PART Ⅰ SINGLE-DEGREE-OF-FREEDOM SYSTEMS 1
1 Equations of Motion，Problem Statement，and Solution Methods 3
1.1 Simple Structures 3
1.2 Single-Degree-of-Freedom System 7
1.3 Force-Displacement Relation 8
1.4 Damping Force 13
1.5 Equation of Motion：External Force 14
1.6 Mass-Spring-Damper System 18
1.7 Equation of Motion：Earthquake Excitation 20
1.8 Problem Statement and Element Forces 23
1.9 Combining Static and Dynamic Responses 25
1.10 Methods of Solution of the Differential Equation 25
1.11 Study of SDF Systems：Organization 29
Appendix 1：Stiffness Coefficients for a Flexural Element 30
2 Free Vibration 35
2.1 Undamped Free Vibration 35
2.2 Viscously Damped Free Vibration 44
2.3 Energy in Free Vibration 52
2.4 Coulomb-Damped Free Vibration 53
3 Response to Harmonic and Periodic Excitations 61
Part A：Viscously Damped Systems：Basic Results 62
3.1 Harmonic Vibration of Undamped Systems 62
3.2 Harmonic Vibration with Viscous Damping 68
Part B：Viscously Damped Systems：Applications 80
3.3 Response to Vibration Generator 80
3.4 Natural Frequency and Damping from Harmonic Tests 83
3.5 Force Transmission and Vibration Isolation 85
3.6 Response to Ground Motion and Vibration Isolation 87
3.7 Vibration-Measuring Instruments 91
3.8 Energy Dissipated in Viscous Damping 94
3.9 Equivalent Viscous Damping 98
Part C：Systems with Nonviscous Damping 100
3.10 Harmonic Vibration with Rate-Independent Damping 100
3.11 Harmonic Vibration with Coulomb Friction 104
Part D：Response to Periodic Excitation 108
3.12 Fourier Series Representation 109
3.13 Response to Periodic Force 109
Appendix 3：Four-Way Logarithmic Graph Paper 113
4 Response to Arbitrary，Step，and Pulse Excitations 119
Part A：Response to Arbitrarily Time-Varying Forces 119
4.1 Response to Unit Impulse 120
4.2 Response to Arbitrary Force 121
Part B：Response to Step and Ramp Forces 123
4.3 Step Force 123
4.4 Ramp or Linearly Increasing Force 125
4.5 Step Force with Finite Rise Time 126
Part C：Response to Pulse Excitations 129
4.6 Solution Methods 129
4.7 Rectangular Pulse Force 131
4.8 Half-Cycle Sine Pulse Force 137
4.9 Symmetrical Triangular Pulse Force 142
4.10 Effects of Pulse Shape and Approximate Analysis for Short Pulses 144
4.11 Effects of Viscous Damping 147
4.12 Response to Ground Motion 149
5 Numerical Evaluation of Dynamic Response 155
5.1 Time-Stepping Methods 155
5.2 Methods Based on Interpolation of Excitation 157
5.3 Central Difference Method 161
5.4 Newmark’s Method 164
5.5 Stability and Computational Error 170
5.6 Analysis of Nonlinear Response：Central Difference Method 174
5.7 Analysis of Nonlinear Response：Newmark’s Method 174
6 Earthquake Response of Linear Systems 187
6.1 Earthquake Excitation 187
6.2 Equation of Motion 193
6.3 Response Quantities 194
6.4 Response History 195
6.5 Response Spectrum Concept 197
6.6 Deformation，Pseudo-velocity，and Pseudo-acceleration Response Spectra 198
6.7 Peak Structural Response from the Response Spectrum 206
6.8 Response Spectrum Characteristics 211
6.9 Elastic Design Spectrum 217
6.10 Comparison of Design and Response Spectra 225
6.11 Distinction between Design and Response Spectra 227
6.12 Velocity and Acceleration Response Spectra 228
Appendix 6：El Centro，1940 Ground Motion 232
7 Earthquake Response of Inelastic Systems 241
7.1 Force-Deformation Relations 242
7.2 Normalized Yield Strength，Yield Reduction Factor，and Ductility Factor 248
