Contents Foreword xxi Preface xxiii Preface to the Second Edition xxv Preface to the First Edition xxvii Acknowledgments xxxiii 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 12 1.5 Equation of Motion: External Force 14 1.6 Mass--Spring--Damper System 19 1.7 Equation of Motion: Earthquake Excitation 23 1.

8 Problem Statement and Element Forces 26 1.9 Combining Static and Dynamic Responses 28 1.10 Methods of Solution of the Differential Equation 28 1.11 Study of SDF Systems: Organization 33 Appendix 1 : Stiffness Coefficients for a Flexural Element 33 2 Free Vibration 39 2.1 Undamped Free Vibration 39 2.2 Viscously Damped Free Vibration 48 2.3 Energy in Free Vibration 56 2.4 Coulomb-Damped Free Vibration 57 3 Response to Harmonic and Periodic Excitations 65 Part A: Viscously Damped Systems: Basic Results 66 3.

1 Harmonic Vibration of Undamped Systems 66 3.2 Harmonic Vibration with Viscous Damping 72 Part B: Viscously Damped Systems: Applications 85 3.3 Response to Vibration Generator 85 3.4 Natural Frequency and Damping from Harmonic Tests 87 3.5 Force Transmission and Vibration Isolation 90 3.6 Response to Ground Motion and Vibration Isolation 91 3.7 Vibration-Measuring Instruments 95 3.8 Energy Dissipated in Viscous Damping 99 3.

9 Equivalent Viscous Damping 103 Part C: Systems with Nonviscous Damping 105 3.10 Harmonic Vibration with Rate-Independent Damping 105 3.11 Harmonic Vibration with Coulomb Friction 109 Part D: Response to Periodic Excitation 113 3.12 Fourier Series Representation 114 3.13 Response to Periodic Force 114 Appendix 3 : Four-Way Logarithmic Graph Paper 118 4 Response to Arbitrary, Step, and Pulse Excitations 125 Part A: Response to Arbitrarily Time-Varying Forces 125 4.1 Response to Unit Impulse 126 4.2 Response to Arbitrary Force 127 Part B: Response to Step and Ramp Forces 129 4.3 Step Force 129 4.

4 Ramp or Linearly Increasing Force 131 4.5 Step Force with Finite Rise Time 132 Part C: Response to Pulse Excitations 135 4.6 Solution Methods 135 4.7 Rectangular Pulse Force 137 4.8 Half-Cycle Sine Pulse Force 143 4.9 Symmetrical Triangular Pulse Force 148 4.10 Effects of Pulse Shape and Approximate Analysis for Short Pulses 151 4.11 Effects of Viscous Damping 154 4.

12 Response to Ground Motion 155 5 Numerical Evaluation of Dynamic Response 165 5.1 Time-Stepping Methods 165 5.2 Methods Based on Interpolation of Excitation 167 5.3 Central Difference Method 171 5.4 Newmark''s Method 174 5.5 Stability and Computational Error 180 5.6 Analysis of Nonlinear Response: Central Difference Method 184 5.7 Analysis of Nonlinear Response: Newmark''s Method 184 6 Earthquake Response of Linear Systems 197 6.

1 Earthquake Excitation 197 6.2 Equation of Motion 203 6.3 Response Quantities 204 6.4 Response History 205 6.5 Response Spectrum Concept 207 6.6 Deformation, Pseudo-velocity, and Pseudo-acceleration Response Spectra 208 6.7 Peak Structural Response from the Response Spectrum 217 6.8 Response Spectrum Characteristics 222 6.

9 Elastic Design Spectrum 230 6.10 Comparison of Design and Response Spectra 239 6.11 Distinction between Design and Response Spectra 241 6.12 Velocity and Acceleration Response Spectra 242 Appendix 6 : ElCentro, 1940 Ground Motion 246 7 Earthquake Response of Inelastic Systems 257 7.1 Force--Deformation Relations 258 7.2 Normalized Yield Strength, Yield Strength Reduction Factor, and Ductility Factor 264 7.3 Equation of Motion and Controlling Parameters 265 7.4 Effects of Yielding 266 7.

5 Response Spectrum for Yield Deformation and Yield Strength 273 7.6 Yield Strength and Deformation from the Response Spectrum 277 7.7 Yield Strength--Ductility Relation 277 7.8 Relative Effects of Yielding and Damping 279 7.9 Dissipated Energy 280 7.10 Energy Dissipation Devices 283 7.11 Inelastic Design Spectrum 288 7.12 Applications of the Design Spectrum 295 7.

13 Comparison of Design and Response Spectra 301 8 Generalized Single-Degree-of-Freedom Systems 305 8.1 Generalized SDF Systems 305 8.2 Rigid-Body Assemblages 307 8.3 Systems with Distributed Mass and Elasticity 309 8.4 Lumped-Mass System: Shear Building 321 8.5 Natural Vibration Frequency by Rayleigh''s Method 328 8.6 Selection of Shape Function 332 Appendix 8 : Inertia Forces for Rigid Bodies 336 PART II MULTI-DEGREE-OF-FREEDOM SYSTEMS 343 9 Equations of Motion, Problem Statement, and Solution Methods 345 9.1 Simple System: Two-Story Shear Building 345 9.

2 General Approach for Linear Systems 350 9.3 Static Condensation 367 9.4 Planar or Symmetric-Plan Systems: Ground Motion 370 9.5 Unsymmetric-Plan Buildings: Ground Motion 375 9.6 Symmetric-Plan Buildings: Torsional Excitation 383 9.7 Multiple Support Excitation 384 9.8 Inelastic Systems 389 9.9 Problem Statement 389 9.

10 Element Forces 390 9.11 Methods for Solving the Equations of Motion: Overview 390 10 Free Vibration 401 Part A: Natural Vibration Frequencies and Modes 402 10.1 Systems without Damping 402 10.2 Natural Vibration Frequencies and Modes 404 10.3 Modal and Spectral Matrices 406 10.4 Orthogonality of Modes 407 10.5 Interpretation of Modal Orthogonality 408