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Seismic Isolation

fo r Designers

a nd Structural Engineers

R. Ivan Skinner

Trevor E. Kelly

Bill (W.H.) Robinson



Seismic Isolation

fo r Designers

a nd Structural Engineers

R. Ivan Skinner

Trevor E. Kelly

Holmes Consulting Groupwww.holmesgroup.com

Bill (W.H.) Robinson

Robinson Seismic Ltd

www.rslnz.com



CONTENTS

Preface (i)

Acknow ledgemen t s (iii)

Author Biograp hies (iv)

Freque nt ly Used Sym bo ls And Ab breviat ions (v )

CHAPTER 1: INTRODUCTION.........................................................................................................1

1.1 Seismic Isolation in Context........................................................................................................................... 11.2 Flexibility, Damping and Period Shift ...........................................................................................................3

1.3 Comparison of Conventional & Seismic Isolation Approaches.............................................................5

1.4 Components in an Isolation System ............................................................................................................6

1.5 Prac tical Applica tion of the Seismic Isolation Concept..........................................................................71.6 Topics Covered in this Book..........................................................................................................................9

CHAPTER 2: GENERAL FEATURES OF STRUCTURES WITH SEISMIC ISOLATION.............................11

2.1 Introduction ..................................................................................................................................................... 112.2 Role of Earthquake Response Spec tra and Vibrational Modes in the Performance

of Isolated Structures......................................................................................................................................112.2.1 Earthquake Response Spectra ...................................................................................................11

2.2.2 General Effects of Isolation of the Seismic Responses of Structures....................................15

2.2.3 Parameters of Linear and Bilinear Isolation Systems ...............................................................162.2.4 Calculation of Seismic Responses..............................................................................................20

2.2.5 Contributions of Higher Modes to the Seismic Responses of Isolated Structures...............21

2.3 Natural Periods and Mode Shapes of Linear Structures – Unisolated and Isolated............................22

2.3.1 Introduction....................................................................................................................................222.3.2 Structural Model and Controlling Equations ............................................................................22

2.3.3 Natural Periods and Mode Shapes............................................................................................24

2.3.4 Example – Modal Periods and Shapes......................................................................................252.3.5 Natural Periods and Mode Shapes with Bilinear Isolation......................................................26

2.4 Modal and Total Seismic Responses ...........................................................................................................272.4.1 Seismic Responses Important for Seismic Design.....................................................................27

2.4.2 Modal Seismic Responses............................................................................................................28

2.4.3 Structural Responses for Modal Responses...............................................................................302.4.4 Example – Seismic Displacements and Forces........................................................................30

2.4.5 Seismic Responses with Bilinear Isolators...................................................................................31

2.5 Comparisons of Seismic Responses of Linear and Bilinear Location Systems......................................34

2.5.1 Comparative Study of Seven Cases..........................................................................................342.6 Guide to Assist the Selection of Isolation Systems.....................................................................................38

CHAPTER 3: ISOLATOR DEVICES AND SYSTEMS........................................................................... 43

3.1 Isolator Components and Isolator Parameters..........................................................................................43

3.1.1 Introduction....................................................................................................................................43

3.1.2 Combination of Isolator Components to Form Different Isolation Systems ........................433.2 Plasticity of Meta ls..........................................................................................................................................46

3.3 Steel Hysteretic Dampers..............................................................................................................................49

3.3.1 Introduction....................................................................................................................................49

3.3.2 Types of Steel Damper ................................................................................................................. 513.3.3 Approximate Force-Displacement Loops for Steel-Beam Dampers....................................52

3.3.4 Bilinear Approximation to Force-Displacement Loops...........................................................553.3.5 Fatigue Life of Steel-Beam Dampers.........................................................................................57

3.3.6 Summary of Steel Dampers.........................................................................................................593.4 Lead Extrusion Dampers................................................................................................................................59

3.4.1 General........................................................................................................................................... 59

3.4.2 Properties of the Extrusion Damper............................................................................................62

3.4.3 Summary and Discussion of Lead Extrusion Dampers.............................................................65



3.5 Laminated-Rubber Bearings for Seismic Isolators......................................................................................66

3.5.1 Rubber Bearings for Bridges and Isolators.................................................................................66

