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Practitioners’ guide to
finite element modelling
of reinforced concrete
structures
State-of-art report prepared by
Task Group 4.4
June 2008
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Subject to priorities defined by the Technical Council and the Presidium, the results of fib’s work in
Commissions and Task Groups are published in a continuously numbered series of technical publications
called 'Bulletins'. The following categories are used:
category minimum approval procedure required prior to publication
Technical Report approved by a Task Group and the Chairpersons of the Commission
State-of-Art Report approved by a Commission
Manual, Guide (to good practice)
or Recommendation
approved by the Technical Council of fib
Model Code approved by the General Assembly of fib
Any publication not having met the above requirements will be clearly identified as preliminary draft.
This Bulletin N° 45 was approved as an fib State-of-art report by Commission 4 in April 2004.
This report was drafted by Task Group 4.4, Computer based modelling and design, in Commission 4, Modelling
of structural behaviour and design:
Koichi Maekawa 10, 1, 3, 5, 6 (Univ. of Tokyo, Japan, Co-Convener), Frank Vecchio 1, 3, 5, 6 , 10 (Univ. of
Toronto, Canada, Co-convener)
Stephen Foster2, 6, 3, 4, 5, 8
(Univ. of New South Wales, Australia, Editor)
Oguzhan Bayrak 4, 6 (Univ. of Texas at Austin, USA), Evan Bentz 3, 4 (University of Toronto, Canada),
Johan Blaauwendraad 9 (Delft Univ. of Technology, The Netherlands), Jan Cervenka 5 (Cervenka
Consulting, Czech Republic), Vladimir Cervenka5, 6 , 10
(Cervenka Consulting, Czech Republic), Tetsuya
Ishida 6 (Univ. of Tokyo, Japan), Milan Jirasek 6 (Czech Technical Univ. in Prague, Czech Republic),
Walter Kaufmann 2 (dsp Ingenieure & Planer AG, Switzerland), Johann Kollegger 5 (Technische Univ.
Wien, Austria), Daniel Kuchma 7, 8 (Univ. of Illinois, USA), Ho Jung Lee 7 (SC Solutions, Inc., USA),
Giuseppe Mancini 3 (Politecnico Torino, Italy), Giorgio Monti (Sapienza Università di Roma, Italy) 4, 6 ,
Josko O! bolt5, 6
(Univ. Stuttgart, Germany), Clemens Preisinger5 (Technische Univ. Wien, Austria),
Enrico Spacone 4 (Univ. of Chieti-Pescara, Italy), Tjen Tjhin 8 (Buckland and Taylor Ltd. Bridge
Engineering, USA)
1, 2, 3 ... Chapter number for which this member was the main preparing author
1, 2, 3 ... Chapter number for which this member provided contributions
Full address details of Task Group members may be found in the fib Directory or through the online services on
fib's website, www.fib-international.org.
Cover image: FE modelling of high strength squat shear walls (image courtesy of S. Foster)
© fédération internationale du béton ( fib), 2008
Although the International Federation for Structural Concrete fib - féderation internationale du béton - does its best to ensure that any information given is accurate, no liability or responsibility of any kind (including liabilityfor negligence) is accepted in this respect by the organisation, its members, servants or agents.
All rights reserved. No part of this publication may be reproduced, modified, translated, stored in a retrievalsystem, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, orotherwise, without prior written permission.
First published in 2008 by the International Federation for Structural Concrete ( fib) Postal address: Case Postale 88, CH-1015 Lausanne, SwitzerlandStreet address: Federal Institute of Technology Lausanne - EPFL, Section Génie CivilTel +41 21 693 2747 • Fax +41 21 693 [email protected] • www.fib-international.org
ISSN 1562-3610
ISBN 978-2-88394-085-7
Printed by Sprint-Digital-Druck, Stuttgart
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fib Bulletin 45: Practitioners’ guide to finite element modelling of reinforced concrete structures iii
Preface
In September 2000, fib Commission 4 established a task group (TG4.4) with the objective of
preparing a report for guiding design engineers in the safe use of computer-based analysis
procedures for design of reinforced concrete structures. The working party that first met in
Berlin 2001 brought together a group of highly regarded researchers from Europe, the
Americas, East Asia and Australasia with the objective of producing a document for use byengineers with some background in numerical modelling. In the six years since work startedon this report, advanced models have continued to be developed; however, this report is not
about picking one model over another but, rather, how designers can use existing and future
models as tools in design practice, in benchmarking of their models against established and
reliable test data and in selecting an appropriate safety factor as well as recognising various
pitfalls.
