TABLE OF CONTENTS SECTION TITLE PAGE 2 PRINCIPLES OF SEISMIC ISOLATION OF BRIDGES 3

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1 TABLE OF CONTENTS SECTION TITLE PAGE 1 INTRODUCTION 1 2 PRINCIPLES OF SEISMIC ISOLATION OF BRIDGES 3 3 ANALYSIS METHODS OF SEISMICALLY ISOLATED BRIDGES Introduction Loadings for the Analysis and Design of Seismically Isolated Bridges Modification of Response Spectrum for Higher Damping Maximum Velocity and Maximum Force in Isolation Systems with Viscous Damping Devices Re-centering Capability Response Modification Factor Single Mode Method of Analysis Multimode Method of Analysis Response History Analysis Method Use of Methods of Analysis 22 4 MECHANICAL PROPERTIES OF ISOLATORS Introduction Nominal Properties of Lead-Rubber Bearings Upper and Lower Bound Properties of Lead-Rubber Bearings Basic Behavior of Single and Double Friction Pendulum Bearings Basic Behavior of Triple Friction Pendulum Bearings Nominal Properties of Friction Pendulum Bearings Upper and Lower Bound Properties of FP Bearings Example 37 5 ELASTOMERIC SEISMIC ISOLATION BEARING ADEQUACY ASSESSMENT Introduction Calculation of Shear Strains Calculation of Buckling Loads Calculation of Critical Displacements Stresses in Reinforcing Shim Plates 52 ix

2 TABLE OF CONTENTS (CONT D) SECTION TITLE PAGE 5.6 Assessment of Adequacy of Elastomeric Seismic Isolation Bearings Introduction Adequacy Criteria Example of Elastomeric Bearing Adequacy Assessment Assessment of Adequacy of End Plates of Elastomeric Bearings Introduction Reduced Area Procedure Load-Moment Procedure Example 73 6 ELASTOMERIC BRIDGE BEARING ADEQUACY ASSESSMENT Introduction Assessment of Adequacy of Steel Reinforced Elastomeric Bridge Bearings Example Example Example Example SOME ASPECTS OF BEHAVIOR OF PTFE SPHERICAL BEARINGS Introduction Types of PTFE Spherical Bearings Design Considerations for Spherical Bearings Lateral Load Resistance Resistance to Rotation Eccentricity due to Rotation at the Spherical Surface PROCEDURE FOR DESIGN OF END PLATES OF SLIDING BEARINGS Transfer of Force in Sliding Bearings Procedure for Design of End Plates of Sliding Bearings Example of Assessment of Adequacy of End Plate under Service Load Conditions Example of Assessment of Adequacy of End Plate under Seismic Conditions Example of Assessment of Adequacy of End Plate Using Load-Moment Procedure 127 x

3 TABLE OF CONTENTS (CONT D) SECTION TITLE PAGE 8.6 Plastic Analysis of End Plates Stiffness Considerations in the Design of End Plates of Sliding Bearings Summary and Recommendations PROCEDURE FOR DESIGN OF PTFE SPHERICAL BEARINGS Introduction Materials Used in PTFE Spherical Bearings and Limits of Pressure on PTFE Coefficient of Friction PTFE Spherical Bearing Design Procedure Example DESCRIPTION OF EXAMPLE BRIDGE Introduction Description of the Bridge Analysis of Bridge for Dead, Live, Brake and Wind Loadings Seismic Loading DESIGN AND ANALYSIS OF TRIPLE FRICTION PENDULUM ISOLATION SYSTEM FOR EXAMPLE BRIDGE Single Mode Analysis Multimode Response Spectrum Analysis Dynamic Response History Analysis DESIGN AND ANALYSIS OF LEAD-RUBBER ISOLATION SYSTEM FOR EXAMPLE BRIDGE Single Mode Analysis Multimode Response Spectrum Analysis Dynamic Response History Analysis DESIGN AND ANALYSIS OF SINGLE FRICTION PENDULUM ISOLATION SYSTEM FOR EXAMPLE BRIDGE Single Mode Analysis Multimode Response Spectrum Analysis Dynamic Response History Analysis 201 xi