3.5.2 Rubber Bearing, Weight Capacity Wmax................................................................................... 673.5.3 Rubber Bearing Isolation: Stiffness, Period and Damping.....................................................68

3.5.4 Allowable Seismic Displacement Xb ..........................................................................................70

3.5.5 Allowable Maximum Rubber Strains..........................................................................................723.5.6 Other Fac tors in Rubber Bearing Design...................................................................................74

3.5.7 Summary of Laminated Rubber Bearings.................................................................................743.6 Lead Rubber Bearings....................................................................................................................................74

3.6.1 Introduction....................................................................................................................................743.6.2 Properties of the Lead Rubber Bearing .....................................................................................77

3.7 Further Isolator Components and Systems.................................................................................................83

3.7.1 Isolator Damping Proportional to Veloc ity ...............................................................................83

3.7.2 PTFE Sliding Bearings ..................................................................................................................... 84

3.7.3 PTFE Bearings Mounted on Rubber Bearings............................................................................853.7.4 Tall Slender Structures Rocking with Uplift ................................................................................. 85

3.7.5 Further Components for Isolator Flexibility ................................................................................86

3.7.6 Buffers to Reduce the Maximum Isolator Displacement........................................................873.7.7 Active Isolation Systems............................................................................................................... 88

CHAPTER 4: ENGINEERING PROPERTIES OF ISOLATORS.............................................................. 89

4.1 Sources of Information...................................................................................................................................894.2 Engineering Properties of Lead Rubber Bearings......................................................................................89

4.2.1 Shear Modulus...............................................................................................................................90

4.2.2 Rubber Damping........................................................................................................................... 904.2.3 Cyclic Change in Properties.......................................................................................................91

4.2.4 Age Change in Properties...........................................................................................................934.2.5 Design Compressive Stress...........................................................................................................94

4.2.6 Design Tension Stress..................................................................................................................... 94

4.2.7 Maximum Shear Strain.................................................................................................................. 95

4.2.8 Bond Strength ................................................................................................................................974.2.9 Vertical Deflections.......................................................................................................................97

4.3 Engineering Properties of High Damping Rubber Isolators......................................................................100

4.3.1 Shear Modulus...............................................................................................................................100

4.3.2 Damping .........................................................................................................................................1014.3.3 Cyclic Change in Properties.......................................................................................................102

4.3.4 Age Change in Properties...........................................................................................................1034.3.5 Design Compressive Stress...........................................................................................................103

4.3.6 Maximum Shear Strain.................................................................................................................. 1034.3.7 Bond Strength ................................................................................................................................103

4.3.8 Vertical Deflec tions....................................................................................................................... 103

4.3.9 Wind Displacements..................................................................................................................... 104

4.4 Engineering Properties of Sliding Type Isolators.........................................................................................1044.4.1 Dynamic Friction Coefficient ......................................................................................................105

4.4.2 Static Friction Coefficient.............................................................................................................106

4.4.3 Effect of Static Friction on Performance ...................................................................................1084.4.4 Check on Restoring Force ...........................................................................................................110

4.4.5 Age Change in Properties...........................................................................................................1104.4.6 Cyclic Change in Properties.......................................................................................................1114.4.7 Design Compressive Stress...........................................................................................................111

4.4.8 Ultimate Compressive Stress........................................................................................................1114.5 Design Life of Isolators....................................................................................................................................111

4.6 Fire Resistance ................................................................................................................................................. 111

4.7 Effects of Temperature on Performance....................................................................................................1124.8 Temperature Range for Installation.............................................................................................................112

CHAPTER 5: ISOLATION SYSTEM DESIGN.....................................................................................113

5.1 Introduction ..................................................................................................................................................... 113

5.1.1 Assessing Suitability........................................................................................................................113

5.1.2 Design Development for an Isolation Projec t ..........................................................................115



5.2 Design Equations for Elastomeric Bearing Types.......................................................................................116

5.2.1 Codes..............................................................................................................................................116

5.2.2 Empirical Data ...............................................................................................................................1165.2.3 Definitions........................................................................................................................................ 116

5.2.4 Range of Rubber Properties........................................................................................................117

5.2.5 Vertical Stiffness and Load Capacity........................................................................................1185.2.6 Vertical Stiffness............................................................................................................................. 118

