basic creep can be written as follows: C(t  t0, rt ,  )  0(rt ,  )( 0

t  t0 )0.35 1(rt )  t  t0

(11)

where

1(rt )  600rt3 0

(12)

0(rt ,  )  0

1 P (r )(1  P2(rt ) 2 ) 0 E28 1 t0

(13)

Parameter μ1 depends on the degree of hydration rt0 at the moment of loading t0, whereas parameter μ0 also depends on the stress level α at the moment of loading. The creep development is thus influenced by both rt0 and the stress level α. Parameters P1(rt0) and P2(rt0) for the concrete used in the GZM project have been obtained in a creep test: P1(rt )  9.2  109  rt17.87  0.857rt  0.381

(14)

P2(rt )  0

(15)

fc(r = 1) tensile strength at degree of reaction r = 1 r0 percolation threshold for degree of reaction b parameters r0 = 0.25, b = 0.5 for the type of concrete Therefore, the age-dependent behaviour of early-age concrete, such as modulus of elasticity, autogenous shrinkage, creep under varying stress levels and splitting tensile and fracture energy can be modelled as outlined above. So once the age-dependent behaviour of materials at a standard condition is known, the corresponding properties at the real condition can be extrapolated via the link of degree of hydration. In this way, the effects of age and curing temperature can be considered simultaneously.

3.3

Model parameter estimation

According to the degree of hydration-based description for the constitutive model, the related model parameters need to be tested to estimate the input parameters.

3.3.1 Materials High-strength concrete (HSC) is used for the tube. An overview of the HSC, to which fly ash and ground slag are added, is given in Table 1.

3.3.2 Determining the heat of hydration

Creep models for concrete typically predict the evolution of the deformation for a constant stress. However, in reality, stress levels do not remain constant [30], especially during the early-age stage. Accordingly, an incremental calculation model for creep is developed here, which gives a direct relation between stress and strain increment. The fictitious degree of hydration method and principle of superposition have been applied to take into account both the build-up and relieving of stress during the stress development in the tube. More details can be found in [31].

Isothermal hydration tests were performed on cement paste according to the given mix. The tests were carried out at 20 °C and lasted for 14 days. Measurement of the heat production rate q (J/(g · h) proceeds continuously, starting immediately after adding the water. The heat production rates are calculated per unit weight of binder. The first (wetting) peak of the heat production is not considered here. The degree of hydration (degree of reaction) of the mix proportion can be thus obtained (shown in Figs. 4 and 5).

3.3.3 Early-age creep measured on laboratory specimens 3.2.5 Tensile strength The splitting tensile strength of the concrete used in the project is modelled as follows: fct(r) r  r0 c ) ( fct(r  1) 1  r0 where: tensile strength at degree of reaction r fc(r)

Structural Concrete 15 (2014), No. 1

(16)

Concrete specimens used for the creep tests are prisms measuring 100 × 100 × 515 mm. All specimens were cast and stored in a curing chamber at 20 ± 2 °C and > 90 % R.H. for one day. Afterwards, they were removed from their moulds and sealed by means of self-adhesive aluminium sheets in order to prevent moisture exchange with the environment. After being equipped with the measuring devices, each specimen is placed in the creep apparatus immediately, in a controlled atmosphere at 20 ± 2 °C

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 7

Heat production rate (J/gh)

6 5 4 3 2 1

Fig. 6. Shrinkage (left) and creep (right) test setups

0 0

24 48 72 96 120 144 168 192 216 240 264 288 312 336 360

Time (h)

thermal problem is assumed to be independent of the mechanical one. And the corresponding thermal analysis can be described as follows. At an early age, a great deal of heat will be generated as the cement hydrates, and the temperature inside the tubes would vary over time. With the help of heat conduction theory [32], the transient heat conduction within the tubes can be expressed by the following heat diffusion equation:

Fig. 4. Heat production rate q(t) as a function of time 5.0

Heat production rate q (J/gh)

4.5 4.0 3.5 3.0

k  (T )  Q   cT

2.5

1.5 1.0 0.5 0.0 0.0

0.2

0.4

0.6

0.8

1.0

Degree of reaction Fig. 5. Heat production rate q(t) as a function of degree of reaction

and 60 ± 5 % R.H. A sealed dummy specimen is used to monitor the deformations due to temperature changes and autogenous shrinkage (shown in Fig. 6). In order to study the basic creep behaviour at early age, creep tests at constant stress level were carried out for a loading age varying from 12 hours to 14 days. Four groups of concrete compressive creep tests were conducted at different ages of loading (1 d, 2 d, 3 d and 7 d) and lasted for 28 days. The stress/strength ratio at the age of loading is 40 %.

4 4.1

(17)

2.0

Application to precast immersed tunnel Early-age behaviour within the tubes

After defining the early-age behaviour of the materials, the behaviour of the structure could be modelled through the process of heat transfer and the stress increase caused by different volume changes, which is a typical coupled-field problem. As the evolution of the hydration reaction is practically independent of the strains and stresses that develop in concrete, it is usual to consider a unidirectional coupling in which the mechanical analyses are performed after the thermal computations. With such an option, the

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 be represented according to Eq. (1) The sequentially coupled thermal stress analysis is carried out after the heat transfer analysis. As far as the mechanical analysis is concerned, it can only be activated after the thermal model, from which it receives the local temperatures indispensable for computing the thermal strain based on Eq. (3) together with autogenous shrinkage and creep strain. The basic procedure described above for modelling the early-age behaviour of concrete structures will be applied to all the fabrication procedures for the immersed tunnel. The strain and stress that develop in the segments during the first 30 days after the setting phases can thus be predicted. During the numerical simulation, the hydration process is separated by several calculation steps (1…n…). The stress at step n + 1 can be expressed by subtracting the strains due to temperature, shrinkage and creep from the total strain:

 n1  D  [  n1   nT1   nsh1   ncr1]

(18)

where: D stiffness matrix of material Δε Tn+1 thermal stain increment sh , Δε cr Δε n+1 n+1 shrinkage and creep strain increment during step respectively

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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

4.2.1 Thermal analysis

Fig. 7. Finite element mesh for segment

As the degree of hydration is used as a measure of time during the simulation, the behaviour of early-age concrete is modelled as a function of the degree of hydration. The analyses were carried out using a three-dimensional model of the segment, with discretization using 8noded elements. Appropriate attention was paid to ensuring that the thermal and mechanical meshes overlap perfectly, see Fig. 7. The mesh fineness, with respect to mesh sensitivity and accuracy of the simulation results, is checked in a separate numerical study. The details of the study are beyond the scope of this contribution.

4.2

Boundaries

The fabrication of the immersed tunnel can be separated into several stages, each of which can have some kind of influence on the occurrence of early-age cracking. In the proposed numerical model, besides the difference in the degree of hydration at each stage, the boundary conditions should also be changed with different stages. For the GZM Link, the fabrication stages connected to the early-age behaviour can be described as follows. (The other stages, including reinforcing steel cage preparation 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 a continuous or discontinuous process. (2) Indoor curing stage: after several days, the specified formwork striking time, the formwork is struck and the completed segment is ready to be jacked out of the casting pit. During jacking, the segments are supported on 36 active hydraulic jacks connected together in three groups of 12. After jacking, the completed segment is still in the factory building. (3) Outdoor curing stage: after jacking the completed segment through 22.5 m, the following segment can be made. The above process is repeated. When the growing tunnel element is jacked for the third time, the first segment begins to leave the casting hall for further curing outside the factory building. Once eight segments have been cast, they are held together with temporary prestressing cables. The whole element is then pushed further to the dock area in preparation for flotation of the elements inside the basin. According to the above description, the corresponding boundary conditions can be defined below.

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Concerning the thermal analysis, different boundaries were considered depending on the fabrication stages: (1) Casting stage: concerning the formwork adopted for the outer and inner surfaces, which are used as curing measures. Thus the ‘equivalent boundary coefficient’ heq can be modified according to the formwork conductivity properties. For practical use, the formwork layers existing between the tunnel surface and the air may be viewed as associated in series, and the equivalent boundary coefficient can be computed accordingly as heq  (

1  hA

i1 ki Ai )1 n

(19)

where: h heat exchange coefficient between concrete surface and environment (9.9∼17.9 W/m2K) A unit area through which heat transfer occurs Li thickness of each ith layer ki conduction coefficient for each ith layer In the case of steel formwork with a thickness of only millimetres, the equivalent boundary coefficient is computed as 9.9 W/m2K, and 2.6 W/m2K for timber formwork according to Eq. (18). (2) Indoor curing stage: where the formwork is stripped and all the surfaces of segments are assumed to be in direct contact with the air. As the segment is still inside the factory, a heat exchange coefficient heq = W/(m2 · K) and indoor temperature Tin were adopted. (3) Outdoor curing stage: where the segment is pushed outside of the casting hall, a heat exchange coefficient heq = W/(m2 · K) and outdoor temperature Tout were used, which also considers the possible wet burlap/ plastic membrane which covered the outer surface during 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 displacements were restrained at all points on the outline of the base slab. Besides, between the base slab and the bottom formwork, special contact elements were adopted that allow limited sliding at this stage. (2) Indoor and outdoor curing stages: during these later fabrication stages, the base formwork is released, and the segment then rests on six skidding beams positioned underneath the tunnel walls. These supporting concrete beams are continuous over a certain length and are provided with stainless steel plates on top. Six bearing pads per section are placed on each beam so that a total of 36 pads carry one segment. Jacking forwards is performed by pressing against the segment joint, moving the pads along the steel plate. Thus, the points supported by the pads at the base slab are re-

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

strained vertically and the other constraints are released. When applying the above restraint condition to the FEM modelling, different springs are employed to simulate the restraint effect at the corresponding stages. For example, the stiffness coefficient for the springs restraining the vertical displacements is set to be large enough such that no vertical displacement is allowed at the bottom of the base slab. The stiffness coefficient for the springs restraining the horizontal displacements can be calculated as follows: k

N A

(20)

where: μ friction factor N weight of tube A base area of tube tunnel A stiffness coefficient of 3.8 × 105 N/m2 is set during the modelling.

5 5.1

Results and discussion Simulation results

To perform the proposed numerical procedure, a general case was set as the reference one with the fabrication parameters as follows: fresh concrete temperature 20 °C, formwork conductivity 9.9 W/m2K; indoor curing temperature 20 °C, ambient temperature 30 °C. A whole picture of behaviour development during the fabrication stages can thus be plotted in the following.

5.1.1 Temperature field As the length of segment (22.5 m) is larger than the thickness of slabs and walls (1.5 m), it can be expected that the heat transfer essentially occurs in directions X and Y, i.e. the direction of thickness. The evolution of early-age temperatures is predicted numerically on the segment at the

1 day

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 together for comparison. It can be seen from Fig. 8 that the temperature distributions along the base slab, side walls and top slab are symmetrical, with the middle parts having a higher temperature, because the curing conditions both inside and outside the elements are the same during fabrication. It should be pointed out that in Fig. 8 the inner wall temperatures are observed to be lower than those of the other segment elements. This is because the inner wall thickness is less than the other segmental elements, thus less heat cumulates during hydration. As the fabrication stages progress, so the temperature increases at first because of the release of hydration heat. A peak value of 65 °C is reached at the centre of the base slab, side walls and top slab simultaneously at an age of 2.4 days. After demoulding, the temperature at the surface of the segment decreases to the curing temperature until the centre and the surface have the same temperature in the later fabrication stages. To ascertain the influence of the fabrication more clearly, the temperature distribution and variation obtained at the core and near the surface of the side wall are presented in Fig. 9. It can be seen that owing to its large dimensions, the structure undergoes a large increase in temperature, mainly in the core. A maximum temperature of 51.5 °C is reached at an age of 2.4 days. The surfaces experience thermal transfer by convection with the environment and have a lower temperature than the core. A sudden temperature increase is found at an age of 7 days. The reason for this lies in the fact that at this stage the segment is jacked out of the casting hall and the ambient temperature is set higher than that of the indoor curing temperature in the reference case.

5.1.2 Stress field The discussion on the numerical results from the mechanical model is carried out by analysing the normal

2.4 days

5 days

7 days

14 days

28 days

Temperature + 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

Fig. 8. Temperature development at different fabrication stages (1, 2.4, 5, 7, 14 and 28 days)

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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 55

middle surface

Temperature/ oC

50 45 40 35 30 25 20 0

time /d Fig. 9. Temperature distribution and variation along the side wall

stresses that develop over time in the three directions of the finite element mesh: X (horizontal), Y (vertical) and Z (longitudinal). It should be noted that due to the geometry difference of the segment, the stresses σx and σz are of utmost relevance, with greater values (both in tension and compression) than σy. The evolution of stress σx can be observed in Fig. 10. During the heating phase (between pouring and an age of 3 days), and due to the fact that the thermal volumetric expansion of the core is significantly larger than that of the surface areas, tensile stresses arise near the segment surfaces. After 3 days (onset of cooling phase) this process is reversed: the volumetric contraction of the slab core becomes larger than that of the surface areas (due to the higher temperatures in the core); accordingly, compressive stresses develop in the surface and tensile stresses in the core. A detailed analysis of the stress sign inversions is possible by observing Fig. 11, which reproduces the calculated evolution of the horizontal stress for a specific point on the side wall.

1 day

The difference between the surface and core temperatures observed in Fig. 9 generates a system of self-balancing stresses, with tension at the surface and compression at the core. An abrupt change in stress can be found, which is caused by the sudden temperature difference after the segment is jacked outside of the casting hall. However, even in the most unfavourable instance of analysis, compressive stresses σx do not reach 2 MPa. The interpretation of the normal stress σz that develops can be carried out analogously to that for stress σx because the respective volumetric restraints to deformation are quite similar. This resemblance is reflected in the very similar distribution of σx and σz, depicted in Figs. 12 and 13. Nevertheless, as the volumetric restraints in direction X are larger than those in direction Z (see Fig. 11), and so on, normal stress σz is less than σx. In terms of results, attention is drawn to the stresses in the X and Z directions, depicted in Figs. 10 and 12 for 2.4 days when maximum tensile stresses are observed in Figs. 11 and 13. The simulated stress is up to 2.5 MPa at the surface. These larger tensile stresses are the consequence of the higher thermal gradient resulting from the lower thermal insulation value of the formwork.

5.2 Discussion The questions raised relating to the early-age cracking control in section 2 can be answered based on the numerical analysis performed. An index Icr, called the cracking risk index, is defined as the ratio of the principal tensile stress (which is obtained from the numerical modelling) to the splitting tensile strength for comparative study later. Icr 

 1(r) ft(r)

where σ1(r) and f1(r) are the first principal tensile stress and tensile strength at reaction degree r respectively. How several factors influence the structural performance of concrete at an early age is discussed below, considering three types of parameter.