Non-linear computer analysis methods have seen remarkable advancement in the last half-
century with much research activity in the manner of constitutive modelling of reinforced
concrete behaviour and in the development of sophisticated analysis algorithms. These
advancements are well documented in various state-of-the-art reports and remain the subjectof intensive research today. Linear and non-linear analysis methods, combined with plasticity
design processes, and with local detailing methods such as strut-and-tie modelling, can form
the basis of design of new, complex, structures that are not easily dimensioned using other
rational design methods.
The state-of-the-art in non-linear finite element analysis of reinforced concrete has progressed
to the point where such procedures are close to being practical, every-day tools for design
office engineers. No longer solely within the domain of researchers, they are finding use in
various applications; many relating to our aging infrastructure. Non-linear computer analysis
procedures can be used to provide reliable assessments of the strength and integrity of
damaged or deteriorated structures, or of structures built to previous codes, standards or practices deemed to be deficient today. They can serve as valuable tools in assessing theexpected behaviour from retrofitted structures, or in investigating and rationally selecting
amongst various repair alternatives. Non-linear finite element analysis procedures are also
proving particularly valuable in forensic analyses. In the near future, they will likely form the
main engine in computer-based automated design software, although in a form likely invisible
to the user.
This report provides an overview of concepts and techniques relating to computer-based
modelling of structural concrete. It attempts to provide a diverse and balanced portrayal of the
current technical knowledge, recognizing that there are often competing and conflicting
viewpoints. The report is written primarily for the benefit of the practicing engineer, rather
than as a state-of-the-art for researchers, concentrating more on practical application and lesson subtleties in constitutive modelling. To the members of the working party, our sincere
thanks for the extensive and voluntary work undertaken over an extended period to get this
report competed.
Stephen Foster, Editor, chair of fib Commission 4
Koichi Maekawa, co-convener of TG 4.4
Frank Vecchio, deputy chair of fib Commission 4 and co-covener of TG 4.4
14 November 2007
.
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iv fib Bulletin 45: Practitioners’ guide to finite element modelling of reinforced concrete structures
Contents
1 Introduction 1
1.1 Preamble 1
1.2 Notation 2
1.3 Sample applications 2
(1.3.1 Kimberley!
Clark warehouse – 1.3.2 Sleipner A offshore platform –1.3.3 Frame corner – 1.3.4 Base slabs in LNG storage tank)
1.4 The question of accuracy (1.4.1 – Reasons for caution) 20
1.5 Challenges remaining 27
1.6 Objectives 29
1.7 Scope of report 30
1.8 References 30
2 Design using linear stress analysis 33
2.1 Introduction 33
2.2 Membrane structures 34(2.2.1 Notation – 2.2.2 General – 2.2.3 Reinforcement in one direction –2.2.4 Isotropically reinforced panels – 2.2.5 The general solution –2.2.6 Some comments on the angle ! – 2.2.7 The design concretecompression strength, f cd. – 2.2.8 Example – Design of a reinforced concretesquat shear wall)
2.3 Slabs and shells 52(2.3.1 General – 2.3.2 Stress resultants – 2.3.3 Equilibrium, stresstransformation and boundary conditions for slabs – 2.3.4 Normal momentyield criterion for slabs – 2.3.5 Sandwich model for the dimensioning of shellelements – 2.3.6 Dimensioning of slab and shell elements in design practice –2.3.7 Example 1 – 2.3.8 Example 2)
2.4 3D solid modelling 70
(2.4.1 Introduction – 2.4.2 Background – 2.4.3 Application to reinforcedconcrete – 2.4.4 Reinforcement dimensioning for 3D stresses ! example 1 –2.4.5 Reinforcement dimensioning for 3D stresses ! example 2)
2.5 References 78
3 Essential nonlinear modelling concepts 83
3.1 Introduction 83
3.2 Nonlinear concrete behaviour 84(3.2.1 Concrete in compression – 3.2.2 Concrete in tension –3.2.3 Modelling of tension stiffening – 3.2.4 Modelling of concrete cracks –3.2.5 Modelling of reinforcement)
3.3 Nonlinear concrete modelling framework 98
(3.3.1 Elasticity – 3.3.2 Plasticity – 3.3.3 Damage – 3.3.4 Mixed models –3.3.5 Discrete modelling frameworks)
3.4 Solution methods 102(3.4.1 Newton!Raphson method – 3.4.2 Modified Newton!Raphsonmethod)
3.5 Precision of nonlinear concrete FE analyses 104
3.6 Safety and reliability 105
3.7 Statistical analyses 114
3.8 Concluding remarks 115
3.9 References 115
4 Analysis and design of frame structures using non linear models 121
4.1 Introduction 121
4.2 Notation 122