5.2.7 Compressive Rated Load Capacity..........................................................................................1195.2.8 AASHTO 1999 Requirements........................................................................................................ 120

5.2.9 Tensile Rated Load Capacity......................................................................................................1215.2.10 Bucking Load Capacity...............................................................................................................121

5.2.11 Lateral Stiffness and Hysteresis Parameters for Bearing..........................................................1225.2.12 Lead Core Confinement..............................................................................................................125

5.3 Basis of an Isolation System Design Procedure..........................................................................................126

5.3.1 Elastomeric Based Systems.......................................................................................................... 1275.3.2 Sliding and Pendulum Systems....................................................................................................127

5.3.3 Other Systems.................................................................................................................................127

5.4 Step-By-Step Implementation of a Design Procedure.............................................................................1275.4.1 Example of Illustrate Calculations..............................................................................................128

5.4.2 Design Code ..................................................................................................................................1295.4.3 Units..................................................................................................................................................129

5.4.4 Seismic and Building Definition ...................................................................................................130

5.4.5 Material Definition......................................................................................................................... 1315.4.6 Isolator Types and Load Data .....................................................................................................133

5.4.7 Isolator Dimensions........................................................................................................................134

5.4.8 Calculate Bearing Properties......................................................................................................136

5.4.9 Gravity Load Capacity................................................................................................................1385.4.10 Calculate Seismic Performance.................................................................................................139

5.4.11 Seismic Load Capacity................................................................................................................143

5.4.12 Assess Fac tors of Safety and Performance ..............................................................................1445.4.13 Properties for Analysis................................................................................................................... 146

5.4.14 Hysteresis Properties...................................................................................................................... 147

CHAPTER 6: EFFECT OF ISOLATION ON BUILDINGS..................................................................... 149

6.1 Prototype Buildings.........................................................................................................................................1496.1.1 Building Configuration..................................................................................................................1496.1.2 Design of Isolators.......................................................................................................................... 150

6.1.3 Evaluation Procedure...................................................................................................................1566.1.4 Comparison with Design Procedure..........................................................................................158

6.1.5 Isolation System Performance.....................................................................................................164

6.1.6 Building Inertia Loads.................................................................................................................... 166

6.1.7 Floor Accelerations.......................................................................................................................1756.1.8 Optimum Isolation Systems.......................................................................................................... 180

6.2 Example Assessment of Isolator Properties................................................................................................. 182

CHAPTER 7: SEISMIC ISOLATION OF BUILDINGS AND BRIDGES..................................................185

7.1 Introduction to Isolation of Buildings............................................................................................................185

7.2 Scope of Building Example ...........................................................................................................................185

7.3 Seismic Input.................................................................................................................................................... 1867.4 Design of Isolation System .............................................................................................................................187

7.5 Analysis Models...............................................................................................................................................189

7.6 Analysis Results................................................................................................................................................191

7.6.1 Summary of Results....................................................................................................................... 1957.7 Test Conditions................................................................................................................................................ 195

7.8 Production Test Results...................................................................................................................................196

7.9 Summary .......................................................................................................................................................... 1977.10 Implementation in Spreadsheet ..................................................................................................................198

7.10.1 Material Definition......................................................................................................................... 1987.10.2 Project Definition ........................................................................................................................... 199

7.10.3 Isolator Types and Load Data .....................................................................................................200

7.10.4 Isolator Dimensions........................................................................................................................2017.10.5 Isolator Performance ....................................................................................................................203

7.10.6 Properties for Analysis................................................................................................................... 205

7.11 Introduction to Isolation for Bridges.............................................................................................................207

7.12 Seismic Separation of Bridges.......................................................................................................................208



7.13 Design Spec ifications for Bridges.................................................................................................................209

7.13.1 The 1991 AASHTO Guide Specifica tions....................................................................................209

7.13.2 The 1999 AASHTO Guide Specifications....................................................................................2107.14 Use of Bridge Specifica tions for Building Isolator Design .........................................................................210

7.15 Design of Isolation Systems............................................................................................................................212

7.15.1 Non-Seismic Loads........................................................................................................................2127.15.2 Effec t of Bent Flexibility.................................................................................................................213

7.16 Analysis of Isolated Bridges ...........................................................................................................................2157.17 Design Procedure for Bridge Isolation.........................................................................................................216