4 TABLE OF CONTENTS (CONT D) SECTION TITLE PAGE 14 SUMMARY AND CONCLUSIONS REFERENCES 205 APPENDICES A B C D E (Provided on attached CD) DEVELOPMENT AND VERIFICATION OF SIMPLIFIED EXPRESSIONS FOR SHEAR STRAIN IN RUBBER LAYERS FOR USE IS DESIGN OF ELASTOMERIC BEARINGS A-1 SERVICE LOADS, DISPLACEMENTS AND ROTATIONS FOR BEARINGS THREE-SPAN BRIDGE WITH SKEW B-1 TRIPLE FRICTION PENDULUM SYSTEM CALCULATIONS THREE-SPAN BRIDGE WITH SKEW C-1 LEAD-RUBBER SYSTEM CALCULATIONS THREE- SPAN BRIDGE WITH SKEW D-1 SINGLE FRICTION PENDULUM SYSTEM CALCULATIONS THREE-SPAN BRIDGE WITH SKEW E-1 xii

5 LIST OF ILLUSTRATIONS FIGURE TITLE PAGE 2-1 Principles of Seismic Isolation Hysteretic Damping in LR and FP Bearings Idealized Force-Displacement Relation of Typical Seismic Isolation System Structural Response of a Yielding System Seismically Isolated Bridge with a Flexible Substructure and its Deformation under Lateral Force Response Spectrum for Multimode Analysis of a Seismically Isolated Bridge Internal Construction of a Lead-Rubber Bearing (Courtesy of DIS) Cross Sections of Single and Double Friction Pendulum Bearings and Definition of Dimensional and Frictional Properties Cross Section of Triple Friction Pendulum Bearing and Definition of Dimensional and Frictional Properties Force-Displacement Loops of Triple FP Bearing Force-Displacement Loop of Special Triple FP Isolator Internal Construction of Elastomeric Bearing Shapes and Dimensions of Single Rubber Layers Locations of Maximum Shear Strain in Bonded Rubber Layers Characteristics of Dowelled and Bolted Elastomeric Bearings Overturning of Dowelled Bearing and Lateral Force- Displacement Relationships Tractions Acting on Circular Shim and Resulting Stresses Example Lead-Rubber Bearing Deformed Bearing and Forces Acting on End Plates End Plate Design Using Reduced Area Procedure Free Body Diagram of End Plate without Bolt Tension Free Body Diagram of End Plate with Bolt Tension Simplified Procedure for Checking a Mounting Plate Bearing for End Plate Adequacy Assessment Example Bridge Elastomeric Bearing Internal Construction and Connection Details (adapted from Konstantinidis et al, 2008) 79 xiii

6 LIST OF ILLUSTRATIONS (CONT D) FIGURE TITLE PAGE 7-1 Fixed Spherical Bearing (Caltrans, 1994) Multidirectional PTFE Sliding Spherical Bearing (Caltrans, 1994) Definition of Geometric Parameters of Spherical Bearings Lateral Load Resistance of a Spherical Bearing without Bearing Rotation Lateral Load Resistance of a Spherical Bearing with Bearing Rotation Spherical Coordinate System for Moment Calculation Moment Resistance of Spherical Bearing for Varying Bearing Subtended Semi-angle Moment Resistance of Spherical Bearings with or without a Flat Sliding Surface Free Body Diagram of Spherical Bearing under Vertical Load and Rotation Free Body Diagram of Concave Plate Showing Eccentricity Friction Pendulum Bearing and the Procedure for End Plate Design Transfer of Force in Flat Spherical Bearing with Stainless Steel Surface Facing Down Transfer of Force in Flat Spherical Bearing with Stainless Steel Surface Facing Up Transfer of Force in Double or Triple Friction Pendulum Bearing Comparison of Moment in End Plate Calculated by the Exact Solution and by the Simplified Theory and Correction Factor for ν= End Plate Adequacy Assessment in Deformed Position Using Centrally Loaded Area Procedure End Plate Adequacy Assessment Using Load-Moment Procedure End Plate Adequacy Assessment Using Load-Moment Procedure for Higher Load Loaded End Plate Polygon-Shaped Plate Yielding Yield Line Analysis of Hollow Circular Plate Comparison of Yield Line Solution and Exact Solution for Plate Plastic Collapse 134 xiv

