1 Volume 16 March 2015 ISSN 14644177
 Eurocode 2 – analysis of National Annexes  Extended design parameters for columns in fire with 2nd order effects  Lowstrength mortars – EC/US code approaches  Bond/Anchorage of steel bars in fib Model Code 2010  Bond behaviour of normal and highstrength RAC  5spring model for full shear behaviour of deep beams  Transverse stresses and bursting forces in posttensioned anchorages  Derivation of σw relationship for SFRC with bending tests  Thinwalled TRC shells – Part I: Design and construction  Thinwalled TRC shells – Part II: ULS assessment, simulation  Quality assessment of material models for RC flexural members  Smallscale tests for composite slab design
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Contents
They have already become a new landmark: The six new water towers in the Al Jahra area in Kuwait City. Their mushroomshaped water tanks were posttensioned using DYWIDAG Strand Tendons. It goes without saying, that these buildings are of decisive importance for the inhabitants of cities in Kuwait, see page A5 (photo: DSI).
Structural Concrete Vol. 16 / 1 March 2015 ISSN 14644177 (print) ISSN 17517648 (online)
1
Message from the president Harald S. Müller From accomplishments to challenges
3
Technical Papers Anett Ignatiadis, Frank Fingerloos, Josef Hegger, Frederik Teworte Eurocode 2 – analysis of National Annexes
17
Lijie Wang, Robby Caspeele, Ruben Van Coile, Luc Taerwe Extension of tabulated design parameters for rectangular columns exposed to fire taking into account secondorder effects and various fire models
36
François Duplan, Ariane AbouChakra, Anaclet Turatsinze, Gilles Escadeillas, Stéphane Brûlé, Emmanuel Javelaud, Frédéric Massé On the use of European and American building codes with lowstrength mortars
45
John Cairns Bond and anchorage of embedded steel reinforcement in fib Model Code 2010
56
M. John Robert Prince, Bhupinder Singh Bond behaviour of normal and highstrength recycled aggregate concrete
71
Boyan Mihaylov Fivespring model for complete shear behaviour of deep beams
84
LinYun Zhou, Zhao Liu, ZhiQi He Further investigation of transverse stresses and bursting forces in posttensioned anchorage zones
93
Ali Amin, Stephen J. Foster, Aurelio Muttoni Derivation of the σw relationship for SFRC from prism bending tests
106
Alexander Scholzen, Rostislav Chudoba, Josef Hegger Thinwalled shell structures made of textilereinforced concrete Part I: Structural design and construction
115
Alexander Scholzen, Rostislav Chudoba, Josef Hegger Thinwalled shell structures made of textilereinforced concrete Part II: Experimental characterization, ultimate limit state assessment and numerical simulation
125
Bastian Jung, Guido Morgenthal, Dong Xu, Hendrik Schröter Quality assessment of material models for reinforced concrete flexural members
137
Josef Holomek, Miroslav Bajer, Jan Barnat, Pavel Schmid Design of composite slabs with prepressed embossments using smallscale tests
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Peer reviewed journal Since 2009, Structural Concrete is indexed in Thomson Reuter’s Web of Knowledge (ISI Web of Science). Impact Factor 2013: 0.857 fédération internationale du béton International Federation for Structural Concrete www.fibinternational.org
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149 150 151 151 152 152 153 153 155 156 157
fibnews The fib in Russia: new standards Worldwide representation at ACF 2014 DISC2014: the past and the future Old for new: Penang Bridge A venerable institute turns 80 JPEE2014 in Lisbon fib MC2010 course in Brazil Short notes Nigel Priestley † 1943–2014 Congresses and symposia Acknowledgement
A5
Products and Projects
Bautechnik 81 (2004), Heft 1
3
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.ernstundsohn.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 EditorinChief Luc Taerwe (Belgium), email: Luc.Taerwe@UGent.be Deputy Editor Steinar Helland (Norway), email: steinar.helland@skanska.no Members György L. Balázs (Hungary) Josée Bastien (Canada) Mikael Braestrup (Denmark) Tom d’ Arcy (USA) Michael Fardis (Greece) Stephen Foster (Australia) Sung Gul Hong (Korea) Tim Ibell (UK) S.G. Joglekar (India) Akio Kasuga (Japan) Daniel A. Kuchma (USA) Gaetano Manfredi (Italy) Pierre Rossi (France) Guilhemo Sales Melo (Brazil) Petra Schumacher (Secretary General fib) Tamon Ueda (Japan) Yong Yuan (China)
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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 2015. 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 Structural Concrete, ISSN 14644177, is published quarterly. US mailing agent: SPP, PO Box 437, Emigsville, PA 17318. Periodicals postage paid at Emigsville PA. Postmaster: Send all address changes to Structural Concrete, John Wiley & Sons Inc., c/o The Sheridan Press, PO Box 465, Hanover, PA 17331. Service for customers and readers WileyVCH Customer Service for Ernst & Sohn Boschstrasse 12, D69469 Weinheim Tel.: +49 (0)800 1800 536 (within Germany) Tel.: +44 (0)1865476721 (outside Germany) Fax: +49 (0)6201 606184 csgermany@wiley.com Quicklink: www.wileycustomerhelp.com © 2015 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin
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Structural Concrete 16 (2015), No. 1
Products & Projects
DYWIDAG Ring Tendons stabilize Kuwait’s new Landmark
Fig. 1. They are an investment of decisive importance for cities in Kuwait: the six new water towers that were built in the Al Jahra area, Kuwait City
Water is a valuable commodity in Kuwait – bottled water is even more expensive than petrol. Consequently, the six new water towers that were built in the Al Jahra area in Kuwait City are an investment of decisive importance for cities in that country. The huge, mushroomshaped water tanks have already become a new landmark of the country and can be seen from afar thanks to their blue and white stripes. The elevated tanks are 38.5m high and have diameters of 32m at the upper rim of the water tanks. This way, the tanks can store more than 2.4 million liters or 650,000 gallons of fresh water. The towers’ mushroomshaped water tanks were posttensioned using DYWIDAG Strand Tendons. DSI supplied 66 60.5“ DYWIDAG Ring Tendons with anchorages and accessories to posttension each tank. Initially, the ducts and tendons were installed into the formwork at ground level. They were then hydraulically lifted onto the pillars of the water towers. Fig. 2. A new landmark of the country
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Fig. 3. The tanks are 38.5m high and have diameters of 32m at the upper rim of the water tanks. (© DSI)
Afterwards, concreting, posttensioning and grouting of the tendons were carried out using the equipment that had been supplied by DSI. Further Information: DSI Holding GmbH, Destouchesstrasse 68, 80796 Munich, Germany, Tel. +49 (0)89 – 30 90 50200, Fax +49 (0)89 – 30 90 50215, info@dywidagsystems.com, www.dywidagsystems.com
Structural Concrete 16 (2015), No. 1
A5
Products & Projects
Generation of Moving Loads on Surfaces The RFEM addon module RFMOVE Surfaces creates load cases from various positions of moving loads such as vehicles on bridges. It is also possible to create an enveloping result combination.
You can define the „lane” by using sets of lines. They can be selected graphically in the model. The moving step of single load steps is also specified. RFMOVE Surfaces provides several load types such as single, linear, rectangular, circular loads as well as different axle loads. They can be applied in local and in global directions. The different loads are summarized in load models. The defined load models are allocated to the sets of lines and on the basis of this information, individual load cases are generated. With a single mouse click, you can create a variety of load cases. When the generation has been completed, RFMOVE Surfaces displays the numbers of the created load cases for information. The descriptions of the individual moving loads are deduced from the respective load step number. It is possible, however, to replace those names in RFEM by other load case descriptions. Finally, the entire window input can be exported to MS Excel or OpenOffice.org.Calc. More Information and Trial Versions: Dlubal Software GmbH, Am Zellweg 2, 93464 Tiefenbach, Tel. +49 (0)96 73 – 92 030, Fax +49 (0)96 73 – 92 0351, info@dlubal.com, www.dlubal.de
Fig. 1. Definition of the lane using sets of lines in RFMOVE Surfaces
The data is entered in only four input windows. In this way, and due to the quick load case generation for RFEM, you can save a lot of time.
Features – Parameterized load positions for different concentrated, distributed, surface and axle loads – Access to different stored axle load models (database) – Favorable or unfavorable load application taking into account influence lines and surfaces – Summarizing several moving loads in one load scheme – Generation of a result combination to determine the most unfavorable internal forces – Option to save different sets of movements to use them in other structures
Working with RFMOVE Surfaces The surfaces on which the load is moving are selected graphically in the RFEM model. It is possible to define a load on a surface with several different sets of movements at the same time.
Fig. 2. Generated Loads in RFEM (© Dlubal)
A6
Structural Concrete 16 (2015), No. 1
MAURER AG: Change of corporate form with a view to the future With effect from 15. December 2014 the tradition steeped Munich firm specializing in steel construction, mechanical and plant engineering, Maurer Söhne GmbH & Co. KG will become the MAURER AG. The change in corporate form to a stock corporation denotes a milestone in the company`s strategy: The path is leading in the direction of further internationalization and the internationally recognized legal form of stock corporation is a logical step on this path. Maurer AG will be represented by a new Logo and a new internet presence. The new Logo of the renamed MAURER AG. The M can stand alone. (© Maurer)
Dr. Holger Krasmann (Chairman of the Executive board) and Dr. Christian Braun, the former managing directors, have been appointed to the board of the renamed Maurer AG. The company will remain in the ownership of the Beutler and Grill families, with Jörg Beutler as Chairman of the Supervisory Board. A new, clearer brand image will support the changeover to a stock corporation. The Logo has been reworked: Clear, contemporary and distinctive, the Logo communicates strength and unity. The company name now only consists of the name Maurer. The new internet presence www.maurer.eu gives a clear visual message of technological orientation. “However it is not only a visual concept” explains head of marketing Judith Klein, “rather that we want to present a company cast from one piece, no longer separated into subdivisions but one homogenous Company.” Naturally the new website is also optimized for mobile devices. Further Information: MAURER AG, Frankfurter Ring 193, 80807 München, Tel. +49 (0)89 – 323 940, info@maurersoehne.de, www.maurer.eu
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Products & Projects
Strasbourg receives another clinic PASCHAL gets things moving on the construction site in the Strasbourg district of Cronenbourg with its “TTR” Trapezoidal girder circular formwork and the speedy construction progress for column formwork is supported with the multipurpose panel.
Fig. 2. The small ellipse with half of a Trapezoidal girder circular formwork unit in the foreground; the assembled recess formwork for the penetrations is subsequently reinforced.
Fig. 1. The small ellipse is rounder and has 5 x 4 = 20 radii.
EPSAN and ARS Alsace, partners for psychiatric care, commissioned the construction of a 140bed hospital to provide better patient care.
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The Alsace branch of the construction company EIFFAGE CONSTRUCTION in Strasbourg prepared the project for the clinic, which is scheduled to open at the end of 2015. The square building structure is broken up by two twostorey, elliptical reinforced concrete constructions and a rounded reinforced concrete construction.
First choice for rounded reinforced concrete constructions To form the two ellipses and the semicircular reinforced concrete wall, Eiffrage, the construction company in charge, used the TTR Trapezoidal girder circular formwork from PASCHAL. The construction company relied on the materials being delivered and also profited from PASCHAL’s specialist knowledge and experience, which they used for the preparations and compliance with the work safety regulations. The application engineering department at PASCHAL was therefore involved in the construction project from the very beginning and delivered a detailed and practical formwork concept in close coordination with the other parties involved in the project.
Individual columns on individual foundations Right at the start of the shell construction, the slim reinforced concrete columns (dimensions: 35 × 65 cm) were formed and concreted with the multipurpose panel from the LOGO.3 formwork system. Four multipurpose panels can be used to form rectangular and square columns with edge lengths from 20 cm to 75 cm quickly and easily using the “windmill vane principle”. This was applied on the construction site in Strasbourg. To speed up the work progress and to meet the strict French accident prevention regulations, the column forms were each fitted with two preassembled work platforms opposite each other.
Curved concrete constructions Anchor Profi is probably the best tool available to you to meet your future requirements in anchorage design, anchor comparison and selection from all major European anchor manufacturers. For further information, please contact: Dr. Li Anchor Profi GmbH GustavStollWeg 7, D72250 Freudenstadt Phone: +49 7441 4073833, Fax: +49 7441 4077139 Internet: www.anchorprofi.de, Email: info@anchorprofi.de
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Structural Concrete 16 (2015), No. 1
Both ellipses consist of a 20 cm thick C25/30 reinforced concrete wall. The large ellipse has a length of 13.352 m and a width of 5.825 m. The small construction has a length of 6.50 m and a width of 4.26 m. Both ellipses have a height of 9.39 m to 9.75 m. The height difference is due to the sloping upper connecting wall. To optimally support the construction progress, PASCHAL supplied completely preassembled and rounded TTR formwork units for the first step, including preassembled folding work platforms for the construction site. For the height intervals of the working levels, attention was paid to the easy accessibility of
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Fig. 3. Completely preassembled formwork units of the Trapezoidal girder circular formwork with plywood and builton, folding work platforms are ready for use.
The Ultimate FEA Program
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Steel Construction
Fig. 4. To the left, the dismantled “large ellipse”. To the right, the mounted formwork unit consisting of TTR segments for the rounded reinforced concrete wall in “Block 11”. The three working levels were coordinated with the formwork and reinforcements to be executed so that the builders could work quickly and safely. (© Paschal)
CrossSections
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Bridge Construction
To shape each ellipse as planned, the engineers in application engineering “mirrored” each ellipse along the longitudinal axis. To form the large ellipse, the two infinitely “adjustable ranges” were combined with the “adjustable range” up to 5 metres inside diameter. When added together, this ellipse comprises 8 × 4 = 32 radii. To ensure a smooth transition at the concrete sections to the left and right of the longitudinal axis, the inner and outer formworks extended beyond the actual concrete section and 3/4 were covered with a panel of 1.25 m during concreting of the opposite halves of the formwork with the two formwork units. All three rounded structural parts were built with system formwork and form
These possible combinations allow all curvatures to be shaped exactly, as there is a matching outside segment for each inside segment. The system only uses a few ties and reliably absorbs fresh concrete pressure of up to 60 kN/m². Further information: PASCHALWerk G. Maier GmbH, Kreuzbühlstraße 5, 77790 Steinach, Tel. +49 (0)78 32 – 710, Fax +49 (0)78 32 – 71209, service@paschal.de, www.paschal.de
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3D Frameworks
Stability and Dynamics
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Column Bases
Formwork planning for ellipses
work filler plates supplied by PASCHAL were used for compensation. As the pioneer of circular formwork with adjustable radii, PASCHAL is constantly faced with diverse reinforced concrete construction shapes, as highlighted by the Strasbourg clinic example. Thanks to extensive practical experience, PASCHAL’s specialist team is able to prepare system formwork even for such unusual shapes. The invaluable benefits come from the Trapezoidal girder circular formwork available in two versions: – For inside diameters from 5.00 m (r = 2.50 m) to infinity (straight). – For inside diameters from 2.00 m (r = 1.00 m) to inside diameters of 5.00 m.
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the ties during formwork planning, so that the formwork tasks could be completed quickly and safely. For each preassembled formwork unit, the dead weight and the admissible capacity of the crane lifting eyes were calculated exactly and recorded on the formwork drawings for the work phases. In this way, the crane operator knew the lifting weight for each moving process of the formwork units.
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Products & Projects
Toppingout ceremony for New Office Airport Stuttgart Last year’s November saw the toppingout ceremony for New Office Airport Stuttgart (NOAS), a new office building and one of the largest construction projects at Stuttgart Airport in recent years. With its rounded contours, the striking new building will redefine the character of the entrance to Stuttgart’s Airport City. Züblin completed the structural works on time within the schedule provided and the building’s first tenant, financial audit firm Ernst & Young, is slated to move its Germany headquarters into the complex in early 2016.
Fig. 2. With its rounded contours, the striking new building will redefine the character of the entrance to Stuttgart’s Airport City.The structural works have been completed by Züblin on time within the schedule provided. (© Stuttgart Airport)
Fig. 1. Bird’s eye view on one of the largest construction projects at Stuttgart Airport in recent years
In his ceremonial speech, Walter Schoefer, managing director of Stuttgart Airport, stressed: “We are investing about € 130 million in this excellent office property as a symbol for the further statedriven development of our airport site. Over 1,500 employees of Ernst & Young will relocate here in 2016, giving the campus enormous economic strength. The move shows that optimal infrastructure and mobility are extremely important for globally positioned companies. In this respect, Stuttgart Airport is one of the bestdeveloped locations in the state of BadenWürttemberg.”
A10 Structural Concrete 16 (2015), No. 1
Michael Marbler, lead partner for southwest Germany at Ernst & Young, and Roland Wiehl, business unit manager for turnkey construction at Züblin, which is handling the project turnkey as general contractor, expressed their thanks to the workers for helping to complete the structural works so swiftly and perfectly. The new office building was planned and is being built according to the latest standards in terms of efficiency, sustainability and comfort. The architectural design by Hascher Jehle Architekten consists of two building complexes in the form of a reclining figure eight plus a third complex housing a conference centre. The office building, which is clearly visible as a new landmark from the A8 motorway, comprises an aboveground area of around 40,000 m2 as well as two underground floors with approximately 20,000 m2 for parking, storage and cellar rooms. Further Information: Ed. Züblin AG, Albstadtweg 3, 70567 Stuttgart, Tel. +49 (0)711 – 78 830, Fax +49 (0)711 – 78 83390, info@zueblin.de, www.zueblin.de
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Provider directory products & services
bridge accessories
Maurer Söhne GmbH & Co. KG Frankfurter Ring 193 D80807 München Phone +49(0)89 32394341 Fax +49(0)89 32394306 Mail: ba@maurersoehne.de Web: www.maurersoehne.de Structural Protection Systems Expansion Joints Structural Bearings Seismic Devices Vibration Absorbers
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HALFEN Vertriebsgesellschaft mbH Katzbergstraße 3 D40764 Langenfeld Phone +49 (0) 21 73 9 700 Fax +49 (0) 21 73 9 702 25 Mail: info@halfen.de Web: www.halfen.de concrete: fixing systems facade: fastening technology framing systems: products and systems
posttensioning Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG Rotherstraße 21 10245 Berlin Phone +49 (0) 30 4 70 312 00 Fax +49 (0) 30 4 70 312 70 Email: info@ernstundsohn.de Web: www.ernstundsohn.de
DYWIDAGSystems International GmbH MaxPlanckRing 1 40764 Langenfeld/Germany Phone +49 (0)21 73/7 90 20 Mail: dsihv@dywidagsystems.com Web: www.dywidagsystems.de
prestressed concrete
HALFEN Vertriebsgesellschaft mbH Katzbergstraße 3 D40764 Langenfeld Phone +49 (0) 21 73 9 700 Fax +49 (0) 21 73 9 702 25 Mail: info@halfen.de Web: www.halfen.de concrete: fixing systems facade: fastening technology framing systems: products and systems
Max Frank GmbH & Co. KG Technologies for the construction industry Mitterweg 1 94339 Leiblfing Germany Phone +49 (0)94 27/1 890 Fax +49 (0)94 27/15 88 Mail: info@maxfrank.com Web: www.maxfrank.com
sealing technologies Paul Maschinenfabrik GmbH & Co. KG MaxPaulStraße 1 88525 Dürmentingen/Germany Phone +49 (0)73 71/5 000 Fax +49 (0)73 71/5 001 11 Mail: stressing@paul.eu Web: www.paul.eu
software
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Max Frank GmbH & Co. KG Technologies for the construction industry Mitterweg 1 94339 Leiblfing Germany Phone +49 (0)94 27/1 890 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 92 030 Fax +49 (0) 96 73 92 0351 Mail: info@dlubal.com Web: www.dlubal.de
stay cables
DYWIDAGSystems International GmbH MaxPlanckRing 1 40764 Langenfeld/Germany Phone +49 (0)21 73/7 90 20 Mail: dsihv@dywidagsystems.com Web: www.dywidagsystems.de
vibration isolation
BSW GmbH Am Hilgenacker 24 D57319 Bad Berleburg Phone +49(0)2751 803126 Mail: info@berleburger.de Web: www.bswvibrationtechnology.com underscreed impact sound insulation with European Technical Approval, PUR foam & PUR rubber materials for vibration isolation
Structural Concrete 16 (2015), No. 1
A11
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 HäusslerCombe Computational Methods for Reinforced Concrete Structures 2014. 354 pages. € 59,–* ISBN 9783433030547 Also available as
ﬁnite element in a nutschell uniaxial structural concrete behavior 2D structural beams and frames strutandtie models multiaxial concrete material behavior deep beams slabs appendix
Recommendations: fib Model Code for Concrete Structures 2010 Structural Concrete Journal of the fib
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Message from the president
From accomplishments to challenges On 1 January I began my twoyear term as fib president with emotions ranging from deep respect for the office to pleasure at the idea of serving the fib in such a prominent role. This outstanding international association has been my home for many years and I have occupied various positions within it since I started in the CEB in 1979. I am truly humbled to fill the same role as such extraordinary individuals as Gordon Clark, György L. Balázs, and Michael Fardis, to mention but a few. When I think of the fib’s mission and look back at its recent history, I see significant contributions to the advancement of knowledge and technical developments in the field of structural concrete. The greatest accomplishment was the publication of the fib Model Code for Concrete Structures 2010 in September 2013, which exemplified the fib’s ambition to compile the most uptodate knowledge in codetype form to serve as a model for new generations of standards. Following indepth analyses and discussions that began in 2010, the new structure for the fib’s commissions and task groups was implemented at the beginning of this year and will help the fib to run more efficiently. Finally, Structural Concrete, journal of the fib, has made great progress: last year its impact factor increased from 0.289 to 0.857, testimony to the high quality of its articles. Therefore, it would seem that, as president, I have only to steer the association forward with a steady hand on the wheel. Not so. I think such an approach would be hazardous in our rapidly changing world. Stagnation means regression. We have to build on our accomplishments. The true challenge consists of developing a vision that looks beyond the horizon. With this in mind, I would define my main targets in these terms: strategy, development, and globalisation. For me, ‘strategy’ comprises, for example, a concept for continuously updating the fib Model Code. Exactly 20 years elapsed between MC 1990 and MC 2010; MC 1990 was already partially outdated by the end of the 1990s. ‘Strategy’ also means finding the best framework for designating fib membership status and future benefits. By ‘development’, I mean defining the technical advances to be promoted by the fib, one of which is of
course sustainability. Simply partially replacing Portland cement in concrete with other binders will not solve future problems. Since concrete use will increase by a factor of five over the next 30 years, only the development of new concretes and design concepts will help to avert increased environmental troubles. We need task groups to tackle these problems. Developing a model code Harald S. Müller for existing structures is a logical step, as maintenance and rehabilitation are the most effective sustainable measures. Referring to ‘globalisation’, I think firstly of the fib’s role within the international associations scene, where ISO, CEN, the ACI, RILEM, the ACF, and others, have missions that are partially similar and certain publications that are comparable to those of the fib. Defining our own position more clearly and developing closer official contacts, for example through cooperation agreements or memoranda of understanding, appears to be advantageous in many respects. My approach may mean that I, along with my designated successor, current Deputy President Hugo Corres, will face sizable challenges. I am, however, rather confident that we will contribute to the progress of the fib, not because of our own aptitudes, but because of the support of the excellent engineers, scientists, and practitioners from all over the world who form the backbone and strength of the fib.
Univ.Prof. Dr.Ing. Harald S. Müller President, International Federation for Structural Concrete (fib)
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Technical Paper Anett Ignatiadis Frank Fingerloos* Josef Hegger Frederik Teworte
DOI: 10.1002/suco.201400060
Eurocode 2 – analysis of National Annexes Eurocode 2 consists of four parts that have to be applied in conjunction with the respective National Annexes of the CEN member states. The National Annexes were introduced, in particular, to maintain national safety levels and to account for regional aspects in the different states. The CEN (European Committee for Standardization) will revise and extend all structural Eurocodes by 2018. As part of that process, two main objectives for revising Eurocodes have been formulated: a reduction in the number of Nationally Determined Parameters (NDP) and improving the “ease of use”. In order to reduce the number of NDP, improve the ease of use and allow for further harmonization without changing the main structure and the design models of Eurocode 2, the National Annexes of EN 199211 for the different CEN member states have been compared and analysed. Furthermore, the analysis of the National Annexes may help to identify some main aspects for the revision of Eurocode 2. This paper summarizes the analysis of the National annexes of EN 199211 and makes first proposals for further harmonization. Keywords: Eurocode 2, national annexes, NDP comparison, harmonization
1
Reason and introduction
The European Commission has initiated the amendment and evolution of the present Eurocode generation by 2018 in accordance with mandate M/515 [1]. The European standards organization CEN followed up the mandate with detailed proposals for the respective work programmes [2]. As part of that process, two main objectives for the revision of Eurocodes have been formulated: a reduction in the number of Nationally Determined Parameters (NDP) and improving the “ease of use”. In Germany these objectives have been expressly supported. Therefore, the engineering offices and industrial associations chiefly affected by the codes in their everyday business have established the Initiative PRB, an organization that aims to make the Eurocodes easier to use. Based on collecting and evaluating the experience gained with the present Eurocodes, practiceoriented proposals will be developed for the next Eurocode generation.
* Corresponding author: fingerloos@betonverein.de Submitted for review: 21 July 2014 Accepted for publication: 5 September 2014
Looking after concrete construction and Eurocode 2 within this organization are the German Committee for Structural Concrete (DAfStb) and the German Society for Concrete and Construction Technology (DBV). One of the first tasks was to analyse the implementation of Eurocode 2 in the National Annexes of the CEN member states (CENMS). Eurocode 2 consists of four parts ([3], [4], [5], [6]), which have to be applied in conjunction with the respective National Annexes. The National Annexes were introduced, in particular, to maintain national safety levels and to account for regional aspects in the different CENMS. Some CENMS also implemented additional national rules and explanations in the form of NCI (Noncontradictory Complementary Information) for further guidance. In order to reduce the number of NDP, improve the ease of use and allow for further harmonization without changing the main structure and the existing models, the National Annexes of EN 199211 of the different CENMS have been compared and analysed. Furthermore, the analysis of the National Annexes may help to identify some main aspects for the revision of Eurocode 2. The German mirror committee for Eurocode 2 takes the view that, in principle, the present code structure and the design and detailing rules should remain largely unchanged, unless unacceptable safety deficits or other technical and economical reasons exist (e.g. “ease of use”). The following sections summarize the results of an analysis of the National Annexes of EN 199211 and make the first proposals for further harmonization.
2
Analysis and comparison
The National Annexes contain two types of information: the Nationally Determined Parameters (NDP) and the noncontradictory complementary information (NCI). Whereas the NCI may contain additional or specific national rules (e.g. application rules for cases not covered by Eurocode 2, links to national codes or literature), the NDP represent mostly single values, groups of values, tables or methods from which choices can be made. Recommended values are given in Eurocode 2, which can be adopted or changed in the National Annexes of the many CENMS. Background information to the German National Annex [8] can be found in [7].
© 2015 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete (2015), No. 1
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A. Ignatiadis/F. Fingerloos/J. Hegger/F. Teworte Âˇ Eurocode 2 â€“ analysis of National Annexes
Altogether, Eurocode 2 refers to more than 120 NDP in EN 199211 [3] and a further approx. 70 NDP in EN 199212 [4], EN 19922 [5] and EN 19923 [6]. The National Annexes of EN 199211 of 28 states ([8] to [36]) have been compared in the present analysis. Malta and Latvia do not have National Annexes and the Swiss document is still in print. Fig. 2 shows the implementation of the recommended values given in Eurocode 2 in the different National Annexes. The resulting potential for harmonization is shown in Fig. 1. In general, the concepts and models of Eurocode 2 are adopted by all states. Only the informative annexes do not apply in every state, and in some states single paragraphs are omitted via NDP or NCI. In many cases the NDP just change some values compared with [3]. Hence, the number of differences between the National Annexes and [3] does not necessarily reflect the acceptance of EC2 in the different countries. Larger changes to the models and concepts implemented are exceptions (e.g. Finland does not apply the sections concerning punching, which may be solved with the current amendment [37]; Denmark has introduced a more detailed concept for the material safety factors and a design concept based on plastic theory).
E: 5 (4%) A: 8 (6%) B: 23 (18%) D: 44 (34%)
C: 48 (38%)
Key to Fig. 1: Categories A: Harmonization by fixing value B: Harmonization possible by introducing classes C: Good chance for harmonization D: Harmonization may be possible (fixed or classes) E: Harmonization very difficult Fig. 1. Potential for harmonization of NDP in EN 199211 (28 states analysed)
NDP in EN 199211 Hungary Czech Republic Slovenia Slovakia Poland Croatia Spain Portugal Italy Cyprus Romania Greece Bulgaria Netherlands Luxembourg Belgium Norway Lithuania Iceland Finland Estonia Denmark Sweden Ireland United Kingdom France Austria Germany
HU CZ SI SK PL HR ES PT IT CY RO GR BG NL LU BE NO LT IS FI EE DK SE IE UK FR AT DE 0
10
20
30
40
50
60
70
80
90
100
Number of NDP Key: Recommended values adopted In general, recommended values adopted, but special conditions for application or exceptions possible Different values Section does not apply Section not mentioned in NA / information incomplete or ambiguous Fig. 2. Comparison of Nationally Determined Parameters (NDP) with the recommended values in EN 199211
4
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110
120
130
A. Ignatiadis/F. Fingerloos/J. Hegger/F. Teworte · Eurocode 2 – analysis of National Annexes
To outline possibilities for further harmonization and to identify main aspects for revision, the NDP were divided into five categories. NDP with acceptance of the recommended values according to EN 199211 in all states were classified as category A (e.g. safety factor for fatigue). Furthermore, there are several NDP where only two or three different values are used in all states. In this case, harmonization by introducing classes seems possible (category B). This concerns, for example, the factor αcc used when calculating the design value of concrete compressive strength, which only differs between 0.85 and 1.0. Category C describes NDP where the differences are quite small and only a few states do not apply the recommended values, thus leading to a high potential for harmonization (see example in Table 1). The values of NDP in category D show larger differences, so there is greater need for discussion, see Table 2. NDP in categories C and D especially need further investigation concerning the reasons for the differences. The differences, particularly regarding the final result (e.g. dimensions, amount of reinforcing steel), may be identified by means of parameter studies or comparative calculations. For some NDP the chance for further harmonization seems to be rather small (category E). This applies especially to NDP that relate to other codes, e.g. determining the minimum concrete cover depending on the exposure classes with reference to EN 2061:2000 [39] or the properties of reinforcing steel with reference to EN 10080 [40]. Table 3 lists and classifies the NDP of EN 199211 concerning the potential for harmonization applying the five categories A to E described above.
3 3.1
Approaches for reducing the number of NDP and further harmonization General
Different approaches can be applied to reduce the number of NDP, and hence also the volume of Eurocode 2 and the National Annexes. One approach, especially applicable to NDP in category A, is the use of the recommended values as fixed values. However, for safety factors it may be necessary to retain an opening clause for formal reasons. Another approach is the introduction of classes, which seems to be promising for NDP in category B. Furthermore, some NDP may be omitted due to the revision or reduction of the corresponding section (e.g. if special cases or application methods are shortened). After a discussion of the different national provisions, it may be possible to enhance the chance for harmonization by clarifying the corresponding section for some NDP (e.g. different recommended values for different loads). In doing so, the existing concepts and models can generally be retained and there is no need to start harmonization based on a completely new document. Owing to the number of parameters and the complexity of the Eurocodes, it cannot be ruled out that identical or similar influences are considered in different paragraphs in the many CENMS. For this reason, many NDP cannot be dealt with independently, but have to be evaluated according to their final result accounting for the influencing NDP. Therefore, some NDP may be summarized as one NDP without influence on the (national) final re
Table 1. Example of NDP for category C (good chance for harmonization)
Section
5.10.2.2 (5)
Parameter
k6
Description
Coefficient used to determine maximum compressive stress at time of transfer of prestress for pretensioned elements
Recommended value
0.70
Values in National Annexes1) DE, AT, FR, UK, IE, SE, DK, EE, IS, LT, NO, LU, NL, BG, GR, RO, CY, IT, PT, HR, PL, SK, SI, CZ: recommended value FI
0.65
BE
0.667 fcm(t)/fck(t)
ES
0.60
HU
up to 0.90 (under defined conditions)
1)
for CEN Member State codes see Fig. 2
Table 2. Example of NDP for category D (average chance for harmonization)
Section
5.5 (4)
Parameter
k1, k2, k3, k4, k5, k6
Description
Coefficients to limit the redistribution of bending moments without an explicit check of the rotation capacity
Recommended values k1 = 0.44; k2 = 1.25 · (0.6 + 0.0014/εcu2); k3 = 0.54; k4 = 1.25 · (0.6 + 0.0014/εcu2); k5 = 0.7; k6 = 0.8 Values in National Annexes1) AT, FR, SE, DK, EE, IS, LT, BE, LU, BG, GR, RO, CY, PT, HR, PL, SK, SI, CZ, HU: recommended values IT
Recommended values, except k6 = 0.85
NO
Recommended values, except k6 = 0.9
ES
Recommended values, except k6 = 0.8εcu2
DE
k1 = 0.64; k2 = 0.8; k3 = 0.72; k4 = 0.8; k5 = 0.7 and k6 = 0.8 for fck ≤ 50 MPa; k5 = 0.8 and k6 = 1.0 for fck > 50 MPa
UK, IE For reinforcing steel with fyk ≤ 500 MPa: k1 = 0.40, k2 = 0.6 + 0.0014/εcu2; k3 = 0.40, k4 = 0.6 + 0.0014/εcu2; k5 = 0.7; k6 = 0.8 (more restrictive values for fyk > 500 MPa, further guidance in PD 6687 [38]) FI
k1 = 0.44; k2 = 1.10; k3 = 0.54; k4 = 1.25 · (0.6 – 0.0014/εcu2); k5 = k6 = 1.0 for 100 · εuk · ft/fyk < 2.5; k5 = k6 = 0.9 – 3.21· εuk · ft/fyk ≥ 0.67 for 100 · εuk · ft/fyk ≥ 2.5
NL
k1 = f/(500 + f); k2 = 0; k3 = 7f/(εcu · 106 + 7f) with f = [(fpk/γS – σpm,∞) · Ap + fyd · As)]/(Ap + As) k4 = 1.0; k5 = 0.7; k6 = 0.8
1)
for CEN Member State codes see Fig. 2
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Table 3. Analysis of NDP in EN 199211
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Table 3. Analysis of NDP in EN 199211 (Continued)
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sult, whereas in other cases a single NDP cannot be harmonized, instead a group of NDP has to be considered in combination (e.g. the permitted angle of the inclined compression strut determining the shear resistance and the maximum spacing of shear reinforcement). During the revision of Eurocode 2, attention has to be paid to ensuring consistent recommended values in the remaining NDP, which means avoiding mixing up different national methods and philosophies so that the use of all recommended values is possible and on the safe side. Furthermore, the influences on the other parts of Eurocode 2, especially part 2, have to be considered. It cannot be ruled out that new NDP have to be introduced during the revision. However, this may still lead to a reduction in the National Annexes if NCI can be omitted instead. In particular, in cases where NCI in the National Annex contradict the Eurocode or contain more restrictive requirements, the implementation of NDP will be a better solution. Further research concerning the background to the national provisions, parameter studies and in some cases comparative analyses is necessary to make specific proposals. The classification of the NDP into categories A to E is explained in the following section. In addition, NDP related to other NDP are identified. Proposals for harmonization and further procedures are described for certain NDP.
3.2 Specific approach for certain NDP 3.2.1 Basis of design In section 2.3.3 (3) a value of 30 m is recommended as the maximum spacing for joints to preclude temperature and shrinkage effects from the global structural analysis. Although only some CENMS have adopted this value, the chances for harmonization are high (category C). In the states not adopting the recommended value, this value has to be determined for each individual case (e.g. in Germany), or several values dependent on different influences are given (e.g. member geometry, concrete composition, foundation type, regional factors and others). Since this parameter can be dealt with independently from other NDP, the section could be revised, not recommending any specific value but instead pointing out factors to be considered so that the NDP could be omitted. Detailed guidance and recommendations for several cases could be given in background literature. The recommended values for the partial factor for shrinkage action in section 2.4.2.1 (1), for the partial safety factor for fatigue loading in section 2.4.2.3 (1) and for the partial safety factors for materials for serviceability limit states in section 2.4.2.4 (2) have been adopted by all states and could be fixed unless barred for formal reasons (category A). The recommended value of 1.0 for the partial safety factor for favourable prestressing action in section 2.4.2.2 (1) has been adopted by most CENMS. In the United Kingdom, Ireland and Finland, a value of 0.9 is used, while in Norway and Romania values of 0.9 and 1.1 are applied. Therefore, this NDP was classified as category C. The recommended value of 1.3 for the partial safety factor for unfavourable external prestressing action at the stabili
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ty limit state in section 2.4.2.2 (2) has been adopted by many states. The differing values range from 1.0 to 1.3 and so this NDP was classified as category D. The recommended value of 1.2 for the partial safety factor for unfavourable prestressing action for local effects in section 2.4.2.2 (3) has been adopted by most states; only Germany and Norway use other values (category C). These three NDP cannot be observed independently from other NDP concerning prestressing (especially in section 5.10). Since these NDP concern special cases (external prestressing with additional European Technical Approvals (ETAs)) or certain verifications (tensile splitting reinforcement, partly also requirements in ETAs), NDP in sections 2.4.2.2 (2) and (3) may eventually be omitted. The recommended values for the partial safety factors for materials for ultimate limit states in section 2.4.2.4 (1) have been adopted by many states. This NDP was classified as category D even though the differences are not very great. Denmark has applied a more detailed system taking into account the type of failure and the level of inspection. Here, it can be checked whether some of these influences are already covered by the current Annex A of Eurocode 2 as well. The values for reinforcing and prestressing steel with γS = 1.15 for the persistent, transient and fatigue design situations and γS = 1.0 for the accidental design situation have been adopted by all other states, except The Netherlands, where the factor γS = 1.1 is applied for prestressing steel in these situations. Further, γC = 1.5 for concrete in the persistent, transient and fatigue design situations has been adopted by almost all other states, with the following exceptions: Poland: γC = 1.4; Italy: other values for special cases; The Netherlands: γC = 1.35 for fatigue design. The maximum deviation occurs in the accidental design situation, where values of γC higher than the recommended value (1.2) are applied (Germany, Spain: 1.3) as well as values lower than the recommended one (Italy: 1.0). Complete harmonization seems to be quite difficult. In addition, these factors (especially γC) are used several times in Eurocode 2, but eventually some of these values could be fixed unless barred for formal reasons. The recommended value kf = 1.1 for the coefficient for multiplying the partial safety factor for concrete when calculating the design resistance of castinplace piles without a permanent casing in section 2.4.2.5 (2) has been adopted by most CENMS (category C). In Germany and Austria, kf = 1.0 is possible if the bored piles are built according to EN 1536 [41], and in Denmark and Italy a value of 1.0 is applied in general. In France the factor has to be determined according to the national code NF P94262 [42]. It is necessary to check (also in section 9.8) which provisions for foundation members are necessary in Eurocode 2 and what is already covered in Eurocode 7 [43] or in the codes for execution of special geotechnical work (e.g. EN 1536).
3.2.2 Materials The maximum concrete strength class of C90/105 for using Eurocode 2 in section 3.1.2 (2) has been adopted by most CENMS (category C). Germany, Sweden and Norway allow a higher strength class (C100/115 or C95/110). In some states the use of strength classes higher than
A. Ignatiadis/F. Fingerloos/J. Hegger/F. Teworte · Eurocode 2 – analysis of National Annexes
C50/60 requires the approval of the authority responsible and in other states they can be used only with some restrictions. The value for bridges may be different (EN 19922 NDP to 3.1.2 (102)P). Owing to developments in concrete technology, harmonization seems possible by the time the new generation of Eurocodes is published. Factor kt, for reducing coefficients αcc and αct if the concrete strength is determined at age t > 28d, is defined in section 3.1.2 (4). In most of the states the recommended value of 0.85 or a value of 1.0 is applied. In some states the influence is considered by interpolation (Spain, Hungary), determination according to the development of the strength (Germany, Denmark) or by equation 1/αcc(t) (Norway, Slovenia). The introduction of classes might be possible in this case (category B). This NDP could also be included in the NDP αcc in 3.1.6 (1) and αct in 3.1.6 (2) as it only can be observed in relation to these parameters. Coefficient αcc in section 3.1.6 (1) takes into account longterm effects on the compressive strength and unfavourable effects resulting from the load application. The recommended value of 1.0 is adopted in about half the states. Some states apply a value of 0.85 and some states apply values of 0.85 or 1.0 depending on the load (e.g. 0.85 for axial force and bending, 1.0 in other cases). The introduction of classes could be a way of harmonizing here (category B). It has to be considered that this parameter influences many verifications indirectly via fcd. To enhance the chances for harmonization, it has to be checked in the several sections as to whether the reduction in compressive strength is justified and if other NDP in the several sections include a similar reduction, especially in the states that apply αcc = 1.0. For this purpose, careful investigation of which influences are considered precisely by coefficient αcc is necessary. It is the same with coefficient αct in section 3.1.6 (2), which takes into account longterm effects on the tensile strength and unfavourable effects resulting from load application. In most of the states the recommended value of 1.0 is adopted. Only Germany and Norway apply a value of 0.85 and Spain reduces the value for high ratios of permanent and full load. Furthermore, it should be confirmed whether the σs [MPa]
applied values for NDP to 3.1.6 (101)P and NDP to 3.1.6 (102)P in EN 19922 are different in one state. If not, at least this NDP could be eliminated there. The stressstrain diagram for reinforcing steel is defined in section 3.2.7 (2). Apart from the bilinear stressstrain diagram with horizontal top branch without strain limit, a bilinear stressstrain diagram with inclined top branch and limitation of strains may be applied. The strain limit εud depends on the National Annexes. The recommended value εud = 0.9εuk is applied in many states. However, there are also differences, e.g. in Denmark only the stressstrain diagram with horizontal top branch is applied, and in Germany and Finland one absolute value independent of εuk is defined. In Norway, for example, εud is defined depending on the steel class, since different classes exhibit different ductilities. As the steel class used (wire fabrics = class A; reinforcing bars = class B) is not always known during the design process, in Germany this approach was not considered practical, leading to one diagram for all classes (and therefore to identical design tools). Figs. 3 and 4 only reflect how the values determined influence the stressstrain diagrams and do not show the differences in, for example, the amount of reinforcement resulting from this. Hence, the parameter is classified as category D. To identify the potential for harmonization, further investigation is necessary. The impact on the reinforcement required could be figured out by comparative analyses of different member types (e.g. beams, slabs, columns), also considering the minimum reinforcement and, where applicable, the stress limits. Therefore, the stressstrain diagram with horizontal top branch should also be considered. It is conceivable that the differences in the amount of reinforcement will be rather small, so this diagram may be sufficiently accurate in most cases (especially for steel classes A and B) and the NDP could be eliminated. The minimum value k = fpk/f0.1k to ensure adequate ductility in tension for the prestressing tendons is defined in section 3.3.4 (5). The recommended value k = 1.1 has been adopted by all CENMS and could be fixed.
B500A
470
460
DE, BG (*) BE, BG(**)
450
EC2 (a)
FI, EE, ES
440
BE (b) LU (b)
NO
fyd
DK,, HU ((b))
430
EC2 (b)
420 EC2 (a) = AT, FR, UK, IE, SE, EE, IS, LT, LU, NE, BG, GR, RO, CY, IT, PT, HR, PL, SK, SI, CZ, HU BG (*) = ULS for axial force, nonprestressed members BG (**) = ULS for axial force, prestressed members (EE  two options possible)
410
400 0
5
10
15
20
ε uk 25
εs [‰] 30
Fig. 3. Stressstrain diagram for reinforcing steel A (fyk = 500 MPa, γS = 1.15)
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B500B
470 EC2 (a)
460
BE
DE
450
BG (*) BG(**) EE, ES FI EE FI,
440
NO BE (b)
fyd
LU (b)
DK
EC2 (b)
430
420 EC2 (a) = AT, FR, UK, IE, SE, EE, IS, LT, LU, NE, BG, GR, RO, IT, CY, PT, HR, PL, SK, SI, CZ, HU BG (*) = ULS for axial force, nonprestressed members BG (**) = ULS ffor axial i l fforce, prestressed t d members b (EE  two options possible)
410
εuk
400 0
5
10
15
20
25
30
35
40
45
50
εs [‰] 55
Fig. 4. Stressstrain diagram for reinforcing steel B (fyk = 500 MPa, γS = 1.15)
3.2.3 Durability The minimum cover cmin,b for posttensioned ducts and pretensioned tendons in order to transmit bond forces safely and ensure adequate compaction of the concrete is given in section 4.4.1.2 (3). Generally, there is good consensus regarding the values applied in different states, especially concerning posttensioned ducts. However, at least four values have to be defined, and the actual values in altogether 10 states deviate to some degree (category D). For posttensioned circular ducts, the value cmin,b = φduct is adopted by all states except Austria, where 0.5φduct is applied. Also, the upper limit of 80 mm for circular ducts as well as for rectangular ducts is generally accepted. Only The Netherlands does not apply any upper limit and in Denmark the upper limit for circular ducts is 65 mm. Additional lower limits are applied in The Netherlands (25 mm for circular ducts) and Spain (40 mm). Essentially two groups can be identified for pretensioned tendons, i.e. one group adopting the recommended values of 1.5φp (for strands or plain wires) and 2.5φp (for indented wires) and another group (Belgium, Luxembourg, Italy, Cyprus, Spain) applying values of 2.0φp and 3.0φp respectively. No difference between strands, plain and indented wires is made in Germany (generally 2.5φp) and France (generally 2.0φp or maximum aggregate size). Further harmonization seems possible (maybe fixing the values for posttensioned ducts and introducing classes for pretensioned tendons) provided the reasons for the differences are discussed. The minimum concrete covers for reinforcement and prestressing tendons in normalweight concrete, taking into account exposure and structural classes, are determined in section 4.4.1.2 (5). Here, only a few states have adopted the recommended Tables 4.3N to 4.5N without any change. In some parts even the philosophy of the structural classes has not been applied. Therefore, this NDP was classified as category E, also concerning the definition of exposure classes in EN 2061 [39]. In [44] a survey of national requirements used in conjunction with EN 2061 revealed that the application of the exposure classes
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cannot be harmonized further. Therefore, further investigation would seem to be unrewarding. In most of the states the additive safety element for determining minimum concrete cover in section 4.4.1.2 (6) is not used (recommended value 0 mm) or integrated directly into section 4.4.1.2 (5) (category C). Only Germany, Ireland and Spain define values for Δcdur,γ. Concerning the differences in section 4.4.1.2 (5), this NDP may be eliminated and the respective values may be integrated there as already done by some states. Specific values for reducing minimum cover due to the use of stainless steel or other special measures in section 4.4.1.2 (7) or because of additional protection in section 4.4.1.2 (8) are given in a few states only. Most states have adopted the recommended value of 0 mm without further specification (category C). In some states a reduction is possible with further specification (approval, specialist literature or tests). Here, mentioning the general possibility of reducing the minimum cover may be sufficient without giving any recommended value (elimination of NDP). The NDP in sections 4.4.1.3 (1) and 4.4.1.3 (3) concerning the additive value to calculate the nominal cover (accepted negative deviation during execution) could be summarized, so that all cases for Δcdev are covered by one paragraph. This is already done in some states.
3.2.4 Structural analysis The coefficients to limit the redistribution of bending moments without checking the rotation capacity are determined in section 5.5 (4). This NDP consists of six values, k1 to k6, which define four different conditions for the permitted ratio of redistributed moment and elastic bending moment. The recommended values have been adopted in many CENMS, whereas in some states only one or two values differ and in other states all values have been changed (see Table 2). Hence, this NDP is classified as category D. The differences can be evaluated using Fig. 5. It can be seen that the permitted redistribution using rein
A. Ignatiadis/F. Fingerloos/J. Hegger/F. Teworte · Eurocode 2 – analysis of National Annexes 1.00
0.90
δ
NL (B,C)
NO (A)
UK, IE (B,C)
IT (A) DE (A) FI (A)
0.80
EC2 (A)
UK, IE (A)
NL (A) DE (B,C)
EC2 (B,C)
FI (B)
0.70 FI (C) EC2 (B, C) = AT, FR, SE, DK, EE, IS, LT, NO, BE, LU, BG, GR, RO, CY, IT, PT, ES, HR, PL, SK, SI, CZ, HU EC2 (A) = AT, FR, SE, DK, EE, IS, LT, BE, LU, BG, GR, RO, CY, PT, HR, PL, SK, SI, CZ, HU NL for fyk = 500 MPa and without prestressing; UK, IE for fyk = 500 MPa
0.60 0.00
0.05
0.10
0.15
0.20
0.25 xu/d
0.30
0.35
0.40
0.45
0.50
Fig. 5. Permitted ratio δ of redistributed moment and elastic bending moment (fck ≤ 50 MPa)
forcing steel class A is generally lower than for class B or C. Furthermore, it decreases as the ratio between depth of neutral axis and effective section depth xu/d increases in all states, but to a variable extent. This trend is more distinct for concrete with higher strength. The differences between the many CENMS are small (≤ 10 %) for concrete with fck ≤ 50 MPa and moderate degree of utilization (small xu/d) and increase with increasing concrete strength and increasing xu/d. To discuss harmonization, research concerning the background to the differences is necessary. The slenderness criterion in Eq. (5.13N) to check whether secondorder effects may be ignored has been adopted by most CENMS (category C). Only Germany, Norway and Spain use other criteria, and in Slovakia and the Czech Republic an additional limit λlim ≤ 75 has been introduced. Since this is only a limit for using one method, there is no influence on the final result. There may be an influence on the computational cost in some cases. The NDP could be harmonized by getting all states to adopt Eq. (5.13N) or by changing the current voluminous limit to a simpler criterion that is on the safe side. Three different methods considering secondorder effects are introduced in section 5.8.5 (1). Apart from the general method, based on nonlinear secondorder analysis, two simplified methods can be chosen. In most of the states, both methods can be applied without restrictions (category C). In Germany only method (b), based on nominal curvature, is used and in Denmark only method (a), based on nominal stiffness. In The Netherlands both methods apply with some restrictions or changes. In order to reduce the volume of Eurocode 2, one simplified method should be sufficient. Several NDP calculating the permissible prestressing are given in sections 5.10.2, 5.10.3 and 7.2, limiting the stresses in prestressing steel or the compressive stress in the concrete at different times. As in most cases only three or four states define different values, these NDP have mainly been classified as category C. The coefficient to limit the compressive stress in the concrete under the qua
sipermanent combination of loads in section 7.2 (3) can be fixed because all states have adopted the recommended value (category A). Furthermore, upper and lower partial safety factors for the increase in stress are defined in section 5.10.8 (3) and coefficients to consider possible variations in prestress in section 5.10.9 (1). Here, it might be possible to introduce classes (category B). The differences in the final result can only be assessed by comparative analyses of different member types as all these NDP have to be considered together. In general, it should be investigated as to whether so many NDP are needed here or if one general NDP for stresses in the prestressing steel, one general NDP for stresses in the concrete and one or two NDP considering possible variations and safety factors are sufficient.
3.2.5 Ultimate limit states There are several NDP in sections 6.2 and 6.4 for shear and punching design. These sections have already been identified as one main topic for the revision of Eurocode 2. The NDP for shear and punching resistance for members not requiring shear reinforcement in sections 6.2.2 (1) and 6.4.4 (1) respectively are classified as category C. The results do not depend on other NDP except γC. Strength reduction factors for concrete cracked in shear are determined in 6.2.2 (6) and 6.2.3 (3). It should be confirmed whether two NDP or even three, considering ν ′ in 6.5.2 (2) as well, are necessary for this purpose. Since the final results depend on fcd, further NDP have to be considered (see also remarks to 6.5.2 and 6.5.4). The NDP for limiting the angle of the inclined compression strut in section 6.2.3 (2) is classified as category D (see also remarks to sections 9.2.2 (6) to 9.2.2 (8)). The maximum punching shear resistance vRd,max in section 6.4.5 (3) is determined quite differently in several CENMS. This even concerns the applicable control perimeter. Owing to an amendment [37], the general concept at least will be harmonized. However, a new factor kmax for the maximum punching resistance as a multiple of vRd,c had to be introduced as an
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NDP, which can hardly be harmonized since it also depends on the actual punching reinforcement details in the several states (EC2 recommendation: kmax = 1.5, but, for example, Germany has kmax = 1.4). Further comparison of national rules can be found in [45–47]. The design strength of concrete compression struts in strutandtie models in cracked compression zones is determined in section 6.5.2 (2) by the reduction factor ν ′, depending on the characteristic compressive cylinder strength fck. This NDP is classified as category D because the values in some states differ from the recommended value. Furthermore, this parameter not only applies in this section, but in section 6.5.4, too. Hence, it cannot be treated independently regarding the final result (σRd,max) and further NDP have to be considered in this section as well as in section 6.5.4. To evaluate the differences, graphical representation is used (see Figs. 6 and 7).
If only parameter ν ′ is considered, Germany, Spain, Denmark and Italy do not apply the recommended value. Considering the standard cases (DE (b), ES (a)), the differences in the design strength of concrete struts σRd,max vary by approx. 10 and 15 % in relation to the design value of concrete compressive strength fcd for normal concrete and up to 22 % for highstrength concrete (see Fig. 6). However, when relating the design strength of concrete struts σRd,max to the characteristic compressive cylinder strength fck, NDP αcc and γC have to be considered as well. In doing so, a better comparison of the actual permissible stresses is achieved. Taking into account these additional parameters, Finland, Norway and Poland also apply values differing from the recommended ones. The differences between several states considering the standard cases (DE (b), ES (a)) are less than 10 % for concrete strength classes ≥ C30/37 and up to 15 % for the lower
0.80 0.70
DE (a)
0.60 DE (b)
σRd,max / fcd
0.50
IT
DE (c) DK
0.40
EC2 ES (a)
0 30 0.30
ES (b)
EC2 = AT, FR, UK, IE, SE, EE, FI, IS, LT, NO, BE, LU, NL, BG, GR, RO, CY, PT, HR, PL, SK, SI, CZ, HU DE (a) = for concrete struts parallel to cracks DE (b) = for concrete struts crossing the cracks DE (c) = for extensive crack formation with V and T ES (a) = if the crack width is controlled ES (b) = for concrete struts crossing bigger cracks or tension zones
0.20 0.10 0.00 0
10
20
30
40
50 fck [MPa]
60
70
80
90
100
Fig. 6. NDP to determine the design strength of concrete compression struts in strutandtie models in cracked compression zones in relation to fcd, Eq. (6.56) of EN 199211 0.50 0.45
DK PL
0.40
DE (a) ES (a)
0.35 0 35
FI, NO
σRd,max / fck
0.30
DE (c)
DE (b) IT EC2
ES (b)
0.25 0.20 0.15
EC2 = AT, FR, UK (αcc = 1.0), IE (αcc = 1.0), SE, EE, IS, LT, BE, LU, NL, BG, GR, RO, CY, PT, HR, SK, SI, CZ, HU (αcc = 1.0) DE (a) = for concrete struts parallel to cracks DE (b) = for concrete struts crossing the cracks DE (c) = for extensive crack formation with V and T ES (a) = if the crack width is controlled ES (b) = for concrete struts crossing bigger cracks or tension zones
0 10 0.10 0.05 0.00 0
10
20
30
40
50 fck [MPa]
60
70
80
90
100
Fig. 7. NDP to determine the design strength of concrete compression struts in strutandtie models in cracked compression zones in relation to fck, Eq. (6.56) of EN 199211
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A. Ignatiadis/F. Fingerloos/J. Hegger/F. Teworte · Eurocode 2 – analysis of National Annexes
Table 4. Differences in NDP to 6.5.4 (4)
Recommended values
k1 = 1.0; k2 = 0.85; k3 = 0.75
(FR)
Recommended values (in individual cases up to: k1 = 1/ν ′; k2 = 1.0; k3 = 0.9)
DE
k1 = 1.1; k2 = 0.75; k3 = 0.75
AT
k1 = 1.25; k2 = 0.9; k3 = 0.9
DK
k2 = k3 = 1.0 and ν ′ = ν (ν according to NCI to 5.6.1 (3), usually ν = 0.8 for nodes)
ES
k1 = 1.0; k2 = 0.7; k3 = 0.75
concrete strength classes (see Fig. 7). This means that the deviations are overall smaller than they initially seem in Fig. 6. The allowable design values for compressive stresses within nodes of truss models are determined in section 6.5.4 (4). In this context, different values are defined for compression nodes without ties anchored at the node (Eq. (6.60)), compressiontension nodes with ties anchored in one direction (Eq. (6.61)) and compressiontension nodes with ties anchored in more than one direction (Eq. (6.62)). The design values are determined by means of NDP k1 to k3 defined in this section. Furthermore, all three equations consider factor ν ′ (NDP to 6.5.2 (2)). Therefore, this NDP cannot be considered in isolation and is classified as category D, although the differences and the number of states not applying the recommended values seem rather small initially (see Table 4).
1.20
1.10 DE
σRd,max / fcd
1.00
0.90 AT
IT DK
0.80
0.70 EC2
0.60 EC2 = FR, UK, IE, SE, EE, FI, IS, LT, NO, BE, LU, NL, BG, GR, RO, CY, PT, HR, PL, SK, SI, CZ, HU
ES
0.50 0
10
20
30
40
50 fck [MPa]
60
70
80
90
100
Fig. 8. NDP to determine design strength of concrete for compression nodes without ties anchored at the node in relation to fcd, Eq. (6.60) of EN 199211
0.80 0.75 0.70 00.65 65
σRd,max / fck
0.60 DE
0.55
DK AT
FI, NO
0.50 IT
PL
0.45
EC2
0 40 0.40 ES
0.35
EC2 = FR, UK (αcc = 1,0), IE (αcc = 1,0), SE, EE, IS, LT, BE, LU, NL, BG, GR, RO, CY, PT, HR, SK, SI, CZ, HU (αcc = 1.0)
0.30 0
10
20
30
40
50 fck [MPa]
60
70
80
90
100
Fig. 9. NDP to determine design strength of concrete for compression nodes without ties anchored at the node in relation to fck, Eq. (6.60) of EN 199211
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PL
2.00
FR (*)
ES DE (*)
FI, NO
σRd,max / fck
1.50
IT EC2
1.00 DK DE
0.50
EC2 = AT, FR, UK (αcc = 1,0), IE (αcc = 1,0), SE, EE, IS, LT, BE, LU, NL, BG, GR, RO, CY, PT, HR, SK, SI, CZ, HU (αcc = 1.0) DE (*) = with further justification FR (*) = in special cases
0.00 0
10
20
30
40
50 fck [MPa]
60
70
80
90
100
Fig. 10. NDP to determine design strength of concrete for triaxially compressed nodes in relation to fck, according to EN 199211, 6.5.4 (6)
Considering – during the evaluation of Eq. (6.60) – parameter ν ′ in addition to k1 and using σRd,max/fcd, Italy, too, applies different values and the deviations generally increase (Fig. 8). When σRd,max is related to fck instead, meaning that αcc and γC are considered, further states differ from the recommended values. However, the deviations can be put into perspective (Fig. 9). So the differences relating σRd,max to fcd in Fig. 8 depend on the concrete strength and vary between 30 and 45 %. Looking at the ratio of σRd,max to fck in Fig. 9, the differences remain relatively constant, with a value of about approx. 20 % (except Austria for < C50/60). A similar tendency can be observed for Eqs. (6.61) and (6.62). The design value of the allowable compressive stress for triaxially compressed nodes is determined in section 6.5.4 (6). Here, a good consensus seems to be possible at first sight. Only Germany and Denmark apply more conservative values (1.1 and 1.0 respectively) for k4, while all other states use the recommended value of 3.0 (category C). Under certain circumstances, higher values may be used in Germany and France (up to σRd,max = 3.0fcd). The ratio between σRd,max and fck in Fig. 10 reveals that the differences are underestimated if only factor k4 is considered. Generally, the necessity for four NDP in these sections (6.5.2 and 6.5.4) to determine one design stress value has to be questioned. Hence, it should be checked whether the use of fcd in the equations for σRd,max is the best way or if a more convenient solution is reached by using fck or fck/γC instead.
3.2.6 Detailing rules The NDP in section 9 consider mostly the required minimum or maximum values for reinforcement, diameter or spacing. Most of these parameters will need some discussion for harmonization (category D) and in some cases an introduction of classes seems possible (category B, e.g. maximum spacing of transverse reinforcement along the column in section 9.5.3 (3)). These differences are mainly
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Structural Concrete (2015), No. 1
based on experience or are due to regional circumstances (geotechnical conditions, earthquake), but maybe some reduction based on summarizing of NDP is possible (see below). In some cases, mechanical issues and correlation with rules in section 6 or 7 may be the reason (see example below). Maximum spacing between shear reinforcement is determined with three NDP in sections 9.2.2 (6) to 9.2.2 (8). Some CENMS apply values differing from the recommended ones. Additionally, the maximum spacing is defined depending on the utilization of shear resistance in Germany, Croatia and, partly, Spain. Since the detailing of members and the particular rules are based on experience in the several states, these parameters are classified as category D. Furthermore, these detailing rules cannot be observed independently from the design rules in sections 6 and 7. For example, the more restrictive spacing rules for shear reinforcement in Germany go hand in hand with a smaller permitted strut inclination of the compression strut. It has to be investigated whether the differences are mainly based on experience or on mechanical issues. In the first case, harmonization will probably be difficult. In the second case, the introduction of two or three consistent approaches seems a possible solution (e.g. if smaller strut inclinations are used, a smaller spacing is required). These different approaches could be chosen nationally (introduction of classes – category B) or applied by all states and chosen depending on the specific design situation (e.g. existing structure, small spacing not possible for other reasons). Hence, the respective NDP could be eliminated. In both cases, this approach would lead to a reduction in NDP because the corresponding NDP would be merged. Five NDP for defining the minimum reinforcing bar diameters for different members are defined in sections 9.5.2 (1) and 9.8. Complete harmonization does not seem possible, but some groups could be identified (see Table 5). Furthermore, a reduction in NDP should be discussed, especially concerning lines 2 to 4 of Table 5, which
A. Ignatiadis/F. Fingerloos/J. Hegger/F. Teworte · Eurocode 2 – analysis of National Annexes
Table 5. NDP considering minimum reinforcing bar diameters
Member
Section
Reinforcement EC2 PL
columns pile caps column and wall footing tie beams column footings on rocks
9.5.2 (1) 9.8.1 (3)
longitudinal main tensile
UK, BE, NO AT IT SK, ES HR DE BG, PT HU IE,SI LU CZ RO 12 12b) 10 12a) 12 12a) 12 12 12 12 10 8 8 8 8 12 12 12 12 12 8 10 10 12
8 8
6 8
9.8.2.1 (1) main
8
8
8
8
8
12c) 12 12d) 12 12d) 10c)
9.8.3 (1) 9.8.4 (1)
8 8
8 8
8 8
8 8
8 8
12 8
flexural transverse
12 12a) 12 8 8 12
12 10c) 12 10c)
10
10
10
10 8
10 10
10 10
EC2 = FR, SE, DK, EE, FI, IS, NL, GR, CY a) b) 10 mm for h ≤ 20 cm 8 mm for precast concrete elements cast horizontally c) d) 6 mm for wire fabrics 8 mm for wire fabrics
all consider the main reinforcement in foundation elements.
4
Conclusion
The analysis of the National Annexes of EN 199211 reveals the widespread acceptance of the models and concepts of Eurocode 2 and points out the potential for a reduction in NDP. However, the task of reducing or harmonizing NDP is very complex. Using the example of section 6.5, it was shown that the differences between the many CENMS can be overestimated as well as underestimated when comparing only one single NDP. But this complexity also opens up the chance to reduce NDP and enhance the ease of use without changing the final result of the design. So the approaches of reduction, concretization or generalization of sections and summarizing some NDP offer good potential for a reduction in NDP. Where technical changes in some states are needed for further harmonization, the success depends on the reasons for the actual differences (e.g. level of safety, philosophies, experience). Complete harmonization without NDP does not seem possible, especially when regional characteristics are an issue (e.g. influence of earthquakes on minimum diameters and reinforcement ratios, influence of different concrete compositions on exposure classes). Whereas some NDP could be easily eliminated or harmonized right now, others need further discussion, research into the background and, in some cases, comparative analyses.
Acknowledgements The results presented here were developed as part of a research project carried out by Initiative PRB, a German organization that aims to make the Eurocodes easier to use and is sponsored within the “Future Building” research programme of the German Federal Institute for Research on Building, Urban Affairs and Spatial Development (BBSR). References 1. European Commission: Mandate for amending existing Eurocodes and extending the scope of structural Eurocodes (M/515). Brussels, Dec 2012.
2. CEN/TC 250: Response to Mandate M/515 EN, Towards a second generation of EN Eurocodes, May 2013. 3. EN 199211:2004 + AC:2010: Eurocode 2: Design of concrete structures – Part 11: General rules and rules for buildings. 4. EN 199212:2004 + AC:2008: Eurocode 2: Design of concrete structures – Part 12: General rules – Structural fire design. 5. EN 19922:2005 + AC:2008: Eurocode 2: Design of concrete structures – Part 2: Concrete bridges – Design and detailing rules. 6. EN 19923:2006: Eurocode 2: Design of concrete structures – Part 3: Liquid retaining and containment structures. 7. DAfStbHeft 600: Erläuterungen zu DIN EN 199211 und DIN EN 199211/NA (Eurocode 2). BeuthVerlag, Berlin, 2012. 8. DIN EN 199211/NA:201304 (National Annex Germany). 9. ÖNORM B 199211:201112 (National Annex Austria). 10. NF EN 199211/NA Mars 2007 (National Annex France). 11. BS EN 199211:2004/NA:2009 (National Annex United Kingdom). 12. Irish National Annex NA+AC1 to I.S. EN 199211:2005. 13. Swedish National Board of Housing, Building & Planning (www.boverket.se): BFS 2011:10 EKS 8 section D chap. 2.1.1 (National Application rules in Sweden). 14. Swedish Transport Administration (www.trafikverket.se): TRVFS 2011:12, chap. 21 (National Application rules in Sweden). 15. DS/EN 199211 DK NA:2011 (National Annex Denmark). 16. EVSEN 199211/NA:2007 (National Annex Estonia). 17. Finnish National Annex to Standard SFSEN 199211. 18. IST EN 199211:2004/NA:2010 (National Annex Iceland). 19. National provisions of Lithuania (JRCDatabase 201311). 20. NSEN 199211:2004/NA:2008 (National Annex Norway). 21. NBN EN 199211ANB:2010 (National Annex Belgium). 22. EN 199211:2004/ANLU:2011 (National Annex Luxembourg). 23. NENEN 199211 + C2:2011/NB:2011 (National Annex Netherlands). 24. БДС EN 199211/NA:201107 (National Annex Bulgaria). 25. ELOT EN 199211:2005/NA (20101115) (National Annex Greece). 26. National provisions of Romania (JRCDatabase 201309). 27. CYS National Annex to CYS EN 199211:2004 (11/06/2010). 28. UNIEN 199211 Appendice Nazionale (24/09/2010) (National Annex Italy). 29. National provisions of Portugal (JRCDatabase 201309). 30. Anejo Nacional AN/UNEEN 199211 (Feb 2013) (National Annex Spain).
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31. HRN EN 199211:2013/NA (National Annex Croatia). 32. PNEN 199211:2008/NA:2010 (National Annex Poland). 33. Národná príloha STN 199211/NA (2005) (National Annex Slovakia). 34. National provisions of Slovenia (JRCDatabase 201309). 35. CSN EN 199211 NA ed. A: 2011 (National Annex Czech Republic). 36. MSZ EN 199211 NM (20120604) (National Annex Hungary). 37. Draft (Amendment) Eurocode 2: Design of concrete structures – Part 11: General rules and rules for buildings; EN 199211:2004/prA1:2013 38. PD 66871:2010 Background paper to the National Annexes to BS EN 19921 and BS EN 19923. 39. EN 2061:200012: Concrete – Part 1: Specification, performance, production and conformity. 40. EN 10080:2005: Steel for the reinforcement of concrete – Weldable reinforcing steel – General. 41. EN 1536:2010: Execution of special geotechnical work – Bored piles. 42. NF P94262: Justification of geotechnical work – National application standards for the implementation of Eurocode 7 – Deep foundations. 43. EN 1997: Eurocode 7: Geotechnical design. 44. CEN/TR 15868:2009, Survey of national requirements used in conjunction with EN 2061:2000. 45. Gmainer, S., Walraven, J.: Comparison of the National Annexes of Eurocode 2 for shear and punching shear capacity. In: Proc. of 3rd Intl. Workshop Design of Concrete Structures using Eurocodes, Vienna, Sept 2012. 46. Siburg, C., Hegger, J.: Punching design of foundations according to Eurocode 2. In: Proc. of 3rd Intl. Workshop Design of Concrete Structures using Eurocodes, Vienna, Sept 2012. 47. Siburg, C., Ricker, M., Hegger, J. (2014): Punching shear design of footings: critical review of different code provisions. Structural Concrete, 15: 497–508. doi: 10.1002/suco. 201300092
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Structural Concrete (2015), No. 1
Dipl.Ing. Anett Ignatiadis German Committee for Structural Concrete Budapester Str. 31 10787 Berlin anett.ignatiadis@dafstb.de
Dr.Ing. Frank Fingerloos German Society for Concrete & Construction Technology Kurfuerstenstr. 129 10785 Berlin frank.fingerloos@betonverein.de
Prof. Dr.Ing. Josef Hegger RWTH Aachen University Institute of Structural Concrete MiesvanderRoheStr. 1 52074 Aachen jhegger@imb.rwthaachen.de
Dr.Ing. Frederik Teworte H+P Ingenieure GmbH & Co. KG Kackertstr. 10 52072 Aachen fteworte@huping.de
Technical Paper Lijie Wang* Robby Caspeele Ruben Van Coile Luc Taerwe
DOI: 10.1002/suco.201400002
Extension of tabulated design parameters for rectangular columns exposed to fire taking into account secondorder effects and various fire models Fire, as one of the most severe load conditions, has an important impact on concrete structures. Not only does a fire affect the material strength, it affects structural stiffness and stability as well. A concrete column, compared with other structural members, in most cases has to cope with both vertical forces and bending moments transferred by slabs and beams. Consequently, it is essential to find a reliable and practical way of establishing interaction curves for the overall structural behaviour of concrete columns subjected to fire. In this paper, a crosssectional calculation method based on the material models of Eurocode 2 is explained and adopted in order to calculate interaction curves for a typical rectangular column exposed to the ISO 834 standard fire. Subsequently, an iterative approach is introduced to develop interaction curves taking into account secondorder effects in the case of all the four faces of a column exposed to fire. The maximum permissible slenderness ratios for columns in different fire durations are obtained and compared with Eurocode 2 provisions. Finally, this method is used to calculate the maximum permissible slenderness ratios for columns exposed to hydrocarbon and natural fires. Keywords: concrete column, interaction curve, slenderness, secondorder effects, hydrocarbon fire, natural fire, Eurocode
1
Introduction
There are basically three ways of evaluating the fire resistance of structural members: experimental tests, numerical simulations and simplified analytical methods [1]. With respect to concrete columns exposed to fire, Lie [2] has carried out tests to study the influences of concentric loads, crosssection, moisture and aggregate type on the structural fire resistance. Later, experiments on the fire resistance of columns with different slenderness ratios were carried out at TU Braunschweig, Ghent University and the University of Liège [5]. In the meantime, based on other experimental data, a mathematical approach to predict the fire resistance of circular reinforced concrete columns was developed in [3]. This method was further developed in order to include rectangular crosssection columns [4]. Dotreppe et al. [5] developed a computer program to simulate the structural behaviour under fire conditions. Meda * Corresponding author: lijie.wang@ugent.be Submitted for review: 08 January 2014 Revised: 13 May 2014 Accepted for publication: 07 June 2014
et al. [6] made comparisons between the MN interaction curves for normalstrength and highperformance concrete. Most recently, Kodur [7] proposed a simplified approach for predicting the fire resistance of reinforced concrete columns under biaxial bending. Van Coile et al. [8] developed a crosssectional calculation model in order to calculate the bending moment capacity for a concrete beam exposed to fire within the scope of reliability calculations. This model was further used as a basis for the lifetime cost optimization of the structural fire resistance of concrete slabs [9]. In the current contribution, the calculation tool developed by Van Coile et al. is applied and expanded to allow for the calculation of interaction diagrams for concrete columns subjected to fire. Structural fire analysis consists of an integrated approach of both transient thermal analysis and structural analysis. Transient thermal analysis, on the one hand, is a procedure for evaluating the temperature distribution by considering fire effects, the material density, the thermal conductivity, the specific heat capacity and the convection coefficient. On the other hand, the structural deformation as well as the increase in stress and strain during a fire are quantified using a structural analysis. Jeffers [10], [11] introduced a heat transfer element model to account for both transverse and longitudinal temperature variations in a structural member and then implemented this element formulation in a finite element program. In the last two decades, several simplified methods have been introduced to calculate interaction curves for structural members exposed to fire [14]. Nevertheless, these approaches focus on a crosssectional calculation without considering secondorder effects. Even in EN 199212 [13], no detailed calculation guidelines are provided for quantifying secondorder effects during fire exposure. However, secondorder effects cannot be neglected if the slenderness ratio is greater than a certain value λlim [12]. In order to solve this problem, a numerical crosssectional calculation method is proposed in this paper to calculate interaction curves for slender columns incorporating secondorder effects. Furthermore, the proposed calculation model can be widely used and the column properties, boundary conditions and fire scenarios can be easily altered in a flexible way. During heating, moisture movements occur, but these are normally ignored in structural analysis methods, and hence not considered in this paper either.
© 2015 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete (2015), No. 1
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L. Wang/R. Caspeele/R. Van Coile/L. Taerwe · Extension of tabulated design parameters for rectangular columns exposed to fire taking into account secondorder effects and various fire models
2
Calculation model
implemented for calculating interaction curves with those used by Meda in [6].
A numerical calculation tool is proposed to calculate the combined effect of an axial force N and a bending moment M on columns, taking into account material strength reduction and thermal strains during fire. This calculation model takes the material model of EN 199212 [13] as a basis for both the thermal and the structural analysis.
2.1
Material model
The material models are the same as provided in EN 199212 [13]. It should be noted that the tensile strength of concrete is not considered. Table 1 compares the basic assumptions of the properties of concrete and steel
2.2
Transient thermal model
The heat transfer and the temperature calculation is based on Fourier’s law for conduction, Newton’s law for convection and the StefanBoltzmann law for radiation. Consequently, the heat flow between nodes of a crosssection can be calculated by defining a matrix. The formulas for the transient heat calculation differ for the two cases of elements directly exposed to the surroundings and elements located in the interior of the column. The heat flow in the external surface area directly exposed to the fire is determined as follows [13]:
Table 1. Material model comparison
Meda’s model [6] Concrete compressive strength at elevated temperatures
Stress–strain laws for concrete in compression at elevated temperatures
Stress–strain relationships for reinforcing steel in tension at elevated temperatures
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Structural Concrete (2015), No 1
Material model (as implemented in the current contribution)
L. Wang/R. Caspeele/R. Van Coile/L. Taerwe Âˇ Extension of tabulated design parameters for rectangular columns exposed to fire taking into account secondorder effects and various fire models
'H
4 4Âş ÂŞ I Â˜ H m Â˜ H f Â˜ V Â˜ ÂŤ 4 r 273 4 m 273 Âť [W / m 2 ] ÂŹ Âź
(1)
where: Ď† configuration factor Îľm surface emissivity of member, Îľm = 0.8 Îľf emissivity of fire, generally taken as 1.0 Ďƒ StephanBoltzmann constant (= 5.67 Ă— 10â€“8 W/m2K4) Î˜r effective radiation temperature of fire environment [Â°C] Î˜m surface temperature of member [Â°C] The heat flow between internal surfaces is calculated as follows:
ÂŚ
'H
4 higher 4 lower s
OÂ˜
flow in
ÂŚ
O' Â˜
flow out
4 higher' 4 lower' [W / m 2 ] s
(2)
where: Îť, Îť' thermal conductivities Î˜higher, Î˜lower, Î˜higher', Î˜lower' temperatures of member nodes [Â°C] s distance for heat transfer [m]
Fig. 1. Temperature calculation model
the finite element software analysis [16]. As a result, node temperatures from this methodology are implemented in the crosssectional model (also implemented in a routine [15]) to calculate interaction curves for columns exposed to fire. The thermal strain in concrete for different types of aggregate can be considered. Taking siliceous aggregates, for instance, a formula for the thermal strain presented in EN 199212 [13] is adopted in the current calculation: min{1.8 u 104 9 u 106T 2.3 u 1011T 3,
H c(T )
14 u 103 }
(3)
where Î¸ is the node temperature. As the first step in the node temperature calculation, the crosssection under consideration is discretized into small rectangles. A 1 Ă— 1 mm square is set as a basic calculation element. Considering different boundary conditions (fire duration, exposed surface, heat transfer direction, etc.), a program implemented in [15] has been developed to calculate the temperature distribution for different fire exposure surfaces. The temperature distribution of the crosssection is first calculated with the proposed methodology and validated with the finite element program [16] and Eurocode 2 provision (Fig .2). For the temperature simulation, the lower limit of the thermal conductivity, a concrete moisture content of 1.5 % and a concrete density of 2300 kg/m3 are considered. From Fig. 2 it is clear that the temperature distribution prediction of the newly developed routine [15] exhibits good agreement with that of the Eurocode [13] and
2.3
Structural model
The same crosssectional discretization is used for the structural analysis. The mechanical strain is expressed as follows [17]:
H mech
H tot H th
H 0 k0K H th
(4)
where: Îľtot total strain Îľth thermal strain Îľ0 strain at centroid k0 curvature about neutral axis In EN 199212 [13] the transient strain is implicitly considered in the mechanical strain term. The stressâ€“strain curves for concrete and reinforcing bars given in Eu
Fig. 2. Comparison of temperature distributions calculated using the proposed methodology implemented in a Matlab routine, with graphs given in EN 199212 and results obtained with the finite element program DIANA after 30, 60, 90 and 120 min
Structural Concrete (2015), No. 1
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L. Wang/R. Caspeele/R. Van Coile/L. Taerwe Âˇ Extension of tabulated design parameters for rectangular columns exposed to fire taking into account secondorder effects and various fire models
Fig. 3. Total, thermal and mechanical strains
slenderness ratios of 35, 70, 105 and 140 are calculated, most of which can be finished within seven iterations.