7.17.1 Example Bridge..............................................................................................................................2167.17.2 Design of Isolators..........................................................................................................................218

7.17.3 Accounting for Bent Flexibility in Design ...................................................................................2207.17.4 Evaluation of Performance .........................................................................................................224

7.17.5 Effect of Isolation System on Displacements............................................................................228

7.17.6 Effect of Isolation on Forces ........................................................................................................2297.17.7 Summary.........................................................................................................................................231

7.18 Implementation in Spreadsheet ..................................................................................................................231

7.18.1 Material Properties........................................................................................................................ 2327.18.2 Dimensional Properties.................................................................................................................232

7.18.3 Load and Design Data.................................................................................................................2337.18.4 Isolation Solution............................................................................................................................ 234

CHAPTER 8: APPLICATIONS OF SEISMIC ISOLATION...................................................................237

8.1 Introduction ..................................................................................................................................................... 237

8.2 Structures Isolated in New Zealand .............................................................................................................239

8.2.1 Introduction....................................................................................................................................2398.2.2 Road Bridges..................................................................................................................................242

8.2.3 South Rangitikei Viaduct with Stepping Isolation ....................................................................244

8.2.4 William Clayton Building............................................................................................................... 2458.2.5 Union House ...................................................................................................................................247

8.2.6 Wellington Central Police Station...............................................................................................249

8.3 Structures Isolated in J apan..........................................................................................................................2518.3.1 Introduction....................................................................................................................................251

8.3.2 The C-1 Building, Cuchu City, Tokyo ..........................................................................................2558.3.3 The High-Tech R&D Centre, Obayashi Corporation ...............................................................255

8.3.4 Comparison of Three Buildings with Different Seismic Isolation Systems .............................256

8.3.5 Oiles Technical Centre Building ..................................................................................................258

8.3.6 Miyagawa Bridge..........................................................................................................................2598.4 Structures Isolated in the USA ....................................................................................................................... 261

8.4.1 Introduction....................................................................................................................................261

8.4.2 Foothill Communities Law and J ustice Centre, San Bernandino, California ......................2638.4.3 Salt Lake City and Country Building: Retrofit...........................................................................264

8.4.4 USC University Hospital, Los Angeles..........................................................................................2658.4.5 Sierra Point Overhead Bridge, San Francisco...........................................................................266

8.4.6 Sexton Creek Bridge, Illinois.........................................................................................................267

8.5 Structures Isolated in Italy..............................................................................................................................2688.5.1 Introduction ....................................................................................................................................268

8.5.2 Seismically Isolated Bridges.........................................................................................................2688.5.3 The Mortaiolo Bridge..................................................................................................................... 269

8.6 Isolation of Delicate or Potentially Hazardous Structures or Substructures...........................................274

8.6.1 Introduction ....................................................................................................................................2748.6.2 Seismically Isolated Nuclear Power Stations.............................................................................275

8.6.3 Protec tion of Capacity Banks, Haywards, New Zealand.......................................................275

8.6.4 Seismic Isolation of a Printing Press in Wellington, New Zealand ..........................................277

CHAPTER 9: IMPLEMENTATION ISSUES..........................................................................................279

9.1 Introduction ..................................................................................................................................................... 2799.2 Isolator Locations and Types.........................................................................................................................279

9.2.1 Selection of Isolation Plane .........................................................................................................279

9.2.2 Selection of Device Type .............................................................................................................283



9.3 Seismic Input.................................................................................................................................................... 292

9.3.1 Form of Seismic Input.................................................................................................................... 292

9.3.2 Recorded Earthquake Motions...................................................................................................293 9.3.3 Near Fault Effec ts.......................................................................................................................... 300

9.3.4 Variations in Displacements........................................................................................................300

9.3.5 Time History Seismic Input ............................................................................................................3029.3.6 Selecting and Scaling Records for Time History Analysis........................................................302

9.3.7 Selecting Records from a Set......................................................................................................3039.3.8 Comparison of Earthquake Scaling Factors.............................................................................304

9.4 Detailed System Analysis...............................................................................................................................3069.4.1 Single Degree-of-Freedom Model .............................................................................................307

