DYNAMICS OF STRUCTURES
CONTENTS PART I SINGLE-DEGREE-OF-FREEDOM SYSTEMS EQUATIONS OF MOTION, PROBLEM STATEMENT, AND SOLUTION METHODS SIMPLE STRUCTURES SINGLE-DEGREE-OF-FREEDOM SYSTEM FORCE–DISPLACEMENT RELATION DAMPING FORCE EQUATION OF MOTION: EXTERNAL FORCE MASS–SPRING–DAMPER SYSTEM EQUATION OF MOTION: EARTHQUAKE EXCITATION PROBLEM STATEMENT AND ELEMENT FORCES COMBINING STATIC AND DYNAMIC RESPONSES METHODS OF SOLUTION OF THE DIFFERENTIAL EQUATION STUDY OF SDF SYSTEMS: ORGANIZATION APPENDIX 1: STIFFNESS COEF?CIENTS FOR A FLEXURAL ELEMENT FREE VIBRATION UNDAMPED FREE VIBRATION VISCOUSLY DAMPED FREE VIBRATION ENERGY IN FREE VIBRATION COULOMB-DAMPED FREE VIBRATION RESPONSE TO HARMONIC AND PERIODIC EXCITATIONS PART A: VISCOUSLY DAMPED SYSTEMS: BASIC RESULTS HARMONIC VIBRATION OF UNDAMPED SYSTEMS HARMONIC VIBRATION WITH VISCOUS DAMPING PART B: VISCOUSLY DAMPED SYSTEMS: APPLICATIONS RESPONSE TO VIBRATION GENERATOR NATURAL FREQUENCY AND DAMPING FROM HARMONIC TESTS FORCE TRANSMISSION AND VIBRATION ISOLATION RESPONSE TO GROUND MOTION AND VIBRATION ISOLATION VIBRATION-MEASURING INSTRUMENTS ENERGY DISSIPATED IN VISCOUS DAMPING EQUIVALENT VISCOUS DAMPING PART C: SYSTEMS WITH NONVISCOUS DAMPING HARMONIC VIBRATION WITH RATE-INDEPENDENT DAMPING HARMONIC VIBRATION WITH COULOMB FRICTION PART D: RESPONSE TO PERIODIC EXCITATION FOURIER SERIES REPRESENTATION RESPONSE TO PERIODIC FORCE APPENDIX 3: FOUR-WAY LOGARITHMIC GRAPH PAPER RESPONSE TO ARBITRARY, STEP, AND PULSE EXCITATIONS PART A: RESPONSE TO ARBITRARILY TIME-VARYING FORCES RESPONSE TO UNIT IMPULSE RESPONSE TO ARBITRARY FORCE PART B: RESPONSE TO STEP AND RAMP FORCES STEP FORCE RAMP OR LINEARLY INCREASING FORCE STEP FORCE WITH FINITE RISE TIME PART C: RESPONSE TO PULSE EXCITATIONS SOLUTION METHODS RECTANGULAR PULSE FORCE HALF-CYCLE SINE PULSE FORCE SYMMETRICAL TRIANGULAR PULSE FORCE EFFECTS OF PULSE SHAPE AND APPROXIMATE ANALYSIS FOR SHORT PULSES EFFECTS OF VISCOUS DAMPING RESPONSE TO GROUND MOTION NUMERICAL EVALUATION OF DYNAMIC RESPONSE TIME-STEPPING METHODS METHODS BASED ON INTERPOLATION OF EXCITATION CENTRAL DIFFERENCE METHOD NEWMARK’S METHOD STABILITY AND COMPUTATIONAL ERROR NONLINEAR SYSTEMS: CENTRAL DIFFERENCE METHOD NONLINEAR SYSTEMS: NEWMARK’S METHOD EARTHQUAKE RESPONSE OF LINEAR SYSTEMS EARTHQUAKE EXCITATION EQUATION OF MOTION RESPONSE QUANTITIES RESPONSE HISTORY RESPONSE SPECTRUM CONCEPT DEFORMATION, PSEUDO-VELOCITY, AND PSEUDO-ACCELERATION RESPONSE SPECTRA PEAK STRUCTURAL RESPONSE FROM THE RESPONSE SPECTRUM RESPONSE SPECTRUM CHARACTERISTICS ELASTIC DESIGN SPECTRUM COMPARISON OF DESIGN AND RESPONSE SPECTRA DISTINCTION BETWEEN DESIGN AND RESPONSE SPECTRA VELOCITY AND ACCELERATION RESPONSE SPECTRA APPENDIX 6: EL CENTRO, 1940 GROUND MOTION EARTHQUAKE RESPONSE OF INELASTIC SYSTEMS FORCE–DEFORMATION RELATIONS NORMALIZED YIELD STRENGTH, YIELD STRENGTH REDUCTION FACTOR, AND DUCTILITY FACTOR EQUATION OF MOTION AND CONTROLLING PARAMETERS EFFECTS OF YIELDING RESPONSE SPECTRUM FOR