PACIFIC EARTHQUAKE ENGINEERING RESEARCH CENTER Stochastic Dynamic Analysis of Bridges Subjected to Spatially Varying Ground Motions

................................................................................................................................. iii ACKNOWLEDGMENTS ............................................................................................................ v TABLE OF CONTENTS ........................................................................................................... vii LIST OF FIGURES ................................................................................................................... xiii LIST OF TABLES ..................................................................................................................... xxi 1 INTRODUCTION .................................................................................................................1 1.1 MOTIVATION AND BACKGROUND ........................................................................1 1.2 OBJECTIVES AND SCOPE ..........................................................................................5 1.2.1 Development of Analysis Tools ...........................................................................5 1.2.1.1 Response Spectrum Approach ............................................................. 5 1.2.2 Synthetic Motions for RHA .................................................................................6 1.2.3 Parametric Analyses of Real Bridge Models .......................................................6 1.2.4 Investigation of Coherency Models .....................................................................7 1.3 ORGANIZATION OF THE REPORT ...........................................................................7 2 GENERALIZED AND EXTENDED MSRS RULE ........................................................11 2.1 INTRODUCTION ........................................................................................................11 2.2 GENERALIZED FORMULATION OF THE MSRS RULE .......................................12 2.2.1 Equations of Motion ...........................................................................................12 2.2.2 The MSRS Rule .................................................................................................15 2.2.3 The Coherency Function ....................................................................................17 2.2.4 Modeling of the Site Response ...........................................................................19 2.3 MODE TRUNCATION CRITERIA FOR RESPONSE TO DIFFERENTIAL SUPPORT MOTIONS ..................................................................................................21 2.4 EXTENDED MSRS RULE ..........................................................................................22 2.5 PARAMETRIC ANALYSIS OF THE NEW CROSS-CORRELATION COEFFICIENTS ...........................................................................................................25 2.5.1 Cross-correlation Coefficient between Ground Accelerations at Stations k and l .................................................................................................................26 2.5.2 Cross-correlation Coefficient between Ground Displacement at Station k and Ground acceleration at Station l ...............................................................27