Table Of ContentNonlinear Mechanics of
Reinforced Concrete
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Nonlinear Mechanics of
Reinforced Concrete
K. Maekawa, A. Pimanmas and
H. Okamura
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Firstpublished2003
bySponPress
11NewFetterLane,LondonEC4P4EE
SimultaneouslypublishedintheUSAandCanada
bySponPress
29West35thStreet,NewYork,NY10001
This edition published in the Taylor & Francis e-Library, 2004.
Spon Press is an imprint of the Taylor & Francis Group
©2003K.Maekawa,A.PimanmasandH.Okamura
Allrightsreserved.Nopartofthisbookmaybereprintedorreproducedor
utilisedinanyformorbyanyelectronic,mechanical,orothermeans,now
knownorhereafterinvented,includingphotocopyingandrecording,orin
anyinformationstorageorretrievalsystem,withoutpermissioninwriting
fromthepublishers.
BritishLibraryCataloguinginPublicationData
AcataloguerecordforthisbookisavailablefromtheBritishLibrary
LibraryofCongressCataloginginPublicationData
Maekawa,Koichi,1938–
Nonlinearmechanicsofreinforcedconcrete/K.Maekawa,A.Pimanmas,
andH.Okamura.
p.cm.
Includesbibliographicalreferencesandindex.
1.Reinforcedconcreteconstruction.2.Reinforcedconcrete–Mathematicalmodels.
3.Nonlinearmechanics.I.Pimanmas,A.(Amorn)II.Okamura,Hajime,1938–III.Title.
TA683.2.M3452003
(cid:1)
624.1 8341–dc21 2002030206
ISBN 0-203-30288-5 Master e-book ISBN
ISBN 0-203-34659-9 (Adobe eReader Format)
ISBN0–415–27126–6(alk.paper)
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Contents
List of figures xvii
List of tables xxxvii
Preface xxxix
Acknowledgments xliii
PART 1
Analysis and modeling of reinforced concrete 1
1 Introduction 3
1.1 Behavioral simulation of structures 3
1.1.1 Constitutive modeling: how to represent the
nonlinear mechanics of reinforced concrete? 3
1.1.2 Nonlinear structural analysis: how to use
nonlinear mechanics? 4
1.1.3 Verification of nonlinear modeling: applicability
and reliability? 6
1.2 Engineering applications 6
1.2.1 Performance-based design 6
1.2.2 Limit state criteria 9
1.2.3 Performance assessment of existing structures 11
1.3 Organization of the book 12
References 12
2 Two-dimensional analysis of reinforced concrete 13
2.1 The concept of smeared cracks: a space-averaged
constitutive model 13
2.2 Direction of cracking 15
2.3 Implicit formulation: preliminary discussion 17
2.4 Explicit formulation: the active crack approach 18
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vi Contents
2.5 The orthogonal two-way fixed crack model 20
2.5.1 The concrete model before cracking 21
2.5.2 The cracked concrete model 24
2.6 The quasi-orthogonal two-way fixed crack approach 44
2.7 Verification of the two-way fixed crack model 45
2.7.1 Shear panels subjected to monotonic loads 46
2.7.2 Shear panels subjected to reversed cyclic
loading 49
2.7.3 The SE-series panel tested by Stevens et al. 53
2.8 Four-way fixed crack model 54
2.8.1 Basic concept 54
2.8.2 Strategic framework 55
2.9 Verification of the four-way fixed crack model 61
2.9.1 The average shear stress–average shear strain
relation 67
2.9.2 The average shear stress–normal strain
relation 68
2.9.3 Crack angles 68
2.10 Two-dimensional structural analysis 68
2.10.1 Shear walls 69
2.10.2 Shear failure of RC members 74
2.10.3 A five-storied shear wall subjected to dynamic
loading 92
2.10.4 Analysis of scaled-down test structures 94
2.11 Shear failure of a high-strength concrete beam 101
2.11.1 Analytical method and constitutive models 102
2.11.2 Experimental verification 103
2.12 A shear wall subject to horizontal two-directional
loading 112
2.13 An underground box culvert 115
References 121
3 Three-dimensional analysis of reinforced concrete 125
3.1 General concept 125
3.2 An elasto-plastic and continuum-fracture model for
uncracked concrete 126
3.2.1 The modeling concept 126
3.2.2 The elasto-plastic fracture model 126
3.2.3 A three-dimensional multi-directional smeared
crack model 132
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Contents vii
3.3 A three-dimensional zoning concept and anisotropic
post-cracking response 134
3.3.1 Anisotropic tension stiffening/softening
behavior 136
3.3.2 Anisotropic shear fracture 140
3.3.3 Anisotropic average yield strength 141
3.4 Nonlinear structural analysis 144
3.4.1 An RC column subjected to unilateral
loading 144
3.4.2 Torsion of plain and RC members 147
3.4.3 Multi-directional shear failure of a short RC