2.4 days

5 days

7 days

14 days

28 days

Fig. 10. Horizontal stress sx development at different fabrication stages (1, 2.4, 5, 7, 14 and 28 days)

Structural Concrete 15 (2014), No. 1

(21)

S, S33 (Avg: 75%) +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

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

5.2.1 Influence of mix design

2.5

surface point at roof

Horizontal stress /Mpa

2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 0

time /d Fig. 11. Horizontal stress development at specific point

Concrete mix design depends not only on durability requirements, but also refers to the performance of early-age concrete. As the heat of hydration is the main origin of earlyage cracking, the rate of releasing this heat and the maximum heat of hydration, depending on the mix design, have an obvious influence on the performance of early-age concrete. Two kinds of concrete with different cement types and content are compared here (see Table 2); these are common mix proportions for massive concrete structures in China. Although there is a minor difference in the W/B between these two mixes, the release of heat of hydration is quite different. Based on the hydration tests, the adiabatic temperature rise of groups I and II is 41.4 and 60.0 °C respectively. More heat and a faster rate of heat release have

2.4 days

1 day

S, S11 (Avg: 75%)

5 days

7 days

14 days

28 days

+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

Fig. 12. Longitudinal stress σz development at different fabrication stages (1, 2.4, 5, 7, 14 and 28 days)

longitudinal stress /Mpa

2.0

surface point at side wall

1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5

time /d Fig. 13. Longitudinal stress development at specific point

been noticed in group II, which is mainly caused by the different types and various components of cementitious materials. Therefore, the influence of concrete mixes is studied based on these two groups. From the simulation of the thermal fields, the temperature development at the corner of a segment for both groups is shown in Fig. 14. It can be seen that the maximum temperature rise is 52.3 °C at 2.7 days and 67.8 °C at 2.47 days for groups I and II respectively. The difference in maximum temperature is nearly 15.5 °C, which is caused by more hydration heat and a much faster rate of heat release in group II. According to the analysis given in section 5.1, dangerous tensile stresses occur on the surface at the corner (shown in Fig. 15). Therefore, the development of the cracking risk index for groups I and II on the surface at the corner are selected to compare the influence of con-

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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

Table 2. Concrete composition in kg/m3

Group

W/B

Binding material kg/m3

Water kg/m3

Cement

Fly ash

Slag

8 Gravel 5∼10 mm

10∼20 mm

Sand

Superplasticizer

kg/m3

0.34

400

136

497.3

607.9

739.6

3.08

0.37

430

160

480

550

760

4.73

1.2

1.0

Group I Group II

Cracking risk index

Temperature (°C)

Group I Group II

0.8

0.6

0.4

0.2

0.0 0.0

0.2

0.6

0.8

1.0

Degree of reaction

Time (Day) Fig. 14. Temperature development on surface of corner

0.4

Fig. 16. Development of cracking risk index at surface of corner

Y Z

First Placement Second Placement Third Placement

Point selected for analysing surface of corner Fig. 17. Casting the segment in three parts Fig. 15. Specific point selected for analysing surface of corner

crete mixes, (shown in Fig. 16). This is obtained from the simulation results of the precast immersed tunnel based on two mix design groups. It is shown that a higher risk is noted for group II during hydration, which is 1.13 at degree of reaction 0.55 compared with 1.04 at degree of reaction 0.42 for group I. The reason is that a higher thermal gradient between the surface and the core have been reached in the case of group II, which leads to a higher cracking risk index.

5.2.2 Influence of casting scheme Block and continuous concreting methods are two common casting methods for massive concrete structures.

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For the continuous concreting method, the simulated segment was divided into three parts, as shown in Fig. 17. The base slab is cast first, followed by the side walls and then the top slab. Intervals of 3 or 7 days are calculated. The block concreting method is simulated for the case where the segments are cast without intervals. The ambient temperature is set equal to 20 °C during fabrication. As mentioned before, the development of the cracking risk index at the surface of a corner, which is the most dangerous point, has been picked up to compare the two casting schemes. As can be seen in Fig. 18, all the cracking risk indexes are < 1.0 for the three cases. The peak values are 0.6 for

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

block concreting and 0.51 and 0.37 for continuous concreting for 3 and 7 days respectively. The difference can be explained by the development of the temperature, which is shown 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 the base slab decreases for the three cases, being 58.1 °C for block concreting and 46.8 and 43.5 °C for continuous concreting for 3 and 7 days respectively. The reason lies in the superimposed effect of the heat of hydration of the base slab and the side wall. The influence is lower when the interval between base slab and side wall is increased. The conduction of hydration heat in the subsequent part could heat up the prior part, which is advantageous for cracking control due to the reduced temperature difference between surfaces and core. On the other hand, the shrinkage stress has obviously increased because the base concrete cast first restrains the wall concrete cast later, resulting in tension stresses in the side walls. The longitudinal stress development – mainly caused by shrinkage of materials – was obtained from the simulation results in Fig. 22.

As shown in Fig. 22, the highest stress is 0.26 MPa for continuous concreting with a 3-day interval, compared with 0.18 MPa for a 7-day interval. Therefore, compared with the block concreting method, continuous concreting has both advantages and disadvantages. The shrinkage stress in the continuous concreting method will increase with the length of segment and roughness of the interface. Meanwhile, the thermal stress is closely related to the bulk and the hydration heat of parts. It is better to take these factors into account when determining the casting scheme.

5.2.3 Influence of curing conditions (1) Fresh concrete temperature Four groups of calculations have been carried out with fresh concrete temperatures of 20, 22, 25 and 28 °C. As before, the development of the cracking risk index at the surface of a corner was picked up for comparison in Fig. 23. The maximum cracking risk index decreased from 1.35 to 1.32, 1.23 and 1.04 when the fresh concrete temperature was decreased from 28 to 20 °C. The reason is

0.7

60 Block concreting Continuous concreting at 3-day intervals Continuous concreting at 7-day intervals

0.6

50 Base slab Side wall Top slab

Temperature (°C)

Cracking risk index

0.5 0.4 0.3 0.2

0.1 0.0

0 0

Time (Day)

Base slab Side wall Top slab

Temperature (°C)

Base slab Side wall Top slab

Temperature (°C)

Fig. 20. Temperature development with 3-day intervals

Fig. 18. Development of cracking risk index at surface of corner in base slab

40 30 20

10 0

Time (Day)

Time (Day) Fig. 19. Temperature development without casting interval

Time (Day) Fig. 21. Temperature development with 7-day intervals

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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 1.4

0.30

1.2 0.25

15°C 20°C 25°C 30°C 35°C

Cracking risk index

1.0

Stress (MPa)

0.20

0.15

0.10

0.05

0.00

0.6 0.4 0.2

3-day intervals 7-day intervals 0

0.8

0.0 0.0

0.2

0.4

0.6

1.0

Fig. 24. Development of cracking risk index at surface of corner in base slab

Fig. 22. Longitudinal stress development in side wall

1.2

1.6 1.4

8.8 W(m2K) 2.6 W(m2K)

1.0

Cracking risk index

20°C 22°C 25°C 28°C

1.2

Cracking risk index

0.8

Degree of reaction

Time (Day)

0.8 0.6

0.8

0.6

0.4

0.4 0.2 0.2 0.0 0.0

0.2

0.4

0.6

0.8

1.0

Degree of reaction

0.0 0.0

0.2

0.4

0.6

0.8

1.0

Degree of reaction

Fig. 23. Development of cracking risk index at surface of corner in base slab

Fig. 25. Development of cracking risk index at surface of corner in base slab

that the maximum thermal stress decreases with the drop in the fresh concrete temperature. When lowering the fresh concrete temperature, the temperature difference inside a segment will decrease for the same adiabatic temperature, and thus the thermal stress can decrease. It is thus shown that controlling the fresh concrete temperature could be an effective way of controlling early-age cracking.

1.23 to 0.51 has been noticed when the curing temperature increased from 15 to 35 °C. It is shown that the segment is much safer when curing at a higher ambient temperature – due to the minor temperature difference between external surface and core. Therefore, it is necessary to maintain the curing temperature as a higher temperature to lower the temperature difference of the concrete structure.

(2) Curing temperature The curing temperature is closely related to the thermal fields in the structure during hydration. A proper curing temperature will maintain the temperature difference between internal and external structure at a lower level, which is significant for the thermal stresses within the concrete. The influence of ambient temperature is obtained from five groups of calculations for which the ambient temperatures are 20, 25, 30 and 35 °C. The development of the cracking risk index at the surface of a corner has been selected for comparison in Fig. 24. An obvious drop in the cracking risk index from

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(3) Conductivity of formwork The conductivity of the formwork has a distinct influence on the thermal exchange during hydration. It is noticed that a lower formwork conductivity is necessary for controlling early-age cracking of concrete structures. Two groups of calculations have been carried out, for which the equivalent boundary coefficients of the internal surface are 8.8 and 2.6 W/m2K respectively. The development of the cracking risk index at the surface of a corner has been selected for comparison in Fig. 25. It is found that the cracking risk index has been significantly reduced from 1.04 to 0.49 when the formwork conductivity is changed from 8.8 to 2.6 W/m2K.

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

A major temperature difference between core and surface of concrete is avoided when the heat insulation is effective, which leads to only minor thermal stresses at an early age.

for early-age cracking control in engineering practice by providing recommendations on the pertinent curing strategy to minimize the cracking risk.

Acknowledgements 6

Conclusion

The early-age behaviour of precast concrete immersed tunnels during fabrication is influenced by the concrete mix design and also by the construction technology. Early-age cracking control represents a great challenge for engineering practice. Numerical analysis is normally employed to investigate the age-dependent behaviour in structures. In this contribution, the degree of hydration concept is considered for the constitutive model of the hardening concrete. This approach allows the effects of both age and temperature on hydration to be taken into account simultaneously. The numerical procedure is described to simulate the early-age behaviour of the precast immersed tubes illustrated. Based on the proposed numerical model, the influences of mix design, casting scheme and curing conditions on the early-age behaviour of the immersed tubes are investigated. It is found that: (1) Mixes with a higher heat of hydration cause a higher maximum temperature and higher cracking risk index in the immersed tube simulated, which means greater difficulty in controlling early-age cracking. And even minor adjustment of the filler content in mix design can be found to influence the tube’s early-age performance via simulation. Thus, when designing mixes, in practice it is necessary to investigate experimentally the influence of mix compositions on the heat released during hydration. (2) Comparing the results of different casting schemes, it can be found that the segmental concreting method will bring about a lower cracking risk index by decreasing the heat accumulation in the immersed segment simulated, which is more noteworthy with a longer time interval between the casting of the different segments. However, the cracking risk in the longitudinal direction will increase as the deformation in the newly cast segment will be restrained by the segment cast previously. The decision concerning the casting scheme normally depends on several factors, however. Therefore, if the block concreting method is employed in practice, more attention – with emphasis on the curing condition – should be paid to controlling early-age cracking. (3) Controlling the fresh concrete temperature, proper curing temperatures and using formwork with a lower conductivity are all factors that could be employed to control early-age cracking. And their specific determination could be analysed using the method described in this work after setting the control criterion referring to the cracking risk index. Moreover, a sensitivity analysis could be conducted to identify their level of influence. To validate the numerical procedure developed in this contribution, full-scale trial casting is now being conducted. After that, the proposed procedure can be further used

The research was financially supported by the National Natural Science Foundation of China, Ref. Nos. 50908167 and 50838004, the National Science and Technology Support Programme, Ref No. 2011BAG07B04, and the Fundamental Research Funds for the Central Universities of China, all of which is gratefully acknowledged.

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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

15. De Schutter, G., Taerwe, L.: Degree of hydration-based description of mechanical properties of early age concrete. Material Structure, 1996, 29, pp. 335–344. 16. De Schutter, G.: Applicability of degree of hydration concept and maturity method for thermo-visco-elastic behaviour of early-age concrete. Cement and Concrete Composites, 2004, 26, pp. 437–443. 17. Bernard, O., Ulm, F. J., Lemarchand, E.: A multiscale micromechanics-hydration model for the early-age elastic properties of cement-based materials. Cement and Concrete Research, 2003, 33, pp. 1293–1309. 18. De Schutter, G.: Finite element simulation of thermal cracking in massive hardening concrete elements using degree of hydration-based material laws. Computation & Structures, 2002, 80, pp. 2035–2042. 19. De Schutter, G.: Degree of hydration based Kelvin model for the basic creep of early-age concrete. Material Structure, 1999, 32, pp. 260–265. 20. De Schutter, G., Taerwe, L.: Fictitious degree of hydration method for the basic creep of early-age concrete. Material Structure, 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 related to the same concrete. Structural Concrete, 2013, 14 (2), pp. 124–130. 22. Ivindra, P., Will, H.: Investigation of blended cement hydration by isothermal calorimetry and thermal analysis. Cement and Concrete Research, 2005, 35 (6), pp. 1155–1164. 23. Antonio, A. M. N., Maria, A. C., Wellington, R.: Drying and autogenous shrinkage of pastes and mortars with activated slag 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-thermochemo-mechanical modelling of concrete at early ages and beyond. Part II: shrinkage and creep of concrete. Journal for Numerical Methods in Engineering, 2006, 67 (3), pp. 332–363. 26. Waller, V., D’Aloia, L., Cussigh, F., Lecrux, S.: Using the maturity method in concrete cracking control at early ages. Cement and Concrete Composites, 2004, 26 (5), pp. 589–599. 27. Loser, R., Münch, B., Lura, B. P.: A volumetric technique for measuring the coefficient of thermal expansion of hardening cement paste and mortar. Cement and Concrete Research, 2010, 40 (7), pp. 1138–1147. 28. EN 1992-1-1:2004: Eurocode 2: Design of concrete structures. 29. Guenot, L., Torrenti, J. M.: Stresses in concrete at early ages: comparison of different creep models. Proc. of international RILEM symposium on thermal cracking in concrete at early ages, pp. 103–110, Spon, London, 1994. 30. Bazant, Z. P.: Mathematical modeling of creep and shrinkage of concrete. John Wiley & Sons Ltd., New York, 1988.

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31. Jiang, W.: Constitutive model of early age concrete and its structural performance. Ghent University, 2012. 32. Incropera, F. P., DeWitt. D. P.: Introduction to heat transfer. Wiley, New York, 2001.

Xian Liu Department of Geotechnical Engineering Tongji University Shanghai 200092, P.R. China E-mail: xian.liu@tongji.edu.cn Tel: +86-(0)21 6598 0234 Fax: +86-(0)21 6598 0234

Wei Jiang School of Materials Science and Engineering Tongji University Shanghai 201804, P.R. China

Geert De Schutter Magnel Laboratory for Concrete Research Department of Structural Engineering Ghent University Ghent B-9052, Belgium

Yong Yuan Department of Geotechnical Engineering Tongji University Shanghai 200092, P.R. China

Quanke Su Hong Kong-Zhuhai-Macao Bridge Authority Zhuhai 519000, P.R. China

Technical Paper Morteza Aboutalebi* Amir M. Alani Joseph Rizzuto Derrick Beckett

DOI: 10.1002/suco.201300043

Structural behaviour and deformation patterns in loaded plain concrete ground-supported slabs The work presented in this paper is considered to be an attempt to contribute towards a better understanding of the structural behaviour of plain concrete slabs under step loading conditions. The Concrete Society Technical Report TR34 “Concrete Industrial Ground Floors” is in its 3rd edition (2003) and is currently under review. TR34 covers the design of concrete ground-supported slabs containing fibres, both steel and synthetic, as an alternative to mesh reinforcement. This work reports on tests carried out at different critical loading locations, including the centre, edges and corners of a 6.0 × 6.0 × 0.15 m deep plain concrete slab. The test results are compared with theoretical values derived using available design codes and other information sources. The results show a notable difference between the test results and the theoretical values. Keywords: ground-supported slab, displacement, crack propagation, bending, punching

Introduction

More than 30 tests on ground-supported slabs were undertaken at the University of Greenwich between 1989 and 1999 using a test rig capable of applying a concentrated load of up to 600 kN (60 t) at any location within an area having maximum dimensions of 11 m long and 3 m wide. The results of these tests were summarized in the proceedings of the 4th and 5th International Colloquiums on Industrial Floors [1], [2]. Further tests using an upgraded ground slab test rig with similar loading capabilities but significantly larger maximum dimensions, 12 m long and 6 m wide, were published in the proceedings of the 2007 Industrial Floors Colloquium [3]. The majority of the test slabs had dimensions of 3 × 3 × 0.15 m deep and were subject to internal, edge and corner loading. In all cases, the loading plates were 100 × 100 mm, which was intended to simulate single- or double-racking leg loads. The loading tests included plain concrete, fabric (mesh), steel and synthetic fibre reinforcement. The majority of tests were on slabs containing steel fibres of variable geometry, including plain, undulating and hook-ended, with fibre contents ranging between 20 and 40 kg/m3.

