About the Authors ix

Preface xiii

1 History of Multilayer Rubber Bearings 1

2 Behavior of Multilayer Rubber Bearings under Compression 19

2.1 Introduction 19

2.2 Pure Compression of Bearing Pads with Incompressible Rubber 19

2.2.1 Infinite Strip Pad 24

2.2.2 Circular Pad 25

2.2.3 Rectangular Pad (with Transition to Square or Strip) 26

2.2.4 Annular Pad 27

2.3 Shear Stresses Produced by Compression 30

2.4 Pure Compression of Single Pads with Compressible Rubber 33

2.4.1 Infinite Strip Pad 33

2.4.2 Circular Pad 36

2.4.3 Rectangular Pad 39

2.4.4 Annular Pad 40

3 Behavior of Multilayer Rubber Bearings under Bending 45

3.1 Bending Stiffness of Single Pad with Incompressible Rubber 45

3.1.1 Infinite Strip Pad 47

3.1.2 Circular Pad 48

3.1.3 Rectangular Pad 49

3.1.4 Annular Pad 51

3.2 Bending Stiffness of Single Pads with Compressible Rubber 52

3.2.1 Infinite Strip Pad 52

3.2.2 Circular Pad 54

3.2.3 Rectangular Pad 57

3.2.4 Annular Pad 58

4 Steel Stress in Multilayer Rubber Bearings under Compression and Bending 63

4.1 Review of the Compression and Bending of a Pad 64

4.2 Steel Stresses in Circular Bearings with Incompressible Rubber 65

4.2.1 Stress Function Solution for Pure Compression 68

4.2.2 Stress Function Solution for Pure Bending 71

4.3 Steel Stresses in Circular Bearings with Compressible Rubber 73

4.3.1 Stress Function Solution for Pure Compression 73

4.3.2 Stress Function Solution for Pure Bending 76

4.4 Yielding of Steel Shims under Compression 78

4.4.1 Yielding of Steel Shims for the Case of Incompressible Rubber 78

4.4.2 Yielding of Steel Shims for the Case of Compressible Rubber 79

5 Buckling Behavior of Multilayer Rubber Isolators 83

5.1 Stability Analysis of Bearings 83

5.2 Stability Analysis of Annular Bearings 90

5.3 Influence of Vertical Load on Horizontal Stiffness 91

5.4 Downward Displacement of the Top of a Bearing 95

5.5 A Simple Mechanical Model for Bearing Buckling 100

5.5.1 Postbuckling Behavior 104

5.5.2 Influence of Compressive Load on Bearing Damping Properties 106

5.6 Rollout Stability 108

5.7 Effect of Rubber Compressibility on Buckling 110

6 Buckling of Multilayer Rubber Isolators in Tension 113

6.1 Introduction 113

6.2 Influence of a Tensile Vertical Load on the Horizontal Stiffness 115

6.3 Vertical Displacement under Lateral Load 117

6.4 Numerical Modelling of Buckling in Tension 120

6.4.1 Modelling Details 120

6.4.2 Critical Buckling Load in Compression and Tension 122

7 Influence of Plate Flexibility on the Buckling Load of Multilayer

Rubber Isolators 129

7.1 Introduction 129

7.2 Shearing Deformations of Short Beams 130

7.3 Buckling of Short Beams with Warping Included 139

7.4 Buckling Analysis for Bearing 146

7.5 Computation of Buckling Loads 153

8 Frictional Restraint on Unbonded Rubber Pads 159

8.1 Introduction 159

8.2 Compression of Long Strip Pad with Frictional Restraint 160

8.3 The Effect of Surface Slip on the Vertical Stiffness of an Infinite Strip Pad 163

8.4 The Effect of Surface Slip on the Vertical Stiffness of a Circular Pad 169

9 Effect of Friction on Unbonded Rubber Bearings 177

9.1 Introduction 178

9.2 Bearing Designs and Rubber Properties 180

9.3 Ultimate Displacement of Unbonded Bearings 180

9.4 Vertical Stiffness of Unbonded Rubber Bearings with Slip on their Top and Bottom Supports 184

Appendix: Elastic Connection Device for One or More Degrees of Freedom 193

References 209

Photograph Credits 213

Author Index 215

Subject Index 217