YIELD DEFORMATION AND YIELD STRENGTH YIELD STRENGTH AND DEFORMATION FROM THE RESPONSE SPECTRUM YIELD STRENGTH–DUCTILITY RELATION RELATIVE EFFECTS OF YIELDING AND DAMPING DISSIPATED ENERGY SUPPLEMENTAL ENERGY DISSIPATION DEVICES INELASTIC DESIGN SPECTRUM APPLICATIONS OF THE DESIGN SPECTRUM GENERALIZED SINGLE-DEGREE-OF-FREEDOM SYSTEMS GENERALIZED SDF SYSTEMS RIGID-BODY ASSEMBLAGES SYSTEMS WITH DISTRIBUTED MASS AND ELASTICITY LUMPED-MASS SYSTEM: SHEAR BUILDING NATURAL VIBRATION FREQUENCY BY RAYLEIGH’S METHOD SELECTION OF SHAPE FUNCTION APPENDIX 8: INERTIA FORCES FOR RIGID BODIES PART II MULTI-DEGREE-OF-FREEDOM SYSTEMS SIMPLE SYSTEM: TWO-STORY SHEAR BUILDING GENERAL APPROACH FOR LINEAR SYSTEMS STATIC CONDENSATION PLANAR OR SYMMETRIC-PLAN SYSTEMS: GROUND MOTION ONE-STORY UNSYMMETRIC-PLAN BUILDINGS MULTISTORY UNSYMMETRIC-PLAN BUILDINGS MULTIPLE SUPPORT EXCITATION INELASTIC SYSTEMS PROBLEM STATEMENT ELEMENT FORCES METHODS FOR SOLVING THE EQUATIONS OF MOTION: OVERVIEW PART A: NATURAL VIBRATION FREQUENCIES AND MODES SYSTEMS WITHOUT DAMPING NATURAL VIBRATION FREQUENCIES AND MODES MODAL AND SPECTRAL MATRICES ORTHOGONALITY OF MODES INTERPRETATION OF MODAL ORTHOGONALITY NORMALIZATION OF MODES MODAL EXPANSION OF DISPLACEMENTS PART B: FREE VIBRATION RESPONSE SOLUTION OF FREE VIBRATION EQUATIONS: UNDAMPED SYSTEMS SYSTEMS WITH DAMPING SOLUTION OF FREE VIBRATION EQUATIONS: CLASSICALLY DAMPED SYSTEMS PART C: COMPUTATION OF VIBRATION PROPERTIES SOLUTION METHODS FOR THE EIGENVALUE PROBLEM RAYLEIGH’S QUOTIENT INVERSE VECTOR ITERATION METHOD VECTOR ITERATION WITH SHIFTS: PREFERRED PROCEDURE TRANSFORMATION OF K? = ?2M? TO THE STANDARD FORM DAMPING IN STRUCTURES PART A: EXPERIMENTAL DATA AND RECOMMENDED MODAL DAMPING RATIOS VIBRATION PROPERTIES OF MILLIKAN LIBRARY BUILDING ESTIMATING MODAL DAMPING RATIOS PART B: CONSTRUCTION OF DAMPING MATRIX DAMPING MATRIX CLASSICAL DAMPING MATRIX NONCLASSICAL DAMPING MATRIX DYNAMIC ANALYSIS AND RESPONSE OF LINEAR SYSTEMS PART A: TWO-DEGREE-OF-FREEDOM SYSTEMS ANALYSIS OF TWO-DOF SYSTEMS WITHOUT DAMPING VIBRATION ABSORBER OR TUNED MASS DAMPER PART B: MODAL ANALYSIS MODAL EQUATIONS FOR UNDAMPED SYSTEMS MODAL EQUATIONS FOR DAMPED SYSTEMS DISPLACEMENT RESPONSE MODAL ANALYSIS: SUMMARY PART C: MODAL RESPONSE CONTRIBUTIONS MODAL EXPANSION OF EXCITATION VECTOR P(T) = SP(T) MODAL ANALYSIS FOR P(T) = SP(T) MODAL CONTRIBUTION FACTORS MODAL RESPONSES AND REQUIRED NUMBER OF MODES PART D: SPECIAL ANALYSIS PROCEDURES STATIC CORRECTION METHOD MODE ACCELERATION SUPERPOSITION METHOD MODE ACCELERATION SUPERPOSITION METHOD: ARBITRARY EXCITATION EARTHQUAKE ANALYSIS OF LINEAR SYSTEMS PART A: RESPONSE HISTORY ANALYSIS MODAL ANALYSIS MULTISTORY BUILDINGS WITH SYMMETRIC PLAN MULTISTORY BUILDINGS WITH UNSYMMETRIC PLAN TORSIONAL RESPONSE OF SYMMETRIC-PLAN BUILDINGS RESPONSE ANALYSIS FOR MULTIPLE SUPPORT EXCITATION STRUCTURAL IDEALIZATION AND EARTHQUAKE RESPONSE PART B: RESPONSE SPECTRUM ANALYSIS PEAK RESPONSE FROM EARTHQUAKE RESPONSE