These tests and others [4] formed the basis for an appendix in the 2nd edition of TR34 (1994) [5], which introduced a plastic approach to the thickness design of concrete ground slabs based on the work of Meyerhof [6]. The 1st edition of TR34 (1988) [7] used an elastic analysis approach for slab thickness design based on the pioneering work of H. M. Westergaard (1926) [8]. The 3rd edition of TR34 was published in March 2003 and the sections on thickness design and the worked examples were undertaken by Beckett and Clarke [9]. These were in an ultimate limit state format and in line with the draft version of Eurocode 2 [10]. The 3rd edition of TR34 pays greater attention to crack control, deflections and load transfer across joints. In addition, significant emphasis is paid to the use of fibres, steel and synthetic, as an alternative to fabric (mesh) reinforcement. The final version of Eurocode 2 [11] was published in 2004 and now incorporates the Jan 2008 corrigendum. The 2003 edition of TR34 is currently being revised and there are several issues that need resolving. These include the fact that the equation for the characteristic flexural strength of plain concrete in the 2004 edition of EC2 gives significantly lower values than those given in TR34 (2003), which uses the draft EC2 formula. TR34 (2003) recommends that the characteristic 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 concrete fctk (0.05) characteristic axial tensile strength of plain concrete (5 % fractile) EC2 (2004) recommends that the following relationship may be used for calculating the mean axial tensile strength of reinforced concrete: fctm(fl) = max [(1.6 – h/1000) fctm]

Eq. 3.23 EC2 (2004)

* Corresponding author: aboutalebi@greenwich.ac.uk

where: h fctm

Submitted for review: 12 June 2013 Revised: 12 June 2013 Accepted for publication: 6 July 2013

The relation given in Eq, (3.23) also applies for the characteristic tensile strength values. Other issues include the

total member depth in mm mean axial tensile strength (TR34, Table 3.1)

M. Aboutalebi/A. M. Alani/J. Rizzuto/D. Beckett · Structural behaviour and deformation patterns in loaded plain concrete ground-supported slabs

influence of ground support on punching failure, design of piled ground slabs and the effect of creep on the long-term flexural strength of concrete, which is not addressed in TR34 (2003). In addition to the above, no reported work has been identified concerning the punching shear failure of steel and synthetic fibre-reinforced slabs larger than 3.0 × 3.0 m. The limitations of a 3.0 × 3.0 m slab with regard to lifting of the corners and edges were observed during 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 of Greenwich provided the opportunity to cast test slabs with a much larger plan area and more in line with industry practice. Similar to the previous rig, the new facility is capable of applying a load of up to 600 kN (60 t) at any position and the plan dimensions of the test slabs can be increased 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 deep slab tests started in March 2010. One of the main reasons for constructing ground slabs on this scale was to investigate the limitations of the smaller slabs referred to above [12]. In February 2011 the second phase of testing was realized with synthetic fibres [13]. The plain concrete slab was subjected to central, edge and corner loading during the testing. Further tests are planned, including mesh-reinforced concrete.

Fig. 1. CBR-equivalent plate testing of re-engineered soil

The ground slab testing facility is comprised of a flat bed over which a slab can be cast. A single point load can be applied to the test slab via a compressor attached to a transverse plate girder spanning over the slab. The transverse girder can be moved back and forth two steel-plated ground beams, spaced at 8.5 m centres. These ground

(a)

(b)

(c)

(d)

Fig. 2. (a) to (d): concrete placement and cast slab

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Test facility apparatus

M. Aboutalebi/A. M. Alani/J. Rizzuto/D. Beckett · Structural behaviour and deformation patterns in loaded plain concrete ground-supported slabs

beams run either side of the test rig and are restrained against uplift by tension piles. The ground beams are 16 m long and so the point load can be located anywhere within a 6 × 12 m surface area of a slab.

2.1

Ground conditions

The soil type within the test rig can be readily modified by excavation and reinstatement. This exercise can modify the soil compaction level to give any desired compressible conditions. In April 2010 the ground conditions were modified and subsequently re-evaluated using a plate-equivalent CBR test in line with BS 1377, Part 9, 4.1 [14]. The modulus of subgrade reaction k, modified for plate diameter, was found to vary from 44 to 55 MPa/m. Figs. 1 and 2 depict the process of the ground improvement work carried out for the investigation together with the concrete placement and casting of the plain concrete slab.

2.2

Fig. 3. Overview of testing facility together with test in progress, centre punch load application point on slab

Slab loading procedure

The load was applied to the ground-supported slab at a constant rate by the electronic control of the hydraulic compressor. As the load was applied, a load pressure cell, located between hydraulic jack and load plate, recorded the load to which the slab was being subjected. The deflection of the slab was recorded with linear variable differential transducers (LVDTs) at the load point and at various other locations across the slab surface. Figs. 3, 4 and 5 show detailed views of the regions where the load was applied. The precise location of the deflection monitors and the load point was varied in each test (see Fig. 6 and specific load tests for details).

Tests

The slab was cast on 11 January 2012. The following concrete specification was used: – Strength class of concrete C32/40 in accordance with Table 9.1 of TR34 (2003) with a maximum water/cement ratio of 0.55

Fig. 4. Test in progress, 150 mm edge load application point on slab

CBR tests on the subsoil supporting the slab area gave an average modulus of subgrade reaction k = 0.05 N/mm3.

3.1

Slab loading tests

Loading on the slab commenced after a minimum curing period of 28 days and five tests were undertaken with one internal, two edge and two corner loading locations. The load locations were as shown in Fig. 4. The positions of displacement transducers and acoustic sensors are depicted later in the text under the discussion of results as shown in Fig. 5. The 100 × 100 mm steel loading plate was sandwiched between a similar-sized plywood spreader plate to counteract any unevenness on the concrete surface and the 200 × 200 mm steel plate on which four transducers were placed (1–4). The load control was automated and the loading jack was connected via a top plate to the reaction beams. A general view of the test area including the cover, the 6.0 × 6.0 × 0.15 m concrete slab and reaction beams can be seen in Figs. 2 and 3.

Fig. 5. Test in progress, 300 mm edge load application point on slab

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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

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

loading carried out at 49 day; test 5, 150 mm corner loading 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 loading locations) with comments on the modes of failure depicted.

Fig. 6. Loading locations on 6.0 × 6.0 × 0.15 m deep slab

3.2

Compressive strength tests

A total of nine 150 × 150 × 150 mm cubes were tested. The 28-day average compressive strength results are shown in Table 1. The concrete cubes and cylinders were tested at the time the particular slab tests were carried out in order to enable accurate comparison of the experimental and theoretical outputs. The following ages of concrete were used in this work: Ground slab cast on 11 January 2012, test 1, centre loading, test 2, 150 mm edge loading, test 3, 300 mm edge loading, all carried out at 28 days; test 4, 300 mm corner

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 the acoustic sensors utilized during the test. The failure load was 479 kN and no cracks were visible on the top surface of the slab at failure. Deflections due to step loading conditions at the punching shear failure mode are shown in Figs. 8 and 9. Fig. 10 depicts the crack propagation profiles at 300 kN load and 479 kN at failure. Fig. 11 shows surface deformation profiles achieved under 300 kN load and 479 kN at failure. The Meyerhof value for bending is 232.1 kN and for punching shear 290.3 kN. Membrane action influences the failure load for central loading and, further, the use of d = 0.75 h = 112.5 mm for

Table 2. Summary of results for slab tests 1–5 with comments on crack formation

Test

Load at first crack (kN)

Load at failure (kN)

Average deflection (mm), transducers 1–4 at first crack

at failure

Test No. 1 Internal centre punch load (28 days)

–

479.0

–

–5.54

Test No. 2 Edge 1 – 150 mm (28 days)

12.6

407.0

0.5

–18.75

Test No. 3 Edge 2 – 300 mm (28 days)

10.9

443.0

0.5

–18.82

Test No. 4 Corner 1 – 300 mm (49 days)

10.5

262.3.0

0.7

–16.85

Test No. 5 Corner 2 – 150 mm (70 days)

20.0

192.0

1.4

–12.25

Comments

No cracks visible on surface of slab at failure – punching shear mode.

Vertical cracks on side of slab gradually widening with increase in load followed by circumferential & radial cracks up to failure. Vertical cracks followed by circumferential cracks with punching-type failure at 443 kN. Circumferential cracks apparent.

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At failure circumferential, radial & vertical cracks (sides) & punching.

M. Aboutalebi/A. M. Alani/J. Rizzuto/D. Beckett · Structural behaviour and deformation patterns in loaded plain concrete ground-supported slabs

Fig. 7. Central loading location and positions of sensors 08/02/2012

Centre Punch Test W-E Axis

1 0

Depth (mm)

-1 100kN

-2

200kN -3

300kN 400kN

-4

478kN

-5 -6 -3000

-2000

-1000 0 1000 Sensor Posi on (mm)

2000

3000

Fig. 8. Displacement plotted against position along axis 1 (W-E) caused by incremental step loading

the effective depth of the slab is conservative (TR34, 2003). See Table 3 below for all theoretical and test results. Test No. 2 – edge loading (150 mm) Fig. 12 depicts the loading position together with the locations of the displacement transducers and the acoustic sensors utilized during the test. For test No. 2, the loading plate was centred 150 mm from the slab edge. Vertical cracks appeared on the side of the slab, which gradually widened as the load increased, followed by circumferential and radial cracks leading to punching failure at 407.0 kN. Figs. 13 and 14 show the deflections recorded as a result of step loading applied at the edge of the slab.

Test No. 3 – edge loading (300 mm) Fig. 6 depicts the loading position together with the locations of the displacement transducers and the acoustic sensors utilized during the test. For test No. 3, the loading plate was centred 300 mm from the slab edge. Vertical cracks appeared on the side of the slab, which gradually widened as the load increased, followed by circumferential and radial cracks leading to punching failure at 443.3 kN. Figs. 15 and 16 show the deflections recorded as a result of step loading applied at the edge of the slab. Test No. 4 – corner loading (300 mm) Fig. 6 depicts the loading position together with the locations of the displacement transducers utilized during the test.

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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 08/02/2012

Centre Punch Test N-S Axis

1 0

Depth (mm)

-1 100kN

-2

200kN -3

300kN 400kN

-4

478kN

-5 -6 -3000

-2000

-1000 0 1000 Sensor Posi on (mm)

2000

3000

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

145

750

1500

2250

300000 -2250 -1500 -750 -145 0

145 750 1500 2250 3000

-3000

-2250

-1

-1500

-750

-145

145

750

1500

2250

300000 -2250 -1500 -750 -145 0

145 750 1500 2250 3000 -1

2 3 4 5 6

Displacement (mm)

-1-0 0-1 1-2 2-3 3-4 4-5 5-6

3 4 5 6

Displacement (mm) -1-0 0-1 1-2 2-3 3-4 4-5 5-6

Fig. 11. Surface deformation profiles achieved under 300 kN load and 479 kN at failure

For test No. 4, the loading plate was centred 300 mm from the slab corner and circumferential cracks first appeared at 10.5 kN. As the load increased, so circumferential and radial cracks appeared, followed by vertical

Structural Concrete 15 (2014), No. 1

cracks on the side of the slabs, with punching failure at 262.3 kN. Figs. 17 and 18 illustrate the displacements recorded with respect to step loading conditions applied in both axes.

M. Aboutalebi/A. M. Alani/J. Rizzuto/D. Beckett · Structural behaviour and deformation patterns in loaded plain concrete ground-supported slabs

Fig. 12. Edge loading position 300 mm from edge of slab

Edge 150 Test N-S Axis 5

Depth (mm)

-5

100kN 200kN 300kN

-10

400kN 407kN

-15

-20 -3000

-2000

-1000 0 1000 Sensor Posi on (mm)

2000

3000

Fig. 13. Displacement plotted against position along axis 1 (N-S) caused by incremental step loading

Test No. 5 – corner loading (150 mm) Fig. 19 depicts the loading position together with the locations of the displacement transducers utilized during the test. For test No. 5, the loading plate was centred 150 mm from the slab corner and circumferential cracks first appeared at 20.0 kN. As the load increased, so circumferential and radial cracks appeared, followed by vertical cracks on the side of the slabs, with punching failure at 192.0 kN. Figs. 20 and 21 illustrate the displacements recorded with respect to step loading conditions applied in both axes.

Theoretical calculations

Theoretical calculations for the five tests were undertaken in 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

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M. Aboutalebi/A. M. Alani/J. Rizzuto/D. Beckett 路 Structural behaviour and deformation patterns in loaded plain concrete ground-supported slabs 08/02/2012

Edge 150 Test W-E Axis

Depth (mm)

-5

100kN 200kN 300kN

-10

400kN 407kN

-15

-20

500

1000

1500 2000 Sensor Posi on (mm)

2500

3000

3500

Fig. 14. Displacement plotted against position along axis 2 (W-E) caused by incremental step loading 08/02/2012

Edge 300 Test N-S Axis

Depth (mm)

-5

100kN 200kN 300kN

-10

400kN 443kN

-15

-20 -500

500

1000 1500 2000 Sensor Posi on (mm)

2500

3000

3500

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)

Edge 300 Test W-E Axis 5

Depth (mm)

-5

100kN 200kN 300kN

-10

400kN 443kN

-15

-20 -3000

-2000

-1000 0 1000 Sensor Posi on (mm)

2000

3000

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)

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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 29/02/2012

Corner 300 Test North Face

10 5

Depth (mm)

0 50kN -5

100kN 150kN

-10

200kN 250kN

-15 -20

200

400

600 800 1000 Sensor Posi on (mm)

1200

1400

1600

Fig. 17. Displacements recorded as a result of step loading at the loading position 300 mm from the edge

29/02/2012

Corner 300 Test West Face

10 5

Depth (mm)

0 50kN -5

100kN 150kN

-10

200kN 250kN

-15 -20

200

400

600 800 1000 Sensor Posi on (mm)

1200

1400

1600

Fig. 18. Displacements recorded as a result of step loading at the loading position 300 mm from the edge.

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

νmax = 0.5 k2 ƒcd

Eq. 9.28

where: ƒcd design concrete compressive strength (cylinder) = ƒck/γc

For a true free corner load with a/l = 0: Pu = 2 Mn

In accordance with the draft of Eurocode 2, irrespective of the amount of any reinforcement in the slab, the shear stress at the face of the contact area should not exceed a value νmax given by

Eq. 9.12a

k2 = 0.6 (1 – ƒck/250)

a/l > 0.2: Pu = 4.0 Mn/[1 – (a/l)]

where: ƒck characteristic concrete compressive strength (cylinder)

For punching shear, section 9.11 of TR34 (2003) was adopted using Eqs. 9.28 to 9.33 and Fig. 9.11.