7.3 Equation of Motion and Controlling Parameters 249
7.4 Effects of Yielding 250
7.5 Response Spectrum for Yield Deformation and Yield Strength 257
7.6 Design Strength and Deformation from the Response Spectrum 261
7.7 Design Yield Strength 261
7.8 Relative Effects of Yielding and Damping 263
7.9 Dissipated Energy 264
7.10 Inelastic Design Spectrum 269
7.11 Comparison of Design and Response Spectra 274
8 Generalized Single-Degree-of-Freedom Systems 277
8.1 Generalized SDF Systems 277
8.2 Rigid-Body Assemblages 279
8.3 Systems with Distributed Mass and Elasticity 281
8.4 Lumped-Mass System：Shear Building 292
8.5 Natural Vibration Frequency by Rayleigh’s Method 298
8.6 Selection of Shape Function 302
Appendix 8：Inertia Forces for Rigid Bodies 306
PART Ⅱ MULTI-DEGREE-OF-FREEDOM SYSTEMS 311
9 Equations of Motion，Problem Statement，and Solution Methods 313
9.1 Simple System：Two-Story Shear Building 313
9.2 General Approach for Linear Systems 318
9.3 Static Condensation 334
9.4 Planar or Symmetric-Plan Systems：Ground Motion 337
9.5 Unsymmetric-Plan Buildings：Ground Motion 342
9.6 Symmetric-Plan Buildings：Torsional Excitation 350
9.7 Multiple Support Excitation 351
9.8 Inelastic Systems 355
9.9 Problem Statement 356
9.10 Element Forces 356
9.11 Methods for Solving the Equations of Motion：Overview 357
10 Free Vibration 365
Part A：Natural Vibration Frequencies and Modes 366
10.1 Systems without Damping 366
10.2 Natural Vibration Frequencies and Modes 368
10.3 Modal and Spectral Matrices 370
10.4 Orthogonality of Modes 371
10.5 Interpretation of Modal Orthogonality 372
10.6 Normalization of Modes 372
10.7 Modal Expansion of Displacements 382
Part B：Free Vibration Response 383
10.8 Solution of Free Vibration Equations：Undamped Systems 383
10.9 Free Vibration of Systems with Damping 386
10.10 Solution of Free Vibration Equations：Classically Damped Systems 390
Part C：Computation of Vibration Properties 392
10.11 Solution Methods for the Eigenvalue Problem 392
10.12 Rayleigh’s Quotient 394
10.13 Inverse Vector Iteration Method 394
10.14 Vector Iteration with Shifts：Preferred Procedure 399
10.15 Transformation of kφ=ω2mφ to the Standard Form 404
11 Damping in Structures 409
Part A：Experimental Data and Recommended Modal Damping Ratios 409
11.1 Vibration Properties of Millikan Library Building 409
11.2 Estimating Modal Damping Ratios 414
Part B：Construction of Damping Matrix 416
11.3 Damping Matrix 416
11.4 Classical Damping Matrix 417
11.5 Nonclassical Damping Matrix 425
12 Dynamic Analysis and Response of Linear Systems 429
Part A：Two-Degree-of-Freedom Systems 429
12.1 Analysis of Two-DOF Systems without Damping 429
12.2 Vibration Absorber or Tuned Mass Damper 432
Part B：Modal Analysis 434
12.3 Modal Equations for Undamped Systems 434
12.4 Modal Equations for Damped Systems 436
12.5 Displacement Response 438
12.6 Element Forces 438
12.7 Modal Analysis：Summary 439
Part C：Modal Response Contributions 444
12.8 Modal Expansion of Excitation Vector p（t） = sp（t） 444
12.9 Modal Analysis for p（t） = sp（t） 447
12.10 Modal Contribution Factors 448
12.11 Modal Contributions to Response 449
Part D：Special Analysis Procedures 455
12.12 Static Correction Method 455
12.13 Mode Acceleration Superposition Method 458
12.14 Analysis of Nonclassically Damped Systems 459
13 Earthquake Analysis of Linear Systems 467