3 3.1
Fig. 4. a) Temperature distribution over the depth, b) strain profiles and strain limits [17]
rocode [13] are adopted in this paper. Fig. 3 illustrates the relationship between total strain, thermal strain and mechanical strain. The basic calculation model for the crosssectional structural resistance is described in Fig. 4. The compressive strains are considered to be positive. For slender columns, reasonable secondorder effects still need to be considered. In order to solve this problem, the crosssectional calculation tool is developed further to take into account secondorder effects and different slenderness ratios. The deflection is calculated as follows: d
M
Âł m. EI dx Âł m.F dx
Owing to eccentric load effects, additional bending moments occur along the column. As a result, M and, consequently, Ď‡ are not constant along the column as is the case when considering only firstorder effects. MĎ‡ curves are obtained based on the crosssectional calculation. As the first step in the calculations, the curvature Ď‡ for the firstorder bending moment can be obtained based on the crosssectional calculation. Deflections at any position on the column are calculated using Eq.Â (5). Then, additional bending moments caused by deflections under eccentric loads are obtained. Next, a new Ď‡ corresponding to the updated bending moment can be found from a crosssection calculation. This procedure is repeated until the bending moment converges and further iterations do not alter the bending moment significantly. Taking a simply supported column, for instance, the cases of columns for
Structural Concrete (2015), No 1
In order to verify the calculation method, the results obtained for the specific case of a square column with crosssection 600 Ă— 600 mm, 24 bars 20 mm diameter, 50 mm concrete cover, 20Â°C concrete compressive strength fck = 40 MPa, reinforcement yield strength fy = 430 MPa and Youngâ€™s modulus of steel Es = 2 Ă— 105 N/mm2 are compared with the results from Meda [6], where the same column dimensions, reinforcement, strength and Youngâ€™s modulus of concrete and reinforcement at ambient temperature were used for the analysis. There are two differences between the calculation model of Meda [6] and the current calculation: Firstly, the compressive strength of concrete at elevated temperatures in [6] is based on tests by Meda, whereas the current method is based on Eurocode 2 [13]. Secondly, stressâ€“strain laws for concrete in compression at elevated temperatures are different (Table 1) in order to allow comparison with Eurocode 2 prescriptions. The results of the interaction curves in the case of fire exposure on all sides are shown in Fig. 5 considering
(5)
where: M bending moment at local crosssection EI stiffness of crosssection Ď‡ curvature of local crosssection
20
Validation of interaction curves Validation of interaction curves based on crosssection calculations
n'
Nc Ns and mx fc bh
Mc Ms fc bh 2
where Nc, Mc, Ns and Ms are design values of normal forces and bending moments for concrete and steel reinforcement respectively, b is the width of the column and h is the depth of the crosssection. Fig. 5 indicates that interactive curves for 0 and 30 min obtained in [6] are less conservative than results from the proposed analytical method. This is because different material models are chosen. For the stressâ€“strain laws for concrete in compression, elastic and perfectly plastic stressâ€“strain curves are adopted in [6], whereas decreasing branches are considered in the proposed method. As a result, the corresponding maximum permissible bending moments are a little smaller than those in [6]. The differences are apparent when the column temperatures are low. Subsequently, the cases of columns with between one and four exposed surfaces are compared with the data from Caldas [14], who used the same input parameters as Meda [6]. The cases of columns with different exposed surfaces subjected to the ISO standard fire for 90 and 300
L. Wang/R. Caspeele/R. Van Coile/L. Taerwe · Extension of tabulated design parameters for rectangular columns exposed to fire taking into account secondorder effects and various fire models
Fig. 5. Comparison of interaction curves with results available in [6]
Fig. 6. Interaction curves for columns of different slenderness – comparison with Eurocode 2 [13] background documents
min have been illustrated in [18]. The results prove to be very close to results found in [6] and [14].
3.2
Validations of interaction curves based on theoretical and experimental data considering secondorder effects
In EN 199211 [19] it turns out that secondorder effects may be ignored if the slenderness λ is below a certain value λlim:
O
leff
(6)
I/A
λlim = 20 · A · B · C where leff I A
(7)
effective length area moment of inertia crosssectional area A = 1/(1 + 0.2ϕef) B = √(1 + 2ω)/n C = 1.7 – rm
ϕef
effective creep ratio; if ϕ is not known, A = 0.7 ω = Asfyd/(Acfcd) mechanical reinforcement ratio; if ω is not known, B = 1.2 As total area of longitudinal reinforcement n = NEd/(Acfcd) relative normal force rm = M01 / M02 moment ratio M01, M02 firstorder end moments, M02 ≥ M01 In the current study, interaction curves are compared with Eurocode 2 [13] and experimental data [2] respectively. First, based on the interaction curve for λ = 0 at normal temperature and the deflection formula Eq. (5), interaction curves for different slenderness ratios are obtained and compared with the background documents associated with Eurocode 2 [13] (Fig. 6, e0 = initial eccentricity, e2 = additional deflection caused by eccentric loads). Subsequently, this method is adopted for studying the secondorder effects of columns exposed to fire. A basic column with two fixed ends was chosen in accordance with an experiment carried out by Lie [2] in order to vali
Structural Concrete (2015), No. 1
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L. Wang/R. Caspeele/R. Van Coile/L. Taerwe · Extension of tabulated design parameters for rectangular columns exposed to fire taking into account secondorder effects and various fire models
Table 2. Comparison of fire resistance of columns subjected to secondorder effects with experimental test observations [2]
Test case
A
B
Fire duration (h:min)
2:50
2:26
eccentricity (mm)
load (kN)
eccentricity (mm)
load (kN)
0 Current calculation model 1.1
1603
0
1887
1335
1.8
1790
1.9
1237
2.3
1778
2.7
1172
3.1
1758
0–2.5 mm (assumed)
1333
0–2.5 mm (assumed)
1778
Experimental results [2]
date the performance of the crosssectional calculation tool developed. The same experimental fire temperatures as well as geometric and material properties are taken into account. Considering the fixed ends, a factor K = 0.6 was used to calculate the effective length of columns as Lie [2] proposed. A comparison of the results is given in Table 2. Further, two more comparisons have been performed with respect to tests from TU Braunschweig [20] (Table 3) and the University of Liège [21] (Table 4) respectively. From Table 2, Table 3 and Table 4 it can be seen that the experimental results closely correspond to the predictions of the calculation method presented here.
3.3
Comparison of calculated ISO 834 standard fire resistance time of rectangular concrete columns with EN 199212 tabulated guidelines for different slenderness ratios and eccentricities
When it comes to the fire resistance of columns in braced structures, EN 199212 [13] provides tables with the minimum crosssection required for different slenderness ratios and ISO 834 standard fire durations. In order to enable comparisons with EN 199212 [13], the same input data has been used for the analytical method described above. In EN 199212 [13] the moisture content of concrete for all the tabulated tables is 1.5 %, and this value is also adopted for all the fire calculations in this paper. It is worth mentioning that explosive spalling is unlikely to occur when the moisture content of the concrete is less than 3 % [13], [22], so such spalling is not taken into account for any cases in this paper. The effect of imperfections is considered as an eccentricity ei = l0/400, given in EN 199211 [19], where l0 is the effective length of the column. Other parameters, such as reinforcement ratio
Z
As fyd Ac fcd
and load eccentricity e are varied over the different tables, i.e. ω = 0.1, 0.5, 1.0 and e = 0.025b, 0.25b, 0.5b. The cases with the ISO 834 standard fire at 30, 60, 90 and 120 min are illustrated in Tables 5–13, with n = N0Ed,fi / (0.7(Ac fcd + As fyd)) as proposed in EN 199212 [13], where Ac is the crosssectional area of concrete, As the crosssectional area of reinforcing bars, fcd the design value of concrete
Table 3. Comparison of fire resistance of columns subjected to secondorder effects with experimental tests from TU Braunschweig [20]
NO.
1 2 3 4 5 6 7
Cover Crosssection Reinforcement thickness (mm × mm) bar (mm) (mm) 200 ×200 200 ×200 200 ×200 200 ×200 200 ×200 200 ×200 200 ×200
20 20 20 20 20 20 20
4Ф20 4Ф20 4Ф20 4Ф20 4Ф20 4Ф20 4Ф20
fc
fy
(N/mm 2 )
(N/mm 2 )
29.0 29.0 37.0 37.0 37.0 37.0 39.0
487 487 487 462 462 418 443
Height Eccentricity Fire duration (m) (mm) (min) 3.76 4.76 4.76 4.76 4.76 4.76 5.76
0 0 10 20 60 100 10
58 48 49 36 49 53 40
N0 (kN) Experiment Calculation 420 371 340 325 280 281 240 311 170 178 130 126 208 250
Cal / Exp
0.88 0.96 1.00 1.30 1.05 0.97 1.20
Table 4. Comparison of fire resistance of columns subjected to secondorder effects with experimental tests from University of Liège [21]
NO.
1 2 3 4 5 6
22
Cover Crosssection Reinforcement thickness (mm × mm) bar (mm) (mm) 300 ×300 300 ×300 300 ×300 300 ×300 300 ×300 300 ×300
25 25 25 25 40 25
Structural Concrete (2015), No 1
4Ф16 4Ф16 4Ф16 4Ф16 4Ф16 4Ф25
fc
fy
(N/mm 2 )
(N/mm 2 )
31.6 32.3 32.8 32.7 31.8 27.9
576 576 576 576 576 591
Height Eccentricity Fire duration (m) (mm) (min) 3.9 3.9 3.9 3.9 3.9 3.9
20 0 0 20 20 20
0 61 120 125 123 120
N0 (kN) Experiment Calculation 2000 2161 950 1221 622 561 220 221 349 372 475 364
Cal / Exp
1.08 1.29 0.90 1.00 1.07 0.77
30 40 50 60 70 80
30 40 50 60 70 80
30 40 50 60 70 80
R60
R90
R120
200/25 200/40:250/25 250/50:350/25 350/50:500/25 500/50:600/45 550/60 250/25 250/50:300/25 300/50:400/25 500/50:600/25 600/80 600/80 250/25 300/50:350/25 400/50:500/25 550/60 600/80 ①
150/25 200/25 200/25 250/25 200/25 150/35:200/25 200/35:250/25 200/30:250/25 250/50:350/25 250/40:350/25 200/35:250/25 200/25 250/25 200/35:300/25 200/35:250/25 250/50:500/25 350/50:550/25 250/40:300/25 350/50:550/25 500/60:600/45 300/35:350/25 250/50:400/25 250/25 550/60 350/50:500/25 250/30:300/25 550/60:600/60 350/35:400/25
200/25 250/25 250/25 250/25 300/25 250/40:300/25 250/25 300/50:350/25 350/50:400/25 250/40:350/25 250/25 300/25 350/50:600/25 500/60:600/25 250/50:400/25 250/25 350/25 350/50:500/25 250/50:300/25 500/50:600/35 600/60 400/25 600/80 500/25 300/25 600/80 450/40:500/25
200/25 200/25 200/40:250/25 200/40:300/25 250/50:350/25 350/50:550/25
200/25 250/40:300/25 350/35:400/25 500/40:550/25 550/40:600/60 ①
350/25 400/25 550/25 ① ① ①
200/30:250/25 250/50:300/25 350/25 250/25 450/25 300/25 350/30:400/25 550/60:600/25 600/80 450/35:550/25 ① 550/60:600/35
200/50:250/25 250/50:300/25 250/40:300/25 250/30:300/25 350/25 250/25 300/50:350/25 300/25 450/25 300/25 450/50:500/25 350/50:400/25 600/80 350/35:400/25 600/60 450/50:550/25 ① 400/45:550/25 600/40 ① ① ① 550/40:600/25
200/40:250/25 250/50:300/25 350/50:400/25 500/50:550/25 600/60 ①
n=0.7 hydrocarbon fire standard fire hydrocarbon fire Numerical Numerical Numerical Eurocode 2 calculation calculation calculation 200/25 150/25 200/25 200/25 250/25 150/30:200/25 150/25 250/25 200/25 300/35:350/25 300/50:350/25 300/30:350/25 350/50:400/25 250/25 350/50:550/25 350/50:450/25 500/50:550/25 300/25 500/50:600/45 450/50:600/25 550/60:600/45 350/25
300/25 250/50:300/25 250/25 300/50:350/25 300/45:350/25 400/35:450/25 350/25 500/35:550/25 350/25 300/25 400/50:450/25 400/25 600/25 500/25 350/50:400/25 550/40:600/25 550/40:600/25 450/50:500/25 ① ① 600/25 450/40:500/25 600/80 550/50 ① ① ① 600/80 500/60:550/25 ① ① ① 600/45 ①
250/25 250/50:300/25 300/50:450/25 500/60:550/25 550/60:600/80 ①
200/25 200/30:250/25 200/25 250/50:300/25 250/25 350/50:400/25 250/40:300/25 500/60:600/25 300/40:350/25 550/60:600/60 400/30:450/25
Columns exposed on more than one side n=0.3 n=0.5 standard fire hydrocarbon fire standard fire Numerical Numerical Numerical Eurocode 2 Eurocode 2 calculation calculation calculation 150/25 150/25 150/25 150/25 150/25 150/25 150/25 200/25 150/30:200/25 150/25 150/25 250/35:300/25 200/35:250/25 200/25 300/35:350/25 300/50:350/25 200/25 150/25 250/25 350/50:600/35 350/50:500/25 250/30:300/25 250/25 200/25
Minimum dimensions (mm) / Column width bmin [mm]/axis distance a [mm]
150/25 150/30:200/25 150/25 200/30:250/25 200/25 250/40:350/25 200/40:250/25 350/50:400/25 250/30:300/25 500/60:600/45 250/40:300/25
150/25 150/25 150/25 150/30:200/25 150/25 200/25 200/25 200/30:250/25
n=0.15 standard fire hydrocarbon fire Numerical Numerical Eurocode 2 calculation calculation 150/25 150/25 150/25 150/25 150/25 150/25 150/25 150/25 150/25 200/25 150/25 200/25
* x Requires a width > 600 mm
30 40 50 60 70 80
λ
R30
Fire resistance
Table 5. Minimum dimensions and concrete covers for reinforced concrete columns with rectangular section (ISO 834); mechanical reinforcement ratio ω = 0.1, low firstorder moment: e = 0.025b with e ≥ 10 mm L. Wang/R. Caspeele/R. Van Coile/L. Taerwe · Extension of tabulated design parameters for rectangular columns exposed to fire taking into account secondorder effects and various fire models
Structural Concrete (2015), No. 1
23
24
Structural Concrete (2015), No 1
30 40 50 60 70 80
30 40 50 60 70 80
30 40 50 60 70 80
R60
R90
R120
300/35:400/25 400/50:600/35 550/60:600/45 600/80 ① ① 350/50:550/25 500/50:600/45 600/80 ① ① ① 500/50:600/35 550/60:600/80 ① ① ① ①
250/50:400/25 300/50:400/25 300/40:400/25 300/50:600/35 400/50:600/25 350/50:550/25 400/50:600/45 550/60:600/45 500/60:550/25 550/60:600/80 600/80 550/45:600/25 600/80 600/45 ① ① ①
250/50:450/25 250/50:350/25 300/50:350/25 400/50:500/25 400/50:550/25 300/50:500/25 400/50:600/45 500/60:600/25 500/50:550/25 450/50:550/25 400/50:550/25 550/60:600/80 600/60 550/50:600/25 600/80 500/60:600/45 500/50:550/25 600/80 550/55:600/50 ① 550/60:600/80 500/60:600/25 600/60 ① ① ① 600/80 550/50:600/25
200/35:300/25 250/40:400/25 350/50:500/25 400/50:600/45 550/60:600/45 550/60:600/60
200/40:250/25 250/40:350/25 300/40:500/25 300/50:550/25 400/50:550/25 500/60:600/25
150/30:200/25 200/30:250/25 200/40:300/25 250/35:400/25 300/40:500/25 400/40:550/25
200/40:300/25 250/25 200/40:300/25 250/50:350/25 300/50:400/25 300/35:350/25 300/50:600/35 450/50:500/25 350/45:550/25 400/50:600/35 550/60:600/25 450/50:550/25 550/60:600/45 600/80 550/30:600/25 550/60:600/80 600/30 ①
150/25 200/25 200/35:300/25 300/50:500/25 400/50:500/25 500/40:600/45
550/60:600/80 500/60:600/25 550/25 ① 600/80 550/55:600/25 ① 600/60 ① ① ① ① ① ① ①
600/60
550/60:600/45 ① ① ① ① ①
450/50:500/25 500/50:550/25 500/50:600/45 550/60:600/45 550/40:600/25 ① 550/60:600/45 550/35:600/25 600/50 ① ① ① 600/40 ① ① ① ① ① ① ① ① ① ①
① ① ① ① ① ①
① ① ① ① ① ①
500/25 550/60:600/80 350/50:400/25 300/40:500/25 400/50:550/25 ① 500/25 450/50:550/25 550/60:600/80 550/60:600/25 550/40:600/25 ① ① 550/60:600/25 550/30:600/30 600/55 ① ① ① ① 600/35 ① ① ① ① 600/80 ① ① ① ① ①
n=0.7 hydrocarbon fire standard fire hydrocarbon fire Numerical Numerical Numerical Eurocode 2 calculation calculation calculation 300/35:400/25 500/25 400/25 300/30:350/25 400/50:500/25 500/25 500/40:550/25 550/40:600/45 550/40:600/45 550/60:600/25 ① 550/25 ① ① 600/30 ① ① ① ① ① ① ①
Minimum dimensions (mm) / Column width bmin [mm]/axis distance a [mm]
Columns exposed on more than one side n=0.15 n=0.3 n=0.5 standard fire hydrocarbon fire standard fire hydrocarbon fire standard fire Numerical Numerical Numerical Numerical Numerical Eurocode 2 Eurocode 2 Eurocode 2 calculation calculation calculation calculation calculation 150/25 150/25 150/25 200/25 200/25 200/30:250/25 150/25 200/25 300/25 200/25 150/30:200/25 350/35:400/25 300/25 150/25 200/40:250/25 300/25 200/40:250/25 400/35:500/25 450/50:500/25 350/40:500/25 150/25 250/35:350/25 400/50:450/25 500/50:600/35 550/40:600/25 300/25 550/25 200/25 300/50:500/25 500/40:600/25 350/40:500/25 550/60:600/45 550/30:600/25 ① 500/35:600/35 ① ① 300/30:400/25 250/25 600/45 550/25
* x Requires a width > 600 mm
30 40 50 60 70 80
λ
R30
Fire resistance
Table 6. Minimum dimensions and concrete covers for reinforced concrete columns with rectangular section (ISO 834); mechanical reinforcement ratio ω = 0.1, moderate firstorder moment: e = 0.25b with e ≤ 100 mm
L. Wang/R. Caspeele/R. Van Coile/L. Taerwe · Extension of tabulated design parameters for rectangular columns exposed to fire taking into account secondorder effects and various fire models
30 40 50 60 70 80
30 40 50 60 70 80
30 40 50 60 70 80
R60
R90
R120 ① ① ① ①
① ① ① ① ① ①
① ① ① ① ① ①
550/50 600/70
450/50:600/25 550/40:600/30 500/50:600/80 500/60:600/45 550/50:600/45 550/60:600/80 ① 550/60:600/60 550/55:600/50 ① 600/80 550/60:600/50 ① 600/70 ① ① ① 600/60 ①
① ① ① ① ①
①
① ① ① ① ① ①
600/80
550/50:600/40 ① ① ① ① ①
350/50:550/25 400/50:600/45 550/60:600/45 550/45:600/40 450/50:600/45 500/60:600/30 550/60:600/80 550/60:600/50 ① 600/80 550/60:600/45 550/40 600/80 ① ① ① 550/60:600/60 550/50:600/45 ① ① 550/60:600/50 ① ① ① 600/70 ①
500/50:550/25 550/40:600/30 550/50:600/40 600/80 ① ①
①
550/25 600/25 ① ①
① ① ① ① ① ①
① ① ① ① ① ①
① ① ① ① ① ①
① ① ① ① ① ①
① ① ① ① ① ①
① ① ① ① ① ①
① ① ① ① ① ①
① ① ① ① ① ①
① ① ① ① ① ①
Columns exposed on more than one side n=0.3 n=0.5 n=0.7 standard fire hydrocarbon fire standard fire hydrocarbon fire standard fire hydrocarbon fire Numerical Numerical Numerical Numerical Numerical Numerical Eurocode 2 Eurocode 2 Eurocode 2 calculation calculation calculation calculation calculation calculation 500/25 ① ① ① 450/25 400/40:550/25 550/40:600/25 550/25 550/60 ① ① ① 500/40:550/25 550/25 550/35:600/30 ① ① ① ① ① ① 600/25 550/30:600/25 ① ① ① ① ① 600/50 ① ① ① ① ① ① ① ① ① ① ① ① ①
Minimum dimensions (mm) / Column width bmin [mm]/axis distance a [mm]
550/40 ① ① ① ① ①
hydrocarbon fire Numerical calculation 250/35:300/25 300/35:400/25 400/35:500/25 500/50:600/35 550/60:600/45 ①
300/30:400/25 300/35:500/25 350/50:550/25 400/50:550/25 350/40:550/25 500/35:600/35 550/25 450/50:550/25 550/60:600/45 ① 550/40:600/25 550/30 ① 600/60 550/35 ① 550/40 ①
n=0.15 standard fire Numerical Eurocode 2 calculation 150/25 200/25 300/30:400/25 250/30:300/25 400/50:450/25 300/40:550/25 500/40:550/25 400/40:550/25 550/40:600/25 550/25
* x Requires a width > 600 mm
30 40 50 60 70 80
λ
R30
Fire resistance
Table 7. Minimum dimensions and concrete covers for reinforced concrete columns with rectangular section (ISO 834); mechanical reinforcement ratio ω = 0.1, high firstorder moment: e = 0.5b with e ≤ 200 mm L. Wang/R. Caspeele/R. Van Coile/L. Taerwe · Extension of tabulated design parameters for rectangular columns exposed to fire taking into account secondorder effects and various fire models
Structural Concrete (2015)
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Structural Concrete (2015)
30 40 50 60 70 80
30 40 50 60 70 80
30 40 50 60 70 80
R60
R90
R120
200/25 250/30:300/25 250/40:350/25 300/40:400/25 350/40:550/25 350/40:600/45
200/35:250/25 250/35:300/25 250/50:350/25 250/50:450/25 250/50:450/25 250/50:600/40
150/35:200/25 200/25 200/30:250/25 200/40:250/25 200/30:300/25 200/50:250/25 250/30:350/25 250/35:300/25 250/40:400/25 250/45:300/25
200/25
200/25 200/25 200/30:250/25 250/30:300/25 300/30:400/25 300/35:400/25
200/25 200/35:250/25 200/35:300/25 250/35:300/25 250/35:350/25 250/50:400/25
150/25 150/25 150/40:200/25 200/25 200/25 200/35:250/25 200/30:250/25 200/45:250/25 200/40:250/25 250/25 250/45:300/25 300/45:350/25 350/45:450/25 400/50:550/25
150/40:200/25 200/35:250/25 200/45:250/25 250/35:300/25 250/45:350/25 250/50:400/25
150/25 150/25 150/35:200/25 200/25 200/30:250/25 200/25 200/35:250/25 250/25 250/30:300/25
150/25 200/25 200/25 200/35:250/25 200/35:250/25 200/35:250/25
250/35:300/25 250/50:350/25 300/50:450/25 300/50:600/40 400/50:600/40 450/50:600/60
200/35:300/25 250/35:300/25 250/50:400/25 300/35:450/25 300/50:550/25 350/50:600/40
150/40:200/25 200/35:250/25 200/35:250/25 250/35:300/25 250/50:350/25 300/35:400/25
250/35:300/25 300/40:400/25 350/40:500/25 500/50:550/50 600/60 600/80
250/45:300/25 300/45:350/25 350/45:450/25 400/50:550/25 500/50:600/40 500/60:600/45
200/30:250/25 200/40:250/25 250/30:300/25 300/40:400/25 250/45:350/25 350/40:500/25 300/45:400/25 350/40:600/45 350/45:600/25 600/60 400/50:600/35
150/30:200/25 200/25 200/30:250/25 200/40:250/25 250/40:350/25 250/30:300/25 350/40:450/25 250/40:350/25 350/40:550/35 300/40:500/25
150/25
300/50:350/25 350/50:450/25 400/50:600/40 600/60 600/80 ①
250/50:300/25 300/35:400/25 350/50:500/25 600/40 600/60 600/80
200/35:250/25 250/35:300/25 250/50:350/25 350/50:450/25 400/50:600/40 450/50:600/60
200/35:250/25 250/30:300/25 250/40:350/25 300/40:450/25 350/45:600/25 450/50:600/35
250/35:300/25 300/35:400/25 350/50:450/25 450/50:600/40 600/60 600/60
300/40:400/25 350/40:500/25 500/50:600/45 600/80 ① ①
350/45:500/25 350/50:500/25 400/50:550/25 450/50:550/25 600/60 450/50:600/25 ① 500/60:600/35 ① 600/45 ① 600/60
250/35:300/25 250/40:300/25 300/50:400/25 300/40:400/25 350/50:500/25 600/40 350/40:550/25 350/45:550/25 600/60 550/50:600/45 400/50:550/25 600/80 600/60 550/50:600/45 ① ① 600/60
200/25 250/25 300/30:350/25 350/40:450/25 400/50:600/45 400/50:600/45
Columns exposed on more than one side n=0.3 n=0.5 n=0.7 hydrocarbon fire standard fire hydrocarbon fire standard fire hydrocarbon fire standard fire hydrocarbon fire Numerical Numerical Numerical Numerical Numerical Numerical Numerical Eurocode 2 Eurocode 2 Eurocode 2 calculation calculation calculation calculation calculation calculation calculation 150/25 150/25 150/25 150/25 150/25 150/25 200/25 150/25 150/25 150/25 150/25 200/25 150/25 200/25 150/25 150/25 150/25 150/25 200/25 200/25 250/25 150/25 150/25 150/25 150/25 250/25 200/30:250/25 300/35:400/25 150/25 150/25 200/25 300/35:350/25 350/50:450/25 200/25 150/25 300/25 250/25 150/25 150/25 200/35:250/25 250/30:300/25 200/30:250/25 300/50:450/25 350/35:400/25 400/50:600/40 300/25
Minimum dimensions (mm) / Column width bmin [mm]/axis distance a [mm]
150/25 150/25 150/25 150/25 150/25 150/25 150/35:200/25
n=0.15 standard fire Numerical Eurocode 2 calculation 150/25 150/25 150/25 150/25 150/25 150/25
* x Requires a width > 600 mm
30 40 50 60 70 80
λ
R30
Fire resistance
Table 8. Minimum dimensions and concrete covers for reinforced concrete columns with rectangular section (ISO 834); mechanical reinforcement ratio ω = 0.5, low firstorder moment: e = 0.025b with e ≥ 10 mm
L. Wang/R. Caspeele/R. Van Coile/L. Taerwe · Extension of tabulated design parameters for rectangular columns exposed to fire taking into account secondorder effects and various fire models
30 40 50 60 70 80
30 40 50 60 70 80
30 40 50 60 70 80
R60
R90
R120
200/30:250/25 200/30:300/25 250/35:350/25 300/40:450/25 300/40:450/25 350/40:600/25
200/45:300/25 200/50:350/25 250/45:450/25 300/50:500/25 350/50:550/25 400/50:600/25
150/35:200/25 200/25 200/35:250/25 200/30:250/25 200/40:300/25 200/30:300/25 200/50:400/25 250/35:350/25 300/35:500/25 250/40:400/25 300/40:600/25
150/25 150/25 200/25 200/25
150/25 150/25 150/30:200/25 150/35:200/25 200/30:300/25 200/35:300/25
n=0.15 standard fire Numerical Eurocode 2 calculation 150/25 150/25 150/25 150/25 150/25 150/25
* x Requires a width > 600 mm
30 40 50 60 70 80
λ
R30
Fire resistance
200/30:250/25 250/30:300/25 300/30:400/25 350/40:450/25 350/40:550/35 500/50:600/45 250/40:350/25 300/40:450/25 350/40:550/25 350/40:600/45 550/50:600/45 600/60
200/35:300/25 250/35:300/25 250/50:400/25 250/50:450/25 300/50:450/25 300/50:600/25
250/35:300/25 250/50:400/25 250/50:450/25 300/50:600/40 350/50:600/40 400/50:600/40 300/45:550/25 350/50:550/25 450/50:600/25 500/45:600/40 500/50:550/45 500/55:600/40
200/45:300/25 250/45:500/25 300/45:550/25 350/50:600/25 400/50:600/35 500/55:600/40
150/40:200/25 150/25 150/35:200/25 200/25 200/25 200/30:300/25 200/35:250/25 200/25 200/40:350/25 200/35:300/25 250/30:300/25 250/40:500/25 250/35:300/25 300/40:400/25 300/40:500/25 250/35:400/25 350/40:450/25 350/40:600/25
300/50:450/25 350/40:450/25 450/50:600/25 350/50:550/25 350/40:600/45 500/50:600/40 400/50:600/40 550/50:600/45 500/55:550/45 600/60 600/80 550/60:600/60 600/60 ① 600/75 600/80 ①
250/50:400/25 300/40:400/25 300/45:550/25 300/50:450/25 350/40:450/25 350/50:600/25 350/50:500/25 500/35:600/25 500/50:600/35 450/50:600/40 600/45 500/55:550/45 600/40 600/80 600/50 600/60 ① 600/80
200/35:250/25 250/25 250/35:350/25 250/35:300/25 300/25 300/35:500/25 250/50:300/25 350/40:500/25 300/45:550/25 300/25 500/35:550/25 400/45:600/30 400/50:550/25 550/50:600/45 500/40:600/35 450/50:600/40 600/60 550/55:600/40
400/50:600/40 600/40 600/60 ① ① ①
350/50:450/25 450/50:600/40 600/40 600/60 ① ①
300/35:350/25 350/35:450/25 550/25 600/40 600/60 ①
500/50:600/45 500/60:600/50 600/60 600/55 ① 600/80 ① ① ①
450/35:500/25 500/50:600/40 550/50:600/45 550/50:600/45 600/80 600/55 ① ① ①
600/60 ① ① ① ① ①
600/40 600/60 ① ① ① ①
350/30:400/25 350/40:550/25 450/35:500/25 600/40 450/35:500/25 450/50:600/30 600/60 500/50:600/25 500/30:550/25 ① 600/60 600/45 ① ① 600/80 ① ①
Columns exposed on more than one side n=0.3 n=0.5 n=0.7 hydrocarbon fire standard fire hydrocarbon fire standard fire hydrocarbon fire standard fire hydrocarbon fire Numerical Numerical Numerical Numerical Numerical Numerical Numerical Eurocode 2 Eurocode 2 Eurocode 2 calculation calculation calculation calculation calculation calculation calculation 150/25 150/25 150/25 150/25 200/25 300/25 200/25 200/30:250/25 150/25 150/25 150/25 250/25 200/25 150/25 250/25 300/45:350/25 400/35:450/25 150/25 150/25 200/25 300/25 350/40:450/25 450/35:500/25 200/25 200/30:250/25 150/25 150/25 200/35:250/25 600/40 300/25 250/30:300/25 350/50:450/25 450/35:500/25 500/30:550/25 150/25 150/35:200/25 250/35:300/25 350/40:450/25 350/30:400/25 450/35:550/25 550/35:600/25 550/35:600/30 ① 200/25 600/40 ① ① 200/25 200/30:250/25 300/50:400/25 400/35:500/25 400/40:500/25 600/50
Minimum dimensions (mm) / Column width bmin [mm]/axis distance a [mm]
Table 9. Minimum dimensions and concrete covers for reinforced concrete columns with rectangular section (ISO 834); mechanical reinforcement ratio ω = 0.5, moderate firstorder moment: e = 0.25b with e ≤ 100 mm L. Wang/R. Caspeele/R. Van Coile/L. Taerwe · Extension of tabulated design parameters for rectangular columns exposed to fire taking into account secondorder effects and various fire models
Structural Concrete (2015)
27
28
Structural Concrete (2015)
30 40 50 60 70 80
30 40 50 60 70 80
30 40 50 60 70 80
R60
R90
R120
Minimum dimensions (mm) / Column width bmin [mm]/axis distance a [mm]
250/35:350/25 300/40:400/25 300/40:450/25 350/40:500/25 350/40:600/45 350/40:600/45
200/30:250/25 200/30:300/25 300/25 250/35:400/25 300/40:450/25 400/35:450/25
150/25 150/25 200/25 200/25 200/30:250/25 250/30:300/25
250/50:550/25 300/50:600/25 400/50:550/35 450/50:600/40 500/50:550/45 550/50:600/45
200/40:450/25 200/50:500/25 250/45:550/25 250/50:550/30 300/50:550/35 350/50:600/35
150/30:200/25 150/35:200/25 200/35:300/25 200/40:500/25 200/40:550/25 250/40:600/25 350/50:450/25 500/35:550/25 500/55:600/40 400/50:550/25 550/50:600/45 550/60:600/50 600/40 600/80 600/60 600/60 ① 600/80 600/80 ① ① ① 400/50:600/40 550/50:600/45 550/50 450/50:600/40 600/60 550/60:600/55 600/60 ① 600/80 600/60 ① ① ① ① ①
300/30:400/25 300/50:500/25 350/35:450/25 350/50:550/35 450/35:500/25 500/45:550/40 500/50:550/35 500/50:550/45 550/50:600/45 600/80 550/60:600/50
250/50:450/25 350/40:450/25 500/50:550/40 300/50:500/25 350/40:600/25 500/55:550/45 300/50:600/40 500/50:600/45 500/60:600/45 350/50:600/40 600/45 550/50 450/50:600/40 600/80 550/60:600/55 450/50:600/40 ① 600/70
300/35:400/25 450/35:500/25 450/50:550/30 350/35:400/25 500/25 500/40:550/35 400/50:500/25 550/50:600/45 500/55:550/40 450/50:600/25 600/80 550/50:600/45 600/40 ① 600/60 600/60 ①
250/35:400/25 250/50:400/25 250/50:450/25 300/50:500/25 350/50:600/40 400/50:600/40
200/40:450/25 250/40:500/25 300/45:550/25 400/40:600/30 500/40:550/35 500/45:600/35
200/30:250/25 250/30:300/25 350/25 400/35:500/25 500/35:550/25 500/50:600/45
200/35:250/25 200/35:300/25 250/35:300/25 250/35:350/25 300/35:400/25 350/35:500/25
600/60 ① ① ① ① ①
600/40 600/60 ① ① ① ①
450/50:500/25 600/40 600/60 ① ① ①
Columns exposed on more than one side n=0.15 n=0.3 n=0.5 standard fire hydrocarbon fire standard fire hydrocarbon fire standard fire hydrocarbon fire Numerical Numerical Numerical Numerical Numerical Numerical Eurocode 2 Eurocode 2 Eurocode 2 calculation calculation calculation calculation calculation calculation 150/25 150/25 150/25 200/25 400/25 250/25 250/35:300/25 150/25 150/25 150/30:200/25 250/25 450/25 350/40:400/25 300/35:450/25 150/25 150/25 300/25 550/25 200/25 200/30:250/25 450/25 400/40:500/25 150/25 200/25 200/35:250/25 350/35:400/25 500/35:550/25 450/50:550/25 600/40 150/25 200/25 ① 300/30:350/25 250/40:400/25 450/35:500/25 550/35:600/25 500/40:600/30 150/25 200/35:250/25 400/35:450/25 300/40:500/25 450/35:550/25 ① ① 550/50:600/40
* x Requires a width > 600 mm
30 40 50 60 70 80
λ
R30
Fire resistance
①
① ① ① ① ① ①
① ① ① ① ①
600/80
550/50:600/40 ① 600/60 ① ① ① ①
① ① ① ① ① ①
① ① ① ① ① ①
600/60 ① ① ① ① ①
n=0.7 standard fire hydrocarbon fire Numerical Numerical Eurocode 2 calculation calculation 550/25 500/25 500/40:550/25 600/40 550/25 550/30 ① 600/45 550/50:600/40 ① ① ① ① ① ①
Table 10. Minimum dimensions and concrete covers for reinforced concrete columns with rectangular section (ISO 834); mechanical reinforcement ratio ω = 0.5, high firstorder moment: e = 0.5b with e ≤ 200 mm
L. Wang/R. Caspeele/R. Van Coile/L. Taerwe · Extension of tabulated design parameters for rectangular columns exposed to fire taking into account secondorder effects and various fire models
30 40 50 60 70 80
200/25 200/25 200/30:250/25 200/40:300/25 250/35:300/25 250/35:400/25
* x Requires a width > 600 mm
R120
150/25 150/25 200/25 30 150/25 200/25 40 200/25 200/35:250/25 50 150/30:200/25 150/35:200/25 200/40:250/25 200/30:250/25 200/40:250/25 60 200/25 150/40:250/25 200/40:300/25 200/40:250/25 250/55:300/25 70 200/25 200/35:250/25 250/35:300/25 250/35:300/25 300/35:350/25 80 200/30:250/25 200/40:250/25 250/35:400/25 250/50:400/25 300/40:500/25
150/40:200/25 200/30:250/25 200/40:250/25 200/45:250/25 250/25 250/35:300/25
200/25 200/40:250/25 250/35:300/25 250/50:400/25 250/50:450/25 250/50:450/25 200/40:250/25 250/35:300/25 250/35:350/25 250/50:400/25 300/50:450/25 300/50:600/35
200/45:250/25 250/25 250/35:300/25 250/45:400/25 350/35:450/25 350/40:550/25
150/25 150/25 150/25 150/25 150/40:200/25 150/25 150/30:200/25 150/40:200/25 150/30:200/25 150/40:250/25 200/25 200/25 200/35:250/25 200/40:250/25 200/30:250/25 200/40:300/25
R90
150/25 150/25 150/25 150/25 150/25 150/25
30 40 50 60 70 80
250/50:300/25 250/50:350/25 250/50:450/25 300/50:600/25 300/50:600/25 350/50:600/25
200/40:250/25 250/35:300/25 250/50:350/25 250/50:450/25 250/50:450/25 300/50:600/45
250/50:350/25 250/50:400/25 300/50:550/25 400/50:600/35 500/50:600/45 600/60
250/45:400/25 300/45:400/25 350/40:550/25 400/50:600/25 550/40:600/35 550/50:600/45
200/40:250/25 250/35:300/25 250/35:350/25 250/50:400/25 250/45:400/25 300/50:450/25 300/45:550/25 400/50:600/35 350/45:600/35 450/50:600/45 350/50:600/40
250/35:300/25 250/45:600/25 300/50:400/25 300/50:450/25 300/45:600/30 350/50:600/25 400/50:550/25 350/45:600/35 450/50:600/45 600/60 450/50:600/35 400/50:600/40 600/80 600/60 550/50:600/45 ① 600/80 550/65:600/55 300/50:400/25 300/50:400/25 400/40:600/25 350/50:500/25 300/50:500/25 400/50:600/25 400/50:600/30 450/50:600/25 400/50:600/25 450/50:600/45 550/45:600/40 600/25 450/50:600/25 600/80 600/60 550/60:600/50 600/25 ① 600/80 600/70 600/80 ① ①
250/50:350/25 250/50:400/25 300/50:600/25 400/50:600/45 450/50:600/45 600/60
250/35:300/25 300/35:400/25 350/50:450/25 400/50:600/45 500/50:600/45 600/60
n=0.7 hydrocarbon fire standard fire hydrocarbon fire Numerical Numerical Numerical Eurocode 2 calculation calculation calculation 150/25 150/25 200/25 150/25 150/25 200/25 200/25 250/25 200/25 150/30:200/25 200/40:250/25 200/25 200/30:250/25 300/35:350/25 250/35:300/25 250/35:350/25 350/50:450/25 250/25 300/35:350/25 300/35:400/25 250/30:300/25 350/50:550/25
150/40:200/25 150/25 200/40:250/25 200/25 200/40:300/25 200/25 200/25 200/30:250/25 200/40:300/25 250/25 250/35:350/25 200/40:250/25 200/30:250/25 200/40:250/25 250/50:350/25 300/25 250/40:350/25 200/40:300/25 250/35:300/25 300/35:450/25 350/40:450/25 300/40:600/25 250/35:300/25 300/35:400/25 250/40:400/25 350/50:500/25 400/50:600/45 350/40:450/35 250/35:400/25 300/50:450/25 300/40:550/25 400/50:600/45 450/50:600/45 350/45:450/40
Columns exposed on more than one side n=0.3 n=0.5 standard fire hydrocarbon fire standard fire Numerical Numerical Numerical Eurocode 2 Eurocode 2 calculation calculation calculation 150/25 150/25 150/25 150/25 150/25 150/25 150/25 150/25 150/25 150/25 150/25 150/25 150/25 150/25 200/25 150/30:200/25 200/25 150/25 200/25 200/25 200/30:250/25
R60
n=0.15 standard fire hydrocarbon fire Numerical Numerical Eurocode 2 calculation calculation 150/25 150/25 150/25 150/25 150/25 150/25 150/25 150/25 150/25 150/25 150/25 150/25
Minimum dimensions (mm) / Column width bmin [mm]/axis distance a [mm]
30 40 50 60 70 80
λ
R30
Fire resistance
Table 11. Minimum dimensions and concrete covers for reinforced concrete columns with rectangular section (ISO 834); mechanical reinforcement ratio ω = 1.0, low firstorder moment: e = 0.025b with e ≥ 10 mm L. Wang/R. Caspeele/R. Van Coile/L. Taerwe · Extension of tabulated design parameters for rectangular columns exposed to fire taking into account secondorder effects and various fire models
Structural Concrete (2015)
29
30
Structural Concrete (2015)
30 40 50 60 70 80
30 40 50 60 70 80
30 40 50 60 70 80
R60
R90
R120
200/30:250/25 200/40:300/25 250/35:300/25 250/35:400/25 250/50:400/25 250/50:450/25
150/30:200/25 200/25 200/25 200/30:250/25 200/40:300/25 200/40:300/25
200/40:250/25 200/45:300/25 250/40:400/25 250/50:450/25 300/40:500/25 300/50:550/25
200/25 200/30:250/25 200/35:300/25 200/40:400/25 200/45:450/25 200/50:500/25
150/25 150/25 150/25 150/25 150/30:200/25 150/25 150/35:200/25 150/25 200/30:250/25 150/25 150/30:200/25 200/25 200/30:250/25 250/35:300/25 300/35:350/25 200/30:250/25 200/40:300/25 250/35:300/25 300/35:400/25 300/50:450/25 400/50:550/25 250/35:300/25 250/50:400/25 300/50:450/25 400/50:600/25 450/50:600/35 500/50:600/35
200/40:250/25 200/40:300/25 250/35:300/25 250/35:400/25 250/50:450/25 250/50:450/25
250/35:300/25 250/50:400/25 250/50:450/25 250/50:450/25 300/50:600/25 300/50:600/25 250/50:400/25 300/40:500/25 400/40:550/25 400/50:500/35 500/45:600/35 500/60:600/40
200/40:300/25 200/50:400/25 250/50:550/25 300/45:600/25 300/50:600/35 400/50:600/35
150/30:200/25 150/40:250/25 200/35:400/25 200/40:450/25 250/40:550/25 300/40:550/25 250/50:350/25 300/50:450/25 450/50:500/25 500/50:600/35 600/60 600/80
200/25 250/35:300/25 300/25 400/50:450/25 450/50:550/25 500/50:600/35
250/50:350/25 300/35:350/25 300/50:600/30 450/25 300/35:400/25 500/50:600/25 450/25 400/50:600/35 400/50:450/25 500/50:600/25 500/45:600/40 550/50:600/45 450/50:600/25 600/80 600/45 550/40:600/40 550/50:600/45 ① 600/60 ① 600/60 ① 600/80 ①
600/60 ①
550/50:600/25 600/25 ① ① ① ①
250/40:550/25 300/50:450/25 450/50:500/25 500/50:600/45 500/50:600/45 600/45 300/50:600/35 350/50:600/45 500/50:600/35 500/60:600/50 600/80 400/50:600/40 500/50:600/45 600/60 600/55 600/45 ① 500/50:600/45 600/70 ① 600/80 ① ① 550/55:600/50 ① ① ① 600/55
200/40:400/25 250/40:500/25 300/40:600/25 400/40:600/30 450/45:500/35 500/50:600/40
n=0.7 hydrocarbon fire standard fire hydrocarbon fire Numerical Numerical Numerical Eurocode 2 calculation calculation calculation 200/25 300/25 200/25 200/30:300/25 250/25 250/35:300/25 250/30:450/25 350/50:400/25 250/25 350/40:400/25 300/35:500/25 450/50:500/25 300/50:400/25 450/25 400/40:550/25 500/50:600/25 400/50:450/25 500/50:550/25 500/35:600/30 550/50:600/60 450/50:550/25 ① 600/35 500/60:600/35
250/50:450/25 300/50:550/25 450/45:600/30 400/50:600/25 500/50:600/35 300/50:500/25 400/50:600/35 500/50:600/35 450/50:600/25 600/45 350/50:600/25 550/50:600/45 550/50:600/25 ① 400/50:600/25 600/25 ① 600/45 600/55 450/50:600/25 ① ① 600/80 ① 550/50:600/25 ① ① ①
250/35:350/25 250/50:400/25 300/50:450/25 300/50:600/25 400/50:600/45 450/50:600/45
200/40:250/25 200/40:300/25 250/35:300/25 250/50:400/25 300/35:450/25 350/50:450/25
Columns exposed on more than one side n=0.3 n=0.5 standard fire hydrocarbon fire standard fire Numerical Numerical Numerical Eurocode 2 Eurocode 2 calculation calculation calculation 150/25 150/25 150/25 150/25 150/25 150/25 150/25 150/25 200/25 150/25 200/25 250/25 200/30:250/25 150/25 200/40:250/25 300/25 250/35:300/25 250/25 200/25 150/30:250/25 350/40:400/25 300/35:500/25
Minimum dimensions (mm) / Column width bmin [mm]/axis distance a [mm]
150/40:200/25 150/40:200/25 200/40:250/25 200/40:250/25 200/40:300/25 200/40:300/25
n=0.15 standard fire hydrocarbon fire Numerical Numerical Eurocode 2 calculation calculation 150/25 150/25 150/25 150/25 150/25 150/25 150/25 150/25 150/25 150/25 150/25 150/25
* x Requires a width > 600 mm
30 40 50 60 70 80
λ
R30
Fire resistance
Table 12. Minimum dimensions and concrete covers for reinforced concrete columns with rectangular section (ISO 834); mechanical reinforcement ratio ω = 1.0, moderate firstorder moment: e = 0.25b with e ≤ 100 mm
L. Wang/R. Caspeele/R. Van Coile/L. Taerwe · Extension of tabulated design parameters for rectangular columns exposed to fire taking into account secondorder effects and various fire models
30 40 50 60 70 80
30 40 50 60 70 80
30 40 50 60 70 80
R60
R90
R120
250/35:350/25 300/40:400/25 300/40:450/25 350/40:500/25 350/40:600/45 350/40:600/45
200/30:250/25 200/30:300/25 300/25 250/35:400/25 300/40:450/25 400/35:450/25
150/25 150/25 200/25 200/25 200/30:250/25 250/30:300/25
250/50:550/25 300/50:600/25 400/50:550/35 450/50:600/40 500/50:550/45 550/50:600/45
200/40:450/25 200/50:500/25 250/45:550/25 250/50:550/30 300/50:550/35 350/50:600/35
150/30:200/25 150/35:200/25 200/35:300/25 200/40:500/25 200/40:550/25 250/40:600/25
n=0.15 standard fire Numerical Eurocode 2 calculation 150/25 150/25 150/25 150/25 150/25 150/25
* x Requires a width > 600 mm
30 40 50 60 70 80
λ
R30
Fire resistance
350/50:450/25 500/35:550/25 500/55:600/40 400/50:550/25 550/50:600/45 550/60:600/50 600/40 600/80 600/60 600/60 ① 600/80 600/80 ① ① ① 400/50:600/40 550/50:600/45 550/50 450/50:600/40 600/60 550/60:600/55 600/60 ① 600/80 600/60 ① ① ① ① ①
300/30:400/25 300/50:500/25 350/35:450/25 350/50:550/35 450/35:500/25 500/45:550/40 500/50:550/35 500/50:550/45 550/50:600/45 600/80 550/60:600/50
250/50:450/25 350/40:450/25 500/50:550/40 300/50:500/25 350/40:600/25 500/55:550/45 300/50:600/40 500/50:600/45 500/60:600/45 350/50:600/40 600/45 550/50 450/50:600/40 600/80 550/60:600/55 450/50:600/40 ① 600/70
300/35:400/25 450/35:500/25 450/50:550/30 350/35:400/25 500/25 500/40:550/35 400/50:500/25 550/50:600/45 500/55:550/40 450/50:600/25 600/80 550/50:600/45 600/40 ① 600/60 600/60 ①
250/35:400/25 250/50:400/25 250/50:450/25 300/50:500/25 350/50:600/40 400/50:600/40
200/40:450/25 250/40:500/25 300/45:550/25 400/40:600/30 500/40:550/35 500/45:600/35
200/30:250/25 250/30:300/25 350/25 400/35:500/25 500/35:550/25 500/50:600/45
200/35:250/25 200/35:300/25 250/35:300/25 250/35:350/25 300/35:400/25 350/35:500/25
600/60 ① ① ① ① ①
600/40 600/60 ① ① ① ①
450/50:500/25 600/40 600/60 ① ① ①
Columns exposed on more than one side n=0.3 n=0.5 hydrocarbon fire standard fire hydrocarbon fire standard fire hydrocarbon fire Numerical Numerical Numerical Numerical Numerical Eurocode 2 Eurocode 2 calculation calculation calculation calculation calculation 150/25 150/25 200/25 400/25 250/25 250/35:300/25 150/25 150/30:200/25 250/25 450/25 350/40:400/25 300/35:450/25 150/25 300/25 550/25 200/25 200/30:250/25 450/25 400/40:500/25 200/25 200/35:250/25 350/35:400/25 500/35:550/25 450/50:550/25 600/40 200/25 ① 300/30:350/25 250/40:400/25 450/35:500/25 550/35:600/25 500/40:600/30 200/35:250/25 400/35:450/25 300/40:500/25 450/35:550/25 ① ① 550/50:600/40
Minimum dimensions (mm) / Column width bmin [mm]/axis distance a [mm]
①
① ① ① ① ① ①
① ① ① ① ①
600/80
550/50:600/40 ① 600/60 ① ① ① ①
① ① ① ① ① ①
① ① ① ① ① ①
600/60 ① ① ① ① ①
n=0.7 standard fire hydrocarbon fire Numerical Numerical Eurocode 2 calculation calculation 550/25 500/25 500/40:550/25 600/40 550/25 550/30 ① 600/45 550/50:600/40 ① ① ① ① ① ①
Table 13. Minimum dimensions and concrete covers for reinforced concrete columns with rectangular section (ISO 834); mechanical reinforcement ratio ω = 1.0, high firstorder moment: e = 0.5b with e ≤ 200 mm L. Wang/R. Caspeele/R. Van Coile/L. Taerwe · Extension of tabulated design parameters for rectangular columns exposed to fire taking into account secondorder effects and various fire models
Structural Concrete (2015)
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L. Wang/R. Caspeele/R. Van Coile/L. Taerwe · Extension of tabulated design parameters for rectangular columns exposed to fire taking into account secondorder effects and various fire models
compressive strength, fyd the design yield stress of reinforcement and N0Ed,fi the design value of the applied axial force. From the tables above and comparing these with the tabulated data provided in Eurocode 2 [13], it can be seen that the Eurocode 2 [13] tables are not safe for the case of a reinforcement ratio of 0.1 or for a reinforcement ratio of 0.5 when the axial load is large. On the other hand, some minimum dimensions are overly conservative for a reinforcement ratio of 1.0. Further, the present study proves very helpful when providing guidelines for a minimum crosssection design for columns subjected to fire.
4
Extension of the tabulated data for concrete columns exposed to hydrocarbon and natural fires
EN 199212 [13] only provides minimum dimensions with respect to the ISO 834 standard fire, but this standard fire does not represent a true indication of how structural members and assemblies will behave in an actual fire or when exposed to a hydrocarbon fire. As resistance to hydrocarbon fires may be required in specific situations and little data is available on the design of concrete columns exposed to hydrocarbon fires, extending the tables of the Eurocode with respect to this more severe design fire is important. Hence, the same analytical method is used to determine the required crosssection characteristics for columns exposed to these other fire curves. Hydrocarbon fires represent the burning of, for example, gasoline pool fires, and they are widely used when designing technical facilities and tunnels. Natural fires, known as compartment fires, account for the fire load present within a compartment and decrease in intensity once the fuel has been burned. Both of these two types of fire are typical fire events and so they are adopted for the fire resistance of columns. The hydrocarbon temperature–time curve is given in [13] as follows: Qg = 1080 (1 – 0.325 e–0.167t – 0.675 e–2.5t ) + 20 [°C]
Table 14. Occupancyspecific fire load densities [MJ/m2]
Occupancy
Mean
Standard deviation
80 percentile
Dwelling
780
234
948
Office
420
126
511
acteristic value is proposed as the 80 percentile of a Gumbel distribution. In this case the same fire compartment as in [24] is adopted for both the dwelling and the office cases, with Af = 16 m2, height H = 3 m, area of openings Aw = 8 m2 and average height of openings hw = 2.50 m. It is worth noting that these natural fires start to decrease after about 50 min in a dwelling and 30 min in an office. A square column subjected to these fire conditions will be analysed next: 300 × 300 mm crosssection, one 32 mm diameter reinforcing bar in each corner, 25 mm concrete cover, concrete compressive strength fck = 55 MPa, reinforcement yield strength fy = 500 MPa and Young’s modulus of steel Es = 2 × 105 N/mm2. The reinforcement temperature as a function of the fire exposure time is shown in Figs. 7 and 8 for the two fire simulations respectively. It can be seen that the reinforcement temperature begins to decrease after 75 min in the dwelling and 60 min in the office. Considering plastic damage and strength loss
(4)
where Qg is the gas temperature in the fire compartment [°C] and t is the time [min].
4.1
Fire resistance of columns subjected to a hydrocarbon fire
Fig. 7. Temperature–time diagram for reinforcing bar (dwelling)
The same material properties and boundary conditions as for EN 199212 [13] are considered in the case of this hydrocarbon fire. The minimum column crosssections required for 30, 60, 90 and 120 min are shown in the same tables as for the ISO 834 standard fire (Tables 5–13).
4.2
Fire resistance of columns subjected to natural fires
Besides considering standard ISO 834 fires or hydrocarbon fires, this calculation analysis can also be used when columns are subjected to natural fires. Interaction curves for columns are obtained for the case of dwellings and offices. The fire load densities are listed in Table 14 [23]. In EN 199212 [12] the mean value of the fire load density is provided for the typical occupancy and the char
32
Structural Concrete (2015), No 1
Fig. 8. Temperature–time diagram for reinforcing bar (office)
L. Wang/R. Caspeele/R. Van Coile/L. Taerwe Âˇ Extension of tabulated design parameters for rectangular columns exposed to fire taking into account secondorder effects and various fire models
in the concrete, the stressâ€“strain relationship for cooling is not the same as for the increasing fire temperature. However, no specific guidelines are given in the Eurocode for calculating the cooling branch. In order to solve this problem, an analytical method is proposed. This analytical approach supposes, on the one hand, that there is no strength recovery in the concrete and adopts the same stressâ€“strain model to calculate the upper limit curve during the cooling period (assuming perfect recovery). On the other hand, it considers the stressâ€“strain model associated with the maximum local concrete temperature reached during the fire. In this way, a lower limit curve can be obtained (assuming no recovery). As a result, the bending moment capacity of the columns should be located between these two curves. The current analytical tool, however, has not been explored for the full cooling phase yet. The maximum local concrete temperature is a simplified and conservative way of predicting the tendency of fire resistance when the fire temperature begins to decrease. Taking the dwelling, for instance, upper and lower limit curves (Figs. 9 and 10) are calculated for different normal forces, where n = N0Ed,fi / (0.7(Ac fcd + As fyd)) as proposed in EN 199212 [13]. Fig. 9 indicates that the maximum permissible bending moment does not decrease much when the normal force is low (n < 0.3). This is because secondorder effects
are insignificant for loads with small eccentricities. As soon as n reaches 0.3, the maximum permissible bending moment decreases significantly as the eccentric load increases. It is worth mentioning that the lower limit curve increases again as the reinforcing bars cool. It is possible to obtain the minimal curves (the most critical case during a fire). Comparing the curves in Fig. 10, it can be seen that the lower limit curve does not drop much below the most critical point of the upper limit curve. The same analysis has been performed for the office with a natural fire and the maximum permissible bending moments as a function of fire duration are shown in Table 15. The upper limit and lower limit for the maximum permissible bending moment define a range in which the actual design value for the bending moment is situated. This is illustrated in Fig. 11 for n = 0.3 by the shaded area. Finally, the lower limit curve can be adopted to calculate interaction curves for columns with different slenderness ratios. As an example, interaction curves based on the lower limit curve at the most critical time for the dwelling and office are provided in Figs. 12 and 13, with n
Fig. 10. Maximum permissible bending moments in columns during a dwelling fire (n > 0.3)
Mc Ms
0.7 Ac fcd As fyd *h
,
where Nc, Mc, Ns, and Ms are maximum forces and bending moments respectively for concrete and reinforcement, b is the width of the column and h is the depth of the crosssection.
5
Fig. 9. Maximum permissible bending moments in columns during a dwelling fire (n â‰¤ 0.3)
Nc Ns and 0.7( Ac fcd As fyd )
Conclusion
An analytical method has been developed which proves to be an easy way of predicting interaction curves for columns exposed to fire. The minimum dimensions of columns for the ISO 834 standard fire are recalculated and some comparisons with experimental results are provided in order to validate the calculation tool obtained. It is found that, on the one hand, Eurocode provisions are not safe for the case of a reinforcement ratio of 0.1 or reinforcement ratio of 0.5 when the axial load is large. On the other hand, tabulated data is found to be too conservative for high reinforcement ratios Ď‰ = 1.0, which results in inefficient and uneconomical solutions in practice. Considering the economical aspect as well as the safety issue, the tabulated design solutions obtained in the current work provide more precise references for the design of concrete columns exposed to fire. Furthermore, the range of applications is extended to other fire scenarios. The minimum column dimensions are presented for hydrocarbon fires. Comparing the results for the hydrocarbon fire with the tables obtained for the ISO 834 standard fire, it should be noted that fire resistance to the hydrocarbon fire may result in very stringent requirements. Moreover, some specific examples are given for the case of columns subjected to natural fires. Both upper and lower limit curves are introduced dependant on the assumption with respect to recovery in the coding phase to investigate the fire resistance of columns when the fire temperature begins to decrease. The results prove that secondorder effects are insignificant when the normal force is low. When the eccentric loads are large enough, the maximum permissible
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33
34
0 15 30 45 60 75 90
0.3 0.2 0.1 0 t (min)
n
Table 15. Maximum permissible bending moments in columns during an office fire
0.4
0.5
0.6
0.7
0.8
0.9
1
Perfect No Perfect No Perfect No Perfect No Perfect No Perfect No Perfect No Perfect No Perfect No Perfect No Perfect No recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery recovery 188 188 241 241 290 290 326 326 345 345 332 332 301 301 271 271 238 238 199 199 154 154 188 188 241 241 290 290 325 325 342 342 331 331 298 298 265 265 229 229 187 187 143 143 183 183 237 237 278 278 297 297 297 297 270 270 236 236 197 197 158 158 116 116 73 73 182 182 235 234 272 270 283 278 275 266 244 237 200 193 166 156 126 117 86 80 48 41 233 269 274 259 227 188 144 112 75 36 273 259 227 188 143 111 73 33 72 32
L. Wang/R. Caspeele/R. Van Coile/L. Taerwe 路 Extension of tabulated design parameters for rectangular columns exposed to fire taking into account secondorder effects and various fire models
Structural Concrete (2015), No 1
Fig. 11. Range of maximum permissible bending moments during a natural fire for n = 0.3
Fig. 12. Interaction curves for columns after 75 min fire exposure (dwelling)
Fig. 13. Interaction curves for columns after 60 min fire exposure (office)
bending moment in the column first drops continuously during the fire and then rises slightly at a certain point during the cooling phase. As a result, this value based on the lower limit curve could be identified as the design value during this specific fire. In conclusion, the analytical method and calculation tool are both accurate and flexi
L. Wang/R. Caspeele/R. Van Coile/L. Taerwe · Extension of tabulated design parameters for rectangular columns exposed to fire taking into account secondorder effects and various fire models
ble, and could possibly be effective in quantifying the interaction curves of columns exposed to any types of fire when considering secondorder effects.
Acknowledgements The authors would like to thank the China Scholarship Council (CSC) for their financial support. References 1. Franssen, J. M., Dotreppe, J. C.: Fire tests and calculation methods for circular concrete columns. Fire Technology, 2003(39), pp. 89–97. 2. Lie, T. T., Lin, T. D., Allen, D. E., Abrams, M. S.: Fire resistance of reinforced concrete columns. Division of Building Research, DBR paper No. 1167, National Research Council of Canada, Ottawa, Canada, Feb 1984. 3. Lie, T. T., Celikkol, B.: Method to calculate the fire resistance of circular reinforced concrete columns. ACI Materials Journal, 1991, 88(1), pp. 84–91. 4. Lie, T. T., Irwin, R. J.: Method to calculate the fire resistance of reinforced concrete columns with rectangular cross section. ACI Structural Journal, 1993, 90(1), pp. 52–60. 5. Dotreppe, J. C., Franssen, J. M., Vanderzeypen, Y.: Calculation method for design of reinforced concrete columns under fire conditions. ACI Structural Journal, 1999, 96(1), pp. 9–18. 6. Meda, A., Gambarova, P. G., Bonomi, M.: Highperformance concrete in fireexposed reinforced concrete sections. ACI Structural Journal, 2002, 99(3), pp. 277–287. 7. Kodur, V., Raut, N.: A simplified approach for predicting fire resistance of reinforced concrete columns under biaxial bending. Eng Struct, 2012, 41, pp. 428–443. 8. Van Coile, R., Annerel, E., Caspeele, R., Taerwe, L.: FullProbabilistic analysis of concrete beams during fire. Journal of Structural Fire Engineering, 2013, pp. 165–174. 9. Van Coile, R., Caspeele, R., Taerwe, L.: Lifetime cost optimization for the structural fire resistance of concrete slabs. Fire Technology, Jun 2013. 10. Jeffers, A., Sotelino, E.: Fiber heat transfer element for modeling the thermal response of structures in fire. J. Struct. Eng., 2009, 135(10), pp. 1191–1200. 11. Jeffers, A.: Heat transfer element for modeling the thermal response of nonuniformly heated plates. Finite Elements in Analysis and Design. 2013, 63, pp. 62–68. 12. Eurocode 2 – Commentary – European Concrete Platform ASBL, Jun 2008. 13. CEN. EN 199212: Design of concrete structures – Part 12: General rules – Structural fire design. European Committee for Standardization, Brussels, Belgium, 2004. 14. Caldas, R. B., Sousa, J. B. M., Fakury, R. H.: Interaction diagrams for reinforced concrete sections subjected to fire. Eng Struct, 2010, 32(9), pp. 2832–2838. 15. MATLAB version 8.1 (R2013a), The MathWorks Inc., Natick, Massachusetts, 2013. 16. DIANA version 9.4.4, TNO DIANA BV, Delft, The Netherlands, 2012. 17. fib Bulletin No. 46: Fire design of concrete structures – structural behaviour and assessment, State of the art report, 2008.
18. Wang, L. J., Caspeele, R., Taerwe, L.: Development of an Excelbased calculation tool for interaction curves of rectangular concrete columns subjected to fire. IRF’2013, 4th Int. Conf. on Integrity, Reliability & Failure, 2013, pp. 49–50. 19. CEN: EN 199211: Design of concrete structures – Part 11: General rules and rules for buildings. European Committee for Standardization, Brussels, Belgium, 2004. 20. Hass, R.: Zur praxisgerechten brandschutztechnischen Beurteilung von Stützen aus Stahl und Beton. PhD dissertation, 1986. 21. Dotreppe, J.C., Franssen, J.M.: Dimensionnement des colonnes en béton armé en considérant le problème de la résistance au feu. External Report, 1993. 22. fib Bulletin No. 38: Fire design of concrete structures – materials, structures and modeling, State of the art report, 2007. 23. Albrecht, C., Hosser, D.: Riskinformed framework for performancebased structural fire protection according to the Eurocode fire parts, Proc. of 12th Interflam Conf., Nottingham, 5–7 Jul 2010, pp. 1031–1042. 24. Zehfuss, J., Hosser, D.: A parametric natural fire model for the structural fire design of multistorey buildings. Fire Safety Journal, 2007, 42, pp. 115–126.
Lijie Wang Ghent University Department of Structural Engineering Magnel Laboratory for Concrete Research TechnologieparkZwijnaarde 904 9000 Ghent Belgium Email: Lijie.Wang@UGent.be
Robby Caspeele Ghent University Department of Structural Engineering Magnel Laboratory for Concrete Research TechnologieparkZwijnaarde 904 9000 Ghent Belgium
Ruben Van Coile Ghent University Department of Structural Engineering Magnel Laboratory for Concrete Research TechnologieparkZwijnaarde 904 9000 Ghent Belgium
Luc Taerwe Ghent University Department of Structural Engineering Magnel Laboratory for Concrete Research TechnologieparkZwijnaarde 904 9000 Ghent Belgium
Structural Concrete (2015), No. 1
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Technical Paper François Duplan* Ariane AbouChakra Anaclet Turatsinze Gilles Escadeillas Stéphane Brûlé Emmanuel Javelaud Frédéric Massé
DOI: 10.1002/suco.201400020
On the use of European and American building codes with lowstrength mortars The standard European building specifications, grouped in a ninevolume Eurocode, describe different approaches for determining the properties of commonly used building materials such as steel, aluminium, concrete, etc. The American Concrete Institute (ACI) also offers different reports concerning concrete structures (ACI 318R), lightweight concrete (ACI 213R) and the longterm mechanical behaviour (ACI 209R) of concrete. Those reports, used as building codes, are applicable when the properties and composition of the material respect various criteria. All those materials that do not meet the scope criteria of Eurocode 2 or ACI reports because of their composition, property values or application cannot be used in the design of structures with those building codes. Regarding cementbased materials, concretes and mortars whose compressive strength is lower than the minima might not be useful for structures; however, they present an interesting potential for applications such as infrastructure materials, slabsonground, etc. When designing structures and infrastructures in those materials, the accuracy of any formula offered by those building codes should be checked before being used. This article compares experimental measurements and predictive formulas for the engineering properties (compressive and tensile strengths, modulus of elasticity). The results show that the addition of specific aggregates with low stiffness and strength modifies the relation between those engineering properties, thus reducing the accuracy of some of the predictive formulas suggested in ACI reports or Eurocodes.
with s = 0.20 for type R cement s = 0.25 for type N cement s = 0.38 for type S cement
Keywords: Modulus of elasticity, compressive strength, lightweight mortar, rubberized mortar, sand mortar
fcm(t) = βcc(t)fcm
(2)
fctm(t) = (βcc(t))α fctm
(3)
1
Introduction
pose of the current paper is to evaluate the accuracy of those predictive empirical formulas for the mechanical properties of cementbased composites with two types of lowstrength mortar: lightweight and rubberized mortars. The experimental results of the engineering properties (compressive and tensile strengths, modulus of elasticity) are compared with the ones predicted by the empirical formulas of Eurocode 2 Part 11, Eurocode 2 Part 14, ACI 318, ACI 363, ACI 213 and ACI 209. The precision of those formulas for the lowstrength materials investigated is compared with the precision obtained for normal and highstrength concrete.
2 European building codes 2.1 Eurocode 2 2.1.1 Evolution of the mechanical properties over time The evolution of strengths and modulus of elasticity over time is predicted with Eqs. (2), (3) and (4). The exponential term βcc used for all three predictions is defined in Eq. (1): ⎯28/t) βcc(t) = es(1–√
(1)
with α = l for t = 28 days and α = 2/3 for t > 28 days Among the engineering properties of concrete, the most important for the design of structures are the strength (especially in compression), the modulus of elasticity and the unit weight. The strength of the material used for design is a guaranteed value of the mean compressive strength. The other properties (tensile strength and modulus of elasticity) are often estimated by empirical formulas based on the assumed compressive strength of the material. The pur
Ecm(t) = (fcm(t)/fcm)0.3Ecm
(4)
2.1.2 Relationships between the mechanical properties Various strength classes, from C12/15 to C90/105, are defined by their characteristic compressive strengths. Empirical formulas allow their modulus of elasticity to be estimated, as in Eq. (5):
* Corresponding author: francois.duplan86@gmail.com Submitted for review: 3 March 2014 Revised: 20 May 2014 Accepted for publication: 29 June 2014
36
Ecm
§f · 22 ¨ cm ¸ © 10 ¹
0.3
© 2015 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete (2015), No. 1
(5)
F. Duplan/A. AbouChakra/A. Turatsinze/G. Escadeillas/S. BrĂťlĂŠ/E. Javelaud/F. MassĂŠ Âˇ On the use of European and American building codes with lowstrength mortars
Eurocode 2 Part 1â€“4: Lightweight concrete For lightweight concrete (bulk density < 2000 kg/m3) made with closedstructure lightweight aggregates, the strength classes remain the same and range from LC12 to LC50. The modulus of elasticity is determined by multiplying the result of Eq. (5) by a factor gE given by Eq. (6): gE
Â§ q Âˇ Â¨ÂŠ 2200 Â¸Âš
2
(6)
modulus of elasticity should include the additional term Îť for unit weights between 90 and 155 lb/ft3 (1440 and 2480 kg/m3).
3.3
ACI 209 R
This report [3] defines the evolution over time of some concrete properties and gives formulas for the prediction of shrinkage and creep. The evolution of the compressive strength of concrete over time can be expressed using Eqs. (9) and (10): t (f c) D Et c u
Eurocode 2 Part 1â€“6: Plain concrete structures
fcc(t)
When concrete is used without steel reinforcement, or with a quantity less than the minimum specified by Eurocode 2 Part 11, Îłc should be multiplied by 1.2.
with Îą between 0.05 and 9.25 (from Table 1) Î˛ between 0.67 and 0.98 (from Table 1)
3 3.1
fcc(t)
American building codes ACI 318
ACI 318 [1] defines the modulus of elasticity of concrete as the secant slope of the line between the origin and the point at 0.45 fcâ€˛ (45 % of maximum stress). When the unit weight of dry concrete wc is between 90 and 160 lb/ft3 (1440 and 2560 kg/m3), Eq. (7) should be used: Ec = wc1.5 33âˆš âŽŻfcâ€˛
(7)
For normalweight concrete, Eq. (8) can be used; it is the same as Eq. (7) with an assumed unit weight of 144 lb/ft3 (2303 kg/m3): âˆš câ€˛ Ec = 57000âŽŻf
For sandlightweight concrete (only coarse aggregates are light): Îť = 0.85 For alllightweight concrete (fine and coarse aggregates are light): Îť = 0.75 For normalweight concrete: Îť = l Linear interpolation should be used when gravel is substituted by lightweight coarse aggregate and/or the substitution of the sand by fine lightweight aggregate is only partial. When the splitting tensile strength has been measured, then
3.2
fct 6.7 fcc
t ( fcc )u D t E
(10)
with Îą between 0.05 and 9.25 (from Table 1) Î˛ between 0.67 and 0.98 (from Table 1) The coefficients Îą and Î˛ are given for two types of cement (I and III) and two types of curing (steam and moist), as given in Table 1 (taken from [3]). The direct tensile strength ftâ€˛ can be evaluated from the unit weight and the compressive strength using Eq. (11): ft c
1 [wf c ]0.5 3 ct
(11)
(8)
For lightweight concrete, an additional coefficient Îť must be introduced in the above formulas before the term âŽŻf âˆš câ€˛. This coefficient takes the following values:
O
(9)
.
ACI 213 R
This report [2] on lightweight concrete recommends using the formulas of ACI 318. The evaluation formulas for the
The modulus of elasticity is evaluated with Eq. (7) from ACI 318.
4 4.1
Experimental study Experimental mixes
Various cementbased composites were investigated, with different aggregate volumes and properties. The composites included sand, lightweight and rubberized mortar. The cement was a CEM III C 32.5 PMES for all mixes, the limestone filler had a grain size of 0/100 Îźm and the sand was a local river sand from the River Garonne (0/4 mm). The specific aggregates were expanded clay lightweight aggregates (4/8 mm), and the rubber aggregates (0/4 mm) were obtained from the grinding of used tyres. The water/cement (w/c) ratio remained constant for each mortar; therefore, the elastic properties of the cement paste remained unchanged. The amounts of rheologymodifying admixtures were adjusted in order to maintain the slump between 18 and 22 cm; their effect on the elastic properties of the cement paste was presumed to be insignificant. In order to consider the effective w/c ratio of the cement paste, the water absorption of the natural sand was taken into account. It was 1.9 % by weight. The mortar compositions are given in Tables 2, 3 and 4.
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F. Duplan/A. AbouChakra/A. Turatsinze/G. Escadeillas/S. Brûlé/E. Javelaud/F. Massé · On the use of European and American building codes with lowstrength mortars
Table 1. α and β coefficients for the evolution of fc′(t)
Time ratio
(fc′)t/(fc′) 28 Eq. (21)
Type of curing
Moist Cured
Cement Type
Moist Cured Steam Cured
Days
Years 14
21
28
56
91
1
10
α = 4.0 β = 0.85
0.46
0.70
0.88
0.96
1.0
1.08
1.12
1.16
1.17
α = 2.3 β = 0.92
0.59
0.80
0.92
0.97
1.0
1.04
1.06
1.08
1.09 1.09
α = 1.0 β = 0.95
0.78
0.91
0.98
1.0
1.0
1.03
1.04
1.05
1.05 1.05
α = 0.70 β = 0.98
0.82
0.93
0.97
0.99
1.0
1.0
1.01
1.01
1.02 1.02
I
α/β = 4.71
0.39
0.60
0.75
0.82
0.86
0.92
0.95
0.99
1.0
1.0
III
α/β = 2.5
0.54
0.74
0.85
0.89
0.92
0.96
0.97
0.99
1.0
1.0
I
α/β = 1.05
0.74
0.87
0.93
0.95
0.96
0.98
0.99
1.0
1.0
1.0
III
α/β = 0.71
0.81
0.91
0.95
0.97
0.97
0.99
0.99
1.0
1.0
1.0
I
I
Cement (kg/m3)
242
Water (kg/m3)
254
Sand (kg/m3)
1644
Filler (kg/m3)
135
Superplasticizer (kg/m3)
4.73
Table 3. Lightweight mortar mixes
Lightweight aggregates substitution rate (%)
0
30
60
Cement (kg/m3)
242
242
242
Water (kg/m3)
254
254
254
Sand (kg/m3)
1644
1151
658
Filler (kg/m3)
135
135
135
Presaturated lightweight aggregates (kg/m3)
0
222
444
Superplaticizer (kg/m3)
4.73
7.20
7.20
Viscosity agent (kg/m3)
0
1.06
1.06
The lightweight and rubberized mortars were formulated by substituting natural sand by those specific aggregates from a control mix. The control mix is the mortar containing a 62 % volume fraction of natural sand. This method of formulation maintains the properties and volume fraction of the cement paste, whereas the relative volume fractions of sand and specific aggregates were variable.