column 156
3.4.4 Combined torsion and shear 162
3.4.5 RC columns under cyclic combined axial force,
torsion and bending/shear 164
References 173
4 Nonlinear soil–structure interaction 176
4.1 The complete soil–structure system of nonlinearity 176
4.2 Modeling of soil and soil–RC interface 177
4.2.1 Modeling of soil and foundation 177
4.2.2 Soil–structure interface 183
4.2.3 Verification of the RC–soil system: a box culvert
tested by the JSCE committee 185
4.3 Nonlinear static response of underground RC structures
188
4.3.1 Macro indicators 188
4.3.2 Limit state criterion 190
4.3.3 Shear response of the RC box culvert tested by
the JSCE committee 191
4.3.4 Parametric study 192
4.4 A nonlinear dynamic analysis of the RC–soil system 195
4.4.1 Analysis method 195
4.4.2 Nonlinear dynamic response of an underground
RC vertical duct 197
4.4.3 Nonlinear dynamic analysis of an underground
multi-vent box culvert 200
4.5 The failure/collapse mechanism of damaged underground
structures 209
4.5.1 Failure of underground RC culverts in an
earthquake 209
viii Contents
4.5.2 Case study 1: Daikai station 210
4.5.3 Case study 2: Kamisawa station 215
References 223
5 Three-dimensional analysis of shells and frames 225
Part 1: Shell elements 225
5.1 Introduction 225
5.2 Degenerated shell elements and layered formulations 226
5.3 Geometrical nonlinearity 231
5.4 Integration scheme 232
5.5 Crack patterns in a shell element subjected to
out-of-plane transverse loads 233
5.6 Verification of shell element 234
5.6.1 Shell elements under combined out-of-plane
flexure and in-plane forces 234
5.6.2 A shell element subjected to combined transverse
shear and in-plane forces 235
5.6.3 Slabs under cyclic transverse loading 239
5.6.4 A box culvert under cyclic loading 243
5.6.5 An RC cylindrical tank subject to reversed cyclic
loading 244
Part 2: Frame elements 248
5.7 Fiber formulation 248
5.7.1 Degeneration of fields 248
5.7.2 Normal stress, stiffness and fiber assembly 252
5.7.3 Shear stress and the stiffness model 256
5.7.4 Geometrical nonlinearity in a frame element 258
5.7.5 Constitutive modeling and RC zoning 259
5.8 Verification of frame elements 260
5.8.1 Interaction diagram of a column 260
5.8.2 Cyclic loading of a steel tube 260
5.8.3 Cyclic loading of an RC square box-section 261
5.8.4 Three-dimensional cyclic loading of a
concrete-filled tube sub-assemblage 263
5.8.5 Multi-directional flexure subject to eccentric
axial forces 264
5.8.6 Three-dimensional dynamic analysis of a
multi-story frame 275
5.9 Buckling and spalling models 276
5.9.1 The compression envelope of reinforcement and
cyclic loops 276
5.9.2 Cover concrete spalling 279
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Contents ix
5.9.3 Mesh size consistency 280
5.9.4 Giuffre–Menegotto–Pinto model for cyclic loops
281
5.10 Frame members under large lateral deformation 283
5.10.1 An RC column subjected to reversed cyclic
load 283
5.10.2 A high-strength composite RC column subjected
to reversed cyclic load 286
5.10.3 Dynamic analysis of an RC pier 288
5.11 Post-peak cyclic response analysis 288
5.11.1 Experimental set-up and specimen details 289
5.11.2 Numerical simulation of the experiments 291
5.12 Geometrical nonlinearity in the collapse of RC piers 294
References 296
6 Analysis of strengthened and retrofitted structures 300
6.1 Background 300
6.2 A structural steel model 300
6.2.1 Elasto-perfectly plastic plane stress routine 301
6.2.2 Parallel elasto-plastic model 304
6.2.3 Verification of constitutive modeling 306
6.3 A carbon fiber sheet model 308
6.4 A steel–concrete interface model 309
6.4.1 Requirement of modeling 309
6.4.2 A softening plasticity interface model 309
6.4.3 Numerical integration 314
6.4.4 Verification: uniform stress field 315
6.5 Concentric and eccentric compression of strengthened
columns 319
6.5.1 The effect of steel–concrete shear transfer
mechanisms 319
6.5.2 Carbon fiber sheet as confining agents 323
6.5.3 Carbon fiber sheets versus steel jackets 327
6.5.4 Eccentric compression 330
6.6 RC columns strengthened by steel encasement 331
6.6.1 Practical needs 331
6.6.2 Consideration of discontinuities in analysis 332
6.6.3 Overall response 334
6.7 RC columns strengthened by carbon fiber sheet
wrapping 335
6.7.1 Strengthening of RC columns failing in
flexure 335
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