Hence, the maximum load capacity in punching Pp,max is given by

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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

Fig. 19. Corner loading position at 150mm from edge of slab

21/03/2012

Corner 150 Test West Face

4 2 0

Depth (mm)

-2 -4

50kN

-6

100kN 150kN

-8

192kN

-10 -12 -14

200

400

600 800 1000 Sensor Posi on (mm)

1200

1400

1600

Fig. 20. Displacement plotted against position along axis 1 west face due to different loading conditions

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 mm Modulus of subgrade reaction k = 0.05 N/mm3 – average CBR = 8.325, see TR34 (2003), Fig. 6.2 – ‘CBR percentage’ vs. ‘k’ N/mm3 For all five tests, ν = 0.2 – Poisson’s ratio, see TR34 (2003)

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

Structural Concrete 15 (2014), No. 1

For test 4 fcu fck fctk (0.05) Ecm

(49 days) = 46.8 N/mm2 (average) = 37.6 N/mm2 – see Table 3.1, EC2 (2004) = 2.36 N/mm2 = 34.7 kN/mm2

For test 5 (70 days) = 51.7 N/mm2 (average) fcu fck = 40.1 N/mm2 – see Table 3.1, EC2 (2004)

M. Aboutalebi/A. M. Alani/J. Rizzuto/D. Beckett · Structural behaviour and deformation patterns in loaded plain concrete ground-supported slabs 21/03/2012

Corner 150 Test North Face

4 2 0

Depth (mm)

-2 -4

50kN

-6

100kN 150kN

-8

192kN

-10 -12 -14

200

400

600 800 1000 Sensor Posi on (mm)

1200

1400

1600

Fig. 21. Displacement plotted against position along axis 2 north face due to different loading conditions

fctk (0.05) = 2.46 N/mm2 Ecm = 35.2 kN/mm2 The summary of calculations tabulated in Table 3 is based on TR34 (2003). However, the characteristic strength of plain concrete was calculated using EC2 (2004) for comparison purposes. From TR34 (2003), the characteristic flexural strength 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

For tests 1–3: = 12.79 kNm/m Mn Mp = 12.79 kNm/m Mp + Mn = 25.58 kNm/m For test 4: Mn = 12.70 kNm/m Mp = 12.70 kNm/m Mp + Mn = 25.40 kNm/m For test 5: Mn = 13.25 kNm/m Mp = 13.25 kNm/m Mp + Mn = 26.50 kNm/m

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 mm square 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 automatically. As there was no reinforcement present, using Eq. 9.6 (TR34, 2003), the positive and negative moments (Mp and Mn) are taken as equal and are as follows:

Table 3 depicts the theoretical values for bending using the Meyerhof equations together with the punching shear values in comparison with the test results. By reference to Tables 2 and 3, the disparity between the test results and those obtained from TR34 (2003) for punching are apparent. In 1997 Shentu et al. [15] used a finite element model, assuming a Winkler slab, to develop a simple formula to determine the load-carrying capacity of a plain concrete slab on grade subjected to an interior concentrated load. The load capacity P can be expressed as P = 1.72 [(k · r/Ec) × 104 + 3.6] f1t · h2 where: k modulus of subgrade reaction r radius of loaded area Ec modulus of elasticity of concrete f1t uniaxial tensile strength of concrete h 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

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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

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. 1 Internal centre punch load (28 days)

232.1

290.3 (face) 124.5 (critical section)

–

479.0

Test No. 2 Edge 1 (150 mm) (28 days)

72.6

217.7 (face) 77.4 (critical section)

–

407.0

Test No. 3 Edge 2 (300 mm) (28 days)

79.6

217.7 (face) 89.7 (critical section)

–

443.0

Test No. 4 Corner 1 (300 mm) (49 days)

45.8

143.8 (face) 76.3 (critical section)

–

262.3

Test No. 5 Corner 2 (150 mm) (70 days)

43.7

151.7 (face) 58.8 (critical section)

–

192.0

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 test value of 479.0 kN. The work of Shentu et al. did not include edge or corner loading and the slab tested was circular.

Acknowledgements The authors would like to express their thanks to Ian Cakebread, Tony Stevens, Bruce Hassan and Marc Van De Peer for setting up the test rig, installing instrumentation, carrying out the loadings and recording the results for the tests. References

Discussion of results

With the load centred at 300 mm from the edge of the slab, the failure load of 443 kN was 92 % of the internal load condition (479.0 kN), whereas the failure load for 150 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 crack was 84 % of that for test No. 3. A similar pattern emerged for test Nos. 4 and 5. The load at first crack for test No. 4 was 47.5 % of that for test No. 5, and the failure load percentage was 63 %. This demonstrates that, in practice, placing racking legs closer than 300 mm from the edges or corners of a ground slab should be avoided if there is no load transfer to adjacent slabs or beams.

Conclusions

The calculations are summarized and it is apparent that the theoretical failure loads are significantly lower than the test values. The results of this research clearly demonstrate the significance of tests at similar scales to those used in practice. The results were conclusive in overcoming the limitations of a 3.0 × 3.0 m slab with regard to lifting of the corners and edges as observed and reported in the earlier works. The significance of loading positions on the edges and corners of slabs in terms of ultimate shear failure achieved has been clearly demonstrated.

Structural Concrete 15 (2014), No. 1

1. Beckett, D.: A comparison of thickness design methods for concrete industrial ground floors. Technische Akademie Esslingen, 4th International Colloquium, 12–14 Jan 1999, Industrial Floors 99, vol. 2, p. 159. 2. Beckett, D.: Strength & serviceability design of concrete industrial ground floors. Teknische Akadamie Esslingen, 5th International Colloquium, 21–23 Jan 2003, Industrial Floors 03, vol. 2, p. 601. 3. Beckett, D.: Concrete ground slab test facilities at the University of Greenwich: an update. Technische Akademie Esslingen, 6th International Colloquium, 16–18 Jan 2007, Industrial Floors 07, vol. 2, p. 707. 4. Falkner, H., Teusch, M.: Comparative investigations of plain and steel fibre reinforced industrial ground slabs. TU Braunschweig, 1993. 5. The Concrete Society, Technical Report 34, Concrete industrial ground floor slabs – a guide to their design and construction, 2nd ed., 1994. 6. Meyerhof, G. G. W.: Load-carrying capacity of concrete pavements. Journal of the Soil Mechanics & Foundations Division. Proc. of American Society of Civil Engineers (ASCE), vol. 88, Jun 1962, pp. 89–166. 7. The Concrete Society, Technical Report 34, Concrete industrial ground floor slabs – a guide to their design and construction, 1st ed., 1988. 8. Westergaard, H. M.: Stresses in concrete pavements computed by theoretical analysis. Public Roads, vol. 7, No. 2, Apr 1926. 9. The Concrete Society, Technical Report 34, Concrete industrial ground floor slabs – a guide to their design and construction, 3rd ed., 2003.

M. Aboutalebi/A. M. Alani/J. Rizzuto/D. Beckett · Structural behaviour and deformation patterns in loaded plain concrete ground-supported slabs

10. British Standards Institution, BS EN 1992-1, Draft Eurocode 2, Design of concrete structures – Part 1: General rules and rules for buildings. 11. British Standards Institution, BS EN 1992-1-1: 2004 (incorporating corrigendum Janu 2008), Eurocode 2: Design of concrete structures – Part 1-1: General rules and rules for buildings. 12. Alani, A. M., Beckett, D., Khosrowshahi, F.: Mechanical behaviour of a steel fibre reinforced concrete ground slab. Magazine of Concrete Research, ICE, 2012, pp. 1–12. 13. Alani, A. M., Beckett, D.: Mechanical Properties of a large Scale Synthetic Fibre Reinforced Concrete Ground Slab. Journal of Construction and Building Materials, vol. 41, Apr 2013, pp. 335–344. 14. BS 1377, Part 9: Methods for test for soils for civil engineering purposes – in situ tests; 1990. 15. Shentu, L., Jiang, D., Hsu, C. T. T.: Load-carrying capacity for slabs on grade. ASCE Journal of Structural Engineering, Jan 1997.

Dr. Morteza Aboutalebi B.Sc. (Hons), M.Sc. (Distinction), Ph.D Senior Lecturer, Department of Civil Engineering School of Engineering University of Greenwich Central Avenue, Chatham Maritime Kent. ME4 4TB, UK Tel: +44(0)1634883019 Email: aboutalebi@gre.ac.uk

Professor Amir Alani BSc (Hons), MSc, PhD, CEng, FIMechE, FHEA, MCIHT Head of Department of Civil Engineering The Bridge Wardens’ Chair in Bridge and Tunnel Engineering School of Engineering University of Greenwich Central Avenue, Chatham Maritime Kent. ME4 4TB, UK Tel: +44(0)1634 883293 Email: m.alani@gre.ac.uk Dr Joseph Rizzuto BSc, MSc, PhD, CertEd, CEng, MICE, MIStructE, MCIHT Deputy Head Department of Civil Engineering University of Greenwich Department of Civil Engineering Faculty of Engineering & Science Central Avenue, Chatham Maritime Kent ME4 4TB, UK Email: j.rizzuto@gre.ac.uk Tel. +44(0) 1634 883584 Fax. +44(0) 1634 883153

Derrick Beckett BSc Eng, MPhil, PhD, CEng, MICE, MCIOB Visiting Professor, Department of Civil Engineering School of Engineering University of Greenwich Central Avenue, Chatham Maritime Kent. ME4 4TB, UK

Structural Concrete 15 (2014), No. 1

Technical Paper Ali A. Abbas* Sharifah M. Syed Mohsin Demetrios M. Cotsovos

DOI: 10.1002/suco.201300004

Non-linear analysis of statically indeterminate SFRC columns 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 this work is the consideration of statically indeterminate SFRC columns. Most of the SFRC specimens studied in the literature are simply supported beams, and information on statically indeterminate columns is sparse. In addition, both axial and lateral loads were considered in order to allow for compression and flexural effects on the columns. The aim of the work was to examine the potential for using steel fibres to reduce the amount of conventional transverse steel reinforcement without compromising ductility and strength requirements. To achieve this, the spacing between shear links was increased while steel fibres were added as a substitute (spacing between shear links increased by 50 and 100 % with fibre volume fraction Vf increased to Vf = 1, 1.5, 2 and 2.5 %). The numerical model was carefully calibrated against existing experimental data to ensure the reliability of its predictions. Parametric studies were subsequently carried out, which provided insight into how the steel fibres can help reduce the number of conventional shear links. Keywords: fibre-reinforced concrete, finite element methods, structural analysis

Introduction

Due to the inherent brittle nature of plain concrete, steel fibres are usually provided as a means of enhancing ductility. This paper presents the results of numerical investigations of steel fibre-reinforced concrete (SFRC) twospan columns using non-linear finite element analysis (NLFEA). This arrangement was chosen to allow for a study of statically indeterminate SFRC columns, which has been addressed only occasionally as most of the research work reported in the literature focuses on simply supported beams [1–4]. Axial loads have also been considered (in addition to lateral loads as depicted schematically in Fig. 1), so both compression and bending responses can be modelled (again, previous work predominantly focused on lateral loads on beams). A key issue assessed is the potential for steel fibres to contribute to a reduction in conventional transverse rein* Corresponding author: abbas@uel.ac.uk Submitted for review: 18 January 2013 Revised: 22 August 2013 Accepted for publication: 22 August 2013

forcement without compromising ductility and strength requirements. In this respect, the spacing between shear links was increased while steel fibres were added to see whether or not the loss of strength can be compensated for in this way. This is particularly useful in situations where the conventional transverse reinforcement required can lead to congestion of shear links, e.g. in seismic design [5]. The NLFEA investigations provided insights into how the steel fibres can help reduce the number of conventional shear links. The effect of the steel fibres was directly modelled into an existing concrete material model employed in the ABAQUS [6] software package to describe its non-linear behaviour. This is achieved through appropriate modification of the stress-strain relationship of concrete in uniaxial tension. Initially, column specimens investigated experimentally by Kotsovos et al. [7] were selected to calibrate the numerical model and thus ensure the reliability of its predictions. The experimental data was useful in providing a benchmark to validate the FE results; however, the range of fibre content considered was limited. The present research work, on the other hand, covers the full practical range of fibre contents and reduction in the number of stirrups. Therefore, once the calibration work was concluded, full NLFEA-based parametric studies were subsequently carried out with the spacing between shear stirrups increased by 50 and 100 %, whereas the fibre volume fraction Vf was increased to Vf = 1, 1.5, 2 and 2.5 % to see whether or not fibres can compensate for the reduction in transverse reinforcement. The original stirrup spacing was 40 and 140 mm at support and midspan regions respectively, as depicted in Fig. 1. Thus, the additional spacings adopted were 60 and 210 mm and 80 and 280 mm, corresponding to 50 and 100 % increases respectively. Similarly, the fibre contents used were 80, 120, 160 and 200 kg/m3, corresponding to Vf = 1, 1.5, 2 and 2.5 % 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 high amounts (i.e. Vf > 2%) must be tempered by practical considerations such as workability issues, which are usually addressed by adding water-reducing admixtures. It is also common to use fly ash, slag or silica fume to facilitate the inclusion of fibres and improve workability. Adjustments to the mix design is often needed as well to accommodate high fibre contents, and the mixing method should consider the type and content of fibres used in order to ensure

A. A. Abbas/S. M. Syed Mohsin/D. M. Cotsovos · Non-linear analysis of statically indeterminate SFRC columns

P N

N = constant axial load P = monotonic lateral load Inflexion point Fig. 1. Idealization of SFRC continuous column under gravity and lateral loads

uniform distribution (however, this is beyond the scope of this paper).

Constitutive models for SFRC and numerical modelling strategy

The failure of plain concrete is governed by crack formation (when the maximum principal tensile stress exceeds the tensile strength of the concrete), which continue to extend as the load is increased. In SFRC, after the onset of cracking, the fibres provide a crack-bridging effect to resist further crack opening. There are different potential failure modes depending on the effectiveness of the fibres in bridging the cracks. In order to model the structural response of SFRC structural members, key characteristics were studied and corresponding constitutive models were examined. The effects of fibres were modelled by modifying existing models for plain concrete already available in the ABAQUS software package. In this respect, the “brittle cracking model” in ABAQUS [6] is currently adopted to describe brittle material behaviour dominated by tensile cracking, as is the case for structural concrete. A summary of the constitutive models and the FE modelling strategy is provided next.

2.1

ial tension stress-strain relationships proposed in the model are  2  for(0     to )    ft 2  / to   / to       ft 1  1  ftu/ft    to/ t1   to  for( to     t1)     for( t1     tu)    ftu



 





(1)

where: ft and εto ultimate tensile strength and strain (i.e. at onset of cracking) respectively ftu and εt1 residual strength and corresponding strain of SFRC, defined as [13] ftu   · Vf ·  d · L/d and  t1   d · L/d · 1/Es

(2)

where: η fibre orientation factor that takes account of the three-dimensional (3D) random distribution of the fibres, which takes values between 0.405 and 0.5 [14] Vf fibre volume fraction τd bond stress between concrete and steel fibres L/d aspect ratio of steel fibres modulus of elasticity of steel fibres. Es

Tensile behaviour 2.2

The structural response of SFRC elements is characterized by their tensile post-cracking behaviour. A number of constitutive models available for SFRC have been identified, 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 describe the uniaxial tensile stress-strain relationship of SFRC. In particular, they depict the effect of SFRC on the post-cracking behaviour of concrete from the brittle sharp drop associated with plain concrete to either a tension softening or hardening response depending on fibre content, fibre geometry and shape and bond stress. In these models the residual strength beyond the cracking point of the concrete is made up of two components: the steel fibres bridging the crack and the concrete matrix followed by the pull-out phase (i.e. bond failure). The main characteristics of the models were closely studied and a calibration study was undertaken by Syed Mohsin [15] and Abbas et al. [16, 17] using NLFEA to examine these models and, consequently, the one proposed by Lok and Xiao [14] was selected for the subsequent parametric studies. The uniax-

Compression behaviour

Previous work on SFRC [8, 9, 12, 14] suggests that the compression behaviour of SFRC can be conveniently assumed to be similar to that of plain concrete. Investigations carried out by Bencardino et al. [18] support this conclusion, as the observed results show that the addition of steel fibres does not significantly affect the compressive strength of the concrete (with the potentially improved ultimate strain safely ignored). However, it should be borne in mind that there are several other studies in which an increase in the compressive strength was attained by adding fibres, plus enhanced ductility in compression [19]. Therefore, in the present work, the steel fibres are conservatively considered to have no effect on the compression behaviour 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 aggregate interlock and dowel action. Fibres have a similar

Structural Concrete 15 (2014), No. 1

A. A. Abbas/S. M. Syed Mohsin/D. M. Cotsovos · Non-linear analysis of statically indeterminate SFRC columns

effect on shear response (i.e. in a direction parallel to the crack) and therefore it was modelled using the “shear retention” part of the ABAQUS (2007) concrete model [9, 15, 17]. The shear stiffness of concrete decreases as cracks propagate. Therefore, in order to allow for a degradation in shear stiffness due to crack propagation, the shear modulus was reduced in a linear fashion from full shear retention (i.e. no degradation) at the cracking strain to 50 % at the ultimate tensile strain.

