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Standard Methods for Seismic Analyses
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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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