Friday, March 30, 2018
Concrete Buildings in Seismic Regions
Concrete Buildings in Seismic Regions
Concrete Buildings in Seismic Regions
Contents
1 Introduction
1.1 Historical notes 1
1.2 Structure of this book 4
2 An overview of structural dynamics
2.1 General 5
2.2 Dynamic analysis of elastic single-degree-of-freedom systems 6
2.2.1 Equations of motion 6
2.2.2 Free vibration 7
2.2.3 Forced vibration 10
2.2.4 Elastic response spectra 13
2.2.4.1 Definition: Generation 13
2.2.4.2 Acceleration response spectra 16
2.2.4.3 Displacement response spectra 19
2.2.4.4 Velocity response spectra 20
2.2.4.5 Acceleration-displacement response spectra 21
2.3 Dynamic analysis of inelastic SDOF systems 22
2.3.1 Introduction 22
2.3.2 Viscous damping 22
2.3.3 Hysteretic damping 25
2.3.4 Energy dissipation and ductility 27
2.3.5 Physical meaning of the ability for energy absorption (damping) 32
2.3.6 Inelastic response spectra 35
2.3.6.1 Inelastic acceleration response spectra 35
2.3.6.2 Inelastic displacement response spectra 36
2.4 Dynamic analysis of MDOF elastic systems 37
2.4.1 Introduction 37
2.4.2 Equations of motion of plane systems 37
2.4.3 Modal response spectrum analysis versus time�history analysis 41
2.4.3.1 General 41
2.4.3.2 Modal response spectrum analysis 42
2.4.3.3 Time-history analysis 45
2.4.4 Pseudospatial structural single-storey system 46
2.4.4.1 General 46
2.4.4.2 Static response of the single-storey 3D system 48
2.4.4.3 Dynamic response of a single-storey 3D system 54
2.4.4.4 Concluding remarks 58
2.5 Dynamic analysis of MDOF inelastic systems 62
2.5.1 Introduction 62
2.5.2 Methodology for inelastic dynamic analysis of MDOF plane systems 63
2.5.3 Concluding remarks 69
2.6 Application example 70
2.6.1 Building description 71
2.6.2 Design specifications 71
2.6.3 Modelling assumptions 72
2.6.4 Static response 72
2.6.5 Hand calculation for the centre of stiffness 72
2.6.6 Mass calculation 73
2.6.7 Base shear calculation 73
2.6.8 Computer-aided calculation for the centre of stiffness 76
2.6.9 Dynamic response 79
2.6.10 Estimation of poles of rotation for building B 79
3 Design principles, seismic actions, performance requirements,compliance criteria
3.1 Introduction 83
3.2 Conceptual framework of seismic design: Energy balance 84
3.2.1 General 84
3.2.2 Displacement-based design 88
3.2.2.1 Inelastic dynamic analysis and design 88
3.2.2.2 Inelastic static analysis and design 88
3.2.3 Force-based design 90
3.2.4 Concluding remarks 92
3.3 Earthquake input 93
3.3.1 Definitions 93
3.3.2 Seismicity and seismic hazard 98
3.3.2.1 Seismicity 99
3.3.2.2 Seismic hazard 100
3.3.3 Concluding remarks 102
3.4 Ground conditions and design seismic actions 103
3.4.1 General 103
3.4.2 Ground conditions 105
3.4.2.1 Introduction 105
3.4.2.2 Identification of ground types 105Contents vii
3.4.3 Seismic action in the form of response spectra 105
3.4.3.1 Seismic zones 105
3.4.3.2 Importance factor 106
3.4.3.3 Basic representation of seismic action in the form of a response spectrum 108
3.4.3.4 Horizontal elastic response spectrum 109
3.4.3.5 Vertical elastic response spectrum 111
3.4.3.6 Elastic displacement response spectrum 112
3.4.3.7 Design spectrum for elastic analysis 113
3.4.4 Alternative representation of the seismic action 115
3.4.4.1 General 115
3.4.4.2 Artificial accelerograms 115
3.4.4.3 Recorded or simulated accelerograms 116
3.4.5 Combination of seismic action with other actions 117
3.5 Performance requirements and compliance criteria 118
3.5.1 Introduction 118
3.5.2 Performance requirements according to EC 8-1/2004 120