2.4

FE modelling strategy

The ABAQUS software package offers a few material models for the non-linear analysis of plain concrete and associated cracking processes. The models also allow for the effect of “tension stiffening” to be included (an effect related to the stiffness provided by concrete between cracks or interaction between concrete and reinforcement). This is effectively achieved by modifying the postcracking tensile stress-strain diagram. Therefore, this was conveniently used to input the tensile constitutive models for SFRC. The shear retention values were also adjusted as explained above. The concrete medium was modelled by a mesh of 8-node 3D brick elements, whereas 2-node 1D bar elements representing conventional steel reinforcing bars and shear links were included to mimic the actual arrangement in the specimens modelled (e.g. cover allowed for). The steel properties were modelled using the stress-strain relation recommended in Eurocode 2 [20]. An ultimate tensile strain was also defined to detect any failure of the steel main bars or stirrups. The cracking process that concrete undergoes is modelled by the smeared crack approach. A crack forms when the predicted value of stress developing in a given part of the structure corresponds to a point in the principal stress space that lies outside the surface defining the failure criterion for concrete, thus resulting in localized material failure. The plane of the crack is normal to the direction in which the largest principal tensile stress acts. For the purposes of crack detection, a simple Rankine failure criterion is used to detect crack initiation (i.e. a crack forms when the maximum principal tensile stress attains the specified tensile strength of the concrete). The concrete medium is modelled by a dense mesh of 8-node brick elements, and the element formulation adopts a reduced integration scheme. The concrete model adopts fixed, orthogonal cracks, with the maximum number of cracks at a material point limited by the number of direct stress components present at that material (Gauss) point of the finite element model (a maximum of three cracks in 3D). An iterative procedure based on the well-established NewtonRaphson method is used in order to account for the stress redistributions during which the crack formation and closure 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 for materials that are dominated by tensile cracking, such as concrete. Since the focus is on the all-important brittle tensile aspect of concrete behaviour, a simplification employed in the model is that the behaviour in compression is assumed to be linear elastic. This is justified, particularly for 3D modelling, because at least one of the three pre-

Structural Concrete 15 (2014), No. 1

dicted values of the principal stresses needs to be tensile and greater than the tensile strength required to initiate cracking (whereas the other two principal stresses could be compressive). The main attractive feature of the model is that it focuses on the main mechanisms for failure in concrete, namely its brittleness and cracking (predominantly in tension). Thus, the simplification made with regard to compressive behaviour is intended to make the solution process more efficient without compromising its ability to mimic the non-linear response of concrete structural elements. As a further precaution, the strain results were checked to ensure that the values of ultimate compressive strain did not exceed 0.0035 before failure [20]. In order to improve the efficiency of the numerical solution and to enhance numerical stability (which is adversely affected by cracking), the analysis was carried out using the dynamic solver as a quasi-static one (i.e. at a low rate of loading). This was used in conjunction with the explicit dynamic procedure available in ABAQUS/Explicit [6]. The ratio between kinetic and strain energies was checked to ensure that it remains below ∼5 %, indicating that the analysis remains quasi-static. A similar approach is commonly used in the modelling of RC structures [21]. This was also confirmed by examining both the deformed shape and cracking pattern of the structure. In addition, the load was applied using a displacement-based method to minimize convergence problems.

Calibration with experimental work

A series of statically indeterminate SFRC columns was tested under monotonic loading by Kotsovos et al. [7] to study their structural behaviour. The results of some of these specimens were used to calibrate the present numerical work as discussed next.

3.1

Experimental cases considered

Several two-span continuous columns were tested by Kotsovos et al. [7]. The parameters considered were: concrete strength, longitudinal and shear reinforcement properties and a specimen with fibre-reinforced concrete. The columns were cast and tested as horizontal members. Therefore, the axial force was applied horizontally and lateral loading P was applied vertically as shown in Fig. 2 (thus representing the column idealized in Fig. 1). In the present NLFEA work, one of these columns was selected for the calibration (referred to in the experimental work as D16-FC30-M with the key features depicted in Fig. 2). The steel fibres used were DRAMIX RC80/60BN, which are hooked-end cold-drawn wire fibres with a diameter of 0.75 mm, length of 60 mm and strength of 1050 MPa. The concrete compressive strength for the specimen was approx. 37 MPa. The longitudinal reinforcement has a yield stress fy = 555 MPa, the transverse reinforcement a yield stress fy = 470 MPa. The modulus of elasticity for steel Es is 200 GPa. The axial force N applied at the column ends was taken to be 20 % of the compressive resistance of the column provided by the concrete Nu. The latter can be expressed as Nu = fc bh, where fc is the uniaxial cylinder compressive strength of concrete, and b and h are the crosssectional dimensions of the column. Once the axial force

A. A. Abbas/S. M. Syed Mohsin/D. M. Cotsovos · Non-linear analysis of statically indeterminate SFRC columns

975 mm

975 mm 2 T16

200 mm

2 T16

1950 mm

1200 mm

200 mm R8/40

R8/140

R8/40

R8/140

R8/40

R8/140

R8/40

300 mm

720 mm

560 mm

415 mm

560 mm

495 mm

300 mm

Fig. 2. Loading arrangement and reinforcement details of column

was introduced, the lateral monotonic loading was applied (using a displacement-based method) at point C in Fig. 2. Consequently, the load and deflection values measured to plot the ensuing load-deflection curves were also taken at point C.

3.2

Results of calibration work

A comparison between the load-deflection curves based on the experimental and numerical results are depicted Fig. 3, which shows good agreement between the two sets of data (with the curves almost identical up to a deflection of about 40 mm, whereas the slight discrepancy afterwards, i.e. ∼5 %, is negligible). A summary of the key load and deflection values is provided in Table 1, with Py representing 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 ultimate 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 the failure point, the kinetic energy of the column is plotted against the deflection in Fig. 4. A clear, abrupt rise can be observed, indicating failure (i.e. the presence of extensive/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 in the present research work as it allowed the determination of some parameters needed for the numerical simulations. For instance, the FE mesh adopted (with an element size of 30 mm) was determined based on a sensitivity analysis carried out in order to assess the effect of the mesh size on the accuracy of the numerical predictions. Thus, the calibration work carried out against experimental data was crucial in selecting the best mesh size that represents accurately the true structural response (i.e. the mesh that best replicates experimental results). Similarly, the calibration data was useful in determining a reliable loading rate to be used in the numerical model. The comparison with

200 180 160

Experimental (Vf=0.4%)

Load (kN)

140 120 100 80

FE model (Vf=0.4%)

60 40 20 0 0

30 40 Deflection (mm)

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 FE model

155.0 144.3

11 9.7

158 174.1

65.5 60.3

187 182.9

6.0 6.2

1.21 1.33

Structural Concrete 15 (2014), No. 1

Kinetic energy (J)

A. A. Abbas/S. M. Syed Mohsin/D. M. Cotsovos · Non-linear analysis of statically indeterminate SFRC columns

the stirrups was increased with SI = 0, 50 and 100 %. At the same time, the fibre volume fraction was increased with Vf = 0, 1, 1.5, 2 and 2.5 % to see whether or not fibres can compensate for the reduction in shear reinforcement. The tensile stress-strain relations for each fibre volume fraction are depicted in Fig. 5, with the key values of stress and strain summarized in Table 2. The results obtained are discussed next.

10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0

4.1 0

Deflection (mm) Fig. 4. Kinetic energy plots to determine failure of column

experimental data also helped ascertain the reliability of both the constitutive relationships adopted for SFRC and the brittle cracking model used to implement them in ABAQUS (no alterations to the parameters of the constitutive model summarized in Eqs. (1) and (2) were needed and the values of the parameters were kept the same as the input values used in the experiments).

Parametric studies of statically indeterminate SFRC columns

Following the calibration work, parametric studies were carried out (by means of NLFEA) incorporating two key parameters: increase in spacing SI between shear stirrups and steel fibres volume fraction Vf. The spacing between

6 5

Load-deflection curves

The load-deflection curves for specimens with increased stirrup spacing SI = 0 %, SI = 50 % and SI = 100 % are presented in Figs. 6(a) to (c) respectively. The control column specimen (i.e. the one with no reduction in shear reinforcement and no fibres) is also included in the figures to illustrate whether the addition of fibres can restore the original response. Additionally, a summary of the key load and deflection results is provided in Tables 3(a) to (c). The ratio between the ultimate load (i.e. residual strength) Pu and the maximum load (i.e. strength) Pmax was added to the tables. This is to ensure that the slight softening trend in the load-deflection curves beyond peak (i.e. maximum) load is not significant, so the residual strength and corresponding ductility levels remain of practical value. From the tables it is clear that the residual strength is at least ∼90 % of the peak value, confirming that the softening is negligible. The load-deflection curves show that there is a gradual increase in strength, stiffness and ductility as the fibres content is increased. This will be discussed next.

C Vf = 0%

Stress (MPa)

Vf = 1%

Vf = 1.5%

Vf = 2%

0 0

Vf = 2.5%

D 0.005

0.01 0.015 Strain (-)

0.02

0.025

Fig. 5. Stress–strain relations in tension adopted for parametric studies of statically indeterminate SFRC columns

Table 2. Tensile stress-strain key values adopted

Point

Origin Ultimate tensile strength – Plain (A) Ultimate tensile strain – Plain (B0) Beginning of plateau – SFRC (B) End of plateau – SFRC (C) Ultimate tensile strain – SFRC (D)

Structural Concrete 15 (2014), No. 1

Strain (‰)

0 0.215 2.0 2.12 18 20

Stress (MPa) Vf = 0.0 %

Vf = 1.0 %

Vf = 1.5 %

Vf = 2.0 %

Vf = 2.5 %

0 3.70 0 – – –

0 3.70 – 2.12 2.12 0

0 3.70 – 3.18 3.18 0

0 3.7 – 4.24 4.24 0

0 3.70 – 5.30 5.30 0

A. A. Abbas/S. M. Syed Mohsin/D. M. Cotsovos 路 Non-linear analysis of statically indeterminate SFRC columns

250 Vf = 0% 200

Load (kN)

Vf = 1% 150

Vf = 1.5%

100

Vf = 2%

Vf = 2.5%

0 0

Def lection (mm) Fig. 6(a). Load-deflection curves for columns with SI = 0 %

250 Control column

Load (kN)

200

Vf = 0%

150

Vf = 1%

100

Vf = 1.5% Vf = 2%

50 Vf = 2.5% 0

Def lection (mm) Fig. 6(b). Load-deflection curves for columns with SI = 50 %

250 Control column

200

Load (kN)

Vf = 0% 150

Vf = 1%

100

Vf = 1.5% Vf = 2%

50 Vf = 2.5% 0

Deflection (mm) Fig. 6(c). Load-deflection curves for columns with SI = 100 %

Structural Concrete 15 (2014), No. 1

A. A. Abbas/S. M. Syed Mohsin/D. M. Cotsovos · Non-linear analysis of statically indeterminate SFRC columns

Table 3(a). Summary of load-deflection curves for columns with SI = 0 %

Vf (%)

Py (kN)

δ y (mm)

Pu (kN)

δ u (mm)

Pmax (kN)

Pu /Pmax

μ = δ u /δ y

0 1 1.5 2 2.5

136.3 147.6 155.9 162.1 167.3

9.36 9.34 9.32 9.3 9.3

170.6 180.1 180.7 190.0 195.5

56.4 60.9 59.3 44.1 39.4

179.9 183.2 184.6 192.0 200.7

95 % 98 % 98 % 99 % 97 %

6.03 6.52 6.36 4.74 4.24

Table 3(b). Summary of load-deflection curves for columns with SI = 50 % (* CC is the control column with Vf = 0 % and SI = 0 %)

Vf (%)

Py (kN)

δ y (mm)

Pu (kN)

δ u (mm)

Pmax (kN)

Pu /Pmax

μ = δ u /δ y

CC*

136.3

9.36

170.6

56.4

179.9

95 %

6.03

0 1 1.5 2 2.5

139.4 152.62 162.85 168.4 174.3

9.4 9.33 9.32 9.32 9.31

173.0 182.5 177.7 175.8 189.2

44.4 53.7 62.5 48.2 43.4

176.1 182.5 183.7 192.3 200.6

98 % 100 % 97 % 100 % 94 %

4.72 5.76 6.71 5.17 4.66

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)

δ u (mm)

Pmax (kN)

Pu /Pmax

μ = δ u /δ y

CC*

136.3

9.36

170.6

56.4

179.9

95 %

6.03

0 1 1.5 2 2.5

137.9 155.4 161.6 167.6 173.1

9.12 9.04 9.02 9.01 9.00

170.8 180.3 169.4 179.4 185.4

33.4 48.1 47.7 47.8 42.8

170.8 181.6 183.1 188.7 193.6

100 % 99 % 93 % 95 % 96 %

3.66 5.32 5.29 5.31 4.76

4.2

Strength

The load-deflection curves show that the increase in the amount of fibres provided led to an increase in load-carrying capacity Pmax. Comparing the strength of each SFRC column with the strength of the column with no fibres shows that the load-carrying capacity increased by up to 14 %. In addition, the value of the load at yield Py for the SFRC columns increased gradually up to an average of 23.5 % in comparison to the yield load of columns with no fibres. This shows the effectiveness of fibres in bridging the crack opening, thus enhancing the load at yield of the columns, which leads to enhanced stiffness. Taking the column with conventional reinforcement and no fibres (Vf = 0 %) with a stirrup spacing increase SI = 0 % as the reference or control column specimen (CC), further comparisons were made with columns having varying fibre content and stirrup spacing. From Figs. 6(a) to (c) and Tables 3(a) to (c) it can be seen that the strength properties of the SFRC columns with SI = 50 % and SI = 100 % exhibit a better performance than the control column specimen. The values of Py and Pmax obtained are also higher than the corresponding values for the control column, even at a fibre volume fraction as low as 1 %.

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4.3

Ductility

The ductility of the columns can be analysed by examining the ultimate deflection δu and the ductility ratio μ. An upward trend in both parameters is observed with the increase in fibre volume fraction. However, this pattern is only true up to a certain critical fibre volume ratio; the higher the spacing between the stirrups, the higher the critical fibre volume ratio. In this parametric study the highest ductility ratio is obtained for the column with Vf = 1 % for SI = 0 %, Vf = 1.5 % for SI = 50 %, and Vf = 2 % for SI = 100 %. It is interesting to note that increasing the fibre content beyond 1.5∼2 % has actually led to a reduction (rather than an increase) in ductility. The reduction in ductility is more pronounced in the case of specimens where fibres were added in addition to full conventional shear reinforcement, i.e. SI = 0 % (the response became less ductile even when fibre provision exceeded Vf = 1 %). This suggests that a situation similar to the one experienced when main flexural reinforcement is increased beyond a certain threshold (i.e. over-reinforced), which leads to an increase in strength but reduction in ductility. Furthermore, for every SI value there is a certain fibre volume fraction for which the ductility of the SFRC column is comparable with that associated with the origi-

A. A. Abbas/S. M. Syed Mohsin/D. M. Cotsovos · Non-linear analysis of statically indeterminate SFRC columns

nal control specimen (i.e. with no fibres and full conventional shear reinforcement). This is significant from a practical viewpoint as it indicates that fibres provided in certain amounts can compensate for the decrease in ductility due to a reduction in shear reinforcement. These fibre volume fractions are 1.5 % for SI = 50 % and between 1.5 and 2 % for SI = 100 %.