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fib Bulletin 45: Practitioners’ guide to finite element modelling of reinforced concrete structures v
4.3 Nonlinear models of frame elements 123(4.3.1 Lumped versus distributed plasticity – 4.3.2 Distributed models –4.3.3 Section models: fibre elements vs. strut!and!tie – 4.3.4 Modelling ofshear – 4.3.5 Modelling Bond Slip in Beams – 4.3.6 Analysis of a section)
4.4 Interpretation of results 148(4.4.1 Localisation problems – 4.4.2 Physical characteristics of localisedfailure in concrete – 4.4.3 Regularisation techniques for force! based frameelements – 4.4.4 Practical considerations)
4.5 References 160
5 Analysis and design of surface and solid structures using non linear models 165
5.1 Introduction 165
5.2 Notation 165
5.3 2D Structures with in! plane loading 166
5.4 Plate and shell structures (5.4.1 Layered elements) 170
5.5 Three dimensional solid structures 173(5.5.1 Introduction – 5.5.2 Models based on non!linear elasticity –5.5.3 Fracture! plasticity modelling – 5.5.4 Microplane model –
5.5.5 Examples of the application of 3D FE modeling)
5.6 References 190
6 Advanced modelling and analysis concepts 195
6.1 Introduction 195
6.2 Constitutive frameworks 195(6.2.1 Non!linear elasticity – 6.2.2 Plasticity – 6.2.3 Continuum damagemechanics – 6.2.4 Smeared crack models – 6.2.5 Microplane models)
6.3 Solution strategies 214(6.3.1 Introduction – 6.3.2 Newton!Raphson method – 6.3.3 Modified
Newton!Raphson method – 6.3.4 Incremental displacement method –6.3.5 The constant arc length method – 6.3.6 Line searches –6.3.7 Convergence criteria – 6.3.8 Load
!displacement incrementation)
6.4 Other issues 223(6.4.1 Post peak response of compression elements – 6.4.2 Effects of ageingand distress in concrete – 6.4.3 Effects of ageing and distress in reinforcingsteel – 6.4.4 Second order effects)
6.5 References 227
7 Benchmark tests and validation procedures 233
7.1 Introduction 233
7.2 Calibration and validation of NLFEA models 234(7.2.1 Overview of model calibration and validation process – 7.2.2 Level 1:model calibration with material properties – 7.2.3 Level 2: validation andcalibration with systematically arranged element–level benchmark tests –7.2.4 Level 3: validation and calibration at structural level)
7.3 Selection of global safety factor 239
7.4 Other issues in the use and validation of NLFEA programs 241(7.4.1 Problem definition and model selection – 7.4.2 Working within thedomain of the program’s capability)
7.5 Case 1: Design of a shear wall with openings 244(7.5.1 Objective – 7.5.2 Level 1 calibration – 7.5.3 Level 2 and 3validation – 7.5.4 Evaluation of global safety)
7.6 Case study II: design of simply supported deep beam 250
(7.6.1 Objective – 7.6.2 Calibration and validation of NLFEAP!
1 –7.6.3 Calibration and validation of NLFEAP!2 – 7.6.4 Analysis of deep beam)
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vi fib Bulletin 45: Practitioners’ guide to finite element modelling of reinforced concrete structures
7.7 Summary and future trends in model validation 260
7.8 Future trends in model validation 261
7.9 References 263
8 Strut and tie modelling 265
8.1 Introduction 265
8.2 Notation 266
8.3 Overview of the STM 267(8.3.1 Strut!and!tie models – 8.3.2 Components of strut!and!tie models –8.3.3 Admissible strut!and!tie models)
8.4 STM design steps (8.4.1 Complications in STM design) 270
8.5 Some considerations in using the STM 271(8.5.1 Rules in defining D!regions – 8.5.2 Two! and three!dimensionalD!regions – 8.5.3 Capacity of struts – 8.5.4 Uniqueness of strut!and!tiemodels – 8.5.5 Strain incompatibility of struts and ties – 8.5.6 Tensionstiffening in ties – 8.5.7 Influence of tie anchorages – 8.5.8 Size, geometry,and strength of nodal zones – 8.5.9 Load redistribution and ductilityrequirements)
8.6 Computer ! based STM 279
8.7 Modelling aspects using computer ! based STM 280(8.7.1 Identifying strut!and!tie models – 8.7.2 Refining strut!and!tiemodels – 8.7.3 Other considerations – 8.7.4 Static indeterminacy ofstrut!and!tie models – 8.7.5 Procedures to solve statically indeterminatestrut!and!tie models – 8.7.6 Dimensioning nodal regions)
8.8 Design example using computer ! based tools 298
(8.8.1 Problem statement – 8.8.2 Solution)
8.9 References 303
9 Special purpose design methods for surface structures 307
9.1 Introduction 3079.2 Notation 307
9.3 Design of slabs and shear walls: perfect plastic approach 309(9.3.1 Slabs subjected to bending loads – 9.3.2 Ultimate load determination –9.3.3 Failure mode determination – 9.3.4 Material optimization –9.3.5 Plates subjected to in! plane loads)
9.4 Design of slabs using the reinforcement field approach 318(9.4.1 Linear yield conditions for element nodal forces – 9.4.2 Materialoptimisation through stress redistribution – 9.4.3 Slab subjected to bendingloads – 9.4.4 Dimensioning procedure)
9.5 Design of shear !walls: the stringer ! panel approach 321
(9.5.1 Linear !