9.4.2 Two Dimensional Non-Linear Model ..........................................................................................3079.4.3 Three Dimensional Equivalent Linear Model ............................................................................307

9.4.4 Three Dimensional Model-Elastic Superstructure, Yielding Isolators.....................................308

9.4.5 Fully Non-Linear Three Dimensional Model...............................................................................3089.4.6 Device Modeling...........................................................................................................................308

9.4.7 ETABS Analysis for Buildings..........................................................................................................309

9.4.8 Concurrency Effects.....................................................................................................................3139.5 Connec tion Design ........................................................................................................................................316

9.5.1 Elastomeric Based Isolators..........................................................................................................3169.5.2 Sliding Isolators...............................................................................................................................321

9.5.3 Installation Examples..................................................................................................................... 322

9.6 Structural Design9.6.1 Design Concepts........................................................................................................................... 327

9.6.2 UBC Requirements ........................................................................................................................ 328

9.6.3 MCE Level of Earthquake ............................................................................................................332

9.6.4 Non-Structural Components .......................................................................................................3329.6.5 Bridges.............................................................................................................................................333

9.7 Spec ifications.................................................................................................................................................. 333

9.7.1 General...........................................................................................................................................3339.7.2 Testing.............................................................................................................................................. 335

CHAPTER 10: FEASIBILITY ASSESSMENT, EVALUATION AND FURTHER DEVELOPMENT

OF SEISMIC ISOLATION............................................................................................ 337

10.1 Dec ision-Making in a Seismic Isolation Context........................................................................................337

10.1.1 Seismic Isolation Dec isions to be Made ....................................................................................337

10.1.2 Seismic Isolation Dec isions in the Wellington Area ..................................................................33810.2 Construction Projec ts in New Zealand and India 1992 to 2005..............................................................339

10.2.1 Introduction....................................................................................................................................339

10.2.2 Retrofits............................................................................................................................................33910.2.3 Te Papa Tongarewa ..................................................................................................................... 339

10.2.4 Other Seismically Isolated Buildings ...........................................................................................341

10.2.5 Bhuj Hospital...................................................................................................................................34110.3 A Feasibility Study for Seismic Isolation........................................................................................................343

10.3.1 Te Papa Tongarewa, the Museum of New Zealand ...............................................................34310.3.2 Description...................................................................................................................................... 343

10.3.3 Seismic Design Criteria ................................................................................................................. 344

10.3.4 Feasibility Study.............................................................................................................................. 34510.3.5 Isolation System Design ................................................................................................................34610.3.6 Evaluation of Structural Performance .......................................................................................346

10.3.7 Results of ANSR-II Analysis............................................................................................................. 348

10.3.8 Conclusions....................................................................................................................................34810.4 Performance in Real Earthquakes...............................................................................................................350

10.5 New Approaches to Seismic Isolation.........................................................................................................35310.5.1 Introduction....................................................................................................................................353

10.5.2 The RoBall........................................................................................................................................353

10.5.3 The RoG lider...................................................................................................................................35610.6 Projec t Management Approach.................................................................................................................358

10.7 Future ................................................................................................................................................................359

Reference List………………………………………………………………………………………………………361

Additional Resources…………………………………………………………………………………………….367



(i)

PREFACE This is a revised version of the book “An Introduction to Seismic Isolation” published by Wiley and

Sons in 1993. There have been many changes in the course of this revision and this is reflected inthe changed title - “Seismic Isolation for Designers and Structural Engineers”.

This new book builds on the previous one and uses much of the previous material, but it hasdifferent authorship and more focus on practical applications. It acknowledges the pioneeringwork that has been done over the past 30 to 40 years but a ims to present seismic isolation in adifferent way, as an established technique that could be considered widely, even routinely, asan option by designers and structural engineers. Trevor Kelly’s input as a practising structuralengineer has transformed the book into a modern version that makes full use of computerscience techniques. (A CD Rom is included).

The original book was authored by R I Skinner, W H Robinson and GH McVerry, who were at the

time working at the Department of Scientific and Industrial Research (DSIR) in Wellington, NewZealand. The book recorded the innovative earthquake engineering research that had beencarried out at the DSIR over the previous 25 years (see Chap ter 3 of both books, and Chap ter 8 of this book, which is carried over from the previous Cha pter 6 ). However the book also markedthe end of an era, as it was written at a time when change was in the air and the DSIR wasabout to be disestablished.