3.5.3 Compliance criteria 122
3.5.3.1 General 122
3.5.3.2 Ultimate limit state 122
3.5.3.3 Damage limitation state 124
3.5.3.4 Specific measures 124
4 Configuration of earthquake-resistant R/C structural systems:Structural behaviour
4.1 General 125
4.2 Basic principles of conceptual design 126
4.2.1 Structural simplicity 126
4.2.2 Structural regularity in plan and elevation 126
4.2.3 Form of structural walls 127
4.2.4 Structural redundancy 129
4.2.5 Avoidance of short columns 129
4.2.6 Avoidance of using flat slab frames as main structural systems 130
4.2.7 Avoidance of a soft storey 131
4.2.8 Diaphragmatic behaviour 131
4.2.9 Bi-directional resistance and stiffness 131
4.2.10 Strong columns�weak beams 132
4.2.11 Provision of a second line of defense 132
4.2.12 Adequate foundation system 134
4.3 Primary and secondary seismic members 136
4.4 Structural R/C types covered by seismic codes 137
4.5 Response of structural systems to lateral loading 139
4.5.1 General 139
4.5.2 Plane structural systems 139
4.5.2.1 Moment-resisting frames 140viii Contents
4.5.2.2 Wall systems or flexural systems 141
4.5.2.3 Coupled shear walls 142
4.5.2.4 Dual systems 143
4.5.3 Pseudospatial multistorey structural system 144
4.6 Structural configuration of multi-storey R/C buildings 150
4.6.1 General 150
4.6.2 Historical overview of the development of R/C multi-storey buildings 152
4.6.3 Structural system and its main characteristics 156
4.6.3.1 General 156
4.6.3.2 Buildings with moment-resisting frames 156
4.6.3.3 Buildings with wall systems 157
4.6.3.4 Buildings with dual systems 160
4.6.3.5 Buildings with flat slab frames, shear walls and moment-resisting frames 161
4.6.3.6 Buildings with tube systems 162
5 Analysis of the structural system
5.1 General 163
5.2 Structural regularity 163
5.2.1 Introduction 163
5.2.2 Criteria for regularity in plan 164
5.2.3 Criteria for regularity in elevation 166
5.2.4 Conclusions 166
5.3 Torsional flexibility 167
5.4 Ductility classes and behaviour factors 170
5.4.1 General 170
5.4.2 Ductility classes 171
5.4.3 Behaviour factors for horizontal seismic actions 172
5.4.4 Quantitative relations between the Q-factor and ductility 176
5.4.4.1 General 176
5.4.4.2 M�relation for R/C members under plain bending 177
5.4.4.3 Moment�curvature�displacement diagrams of R/C cantilever beams 180
5.4.4.4 Moment�curvature�displacement diagrams of R/C frames 182
5.4.4.5 Conclusions 183
5.4.5 Critical regions 185
5.5 Analysis methods 187
5.5.1 Available methods of analysis for R/C buildings 187
5.6 Elastic analysis methods 190
5.6.1 General 190
5.6.2 Modelling of buildings for elastic analysis and BIM concepts 190
5.6.3 Specific modelling issues 191
5.6.3.1 Walls and cores modelling 192
5.6.3.2 T-shaped beams 192Contents ix
5.6.3.3 Diaphragm constraint 193
5.6.3.4 Eccentricity 194
5.6.3.5 Stiffness 195
5.6.4 Lateral force method of analysis 195
5.6.4.1 Base shear forces 196
5.6.4.2 Distribution along the height 196
5.6.4.3 Estimation of the fundamental period 197
5.6.4.4 Torsional effects 198
5.6.5 Modal response spectrum analysis 199
5.6.5.1 Modal participation 200
5.6.5.2 Storey and wall shears 200
5.6.5.3 Ritz vector analysis 201
5.6.6 Time�history elastic analysis 201
5.7 Inelastic analysis methods 201
5.7.1 General 201
5.7.2 Modelling in nonlinear analysis 202
5.7.2.1 Slab modelling and transfer of loads 202
5.7.2.2 Diaphragm constraint 203
5.7.2.3 R/C walls and cores 203
5.7.2.4 Foundation 205
5.7.2.5 Point hinge versus fibre modelling 205
5.7.2.6 Safety factors 207
5.7.3 Pushover analysis 209
