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[资源] Standard Methods for Seismic Analyses

João Luís Domingues Costa
Standard Methods for Seismic
Analyses
Report
BYG·DTU R-064
2003
ISSN 1601-2917
ISBN 87-7877-126
Contents
ACKNOWLEDGEMENTS...........................................................................................3
1. INTRODUCTION.....................................................................................................5
2. STRUCTURAL DYNAMICS FUNDAMENTALS.....................................................7
2.1 FORMULATION OF EQUATION OF MOTION FOR SDOF SYSTEMS ...........................7
2.2 UNDAMPED FREE VIBRATIONS...........................................................................8
2.3 DAMPED FREE VIBRATIONS................................................................................9
2.4 RESONANT RESPONSE....................................................................................11
2.5 BASE MOTION FOR SDOF SYSTEMS................................................................14
2.6 FORMULATION OF THE EQUATION OF MOTION FOR MDOF SYSTEMS...................15
2.7 FREQUENCY AND VIBRATION MODE SHAPE ANALYSIS .......................................17
2.8 ORTHOGONALITY CONDITIONS.........................................................................19
Orthogonality with respect to the mass matrix .....................................19
Orthogonality with respect to the stiffness matrix.................................19
2.9 MODAL COORDINATES ....................................................................................20
2.10 EQUATION OF MOTION IN MODAL COORDINATES...............................................21
2.11 BASE MOTION FOR MDOF SYSTEMS ...............................................................23
2.12 VIBRATION ANALYSIS BY THE RAYLEIGH METHOD..............................................26
Basic concepts.....................................................................................26
Approximate analysis of a general system; Selection of the vibration
shape ...................................................................................................26
3. SEISMIC ANALYSIS BY RESPONSE SPECTRA................................................31
3.1 RESPONSE SPECTRUM CONCEPT ....................................................................31
3.2 RESPONSE SPECTRUM ANALYSIS APPLIED TO MDOF SYSTEMS ........................33
1) SRSS (Square Root of Sum of Squares)......................................34
2) CQC (Complete Quadratic Combination)......................................35
3.3 DUCTILE BEHAVIOUR CONSIDERATION .............................................................35
4. SEISMIC RESPONSE BY TIME-HISTORY ANALYSIS .......................................39
4.1 RESPONSE OF A SDOF SYSTEM TO GENERAL DYNAMIC LOADING; DUHAMEL’S
INTEGRAL ......................................................................................................39
4.2 LINEAR TIME HISTORY ANALYSIS FOR MDOF SYSTEMS ....................................41
4.3 TIME HISTORY ANALYSIS FOR EARTHQUAKES ...................................................42
Step-by-step integration method with linear variation of the load.........43

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