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1.18
Table 4. Rubberized mortar mixes
Table 2. Natural sand mortar mix
38
Ultimate (in time)
7
III (fc′)t/(fc′) u, Eq. (22)
Concrete age
3
III Steam Cured
Constants α, and α/β
Rubber aggregates substitution rate (%)
0
5
15
30
Cement (kg/m3)
242
242
242
242
Water (kg/m3)
254
254
254
254
Sand (kg/m3)
1644
1562
1397
1151
Filler (kg/m3)
135
135
135
135
Rubber aggregates (kg/m3)
0
37
111
221
Superplaticizer (kg/m3)
4.73
7.20
7.20
7.20
Viscosity agent (kg/m3)
0
1.06
1.06
1.08
The lightweight aggregates were presaturated before mixing according to their data sheet. Their presaturation water (5 min water absorption ratio of 9 %) does not figure in the mix details in Table 3. The water absorption ratio of the rubber aggregates could not be measured, but is known to be very low since vulcanized rubber is hydrophobic [4]. Without any complementary data, the total water quantity was kept constant.
4.2
Testing methods
The elastic moduli were tested according to the RILEM CPC8 recommendations. The compressive strength and density tests were carried out according to EN 12390.
5
Results taken from the literature
In order to judge the validity of the formulas for lowstrength mortars, it was decided to compare their accuracy with structural concrete data from the literature, and then
F. Duplan/A. AbouChakra/A. Turatsinze/G. Escadeillas/S. Brûlé/E. Javelaud/F. Massé · On the use of European and American building codes with lowstrength mortars
compare it with the accuracy for the mortars investigated. The studies in [5], [6], [7], [8], [9], [10], [11], [12], [13] and [14] investigate normalweight concretes with compressive strengths in the common structural range of 30 to 100 MPa. Those concretes were mainly made with natural aggregates and type I cement. Studies [15] and [16] investigate concrete and mortars with partial substitution of natural aggregates by rubber aggregates. Rubberized concrete is a kind of lightweight concrete that is not considered by either the Eurocode or the ACI building codes. Study [17] investigates the addition of lightweight aggregates to a sand mortar whose relative composition was maintained. Study [18] looked at the effect of cork substitution for sand and stone in mortar and concrete. The first three of these works used type I cement, whereas general use cement was used in [18].
6
Comparison between predictions and experimental mechanical properties 6.1 Comparison with Eurocode 2 6.1.1 Evolution of the compressive strength over time Figs. 1 and 2 show the comparison between the compressive strengths of concrete after 7 and 28 days of curing. Fig. 1 shows the estimation of Eurocode 2 using Eq. (2) for a type I cement. Fig. 2 shows the prediction of Eq. (9) with α and β values corresponding to a moistcured, cement type I concrete. Overall, compared with the results from the literature, the predictions of both codes, which have similar values, are both satisfying when the material compressive strength ranges between 20 and 40 MPa. The prediction of Eq. (2) for type R cement (s = 0.2 in Eq. (1)) has, compared with the results taken from the literature, mean and maximum relative error values of 14 and 47 % respectively. The prediction of Eq. (9) for moistcured type I cement gives mean and maximum relative errors of 15 and 45 % respectively. Figs. 3 and 4 show that, for the lowstrength mortars investigated, the correlation between the 7 and 28day compressive strengths are satisfying with Eurocode 2.
Fig. 1. Correlation between 7 and 28day compressive strengths – results from the literature – Eurocode 2
Fig. 2. Correlation between 7 and 28day compressive strengths – results from the literature – ACI 209
Fig. 3. Correlation between 7 and 28day compressive strengths – experimental results – Eurocode 2
Fig. 4. Correlation between 7 and 28day compressive strengths – experimental results – ACI 209
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F. Duplan/A. AbouChakra/A. Turatsinze/G. Escadeillas/S. Brûlé/E. Javelaud/F. Massé · On the use of European and American building codes with lowstrength mortars
The prediction of Eq. (2) for type S cement (s = 0.38 in Eq. (1)) has, compared with the experimental results, mean and maximum relative error values of 8 and 34 % respectively. When the 28day compressive strength is used as input data for Eq. (9), as suggested by its form, the 7day compressive strength is slightly underestimated, as Eq. (2) would give a slightly lower value than experiments. Nevertheless, since only one of the eight mortar mixes investigated gave a relative error > 30 %, Eq. (2) still seems accurate. The prediction of Eq. (9) for moistcured type I cement gives mean and maximum relative errors of 14 and 20 % respectively. It can be concluded that the use of Eqs. (2) and (9) can be extended to lowstrength mortars, since they present similar accuracies. The compressive strength of concrete is known to depend on the granular skeleton, the amount of entrained air, the interfacial transition zone properties and the cement paste properties. During the curing of the cementbased material, the only parameters that will vary are the two latter ones, because of the hydration process of the cement. As a matter of fact, the evolution of the compressive strength of concrete over time is directly linked to the hydration rate of the cement, which is well known for a given type of cement and curing.
Fig. 5. Correlation between 7 and 28day moduli of elasticity – results from the literature
6.1.2 Evolution of the modulus of elasticity over time The ACI 318, 363, 214 and 209 reports do not offer a predictive formula concerning the time dependence of the modulus of elasticity. Figs. 5 and 6 show the prediction of Eq. (4). Compared with the results taken from the literature, the correlation is satisfying; mean and maximum relative errors have values of 10 and 21 % respectively. However, for the lowstrength mortars investigated, the prediction of Eq. (4) is less efficient; mean and maximum relative errors are 22 and 34 % respectively. When the volume of lightweight or rubber aggregates increases, this error seems to increase as well. As for the compressive strength, only the properties of the cement paste change during curing. However, the modulus of elasticity of concrete depends of the elastic properties of its components (cement paste and aggregates). By modifying the composition of the granular skeleton, the impact of the the elastic properties of the cement paste on the modulus of elasticity of concrete is changed, and the empirical formulas do not work as efficiently. Nevertheless, the relative errors obtained are still acceptable since ACI 318 reported that the measured values are typically between 80 and 120 % of the specified value.
6.1.3 Evaluation of the modulus of elasticity Estimates based on the compressive strength Figs. 7 and 8 show the predictions of Eqs. (5) and (8). For the results taken from the literature, the mean and maximum relative errors are 8 and 56 % respectively for Eq. (5), and 11 and 25 % for Eq. (8). The predictions of both equations seem to overestimate the results from [16], [15]
40
Structural Concrete (2015), No. 1
Fig. 6. Correlation between 7 and 28day moduli of elasticity – experimental results
and [17], which are the ones containing rubber or lightweight aggregates. For the experimental results, the mean and maximum relative errors are 62 and 147 % respectively for Eurocode 2 (Eq. (5)), and 13 and 45 % for ACI 318 (Eq. (7)). As can be seen in Fig. 9, the prediction of Eurocode 2 is an overestimation for all experimental results. As shown in Fig. 10, ACI 318 (Eq. (8)) provides a better estimation for this range of compressive strength (but still overestimates its actual value). It can be seen in the previous section that the impact of the modulus of elasticity of the cement paste on that of the concrete changes when the granular skeleton incorporates lowstiffness aggregates. For those materials, the modulus of elasticity should not be estimated with the compressive strength as the only input data. As will be shown in the next section, the consideration of a second input, the unit weight, allows the estimation of the modulus of elasticity of those materials to be acceptable.
F. Duplan/A. AbouChakra/A. Turatsinze/G. Escadeillas/S. Brûlé/E. Javelaud/F. Massé · On the use of European and American building codes with lowstrength mortars
Fig. 7. Correlation between compressive strength and modulus of elasticity – results from the literature – Eurocode 2
Fig. 9. Correlation between compressive strength and modulus of elasticity – experimental results – Eurocode 2t
Fig. 8. Correlation between compressive strength and modulus of elasticity – results from the literature – ACI
Fig. 10. Correlation between compressive strength and modulus of elasticity – experimental results – ACI
Estimates based on the compressive strength and unit weight For Eurocode 2 Part 14, only concretes with dry densities < 2000 kg/m3 are supposed to be concerned. For ACI 318, Eq. (7) can be used with unit weights between 1440 and 2560 kg/m3. The addition of the correcting factor gE (Eq. (6)) to Eq. (5) significantly improves the prediction for the studies of [16], [15], [17] and [18]: the mean and maximum relative errors are 21 and 78 % respectively, compared with 96 and 132 % when the correcting factor gE was not taken into account. The prediction of Eq. (7) from ACI 318 gives lower results than Eurocode 2 Part 1–4 and seems to be closer to the actual values of the modulus of elasticity of lightweight concrete: the mean and maximum relative errors are 14 and 31 % respectively. The predicted and experimental moduli from the literature are presented in Table 5.
As for the results from the literature, the addition of the coefficient gE to Eq. (5) improves the prediction of the moduli of elasticity of the mortars investigated: mean and maximum relative errors are 15 and 45 % respectively, compared with 62 and 147 % without the correcting factor gE. Eq. (7) underestimates the modulus of elasticity of the mortars investigated. The mean and maximum relative errors were 13 and 45 % respectively, compared with 29 and 41 % for Eq. (7). The predicted and experimental moduli are presented in Table 6.
7
Conclusion
The evolution of the compressive strength of lowstrength mortars over time is predicted with accuracy by Eurocode 2 and ACI 209. The time dependence of the modulus of elasticity can be predicted with the Eurocode 2 formula for normal
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F. Duplan/A. AbouChakra/A. Turatsinze/G. Escadeillas/S. Brûlé/E. Javelaud/F. Massé · On the use of European and American building codes with lowstrength mortars
Table 5. Predicted moduli of elasticity with unit weight and compressive strength – results from the literature
fcm
q (EC2), wc (ACI)
Eexp
EACl
EEC2
error EACl
error EEC2
Reference
(MPa)
(kg/m3)
(GPa)
(GPa)
(GPa)
(%)
(%)
–
63.0
2300
34.0
37.6
41.8
11 %
23 %
[16]
40.0
2150
23.5
26.3
31.8
12 %
36 %
[16]
27.0
2090
18.0
20.4
26.7
13 %
49 %
[16]
18.0
2040
17.0
15.8
22.6
7%
33 %
[16]
44.0
2300
35.0
31.5
37.5
10 %
7%
[15]
34.0
2240
30.0
26.4
32.9
12 %
10 %
[15]
22.5
2190
24.5
20.6
27.8
16 %
13 %
[15]
13.8
2050
19.5
14.5
21.0
26 %
8%
[15]
7.5
1950
13.5
9.8
15.9
27 %
17 %
[15]
6.0
1850
10.0
8.1
13.3
19 %
33 %
[15]
44.0
2300
35.0
31.5
37.5
10 %
7%
[15]
36.0
2170
27.0
25.9
31.4
4%
16 %
[15]
30.0
2050
22.0
21.5
26.6
2%
21 %
[15]
20.0
2008
18.0
16.9
22.6
6%
25 %
[15]
16.0
1975
15.0
14.6
20.4
2%
3%
[15]
12.0
1927
10.0
12.1
17.8
21 %
78 %
[15]
40.2
1970
28.6
23.8
26.8
17 %
6%
[17]
36.5
1850
23.5
20.3
22.9
14 %
2%
[17]
30.8
1720,0
20.7
16.4
18.8
21 %
9%
[17]
27.2
1560
16.7
13.0
14.9
22 %
11 %
[17]
24.9
1530
15.7
11.9
14.0
24 %
11 %
[17]
50.0
2456
45.7
37.0
44.4
19 %
3%
[18]
22.6
2226
22.1
21.5
28.8
3%
30 %
[18]
17.0
2121
23.3
17.3
24.0
26 %
3%
[18]
21.7
2233
22.0
21.1
28.6
4%
30 %
[18]
18.5
2069
25.4
17.4
23.4
31 %
8%
[18]
19.4
2053
17.5
17.6
23.4
1%
34 %
[18]
17.8
2067
21.9
17.1
23.1
22 %
5%
[18]
17.8
2093
18.0
17.4
23.7
3%
32 %
[18]
7.1
1823
10.8
8.9
13.7
17 %
26 %
[18]
weight concretes. When specific (and less stiff) aggregates are incorporated in the cement mix, those formulas lose their precision because the impact of the cement paste hydration on the overall elastic properties of the material is changed. Estimating the modulus of elasticity of lowstrength mortars with Eurocode 2 should take into account their unit weights in order to improve the precision. With ACI building codes, the consideration of the unit weight does
42
Structural Concrete (2015), No. 1
not give a better accuracy, and systematically underestimates the modulus of elasticity.
Acknowledgements The authors would like to thank the Menard company for their financial support and for showing great interest in this work.
F. Duplan/A. AbouChakra/A. Turatsinze/G. Escadeillas/S. Brûlé/E. Javelaud/F. Massé · On the use of European and American building codes with lowstrength mortars
Table 6. Predicted moduli of elasticity with unit weight and compressive strength – experimental results
fcm
ρm
(MPa)
(kg/m3) (GPa) (GPa) (GPa) (%)
(%)
12.8
2030
17.8
14.1
20.2
13 %
21 %
11.9
1806
17.4
11.1
15.6
10 %
36 %
12.9
1763
16.2
10.9
15.2
6%
33 %
11.7
1630
14.8
9.0
12.7
14 %
39 %
12.5
1495
13.5
8.0
10.9
19 %
41 %
12.8
2030
17.8
14.1
20.2
13 %
21 %
10.8
1836
16.3
11.0
15.7
4%
32 %
7.3
1792
11.9
8.6
13.3
11 %
28 %
4.7
1689
7.1
6.2
10.3
45 %
13 %
Eexp
EACl
EEC2
error EACl error EEC2
Notation Eurocode 2 fcm (MPa) average concrete compressive strength after 28 days of curing fctm (MPa) average concrete tensile strength after 28 days of curing Ecm (GPa) average concrete modulus of elasticity after 28 days of curing t days of curing βcc(t) time evolution term fcm(t) (MPa) average concrete compressive strength after t days of curing Ecm(t) (GPa) average concrete modulus of elasticity after t days of curing Eurocode 2 Part 1–4 dry unit weight q (kg/m3) gE reduction factor for lightweight concrete ACI 318 Ec (psi) wc (lb/ft3) fc′ (psi) ACI 209 (fc′)t (psi) (fc′)28 (psi) (fc′)u (psi)
modulus of elasticity of concrete dry unit weight of concrete specified compressive strength of concrete
compressive strength of concrete after t days of curing compressive strength of concrete after 28 days of curing ultimate compressive strength of concrete over time
References 1. ACI Committee 318: American Concrete Institute and International Organization for Standardization. Building Code Requirements for Structural Concrete (ACI 31808) and Commentary, 2008. 2. Guide for structural lightweightaggregate concrete, ACI, 213R03, 2003.
3. ACI Committee 209R92Creep and Shrinkage: Prediction of Creep, Shrinkage, and Temperature Effects in Concrete Structures. ACI standard, American Concrete Institute, 2008. 4. Turatsinze, A., Garros, M.: On the modulus of elasticity and strain capacity of selfcompacting concrete incorporating rubber aggregates. Resour. Conserv. Recycling, 52 (10): 1209–1215, 2008. 5. Panesar, D. K., Shindman, B.: Elastic properties of self consolidating concrete. Construction and Building Materials, 25: 3334–3344, 2011. 6. Parra, C., Valcuende, M., Gomez, F.: Splitting tensile strength and modulus of elasticity of selfcompacting concrete. Construction and Building Materials, 25: 201–207, 2011. 7. Shariq, M., Prasad, J., Masood, A.: Effect of gbbfs on time dependent compressive strength of concrete. Construction and Building Materials, 24: 1469–1478, 2010. 8. Shariq, M., Prasad, J., Masood, A.: Effect of gbbfs on age dependent modulus of elasticity of concrete. Construction and Building Materials, 41: 411–418, 2013. 9. Aslani, F., Nejadi, S.: Self compacting concrete incorporating steel and polypropylene fibers. Composites: Part B, 53: 121–133, 2013. 10. Wild, S., Sabir, B. B., Khatib, J. M.: Factors influencing strength development of concrete containing silica fume. Cement and Concrete Research, 25 (7): 1567–1580, 1995. 11. Malaikah, A. S.: A proposed relationship for the modulus of elasticity of high strength concrete using local materials in Riyadh. Journal of King Saud University, 7, 2004. 12. Nazari, A., Riahi, S.: Improvement compressive strength of concrete in different curing media by Al2O3 nanoparticles. Materials Science and Engineering, 528: 1183–1191, 2011. 13. Kim, J. K., Moon, Y. H., Eo, S. H.: Compressive strength development of concrete with different curing time and temperature. Cement and Concrete Research, 28 (12): 1761–1773, 1998. 14. Zain, M. F. M., Mahmud, H. B., Ilham, A., Faizal, M.: Prediction of splitting tensile strength of highperformance concrete. Cement and Concrete Research, 32: 1251–1258, 2002. 15. Garros, M.: Composites cimentaires incorporant des granulats caoutchouc issus du broyage de pneux usagés: optimisation de la formulation et caractérisation – Cementitious composites incorporating waste tire rubber aggregates. PhD thesis, Université de Toulouse, 2007. 16. Ho, A. C.: Optimisation de la composition et caractérisation d’un béton incorporant des granulats issus du broyage de pneus usagés. Application aux éléments de grande surface. – Mix design optimization and characterization of concrete incorporating waste tire rubber aggregates. PhD thesis, Université de Toulouse, 2010. 17. Ke, Y., Beaucour, A. L., Ortola, S., Dumontet, H., Cabrillac, R.: Influence of volume fraction and characteristics of lightweight aggregates on the mechanical properties of concrete. Construction and Building Materials, 23: 2821–2828, 2009. 18. Panesar, D. K., Shindman, B.: The mechanical, transport and thermal properties of mortar and concrete containing waste cork. Cement and Concrete Composites, 34: 982–992, 2012. Francois Duplan PhD Université de Toulouse, UPS, INSA LMDC (Laboratoire Materiaux et Durabilite des Constructions) 135, Avenue de Rangueil F31 077 Toulouse cedex 4, France Menard, 91 620 Nozay, France francois.duplan86@gmail.com Tel.: +3356 155 9916
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F. Duplan/A. AbouChakra/A. Turatsinze/G. Escadeillas/S. Brûlé/E. Javelaud/F. Massé · On the use of European and American building codes with lowstrength mortars
Ariane AbouChakra, Assistant professor Université de Toulouse, UPS, INSA LMDC (Laboratoire Materiaux et Durabilite des Constructions) 135, Avenue de Rangueil F31 077 Toulouse cedex 4, France abouchak@insatoulouse.fr Tel.: +3356155 9930 Anaclet Turatsinze, Professor Université de Toulouse, UPS, INSA LMDC (Laboratoire Materiaux et Durabilite des Constructions) 135, Avenue de Rangueil F31 077 Toulouse cedex 4, France anaclet@insatoulouse.fr Tel.: +3356155 9934 Gilles Escadeillas, Head of departement Université de Toulouse, UPS, INSA LMDC (Laboratoire Materiaux et Durabilite des Constructions) 135, Avenue de Rangueil F31 077 Toulouse cedex 4, France gilles.escadeillas@insatoulouse.fr Tel.: +3356155 7498
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Structural Concrete (2015), No. 1
Stéphane Brûlé Menard, 91 620 Nozay France stephane.brule@menardmail.com Tel.: +33478513394 Emmanuel Javelaud Menard, 91 620 Nozay France emmanuel.javelaud@menardmail.com Tel.: +33478513394 Frédéric Massé Menard, 150 East Main Street, Suite 500 Carnegie, PA 15106, United States frederic.masse@menardusa.com Tel. : +14126206000
Technical Paper John Cairns
DOI: 10.1002/suco.201400043
Bond and anchorage of embedded steel reinforcement in fib Model Code 2010 This paper describes the changes to design provisions for embedded steel reinforcement in the fib Model Code for Concrete Structures 2010. The changes introduce new coefficients for steel grade and clear spacing between bars, and extend the range of concrete strengths covered. The way in which the contribution of hooks or anchorages is calculated has been revised and the contribution of end bearing to laps and anchorages of compression bars is recognized. The revised rules represent a move away from a distinction between laps and anchorages per se towards a distinction based on the presence or absence of transverse pressure perpendicular to the bar axis within the bond length. The benefits of staggering laps with only a proportion of bars lapped at a section are also reviewed. Finally, the potential impact of lap and anchorage performance on structural robustness is discussed, and it is concluded that this can only be achieved if bar yield precedes splitting mode bond failures. Keywords: fib Model Code, bond, anchorage, lapped joints, hooks and bends
1
Introduction
The fib Model Code for Concrete Structures 2010 [1] was published in its final version in 2013. As part of the revision process, fib Task Group 4.5 “Bond Models” undertook a thorough review of the content for bond of embedded steel reinforcement, the outcome of which has resulted in section 6.1 of fib Model Code 2010. This paper reviews the major changes between MC90 [2] and fib Model Code 2010 with the aim of helping users to understand the revised rules and the underlying physical basis for the changes introduced. The scope of the paper is restricted to conventional noncoated ribbed reinforcing bars. The basic expressions for bond strength in the Model Codes have remained essentially unchanged since MC78 [3]. Since then there has been a general increase in the strengths of both concrete and reinforcement used in construction. For example, the characteristic strength of reinforcement in many European countries was about 410 MPa in 1978, but is currently 500 MPa. The CEB Bulletin on High Performance Concrete [4] recommended that the range of concrete grades covered in the 1990
* Corresponding author: j.j.cairns@hw.ac.uk Submitted for review: 26 May 2014 Accepted for publication: 20 July 2014
Model Code be extended from the limit of C80/100 then up to C100/125 now, and that the validity of current rules for bond and anchorage should be reconsidered. In addition, the source of many rules in MC90 was unknown and evidence to support them lacking. A rigorous review of the Model Code provisions for bond and anchorage was therefore considered necessary.
1.1
Basics of bond and anchorage
Bond and anchorage are the terms used to denote the transfer of force between reinforcement and concrete. Bond is conventionally described as the change in force along a bar divided by the (nominal) area of bar surface over which this change takes place, Eq. (1). This concept represents a major simplification, however, as most bars produced today rely on the bearing of ribs rolled onto the surface of the bar during manufacture to transfer force. Although the transfer of force between reinforcement and concrete depends on adhesion and friction over the whole bar surface at low bond stresses, as the ultimate limit state is approached, so bond relies increasingly on the bearing of the ribs on the concrete. The definition of Eq. (1) is, nonetheless, a convenient one and is used here: fb = Δfs · As/πφlb
(1)
where: fb average bond stress over length lb Δfs change in bar stress over length lb As crosssectional area of bar φ nominal diameter of bar lb bond length over which Δfs takes place The simplicity of Eq. (1) can be misleading; the evaluation of bond resistance is complex. MC90 includes no less than 10 parameters for the calculation of anchorage or lap length. While there is general agreement on the parameters that influence bond resistance, there are inconsistencies in the magnitude of the contribution attributed to each reported by various investigators. The one common conclusion on which all agree, however, is that bond is not a fundamental property of the bar, as has been asserted in the past, but is influenced by bar and concrete section geometry, materials characteristics and stress state as well as the surface characteristics of the steel.
© 2015 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete (2015), No. 1
45
J. Cairns Âˇ Bond and anchorage of embedded steel reinforcement in fib Model Code 2010
ment in the crosssection, cover and spacing between bars, are of markedly greater importance to performance at the serviceability limit state. Broadly similar considerations apply to rotation capacity at the ultimate limit state. No changes to these two aspects have been introduced for conventional ribbed bars in fib Model Code 2010.
2 Fig. 1. Splitting mode of bond failure
There are two broad forms of bond failure depending on whether or not the concrete cover splits. Where confinement is high, typically when concrete cover around the bar exceeds 3â€“4 times the bar diameter, failure of ribbed bars is marked by the concrete shearing on a surface along the tops of the ribs. Where confinement is less than 3 times the bar diameter, radial bursting stresses generated by bond lead to formation of longitudinal cover cracks, Fig.1, and bond strength is limited by the splitting resistance provided by the surrounding cover and confining reinforcement, together with any transverse pressure. The splitting mode is the weaker of the two, and design rules are generally based on the weakest practical detailing arrangements consistent with other code provisions. By contrast, models for local bondslip behaviour have generally been formulated for conditions of high confinement where splitting does not occur, and the local bondslip relationship in the fib Model Code 2010 [1] gives mean rather than characteristic values. These factors, together with differences between the bond lengths required in practical construction and the much shorter lengths used in local bondslip models, resulted in what might be perceived as inconsistencies between bond values in the modelling and detailing sections of MC90. Bond resistance along straight lengths of bar may be supplemented by other features that contribute to transfer of force between bar and concrete and hence to anchorage. These might include welded crossbars, a hook or bend formed close to the end of the bar, a plate or head welded to the end of the bar or, in the case of bars in compression, bearing of the end of the bar on the concrete. Owing to differences in loadslip characteristics, the contributions of these other forms of anchorage cannot be directly summed with that of bond over the straight length of a bar, and it is necessary to consider their interaction in order to determine the combined resistance.
1.2
46
In the calculation of lap and anchorage lengths in fib Model Code 2010 [1], a basic bond strength for a straight length of bar dependent on concrete grade, bar diameter, casting position and reinforcement grade is first determined, subject to various minimum values for confinement by concrete cover, bar spacing and confining reinforcement being satisfied â€“ Eq. 6.120 in fib Model Code 2010, given below as Eq. (2). The basic value is then modified to take account of transverse pressure and confinement in excess of these minima: fbd,0
Structural Concrete (2015), No. 1
Â§ f Âˇ K1 K2 K3 K4 Â¨ c Â¸ ÂŠ 25Âš
0.5
(2)
/J c
The following sections outline the derivation of Eq. (2) and review how the changes influence basic bond resistance in fib Model Code 2010 with respect to the corresponding expression for design bond strength in MC90. A much fuller description of the derivation and validation procedure is given in fib Bulletin 72 [5].
2.1
Derivation of basic bond strength
Eq. (2) is derived from a semiempirical expression developed by fib TG4.5 for the stress developed in a straight length of bar by bond â€“ Eq. 6.119 in fib Model Code 2010, given below as Eq. (3). This states that bar stress is limited by splitting resistance, by the strength of the bar itself and by pullout resistance [1]. Eq. (3) is a mean strength expression and is not intended for design. The expression has been calibrated using the ACI408 bond test database [6] and validated using additional data gathered by fib TG4.5 [7] and compiled by Amin [8]: fstm
Â§f Âˇ 54 Â¨ cm Â¸ ÂŠ 25 Âš
0.25
Â§ 25Âˇ Â¨ÂŠ I Â¸Âš
0.2
Â§ lb Âˇ Â¨IÂ¸ ÂŠ Âš
0.55
0.1 0.25 ÂŞÂ§ Âş Â§ cmax Âˇ ÂŤ cmin Âˇ Âť k K Â¨c Â¸ m tr Âť ÂŤÂ¨ÂŠ I Â¸Âš ÂŠ min Âš ÂŹ Âź
d fy , d 10 fcm
Influence of bond on structural performance
Bond influences the performance of concrete structures in several ways. At the serviceability limit state, bond influences the width and spacing of transverse cracks, tension stiffening and flexural curvature. At the ultimate limit state, bond is responsible for the strength of end anchorages and lapped joints of reinforcement, and influences the rotation capacity of plastic hinge regions. Although bond does influence structural performance under service loadings, its effect is relatively modest. Other factors, particularly the percentage of reinforce
Basic bond strength
where: fstm fcm lb, Ď† cmax, cmin
lb
I
(3)
estimated stress developed in bar (mean value) measured concrete cylinder compressive strength, 15 MPa < fcm < 110 MPa bond length and diameter of lapped or anchored bar respectively as defined in Fig. 2, 0.5 â‰¤ cmin/Ď† â‰¤ 3.5, cmax/cmin â‰¤ 5, limitations imposed by lack of experimental data beyond these values
J. Cairns · Bond and anchorage of embedded steel reinforcement in fib Model Code 2010
Fig. 2. Definition of concrete cover dimensions [1]
Ktr = nl.ng.Asv/(lb.φ.nb) ≤ 0.05, representing the density of transverse reinforcement
columns of structural significance, somewhat greater importance was placed on this situation when deriving fib Model Code 2010 provisions. Basic bond strength is initially derived for minimum cover equal to bar diameter, cmax = cmin, and no confining reinforcement, for which the term in square brackets in Eq. (3) has a value of 1.0. Eq. (3) is a mean strength expression, and is first converted into a characteristic expression by multiplying the mean coefficient 54 in Eq. (3) by the characteristic ratio from Table 1b to obtain a similar expression for lower 5 % characteristic values. The resulting expression is then rearranged to allow basic bond length lb,0 to be determined as a function of the bar stress to be anchored fst, Eq. (4): lb,0
I nt
number of legs of confining reinforcement crossing a potential splitting failure surface at a section crosssectional area of one leg of a confining bar longitudinal spacing of confining reinforcement number of anchored bars or pairs of lapped bars at potential splitting surface “effectiveness factor” for link confinement, taken as 12 where a bar is confined by a link passing through an angle of at least 90° yield strength of reinforcement
Ast st nb km
fy
The coefficient 54 in Eq. (3) has units of MPa. The ratio 25/φ is limited to a maximum of 2.0 on the basis of evidence in the database, the limit probably reflecting the lesser relative rib area of smaller (i.e. ≤ 12 mm) diameter bars. Fig. 3 demonstrates that Eq. (3) provides a reasonable fit to test data, marginally better than that achieved by other investigators for confined situations, Table 1b, although not quite as good as some alternatives for unconfined conditions, Table 1a (data for other investigations [10, 11] is taken from Canbay and Frosch [9]). As confining reinforcement would be required in all beams and
§ fst · ¨ 41¸ © ¹
1.82
§ fc · ¨ 25¸ © ¹
0.45
§ 25· ¨© I ¸¹
0.36
(4)
Setting fst to the design strength fyd = fyk/γst of grade 500 reinforcement and including partial safety coefficients of 1.15 and 1.5 for reinforcement and concrete respectively leads to Eq. (5): lb,0
I
§ 500 · 1.15¸ ¨ ¨ 41 ¸ ¹ © § f · 73.5 ¨ c ¸ © 25¹
1.82
§ fc · ¨ 25¸ © ¹
0.45
§ 25· ¨© I ¸¹
0.45
§ 25· ¨© I ¸¹
0.36
(5)
0.36
Basic bond strength for design is then obtained by inserting bond length lb,0/φ, obtained from Eq. (5), into Eq. (6), which leads to Eq. (7): fbk,0
fbk,0
fyd
§ lb,0 · 4. ¨© I ¸¹
§ f · 1.5 ¨ c ¸ © 25¹
0.45
(6)
§ 25· ¨© I ¸¹
0.36
(7)
Making allowance for the contribution of minimum transverse reinforcement and including a partial safety factor
Rao measured/esmated strength
2.50
2.00
1.50 Laps, conﬁned
1.00
Laps, unconﬁned
0.50
0.00 0
20 40 60 80 100 Concrete cylinder compressive strength (MPa)
120
Fig. 3. Ratio of measured/calculated bond strength vs. concrete cylinder compressive strength [5]
Structural Concrete (2015), No. 1
47
J. Cairns · Bond and anchorage of embedded steel reinforcement in fib Model Code 2010
Table 1. Summary of statistical data (values from other investigations are taken from [9])
Mean Standard deviation Coeff. of variation 5 % characteristic ratio
fib MC2010 [1] (Eq. (3))
Orangun, Jirsa & Breen [10]
Zuo & Darwin [11]
Canbay & Frosch [9]
0.97 0.145 0.150 0.73
1.005 0.215 0.214 0.65
1.005 0.128 0.127 0.79
0.980 0.118 0.120 0.79
fib MC2010 [1] (Eq. (3))
Orangun, Jirsa & Breen [10]
Zuo & Darwin [11]
Canbay & Frosch [9]
1.00 0.132 0.132 0.78
1.060 0.238 0.224 0.67
0.960 0.125 0.130 0.76
0.977 0.149 0.153 0.73
a) bars not confined by secondary reinforcement
Mean Standard deviation Coeff. of variation 5 % characteristic ratio
b) bars confined by secondary reinforcement
γc, and after further calibration and rounding for convenience, Eq. (8) is obtained: fbd,0
§ f · K1 ¨ c ¸ © 25¹
0.5
§ 25· ¨© I ¸¹
0.3
/J c
(8)
where γc is a partial safety factor and η1 = 1.75 MPa. The value of coefficient η1 is reduced from 2.25 in MC90 to 1.75 in fib Model Code 2010, and together with the change from 0.67 to 0.5 in the index for concrete strength, it reduces basic bond strength in fib Model Code 2010 to 40–45 % of that in MC90. At first sight, therefore, design bond strength may appear markedly reduced in fib Model Code 2010. Other changes in design procedures, as will be explained in sections 3.3 and 5.1, mean that the impact on lap and anchorage lengths is much less marked than the difference between basic (fib Model Code 2010) and design (MC90) values for bond strength. The influence of the various parameters that influence basic bond strength and the differences between fib Model Code 2010 and MC90 are summarized in the following sections
2.2
Concrete strength
The CEB Bulletin on High Performance Concrete [4] recommended that the range of concrete grades covered by the fib Model Code 2010 [1] be extended from the limit of C80/100 then up to C100/125 now, and that the validity of current rules for bond and anchorage should be reconsidered. The European standard for design of concrete structures, EC2 [12], is strongly influenced by MC90, but limits bond strength to the value for class C60/75 concrete “unless it can be verified that the average bond strength increases above this limit”. The ratio of measured bond strength to that estimated by Eq. (3) is plotted against concrete cylinder compressive strength in Fig. 3. Results from specimens with and without confining transverse reinforcement are plotted independently. The trend line remains horizontal for concrete strengths up to 110 MPa, and shows Eq. (3) to be valid up to C100/125.
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Structural Concrete (2015), No. 1
2.3
Casting position
Consolidation of fluid concrete around a rigid reinforcement cage may lead to a higher water/binder ratio and to the formation of voids underneath horizontal bars close to the top of a pour, and, consequently, might weaken bond. A reduction factor is applied in these situations. The value of factor η2 in fib Model Code 2010 is unchanged from MC90.
2.4
Bar size
The influence of bar diameter is represented by η3 in Eq. (2). Bond strength exhibits a significant size effect that is not limited to large diameter bars. The bond strength of a 12 mm diameter bar is nearly 27 % higher than that for a 40 mm diameter bar according to Eq. (3). MC90 includes a size factor for large bars only, probably because the code chose to neglect the influence of bar diameter for small size bars for simplicity rather than as a result of an error in the trend represented by coefficient η3. Although the format of the expression for η3 has been modified in fib Model Code 2010, the change has only a minor influence on basic bond strength. The fib Model Code 2010 uses 25 mm as a datum instead of the 32 mm of MC90.
2.5
Reinforcement grade
The solid line in Fig. 4 plots the relationship between mean value of lap strength fstm estimated by Eq. (3) and bond length lb,o/φ for a concrete strength of 32 MPa, a bar diameter of 20 mm, minimum cover and clear spacing between bars of 20 and 40 mm respectively when transverse reinforcement is not present. Average bond strength corresponds to the secant modulus of the plot, as shown by the various dashed lines, and is therefore dependent on the stress to be developed in the bar. As bond length has to increase to develop the design strength of highergrade reinforcing bars, it follows that average bond strength should decrease for higher grades. It is therefore necessary to define the bar stress for which bond strength is derived. The fib Model Code 2010 takes grade 500 reinforcement as a
J. Cairns · Bond and anchorage of embedded steel reinforcement in fib Model Code 2010
700
Bar stress (MPa)
600 500 Eq.3
400
Grade 400 300
Grade 500
200
Grade 600 Grade 700
100 0 0
20
40 Bond length lb,0 /φ
60
80
Fig. 4. Mean bond stress for various reinforcement grades
Table 2. Factor η4 for steel grade
datum, and introduces a new factor η4, Table 2, into the expression for basic design bond strength fbd,0 to adjust bond strength for other reinforcement grades.
is substantially unchanged within the limits imposed by MC90. The wider range of results in the new test database has, however, allowed limiting values imposed by MC90 to be relaxed somewhat in fib Model Code 2010. Bond strength is also influenced by the clear spacing between bars, cs in Fig. 2, and this can be significant, particularly for slabs. This influence is now recognized in fib Model Code 2010 through the inclusion of a term cmax/cmin in factor α2.
3
3.3
fyk (MPa) η4
400 1.2
500 1.0
600 0.85
700 0.75
800 0.68
Design anchorage length of straight bars in tension
Basic bond strength for benchmark conditions of confinement may be modified to take account of minimum cover, bar spacing, transverse reinforcement and confining pressure in excess of their respective minima – according to Eq. 6.121 of fib Model Code 2010, reproduced here as Eq. (9), which represents a trilinear relationship in which fbd = (α2+α3) fbd,0 – 2ptr < 2.0 fbd,0 – 0.4ptr < 1.5/γ⎯f c√ ck
(9)
where α2 and α3 represent the confinement provided by concrete around the bars and by secondary reinforcement respectively and ptr is the average compressive stress on the section acting perpendicular to the bar axes of the bars. Note that compressive stress is taken to be negative; transverse compression hence increases bond strength fbd.
3.2
Confinement by concrete cover and transverse reinforcement
The beneficial influence of secondary reinforcement and increasing concrete cover on bond strength has been recognized for many years, and was included in MC90. Coefficients for minimum cover and transverse reinforcement were combined factorially in MC90, but it was considered more rational for contributions from these components to be summed, as in Eq. (3). Although the format of the expressions for the contributions of minimum cover and secondary reinforcement have changed in fib Model Code 2010, the net influence of minimum cover and transverse reinforcement on bond strength, each taken individually,
Transverse pressure
The effect of transverse compression on bond is twofold: it retards the onset of splitting failure and increases the frictional force at the bar/concrete interface. The first of these mechanisms dominates in situations with low confinement by concrete cover and secondary reinforcement when splitting failure would otherwise occur, with frictional enhancement taking over at higher pressures once the splitting failure mode is suppressed. “Higher” confining pressures may be taken as those that exceed the tensile strength of the concrete. Much of the available data comes from tests with high unidirectional lateral stresses, where bond failure took place either by pullout, or in a splitting mode where the splitting crack ran parallel to the direction of the applied lateral stress, and relate to conditions where confinement was already relatively high, even without applying transverse pressure. The factor α5 in MC90 appears to have been derived for this condition and correlates fairly well with results in such stress environments. However, it underestimates the enhancement in strength where confinement from cover and transverse reinforcement is low, and fib Model Code 2010 includes a trilinear relationship to represent the enhancement in bond due to transverse pressure, Eq. (9) and Fig. 5. A parametric investigation of representative simply supported beams has found that if anchorage demand at an end support or an equivalent situation is high, Figs. 6a and 6b, transverse compression will be sufficient to position the stress environment on the intermediate segment of Fig. 6, but that in other circumstances end anchorage capacity will not be critical. The intermediate segment of
Structural Concrete (2015), No. 1
49
J. Cairns · Bond and anchorage of embedded steel reinforcement in fib Model Code 2010
Fig. 5. Enhancement in bond strength due to transverse compression
by Schiessl [13]. By modelling local bondslip behaviour and bendslip behaviour measured in tests using the finite difference approach, Schiessl determined the relationship between the lengths of straight and bent bar which result in zero slip at the free end of the bar under service load and a limiting slip of 0.1 mm at ultimate load. The model did not represent splitting failure modes, although it is reported that this was taken into consideration in other ways. The fib Model Code 2010 adopts a different format in which the net contribution from a hook or bend is subtracted from the stress to be anchored and the straight length required to carry the difference σsd then calculated – Eq. 6.124 of fib Model Code 2010, reproduced here as Eq. (10):
σsd = α1 fyd – (Fh/Ab) the plot in Fig. 5 takes over at a bond strength corresponding to approximately twice the basic value; consequently, the design bond resistance at a support would be at least double the basic value (assuming all other parameters are identical). In these circumstances the apparent reduction in basic bond strength mentioned in section 2.1 is negated when determining anchorage length. Thus, in fib Model Code 2010, higher bond strengths are permitted at anchorages as a consequence of transverse compression rather than being based on a distinction between laps and anchorages per se as in MC90. In other situations where bars must be anchored, e.g. where hogging reinforcement over a continuous support is curtailed, the enhancement in anchorage resistance provided by transverse compression may not be present, Figs. 6c and 6d. At locations such as these there is generally a greater probability of other modes of failure, but there is relatively little experimental evidence covering such situations. Further work to determine safe bond stresses in such situations is desirable (see also section 5.1).
4
Hooks, bends and end bearing
The rules in MC90 permit a 30 % reduction in anchorage length for bars terminating in a hook or bend, subject to certain restrictions on minimum cover. They were derived principally from numerical analyses of loadslip behaviour
Benefical transverse compression
a) Simply supported end
b) Pilecap Fig. 6. Transverse pressure at support
50
Structural Concrete (2015), No. 1
(10)
where: Fh force developed by a hook, bend or head (Fh = 0 in the case of straight tension bars) Ab crosssectional area of bar α1 stress to be anchored, with α1 = As,cal/As,ef for anchorages and 1.0 for laps The change to the format is adopted for several reasons: 1. The existing format reduces safety margins as the bar strength increases. The capacity of a hook or bend is primarily dependent on the bearing capacity of the concrete, but the MC90 format implies that the contribution varies with reinforcement grade. 2. The introduction of headed bars with a range of dimensions means that a single value for the contribution of a bar termination is no longer sufficient. 3. Consistency with the strategy adopted for laps and anchorages of bars in compression (see section 5.2). This approach permits shorter anchorages at end supports when the force to be anchored is below the full design strength of the reinforcement, although this cannot be applied to laps for the reasons described in section 7. There is currently no consensus model for anchorage of headed bars. The rules presented in fib Model Code 2010 represent a conservative approach based on bars ter
No transverse compression
c) Half jont
d) ‘ Top hat’ section
J. Cairns · Bond and anchorage of embedded steel reinforcement in fib Model Code 2010
minating in a hook or bend. Design by testing may currently offer the best approach for specific situations.
5
Lapped joints
Many design codes, including MC90 [2], EC2 [12] and ACI 318 [14], make a distinction between laps and anchorages with regard to bond length requirements. The required anchorage (or development) lengths are generally shorter than those for lapped joints, particularly where all bars are lapped at the same section. This appears to be inconsistent with a statistical analysis of test data, which demonstrates an insignificant difference between the bond strengths of laps and anchorages. Table 3 summarizes the statistical fit of Eq. (3) to results for laps and anchorages in the ACI 408 database [6], as extended by TG4.5 [7], and in the database compiled by Amin [8]. It is not clear how the distinction between strengths of laps and anchorages has become established in design codes, and there appear to be two possibilities. One derives from the “hydraulic pressure” models for the bursting action of bond proposed by Ferguson and Breen [15] and Tepfers [16], which assumes that the bursting force generated perpendicular to a plane passing through the axes of a pair of lapped bars is double that produced by a single anchored bar, Fig. 7, and, hence, that the splitting resistance available to each of the bars in a lapped pair is half that of a single anchored bar and bond strength in a lap consequently; less than that of an anchorage. The other possibility is that the distinction is based on differences in the stress environment surrounding laps and anchorages which are not specifically defined by MC90; for example, the transverse compression at supports which helps to prevent or delay a splitting mode failure of end anchor
ages is not present at laps. Statistical evidence such as that in Table 3 and tests reported by Reynolds and Beeby [17] disprove the former hypothesis. It is also evident from the work of Magnusson [18] that anchorage is markedly reduced if the end support is indirect rather than direct, Fig. 8. Therefore, fib Model Code 2010 does not distinguish between laps and anchorages on the basis of their function, but instead makes a distinction based on the presence or absence of transverse compression.
5.1
Proportion of bars lapped at a section
In MC90 [2] and many other design codes, e.g. EC2 [12] and ACI 318 [14], lap lengths for tension reinforcement depend on the proportion of bars lapped at a section. Fig. 9 compares values of coefficients for proportion lapped given in various codes, and shows that there are marked differences in the values assigned. Considering that the factor for the proportion of bars lapped can have as great an influence on lap length as confinement factors, surprisingly little research has been undertaken to assess the performance of staggered laps, and attempts to discover the basis for the α6 coefficients in MC90 were fruitless. Investigations by Metelli et al. [19] and Cairns [20] found no evidence that reductions in the proportion of bars lapped at a section had any beneficial influence on lap strength, even though the clear spacing cs between pairs of lapped bars was increased where only a proportion of bars was lapped at a section, Fig. 10. Indeed, if Eq. (3) is used to take account of the increase in clear spacing where laps are staggered, it appears that staggering reduces lap strength. Cairns suggests that this is attributable to lapped bars being stiffer and attracting a disproportionate share of force compared with the continuous
Table 3. Statistical summary of fit of Eq. (3) to test data
Source
ACI408/TG4.5 test database [7]
Mean Standard deviation Coefficient of variation Minimum 5 % characteristic ratio No. of results
Amin [8]
Laps with links
Laps w/o links
Anchorages with links
Anchorages w/o links
Anchorages
0.99 0.130 0.132 0.68 0.77 286
0.97 0.145 0.150 0.62 0.73 255
0.97 0.171 0.176 0.62 0.69 18
0.92 0.109 0.118 0.75 0.75 21
1.01 0.16 0.160 0.61 0.74 164
φ.σsplit
φ.σsplit
σsplit
2.φ .σsplit
φ.σsplit
φ.σsplit
φ.σsplit
σsplit
σsplit
φ.σsplit
2.φ .σsplit
Fig. 7. Hydraulic pressure analogy for bond
Structural Concrete (2015), No. 1
51
J. Cairns · Bond and anchorage of embedded steel reinforcement in fib Model Code 2010
Load
Load Reaction
Reaction ‘Direct Support’
‘Indirect Support’
Fig. 8. Direct and indirect support arrangements, Magnusson’s tests [18], redrawn
450
Lap Strength (MPa)
400 350 300 250 200 150 100 50 0 0% Fig. 9. Coefficients for proportion lapped in various codes
20%
40%
60%
80%
100%
120%
Proporon lapped
bars [20]. In the absence of any evidence to support its continued inclusion, the proportion lapped factor α6 given in MC90 has been discontinued. As the proportion lapped coefficient α6 in MC90 effectively halved basic bond strength when all bars were lapped at a section, the lower basic bond strength of fib Model Code 2010 mentioned in section 2.1 is largely negated when determining lap length.
5.2
Compression laps
Eq. (3) for the stress developed by bond over a straight length of bar is broadly applicable whether lapped bars are in tension or in compression, although there are differences between the two. The major factor is that bearing of the ends of compression bars on concrete provides an additional contribution to load transfer. Several other differences are probably of secondary importance; “in and out” bond stresses in the vicinity of transverse cracks are absent in compression laps, the transfer of force between bars is less uniform within a compression lapped joint, splitting resistance of the concrete cover is reduced due to biaxial tension/compression in the case of compression laps and the contribution from links in compression laps and anchorages is enhanced by increases in their bond stiffness as a result of compression transverse to the plane of the links [21]. These secondary effects are believed to be relatively modest, and analysis of test data has not found any justification to make explicit allowance for them. The
52
Structural Concrete (2015), No. 1
Rao measured/esmated lap strengt
Fig. 10. How proportion of bars lapped influences strength [20]
1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0
1 2 No. transverse bars within 3 diameters of ends
3
Fig. 11. Influence of number of links located close to ends of compression lap [5]
contribution of end bearing of the bar in fib Model Code 2010 is allowed for by the same approach as that used for hooks and bends, Eq. (10), subject to the condition that the distance along the bar axis from the end of the bar to the nearest face exceeds a specified minimum. The requirement for multiple links to be located near the ends of compression laps has been eased in fib Model Code 2010 as the available evidence suggests that the additional links are of little benefit. Fig. 11 compares strengths of compression laps with and without links
J. Cairns · Bond and anchorage of embedded steel reinforcement in fib Model Code 2010
Detailing considerations Minimum detailing requirements
A number of detailing provisions regarding bar spacing and transverse reinforcement have been tightened with respect to fib Model Code 2010 with the aim of constraining brittleness of the splitting failure mode of laps and anchorages. The requirements are relaxed where transverse pressure constrains the splitting mode.
6.2
Bars in bundles
Two distinct situations have to be considered: firstly, where it is necessary to anchor all bars in a bundle at the same location and, secondly, where individual bars in a bundle are to be lapped and the laps are staggered. In the first case the wellestablished “equivalent bar” approach is adopted, as in MC90. However, MC90 did not specifically consider the second situation, and the requirements of fib Model Code 2010 are based on the work of Cairns [22], who demonstrated that bond strength is not reduced where an individual bar within a pair or bundle of three bars is lapspliced and appropriate allowance is made for differences in confinement and the proportion of bars spliced at a section, Fig. 12.
6.3
Bars in layers
Although data is scarce, there is no convincing argument in favour of modifying bond length where more than a single layer of reinforcement is present.
6.4
Lapped bars of different diameter
If lapped bars are of different diameters, lap length may be based on the diameter of the smaller bar.
7
Ductility and robustness
The splitting mode of bond failure is invariably nonductile, even where relatively large amounts of confining reinforcement are present. The options for ensuring ductility are a) to provide sufficient confinement for a pullout mode of failure and b) to ensure the bonded length is long enough for the bar to reach yield. Although it is believed that one of the justifications for the lower values of the coefficient α6 in MC90 when only a proportion of bars is lapped was that bars continuous through the lapped joint would maintain some postpeak capacity in the event of a failure of the lapped proportion, the available evidence shows that where laps are staggered with only 50 % of bars lapped at a section, beams behave in a manner nearly as brittle as those beams with 100 % of bars lapped at the same section [20], Fig 13. Fig. 14 shows the method of determining the ductility index Dres used in Fig. 13.
5.00
Bond strength (MPa)
6 6.1
6.00
4.00 3.00 2.00 1.00 0.00 0
1
2
3
No. in bundle
Fig. 12. Influence of bundle size on bond strength of lapped joint [22]
1.0 0.8
Duclity Index Dres
located within a distance of 3 bar diameters from the end of a lap. The importance of locating a link near each end of a compression lap is evident, but there is no significant gain when more than a single link is provided at each end.
0.6 Bundle
0.4
Individual
0.2 0.0 0%
25%
50% 75% Proporon lapped
100%
Fig. 13. How proportion of bars lapped at a section influences postpeak resistance [19]
At end anchorages at supports, Figs. 6a and 6b, parametric investigations show that where bond demand exceeds basic bond strength, transverse compression will be sufficient to preclude a splitting failure mode. In such situations a moderately ductile failure mode would be obtained without the need to design for the bar yielding, and the design stress may be taken as α1.fyd, with α1 = As,cal/As,ef, where As,cal is the calculated area of reinforcement required by the design and As,ef is the area of reinforcement provided. Bond failure of a lapped joint is likely to occur in a splitting mode for all except the smallest diameter bars; hence, they should be designed to ensure an adequate probability that bars can reach yield. Lap length should therefore not be reduced if the area of reinforcement provided exceeds that required by design, as was permitted in MC90.
8
Economy and constructability
Although the contribution of lapped joints to material costs is small in relation to the overall costs of construction, laps may have a significant impact on locations of construction joints and hence on a construction programme. Contractors therefore wish to minimize lap lengths consistent with maintaining an appropriate level
Structural Concrete (2015), No. 1
53
J. Cairns · Bond and anchorage of embedded steel reinforcement in fib Model Code 2010
Fig. 14. Typical plot of load vs. deflection, showing calculation of deformability index Dres
of safety. Good detailing practice locates laps where stress in reinforcement is low, e.g. near points of contraflexure in continuous beams. Stresses in lapped bars at such locations will never approach the design strength of reinforcement under normal service conditions. It is only in the event of accidental loading or damage that bars would be highly stressed, e.g. if an intermediate support were to fail. In such situations the lap should still be designed so that the bar reaches yield, but the partial safety factor used when determining the basic bond strength should be that appropriate to accidental rather than transient and persistent situations. A coefficient α4 = 0.7 has been introduced for such circumstances to permit shorter laps where it is safe to do so, and will encourage detailers to locate laps at positions of low reinforcement stress.
9
Local bondslip relationship
In MC90 it was not apparent how the bond strengths for laps or anchorages presented in section 6.9 related to the local bondslip relationship presented in section 3. The basic design bond strength for a grade 30 concrete in MC90 is 3.0 MPa, while the peak bond stress τmax from the local bondslip relationship is 12.3 MPa – over four times greater; hence, the two sections might be perceived to be inconsistent. There are several reasons for the difference. The local bondslip relationship gives a mean value, whereas the basic bond strength is a characteristic value. The local bondslip relationship is based on a test specification such as that for the RILEM pullout test which has a short bond length of 5φ and a relatively thick concrete cover equal to 4.5φ. As demonstrated in Fig. 4, average bond strength decreases with increasing bond length. The thick cover, together with arching action within the specimen, provides high confinement. By contrast, the application rules provide design values based on the minimum permissible cover of 1φ and thus correspond to a much lower confinement, and are also derived for much longer bond lengths. The values for τbu,split given in the local bondslip relationship and design bond strengths given in fib Model Code 2010 are both derived from Eq. (3), so the common origin
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Structural Concrete (2015), No. 1
of these two parts of the fib Model Code 2010 provisions is now explicit.
10
Simplified rules
While it is essential that design rules for bond of embedded reinforcement be based on rational physical models of the relevant physical phenomena, refinement of design rules invariably leads to increasing complexity in the calculations associated with the detailing process for laps and anchorages, which brings with it an increased possibility of errors. There is therefore an incentive to derive simplified requirements for more common situations and to develop a system of classification to define them. Detailing rules in sections 7.13.2.5 and 7.13.2.6 of fib Model Code 2010 are derived from the provisions of section 6.1 for the most common situations and represent a basic attempt at classification.
11
Conclusions
This paper provides an overview of the rationale underpinning the requirements of fib Model Code 2010 for the design of laps and anchorages of embedded ribbed steel reinforcement. The reader should refer to fib Bulletin 72 [5] for a more comprehensive and detailed review. It is demonstrated that fib Model Code 2010 design rules are linked back to evidence from a large number of physical tests. The most significant changes from MC90 are: 1. An extension of the range of concrete strengths covered. 2. The introduction of a new coefficient η4 for steel grade to allow for the nonlinear relationship between bond length and the stress developed in a bar. 3. Revisions to the expressions allowing for confinement by concrete and secondary reinforcement and to their respective limiting values, plus the introduction of a clear spacing parameter cmax/cmin which permits shorter laps in slabs. 4. A change in the way the contribution of hooks or anchorages is determined.
J. Cairns · Bond and anchorage of embedded steel reinforcement in fib Model Code 2010
5. Recognition of the contribution of end bearing to laps and anchorages for compression bars. 6. A distinction between laps and anchorages based on the presence or absence of transverse pressure instead of function. 7. Discontinuation of the α6 coefficient for staggered laps. 8. Recognition of the need to avoid brittle failures of lapped joints and that structural robustness requires bar yield to precede a splitting mode bond failure. 9. A clear link between design rules and the local bondslip relationship.
Acknowledgements The author wishes to record his appreciation for the contributions to the work summarized in this paper made by members of TG4.5, in particular G. Balazs, R. Eligehausen, S. Lettow, G. Metelli, S. Pantazopoulou and G. Plizzari. References 1. fib – International Federation for Structural Concrete. fib Model Code for Concrete Structures 2010. Berlin: Verlag Ernst & Sohn, 2013. 2. CEBFIP Model Code 90. CEB, Lausanne, 1993. 3. CEBFIP Model Code for concrete structures. CEB, 1978. 4. CEB Bulletin 228: High Performance Concrete. Recommended Extensions to the Model Code 90 – Research Needs, 1995, ISBN 9782883940314. 5. fib: Bond and anchorage of embedded reinforcement: Background to the fib Model Code 2010. fib Bulletin fib, Lausanne, May 2014 170pp. ISBN 9782883941120 6. ACI 408 bond database – may be obtained from: http://www.concrete.org/technical/ckc/Additional_Data_R eferenced_from_Technical_Committee_Documents.htm 7. fib TG4.5 bond test database – may be obtained from: http://fibtg45.dii.unile.it/files%20scaricabili/Database_splic etest%20Stuttgart% 20sept%202005.xls 8. Amin, R.: End Anchorage At Simple Supports In Reinforced Concrete. PhD thesis, London South Bank University, Nov 2009. 9. Canbay, E., Frosch, R. J.: Bond Strength of LapSpliced Bars. ACI Structural Journal, vol. 102, No. 4, Jul 2005. 10. Orangun, C. O., Jirsa, J. O., Breen, J. E.: ‘A Reevaulation of Test Data on Development Length and Splices’, Proceedings American Concrete Institute. Vol. 74, No. 3, March 1977.
11. Zuo, J., Darwin, D.: ‘Splice Strength of Conventional and High Relative Rib Area Bars in Normal and HighStrength Concrete’, ACI Structural Journal. Vol. 97, No. 4, July 2000. 12. Eurocode 2: Design of concrete structures – Part 11: General rules and rules for buildings. BS EN 199211:2004. British Standards Institution, London, 2004. 13 Schiessl, P.: Interaction between anchorage of bond, hooks and welded transverse bars. Proc. of Intl. Conf. on Bond in Concrete. Paisley, Applied Science Publishers, London, 1982, pp. 424–433. 14. American Concrete Institute. ACI 31811: Building Code Requirements for Structural Concrete and Commentary. ACI, Michigan, USA, 2008. 15. Ferguson, P. M., Breen, J.: Lapped Splices For High Strength Reinforcing Bars. ACI Proc., vol. 62, No. 9, 1965, pp. 1063–1078. 16. Tepfers, R.: A Theory of bond applied to overlapped reinforcement splices for deformed bars. Chalmers Technical University, Institution for Betonbyggnad. Pub. No. 73:2, Gothenburg, 1973. 17. Reynolds, G., Beeby, A. W.: Proc. of Intl. Conf. on Bond in Concrete. Paisley, Applied Science Publishers, London, 1982. 18. Magnusson, J.: Bond and anchorage of ribbed bars in high strength concrete. PhD thesis, Div. of Concrete Structures, Chalmers University of Technology, Gothenburg, 2000. 19. Metelli, G., Cairns, J., Plizzari, G.: The influence of percentage of bars lapped on performance of splices. Materials and Structures, June 2014. DOI: 10.1617/s115270140371y 20. Cairns, J. (2014), Staggered lap joints for tension reinforcement. Structural Concrete, 15: 45–54. doi: 10.1002/suco. 201300041. 21. Cairns, J.: Bond Strength Of Compression Splices: A Reevaluation Of Test Data. ACI Proc., Jul/Aug 1985, pp. 510–516. 22. Cairns, J.: Lap Splices of Bars in Bundles. ACI Structural Journal (110S16), Mar/Apr 2013.
John Cairns School of the Built Environment HeriotWatt University Edinburgh EH14 4AS, UK j.j.cairns@hw.ac.uk
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Technical Paper M. John Robert Prince Bhupinder Singh*
DOI: 10.1002/suco.201300101
Bond behaviour of normal and highstrength recycled aggregate concrete The effect of concrete grade on the bond between 12 mm diameter deformed steel bars and recycled aggregate concrete (RAC) has been investigated with the help of 45 pullout tests with concentric rebar placement for coarse recycled concrete aggregate (RCA) replacement levels of 25, 50, 75 and 100 %. For all the three concrete grades, the measured bondslip relationships indicate similar mechanisms of bond resistance in the RAC and the natural aggregate (NA) concrete. The most accurate and least conservative predictions of the measured bond strengths were obtained from the local bondslip model in the fib Model Code for Concrete Structures 2010. Bond strength normalized to fc(3/4) resulted in an improved match with test data and increased with an increase in the RCA replacement levels and decreased with an increase in compressive strength. An attempt to explain this behaviour has been sought in terms of brittleness index, an analogous parameter from rock mechanics. An empirical bond stress versus slip relationship has been proposed for the 12 mm diameter bar and it is conservatively suggested that similar anchorage lengths for this bar in all three concrete grades can be adopted for the RAC and the NA concretes. Keywords: coarse recycled concrete aggregate, replacement level, natural coarse aggregate, bond, pullout failure, normalized bond strength
1
Introduction
Traditionally, bond strength between steel bars and conventional concrete (made with natural coarse aggregates) has been normalized to the square root of the concrete compressive strength fc [1–7], although this practice has not been universal. Zsutty [8], for example, found that fc1/3 provided a better match with data compared with fc1/2.On the basis of a review of a large number of bond test results of concretes with strengths between 17 and 110 MPa, Darwin et al. [9] and Zuo and Darwin [10] have reported that the effect of concrete grade on splice strength for normalstrength as well as highstrength concrete is more accurately represented if the bond strength data are normalized to fc1/4. The bond test results of Harajli and AlHajj [11] show that as the compressive strength of concrete increased from about 28 MPa to about 55 MPa, the local
* Corresponding author: bhupifce@iitr.ernet.in Submitted for review: 11 December 2013 Revised: 7 May 2014 Accepted for publication: 28 May 2014
56
splice strength increased in proportion to fcp, with p > 1/2. These authors found that for all the parameters they investigated, whenever the local splice strengths were normalized to fc1/2, the results of highstrength concrete were about 23 % higher than those of normalstrength concrete. On the other hand, according to Azizinamini et al. [12], the normalized average bond strength at failure in highstrength concrete reduces relative to normalstrength concrete, and this reduction in bond strength increases with an increase in splice length. In contrast to the results of Azizinamini et al. [12], Esfahani and Rangan [13] found that the average bond stress at failure normalized with respect to fc1/2 is higher for highstrength concrete than for normalstrength concrete. According to the literature, fc1/2 does not accurately represent the effect of concrete strength on bond, and ACI Committee 408 [14] states that “when bond strengths are normalized with respect to fc1/2, the effect of concrete strength is exaggerated, resulting in an overestimation of bond strength for higher strength concretes”. The brief review presented above indicates the complexity of the relationship between local bond strength of deformed steel bars and grade of concrete (made with natural coarse aggregates). In recent years, considerable effort has been directed towards investigating the possibility of using coarse recycled concrete aggregate (RCA) as a substitute for natural coarse aggregate (NCA) in concrete construction. Although the bond behaviour between NCA concrete and steel rebars has been extensively studied [14–16], only a few investigations have looked at the bond between RCA concrete and steel reinforcement [17–21]. This situation is further compounded by the fact that even less information is available in the literature on the bond strength of deformed steel bars embedded in highstrength recycled aggregate concrete (RAC). Since bond behaviour is heavily influenced by the tensile strength and fracture energy of concrete, which besides other parameters also depends upon the characteristics of the coarse aggregates in the concrete, there is the possibility that bond strength and its variation with concrete grade in RAC made with the relatively porous and softer coarse recycled concrete aggregates may be significantly different or even inferior to that of conventional concrete made with natural coarse aggregates. The objective of this experimental study has been to investigate the effect of the grade of recycled aggregate
© 2015 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete (2015), No. 1
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Portland cement and the aggregates are presented in Tables 1 and 2 respectively. The aggregate crushing and impact values listed in Table 2 were measured using the procedure given in IS 2386 (Part IV) 1963 [26] and the residual mortar content of the RCA particles was found using the hydrochloric acid dissolution method of Nagataki et al. [27]. The natural coarse aggregates consisted of locally available crushed rock (fineness modulus = 6.38) and the coarse RCA was generated by using a jaw crusher to process waste specimens obtained from the concrete laboratory of the authors’ host institute. The nominal maximum size of the NCA and RCA particles was kept to 12.5 mm and the size fractions of the RCA particles obtained from the jaw crusher were blended in such a way that the grading curves of both coarse aggregate types, besides being similar to each other, were also within the specified coarse aggregate grading limits of IS 3831970 [28], see Fig. 1. Crescentribbed deformed steel bars (ultimate tensile strength = 616 MPa) with 12 mm nominal diameter and having ribs of the same orientation on both sides of the longitudinal axis of the bars, Fig. 2, and whose measured surface characteristics are given in Table 3, were used as the reinforcement in the pullout tests.
concrete on the local bond strength of a deformed steel bar, with the RCA replacement level being the other parameter investigated besides the concrete grade. The rebar diameter ϕ and its cover have been kept nominally constant during the investigation. Further, on the basis of the results of 45 pullout tests performed according to IS 2770 (Part 1) 1967 [22], the relationship between the parameters under investigation and bond strength has been explored and an attempt has been made to correlate the trends in the measured bond strengths with the fracture toughness of concrete. As a calibration exercise, the measured bond strengths have been compared with predictions from the local bondslip models in the fib Model Code for Concrete Structures 2010 [23] and the literature [4, 24]. The observed slip behaviour of the rebar has been used to propose an empirical bond stress versus slip relationship between the recycled aggregate concrete and the steel rebar.
2 2.1
Experimental programme Materials
The materials and the methodology used in this investigation were similar to those used in an earlier investigation by the same authors [20, 21], although for the sake of completeness, the relevant details are briefly repeated here. The concrete mixes used in the pullout specimens were made using Portland cement conforming to IS 81121989 [25], coarse aggregates, clean river sand (fineness modulus = 2.68) and potable water. The physical properties of the
2.2
Mix proportions
Three concrete grades representative of normalstrength (mix A), mediumstrength (mix B) and highstrength concrete (mix C), having target cylinder strengths of 36, 51 and 68 MPa respectively, were investigated. For each of
Table 1. Physical properties of the Portland cement [21]
Property
Unit
Test result
Limiting values specified in IS 8112:1989 [25]
Specific gravity
–
3.14
–
Fineness by Blaine’s Air permeability test
m2/kg
285
≥ 225
Soundness, LeChatelier
mm
1
≤ 10
Standard consistency
%
28
–
Initial setting time
min
74
≥ 30
Final setting time
min
168
≤ 600
72 ± 1 h compressive strength
MPa
25.2
≥ 23
168 ± 2 h compressive strength
MPa
37.5
≥ 33
672 ± 4 h compressive strength
MPa
45.8
≥ 43
Table 2. Physical properties of the aggregates [21]
Property
Fine aggregate
Natural coarse aggregate (NCA)
Recycled concrete aggregate (RCA)
Bulk density (kg/m3)
1866
1630
1385
Bulk specific gravity
2.68
2.67
2.5
Water absorption (%)
0.7
1.0
6.0
Crushing value (%)
–
21.2
21.7
Impact value (%)
–
17.3
22.2
Residual mortar content (%)
–
–
32.2
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M. J. R. Prince/B. Singh · Bond behaviour of normal and highstrength recycled aggregate concrete
Table 3. Surface characteristics of the rebar
Cumulative passing (%)
120 100
Property
Measured value
Rib height*
0.7 mm
IS 383 upper limit for CA
Rib width
1.43 mm
IS 383 lower limit for CA
Rib spacing**
7.28 mm
Relative rib area
0.096 mm2
Rib face angle
45°
80 NCA
60 40
RCA 20 0 0
5
10
15
20
25
Sieve size (mm)
**
Fig. 1. Grading curves of the natural coarse aggregates and coarse recycled concrete aggregates [21]
Fig. 2. Orientation of ribs on the deformed steel bar used in the investigation [21]
**
Ribs on both sides of the longitudinal axis of a bar have the sameorientation Centretocentre distance between ribs
the three grades, the control concrete mix designed using the absolute volume method was made using NCA. The mix design of the RCA concrete was carried out using equivalent mix proportions, with the mix proportions of the NCA and RCA concretes being kept nominally the same except for substitution of NCA with RCA in accordance with the desired RCA replacement level. The RCA replacement level is defined as the weight ratio of RCA to the total coarse aggregates in the concrete mix and, depending upon the selected replacement level, direct substitution of NCA with an equal weight of RCA particles was carried out. The following five weight combinations of NCA and RCA were investigated for each grade of concrete: 100 % NCA (control mix), 75 % NCA + 25 % RCA, 50 % NCA + 50 % RCA, 25 % NCA + 75 % RCA, 100 % RCA. The concrete mix proportions are presented in Table 4. The RCA particles were used in the saturated
Table 4. Concrete mix proportions
mix ID
RCA replacement level, r (%)
Cement (kg/m3)
Fine aggregate (kg/m3)
NCA (kg/m3)
RCA (kg/m3)
Mixing water including HRWRA* (kg/m3)
HRWRA* (ml/m3)
AR0
0
369
854
912
0
199
–
AR25
25
369
854
684
228
199
–
AR50
50
369
854
456
456
199
–
AR75
75
369
854
228
684
199
–
AR100
100
369
854
0
912
199
–
BR0
0
379
790
1100
0
159
1516
BR25
25
379
790
825
275
159
1516
BR50
50
379
790
550
550
159
1516
BR75
75
379
790
275
825
159
1516
BR100
100
379
790
0
1100
159
1516
CR0
0
430
746
1100
0
159
1720
CR25
25
430
746
825
275
159
1720
CR50
50
430
746
550
550
159
1720
CR75
75
430
746
275
825
159
1720
CR100
100
430
746
0
1100
159
1720
*
58
high range water reducing admixture
Structural Concrete (2015), No. 1
36.91
28.88
24.04
26.16
24.71
51.14
46.70
41.96
36.97
35.58
68.65
65.60
57.54
54.20
50.30
A12R0
A12R25
A12R50
A12R75
A12R100
B12R0
B12R25
B12R50
B12R75
B12R100
C12R0
C12R25
C12R50
C12R75
C12R100
45
40
35
60
70
45
55
40
60
70
52
80
65
70
70
(mm)
Initial slump
5.31
4.89
4.89
4.79
4.47
4.23
3.81
3.80
3.87
3.74
3.34
2.85
2.99
2.96
2.83
Splitting tensile strength of concrete, fct,sp (MPa)
22.12
22.62
23.48
26.19
26.08
19.56
21.19
16.91
20.38
19.78
19.11
19.01
18.87
19.54
18.68
Ultimate bond stress, fbu (MPa)
9.44
11.04
10.52
9.48
7.12
6.88
10.55
10.18
8.74
7.23
3.01
15.17
3.84
1.77
4.39
Coefficient of variation, fbu (%)
0.443
0.394
0.418
0.481
0.464
0.497
0.543
0.432
0.475
0.456
0.636
0.710
0.657
0.651
0.561
Unloaded end slip at ultimate load, su (mm)
9.47
11.08
11.77
13.70
15.36
8.41
9.70
11.04
12.07
13.67
7.40
9.18
8.04
9.76
13.04
Brittleness index
1.17
1.13
1.12
1.14
1.09
1.34
1.41
1.03
1.14
1.03
1.72
1.64
1.74
1.57
1.25
Normalized bond strength, fbun (MPa(3/4))
* Specimen ID: The first letterrepresents concrete grade (A: normalstrength, B: mediumstrength, C: highstrength), the next two numerals represent the nominal rebar diameter (12 mm) and the remaining characters represent the RCA replacement levels (0: 0 %; 25: 25 %; 50: 50 %; 75: 75 % and 100: 100 %). Note: Pullout failure induced by throughsplitting was observed in all the specimens.
Cylinder compressive strength of concrete, fc (MPa)
Specimen ID*
Table 5. Experimental results of pullout specimens (reported values are averages of measured results of three nominally identical replicate specimens)
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surfacedry (SSD) moisture state achieved by presoaking the aggregates in water for a period of 24 h prior to casting. The initial slumps and the 56day compressive strengths of the concrete mixes listed in Table 4, obtained as the average of the measured strength of three replicate cylinders (100 mm dia. × 200 mm high), are given in Table 5.
2.3
Pullout specimens
The pullout tests were carried out using cylindrical specimens 100 mm dia. × 200 mm long with concentric rebar placement. Pullout specimens are widely used for investigating bond behaviour because of their ease of fabrication and the simplicity of the test, and they provide a simple means of comparing normalized bond behaviour. However, these specimens are the least realistic because the stress fields in them do not accurately simulate bond conditions in actual structures [14]. Nevertheless, some of the drawbacks of pullout tests can be overcome by suitable modifications to the test specimens which serve to mitigate the effect of the compressive struts that subject the bar surface to compression during pullout. The pullout specimens were cast in a vertical position in the laboratory using steel moulds. During casting and subsequent compaction, the concentrically placed steel bars were nominally held in position using a specially designed steel fixture. The bonded length of the rebars in the pullout specimens was five times the rebar diameter, Fig. 3, and was selected in order to reduce any possibility of yielding during pullout. It should be noted that al
though the selected bonded length helps to prevent yielding and ensures an almost uniform bond stress distribution, particularly in normalstrength concrete, a shorter bonded length of the order of three times the rebar diameter would be more compatible with the relatively smaller mass of the pullout specimens used in this investigation. This is expected to result in more accurate ultimate bond stress values. In order to mitigate the effect of the aforementioned compressive struts, contact between the concrete and the rebar along the debonded length in the pullout specimens was broken by placing a soft plastic tube around the rebar and filling the annular space between rebar and plastic tube with clay, which was removed after curing. The concrete was mixed in the laboratory using a tilting drumtype mixer, poured into the moulds and compacted using a vibrating table. To prevent excessive evaporation from the fresh concrete, the pullout specimens were covered with a plastic sheet soon after casting and demoulded after 24 h. Afterwards, they were moistcured in the laboratory for a nominal period of 56 days from the day of casting by immersing them in a curing tank in which the temperature of water was maintained at 27 ± 2 °C. The curing tank water was replaced every week. To help ensure the repeatability of the results, three nominally identical companion pullout specimens were cast for each parameter under investigation. The identification of the pullout specimens is presented in Table 5. Control cylindrical specimens for finding the compressive and the splitting tensile strengths of the concretes were also cast together with the pullout specimens and the measured strengths are given in Table 5.
P LVDT 1
LVDT 2
MS angle attached to rebar MS restrainer plate, 40 thick
Bonded length, 5 ϕ
100 dia. cylindrical specimen
Steel bar, diameter ϕ
Bond breaker
200
Pipe sleeve as bond breaker
Clay filling LVDT 3 LVDT 4 All dimensions in mm Fig. 3. Pullout test setup configuration in elevation [21]
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Bond stress (MPa)
28
A12
24 20 16 12
A12R0 A12R25 A12R50 A12R75 A12R100
8 4 0 0
4
a)
2.4
Test setup
The pullout tests were carried out in a stiff electrohydraulic test frame using a specially fabricated mild steel jig rigidly connected to the testing machine. Fig. 3 shows the test setup configuration and Fig. 4 a pullout test in progress. During loading, which was applied in a monotonically increasing manner in loadcontrolled mode, the top crosssection of the cylindrical pullout specimen was pressed against a stiff 40 mm thick mild steel restrainer plate, Fig. 3, with a thin sheet of softwood and a layer of grease between the underside of the restrainer plate and the pullout specimen to ensure uniform contact and minimize platen friction respectively. The test was performed by pulling the embedded rebar uniformly upwards from the specimen and the applied load was measured with the help of a pressure sensor whose output was fed to an automatic data acquisition system. The loadedend slip was measured as the average of the output of LVDTs 1 and 2 (see Fig. 3) and the net slip at the unloaded end was found as the difference between the readings from LVDTs 3 and 4. The output of all LVDTs was recorded with the help of the data acquisition system. After reaching the ultimate load, each specimen was subjected to a further increase in displacement to include the descending branch of the loadslip relationship. The failure mode was noted. A pullout test was terminated when one of the following conditions occurred first: i) pullthrough or rupture of the rebar, ii) splitting of the concrete enclosing the rebar, iii) unloaded end slip in the range 10–16 mm.
