Contents
1 Earthquakes 1
1.1 Concise Historical Review of Seismic Design 1
1.2 Understanding Earthquakes 1
1.2.1 Earth Interior 4
1.2.2 Plate Tectonics 4
1.2.3 Faults 5
1.2.4 Predicting Earthquake Occurrence 6
1.2.5 Earthquake Effects 7
1.2.6 Seismic Zoning 8
1.3 Earthquake Features 8
1.3.1 Seismic Waves 8
1.3.2 Locating an Earthquake's Epicentre 9
1.4 Quan ti ti cation of the Shake 11
1.4.1 Measuring Ground Motion 11
1.4.2 Intensity Scale 12
1.4.3 Magnitude Scale 13
1.5 Illustrative Examples 14
Ex 1.5.1 Locating the Epicenter 14
Ex 1.5.2 Evaluating Moment Magnitude 14
2 Important Attributes for Seismic Design 15
2.1 Introduction 15
2.2 Material Attributes 16
2.2.1 Need for Yogic Concrete 16
2.2.2 Steel Reinforcement 18
2.2.3 Bond and Shear 19
2.2.4 Masonry Components 20
2.3 Damping 21
2.3.1 Types of Damping 21
2.3.2 Damping Ratio 22
2.3.3 Critical Damping 23
2.3.4 Logarithmic Decrement (8) 24
2.3.5 Magnitude of Damping 26
2.3.6 Proportional Damping 26
2.4 Ductility 28
2.4.1 Importance of Ductility 28
2.4.2 Classification of Ductility 29
2.4.3 Ensuring Adequate Ductility 34
2.5 Lateral Stiffness 35
2.5.1 Nature of Stiffness 35
2.5.2 Lateral Stiffness Values 38
2.6 Strength 42
2.6.1 Characteristic Strength 43
2.6.2 Target Strength 43
2.6.3 Overstrength 44
2.7 Mass 44
2.7.1 Lumped Mass 44
2.7.2 Mass Moment of lnertia (mo) 45
2.8Degrees of Freedom (DOF) 46
2.8.1 Description of Degrees of Freedom 46
2.8.2 Natural Vibration Frequencies in Six DOF 47
2.9 Illustrative Examples 48
Ex 2.9.1 Determination of Nature of Damping and Damped Frequency 48
Ex 2.9.2 Calculation of Critical Damping, Damping Coefficient and Logarithmic Decrement 49
Ex 2.9.3 Obtaining Undamped and Damped Frequencies and Vibration Period with Damping 49
Ex 2.9.4 Finding Time Period required for Specified Reduction in Amplitude 50
Ex 2.9 .5 Calculating Energy Dissipated in a Cycle 50
Ex 2.9.6 Deriving Damping Ratios and Rayleigh Damping Matrix 50
Ex 2.9.7 Calculation of Curvature Ductility 52
Ex 2.9.8 Calculation of Rotational Ductility 52
Ex 2.9.9 Evaluation of Frequencies for Six Degrees of Freedom 53
3 Vibration Concepts: Linear Systems 57
3.1 Introduction 57
3.2 Simple Harmonic Motion (SHM) 58
3.2.1 Equation of a Simple Harmonic Motion 59
3.3 Combining Gravity and Dynamic Loads 60
3.4 Single Degree-of-Freedom (SDOF) Systems 62
3.4.1 Equation of Motion of a SDOF System 62
3.4.2 Undamped Free Vibrations 64
3.4.3 Damped Free Vibrations 65
3.4.4 Damped Free Vibrations Under Impulse Loading 66
3.4.5 Damped Free Vibrations Under Earthquake Excitation 67
3.4.6 Resonance 69
3.5 Two Degree-of-Freedom (Two DOF) System 69
3.5.1 Undamped Free Vibrations 69
3.6 Multi-Degree-of-Freedom (MDOF) System 73
3.6.1 Undamped Free Vibrations 74
3.6.2 Damped System Under Free Vibrations 74
3.6.3 Damped Vibrations Under Earthquake Excitation 75
3.7 Torsional Vibrations 77
3.7.1 Equations of Motion for an Undamped System 77
3.8 Rocking Motion 79
3.9 Illustrative Examples 83
Ex 3.9.1 Evaluation of Frequency and Frame Side Sway 83
Ex 3.9.2 Computation of Displacement Response due to a Seismic Impulse 84
Ex 3.9.3 Calculation of Inertia Forces, Base Shear, Displacement and Drift for a Two DOF Shear Frame 85
3.9.4 Calculation of Frequencies with Torsion 87
3.9.5 Computation of Rocking Frequency 88
4 Response Evaluation 89
4.1 Introduction 89
4.2 Elastic Response Spectrum 90
4.2.1 Concept 90
4.2.2 Relationship Between Spectral Quantities 91
4.2.3 Linear Design Acceleration Spectrum 93