5.7.4 Pros and cons of pushover analysis 210
5.7.5 Equivalent SDOF systems 212
5.7.5.1 Equivalent SDOF for torsionally restrained buildings 212
5.7.5.2 Equivalent SDOF for torsionally unrestrained buildings 216
5.7.6 Time�history nonlinear analysis 224
5.7.6.1 Input motion-scaling of accelerograms 224
5.7.6.2 Incremental dynamic analysis IDA 226
5.8 Combination of the components of gravity loads and seismic action 229
5.8.1 General 229
5.8.2 Theoretical background 232
5.8.3 Simplified procedures 234
5.8.3.1 Combination of the extreme values of the interacting load effects 235
5.8.3.2 Combination of each extreme load effect with the corresponding values of the interacting
5.8.3.3 Gupta�Singh procedure 236
5.8.3.4 Rosenblueth and Contreras procedure 237
5.8.3.5 Extreme stress procedure 238
5.8.4 Code provisions 239
5.8.4.1 Suggested procedure for the analysis 239
5.8.4.2 Implementation of the reference method in case of horizontal seismic actions 240x Contents
5.8.4.3 Implementation of the alternative method in the case of horizontal seismic actions 241
5.8.4.4 Implementation of the alternative method for horizontal and vertical seismic action 245
5.9 Example: Modelling and elastic analysis of an eight-storey RC building 245
5.9.1 Building description 245
5.9.2 Material properties 247
5.9.3 Design specifications 247
5.9.4 Definition of the design spectrum 247
5.9.4.1 Elastic response spectrum (5% damping) 247
5.9.4.2 Design response spectrum 247
5.9.5 Estimation of mass and mass moment of inertia 248
5.9.6 Structural regularity in plan and elevation 248
5.9.6.1 Criteria for regularity in plan 248
5.9.6.2 Criteria for regularity in elevation 250
5.9.7 Determination of the behaviour factor q (Subsection 5.4.3) 251
5.9.8 Description of the structural model 252
5.9.9 Modal response spectrum analysis 254
5.9.9.1 Accidental torsional effects 254
5.9.9.2 Periods, effective masses and modes of vibration 255
5.9.9.3 Shear forces per storey 255
5.9.9.4 Displacements of the centres of masses 255
5.9.9.5 Damage limitations 256
5.9.9.6 Second-order effects 258
5.9.9.7 Internal forces 259
5.10 Examples: Applications using inelastic analysis 259
5.10.1 Cantilever beam 259
5.10.1.1 Modelling approaches 259
5.10.1.2 Results 260
5.10.2 2-D MRF 261
5.10.2.1 Modelling approaches 261
5.10.2.2 Results 263
5.10.3 Sixteen-storey R/C building 264
5.10.3.1 Modelling approaches 264
5.10.3.2 Nonlinear dynamic analysis 271
5.10.3.3 Nonlinear static analysis 271
5.10.3.4 Results: Global response 272
5.10.3.5 Results: Local response 274
6 Capacity design � design action effects � safety verifications
6.1 Impact of capacity design on design action effects 277
6.1.1 General 277
6.1.2 Design criteria influencing the design action effects 278
6.1.3 Capacity design procedure for beams 279
6.1.4 Capacity design of columns 281Contents xi
6.1.4.1 General 281
6.1.4.2 Bending 282
6.1.4.3 Shear 285
6.1.5 Capacity design procedure for slender ductile walls 287
6.1.5.1 General 287
6.1.5.2 Bending 287
6.1.5.3 Shear 289
6.1.6 Capacity design procedure for squat walls 290
6.1.6.1 DCH buildings 291
6.1.6.2 DCM buildings 291
6.1.7 Capacity design of large lightly reinforced walls 291
6.1.8 Capacity design of foundation 292
6.2 Safety verifications 294
6.2.1 General 294
6.2.2 Ultimate limit state 294
6.2.2.1 Resistance condition 295
6.2.2.2 Second-order effects 295
6.2.2.3 Global and local ductility condition 297
6.2.2.4 Equilibrium condition 298
6.2.2.5 Resistance of horizontal diaphragms 298
6.2.2.6 Resistance of foundations 299