3 3.1
Results and discussion Measured bond stressslip relationship
The measured load versus unloadedend slip curves of all three concrete grades, after eliminating outliers, is presented in Fig. 5. They are similar to each other, especially in the ascending branch of the relationships, across the two types as well as the three grades of concretes. This trend in Fig. 5 supports the observation of Xiao and Falkner [19] that bond development and deterioration between RCA concrete and deformed steel bars is fundamentally similar to that observed in NCA concrete and the following stages of bond behaviour can be identified in the measured loadslip relationships: i) microslip, ii) internal cracking, iii)
B12
24 20 16 12
16
B12R0 B12R25 B12R50 B12R75 B12R100
8 4 0 0
4
b)
28
Bond stress (MPa)
Fig. 4. Pullout test setup [20]
Bond stress (MPa)
28
8 12 Unloaded end slip (mm)
8 12 Unloaded end slip (mm)
C12
24 20 16 12
16
C12R0 C12R25 C12R50 C12R75 C12R100
8 4 0 0
c)
4
8 12 Unloaded end slip (mm)
16
Fig. 5. Bondslip curves for the 12 mm dia. deformed bars: a) normalstrength concrete, mixA, b) mediumstrength concrete, mix B, c) highstrength concrete, mix C
pullout, iv) descending and v) residual. Phase I of the loadslip behaviour in Fig. 5 consists of that part of the relationship which is ascending steeply (due to adhesion) and nearly linear up to about 60–70 % of the ultimate load. This phase encompasses microslip (load is small and no obvious slip occurs at free end) in the initial part followed by internal cracking in the later part, which results in slip of the free end of the rebar, i.e. the adhesion mechanism of bond resistance has been exhausted. After phase I, the rate of slip begins to increase in phase II, in which the ascending branch of the curve becomes distinctly nonlinear with a relatively small increase in bond resistance such that the pullout load reaches an ultimate value Qu and is accompanied by the formation of a splitting crack. The dominant mechanism of bond resistance in phase II can be attributed to mechanical interlock accompanied by some contribution from frictional resistance due to displaced mortar particles becoming wedged between the rebar and the surrounding concrete. As the load increased further, so the loadslip relation
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ships were seen to undergo a sharp change in slope, signifying a breakdown of bond strength and development of significant nonrecoverable slip. The descending branch of the loadslip relationships represents phase III in which an approximately linear decrease in bond resistance with rapid increase in slip occurred (accompanied by widening
of the splitting crack), culminating in varying degrees of residual slip. Following that, the residual phase set in, with the pullout load becoming nearly constant and reaching approximately onefifth of the ultimate load. Although visible splitting cracks were noticed in the test specimens, which can be considered to be moderately confined (cov
Fig. 6. Interfaces in NCA and RCA concretes showing crushing of concrete in front of ribs: a) A12R01, b) A12R1002, c) B12R01, d) B12R1001, e) C12R01, f) C12R1001
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er being approximately four times the rebar diameter), they were not severe enough to result in spalling of the concrete cover over the rebars (as happens in a classical splitting failure). Therefore, it would be more accurate to define the failure mode observed in the test specimens as being essentially a pullout failure induced by throughsplitting. This reasoning is further supported by the residual tail in the measured bond stressslip relationships, which is indicative of frictional resistance due to concrete slip on rib faces during the course of rebar pullout. All the specimens tested were dissected to examine the interface between the steel bar and the concrete. The specimens were cut using a watercooled diamondtipped saw and then pried open to reveal the interface. Fig. 6, which presents a selection of interfaces in the NCA and the RCA concrete specimens, shows varying degrees of crushing of the concrete in front of the ribs and a closer examination of this figure reveals that the degree of crushing was more sensitive to concrete grade rather than concrete type (NCA or RCA concrete). In Fig. 6, for both the NCA as well as the RCA concrete specimens, crushing is least in the highstrength concrete specimens, followed by the mediumstrength concrete specimens, and maximum crushing is seen in the normalstrength concrete pullout specimens. This behaviour is similar to that observed by Esfahani and Rangan [13] in their pullout specimens made of (NCA) concrete with cylinder crushing strengths of 26, 50 and 75 MPa, which are approximately analogous to the normal, mediumand highstrength concretes of this investigation. Azizinamini et al. [12] have also reported a relatively higher degree of concrete crushing in front of the ribs in normalstrength concrete compared with that in highstrength concrete. Unlike Esfahani and Rangan [13] and Azizinamini et al. [12], no definite conclusions with respect to the relative bond strength of normaland highstrength concrete could be drawn on the basis of the observed trends in crushing of concrete in front of ribs, although Table 5 shows ultimateload slip values (and hence the degree of concrete crushing in front of the ribs) to be inversely proportional to the concrete grade.
3.2
Bond strength
Assuming a uniform bond stress distribution over the (short) embedded length of the rebar in the concrete, the bond strength is given by the following relationship: fbu = Qu/(πϕ l)
(1)
where: fbu ultimate bond stress (MPa) between concrete and steel rebar, also called the bond strength Qu ultimate load (N) ϕ nominal rebar diameter (mm) l bonded length (mm), taken as 5ϕ in this investigation The averages of the ultimate bond stresses fbu given in Table 5 are the bond strengths of the companion pullout specimens and are compared with predictions from fib Model Code 2010 and selected local bond strength models in the literature in Fig. 7. The trends in this figure show that the most accurate and least conservative bond
strength predictions were obtained from the local bondslip model in fib Model Code 2010 [23]. It should be noted, however, that the local bond strength prediction model in fib Model Code 2010 is valid for wellconfined concrete (cover ≥ 5ϕ), whereas the pullout specimens of this investigation with a cover of approx. 4ϕ may be considered to be “moderately confined”, and therefore the predictive appraisal of fib Model Code 2010 presented in Fig. 7 may not be strictly valid. Fig. 8 shows trends in the normalized bond strengths when the ultimate bond stress values were normalized to fc(3/4), unlike the traditional use of fc1/2, which tends to exaggerate the effect of concrete strength and leads to the bond strength being overestimated for higherstrength concrete. It should also be pointed out that fc(3/4) provided an improved match with the test data compared with fc1/2. Although normalizing measured bond strengths may help explain trends in local bond behaviour associated with short bond lengths, it is not valid when analysing fullstrength laps and anchorages. The bestfit lines in Fig. 8 are indicative of the following trends: i) Across all the RCA replacement levels, the normalized bond strength of the normalstrength concrete (mix A) is higher relative to that of the medium (mix B) and highstrength (mix C) concretes, although the difference between the trends for mix B and mix C is less pronounced. ii) For the results from this investigation (particularly the normal and mediumstrength concretes) as well those of Xiao and Falkner [19], the normalized bond strength is seen to increase with an increase in the RCA replacement level. According to Xiao and Falkner [19], the superior bond strength of RCA concrete relative to NA concrete is due to the similar elastic moduli of coarse RCA and the cement paste of the recycled aggregate concrete, although a more objective explanation for this observed behaviour has been sought here in the mechanical properties of concrete. It is well established that the tensile properties of concrete, in particular its fracture toughness, play a significant role when determining bond strength [14]. Brittleness is an important attribute of concrete related to its fracture toughness and, drawing upon an analogy with rock mechanics, the brittleness of the NA and RCA concretes has been evaluated in terms of the brittleness index BI, which is a widely used parameter for quantifying rock brittleness and is calculated as follows [21]: BI = fc/fct,sp
(2)
where fc and fct,sp are the compressive and splitting tensile strengths of concrete respectively. The higher the brittleness index, the more brittle the material can be expected to be and therefore the lower its fracture toughness. It is reckoned in rock mechanics that as the brittleness index increases, so the size of the crushed zone as well as the number and length of main cracks outside the crushed zone also increase [29]. In this context it can be expected that the bond strength of concrete should increase as its brittleness index decreases. The trend lines for the brittleness indexes givenin Table 5
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M. J. R. Prince/B. Singh · Bond behaviour of normal and highstrength recycled aggregate concrete
A12
Bond Stress (MPa)
24 20 16
Test
12
fib MC2010
8
Kim et al. [24]
4
Esfahani and Rangan [4]
0 0 a)
25 50 75 100 RCA replacement percentage (%)
B12 Bond Stress (MPa)
24 20 16
Test
12
fib MC2010
8
Kim et al. [24]
4
Esfahani and Rangan [4]
0 0 b)
25 50 75 100 RCA replacement percentage (%)
C12 28 Bond Stress (MPa)
24 20
Test
16
fib MC2010
12 Kim et al. [24] 8 Esfahani and Rangan [4]
4 0 0 c)
25 50 75 100 RCA replacement percentage (%)
Fig. 7. Comparison of measured and predicted bond stress values: a) normalstrength concrete, mix A, b) mediumstrength concrete, mix B, c) highstrength concrete, mix C
as well as those obtained from the data of Kim and Yun [30] are plotted in Fig. 9, which shows a steady decrease in brittleness index with the increase in RCA replacement level. On the basis of the fracture toughness hypothesis postulated above, the trends in Fig. 9 are indicative of an increase in bond strength with increase in RCA replacement level, which lends support to the trends in the normalized bond strength observed in Fig. 8. It should also be noted in Fig. 9 that across all the RCA replacement levels, the lowest BI values were obtained for the normalstrength
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Structural Concrete (2015), No. 1
concrete and the highest for the highstrength concrete, with the values for mediumstrength concrete lying in between; this agrees with the known trends for these grades of concrete. These observations suggest that brittleness index may be a valid predictor of bond strength visàvis concrete grade and RCA replacement level. An attempt has been made to derive some measure of the brittleness of bond behaviour from the measured local bond stressslip relationship. To this end, the parameter “(normalized) toughness in bond”, taken as the area
M. J. R. Prince/B. Singh Âˇ Bond behaviour of normal and highstrength recycled aggregate concrete
Normalised bond strength [Ď„max /{(fcâ€™)(3/4)}]
2,0 RÂ˛ = 0,6598
1,8 1,6
Mix A RÂ˛ = 0,6227
1,4
Mix B
RÂ˛ = 0,737
1,2 1,0
Mix C Xiao and Falkner [19]
RÂ˛ = 0,9774
0,8
Linear, Mix A
0,6
Linear, Mix B
0,4
Linear, Mix C Linear, Xiao and Falkner [19]
0,2 0,0 0
25
50 75 RCA replacement level (%)
100
Fig. 8. Normalized bond strengths for various RCA replacement levels (mixA â€“ normalstrength concrete; mix B â€“ mediumstrength concrete; mix C â€“ highstrength concrete)
Brittleness Index ( fc'/ft )
20
Mix A RÂ˛ = 0,9828
16
Mix B RÂ˛ = 0,8274
Mix C
12
Kim and Yun [30] Linear (Mix A)
8 RÂ˛ = 0,9966
Linear (Mix B) RÂ˛ = 0,731
4
Linear (Mix C) Linear (Kim and Yun [30])
0 0
25
50 75 RCA replacement level (%)
100
Fig. 9. Variation inbrittleness index with RCA replacement levels
under the local bond stressslip relationship up to the beginning of the residual tail normalized to fc(3/4), has been calculated and plotted against the RCA replacement level for all three concrete grades in Fig. 10, which also includes the trend lines for the variation in the brittleness indexes calculated using Eq. (2). Fig. 10 shows that the trends for the normalized toughness and the brittleness index complement each other in the case of the normal (mix A) and the mediumstrength (mix B) concrete, although they was disagreement in the case of the highstrength concrete (mix C).
3.3
fb
s
s su
(3)
where su is the slip corresponding to ultimate bond stress fbu. A model for the ascending and descending branches of the measured bond stressslip relationships is presented in the following equations. The ascending branch has been modelled by estimating, on the basis of a regression analysis of test data, the constant a in the following constitutive equation for normalstrength concrete proposed by Harajli [31]:
Modelling the bondslip relationship
Modelling of bond behaviour at the steelconcrete interface is necessary for the numerical analysis of reinforced RCA concrete members. To this end, a normalized bondslip relationship is proposed in terms of the following dimensionless parameters of Xiao and Falkner [19]:
fb , fbu
fb
Â a Â°Â° s ÂŽÂ§ 1 Âˇ Â°Â¨ Â¸ 0.15fbu ÂŻÂ°ÂŠ s Âš
s d1 (4)
s !1
where a is a function of the slope of the ascending branch of the measured bond stressslip relationship. The de
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M. J. R. Prince/B. Singh · Bond behaviour of normal and highstrength recycled aggregate concrete
14
14
A12 10
10
8
8 R² = 0,731
6
6
4
4 Toughness Linear (Toughness)
2
BI Linear (BI)
2
0
0 0
a)
25 50 75 RCA replacement level (%)
100
16
5 R² = 0,6166
14
4
12 10
3
8
R² = 0,9966 2
6 Toughness Linear (Toughness)
1
4
BI Linear (BI)
2
0
0 0
25
b)
50 75 RCA replacement level (%)
100
8
18
C12
7 Normalised toughness
Brittleness Index, BI
Normalised toughness
B12
16 14
6
R² = 0,4291
12
5
10
R² = 0,9828
4
8
3
6
2
Toughness Linear (Toughness)
1
4
BI Linear (BI)
2 0
0 0 c)
Brittleness Index, BI
12 R² = 0,6985
Brittleness Index, BI
Normalised toughness
12
25
50 75 RCA replacement level (%)
100
Fig. 10. Variation in normalized toughness in bond and brittleness index with RCA replacement levels: a) normalstrength concrete, mix A, b) mediumstrength concrete, mix B, c) highstrength concrete, mix C
scending branch is proposed as a function of the normalized slip and the peak bond stress. The estimated value of the regression parameter a was found to be 0.2 for the normal (mix A) and highstrength (mix C) concretes, whereas the value for the mediumstrength concrete (mix B) was 0.3. The normalized bondslip relationships of the companion specimens with various RCA replacement levels for the normal, medium and highstrength concretes shows good correlation with the predictions from Eqs. (3) and (4) in Figs. 11, 12 and 13 respectively. It should be not
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ed that only selected test results have been compared with predictions in Fig. 11, whereas in Figs. 12 and 13 the average of the response of the three replicate specimens for each RCA replacement ratio has been compared with the predictions. Xiao and Falkner [19] have also reported accurate predictions of the measured bondslip relationships of their RCA concretes with the help of Eq. (3), which therefore lends support to the validity of this equation for predictive assessment of the bondslip behaviour of RCA concrete.
M. J. R. Prince/B. Singh · Bond behaviour of normal and highstrength recycled aggregate concrete
1.2
1.2
Test Predicted
A12R02
1
1 0.8 τ/τmax
τ/τmax
0.8 0.6
0.4
0.2
0.2 0
0 0
5
1.2
10
s/smax
15
20
25
τ/τmax
τ/τmax
0.2
0.2 0
5
1.2
10
s/smax
15
20
25
14
16
Test Predicted
B12R25
0
b)
2
4
1.2
Test Predicted
A12R503
1
6
8 10 s/smax
12
14
16
Test Predicted
B12R50
1 0.8 τ/τmax
0.8 τ/τmax
12
0
0
0.6
0.6
0.4
0.4
0.2
0.2 0
0 0
5
1.2
10
s/smax
15
20
25
0
c)
2
4
1.2
Test Predicted
A12R752
1
6
8 10 s/smax
12
14
16
Test Predicted
B12R75
1 0.8 τ/τmax
0.8 τ/τmax
8 10 s/smax
0.6 0.4
0.6
0.6
0.4
0.4
0.2
0.2 0
0 0
d)
6
1
0.4
c)
4
0.8
0.6
b)
2
1.2
0.8
5
1.2
10
s/smax
15
A12R1001
1
20
25
0
d)
2
4
1.2
Test Predicted
6
8 10 s/smax
12
14
16
Test Predicted
B12R100
1
0.8
0.8 τ/τmax
τ/τmax
0
a)
Test Predicted
A12R253
1
0.6
0.6
0.4
0.4
0.2
0.2
0 e)
0.6
0.4
a)
Test Predicted
B12R0
0 0
5
10
s/smax
15
20
25
Fig. 11. Measured vs. predicted bondslip relationships for the 12 mm dia. deformed bars: a) A12R0, b) A12R25, c) A12R50, d) A12R75, e) A12R100 [21]
e)
0
2
4
6
8 10 s/smax
12
14
16
Fig. 12. Measured vs. predicted bondslip relationships for the 12 mm dia. deformed bars: a) B12R0, b) B12R25, c) B12R50, d) B12R75, e) B12R100
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M. J. R. Prince/B. Singh · Bond behaviour of normal and highstrength recycled aggregate concrete
1.2
Test Predicted
C12R0
1 τ/τmax
0.8 0.6 0.4 0.2 0 0
a)
5
1.2
10
s/smax
15
20
25
Test Predicted
C12R25
1 τ/τmax
0.8 0.6 0.4 0.2 0 0
b)
5
1.2
10
s/smax
15
20
25
Test Predicted
C12R50
1 τ/τmax
0.8 0.6
0.2 0 0
5
1.2
10
s/smax
15
20
25
Test Predicted
C12R75
1 τ/τmax
0.8 0.6 0.4 0.2 0 0
d)
5
1.2
10
s/smax
15
20
25
Test Predicted
C12R100
1 τ/τmax
0.8 0.6 0.4 0.2 0 e)
0
5
10
15
20
25
s/smax
Fig. 13. Measured vs. predicted bondslip relationships for the 12 mm dia. deformed bars: a) C12R0, b) C12R25, c) C12R50, d) C12R75, e) C12R100
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Structural Concrete (2015), No. 1
Anchorage length in RCA concrete
Rebar anchorage in RCA concrete is of practical interest and, in general, anchorage length is influenced by a number of parameters, including the compressive strength of concrete and yield strength of rebars, which are the material parameters of interest. Although the anchorage characteristics have not been considered explicitly in this investigation, some relevant suggestions implied by the observed behaviour of the RCA concretes are made here. Since the RCA concrete was designed on the basis of equivalent mix proportions, a perusal of Table 5 reveals that its compressive strength was lower than that of the control NCA concrete for all three grades and, further, the compressive strength of the RCA concrete decreased with the increase in the RCA replacement level. However, when the ultimate bond stress values were normalized with the respective compressive strengths and plotted in Fig. 8, then for all three concrete grades the normalized bond strengths of the RCA concretes across all replacement levels were higher than that of the NCA concrete. Further, the trends in brittleness index in Fig. 9 indicate that fracture toughness of the concretes increased with an increase in the RCA replacement level, which supports the trends in normalized bond strength. The limited results from this investigation suggest that the anchorage lengths of the 12 mm diameter deformed rebars can be short in RCA concrete compared with those for NCA concrete. However, more tests are required to confirm the validity of this hypothesis.
4
0.4
c)
3.4
Conclusions
1. When designed using equivalent mix proportions, the compressive strengths of the three concrete grades representative of normal, medium and highstrength concrete decreased with an increase in the RCA replacement level by weight. 2. For all three concrete grades, bond behaviour between the 12 mm diameter deformed steel bar and the RCA concrete was similar to that of the NCA concrete, and across both these concrete types, bondslip behaviour corresponding to the stages of microslip, internal cracking, pullout, descending and residual could be identified in the measured relationships. Pullout failure induced by throughsplitting was observed in the NCA as well as the RCA concrete. Varying degrees of crushing of the concrete in front of the ribs was observed at the interface between rebar and surrounding concrete irrespective of the concrete type (NCA or RCA). The degree of concrete crushing was most prominent in the normalstrength concrete and least in the highstrength concrete, with the mediumstrength concrete lying in between. Correspondingly, ultimateload slip values were lowest for the highstrength concrete and highest for the normalstrength concretes. 3. Among the bond strength models under appraisal, the most accurate and least conservative predictions for the NCA and RCA concretes of this investigation were obtained from the local bondslip model in fib Model Code 2010. 4. Compared with fc1/2, normalization of the measured bond strengths to fc(3/4) produced a better match with the
M. J. R. Prince/B. Singh · Bond behaviour of normal and highstrength recycled aggregate concrete
5.
6.
7.
8.
test data. The normalized bond strengths across all RCA replacement levels were highest for the normalstrength concrete and lowest for the highstrength concrete (beyond RCA replacement levels of 25 %), with the results for the mediumstrength concrete lying in between. For the normal and mediumstrength concretes in particular, the normalized bond strengths across all RCA replacement levels were higher than the corresponding values for the NA concretes. These bond strengths were observed to increase with an increase in the RCA replacement level such that the highest values of this parameter were obtained when all the natural coarse aggregate in the concrete was replaced with coarse recycled concrete aggregate particles in the saturated surfacedry moisture condition. However, such a trend was not evident in the case of the highstrength concrete. The fracture toughness of concrete has been characterized in terms of the brittleness index calculated as the ratio of the compressive and the splitting tensile strengths. It has been shown in terms of this parameter that for all three concrete grades, the fracture toughness of the RCA concretes of this investigation was higher than that of the NA concretes and increased with an increase in the RCA replacement level. The normalstrength concrete has been shown to be the least brittle, followed by the medium and highstrength concretes. These observations lend support to the recorded trends in the normalized bond strength visàvis concrete grade and RCA replacement level and suggest that brittleness index may be a valid predictor of bond strength visàvis concrete grade and RCA replacement level. Accurate predictions of the bondslip relationships of the 12 mm diameter deformed steel bars embedded in both concrete types were obtained by empirically selecting the constants in a constitutive model for concrete available in the literature. It is suggested that for all three concrete grades, the anchorage lengths of the 12 mm diameter rebars embedded in the RCA concretes can be conservatively taken to be equal to those for NCA concrete.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Acknowledgements The support and cooperation of the staff of the concrete laboratory at the Department of Civil Engineering, Indian Institute of Technology (I.I.T.) Roorkee, Roorkee, in this experimental investigation is gratefully acknowledged.
14.
15. 16.
Notation 17.
ϕ l fc fct,sp Qu fbu fbun
nominal rebar diameter embedded length cylinder compressive strength of concrete splitting tensile strength of concrete ultimate load ultimate bond stress normalized bond strength
18.
19.
References 20. 1. Tepfers, R.: A Theory of Bond Applied to Overlapping Tensile Reinforcement Splices for Deformed Bars. Thesis, Divi
sion of Concrete Structures, Chalmers University of Technology, Pub. 73:2, Gothenburg, Sweden, May 1973. Orangun, C. O., Jirsa, J. O., Breen, J. E.: A revaluation of test data on development length and splices. ACI Journal, 1977, vol. 74, No. 3, pp. 114–122. Darwin, D., McCabe, S. L., Idun, E. K., Schoenekase, S. P.: Development length criteria: Bars not confined by transverse reinforcement. ACI Structural Journal, 1992, vol. 89, No. 6, pp. 709–720. Esfahani, M. R., Rangan, V. B.: Local bond strength of reinforcing bars in normalstrength and highstrength concrete (HSC). ACI Structural Journal, 1998, vol. 95, No. 2, pp. 96–106. Esfahani, M. R., Rangan, V. B.: Bond between normalstrength and highstrength concrete (HSC) and reinforcing bars in splices in beams. ACI Structural Journal, 1998, vol. 95, No. 3, pp. 272–280. ACI Committee 318: ACI 31808. Building Code Requirements for Structural Concrete and Commentary. Farmington Hills (MI), 2008. Harajli, M. H.: Comparison of bond strength of steel bars in normal and highstrength concrete. Journal of Materials in Civil Engineering, 2005, vol. 16, No. 4, pp. 365–374. Zsutty, T.: Empirical study of bar development behavior. Journal of Structural Engineering, ASCE, 1985, vol. 111, No. 1, pp. 205–219. Darwin, D., Zuo, J., Tholen, M. L., Idun, E. K.: Development length criteria for conventional and high relative rib area reinforcing bars. ACI Structural Journal, 1996, vol. 93, No. 3, pp. 347–359. Zuo, J., Darwin, D.: Splice strength of conventional and high relative rib area bars in normaland highstrength concrete. ACI Structural Journal, 2000, vol. 97, No. 4, pp. 630–641. Harajli, M., AlHajj, J.: Bond–slip response of reinforcing bars embedded in highstrength concrete. Proc. of Int. Symposium “Bond in concrete – From Research to Standards”, Budapest University of Technology & Economics, Budapest, Hungary, 2002. Azizinamini, A., Stark, M., Roller, J. J., Ghosh, S. K.: Bond performance of reinforcing bars embedded in highstrength concrete. ACI Structural Journal, 1993, vol. 90, No. 5, pp. 554–561. Esfahani, M. R., Rangan, V. B.: Studies on bond between concrete and reinforcing bars. School of Civil Engineering, Curtin University of Technology, Perth, Western Australia, 1996. ACI Committee 408: ACI 408R03. Bond and development of straight reinforcing bars in tension. Farmington Hills (MI), 2003. ACI Committee 408: Bond stress – the stateoftheart. ACI Journal, 1966, vol. 63, No. 11, pp. 1161–1190. ACI Committee 408: Opportunities in bond research. ACI Journal, 1970, vol. 67, No. 11, pp. 857–867. Mukai, T., Kikuchi, M.: Fundamental study on bond properties between recycled aggregate concrete and steel bars. Cement Association of Japan, 1978, 32nd review. Roos, F.: Beitrag zur Bemessung von Beton mit Zuschag aus rezyklierter Gesteinskörnung nach DIN 10451(Contribution to design of concrete with additive of recycled aggregate according to DIN 10451), Thesis, TU Munich, 2002 (in German). Xiao, J., Falkner,H.: Bond behaviour between recycled aggregate concrete and steel rebars. Construction and Building Materials, 2007, vol. 21, pp. 395–401. Prince, M. J. R., Singh, B.: Bond behaviour between recycled aggregate concrete and deformed steel bars. Materials and Structures, 2014, vol. 47, pp. 503–516.
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21. Prince, M. J. R., Singh, B. (2014): Investigation of bond behaviour between recycled aggregate concrete and deformed steel bars. Structural Concrete, 15: 154–168. doi: 10.1002/ suco.201300042. 22. Bureau of Indian Standards: IS 2770 (Part I) 1967 (reaffirmed 2002). Methods of Testing Bond in Reinforced Concrete Part I Pullout Test. New Delhi, India, 1967. 23. fib: Model Code for Concrete Structures 2010. Ernst & Sohn, Berlin, 2013. 24. Kim, Y., Sim, J., Park, C.: Mechanical properties of recycled aggregate concrete with deformed steel rebar. Journal of Marine Science and Technology, 2012, vol. 20, No. 3, pp. 274–280. 25. Bureau of Indian Standards: IS 81121989 (reaffirmed 2005). 43 Grade Ordinary Portland CementSpecification. New Delhi, India, 1989. 26. Bureau of Indian Standards: IS 2386 (Part IV) – 1963 (Reaffirmed 2007). Methods of test for aggregates for concrete. Part IV Mechanical properties. New Delhi, India 1963. 27. Nagataki, S., Saeki, T., Iida, K.: Recycled Concrete as Aggregate. CANMET/ACI International Symposium on Sustainable Development of the Cement and Concrete Industry, Ottawa, Canada, 1998, pp. 131–146. 28. Bureau of Indian Standards: IS 3831970 (reaffirmed 2002). Specification for Coarse and Fine Aggregate from Natural Sources for Concrete. New Delhi, India, 1970. 29. Perera, S. V. T. J., Mutsuyoshi, H.: Shear behavior of reinforced highstrength concrete beams. ACI Structural Journal, 2013, vol. 110, No. 1, pp. 43–52.
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30. Kim, S. W., Yun. H. D.: Influence of recycled coarse aggregates on the bond behavior of deformed bars in concrete. Engineering Structures, 2013, vol. 48, pp. 133–143. 31. Harajli, M. H.: Development/splice strength of reinforcing bars embedded in plain and fibre reinforced concrete. ACI Journal, 1994, vol. 91, No. 5, pp. 511–520.
M. John Robert Prince, M.Engg. Research Scholar Department of Civil Engineering Indian Institute of Technology Roorkee Roorkee 247 667, India Tel: +91 9458947809 princeiitr@gmail.com
Bhupinder Singh, PhD (corresponding author) Associate Professor Department of Civil Engineering Indian Institute of Technology Roorkee Roorkee 247 667, India Telefax: +91 1332 285885 bhupifce@iitr.ernet.in, bsiitr@gmail.com
Technical Paper Boyan Mihaylov
DOI: 10.1002/suco.201400044
Fivespring model for complete shear behaviour of deep beams This paper presents a fivespring model capable of predicting the complete pre and postpeak shear behaviour of deep beams. The model stems from a twoparameter kinematic theory (2PKT) for the shear strength and displacement capacity of deep beams under single curvature. Four of the springs of the model represent the shear resistance mechanisms of the beam, while the fifth spring models the flexural behaviour. The model predicts not only the load–displacement response, but also the deformation patterns of the beam and how these patterns change with increasing load. Validation studies are performed by using 28 tests from the literature, showing excellent results. The model is used to interpret the tests and to draw conclusions about the behaviour of deep beams. It is shown that shear strength variations of up to 60 % between nominally identical specimens can be caused by variations in the path of the critical shear cracks. It is also demonstrated that loss of bond of large reinforcing bars increases the shear capacity of deep beams. Finally, the fivespring model is shown to predict the postpeak shear behaviour effectively, which is important for the analysis of structures under extreme loading. Keywords: deep beams, shear, kinematic model, displacement capacity, postpeak response
1
Introduction
Deep beams have relatively small shearspantodepth ratios (a/d < approx. 2.5) and carry shear by direct compression between the loads and the supports. This loadbearing mechanism is associated with large stiffness and large shear strength compared with beams with larger a/d ratios (slender beams). Owing to these properties, deep beams are used, for example, as transfer girders in buildings, carrying heavy loads from discontinuous columns or shear walls, see Fig. 1. Such girders are essential for structural safety as their failure can result in the partial or complete collapse of the structure. Even though transfer girders are usually conservatively designed, they can be overloaded by rare events such as the February 2011 earthquake in Christchurch, New Zealand, which produced unforeseen vertical ground accelerations of up to 1.8g. As buildings
* Corresponding author: boyan.mihaylov@ulg.ac.be Submitted for review: 02 June 2014 Revised: 13 August 2014 Accepted for publication: 18 August 2014
are typically designed with little or no consideration of vertical ground accelerations, a number of structures with transfer girders were on the verge of collapse and had to be demolished. In such extreme events the ability of the structure to remain standing depends on its capacity to redistribute the forces from the damaged transfer girders to other structural members. The extent of such force redistribution in turn depends on the displacement capacity and postpeak behaviour of the transfer girders. For this reason, the evaluation of complex structures with deep beams requires accurate and computationally effective models for predicting the complete nonlinear behaviour of the beams. The behaviour of deep beams can be predicted by using nonlinear finite element models. Such models, however, require significant time for modelling and computation, and thus become impractical when complex structures need to be analysed under various loads. In addition, FE models are not effective in capturing the postpeak behaviour of shearcritical deep beams. Postpeak shear behaviour is characterized by large sliding deformations along a few (typically one) wide diagonal cracks, whereas FE models are better suited to situations with distributed deformations. Taking this into account, Kaneko and Mihashi [1] have proposed a simplified mechanical model based on the FE approach where the deformations away from the critical diagonal cracks are neglected. In this model the damage along the critical crack is represented by a band of cracked concrete that is modelled with a smeared rotating crack formulation. Another approach that can be viewed as a simplified version of nonlinear FE models is stress field modelling [2]. This approach neglects the tensile stresses in the concrete and provides a clear visualization of the flow of forces in the member. Strutandtie models, which are typically used for strength calculations and design [3]–[6], have also been used for the analysis of deep beams. In order to predict the complete behaviour of the member, researchers have proposed nonlinear constitutive relationships for the struts and ties [7]–[10]. However, this approach faces significant difficulties related to the modelling of the complex distribution of deformations in the cracked concrete of deep beams by using simple constant strain struts. Furthermore, important phenomena such as sliding displacements and aggregate interlock along the critical diagonal cracks are not accounted for in strutandtie models.
© 2015 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete (2015), No. 1
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B. Mihaylov · Fivespring model for complete shear behaviour of deep beams
slender beam transfer girder
deep beam
Fig. 1. A deep beam in a building
Explicit modelling of the critical diagonal cracks in deep beams has recently been included in a twoparameter kinematic theory (2PKT) proposed by Mihaylov et al. [11]. This rational approach focuses on the ultimate shear strength and displacement capacity of deep beams subjected to single curvature. The 2PKT also includes explicit modelling of the critical loading zones (CLZ) that trigger the shear failure of deep beams. In this paper the 2PKT approach will be extended to a nonlinear fivespring model to capture the complete pre and postpeak behaviour of shearcritical deep beams. The fivespring model aims to combine simplicity with accuracy as required for the analysis of complex structures with deep beams such as the structure shown in Fig. 1.
2
Kinematic model for deep beams
The fivespring model is based on a kinematic model for the shear spans of deep beams subjected to single curvature [11], [12], Fig. 2. The kinematic model describes the
Fig. 2. Kinematic model for deep beams under single curvature
72
Structural Concrete (2015), No. 1
complete deformed shape of the shear span with the help of the two deformation patterns shown in Fig. 2a. Each of these patterns is defined by a single kinematic parameter or degree of freedom (DOF). The upper deformation pattern is a function of the average strain in the bottom flexural reinforcement εt,avg within the cracked portion of the shear span. The lower pattern is a function of the vertical displacement Δc that develops in the CLZ of the beam. The complete deformed shape of the shear span is obtained by superimposing the two deformation patterns. The main assumptions underlying the kinematic model are that the beam develops a critical diagonal crack and that the concrete above this crack behaves like a rigid block. The concrete below the critical crack, on the other hand, is characterized by a pattern of radial flexureshear cracks with their centre at the loading point. This zone is modelled as a “fan” of rigid radial struts pinned at the loading point and connected to the bottom reinforcement. In the deformation pattern associated with DOF εt,avg, the rigid block and struts rotate about the loading point relative to the section with maximum bending moment. In the deformation pattern associated with DOF Δc, the fan remains undeformed and the rigid block translates vertically relative to the fan. It can be seen from Fig. 2a that DOF εt,avg can be associated with flexural deformations, DOF Δc with shear deformations. Fig. 2b summarizes the geometry of the kinematic model which has been defined elsewhere [11], [12]. The effective width of the loading plate lb1e given by Eq. (1) corresponds to the portion of the plate responsible for the shear force V (with the pressure under the plate assumed to be uniformly distributed). As will be discussed later, lb1e determines the size of the CLZ and has a significant influence on the behaviour of deep beams. Another important geometrical parameter is the angle θ1 between the critical crack and the axis of the beam, given by Eq. (2). This angle is determined with the help of two other angles: angle
B. Mihaylov Âˇ Fivespring model for complete shear behaviour of deep beams
Îą of the diagonal of the shear span and angle Î¸ of the shear cracks obtained from sectional shear models for slender beams. In deep beams the critical crack typically propagates from the inner edge of the support plate and therefore Îą1 = Îą. In order to capture the transition from deep to slender beams, however, Îą1 should not be taken smaller than the angle Î¸ valid for zones away from concentrated loads. Angle Î¸ is obtained from a shear strength calculation according to the sectional shear provisions of Canadian code CSA 2004 [4] or level of approximation 3 in fib Model Code for Concrete Structures 2010 [13], [14]. Both of these provisions are based on the simplified modified compression field theory [15], which relates the inclination of the shear cracks to the strain in the flexural reinforcement at shear failure. The calculation of Î¸ is performed for a section at a distance 0.9d from the inner edge of the loading plate but no further than onehalf of the clear shear span. The sectional shear strength Vsect obtained from this calculation will also be used for evaluating the behaviour of deep beams as explained in section 4.1. Eqs. (3) and (4) define additional geometrical parameters shown in Fig. 2a. With the geometry of the kinematic model defined, the deformations of the shear span of the beam can be obtained from the equations in Fig. 2c. These equations are derived by using small displacement kinematics based on the assumptions of the kinematic model [11], [12]. All deformations are expressed as functions of DOFs Îľt,avg and Î”c. Eqs. (5)â€“(8) define the complete displacement field of the shear span in an xz coordinate system attached to the section with maximum bending moment. These equations can be used to derive important relationships such as Eq. (9) for the strain Îľv in the transverse reinforcement (stirrups) halfway along the critical crack. The fraction in this equation is the average strain along the length of the stirrup and the factor 2 accounts approximately for the strain concentration at the critical crack. Strain Îľv will be used later to evaluate the shear force transferred across the critical crack by the stirrups. The shear transferred by aggregate interlock, on the other hand, will be evaluated as a function of the width of the critical crack w and the slip at crack s halfway along the critical crack, given by Eqs. (10) and (11) respectively. It can be seen from these equations that the widening of the crack is associated with both DOFs of the kinematic model, whereas the slip at the crack depends on DOF Î”c and the strain Îľd in the strut adjacent to the critical crack. The shortening of the strut below the critical crack reduces the slip at the crack caused by DOF Î”c. Note that strain Îľd is generally neglected in the kinematic model except for the calculation of the slip at the crack. Finally, the kinematic model can be used to express the deflection Î” of the shear span of the beam as a function of DOFs Îľt,avg and Î”c. The deflection is defined as the relative vertical displacement between the support and the section with maximum bending moment, assuming that the latter section remains vertical. This displacement can be obtained directly from Eq. (8) by replacing coordinate x with the length of the shear span a:
'
H t, avglt a 'c d
't 'c
(12)
V CLZ Vci
V, Î”
Vd Vs
Î”c
shear behaviour
flexural behaviour
Î”c
Î” t = Î”  Î”c
V= ÎŁ Vi
V=T (0.9d)/a
Î”c
Î” d Îľ t,avg = at l t
displ. shear DOFs kinematic model
VCLZ CLZ d
Vci
Îą =Îą
Vs
1
V
Vd
VCLZ cot Îą C ~ ~ 0.9d T
lt a
Fig. 3. Fivespring model for deep beams
where Îľt,avglt is the elongation of the flexural reinforcement and Îľt,avglt/d is the angle of rotation of the rigid block about the loading point. When the rotation is multiplied by the distance from the loading point to the support, it produces the deflection Î”t associated with DOF Î”t,avg. The deflection is increased by the vertical displacement Î”c in the CLZ. Eq. (12) forms the basis of the fivespring model for deep beams.
3 3.1
Fivespring model Main assumptions
According to Eq. (12), the deflection of the shear span of a deep beam consists of two components: Î”t related to the strains in the flexural reinforcement and Î”c related to the shear deformations. Based on this, the shear span can be represented by two sets of springs connected in series and loaded by shear force V, see Fig. 3. The set of four parallel springs elongates by Î”c and represents the shear behaviour of the member; the fifth spring of the model elongates by Î”t and represents the flexural behaviour of the beam. The forces in the four parallel springs are shown in the freebody diagram of the rigid block in Fig. 3. Force VCLZ is the shear carried in the critical loading zone, Vci is the aggregate interlock shear along the critical crack, Vs is the shear carried by the stirrups and Vd is the shear resisted by the dowel action of the flexural reinforcement. The sum of these forces is the shear V obtained from vertical equilibrium of the rigid block. The force in the flexural spring, on the other hand, is the shear derived from moment equilibrium of the shear span. The
Structural Concrete (2015), No. 1
73
B. Mihaylov Âˇ Fivespring model for complete shear behaviour of deep beams
equilibrium is calculated about the point of application of the compression force C in the section with maximum moment. This equilibrium results in a shear force V = T(0.9d)/a, where T is the tension force in the flexural reinforcement and 0.9d is the estimated lever arm between forces C and T. Based on the above, the equilibrium of the forces in the fivespring model can be expressed as follows: VCLZ Vci Vs Vd
Es AsH t, avg
0.33 fc 1 200H t, avg
Ac, eff d As fy
(14)
where the first term of this expression models the behaviour of bare elastic reinforcement, the second term accounts for the tension stiffening effect of the concrete [16], Asfy is the yield force of the bottom reinforcement and Ac,eff is the area of the concrete around the bottom reinforcing bars which provides tension stiffening for the bars. The width of this area is taken as equal to the width of the section b and the depth of the area is estimated as the minimum of 2.5(hd) and h/2 [5]. The shear VCLZ carried by the CLZ is derived with the help of Fig. 4 as a function of DOF Î”c. The CLZ has a triangular shape that depends on the effective width of the loading plate lb1e and the angle of the critical crack in the vicinity of the load approximated by angle Îą [11]. The concrete in the CLZ is subjected to diagonal compressive stresses Ďƒ and strains Îľ. The strains are assumed to vary linearly from zero at the top face of the beam to Îľmax along the bottom inclined face of the zone. Taking into account the deformed configuration of the CLZ, strain Îľmax is expressed as a function of DOF Î”c as shown in Fig.Â 4. The diagonal compressive stresses Ďƒ are calculated from the strains Îľ by using an appropriate stressâ€“strain relationship for the concrete under uniaxial compression [17]. In order to evaluate the diagonal compressive force in the CLZ, the average stress in the concrete Ďƒavg is multiplied by the area of the section passing through the edge of the loading plate and perpendicular to the bottom face of the CLZ. This diagonal force is shown in the triangle of forces in Fig. 4. Based on this triangle, the shear carried in the critical loading zone VCLZ is expressed as follows:
74
Îľm
Îą
ax
Î”c
sÎą co
b
tan Îą
3l b1e
sin
1e
(Îľ m
g Ďƒ av
)b
ax
Îą
l b1e
Îą
VCLZ
Fig. 4. Critical loading zone (CLZ)
VCLZ
kV avg[H max('c )]blb1e sin 2 D
(15)
Constitutive relationships for the springs
In order to evaluate the equilibrium given by Eq. (13), forces VCLZ, Vci, Vs, Vd and T need to be expressed as functions of displacements Î”c and Î”t or, equivalently, as functions of the DOFs of the kinematic model Î”c and Îľt,avg. DOF Îľt,avg can be obtained from Î”t based on Eq. (12) as shown in Fig. 3. In the cracked stage of the behaviour of the member, the force in the flexural reinforcement T is expressed with strain Îľt,avg as follows: T
Ďƒ
3l
(13)
If the four parallel springs fail first, the beam is predicted to fail in shear along a critical diagonal crack. If the flexural spring yields first, this would mean that the bottom flexural reinforcement has yielded at the section with maximum moment.
3.2
Îą
Îľ
Îľ max =
sÎą co
T(0.9d) / a
Î”c
Î”c
V
VCLZ l b1e
Structural Concrete (2015), No. 1
The additional coefficient k in this expression accounts for the fact that in slender beams the angle of the critical crack in the vicinity of the load is typically smaller than angle Îą. This is because the cracks in slender members are not straight, as assumed in the kinematic model, but have an â€œsâ€? shape. Coefficient k is calculated as proposed in the 2PKT [11]: k
^
`
min max ÂŞ1 2 cot D 2 , 0Âş ,1 ÂŹ Âź
(16)
Based on the above, it follows that the relationship between VCLZ and Î”c has the same shape as the relationship between average stress and maximum strain. The latter relationship is obtained from the stressâ€“strain diagram for concrete in compression by averaging the stresses from zero strain up to the current strain. Note that owing to this averaging, the behaviour of the CLZ is predicted to be less brittle than that of a concrete cylinder. The shear carried by aggregate interlock Vci is the next component in the equilibrium condition Eq. (13). This force is expressed with the average shear stress vci transferred across the critical crack by means of interlocking of the rough crack surfaces: Vci
0.18vcibd
(17)
The stress vci is evaluated halfway along the critical crack as a function of crack width w and crack slip s given by Eqs. (10) and (11) respectively. Relationship vci (w,s) is computed according to the contact density model (CDM) proposed by Li et al. [18]. In the CDM the crack surfaces are represented by a series of planes at different angles. Planes at the same angle on each side of the crack are connected by contact springs that have an elasticâ€“perfectly plastic behaviour in compression and zero resistance in tension. Depending on the crack width and the direction of the movement at the crack, some of the springs are active (planes are in contact) while others are at zero stress (no contact). The forces in the springs are projected on axes perpendicular and parallel to the crack direction. In this way the CDM accounts for compressive stresses on the crack surfaces (clamping stresses) which enhance the shear resistance vci. As the clamping stresses are neglected in the fivespring model, the shear resistance obtained
B. Mihaylov Âˇ Fivespring model for complete shear behaviour of deep beams
Hd
C VCLZ cot D
(18)
Ecbc
where ICI = T is the compression force in the section with maximum bending moment and VCLZ.cotÎą is the horizontal component of the compression force in the CLZ, see Fig. 3. The difference between these two forces is the horizontal component of the compression force in the radial struts. In order to estimate Îľd, this force is divided by the area of the compression zone (b.c) where the struts join, and by the elastic modulus of the concrete Ec. The depth of the compression zone c is estimated as in the flexural theory for cracked sections: c
nU
2 2 l
2nUl nUl d
V v Uvb(d cot D1 l0 1.5lb1e )
Vd
Equilibrium
1000
V=ÎŁVi 800 600
w/o tension stiffening
VCLZ
400
Vs
200
Vci Vd
0 0
0.2
0.4
0.6
Î” /Î” c
0.8
1
(Î” = 8.0 mm)
Fig. 5. Equilibrium of forces in fivespring model for an applied displacement Î”
3.3
(20)
where the transverse reinforcement ratio Ď v should not be taken larger than 0.15fc/fyv and the value in the brackets should not be less than 0.5dcotÎą1. For members without transverse reinforcement, Vs is zero and the fivespring model reduces to a fourspring model. Finally, the dowel action force Vd in Eq. (13) is expressed as follows: 2Âş ÂŞ 12EsS db4 db3 ÂŤ Â§ T Âˇ Âť nb 'c d nb fy 1 Â¨ Â¸ 3lk ÂŤ ÂŠ As fy Âš Âť 64lk3 ÂŤÂŹ ÂťÂź
V=T(0.9d)/a
1200
Overview of solution procedure
(19)
where Ď l = As/bd is the ratio of flexural reinforcement and n = Es/Ec. The next term in Eq. (13) is the shear Vs carried across the critical diagonal crack by the stirrups. The strain in the stirrups Îľv is given by Eq. (9) as a function of DOFs Îľt,avg and Î”c. The stress in the stirrups Ďƒv is obtained from Îľv on the basis of an elasticâ€“perfectly plastic stressâ€“strain relationship for the steel. The shear Vs is then expressed by multiplying stress Ďƒv by the area of the stirrups that are effective in providing shear resistance [11]: Vs
1400
Shear forces, kN
from the CDM is reduced by a factor of 0.18 adopted from Vecchio and Collins [16]. When calculating vci, special consideration needs to be given to Eq. (11) for the slip at the critical crack. The second term of this equation depends on strut strain Îľd, which is not a direct function of the DOFs of the kinematic model. This strain is estimated in the following approximate manner:
(21)
where nb is the number of bottom flexural bar dowels, db the bar diameter and lk the length of the bar dowels given by Eq. (4). The first part of Eq. (21) is derived by assuming that the dowels behave like elastic fixedfixed beams subjected to a relative transverse support displacement Î”c. The upper limit on force Vd corresponds to the formation of plastic hinges at the ends of the dowels. The expression in the square brackets of this limit accounts for the reduced moment capacity of the plastic hinges due to the tension in the bars T [11] and should not be less than zero.
The fivespring model of Fig. 3 is solved under increasing deflection Î” to obtain the complete shear force vs. deflection response for the shear spans of deep beams. Since the deflection of the shear span is imposed, the only kinematic unknown of the model is the elongation of the set of four parallel springs Î”c (elongation of flexural spring Î”t equals Î”Î”c). Elongation Î”c and shear force V are obtained by solving equilibrium equation Eq. (13). The solution of this equation for a given Î” is explained with the help of Fig. 5 prepared for a sample deep beam. The horizontal axis of the figure shows the full range of possible values of Î”c from zero to Î”, normalized with respect to Î”. The vertical axis reproduces the shear forces in Eq. (13) obtained from Eqs. (14), (15), (17), (20) and (21). These forces are functions of the DOFs of the kinematic model Î”c and Îľt,avg, where the latter DOF is obtained from the elongation of the flexural spring Î”t as shown in Fig. 3. When Î”c is zero, DOF Îľt,avg has a maximum and the deformed shape of the beam is described by the upper deformation pattern in Fig. 2a only (pure flexural deformations). Since Îľt,avg is a maximum, the tension in the bottom reinforcement T and the corresponding shear T(0.9d)/a also have a maximum, as is evident from the thick black line in Fig. 5. Contrary to this, the sum of the shear forces transferred across the critical crack ÎŁVi (thick red line) has a minimum as these forces depend mainly on DOF Î”c. For example, the shear Vci carried by aggregate interlock is zero because the critical crack is open and slip at the crack is zero. The only nonzero shear component is Vs since the stirrups are strained when Î”c = 0. In the other limit case when Î”c = Î”, DOF Îľt,avg is zero and the deformed shape of the beam is described only by the lower deformation pattern in Fig. 2a (pure shear deformations). In this case the thick black line is at zero whereas the shear resistance ÎŁVi is either in the pre or postpeak regime depending on the magnitude of Î”. Since the thick black and red lines represent the two sides of equilibrium equation Eq.Â (13), the intersection of the lines corresponds to the solution of the
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75
B. Mihaylov Âˇ Fivespring model for complete shear behaviour of deep beams
equation. The intersection is found iteratively by using the bisection method. The ordinate of the intersection point is the shear force V corresponding to the imposed deflection Î”. The bisection method is applied with increasing values of Î” to compute the complete VÎ” response of the member.
shear at diagonal cracking Vcr,sh is proportional to the cracking force Ncr of the zone influenced by the bottom reinforcement:
4 4.1
where
Comparisons of predicted and measured behaviour Specimens S1M and S1C
Vcr,sh
N cr The fivespring model is used to predict the behaviour of two deep beam specimens, S1M and S1C, tested to failure at the University of Toronto [19]. These beams were simply supported and loaded with a point load in the middle of the span. The only difference between the two tests was that specimen S1M was loaded monotonically whereas S1C was subjected to reversed cyclic loading. The effective depth of the section was d = 1095 mm (h = 1200 mm) and the shearspantodepth ratio a/d was 1.55. The beams had symmetrical top and bottom longitudinal reinforcement with a ratio Ď l = 0.70Â % and stirrups with a ratio Ď v = 0.10Â %. The compressive strength of the concrete on the day of beam testing was fc = 33.0Â MPa. Table 1 summarizes the properties of the specimens as well as the measured and predicted failure loads. Both specimens failed in shear along critical diagonal cracks prior to yielding of the flexural reinforcement. As the beams were symmetrical, the fivespring model is used to model onehalf of the beams (one shear span). The upper plot in Fig. 6 shows the measured and predicted responses of specimens S1M and S1C. The horizontal axis is the midspan deflection of the beams, the vertical axis is the shear force. It can be seen that the two green curves, which represent the envelopes of the measured responses, almost overlap. This shows that the load reversals applied to specimen S1C did not cause significant strength or stiffness degradation. It can also be seen that the red prediction curve matches the experimental curves well in both the prepeak and postpeak regimes. The prediction curve consists of a nonlinear part produced by the fivespring model and a trilinear curve for the initial response. The latter curve models the behaviour prior to the development of the deformation patterns assumed in the kinematic model. The first point along this curve corresponds to the flexural cracking at the section with maximum moment (shear Vcr,fl). This point is obtained based on flexural beam theory by using transformed sectional properties. The cracking is assumed to occur when the stress in the concrete at the bottom of the section reaches 0.63âˆš âŽŻfc [6]. The flexural cracking is followed by the propagation of the first radial flexureshear crack at a distance scr from the midspan section along the bottom reinforcement, see Fig. 2a. Further load increments result in the propagation of more radial cracks away from the flexural crack until the critical diagonal crack forms under a shear force Vcr,sh. This load level corresponds to the second point in the initial trilinear response. The radial cracks and the critical crack initiate at the bottom of the section in the zone influenced by the flexural reinforcement. In beams without web reinforcement, these cracks propagate almost instantaneously to the vicinity of the load. Therefore, it is assumed that the
76
Structural Concrete (2015), No. 1
1.5N cr
0.9d a
(22)
[ Ac, eff (n 1)As ]0.63 fc
(23)
The factor of 1.5 in Eq. (22) accounts approximately for the load increase between the occurrence of the first radial crack and the propagation of the critical diagonal crack. The deflection Î”cr,sh under shear Vcr,sh is obtained from Eq. (12) of the kinematic model by taking Î”c = 0 and assuming a shorter cracked length along the bottom reinforcement:
'cr,sh
H t, avg lt lk scr d
a
(24)
The last point from the initial trilinear response corresponds to the breakdown of beam action and the transition to the deformation patterns assumed in the fivespring model. This point is defined by the sectional shear capacity Vsect obtained from the Canadian code or fib Model Code 2010 [4], [13]. If Vsect is larger than the peak resistance obtained from the fivespring model, the beam is considered slender and the fivespring model is not applicable. It can be seen from the plot that the trilinear curve matches the initial response of specimens S1M/S1C well. The upper plot in Fig. 6 also shows the predicted shear resistance mechanisms and how they vary with increasing deflection. The main contribution to the shear resistance is provided by the critical loading zone (VCLZ) whose failure is predicted to trigger the shear failure of the beam. This result is consistent with the main assumption underlying the 2PKT: the peak shear response of the member coincides with the peak response of the CLZ. Significant shear resistance is also provided by the stirrups (shear Vs), which are predicted to yield at a deflection of about 3.5 mm. The aggregate interlock mechanism Vci reaches its maximum when the member is in the postpeak regime, and vanishes at a deflection of about 14.5 mm. At this deflection the critical crack is very wide (w â‰ˆ 10 mm) and thus the crack surfaces are not in contact any more, regardless of the large slip at the crack (s â‰ˆ 7 mm). Finally, the dowel action shear Vd is predicted to have an effect mainly on the postpeak behaviour of beams S1M and S1C. The lower plot in Fig. 6 shows the evolution of the deflections in specimens S1M and S1C associated with the two deformation patterns of the kinematic model. Ratio Î”t/Î” shows the portion of the deflection due to the flexural deformation pattern, whereas Î”c/Î” is the portion due to the shear pattern. It can be seen from the prediction line that, initially, the deformations are mostly flexural. The shear deformations begin to develop rapidly just prior to shear failure, and at the end of the test they account for almost 90Â % of the total deflection. It can also be
400 400 400 400 400 400 400 400 400 400 600 600 800 800 1000 1000 1200 1400 1400
1095 1095 1095 1095 1095 1095 1095 1095 1070
d (mm)
475 475 475 475 475 475 475 475 475 475 675 675 905 905 1105 1105 1305 1505 1505
1200 1200 1200 1200 1200 1200 1200 1200 1200
h (mm)
200 200 200 400 400 400 600 600 600 600 900 900 1200 1200 1500 1500 1800 2100 2100
1700 1700 1700 1700 2500 2500 2500 2500 1700
a (mm)
100 100 100 100 100 100 100 100 100 100 150 150 200 200 250 250 300 350 350
300 300 300 300 300 300 300 300 300
lb1* (mm)
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
V/P
** Obtained with α1 = 50° and lt = 1850 mm based on experimental observations.
* lb2 = 150 mm for tests by Mihaylov et al. and lb2 = lb1 for tests by Salamy et al.
240 240 240 240 240 240 240 240 240 240 360 360 480 480 600 600 720 840 840
Salamy et al. [21] B2 0.50 B3 0.50 B4 0.50 B6 1.00 B7 1.00 B8 1.00 B101 1.50 B102 1.50 B11 1.50 B12 1.50 B10.31 1.50 B10.32 1.50 B131 1.50 B132 1.50 B14 1.50 B17 1.50 B15 1.50 B16 1.50 B18 1.50
b (mm)
400 400 400 400 400 400 400 400 400
a/d
Mihaylov et al. [19], [20] S1M 1.55 S1C 1.55 S0M 1.55 S0C 1.55 L1M 2.28 L1C 2.28 L0M 2.28 L0C 2.28 SB 1.59
Beam
Table 1. Test specimens investigated
2.02 2.02 2.02 2.02 2.02 2.02 2.02 2.02 2.02 2.02 2.11 2.11 2.07 2.07 2.04 2.04 1.99 2.05 2.05
0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.60
ρl (%)
5 5 5 5 5 5 5 5 5 5 9 9 10 10 14 14 18 18 18
6 6 6 6 6 6 6 6 1
nb
376 376 376 376 376 376 376 376 376 376 388 372 398 398 398 398 402 394 398
652 652 652 652 652 652 652 652 652
fy (MPa)
20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
20 20 20 20 20 20 20 20 20
ag (mm)
36.2 36.2 31.3 31.3 31.3 37.8 29.2 23.0 29.2 31.3 37.8 31.2 31.6 24.0 31.0 28.7 27.0 27.3 23.5
33.0 33.0 34.2 34.2 37.8 37.8 29.1 29.1 30.5
fc (MPa)
0 0.4 0.8 0 0.4 0.8 0 0 0.4 0.8 0 0 0 0 0 0.4 0 0 0.4
0.10 0.10 0 0 0.10 0.10 0 0 0
ρv (%)
398
398
376 376
376 376
376 376
490 490
490 490
fyv (MPa)
0.61 0.60 0.78 0.84 0.94 1.17 0.75 0.90 1.24 1.39 0.95 0.93 0.84 0.67 0.72 0.96 0.71 0.57 0.83
0.80 0.80 0.61 0.98 0.82 0.79 0.52 0.62 0.74 775.0 768.0 975.5 525.0 590.5 750.5 308.0 351.5 512.5 580.5 980.0 893.5 1492.5 1128.5 1984.5 2607.0 2695.0 2987.5 4198.0
941.0 943.0 721.0 1162.0 663.0 642.0 416.0 492.0 715.7
Mmax/Mn Vexp (kN)
761.4 761.4 699.6 452.2 464.8 – 293.6 259.8 – – 743.4 664.5 1191.6 1028.1 1790.0 2295.4 2330.9 3195.8 4232.4
909.3 909.3 770.3 770.3 652.4 652.4 404.6 404.6 724.7**
Vpred (kN)
3.2 4.8 1.9 2.8 2.8 3.3 3.8 5.3 14.7 7.1 6.6 8.6 11.9 9.3 9.3 11.9 11.9 10.6 15.8
7.7 8.4 6.4 10.9 14.2 13.7 10.0 11.1 9.5
Δexp (mm)
1.0 1.0 1.1 2.5 2.6 – 4.1 4.5 – – 6.0 6.1 8.0 8.6 10.1 12.4 12.2 14.1 17.6
7.5 7.5 6.7 6.7 12.6 12.6 9.6 9.6 8.9**
Δpred (mm)
B. Mihaylov · Fivespring model for complete shear behaviour of deep beams
Structural Concrete (2015), No. 1
77
B. Mihaylov · Fivespring model for complete shear behaviour of deep beams 1000 900 800
exp.
700
V, kN
600
Vsect
500
model
VCLZ 400
Vcr,sh 5sm
300
Vs
V cr,fl
200
Vci
100
Vd
0 0
2
4
6
8
10
12
14
16
18
Δ, mm
Normalized deflection
1
4.2
0.8
model
Δt /Δ
0.6 0.4
exp S1C
Δc /Δ
0.2 0 0
2
4
6
8
10
12
14
16
18
Δ, mm Fig. 6. Measured and predicted responses of specimens S1M and S1C
Δ = 4.3 mm exp.
Δ = 6.2 mm model
Δ = 8.2 mm (shear failure)
Δ = 11.0 mm (postpeak)
Fig. 7. Measured (triangular mesh) and predicted (green dots) deformed shapes x30 – specimen S1C
seen that the model matches well the experimental points from test S1C, with the exception of the first point, which is overpredicted. The sudden increase in shear deformations between the first and second points can be attributed to the breakdown of beam action at V = Vsect. Fig. 7 shows the complete deformed shapes of specimen S1C for four displacement levels. The triangular meshes show the measured deformed shapes and the green dots show the predicted locations of the vertices of
78
the triangles. The first three diagrams correspond to the second, third and fifth experimental points in the lower plot of Fig. 6. The diagram at bottom right shows the predicted deformations only since measurements of deformed shapes were not performed in the postpeak regime of the beam. It can be seen that the fivespring model provides excellent approximations for the measured deformed shapes of specimen S1C from the stage of breakdown of beam action to the shear failure of the beam. The first deformed shape resembles the flexural deformation pattern of the kinematic model since, initially, DOF Δc is relatively small. The shear deformation pattern emerges clearly in the diagram at bottom left, which corresponds to the shear failure of the beam. In the postpeak regime, the shear deformations continue to increase, whereas the bottom reinforcement unloads and the flexural deformations decrease.
Structural Concrete (2015), No. 1
Effect of size of CLZ
As discussed in relation to Fig. 6, the critical loading zone (CLZ) is predicted to have a major effect on the behaviour of deep beams. At the same time, the size and shape of this zone is very sensitive to the exact location of the critical diagonal crack in the vicinity of the loading plate, see Fig. 4. The fivespring model can therefore be used to investigate the effect of variations in the path of the critical crack on the shear response of deep beams. Such an analysis is performed for two other tests performed at the University of Toronto: specimens S0M and S0C [19]. These beams were very similar to specimens S1M and S1C except that they did not have stirrups, see Table 1. As before, specimen S0M was loaded monotonically whereas S0C was subjected to reversed cyclic loading. The envelopes of the measured load–displacement responses of these beams are shown in Fig. 8. It can be seen from the green and blue curves in Fig. 8 that specimens S0M and S0C behaved in an almost identical manner up to a shear force of about 550 kN. Following this load level, however, the cyclically loaded specimen exhibited a much stronger response than the specimen loaded monotonically (60 % greater shear strength). This counterintuitive result can be explained with the help of the fivespring model. The prediction of the model without modifications is shown by the red line in the plot. This prediction slightly overestimates the shear strength of specimen S0M and significantly underestimates that of S0C. The two black prediction lines in the plot are obtained by scaling the effective width of the loading plate lb1e from Eq. (1). A smaller lb1e means that the critical crack propagates towards a point that is closer to the inner edge of the loading plate, and thus the CLZ is smaller, see Fig. 4. Inversely, a larger lb1e means a larger CLZ because the critical crack propagates towards a point that is further along the loading plate. It can be seen from the lower black line that a scale factor of 0.85 results in an accurate prediction of the response of specimen S0M. Similarly, a factor of 2 allows for an accurate prediction of the response of specimen S0C. These results are consistent with the two photographs in Fig. 8, which show the CLZs of the beams after failure. It can be seen that the CLZ of specimen S0M was significantly smaller than that of S0C due to
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Fig. 9. Measured and predicted VΔ responses of Toronto test series
Fig. 8. Effect of size of critical loading zone (CLZ) lb1e on shear behaviour of deep beams
the different paths of the critical cracks in the vicinity of the loading plates. This difference cannot be attributed to the load reversals in test S0C because the reversals were performed after the critical diagonal crack had fully propagated. The difference is instead explained by local variations in the concrete properties which affected the path of the critical cracks. By comparing the curves in Figs. 8 and 6, it can be concluded that the addition of 0.10 % of stirrups in specimens S1M and S1C effectively eliminated this effect.
4.3
Effect of spantodepth and transverse reinforcement ratios
Specimens S0M/C and S1M/C were part of a larger experimental programme that involved nine shearcritical deep beam specimens, see Table 1. The first eight of these specimens were designed to study the effect of loading history (monotonic vs. reversed cyclic loading), amount of transverse reinforcement (no stirrups vs. ρv = 0.10 %) and effect of shearspantodepth ratio (a/d = 1.55 vs. 2.28) [19]. The envelopes of the measured load–displacement responses of these beams (except for S0C) are shown by thin lines in Fig. 9, whereas the predictions of the fivespring model are shown by thick lines. The red and green curves were already discussed in reference to Figs. 6 and 8 respectively. By comparing these curves once again, it can be seen that the stirrups in specimens S1M/C resulted in a significant increase in shear strength, also slightly less brittle postpeak behaviour. Specimens L1M and L1C were
similar to S1M and S1C but had a longer shear span a. These members with a/d = 2.28 can be considered as being in the transition zone between deep and slender beams. The fivespring model provides excellent predictions for the prepeak behaviour of the two beams but underestimates their postpeak resistance. This conservative prediction is attributed to the modelling of the shear resistance provided by the transverse reinforcement. The large deformations in the postpeak regime of slender beams result in the activation of more stirrups along the shear span than assumed in Eq. (20). Specimens L0M and L0C, on the other hand, had no stirrups and exhibited a more brittle response, captured by the fivespring model. Similarly to specimens S0M/C, the two longer beams without stirrups had significantly different shear strengths, which were attributed to variations in the path of the critical diagonal cracks.
4.4
Effect of bond between flexural reinforcement and concrete
The last specimen from the Toronto series discussed in this paper is specimen SB [20], see Table 1. This beam had the same overall dimensions as specimens S0M/C but was reinforced with a single #18 (57 mm dia.) headed bar placed 130 mm from the bottom of the section. Fig. 10 shows the load–displacement response of the specimen and the measured crack pattern of the beam at shear failure. The big bar caused splitting of the concrete cover on the bottom face of the beam, which resulted in an almost complete loss of bond between bar and concrete. This was confirmed by strain gauge measurements along the bar which showed a nearly constant strain profile from anchor head to anchor head prior to failure. Owing to the loss of bond, the beam did not develop diagonal cracks but only two steep flexureshear cracks, one on each side of the midspan section. The shear failure occurred along one of these cracks, with crushing of the concrete in the CLZ.
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Fig. 10. Response of specimen SB reinforced with a single #18 (57 mm dia.) headed bar
Fig. 11. Response of beams from size effect series
If the fivespring model is applied to specimen SB without modifications, the angle of the critical crack Îą1 is predicted to be 36.4Â° (Eq. (2)) and the length of the bottom reinforcement lt in the cracked part of the shear span is 1450 mm (Eq. (3)). With these values, the model significantly underestimates the shear strength of the beam, as is evident from the dotted red line in Fig. 10. In order to improve this prediction, a second analysis is performed with geometrical parameters Îą1 and lt estimated from the test. The angle of the critical crack is estimated to be 50Â° based on the crack diagram of the beam at shear failure. Since the strains in the reinforcing bar were constant from anchor head to anchor head, lt is taken as equal to the full length of the bar in the shear span (lt = 1850 mm). It can be seen from Fig. 10 that with these input parameters, the fivespring model provides an excellent approximation of the measured loadâ€“displacement response of specimen SB for shear forces > approx. 450 kN. Note that the prediction curves do not include the initial trilinear part of the response used in the previous comparisons because this approach does not account for splitting of the concrete cover. The difference between the two prediction curves is mainly due to the shear resisted by aggregate interlock. According to Eqs. (10) and (11), the steeper the critical crack (larger Îą1), the larger is the slip at the crack in comparison to the width of the crack. This results in more effective interlocking of the rough crack surfaces and thus a larger shear resistance component Vci. Comparing the two prediction curves in Fig. 10 allows us to conclude that the loss of bond between the flexural reinforcement and the concrete enhanced the shear strength of specimen SB.
fourpoint bending. The main variables in the tests were the shearspantodepth ratio (a/d = 0.5â€“1.5), the effective depth of the section (d = 400â€“1400 mm) and the ratio of transverse reinforcement (Ď v = 0â€“0.8%). The behaviour of two of these beams, B17 and B18, is shown in Fig. 11 in terms of shear force vs. midspan deflection. The difference between the two beams was the effective depth of the section (d = 1000 mm for B17 vs. d = 1400 mm for B18) and the compressive strength of the concrete (fc = 28.7 MPa vs. fc = 23.5 MPa). Both beams failed in shear but exhibited a relatively ductile postpeak response, as is evident from the green experimental curves in Fig. 11. The fivespring model is used to predict the behaviour of the shear spans of beams B17 and B18 in the same way as was done for the Toronto specimens. In order to predict the behaviour of the entire member, however, the deformations in the pure bending region between the two shear spans also need to be taken into account. The constant curvature Ď† in this region of length Lf contributes to the midspan deflection of the beams as follows:
4.5
Tests by Salamy et al.
The fivespring model is further validated with the help of 19 tests on deep beams reported by Salamy et al. [21]. The properties of the test specimens are summarized in Table 1. The beams were loaded to failure under symmetrical
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'
Â§ L2 L a Âˇ '5sm I Â¨ f f Â¸ Â¨ÂŠ 8 2 Â¸Âš
(25)
where Î”5sm is the deflection of the shear spans of length a modelled with the fivespring model. Curvature Ď† is estimated by assuming that the section has cracked and that the concrete and steel behave linearly:
I
Va Ec Icr
(26)
where V is the shear force obtained from the fivespring model for given deflections of the shear span Î”5sm and (V.a) is the bending moment in the constant moment region. The cracked moment of inertia of the section Icr is obtained from Icr
bc 3 / 3 nAs d c
2
(27)
B. Mihaylov · Fivespring model for complete shear behaviour of deep beams
'cx  0.5'c cot D1
(28)
Displacement Δcx of the CLZ increases the deflection of the shear span as shown by the deformed shape in Fig. 11. If Δcx ≠ 0 and Δc = εt,avg = 0, the rigid block of the kinematic model rotates about fulcrum O through an angle Δcx/d. This angle, multiplied by the distance from O to the support, produces an additional deflection Δcxa/d; this deflection is added to the deflection from Eq. (25). The prediction curves for specimens B18 and B17 with the additional deflection are shown by thick red lines in Fig. 11. It can be seen that the suggested simple approximation for Δcx is very effective for capturing the complete load–deflection response of the beams, including their relatively ductile postpeak behaviour. Finally, this procedure is applied to all 19 specimens tested by Salamy et al. [21] and the results are summarized in Table 1 and Fig. 12. Three of the specimens (B8, B11, B12) are excluded from the comparisons because the measured loadbearing capacity significantly exceeded the predicted flexural capacity (Mmax/Mn = 1.17, 1.24 and 1.39 respectively). The left plot in Fig. 12 compares the experimentally measured and predicted shear strengths of the specimens. It can be seen that the fivespring model predicts the peak resistance of the beams very well, since the dots corresponding to the tests are grouped along the diagonal of the plot. The plot on the right shows that the deflections at shear failure are also reasonably well predicted, with the exception of the smallest specimens, which showed very large experimental scatter.
5
Conclusions
This paper presents a physical fivespring model for predicting the complete load–deflection response of deep beams under single curvature. The model is based on a kinematic model with two degrees of freedom (DOF)
5000
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, kN
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pred
3000
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4000
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V
where the depth of the compression zone c is evaluated using Eq. (19). The result from the above procedure for specimen B18 is shown by the dotted red line in Fig. 11. The dotted black line in the plot shows the predicted contribution of the curvature φ to the midspan deflection of the beam. It can be seen that the model predicts the shear strength well but underestimates the total deflections. This result is attributed to the assumption that the critical loading zones undergo a pure vertical displacement Δc. This assumption is suitable for the Toronto beams because they had large amounts of top longitudinal reinforcement, which stiffened the CLZ against horizontal deformations. For the tests by Salamy et al., however, it is suggested that the horizontal shortening of the CLZ, denoted by Δcx, be taken into account in a simple manner. It is assumed that the direction of the displacement in the CLZ remains constant throughout the loading history, and thus Δcx is proportional to Δc. Based on this assumption, the limiting cases for Δcx are zero (vertical displacement in CLZ) or Δc cotα1 (displacement parallel to critical diagonal crack). For the sake of simplicity, it is assumed that the actual displacement is the average of these two limiting displacements and thus
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Fig. 12. Experimental and predicted shear strengths and displacement capacities – tests by Salamy et al.
which describes the deformation patterns in deep beams. The two DOFs are the average strain in the bottom flexural reinforcement and the vertical displacement in the critical loading zone (CLZ). The fivespring model was applied to 28 tests from the literature and produced excellent predictions of both pre and postpeak shear behaviour. The model also predicts the components of shear resistance and how they vary with increasing deflections. This feature of the model was used to interpret the results from the tests and to draw the following conclusions regarding the behaviour of deep beams: The CLZs in deep beams have a major effect on the shear behaviour. At the same time, the shapes and sizes of these zones are very sensitive to the exact location of the critical diagonal crack in the vicinity of the loads. It was shown with the help of the model that random variations in the path of the critical crack can explain differences in shear strength of up to 60 % observed between nominally identical specimens without web reinforcement. Large diameter bars in deep beams can result in splitting of the concrete cover and loss of bond between reinforcement and concrete. The fivespring model was adapted to capture the response of such a beam. With the help of the model it was shown that the loss of bond in deep beams results in an increased shear strength. It was shown that in some cases an accurate prediction of the deflections in deep beams may require the introduction of a third DOF in the kinematic model: the horizontal displacement in the CLZ. Such displacement was accounted for in a simple manner, resulting in accurate predictions. A more explicit account of this DOF can provide further insights into the behaviour of deep beams.
Notation a shear span ag maximum size of coarse aggregate Ac,eff area of concrete providing tension stiffening for bottom reinforcement As area of longitudinal bars on flexural tension side b width of crosssection d effective depth of section C compression force in section with maximum moment c depth of compression zone db diameter of bottom longitudinal bars Ec elastic modulus of concrete
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Es fc fy fyv h Icr k Lf l0 lb1 lb1e lb2 lk lt Mmax Mn Ncr n nb P s scr T V Vexp Vpred Vcr,fl Vcr,sh Vsect VCLZ Vci vci Vd Vs w α α1 δx δz φ θ Δ Δexp Δpred Δcr,sh Δ5sm Δc Δt
82
elastic modulus of steel concrete cylinder strength yield strength of bottom longitudinal bars yield strength of stirrups total depth of section moment of inertia of cracked section crack shape factor length of pure flexure region length of heavily cracked zone at bottom of critical diagonal crack width of loading plate parallel to longitudinal axis of member effective width of loading plate parallel to longitudinal axis of member width of support plate parallel to longitudinal axis of member length of dowels provided by bottom longitudinal reinforcement length of bottom reinforcement within cracked part of shear span maximum bending moment in beam corresponding to measured shear strength predicted flexural capacity of section cracking force of zone influenced by bottom reinforcement ratio of elastic moduli of steel and concrete number of bottom longitudinal bars applied concentrated load slip displacement in critical diagonal crack distance between radial cracks along bottom longitudinal reinforcement tensile force in bottom reinforcement shear force measured shear strength predicted shear strength shear corresponding to flexural cracking shear corresponding to the propagation of critical diagonal crack sectional shear strength shear resisted by CLZ shear resisted by aggregate interlock aggregate interlock shear stress shear resisted by dowel action shear resisted by stirrups width of critical diagonal crack halfway along crack angle of line extending from inner edge of support plate to far edge of tributary area of loading plate responsible for shear force V angle of critical diagonal crack displacement along x axis displacement along z axis curvature in pure flexure region angle of diagonal cracks in uniform stress field midspan deflection of beam measured midspan deflection at shear failure predicted midspan deflection at shear failure midspan deflection corresponding to Vcr,sh deflection of shear span given by fivespring model transverse displacement of CLZ deflection of shear span due to elongation of bottom longitudinal reinforcement
Structural Concrete (2015), No. 1
ε εmax εd εt,avg εv ρl ρv σ σavg σv
diagonal compressive strains in CLZ maximum diagonal compressive strain in CLZ average compressive strain along radial strut adjacent to critical diagonal crack average strain in bottom longitudinal reinforcement strain in transverse reinforcement in critical diagonal crack halfway along crack ratio of bottom longitudinal reinforcement ratio of transverse reinforcement diagonal compressive stress in CLZ average diagonal compressive stress in CLZ stress in transverse reinforcement
References 1. Kaneko, Y., Mihashi, H.: Shear Softening Characteristics of Reinforced Concrete Deep Beams. Finite Element Analysis of RC Structures, American Concrete Institute, SP23714, 2006, pp. 205–225. 2. Ruiz, M. F., Muttoni, A.: On Development of Suitable Stress Fields for Structural Concrete. ACI Structural Journal, vol. 104, No. 4, 2007, pp. 495–502. 3. Schlaich, J., Schäfer, K., Jennewein, M.: Toward a Consistent Design of Structural Concrete. PCI Journal, vol. 32, No. 3, 1987, pp. 74–150. 4. CSA Committee A23.3.: Design of Concrete Structures, Canadian Standards Association, Mississauga, Ontario, 2005. 5. European Committee for Standardization: EN 199211 Eurocode 2: Design of Concrete Structures – Part 11: General Rules and Rules for Buildings. CEN, Brussels, 2004. 6. ACI Committee 318: Building Code Requirements for Reinforced Concrete (ACI 31808) and Commentary (318R08). American Concrete Institute, Farmington Hills, Mich., 2008. 7. Salem, H. M., Maekawa, K.: ComputerAided Analysis of Reinforced Concrete Using a Refined Nonlinear Strut and Tie Model Approach. Journal of Advanced Concrete Technology, vol. 4, No. 2, 2006, pp. 325–336. 8. Eom, T. S., Park, H. G.: Secant Stiffness Method for Inelastic Design of StrutandTie Model. ACI Structural Journal, vol. 107, No. 6, 2010, pp. 689–698. 9. Scott, R. M., Mander, J. B., Bracci, J. M.: Compatibility StrutandTie Modeling: Part I – Formulation. ACI Structural Journal, vol. 109, No. 5, 2012, pp. 635–644. 10. Barbachyn, S. M., Kurama, Y. C., Novak, L. C.: Analytical Evaluation of Diagonally Reinforced Concrete Coupling Beams under Lateral Loads. ACI Structural Journal, vol. 109, No. 4, 2012, pp. 497–507. 11. Mihaylov, B. I., Bentz, E. C., Collins, M. P.: TwoParameter Kinematic Theory for Shear Behavior of Deep Beams. ACI Structural Journal, vol. 110, No. 3, 2013, pp. 447–456. 12. Mihaylov, B. I., Bentz, E. C., Collins, M. P.: A Two Degree of Freedom Kinematic Model for Predicting the Deformations of Deep Beams. CSCE 2nd Intl. Engineering Mechanics & Materials Specialty Conf., Jun 2011. 13. fib  International Federation for Structural Concrete. fib Model Code for Concrete Structures 2010. Berlin: Verlag Ernst & Sohn, 2013. 14. Sigrist, V., Bentz, E. C., Ruiz, M. F., Foster, S., Muttoni, A.: Background to the fib Model Code 2010 Shear Provisions – Part I: Beams and Slabs. Structural Concrete, vol. 14, No. 3, 2013, pp. 195–203. 15. Bentz, E. C., Vecchio, F. J., Collins, M. P.: Simplified Modified Compression Field Theory for Calculating Shear
B. Mihaylov · Fivespring model for complete shear behaviour of deep beams
16.