4.2.4 Tripartite Plot 93
4.2.5 Merits and Limitations of a Design Response Spectrum 95
4.2.6 Effect of Vertical Ground Motion 95
4.3 Inelastic Response Spectrum 97
4.3.1 Effect of Ductility 97
4.3.2 Deducing Inelastic Design Response Spectrum 99
4.4 Estimate of Fundamental Time Period of Vibration 99
4.4.1 Effect of Masonry Infill 100
4.4.2 Effect of Shear Walls 101
4.5 Linear Static Procedure (LSP) 101
4.5.1 Design Horizontal Seismic Coefficient 101
4.5.2 Response Reduction Factor 103
4.5.3 Evaluation of Base Shear 105
4.5.4 Distribution of Base Shear 105
4.5.5 Linear Static Design Procedure 106
4.6 Modal Analysis 107
4.6.1 Basic Principles 107
4.6.2 Modal Equation of Motion 107
4.6.3 Mode Shapes 109
4.6.4 Modal Frequencies 110
4.6.5 Orthogonality of Modes 110
4.6.6 Normalisation of Modes 111
4.6.7 Modal Participation Factor 112
4.6.8 Modal Mass 112
4.6.9 Modal Height and Moment 114
4.6.10 Combining Modal Responses 114
4.6.11 Modal Analysis Procedure 116
4.6.12 Missing Mass Correction 118
4.7 Numerical Time History Analysis 118
4.7.1 Newmark's Numerical Methods 119
4.7.2 Linear Acceleration Method 120
4.7.3 Average Acceleration Method 122
4.8 Nonlinear Time History Analysis 123
4.8.1 Nonlinear SDOF System 123
4.8.2 Nonlinear MDOF System 125
4.9 Illustrative Examples 127
Ex 4.9.1 Use of Tripartite Plot 127
Ex 4.9.2 Effect of Ductility on Magnitude of Lateral Force 127
Ex 4.9.3 Evaluation of Mode Shapes and Modal Frequencies 128
Ex 4.9.4 Demonstration of Mode Orthogonality 130
Ex 4.9.5 Different Methods for Normalizing Mode Shape 131
Ex 4.9.6 Calculation of Participation Factors 132
Ex 4.9.7 Determining Modal Masses and Modal Height 133
Ex 4.9.8 Comparison of SRSS and CQC Methods 134
Ex 4.9.9 Use of Missing Mass Method 135
Ex 4.9.10 Time History Calculations for a Linear SDOF System using Linear Acceleration Method 138
Ex 4.9.11 Time History Calculations for an Elasto - Plastic SDOF System 141
Ex 4.9.12 Time History Computation for a MDOF system 147
5 Planning for Aseismic Buildings 155
5.1 Introduction 155
5.2 Building Configuration 156
5.2.1 Architectural Planning for Earthquakes 156
5.2.2 Structural Planning 158
5.2.3 Irregularity 160
5.3 Pounding 165
5.4 Horizontal Torsion 167
5.4.1 Torsion Computation for a Multi-storey Building 167
5.4.2 Design Forces Including for Torsion 171
5.4.3 Effects of Horizontal Torsion 173
5.5 Structural Anatomy 174
5.5.1 Soft and Weak Storeys 174
5.5.2 Short Column 176
5.5.3 Floating Column 178
5.5.4 Load Path Integrity and Redundancy 179
5.5.5 Staircases 181
5.6 Force-Based Design 184
5.6.1 Design Philosophy 184
5.6.2 Selection of a Design Earthquake 185
5.6.3 Direction of Ground Motion 185
5.6.4 Inertia Effects 185
5.6.5 Load Combinations 189
5.7 Illustrative Examples 190
Ex 5.7.1 Effect of Vertical Irregularity 190
Ex 5.7.2 Evaluation of Torsional Moment at a Floor in a Multistorey Building 190
Ex 5.7.3 Sharing of Forces among Walls due to Torsion 193
Ex 5.7.4 Checking for Existence of a Soft Storey 196
Ex 5.7 .5 Checking for Existence of a Weak Storey 196
6 Frames and Diaphragms: Design and Detailing 199
6.1 Introduction 199
6.2 Moment-Resisting Frames (MRFs) 200
6.2.1 Types of Moment-Resisting Frames 200
6.2.2 Seismic Analysis Procedures 201
6.2.3 Design and Ductile Detailing Principles 204
6.3 Diaphragms 206
6.3.1 Flexible Diaphragm 207
6.3.2 Rigid Diaphragm 207
6.3 .3 Flat Slab Diaphragm 210
6.3.4 Transfer Diaphragm 212
6.3 .5 Collectors and Chord Elements 212
6.4 Beams 214
