James M. Kelly & Dimitrios Konstantinidis 
Mechanics of Rubber Bearings for Seismic and Vibration Isolation 

Widely used in civil, mechanical and automotive engineer-ing
since the early 1980s, multilayer rubber bearings have been used as
seismic isolation devices for buildings in highly seismic areas in
many countries. Their appeal in these applications comes from their
ability to provide a component with high stiffness in one direction
with high flexibility in one or more orthogonal directions. This
combination of vertical stiffness with horizontal flexibility,
achieved by reinforcing the rubber by thin steel shims
perpendicular to the vertical load, enables them to be used as
seismic and vibra-tion isolators for machinery, buildings and
bridges.

Mechanics of Rubber Bearings for Seismic and Vibration
Isolation collates the most important information on the
mechanics of multilayer rubber bearings. It explores a unique and
comprehensive combination of relevant topics, covering all
prerequisite fundamental theory and providing a number of
closed-form solutions to various boundary value problems as well as
a comprehensive historical overview on the use of isolation.

Many of the results presented in the book are new and are
essential for a proper understanding of the behavior of these
bearings and for the design and analysis of vibration or seismic
isolation systems. The advantages afforded by adopting these
natural rubber systems is clearly explained to designers and users
of this technology, bringing into focus the design and
specification of bearings for buildings, bridges and industrial
structures.

This comprehensive book:

* includes state of the art, as yet unpublished research along
with all required fundamental concepts;

* is authored by world-leading experts with over 40 years of
combined experience on seismic isolation and the behavior of
multilayer rubber bearings;

* is accompanied by a website at www.wiley.com/go/kelly

The concise approach of Mechanics of Rubber Bearings
for Seismic and Vibration Isolation forms an invaluable
resource for graduate students and researchers/practitioners in
structural and mechanical engineering departments, in particular
those working in seismic and vibration isolation.

Table of Content

About the Authors ix

Preface xiii

1 History of Multilayer Rubber Bearings 1

2 Behavior of Multilayer Rubber Bearings under Compression19

2.1 Introduction 19

2.2 Pure Compression of Bearing Pads with Incompressible Rubber19

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 Rubber33

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 Bending45

3.1 Bending Stiffness of Single Pad with Incompressible Rubber45

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 Rubber52

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 Rubber73

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 Tension113

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 Restraint160

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 ontheir Top and Bottom Supports 184

Appendix: Elastic Connection Device for One or More Degreesof Freedom 193

References 209

Photograph Credits 213

Author Index 215

Subject Index 217

About the author

James M Kelly & Dimitrios A Konstantinidis, University of California at Berkeley, USA
James M Kelly is a Professor in the Graduate School, Department of Civil and Environmental Engineering, Division of Structural Engineering Mechanics and Materials at the University of California at Berkeley, and a Participating Faculty Member at the Earthquake Engineering Research Center, University of California at Berkeley. He has authored over 300 refereed journal papers and 2 books, Earthquake-Resistant Design with Rubber 2nd ed 1996 (Springer Verlag) and Design of Seismic Isolated Structures, 1999, Wiley. He has led the way in experimental investigations of elastomeric seismic isolation bearings by conducting many pioneering studies of seismically isolated structures and structures with energy dissipators. In testing hundreds of bearings he achieved numerous advances, including the application of high-damping rubber for seismic isolation bearings – used in the first U.S. isolated building and in more than 100 structures around the world and the understanding of the dynamic and ultimate behavior of elastomeric seismic isolation at large deformation.

Dimitrios A Konstantinidis is a Postdoctoral Researcher on health monitoring at University of California, Berkeley, working on the development and testing of a reliable scheme for monitoring the health of fluid viscous dampers in bridges via wireless communication.