6.2.2.7 Seismic joint condition 299
6.2.3 Damage limitation 299
6.2.4 Specific measures 302
6.2.4.1 Design 302
6.2.4.2 Foundations 302
6.2.4.3 Quality system plan 302
6.2.4.4 Resistance uncertainties 303
6.2.4.5 Ductility uncertainties 303
6.2.5 Concluding remarks 303
7 Reinforced concrete materials under seismic actions
7.1 Introduction 305
7.2 Plain (unconfined) concrete 307
7.2.1 General 307
7.2.2 Monotonic compressive stress�strain diagrams 307
7.2.3 Cyclic compressive stress�strain diagram 308
7.2.4 Provisions of Eurocodes for plain (not confined) concrete 311
7.3 Steel 314
7.3.1 General 314
7.3.2 Monotonic stress�strain diagrams 314
7.3.3 Stress�strain diagram for repeated tensile loading 314
7.3.4 Stress�strain diagram for reversed cyclic loading 316
7.3.5 Provisions of codes for reinforcement steel 317
7.3.6 Concluding remarks 318xii Contents
7.4 Confined concrete 321
7.4.1 General 321
7.4.2 Factors influencing confinement 322
7.4.3 Provisions of Eurocodes for confined concrete 323
7.4.3.1 Form of the diagram
7.4.3.2 Influence of confinement 325
7.5 Bonding between steel and concrete 329
7.5.1 General 329
7.5.2 Bond�slip diagram under monotonic loading 332
7.5.3 Bond�slip diagram under cyclic loading 334
7.5.4 Provisions of Eurocodes for bond of steel to concrete 335
7.5.4.1 Static loading 335
7.5.4.2 Seismic loading 337
7.6 Basic conclusions for materials and their synergy 337
8 Seismic-resistant R/C frames
8.1 General 339
8.2 Design of beams 340
8.2.1 General 340
8.2.2 Beams under bending 343
8.2.2.1 Main assumptions 343
8.2.2.2 Characteristic levels of loading to failure (limit states) 344
8.2.2.3 Determination of the characteristic points diagram and ductility in terms of curvature for orthogonal cross section 348
8.2.2.4 Determination of the characteristic points diagram and ductility in terms of curvature for a generalised cross section 354
8.2.3 Load�deformation diagrams for bending under cyclic loading 359
8.2.3.1 General 359
8.2.3.2 Flexural behaviour of beams under cyclic loading 360
8.2.4 Strength and deformation of beams under prevailing shear 361
8.2.4.1 Static loading 361
8.2.4.2 Cyclic loading 369
8.2.4.3 Concluding remarks on shear resistance 370
8.2.5 Code provisions for beams under prevailing seismic action 371
8.2.5.1 General 371
8.2.5.2 Design of beams for DCM buildings 372
8.2.5.3 Design of beams for DCH buildings 376
8.2.5.4 Anchorage of beam reinforcement in joints 379
8.2.5.5 Splicing of bars 381
8.3 Design of columns 382
8.3.1 General 382
8.3.2 Columns under bending with axial force 383
8.3.2.1 General 383Contents xiii
8.3.2.2 Determination of characteristic points of M�diagram and ductility in terms of curvature under axial load for an orthogonal cross-section 386
8.3.2.3 Behaviour of columns under cyclic loading 392
8.3.3 Strength and deformation of columns under prevailing shear 393
8.3.3.1 General 393
8.3.3.2 Shear design of rectangular R/C columns 395
8.3.4 Code provisions for columns under seismic action 399
8.3.4.1 General 399
8.3.4.2 Design of columns for DCM buildings 399
8.3.4.3 Design of columns for DCH buildings 407
8.3.4.4 Anchorage of column reinforcement 409
8.3.4.5 Splicing of bars 409
8.3.5 Columns under axial load and biaxial bending 410
8.3.5.1 General 410
8.3.5.2 Biaxial strength in bending and shear 410
8.3.5.3 Chord rotation at yield and failure stage: Skew ductility
8.3.5.4 Stability of M diagrams under cyclic loading: Form of the hysteresis loops 415
8.3.5.5 Conclusions 415
8.3.6 Short columns under seismic action 415
8.3.6.1 General 415