6.4.1 Design for Moment 214
6.4.2 Design for Shear 216
6.4.3 Design for Bond 217
6.4.4 Tension Shift 218
6.4.5 Ductile Detailing 219
6.5 Columns 220
6.5.1 Column Design 220
6.5.2 Ductile Detailing 224
6.6 Beam- Column Joints 225
6.6.1 Joint Types 227
6.6.2 Joint Behaviour Mechanism 228
6.6.3 Joint Design 231
6.6.4 Ductile Detailing of a Joint 233
6.6.5 Joint Constructability 234
6.7 Facade Skin 235
6.7.1 Rigid Masonry Infill 235
6.7.2 Curtain Wall 236
6.8 Tall Frames 238
6.8.1 Introduction 238
6.8.2 Structural Forms 239
6.9 Special Aspects Relevant to Tall Frames 242
6.9.1 Damping 242
6.9.2 Effect of Higher Modes 243
6.9.3 Reduction of Frames 243
6.9.4 Shear Lag Effect 247
6.9.5 P-t-. Translational Effect 248
6.9.6 P-t-. Torque Effect 251
6.9.7 Drift and Deformation 251
6.9.8 Podium 252
6.10 Illustrative Examples 253
Ex 6.10.1 Analysis using Linear Static Procedure 253
Ex 6.10.2 Evaluation of vibration frequencies 256
Ex 6.10.3 Analysis using Linear Dynamic Procedure 256
Ex 6.10.4 Load Distribution among Walls Depending on Diaphragm Rigidity 259
Ex 6.10.5 Analysis of a Collector and a Chord 261
Ex 6.10.6 Design of a Beam-Column Joint 262
Ex 6.10.7 Evaluation of P-Delta Translational Effect v265
7 Shear Walls: Aseismic Design and Detailing 269
7.1 Introduction 269
7.2 Functional Layout and Configuration 270
7.3 Classification of Shear Walls 272
7.3.1 Aspect Ratio 272
7.3.2 Shape in Plan 273
7 .3.3 Ductility Class 273
7.4 Design of Cantilever Walls in Flexure 274
7.4.1 Important Design Considerations 274
7.4.2 Flexural Stress Analysis 275
7.4.3 Detailing for Flexure 279
7.4.4 Boundary Elements 282
7 .5 Capacity-Based Shear Design of Cantilever Walls 284
7.5. l Design for Diagonal Tension 284
7.5.2 Design for Sliding Shear 286
7.6 Design of Squat Walls 287
7.6. l Design for Flexure 287
7.6.2 Design for Diagonal Tension 287
7.7 Coupled Shear Walls 289
7.7.1 Degree of Coupling 290
7 .7 .2 Design of Coupling Beams 290
7.8 Walls with Openings 293
7.9 Illustrative Examples 294
Ex 7.9.1 Design of a Cantilever Shear Wall 294
Ex 7.9.2 Design of a Squat Wall 298
8 Substructure Design and Soil-Structure Coupling 301
8.1 Introduction 301
8.2 Parameters of Strong Ground Motion 302
8.2.1 Amplitude and Frequency Content 303
8.2.2 Effective Duration of Strong Motion 304
8.2.3 Time History of Motion 304
8.3 Important Subsoil Parameters 305
8.3.1 Depth of Soil Overlay and Its Stratification 305
8.3.2 Dynamic Shear Modulus (G) 306
8.3.3 Poisson's Ratio 306
8.3.4 Particle Grain Size Distribution 307
8.3.5 Soil Damping 307
8.3.6 Relative Density 308
8.3.7 Water Depth 308
8.3.8 Soil Bearing Capacity 309
8.4 Soil Liquefaction 309
8.4.1 Causes of Liquefaction 309
8.4.2 Determining Liquefaction Potential 310
8.5 Open Foundations 310
8.5.1 Tie Beams 312
8.6 Piles 314
8.6.1 Pile Loads 314
8.6.2 Pile Design Criteria 315
8.6.3 Analysis of Laterally Loaded Piles 316
8.6.4 Pile Group Effect 321
8.6.5 Pile and Pile Cap Details 322
8.7 Retaining Walls 323
8.7.1 Yielding Walls (Cantilever Walls) 323
8.7.2 Non-yielding Walls (Basement Walls) 328
8.8 Soil- Structure Coupling (SSC) 329
8.8.1 Dynamics of Soil- Structure Coupling 330
8.8.2 Evaluating Effect of Soil-Structure Coupling 331
8.9 Illustrative Examples 340
Ex 8.9.1 Characteristic Load Method for Piles 340
Ex 8.9.2 Active Earth Pressure and Base Moment on a Retaining 341
Ex 8.9.3 Active Earth Pressure on a Retaining Wall with Submerged Soil 342
Ex 8.9.4 Soil Structure Interaction for a MDOF System 343
