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Page 1: FIB Guide to Finite Element

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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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34 2 Design using linear stress analysis

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60 2 Design using linear stress analysis

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ib Bulletin 45: Practitioners’ guide to finite element modelling of reinforced concrete structures   61

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68 2 Design using linear stress analysis

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106 3 Essential nonlinear modelling concepts

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118 3 Essential nonlinear modelling concepts

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176 5 Analysis and desing of surface and solid structures using non-linear models

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ib Bulletin 45: Practitioners’ guide to finite element modelling of reinforced concrete structures   177

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178 5 Analysis and desing of surface and solid structures using non-linear models

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ib Bulletin 45: Practitioners’ guide to finite element modelling of reinforced concrete structures   179

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ib Bulletin 45: Practitioners’ guide to finite element modelling of reinforced concrete structures   181

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ib Bulletin 45: Practitioners’ guide to finite element modelling of reinforced concrete structures   183

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184 5 Analysis and desing of surface and solid structures using non-linear models

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ib Bulletin 45: Practitioners’ guide to finite element modelling of reinforced concrete structures   187

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264 7 Benchmark tests and validation procedures

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266 8 Strut-and-tie modelling 

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268 8 Strut-and-tie modelling 

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 fib Bulletins published since 1998

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