4.4

Principal strain vectors and crack patterns

The principal strain vectors at failure were studied and the data provided an insight into the failure mechanism as well as cracking formation and patterns. The principal strain vectors for columns with SI = 0 %, SI = 50 % and SI = 100 % are presented in Figs. 7, 8 and 9 respectively. From these figures it can be seen that the failure of the columns is characterized by tensile cracking in two regions: (i) the top of the section at the intermediate support and (ii) the bottom of the section where the lateral load P is applied. The principal strain vectors are also highlighted in the column’s span between these two regions for the column with no fibres, indicating some cracks propagated in this span, especially in the column with SI = 100 %. The strain vectors depict the cracks that developed in the span between the intermediate support and the point where lateral load is applied. Thus, it can be concluded that in this particular column with no fibres for the column with SI = 100 %, the cracking pattern suggested a bendingshear failure. However, the inclusion of steel fibres, even a fibre volume ratio of just 1 %, improves the crack propagation and changes the mode of failure of the SFRC columns from shear to bending. Based on the cracking pattern observed in these figures it can be concluded that all columns show a bending failure mode, except the column with no fibres and the most critical stirrups spacing (i.e. SI = 100 %). Thus, it can be concluded that the addition of fibres reduces the crack propagation and limits it to regions local to the intermediate support and the lateral loading point.

4.5

Comparative study with control specimen using non-dimensional ratios

In this section, an overall comparison is made between the control column specimen (i.e. the one with no fibres and full conventional shear reinforcement) and the columns with various fibre dosages and increased stirrup spacing. The strength, ductility and energy absorption values were normalized by dividing them by the corresponding control specimen values. This allowed overall conclusions to be reached regarding the potential of fibres to compensate for a reduction in conventional transverse reinforcement.

(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) (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 %

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 %

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4.5.1 Strength ratio The ratio between the maximum load Pmax of each column and that of the control column specimen Pmax,o is depicted in Fig. 10, which shows that there is an upward trend in the Pmax/Pmax,o ratio for all columns as the fibre percentages are increased. It can also be seen that the columns with SI = 100 % result in lower strength increases than the other columns. From Fig. 10 it can be concluded that the Pmax/Pmax,o ratio for all SFRC columns is higher than the corresponding ratio for the control specimen (i.e. Pmax/Pmax,o = 1.0) when fibres are provided with a minimum value Vf = ∼0.8 %. This indicates that the fibres at this dosage compensate for the loss of strength due to the reduction in conventional shear reinforcement for the specimens considered in the present parametric studies.

4.5.2 Ductility ratio The ductility ratios of all the columns were normalized by dividing them by the ductility ratio of the control specimen, i.e. μ/μo, and the results were plotted against the change in fibre volume fraction as depicted in Fig. 11. The

values of the ductility ratios for all columns considered are also included in Fig. 11, which were all > 3 and thus the vertical axis was truncated to aid clarity. It can be concluded that the addition of fibres improved the ductility of the specimens provided the fibre amount does not exceed a certain threshold. Therefore, an optimum ratio of fibres was determined in all specimens (i.e. for columns with SI = 0, 50 and 100 %, the optimum fibre volume fractions are 1, 1.5 and 2 % respectively). The addition of steel fibres above these fibre dosages led to a reduction in the ductility ratio, with the worst decease in SFRC columns with Vf = 2.5 %, as can be seen in Fig. 11. This can be explained by recalling that a higher fibre ratio leads to a much stiffer response, causing the column to deflect less. This is similar to the brittle “over-reinforced” response experienced in RC design when main flexural reinforcement is increased beyond a certain threshold, leading to a reduction in ductility. Moreover, it is interesting to note that columns with SI = 50 % strengthened with fibres with a Vf = 1.5 % dosage show better performance in term of ductility than the control specimen (i.e. the one with no spacing increase and no fibres). Additionally, in the columns with a

1.14 1.12

Pmax / Pmax,o

1.1 1.08

SI=0%

1.06 1.04

SI=50%

1.02 1

SI=100%

0.98 0.96 0.94 0

0.5

1.5

2.5

Vf (%)

1.17

1.00

0.83

0.67

SI=0%

SI=50%

µ/ µ,o

Fig. 10. Ratio between the maximum load and that in the control column (SI = 0 %, Vf = 0 %) plotted against fibre volume fraction

SI=100%

0.50 0

0.5

1.5

2.5

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)

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A. A. Abbas/S. M. Syed Mohsin/D. M. Cotsovos · Non-linear analysis of statically indeterminate SFRC columns

considerable spacing increase (i.e. SI = 100 %), the provision of fibres has led to ductility levels that are close (∼85 %) to the initial ductility level associated with the control specimen. It is also interesting to note that the ductility levels associated with the columns with no spacing increase (i.e. SI = 0 %) are worse than those related to columns with SI = 50 % if fibre dosage is Vf = 1.5 % or more (similarly, they are worse than columns with SI = 100 % if fibre dosage is Vf = 2 % or more). This indicates that, in terms of ductility, the combination of full conventional transverse reinforcement and fibres at high dosages will lead to reduced – rather than increased – ductility. Thus, it can be concluded that fibres have the potential to replace conventional reinforcement if excessive combinations of the two types of reinforcement are avoided (i.e. fibres should be provided to replace a reduced amount of conventional reinforcement but not in addition to full amounts of the latter). Notwithstanding the above observations, adding fibres will lead to ductility ratios μ > 4, as presented in Tables 3(a) to (c) and Fig. 11, which will be useful in practice. This is true even for high dosages such as Vf = 2.5 %, which could be used for strength enhancement purposes.

4.5.3 Energy absorption The ratio between the energy absorption Ea in each column and that in the control column Ea,o is depicted in Fig. 12. In columns with SI = 0 %, the energy absorption ratio increases by up to 15 %, but decreased by 25 % when the fibre volume fractions exceeded 1.5 %. In columns with SI = 50 %, a fibre dosage Vf = 1.5 % led to a ratio larger than the one associated with the control specimen, whereas for columns with SI = 100 %, a fibre dosage Vf = 2 % led to a ratio close to that of the control specimen. The trend in the energy absorption data is similar to the one for ductility discussed in the previous section. To investigate the energy absorption response further, another comparison was made, but now the energy absorption ratio for every SFRC column is normalized by that for its counterpart column with the same SI value but without fibres (i.e. Vf = 0 %) as shown in Fig. 13. It is clear that the energy absorption for SFRC columns increased significantly, up to 61 and 77 % for SI = 50 % and SI = 100 % respectively. It is interesting to note that the energy absorption ratio for the columns with SI = 100 % provides the greatest enhancement. This demonstrates

1.40 1.20 SI=0%

Ea / Ea,o

1.00 0.80

SI=50%

0.60 SI=100%

0.40 0.20 0.00

0.5

1.5

2.5

Vf (%) 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

2 1.8 SI=0%

Ea / Ea,Vf=0%

1.6 1.4

SI=50%

1.2 1

SI=100%

0.8 0.6

0.5

1.5

2.5

Vf (%) 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

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that there is more room for enhancement by fibres as conventional reinforcement is reduced. This confirms the finding that fibres will absorb more energy and improve ductility as conventional reinforcement is reduced. Conversely, the response becomes less ductile if the fibres are provided in addition to full conventional reinforcement. Additionally, Fig. 13 also confirms that there is an optimum 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 of an inherently brittle and crack-prone cement-based matrix. Parametric studies of two-span continuous (i.e. statically indeterminate) SFRC columns were carried out by means of NLFEA, which were initially calibrated and verified against existing experimental data. Despite the simplicity of the constitutive model used for the concrete, the proposed NLFEA model employed was capable of yielding realistic predictions of the responses of several SFRC columns. A key aim of the research work was to examine the effect of fibres on the structural response and, in particular, their potential to compensate for a reduction in conventional transverse reinforcement without compromising ductility and strength requirements. This was investigated by increasing the spacing between shear links while adding steel fibres to see whether or not the loss in strength and ductility can be compensated for in this way. Based on the results obtained, it can be concluded that the strength of the columns is consistently enhanced as the amount of fibres is increased. It was also found that the original strength level associated with the control specimen (with no spacing increase and no fibres) can be restored when the spacing is increased by 50∼100 % by adding fibres at a volume fraction of ∼0.8 % for the present study. Moreover, it was found that the stiffness and ductility of the columns improved with the addition of fibres. This indicates that the addition of fibres has led to improvements at both the serviceability and ultimate limit states. Interestingly, however, it was found that the increase in ductility seems to drop if excessive amounts of fibres are provided (so excessive amounts of fibres result in the columns becoming much stiffer and deflecting less). This suggests that there is an optimum amount of fibres that can be added to enhance ductility, but adding fibres beyond this threshold should be avoided. This is similar to the situation experienced in RC design when reinforcement is increased beyond a certain threshold (i.e. “over-reinforced”), which leads to an increase in strength but reduction in ductility. For the columns with SI = 0, 50 and 100 %, the optimum fibre volume fraction values obtained were Vf = 1 %, Vf = 1.5 % and Vf = 2 % respectively. Nevertheless, adding fibres resulted in ductility ratios μ > 4 in the present study, which is substantial and will be useful in practice. This is even true for dosages as high as Vf = 2.5 %, which could be used for strength enhancement purposes. However, it must be pointed out that the provision of high fibre dosages (in excess of Vf = 2∼2.5 %) in the concrete mix can lead to practical mixing difficulties. So to improve the workability of mixes with such high fibre volumes, water-reducing admixtures are often used. Care

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is also needed to ensure that the mix composition is adjusted taking into account the natural disturbing effect that fibres have on the arrangement of the granular material. In general, the mixing method should consider the type and content of fibres used in order to ensure uniform distribution and bonding within the concrete paste. Based on the above analysis of the numerical predictions, it is interesting to point out that apart from mixing difficulties, the use of excessive fibre contents can also result in a reduction in the ductility of the structural elements presently considered once an optimum fibre content value is passed. A similar pattern was observed for energy absorption, which, alongside ductility, is an important indicator of structural performance. Additionally, it was found that the energy absorption ratio for the columns with SI = 100 % provided the greatest enhancement. This demonstrates that there is more room for enhancement by fibres as conventional reinforcement is reduced, and indicates that fibres will provide higher energy absorption and ductility improvement as the conventional reinforcement is reduced. Conversely, the response becomes less ductile if excessive fibres are provided in addition to full conventional reinforcement as discussed earlier. Furthermore, it was observed that fibres help control the cracking and minimize crack opening especially in the section between the intermediate support and the point where the lateral load is applied. Most of the cracking develops in two main regions, which are the intermediate support and the point where the lateral load is applied. In the column with SI = 100 % it was clear that the inclusion of fibres improved the cracking pattern of the column, even at a low fibre volume fraction of 1 %. Summing up, it can be concluded that the addition of steel fibres improves the strength of the columns consistently. A similar trend is observed with regard to the stiffness and ductility of the SFRC columns. A critical threshold was found, however, beyond which the addition of more fibres led to a less ductile response. Interestingly, the threshold seems to be of the same order of magnitude as that associated with practical mixing difficulties (thus, providing fibres at Vf > 2∼2.5 % can be regarded as both impractical and counterproductive from a ductility viewpoint). Nevertheless, the study has also confirmed the potential for fibres to compensate for a reduction in conventional transverse reinforcement. This can be useful in situations where the number of stirrups required can lead to congestion, whereas the use of fibres can resolve this and also simplify complex construction arrangements (e.g. beam-column joints).

Notation Ea Ea,0 Es L/d N Nu P SI Py

energy absorption energy absorption of control specimen Young’s modulus for steel aspect ratio of steel fibre axial force applied to column compression resistance of column provided by concrete lateral monotonic load increase in stirrup spacing load at yield

A. A. Abbas/S. M. Syed Mohsin/D. M. Cotsovos · Non-linear analysis of statically indeterminate SFRC columns

load-carrying capacity load-carrying capacity of control specimen ultimate load volume fraction of fibres cross-sectional dimensions of column uniaxial cylinder compressive strength of concrete ft ultimate tensile strength of SFRC ftu residual tensile strength of SFRC fy steel yield stress δy deflection at yield δu ultimate deflection εto ultimate tensile strain in SFRC εt1 residual tensile strain in SFRC η fibre orientation factor μ ductility ratio μ,o ductility ratio of control specimen τd bond stress between concrete and steel fibres CC control column specimen FEA finite element analysis SFRC steel fibre-reinforced concrete NLFEA non-linear finite element analysis RC reinforced concrete Pmax Pmax,0 Pu Vf b and h fc

References 1. Campione, G., Mangiavillano, M.: Fibrous reinforced concrete beams in flexure: Experimental investigation, analytical modelling and design considerations. Engineering Structures, 2008, 30, pp. 2970–2980. 2. Cho, S. H., Kim, Y. I.: Effect of steel fibres on short beams loaded in shear. ACI Structural Journal, 2003, 100, pp. 765–774. 3. Trottier, J. F., Banthia, N.: Toughness Characterization of Steel 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 Reinforced Concrete Beams. ACI Journal, 1986, 83, pp. 624–628. 5. BS EN 1998-1: Eurocode 8: Design of structures for earthquake resistance – Part 1: General rules, seismic actions and rules for buildings. BSI, London, 2004. 6. ABAQUS Version 6.7 Documentation, 2007. Available at www.engine.brown.edu:2080/v6.7/index.html. 7. Kotsovos, G., Zeris, C., Kotsovos, M.: The effect of steel fibres on the earthquake-resistant design of reinforced concrete structures. Materials and Structures, RILEM, 2007, 40, pp. 175–188. 8. RILEM Technical Committees, RILEM TC 162-TDF: Test and Design Methods for Steel Fibre-Reinforced Concrete, Recommendation: s-e Design Method. Materials and Structures, RILEM, 2000, 33, pp. 75–81. 9. RILEM Technical Committees, RILEM TC 162-TDF: Test and Design Methods for Steel Fibre-Reinforced Concrete, Final Recommendation: s-e Design Method. Materials and Structures, RILEM, 2003, 36, pp. 560–567. 10. Barros, J. A., Figueiras, J. A.: Flexural behavior of SFRC: Testing and modelling. Journal of Materials in Civil Engineering ASCE, 1999, 11, No. 4, pp. 331–339. 11. Barros, J. A., Figueiras, J. A.: Model for the Analysis of Steel Fibre Reinforced Concrete Slabs on Grade. Computers and Structures, 2001, 79, No. 1, pp. 97–106. 12. Tlemat, H., Pilakoutas, K., Neocleous, K.: Modelling of SFRC using Inverse Finite Element Analysis. Materials and Structures, RILEM, 2006, 39, pp. 221–233.

13. Lok, T. S., Pei, J. S.: Flexural Behavior of Steel Fiber-Reinforced Concrete. Journal of Materials in Civil Engineering ASCE, 1998, 10, No. 2, pp. 86–97. 14. Lok, T. S., Xiao, J. R.: Flexural Strength Assessment of Steel Fiber-Reinforced Concrete. Journal of Materials in Civil Engineering ASCE, 1999, 11, No. 3, pp. 188–196. 15. Syed Mohsin, S. M.: Behaviour of fibre-reinforced concrete structures under seismic loading. PhD thesis, Imperial College London, 2012. 16. Abbas, A. A., Syed Mohsin, S. M., Cotsovos, D. M.: Numerical modelling of fibre-reinforced concrete. Proc. of International Conference on Computing in Civil & Building Engineering icccbe 2010, (ed W. Tizani), University of Nottingham 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 comparative study on modelling approaches for fibre-reinforced concrete. Proc. of 9th HSTAM International Congress on Mechanics, Limassol, Cyprus, 12–14 July 2010. 18. Bencardino, F., Rizzuti, L., Spadea, G., Ramnath, N.: StressStrain Behavior of Steel Fiber-Reinforced Concrete in Compression. Journal of Materials in Civil Engineering ASCE, 2008, 20, No. 3, pp. 255–262. 19. Ghosh, S., Bhattacharjya, S., Chakraborty, S.: Compressive behaviour of short-fibre-reinforced concrete. Magazine of Concrete 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, London, 2004. 21. Zheng, Y., Robinson, D., Taylor, S., Cleland, D.: Non-linear finite-element analysis of punching capacities of steel-concrete bridge deck slabs. Structures and Buildings, ICE Proc., 2012, 165, No. 5, pp. 255–259.