17. 18.
19.
20.
Strength of Reinforced Concrete Elements. ACI Structural Journal, vol. 103, No. 4, 2006, pp. 614–624. Vecchio, F. J., Collins, M. P.: The Modified CompressionField Theory for Reinforced Concrete Elements Subjected to Shear. ACI Structural Journal, vol. 83, No. 2, 1986, pp. 219–231. Popovics, S.: A Review of Stress–strain Relationships for Concrete. ACI Journal, vol. 67, No. 3, 1970, pp. 243–248. Li, B., Maekawa, K., Okamura, H.: Contact Density Model for Stress Transfer Across Cracks in Concrete. J. Faculty Eng., University of Tokyo (B), vol. 40, No. 1, 1989, pp. 9–52. Mihaylov, B. I., Bentz, E. C., Collins, M. P.: Behavior of Large Deep Beam Subjected to Monotonic and Reversed Cyclic Shear. ACI Structural Journal, vol. 107, No. 6, 2010, pp. 726–734. Mihaylov, B. I., Bentz, E. C., Collins, M. P.: Behavior of Deep Beams with Large Headed Bars. ACI Structural Journal, vol. 110, No. 6, 2013, pp. 1013–1021.
21. Salamy, M. R., Kobayashi, H., Unjoh, S.: Experimental and Analytical Study on RC Deep Beams. Asian Journal of Civil Engineering (AJCE), vol. 6, No. 5, 2005, pp. 409–422.
Boyan Mihaylov, PhD Assistant Professor University of Liege Department of ArGEnCo Building B52, Room +1/417 Chemin des Chevreuils, 1 B4000 Liège, Belgium boyan.mihaylov@ulg.ac.be
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Technical Paper LinYun Zhou Zhao Liu* ZhiQi He
DOI: 10.1002/suco.201400005
Further investigation of transverse stresses and bursting forces in posttensioned anchorage zones In the posttensioned anchorage zone, the load transfer path of an anchor force can be visualized by an infinite number of isostatic lines of compression (ILCs). The method was initially proposed by Guyon and recently attracted significant interest from a number of researchers. Based on the work of these predecessors, an updated mathematical model has been proposed in order to analyse the bursting forces and the distribution of transverse stresses in the anchorage zone. Compared with the results of a finite element analysis, the updated equations are more accurate than the previous ones. Based on the observation that the sixthorder polynomial expression is better than the fourthorder one, as far as the solution of bursting stresses is concerned, it can be reasonably postulated that a de facto function of the ILCs must exist. Additionally, it is equally interesting that the bursting forces derived with the updated analytical model are the same as those obtained with the formula in the current AASHTOLRFD Bridge Design Specifications based on numerical stress analyses. Keywords: anchorage zones, isostatic lines of compression, distribution of transverse stresses, bursting forces
1
Introduction
In a posttensioned anchorage zone, the spread of a concentrated force from the body of the member produces transverse tensile stresses, also known as bursting stresses, along the tendon path. The resultant of the bursting stresses is usually called the bursting force. In practice, both the bursting force and the distribution of bursting stresses are used to plan the reinforcing details in the anchorage zone. Over the past decades, considerable efforts have been made to quantify the bursting forces and transverse stress distributions in the posttensioned anchorage zone. Unfortunately, theoretical solutions of elasticity were hardly available in this scenario because of formulaic obstacles [1]. Therefore, numerical and experimental methods have been sought by many researchers. Christodoulides [2] studied the distribution of transverse stresses in the anchorage zone via photoelastic tests. Based on experimental studies, Zielinski and Rowe [3, 4] proposed an
* Corresponding author: mr.liuzhao@seu.edu.cn Submitted for review: 23 January 2014 Revised: 21 April 2014 Accepted for publication: 25 May 2014
84
empirical formula for calculating bursting forces. Yettram [5] demonstrated transverse stress distributions for multiple and eccentric anchorages by using finite element analysis. After substantial numerical investigations, Foster [6] found that the distribution of bursting stresses was flatter and occurred over a longer disturbed region than is predicted by the linear solution. Since the 1980s, strutandtie models (STMs) have been emerging as an efficient tool for modelling and detailing Dregions in structural concrete members. Some typical STMs for obtaining the bursting forces behind the anchorage devices have been suggested by Marti [7], Schlaich [8] and Breen [9]. In the early 1990s The University of Texas at Austin carried out dozens of model tests of anchorage zones [10]. Based on the results of those tests and finite element analyses, Eq. (1) was proposed for calculating the bursting forces for a typical anchorage zone, and this has been adopted in the AASHTOLRFD Bridge Design Specifications [11] since 1994. Tb
ÂŚ P(1 ha ) 0.5ÂŚ (P sin D )
0.25
(1)
for which the location of the bursting force is taken as db
0.5(h 2e) 5e sin D
(2)
where: P anchor force of a single anchor P sum of anchor forces of a group of anchors h depth of beam a width of bearing plate in direction of beam depth Îą tendon inclination e eccentricity
ÎŁ
In the case of a concentric anchorage zone as shown in Fig. 1, Eqs. (1) and (2) can be reduced to Tb
0.25P(1
db
0.5h
a ) h
(3) (4)
Table 1 summarizes formulas for calculating the bursting forces currently specified in several codes (AASHTO 2010, ACI 31808 2008, CEB FIP 1993 and PTI 2000). However, no strict theoretical derivation can be found in current literature from the perspective of elasticity.
ÂŠ 2015 Ernst & Sohn Verlag fĂźr Architektur und technische Wissenschaften GmbH & Co. KG, Berlin Âˇ Structural Concrete (2015), No. 1
L.Y. Zhou/Z. Liu/Z.Q. He · Further investigation of transverse stresses and bursting forces in posttensioned anchorage zones
Fig. 1. A strutandtie model for the concentric anchorage zone
As a matter of fact, as early as the 1950s, an alternative conceptual model depicting the force flow for the anchorage zone was proposed by Guyon [15, 16], a wellknown French engineer. In his monographs, isostatic lines of compression (ILCs) were used to describe the stress dispersion path in the anchorage zone. Unfortunately, the idea of ILCs did not attract attention until recent advancements in quantifying the ILCs in polynomial expressions by Sahoo et al. [17] and He et al. [18].
2 2.1
Existing equations for ILCs Original isostatic lines of compression
As shown in Fig. 2, Guyon used the ILCs to describe the dispersion of tensile and compressive stresses in a typical anchorage zone [15], which is a disturbed region with an approximately square shape. There are infinite ILCs throughout the anchorage zone. Guyon reasoned that all the ILCs must be parallel to the anchor force at both the nearend section AB and farend section CD. Each individual isostatic line transfers an equal share of the force, which induces a certain amount of transverse stress, the magnitude of which will depend on the curvatures of the ILCs. Therefore, the distribution of transverse stresses along the Xaxis can be sketched as shown in Fig. 2b, which has been verified by Tesar’s photoelastic experiments. Although the ILCs can be used to visualize the internal load transfer path in the anchorage zone and describe the transverse stress distribution along the tendon axis, no mathematical equations for the ILCs are given in Guyon’s monographs.
2.2
Fig. 2. Dispersion of compression in an anchorage zone: a) isostatic lines of compression, b) distribution of transverse stresses along the tendon axis
Equations proposed by Sahoo et al.
Fig. 3. ILCs in the concentric anchorage zone as proposed by Sahoo et al.
the bursting forces by introducing certain boundary conditions. For the Cartesian coordinate system adopted in a typical anchorage zone as shown in Fig. 3, the vertical ordinate of an ILC at section AB is yi, and its vertical ordinate at section CD, yi, can be obtained by using the principle of geometric similarity such that
y
yi , y
x 0
a ha (y ) h i 2
yj
x l
(5)
The ILCs must be parallel to the anchor force P at section AB and section CD, which requires that
Following Guyon’s original concept, Sahoo et al. presented a mathematical expression for the ILCs for concentric anchorage zones and derived an equation for estimating
dy dx x
0, 0
dy dx x
0
(6)
h
Table 1. Four different formulas for bursting forces in different codes
Code
AASHTO
ACI 31808
CEB FIP
PTI
Bursting force Tb
a) 0.25P(1 – – h
a) 0.25P(1 – – h
a) 0.25P(1 – – h
a) 0.35P(1 – – h
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L.Y. Zhou/Z. Liu/Z.Q. He Âˇ Further investigation of transverse stresses and bursting forces in posttensioned anchorage zones
By assuming the curvatures of the ILCs are zero at section AB, we get d2y dx2 x
0
(7)
0
Further, the transverse stresses should vanish at section CD, i.e. d2y dx2 x
0
(8)
h
Using the previous six boundary conditions, a fifthorder polynomial equation can be obtained for the ILCs: y
(2 yi h)(h a)x3 (5h2 30hx 12x2 ) 4ah5
yi
(9)
Based on the relationship between the curvature of the ILCs and the transverse stresses in the monographs of Guyon, the distribution of transverse stresses along the tendon path ĎƒT can be derived as h/2
Âł0
VT
d2y V dy dx2 CD i
a 15P 4 (1 )(h2x 3hx2 2x3) (10) h 2h t
Âłh/2 V T t dx
Tb
Tb
(11)
h
2.3
Modified equations proposed by He et al.
0.79h
(12)
Comparing the transverse stress distribution behind the bearing plate predicted by Eq. (10) with the numerical solution obtained by finite element analysis (FEA) revealed an imperfection hidden in Sahooâ€™s mathematical model [19]. He et al. modified the equations by abandoning the questionable boundary condition, Eq. (7), used by Sahoo et al. By relocating the Cartesian coordinates as shown in Fig. 4 and denoting the vertical ordinate of the ILCs at section CD as yi, the vertical ordinate at section AB can be derived: y
x h
y j, y
x 0
yi
a y h j
(13)
Now, using the five boundary conditions of Eqs. (6), (8) and (13), a fourthorder polynomial equation for the ILCs can be written:
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Structural Concrete (2015), No. 1
(14)
h/2
Âł0
d2y V dy dx2 CD i
3P(h a) (3x2 4hx h2 ) 2h4t
(15)
h
Âłh/3 V T t dx
a 2P (1 ) h 9
(16)
The location of the bursting force db can be taken as h
The location of the bursting force db can be expressed as follows: db
(h a)x2 3 2 8 a ( 2 x x 6) ] h h h3 h
Then, the transverse stress distribution along the tendon axis ĎƒT can be expressed as
db
Âłh/2 xV T t dx h Âłh/2 V T t dx
y j[
The bursting force Tb can be found using
By integrating the transverse tensile stresses along the tendon path, the bursting force Tb can be obtained from a 15P (1 ) h 64
y
VT
where: ĎƒCD = P/(ht) normal stresses at section CD t thickness of anchorage zone a/h bearing plate ratio
h
Fig. 4. ILCs in the concentric anchorage zone
Âłh/3 xV T t dx h Âłh/3 V T t dx
0.67h
(17)
For the case of an eccentric anchorage zone, He et al. have also established the mathematic expressions for the bursting stresses, bursting forces and their locations as follows [18]: h 2e 9P(h 2e a)(h 2e)2 (x )[ x (h 2e)] (18) 3 3 3 2h (h 2e) t
VT
Tb
2P a (1 J )2(1 J ) 9 h
(19)
db
0.67h(1 J )
(20)
where e is the eccentricity and Îł = 2e/h the tendon eccentricity ratio.
2.4
Verification of existing equations
In order to check the accuracy of the equations proposed by Sahoo et al and He et al, a typical anchorage zone was analysed using their proposed equations and a finite element analysis. For the twodimensional finite model shown in Fig. 5, the concrete body, taken as h Ă— 2h, is
L.Y. Zhou/Z. Liu/Z.Q. He Âˇ Further investigation of transverse stresses and bursting forces in posttensioned anchorage zones
the FEA results. Similarly, the transverse stress distribution using the modified equations of He et al. is also far from satisfactory when compared with the FEA results.
3 3.1
Updated equations for ILCs Equations for concentric loading
Fig. 5. Finite element model for the anchorage zone (30 Ă— 60 elements)
For the same problem as depicted in Fig. 4, in accordance with St. Venantâ€™s principle, section CD is the interface between the zone of disturbed stresses and the uniformly distributed stress zone, which means that the transverse stresses at this section should have diminished. As a result, the rate of transverse stress change along the Xaxis should approach zero as it approaches section CD, i.e.
Table 2. Bursting forces and their locations
wV y
Method
Bursting force Tb /P
Location db /h
Sahoo et al. He et al. FEA
0.14 0.13 0.15
0.79 0.67 0.5
Noting that the transverse stress is proportional to the curvature of the ILCs, this leads to d3 y dx3 x
modelled by fournode plane stress elements. The bearing plate ratio a/h is taken to be 0.4, Youngâ€™s modulus of concrete as 3.0 Ă— 104 MPa and Poissonâ€™s ratio as 0.2. The anchor force is applied as a uniform load within the footprint of the anchor plate, and the boundary conditions at the farend are restrained as shown in Fig. 5. The bursting forces and their locations calculated by the equations of Sahoo et al and He et al are summarized in Table 2. It can be seen that the bursting forces estimated by either Eq. (11) or Eq. (16) are in good agreement with the FEA results. However, the locations of the bursting forces obtained by Eqs. (12) and (17) are significantly different from the FEA results. The relative error is 58Â % and 34Â % for the equations of Sahoo et al. and He et al. respectively. Fig. 6 shows the distributions of the transverse stresses obtained along the tendon axis. The diagram indicates that there is a substantial discrepancy between the transverse stresses given by the equations of Sahoo et al. and
(21)
0
wx
(22)
0 h
According to the theory of elasticity [1], the compatibility equation and equilibrium differential equations for the planar stress problems can be obtained as follows: w2W xy w2 w2 ( V â€“ PV ) ( V â€“ PV ) 2(1 P ) x y y x wx w y wx 2 wy2 wW xy
wV y
Y wy wV xX wx
wx wW xy wy where: Îź Ďƒx Ďƒy â€“ X â€“ Y
(23)
(24)
Poissonâ€™s ratio normal stress in x direction normal stress in y direction sum of external forces in x direction sum of external forces in y direction
0.50
ĎƒT /Ďƒ 0
0.00 Sahoo et al. He et al. FEA
0.50 1.00
hP
a
x
1.50
Ďƒ 0 = P / (ht)
l h
2.00 0
0.1
0.2
0.3
0.4
0.5
Relative distance,
0.6
0.7
0.8
0.9
1
x/h
Fig. 6. Distribution of transverse stresses along the tendon axis
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L.Y. Zhou/Z. Liu/Z.Q. He Âˇ Further investigation of transverse stresses and bursting forces in posttensioned anchorage zones
Fig. 7. ILCs in the eccentric anchorage zone: a) small eccentric loading, b) large eccentric loading
Taking the derivative of Eq. (24) with respect to x and y, then, respectively,
Therefore, the bursting force along the tendon axis Tb,1 can be written as
w2W xy
Tb,1
wx w y w2W xy
wx w y
w2V y wy2
(25)
0
(26)
And therefore d4y dx4 x
0
(27)
h
Using all seven boundary conditions, Eqs. (6), (8), (13), (22) and (27), a sixthorder polynomial equation for the ILCs can be derived as follows: y
ÂŞ(h a)x2 5x4 24x3 45x2 40x aÂş yi ÂŤ 15) Âť ( 4 3 2 3 h h h h h ÂŹ h Âź
(28)
where yi is vertical ordinate of an individual ILC at section CD. Since yi varies between â€“h/2 and h/2, all the ILCs can be expressed by Eq. (28). Using Eq. (28), the distribution of transverse stresses along the tendon path ĎƒT,1 can be derived: h/2
Âł0
V T ,1
h d2y 15P(h a) V dy  (x )(x h)3 5 h6t dx2 x i
(29)
Eq. (29) suggests two points of zero transverse stress: firstly, at x = h/5, i.e. the point of inflection on the ILCs, and, secondly, at x = h, the farend of the disturbed region. It can be shown that the transverse stress reaches its maximum value ĎƒT,max at x = 2h/5:
V T ,max
88
0.6P(h a) / (h2t)
Structural Concrete (2015), No. 1
a ) h
(31)
h
(30)
Âłh/5 xV T ,1t dx h Âłh/5 V T ,1t dx
db,1
3.2
wx 2
0.25P(1
Finally, the location of the bursting force db,1 can be expressed in the form
w2V x wx 2
Substituting Eq. (25) and the boundary conditions of secâ€“ â€“ tion CD (as shown in Fig. 4), i.e. X = 0, Y = 0, and Ďƒx = P/(ht) into Eq. (23) leads to w2V y
h
Âłh/5 V T ,1tdx
(32)
0.48h
Equations for eccentric loading
For some practical applications, the anchor force can be applied eccentrically on the end face. Guyon tactically transformed the case of eccentric into concentric by using the symmetrical prism approach [15]. The rules of the symmetrical prism state that the transverse dimension of the prism is equal to twice the smallest distance from the centreline of the tendon to the closest edge of the anchorage zone (the square area ACNM in Fig .7). It can be assumed that the dispersion of the anchor load would vanish at a longitudinal distance h2e from the anchor plate. In the case of an eccentric loading as shown in Fig. 7, a set of seven boundary conditions can be established for an ILC in an eccentric anchorage zone: y
y j, y
x h 2e
dy dx x
0, 0
d2y dx2 x
dy dx x 0,
h 2e
x 0
yi
yj
a (h 2e)
(33)
(34)
0 h 2e
d 3y dx3 x
0, h 2e
d4y dx4 x
0
(35)
h 2e
A sixthorder polynomial equation can be written to satisfy the seven boundary conditions above. It can be proved that the equations for ILCs in eccentric anchorage zones can be attained by replacing h in Eq. (28) with h â€“ 2e. Therefore, the distribution of the transverse stresses along the tendon path in the eccentric anchorage zone ĎƒT,2 can be derived as
L.Y. Zhou/Z. Liu/Z.Q. He Âˇ Further investigation of transverse stresses and bursting forces in posttensioned anchorage zones
Fig. 8. ILCs in the concentric anchorage zone with inclined tendon
d2y V dy dx2 x i 15P(1 J a / h)(1 J )2 x 1 J x ( )[ (1 J )]3 h h 5 h(1 J )5t h/2 e
Âł0
V T ,2
(36)
where Ďƒx is normal stress at section CD, Îł = 2e/h the tendon eccentricity ratio and 0 â‰¤ Îł < 1. The transverse stress reaches its maximum value ĎƒT,max when x = 2(h â€“ 2e)/5:
V T ,max
0.6P a (1 ) h(1 J )t h
(37)
The bursting force in the eccentric anchorage zone Tb,2 can be obtained as follows: Tb,2
h 2e
0.25P(1 J )2(1 J
Âł(h2e)/5 V T ,2tdx
a ) h
(38)
Finally, the location of the bursting force db,2 can be expressed as h 2e
db,2
3.3
Âł(h2e)/5 xV T ,2tdx h 2e Âł(h2e)/5 V T ,2tdx
0.48h(1 J )
(39)
x h
y j, y
x 0
yi
a( y j h tan T ) h(1 2 tan T )
(40)
tan T , 0
d2y dx2 x
0, h
dy dx x
d 3y dx3 x
h
W CD V CD
0, h
(41)
d4y dx4 x
0
(42)
h
where ĎƒCD and Ď„CD are the normal and shear stress respectively at the end of the body. Equations for the ILCs and the distribution of transverse stresses along the tendon axis can then be written (these equations are not shown here because of their complex form). The bursting force in the concentric anchorage zone with inclined tendon can be derived as Tb,3  0.25P(1
3.4
a a ) 0.5sin T(1 ) h h
(43)
Unified equation for bursting forces and locations
Based on updated equations for rectangular anchorage zones with single concentric, eccentric and inclined tendons, a unified equation for calculating bursting forces can be expressed as Tb
Equations for inclined loading
In the case of an anchorage zone with inclined tendons, both the horizontal and vertical components of the anchor force will determine the flow of the loads. As shown in Fig. 8, in the case of a concentric load with an inclination Î¸ applied to the rectangular anchorage zone, the ILCs must be parallel to the applied load at section AB and parallel to the direction of the principal compressive stress at section CD. Therefore, the boundary conditions for an ILC can be given by y
dy dx x
0.25P(1 J )2(1 J
a a ) 0.5sin T(1 ) h h
(44)
For the eccentric anchorage zone with inclined tendons, the location of the bursting force can be derived by integrating the transverse stress distribution along the tendon path: db  0.48h(1 J )
8e(1 J )2 sin T (1 J a / h)
(45)
In the case of concentric anchorage zones Îł = 0, Eq. (44) can be reduced to Eq. (43) for concentric anchorage zones with inclined tendons. Further, Eq. (43) can be simplified to Eq. (31) for concentric anchorage zones when Î¸ = 0.
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L.Y. Zhou/Z. Liu/Z.Q. He · Further investigation of transverse stresses and bursting forces in posttensioned anchorage zones 0.50
0.50 0.00
0.00 Sahoo et al. He et al. Eq. (36) FEA
1.00 1.50 2.00
σT /σ 0
σT /σ 0
0.50
σ 0 = P / (ht)
2.50
Sahoo et al. He et al. Eq. (36) FEA
0.50 1.00
σ 0 = P / (ht)
1.50 2.00
3.00 0
0.1
0.2
0.3
0.4
0.5
0.6
Relative distance,
x/h
0.7
0.8
0.9
0
1
0.1
0.2
0.3
0.5
0.6
Relative distance,
x/h
a / h = 0.2
0.7
0.8
0.9
1
a / h = 0.4
0.20
0.15
0.05
0.00
0.10
Sahoo et al. He et al. Eq. (36) FEA
0.25 0.40
σT /σ 0
σT /σ 0
0.4
0.30 0.45
σ 0 = P / (ht)
0.55
Sahoo et al. He et al. Eq. (36) FEA
0.15
σ 0 = P / (ht)
0.60
0.70 0
0.1
0.2
0.3
0.4
0.5
Relative distance,
0.6
0.7
0.8
0.9
0
1
0.1
0.2
0.3
0.4
0.5
Relative distance,
x/h
a / h = 0.6
0.6
0.7
0.8
0.9
1
x/h
a / h = 0.8
Fig. 9. Transverse stress distributions in concentric anchorage zones for different bearing plate ratios
4 4.1
Verification of the updated equations Comparison of distributions of transverse stresses
The aforementioned finite element model shown in Fig. 5 was used again to verify the accuracy of the updated equations. For the concentric case, Fig. 9 compares the transverse stress distribution along the tendon axis for the results of the FEA and the previous analytical equations with different bearing plate ratios. For the eccentric case, Fig. 10 illustrates the comparison of the distributions of transverse stresses with various eccentricities and constant bearing plate ratio a/h = 0.2. Provided that the FEA results represent the true distribution of the transverse stresses, it can be seen from Figs. 9 and 10 that the updated equation, Eq. (36), agrees better with the FEA results than the previous analytical equations proposed by Sahoo et al. and He et al.
4.2
Comparison of the bursting forces
A comparison of the bursting forces calculated using the FEA and the analytical methods for the concentric anchorage zone is shown in Fig. 11. It can be seen that the updated Eq. (44) agrees better with the FEA results. The average relative deviation is only about 3.8 %, whereas it is 5.7 and 8.6 % for the equations proposed by Sahoo et al. and He et al. respectively.
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Structural Concrete (2015), No. 1
4.3
Comparison of the locations of bursting forces
For the case of eccentric loading with an inclination θ = 10°, Fig. 12 shows the comparison of locations of bursting forces with various eccentricity ratios (the plate ratio is kept constant at a/h = 0.1) and Fig. 13 shows the influence of bearing plate ratio on the locations of bursting forces (the eccentricity is kept constant at 2e/h = 0.3). It can be seen that the results calculated with Eq. (45) are in good agreement with the FEA, whereas the formula in the AASHTO LRFD specifications, Eq. (2), results in a bigger discrepancy in most cases.
5
Towards the existence of an actual solution for ILCs
The major significance of this investigation not only lies in having made some improvements to the ILCs, but also to implying that a de facto function of the ILCs must exist as well. As was discussed, Eq. (14) is better than Eq. (9), and the updated Eq. (28) is better than Eq. (14). Encouraged by such gradual improvements, we may reasonably conceive that a real function for the ILCs would exist. With the help of a Taylor series, a general function of F(x) depicting the ILCs in the anchorage zone can be expressed as follows:
1.00
1.00
0.00
0.00 He et al. Eq. (36) FEA
1.00
ĎƒT /Ďƒ 0
ĎƒT /Ďƒ 0
L.Y. Zhou/Z. Liu/Z.Q. He Âˇ Further investigation of transverse stresses and bursting forces in posttensioned anchorage zones
2.00 3.00
2.00 3.00
Ďƒ 0 = P / (ht)
4.00
Ďƒ 0 = P / (ht)
4.00
0
0.1
0.2
0.3
0.4
0.5
Relative distance,
0.6
0.7
0.8
0.9
1
0
0.1
0.2
x / (h â€“ 2e)
0.3
0.4
1.00
0.80
0.00
0.00
ĎƒT /Ďƒ 0
He et al. Eq. (36) FEA
2.00
Ďƒ 0 = P / (ht)
3.00
0.6
0.7
0.9
1
x / (h â€“ 2e)
He et al. Eq. (36) FEA
0.80 1.60
Ďƒ 0 = P / (ht)
2.40
4.00
0.8
Îł = 0.4
b)
1.00
0.5
Relative distance,
Îł = 0.2
a)
ĎƒT /Ďƒ 0
He et al. Eq. (36) FEA
1.00
3.20
0
0.1
0.2
0.3
0.4
0.5
Relative distance,
0.6
0.7
0.8
0.9
0.1
0.2
0.3
0.4
0.5
Relative distance,
x / (h â€“ 2e)
Îł = 0.6
c)
0
1
0.6
0.7
0.8
0.9
1
x / (h â€“ 2e)
Îł = 0.8
d)
Fig. 10. Transverse stress distributions in the eccentric anchorage zones for different eccentricity ratios
0.25
0.65
Sahoo et al.
AASHTO
He et al.
Eq. (45)
0.60
FEM
Eq. (44)
0.15
db / h
Tb / P
0.20
FEA
0.10
0.55
0.50
0.05 0.00
0.45
0
0.1
0.2
0.3
0.4
Bearing plate ratio,
0.5
0.6
0.7
0.8
0
0.9
a/h
0.1
0.2
0.3
0.4
0.5
Fig. 12. Influence of eccentricity ratio on location of bursting force
Fig. 11. Influence of bearing plate ratio on bursting force
F(x)
F(h) F '(h)(x h) F (n)(h) n!
F ''(h) (x h)2 ... 2!
(46)
(x h)n o[(x h)n ]
where h is the position at the farend of the anchorage zone and o[(x â€“ h]n] is the Peano form of the remainder. Ignoring the Peano form of the remainder, F(x) can then be rewritten as F(x)
a0 a1(x h) a2(x h)2 ... an(x h)n
(47)
where a0, a1, a2, â€Ś, an are the coefficients to be determined by the boundary conditions of the ILCs at x = h. Actually, it can be proved that the modified Eq. (14) for ILCs, in the form of a 4th degree polynomial, is the first four terms of Eq. (47), and a0 = yj, a1 = a2 = 0 can be derived using the boundary conditions. Accordingly, Eq. (28) can be regarded as the first six terms of Eq. (47).
6
Conclusions
Following in the footsteps of Guyon, a further investigation of analytical equations for the transverse stresses and bursting forces has been carried out for anchorage zones
Structural Concrete (2015), No. 1
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L.Y. Zhou/Z. Liu/Z.Q. He · Further investigation of transverse stresses and bursting forces in posttensioned anchorage zones 0.80
AASHTO
0.75
7.
Eq. (45)
db / h
0.70
FEM
8.
0.65 0.60
9.
0.55 0.50
10.
0.45 0
0.1
0.2
0.3
0.4
Fig. 13. Influence of bearing plate ratio on location of bursting force
11.
for both concentric and eccentric forces. The main conclusions can be summarized as follows:
12.
1. The proposed equations for transverse stresses and bursting forces based on the updated ILC model are more accurate than the previous ones, which have been verified by the results of finite element analyses as shown in Figs. 9 and 10. 2. The proposed unified equations, Eqs. (44) and (45), can be used to predict the bursting forces and locations of bursting forces in a rectangular anchorage zone with different loading conditions. 3. It is interesting to note that the bursting forces derived using the updated ILC model is the same as the bursting forces given in the AASHTOLRFD Bridge Design Specifications, which was obtained by numerical elastic stress analyses. 4. It can be reasonably postulated that there exists a de facto function for the ILCs, although not completely revealed up to now.
Acknowledgements This study was supported by the National Natural Science Foundation of China (Grant No. 51278120 and Grant No. 51408116) and Jiangsu Province (Grant No. BK20140630). The authors also express their sincere thanks to Dr. Jianping Jiang of MMM Group Limited, Canada, for his valuable suggestions and the revision of this paper.
13. 14. 15. 16. 17.
18.
19.
zine of Concrete Research, vol. 49, No. 180, 1997, pp. 231–240. Marti, P.: Basic tools of reinforced concrete beam design. ACI Structural Journal, vol. 82, No. 1, 1985, pp. 46–56. Schlaich, J., Schäfer, K., Jennewein, M.: Toward a consistent design of structural concrete. Journal of the Prestressed Concrete Institute, vol. 32, No. 2, 1987, pp. 74–150. Breen, J. E., Burdet, O., Roberts, C., Wollmannn, G.: Anchorage zone reinforcement for posttensioned concrete girders. Rep. for NCHRP 1029, The University of Texas at Austin, Austin (TX), 1991. Burdet, O.: Analysis and design of anchorage zones for posttensioned concrete bridges. PhD thesis, The University of Texas at Austin, Austin (TX), 1990. AASHTO LRFD bridge design specification (SI units, 5th ed.), American Association of State Highway & Transportation Officials, Washington, D.C., 2010. ACI committee 318: Building Code Requirements for Structural Concrete (ACI 31808) and Commentary (ACI 318R08). Farmington Hills (MI), American Concrete Institute, 2008. CEBFIP: Model Code 1990. Thomas Telford Services Ltd, London, 1993. PostTensioning Institute. Anchorage Zone Design. Phoenix, AZ, 2000. Guyon, Y.: Prestressed concrete. Contractor’s Record Ltd, London, 1953, pp. 125–132. Guyon, Y.: Limitstate design of prestressed concrete. Applied Science Publishers Ltd, London, 1974, pp. 351–380. Sahoo, D. K., Singh, B., Bhargav, P.: Investigation of dispersion of compression in bottle shaped struts. ACI Structural Journal, vol. 106, No. 2, 2009, pp. 178–186. He, Z., Liu, Z.: Investigation of bursting force in anchorage zone: compressiondispersion models and unified design equation. ASCE Journal of Bridge Engineering, vol. 16, No. 6, 2011, pp. 820–827. Windisch, A.: Discussion of “Investigation of dispersion of compression in bottleshaped struts” by Dipak Kumar Sahoo, Bhupinder Singh and Pradeep Bhargava. ACI Structural Journal, vol. 107, No. 1, 2010, pp. 124–125.
LinYun Zhou Key Laboratory of Concrete & Prestressed Concrete Structures of Ministry of Education School of Civil Engineering Southeast University, Nanjing 210096, PR China
References 1. Timoshenko, S., Goodier, J. N.: Theory of Elasticity. McGrawHill book company, New York, 1951, pp. 22–26. 2. Christodoulides, S. P.: A photoelastic investigation of prestressesed concrete anchorage. Civil Engineering and Public Works Review, vol. 51, No. 1603, 1956, pp. 994–997. 3. Zielinski, J., Rowe, R. E.: An investigation of the stresses distribution in the anchorage zone of posttensioned concrete members. Res. Rep. Cement & Concrete Association, 1960. 4. Rowe, R. E.: End block stresses in posttensioned concrete beams. Structural Engineer, vol. 41, No. 2, 1963, pp. 54–68. 5. Yettram, A., Robbins, K.: Anchorage zone stresses in posttensioned uniform members with eccentric and multiple anchorages. Magazine of Concrete Research, vol. 22, No. 73, 1970, pp. 209–218. 6. Foster, S. J., Rogowsky, D. M.: Bursting forces in concrete panels resulting from inplane concentrated Loads. Maga
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Zhao Liu Key Laboratory of Concrete & Prestressed Concrete Structures of Ministry of Education School of Civil Engineering Southeast University, Nanjing 210096, PR China Tel. +86 25 8379 0780 Fax +86 25 8739 3718. Email: mr.liuzhao@seu.edu.cn
ZhiQi He Key Laboratory of Concrete & Prestressed Concrete Structures of Ministry of Education School of Civil Engineering Southeast University, Nanjing 210096, PR China
Technical Paper Ali Amin Stephen J. Foster* Aurelio Muttoni
DOI: 10.1002/suco.201400018
Derivation of the σw relationship for SFRC from prism bending tests The material characterization of steel fibrereinforced concrete (SFRC), which is required for its implementation in design codes, should be based on nominal properties that describe its postcracking strength in tension. In the case of brittle and quasibrittle materials, such as concrete, the tensile parameters are often derived indirectly. However, for materials with more ductility, such as SFRC, there is conjecture as to whether or not an indirect measure may be used to establish the stress versus crack opening displacement relationship, such as the use of a three or fourpoint prism test combined with an inverse analysis. In this paper a simple and efficient inverse analysis technique is developed and shown to compare well with data obtained from direct tension tests. Furthermore, the methodology proposed by the fib Model Code for Concrete Structures 2010 has been investigated and recommendations made to improve its accuracy. Keywords: steel fibre, concrete, inverse analysis, bending, uniaxial tension
1
fined deterministic relationship. This is summarized in Fig. 2, where CMOD is the crack mouth opening displacement as measured across the notch at the extreme tensile fibre in a flexural prism test. Although a direct tensile test is the most reliable method for determining the residual (postcracking) properties of SFRC [2–4], it is expensive. It requires specialized testing machines and can be timeconsuming in its preparation. For this reason, extensive efforts have been made to find a reliable model for obtaining the postcracking behaviour based on an inverse analysis of data obtained from either notched or unnotched prism bending tests [5–8]. However, although this methodology has been incorporated in the fib Model Code for Concrete Structures 2010 [8–10], the test data available at the time for full validation was somewhat limited [11].
σ
Introduction
Research in steel fibrereinforced concrete has a history of about 50 years [1] and its adoption in practice is developing. It is well established that the strength of unreinforced concrete in tension reduces quickly to zero after cracking. In steel fibrereinforced concrete (SFRC) the fibres are capable of bridging cracks and transmitting tensile force across them to enhance the postcracking tensile behaviour. One limitation in developing rational design models for SFRC in members and structures is the complexity of the test needed to characterize the fundamental tensile strength properties of the material, i.e. determining its postcracking, or residual, tensile strength. Prior to cracking, the characteristic behaviour of SFRC in tension is typically represented by its stressstrain response. After cracking, behaviour is described by the stress versus crack opening displacement (σw) relationship (Fig. 1). The σw response can be obtained through a uniaxial tension test or possibly by an indirect method using three or fourpoint bending tests on prism beam specimens in conjunction with an inverse analysis that assumes some prede
* Corresponding author: s.foster@unsw.edu.au Submitted for review: 27 February 2014 Accepted for publication: 14 July 2014
fct
matrix + fibres
f (w) fibres matrix
COD (w)
wT Fig. 1. Stress versus crack COD (w) for SFRC
F
F
Inverse Analysis σ CMOD
P
P
Direct w
P
w
Fig. 2. Approaches to determine the tensile properties of SFRC
© 2015 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin · Structural Concrete (2015)
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A. Amin/S. J. Foster/A. Muttoni Âˇ Derivation of the Ďƒw relationship for SFRC from prism bending tests
In this paper a physically based model is developed to predict the tensile response of strainsoftening SFRC from prism bending tests. To validate the model, tests were conducted for six series of matched uniaxial tension and prism bending tests for various fibre types and ratios, and for different flexural prism testing arrangements. The results of these matched tests are reported here and the model predictions presented. Finally, based on the model described, a Ďƒw relationship for the postcracking residual tensile strength of SFRC for use in design is proposed. The material law is compared with test data collected in this study and elsewhere, also with predictions obtained using the fib Model Code 2010 approach, and conclusions are drawn.
2 2.1
The Ďƒw model for SFRC Determination of contribution of fibres to strength of SFRC
h sp
D
dn (b) Stresses at crack
(a) Section
fw
(c) Simplified Model
dn
d r /2
T
fr1 2 fr2 dr 6 fw
(3)
and taking fr1 = fw(1 + Îą) and fr2 = fw(1 â€“ Îą), Eq. (3) becomes dr
3D dr 6
(4)
The shape of the compressive stress block (Fig. 4) changes from elastic to inelastic and depends on the compressive strength of the concrete and the state of loading. When elastic, the stress block is triangular and its centroid is positioned 0.67dn above the neutral axis (NA). If fully inelastic, then using the parabolicrectangular stressblock model of fib Model Code 2010 [10], its centroid is 0.60dn above the NA. For the case of the NA located at 0.2hsp, the internal lever arm changes from 0.92hsp to 0.93hsp, a < 1 % difference. In this paper the height of the stressblock centroid above the NA is taken as 0.64dn. Thus, from equilibrium (M = Tz) we can write fwdrb (0.64dn dr )
(5)
dr
hsp dn
(6)
Examination of Eqs. (4) to (6) reveals that we have three independent variables (fw, dn and Îą) and two dependent
a F/2 F/2
F
z
dr
h sp
dr
d r /2
D
fr1
fw
Fig. 4. Stresses at cracked section for SFRC prism in bending
Structural Concrete (2015)
(2)
a
CMOD
94
dr
C
f r2
fwdrb
where F is the externally applied force and a is the shear span (see Fig. 5). From geometry
Fig. 3. Model for inverse analysis of Ďƒw curve from prism bending tests
w
(1)
The centroid of the tensile stress block measured from the â€“ neutral axis d r is
f r2
notch
(fr1 fr2 )/2
where fr1 is the stress for w = 0 and fr2 is the stress at the notch root. From the sectional stress blocks (Fig. 4)
Fa 2
f r1
f(w)
fw
T
Fig. 3a shows the crosssection of an SFRC prism cracked in bending, where D is the total depth of the prism, hsp the depth minus the notch depth, dn the depth from extreme compressive fibre to neutral axis and b the width of the prism. On the compression side (Fig. 3b), the neutral axis rises in the section as the crack opens; on initial cracking the stress block is linear, becoming nonlinear as CMOD increases. The lever arm z (Fig. 4) is insensitive to the shape of the compressive stress block, however, and it is sufficiently accurate to assume the stress block to be linear throughout the analysis. For a small length on the tension side of the neutral axis (Fig. 3b), the concrete is uncracked and carries tension. At greater distances from the neutral axis, the concrete is cracked and the steel fibres carry a tensile stress f(w) that corresponds to a direct tensile stress for a crack opening w at the level in the section under consideration. Assuming that i) the tensile component of the uncracked concrete can be ignored, ii) the crack width is directly pro
b
portional to the distance from the neutral axis (rigid body rotation) and iii) the Ďƒw relationship is approximately linear over the range of crack widths of interest [12, 13], the tensile stress block can be simplified as shown in Fig. 3c. The stress on the Ďƒw curve for the average crack opening displacement (COD) between the root of the notch and the crack tip is denoted as fw, and is calculated as follows:
F/2
l 3point bending
F/2
F/2
l
F/2
4point bending
Fig. 5. Forces applied to threepoint and fourpoint bending prism specimens
A. Amin/S. J. Foster/A. Muttoni Âˇ Derivation of the Ďƒw relationship for SFRC from prism bending tests
â€“ variables (dr, d r), with one independent equation (Eq. (5)) to solve. The problem is twofold indeterminate and the solution thus intractable. Eq. (5) may be written as k1k2 2M 2 b hsp
k1k2Fa 2 b hsp
(7)
where k1 is a function of dn/hsp and Îą (k1 â‰Ľ 1), and can be determined from Eqs. (4) and (5) as 3 ÂŞÂŹ3.9 (0.85 D ) E ÂşÂź E
w
CMOD (hsp dn ) Â˜ 2 ( D dn )
Îą = 0.15
(8)
where Î˛ = 1 â€“ dn/hsp. Coefficient k2 is included in Eq. (7) to account for the influence of the notch on defining the crack path and the resulting influence on the measured tensile strength, as described in [14]. For the case of unnotched specimens, the critical crack will find a path of least resistance and failure occurs at sections where fibre distributions are at their lowest and thus the equivalent fibre dosage at the failure section is less than the average fibre dosage for the specimen. By contrast, in notched specimens the location of the failure plane is predefined by the location of the notch and the fibre volume fraction at the failure section will, on average, equal the supplied fibre dosage for the specimen. To convert the results of notched prism tests to those of unnotched uniaxial tensile tests, the factor k2 = 0.82 is applied, as described in [14, 15]. We shall now look more closely at parameter Îą and the location of the neutral axis depth dn. In Fig. 6 the value of k1 is plotted for different values of dn/hsp and varying Îą. The figure shows that over the range of interest k1 at 1.2 Âą 20 %, is relatively insensitive to the combination of Îą and dn. Hence, the determination of fw is somewhat insensitive to the values selected for Îą and dn. Taking Îą = 0.2 and dn = 0.2hsp results in k1 = 1.25 and k1k2 â‰ˆ 1. This is similar to the value determined in [8, 11] for the case where Îą = 0.2 and dn = 0.2hsp and where the notch effect is ignored (i.e. k2 = 1.0). To determine the crack opening displacement corresponding to the calculated value of fw, we assume i) rigid body rotations of the two prism halves centred about the crack tip and ii) failure occurs along a single dominant crack. The COD (w) for our Ďƒ w curve is obtained from the measured crack mouth opening displacement (CMOD) as shown in Fig. 4:
1.20
1.00
Îą = 0.0
0.80 0.00
0.10
0.20
Fig. 6. Ratio of the internal tensile force to the external applied force versus the neutral axis depth ratio dn/hsp for various values of Îą
1.4
1.2
hsp /D = 0.83 (EN 146512007)
1.0
0.8
hsp /D = 0.70 (JCIS0022003)
0.6 0.00
0.10
0.20
0.30
In Fig. 7 the ratio w/CMOD from Eq. (9) is plotted against the ratio dn/hsp for prisms with hsp/D = 0.83 (as per EN 14651 [9]) and hsp/D = 0.70 (as per JCIS002 [16]) and normalized against the value calculated for dn = 0. For the EN 14651 [9] testing configuration, the change in the ratio w/CMOD with hsp/D = 0.83 is 10 % from the condition soon after cracking (taken at dn/hsp = 0.4) to the time when the neutral axis is high in the section. For the JCIS002 configuration [16] the change is 17 %. Again, the results are somewhat insensitive to the neutral axis depth.
0.40
dn /h sp Fig. 7. Ratio of w/CMOD versus dn /hsp for prisms with hsp /D = 0.83 and hsp /D = 0.70
For design, an appropriately conservative value is recommended and entering dn = 0.3hsp in Eq. (9) results in w
2.2
CMOD u 0.35hsp
(10)
D 0.3hsp
StressCOD relationship for SFRC
The strength of the composite for a given COD can be determined from
V (w) V c(w) V f(w) (9)
0.30
dn/hsp
w/(wdn=0 . CMOD)
k1
Îą = 0.3
1.40
k1
fw
1.60
(11)
where Ďƒc(w) is the concrete component for a given COD, including any beneficial coupling effect that the fibres might have on the matrix, and Ďƒf(w) is the nominal stress carried by the fibres. In the prism tests, during the early stages of the test postcracking, consideration of the matrix component is significant when interpreting the resulting moment versus CMOD response. At later stages of the test, the influence of the matrix component is less significant and may be obtained from Eq. (11), taking Ďƒf (w) = fw for the COD (w) given by Eq. (10). This response is depicted in Fig. 8, with a transition zone between the cracking point CMOD0 and a point CMODT where the influence of
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A. Amin/S. J. Foster/A. Muttoni · Derivation of the σw relationship for SFRC from prism bending tests
transition
M
fibres component dominates
proach for determining the residual direct tensile strength from prism bending tests. For plain concrete, the tensile softening stress can be taken as [17, 19–21]
V c(w)
Mcr uncracked matrix controls CMOD0
CMOD CMODT
Fig. 8. Simplified approach for the transition in the momentCMOD response of the prism test being influenced by the uncracked concrete component to the stress block to the point where the uncracked concrete component is insignificant
the uncracked concrete on the momentCMOD response may be considered to be insignificant. Voo and Foster [17] and Foster et al. [18] observed that the takeup, or engagement, of fibres is delayed from the initial point of cracking, with the length of the delay dependent on the angle of a fibre with respect to the cracking plane, and with the complete response determined by integrating the individual fibre responses. The result of this is a progressive takeup of the fibres component from the initial point of cracking to a peak, as shown in Fig. 1. To develop the first part of the curve, we take the fibres component to be
V f(w) ] (w) fw
(12)
where fw is obtained from Eq. (9) and ζ (w) is a transition function. In this paper we adopt an elliptical transition function:
] (w)
2 °° 1 (wT w) 2 wT ® ° °¯ 1
if w wT
(13)
if w t wT
where wT (see Fig. 1) is the point on the σ w curve where the fibres have achieved their maximum effectiveness. It should be noted that this transition only influences the initial part of the response after cracking and is not overly significant in the development of a simple design ap
c1fct e c2w
(14)
where fct is the tensile strength of the concrete without fibre reinforcement and c1 and c2 are coefficients. Coefficient c1 accounts for any beneficial effect of the fibres on the peak matrix strength and c2 is a factor that controls the steepness of the descending branch and is influenced by the volume of fibres and the cementitious matrix composition. For Mode I fracture, Voo and Foster [17, 19, 22] adopted c1 as unity. For c2, Ng et al. [23] proposed the following: c2 = 30/(1 + 100ρf) ... for mortar and concrete with ag ≤ 10 mm c2 = 20/(1 + 100ρf) ... for concrete with ag > 10 mm
(15a) (15b)
where ag is the maximum size of the aggregate particles.
3
Experimental validation
Specimens were cast for direct tension tests and notched prism tests using six SFRC mix designs. The SFRC mixes were fabricated using two types of commercially available steel fibres: endhooked (EH) Dramix® RC65/35BN colddrawn wire fibres and OL13/0.20 straight (S) highcarbon steel fibres, both manufactured by Bekaert. The EH fibres were 0.55 mm in diameter, 35 mm long and had a tensile strength of 1340 MPa. The S fibres were 0.2 mm in diameter, 13 mm long and had a tensile strength > 1800 MPa. The tests are categorized in two series: series AM and series DA. The fibre volumetric dosages adopted in this study were 0.4, 0.5, 0.8 and 1.0 % for the EH fibres and 0.5 and 1.0 % for the S fibres. The aggregate used was basalt with a maximum particle size of 10 mm. The compressive strength characteristics of the concrete used in the study were determined from 100 mm diameter × 200 mm high cylinders tested after 28 days of moist curing at 23 °C; the results are summarized in Table 1. The mean compressive strength fcm was determined from three cylinders tested with load control at a rate of 20 MPa/min, as per AS1012.9 [24]. The modulus of
Table 1. Mechanical properties of SFRC mixes
Mix
Fibre type
Fibre vol. (%)
fcm (MPa)
lf (mm)
df (mm)
Eo (GPa)
fct (MPa)
DA0.5EH
endhooked
0.5
56.2
35
0.55
33.0
3.85
DA1.0EH
endhooked
1.0
60.1
35
0.55
31.5
3.92
DA0.5S
straight
0.5
63.7
13
0.20
34.7
4.03
DA1.0S
straight
1.0
63.0
13
0.20
35.8
4.30
AM0.4EH
endhooked
0.4
61.3
35
0.55
33.5
4.15
AM0.8EH
endhooked
0.8
63.8
35
0.55
34.0
4.52
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A. Amin/S. J. Foster/A. Muttoni · Derivation of the σw relationship for SFRC from prism bending tests
elasticity Eo was obtained in accordance with AS1012.17 [25]. The tensile strength of the matrix fct was obtained from dogbone tests (described below). The uniaxial tensile test was conducted on hour glassshaped “dogbone” specimens with the shape introduced by van Vliet [26]. Fig. 9a shows the specimen size and test setup details adopted in this study. Four specimens were cast and tested for each of the DA mixes; six specimens were cast and tested for each of the AM mixes. The specimens were filled using the procedure outlined in [9], i.e. the centre portion of the mould was filled to approx. 90 % of the height of the specimen, which was then followed by pouring of the ends. The moulds were compacted using a vibrating table. The dogbone specimens were tested in an Instron servohydraulic universal testing machine (UTM). Prior to
P
P
125
Universal joint
125 200
R145
125
125
215
16 mm dia. threaded rod
casting, four 16 mm threaded rods were embedded 100 mm in each end of the sample. Upon testing, the specimen was bolted to end plates and connected to the UTM. One end of the test arrangement was connected to the testing machine through a universal joint, the other through a fixed platen. This arrangement was used to ensure that no stresses were transferred to the specimen during the connection to the UTM. To measure the COD, two LVDTs were attached to the north and south faces and two LSCTs on the east and west faces of the specimen. The gauges were centred on the specimen and had gauge lengths of 230 mm (Fig. 9b). Loading was applied using displacement control, initially at a rate of 0.12 mm/min, until the formation of the dominant crack. After cracking, the rate was increased to 0.2 mm/min, with additional rate increases introduced as the test progressed. The notched threepoint beam tests were performed on two different prism sizes for the DA series: 150 × 150 × 500 mm long prisms, with a notch depth of 45 mm and spanning 456 mm, and 100 × 100 × 500 mm long prisms, with a notch depth of 30 mm and spanning 400 mm (as per [16]). For the AM series, the prism beam tests were performed on 150 × 150 × 600 mm long prisms, with a notch depth of 25 mm and spanning 500 mm, and tested to EN 14651 [9]. The notches were cut with a diamondtipped sawblade. In the DA series of tests, two prism tests were carried out for each specimen size and test configuration; for the AM series of tests, six specimens were cast and tested for each fibre dosage. The prismatic specimens were tested using a closed loop test system by attaching a clip gauge to the underside of the beam at the notch to measure and control the CMOD at the extreme tensile fibre. The test was operated such that the CMOD increased at a constant rate of 0.05 mm/min for the first 2 min and then increased to 0.2 mm/min until the CMOD reached 4 mm for the DA series of tests and 13 mm for the AM series of tests.
4
P
a)
107.5
62.5
230
245
Test results
P
155
b)
Fig. 9. Details of uniaxial tension test specimens: a) specimen dimensions, b) displacement transducer locations
The experimental results for the uniaxial tests are presented in Fig. 10; the points plotted on the axes of the figures are the tensile strengths of the matrix, with the averages for each series given in Table 1. The fracture processes of all the specimens consisted of three key stages. The first stage involved the formation of meso or hairline cracks < 0.05 mm wide; once initiated, the crack propagated along the weakest crosssection along a surface. At this stage the peak stress had been reached. This was quickly followed by a sharp reduction in load, coinciding with a significant opening of the crack, as the elastic strain energy stored in the specimen and testing rig was recovered. Thus, no displacement data is available between the peak load and that corresponding to the stabilized crack. It was observed, however, that the initial load after cracking had dropped below that of the peak residual strength of the SFRC specimens with low fibre dosages. The results are presented in Table 2 to highlight the inplane and outofplane rotations of the uniaxial specimens at an average COD equal to 1.5 mm. After the crack had stabilized, the load again increased as the fibres became engaged. The long tail of each curve reflects the progressively smooth
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A. Amin/S. J. Foster/A. Muttoni Âˇ Derivation of the Ďƒw relationship for SFRC from prism bending tests
5
Tensile Stress (MPa)
Tensile Stress (MPa)
5 4 3 2 1 0 a)
1 2 3 4 5 6 7 8 Crack Opening Displacement, w (mm)
1
0
1
2
3
4
5
6
7
8
Crack Opening Displacement, w (mm)
5
Tensile Stress (MPa)
Tensile Stress (MPa)
2
b)
5 4 3 2 1 0
4 3 2 1 0
0 c)
1
2
3
4
5
6
7
8
0 d)
Crack Opening Displacement, w (mm)
5
1
2
3
4
5
6
7
8
Crack Opening Displacement, w (mm)
5
Tensile Stress (MPa)
Tensile Stress (MPa)
3
0
0
4 3 2 1 0
4 3 2 1 0
0 e)
4
1
2
3
4
5
6
7
Crack Opening Displacement, w (mm)
8
0 f)
1
2
3
4
5
6
7
8
Crack Opening Displacement, w (mm)
Fig. 10. Uniaxial test results: a) mix DA0.5EH, b) mix DA1.0EH, c) mix DA0.5S, d) mix DA1.0S, e) mix AM0.4EH, f) mix AM0.8EH
residual capacity of the specimens. Soon after cracking it was clear that the concrete provided no contribution to the tensile strength and that the strength was due to the fibres alone. Following the conclusion of testing of uniaxial specimens with endhooked fibres, the number of fibres crossing the plane of the dominant crack was recorded. The results are presented in Table 3. The experimental results for the prism bending tests are shown in Fig. 11. Three distinct phases describe the response of the threepoint notched bending test: i) an elastic phase up to cracking, ii) a flexural hardening response up to peak load and iii) a reduction in load with increasing CMOD. Before comparing the results from the inverse analysis of the bending tests, the uniaxial test data needs to be compensated for the boundary (wall) effect. The presence of a boundary restricts a fibre from being freely orientated [23, 27â€“30]. An orientation factor kt must be applied to the
98
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uniaxial test results to remove this influence, thus converting the results to those of an equivalent 3D fibre distribution free of boundary factors. For an element approximately square in section and tested in tension, as is the case in this study, the boundary influence found in Lee et al. [30] can be approximated as follows: kt
0.5 d
1 d1 0.94 0.6 lf b
(16)
It is worth noting that for the prism tests, the wall effect is largely mitigated by the influence of the notch at the bottom and compressive region at the top; in this case only the side walls provide significant influence and the wall effect can be approximated as a 2D problem. For the case of prism tests, provided that lf/b â‰¤ 1, the boundary influence factor may be adapted from the 2D approximation of Ng et al. [23] as
A. Amin/S. J. Foster/A. Muttoni Âˇ Derivation of the Ďƒw relationship for SFRC from prism bending tests
Table 2. LSCT readings from uniaxial tests at COD = 1.5 mm
Dogbone ID
North (mm)
South (mm)
East (mm)
West (mm)
Outofplane rotation (rad)
Inplane rotation (rad)
DA0.5EHâ€“1
1.79
1.23
1.12
1.85
0.00361
0.00298
DA0.5EHâ€“2
1.32
1.67
1.26
1.76
â€“0.00226
â€“0.00204
DA0.5EHâ€“3
â€“0.12
3.15
2.14
0.83
â€“0.02109
0.00535
DA0.5EHâ€“4
0.76
â€“
1.97
1.77
â€“
0.00082
DA1.0EHâ€“1
1.41
1.57
0.51
2.51
â€“0.00103
â€“0.00816
DA1.0EHâ€“2
1.50
1.48
2.12
0.90
0.00013
0.00498
DA1.0EHâ€“3
2.37
0.61
1.12
1.90
0.01135
0.00318
DA1.0EHâ€“4
1.62
â€“
1.40
1.49
â€“
â€“0.00037
DA0.5Sâ€“1
0.87
2.10
1.30
1.74
â€“0.00794
â€“0.00180
DA0.5Sâ€“2
0.62
2.45
1.09
1.86
â€“0.01181
â€“0.00314
DA0.5Sâ€“3
1.59
â€“
0.87
2.04
â€“
â€“0.00478
DA0.5Sâ€“4
0.58
â€“
2.03
1.92
â€“
0.00045
DA1.0Sâ€“1
1.40
1.60
â€“
â€“
â€“0.00129
â€“
DA1.0Sâ€“2
0.94
2.08
1.03
1.96
â€“0.00735
â€“0.00380
DA1.0Sâ€“3
1.30
1.71
1.51
1.50
â€“0.00265
0.00004
DA1.0Sâ€“4
1.50
â€“
0.91
2.12
â€“
â€“0.00494
AM0.4EHâ€“2
1.95
0.93
1.44
1.69
0.00658
â€“0.00102
AM0.4EHâ€“3
0.79
2.13
1.38
1.59
â€“0.00864
â€“0.00086
AM0.4EHâ€“4
1.51
1.49
2.48
0.52
0.00013
0.00800
AM0.4EHâ€“5
1.65
1.36
1.73
1.27
0.00187
0.00188
AM0.4EHâ€“6
0.99
1.98
1.91
1.12
â€“0.00639
0.00322
AM0.8EHâ€“1
1.05
1.96
3.43
â€“0.43
â€“0.00587
0.01575
AM0.8EHâ€“2
2.30
0.67
2.56
0.47
0.01052
0.00853
AM0.8EHâ€“3
1.65
1.30
3.12
â€“0.06
0.00226
0.01298
AM0.8EHâ€“4
2.42
0.54
0.61
2.44
0.01213
â€“0.00747
AM0.8EHâ€“5
0.50
2.50
0.81
2.19
â€“0.01290
â€“0.00563
AM0.8EHâ€“6
0.23
2.75
1.93
1.09
â€“0.01626
0.00343
kb
S d1 3.1 0.6 lf b
(17)
Applying the inverse analysis technique to a notched SFRC beam in bending described by Eqs. (12) to (14) is illustrated in Fig. 12 for wT = 0.3 mm. It can be seen that the proposed model fits well within the data obtained from the uniaxial tensile test data, compensated for the boundary effect.
5
Simplified model for design
In the establishment of Eqs. (7) and (10) it is assumed that sufficient cracking has occurred such that the neutral axis is sufficiently high in the section and thus the contribution
of the uncracked concrete to the bending moment is small compared with that provided by the fibres. In determining a simple model we can adopt points corresponding to CMODs of 1.5 and 3.5 mm, which correspond to points CMOD2 and CMOD4 according to [9] and shown in Fig. 13. These points are selected to be sufficiently separated from each other so as to provide reasonable modelling over the most important region of the Ďƒ w curve for both service and strength limit design and with point CMOD2 being sufficiently distant from initial cracking such that the contribution of the uncracked concrete to the section capacity of the prism is small [31]. Considering Eqs. (7) to (10) with a linear constitutive law interpolating between points CMOD2 and CMOD4, with k1k2 = 1, results in
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A. Amin/S. J. Foster/A. Muttoni Âˇ Derivation of the Ďƒw relationship for SFRC from prism bending tests
Table 3. Number of fibres crossing failure plane in uniaxial tests
Specimen ID
Number of fibres
Specimen ID
DA0.5EHâ€“1
126
AM0.4EHâ€“3
94
DA0.5EHâ€“2
162
AM0.4EHâ€“4
51
DA0.5EHâ€“3
169
AM0.4EHâ€“5
86
DA0.5EHâ€“4
131
AM0.4EHâ€“6
84
Number of fibres
DA1.0EHâ€“1
208
AM0.8EHâ€“1
175
DA1.0EHâ€“2
228
AM0.8EHâ€“2
169
DA1.0EHâ€“3
265
AM0.8EHâ€“3
158
DA1.0EHâ€“4
231
AM0.8EHâ€“4
131
AM0.4EHâ€“1
57
AM0.8EHâ€“5
158
AM0.4EHâ€“2
79
AM0.8EHâ€“6
138
fR, j
20
20
0
1
2
a)
3
.... j
2, 4
(19)
15 10
0
4
1
CMOD (mm) 25
25
20
20
15 10 5
2
3
4
CMOD (mm)
b)
Load (kN)
Load (kN)
2 b hsp
0
0
15 10 5
0 0
1
c)
2
3
0
4
0
1
d)
CMOD (mm)
35
30
30
25
25
20 15
3
4
20 15
10
10
5
5
0
2
CMOD (mm)
35
Load (kN)
Load (kN)
3 Fj a
5
5
0 0
e)
(18b)
For threepoint bending, the shear span a = l/2. The model of Eqs. (18) and (19) is compared with the direct tension test data â€“ with the boundary effect compensated for by Eq. (16) â€“ in Fig. 14 for the domain w âˆˆ[0, 2.0] mm. The prediction according to fib Model Code 2010 [10] is also plotted, with the Model Code model multiplied by factor k2 to include the influence of the notch in
25
10
(18a)
w (D dn ) 1 Â˜ 3 (hsp dn ) 4
[ (w)
25
15
fR2 ( fR4 fR2 ) [ (w) t 0 3
with fR2 and fR4 calculated in accordance with EN 14651 [9] (Fig. 13) as
Load (kN)
Load (kN)
fw
1
2
3
4
CMOD (mm)
5
6
0
f)
1
2
3
4
5
6
CMOD (mm)
Fig. 11. Prism bending test results: a) mix DA0.5EH, b) mix DA1.0EH, c) mix DA0.5S/mix DA1.0S (higher curves 150 mm square prisms/ lower curves 100 mm square prisms), e) mix AM0.4EH, f) mix AM0.8EH
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3
Data range direct tension test x kt
2 1
0
0.5 1 COD, w (mm)
a)
Data range direct tension test x k t
1 0
0
0.5 1 COD, w (mm)
c)
5
Data range direct tension test x kt
1 0
0
1
2 3 COD, w (mm)
0
0.5 1 COD, w (mm)
4 3
Data range direct tension test x kt
2 1
0
0.5 1 COD, w (mm)
5
1.5
0.8% EH Fibres 150 mm sq. prisms EN 14651
4
Data range direct tension test x kt
3 2 1 0
4
1.5
1.0% S Fibres 150 mm sq. prisms 100 mm sq. prisms
d)
3 2
Data range direct tension test x kt
1
0
1.5
0.4% EH Fibres 150 mm sq. prisms EN 14651
4
2
5
3 2
3
b)
0.5% S Fibres 150 mm sq. prisms 100 mm sq. prisms
4
1.0% EH Fibres 150 mm sq. prisms 100 mm sq. prisms
4
0
1.5
Tensile Stress (MPa)
Tensile Stress (MPa)
5
Tensile Stress (MPa)
Tensile Stress (MPa)
4
0
e)
5
0.5% EH Fibres 150 mm sq. prisms 100 mm sq. prisms
Tensile Stress (MPa)
Tensile Stress (MPa)
5
0
f)
1
2 3 COD, w (mm)
4
Fig. 12. Comparison of predicted uniaxial σw curves obtained from inverse analysis of prism bending tests with uniaxial test data: a) mix DA0.5EH, b) mix DA1.0EH, c) mix DA0.5S, d) mix DA1.0S, e) mix AM0.4EH, f) mix AM0.8EH
the prism tests (referred to as Modified fib MC2010 in Figs. 14 and 15). The simplified model developed above compares reasonably with the tensile test data over the range 0.5 mm ≤ w ≤ 1.5 mm. Beyond 1.5 mm the results are somewhat conservative; this could be improved by selecting a second calibration point beyond CMOD4 (i.e. > 3.5 mm) on the moment versus CMOD plot. On the other hand, the fib Model Code 2010 relationship generally overestimates the tensile capacity at a given COD. The importance of the observation above should not be underestimated. When relying on physical models to
describe behaviour, e.g. shear and punching shear [32, 33], the material laws must first be accurately established. To further validate the model, data was collated from the studies of Colombo [34] (used in di Prisco et al. [11] for comparison with fib Model Code 2010 [10] model) and Deluce [35]. In these studies, both indirect and direct tension tests were performed on SFRC produced from the same mix. The indirect tension tests of [34] were performed on three 150 mm square notched prisms spanning 450 mm under a fourpoint loading configuration. The prisms had
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Load, F (kN)
a notch depth of 45 mm. The direct tension tests of [34] used 3 × 75 mm diameter core samples taken from cast prisms and notched at midheight; the cylinders were tested with both ends fixed to the loading platens. As the tensile specimens were obtained using cores from a larger section, the boundary influence is eliminated in this case, i.e. kt = 1.0. In addition k2 = 1.0, as both the prism tests and tension tests are on notched specimens. Deluce [35] presented the results of direct tension tests on three dogbone specimens and a single notched prism bending test. The prism specimens spanned 456 mm, had a crosssection of 150 × 150 mm and a notch depth of 25 mm.
CMOD (mm) 0.5 CMOD1
1.5
CMOD2
2.5
CMOD3
3.5
CMOD4
Fig. 13. Definitions of key points on the applied force versus CMOD curve for flexural testing of prisms according to fib Model Code 2010 [10]
Data range direct tension test x kt
2 1
0
0.5
a)
T ensile Str ess (M Pa)
5
1 1.5 COD, w (mm)
3 2
Data range direct tension test x kt
1
0
0.5
c)
5
1 1.5 COD, w (mm)
Data range direct tension test x kt
1 0
0
0.5
1 1.5 COD, w (mm)
2 Data range direct tension test x kt
1
0 b)
2
0.5
1 1.5 COD, w (mm)
2
1.0% S Fibres Simplified Model (this study) fib MC2010 Modified fib MC2010
4 3
Data range direct tension test x kt
2 1 0
0 d)
5
3 2
3
5
2
0.4% EH Fibres Simplified Model (this study) fib MC2010 Modified fib MC2010
4
1.0% EH Fibres Simplified Model (this study) fib MC2010 Modified fib MC2010
4
0
2
0.5% S Fibres Simplified Model (this study) fib MC2010 Modified fib MC2010
4
0
T ensile Str ess (M Pa)
T ensile Str ess (M Pa)
3
T ensile Str ess (M Pa)
4
0
e)
5
0.5% EH Fibres Simplified Model (this study) fib MC2010 Modified fib MC2010
T ensile Str ess (M Pa)
T ensile Str ess (M Pa)
5
0.5
1 1.5 COD, w (mm)
2
4
0.8% EH Fibres Simplified Model (this study) fib MC2010 Modified MC2010
3
Data range direct tension test x kt
2 1 0
0 f)
0.5
1 1.5 COD, w (mm)
2
Fig. 14. Comparison of simplified design model with the uniaxial test data: a) mix DA0.5EH, b) mix DA1.0EH, c) mix DA0.5S, d) mix DA1.0S, e) mix AM0.4EH, f) mix AM0.8EH
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di Prisco et al. (2013)  M3F20.62 Simplified Model (this study) fib MC2010 Modified fib MC2010
Tensile Stress (MPa)
5 4
Direct tension test data
3 2 1 0
0
a)
0.5 1 COD, w (mm)
Deluce (2011)  FRC4 Simplified Model (this study) fib MC2010 Modified fib MC2010
5
Tensile Stress (MPa)
6
4 3 2 1 0
1.5
Data range direct tension test x kt
0
0.5
b)
1 1.5 COD, w (mm)
2
Fig. 15. Comparison of simplified design model with data obtained from: a) di Prisco et al. [11] mix M3F20.62, b) Deluce [35] mix FRC4
Table 4. Comparison of residual tensile strength at crack opening displacements (COD) of 0.5 and 1.5 mm
Researchers
Test
at w = 0.5 mm
at w = 1.5 mm
Exp.
fib model
Proposed model
Exp.
fib model
Proposed model
ftf (MPa) A
ftf (MPa) BB/A
ftf (MPa) CC/A
ftf (MPa) D
ftf (MPa) EE/D
ftf (MPa) FF/D
Colombo [34]
M3F20.62
1.74
2.12
1.22
1.52
0.87
0.33
1.12
3.39
0.30
0.91
Deluce [35]
FRC1
1.85
3.53
1.91
2.63
1.42
1.23
2.56
2.08
1.66
1.35
FRC2
2.52
3.94
1.56
3.36
1.33
1.98
3.22
1.63
2.29
1.16
FRC3
2.85
2.99
1.05
2.47
0.87
2.10
2.39
1.14
1.66
0.79
FRC4
1.89
2.56
1.35
1.83
0.97
1.23
1.73
1.41
1.07
0.87
FRC5
1.87
3.04
1.63
2.27
1.21
1.31
2.25
1.72
1.37
1.05
DA0.5EH
1.15
1.92
1.67
1.64
1.43
0.97
1.57
1.62
1.24
1.28
DA1.0EH
2.44
3.11
1.27
2.59
1.06
1.70
2.36
1.39
1.53
0.90
DA0.5S
0.60
1.39
2.32
0.94
1.57
0.60
0.82
1.37
0.40
0.67
DA1.0S
1.39
1.98
1.42
1.38
0.99
0.67
1.22
1.82
0.67
1.00
AM0.4EH
–
1.93
–
1.38
–
0.74
1.30
1.76
0.80
1.08
AM0.8EH
2.78
2.95
1.06
2.63
0.95
1.97
2.15
1.09
1.54
0.78
This study
Mean COV
1.50 0.25
The predictions of the simplified model as given Eq. (18) are compared with the results for the Colombo [34] data in Fig. 15a, the Deluce [35] mix FRC4 in Fig. 15b and for all data, at the key points w = 0.5 mm and w = 1.5 mm, in Table 4. The predictions of fib Model Code 2010 [10] are also provided. It can be seen that the simplified model proposed predicts the residual tensile strength of SFRC concrete consistently, whereas fib Model Code 2010 [10] consistently overestimates the capacity.
6
Discussion of the simplified model
It is important to recognize that the philosophy adopted in fib Model Code 2010 for predicting the tensile strength
1.15 0.22
1.70 0.36
0.99 0.21
is a sound one and, indeed, the simplified model presented here is adapted from that model. The key difficulty in the fib Model Code 2010 approach can be attributed to two conditions. The first is the adoption of CMOD1, corresponding to a crack mouth opening displacement of 0.5 mm, as the first key sampling point. Adjusting for the depth of the notch, this leads to an average crack width of about 0.2 mm; at this crack width the tensile strength of the cementitious matrix remains a significant contributor to the flexural resistance of the member. Moving this first sampling point back to CMOD2 (CMOD = 1.5 mm) corrects this. Similarly, CMOD4 is adopted, rather than CMOD3, to maximize the distance between the first and second key points and increase the reliability of the ap
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proach. The second condition is the influence of testing on notched specimens, where the failure section is defined by the location of the notch and not by probabilities related to fibre distributions and scatter. When tested against the available data collected in this study and elsewhere, at the key point w = 1.5 mm (Table 4), the model prediction to experimental ratio is 0.99 and has a COV of 0.21.
7
Conclusions
In order to increase the utilization of SFRC in structural applications, it is important to establish the postcracking, or residual, tensile strength of SFRC correctly. The postcracking behaviour of SFRC can be obtained directly from uniaxial tensile tests or indirectly, following an inverse analysis of notched beams in bending. Consequently, reliable methods to attain these results are required. Following an experimental investigation of six softening SFRC mixes and a subsequent analysis that examined the applicability of inverse analysis techniques found in the literature, i.e. ones that led to the approach adopted in fib Model Code 2010 [10], it was found that the fib Model Code 2010 results might overestimate the residual tensile strength that forms the basis of physical models for SFRC. To address this, a simple yet effective inverse analysis procedure was derived to find the σ w relationship for SFRC from prism bending tests. The model considers the influence of fibres on the moment carried by the specimen from the point in the test where the uncracked concrete has little influence on its capacity and considers rigid body rotations. In the development of the model it is important to note that the measurement point for the CMOD is not at the notch root (i.e. the location of the true crack mouth) but at a certain distance from it. Using this observation, a rational model is derived which is independent of specimen geometry, testing span and method of testing, i.e. three or fourpoint bending. The model was validated against experimental data obtained from direct tension tests on six SFRC mixes carried out in this study and six SFRC mixes obtained from results presented in the literature. For all 12 mixes tested, each of varying fibre type and dosage, and for five different prism geometries tested, the model predicted the results well and generally within the range of scatter of the collected data.
References 1. Romualdi, J. P., Batson. G. B.: Behaviour of reinforced concrete beams with closely spaced reinforcement. Proc., ACI Journal, 60 (6), 1963, pp. 775–789. 2. van Mier, J. G. M.: Concrete Fracture: a Multiscale Approach. CRC Press, Boca Raton, Florida, USA, 2013. 3. van Vliet, M. R. A., van Mier, J. G. M.: Effect of strain gradients on the size effect of concrete in uniaxial tension. International Journal of Fracture, 95, 1999, pp. 195–219. 4. van Mier, J. G. M., van Vliet, M. R. A.: Uniaxial tension test for the determination of fracture parameters of concrete: state of the art. Engineering Fracture Mechanics, 69, 2002, pp. 235 –247.
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5. Zhang, J., Stang. H.: Application of stress crack width relationship in predicting the flexural behavior of fiber reinforced concrete. Journal of Cement and Concrete Research, 28 (3), 1998, pp. 439–452. 6. Planas, J., Guinea, G. V., Elices, M.: Size effect and inverse analysis in concrete fracture. International Journal of Fracture, 95, 1999, pp. 367–378. 7. de Oliveira e Sousa, J. L. A., Gettu, R., Barragán, B. E.: Inverse analysis of the notched beam response for determining the σw curve for plain and fiber reinforced concretes. Anales de Mecánica de la Fractura, 19, 2002, pp. 393–398. 8. di Prisco, M., Plizzari, G., Vandewalle, L.: Fibre reinforced concrete: new design perspectives. Materials and Structures, 42, 2009, pp. 1261–1281. 9. EN 14651:2007: Test Method for Metallic Fibre Concrete – Measuring the Flexural Tensile Strength (Limit of Proportionality (LOP), Residual). European Committee for Standardization. 10. fib – International Federation for Structural Concrete. fib Model Code for Concrete Structures 2010. Berlin: Verlag Ernst & Sohn, 2013. 11. di Prisco, M., Colombo, M., Dozio, D. (2013): Fibrereinforced concrete in fib Model Code 2010: principles, models and test validation. Structural Concrete, 14, pp. 342–361. 12. Zhu, Y.: The Flexural Strength Function for Concrete Beams: A Closed Form Solution Based on the Fictitious Crack Model. Bulletin No. 157, Department of Structural Mechanics & Engineering, The Royal Institute of Technology, Stockholm, Sweden, 1991, pp. B2–B23. 13. Sigrist, V.: Zum Verformungsvermögen von Stahlbetonträgern (On the Deformation Capacity of Reinforced Concrete Beams). PhD dissertation, IBK Report No.210, Swiss Federal Institute of Technology, Switzerland, 1995 (in German). 14. Foster, S. J, Htut, T. N. S., Ng, T. S.: High Performance Fibre Reinforced Concrete: Fundamental Behaviour and Modelling. Proc. of 8th Int. Conf. on Fracture Mechanics Concrete and Concrete Structures (FraMCoS8), Toledo, Spain, 10–14 Mar 2013, pp. 69–78. 15. Htut, T. N. S.: Fracture processes in steel fibre reinforced concrete. PhD dissertation, School of Civil & Environmental Engineering, The University of New South Wales, Australia, 2010. 16. JCIS0022003: Method of test for loaddisplacement curve of fiber reinforced concrete by use of notched beam. Japan Concrete Institute, 2003. 17. Voo, J. Y. L., Foster, S. J.: Tensile fracture of fibre reinforced concrete: variable engagement model. In: di Prisco, M., Felicett, R. Plizzari, G.A. (eds.), 6th Rilem Symposium on Fibrereinforced Concrete (FRC), Varenna, Italy, 20–22 Sept 2004, pp. 875–884. 18. Foster, S. J., Voo, Y. L. Chong, K. T.: Analysis of Steel Fiber Reinforced Concrete Beams Failing in Shear: Variable Engagement Model, chap. 5: Finite Element Analysis of Reinforced Concrete Structures, Lowes, L., Filippou, F. (eds.), ACI SP237, 2006, pp. 55–70 (CDROM). 19. Voo, Y. L., Foster, S. J.: Reactive powder concrete: analysis and design of RPC girders. Lambert Academic Publishing, 2009, ISBN 9783838324067. 20. Lee, G. G., Foster, S. J.: Behaviour of steel fibre reinforced mortar III: variable engagement model II. UNICIV report R448, School of Civil & Environmental Engineering, The University of New South Wales, Australia, 2007. 21. Lee, G. G., Foster, S. J.: Modelling of shearfracture of fibrereinforced concrete. Int. fib Symposium, CRC Press, 2008, pp. 493–499. 22. Voo, J. Y. L., Foster, S. J.: Variable engagement model for fibrereinforced concrete in tension. UNICIV report R420,
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23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
School of Civil & Environmental Engineering, The University of New South Wales, Australia, 2003. Ng, T. S., Htut, T. N. S., Foster, S. J.: Fracture of steel fibrereinforced concrete – the unified variable engagement model. UNICIV report R460, School of Civil & Environmental Engineering, The University of New South Wales, Australia, 2012. AS1012.9: Methods of Testing Concrete – Determination of the compressive strength of concrete specimens. Standards Australia, 1999. AS1012.17: Methods of Testing Concrete – Determination of the static chord modulus of elasticity and Poisson’s ratio of concrete specimens. Standards Australia, 1997. van Vliet, M. R. A.: Size effect in tensile fracture of concrete and rock. PhD dissertation, Delft University, The Netherlands, 2000. Romualdi, J. P., Mandel, J. A.: Tensile strength of concrete affected by uniformly distributed and closely spaced short length wire reinforcement. Journal of American Concrete Institute Proc., 61 (6), 1964, pp. 657–671. Aveston, J., Kelly, A.: Theory of multiple fracture of fibrous composites. Journal of Materials Science, 8 (3), 1973, pp. 352–362. Stroeven, P.: Stereological principles of spatial modelling applied to steel fibrereinforced concrete in tension. ACI Materials Journal, 106 (3), 2009, pp. 213–222. Lee, S. C., Cho, J., Vecchio, F. J.: Diverse embedment model for steel fibrereinforced concrete in tension: model development. ACI Materials Journal, 108 (5), 2011, pp. 516–525. Amin, A., Foster, S. J., Muttoni, A.: Evaluation of The Tensile Strength of SFRC as derived from Inverse Analysis of Notched Bending Test. Proc. of 8th Int. Conf. on Fracture Mechanics Concrete & Concrete Structures (FraMCoS8), Toledo, Spain, 10–14 Mar 2013, pp. 1049–1057. Foster, S. J.: Design of FRC Beams for Shear using the VEM and the Draft Model Code Approach, chapter 12: Recent Developments on Shear and Punching Shear on RC and FRC Elements, Minelli, F., Plizzari, G. (eds.), fib Bulletin 57, Fédération Internationale du Béton, Lausanne, Switzerland, 2010.