8.3.6.2 Shear strength and failure mode of conventionally reinforced squat columns 418
8.3.6.3 Shear strength and failure mode of alternatively reinforced short columns 425
8.3.6.4 Code provisions for short columns 427
8.4 Beam�Column joints 428
8.4.1 General 428
8.4.2 Design of joints under seismic action 429
8.4.2.1 Demand for the shear design of joints 429
8.4.2.2 Joint shear strength according to the Paulay and Priestley method 431
8.4.2.3 Background for the determination of joint shear resistance according to ACI 318-2011
8.4.2.4 Joint shear strength according to A.G. Tsonos 437
8.4.3 Code provisions for the design of joints under seismic action 440
8.4.3.1 DCM R/C buildings under seismic loading according to EC 8-1/2004 440
8.4.3.2 DCH R/C buildings under seismic loading according to EC 8-1/2004 441
8.4.4 Non-conventional reinforcing in the joint core 443
8.5 Masonry-infilled frames 444
8.5.1 General 444xiv Contents
8.5.2 Structural behaviour of masonry infilled frames under cyclic loading reversals 446
8.5.3 Code provisions for masonry-infilled frames under seismic action 452
8.5.3.1 Requirements and criteria 452
8.5.3.2 Irregularities due to masonry infills 453
8.5.3.3 Linear modeling of masonry infills 454
8.5.3.4 Design and detailing of masonry-infilled frames 454
8.5.4 General remarks on masonry-infilled frames 456
8.6 Example: Detailed design of an internal frame 456
8.6.1 Beams: Ultimate limit state in bending 457
8.6.1.1 External supports on C2 and C28 (beam B8-left, B68-right) 457
8.6.1.2 Internal supports on C8 and on C22
8.6.1.3 Internal supports on C14 and C18 (beam
8.6.1.4 Mid-span (beams B8, B68) 461
8.6.1.5 Mid-span (beams B19, B37, B57) 461
8.6.2 Columns: Ultimate limit state in bending and shear 461
8.6.2.1 Column C2 (exterior column) 462
8.6.2.2 Design of exterior beam�column joint 466
8.6.2.3 Column C8 (interior column) 469
8.6.2.4 Design of interior beam�column joint 474
8.6.3 Beams: Ultimate limit state in shear 476
8.6.3.1 Design shear forces 476
8.6.3.2 Shear reinforcement 481
9 Seismic-resistant R/C walls and diaphragms
9.1 General 485
9.2 Slender ductile walls 486
9.2.1 A summary on structural behaviour of slender ductile walls 486
9.2.2 Behaviour of slender ductile walls under bending with axial load 488
9.2.2.1 General 488
9.2.2.2 Dimensioning of slender ductile walls with orthogonal cross-section under bending with axial
9.2.2.3 Dimensioning of slender ductile walls with a composite cross-section under bending with
9.2.2.4 Determination of M�diagram and ductility in terms of curvature under axial load for orthogonal cross-sections 493
9.2.3 Behaviour of slender ductile walls under prevailing shear 494
9.2.4 Code provisions for slender ductile walls 495
9.2.4.1 General 495
9.2.4.2 Design of slender ductile walls for DCM buildings 495
9.2.4.3 Design of slender ductile walls for DCH buildings 503Contents xv
9.3 Ductile coupled walls 509
9.3.1 General 509
9.3.2 Inelastic behaviour of coupled walls 510
9.3.3 Code provisions for coupled slender ductile walls 512
9.4 Squat ductile walls 513
9.4.1 General 513
9.4.2 Flexural response and reinforcement distribution 514
9.4.3 Shear resistance 515
9.4.4 Code provisions for squat ductile walls 515
9.5 Large lightly reinforced walls 517
9.5.1 General 517
9.5.2 Design to bending with axial force 518
9.5.3 Design to shear 519
9.5.4 Detailing for local ductility 519
9.6 Special issues in the design of walls 520
9.6.1 Analysis and design using FEM procedure 520
9.6.2 Warping of open composite wall sections 523
9.6.2.1 General 523