Ali A. Abbas BSc(Eng.), DIC, PhD, FHEA Senior Lecturer in Structural Engineering School of Architecture, Computing & Engineering University of East London London E16 2RD, UK Tel.: 020 8223 6279 Fax: 020 8223 2963 E-mail: abbas@uel.ac.uk

Sharifah M. Syed Mohsin BSc(Eng.), DIC, PhD Senior Lecturer Faculty of Civil & Earth Resources Universiti Malaysia Pahang Lebuhraya Tun Razak, 26300 Gambang Kuantang, Pahang, Malaysia E-mail: maszura@ump.edu.my

Demetrios M. Cotsovos Dipl Ing, MSc, DIC, PhD, CEng Lecturer in Structural Engineering Institute of Infrastructure & Environment School of the Built Environment Heriot-Watt University Edinburgh, EH14 4AS, UK E-mail: d.cotsovos@hw.ac.uk

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2014 fib Congress, Mumbai: Improving performance of concrete structures Contents

Issue 1 (2014)

2014 fib Congress, Mumbai

106

2014 Freyssinet Medals

107

ConLife and 70th anniversary of NIISK

109

fibUK seminar report

109

20th anniversary of CBS

110

Report from the Spanish NMG

111

2015 fib Symposium

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fib Bulletins

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Congresses and symposia

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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

Held from 10 to 13 February 2014 in Mumbai, India, the fourth fib International Congress and Exhibition was a memorable event from start to finish, with high level technical presentations, special invited lectures, valuable opportunities for networking and exchanges, as well as a rich offering of cultural activities, culinary delights and a picturesque lakeside venue. Organised around the theme, “Improving performance of concrete structures”, the Congress focused on the needs of today’s changing society. Topics covered during the four- day event included, among others: – Existing concrete structures: repair, rehabilitation, retrofitting, – Model Codes and their influence on national codes, – Design, construction and maintenance of large and/or innovative structures precast concrete structures, – Steel-concrete hybrid structures, 106

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– Improvements in prestressing systems, – Improved understanding of new materials, – High Performance and Ultra High Performance Concretes. The Congress commenced on Monday 10 February with the ceremonial lighting of the Lamps of Knowledge. C.R. Alimchandani (Chairman of the Organising Committee and of IMC-fib), Ashok Basa (President of IE(I)), and Gordon Clark (President of fib) conveyed their warm welcomes to the delegates, noting the welcome return of fib to India following the 1986 FIP Congress and 2004 Symposium in New Delhi. Gordon Clark also drew attention to the combined 60-year anniversary of fib-CEB-FIP with a presentation on the history and highlights of the association. Also present to offer their welcome wishes to the delegates were Immediate 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 presented the 2014 Freyssinet Medals to Joost Walraven and Armando Rito and Honorary Memberships to Arnold van Acker (in absentia), Fernando Stucchi and C.R. Alimchandani (see report on pp 107–109). One of the highlights of the inaugural session was the presentation of the 2014 fib Awards for Outstanding Concrete Structures by the jury chairman and Immediate Past President of fib, György L. Balázs. This edition of the prestigious award recognised five winning structures and six special mention recipients; see the December 2013 issue of fib-news (http://www.fib-international.org/fib_news_Dec2013.pdf) for the full results of the competition. The afternoon sessions were devoted to plenary lectures by Giuseppe Mancini (A sustainable approach to existing structures), Hideki Kimura (Large scale application of HS-HP

fib-news

Handover of the Congress bell (from left to right: Stephen Foster, C.R. Alimchandani, S.G. Joglekar)

In additional to the usual business of budget and balance approvals, the General Assembly approved three Honorary Memberships (see next article). Elections for the next terms were held by secret ballot and the following officers were elected:

FRC in Japan) and Joost Walraven (Dealing with the service life of concrete structures – a continuous adventure). The cultural programme included performances of Indian dance, drama and music held on the Monday and Tuesday evenings, providing festive conclusions to the events of the day. The Gala dinner on Wednesday evening was a sumptuous offering of Indian specialities in the multicourse meal. From Tuesday to Thursday, over 250 papers were presented in about 50 parallel sessions, in addition to special invited “on forefront of technology” lectures that included reports from selected fib Commissions, Special Activity Groups and Task Groups. National reports were also presented by fib National Member Groups: Brazil, Czech Republic, Denmark, France, Hungary, India, Japan, Norway, Portugal, Slovakia, Switzerland and the UK. The valedictory session gave the opportunity for fib President Gordon Clark, fib President-elect Harald S. Müller, Organising Committee chairman C.R. Alimchandani and selected delegates to give their impressions of this milestone event and congratulate the organisers. Following a vote of thanks, the traditional fib Congress bell was handed over to Stephen Foster and David Millar, representing the organisers

of the 2018 congress in Melbourne, Australia. Upcoming fib events were announced and previewed, the next of which will be the 2015 symposium in Copenhagen (see call for papers announcement on page 112), to be followed by symposia in Cape Town (2016) and Maastricht (2017). Events continued even after the end of the Congress: three successful workshops on highly relevant topics were held on 13 and 14 February: - fib Model Code for Concrete Structures 2010 short course, - Workshop on durability, - Workshop on High Performance Fiber Reinforced Cementitious Composites.

Technical Council, General Assembly and Elections In conjunction with the Congress, meetings were held by fib Commissions and Task Groups, as well as the Technical Council and General Assembly. The Technical Council approved a major initiative of the Presidium to restructure fib‘s Commissions and Task Groups. The details of the new structure will be given in an upcoming issue of fib-news. The Technical Council appointed new Chairs and Deputy Chairs for 2015–2018 as well as electing their two new Deputy-Chairs, Stephen Foster and Frank Dehn to represent the Technical Council on the Presidium for the same term.

– President, 1st January 2015 – 31 December 2016: Harald S. Müller; – Deputy-President, 1st January 2015 – 31 December 2016: Hugo Corres Peiretti (Spain); – Four elected Presidium Members, 1st January 2015 – 31 December 2018: Josée Bastien (Canada), Akio Kasuga (Japan), Aurelio Muttoni (Switzerland), Tor Ole Olsen (Norway); – Honorary treasurer 1st January 2015 – 31 December 2018: Hans Rudolf Ganz (Switzerland).

2014 Freyssinet Medals Awarded every four years at the occasion of an fib Congress, the Freyssinet Medal is the highest distinction awarded by fib. It is given “in recognition of outstanding technical contributions in the field of structural concrete”, and is a continuation of the Freyssinet Medals awarded by fib’s predecessor FIP (Fédération Internationale de la Précontrainte), since 1970. The two 2014 Freyssinet Medals were awarded by fib President Gordon Clark to Joost Walraven (the Netherlands) and Armando Rito (Portugal) during the inaugural session of the recent 2014 Congress in Mumbai. Structural Concrete 15 (2014), No. 1

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decks in span-by-span construction and box girders of balanced cantilever construction, new cross sections on the designs of high-rise piers, refinements on box girders for the arrangement of prestressing cables.

Left: Gordon Clark with Joost and Rose Walraven; right: with Isabel and Armando Rito

Joost Walraven received his PhD from the Technical University of Delft, the Netherlands, in 1980. After several years as a design engineer for Corsmit Consulting Engineers, he began his academic career in 1985 as a professor at the Technical University of Darmstadt, Germany. In 1989 he returned to Delft as professor of concrete structures, where he was selected for the “Distinguished Teacher Award” in 2005. He held this professorship until his retirement in 2012, when he became Emeritus Professor. He is the author or co-author of 400 publications in scientific and professional journals and conference proceedings, and advisor or co-advisor for over 50 PhDs in the Netherlands, Germany, Belgium, Sweden and Norway. He has been prominently involved in the work of CEB and fib for well over two decades as Head of the Dutch National Member group since 1991, member of the CEB and then fib Presidium from 1992 to 2006, and President of fib from 2000 to 2002. He has been and continues to be a member of numerous fib Task Groups and Special Activity Groups in fib, contributing to bulletins on service life design, retrofitting of concrete structures, constitutive modeling of HS/HPC, shear and punching shear, and the two edition of the fib Structural Concrete textbook.

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His most notable contribution in recent years has been as the convener of Special Activity Group 5, New Model Code. In this role he headed, during a period of nearly ten years, the development and drafting of the 2010 fib Model Code for Concrete Structures which was approved by the fib General Assembly in 2011 and published in hardcover and ebook editions in 2013. Joost Walraven has been awarded numerous honours and distinctions around the world, including the FIP Medal in 1998. Armando Rito received his civil engineering degree in 1969 at the Technical University of Lisbon. He founded his design office soon after, in 1971, and devoted his work mainly to bridge design with a focus on simplicity of design and construction, feasibility, functionality, durability, economy and aesthetical value. To date, several hundred of his bridge and viaduct designs have been built, including the Miguel Torga bridge, the Arade River bridge, the Vila Pouca de Aguiar viaduct and the 4th April bridge over the Catumbel river in Angola. He has introduced and developed several new bridge design concepts that were adopted as standards by Portuguese bridge designers, for example two-beam (Π) decks, the pile/pier where the pier is the natural extension of the pile, the structural and visual continuity between Π

In addition to his design work, he was an invited professor of bridge design at ISEL – Lisbon Polytechnic Institute and at the Portuguese Catholic University, retired since 2008. He was an expert member of the “Project Team 2”, EC2 – Part 2: Concrete bridges, member of fib Task Group 1.2 “Bridges”, and has published over 70 papers and keynote lectures on the subject of bridge design and construction. Armando Rito has been lauded through a number of international prizes and honours; he was also awarded the FIP Medal in 1998.

Honorary Memberships Honorary life memberships are given by the fib General Assembly in recognition of significant personal contributions to the work of fib. At the 2014 General Assembly, honorary memberships were bestowed on C.R. Alimchandani (India), Fernando Stucchi (Brazil) and Arnold van Acker (Belgium). C.R. Alimchandani was awarded Honorary Membership in recognition of his invaluable roles as FIP Vice President, Head of the Indian National Member Group, organiser of the 1986 FIP Congress in New Delhi and of the 2014 fib Congress in Mumbai, and member of fib Commission 1. Fernando Stucchi was awarded Honorary Membership in recognition of his invaluable roles as Head

fib-news

of the Brazilian National Member Group and jury chairman for the 2013 and 2015 editions of the fib Achievement Awards for Young Engineers, as well as his contributions to the fib Model Code for Concrete Structures 2010. Arnold van Acker was awarded Honorary Membership (in absentia) in recognition of his invaluable chairmanship of the Prefabrication Commission for many years, his role as ex-officio member of the fib Steering Committee and his authorship of several important fib bulletins on prefabrication.

ConLife and 70th anniversary of NIISK fib President Gordon Clark travelled to give presentations in Moscow and Kiev during November and December. He was invited as a keynote speaker at the opening of the conference “ConLife” in Moscow on 27 November, which is an annual 4-day conference and exhibition for the Concrete Industry. After the welcome by an official from the organisation responsible for Russian Building Standards, during which it was announced that Russia have signed an agreement with CENELEC to adapt Eurocodes for use in Russia, he spoke about fib, its organisation and activities, and the new Model Code 2010, explaining that it is expected to form the basis for the next revision of the Concrete Eurocode.

In Kiev, Gordon was invited by the Ukraine Research Institute for Building Construction “NIISK” to give a welcome and congratulatory speech on the occasion of the 70th Anniversary of their foundation in 1943. The Institute was founded during the Second World War with a remit to set standards and assist in reconstruction of the damaged Infrastructure in the country. Since then it has now taken responsibility in the post-Soviet era for the Ukraine Building Standards and holds the fib National Membership. He specially welcomed the long-standing support by the Institute for fib and formerly for FIP since the 1960’s. About 200 invited guests were present at the event from across the Ukraine and Russia, as well as other European guests.

fibUK seminar hailed a success fibUK held its first half-day seminar “DISC2013 – Developments in Structural Concrete” on 6th Nov 2013. Such was its success that it will become an annual event, scheduled on the day of the group’s Annual General Meeting. DISC2013 covered off-site manufacture, service life design, shear in beams and concrete cable stayed bridges. The structure of the afternoon worked well with each of the two sessions consisting of two 30minute technical presentations and one 15-minute presentation on an aspect of fib, followed by time for questions. Presentations and other useful documents were made available to feepaying delegates on a fibUK branded flashdrive. Members of the UK Group can view videos of the presentations on the group’s website

(www.fibuk.org). An outline of the seminar presentations is given below.

Session 1 Laing O’Rourke’s Dr. John Stehle discussed the off-site manufacturing processes at its UK factories and presented two case studies highlighting how complex design and construction issues were overcome by a one team approach. Prof. Tom Harrison, visiting professor at Dundee University, described the challenges and limitations on serviceability design by carbonation, corrosion (chloride induced or otherwise) and chemical attacks. He showed the differences in current requirements in the fib model code, ISO16204 & Eurocodes. fib President Gordon Clark briefed the audience on the wide range of fib activities, the history of the fib’s formation and its achievements.