33. Maya, L. F., Fernández Ruiz, M., Muttoni, A., Foster, S. J.: Punching shear strength of steel fibrereinforced concrete slabs. Engineering Structures, 40, 2012, pp. 83–94. 34. Colombo, M.: FRC Bending Behaviour: a Damage Model for High Temperatures. PhD dissertation, Politecnico di Milano, Italy, 2006. 35. Deluce, J.: Cracking Behaviour of Steel Fibrereinforced Concrete Containing Conventional Steel Reinforcement. MASc dissertation, The University of Toronto, Canada, 2011.
Ali Amin, Research Student Centre for Infrastructure Engineering & Safety School of Civil & Environmental Engineering The University of New South Wales Sydney NSW 2052, Australia Ali.Amin@unsw.edu.au
Stephen J. Foster, Professor, Head of School Civil & Environmental Engineering The University of New South Wales Sydney NSW 2052, Australia Phone +61 2 9385 5059 S.Foster@unsw.edu.au
Aurelio Muttoni, Professor School of Architecture Civil & Environmental Engineering École Polytechnique Fédérale de Lausanne, CH1015 Lausanne, Switzerland
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Technical Paper Alexander Scholzen* Rostislav Chudoba Josef Hegger
DOI: 10.1002/suco.201300071
Thinwalled shell structures made of textilereinforced concrete Part I: Structural design and construction At RWTH Aachen University recently, a pavilion was constructed with a roof shell made of textilereinforced concrete (TRC), a composite material consisting of a finegrained concrete and highstrength, noncorroding textile reinforcement in the form of carbon fibres. The thinwalled TRC shell structure demonstrates impressively the loadbearing capacity of this innovative composite material. The present paper discusses the practical issues concerning the construction, such as the fabrication of the TRC shells using shotcrete, the concepts developed for the arrangement of the textile reinforcement and the erection of the shells on top of the precast concrete columns. The issues concerning the design, assessment and numerical simulation of the loadbearing behaviour of TRC shells are presented in the companion paper (Part II). Keywords: cementitious composites, textilereinforced concrete, hyperbolic paraboloid, finite element simulation, manufacturing technology, shotcrete, carbon fabrics, industrial textiles
1
Introduction
During the last decades, intensive research has been conducted on cementitious composites, leading to the development of strain hardening materials with high compressive and tensile strengths and better ductility and energy absorption capacity. The ductile tensile response of the composite required for applications with a loadcarrying function in civil engineering structures can be achieved by combining continuous fabrics and shortfibre reinforcement with a finegrained matrix [1]. Based on advances in the characterization and modelling methods, e.g. [2, 3, 4], a wide range of applications demonstrating the design possibilities of these highperformance composites have emerged. Examples include a slim TRC footbridge [5, 6], façades of large TRC elements [7] and sandwich panels [8]. Further, textile reinforced concrete has been successfully used in many cases as a retrofitting system for existing steel reinforced concrete structures, such as in the renovation of a heritagelisted barrelshaped roof [9]. A detailed review of applications of textilereinforced concrete recently carried out in Germany is given in [10].
The present paper describes in detail the structural design and construction of a pavilion with an ambitious roof structure made of textilereinforced concrete recently built on the campus of RWTH Aachen University. Once glazed on all sides, the pavilion will be used as a room for seminars and events (Fig. 1). The design by the Institute of Building Construction of RWTH Aachen University (bauko 2) uses umbrellalike shells as basic elements, each of which consists of an addition of four surfaces in double curvature, known as hyperbolic paraboloids (hypar surfaces). This shape refers to designs by the Spanish architect Félix Candela (1910–1997) who, especially in the 1950s and 1960s, created many buildings in Mexico which are based on variations of such hypar shells [11] (Fig. 2). Such shell structures made of reinforced concrete have almost completely vanished from the current construction scene because of the corrosion problems of steel reinforced concrete and because of the labourintensive fabrication of the complex in situ formwork. Here, TRC with noncorroding textile reinforcement provides new possibilities for the efficient realization of loadbearing systems with a small crosssectional thickness. Owing to their low weight, such filigree loadbearing structures are particularly suitable for economical prefabricated construction
* Corresponding author: ascholzen@imb.rwthaachen.de Submitted for review: 10 September 2013 Revised: 6 June 2014 Accepted for publication: 17 July 2014
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Fig. 1. Roof structure consisting of four large precast TRC shells (photo: bauko 2, RWTH Aachen University)
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A. Scholzen/R. Chudoba/J. Hegger · Thinwalled shell structures made of textilereinforced concrete
the quasiductile behaviour and the associated stress redistribution within the TRC shell.
2 2.1
Fig. 2. Experimental shell structure by the Spanish architect Félix Candela, Las Aduanas, Mexico, 1953 [11]
and segmentation. In contrast to conventional reinforced concrete shells, which require elaborate falsework and formwork, the spectrum of questions to be addressed for textilereinforced loadbearing structures shifts to issues of assembly, alignment and joining of the individual finished parts. The present paper significantly extends the previous publication in the German language [12]. The structural design of TRC shells is discussed in section 2, dealing with the description and analysis of the loadbearing structure within the preliminary design, resulting in the chosen crosssectional layout of the TRC shell structure. The spatial arrangement of the textile reinforcement within the shell to reflect the stress flow is described in section 2.4. Section 3 covers the issues concerning fabrication of TRC shells using shotcrete technology as well as the erection of the precast structural elements. The ultimate limit state assessment of a TRC shell structure as well as the underlying design approach are described in detail in the companion paper [13]. That paper also addresses the issue of the loadbearing reserves due to
Structural design Description of the loadbearing structure
The loadbearing structure of the pavilion is composed of four TRC shells, each of which is supported at its centre by a steelreinforced concrete column. Each shell is 7 × 7 m on plan and is 6 cm thick. At the centre of the shell the thickness increases to 31 cm in order to ensure a sufficient crosssectional capacity for transferring the loads from the shell to the reinforced concrete column (Fig. 3) [14]. Arranging the four umbrellas in a 2 × 2 layout results in overall plan dimensions of 14 × 14 m and a structure height of 4 m. The basic geometric shape of the TRC shells leads, in particular, to straight shell boundaries, facilitating flush alignment between the individual umbrellas and a simple connection to the façade. The TRC shells were produced as precast parts. The rigid connection between TRC shell and reinforced concrete column as well as the connections between each column and its pad foundation were achieved using prestressed bolts (Fig. 3). Construction planning was carried out in collaboration with the Institute for Steel Construction of RWTH Aachen University. The four TRC umbrellas were subsequently joined by cylindrical steel hinges, significantly increasing the rigidity of the overall system with respect to windinduced horizontal loads. The coupling prevents vertical displacement between adjacent umbrellas and reduces vertical as well as horizontal edge displacements in the transition to the façade (see Fig. 4). In addition, it is no longer necessary to absorb asymmetrical loads solely by bending moments at the fixed column bases, which would have required larger column crosssections. By coupling the umbrellas, the moment load in the column bases is considerably decreased because the normal forces in the total loadbearing structure are activated. It was therefore also possible to reduce
Fig. 3. Diagonal section through the structure consisting of TRC shell, RC column and foundation
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A. Scholzen/R. Chudoba/J. Hegger 路 Thinwalled shell structures made of textilereinforced concrete
Fig. 4. Displacements of the structure under horizontal load with and without coupling of the shells
the column crosssection from top to bottom, thus emphasizing the lightness of the loadbearing structure from an architectural point of view. The umbrellas are joined at seven points at 1 m spacing along the adjacent edges of each shell as depicted in Fig. 5a. Each steel hinge was subsequently fixed to the TRC shell on the upper shell surface with four bolts (Figs. 5b and 5c).
2.2
Analysis of loadbearing behaviour for preliminary design
The advantageous loadbearing characteristics of shell structures are based on their ability to carry the loads ap
plied mainly through membrane stresses. During the preliminary design phase, the effect of the shell thickness and the rise of the hypar shell on the stress distribution due to vertical uniform loads was analysed in order to identify a shell geometry with a prevailing membrane stress state for vertical loads. Fig. 6 shows the distribution of the principal tensile stresses due to selfweight as obtained by linearelastic FE simulation for the shell geometry chosen. Since this stress state is symmetric with respect to the common edges, only one umbrella is shown. Owing to the high compressive strength of the fine concrete used and the lightweight nature of the structure, it was assumed that the tensile stresses would be critical for the ultimate limit state design. Therefore, only the distribution of positive princi
Fig. 5. Cylindrical steel hinges used for coupling the TRC shells: a) arrangement of steel hinges on top surface, b, c) details of a single hinge
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Fig. 7. Crosssectional makeup of TRC shell
Fig. 6. Distribution of the principal tensile stresses in the shell structure due to selfweight
pal stresses (σl > 0) are shown in Fig. 6 in order to indicate the critical crosssections within the shell. As the stress distribution indicates, tensile bands develop along the shell edges, whereas in the centre of the shell only compressive stresses occur. The highest value of tensile stress occurs in the middle of each shell edge in the direction parallel to the edge. In those areas the stress distribution over the depth of the crosssection is almost uniform. Besides the shell geometry, several options for the coupling between the shells was also thoroughly analysed during the preliminary design phase. As a result, a cylindrical hinge was designed with the aim of enabling unrestrained rotation and relative inplane displacement along the shell edges (y axis in Figs. 5b and 5c). The kinematics of the joint preserves the membrane state of the single shell and avoids additional stresses due to temperature and shrinkage. With the given coupling kinematics, numerical analyses of the joint spacing were performed in order to identify an equidistant arrangement of joints with minimized hinge forces (Fig. 5a). Furthermore, the butt straps were designed to taper towards their ends (Fig. 5c) in order to avoid additional bending stresses in the connection between butt strap and shell.
2.3
Technology (ITA) of RWTH Aachen University, was selected as the reinforcement. The individual rovings have a linear density of 800 tex (= g/km) and their spacing in the longitudinal direction (0° direction) is 8.3 mm and in the transverse direction (90° direction) 7.7 mm. The warpknitted fabrics used with their plain stitch bond [15] exhibit an especially flat and open yarn structure, thus resulting in a higher penetration of the cementitious matrix into the interstitial spaces between individual filaments of the yarns and leading to a significantly higher bond strength when compared with the more common pillar and tricot stitch types. The composite strength was investigated experimentally for various reinforcement ratios using dog bonetype tensile tests as described in the companion paper [13]. A maximum composite tensile stress of 24.1 MPa could be reached in tensile tests with specimens 4 cm thick and 12 layers of reinforcement, corresponding to a textile strength of 1625 MPa (see companion paper [13], Fig. 2). Based on the results of the tests performed and considering the production constraints, a 6 cm thick crosssection with 12 layers of textile fabric equally spaced at 4.6 mm was chosen, see Fig. 7. The crosssectional layout requires an appropriate production procedure allowing for simple insertion of the thin concrete layers one by one. An obvious choice is to use shotcrete technology. Hence, the fresh concrete properties of the fine concrete were optimized for shotcrete production of the shells. The concrete mix developed by the Institute for Building Research (ibac) of RWTH Aachen University (see details in Table 1) has a maximum grain diameter of 0.8 mm and contains short fibres of al
Material components and their crosssectional layout
In the preliminary design of the TRC shells, the highest tensile stress due to selfweight, snow and wind was evaluated for symmetrical boundary conditions at the TRC shell edges and compared with the tensile strength determined experimentally using TRC specimens with different types of reinforcement and different reinforcement ratios. Besides the requirements for a high loadbearing capacity of the textile reinforcement, a high shape flexibility of the fabrics was also required due to the doublecurvature geometry of the shell. Therefore, only nonimpregnated fabrics were considered which can be easily adapted to the shell geometry. Even though fabrics impregnated with epoxy or styrene butadiene exhibit a higher efficiency due to a larger number of activated filaments, they do not provide the sufficient form flexibility for the given curvature. Based on the preliminary tests, a nonimpregnated carbon warpknitted fabric, developed at the Institute for Textile
Table 1. Composition of the cementitious matrix
material component
unit
value
Portland cement CEM I 52.5 N (c)
490
fly ash (f)
175
silica fume (s)
kg/m3
35
aggregate 0.0–0.8 mm
1249
water (w)
280
admixture
% by wt. of c
3.8
short fibres (AR glass, 6 mm)
% by vol.
0.5
w/c ratio w/ceq ratio = w/(c + 0.4f + s)
–
0.57 0.47
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kalineresistant (AR) glass with a diameter of 14 μm, length of 6 mm and a volume fraction of 0.5 %. Regarding its compressive strength, with a mean value of fcm, cube, dry = 89.0 MPa the concrete is equivalent to highperformance concrete of strength class C55/67.
2.4
Reinforcement concept
The textile reinforcement is activated optimally only if the principal tensile direction coincides with the 0° direction of the fabric. As explained earlier, in the case of a symmetrical load at the point of maximum stress, the principal tensile stresses run parallel to the shell edges. Therefore, in the production of the TRC shells, the reinforcement layers were all inserted parallel to the shell edges, and discontinuities of the reinforcement in the middle of the shell edges were avoided (Fig. 8). Hence, all 12 layers are available for the load transfer. In general, in the reinforcement concept, butt jointing was used for all adjacent reinforcement fabrics on all sides (Fig. 8). In order to avoid multiple joints in a single crosssection, consecutive layers were laid on top of each other with an offset as shown in Fig. 9, a schematic section through the TRC crosssection at the shell edges. By using a total of six different widths for the edge fabrics, the reinforcement design could be optimized in such a way that at any point in the shell no more than two joints occur in a crosssection, meaning that at least 10 reinforcement layers are available for load transfer. It should be noted that overlapping joints at the transitions of reinforcement fabrics were not used because of the small distance of only 4.6 mm in the thickness direc
tion between the reinforcement layers. Overlapping joints would have led to an insufficient thickness of the concrete layers between the fabrics, inducing delamination at an early load level as observed in experiments. In the shell centre where the crosssectional thickness is locally increased, the textile reinforcement is divided into six layers that follow the shell geometry at the upper and also lower surface (Fig. 10). In this region there is a transition from a state of predominant membrane stress to a multiaxial stress state at the connection to the reinforced concrete column. This area of the structure was therefore locally reinforced with a prefabricated steel cage measuring 1.2 × 1.2 m (Fig. 11) in order to transfer the forces in a concentrated way into the reinforced concrete column. The bars of the lower reinforcement layer of the steel cage form a polygonal pattern and follow the hyperbolic shell geometry precisely. The bars of the upper steel reinforcement follow a straight line and at the same time define the level of the textile reinforcement on top of it. On account of the increased thickness of the TRC shell at its centre, the concrete cover necessary for the steel reinforcement was easily guaranteed. The reinforcement cage enclosed a steel component positioned at the centre of the shell (Fig. 11). The steel component served as an opening for rainwater drainage and was also used for transferring the TRC shell out of the formwork onto the column as will be described in section 3.2. A detailed ultimate limit state assessment was performed for the crosssectional layup designed for the TRC shell as described above. The underlying design approach based on the crosssectional strength characteristics deter
Fig. 8. Offsets of the butt joints between the fabric layers shown in a schematic section through the TRC shell crosssection at the edge
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Fig. 11. Exploded view of the connection detail between TRC shell and RC column
3 3.1
Fig. 9. Reinforcement concept of TRC shells shown for the first two layers of the textile reinforcement as an example
mined experimentally as well as the numerical evaluation for all load case combinations are shown in detail in the companion paper [13].
Implementation in practice Production of textilereinforced concrete shells
The most challenging task concerning the production of the large (49 m2) TRC shells was the stringent requirement for the positional accuracy of the textile reinforcement with tolerances as tight as 3 mm. In collaboration with the contractor (GQ Quadflieg GmbH, Aachen, Germany) a precast concept was developed which allowed for constantly highquality production of all four shells under realistic building conditions. For this purpose, a temporary production tent was built with the formwork for the TRC
Fig. 10. Section through TRC shell showing the arrangement of the upper and lower textile reinforcement layers at the centre
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shells at its centre. Since the shell could not be walked on during the production process, a movable working platform was installed from which every point of the shell could be reached (Fig. 12). Layers of shotcrete approx. 5 mm thick were sprayed from the platform, and the textile reinforcement was laid in this afterwards. To do this, the rolls pf textile fabrics were attached to the scaffolding so that they could be easily unrolled into the shotcrete (Fig. 13). Subsequently, the textile fabrics were laminated with rolls in the fresh concrete matrix in order to achieve a high penetration of the multifilament yarns by the cementitious matrix. Each new layer of reinforcement was started by inserting the peripheral edge fabric. Then the inner layers were aligned with their long sides flush with the edge fabric (Fig. 8). The varying width of the edge fabric resulted in the desired offset of the butt joints as explained in section 2.4. The edge fabrics were prefabricated in the widths required, which were chosen such that two edge fabrics with different widths could be produced simultaneously from a single textile roll 1.23 m wide (Fig. 9).
At the front ends the textiles were initially rolled out with an overlap, and a flush butt joint was achieved with electric fabric scissors. The required positional accuracy of the reinforcement could be ensured through continuous measurement of the layer thickness. After inserting the first six textile reinforcement layers, the preassembled steel reinforcement cage was installed in the centre of the shell (Fig. 11). The spacing of the reinforcing bars of the cage were adjusted in such a way that the reinforcement cage fitted precisely between the guiding tubes of the steel component. After installation, the reinforcement cage was completely encased in concrete and the production process of the TRC shell was continued by inserting the six further textile reinforcement layers (Fig. 10). Thus, each of the four TRC shells was completed within one working day in a continuous production process. The precast approach developed made it possible to produce all four shells with a single formwork. Production of the shells in situ would have required a continuous formwork for all four shells and elaborate falsework at the final height of 4 m. Furthermore, the heated production tent made it possible to produce the shells during the cold winter months. Stripping could be carried out after only 10 days of curing because – owing to the use of highstrength concrete – the TRC shell then already had sufficient strength to accommodate the stresses induced by the stripping process.
3.2
Fig. 12. Timber formwork for TRC shell in fabrication tent with movable working platform
Fig. 13. Production of the TRC shell using shotcrete
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Erection of the TRC shells
Prior to the erection of the TRC shells, the four reinforced concrete columns were levelled, aligned and brought to the desired height. The columns were then joined to the concrete foundation with threaded bars anchored in the concrete foundation. In particular, the steel base plate welded to the column reinforcement at the bottom of the columns was bolted to the pad foundation (Fig. 3). In order to transfer the largeformat TRC shell from the production tent to the reinforced concrete columns, the movable roof of the production tent was opened and the shell was lifted off its formwork with a mobile crane (Fig. 14).
Fig. 14. Transferring a TRC shell from the production tent to the top of the RC column using a mobile crane
A. Scholzen/R. Chudoba/J. Hegger · Thinwalled shell structures made of textilereinforced concrete
aligning the shells has been proposed and realized as well. Issues concerning the material behaviour and ultimate limit state assessment are presented in the companion paper [13]. These large shells demonstrate the application potential of this innovative, highperformance composite material. The present example of the TRC pavilion is intended to inspire designers and architects to implement further new applications of textilereinforced concrete in practice.
Acknowledgements
Fig. 15. Loadbearing structure after final adjustment and coupling of the TRC shells (photo: bauko 2, RWTH Aachen University)
The TRC shells were lifted with the crane at a single point only: the centre. From a structural point of view, the load during stripping corresponded to the final stress state with predominant membrane stresses. In this way no additional transportation anchors were needed for lifting. Instead, the connection of the TRC shell to the crane was realized using a thickwalled hollow steel profile, which was inserted into the embedded steel component and fixed by three steel bolts. The hollow steel profile about 1.20 m high automatically stabilized the shell during the stripping and erection process. The embedded steel component was also used for the final positional adjustment of the shells and the structural connection between shell and column. For this purpose, the four threaded bars protruding from the column were fed through the four guide tubes of the steel component during erection (Fig. 11). In the final state it was then possible to align the shells accurately using nuts which were placed under the steel component, so that a planned gap of 2 cm between the shells was attained (Fig. 15). After final adjustment of the umbrellas, the joints were sealed at each column head and base, and the TRC umbrellas were bolted together with steel joints as explained in section 2.1. Temporary scaffolding was necessary for erecting and coupling the TRC shells, which was dismantled after completion of the work.
4
Conclusions
This paper describes the structural design as well as the construction of a demonstration structure with a roof consisting of textilereinforced concrete (TRC) shells. Based on the analysis of the loadbearing behaviour of the hypar shells, a reinforcement concept was developed reflecting the flow of the principal stresses within the shell structure. Furthermore, a fabrication technique for the TRC shells as precast elements was developed together with the contractor which met the high requirements regarding the positional accuracy of the textile reinforcement layers over the filigree shell thickness. Besides the issues concerning the structural design and production of the shells as precast elements, it was also necessary to address the appropriate design of the connections. A solution for erecting and
The authors wish to thank the German Research Foundation (DFG) for financial support within the collaborative research centre SFB 532 “Textilereinforced concrete – development of a new technology” and DFG project CH 276/22.
References 1. Hinzen, M., Brameshuber, W.: LoadBearing Behaviour of Textile Reinforced Concrete with Short Fibres. In[a1]: Fibre Reinforced Concrete: Challenges and Opportunities. Proc. of 8th RILEM Int. Symposium, Barros, J. A. O. (ed.), Portugal, 19–21 Sept 2012. 2. Rypl, R., Chudoba, R., Scholzen, A., Voˇrechovsky´, M.: Brittle matrix composites with heterogeneous reinforcement: Multiscale model of a crack bridge with rigid matrix. Composites Science and Technology, 2013, 89, pp. 98–109. 3. Soranakom, C., Mobasher, B.: Correlation of tensile and flexural responses of strain softening and strain hardening cement composites. Cement & Concrete Composites, 2008, 30, pp. 465–477. 4. Larrinaga, P., Chastre, C., SanJose, J. T., Garmendia, L.: Nonlinear analytical model of composites based on basalt textile reinforced mortar under uniaxial tension. Composites: Part B, 2013, No. 55, pp. 518–527. 5. Hegger, J., Goralski, C., Kulas, C.: Schlanke Fußgängerbrücke aus Textilbeton – Sechsfeldrige Fußgängerbrücke mit einer Gesamtlänge von 97 m (A Pedestrian Bridge Made of Textile Reinforced Concrete). Beton und Stahlbetonbau, 2011, 106, No. 2, pp. 64–71 (in German). 6. Hegger, J.; Kulas, C.; Raupach, M., Büttner, T.: Tragverhalten und Dauerhaftigkeit einer schlanken Textilbetonbrücke (LoadBearing Behavior and Durability of a Slender Textile Reinforced Concrete Bridge). Beton und Stahlbetonbau, 2011, 106, No. 2, pp. 72–80 (in German). 7. Kulas, C., Schneider, M., Will, N., Grebe, R.: Hinterlüftete Vorhangfassaden aus Textilbeton – Tragverhalten und Ausführung (Ventilated façade structures made of textile reinforced concrete – structural behavior and construction). Bautechnik, 2011, 88, No. 5, pp. 271–280 (in German). 8. Horstmann, M., Hegger, J.: Sandwichfassaden aus Textilbeton – experimentelle Untersuchungen (Sandwich façades made of Textile Reinforced Concrete – Experimental investigations). Bautechnik, 2011, 88, No. 5, pp. 281–291 (in German). 9. Schladitz, F., Lorenz, E., Jesse, F., Curbach, M.: Verstärkung einer denkmalgeschützten Tonnenschale mit Textilbeton. Beton und Stahlbetonbau, 2009, 104, No. 7, pp. 432–437. 10. Ehlig, D., Schladitz, F., Frenzel, M., Curbach, M.: Textilbeton – Praxisprojekte im Überblick (Textile concrete – an overview of executed projects). Beton und Stahlbetonbau, 2012, 107, No. 11, pp. 777–785 (in German).
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11. Cassinello, P., Schlaich, M., Torroja, J. A.: Félix Candela. In memoriam (1910–1997). From thin concrete shells to the 21st century lightweight structures. Informes de la Construcctión, 2010, 62, No. 519, pp. 5–26. 12. Scholzen, A., Chudoba, R., Hegger, J.: Dünnwandiges Schalentragwerk aus Textilbeton: Entwurf, Bemessung und baupraktische Umsetzung. Beton und Stahlbetonbau, 2012, 107, No. 11, pp. 767–776. 13. Scholzen, A., Chudoba, R., Hegger, J. (2015): Thinwalled shell structures made of textilereinforced concrete – Part II: Experimental characterization, ultimate limit state assessment and numerical simulation. Structural Concrete, 16: 115–124. doi: 10.1002/suco.201400046. 14. Schätzke, C., Schneider, H. N., Joachim, T., Feldmann, M., Pak, D., Geßler, A.; Hegger, J., Scholzen, A.: Doppelt gekrümmte Schalen und Gitterschalen aus Textilbeton. In: Proc. of 6th Colloquium on Textile Reinforced Structures, Curbach, M., Ortlepp, R. (eds.), Berlin, 2011, pp. 315–328. 15. Schnabel, A., Grieß, T.: Production of noncrimp fabrics for composites. In: Noncrimp fabric composites: manufacturing, properties and applications, Lomov, S. V. (ed.), Woodhead Publishing Series in Composites Science and Engineering, No. 35, Woodhead, Oxford, 2011.
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Dipl.Ing. Alexander Scholzen RWTH Aachen University Institute of Structural Concrete (IMB) MiesvanderRoheStr. 1 52074 Aachen Germany ascholzen@imb.rwthaachen.de
Dr.Ing. Rostislav Chudoba RWTH Aachen University Institute of Structural Concrete (IMB) MiesvanderRoheStr. 1 52074 Aachen Germany rostislav.chudoba@rwthaachen.de
Prof. Dr.Ing. Josef Hegger RWTH Aachen University Institute of Structural Concrete (IMB) MiesvanderRoheStr. 1 52074 Aachen Germany heg@imb.rwthaachen.de
Technical Paper Alexander Scholzen* Rostislav Chudoba Josef Hegger
DOI: 10.1002/suco.201400046
Thinwalled shell structures made of textilereinforced concrete Part II: Experimental characterization, ultimate limit state assessment and numerical simulation The present paper describes a design approach for textilereinforced concrete (TRC) shells which reflects the interaction between normal forces and bending moments based on the crosssectional strength characteristics of the material determined experimentally. The influence of oblique loading on the composite strength of TRC elements with flexible reinforcement is included in a normalized interaction diagram for combined loading. As an example, the design approach is applied to the ultimate limit state assessment of a TRC shell in double curvature. Furthermore, the general applicability of the design approach is discussed in the light of the nonlinear loadbearing behaviour of TRC. Due to its strainhardening tensile response, stress redistributions within the shell result in loadbearing reserves. Details of the structural design and production solutions developed and applied during the realization of the TRC shell structure are described in the companion paper (Part I). Keywords: cementitious composites, strainhardening composites, textilereinforced concrete, hypar shells, design of concrete shells, numerically based assessment, anisotropic damage model
1
Introduction
Assessment rules are needed for the design of textilereinforced concrete (TRC) shell structures in order to introduce this innovative composite material successfully into engineering practice. Engineering models that reflect the tensile, bending and shear strength of TRC elements have already been developed in recent years in analogy to those for conventional steel reinforced concrete structures. Crosssectional idealizations for design have been provided for loadbearing TRC beam elements [1, 2, 3], steel reinforced concrete structures retrofitted with TRC [4] and TRC sandwich panels [5]. Whereas steelreinforced concrete crosssections can be designed and dimensioned solely based on the material laws for steel and concrete, the direct design of TRC crosssections using the component characteristics is not yet possible. The reason or this is the existence of a wide vari
* Corresponding author: ascholzen@imb.rwthaachen.de Submitted for review: 6 June 2014 Accepted for publication: 17 July 2014
ety of textile fabrics [6] differing in material, type of weave and coating, which affect the stressstrain response of the composite quite significantly. Therefore, the crosssectional strength characteristics of TRC have to be determined experimentally for each material combination considered. For this purpose, several types of test setup have been developed recently [3, 7, 8, 9]. The existing engineering models for TRC [1, 2, 3] have been derived mostly for relevant uniaxial stress states, e.g. for TRC beam or truss elements. However, as documented in [10], by using simple linear finite element analyses, it is possible to exploit the high potential of this composite material, especially in thin shell structures. However, engineering models and design tools for TRC shell structures are still lacking. In this paper, we propose a systematic approach to the ultimate limit state assessment of spatial TRC structures with complex loading scenarios. Compared with the engineering models mentioned, two additional important effects are included in the design approach: i) simultaneous action of normal forces and bending moments on a TRC shell crosssection and ii) a strength reduction due to the direction of loading not being aligned with the orientation of the textile fabrics. The paper starts with a review of the test setups used for deriving the strength characteristics of the TRC crosssection (section 2.1). This is followed by a brief discussion of the test data interpretation (section 2.2). A simplified nm interaction diagram for combined loading is introduced in section 3.1 and extended with the effect of oblique loading and butt joints between the fabrics in sections 3.2 and 3.3 respectively. The general assessment criterion is then given in section 3.4. The proposed automated assessment procedure accounting for the anisotropy of the TRC shell exposed to general loading conditions is described in section 3.5. An example of the application of the assessment procedure is given in section 4 for a roof structure in double curvature, including the evaluation of the crosssectional strength characteristics in section 4.1 and the evaluation of the utilization ratio in section 4.2. The nonlinear loadbearing behaviour of TRC and the structural reserves available due to stress redistributions within the shell are studied numerically in section 4.3. The present paper extends and generalizes the concepts originally published in the German language [11].
ÂŠ 2015 Ernst & Sohn Verlag fĂźr Architektur und technische Wissenschaften GmbH & Co. KG, Berlin Âˇ Structural Concrete (2015), No. 1
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2 2.1
Experimental characterization of TRC Test setups for tensile and bending loads
The strength characteristics of a TRC crosssection needed for the ultimate limit state assessment of the roof shell structure described in [12] have been determined using the tensile and bending tests depicted in Figs. 1 and 2 respectively. Whereas the design of the bending test setup is relatively simple, the design of the tensile test setup represents a nontrivial problem. A variety of setups have been presented in recent years [3, 8, 9]; an overview and classification is provided in [7]. The primary goal in the design of the setup is to induce a uniaxial stress state within the tested length. In the literature, two alternative approaches to the design of the clamping can be distinguished: i) load introduction through butt strap clamps or ii) load transfer using a waisted specimen shape. The setup with butt strap clamps [7, 9] is appealing owing to the simplicity of specimen production and the gradual and smooth load transfer into the specimen along the clamped zone. It is especially suitable for thin crosssections with only a few layers of textile fabrics. However, this setup could not be used in the present case of the 6 cm thick crosssections with 12 layers of carbon fabrics. The main reason was that the maximum achievable load that can be transferred through the butt strap clamps is too low. Even when using a high lateral pressure (limited by the compressive strength of the concrete) or glue to maximize the force transfer between butt strap and concrete surface, the achievable load would not be sufficient.
Fig. 1. Bending test setups used: a) threepoint bending test, b) fourpoint bending test
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Another deficiency in the setup for the relatively thick crosssection is the fact that the stress profile over the crosssectional thickness becomes nonuniform, leading to significant stress concentrations in the outer fabric layers. Therefore, the test setup with dogbone specimens depicted in Fig. 2a was used, with the load transmitted through round steel parts adjusted to the waisted shape. It
Fig. 2. a) Tensile test setup with waisted specimens, b) composite stressstrain response, c) textile stressstrain response
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should be noted that this setup certainly has limitations, too. In particular, the load transfer through the steel parts into the anchorage zones of the waisted specimen induces a multiaxial stress state at the transition from the tested zone to the anchorage zone. The resulting nonuniform stress profile in the rovings over the width of the specimen crosssection results in the maximum achievable tensile force being underestimated. Another issue to consider in the test design is the activation of the inner filaments of the yarns by providing a sufficient anchorage length at the ends of the dogbone specimens. For the type of fabric chosen, the anchorage length of 20 cm turned out to be appropriate. For other types of fabric, e.g. consisting of yarns penetrated by epoxy resin, a significantly shorter anchorage length would be required. Obviously, a tensile test setup inducing a perfectly uniaxial stress state over the whole tested zone is difficult to realize. Moreover, even for a carefully designed setup with a very smooth transfer of stresses into the specimen and then into the fabric, the failure will still most probably be observed at the crack near the clamps. This can be explained by the fact that the periodicity of the stress field in the fabric along the specimen with multiple cracks contributes to the activation of the inner filaments. At the boundary crack, the periodicity is lost and the positive effect of a neighbouring crack is not available any more [13]. In view of the design and the safety assessment, we can conclude that the measured strength represents a lower bound of the true crosssectional strength. However, in order to exploit the whole potential of the composite, a careful design of the test setup minimizing the deficiencies inherent to the tensile load introduction is necessary. Therefore, the characteristics of the tensile response that can be used for a quick assessment of the quality of the measured tensile strength will be reviewed.
2.2
Quality of the measured tensile test data
A detailed interpretation of the stressstrain response enables an assessment of the quality of the tensile test performed. In order to explain the concept, let us briefly review the strainhardening behaviour of the brittle matrix composite depicted in Figs. 2b and 2c with three distinct stages [7, 8, 14, 15]: I) uncracked stage, IIa) distributed cracking of the concrete matrix and IIb) postcracking stage with a saturated crack pattern. The composite stresses shown in Fig. 2b are evaluated using Ďƒc = F/A, with F representing the measured tensile force. The same experiments are also shown for textile stresses evaluated with Ďƒtex = F/A in Fig. 2c. The direct link between the composite stress and the textile stress is Ďƒc = Ď Âˇ Ďƒtex. Figs. 2b and 2c show the responses of two test series with different reinforcement ratios. In both series, 12 layers of carbon fabric were used [12]. The total crosssectional area of the 800 tex carbon rovings, each with a crosssectional area of 0.447 mm2, was Atex = 85.8 mm2. The parameter that was varied was the thickness of the specimens, with values of h1 = 6 cm and h2 = 4 cm, corresponding to crosssectional areas A1 = 8400 mm2 and A2 = 5600 mm2 and reinforcement ratios Ď 1 = 1.02 % and Ď 2 = 1.53 % respectively.
The quality of the test results can be easily verified by comparing the initial and final stiffnesses of the strainhardening response obtained with analytically calculated values. For a given reinforcement ratio, the initial composite stiffness EIc of a TRC specimen is obtained using the rule of mixture as follows: EcI
Etex Â˜ U Em Â˜ 1 U
(1)
where Em and Etex denote the Youngâ€™s modulus of the concrete matrix and the textile fabric respectively. For the material components used, the Youngâ€™s modulus of concrete at the age of testing was Em = 28 427 MPa and the mean Youngâ€™s modulus of the carbon rovings measured in a yarn tensile test with a length of 300 mm was Etex = 180 862 MPa [16]. For the two reinforcement ratios used, the composite stiffness in the initial, uncracked stage are calculated as EIc, 1 = 30 764 MPa and EIc, 2 = 29 983 MPa respectively. As indicated in Figs. 2b and 2c, these values fit well with the composite stiffness obtained in the test. Another verification possibility is provided by the fact that the final stiffness in the postcracking regime (saturated cracking state, IIb) should be equal to the stiffness of the textile reinforcement Etex (Fig. 2c). The horizontal shift between the stressstrain curves of the composite and the yarn is caused by the socalled tension stiffening effect. For completeness, the equivalent reinforcement stiffness EcIIb = Etex Âˇ Ď is also plotted in Fig. 2b. The observation that the tests performed reproduce the stiffness of the reinforcement in the postcracking regime can be regarded as confirmation of full activation of the multifilament yarns within the tested zone. In some published results [3, 7, 8] the measured final stiffness was significantly lower than the stiffness of the reinforcement. This kind of response indicates some source of distortion in the test results, either due to an insufficient anchorage length or a significantly nonuniform stress profile within the composite crosssection in the load transfer area between the clamps. Summarizing, the test programme performed with different fabrics and reinforcement ratios and a detailed interpretation of the test results established the basis for the evaluation of the crosssectional strength characteristics relevant for the ultimate limit state assessment. With reference to Figs. 1 and 2, the values of tensile and bending strength were obtained as follows: nR
FuTT b
mR
min Fu3Pl 4b , Fu4Pl 6b
(2)
where FuTT, Fu3P and Fu4P denote the ultimate loads achieved in the tensile, threepoint and fourpoint bending tests respectively.
3 3.1
Method for ultimate limit state assessment Interaction of normal and bending loads
In a general loading scenario in an arbitrary crosssection of a TRC shell, normal forces and bending moments act simultaneously. For such a combined loading, an nm interaction needs to be considered in the ultimate limit state assessment in a similar way to the design codes for steel re
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Fig. 3. Design approach for TRC shell structures based on a simplified nm interaction diagram
inforced concrete [17]. A simplified nm interaction diagram for TRC can be constructed using the strength characteristics obtained experimentally for uniaxial tension nt,Rd [kN/m], uniaxial compression nc,Rd [kN/m] and pure bending mRd [kNm/m], assuming linear interpolation between these values in the nm interaction diagram (see Fig. 3a). Let us remark here that such a simplified linear nm interaction diagram must represent a lower bound of the real nonlinear interaction between normal force and bending moment. A more accurate representation of the interaction diagram can be obtained by using a numerical model of a crosssection employing the equilibrium conditions of normal forces and bending moments at the ultimate limit state. As a thorough presentation of the numerical studies performed and the accompanying validation tests with combined tensile and bending loads would go beyond the scope of this paper, they will be provided in a subsequent publication. Here, only the two most important conclusions apparent from Fig. 3a are summarized in order to justify the simplifying assumption:
As apparent from Fig. 3b, the normalized stress resultants represent the utilization ratio of the crosssection with respect to the design values of the strength characteristics for tension nt,Rd, compression nc,Rd and bending mRd. Considering the fact that the values of the strength characteristics are all positive, the normalized stress resultants attain their ultimate strength values at Îˇ(.) = 1.0. For a combined loading on a crosssection with normal force and bending moment, the total utilization ratio Îˇnmd is defined as follows:
i) For combined tension and bending, the linear form of the nm interaction diagram can represent the real behaviour relatively well. ii) For combined compression and bending, the linear approximation leads to an underestimation of the ultimate crosssectional strength and is on the safe side.
In the design procedure described here we tacitly assume isotropic material properties with crosssectional strength characteristics nt,Rd, nc,Rd and mRd independent of the loading direction. However, a TRC shell crosssection with orthotropic reinforcement structure exhibits an anisotropic behaviour due to the misfit between the direction of the principal tensile stresses given by angle Ď•1 and the orientation of the fabrics Î´ (Fig. 4). In particular, the deviation angle Îą is equal to
Based on the proposed nm interaction diagram in Fig. 3a, the ultimate limit state assessment can be performed by verifying that the design values of the stress resultants nEd [kN/m] and mEd [kNm/m] lie within the admissible range (shaded area in Fig. 3a) for all load cases. For convenience, the linear nm interaction diagram has been transformed into a normalized form using the normalized stress resultants:
Kntd
118
nEd nt,Rd
Kncd
nEd nc,Rd
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Kmd
mEd mRd
(3)
Knmd
max Kntd , Kncd Kmd
(4)
In analogy to Fig. 3a, it must be verified in the ultimate limit state assessment of the TRC shell that the design values of the total utilization ratio Îˇnmd for all elements and all load case combinations lie within the admissible range Îˇnmd â‰¤ 1.0 (shaded area in Fig. 3b).
3.2
D
Strength reduction for oblique loading
M1 G
(5)
where Ď•1 is obtained as follows:
M1
Â§ V xy Âˇ S arctan Â¨ Â¸ with M1 d V V 2 ÂŠ x 2Âš
(6)
The deviation of the textile reinforcement leads to an increased stress concentration in the outer filaments of the
A. Scholzen/R. Chudoba/J. Hegger Âˇ Thinwalled shell structures made of textilereinforced concrete
Fig. 4. Angle between direction of principal stresses and orientation of fabric
roving at the crack edges, thus reducing the total loadbearing capacity [2]. This can be taken into account through the reduction factor kÎą depending on the deviation angle Îą [1, 2, 3]: kD
1
D  90q
(7)
For the ultimate limit state assessment, this leads to a dependency between the deviation angle and the crosssectional strength characteristics for tensile normal force and bending moment in the Ďƒ1 direction, i.e. nt,Rd(Îą) and mRd(Îą). Assuming full alignment of the rovings with the principal stress direction Ď•1 as depicted in Fig. 4, the strength values can be obtained as the sum of the strength contributions of the rovings in the 0Â° and in 90Â° directions reduced by the factors kÎą and 1 â€“ kÎą respectively: nt,Rd(D ) mRd(D )
mRd,0q Â˜ cos(D ) Â˜ kD mRd,90q Â˜ sin(D ) Â˜ 1 kD
nt,Rd,0q Â˜ cos(D ) Â˜ kD nt,Rd,90q Â˜ sin(D ) Â˜ 1 kD
(8)
The compressive strength nc,Rd of the TRC crosssection is independent of the loading direction in the shell plane and can be obtained as follows:
Part I, the major goal in the design of the reinforcement layout is to minimize the number of interruptions to the reinforcement layers in a crosssection. Regarding the case of a uniform layup with nf fabric layers and, at most, nf,int interruptions within a crosssection, we can introduce a strength reduction factor in the form kb
nf nf,int
For the sake of simplicity, we shall consider this factor to be constant over the whole shell and will not introduce it as a variable. Let us also emphasize that this simple treatment of the interruptions is possible only if the offset between the butt joints in different layers is equal to or greater than the anchorage length of the fabric.
3.4
Assessment criterion for a crosssection of the shell
In order to include the effects of oblique loading and the fabric discontinuities in the assessment, the utilization ratio introduced in Eq. (3) can be rewritten using Eqs. (8) and (10) as
(9)
Kntd(D )
nEd(M1) kb nt,Rd(D )
where fcd stands for the concrete compressive strength and h for the shell thickness.
Kncd(D )
Kmd(D )
mEd(M1) kb mRd(D )
nc,Rd
3.3
fcd Â˜ h
Strength reduction due to the discontinuities in the reinforcement layers
Since the discontinuities in the reinforcement layers cannot be avoided due to the limited width of the textile fabrics, their effect on the crosssectional strength must be considered in the assessment procedure. As described in
(10)
nf
nEd(M1) nc,Rd
(11)
In analogy to Eq. (4) the sum of the utilization ratios for normal forces and bending moments is evaluated as the total angledependent utilization ratio
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(12)
Knmd(D ) d 1.0
thus establishing the basis for an automated assessment of TRC shell structures. It should not be forgotten that both the stress resultants and the strength characteristics are field variables. Therefore, software support for implementing the assessment criterion in Eq. (12) is required when assessing real structures.
3.5
Automated assessment procedure
Since the design values of the composite strength depend on the orientation of the textile fabric, it is not possible to identify a priori the critical shell crosssections relevant for the ultimate limit state assessment. Whereas the point of maximum principal tensile stresses can be determined for each load case combination, this point does not necessarily govern the design because the largest deviation in the fabric orientation may occur at some other point in the shell. As a consequence, the design values of the stress resultants must be evaluated for all possible load case combinations constructed in accordance with DIN EN 1990 [18] and for all points of the TRC shell taking into account the aforementioned directional dependency of the strength values (Eq. (8)). The design values of the normal forces and bending moments are derived by setting up the permutation of the individual load cases distinguishing permanent loads Gk,j, the leading variable load Qk,1 and accompanying additional variable loads Qk,i>1: Ed
ÂŚ jt1 J G,j Â˜ Gk,j J Q,1 Â˜ Qk,1 ÂŚi!1\ 0,i Â˜ J Q,i Â˜ Qk,i
(13)
where ÎłG,j and ÎłQ,i are the partial safety factors and Ďˆ0,i the combination coefficient. In order to handle the increased complexity of the ultimate limit state assessment of TRC shell structures efficiently, a numerical tool has been implemented to perform the following calculation steps: 1. Characteristic values of the stress resultants Ek = {mx, my, mxy, nx, ny, nxy} for all load cases nlc are imported from the linearelastic finite element analysis. 2. Using the field variables obtained, the design values of the stress resultants Ed are generated according to Eq. (13) for all possible load case combinations nlc. 3. The direction of the principal stresses Ď•1 and the deviation angle Îą are calculated using Eqs. (5) and (6) for each element of the finite element discretization nelem and each load case combination nlcc. 4. The fields of normal forces and bending moments are transformed into the direction of the principal stresses applying coordinate transformation with respect to the global coordinate system (x, y): nEd(M1)
1 1 Â˜ (nx ny ) Â˜ (nx ny ) Â˜ cos(2M1) 2 2 nxy Â˜ sin(2M1) (14)
mEd(M1)
120
1 1 Â˜ (mx my ) Â˜ (mx my ) Â˜ cos(2M1) 2 2 mxy Â˜ sin(2M1)
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5. The directiondependent utilization ratios are calculated by substituting the results of Eqs. (8) and (13) in Eq. (11). 6. Finally, using (Eq. (12), it must be verified that the total utilization ratio Îˇnmd(Îą) lies within the admissible range for all elements and all loading case combinations considered. Let us remark here that for the sake of simplicity, this explanation only includes the direction of the maximum principal tensile stress. However, in order to cover all possible combinations of tension and compression loads (i.e. tension/tension, tension/compression, compression/compression) the second principal stress direction Ď•2 is also included in the evaluation, which allows the largest value of the compressive normal force to be included in the assessment as well. Furthermore, as the direction of the principal stresses calculated from the stress resultants might also vary for the top and bottom surfaces of a TRC shell, the assessment procedure described is performed for both sides. In order to demonstrate the design procedure described, the following section shows the ultimate limit state assessment of the TCR shell structure actually built (described in [12]).
4 4.1
Application of the assessment method to the built shell Determination of the crosssectional strength characteristics
For the given application example, the crosssectional strength characteristics nt,Rd [kN/m], nc,Rd [kN/m] and mRd [kNm/m] have been determined experimentally using tensile, compressive and bending tests as described in section 2. The crosssectional thickness, reinforcement layout and production process of the tensile and bending specimens tested were equal to the conditions of the built shell. The crosssectional strength values for tension and bending were evaluated for both the 0Â° and 90Â° orientations of the textile fabric. As the spacing of the rovings was slightly larger in the 0Â° direction [12] due to manufacturing constraints, the strength values determined in the 0Â° direction were slightly lower than those in the 90Â° direction. For the sake of simplicity, only the lower values obtained for the 0Â° orientation were considered in the ultimate limit state assessment. The mean values of the ultimate tensile and bending strengths of a unit crosssectional width were nt,Rm
min(nt,R,0q,nt,R,90q )
996 kN/m
mRm
min(mR,0q,mR,90q ) 15.6 kNm/m
(15)
The corresponding characteristic values (5 % quantiles) were obtained using the statistical evaluation of the measured ultimate loads in accordance with DIN EN 1990 [18], leading to a reduction factor Ď‡ due to scatter of the test results: Ď‡n = 0.81 for the tensile tests and Ď‡m = 0.80 for the bending tests. Considering a partial safety factor Îłtex = 1.5, the design values of the crosssectional strength characteristics were obtained as nt,Rd
F n Â˜ nt,Rm / J tex
539 kN/m
mRd
F m Â˜ mRm / J tex
8.3 kNm/m
(16)
A. Scholzen/R. Chudoba/J. Hegger · Thinwalled shell structures made of textilereinforced concrete
The compressive strength of the TRC shell crosssection was calculated according to Eq. (6). In the given case, the finegrained concrete described in [12] belonged to strength class C55/67, so the design value for the compressive strength of a unit crosssectional width equates to nc,Rd fck /J c h 55MPa/1.5 0.06 m 2200 kN/m
(17)
Further input needed for the assessment procedure is the strength reduction factor due to discontinuities in the fabric layers kb given in Eq. (10). With a number of layers nf = 12 and nf,int = 2 butt fabric joints in a crosssection (see companion paper [12], Fig. 8) and an offset of the butt joints greater than the required anchorage length (see section 2.1), the reduction factor equates to kb = 0.83
(18)
Let us remark here that this reduction was carried out for all crosssections independently of the local reinforcement layout so that it was very simple to implement in the assessment code. It should be noted, however, that (as described in the companion paper) the layout of the fabrics followed the direction of tensile stresses along the shell edges [12]. No butt joints were located at these crosssections, so the overall strength reduction described was too severe. A more detailed treatment of the strength reduction, including the location of joints and orientation of the butt joints with respect to the direction of the principal stresses would allow for a higher utilization of the composite.
4.2
Fig. 5. Numerical assessment of the TRC roof structure for all elements of the finite element discretization and all load case combinations
Ultimate limit state assessment
For the ultimate limit state assessment of the TRC roof structure, wind, snow and imposed loads were analysed using a linear finite element model. Furthermore, restraint stresses due to shrinkage and temperature changes were imposed. In total, 12 different loading cases were defined, resulting in 740 load case combinations according to Eq. (13). Owing to the symmetry of the roof structure, only two of the doublecurvature shells were modelled in the finite element analysis using linear shell elements. The stress resultants were evaluated on a regular grid of crosssectional points with a spacing of 12.5 × 12.5 cm. The result of the numerical assessment is shown in the ηnd–ηmd interaction diagram in Fig. 5. Each dot in the diagram corresponds to a particular crosssectional point of the TRC shell and a particular load case combination evaluated for the first and second principal directions on the top and bottom of the shell. The highest utilization ratio equated using Eq. (12) was ηnmd = 0.604. In order to assign a spatial context to the utilization ratios depicted in Fig. 5, the maximum values of the total utilization ratio ηnmd(x) in each crosssection x for all load case combinations, i.e. max(x ) Knmd
max j
ªK D (x ),x º» 1..nlcc ¬ « nmd,j j ¼
(19)
are shown as field variables in Fig. 6. As expected, the highest utilization ratios arise along the tensile ring running parallel to the shell edges, since in these regions the
Fig. 6. Spatial distribution of the maximum utilization ratio in the TRC shell structure for all load case combinations (plan view)
maximum principal stresses occur for symmetric loading conditions as shown in Fig. 6 in the companion paper [12]. It must be noted, though, that the highest utilization ratio ηnmd = 0.604 does not occur exactly at the middle of a shell edge, where the highest principal tensile stresses occur, but that the critical crosssection shifts to the position
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marked in Fig. 6 due to the assumed strength reduction in the composite material for oblique loading (Eq. (8)).
4.3
Comparison with the nonlinear structural response
Motivated by the need for load case superposition within load case combinations, the ultimate limit state assessment approach described in the previous section was based on linearelastic finite element analysis even though the material behaviour is highly nonlinear (section 2.2). It must be said that the use of linearelastic analysis when designing TRC composites is on the safe side due to the underlying strainhardening material response in tension. Indeed, stress redistributions within the shell lead to a larger loadcarrying capacity than predicted by the linearelastic analysis. In order to investigate the structural redundancies for the given TCR roof structure and to provide a realistic prediction of the shell deflections for the serviceability limit state, nonlinear simulations were performed for selected horizontal and vertical load case combinations. For this purpose an anisotropic damage model of the microplane type [19, 20], reflecting the evolution of finely distributed, oriented cracks as directiondependent damage variables, has been formulated and implemented [21, 22]. The materialspecific damage function reflecting the strainhardening tensile response was calibrated based on the stressstrain curves obtained from the TRC tensile tests described in section 2.2 (Fig. 2b). To evaluate the loadbearing reserves of the TRC roof structure assessed in section 4.2, let us consider a load case consisting of only permanent loads, including selfweight of the shell (material density ρ = 0.224 kN/m3), additional load on top of the shell (distributed load gk = 0.20 kn/m2) and vertical load due to the attached façade (line load gb = 0.35 kN/M). The utilization ratio obtained for this load case using the assessment procedure described based on a fine finite element discretization, which includes the stress peak values at the shell edges, equates to ηnmd = 0.27. In the subsequent nonlinear analysis this load case has been considered as a reference load with the load factor λref = 1.0. Fig. 7 shows the dependency between the increasing load factor λ and the corner deflection w obtained from
Fig. 7. Evaluation of structural reserves using the nonlinear, anisotropic strainhardening damage model for increasing vertical loading
the nonlinear simulation. As mentioned above, the parameters of the anisotropic damage model were identified based on the tensile tests conducted and therefore reflect the material behaviour corresponding to the mean values of the crosssectional strength characteristics in Eq. (14). Ultimate failure was reached for the load factor λinel = 9.08. For the comparison with the linear analysis, let us first determine the load factor corresponding to full utilization at the ultimate limit state for the design values of material strength (Eq. 16), which is λuls = l/ηnmd = 3.7. Further, the load factor corresponding to the mean strength characteristics (see Eq. (15)) is obtained as λel = γtex/χ · λuls = 1.5/0.81 · 3.7 = 6.85. Comparing this load factor with the prediction obtained using the nonlinear model (λinel = 9.08), the structural reserves due to stressredistribution within the shell can be evaluated for the load case considered as λinel/λel = 1.32. Fig. 8 depicts the spatial distribution of damage calculated using the nonlinear simulation for the load levels specified in Fig. 7. The distribution of the maximum value of the microplane damage, i.e. max(ω), on the top and bottom surfaces of the quarter of the shell is depicted for each load level. The analysis shows that the propagation of damage, i.e. matrix cracking, starts in the middle of the
Fig. 8. Distribution of the maximum damage within the TRC shell for the four loading levels given in Fig. 7
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shell edges and propagates along the ring of principal tensile stresses obtained using the linear FE analysis (see companion paper [12], Fig. 7). At the ultimate limit state the damage spreads over a large area of the shell, indicating a high amount of stress redistribution during the loading process. These redistributions, not reflected in the linearelastic design, are the source of the loadbearing reserves identified using the nonlinear simulation. Let us finally remark that the degree of structural redundancy depends on the smoothness of the stress field induced by a particular load case. When a concentrated local load with highly localized stresses is considered, the effect of the inplane stress redistribution might also be less pronounced or even negligible. Furthermore, no redundancy can be expected for pure uniaxial bending of the shell without any membrane stresses and, thus, no possibility for the damage to propagate to other zones of the shell. Nevertheless, the study performed demonstrates that the linearelastic design approach used provides a lower bound estimate of the ultimate load level.
5
Further issues addressed in the structural assessment
Due to limitations of space, the present paper could not cover all aspects included in the design and assessment of the TRC structure actually built. Special attention has been paid to the design and assessment of joints with the aim of assuring a smooth load transfer between structural elements. Further, the serviceability limit state assessment was performed based on the maximum deflections evaluated, also including the effect of creep. Another issue to be considered in a general assessment method are zones exposed to a significant biaxial tensile loading that might lead to a strength reduction in one direction due to longitudinal cracks induced by the tensile load in the perpendicular direction.
6
Conclusions
The present paper introduces a design approach for TRC shell structures based on crosssectional strength characteristics determined experimentally. The description of the design focuses on the assessment at the ultimate limit state considering the interaction between normal forces and bending moments. In order to take into account all load case combinations and at the same time the orientation of the stress resultants with respect to the orientation of the reinforcing fabrics, an automated assessment tool has been formulated and implemented. The design approach described has been successfully applied and tested with respect to its practical feasibility for the TRC pavilion built at RWTH Aachen University.
Acknowledgements The authors wish to thank the German Research Foundation (DFG) for financial support within the collaborative research centre SFB 532 “Textile reinforced concrete – development of a new technology” and DFG project CH 276/22.
References 1. Hegger, J., Voss, S.: Investigation of the loadbearing behaviour and potential of Textile Reinforced Concrete. Engineering Structures, 2008, 30, No. 7, pp. 2050–2056. 2. Hegger, J., Will, N., Bruckermann, O., Voss, S.: Loadbearing behaviour and simulation of textile reinforced concrete. Material and Structures, 2006, 39, No. 8, pp. 765–776. 3. Voss, S.: Ingenieurmodelle zum Tragverhalten von textilbewehrtem Beton (Design models for the loadbearing behaviour of textile reinforced concrete). Dissertation, Institute of Structural Concrete (IMB), RWTH Aachen University, 2008, ISBN 3939051039, ISSN 09497331 (in German). 4. Schladitz, F., Lorenz, E., Curbach, M.: Biegetragfähigkeit von textilbetonverstärkten Stahlbetonplatten (Bending Capacity of Reinforced Concrete Slabs Strengthened with Textile Reinforced Concrete). Beton und Stahlbetonbau, 2011, 106, No. 6, pp. 377–384 (in German). 5. Hegger, J., Horstmann, M.: Sandwichfassaden aus Textilbeton – Numerik und Ingenieurmodelle (Sandwich facades made of Textile Reinforced Concrete – numerical investigations and engineering models). Bautechnik, 2011, 88, No. 6, pp. 373–384 (in German). 6. Schnabel, A., Grieß, T.: Production of noncrimp fabrics for composites; In: Noncrimp fabric composites: manufacturing, properties and applications, Lomov, S. V. (ed.), Woodhead Publishing Series in Composites Science and Engineering, No. 35, Woodhead, Oxford, 2011. 7. Hartig, J., Jesse, F., Schicktanz, K., HäußlerCombe, U.: Influence of experimental setup on the apparent uniaxial tensile loadbearing capacity of Textile Reinforced Concrete specimens. Materials and Structures, 2012, 45, pp. 433–446. 8. Colombo, I. G.., Magri, A., Zani, G., Colombo, M., di Prisco, M.: Textile Reinforced Concrete: experimental investigation on design parameters. Materials and Structures, 2013, 46, pp. 1953–1971. 9. Larrinaga, P., Chastre, C., SanJose, J. T., Garmendia, L.: Nonlinear analytical model of composites based on basalt textile reinforced mortar under uniaxial tension. Composites: Part B, 2013, No. 55, pp. 518–527. 10. Tysmans, T., Adriaenssens, S., Cuypers, H., Wastiels, J.: Structural analysis of small span textile reinforced concrete shells with double curvature. Composites Science and Technology, 2009, 69, pp. 1790–1796. 11. Scholzen, A., Chudoba, R., Hegger, J.: Dünnwandiges Schalentragwerk aus Textilbeton: Entwurf, Bemessung und baupraktische Umsetzung. Beton und Stahlbetonbau, 2012, 107, No. 11, pp, 767–776. 12. Scholzen, A., Chudoba, R., Hegger, J. (2015): Thinwalled shell structures made of textilereinforced concrete – Part I: Structural design and construction. Structural Concrete, 16: 106–114. doi: 10.1002/suco.201300071. 13. Rypl, R., Chudoba, R., Mörschel, U., Stapleton, S. E., Gries, T., Sommer, G.: A novel tensile test device for effective testing of highmodulus multifilament yarns. Journal of Industrial Textiles, 2014, published online, doi: 10.1177/ 1528083714521069. 14. Hinzen, M., Brameshuber, W.: Loadbearing Behaviour of Textile Reinforced Concrete with Short Fibres. In: Fibre Reinforced Concrete: Challenges and Opportunities, Proc. of 8th RILEM Int. Symposium, Barros, J. A. O., (ed.), Portugal, 19–21 Sept 2012. 15. Mobasher, B., Peled, A., Pahilajani, J.: Distributed cracking and stiffness degradation in fabriccement composites. Materials and Structures, 2006, 39, pp, 317–331. 16. Rypl, R., Chudoba, R., Scholzen, A., Voˇrechovsky´, M.: Brittle matrix composites with heterogeneous reinforcement: Multi
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17.
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scale model of a crack bridge with rigid matrix. Composites Science and Technology, 2013, 89, pp. 98–109. DIN EN 199211, Eurocode 2: Design of concrete structures – Part 11: General rules and rules for buildings; German version EN 199211:2004 + AC:2010. DIN EN1990, Eurocode: Basis of structural design; German version EN 1990:2002 + A1:2005 + A1:2005/AC:2010. Jirásek, M.: Comments on microplane theory. Mechanics of Quasibrittle Materials and Structures, Hermes Science Publications, 1999, pp. 55–77. Carol, I., Jirásek, M., Bazˇant, Z.: A thermodynamically consistent approach to microplane theory. Part I. Free energy and consistent microplane stresses. International Journal of Solids and Structures, 2001, 38, No. 17, pp. 2921–2931. Scholzen, A., Chudoba, R., Hegger, J.: Damage Based Modeling of Planar TextileReinforced Concrete Structures. In: Proc. of Int. RILEM Conference on Material Science, Brameshuber, W. (ed.), Aachen, 2010, pp. 362–370. Scholzen, A., Chudoba, R., Hegger, J.: Calibration and Validation of a Microplane Damage Model for cementbased Composites applied to Textile Reinforced Concrete, In: Proc. of Int. Conf. on Recent Advances in Nonlinear Models – Structural Concrete Applications, Barros, H. Faria, R., Pina, C., Ferreira, C. (eds.), ECCOMAS thematic conf., 2011, Coimbra, pp. 417–427.
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Dipl.Ing. Alexander Scholzen RWTH Aachen University Institute of Structural Concrete (IMB) MiesvanderRoheStr. 1 52074 Aachen Germany ascholzen@imb.rwthaachen.de
Dr.Ing. Rostislav Chudoba RWTH Aachen University Institute of Structural Concrete (IMB) MiesvanderRoheStr. 1 52074 Aachen Germany rostislav.chudoba@rwthaachen.de
Prof. Dr.Ing. Josef Hegger RWTH Aachen University Institute of Structural Concrete (IMB) MiesvanderRoheStr. 1 52074 Aachen Germany heg@imb.rwthaachen.de
Technical Paper Bastian Jung* Guido Morgenthal Dong Xu Hendrik Schröter
DOI: 10.1002/suco.201300066
Quality assessment of material models for reinforced concrete flexural members Nonlinear constitutive models for concrete in compression are frequently defined in design codes. The engineer generally uses either the linear (in SLS) or nonlinear (in ULS) compression model. However, a large variety of different approaches exists for describing the behaviour of the cracked concrete tension zone, and the selection of a corresponding model is usually based on qualitative engineering judgement. The aim of this paper is to assess the prediction quality of several concrete material models in order to provide a quantitative model selection. Therefore, uncertainty analysis is applied in order to investigate the model and parameter uncertainty in the bending stiffness prognosis for flexural members. The total uncertainty is converted into a prognosis model quality that allows a quantitative comparison between the material models considered. The consideration of the reinforced concrete in tension is based on the characterization of the tension stiffening effect, which describes the cracking in an average sense. In the interest of the practical applicability of the models considered, even for large structures, no discrete crack simulations based on fracture mechanics are considered. Finally, the assessment identifies that the prediction quality depends on the loading level and, furthermore, the quality across the models can be quantitatively similar as well as diverse. Keywords: model evaluation, model quality, model uncertainty, parameter uncertainty, tension stiffening
1
Introduction
Numerical simulations are commonly used for analysing structural loaddeformation behaviour, particularly in the case of complex systems with a high number of unknowns, geometrical and material nonlinear behaviour, an irregular geometry of the structure and a large number of load cases and combinations. In the field of structural design, a structural engineer has to decide which phenomena – represented by partial models (PM), e.g. material models, soil models, interaction models, load models – should be considered in the numerical simulation of the global structural model (GM) under different conditions and load cases. In general, a high number of analytical and numerical models for each of these partial models are applied in
* Corresponding author: bastianjung85@gmail.com Submitted for review: 22 August 2013 Revised: 2 May 2014 Accepted for publication: 28 May 2014
construction projects and research studies. In addition, new models are being developed with additional knowledge according to the “real” phenomena. Therefore, the selecting adequate partial models in the global model is not a simple and trivial task. The importance of these partial models according to the global response of the structure can be quantified using variancebased sensitivity analysis. In the case that a PM influences the structural behaviour, it is necessary to quantify its prediction quality MQPM and then subsequently combine both sets of information into the global model quality MQGM for the entire structure [1]. When analysing the uncertainty in the model output, the quantitative model evaluation poses the question as to which model should be chosen in comparison to the other models considered. This study considers the uncertainties due to the nondeterministic input parameters and also uncertainties due to the model prediction error. This probabilistic model evaluation helps to achieve a definite model selection in a quantitative manner. Hence, the question as to which model is the most adequate of the ones considered can be answered by the use of uncertainty analysis. This most adequate model with highest prediction quality should be used in structural engineering problems in order to achieve a greater confidence in the simulation results and to ensure a reliable structural design. Material modelling is a partial model with a potentially strong influence on the computational results and reliable prognosis models [2, 3, 4]. For instance, the analysis of internal section forces for restraintsensitive structures, e.g. pavements, bridge decks, walls, industrial floors, constrained slabs or integral and semiintegral bridges, is crucially dependent on the material model prediction [5]. Therefore, the evaluation of the partial model’s quality for reinforced concrete is the focus of this paper. Either purely linear models, nonlinear compressive models or nonlinear models considering the tension stiffening effect are considered in the evaluation. The uncertainty assessment on a structural level (continuous beams, frames) for the material nonlinear simulation is not exclusively influenced by the partial model’s prediction of a certain structural element or crosssection. Owing to concrete cracking and internal force redistribution, the uncertainty in the structural simulation is mainly influenced by several coupled elements
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(beam, column), which are represented by the partial models. Therefore, the sensitivity analysis determines the influence of each partial model on the global model. The sensitivity indices can be used as weighting factors for the partial model quality in the structural model [1]. Depending on the type of structure and conditions, different phenomena are more or less significant for structural responses such as displacements or stresses. This effect is quantified by the sensitivity indices and turns the partial model quality for a certain phenomenon into a global model quality of the structural model. In order to evaluate just the partial model quality of a certain structural member, it is necessary to analyse the loaddeformation behaviour of the crosssection. Therefore, the material models assessment in this study is investigated according to the bending stiffness prediction for a common reinforced concrete crosssection. Nevertheless, the evaluation method presented using the uncertainty analysis is generally applicable to any type of structural member under various conditions.
2 2.1
Uncertainty analysis General statements
In order to evaluate how closely a model approximates the real system of interest, it is not simply a matter of comparing model results and empirical data [6]. The identification and assessment of the uncertainties on which the model is based is a necessary and helpful methodology for the development and application of engineering models. The uncertainty analysis considers the complexity of the models (epistemic uncertainty, afterwards referred to as model uncertainty, also known as reducible uncertainty, subjective uncertainty, stateofknowledge uncertainty [7]) and the influence of probabilistic input parameters concerning the model output (aleatoric uncertainty, afterwards referred to as parameter uncertainty, also known as variability, irreducible uncertainty, inherent uncertainty, stochastic uncertainty [7]). In general, increasing the complexity in the model description reduces model uncertainty because the accuracy is increased when describing the â€œrealâ€? phenomenon (e.g. material behaviour). However, more and more model input parameters are necessary for the analysis of sophisticated models, which cause a higher parameter uncertainty due to imprecision and randomness in the input parameters, see Fig. 1. The most adequate model of the ones considered is the model with acceptable model uncertainty and suitable parameter uncertainty. This relation between both sources of uncertainties is taken into account in the total uncertainty. Finally, the assessment of model, parameter and total uncertainty achieve the quantification of model prediction quality and subsequently assist model selection based on a quantitative approach. Hence, the most adequate model should be used for structural analysis, design, reliability assessment and, indeed, all other purposes. There are many engineering fields and applications where researchers and engineers state the substantial and crucial importance of the uncertainty assessment in numerical simulations, which affects the decisionmaking process in various engineering issues. For example, the un
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Fig. 1. Relation between model complexity and model uncertainty, based on [6]
certainty analysis is applied to hydrological, hydraulic and environmental simulations [8], reliability and risk analyses [9, 10, 11] and road safety assessment [12]. An overview of the existing uncertainty quantification methods is presented in a paper by Riley [13]. The Bayesian model averaging [14] and the adjustment factor approach [15] are methods commonly used. The limited availability of experimental data for approaches such as the Bayesian model averaging is clearly recognizable in the preliminary design phase of engineering structures. In this phase of a construction project, the engineer can hardly compare the results of numerical models due to the lack of measurement data. Therefore, the authors used the adjustment factor approach, which allows a quantitative comparison between several models without specific experimental data. For the response of a certain model YMi, this method introduces a sort of additive Ea* â€œadjustmentâ€? which is applied directly to the prediction of a reference model YMref in order to account for the uncertainty associated with it [15]: Y
M
i
Y
M
ref
Ea*
(1)
Only one source of uncertainty, the model uncertainty, is included in this approach. Using the concept of additive model framework uncertainty, Most [16] enhanced this approach by additionally taking into account the parameter uncertainty. Assuming an additive total uncertainty, the output of a single model can be approximated by Y
M* i
Y
M
i
M
H' i H
M
ref ,
(2)
where ÎľÎ”Mi is the model uncertainty with respect to the reference model. The error in the reference model itself Îľ Mref is assumed to be a constant additive term for each model [16]. Therefore, knowledge about the exact value of the reference model error is unnecessary. If the differentiation between the model complexity (selection of reference model) cannot be carried out with consistent argumentation, the evidence theory initiated by Dempster [17] and developed by Shafer [18] can be used
B. Jung/G. Morgenthal/D. Xu/H. SchrĂśter Âˇ Quality assessment of material models for reinforced concrete flexural members
for the uncertainty quantification with the extension by Park and Grandhi [19].
2.2
Aleatoric parameter uncertainty
In general, the parameter uncertainty is quantified by the variance in each model output caused by the underlying probabilistic input parameters. The aleatoric parameter uncertainty is computed from the quotient of the standard deviation and the mean value, which leads to the dimensionless coefficient of variation (CoV). Therefore, the parameter uncertainty is defined as M
i CoVparameter
V P
M M
i
(3)
.
i
In order to analyse the model with the nondeterministic input parameters, it is necessary to compute a set of probabilistic input parameters using a sampling method. Latin hypercube sampling (LHS) [20] is an effective sampling method that enables a reliable approximation of the stochastic properties â€“ even for a small number of samples and highly dimensional random variables. Further development of this method in [21] improves the accurate consideration of the correlation between the input parameters. This sampling strategy is independent of the dimensions of the random vectors. Furthermore, its independence is related to the number of random variables included in the analysis. This significantly reduces the number of simulations required in the uncertainty analysis. Hence, LHS is used in the assessment of aleatoric parameter uncertainty.
2.3
Epistemic model uncertainty
According to the estimation of the model uncertainty, a certain model is used as the reference model Mref in order to evaluate the differences in the varying model predictions. These different model outputs are caused by the lack of knowledge of the simplified models in relation to the most complex model considered in the evaluation. Experimental data could be used for this purpose, but no specific measurement data are usually available in the design process. Therefore, the most complex model is fixed in this study as a benchmark. By using the model with the highest complexity, it is safe to assume that the accuracy of describing the physical phenomena should also be the highest. The model uncertainty of the other more simplified models Mi is defined as [16] M Âˇ Â§ M Â§ MÂˇ V Â¨ H ' i Â¸  b2 Â¨Y i Y ref Â¸ ÂŠ Âš ÂŠ Âš
M CoV Â§Â¨ H ' i ÂˇÂ¸ Âš ÂŠ
M i CoVmodel

2
(4)
M Âˇ Â§ M b Â˜ Â¨Y i Y ref Â¸ ÂŠ Âš
Y
M
(5)
ref
This model uncertainty is computed using the mean responses of the models. The absolute difference between the reference model and the more simplified models forms the basis for determining the model uncertainty.
The variance in the model uncertainty is unknown and therefore it is necessary to make an assumption about the form of the underlying distribution in order to obtain a valid confidence level. In engineering applications, a reasonable assumption is that the underlying distribution is normal, because many simulation results encountered in practice can be well approximated by this type of distribution [22]. A moderate divergence from normality will have little effect on the validity of this assumption. Based on this assumption, factor b in Eq. (5) can be chosen corresponding to a certain onesided quantile value (confidence bound defined by percentage points tÎą,Î˝ [22]) as follows: 97.5% o b 1 / t0.025,f
1 /1.960
0.510
95.0% o b 1 / t0.050,f
1 /1.645
0.608
90.0% o b 1 / t0.100,f
1 /1.282
0.780
These assumptions for the model uncertainty quantification are suitable for the assessment in the range of the mean values of the input parameters [16]. Furthermore, theoretical studies as published by Kiureghian and Ditlevsen [23] have to be performed for a reliability analysis. Owing to the significant influence of the type of distribution and the bias on the failure probability, the assumptions according to the model uncertainty should be redefined in order to quantify a model quality in the failure regions.
2.4
Total uncertainty and partial model quality
The total variance in a certain model considering the parameter uncertainty, model uncertainty and the variance in the error of the reference model itself is approximately as follows [16]: M*
V (Y i )  M CoV i total
M
V (Y i )
M CoV i parameter
M
M
2(Y i Y ref )2 b M CoV i model
M
ref ) V ( H
(6)
not considered
The total uncertainty defined as the variance is redefined as the dimensionless coefficient of variation, see Eq. (7). Reformulating the dimensional expression of the uncertainty as the dimensionless indication enables a more precise quantification with respect to the relative model responses. Otherwise, the dimensional uncertainty is related to the magnitude of the model output: M
i CoVtotal
M
M
2 CoV i 2 i CoVparameter model
(7)
The most adequate model of all the models considered is the one with the smallest sum of the model and parameter uncertainty. This leads to the following definition of the model quality based on the corresponding total uncertainty: M
M
i MQPMi =1 CoVtotal
(8) M
i For high total uncertainties CoV total > 1.0, the model quality for each partial model can also be related to the minimum total uncertainty of all the models [24].
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3
Analysis method â€“ energy method with integral description of the material behaviour (EIM)
Generally, numerical analyses such as the finite element method solve a system of equations based on equilibrium conditions. Another method for the computation of numerical solutions is solving an optimization problem based on extremum principles. A representation of this principle is the energy method with integral description of the material behaviour (EIM [25, 26]). The extremum formulation is based on Lagrangeâ€™s principle of the minimum of total potential energy [25]. Using nonlinear optimization, the values Îľ0, Îşy and Îşz are found to minimize the following function: C 3 total
3 iC H 0,N y ,N z 3 aC H 0,N y ,N z Â&#x; MIN
(9)
The material models are described by an integral formulation of the stressstrain relation depending on the strain Îľ(y,z) considering the Bernoulli hypothesis. Therefore, the functions W(Îľ), F(Îľ) and ÎŚ(Îľ) are introduced to describe a unique and complete representation of the material behaviour similar to the stressstrain relation. They are defined as the following integrals:
Fig. 2. Rectangular reinforced concrete crosssection
These integrals enable the strain energy Î iC of a crosssection with the region B to be obtained by integrating the specific strain energy W.
crosssection (see Fig. 2), which is simulated under an increasing bending moment (Î”My = 1 kNm). The simulations are performed with MATLAB (MathWorks). This load increase makes it possible to assess the quality of the material models for the uncracked stage, the crack formation stage, the stabilized cracking stage and the steel yielding stage. The material models are associated with the specific subsections of the crosssection, see Fig. 2. For the concrete in compression (concrete compression, CC), the behaviour is simulated by the nonlinear broken rational function of EC 2 [27] or the fib Model Code for Concrete Structures 2010 [28]. For the plain concrete in tension, the linearelastic material description is applied until the tensile strength fctm is reached (concrete tension, CT). Different tension stiffening models are applied according to the reinforced concrete subsection in tension (reinforced concrete tension, RCT). The depth of the reinforced subsection is defined as hc,eff = 2.5 Âˇ d1 [28, 29].