7 LIST OF ILLUSTRATIONS (CONT D) FIGURE TITLE PAGE 8-13 Prediction of Ultimate Moment by Elastic and Plastic Solutions Basic Dimensional Properties of Concave Plate Definition of Dimensional Quantities DB act, R, Y and M m Definition of Dimensional Quantities T min, T max, L cp, H, H act, D m, γ and C m Definition of Dimensional Quantity c Typical Detail of Bearing Anchorage with Shear Lug Projected Area A Vc of Failure Surface on Side of Concrete Pedestal Typical Detail of Bearing Anchorage with Coupling Nut and Bolt Example Multidirectional PTFE Spherical Bearing (units: inch) Connection Details of Multidirectional PTFE Spherical Bearing with Shear Lugs Bridge Plan and Elevation Sections at Abutment Cross Section at Intermediate Bent Model of Bridge for Multimode or Response History Analysis Horizontal 5%-Damped Response Spectrum of the Design Earthquake Comparison of Average SRSS Spectra of 7 Scaled Ground Motions that Meet Minimum Acceptance Criteria to 90% of Target Spectrum Multiplied by Comparison of Average Geometric Mean Spectra of 7 Scaled Ground Motions to Target DE Spectrum Triple Friction Pendulum Bearing for Bridge Example Lead-Rubber Bearing for Bridge Example Single Friction Pendulum Bearing for Bridge Example 197 xv

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9 LIST OF TABLES TABLE TITLE PAGE 3-1 Values of Damping Reduction Factor B in Codes and Specifications Values of Parameter λ Velocity Correction Factor CFV Applicability Criteria for Methods of Analysis Lower-Bound Limits on Multimode and Response History Analysis Methods Specified in Relation to Single Mode Method Requirement Summary of Triple FP Bearing Behavior (Nomenclature Refers to Figure 4-3) Partial List of Standard Sizes of FP Bearing Concave Plates Coefficient f 1 for Circular Bearings Coefficient f 1 for Circular Hollow Bearings (inner surface location) Coefficient f 1 for Circular Hollow Bearings (outer surface location) Coefficient f 1 for Rectangular Bearings with K/G= Coefficient f 1 for Rectangular Bearings with K/G= Coefficient f 1 for Rectangular Bearings with K/G= Coefficient f 1 for Rectangular Bearings with K/G= (incompressible material) Coefficient f 2 for Circular Bearings Coefficient f 2 for Circular Hollow Bearings (outer surface location) Coefficient f 2 for Circular Hollow Bearings (inner surface location) Coefficient f 2 for Rectangular Bearings with K/G= Coefficient f 2 for Rectangular Bearings with K/G= Coefficient f 2 for Rectangular Bearings with K/G= Coefficient f 2 for Rectangular Bearings with K/G= (incompressible material) Summary of Design Requirements Limits of Average and Edge Unfactored Stress on Woven PTFE (1ksi=6.9MPa) 138 xvii

10 LIST OF TABLES (CONT D) TABLE TITLE PAGE 9-2 Recommended Values of Friction Coefficient for PTFE Spherical Bearings Used in Conventional Applications (not seismic isolation) Design Shear Strength (φr n ) and Minimum Edge Distance for High Strength A325N Bolts Cross Sectional Properties and Weights in Bridge Model Foundation Spring Constants in Bridge Model Bearing Loads and Rotations due to Dead, Live, Brake and Wind Loads Bearing Loads, Displacements and Rotations for Service Conditions Seed Accelerograms and Scale Factors Calculated Response using Simplified Analysis and Effective Properties of Triple FP Isolators Values of Parameters h, A, I and E for Each Bearing in Response Spectrum Analysis of Triple FP System Spectral Acceleration Values for Use in Response Spectrum Analysis of Isolated Bridge with Triple FP System Parameters of Parallel Model of Triple FP Bearing in SAP Parameters of Triple FP Bearings for Response History Analysis Response History Analysis Results for Lower Bound Properties of the Triple FP System in the Design Earthquake Response History Analysis Results for Upper Bound Properties of the Triple FP System in the Design Earthquake Calculated Response using Simplified and Response History Analysis Calculated Response using Simplified Analysis and Effective Properties of Lead-Rubber Isolators Values of Parameters h, A, I and E Used in Response Spectrum Analysis of Lead-Rubber Bearing Isolation System Spectral Acceleration Values for Use in Response Spectrum Analysis of Isolated Bridge with Lead-Rubber Bearing System Parameters of Lead-Rubber Bearings used in Response History Analysis in Program SAP xviii

11 LIST OF TABLES (CONT D) TABLE TITLE PAGE 12-5 Response History Analysis Results for Lower Bound Properties of the Lead-Rubber System in the Design Earthquake Response History Analysis Results for Upper Bound Properties of the Lead-Rubber System in the Design Earthquake Calculated Response using Simplified and Response History Analysis Calculated Response using Simplified Analysis and Effective Properties of Single FP Isolators Values of Parameters h, A, I and E for Each Bearing in Response Spectrum Analysis of Single FP System Spectral Acceleration Values for Use in Response Spectrum Analysis of Isolated Bridge with Single FP System Parameters of Single FP Bearings for Response History Analysis 202 xix

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