elastic version – 9.5.2 Non!
linear version –9.5.3 A three!step design procedure – 9.5.4 Example)
9.6 References 329
10 Concluding remarks 331
10.1 Introduction 331
10.2 Structural performance based design in practice 331
10.3 Benefits of non!linear modelling and analyses 333
10.4 Code provisions 335
10.5 Specification of design loads 335
10.6 Maintenance 336
10.7 References 337
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18 1 Introduction
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fib Bulletins published since 1998
N° Title
1 Structural Concrete – Textbook on Behaviour, Design and Performance;
Vol. 1: Introduction - Design Process – MaterialsManual - textbook (244 pages, ISBN 978-2-88394-041-3, July 1999)
2 Structural Concrete – Textbook on Behaviour, Design and Performance
Vol. 2: Basis of DesignManual - textbook (324 pages, ISBN 978-2-88394-042-0, July 1999)
3 Structural Concrete – Textbook on Behaviour, Design and Performance
Vol. 3: Durability - Design for Fire Resistance - Member Design - Maintenance, Assessment
and Repair - Practical aspectsManual - textbook (292 pages, ISBN 978-2-88394-043-7, December 1999)
4 Lightweight aggregate concrete: Extracts from codes and standards
State-of-the-art report (46 pages, ISBN 978-2-88394-044-4, August 1999)
5 Protective systems against hazards: Nature and extent of the problem
Technical report (64 pages, ISBN 978-2-88394-045-1, October 1999)
6 Special design considerations for precast prestressed hollow core floorsGuide to good practice (180 pages, ISBN 978-2-88394-046-8, January 2000)
7 Corrugated plastic ducts for internal bonded post-tensioning
Technical report (50 pages, ISBN 978-2-88394-047-5, January 2000)
8 Lightweight aggregate concrete: Part 1 (guide) – Recommended extensions to Model Code 90;
Part 2 (technical report) – Identification of research needs; Part 3 (state-of-art report) – Application of
lightweight aggregate concrete (118 pages, ISBN 978-2-88394-048-2, May 2000)
9 Guidance for good bridge design: Part 1 – Introduction, Part 2 – Design and construction
aspects. Guide to good practice (190 pages, ISBN 978-2-88394-049-9, July 2000)
10 Bond of reinforcement in concrete
State-of-art report (434 pages, ISBN 978-2-88394-050-5, August 2000)
11 Factory applied corrosion protection of prestressing steel
State-of-art report (20 pages, ISBN 978-2-88394-051-2, January 2001)
12 Punching of structural concrete slabs
Technical report (314 pages, ISBN 978-2-88394-052-9, August 2001)
13 Nuclear containments State-of-art report (130 pages, 1 CD, ISBN 978-2-88394-053-6, September 2001)
14 Externally bonded FRP reinforcement for RC structures
Technical report (138 pages, ISBN 978-2-88394-054-3, October 2001)
15 Durability of post-tensioning tendons
Technical report (284 pages, ISBN 978-2-88394-055-0, November 2001)
16 Design Examples for the 1996 FIP recommendations Practical design of structural concreteTechnical report (198 pages, ISBN 978-2-88394-056-7, January 2002)
17 Management, maintenance and strengthening of concrete structures
Technical report (180 pages, ISBN 978-2-88394-057-4, April 2002)
18 Recycling of offshore concrete structures
State-of-art report (33 pages, ISBN 978-2-88394-058-1, April 2002)
19 Precast concrete in mixed construction
State-of-art report (68 pages, ISBN 978-2-88394-059-8, April 2002)
20 Grouting of tendons in prestressed concrete
Guide to good practice (52 pages, ISBN 978-2-88394-060-4, July 2002)
21 Environmental issues in prefabricationState-of-art report (56 pages, ISBN 978-2-88394-061-1, March 2003)