3 iC
4.2
H
W(H )
Âł0V (H )dH
W(H )
Âł0V (H )dH
F(H )
Âł0 W(H )dH
(10)
H
(11)
H
(12)
ÂłÂłBW( y, z)dydz = ÂłÂłBW ÂŞÂŹH( y, z)ÂşÂź dydz
(13)
The double integral is transformed into an integral along the contour by the Gauss theorem according to Eq. (14):
Ny
Â§ N
Âˇ
ÂłÂłBW( y, z)dydz ÂłL Â¨ÂŠ N 2z F dy N 2 FdzÂ¸Âš
(14)
where the magnitude Îş of the gradient is determined by
N
N y2 N z2
(15)
The potential energy of the external forces of a crosssection loaded by a normal force N and the two bending moments My and Mz is defined by following equation:
3 aC
4 4.1
N Â˜ H 0 M y Â˜ N z Mz Â˜ N y
(16)
Material modelling of reinforced concrete Crosssection
Several crosssection types, e.g. rectangular crosssections, circular crosssections, Tbeams or box girders, can be assessed using the uncertainty analysis, see section 2. The results in this paper (see section 5) focus on a rectangular
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Material modelling of reinforced concrete
The energy method (EIM) introduced above allows the material nonlinearities to be considered, including cracking and tension stiffening. Therefore, the method is used for simulating the loaddeformation behaviour of the rectangular crosssection. The material models considered in this study are listed in Table 1 and some comments on the model characteristics are mentioned in the following paragraphs. The choice of model is carried out in order to compare the prediction quality of linear and nonlinear models, to analyse the effect of compressive stiffness degradation and to quantify the prognosis of several tension stiffening models. However, the model assessment presented in this study has to be seen as a quantitative comparison between the material models considered. Since a variety of other material models exists which are not studied here, the model with the best prediction quality in this study cannot be identified as the best model in general for characterizing the phenomenon. The aim of the evaluation is to present a reasonable method that allows for the quantitative model comparison of certain models. Therefore, the material models for reinforced concrete are chosen in order to emphasize model benefits of different complexity and accuracy.
B. Jung/G. Morgenthal/D. Xu/H. SchrĂśter Âˇ Quality assessment of material models for reinforced concrete flexural members
Table 1. Material models considered for evaluation of prognosis model quality
Partial Model
Concrete
Reinforcement
CC
CT
RCT
linel
linearelastic
linearelastic
linearelastic
linearelastic
brfunc
broken rational function [27, 28]
linearelastic
linearelastic
linearelastic
efunc
broken rational function [27, 28]
linear up to fctm
exponential function [30]
bilinear
multilin
broken rational function [27, 28]
linear up to fctm
multilinear stressstrain diagram [28, 31]
bilinear
modsteel
broken rational function [27, 28]
â€“
â€“
modified steel strains [28, 31, 32]
In the case of linearelastic material modelling, all subsections are modelled assuming linearelastic material behaviour. This material model does not allow any cracking of the concrete due to tension and compression. Therefore, the bending stiffness degradation is excluded for all loading levels, which leads to the simplest material model. This model is denoted as the partial model with the abbreviation â€œlinelâ€?. The material model â€œbrfuncâ€? takes the stressstrain nonlinearity in compression into account. The nonlinear broken rational function of Eurocode 2 [27] or fib Model Code 2010 [28] is applied in order to describe the nonlinear material behaviour of concrete in the compression zone. In contrast, any type of cracking in tension is excluded from this material model. The nonlinear material models (â€œefuncâ€?, â€œmultiinâ€?, â€œmodsteelâ€?) additionally consider the stiffness degradation due to tension cracking as well as the tension stiffening effect. These models consist of the same material descriptions in the plain concrete subsections (CC and CT). Differences between these nonlinear material models exist when considering the tension stiffening effect. The characteristic stages of the reinforced concrete crosssections are the uncracked stage, crack formation stage, stabilized cracking stage and steel yielding stage. In general it is possible to compute strain values to describe the transitions between the cracking stages of the crosssection. The characteristic strains are defined as follows [28, 31]: uncracked stage
H s1
I H sr ,bar Â˜
d xI h xI
(17)
crack formation stage H s2
V s2 Et Â˜ 'H Es
(18)
stabilized cracking stage
H s3
fy Es
Et Â˜ 'H
(19)
steel yielding stage fy
H s4
Es
fy Âˇ Â§ V Âˇ Â§ Et Â˜ 'H G Â˜ Â¨1 s1 Â¸ Â˜ Â¨ H su Â¸ f E ÂŠ sÂš y Âš ÂŠ
(20)
fctm Ec0m
(21)
where: I H sr ,bar
II H sr ,bar
fctm Â˜ Ac, eff
(22)
As1 Â˜ Es
I H sr ,beam
I H sr ,bar
II H sr ,beam
fctm Â˜ Ii As1 Â˜ Es Â˜ ziu Â˜ h d1 x II / 3
'H
(23)
(24)
II I II I MIN H sr ,bar H sr,bar ; H sr,beam H sr,beam
(25)
The characteristics of the crosssection are considered in the computation of the strain values through the amount of tensile reinforcement As1, the moment of inertia Ii, the effective area of concrete in tension Ac,eff and the depth of the compression zone in the uncracked stage xI as well as the cracked stage xII. The ductility of the reinforcement is defined by the coefficient Î´ , and for the highductility reinforcing steels commonly used Î´ = 0.8. The indexes â€œbarâ€? and â€œbeamâ€? express the solution for the strains with respect to a tension bar or flexural member respectively. The coefficient Î˛t,m defines the completeness of the concrete stress distribution over the crack spacing sr,max. The assumptions of constant bond stresses and linear stress distributions in the crack discontinuity areas for all cracking stages leads to Î˛t,m = 0.6 according to Model Code 1990 [31] and fib Model Code 2010 [28] in the case of deformed reinforcing bars and the shortterm (instantaneous) loading condition. The simulation of structures with potentially various cracks generally focuses on the average structural behaviour [33]. Instead of the maximum crack spacing sr,max, the average crack spacing sr,max â‰ˆ 2/3 Âˇ sr,max is used for describing the concrete strain be
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Fig. 4. Stressstrain diagram for concrete in tension considering the effect of tension stiffening according to efunc [30], multilin [28, 31]
Fig. 3. Modified stressstrain diagram for reinforcing bars considering the effect of concrete between the cracks (tension stiffening) according to [28, 31, 32]
tween adjacent cracks. Therefore, the average concrete strain between the cracks reaches εct,m ≈ 2/3 · εct and, consequently, βt = 2/3 · 0.6 = 0.4 [28, 32]. The completeness factor βt = 0.4 is used for all tension stiffening models considered. Based on the strain values for the characteristic cracking stages, varying tension stiffening models are available for the nonlinear simulation of reinforced concrete structures. The material models considered in this paper for describing the tension stiffening effect are introduced in the following paragraphs. The material model considering the modified reinforcing steel strains (“modsteel”) [28, 31, 32] takes into account the tension stiffening effect by reducing the strains in the nonembedded reinforcing bars. The stressstrain relation for the modified steel strains and the nonembedded reinforcing steel are shown in Fig. 3. In order to establish the stressstrain relation for the “modsteel” material model, the strain values Eq. (17) to Eq. (25) and the corresponding stress values Eq. (26) to Eq. (29) are considered in this model. uncracked stage σsl = εII sr,beam · Es
(26)
crack formation stage σs2 = σsl · 1.3
(27)
stabilized cracking stage σs3 = fy
(28)
steel yielding stage σs4 = ft
(29)
The cracking stage strain values are considered in the tension stiffening model “multilin” [28, 31] for the stressstrain relation of the concrete, see Fig. 4. The model is applied to the subsection of the effective area of concrete in tension (RCT, see Fig. 2). Therefore, the tension stiffening
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effect is not considered by reducing the strain values of the reinforcing bars, but is taken into account in the concrete stressstrain relation. The strain values are similarly computed according to Eq. (17) to Eq. (25), and the corresponding stress values are illustrated in Fig. 4. Another model is an exponential function (“efunc”) by Pölling [30], which was originally developed for the stressstrain relation of plain concrete after reaching its tensile strength. In this function, parameter α (see Fig. 4) controls the angle of the descending branch. In this paper the value is computed so that the models “multilin” and “efunc” have the same intersection at strain magnitude εc2. Therefore, this model for the cracked plain concrete is adopted for the description of the tension stiffening effect. However, a clear differentiation in the stressstrain relationship between the crack formation stage and the stabilized cracking stage is not possible. The “efunc” model is applied to the concrete subsection (RCT, see Fig. 2). Comparing the model attributes leads to the conclusion that the model with the modified steel strains (“modsteel”) and the model with the multilinear definition of the concrete (“multilin”) are the most complex of the material models considered. A clear distinction between the cracking stages and the consideration of all crosssection and material parameters allow for more considerable physical phenomena in comparisons with the other models (“linel”, “brfunc”, “efunc”). In general, no difference in the phenomena considered exists between the “modsteel” and “multilin” models when considering the nonlinear material behaviour. It should be noted that owing to the continuously increasing potential for all loading levels, a unique numerical solution can be simulated using the “modsteel” model. In contrast, in the “multilin” material model the uniqueness of the solution close to the concrete tensile strength cannot be guaranteed in principle. Consequently, the “modsteel” model with adequate accuracy and numerical robustness is fixed as the reference model for the other material models considered (model uncertainty assessment, see section 5.2). In order to clarify the choice of the reference model, for the bending moment loading condition, the analysis by Quast [34] emphasizes the model with the modified steel strain to be a more adequate model when compared with other tension stiffening models and experimental results. In general, a comparison by Balázs et al. [35] between the results of a fracture mechanics approach and the more simplified tension stiffen
B. Jung/G. Morgenthal/D. Xu/H. SchrĂśter Âˇ Quality assessment of material models for reinforced concrete flexural members
(a)
(b)
Fig. 5. Deterministic and probabilistic loaddeformation behaviour of a rectangular crosssection
ingbased models illustrates the generally applicability of the simplified models for predicting the average response of a reinforced concrete member.
4.3
Deterministic loaddeformation behaviour
The prediction of the bending stiffness and the stiffness degradation due to concrete cracking is an important response quantity of flexural structural components. This phenomenon has a strong effect on the overall structural response of, for example, restraintsensitive structures [5]. Hence, the results according to the model quality evaluation for the reinforced concrete material models (see section 5) are based on the prediction of the crosssection bending stiffness. The simulation with the deterministic input parameters (mean values, see Table 2) according to the bending stiffnessbending moment relation (see Fig. 5a) shows the different prognoses of the partial models. The bending stiffness is simulated with the help of the energy method (EIM) and the optimized solution is related to the uncracked analytical solution (EII = Ii Âˇ Ec = 143.66 MNm2). In the case where the stiffness ratio EI/EII = 1.0, the predicted numerical and the analytical uncracked stiffnesses are equal. This ratio is visible in the range of small bending moments and, consequently, the numerical solution achieves the analytical initial bending stiffness. Owing to the increasing bending moment, the ratio EI/EII is decreasing â€“ caused by the concrete cracking, see Fig. 5.
5 5.1
Model quality evaluation using uncertainty analysis Parameter uncertainty
The quantification of the parameter uncertainty is simulated with 1000 samples of the probabilistic concrete and reinforcing steel material properties according to Table 2. Comparing the model output for 100, 200, 500 and 1000 samples indicates accurate results for 1000 input samples because the difference in the uncertainty for 500 and 1000 samples is negligible, see Fig. 6c. The probabilistic input parameters for assessing parameter uncertainty are the mean concrete compressive strength fcm, the mean concrete tensile strength fcm, the secant modulus of elasticity
of the concrete Ecm, the yield strength of the reinforcing steel fy, the tensile strength of the reinforcing steel ft and the modulus of elasticity of the reinforcing steel Es. The sampling of the input parameters for the material models with their underlying correlation is performed using LHS [20, 21]. The mean values of the material parameters for concrete class C 30/37 are fcm = 38.0 MN/m2, fctm = 2.90 MN/m2, Ec0m = 32,837 MN/m2, and for reinforcing steel grade B500B Es = 200 000 MN/m2 [29]. The global safety concept for nonlinear simulations according to Eurocode 2 and the German National Annex [29] defines the â€œcalculationâ€? material properties (expressed by index â€œRâ€?) as the mean material properties. Therefore, the mean material properties for concrete C 30/37 are fcR = 21.68 MN/m2 and Ec0mR = 29 307 MN/m2. For reinforcing steel B500B, the mean material properties are fyR = 550 MN/m2 and ftR = 594 MN/m2. More information on the nonlinear safety concept for concrete structures can be found in Cervenka [36] and Allaix et al. [37]. In the study by Tue et al. [38], the variance in the concrete compressive strength is analysed for 173 construction projects with a total of 5027 test specimens. The coefficient of variation for the laboratory compressive test is assessed with CoVf ,test c
2.80MN / m2 1 fck 48.44
(30)
In general, the characteristic structural strength is approx. 85 % of the characteristic cylinder compressive strength due to additional uncertainties such as the quality of placing the concrete in the structure or the various effects of concrete curing. Therefore, the variance in the compressive strength in the structure is increasing and can be defined as [38] CoVf ,str c
0.091 0.85 Â˜ CVf ,test c
(31)
For the given concrete class C 30/37, the coefficient of variation is CVfc,str = 0.19 and the variance in all the other material properties is based on the studies [39, 40, 41], see Table 2.
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Table 2. Material input parameters for probabilistic analysis according to [38, 39, 40, 41], LN... LogNormal, N... Normal
Mat. Prop.
fX(x)
CoV
Correlation ρXiXi+1 [–] concrete: [39], steel: [40]
[–]
fcR
fctm
Ec0mR
fyR
ftR
Es
fcR
LN
0.19 [38]
1
0.82
0.80
0
0
0
fctm
LN
0.29 [39]
0.82
1
0.65
0
0
0
Ec0mR
LN
0.24 [38]
0.80
0.65
1
0
0
0
fyR
N
0.05 [40, 41]
0
0
0
1
0.85
0
ftR
N
0.03 [40, 41]
0
0
0
0.85
1
0
Es
N
0.01 [38, 40]
0
0
0
0
0
1
In general, the method of evaluation is applicable for other concrete strength classes and different reinforcing steel grades, crosssection types and geometric conditions. The conditions in this paper are examples only, chosen in order to present the concept and the results of the uncertainty analysis for a common flexural crosssection. In the case of the “modsteel” material model, the prediction of the bending stiffness due to the uncertain input parameters is shown in Fig. 5b with respect to the loaddeformation behaviour. The influence of the probabilistic material properties on the prediction of the bending stiffness differs with respect to the loading level. The effect in the linearelastic stage is significantly higher in comparison to the stabilized cracking stage. Therefore, the variance in the model response is higher in the uncracked stage, which is caused by the influence of all uncertain input parameters in this stage. In contrast, for higher load levels, some uncertain parameters have less influence on the bending stiffness prediction. Therefore, the variance in the model response decreases. For high loading levels (My > 250 kNm, see Fig. 5b), it is obvious that not all 1000 samples reach the equilibrium condition, because the failure of the crosssection initiated by the maximum material strains is reached. The quantification of the model quality is limited to the loading level, where 90 % of all samples for all models reach a solution without a bending failure. Hence, the results in the uncertainty graphs are limited up to loading level My ≤ 299 kNm, which is illustrated by the “cutoff” in the uncertainty assessment graphs, see Figs. 6 and 7. The linearelastic material model (“linel”) does not take any type of stiffness reduction into account and, consequently, the influence of the scatter of the input parameters is not dependent on the loading level. The parameter uncertainty for the linearelastic material model is conM lin–el stant and has the magnitude CoV para meter , see Fig. 6b, whereas the stiffness degradation due to compression in the “brfunc” material model shows a slight increase in the parameter uncertainty for loading levels My > 100 kNm. The variance in the bending stiffness prediction increases for these loading levels, which is caused by the more nonlinear stressstrain relationship of the broken rational function in the range σc > 0.4 · fcm. In the case of the nonlinear tension stiffening material models, the parameter uncertainty is strongly affected by the loading level. For the same loading level in the
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range of the crack initiation moment, some samples remain in the uncracked stage and other samples already exhibit cracking due to tension. The bending stiffness for both stages varies greatly and therefore the uncertainty increases. A difference between the “modsteel”, “efunc” and “multilin” models is obvious in this stage, which results from the higher variance in the concrete material properties and their stronger influence on the “efunc” and “multi lin” material models. In the stabilized cracking stage, the parameter uncertainties of the tension stiffening models are similar, and even lower than the variance in the linearelastic material modelling and the “brfunc” model. The influence of the concrete’s tensile strength and modulus of elasticity decrease significantly in this stage. In the range of the yielding bending moment, an analogous relation compared with the crack initiation moment occurs. For the same bending moment in this range of the loading level, some samples remain in the stabilized crack stage and some samples exhibit plastic stains in the steel reinforcing bars. The prediction of the bending stiffness for both stages differs significantly and therefore the parameter uncertainty increases.
5.2
Model uncertainty
The loaddeformation analysis predicts the crosssection resistance, which is generally influenced by the model and material characteristics. Material properties such as concrete compression are defined in the design guidelines as that strength below which 5 % of all test specimens may be expected to fail. In a similar way, the onesided 95 % quantile (or 5 % respectively) is used for quantifying the model uncertainty and therefore b = 0.608 (see section 2.3). Nevertheless, a comparative study between the assumptions of the 90 and 97.5 % quantile values resulted in a difference of less than 0.08 in the assessment of model uncertainty. The discussion of the model benefits (see section 4.2) leads to the conclusion that the model with the modified steel strains is the most complex model among the ones considered. Therefore, this model is fixed as a benchmark (reference model) for the other models. The results of the model uncertainty are shown in Fig. 6a. In the uncracked stage, the prediction of the bending stiffness of the purely linearelastic model and the nonlinear models compared with the reference model are similar
B. Jung/G. Morgenthal/D. Xu/H. Schröter · Quality assessment of material models for reinforced concrete flexural members
(a)
(a)
(b)
(b) Fig. 7. Load level dependency of total uncertainty and model quality for material models
“linel” model increases and that of the “brfunc” model is close to being constant after crack formation. The deterministic prediction of the bending stiffness of all tension stiffening models is comparable in the stabilized cracking stage (see Fig. 7a). Differences exist for loading conditions close to the crack initiation moment. Therefore, the tension stiffening models “efunc” and “multilin” have a considerable model uncertainty with respect to the “modsteel” model. (c)
5.3
Fig. 6. Load level dependency of model uncertainty and parameter uncertainty for material models
The total uncertainty of the material models is shown in Fig. 7a. The model quality illustrated in Fig. 7b is another expression of the total uncertainty (inversion of total uncertainty) in order to quantify the prediction quality. If the uncertainty of a model output is low, it means the model prediction has a high reliability and, consequently, a high prognosis quality is quantified. When the scatter of the model output due to the model error (model uncertainty) and the uncertain input parameters (parameter uncertainty) is lower, then the model prediction is more reliable. The scale of the model quality varies significantly between the uncracked stage and the crack formation stage as well as between the stabilized cracking stage and the
in magnitude. Hence, the model uncertainty is very low and even negligible. This relation in the model error changes in the cracked stages. The linearelastic model (“linel”) cannot account for any type of cracking and the model uncertainty increases from the crack formation stage to the stabilized cracking stage. In the case of the “brfunc” model, the bending stiffness degradation is caused by the loss of stiffness in the concrete compression zone. As a consequence, the model uncertainty of the
Total uncertainty and model quality evaluation
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steel yielding stage. For the same load level, some samples remain in the uncracked stage and others have already reached tensile strains above the strains corresponding to the tensile strength. This behaviour results in a significant bending stiffness difference and recognizable variance (uncertainty). A similar behaviour occurs in the loading level between the stabilized cracking stage and the steel yielding stage. The model quality tends to drop in the range of the crack initiation bending moment and the yielding bending moment. The consequence of the simplified linearelastic material model is a significant reduction in the prognosis quality initiated with the beginning of the first bending stiffness degradation (caused by high model uncertainty). The lower model uncertainty of the “brfunc” model compared with the “linel”“ model in the stabilized cracking stage is overlapped by the higher parameter uncertainty. Therefore, the partial model quality of both models is similar: M
M
MQPMlin el  MQPMbr func The highest prediction qualities of the tension stiffening models “efunc”, “multilin” and “modsteel” are found in the stage of stabilized cracking. The low parameter uncertainty and the comparable prediction of the bending stiffness (model uncertainty) lead to a similar partial model quality. The quality of the more complex model with the modified steel strains (“modsteel”) show the overall best model prediction quality over the entire loading level.
6
Conclusions
A comparatively large number of different models exist for the nonlinear modelling of reinforced concrete crosssections and structures. For each application, it is not obvious which model is the most appropriate one for describing the physical phenomena. Therefore, model evaluation with the aid of uncertainty analysis is a powerful methodology for comparing various model predictions in a quantitative manner. In the design process of engineering structures there is often a lack of experimental data, particularly during the preliminary design phase. The focus of this paper is the assessment of the material models without experimental data in order to assist model selection in these project phases. Uncertainty analysis [16] according to the models of a reinforced crosssection enables a clear quantitative differentiation between the different model prognoses for all loading levels up to the steel yield stage. The results show that the model quality of the purely linearelastic material model is generally opposite to that of the nonlinear tension stiffening material models. Furthermore, exclusive consideration of the concrete compressive nonlinear behaviour does not improve the overall prediction quality. Using such simplified models for the simulation of structures with a potentially nonlinear response will lead to unreliable prognoses and should not be used for the simulation of, for example, restraintsensitive structures. Material models with a high quantitative model quality provide reliable predictions and should be used in global structural models.
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Owing to the crucial influence of the loading level on the loaddeformation behaviour of a flexural reinforced concrete member, a clear assignment between the complexity and quality of models does not exist in general. Further research is necessary in order to investigate the effect of several crosssection types, reinforcing steel grades, stirrups, compression steel, concrete strength class and loading conditions. In addition, different material models for reinforced, prestressed, normalstrength and highstrength concrete can be generally assessed by the evaluation method presented in future work.
Acknowledgements The first two authors gratefully acknowledge the support for this research provided by the German Research Foundation (DFG) via the research training group “Assessment of Coupled Experimental and Numerical Partial Models in Structural Engineering (GRK 1462)”. The close collaboration between BauhausUniversität Weimar and Tongji University is also acknowledged.
Notation EIM
energy method with integral description of the material behaviour GM global model LHS Latin hypercube sampling PM partial model b onesided quantile value CoV (…) coefficient of variation εΔMi model error with respect to reference model ε Mref error of reference model Mi one specific model Mref reference model μMi mean value of model response M MQPMi partial model quality σ Mi standard deviation of model response V(…) variance of model response Y model response – Y mean model response βt completeness factor δ ductility factor of reinforcing steel Ecm secant modulus of elasticity of concrete Es modulus of elasticity of steel fcm mean compressive strength of concrete fctm mean tensile strength of concrete fy yield strength of steel ft tensile strength of steel hc,eff effective depth of reinforced concrete subsection κ curvature References 1. Keitel, H., Jung, B., Motra, H. B., Stutz, H.: Quality assessment of coupled partial models considering soilstructure coupling. Engineering Structures, vol. 59, No. 2, 2014, pp. 565–573. 2. Dede, T., Ayvaz, Y.: Nonlinear analysis of reinforced concrete beam with/without tension stiffening effect. Materials & Design, vol. 30, No. 9, 2009, pp. 3846–3851.
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3. Tsang, S. W., Chu, L. Y.: An experimental study of the Tension Stiffening effect on the structural stiffness of Reinforced Concrete Cantilevered Balcony Structures using resonant frequency measurement approach. Construction and Building Materials, vol. 25, No. 5, 2011, pp. 2690–2699. 4. Wu, H. Q., Gilbert, R. I.: Modeling shortterm tension stiffening in reinforced concrete prisms using a continuumbased finite element model. Engineering Structures, vol. 31, No. 10, 2009, pp. 2380–2391. 5. Jung, B., Morgenthal, G, Xu, D.: Integrative Sensitivity Analysis Applied to SemiIntegral Concrete Bridges. Journal of Bridge Engineering, vol. 19, No. 6, 04014014, 2014. 6. United States Environmental Protection Agency: Guidance on the Development, Evaluation, and Application of Environmental Models. Council for Regulatory Environmental Modeling, 2009. 7. Oberkampf, W. L., Helton, J. C., Joslyn, C. A., Wojtkiewicz, S. F., Ferson, S.: Challenge problems: uncertainty in system response given uncertain parameters. Reliability Engineering & System Safety, vol. 85, No. 1–3, 2004, pp. 11–19. 8. Willems, P.: Model uncertainty analysis by variance decomposition. Physics and Chemistry of the Earth, Parts A/B/C, vol. 42–44, 2012, pp. 21–30. 9. Nilson, T., Aven, T.: Models and model uncertainty in the context of risk analysis. Reliability Engineering & System Safety, vol. 79, 2003, pp. 309–317. 10. Ferson, S., Joslyn, C. A., Helton, J. C., Oberkampf, W. L., Sentz, K.: Summary from the epistemic uncertainty workshop: consensus amid diversity. Reliability Engineering & System Safety, vol. 85, No. 1–3, 2004, pp. 355–369. 11. Durga Rao, K., Kushwaha, H. S., Verma, A. K., Srividya, A. K.: Quantification of epistemic and aleatory uncertainties in level1 probabilistic safety assessment studies. Reliability Engineering & System Safety, vol. 92, No. 7, 2007, pp. 947–956. 12. Hermans, E., van den Bossche, F., Wets, G.: Uncertainty assessment of the road safety index. Reliability Engineering & System Safety, vol. 94, No. 7, 2009, pp. 1220–1228. 13. Riley, M. E., Grandhi, R. V.: Quantification of modelform and predictive uncertainty for multiphysics simulation. Computers & Structures, vol. 89, No. 11/12, 2011, pp. 1206–1213. 14. Leamer, E. E.: Specification searches: Ad hoc inference with nonexperimental data. Wiley series in probability and mathematical statistics, Wiley, New York, 1978. 15. Zio, E., Apostolakis, G. E.: Two methods for the structured assessment of model uncertainty by experts in performance assessments of radioactive waste repositories. Reliability Engineering & System Safety, vol. 54, 1996, pp. 225–241. 16. Most, T.: Assessment of structural simulation models by estimating uncertainties due to model selection and model simplification. Computers & Structures, vol. 89 No. 17/18, 2011, pp. 1664–1672. 17. Dempster, A. P.: A generalization of Bayesian inference. Journal of the Royal Statistical Society, Series B (Methodological), vol. 30, 1968, pp. 205–247. 18. Shafer, G.: A mathematical theory of evidence. Princeton Univ. Press, 1976. 19. Park, I., Grandhi, R. V.: Quantification of modelform and parametric uncertainty using evidence theory. Structural Safety, vol. 39, 2012, pp. 44–51. 20. MacKay, M. D., Beckham, R. J., Conover, W. J.: Comparison of three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer. Technometrics, vol. 21, 1979, pp. 239–245. 21. Iman, R. L., Conover, W. J.: Small sample sensitivity analysis techniques for computer models with an application to risk assessment. Communications in Statistics – Theory and Methods, vol. 17, No. A9, 1980, pp. 1749–1842.
22. Montgomery, D. C., Runger, G. C.: Applied statistics and probability for engineers, 3rd ed., Wiley, New York/Chichester, 2003. 23. Kiureghian, A. D., Ditlevsen, Q.: Aleatory or epistemic? Does it matter? Structural Safety, vol. 31, No. 2, 2009, pp. 105–112. 24. Keitel, H.: Evaluation Methods for Prediction Quality of Concrete Creep Models. PhD thesis, Univ. press, Weimar, 2012. 25. Raue, E.: Nonlinear analysis of composite crosssections by nonlinear optimization. Proceedings of Modern Building Materials, Structures and Techniques, Vilnius Gediminas Technical University, 2007. 26. Raue, E.: Nichtlineare Querschnittsanalyse als Optimierungsproblem (Nonlinear analysis of crosssections as an optimisation problem). Bautechnik, vol. 82, No. 11, 2005, pp. 796–809 (in German). 27. German Institute for Standardisation: DIN EN 199211:201101: Eurocode 2: Design of concrete structures – Part 11: General rules and rules for buildings, Beuth, Berlin, 2011. 28. International Federation for Structural Concrete: Model Code 2010, final draft, Bulletin vol. 65/66, International Federation for Structural Concrete, Lausanne, 2012. 29. German Institute for Standardisation: DIN EN 199211/NA:201101: National Annex – Eurocode 2: Design of concrete structures – Part 11: General rules and rules for buildings, Beuth, Berlin, 2011. 30. Pölling, R.: Eine praxisnahe, schädigungsorientierte Materialbeschreibung von Stahlbeton für Strukturanalysen, PhD thesis, RuhrUniversität Bochum, 2001. 31. Comité EuroInternational du Béton: CEBFIP model code 1990, design code. Telford, 1993. 32. German Board for Reinforced Concrete: Comments according DIN 10451, 2nd, rev. ed. Beuth, 2010. 33. Zilch, K., Zehetmaier, G.: Bemessung im konstruktiven Betonbau: Nach DIN 10451 (Fassung 2008) und EN 199211 (Eurocode 2), 2nd ed., Springer, Berlin, 2010. 34. Quast, U.: Zur Auswahl eines geeigneten Verfahrens für die Berücksichtigung der Mitwirkung des Betons auf Zug (On the selection of an adequate method for considering the contribution of concrete in tension). Bautechnik, vol. 87, No. 7, 2010, pp. 397–403 (in German). 35. Balázs, G. L. et al.: Design for SLS according to fib Model Code 2010. Structural Concrete, vol. 14, No. 2, 2013, pp. 99–123. 36. Cervenka, V.: Reliabilitybased nonlinear analysis according to fib Model Code 2010. Structural Concrete, vol. 14, No. 1, 2013, pp. 19–28. 37. Allaix, D. L., Carbone, V. I., Mancini, G.: Global safety format for nonlinear analysis of reinforced concrete structures. Structural Concrete, vol. 14, No. 1, 2013, pp. 29–42. 38. Tue, N.T., Schenck, G., Schwarz, J.: Absicherung der statistisch erhobenen Festbetonkennwerte für die neue Normengeneration, FraunhoferIRBVerlag, Stuttgart, 2005. 39. Strauss, A., Bergmeister, K., März, S.: Zuverlässigkeitsbetrachtung exzentrisch belasteter Stahlbetonstützen (Reliability Assessment of Eccentric loaded Columns). Beton und Stahlbetonbau, vol. 102, No. 4, 2007, pp. 223–230 (in German). 40. Faber, M., Vrouwenvelder, T.: Probabilistic Model Code, 12th draft, Joint Committee on Structural Safety, 2001. 41. AlavizadehFarhang, A.: Concrete structures subjected to combined mechanical and thermal loading, PhD thesis, Royal Institute of Technology, Stockholm, 2000.
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Bastian Jung, PhD student Research Training Group 1462 BauhausUniversität Weimar Berkaer Str. 9, 99425 Weimar, Germany Tel.: +49 (0) 3643 584107 Fax: +49 (0) 3643 584101 bastianjung85@gmail.com
Dong Xu, Prof. PhD Department of Bridge Engineering Tongji University Shanghai 200092, 1239 Siping Road, PR China xu_dong@tongji.edu.cn
Guido Morgenthal, Prof. Dr. Institute of Modelling & Simulation of Structures BauhausUniversität Weimar Marinenstr. 13, 99421 Weimar, Germany guido.morgenthal@uniweimar.de
Hendrik Schröter, PhD student Institute of Modelling & Simulation of Structures BauhausUniversität Weimar Marinenstr. 13, 99421 Weimar, Germany hendrik.schroeter@uniweimar.de
Structural Concrete (2015), No. 1
Technical Paper Josef Holomek* Miroslav Bajer Jan Barnat Pavel Schmid
DOI: 10.1002/suco.201400042
Design of composite slabs with prepressed embossments using smallscale tests The loadbearing capacity of steelconcrete composite slabs using thinwalled steel sheeting with prepressed embossments is in most cases determined by their resistance in longitudinal shear. The design of composite slabs still requires fullscale laboratory bending tests to be performed. Smallscale shear tests cannot include all of the influences affecting the bent slab. However, by using an appropriate procedure, the shear characteristics obtained from such tests can be used to determine the bending capacity of the slab. Two such procedures are compared in this paper. End restraints effectively increase the loadbearing capacity of the composite slabs. Two different types of easily assembled additional end constraints are also tested and compared in this paper. Smallscale tests are used to obtain their shear bearing characteristics and to predict the loadbearing capacity of bent slabs using these restraints. Keywords: composite slab, prepressed embossment, thinwalled, longitudinal shear, smallscale test, loadbearing capacity, end restraints
1
Introduction
There are three failure modes affecting composite slabs in general: vertical shear failure mode, bending failure mode and longitudinal shear failure mode. The latter is typical for composite slabs, and means that the longitudinal shear resistance at the interface between steel and concrete has been reached. At first, the adhesive bond fixes the interface. The adhesive bond is brittle and heavily dependent on casting conditions; it is therefore not included in shear bearing resistance calculations. When the adhesive bond fails, frictional resistance and mechanical interlock become active. As the load increases, so slip occurs between the sheeting and the concrete. The contribution of friction is dependent on the magnitude of the support reaction and acts mainly above the support [1]. The failure mode in longitudinal shear is usually indicated by the sheeting separating from the concrete surface around the embossments (Fig. 1). Concrete cracking may occur simultaneously with slip in the form of macrocracks due to bending and microcracks around emboss
* Corresponding author: holomek.j@fce.vutbr.cz Submitted for review: 12 April 2014 Accepted for publication: 14 July 2014
ments â€“ in a similar way to around a reinforcing bar in reinforced concrete [2]. Microcracks can result in abrasion around embossment edges or local concrete peeling when the embossments are close to each other [3]. The number of factors influencing the bearing capacity makes it difficult to describe slab behaviour analytically. The use of traditional shear studs as end anchorages is limited to steel beams and requires special welding equipment. The small thickness of the sheeting enables the use of common screws, which can be easily drilled into the sheeting before casting. Another possibility is to restrain the sheeting at the webs so that it cannot easily separate from the concrete surface. The effect of these two types of restraint is compared in this paper.
2 2.1
Bending tests Design methods using bending tests
The Eurocode proposes two methods for composite slab design: the mk method (also known as the shear bond method) and the partial connection method. Both require fullscale bending tests to be performed. The partial connection method is only applicable to slabs with ductile behaviour. On the other hand, it can easily include the effect of end restraints by shifting the diagram horizontally through a distance corresponding to the longitudinal shear bearing capacity of the end restraints [4]. An American standard proposes an empirically derived method, which estimates the final bearing capacity for a given geometry of the sheeting and embossments [5]. However, the method is limited to the given range of geometries. The equation for the mk method in EN 199411 for design vertical shear force is V1, Rd
Âş bdp ÂŞ mAp kÂť ÂŤ J VS ÂŤ bLs ÂťÂź ÂŹ
(1)
The linear relationship for ultimate vertical shear resistance is inversely dependent on the shear span length Ls, which reflects the effect of load position. The shear span length Ls is the distance between loading point and support in a fourpoint bending test or onequarter of the span in the case of a uniformly distributed load [4]. Only one sheeting profile type (Cofraplus 60, Arval, ArcelorMittal) was used in all the tests in our laboratory to enable com
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Fig. 1. Separation of the sheeting from the concrete in the area of embossments after the onset of slip
a)
b)
Fig. 2. a) Apparatus for vacuum loading before placing specimen, b) apparatus for vacuum loading with specimen and transducers prepared for the test
parison of results from different test procedures. The sheeting has a trapezoidal shape, is 1 mm thick and has a galvanized surface [6]. The reference slab had a width b = 1.08 m, span length l = 2 m and thickness h = 110 mm. Using the data from the manufacturer [7] for the mk method and considering a shear span length Ls = 0.5 m resulted in Vl,Rk = 25.95 kN. In order to compare the results from different methods, the load obtained was converted into a corresponding uniformly distributed load per unit area, which is qm,k = 24.03 kN/m2 in this case. The evaluation of results using the partial connection method is carried out using a moment diagram. The input values for the diagram were the ultimate moment with full connection Mu = 32.21 kNm and the moment for the sheeting without composite action Mpa = 11.83 kNm.
2.2
Experimental investigation
Two types of bending tests were performed: vacuum loading and fourpoint bending. The vacuum loading procedure developed by Prof. Melcher, produces an ideal uniformly distributed load over the area. A special loading device is used; during the test the specimen is covered with plastic foil and air is extracted from below so that atmospheric pressure produces load on the specimen (Fig. 2) [8].
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The fourpoint bending test setup and the loading procedure from EN 199411 were adopted. This means that two static tests are carried out first to adjust the magnitude of the cyclic load. The other specimens were subjected to cyclic loading and then to static loading up to total collapse. The shear span length was chosen to be onequarter of the span length. Fig. 3 shows the resulting load vs. end slip diagrams for vacuum loading and Fig. 4 shows the diagrams for fourpoint bending. In the mk method the resulting shear force for a slab with ductile behaviour is considered to be half the failure load [9]. However, the mean value of the ultimate bending moment is presented because of easier comparison with other results; it was Mu = 21.84 kNm for vacuum loading and Mu = 19.51 kNm in the fourpoint bending test (static load after cycling) [10]. After converting the load at failure to a uniformly distributed load per unit area it was qv = 40.45 kN/m2 for vacuum loading and q4 = 36.13 kN/m2 for fourpoint bending.
3 3.1
Smallscale tests Design methods using smallscale tests
One way of avoiding fullscale testing is to use smallscale shear tests. Efforts to develop a design method based on smallscale tests have been seen from the beginning of the
J. Holomek/M. Bajer/J. Barnat/P. Schmid · Design of composite slabs with prepressed embossments using smallscale tests
Fig. 3. Load – end slip diagram for vacuumloaded specimens
Fig. 4. Load – end slip diagram for specimens in fourpoint bending test
development of design methods for composite slabs, see Schuster [11]. However, the test results did not correspond with the results from bending tests. Over the period during which composite slab design methods have been developed, various test setups have been presented and used for determining maximum shear force, for comparing the effects of various geometries of mechanical interlocking or for determining shear–slip diagrams for sheeting [12]. A simple and transparent method called the SlipBlock Test was derived by Patrick and Bridge [12]. It uses a special procedure and test setup to obtain the coefficient of friction and the contribution of mechanical interlock separately [13]. Crisinel and Marimon [14] have presented a New Simplified Method which is based on smallscale tests and material characteristics. This method uses a calcula
tion model in a spreadsheet to obtain the momentcurvature relationship at the critical crosssection [14].
3.2
Description of SlipBlock Test
The SlipBlock Test procedure differs from other test procedures mainly in that it requires a changing magnitude of vertical clamping force V (Fig. 10b). The specimen (one rib wide, length b1 = 300 mm) is fixed to a base plate and the concrete block is pushed out of the sheeting horizontally. The vertical clamping force is induced through a roller bearing which enables the horizontal movement of the concrete block. The magnitudes of horizontal force H, vertical clamping force V and slip s are measured. At first, the vertical clamping force V is held constant at 27 kN and the horizontal force H is increased up to the
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onset of slip of about 1 mm, causing the adhesive bond to fail. Then V is increased up to 52Â kN and the corresponding horizontal force is set to reach 1 mm slip again. Thereafter, the magnitude of V is reduced in 10 kN steps and the corresponding values of H are measured. The points corresponding to the stepped vertical force should form a line when plotting the HV diagram. The slope of the line represents the coefficient of friction Îź and the intersection of the line with the horizontal load axis represents the value of the mechanical resistance of the embossments in one rib Hrib [15]. The equation for calculating horizontal resistance to slip is then as follows [15]: H
b1Hrib PV
(2)
The SlipBlock Test design procedure is simple and transparent. The equation for tensile force in the sheeting is derived from the equilibrium of horizontal forces in the bent slab [15]: T
Hrib x Lc P Ru br
Ilim, f,0
Ilim,sl,0
Ilim,sl,0
Fl Ea
(5)
Âł
Ap
z dA
(6)
The contribution of friction above the support of the additional shear anchor can be easily included in the calculation by increasing the value of Fl. The limiting bending moment for phase II is calculated from Mlim,2
Âł
Aequ
(7)
zf Ilim,2z dA
The section properties for the idealized Isection are reduced because of cracking.
3.2.3 Phase III (3)
In order to calculate the loadbearing capacity of the bent slab, rectangular stress block theory is used.
3.3
Fl (longitudinal shear force obtained from smallscale test):
Description of New Simplified Method
A pullout test setup is used in the New Simplified Method, but the authors of the method also permit the use of a different smallscale shear test setup. The SlipBlock Test setup was used in our laboratory with a constant clamping force value of 1.6Â kN [16]. The method uses an equivalent Isection as a substitute for the sheeting and an equivalent rectangular section to represent the concrete part. The slab behaviour is described in three linear phases with a momentcurvature diagram. Limiting points for these phases are calculated iteratively. The following description of the three phases is taken from the ICOM report [17].
The behaviour of the slab in this phase is nonlinear elastoplastic, with concrete cracking and slip. A limiting value for this phase is obtained using the maximum shear stress value from a pullout test. Initial strain in the sheeting Îľa,ini and initial curvature Ď†0 are found iteratively. Two conditions must be fulfilled for this purpose. The first condition is that the horizontal force in the sheeting must have the same magnitude as the horizontal force in the concrete. The second condition is that the horizontal force in sheeting/concrete equals the minimum value of the longitudinal shear resistance, the plastic resistance of the sheeting or plastic resistance of the concrete. The contribution of friction and additional anchorage can be included in the calculation by increasing Fl similarly to phase II. The authors derive maximum strain Îľs from maximum slip before failure smax, which is considered to be 3Â mm for ductile profiles. The limiting bending moment for phase III, which is also ultimate bending moment for the slab, is as follows:
3.2.1 Phase I The behaviour of the slab in this phase is linear elastic, without concrete cracking and without slip. A limiting bending moment for this phase is obtained when the strain corresponding to the tensile strength of the concrete is reached in the extreme fibre of the concrete: Mlim,1
EaIa, eq, yIlim,1
(4)
3.2.2 Phase II The behaviour of the slab in this phase is elastic or elastoplastic, with concrete cracking but no slip. A limiting bending moment for this phase is obtained using the shear stress value corresponding to the first slip from a smallscale test. The depth of cracked concrete has to be found iteratively by taking into account the equality of the curvature Ď†lim,f,0 calculated from maximum strain before tension cracking and curvature Ď†lim,sl,0 calculated using
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Mlim,3
Âł
Ap
zV a(z) dA
Âł
Ac
zV b(z) dA
0
(8)
A calculation model is needed to find the solution iteratively. The advantage of this method is that it also describes the behaviour of the slab before total collapse and the designer has also information about slab curvature corresponding to the calculated moment resistance. Unfortunately, test results exhibit large scatter of the shear force at the level of first slip, which is the input value for phase II [15]. The disadvantage, from a practical point of view, is that the method is significantly more complicated in comparison to the SlipBlock Test. Design, especially the creation of the calculation model, is not so transparent and it is vital to ensure that no mistakes are made while setting up equations for calculating crosssection characteristics, summation of forces and bending moments in the section.
J. Holomek/M. Bajer/J. Barnat/P. Schmid · Design of composite slabs with prepressed embossments using smallscale tests a)
b)
Fig. 5. a) Dimensions of test specimens, b) wooden wedges as additional end restraints
3.4
Experimental investigation
The test setup used in our laboratory was very similar to that of Patrick and Bridge. The loading apparatus consisted of a base plate for fastening specimens with bolts, a cantilever for fixing the horizontal hydraulic cylinder and four steel rods with a crossgirder to fix the vertical hydraulic cylinder. The base plate and the cantilever were welded to a massive steel section which held all the parts of the apparatus together. The specimens were 0.33 m long and two ribs of trapezoidal sheeting, i.e. about 0.4 m, wide. The concrete part of each specimen was b1 = 0.2 m long. The overlapping part of the sheeting allowed the specimens to be fixed to the base plate by M10 bolts (Fig. 5a). A roller bearing was inserted between the vertical cylinder and the specimen to enable horizontal movement of the concrete block. Handoperated hydraulic cylinders were used in these tests. Two pairs of displacement measuring devices were installed, the first pair a for measuring concrete movement and the second pair for measuring sheeting movement. Two forces were measured – vertical and horizontal (Fig. 6). The advantage of this setup is that only one base plate is used for all the specimens. The two ribs of the specimens enable the investigation of the effects of shear
mechanical interlock on the inner rib. Only one application point for horizontal load is needed because the horizontal force is introduced into the middle rib, which facilitates the procedure.
3.5
Test series
The shear tests were performed in several series using: A. Zero vertical clamping force B. Constant vertical clamping force C. Constant vertical clamping force with cast screws as additional end restraints D. Constant vertical clamping force with inserted wooden wedge E. Changing vertical clamping force – SlipBlock Test
3.5.1 Series A – Zero vertical clamping force Three specimens were tested without any restraints in the vertical direction (Fig. 7a – continuous lines). The adhesive bond could be clearly observed in the results because it was not damaged by the application of vertical force as happened with other series. The next three specimens were restricted by the hydraulic jack to vertical movement only, and the vertical reaction occurring during the test was measured (Fig. 7a – dashed lines). To ensure contact between the measuring device and the specimen, the starting value of the vertical force was set to 0.7 kN. The relationship obtained is similar up to 5 mm slip. With major slip, the specimens without restraints started to lift up and their resistance dropped to zero. On the other specimens with restrained vertical movement, the reaction increased to 3 kN on average. For these specimens, the resistance for major slip remained relatively constant.
3.5.2 Series B – Constant vertical clamping force
Fig. 6. Loading apparatus used in pushout tests
The initial clamping force was 1.6 kN, which was the same magnitude as used in the pullout tests for the New Simplified Method (Fig. 7b). During the test, the magnitude of the vertical force also increased with increasing slip. The increase in vertical force usually occurred after slips of about 3 mm.
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a)
b)
Fig. 7. a) Loadslip relationships for specimens in series B with zero clamping force, b) loadslip relationships for specimens in series A with constant clamping force V = 1.6 kN
a)
b)
Fig. 8. Loadslip relationships for specimens: a) with constant vertical clamping force and cast screws, b) with constant vertical clamping force and inserted wooden wedges (the black dashed lines represent specimens without wooden wedges)
3.5.3 Series C – Constant vertical clamping force with cast screws as additional end restraints The cast screws used as additional end restraints caused a very substantial increase in horizontal shear resistance (Fig. 8a). A total of 28 screws 3.5 mm in diameter increased the horizontal force by V1 = 65 kN compared with the specimens without screws. This implies that the shear resistance per screw is V1,1 = 2.32 kN. When reaching slips of about 2 mm, the shear bearing resistance suddenly dropped. The screws sheared off and their effect for higher values of slip was very low. The heads of the screws protruded from the sheeting, which increased the ductility of this connection (Fig. 9a). Nevertheless, the ductile behaviour of the slab should be verified.
3.5.4 Series D – Constant vertical clamping force with inserted wooden wedge As the sheeting usually separates from the concrete in the area of the embossments, it was decided that it was also necessary to investigate how the effect of embossments could be enhanced by inserting a wooden wedge under the ribs (Fig. 5b). Each wedge must fit the dimensions of the rib well, especially in the area of the embossments. The effect of these restraints doubled the magnitude of the re
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sulting horizontal shear resistance (Fig. 9b – continuous lines). The length of each wooden wedge was the same as the length of the concrete block (200 mm). Compared with the cast screws, the effect of wooden wedges increased more slowly and did not diminish when the slip rose to higher values.
3.5.5 Series E – Changing vertical clamping force The vertical clamping force had been changed during the test according to the SlipBlock Test procedure presented in section 3.2. The vertical clamping force was recalculated according to the plan areas of the specimens. These experiments were also performed in the laboratory of the Addis Ababa Institute of Technology (AAiT) in Ethiopia (Fig. 10a), where the loading procedure was slightly modified. The magnitude of the clamping force started at a low level and was gradually increased instead of decreased. This eliminated additional slip caused by transition between steps and enabled the loading cycle to be repeated several times per specimen. Fig. 11 displays the change in the rib resistance and friction depending on the magnitude of the slip for six specimens. The characteristics obtained exhibit a large scatter for low values of slip – probably caused by the residual chemical bond and nonuniform movement of the specimens. Therefore, only val
J. Holomek/M. Bajer/J. Barnat/P. Schmid · Design of composite slabs with prepressed embossments using smallscale tests
a)
b)
Fig. 9. a) Cast screws with heads protruding from sheeting, b) concrete block with cast screws after test
a)
b)
Fig. 10. a) Test setup in AAiT laboratory, b) friction line obtained from the tests
a)
b)
Fig. 11. a) Shear force vs. slip diagram, b) coefficient of friction vs. slip diagram
ues of slip > 2 mm were included in the calculations. The friction line resulting from all the tests can be seen in Fig. 10b. The summarized results displayed show significant scatter. However, the friction line can be obtained when setting linear regression using Eq. (2):
the sheeting using Eq. (3) was T = 181.09 kN, and considering the magnitude of the support reaction Ru = 26.25 kN, the ultimate bending moment is Mu = 13.12 kNm. The uniformly distributed load for comparison with other results is then qs = 24.30 kN/m2.
H = 0.46V + 12.95
3.6
(9)
where m = 0.46 and b1Hrib = 12.95 kN, from which it follows that Hrib = 64.75 kN/m. The resultant tensile force in
End restraints’ contribution to bearing resistance
The reference slab was considered with end restraints in a form of 60 cast screws each side of the slab. Therefore,
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b)
a)
Fig. 12. a) Partial connection evaluation diagram, b) contribution of cast screws to loadbearing capacity in a partial connection diagram
the additional longitudinal shear resistance was V1 = 139.2 kN.
had increased from MRk,s = 15.74 kNm without end anchorage to MRk,s = 22.08 kNm using the cast screws.
3.6.1 Partial connection method
3.6.2 SlipBlock Test
A comparison of bent slabs with and without end anchorage using the partial connection method can be seen in Fig. 12. Using the data from the manufacturer, the limiting moments were given as discussed in section 2.1. The length of the full shear connection Lsf was then calculated with this formula:
The shear resistance V1 is added to the tensile force in the sheeting, so the increased value is T = 329.21 kN. The reaction above the support is Ru = 45.44 kN and the ultimate bending moment Mu,s = 22.72 kNm. A corresponding uniformly distributed load would be qs = 42.08 kN/m2.
Lsf
N cf /bW u, Rk
Ap fy /bW u, Rk
1393.1 350/1000 0.125/1000
(10)
3.9 m
In the case of cast screws being used as additional end restraints, the diagram was shifted by the following distance: V1 bW u, Rk
139.2 1000 0.125 /1000
(11)
1.11m
The specimen span length l = 2 m and a moment distribution similar to that for fourpoint bending are considered. The corresponding maximum bending moment is obtained from the diagram. The resulting ultimate moment
a)
4 4.1
Comparison of results Visual comparison
From a visual comparison of the concrete blocks it can be seen that the specimens from series A with zero vertical force were almost undamaged (Fig. 13a). The specimens from series B, with a constant vertical force of 1.6 kN, displayed a minor amount of abrasion around the edges of the indentations in the concrete (Fig. 13b). The specimens from series E with changing vertical force magnitudes of up to 50 kN had more intensive abrasion around the embossments (Fig. 14a). Finally, the blocks from series D with inserted wooden wedges exhib
b)
Fig. 13. a) State of embossments after testing with zero vertical clamping force, b) state of embossments after testing with constant vertical clamping force
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J. Holomek/M. Bajer/J. Barnat/P. Schmid · Design of composite slabs with prepressed embossments using smallscale tests a)
b)
Fig. 14. State of embossments after testing with a) changing vertical clamping force, b) constant clamping force and wooden wedge blocks inserted as additional end restraints
Table 1. Comparison of results of tests and design methods considering simply supported slab (2 m span) converted to a corresponding uniformly distributed load per unit area
ultimate bending moment [kNm]
corresponding uniform load [kN/m2]
results of vacuum loading tests results of fourpoint bending tests mk method (data from manufacturer) [7] partial connection method (data from manufacturer) [7]
21.84 19.51 12.98 16.43
40.45 36.13 24.03 30.42
SlipBlock Test New Simplified Method New Simplified Method + friction above support
13.12 16.58 17.76
24.30 30.79 32.89
SlipBlock Test + cast screws New Simplified Method + cast screws partial connection method + cast screws
22.72 24.71 23.06
42.08 45.75 42.70
New Simplified Method + inserted wedges plastic bending moment (full composite action)
19.84 32.21
36.57 59.65
ited slight peelingoff of the concrete at the edges of the indentations. Moreover, the side ribs could not bear a higher transverse reaction from the embossments. Cracks formed at the corners of the ribs and a tendency for whole ribs to separate from the sheeting was observed (Fig. 14b). This effect decreased the influence of the wedges on the shear resistance obtained.
4.2
Numerical comparison
All the results are related to a reference slab of 2 m span and 1.08 m width. A comparison of the results from bending tests and design methods can be seen in the first part of Table 1. Results using smallscale test data are displayed in the other parts of the table. Finally, the magnitude of the plastic bending moment considering full composite action is shown. The SlipBlock Test is older and simpler than the New Simplified Method. However, the bending resistance obtained from the SlipBlock Test is similar to that of the
mk and partial connection methods. The bending resistance obtained using the New Simplified Method is less conservative, especially when the friction contribution above the support is included. All the test results are obtained using the test setup corresponding to the SlipBlock Test, which may influence the results. Another important factor influencing results is that embossment geometry, mainly the distance from the longitudinal edge of the trapezoidal sheeting, differed from officially declared geometry. Therefore, a sensitivity study is a very convenient tool for a better understanding and comparison of the methods [18]. The effect of the selected input parameters (shear resistance τmax, maximum slip before failure smax and friction above support m) on the bending resistance can be observed in Fig. 15. Here, the bending resistance corresponding to τmax = 0.127 MPa and smax = 3 mm without considering friction above the support is taken as a reference value. The sensitivity of the shear resistance of mechanical interlock Hrib and the sensitivity of the coefficient of friction m in the SlipBlock
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a)
b)
Fig. 15. a) Influence of shear strength tmax on bending resistance, b) influence of assumed level of maximum slip before failure smax on bending resistance in New Simplified Method
a)
b)
Fig. 16. a) Influence of shear resistance Hrib of mechanical interlock on bending resistance, b) influence of coefficient of friction m on bending resistance in SlipBlock Test method
Test can be observed in Fig. 16. The reference value is calculated using Hrib = 64.74 kN/m and m = 0.46 in this case. It is obvious that the resulting bending resistance is influenced much more by changes in the shear resistance of the mechanical interlock in both methods.
5
Conclusions
Smallscale shear tests on composite slabs represent a less expensive alternative to fullscale bending tests. Two design methods based on smallscale tests results were chosen to compare: the SlipBlock Test method and the New Simplified Method. The SlipBlock Test gives the designer specific information about the contribution of friction and mechanical interlock to the resulting shear bearing capacity. The test procedure is more intensive than most other smallscale test procedures because the magnitude of the vertical clamping force is changed during the testing of each specimen. On the other hand, the corresponding design method is simple and transparent. The loading procedure can be modified so that the clamping force is gradually increased instead of decreased. It is more effective and en
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ables several loading series to be performed per specimen. A disadvantage is that the values obtained from the tests correspond to higher magnitudes of slip, whereas in a real situation, lower values of slip are dominant. The New Simplified Method describes slab behaviour in three phases. An iterative mathematical model is needed to calculate section properties and find the solution. The solution is based on the strength of concrete in tension, equality of curvatures and force equilibrium at the critical section. The method is more sophisticated and describes the real behaviour of the slab, also before reaching the ultimate bending moment. Moreover, it supplies information about curvature corresponding to calculated moment resistance, and so the deflection of the slab can be calculated as well. However, design using the New Simplified Method is generally more complicated and less transparent in comparison to the SlipBlock Test method, which could be an obstacle in practical usage. Comparison of ultimate moments calculated using these methods and data from smallscale tests with the same arrangement show that the New Simplified Method is less conservative. A sensitivity study indicates that friction above the support has a smaller influence on the bending resistance
J. Holomek/M. Bajer/J. Barnat/P. Schmid · Design of composite slabs with prepressed embossments using smallscale tests
than the shear resistance in both methods. Both design methods enable additional end restraints to be taken into account. The performance of smallscale tests may still present a significant uncertainty. The results exhibit a large scatter, especially for the magnitude of the shear force before reaching slip in the case of constant clamping force or for low values of slip in the case of changing clamping force. The features that ought to be specified are, for example, optimal loading speed and conditions for casting and placing the specimens for the test setup. Two types of easily assembled end restraints are compared in this paper: cast screws and inserted wooden wedges. Adding a sufficient number of screws enables the bearing capacity of the sheeting with low bond to be easily enhanced – even up to full composite action. A disadvantage is that it changes the behaviour of the slab from ductile to brittle. The ductility of the screws can be slightly increased by allowing their heads to protrude from the slab. Inserting wooden wedges comes from the idea that the shear bearing capacity of the indentations in concrete is usually unused, as can be observed from visual comparisons. By filling the ribs in the area above the support it is possible to prevent the sheeting from separating from the concrete surface. The loadbearing capacity of a slab with prepressed embossments can be effectively increased in this way. Inserting wooden wedges increases the shear bearing capacity while preserving ductile behaviour.
Acknowledgements This paper has been worked out under the project No. LO1408 “AdMaS UP – Advanced Materials, Structures and Technologies”, supported by Ministry of Education, Youth and Sports under the “National Sustainability Programme I” and under the project FASTJ131918 and FASTS132077.
Notation Ap Ac Aequ Ea Fl Hrib Ia,eq,y Ls Lsf Mlim,1 Mlim,2 Mlim,3 Nc Ncf Ru Vl b b1
crosssectional area of sheeting crosssectional area of concrete crosssectional area of equivalent section modulus of elasticity of steel longitudinal shear resistance of sheeting rib resistance per unit length due to mechanical interlock moment of inertia of equivalent section shear span length limiting length for full composite action limiting bending moment for phase I limiting bending moment for phase II limiting bending moment for phase III longitudinal shear force in partial composite action longitudinal shear force in full composite action ultimate vertical reaction at end support per unit width of slab additional longitudinal shear resistance from end anchoring slab width length of slip block specimen
br dp fy x + Lc z gVS φlim,1 φlim,f,0
φlim,sl,0 μ σa σb τmax
τu,Rk
average steel rib spacing distance from top of sheeting to centroid of effective area of steel sheeting yield strength shear span length (including length beyond support) vertical coordinate of crosssection partial safety factor limiting curvature for phase I limiting curvature calculated from maximum tensile strain before cracking (phase II) limiting curvature calculated using shear resistance of sheeting (phase II) coefficient of friction longitudinal stress in sheeting longitudinal stress in concrete maximum longitudinal shear strength for New Simplified Method longitudinal shear strength for partial connection method (characteristic value)
References 1. Patrick, M., Poh, W.: Parameters affecting the design and behaviour of composite slabs. IABSE reports, Zurich, 60, 1990, pp. 220–225. 2. Maekawa, K., Okamura, H., Pimanmas, A.: NonLinear Mechanics of Reinforced Concrete. CRC Press, 2003, p. 768. 3. Ferrer, M., Marimon, F., Crisinel, M.: Designing coldformed steel sheets for composite slabs: An experimentally validated FEM approach to slip failure mechanics. ThinWalled Structures, vol. 44, No. 12, Elsevier, 2001, p. 1261–1271. 4. European Convention for Constructional Steelwork (ECCS): Design Manual for Composite Slabs, No. 87, Brussels, 1995. 5. ANSI/SDI TCD2011: Test Standard for Composite Steel Deck – Slabs. Steel Deck Institute, 2012, available at http://www.sdi.org/publications2/standards/ 6. CSTB Technical report Cofraplus 60, 3/03390, PAB, ARCELOR Group, 32 rue Gambetta BP 62, F59264 Onnaing, 2004, pp. 27–34. 7. Cofraplus 60. Statické tabulky, Arval ArcelorMittal Construction Solutions, Biskupsky´ dvu° r 7, 110 00 Praha 1, Czech Republic, available at: http://ds.arcelormittal.com/construction/arval_easterneurope/10642/10643/language/CZ 8. Melcher, J.: FullScale Testing of Steel and Timber Structures: Examples and Experience, Structural Assessment – The Role of Large and Full Scale Testing, K. S. Virdi et al. (eds.), E&FN SPON, London, 1997, pp. 301–308. 9. European Convention for Constructional Steelwork (ECCS): Longitudinal Shear Resistance of Composite Slabs: Evaluation of Existing Tests, Brussels, 1998. 10. Holomek, J., Bajer, M.: Experimental and Numerical Investigation of Composite Action of Steel Concrete Slab. Procedia Engineering, Elsevier, vol. 40, 2012, pp. 143–147. 11. Abdullah, R.: Experimental Evaluation and Analytical Modeling of Shear Bond in Composite Slabs. Dissertation, Virginia Polytechnic Institute & State University, Blacksburg, 2004. 12. Patrick, M., Bridge, R.: Review of Concepts Concerning Bond of Steel Decking. 12th Intl. Specialty Conf. on ColdFormed Steel Structures, St. Louis, Missouri, 1994. 13. Patrick, M., Poh, W.: Controlled test for composite slab design parameters. IABSE reports, Zurich, 60, 1990, pp. 227–231. 14. Crisinel, M., Marimon, F.: A new simplified method for the design of composite slabs. Journal of Constructional Steel Research, 60, 2004, pp. 481–491.
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15. Patrick, M., Bridge, R.: Partial shear connection design of composite slabs. Engineering Structures, vol. 16, No. 5, 1994, pp. 348–362. 16. Crisinel, M., Edder, P.: New Method for the Design of Composite Slabs. Composite Construction in Steel and Concrete V, 2006, pp. 166–177. 17. Guignard, P., Schumacher, A., Crisinel, M.: Etude des dalles mixtes et développement d’une méthode de calcul basée sur la relation momentcourbure. ICOM REPORT, Lausanne, 2003. 18. Kala, Z., Kala J.: Sensitivity Analysis of Stability Problems of Steel Columns using Shell Finite Elements and Nonlinear Computation Methods. Proc. of 17th Intl. Conf. on Engineering Mechanics, Svratka, Czech Republic, 2011, pp. 271–274.
Josef Holomek, PhD student Institute of Metal & Timber Structures Faculty of Civil Engineering Brno University of Technology Veverˇi 331/95, 602 00 Brno, Czech Republic Tel. +420541147330 holomek.j@fce.vutbr.cz (corresponding author)
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Miroslav Bajer, Assoc. Professor Institute of Metal & Timber Structures Faculty of Civil Engineering Brno University of Technology Veverˇi 331/95, 602 00 Brno, Czech Republic Tel. +420541147311 bajer.m@fce.vutbr.cz
Jan Barnat, Assistant Institute of Metal & Timber Structures Faculty of Civil Engineering Brno University of Technology Veverˇi 331/95, 602 00 Brno, Czech Republic Tel. +420541147305 barnat.j@fce.vutbr.cz
Pavel Schmid, Assoc. Professor Institute of Building Testing Faculty of Civil Engineering Brno University of Technology Veverˇi 331/95, 602 00 Brno, Czech Republic Tel. +420541147491 schmid.p@fce.vutbr.cz
fibnews fibnews is produced as an integral part of the fib Journal Structural Concrete.
The fib in Russia: new standards In 1993 the Ministry of Justice officially registered the Structural Concrete Association, the fib National Member Group for Russia. However, a true history of the association goes back as far as 1957, when the Academy of Construction and Architecture of the USSR created the Commission for Prestress Concrete, which later became the National Committee of the FIP, chaired by Professor K. Mikhailov. In 1969 the Coordinating Scientific and Technical Council for concrete and reinforced concrete was created. It was composed of delegates appointed by over 500 organizations from the Republics of the Soviet Union and established close contact with the FIP, the CEB, IASS, RILEM and other international organizations. With the dissolution of the Soviet Union, the council was practically discontinued. For this reason, in 1991, it merged with the FIP National Committee to become the Structural Concrete Association and was reorganized again in 1999 under a new Russian law. Since it has come into existence the Structural Concrete Association have organized nearly forty large conferences and congresses. Its major achievements are the all
Russian (international) conferences on concrete and reinforced concrete, supported by the fib, RILEM and the ACI, and the 59th RILEM annual meeting in Moscow. [A detailed account of the 3rd AllRussian (International) Conference on Concrete and Reinforced Concrete can be found in the September 2014 issue of fibnews.]
Contents
Issue 1 (2015)
The fib in Russia: new standards
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Worldwide representation at ACF 2014
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DISC2014: the past and the future
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One of the association’s main objectives is to implement international norms. This year the Eurocodes will be adopted in Russia.
Old for new: Penang Bridge
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A venerable institute turns 80
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JPEE2014 in Lisbon
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A major benefit to the application of the codes is the ease with which European construction companies will be able to bring their own projects into Russia. Substantial sections of edifices will be designed at home, thereby speeding up overall construction.
fib MC2010 course in Brazil
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Short notes
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Nigel Priestley † 1943–2014
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Congresses and symposia
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Acknowledgement
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The introduction of the Eurocodes does not mean that the Russian codes will disappear in 2015; rather, the two systems will coexist, with a possible phasing out of one of them, should it become irrelevant. One of the issues that the Eurocodes might encounter is the variety in climatic conditions in Russia. The northern territories have extreme
weather conditions and standards for infrastructure need to be met to ensure inhabitants’ safety. Steel towers, pipes, storage units and all matter of buildings and bridges exist in regions where winter temperatures can drop below – 50 ºC. Some sections of the Eurocodes limit the use of steel to temperatures ranging from – 40 to – 50 º C, and no lower. Regrettably, these limitations could
A recent highway overpass in the small city of Podolsk, 15 km to the south of Moscow. The Eurocodes were used for guidance in the experimental calculations for the structure Photo credit: V P Korotikhin
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Worldwide representation at ACF 2014 ACF 2014 (The 6th International Conference of Asian Concrete Federation) was held in Korea from 21 to 24 September 2014.
The Lower Bureya hydroelectric power plant in the early stages of construction. Russian civil engineers have to take extreme climatic conditions into consideration Photo credit: V P Korotikhin
not be changed in the usual National Annexes of the Eurocodes. Snow loads (80–560 kg/m2) are also a big problem because they can be much higher in Russia than in the north of Europe. Eighty per cent of Russian territory has saturations and floods, 80 % has dangerous slope processes, 65 % has permafrost, 40 % has particular soil conditions and 35 % lies in karst zones. The CEN has not yet given directions on how the Eurocodes and other standards may be changed for severe climatic conditions. On the Russian side, civil engineers lack experience of the Eurocodes and will have to get used to working with them. A last issue concerns the public availability of codes and standards in Russia. The CEN has recognized the precedence of Russian law but has specified that Russian versions of the codes should not go beyond its borders. Enforcing this will be problematic. We hope to start longrunning professional cooperation with representatives of international organizations and companies to promote Russian involvement in the next generation of codes, implement 150
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design and calculation software, determine which standards should be adopted first and organize workshops for civil engineers. The fib Model Code for Concrete Structures 2010 can play a role in the development of new national codes and the revision of existing ones. We plan to translate fib MC2010 into Russian and organize special courses with the support of fib Commission 9 ‘Dissemination of knowledge’. The year 2014 was a very productive and rewarding time for us, what with the 3rd AllRussian (International) Conference in Moscow and the 4th International ScientificPractical Conference ‘Development of largepanel housing construction in Russia’ (InterConPan2014) in Saint Petersburg. An adhoc meeting of fibRILEM representatives on 13 May, at the Russian Academy of Sciences in Moscow, will make way for greater cooperation between the two organizations. I hope that 2015 will bring prosperity and success to all our and your endeavours. Professor Vyacheslav Falikman, fib Head of the Russian National Delegation
The conference chair was Professor Jongsung Sim (Hanyang University) and the international organizing committee and scientific committee chairs were, respectively, Professors Manyop Han (Ajou University) and Donguk Choi (Hankyong National University). In total, 261 papers from 27 countries were submitted – the largest number received at any ACF conference so far. Among the concrete institutes represented were the ACF, the ACI, the fib and RILEM. The papers were presented in 7 parallel sessions on 22 and 23 September. Six categories were covered: – Concrete structures – Concrete materials and technologies – Maintenance, monitoring, repair and strengthening – Sustainability – Construction and engineering – Recent research and related topics
Twelve papers were honoured with a Best Papers Award. The international event was a great success. The next ACF conference will be held in Hanoi, Vietnam, in 2016. Professor SeJin Jeon Ajou University, Korea
fibnews
DISC2014: the past and the future
Speakers at DISC2014: Steve Denton, Chris Burgoyne, Kenny Arnott, Stuart Matthews, John Orr and Chris Hendy
Aimed at providing practitioners with a valuable update on developments in the design and construction of structural concrete, the annual fibUK Developments in Structural Concrete 2014 seminar (DISC2014) took place on 27 November 2014 at St MartinintheFields in London. ‘Learning from the past – looking to the future’ attracted 90 delegates. Mr Kenny Arnott gave an international perspective on reinforcement detailing past and future, covering how designers and contractors communicate about reinforcement, the different styles of detailing (notably top bars in continuous members) and the need for standardization. Dr Chris Burgoyne spoke about the collapse of Palau Bridge and asked why we have not been able to learn the lessons. Built in 1977 and repaired in 1996, this bridge between two Pacific islands collapsed six weeks after repairs were completed. Having introduced the first two speakers, Professor Steve Denton, Past Chairman of fibUK, gave a briefing on the activities of the fib and fibUK. Mr Chris Hendy, newly inaugurated fibUK Chairman, took the chair while Dr Stuart Matthews described recent and ongoing developments in the structural assessment of buildings and other constructed assets. Dr Matthews went through why, when and how assessment might be undertaken, a topic five fib task groups are currently addressing.
Finally, Dr John Orr advocated efficiency through structural form. He showed how ‘equal strength’ beams (Rd = k · Ed everywhere) may be formed using tensile fabrics. Questions and lively discussions followed. Mr Charles Goodchild MPA – The Concrete Centre
Old for new: Penang Bridge Although new bulletins are constantly being written to offer future solutions to current problems, past CEB, FIP and fib publications continue to be useful. When dealing with existing structures that need maintenance or renovation, engineers frequently turn to older bulletins to understand contemporaneous construction choices and to find calculations that may have fallen out of use. In a presentation given on 11 April 2013 Chris Hendy of Atkins spoke of how the consultancy turned to fib Bulletins 30, 35 and 58 for help with replacing the cable stays of the Penang Bridge, the only existing fixed link between Penang Island and the mainland of Peninsular Malaysia. [A webinar of this talk is available on iStructE: http://www.istructe.org/ resourcescentre/webinars]
The bridge, 13.5 km long and with a span of 225 metres, was built out of reinforced concrete between 1983 and 1986. It was a typical cablestay bridge with a twist: the stays used an experimental system of bars instead of strands. The bars were coupled together in 12metre lengths and then encased in an outer steel tube, which was grouted up. Both the bars and casing carried load. Only the force of the bars was anchored off at the end plates and the force from the steel tubes was anchored off in bonds to the concrete. The cables were not designed to be replaceable. There were already problems with bars and couplers breaking during construction. All the bars were tested to 80% of load and quite a few failed, mainly at the couplers, due to brittle failure. The solution found at the time was to inject couplers with resin. It worked in the laboratory but was harder to achieve on site. In a 1999 study of the load, Atkins discovered that the shorter stays were heavily overstressed. The company Freyssinet installed some new bearings at the pylons to relieve
The Penang Bridge, built out of reinforced concrete between 1983 and 1986, is the only existing fixed link between Penang Island and mainland Malaysia Photo credit: Cmglee
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A venerable institute turns 80 The Eduardo Torroja Institute for Construction Science in Madrid celebrated its 80th anniversary in 2014. Gordon Clark, fib President, was invited to give a plenary address during the final session of the commemorative event on 14 November. His presentation was streamed live over the Internet to an extended audience across Spain.
fib Bulletins 30, 35 and 58 “offered guidance based on sound engineering principles rather than rigid and inflexible codified rules,” according to Chris Hendy of Atkins
load from the short stays. Acoustic monitoring was also installed and gave indications that bars were breaking. A more detailed assessment in 2005 suggested that there were also fatigue problems with the cables as well as static overstressed. The bridge was not closed to traffic because analysis showed that in spite of the huge amount of damage it would suffer, it would remain standing if a cable failed. However, it was agreed by all relevant parties that the cables would all have to be replaced to provide a safe and serviceable future for the bridge.
30 also offered valuable data for the fatigue test for these deviation devices. During cable replacement, temporary stays had to be installed. This required a number of large temporary bolted fixings and fib Bulletin 58 ‘Design of anchorages in concrete’ was instrumental in the calculations for the fixings that had to be installed right next to the free edges of sections for the temporary works. It was able to give the pullout forces of the anchorages.
Replacement of the 117 cables started in 2007. The new cables were designed to EN 1993111, which had been informed by fib Bulletin 30 ‘Acceptance of stay cable systems using prestressing steels’. The bulletin aided with damping requirements and angular tolerances, among other things, but most importantly, with material specifications for polyethylene sheeting.
Installation of the new stays required coring through the main deck edge girders. The cores were close to the prestressing strands in the deck transverse beams with the potential for them to be cut during coring operations. To offset damage to the posttensioning, carbon fibre was used to strengthen the transverse beams. fib Bulletin 35 ‘Retrofitting of concrete structures by externally bonded FRPs’ significantly helped with this design.
The new cables, twice as strong as the existing ones, were also lighter and had less sag. Consequently, despite the best efforts of the designers and contractors, one new cable ended up misaligned with the replacement anchorage and a deviation device with a radius had to be created to correct the angle at which it exited the anchorage. fib Bulletin
Chris Hendy commented “The fib Bulletins offered guidance based on sound engineering principles rather than rigid and inflexible codified rules, which was exactly what was required on this project where nothing was standard. Their guidance was invaluable.”