The DSIR was closed down mid-1992 as part of a New-Zealand wide drive to making sciencemore commercial. Bill Robinson has risen to this challenge by forming Robinson Seismic Limited(RSL), an engineering company specialising in applications of seismic isolation to protectstructures from earthquake damage. Bill has continued as one of the authors of this new book. The new author is Trevor Kelly, a structural engineer with Holmes Consulting, which has beeninvolved in the design and supply of seismic isolation systems for almost 20 years. Trevor’sinterest is in the structural engineering aspects of applying seismic isolation/damping and thenew chapters that he has written emphasise the engineering aspects.

The new book therefore retains the mathematical tools in Chapters 1, 2 and 3 of “AnIntroduction to Seismic Isolation” but replaces the empirical methods of succeeding chapterswith detailed design and documentation material of the type that a structural engineer wouldneed to implement isolation. This is followed through with examples of practical designs.

This book provides both theory and design aspects of seismic isolation. This will be useful forstructural engineers and teachers of engineering courses. For other structural components(concrete frames, steel braces etc) the engineering student is taught the theory (lateral loads,bending moments) but then also the design (how to select sizes, detail reinforcing, bolts). This

book will do the same for seismic engineering.

The book provides practical examples of computer applications as well as device designexamples so that the structural engineer is able to do a preliminary design that won’t specifyimpossible constraints. The book also addresses the steps that need to be taken to ensure thedesign is code compliant.

The structural engineer is the key to adoption of seismic isolation technology. The book aims toprovide enough design information so that the structural engineer can be confident onimplementing seismic isolation; otherwise he/she won’t want to take the risk even if the architector owner is enthusiastic. Firms like RSL and Holmes Consulting will continue to be available toprovide expert advice and the benefits of their considerable experience in the field of device

design and seismic isolation.



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The engineering credentials and expertise of Bill Robinson and his company, RSL, are evidentfrom Cha pte rs 3 and 8 (which describe the invention and development of the Lead RubberBearing). Bill Robinson has been honoured world wide for this work and has received recognitionin New Zealand from the scientific community and the business community. There has also beenconsiderable interest in the public domain, in the display of seismic isolation in Te Papa

Tongarewa, the Museum of New Zealand on the waterfront in Wellington, which was built onLead Rubber Bearings (see Cha pter 9 ).

The engineering credentials of Trevor Kelly are evident from his work as Technical Director ofHolmes Consulting Group (HCG), part of the Holmes Group, which is New Zealand's largestspecialist structural engineering company, with over 90 staff in three main offices in NewZealand plus 25 in the San Francisco office. Trevor heads the seismic isolation division of HCGin the Auckland office. He has over 15 years experience in the design and evaluation ofseismic isolation systems in the United States, New Zealand and other countries and is alicensed Structural Engineer in California.

Since 1954 the company has designed a wide range of structures in the commercial andindustrial fields. HCG has been progressive in applications of seismic isolation and since its first

isolated project, Union House, in 1982, has completed six isolated structures. On theseprojects HCG provided full structural engineering services. In addition, for over 8 years HCGprovided design and analysis services to Skellerup Industries of New Zealand and laterSkellerup O iles Seismic Protection (SOSP), a San Diego based manufacturer of seismicisolation hardware. Isolation hardware used on their projects included Lead Rubber Bearings(LRBs), High Damping Rubber Bearings (HDR), Teflon on stainless steel sliding bearings, sleevedpiles and steel cantilever energy dissipators.

The company has developed design and analysis software to ensure effective andeconomical implementation of seismic isolation for buildings, bridges and industrialequipment. Expertise encompasses the areas of isolation system design, analysis,specifications and evaluation of performance. In writing C hapters 4, 5, 6 and 7 of this book

Trevor has drawn on his practical experience in the field and explains methods of calculatingseismic responses using state-of-the-art computer software such as ETABS, used for the linearand nonlinear analysis of buildings.

This book is the product of three expert engineers who have, over a long period of years,worked separately and collaboratively to design and develop earthquake isolation solutionsand to incorporate them into existing and new structures. Collaboration on this book is afurther joint venture and has a two-fold aim — to be used for the benefit of professionalslooking to apply earthquake isolation techniques, and to be used in educating a newgeneration of structural engineers and designers.