SPECTRUM A RESPONSE-SPECTRUM-BASED ENVELOPE FOR SIMULTANEOUS RESPONSES RESPONSE TO MULTICOMPONENT GROUND MOTION ANALYSIS OF NONCLASSICALLY DAMPED LINEAR SYSTEMS PART A: CLASSICALLY DAMPED SYSTEMS: REFORMULATION UNIT IMPULSE RESPONSE EARTHQUAKE RESPONSE PART B: NONCLASSICALLY DAMPED SYSTEMS SYSTEMS WITH REAL-VALUED EIGENVALUES RESPONSE SPECTRUM ANALYSIS SUMMARY APPENDIX 14: DERIVATIONS REDUCTION OF DEGREES OF FREEDOM KINEMATIC CONSTRAINTS MASS LUMPING IN SELECTED DOFS RAYLEIGH–RITZ METHOD SELECTION OF RITZ VECTORS DYNAMIC ANALYSIS USING RITZ VECTORS LINEAR SYSTEMS WITH NONCLASSICAL DAMPING NONLINEAR SYSTEMS EQUATION OF UNDAMPED MOTION: APPLIED FORCES EQUATION OF UNDAMPED MOTION: SUPPORT EXCITATION MODAL ORTHOGONALITY MODAL ANALYSIS OF FORCED DYNAMIC RESPONSE EARTHQUAKE RESPONSE HISTORY ANALYSIS EARTHQUAKE RESPONSE SPECTRUM ANALYSIS DIF?CULTY IN ANALYZING PRACTICAL SYSTEMS INTRODUCTION TO THE FINITE ELEMENT METHOD PART A: RAYLEIGH–RITZ METHOD FORMULATION USING CONSERVATION OF ENERGY FORMULATION USING VIRTUAL WORK DISADVANTAGES OF RAYLEIGH–RITZ METHOD PART B: FINITE ELEMENT METHOD FINITE ELEMENT APPROXIMATION ANALYSIS PROCEDURE ELEMENT DEGREES OF FREEDOM AND INTERPOLATION FUNCTIONS ELEMENT STIFFNESS MATRIX ELEMENT MASS MATRIX ELEMENT (APPLIED) FORCE VECTOR COMPARISON OF FINITE ELEMENT AND EXACT SOLUTIONS DYNAMIC ANALYSIS OF STRUCTURAL CONTINUA PART III EARTHQUAKE RESPONSE, DESIGN, AND EVALUATION OF MULTISTORY BUILDINGS EARTHQUAKE RESPONSE OF LINEARLY ELASTIC BUILDINGS SYSTEMS ANALYZED, DESIGN SPECTRUM, AND RESPONSE QUANTITIES IN?UENCE OF T1 AND ? ON RESPONSE IN?UENCE OF T1 ON HIGHER-MODE RESPONSE IN?UENCE OF ? ON HIGHER-MODE RESPONSE HEIGHTWISE VARIATION OF HIGHER-MODE RESPONSE HOW MANY MODES TO INCLUDE EARTHQUAKE ANALYSIS AND RESPONSE OF INELASTIC BUILDINGS PART A: NONLINEAR RESPONSE HISTORY ANALYSIS EQUATIONS OF MOTION: FORMULATION AND SOLUTION COMPUTING SEISMIC DEMANDS: FACTORS TO BE CONSIDERED STORY DRIFT DEMANDS STRENGTH DEMANDS FOR SDF AND MDF SYSTEMS PART B: APPROXIMATE ANALYSIS PROCEDURES MOTIVATION AND BASIC CONCEPT UNCOUPLED MODAL RESPONSE HISTORY ANALYSIS MODAL PUSHOVER ANALYSIS EVALUATION OF MODAL PUSHOVER ANALYSIS SIMPLI?ED MODAL PUSHOVER ANALYSIS FOR PRACTICAL APPLICATION EARTHQUAKE DYNAMICS OF BASE-ISOLATED BUILDINGS ISOLATION SYSTEMS BASE-ISOLATED ONE-STORY BUILDINGS EFFECTIVENESS OF BASE ISOLATION BASE-ISOLATED MULTISTORY BUILDINGS APPLICATIONS OF BASE ISOLATION STRUCTURAL DYNAMICS IN BUILDING CODES PART A: BUILDING CODES AND STRUCTURAL DYNAMICS INTERNATIONAL BUILDING CODE (UNITED STATES), NATIONAL BUILDING CODE OF CANADA, MEXICO FEDERAL DISTRICT CODE, EUROCODE 8, PART B: EVALUATION OF BUILDING CODES BASE SHEAR STORY SHEARS AND EQUIVALENT STATIC FORCES OVERTURNING MOMENTS CONCLUDING REMARKS STRUCTURAL DYNAMICS IN BUILDING EVALUATION GUIDELINES NONLINEAR DYNAMIC PROCEDURE: CURRENT PRACTICE SDF-SYSTEM ESTIMATE OF ROOF DISPLACEMENT ESTIMATING DEFORMATION OF INELASTIC SDF SYSTEMS NONLINEAR STATIC PROCEDURES