Session 2 Prof. Steve Denton explained how the new CEN/TC250 commission was focussing on ease of use of the Eurocodes for the second generation of Eurocodes. Dr. Tony Jones of Arup presented on shear. He illustrated the shear reinforcement against shear stress for variable strut inclinations and compared this against traditional Vc+Vs. He discussed the effect of pre-stress on shear (benefit/loss) comparing EN1991-1-1 to the model code and identified this as one of the areas for improvement along with shear for circular sections. David MacKenzie from Flint & Neill argued that the recent developments in concrete cable stayed bridges made them an economic alternative to other materials. He also explained the contribution made by the Model Code in bridge designs. Structural Concrete 15 (2014), No. 1

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20th Anniversary of the Czech Concrete Society In November 2013 the Czech Concrete Society (CˇBS), in conjunction with many Czech technical experts, local collaborators and international partners, commemorated the 20th anniversary of its founding. The occasion was an opportunity to recall and pay tribute to twenty years of efforts by CˇBS to maintain the excellent level of Czech concrete structures within the local construction market. CˇBS was founded on 8th December 2002, under umbrella of the CSSI (Czech Society of Civil Engineers), by several professionals including both academics and engineers from the Czech construction industry. They formulated three principal goals for CˇBS that have determined the character of the Society up to the present: (1) to maintain the traditionally high level of Czech concrete structures; (2) to promote concrete as an efficient building material; (3) to create a social and communication platform for all Czech professionals involved in concrete construction. There were two more key features of CˇBS inscribed into its statutes at that time: (a) independence from any commercial

groups on the market, (b) focus on technical matters only. The first 5-6 years of CˇBS’ existence was marked by a quest for a stable position, both in terms of financing and production of viable projects. Other significant factors for the period of 1994–1999 were the search for a sound status and significant and sharp changes in CˇBS membership. Soon it became obvious that increasing CˇBS aspirations and the expectations of its members surpassed the possibilities of its representatives, who were still just volunteers. Despite its non-professional administrative base, CˇBS founded and maintained several successful and appreciated projects, namely its annual (Czech) Concrete Day conference, the “Beton a zdivo” (Concrete and Masonry) journal and an Outstanding Concrete Structure Award. Also, multiple contacts and participation in the international activities of IABSE, CEB and especially of FIP/fib were kept and enhanced. Since 2000 CˇBS developed steadily and rapidly, primarily thanks to of increasing Czech construction market and growing economy. A booming government investment into infrastructure at that time generated an abundance of both technical knowledge and business informa-

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 Past President), Jan L. Vítek (CBS Past President), Pavel Cížek (first CBS President), Michael Pauser (Austrian Concrete Society), Vlastimil Šru˚ma (Director CBS) and Lars Meyer (DBV Germany) 110

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tion, attracting a huge attendance at CˇBS events. But also a brand new CˇBS organization and internal regulations focused on financing, division of responsibility, etc., led to quite long period of expansion and growth. A new, professional CˇBS office was opened in Prague, and its full-time staff, under the guidance of Dr. Vlastimil Šru˚ma, Managing Director of CˇBS, succeeded in managing the expanding portfolio of CˇBS projects and events. Consequently both the numbers of CˇBS members and participants in CˇBS activities expanded substantially between 2000 and 2008. For the last five years CˇBS has been facing bitter impacts of the considerable depression of the Czech construction market. There are also, partly as a consequence of the broader European financial crisis, more general changes in companies’ and individuals’ behaviour in the construction market and in the spreading of information. As a result of all these impacts, it seems to be almost necessary at least to rethink, and maybe also to redefine, the twenty-year old key principles of the current CˇBS. Thus also the Czech Concrete Society is searching again for long-term stability and efficiency for the demanding years to come. The main celebration of the 20th CˇBS anniversary took place in Hradec Kralove on 27–28 November 2013. Among CˇBS representatives, CˇBS honorary members and numerous leading personalities from the Czech construction industry and technical universities, there were also some close friends and partners of CˇBS present from abroad: Mr. Gordon Clark, President of fib, Prof. György L. Balázs, Past-president of fib, Dr. Lars Mayer and Ing. Michael Pauser, directors of concrete/construction societies of Germany and Austria. Dr. Vlastimil Šru˚ma, CˇBS Managing Director

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Report from the Spanish fib Member Group This report describes the activities of ACHE (Spanish abbreviation for Scientific and Technical Association for Structural Concrete, www.eache.com). This association is the result of merging the two parent associations: GEHO (the Spanish subsidiary of CEB) and ATEP (the Spanish subsidiary of FIP). It has over 900 members; most of them are individuals but there is also an important participation of institutions: consulting companies, contractors, fabricators, suppliers, software companies, etc. ACHE’s income mainly comes from the member fees and conferences. Its activities are organized on the basis of three-year terms. At the end of each term a congress is organized (the next is 17–19 June 2014) and half of the Council of the association, including the President, is renovated. The congress is a big event with over 400 participants and about the same number of papers being presented. Every year ACHE also organizes at least one symposium on a specific topic, generally related to the activities of one of its work groups. Finally, ACHE also organizes courses, generally related to the publication of new concrete codes. The secretariat of ACHE includes one full-time and two part-time positions, but most of its activities are based on voluntary work. The most important results come from the work groups. They are organized in five commissions: design, materials, execution, maintenance and structural elements. Each of these commissions monitors a number of working groups and reports on progress every two months. The total number of working groups which are active at this moment is 26. The activities of each working group end when a monograph is published and distributed among the members of the Association. These activities are the base for interchanging new developments and for including them in future standards. These documents are an im-

portant reference in Spain for the whole concrete related industry. Among the last monographs which have been published we might mention a compilation of all topics related to the design and construction of high rise buildings (two books of about 500 pages each) which was the result of efforts by many different professionals, as is the case when such a building has to be planned, designed and built. These monographs may also consist of a theoretical development related to concrete such as a recent one on statistical methods or they also may include some contributions to controversial topics which may be debated in international groups such as two recently published monographs on imposed deformations in concrete structures or on shear strength of elements without transverse reinforcement. A reduced list of active working groups which should end their work in a short delay would include: Graphic representation of concrete structures, Design of concrete structures in seismic areas, Aggregates for structural concrete, Movement of great weights, External aspect of concrete, Systems for increasing the durability of existing structures, Maintenance manuals, Retrofitting of columns, Examples of application of Eurocode 2. Newly formed working groups include the following topics: Nanotechnology, Fibre-reinforced concrete, Materials for thermal insulation, Execution of incrementally launched decks, Self launching gantries and travellers, Inspection and monitoring techniques. The most significant product of ACHE is the quarterly Journal “Hormigón y Acero” (Concrete and Steel in Spanish) which was founded in 1950. This journal accepts contributions from the industry as well as from the universities and research institutes. Consequently it is usual to see papers on the design and con-

struction of structures along with research papers. This possibility of communication between all the different participants in the construction industry and the researchers of Universities and Institutes is very profitable for all of them and is one of the main assets of the Association and of the “Hormigón y Acero”. The journal is published in Spanish although each paper includes an abstract in English. Every issue of the journal includes a first principal paper, which is published in Spanish and in English; this paper generally consists in the presentation of a very relevant project and, as it is only limited to 10000 words, it usually presents many interesting details of the corresponding project. These principal papers are freely accessible through the web (http://eache.com/mod-ules/pddownloads/viewcat. php?cid=1). All the details of the journal may be found in http://e-ache.com/modules/smartsection/item.php?itemid=9 9. Beginning in 2014, “Hormigón y Acero” will be edited by Elsevier. Like other fib National Member Groups, ACHE occasionally publishes a national report on the most interesting project that were completed in the corresponding time period. The last one covers the period between 1998 and 2008; it includes 140 works and was presented at the 2010 fib Congress. The projects included show the extraordinary development experienced by Spanish structural engineering in recent years. We wish to spread and share our experience with our colleagues around the world which is why we have provided a bilingual SpanishEnglish publication. Details on this book may be found at http://eache.com/modules/smartsection/item.php?itemid=119 ACHE is currently making an effort Structural Concrete 15 (2014), No. 1

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fib Bulletins to promote its activities through the web to make all its publications more accessible to foreign individuals and institutions and it also acts as the distribution node for the publications and activities of fib to promote the progress of structural concrete in Spain. Foreign engineers and architects are invited to participate in our activities and to publish their work in our Journal or to present it in our Congresses.

fib Bulletin 70: Code-type models for structural behaviour of concrete – Background of the constitutive relations and material models in MC2010. State-of-art report, November 2013. 196 pages, ISBN 978-2-88394-110-6, Non-member price: 120 CHF.

Miguel A. Astiz, President of ACHE

The fib Model Code for Concrete Structures 2010 (MC2010) represents the state-of-the-art of code-type models for structural behaviour of concrete, providing constitutive relations and material models together with the most important explanatory notes. However the underlying normative work, i.e. the fundamental data as well as the considerations and discussions behind the formulas, could not be given within the Model Code text. Based on experience gained after the publication of Model Code 1990, this will lead to numerous questions arising from Model Code users.

2015 symposium: call for papers Abstracts are now being accepted for the 2015 fib Symposium, taking place in Copenhagen, Denmark, from 18 to 20 May 2015. The abstract text must be max. 500 words with no tables or pictures; the deadline for submission is 1st May 2014. The symposium theme is “Concrete: Innovation and Design”, with the following 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 offered for oral presentations of structural concrete projects, under execution or recently completed, without a submitted paper. The PowerPoint presentation is subject to review by the Scientific Committee. To submit an abstract and for further information about the event, visit www.fibcopenhagen2015.dk. 112

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fib Bulletin 70 aims to conquer this general weakness of codes in a way to guard against future misunderstandings of MC2010 chapter 5.1 (Concrete). It discusses the given formulas in connection with experimental data and the most important international literature. The constitutive relations or material models, being included in MC1990 and forming the basis and point of origin of the Task Group’s work, were critically evaluated, if necessary and possible adjusted, or replaced by completely new approaches. Major criteria were physical and thermodynamical soundness and practical considerations like simplicity and operationality. Besides being a background document for Chapter 5.1 of MC2010, Buletin 70 will provide an important foundation for the development of future generations of code-type mod-

els related to the characteristics and the behaviour of structural concrete.

fib Bulletin 71: Integrated Life Cycle Assessment of concrete structures. State-of-art report, December 2013. 64 pages, ISBN 978-288394-111-3, Non-member price: 80 CHF. Concrete is after water the second most used material. The production of concrete in the industrialized countries annually amounts to 1.5-3 tonne per capita and is still increasing. This has significant impact on the environment. Thus there is an urgent need for more effective use of concrete in structures and their assessment. The scope of fib Task Group 3.7’s work was to define the methodology for integrated life-cycle assessment of concrete structures and to set up basic methodology to be helpful in development of design and assessment tools focused on sustainability of concrete structure within the whole life cycle. Integrated Life Cycle Assessment (ILCA) represents an advanced approach integrating different aspects of sustainability in one complex assessment procedure. The integrated approach is necessary to insure that the structure will serve during the whole expected service life with a maximum functional quality and safety, while environmental and economic loads will be kept at a low level. The effective application and quality of results are dependent on the availability of relevant input data obtained using a detailed inventory analysis, based on specific regional conditions. The evaluation of the real level of total quality of concrete structure should be based on a detailed ILCA analysis using regionally or locally relevant data sets.

fib-news

Congresses and symposia Date and location

Event

Main organiser

Contact

12–16 May 2014 Moscow, Russia

3nd All-Russia (International) Conference on Concrete and Reinforced Concrete

Russian Academy of Science and others

http://concrete2014.mgsu.ru

11–13 June 2014 Oslo, Norway

Concrete Innovation Conference (CIC2014)

Norwegian Concrete Assocation

www.cic2014.com

16–18 June 2014 Wroclaw, Poland

AMCM 2014: Analytical Models and New Concepts in Concrete and Masonry Structures

fib Group Poland

www.amcm2014.pwr.wroc.pl

21–23 July 2014 Quebec, Canada

10th fib International Ph.D. Université Laval Symposium in Civil Engineering

www.fib-phd.ulaval.ca

24–25 July 2014 Montreal, Canada

2nd FRC Int. Workshop (1st ACI–fib Joint Workshop) on Fibre Reinforced Concrete

www.polymtl.ca/frc2014

14–17 September 2014 Dresden, Germany

Int. Conf. on Application of TU Dresden superabsorbent polymers and other new admixtures in concrete construction

15–18 September 2014 Beijing, China

10th International symposium on Utilization of HS/HPC

Beijing Jiaotong University www.hpc-2014.com

21–24 September 2014 Seoul, Korea

6th International Conference of Asis Concrete Federation

Asian Concrete Federation www.acf2014.kr Korea Concrete Institute

18–20 May 2015 Copenhagen, Denmark

fib Symposium: Concrete – innovation and design

Danish Concrete Society

24–26 May 2015 Chicago, USA

5th Int. Symposium on Nanotechnology in Construction – NICOM5

5–7 October 2015 Leipzig, Germany

4th Int. Conf. on Concrete Repair, Rehabilitation and Retrofitting (ICCRRR 2015)

MFPA Leipzig GmbH University of Cape Town

dehn@mfpa-leipzig.de

8–9 October 2015 Leipzig, Germany

4th International Workshop on Concrete Spalling due to Fire Exposure

MFPA Leipzig GmbH TU Delft

dehn@mfpa-leipzig.de

21–23 November 2016 fib Symposium Cape Town, South Africa

fib Group South Africa

To be announced

13–17 June 2017 Maastricht, Netherlands

fib Symposium

fib Group Netherlands

To be announced

6–12 October 2018 Melbourne, Australia

5th fib Congress and Exhibition

fib Group Australia

www.fibcongress2018.com

ACI-fib

conference2014@tu-dresden.de

www.fibcopenhagen2015.dk

www.nicom5.org

The calendar lists fib congresses and symposia, co-sponsored events and, if space permits, events supported by fib or organised by one of its National Member Groups. It reflects the state of information available to the Secretariat at the time of printing; the information given may be subject to change. The calendar of events on the fib website (www.fib-international.org/upcoming-event) is updated continuously. Structural Concrete 15 (2014), No. 1

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Preview

Structural Concrete 2/2014 Giancarlo Groli, Caldentey Pérez, Giraldo Alejandro, Alejandro Soto Cracking Performance of SCC reinforced with recycled fibres: an experimental study Xian Liu, Yong Yuan, Ke Su Sensitivity analysis of the early-age cracking risk in immersed tunnel Günther Meschke, Rolf Breitenbücher, Fanbing Song, Yjian Zhan Experimental, analytical and numerical analysis of the pullout behavior of steel fibers considering different fiber types, inclinations and concrete strengths Sevket Ozden, Hilal M. Atalay, Erkan Akpinar, Hakan Erdogan, Yilmaz Zafer Vulas Shear Strengthening of RC T-Beams with Fully or Partially Bonded FRP Composites

The paper by Alfred Strauss, Jan Podrouzek and Konrad Bergmeister presents strategies for robustness based performance assessment using nonlinear modeling. It also discusses relevant reliabilitybased 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 describes strategies on the basis of the novel approach for general complex engineering structures.

Alfred Strauss, Jan Podrouzek, Konrad Bergmeister Robustness based performance assessment of concrete bridges

Jianzhuang Xiao, Yuhui Fan, Vivian Tam Effect of old attached mortar on the creep of recycled aggregate concrete

Bhupinder Singh, M. John Robert Prince Investigation of bond behaviour between recycled aggregate concrete and deformed steel bars

Vladimir Cervenka, Hans Ganz Validation of post-tensioning anchorage zones by laboratory testing and numerical simulation

Yong Yuan, Yang Chi Water permeability of concrete under uniaxial tension Morteza Aboutalebi, Amir Alani, Gokhan Kilic Applications of non-contact senor (IBIS-S) and finite element method in assessment of bridge deck structures

The potential and the limitations of numerical methods The book gives a compact review of ﬁnite element and other numerical 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 Python 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:

Ulrich Häußler-Combe Computational Methods for Reinforced Concrete Structures 2014. approx. 300 pages. approx. € 59,–* Available summer 2014 ISBN 978-3-433-03054-7 Also available as

ﬁnite 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

Recommendations: fib Model Code for Concrete Structures 2010 Structural Concrete Journal of the fib

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

Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG

Customer Service: Wiley-VCH Boschstraße 12 D-69469 Weinheim

Tel. +49 (0)6201 606-400 Fax +49 (0)6201 606-184 service@wiley-vch.de

*€ Prices are valid in Germany, exclusively, and subject to alterations. Prices incl. VAT. excl. shipping. 1044106_dp

Structurae’s 15th Anniversary Structurae is an information network for civil & structural engineers and everybodyelse interested in these topics. Since 1998 Structurae has been offering detailed information about structures from around the world. Below is a selection of structures – one for each year since Structurae’s inception. www.structurae.net

1998

1999

2000

2001

Akashi Kaikyo Bridge

Engelberg Base Tunnel

London Eye

Milwaukee Art Museum

Japan / Asia

Germany / Europe

England / Europe

USA / America

2002

2003

2004

2005

Magdeburg Canal Bridge

Leonard P. Zakim

Millau Viaduct

Allianz Arena

Bunker Hill Bridge

France / Europe

Germany / Europe

USA / America

2006

2007

2008

2009

Orinoquia Bridge

High Speed 1

Caserne Dam

Cape Town Stadium

Venezuela / America

England / Europe

France / Europe

South-Africa

2010

2011

2012

2013

Burj Khalifa

Térénez Bridge

Warsaw National Stadium

MuCEM

UAE / Europe

France / Europe

Poland / Europe

France / Europe A Product of

More detailed information about the above structures can be found at www.structurae.net