Basic Structural Dynamics

James C. Anderson is Professor of Civil Engineering at USC and is the author of, and contributor to, numerous book and journal articles.Farzad Naeim is Vice President and General Counsel at John A. Martin & Associates, Inc., a consulting structural engineering firm headquartered in Los Angeles, California. He has received numerous awards for his contributions to earthquake engineering, including the 2007 Fazlur R. Khan Lifetime Achievement Medal by the Council on Tall Buildings and Urban Habitat.

• PREFACE xi1 BASIC CONCEPTS OF STRUCTURAL DYNAMICS 11.1 The Dynamic Environment 11.2 Types of Dynamic Loading 21.3 Basic Principles 31.4 Dynamic Equilibrium 92 SINGLE-DEGREE-OF-FREEDOM SYSTEMS 132.1 Reduction of Degrees of Freedom 132.2 Time-Dependent Force 152.3 Gravitational Forces 172.4 Earthquake Ground Motion 182.5 Formulation of Equation of Motion 192.5.1 d’Alembert’s Principle 192.5.2 Virtual Work (Virtual Displacements) 202.6 Generalized Coordinates 222.6.1 Discrete Parameters 232.6.2 Continuous Parameters 312.6.3 Transformation Factors 382.6.4 Axial Load Effect 422.6.5 Linear Approximation 443 FREE-VIBRATION RESPONSE OF SINGLE-DEGREE-OF-FREEDOM SYSTEMS 513.1 Undamped Free Vibration 513.1.1 Alternate Solution 533.1.2 Rayleigh’s Method 583.1.3 Selection of Deflected Shape 603.2 Damped Free Vibration 613.2.1 Rotating Vector Form 633.2.2 Logarithmic Decrement 663.2.3 Radical Positive 674 RESPONSE TO HARMONIC LOADING 774.1 Undamped Dynamic System 774.2 Damped Dynamic System 844.3 Tripartite Logarithmic Plot 914.4 Evaluation of Damping 914.5 Seismic Accelerometers and Displacement Meters (Seismographs) 955 RESPONSE TO IMPULSE LOADS 1015.1 Rectangular Pulse 1045.2 Damped Rectangular Pulse 1085.3 Triangular Pulse 1095.4 Approximate Analysis for Short-Duration Impulse Load 1126 RESPONSE TO ARBITRARY DYNAMIC LOADING 1216.1 Duhamel Integral 1216.2 Numerical Formulation of the Equation of Motion 1236.3 Numerical Integration Methods 1246.4 Newmark’s Numerical Method 1277 MULTIPLE-DEGREE-OF-FREEDOM SYSTEMS 1377.1 Elastic Properties 1377.1.1 Flexibility 1377.1.2 Stiffness 1387.1.3 Inertia 1397.1.4 Viscous Damping 1397.2 Undamped Free Vibration 1417.3 Free Vibration 1497.4 Betti’s Law 1537.5 Orthogonality Properties of Mode Shapes 1557.6 Changing Coordinates (Inverse Transformation) 1567.7 Holzer Method for Shear Buildings 1597.8 Axial Load Effects (Linear Approximation) 1627.9 Modal Equations for Undamped Time-Dependent Force Analysis 1657.10 Modal Equations of Damped Forced Vibration 1747.11 Modal Equations for Seismic Response Analysis 1798 NONLINEAR RESPONSE OF MULTIPLE-DEGREE-OF-FREEDOM SYSTEMS 1838.1 Static Nonlinear Analysis 1848.2 Dynamic Nonlinear Analysis 1858.3 Gauss Reduction 1898.4 MATLAB Applications 1909 SEISMIC RESPONSE OF STRUCTURES 2019.1 Introduction 2019.2 Linear Elastic Response Spectra 2039.3 Elastic Design Response Spectrum 2089.4 Earthquake Response of SDOF Systems 2159.5 Earthquake Response Analysis of MDOF Systems 2199.5.1 Time History Modal Analysis 2219.5.2 Modal Combinations for Spectral Analyses 2229.6 Structural Dynamics in the Building Code 2329.6.1 Equivalent Lateral Force Procedure 2349.6.2 Modal Response Spectrum Procedure 237APPENDIX—HISTORICAL DEVELOPMENT OF BUILDING CODE SEISMIC PROVISIONS 249SELECTED REFERENCES 263INDEX 265