Part A：Response History Analysis 468
13.1 Modal Analysis 468
13.2 Multistory Buildings with Symmetric Plan 474
13.3 Multistory Buildings with Unsymmetric Plan 492
13.4 Torsional Response of Symmetric-Plan Buildings 503
13.5 Response Analysis for Multiple Support Excitation 508
13.6 Structural Idealization and Earthquake Response 513
Part B：Response Spectrum Analysis 514
13.7 Peak Response from Earthquake Response Spectrum 514
13.8 Multistory Buildings with Symmetric Plan 519
13.9 Multistory Buildings with Unsymmetric Plan 532
14 Reduction of Degrees of Freedom 549
14.1 Kinematic Constraints 550
14.2 Static Condensation 551
14.3 Rayleigh-Ritz Method 551
14.4 Selection of Ritz Vectors 554
14.5 Dynamic Analysis Using Ritz Vectors 560
15 Numerical Evaluation of Dynamic Response 565
15.1 Time-Stepping Methods 565
15.2 Analysis of Linear Systems with Nonclassical Damping 567
15.3 Analysis of Nonlinear Systems 574
16 Systems with Distributed Mass and Elasticity 585
16.1 Equation of Undamped Motion：Applied Forces 586
16.2 Equation of Undamped Motion：Support Excitation 587
16.3 Natural Vibration Frequencies and Modes 588
16.4 Modal Orthogonality 595
16.5 Modal Analysis of Forced Dynamic Response 596
16.6 Earthquake Response History Analysis 600
16.7 Earthquake Response Spectrum Andlysis 604
16.8 Difficulty in Analyzing Practical Systems 607
17 Introduction to the Finite Element Method 613
Part A：Rayleigh-Ritz Method 613
17.1 Formulation Using Conservation of Energy 613
17.2 Formulation Using Virtual Work 617
17.3 Disadvantages of Rayleigh-Ritz Method 618
Part B：Finite Element Method 619
17.4 Finite Element Approximation 619
17.5 Analysis Procedure 621
17.6 Element Degrees of Freedom and Interpolation Functions 622
17.7 Element Stiffness Matrix 624
17.8 Element Mass Matrix 625
17.9 Element（Applied） Force Vector 626
17.10 Comparison of Finite Element and Exact Solutions 630
17.11 Dynamic Analysis of Structural Continua 632
PART Ⅲ EARTHQUAKE RESPONSE AND DESIGN OF MULTISTORY BUILDINGS 639
18 Earthquake Response of Linearly Elastic Buildings 641
18.1 Systems Analyzed，Design Spectrum，and Response Quantities 641
18.2 Influence of T1 and p on Response 646
18.3 Modal Contribution Factors 647
18.4 Influence of T1 on Higher-Mode Response 649
18.5 Influence of p on Higher-Mode Response 652
18.6 Heightwise Variation of Higher-Mode Response 653
18.7 How Many Modes to Include 655
19 Earthquake Response of Inelastic Buildings 659
19.1 Allowable Ductility and Ductility Demand 660
19.2 Buildings with “Weak” or “Soft” First Story 665
19.3 Buildings Designed for Code Force Distribution 670
19.4 Limited Scope 680
20 Earthquake Dynamics of Base-Isolated Buildings 683
20.1 Isolation Systems 683
20.2 Base-Isolated One-Story Buildings 686
20.3 Effectiveness of Base Isolation 691
20.4 Base-Isolated Multistory Buildings 695
20.5 Applications of Base Isolation 701
21 Structural Dynamics in Building Codes 703
Part A：Building Codes and Structural Dynamics 704
21.1 Uniform Building Code（United States），1994 704
21.2 National Building Code of Canada，1995 707
21.3 Mexico Federal District Code，1987 711
21.4 Structural Dynamics in Building Codes 713
Part B：Evaluation of Building Codes 720
21.5 Base Shear 720
21.6 Story Shears and Equivalent Static Forces 723
21.7 Overturning Moments 726
21.8 Concluding Remarks 728
A Notation 731
B Answers to Selected Problems 743
Index 753