9.6.2.2 Saint-Venant uniform torsion 524
9.6.2.3 Concept of warping behaviour 526
9.6.2.4 Geometrical parameters for warping bending 534
9.6.2.5 Implications of warping torsion in analysis and design to seismic action of R/C buildings
9.7 Seismic design of diaphragms 541
9.7.1 General 541
9.7.2 Analysis of diaphragms 542
9.7.2.1 Rigid diaphragms 542
9.7.2.2 Flexible diaphragms 543
9.7.3 Design of diaphragms 544
9.7.4 Code provisions for seismic design of diaphragms 544
9.8 Example: Dimensioning of a slender ductile wall with a composite cross-section 544
9.8.1 Ultimate limit state in bending and shear 545
9.8.2 Estimation of axial stresses due to warping torsion 548
9.8.2.1 Estimation of the geometrical parameters for warping bending of an open composite C-shaped wall section 548
9.8.2.2 Implementation of the proposed methodology for deriving the normal stresses due to warping 550
10 Seismic design of foundations
10.1 General 553
10.2 Ground properties 554
10.2.1 Strength properties 554
10.2.1.1 Clays 554
10.2.1.2 Granular soils (sands and gravels) 555xvi Contents
10.2.1.3 Partial safety factors for soil 555
10.2.2 Stiffness and damping properties 555
10.2.3 Soil liquefaction 557
10.2.4 Excessive settlements of sands under cyclic loading 558
10.2.5 Conclusions 558
10.3 General considerations for foundation analysis and design 558
10.3.1 General requirements and design rules 558
10.3.2 Design action effects on foundations in relation to ductility and capacity design 559
10.3.2.1 General 559
10.3.2.2 Design action effects for various types of R/C foundation members 560
10.4 Analysis and design of foundation ground under the design action effects 563
10.4.1 General requirements 563
10.4.2 Transfer of action effects to the ground 563
10.4.2.1 Horizontal forces 563
10.4.2.2 Normal force and bending moment 564
10.4.3 Verification and dimensioning of foundation ground at ULS of shallow or embedded foundations 564
10.4.3.1 Footings 564
10.4.3.2 Design effects on foundation horizontal connections between vertical structural elements
10.4.3.3 Raft foundations 566
10.4.3.4 Box-type foundations 566
10.4.4 Settlements of foundation ground of shallow or embedded foundations at SLS 567
10.4.4.1 General 567
10.4.4.2 Footings 567
10.4.4.3 Foundation beams and rafts 568
10.4.5 Bearing capacity and deformations of foundation ground in the case of a pile foundation 570
10.4.5.1 General 570
10.4.5.2 Vertical load resistance and stiffness 570
10.4.5.3 Transverse load resistance and stiffness 572
10.5 Analysis and design of foundation members under the design action effects 575
10.5.1 Analysis 575
10.5.1.1 Separated analysis of superstructure and foundation 575
10.5.1.2 Integrated analysis of superstructure and foundation (soil�structure interaction) 576
10.5.1.3 Integrated analysis of superstructure foundation and foundation soil 577
10.5.2 Design of foundation members 578
10.5.2.1 Dissipative superstructure � non-dissipative foundation elements and foundation ground
10.5.2.2 Dissipative superstructure � dissipative foundation elements � elastic foundation ground
10.5.2.3 Non-dissipative superstructure � non-dissipative foundation elements and foundation ground 582
10.5.2.4 Concluding remarks 582
10.6 Example: Dimensioning of foundation beams 582
10.6.1 Ultimate limit state in bending 583
10.6.2 Ultimate limit state in shear 586
11 Seismic pathology
11.1 Classification of damage to R/C structural members 589
11.1.1 Introduction 589
11.1.2 Damage to columns 590
11.1.3 Damage to R/C walls 596
11.1.4 Damage to beams 600