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Mr Clark congratulated the institute and spoke of Eduardo Torroja, a cofounder of both the CEB and FIP. In 1958, following the term of his friend Eugène Freyssinet, this eminent Spanish engineer became the second president of the FIP. In his address Mr Clark also spoke of the challenges for structural concrete in the future and referred specifically to the megastructures he had seen during his presidential trips and the critical state of certain infrastructures. Most will need maintenance, which will have to be carried out without causing disruption. Mr Clark’s presentation is available on YouTube: https://www.youtube. com/watch?v=iV6vcXOgBsQ
JPEE2014 in Lisbon fib President Gordon Clark was invited to make a keynote presentation at the opening of JPEE2014 (5th Portuguese Conference on Structural Engineering) in Lisbon on 26 November. Mr Clark spoke about longlasting concrete structures, focussing on lessons that can be drawn from past experience to help with future projects. The conference, organized by GPBE (the Portuguese national member group of the fib), among others, lasted three days and was very well
fibnews
Short notes attended, attracting 330 Portuguese and international delegates. Mr Clark and Dr Manuel Pipa, President of GPBE, awarded the GPBE Medal of Merit to Dr João Almeida, fib Head of Delegation for Portugal (see Short notes). Several other fib members were present, including Dr Eduardo Carvalho and Professor Julio Appleton, both past presidents of GPBE.
fib MC2010 course in Brazil Between 2011 and 2013, when it came to approving the fib Model Code for Concrete Structures 2010 as well as the latest version of the Brazilian Standard NBR6188 ‘Design of concrete structures’ there were intense discussions in the fib National Member Group for Brazil, composed of ABECE (Brazilian Association of Structural Engineering and Consulting) and ABCIC (Brazilian Association of Industrialized Concrete Construction). To stimulate further debate and find answers to some of the questions
raised, we hosted an fib MC2010 course in São Paolo on 27 and 28 November 2014. The course was a great success thanks to the support of Professor György Balázs (former SAG 2 Convener, current Commission 9 Chair), the sponsorship of the companies Odebrecht and Andrade Gutierrez, the coordination of Professor Joost Walraven and the participation of Professors Aurelio Muttoni, Giuseppe Mancini, Harald Müller and Hugo Corres. Indeed, the discussions were so lively that the last part of the course was cancelled so as not to disrupt them. Based on the interest shown, the Brazilian group will host future courses on related technical issues. Such discussions contribute significantly to the advancement of technical standardization in concrete structures in Brazil, not only for standard elements or codes of practice, but also for innovation and technological development. As a worldwide organization with operations on all the continents, the fib allows its members to connect internationally. Mr Fernando Stucchi fib Delegate for Brazil
In the foreground: Harald Müller, fib President, and Hugo Corres, fib Deputy President (both in office since January 2015) at the fib MC2010 course in São Paolo, where discussions were lively
Professor Koji Sakai receives the ACI Concrete Sustainability Award from ACI President William E Rushing Jr
Koji Sakai – Kudos Professor Koji Sakai, the representative of the Japan Sustainability Institute (JSI), fib TC Deputy Chair (2011–2014) and Professor Emeritus of the University of British Columbia, received the ACI Concrete Sustainability Award during the American Concrete Institute (ACI) Fall 2014 Convention Opening Session, held in Washington DC on 26 October 2014. The award, established in 2010, honours individuals or teams who highlight the role of concrete in sustainability. Professor Sakai’s interest in sustainability can be traced back to his launching of the International Conference on Concrete Under Severe Conditions (CONSEC) in Sapporo, in 1995. In a paper for the workshop that followed CONSEC95 he outlined the following tasks as future research subjects: the effective use of resources, the control of CO2 emissions, the development of highperformance concrete and its utilization, the development of environmentally friendly concrete, interfaces between durability design and structural design, energysaving construction methods and rational maintenance systems. He tackled most of the current major issues in concrete sustainability 20 years ago. Structural Concrete 16 (2015), No. 1
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Since then Professor Sakai has organized 25 international conferences, workshops and forums, and given more than a hundred lectures worldwide to promote environmental consciousness and sustainability in the field of concrete. He was the chair of fib SAG8 ‘Sustainability initiative’ (2011–2014) and of Commission 3 ‘Environmental aspects of design and construction’ (2002–2010) and head of the Japanese national delegation. As well as actively leading concrete sustainability in the fib, he has instigated work in this field in the ACI, ISO and Asian Concrete Federation as well as in the Japan Concrete Institute. Professor Takafumi Noguchi, University of Tokyo Deputy Chair of fib Commission 7 ‘Sustainability’
Tor Ole Olsen and Tor Arne MartiusHammer – Kudos On 30 October 2014 the Norwegian Concrete Association (NB – Norsk Betongforening) honoured two very active members of the fib. Tor Ole Olsen received an honorary membership and Tor Arne MartiusHammer an award for outstanding contribution. The Norwegian Concrete Association bestows honorary membership on those who have rendered long
and notable service to the association itself and the concrete industry at large by disseminating knowledge of concrete and bringing Norway to the fore of the industry. Mr Olsen was commended for his international commitment, the number of offices he has held in various bodies and associations, his active participation in organizing conferences, his valuable contributions to the industry, and the numerous publications he has written and presentations given.
Dr MartiusHammer received his degree in engineering from the Norwegian Institute of Technology in 1981 and his PhD in 2007. Since 1985 he has worked for the largest Scandanavian independent research institution and has led its innovation centre, COIN, for eight years. He is an active member of RILEM and is the deputy chair of fib Commission 4 and the convener of fib Task Group 4.6.
João Almeida – Kudos Mr Olsen received his engineering degree from the University of Toronto, Canada, in 1975, and has since worked for Dr. Techn. Olav Olsen, a consultancy founded by his father (a 1980 FIP medallist) and specializing in large onshore and offshore structures and facilities. He is currently an elected member of the fib Presidium as well as an active member of the ACI and IAB. He was Chairman of the Norwegian Concrete Association from 1995 to 1997. A prize for his achievements in and contributions to the field of structural concrete and the Norwegian Concrete Association was awarded at the same ceremony to Dr MartiusHammer. The association highlighted his assiduity within the organization and international bodies, the numerous articles he has written and his role as the managing director of COIN – Concrete Innovation Centre.
On 26 November 2014, during the Portuguese symposium on structural concrete held at the Portuguese Conference on Structural Engineering (JPEE2014), the GPBE Medal of Merit was awarded to João Almeida.
From left to right: Gordon Clark, João Almeida and Manuel Pipa at the GPBE Medal of Merit ceremony
This honour has been awarded every two years since 2000 at GPBE (Portuguese Group on Structural Concrete) national meetings in Portugal in recognition of outstanding contributions to the field of structural concrete. Dr Almeida is a professor at the Instituto Superior Técnico Lisboa, Portugal. In his career as structural engineer he has designed a number of major buildings and bridges.
Tor Ole Olsen at the award ceremony for his honorary membership
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Tor Arne MartiusHammer receives an award for outstanding work
A longstanding active member of the fib and the FIP and currently head of the Portuguese national delegation, he was the convener of
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Task Group 1.1 from 1998 to 2008 and has coauthored six bulletins. In Stockholm, in 2012, Dr Almeida was awarded the fib Medal of Merit. Dr Manuel Pipa President of GPBE
Marco Menegotto – 75th birthday The fib wishes Marco Menegotto a very happy birthday. Professor Menegotto received the fib Medal of Merit in 2009. A member of various CEB, FIP and fib Commissions since 1972, he has contributed to CEBFIP MC78 and MC90 and fib MC2010 as well as several FIP, CEB and fib reports and bulletins. From 2005 to 2014 he served as Chair of fib Commission 6 ‘Prefabrication’ and has also chaired IABSE and RILEM committees. He has contributed to CEN Structural Eurocodes and is the moderator of the CEN TC229TC250 Ad Hoc Group. Professor Menegotto is coauthor of the most used model for steel constitutive law, known as the MenegottoPinto Model. In 2010, after 30 years of teaching as Full Professor of Structural Engineering, Professor Menegotto retired from Sapienza University of Rome. Today he is Chairman of AICAP (Italian Association for Structural Concrete) and the head of the Italian delegation for the fib.
HansWolf Reinhardt – 75th birthday Congratulations to HansWolf Reinhardt on his birthday. Professor Reinhardt taught at the Delft University of Technology, Nether
lands, then at the University of Technology Darmstadt, Germany, before becoming Dean of the Department of Civil Engineering and Head of the OttoGraf Institute of the University of Stuttgart, Germany, in 1992. He retired officially in 2012. Professor Reinhardt has been a very active member of the fib (and the CEB before it) and coauthored fib MC2010 and several bulletins. Outside the fib he headed the German delegation of the DIN Committee Concrete Technology as part of CEN/TC 104 ‘Concrete’ preparing EN 206. Honoured with the EmilMörsch Commemorative Medal in 2013, he also received an honorary doctorate from the Braunschweig University of Technology, Germany, in 2004, and an honorary professorship from Dalian University, China, in 2002.
Nigel Priestley † 1943–2014 Nigel enrolled for engineering at the University of Canterbury, New Zealand, at the age of 16 and completed his PhD at the age of 23. He headed extensive studies on bridges and buildings for 10 years at the Structures Laboratory of the Ministry of Works before returning to the University of Canterbury’s engineering faculty as a lecturer in 1976. There he and Professor Tom Paulay conducted comprehensive
research into the seismic behaviour of masonry structures. Nigel also studied the behaviour of reinforced concrete columns and a number of his research papers are now recognized as the basis for current understanding on the topic. From 1985 to 1986 he was the president of the New Zealand Society for Earthquake Engineering. In 1986 Nigel was named Professor at the University of California, San Diego, and later became Professor Emeritus. During his 14 years there he conducted extensive research into the seismic design of concrete bridges and for the last three years was a visiting fellow funded by the New Zealand Earthquake Commission. He left UCSD to become the codirector of the ROSE School in Pavia, Italy, where he taught courses in earthquake engineering. Nigel received numerous honours, including honorary doctorates from ETH Zurich and UNCuyo, Argentina. In May 2010 he was awarded the Freyssinet Medal at the fib Congress in Washington DC. He was a coauthor of three seismic design books: ‘Seismic Design of Concrete and Masonry Buildings’, ‘Seismic Design and Retrofit of Bridges’, and ‘DisplacementBased Seismic Design of Structures’. He was also a member of CEB Task Group 3.2: ‘Seismic design of reinforced concrete structures’ and coauthored Bulletin 240: ‘Seismic Design’. A fellow of the ACI, IPENZ, NZ Society for Earthquake Engineering and NZ Concrete Society, and Honorary Fellow of the Royal Society of New Zealand, he was made an Officer of the New Zealand Order of Merit in 2014 for his services to structural engineering. He left behind his wife, Jan, his children, stepchildren and grandchildren. Professor Jason Ingham University of Auckland Structural Concrete 16 (2015), No. 1
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Congresses and symposia Date and location
Event
Main organiser
Contact
24–26 February 2015
59th BetonTage Ulm, Germany
FBF Betondienst GmbH Concretes of the Future
info@betontage.de www.betontage.com
18–20 May 2015 Copenhagen, Denmark
fib Symposium: Concrete innovation and design
Danish Concrete Society
www.fibcopenhagen2015.dk
23–24 April 2015 Düsseldorf, Germany
Deutscher BautechnikTag 2015
DBV
www.bautechniktag.de
24–26 May 2015 Chicago, USA
5th International Symposium on Nanotechnology in Construction (NICOM5)
University of WisconsinMilwaukee, Northwestern University
www.nicom5.org
1–3 July 2015 Porto, Portugal
Multispan Large Bridges
Faculty of Engineering University of Porto
www.fe.up.pt/mslb2015
1–2 October 2015 Hainburg, Austria
11th Central European Congress on Concrete Engineering
OBV Austrian Society for Construction Technology
www.ccc2015.at
5–7 October 2015 Leipzig, Germany
4th Int. Conf. on Concrete Repair, Rehabilitation and Retrofitting (ICCRRR 2015)
MFPA Leipzig GmbH University of Cape Town
www.iccrrr.com
8–9 October 2015 Leipzig, Germany
4th Int. Workshop on Concrete Spalling due to Fire Exposure
MFPA Leipzig GmbH TU Delft
www.iccrrr.com
13–15 June 2016 Madrid, Spain
ICCS16 Second International Conference on Concrete Sustainability
Universidad Politecnica de Madrid
To be announced
29–31 August 2016 Tokyo, Japan
11th fib International Ph.D. Symposium
Nihon University Tokyo University
concrete.t.utokyo.ac.jp/fib _PhD2016
12–14 September 2016 Lecco, Italy
CONSEC2016
Politecnico di Milano
To be announced
21–23 November 2016 Cape Town, South Africa
fib Symposium Performancebased approaches for concrete structures
University of Cape Town
fibcapetown2016.com/
12–15 June 2017 Maastricht, Netherlands
fib Symposium fib National Member High tech concrete: Where Group Netherlands technology and engineering meet
info@symposium2017.com www.fibsymposium2017.com
6–12 October 2018 Melbourne, Australia
5th fib Congress and Exhibition
www.fibcongress2018.com
fib National Member Group Australia
The calendar list with fib Congresses and Symposia, cosponsored events and, if space permits, events supported by the fib or organized by one of its national member groups reflects the state of information available to the secretariat at the time of printing. The information given is subject to change.
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fibnews
Acknowledgement fib – Fédération internationale du béton – the International Federation for Structural Concrete – is grateful for the invaluable support of the following national member groups and sponsoring members, which contributes to the publication of fib Technical Bulletins, the Structural Concrete journal, and fibnews.
National member groups AAHES – Asociación Argentina del Hormigón Estructural CIA – Concrete Institute of Australia ÖBV – Österreichische Bautechtechnik Vereinigung, Austria GBB – Groupement Belge du Béton, Belgium ABCIC – Associação Brasileira da Construção Industrializada de Concreto, Brazil ABECE – Associação Brasileira de, Engenharia e Consultoria Estrutural, Brazil fib Group of Canada CCES – China Civil Engineering Society Cyprus University of Technology CBS – Ceska Betonarska Spolecnost, Czech Republic DBF – Dansk Betonforening DBF, Denmark Suomen Betoniyhdistys R.Y., Finland AFGC – Association Française de Génie Civil, France DBV – Deutscher Beton und Bautechnik Verein, Germany Deutscher Ausschuss für Stahlbeton e.V., Germany FDB – Fachvereinigung Deutscher, Betonfertigteilbau e.V., Germany Technical Chamber of Greece University of Patras, Greece Hungarian Group of fib The Institution of Engineers (India) Dept. of Technical Affairs, Iran IACIE – Israeli Association of Construction, and Infrastructure Engineers Consiglio Nazionale delle Ricerche, Italy
JCI – Japan Concrete Institute JPCI – Japan Prestressed Concrete Institute Lebanese Concrete Society Administration des Ponts et Chaussées, Luxembourg fib Netherlands NZCS – New Zealand Concrete Society Norsk Betongforening, Norway Committee of Civil Engineering, Poland GPBE – Grupo Portugês de Betão Estrutural, Portugal Society for Concrete & Prefab Units of Romania Technical University of Civil Engineering, Romania Transylvania University of Brasov, Romania Association for Structural Concrete, Russia Association of Structural Engineers, Serbia Slovak Union of Civil Engineers Slovenian Society of Structural Engineers University of Cape Town, South Africa KCI – Korean Concrete Institute ACHE – Asociación CientificoTécnica del Hormigón Estructural, Spain Svenska Betongföreningen, Sweden Délégation nationale suisse de la fib, Switzerland TCA – Thailand Concrete Association, Thailand Université de Tunis El Manar, Tunisia ITU – Istanbul Technical University, Turkey NIISK – Research Institute of Building Constructions, Ukraine
fib UK Group ASBI – American Segmental Bridge Institute, USA PCI – Precast/Prestressed Concrete Institute, USA PTI – Post Tensioning Institute, USA
Sponsoring members Liuzhou OVM Machinery Company Ltd, China Consolis Oy Ab,Finland ECS – European Engineered Construction Systems (formerly VBBF), Germany FBF Betondienst GmbH, Germany FiReP Rebar Technology GmbH, Germany MKT MetallKunststoffTechnik GmbH, Germany Larsen & Toubro Ltd ECC Division, India ATP s.r.l, Italy Fuji P. S. Corporation, Japan IHI Construction Service Company Ltd, Japan Obayashi Corporation, Japan Oriental Shiraishi Corporation, Japan P. S. Mitsubishi Construction Company Ltd, Japan SE Corporation, Japan Sumitomo Mitsui Constructruction Company Ltd, Japan Hilti Corporation, Liechtenstein Patriot Engineering, Russia BBR VT International Ltd, Switzerland SIKA Services AG, Switzerland VSL International Ltd, Switzerland China Engineering Consultants, Inc., Taiwan (China) PBL Group Ltd, Thailand CCL Stressing Systems Ltd, United Kingdom
Structural Concrete 16 (2015), No. 1
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Preview
Structural Concrete 2/2015 Dirk Schlicke, Nguyen Viet Tue Minimum reinforcement of concrete members regarding hardening caused stresses and member dimensions
Benjamin Kromoser, Johann Kollegger Pneumatic forming of hardened concrete – building shells in the 21st century
Ricardo Costa, Paulo Providência, Alfredo Dias Consideration of strength and size of beamcolumn joints in the design of RC frames
Kim Van Tittelboom, Elke Gruyaert, Pieter De Backer, Wim Moerman, Nele De Belie Selfrepair of thermal cracks in concrete sandwich panels
Paolo Martinelli, Matteo Colombo, Marco Di Prisco A design approach for tunnels exposed to blast and fire
Andreas Galmarini, Daniel Locher, Peter Marti Predicting the response of reinforced concrete slab strips subjected to axial tension and transverse load: a competition
Jianzhuang Xiao, Chang Sun, Xinghan Jiang Flexural behavior of recycled aggregate concrete gradient slabs
Li Yunpan, Xu Gang, Su Yibiao, Xu Ke Chloride ion transport mechanism under different dryingwetting cycles
Caesar Abi Shdid, Masood Hajali, Ali Alavinasab Effect of the location of broken wire wraps on the failure pressure of prestressed concrete cylinder pipes Martin Classen Shear force carrying of composite dowels in transversely cracked concrete Elena Diaz, David Fernandez, Enrique Gonzalez Influence of axial tension on the shear strength of floor joists without transverse reinforcement Wael Kassem Shear strength of deep beams: a mathematical model and design formula
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forces in motion
2014 Volume 15 No. 1–4 ISSN 14644177
Annual table of contents EditorinChief: Luc Taerwe
Deputy Editor: Steinar Helland Members: György L. Balázs Josée Bastien Mikael Braestrup Tom d’ Arcy Michael Fardis
Stephen Foster Sung Gul Hong Tim Ibell S.G. Joglekar Akio Kasuga Daniel A. Kuchma Gaetano Manfredi Pierre Rossi Guilhemo Sales Melo Petra Schumacher Tamon Ueda Yong Yuan
Annual table of contents 2014
Structural Concrete: Annual table of contents Volume 15 (2014) List of authors (T = Technical Paper, E = Editorial)
Abbas, Ali A.; Mohsin, Sharifah M. Syed; Cotsovos, Demetrios M.: Nonlinear analysis of statically indeterminate SFRC columns Issue 1 Abdellahi, Majid; Heidari, Javad; Bahmanpour, Maryam: A new predictive model for the bond strength of FRPtoconcrete composite joints Issue 4 Aboutalebi, Morteza; Alani, Amir M.; Rizzuto, Joseph; Beckett, Derrick: Structural behaviour and deformation patterns in loaded plain concrete groundsupported slabs Issue 1 Aboutalebi, Morteza; see Alani, Amir M. Ahuja, Ashok K.; see Gupta, Pramod K. Akpinar, Erkan; see Ozden, Sevket Alani, Amir M.; Aboutalebi, Morteza; Kilic, Gokhan: Use of noncontact sensors (IBISS) and finite element methods in the assessment of bridge deck structures Issue 2 Alani, Amir M.; see Aboutalebi, Morteza Almeida, João F.; see Gama, David Andreatta, Andreas; see Theiner, Yvonne Ansell, Anders; see Magnusson, Johan Atalay, Hilal M.; see Ozden, Sevket Bahmanpour, Maryam; see Abdellahi, Majid Beckett, Derrick; see Aboutalebi, Morteza Belletti, Beatrice; Damoni, Cecilia; Hendriks, Max A. N.; de Boer, Ane: Analytical and numerical evaluation of the design shear resistance of reinforced concrete slabs Issue 3 Bergmeister, Konrad: The service life of any structure is due to the genius of the engineer who designs it – and should not be at the expense of the engineer maintaining it. Issue 2 Bergmeister, Konrad; see Podroužek, Jan Bergmeister, Konrad; see Urban, Susanne
2
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94–105
T
509–521
T
81–93
240–247
T
T
317–330
T
115–116
E
Biliszczuk, Jan; see Onysyk, Jerzy Bittencourt, Túlio Nogueira; see Meneghetti, Leila Cristina Boel, Veerle; see Korte, Sara Bollinger, Klaus; see MessariBecker, Lamia Breitenbücher, Rolf; Meschke, Günther; Song, Fanbing; Zhan, Yijian: Experimental, analytical and numerical analysis of the pullout behaviour of steel fibres considering different fibre types, inclinations and concrete strengths Issue 2 Cadamuro, Erica; see Carpinteri, Alberto Cairns, John: Staggered lap joints for tension reinforcement Issue 1 Carpinteri, Alberto; Cadamuro, Erica; Corrado, Mauro: Minimum flexural reinforcement in rectangular and Tsection concrete beams Issue 3 Caspeele, Robby; see Van Coile, Ruben Castberg, Andreas; see Hertz, Kristian Castel, Arnaud; Gilbert, Raymond Ian: Influence of timedependent effects on the crack spacing in reinforced concrete beams Issue 3 Castel, Arnaud; Gilbert, Raymond Ian: Influence of timedependent effects on the crack spacing in reinforced concrete beams Issue 3 Cervenka, Vladimir; Ganz, Hans Rudolf: Validation of posttensioning anchorage zones by laboratory testing and numerical simulation Issue 2 Chen, Genda; see Yan, Dongming Chi, Yang; see Yuan, Yong Christensen, Jacob; see Hertz, Kristian Clark, Gordon: Challenges for concrete in tall buildings Issue 4 Corrado, Mauro; see Carpinteri, Alberto Cotsovos, Demetrios M.; see Abbas, Ali A. Curbach, Manfred; see Wilhelm, Sebastian da Silva Filho, Luiz Carlos Pinto; see Meneghetti, Leila Cristina Dahl, Kaare K. B.: Bella Sky Hotel – taking precast concrete to the limit Issue 4 Damoni, Cecilia; see Belletti, Beatrice
126–135
T
45–54
T
361–372
T
373–379
T
373–379
T
258–268
T
448–453
T
441–447
T
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Annual table of contents 2014
de Boer, Ane; see Belletti, Beatrice De Corte, Wouter; see Korte, Sara De Schutter, Geert; see Korte, Sara De Schutter, Geert; see Liu, Xian Dehlinger, Christian; see Urban, Susanne Erdogan, Hakan; see Ozden, Sevket Fan, Yuhui; Xiao, Jianzhuang; Tam, Vivian W. Y.: Effect of old attached mortar on the creep of recycled aggregate concrete Issue 2 Farkas, György; see Völgyi, István Foremniak, Sara; see Kollegger, Johann Gama, David; Almeida, João F.: Concrete integral abutment bridges with reinforced concrete piles Issue 3 Ganz, Hans Rudolf; see Cervenka, Vladimir Garcez, Mônica Regina; see Meneghetti, Leila Cristina Gastal, Francisco de Paula Simões Lopes; see Meneghetti, Leila Cristina Gilbert, Raymond Ian; see Castel, Arnaud Glavind, Mette: Innovations in concrete for sustainable infrastructure constructions Issue 4 Gmainer, Susanne; see Kollegger, Johann González, Dorys C.; see Vicente, Miguel A. Grohmann, Manfred; see MessariBecker, Lamia Groli, Giancarlo; Pérez Caldentey, Alejandro; Soto, Alejandro Giraldo: Cracking performance of SCC reinforced with recycled fibres – an experimental study Issue 2 Gupta, Pramod K.; Ahuja, Ashok K.; Khaudhair, Ziyad A.: Modelling, verification and investigation of behaviour of circular CFST columns Issue 3 Hallgren, Mikael; see Magnusson, Johan Han, SangHun; see Won, Deok Hee Han, Taek Hee; see Won, Deok Hee Heek, Peter; see Winkler, Karsten Hegger, Josef; see Siburg, Carsten Heidari, Javad; see Abdellahi, Majid Helland, Steinar; see Taerwe, Luc Hendriks, Max A. N.; see Belletti, Beatrice Hertz, Kristian; Castberg, Andreas; Christensen, Jacob: Superlight concrete decks for building floor slabs Issue 4 Hofstetter, Günter; see Theiner, Yvonne
www.ernstundsohn.de
169–178
292–304
439–440
136–153
340–349
522–529
T
T
E
T
T
T
Hölmebakk, CarlViggo; see Krokstrand, Ole H. Jang, InSung; see Won, Deok Hee Jiang, Wei; see Liu, Xian Keršner, Zbyneˇk; see Strauss, Alfred Khaudhair, Ziyad A.; see Gupta, Pramod K. Kilic, Gokhan; see Alani, Amir M. Knappe, Florian; see MessariBecker, Lamia Kollegger, Johann; Foremniak, Sara; Suza, Dominik; Wimmer, David; Gmainer, Susanne: Building bridges using the balanced lift method Korte, Sara; Boel, Veerle; De Corte, Wouter; De Schutter, Geert: Behaviour of fatigue loaded selfcompacting concrete compared to vibrated concrete Krokstrand, Ole H.; Ramstad, Reiulf; Hölmebakk, CarlViggo: Splendid concrete architecture in National Tourist Routes in Norway Kunz, Jakob; see Randl, Norbert Lehký, David; see Strauss, Alfred Li, Hedong; see Yan, Dongming Li, Hong; see Xiao, Jianzhuang Li, Long; see Xiao, Jianzhuang Litzner, HansUlrich: Tempora mutantur...... Liu, Xian; Jiang, Wei; De Schutter, Geert; Yuan, Yong; Su, Quanke: Earlyage behaviour of precast concrete immersed tunnel based on degree of hydration concept Liu, Xian; Yuan, Yong; Su, Quanke: Sensitivity analysis of the earlyage cracking risk in an immersed tunnel Lu, Xilin: Precast concrete structures in the future Magnusson, Johan; Hallgren, Mikael; Ansell, Anders: Shear in concrete structures subjected to dynamic loads Mancini, Giuseppe; Tondolo, Francesco: Effect of bond degradation due to corrosion – a literature survey Mark, Peter; see Winkler, Karsten Martínez, José A.; see Vicente, Miguel A. Meneghetti, Leila Cristina; Garcez, Mônica Regina; da Silva Filho, Luiz Carlos Pinto; Gastal, Francisco de Paula Simões Lopes; Bittencourt, Túlio Nogueira: Fatigue life of RC beams strengthened with FRP systems Meschke, Günther; see Breitenbücher, Rolf MessariBecker, Lamia; Mettke, Angelika; Knappe, Florian;
Issue 3 281–291
T
Issue 4 575–589
T
Issue 2 117–125
T
Issue 3 277–278
E
Issue 1 66–80
T
Issue 2 179–190
T
Issue 1 1–2
E
Issue 1 55–65
T
Issue 3 408–418
T
Issue 2 219–228
T
Structural Concrete 15
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Annual table of contents 2014
Storck, Ulrich; Bollinger, Klaus; Grohmann, Manfred: Recycling concrete in practice – a chance for sustainable resource management Mettke, Angelika; see MessariBecker, Lamia Mohsin, Sharifah M. Syed; see Abbas, Ali A. Mínguez, Jesús; see Vicente, Miguel A. Novák, Drahomír; see Strauss, Alfred Nyhus, Bente Skovseth: Consistent practical design of concrete structures Onysyk, Jerzy; Biliszczuk, Jan; Prabucki, Przemyslaw; Sadowski, Krzysztof; Toczkiewicz, Robert: Strengthening the 100yearold reinforced concrete dome of the Centennial Hall in Wrocław Ozden, Sevket; Atalay, Hilal M.; Akpinar, Erkan; Erdogan, Hakan; Vulas¸ , Yılmaz Zafer: Shear strengthening of reinforced concrete Tbeams with fully or partially bonded fibrereinforced polymer composites Park, Woo Sun; see Won, Deok Hee Podroužek, Jan; Strauss, Alfred; Bergmeister, Konrad: Robustnessbased performance assessment of a prestressed concrete bridge Prabucki, Przemyslaw; see Onysyk, Jerzy Prince, M. John Robert; Singh, Bhupinder: Investigation of bond behaviour between recycled aggregate concrete and deformed steel bars Pérez Caldentey, Alejandro; see Groli, Giancarlo Ramstad, Reiulf; see Krokstrand, Ole H. Randl, Norbert; Kunz, Jakob: Postinstalled reinforcement connections at ultimate and serviceability limit states Reinhardt, HansWolf: Aspects of imposed deformation in concrete structures – a condensed overview Ricker, Marcus; see Siburg, Carsten Rizzuto, Joseph; see Aboutalebi, Morteza Rohländer, Sandra; see Winkler, Karsten Sadowski, Krzysztof; see Onysyk, Jerzy Schütz, Robert; see Urban, Susanne Scott, Richard: Serviceability uncertainties in flat slabs
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Issue 4 556–562
T
Issue 3 305–316
T
Issue 1 30–37
T
Issue 2 229–239
T
Issue 2 248–257
T
Issue 2 154–168
T
Issue 4 563–574
T
Issue 4 454–460
T
Issue 4 469–483
T
Siburg, Carsten; Hegger, Josef: Experimental investigations on the punching behaviour of reinforced concrete footings with structural dimensions Issue 3 Siburg, Carsten; Ricker, Marcus; Hegger, Josef: Punching shear design of footings: critical review of different code provisions Issue 4 Silva Filho, Júlio Jerônimo Holtz; see Souza, Osvaldo Luiz de Carvalho Singh, Bhupinder; see Prince, M. John Robert Sommer, Simone; see Winkler, Karsten Song, Fanbing; see Breitenbücher, Rolf Soto, Alejandro Giraldo; see Groli, Giancarlo Souza, Osvaldo Luiz de Carvalho; Sánchez Filho, Emil de Souza; Vaz, Luiz Eloy; Silva Filho, Júlio Jerônimo Holtz: Reliability analysis of RC beams strengthened for torsion with carbon fibre composites Issue 1 Storck, Ulrich; see MessariBecker, Lamia Strauss, Alfred; Zimmermann, Thomas; Lehký, David; Novák, Drahomír; Keršner, Zbyneˇk: Stochastic fracturemechanical parameters for the performancebased design of concrete structures Issue 3 Strauss, Alfred; see Podroužek, Jan Strauss, Alfred; see Urban, Susanne Su, Quanke; see Liu, Xian Suza, Dominik; see Kollegger, Johann Sánchez Filho, Emil de Souza; see Souza, Osvaldo Luiz de Carvalho Taerwe, Luc; Helland, Steinar: Structural Concrete makes impact Issue 3 Taerwe, Luc; see Van Coile, Ruben Tam, Vivian W. Y.; see Fan, Yuhui Tam, Vivian W.Y.; see Xiao, Jianzhuang Theiner, Yvonne; Andreatta, Andreas; Hofstetter, Günter: Evaluation of models for estimating concrete strains due to drying shrinkage Issue 4 Toczkiewicz, Robert; see Onysyk, Jerzy Tondolo, Francesco; see Mancini, Giuseppe Urban, Susanne; Strauss, Alfred; Schütz, Robert; Bergmeister, Konrad; Dehlinger, Christian: Dynamically loaded concrete structures – monitoringbased
331–339
T
497–508
T
38–44
T
380–394
T
279–280
E
461–468
T
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Annual table of contents 2014
assessment of the real degree of fatigue deterioration Van Coile, Ruben; Caspeele, Robby; Taerwe, Luc: Towards a reliabilitybased postfire assessment method for concrete slabs incorporating information from inspection Vaz, Luiz Eloy; see Souza, Osvaldo Luiz de Carvalho Vicente, Miguel A.; González, Dorys C.; Mínguez, Jesús; Martínez, José A.: Residual modulus of elasticity and maximum compressive strain in HSC and FRHSC after highstresslevel cyclic loading Vulas¸ , Yılmaz Zafer; see Ozden, Sevket Völgyi, István; Windisch, Andor; Farkas, György: Resistance of reinforced concrete members with hollow circular crosssections under combined bending and shear – Part I: experimental investigation Völgyi, István; Windisch, Andor: Resistance of reinforced concrete members with hollow circular crosssection under combined bending and shear – Part II: New calculation model Wilhelm, Sebastian; Curbach, Manfred: Review of possible mineral materials and production techniques for a building material on the moon Wimmer, David; see Kollegger, Johann
www.ernstundsohn.de
Issue 4 530–542
T
Issue 3 395–407
T
Issue 2 210–218
T
Issue 1 13–20
T
Issue 1 21–29
T
Issue 3 419–428
T
Windisch, Andor; see Völgyi, István Winkler, Karsten; Mark, Peter; Heek, Peter; Rohländer, Sandra; Sommer, Simone: Punching shear tests on symmetrically reduced slab quarters Won, Deok Hee; Park, Woo Sun; Jang, InSung; Han, SangHun; Han, Taek Hee: Fire resistance performance of steel composite hollow RC column with inner tube under ISO 834 standard fire Won, Deok Hee; Park, Woo Sun; Yi, JinHak; Han, SangHun; Han, Taek Hee: Effect of welding heat on precast steel composite hollow columns Xiao, Jianzhuang; Li, Long; Tam, Vivian W.Y.; Li, Hong: The state of the art regarding the longterm properties of recycled aggregate concrete Xiao, Jianzhuang; see Fan, Yuhui Xu, Shilang; see Yan, Dongming Yan, Dongming; Xu, Shilang; Chen, Genda; Li, Hedong: Biaxial behaviour of plain concrete subjected to dynamic compression with constant lateral stress Yi, JinHak; s. Won, Deok Hee Yuan, Yong; Chi, Yang: Water permeability of concrete under uniaxial tension Yuan, Yong; s. Liu, Xian Zhan, Yijian; s. Breitenbücher, Rolf Zimmermann, Thomas; s. Strauss, Alfred
Issue 4 484–496
T
Issue 4 543–555
T
Issue 3 350–360
T
Issue 1 3–12
T
Issue 2 202–209
T
Issue 2 191–201
T
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Subject codes and keywords
Analysis and design methods Abbas, Ali A.; Mohsin, Sharifah M. Syed; Cotsovos, Demetrios M.: Nonlinear analysis of statically indeterminate SFRC columns [fibrereinforced concrete; finite element methods; structural analysis] Issue 1 Aboutalebi, Morteza; Alani, Amir M.; Rizzuto, Joseph; Beckett, Derrick: Structural behaviour and deformation patterns in loaded plain concrete groundsupported slabs [groundsupported slab; displacement; crack propagation; bending; punching] Issue 1 Alani, Amir M.; Aboutalebi, Morteza; Kilic, Gokhan: Use of noncontact sensors (IBISS) and finite element methods in the assessment of bridge deck structures [finite element modelling; bridge health monitoring; IBISS sensor; ANSYS] Issue 2 Belletti, Beatrice; Damoni, Cecilia; Hendriks, Max A. N.; de Boer, Ane: Analytical and numerical evaluation of the design shear resistance of reinforced concrete slabs [reinforced concrete slabs; nonlinear finite element analysis; shear resistance evaluation; guidelines; safety formats; design] Issue 3 Breitenbücher, Rolf; Meschke, Günther; Song, Fanbing; Zhan, Yijian: Experimental, analytical and numerical analysis of the pullout behaviour of steel fibres considering different fibre types, inclinations and concrete strengths [steel fibre; pullout behaviour; laboratory test; analytical modelling; numerical simulation] Issue 2 Castel, Arnaud; Gilbert, Raymond Ian: Influence of timedependent effects on the crack spacing in reinforced concrete beams [reinforced concrete; crack spacing; shrinkage; sustained loading; stirrup spacing; fib Model Code 2010] Issue 3 Cervenka, Vladimir; Ganz, Hans Rudolf: Validation of posttensioning anchorage zones by laboratory testing and numerical simulation [anchorage; numerical analysis; testing] Issue 2 Fan, Yuhui; Xiao, Jianzhuang; Tam, Vivian W. Y.: Effect of old attached mortar on the creep of recycled aggregate concrete 6
Structural Concrete 15
94–105
81–93
240–247
317–330
126–135
373–379
258–268
[recycled aggregate concrete; old adhering mortar; shrinkage; creep; influence mechanism] Issue 2 Gama, David; Almeida, João F.: Concrete integral abutment bridges with reinforced concrete piles [prestressed concrete bridges; integral abutment bridges; reinforced concrete piles; imposed deformations; soilstructure interaction; levels of approximation] Issue 3 Gupta, Pramod K.; Ahuja, Ashok K.; Khaudhair, Ziyad A.: Modelling, verification and investigation of behaviour of circular CFST columns [concretefilled tube; CFST column; simulation; CFT; composite columns; confinement; confined concrete; circular columns] Issue 3 Liu, Xian; Jiang, Wei; De Schutter, Geert; Yuan, Yong; Su, Quanke: Earlyage behaviour of precast concrete immersed tunnel based on degree of hydration concept [precast immersed tunnel; earlyage cracking; degree of hydration; creep under varying stress levels] Issue 1 Liu, Xian; Yuan, Yong; Su, Quanke: Sensitivity analysis of the earlyage cracking risk in an immersed tunnel [immersed tunnel; earlyage cracking; sensitivity analysis; curing scheme] Issue 2 Magnusson, Johan; Hallgren, Mikael; Ansell, Anders: Shear in concrete structures subjected to dynamic loads [dynamic loads; impulsive loads; rise time; shear; initial response; support reactions; arch action] Issue 1 Nyhus, Bente Skovseth: Consistent practical design of concrete structures [concrete design; practical design; consistent stiffness method; nonlinear analysis; shear design; MCFT; safety; cost effective] Issue 3 Onysyk, Jerzy; Biliszczuk, Jan; Prabucki, Przemyslaw; Sadowski, Krzysztof; Toczkiewicz, Robert: Strengthening the 100yearold reinforced concrete dome of the Centennial Hall in Wrocław [pioneering concrete structure; renovation; FEM analysis; strengthening] Issue 1 Podroužek, Jan; Strauss, Alfred; Bergmeister, Konrad: Robustnessbased performance assessment of a prestressed concrete bridge [robustness; existing
169–178
292–304
340–349
66–80
179–190
55–65
305–316
30–37
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Annual table of contents 2014
structure; reliability; performance indicators; safety; stochastic methods] Issue 2 Randl, Norbert; Kunz, Jakob: Postinstalled reinforcement connections at ultimate and serviceability limit states [postinstalled reinforcement; anchorage; splitting; pullout; serviceability limit state] Issue 4 Reinhardt, HansWolf: Aspects of imposed deformation in concrete structures – a condensed overview [imposed deformation; fresh concrete; shrinkage; young concrete; cracking] Issue 4 Scott, Richard: Serviceability uncertainties in flat slabs [load tests; finite element analysis; codes of practice] Issue 4 Siburg, Carsten; Ricker, Marcus; Hegger, Josef: Punching shear design of footings: critical review of different code provisions [punching; footing; fib Model Code 2010; Eurocode 2; tests] Issue 4 Souza, Osvaldo Luiz de Carvalho; Sánchez Filho, Emil de Souza; Vaz, Luiz Eloy; Silva Filho, Júlio Jerônimo Holtz: Reliability analysis of RC beams strengthened for torsion with carbon fibre composites [reliability index; torsion in RC beams; carbon fibre composites] Issue 1 Van Coile, Ruben; Caspeele, Robby; Taerwe, Luc: Towards a reliabilitybased postfire assessment method for concrete slabs incorporating information from inspection [fire; postfire assessment; residual strength; safety level; concrete slab] Issue 3 Vicente, Miguel A.; González, Dorys C.; Mínguez, Jesús; Martínez, José A.: Residual modulus of elasticity and maximum compressive strain in HSC and FRHSC after highstresslevel cyclic loading [fatigue; highstrength concrete; fibrereinforced highstrength concrete; modulus of elasticity; maximum compressive strain] Issue 2 Völgyi, István; Windisch, Andor: Resistance of reinforced concrete members with hollow circular crosssection under combined bending and shear – Part II: New calculation model [behaviour under combined bending and shear; hollow circular crosssection; contribution of compressed concrete to shear resistance; sliding surface] Issue 1 Winkler, Karsten; Mark, Peter; Heek, Peter; Rohländer, Sandra;
www.ernstundsohn.de
248–257
563–574
454–460
469–483
497–508
38–44
395–407
Sommer, Simone: Punching shear tests on symmetrically reduced slab quarters [punching shear; innovative test setup; axis symmetry; experiments; quartered slab] Issue 4 484–496
Anchorage Cairns, John: Staggered lap joints for tension reinforcement [lapped joints; bond; detailing] Issue 1 Cervenka, Vladimir; Ganz, Hans Rudolf: Validation of posttensioning anchorage zones by laboratory testing and numerical simulation [anchorage; numerical analysis; testing] Issue 2 Hertz, Kristian; Castberg, Andreas; Christensen, Jacob: Superlight concrete decks for building floor slabs [superlight structures; deck structures; precast concrete; lightweight concrete; prestressed concrete; structural design; testing structural elements] Issue 4 Mancini, Giuseppe; Tondolo, Francesco: Effect of bond degradation due to corrosion – a literature survey [bond degradation; corrosion rate; experimental procedure] Issue 3 Prince, M. John Robert; Singh, Bhupinder: Investigation of bond behaviour between recycled aggregate concrete and deformed steel bars [coarse recycled concrete aggregate; replacement percentage; natural coarse aggregate; bond; pullout failure; splitting failure; normalized bond strength] Issue 2 Randl, Norbert; Kunz, Jakob: Postinstalled reinforcement connections at ultimate and serviceability limit states [postinstalled reinforcement; anchorage; splitting; pullout; serviceability limit state] Issue 4
45–54
258–268
522–529
408–418
154–168
563–574
Art of engineering 210–218
21–29
Dahl, Kaare K. B.: Bella Sky Hotel – taking precast concrete to the limit [precast concrete; structural behaviour; hotel; complex geometry; leaning building] Issue 4 441–447 Kollegger, Johann; Foremniak, Sara; Suza, Dominik; Wimmer, David; Gmainer, Susanne: Building bridges using the balanced lift method [precast concrete elements; posttensioning; bridge construction method; largescale test] Issue 3 281–291
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Krokstrand, Ole H.; Ramstad, Reiulf; Hölmebakk, CarlViggo: Splendid concrete architecture in National Tourist Routes in Norway [concrete architecture; scenic view; tourist routes; Norway] Issue 2 117–125 MessariBecker, Lamia; Mettke, Angelika; Knappe, Florian; Storck, Ulrich; Bollinger, Klaus; Grohmann, Manfred: Recycling concrete in practice – a chance for sustainable resource management [recycled concrete; grey energy; sustainable construction; building materials; resource management; life cycle assessment] Issue 4 556–562 Winkler, Karsten; Mark, Peter; Heek, Peter; Rohländer, Sandra; Sommer, Simone: Punching shear tests on symmetrically reduced slab quarters [punching shear; innovative test setup; axis symmetry; experiments; quartered slab] Issue 4 484–496
Bridge construction Gama, David; Almeida, João F.: Concrete integral abutment bridges with reinforced concrete piles [prestressed concrete bridges; integral abutment bridges; reinforced concrete piles; imposed deformations; soilstructure interaction; levels of approximation] Issue 3 292–304 Kollegger, Johann; Foremniak, Sara; Suza, Dominik; Wimmer, David; Gmainer, Susanne: Building bridges using the balanced lift method [precast concrete elements; posttensioning; bridge construction method; largescale test] Issue 3 281–291 Podroužek, Jan; Strauss, Alfred; Bergmeister, Konrad: Robustnessbased performance assessment of a prestressed concrete bridge [robustness; existing structure; reliability; performance indicators; safety; stochastic methods] Issue 2 248–257
Building maintenance/refurbishment Alani, Amir M.; Aboutalebi, Morteza; Kilic, Gokhan: Use of noncontact sensors (IBISS) and finite element methods in the assessment of bridge deck structures [finite element modelling; bridge health monitoring; IBISS sensor; ANSYS] Issue 2 240–247 Onysyk, Jerzy; Biliszczuk, Jan; Prabucki, Przemyslaw; Sadow8
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ski, Krzysztof; Toczkiewicz, Robert: Strengthening the 100yearold reinforced concrete dome of the Centennial Hall in Wrocław [pioneering concrete structure; renovation; FEM analysis; strengthening] Issue 1 30–37 Van Coile, Ruben; Caspeele, Robby; Taerwe, Luc: Towards a reliabilitybased postfire assessment method for concrete slabs incorporating information from inspection [fire; postfire assessment; residual strength; safety level; concrete slab] Issue 3 395–407
Building materials/construction materials Abdellahi, Majid; Heidari, Javad; Bahmanpour, Maryam: A new predictive model for the bond strength of FRPtoconcrete composite joints [bond strength; model; GEP; FRP; composite] Issue 4 Breitenbücher, Rolf; Meschke, Günther; Song, Fanbing; Zhan, Yijian: Experimental, analytical and numerical analysis of the pullout behaviour of steel fibres considering different fibre types, inclinations and concrete strengths [steel fibre; pullout behaviour; laboratory test; analytical modelling; numerical simulation] Issue 2 Fan, Yuhui; Xiao, Jianzhuang; Tam, Vivian W. Y.: Effect of old attached mortar on the creep of recycled aggregate concrete [recycled aggregate concrete; old adhering mortar; shrinkage; creep; influence mechanism] Issue 2 Groli, Giancarlo; Pérez Caldentey, Alejandro; Soto, Alejandro Giraldo: Cracking performance of SCC reinforced with recycled fibres – an experimental study [FRC; recycled steel fibres; crack width control; φ/ρs,ef; cover; sustainability; fib Model Code 2010] Issue 2 Gupta, Pramod K.; Ahuja, Ashok K.; Khaudhair, Ziyad A.: Modelling, verification and investigation of behaviour of circular CFST columns [concretefilled tube; CFST column; simulation; CFT; composite columns; confinement; confined concrete; circular columns] Issue 3 Korte, Sara; Boel, Veerle; De Corte, Wouter; De Schutter, Geert: Behaviour of fatigue loaded selfcompacting concrete compared to vibrated concrete [selfcompacting concrete; vibrated concrete; cyclic
509–521
126–135
169–178
136–153
340–349
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Annual table of contents 2014
loading; fatigue; SN curve; crack growth] Issue 4 Krokstrand, Ole H.; Ramstad, Reiulf; Hölmebakk, CarlViggo: Splendid concrete architecture in National Tourist Routes in Norway [concrete architecture; scenic view; tourist routes; Norway] Issue 2 MessariBecker, Lamia; Mettke, Angelika; Knappe, Florian; Storck, Ulrich; Bollinger, Klaus; Grohmann, Manfred: Recycling concrete in practice – a chance for sustainable resource management [recycled concrete; grey energy; sustainable construction; building materials; resource management; life cycle assessment] Issue 4 Ozden, Sevket; Atalay, Hilal M.; Akpinar, Erkan; Erdogan, Hakan; Vulas¸, Yılmaz Zafer: Shear strengthening of reinforced concrete Tbeams with fully or partially bonded fibrereinforced polymer composites [reinforced concrete; beam shear strengthening; fibrereinforced polymer; anchorage; partially bonded FRP; modulus of elasticity; composite] Issue 2 Prince, M. John Robert; Singh, Bhupinder: Investigation of bond behaviour between recycled aggregate concrete and deformed steel bars [coarse recycled concrete aggregate; replacement percentage; natural coarse aggregate; bond; pullout failure; splitting failure; normalized bond strength] Issue 2 Randl, Norbert; Kunz, Jakob: Postinstalled reinforcement connections at ultimate and serviceability limit states [postinstalled reinforcement; anchorage; splitting; pullout; serviceability limit state] Issue 4 Reinhardt, HansWolf: Aspects of imposed deformation in concrete structures – a condensed overview [imposed deformation; fresh concrete; shrinkage; young concrete; cracking] Issue 4 Souza, Osvaldo Luiz de Carvalho; Sánchez Filho, Emil de Souza; Vaz, Luiz Eloy; Silva Filho, Júlio Jerônimo Holtz: Reliability analysis of RC beams strengthened for torsion with carbon fibre composites [reliability index; torsion in RC beams; carbon fibre composites] Issue 1 Strauss, Alfred; Zimmermann, Thomas; Lehký, David; Novák, Drahomír; Keršner, Zbyneˇk: Stochastic fracturemechanical parameters for the perform
www.ernstundsohn.de
575–589
117–125
556–562
229–239
154–168
563–574
454–460
ancebased design of concrete structures [fracturemechanical parameters; reliability; inverse analysis; fracture energy; materials database] Issue 3 Urban, Susanne; Strauss, Alfred; Schütz, Robert; Bergmeister, Konrad; Dehlinger, Christian: Dynamically loaded concrete structures – monitoringbased assessment of the real degree of fatigue deterioration [concrete fatigue; monitoring; deterioration assessment] Issue 4 Wilhelm, Sebastian; Curbach, Manfred: Review of possible mineral materials and production techniques for a building material on the moon [mineral materials; lunar base design; building materials; lunar concrete; cast basalt; sulphur concrete; moon; lunar environment; lunar cement; DMSI] Issue 3 Won, Deok Hee; Park, Woo Sun; Jang, InSung; Han, SangHun; Han, Taek Hee: Fire resistance performance of steel composite hollow RC column with inner tube under ISO 834 standard fire [fire resistance; concrete; ISO 834; Eurocode] Issue 4 Won, Deok Hee; Park, Woo Sun; Yi, JinHak; Han, SangHun; Han, Taek Hee: Effect of welding heat on precast steel composite hollow columns [welding; heat; column; precast; concrete] Issue 3 Xiao, Jianzhuang; Li, Long; Tam, Vivian W.Y.; Li, Hong: The state of the art regarding the longterm properties of recycled aggregate concrete [recycled aggregate concrete; longterm properties; shrinkage and creep; carbonation resistance; impermeability; fatigue behaviour] Issue 1 Yan, Dongming; Xu, Shilang; Chen, Genda; Li, Hedong: Biaxial behaviour of plain concrete subjected to dynamic compression with constant lateral stress [biaxial stress state; strain rate; dynamic strength; stressstrain curve; failure mode; concrete] Issue 2 Yuan, Yong; Chi, Yang: Water permeability of concrete under uniaxial tension [reinforced concrete; structural member; water permeability; tensioned element; permeating test] Issue 2
380–394
530–542
419–428
543–555
350–360
3–12
202–209
191–201
38–44
Corrosion Castel, Arnaud; Gilbert, Raymond Ian: Influence of timedependent effects on the crack spacing
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Annual table of contents 2014
in reinforced concrete beams [reinforced concrete; crack spacing; shrinkage; sustained loading; stirrup spacing; fib Model Code 2010] Castel, Arnaud; Gilbert, Raymond Ian: Influence of timedependent effects on the crack spacing in reinforced concrete beams [reinforced concrete; crack spacing; shrinkage; sustained loading; stirrup spacing; fib Model Code 2010] Mancini, Giuseppe; Tondolo, Francesco: Effect of bond degradation due to corrosion – a literature survey [bond degradation; corrosion rate; experimental procedure] Xiao, Jianzhuang; Li, Long; Tam, Vivian W.Y.; Li, Hong: The state of the art regarding the longterm properties of recycled aggregate concrete [recycled aggregate concrete; longterm properties; shrinkage and creep; carbonation resistance; impermeability; fatigue behaviour]
Issue 3 373–379
Issue 3 373–379
Issue 3 408–418
Issue 1 3–12
Design and construction Abbas, Ali A.; Mohsin, Sharifah M. Syed; Cotsovos, Demetrios M.: Nonlinear analysis of statically indeterminate SFRC columns [fibrereinforced concrete; finite element methods; structural analysis] Abdellahi, Majid; Heidari, Javad; Bahmanpour, Maryam: A new predictive model for the bond strength of FRPtoconcrete composite joints [bond strength; model; GEP; FRP; composite] Aboutalebi, Morteza; Alani, Amir M.; Rizzuto, Joseph; Beckett, Derrick: Structural behaviour and deformation patterns in loaded plain concrete groundsupported slabs [groundsupported slab; displacement; crack propagation; bending; punching] Carpinteri, Alberto; Cadamuro, Erica; Corrado, Mauro: Minimum flexural reinforcement in rectangular and Tsection concrete beams [reinforced concrete; code provisions; minimum reinforcement; dimensional analysis; size effects; cohesive crack] Clark, Gordon: Challenges for concrete in tall buildings [tall buildings; design; concrete floors; verticality] Dahl, Kaare K. B.: Bella Sky Hotel – taking precast concrete to the
10
Structural Concrete 15
Issue 1 94–105
Issue 4 509–521
Issue 1 81–93
Issue 3 361–372
Issue 4 448–453
limit [precast concrete; structural behaviour; hotel; complex geometry; leaning building] Issue 4 Gama, David; Almeida, João F.: Concrete integral abutment bridges with reinforced concrete piles [prestressed concrete bridges; integral abutment bridges; reinforced concrete piles; imposed deformations; soilstructure interaction; levels of approximation] Issue 3 Groli, Giancarlo; Pérez Caldentey, Alejandro; Soto, Alejandro Giraldo: Cracking performance of SCC reinforced with recycled fibres – an experimental study [FRC; recycled steel fibres; crack width control; φ/ρs,ef; cover; sustainability; fib Model Code 2010] Issue 2 Gupta, Pramod K.; Ahuja, Ashok K.; Khaudhair, Ziyad A.: Modelling, verification and investigation of behaviour of circular CFST columns [concretefilled tube; CFST column; simulation; CFT; composite columns; confinement; confined concrete; circular columns] Issue 3 Hertz, Kristian; Castberg, Andreas; Christensen, Jacob: Superlight concrete decks for building floor slabs [superlight structures; deck structures; precast concrete; lightweight concrete; prestressed concrete; structural design; testing structural elements] Issue 4 Liu, Xian; Jiang, Wei; De Schutter, Geert; Yuan, Yong; Su, Quanke: Earlyage behaviour of precast concrete immersed tunnel based on degree of hydration concept [precast immersed tunnel; earlyage cracking; degree of hydration; creep under varying stress levels] Issue 1 Liu, Xian; Yuan, Yong; Su, Quanke: Sensitivity analysis of the earlyage cracking risk in an immersed tunnel [immersed tunnel; earlyage cracking; sensitivity analysis; curing scheme] Issue 2 Magnusson, Johan; Hallgren, Mikael; Ansell, Anders: Shear in concrete structures subjected to dynamic loads [dynamic loads; impulsive loads; rise time; shear; initial response; support reactions; arch action] Issue 1 Nyhus, Bente Skovseth: Consistent practical design of concrete structures [concrete design; practical design; consistent stiffness method; nonlinear analysis; shear design; MCFT; safety; cost effective] Issue 3
441–447
292–304
136–153
340–349
522–529
66–80
179–190
55–65
305–316
www.ernstundsohn.de
Annual table of contents 2014
Podroužek, Jan; Strauss, Alfred; Bergmeister, Konrad: Robustnessbased performance assessment of a prestressed concrete bridge [robustness; existing structure; reliability; performance indicators; safety; stochastic methods] Issue 2 Siburg, Carsten; Hegger, Josef: Experimental investigations on the punching behaviour of reinforced concrete footings with structural dimensions [Eurocode 2; footings; punching shear; shear slenderless; size effect; fib Model Code 2010] Issue 3 Vicente, Miguel A.; González, Dorys C.; Mínguez, Jesús; Martínez, José A.: Residual modulus of elasticity and maximum compressive strain in HSC and FRHSC after highstresslevel cyclic loading [fatigue; highstrength concrete; fibrereinforced highstrength concrete; modulus of elasticity; maximum compressive strain] Issue 2 Wilhelm, Sebastian; Curbach, Manfred: Review of possible mineral materials and production techniques for a building material on the moon [mineral materials; lunar base design; building materials; lunar concrete; cast basalt; sulphur concrete; moon; lunar environment; lunar cement; DMSI] Issue 3 Won, Deok Hee; Park, Woo Sun; Jang, InSung; Han, SangHun; Han, Taek Hee: Fire resistance performance of steel composite hollow RC column with inner tube under ISO 834 standard fire [fire resistance; concrete; ISO 834; Eurocode] Issue 4 Won, Deok Hee; Park, Woo Sun; Yi, JinHak; Han, SangHun; Han, Taek Hee: Effect of welding heat on precast steel composite hollow columns [welding; heat; column; precast; concrete] Issue 3
248–257
331–339
Eurocode 210–218
419–428
543–555
350–360
Dynamic actions/earthquakes Korte, Sara; Boel, Veerle; De Corte, Wouter; De Schutter, Geert: Behaviour of fatigue loaded selfcompacting concrete compared to vibrated concrete [selfcompacting concrete; vibrated concrete; cyclic loading; fatigue; SN curve; crack growth] Issue 4 575–589 Magnusson, Johan; Hallgren, Mikael; Ansell, Anders: Shear in concrete structures subjected to dynamic loads [dynamic loads; impulsive loads; rise time; shear;
www.ernstundsohn.de
initial response; support reactions; arch action] Issue 1 55–65 Vicente, Miguel A.; González, Dorys C.; Mínguez, Jesús; Martínez, José A.: Residual modulus of elasticity and maximum compressive strain in HSC and FRHSC after highstresslevel cyclic loading [fatigue; highstrength concrete; fibrereinforced highstrength concrete; modulus of elasticity; maximum compressive strain] Issue 2 210–218 Yan, Dongming; Xu, Shilang; Chen, Genda; Li, Hedong: Biaxial behaviour of plain concrete subjected to dynamic compression with constant lateral stress [biaxial stress state; strain rate; dynamic strength; stressstrain curve; failure mode; concrete] Issue 2 202–209
Carpinteri, Alberto; Cadamuro, Erica; Corrado, Mauro: Minimum flexural reinforcement in rectangular and Tsection concrete beams [reinforced concrete; code provisions; minimum reinforcement; dimensional analysis; size effects; cohesive crack] Scott, Richard: Serviceability uncertainties in flat slabs [load tests; finite element analysis; codes of practice] Siburg, Carsten; Hegger, Josef: Experimental investigations on the punching behaviour of reinforced concrete footings with structural dimensions [Eurocode 2; footings; punching shear; shear slenderless; size effect; fib Model Code 2010] Siburg, Carsten; Ricker, Marcus; Hegger, Josef: Punching shear design of footings: critical review of different code provisions [punching; footing; fib Model Code 2010; Eurocode 2; tests] Souza, Osvaldo Luiz de Carvalho; Sánchez Filho, Emil de Souza; Vaz, Luiz Eloy; Silva Filho, Júlio Jerônimo Holtz: Reliability analysis of RC beams strengthened for torsion with carbon fibre composites [reliability index; torsion in RC beams; carbon fibre composites] Theiner, Yvonne; Andreatta, Andreas; Hofstetter, Günter: Evaluation of models for estimating concrete strains due to drying shrinkage [shrinkage; prediction models; experiments]
Issue 3 361–372
Issue 4 469–483
Issue 3 331–339
Issue 4 497–508
Issue 1 38–44
Issue 4 461–468
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Annual table of contents 2014
Völgyi, István; Windisch, Andor; Farkas, György: Resistance of reinforced concrete members with hollow circular crosssections under combined bending and shear – Part I: experimental investigation [combined bending and shear behaviour; parametric experimental study; hollow circular crosssection; failure section; sliding surface] Issue 1 13–20 Won, Deok Hee; Park, Woo Sun; Jang, InSung; Han, SangHun; Han, Taek Hee: Fire resistance performance of steel composite hollow RC column with inner tube under ISO 834 standard fire [fire resistance; concrete; ISO 834; Eurocode] Issue 4 543–555
Execution of construction works Clark, Gordon: Challenges for concrete in tall buildings [tall buildings; design; concrete floors; verticality]
Issue 4 448–453
fib Model Code 2010 Belletti, Beatrice; Damoni, Cecilia; Hendriks, Max A. N.; de Boer, Ane: Analytical and numerical evaluation of the design shear resistance of reinforced concrete slabs [reinforced concrete slabs; nonlinear finite element analysis; shear resistance evaluation; guidelines; safety formats; design] Cairns, John: Staggered lap joints for tension reinforcement [lapped joints; bond; detailing] Castel, Arnaud; Gilbert, Raymond Ian: Influence of timedependent effects on the crack spacing in reinforced concrete beams [reinforced concrete; crack spacing; shrinkage; sustained loading; stirrup spacing; fib Model Code 2010] Castel, Arnaud; Gilbert, Raymond Ian: Influence of timedependent effects on the crack spacing in reinforced concrete beams [reinforced concrete; crack spacing; shrinkage; sustained loading; stirrup spacing; fib Model Code 2010] Groli, Giancarlo; Pérez Caldentey, Alejandro; Soto, Alejandro Giraldo: Cracking performance of SCC reinforced with recycled fibres – an experimental study [FRC; recycled steel fibres; crack width control; φ/ρs,ef; cover; sustainability; fib Model Code 2010] 12
Structural Concrete 15
Issue 3 317–330 Issue 1 45–54
Issue 3 373–379
Meneghetti, Leila Cristina; Garcez, Mônica Regina; da Silva Filho, Luiz Carlos Pinto; Gastal, Francisco de Paula Simões Lopes; Bittencourt, Túlio Nogueira: Fatigue life of RC beams strengthened with FRP systems [fibrereinforced polymers; RC beams; aramid; carbon; fatigue] Issue 2 Randl, Norbert; Kunz, Jakob: Postinstalled reinforcement connections at ultimate and serviceability limit states [postinstalled reinforcement; anchorage; splitting; pullout; serviceability limit state] Issue 4 Siburg, Carsten; Ricker, Marcus; Hegger, Josef: Punching shear design of footings: critical review of different code provisions [punching; footing; fib Model Code 2010; Eurocode 2; tests] Issue 4 Strauss, Alfred; Zimmermann, Thomas; Lehký, David; Novák, Drahomír; Keršner, Zbyneˇk: Stochastic fracturemechanical parameters for the performancebased design of concrete structures [fracturemechanical parameters; reliability; inverse analysis; fracture energy; materials database] Issue 3 Theiner, Yvonne; Andreatta, Andreas; Hofstetter, Günter: Evaluation of models for estimating concrete strains due to drying shrinkage [shrinkage; prediction models; experiments] Issue 4 Urban, Susanne; Strauss, Alfred; Schütz, Robert; Bergmeister, Konrad; Dehlinger, Christian: Dynamically loaded concrete structures – monitoringbased assessment of the real degree of fatigue deterioration [concrete fatigue; monitoring; deterioration assessment] Issue 4 Völgyi, István; Windisch, Andor; Farkas, György: Resistance of reinforced concrete members with hollow circular crosssections under combined bending and shear – Part I: experimental investigation [combined bending and shear behaviour; parametric experimental study; hollow circular crosssection; failure section; sliding surface] Issue 1
219–228
563–574
497–508
380–394
461–468
530–542
13–20
Issue 3 373–379
Fire protection
Issue 2 136–153
Hertz, Kristian; Castberg, Andreas; Christensen, Jacob: Superlight concrete decks for building floor slabs [superlight structures; deck structures; precast concrete; lightweight concrete;
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Annual table of contents 2014
prestressed concrete; structural design; testing structural elements] Issue 4 Van Coile, Ruben; Caspeele, Robby; Taerwe, Luc: Towards a reliabilitybased postfire assessment method for concrete slabs incorporating information from inspection [fire; postfire assessment; residual strength; safety level; concrete slab] Issue 3 Won, Deok Hee; Park, Woo Sun; Jang, InSung; Han, SangHun; Han, Taek Hee: Fire resistance performance of steel composite hollow RC column with inner tube under ISO 834 standard fire [fire resistance; concrete; ISO 834; Eurocode] Issue 4 Won, Deok Hee; Park, Woo Sun; Yi, JinHak; Han, SangHun; Han, Taek Hee: Effect of welding heat on precast steel composite hollow columns [welding; heat; column; precast; concrete] Issue 3
522–529
395–407
543–555
350–360
General Clark, Gordon: Challenges for concrete in tall buildings [tall buildings; design; concrete floors; verticality] Dahl, Kaare K. B.: Bella Sky Hotel – taking precast concrete to the limit [precast concrete; structural behaviour; hotel; complex geometry; leaning building] Hertz, Kristian; Castberg, Andreas; Christensen, Jacob: Superlight concrete decks for building floor slabs [superlight structures; deck structures; precast concrete; lightweight concrete; prestressed concrete; structural design; testing structural elements] Krokstrand, Ole H.; Ramstad, Reiulf; Hölmebakk, CarlViggo: Splendid concrete architecture in National Tourist Routes in Norway [concrete architecture; scenic view; tourist routes; Norway] Mancini, Giuseppe; Tondolo, Francesco: Effect of bond degradation due to corrosion – a literature survey [bond degradation; corrosion rate; experimental procedure] Meneghetti, Leila Cristina; Garcez, Mônica Regina; da Silva Filho, Luiz Carlos Pinto; Gastal, Francisco de Paula Simões Lopes; Bittencourt, Túlio Nogueira: Fatigue life of RC beams strengthened with FRP systems
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Issue 4 448–453
Issue 4 441–447
Issue 4 522–529
Issue 2 117–125
Issue 3 408–418
[fibrereinforced polymers; RC beams; aramid; carbon; fatigue] Issue 2 219–228 Völgyi, István; Windisch, Andor: Resistance of reinforced concrete members with hollow circular crosssection under combined bending and shear – Part II: New calculation model [behaviour under combined bending and shear; hollow circular crosssection; contribution of compressed concrete to shear resistance; sliding surface] Issue 1 21–29 Wilhelm, Sebastian; Curbach, Manfred: Review of possible mineral materials and production techniques for a building material on the moon [mineral materials; lunar base design; building materials; lunar concrete; cast basalt; sulphur concrete; moon; lunar environment; lunar cement; DMSI] Issue 3 419–428
History of building Onysyk, Jerzy; Biliszczuk, Jan; Prabucki, Przemyslaw; Sadowski, Krzysztof; Toczkiewicz, Robert: Strengthening the 100yearold reinforced concrete dome of the Centennial Hall in Wrocław [pioneering concrete structure; renovation; FEM analysis; strengthening] Issue 1 30–37
Prestressed concrete Cervenka, Vladimir; Ganz, Hans Rudolf: Validation of posttensioning anchorage zones by laboratory testing and numerical simulation [anchorage; numerical analysis; testing] Issue 2 258–268 Gama, David; Almeida, João F.: Concrete integral abutment bridges with reinforced concrete piles [prestressed concrete bridges; integral abutment bridges; reinforced concrete piles; imposed deformations; soilstructure interaction; levels of approximation] Issue 3 292–304 Podroužek, Jan; Strauss, Alfred; Bergmeister, Konrad: Robustnessbased performance assessment of a prestressed concrete bridge [robustness; existing structure; reliability; performance indicators; safety; stochastic methods] Issue 2 248–257
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Reinforcement Abbas, Ali A.; Mohsin, Sharifah M. Syed; Cotsovos, Demetrios M.: Nonlinear analysis of statically indeterminate SFRC columns [fibrereinforced concrete; finite element methods; structural analysis] Issue 1 Abdellahi, Majid; Heidari, Javad; Bahmanpour, Maryam: A new predictive model for the bond strength of FRPtoconcrete composite joints [bond strength; model; GEP; FRP; composite] Issue 4 Cairns, John: Staggered lap joints for tension reinforcement [lapped joints; bond; detailing] Issue 1 Carpinteri, Alberto; Cadamuro, Erica; Corrado, Mauro: Minimum flexural reinforcement in rectangular and Tsection concrete beams [reinforced concrete; code provisions; minimum reinforcement; dimensional analysis; size effects; cohesive crack] Issue 3 Groli, Giancarlo; Pérez Caldentey, Alejandro; Soto, Alejandro Giraldo: Cracking performance of SCC reinforced with recycled fibres – an experimental study [FRC; recycled steel fibres; crack width control; φ/ρs,ef; cover; sustainability; fib Model Code 2010] Issue 2 Mancini, Giuseppe; Tondolo, Francesco: Effect of bond degradation due to corrosion – a literature survey [bond degradation; corrosion rate; experimental procedure] Issue 3 MessariBecker, Lamia; Mettke, Angelika; Knappe, Florian; Storck, Ulrich; Bollinger, Klaus; Grohmann, Manfred: Recycling concrete in practice – a chance for sustainable resource management [recycled concrete; grey energy; sustainable construction; building materials; resource management; life cycle assessment] Issue 4 Ozden, Sevket; Atalay, Hilal M.; Akpinar, Erkan; Erdogan, Hakan; Vulas¸, Yılmaz Zafer: Shear strengthening of reinforced concrete Tbeams with fully or partially bonded fibrereinforced polymer composites [reinforced concrete; beam shear strengthening; fibrereinforced polymer; anchorage; partially bonded FRP; modulus of elasticity; composite] Issue 2 Reinhardt, HansWolf: Aspects of imposed deformation in concrete structures – a condensed overview [imposed deformation;
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94–105
509–521 45–54
fresh concrete; shrinkage; young concrete; cracking] Issue 4 454–460 Völgyi, István; Windisch, Andor: Resistance of reinforced concrete members with hollow circular crosssection under combined bending and shear – Part II: New calculation model [behaviour under combined bending and shear; hollow circular crosssection; contribution of compressed concrete to shear resistance; sliding surface] Issue 1 21–29 Yuan, Yong; Chi, Yang: Water permeability of concrete under uniaxial tension [reinforced concrete; structural member; water permeability; tensioned element; permeating test] Issue 2 191–201
Standards, regulations, guidelines, directives
361–372
136–153
408–418
556–562
229–239
Aboutalebi, Morteza; Alani, Amir M.; Rizzuto, Joseph; Beckett, Derrick: Structural behaviour and deformation patterns in loaded plain concrete groundsupported slabs [groundsupported slab; displacement; crack propagation; bending; punching] Issue 1 Belletti, Beatrice; Damoni, Cecilia; Hendriks, Max A. N.; de Boer, Ane: Analytical and numerical evaluation of the design shear resistance of reinforced concrete slabs [reinforced concrete slabs; nonlinear finite element analysis; shear resistance evaluation; guidelines; safety formats; design] Issue 3 Carpinteri, Alberto; Cadamuro, Erica; Corrado, Mauro: Minimum flexural reinforcement in rectangular and Tsection concrete beams [reinforced concrete; code provisions; minimum reinforcement; dimensional analysis; size effects; cohesive crack] Issue 3 Nyhus, Bente Skovseth: Consistent practical design of concrete structures [concrete design; practical design; consistent stiffness method; nonlinear analysis; shear design; MCFT; safety; cost effective] Issue 3 Theiner, Yvonne; Andreatta, Andreas; Hofstetter, Günter: Evaluation of models for estimating concrete strains due to drying shrinkage [shrinkage; prediction models; experiments] Issue 4 Völgyi, István; Windisch, Andor; Farkas, György: Resistance of reinforced concrete members with hollow circular crosssections under combined bending and shear – Part I: experimen
81–93
317–330
361–372
305–316
461–468
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Annual table of contents 2014
tal investigation [combined bending and shear behaviour; parametric experimental study; hollow circular crosssection; failure section; sliding surface]
Issue 1 13–20
Testing/experiments Aboutalebi, Morteza; Alani, Amir M.; Rizzuto, Joseph; Beckett, Derrick: Structural behaviour and deformation patterns in loaded plain concrete groundsupported slabs [groundsupported slab; displacement; crack propagation; bending; punching] Issue 1 Alani, Amir M.; Aboutalebi, Morteza; Kilic, Gokhan: Use of noncontact sensors (IBISS) and finite element methods in the assessment of bridge deck structures [finite element modelling; bridge health monitoring; IBISS sensor; ANSYS] Issue 2 Breitenbücher, Rolf; Meschke, Günther; Song, Fanbing; Zhan, Yijian: Experimental, analytical and numerical analysis of the pullout behaviour of steel fibres considering different fibre types, inclinations and concrete strengths [steel fibre; pullout behaviour; laboratory test; analytical modelling; numerical simulation] Issue 2 Cairns, John: Staggered lap joints for tension reinforcement [lapped joints; bond; detailing] Issue 1 Cervenka, Vladimir; Ganz, Hans Rudolf: Validation of posttensioning anchorage zones by laboratory testing and numerical simulation [anchorage; numerical analysis; testing] Issue 2 Fan, Yuhui; Xiao, Jianzhuang; Tam, Vivian W. Y.: Effect of old attached mortar on the creep of recycled aggregate concrete [recycled aggregate concrete; old adhering mortar; shrinkage; creep; influence mechanism] Issue 2 Groli, Giancarlo; Pérez Caldentey, Alejandro; Soto, Alejandro Giraldo: Cracking performance of SCC reinforced with recycled fibres – an experimental study [FRC; recycled steel fibres; crack width control; φ/ρs,ef; cover; sustainability; fib Model Code 2010] Issue 2 Hertz, Kristian; Castberg, Andreas; Christensen, Jacob: Superlight concrete decks for building floor slabs [superlight structures; deck structures; precast concrete; lightweight concrete; prestressed concrete; structural
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81–93
240–247
126–135 45–54
258–268
169–178
136–153
design; testing structural elements] Issue 4 Kollegger, Johann; Foremniak, Sara; Suza, Dominik; Wimmer, David; Gmainer, Susanne: Building bridges using the balanced lift method [precast concrete elements; posttensioning; bridge construction method; largescale test] Issue 3 Korte, Sara; Boel, Veerle; De Corte, Wouter; De Schutter, Geert: Behaviour of fatigue loaded selfcompacting concrete compared to vibrated concrete [selfcompacting concrete; vibrated concrete; cyclic loading; fatigue; SN curve; crack growth] Issue 4 Magnusson, Johan; Hallgren, Mikael; Ansell, Anders: Shear in concrete structures subjected to dynamic loads [dynamic loads; impulsive loads; rise time; shear; initial response; support reactions; arch action] Issue 1 Meneghetti, Leila Cristina; Garcez, Mônica Regina; da Silva Filho, Luiz Carlos Pinto; Gastal, Francisco de Paula Simões Lopes; Bittencourt, Túlio Nogueira: Fatigue life of RC beams strengthened with FRP systems [fibrereinforced polymers; RC beams; aramid; carbon; fatigue] Issue 2 Ozden, Sevket; Atalay, Hilal M.; Akpinar, Erkan; Erdogan, Hakan; Vulas¸, Yılmaz Zafer: Shear strengthening of reinforced concrete Tbeams with fully or partially bonded fibrereinforced polymer composites [reinforced concrete; beam shear strengthening; fibrereinforced polymer; anchorage; partially bonded FRP; modulus of elasticity; composite] Issue 2 Prince, M. John Robert; Singh, Bhupinder: Investigation of bond behaviour between recycled aggregate concrete and deformed steel bars [coarse recycled concrete aggregate; replacement percentage; natural coarse aggregate; bond; pullout failure; splitting failure; normalized bond strength] Issue 2 Scott, Richard: Serviceability uncertainties in flat slabs [load tests; finite element analysis; codes of practice] Issue 4 Siburg, Carsten; Hegger, Josef: Experimental investigations on the punching behaviour of reinforced concrete footings with structural dimensions [Eurocode 2; footings; punching shear; shear slenderless; size effect; fib Model Code 2010] Issue 3
522–529
281–291
575–589
55–65
219–228
229–239
154–168
469–483
331–339
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Siburg, Carsten; Ricker, Marcus; Hegger, Josef: Punching shear design of footings: critical review of different code provisions [punching; footing; fib Model Code 2010; Eurocode 2; tests] Issue 4 Strauss, Alfred; Zimmermann, Thomas; Lehký, David; Novák, Drahomír; Keršner, Zbyneˇk: Stochastic fracturemechanical parameters for the performancebased design of concrete structures [fracturemechanical parameters; reliability; inverse analysis; fracture energy; materials database] Issue 3 Theiner, Yvonne; Andreatta, Andreas; Hofstetter, Günter: Evaluation of models for estimating concrete strains due to drying shrinkage [shrinkage; prediction models; experiments] Issue 4 Urban, Susanne; Strauss, Alfred; Schütz, Robert; Bergmeister, Konrad; Dehlinger, Christian: Dynamically loaded concrete structures – monitoringbased assessment of the real degree of fatigue deterioration [concrete fatigue; monitoring; deterioration assessment] Issue 4 Vicente, Miguel A.; González, Dorys C.; Mínguez, Jesús; Martínez, José A.: Residual modulus of elasticity and maximum compressive strain in HSC and FRHSC after highstresslevel cyclic loading [fatigue; highstrength concrete; fibrereinforced highstrength concrete; modulus of elasticity; maximum compressive strain] Issue 2 Völgyi, István; Windisch, Andor; Farkas, György: Resistance of reinforced concrete members with hollow circular crosssections under combined bending and shear – Part I: experimental investigation [combined bending and shear behaviour; parametric experimental study; hollow circular crosssection; failure section; sliding surface] Issue 1
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497–508
380–394
461–468
530–542
Winkler, Karsten; Mark, Peter; Heek, Peter; Rohländer, Sandra; Sommer, Simone: Punching shear tests on symmetrically reduced slab quarters [punching shear; innovative test setup; axis symmetry; experiments; quartered slab] Issue 4 Xiao, Jianzhuang; Li, Long; Tam, Vivian W.Y.; Li, Hong: The state of the art regarding the longterm properties of recycled aggregate concrete [recycled aggregate concrete; longterm properties; shrinkage and creep; carbonation resistance; impermeability; fatigue behaviour] Issue 1 Yan, Dongming; Xu, Shilang; Chen, Genda; Li, Hedong: Biaxial behaviour of plain concrete subjected to dynamic compression with constant lateral stress [biaxial stress state; strain rate; dynamic strength; stressstrain curve; failure mode; concrete] Issue 2 Yuan, Yong; Chi, Yang: Water permeability of concrete under uniaxial tension [reinforced concrete; structural member; water permeability; tensioned element; permeating test] Issue 2
484–496
3–12
202–209
191–201
Tunnelling
210–218
Liu, Xian; Jiang, Wei; De Schutter, Geert; Yuan, Yong; Su, Quanke: Earlyage behaviour of precast concrete immersed tunnel based on degree of hydration concept [precast immersed tunnel; earlyage cracking; degree of hydration; creep under varying stress levels] Issue 1 66–80 Liu, Xian; Yuan, Yong; Su, Quanke: Sensitivity analysis of the earlyage cracking risk in an immersed tunnel [immersed tunnel; earlyage cracking; sensitivity analysis; curing scheme] Issue 2 179–190
13–20
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Structural Concrete, the official journal of the fib, provides conceptual and procedural guidance in the field of concrete construction, and...