9 Confined and Reinforced Masonry Buildings 349
9.1 Introduction 349
9 .2 Seismic Considerations 351
9.2.1 Building Configuration 351
9.2.2 Walls 352
9.2.3 Roofs 353
9.3 Confined Masonry 354
9.3.1 Tie Columns 355
9.3.2 Tie Beams 355
9.4 Sharing of Lateral Force Among Co-planer Walls 355
9.4.1 Rigidity of a Solid Cantilever Shear Wall 357
9.4.2 Rigidity of a Wall with Openings 358
9.4.3 Distribution of Lateral Force Among Masonry Piers 359
9.4.4 Walls Connected by a Drag Member 360
9 .4.5 Design of a Wall Pier 360
9.5 Reinforced Masonry 361
9.5.1 Wall Formation 361
9.5.2 Special Reinforced Masonry Shear Wall 362
9.6 Shear Wall: Working Stress Design 363
9.6.1 Design Parameters 363
9.6.2 Design of a Wall Subjected to Axial Load and In-Plane Flexure 365
9.6.3 Design of a Wall Subjected to Out-of-Plane Forces 368
9.6.4 Flanged Wall 368
9.7 Slender Shear Wall: Strength Design 369
9.7.1 Limit States 369
9.7.2 Strength Design for Flexure 370
9.8 lllustrative Examples 372
Ex 9.8.1 Sharing of Inertia Forces between Piers 372
Ex 9.8.2 Drag Forces in Member Connecting Masonry Shear Walls 375
Ex 9.8.3 Checking Adequacy of a Selected Pier 377
Ex 9.8.4 Design of a Masonry Shear Wall – Working Stress Method 380
Ex 9.8.5 Design of a Wall For Out Of Plane Forces 381
Ex 9.8.6 Strength Design of a Masonry Shear Wall 382
10 Base Isolation 387
10.1 Introduction 387
10.2 Brief History 388
10.3 Concept of Base Isolation 389
10.4 Passive Base Isolators 391
10.4. l Elastomeric Isolators 392
10.4.2 Sliding Isolators 392
10.4.3 Primary Isolator Requirements 393
10.5 Merits and Demerits of Isolators 394
10.5.1 Merits 394
10.5.2 Demerits 395
10.6 Characteristics of Elastomeric Isolators 395
10.6.1 Isolator Stiffness 396
10.6.2 Isolator Damping 397
10.6.3 Time Period of Isolator Supported Building 397
10.7 Analysis of a SDOF Frame on Elastomeric Isolators 397
10.7.J Equation of Motion 398
10.7.2 Evaluation of Natural Frequencies 399
10.7.3 Mode Shapes 400
10.7.4 Roof Displacement 401
10.8 Analysis of a MDOF Frame on Elastomeric Isolators 401
10.8.1 Equations of Motion 402
10.8.2 Evaluation of Natural Frequencies 403
10.9 Analysis of a SDOF Building Frame on Sliding (FPS) Isolators 405
10.9.1 Evaluation of Slider Parameters 405
10.9.2 Equations of Motion in Different Phases 408
10.10 Analysis of a MDOF Building Frame on Sliding (FPS) Isolators 410
10.10.1 Equation of Motion in Different Phases 410
10.11 Illustrative Examples 412
Ex 10.11.1 Determining Elastomeric Isolator Stiffness 412
Ex 10.11.2 Frequencies of an Isolator Supported Building 412
Ex 10. 11.3 Evaluation of Displacement, Stiffness and Damping of a FPS Isolator 415
11 Performance-Based Seismic Design 417
11. 1 Introduction 417
11.2 Description of the Procedure 418
11.2.1 Need for This Approach 418
11.2.2 Performance Levels 419
11.2.3 Hazard Levels 421
11.2.4 Quantifying Performance Objectives 422
11.2.5 Preliminary Building Design 422
11.3 Nonlinear Static Procedure (NSP) - Pushover Analysis 423
11.3.1 Capacity Evaluation 423
11.3.2 Demand Evaluation 427
11.3.3 Conducting a Pushover Analysis 427
11.4 Capacity Spectrum Method 429
11.4.1 Conversion of Spectra to ADRS Format 430
11.4.2 Conversion of Demand Spectrum 430
11.4.3 Conversion to Capacity Spectrum 431
11.4.4 Locating the Performance Point 432
11.5 Seismic Coefficient Method 434
11.5.1 Equivalent Stiffness and Equivalent Time Period 434
11.5.2 Prediction of Target Displacement 435
11.5.3 Evaluation of Performance 436
References 439
Index 445