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ACKNOWLEDGEMENTS

In presenting this new book, which builds on and revises the previous book “An Introduction to

Seismic Isolation”, thanks are due to all those who made the previous book possible, especiallyGraeme McVerry, as well as those who have been involved in its revision. Thanks to BarbaraBibby who again provided editing services, to Heather Naik and the staff and shareholders ofRobinson Seismic Ltd and Holmes Consulting Group, to the Book Committees at RSL and HolmesConsulting who have reviewed it, and to FORST for providing funding for its production.

Trev o r Kelly

Holm es Con sult ing G roup

34 Wa im arei Aven ue

Paeroa

NEW ZEALAND

ww w.ho lme sgroup .c om

Bill Rob inson

Rob inson Se ism ic Ltd

P O Box 33093

Petone

NEW ZEALAND

www.rslnz.com

Iva n Skinne r

31 Blue Mo unta ins Roa d

Silve rstream

Well ington

New Zea land



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AUTHOR BIOGRAPHIES

Trevor E Kelly, Technical Director, Holmes Consulting Group34 Waimarei Avenue, Paeroa, New Zealandwww.holmesgroup.com

Trevor completed a BE at the University of Canterbury in 1973 and an ME in 1974. His researchreport, related to the nonlinear analysis of concrete structures, initiated an interest in this fieldwhich has continued throughout his career. He has worked as a structural engineer in NewZealand and California and is a Chartered Engineer in NZ and licensed Structural Engineer inCalifornia. Over the last 20 years, he has specialised in structural engineering fields whichutilise nonlinear analysis, such as base isolation, energy dissipation and performance basedevaluation of existing buildings. In his current position, Trevor directs the technicaldevelopments at Holmes Consulting G roup, particularly as they relate to structural analysisand computer software development.

Dr William H Robinson, Founder & Chief Engineer, Robinson Seismic Ltd

P O Box 33093, Petone, New Zealandwww.rslnz.com

Bill began his career as a mechanical engineer, graduating ME at the University of Aucklandbefore working for two construction companies. He then changed fields to physicalmetallurgy, completing a PhD in 1965 at the University of Illinois. Two years as a researchfellow followed, working in solid-state physics at the University of Sussex before returning toNew Zealand to work as a scientist with the Physics and Engineering Laboratory (PEL) at theDepartment of Scientific and Industrial Research (DSIR) in December 1967.

Bill’s interest in seismic isolation led to the invention and development of the lead extrusiondamper (1970) and the lead-rubber bearing (1974) (See Chapter 3) and has become hismajor research and engineering interest. Other research during his career as a scientist andlater Director of PEL has included Antarctic sea-ice research, attempts to detectgravitational waves, the successful development of an ultrasonic viscometer andultrasonically modulated ESR. The first version of this book was written with Ivan Skinner andGraeme McVerry in the last days of the DSIR. Ten years ago Bill founded Robinson SeismicLtd, which is based in Lower Hutt, New Zealand and has contacts and clients all over theworld.

Dr R Ivan Skinner31 Blue Mountains Road, Silverstream, Wellington, New Zealand

Ivan’s early activities prepared him for a contribution towards reducing earthquake impactson structures, including early applications of seismic isolation such as the Rangitikei stepping

bridge and the William Clayton building. He obtained a BE Hons in 1951, and a DSc in 1976,from the University of Canterbury, New Zea land. In 1953 he joined the Physics & EngineeringLaboratory, PEL, in Lower Hutt where his wide-ranging activities included designing avibration isolation system for the lab’s new electron microscope.

During 1959-78 he led the Engineering Seismology Sec tion of PEL where he applied hisknowledge of electrodynamics to modelling structures and their dynamic responses tosevere earthquakes. Other sec tion priorities included the development of a New Zealandstrong-motion earthquake recording network used throughout NZ and overseas; engineeringstudies of informative earthquake attacks worldwide; contributions as a UNESCO expert inearthquake engineering and developing special components for seismic isolation to givemore reliable earthquake resistance at lower cost.

After the completion of the Seismic Isolation book with Robinson and McVerry in 1993, Ivanbecame Direc tor of the New Zealand Earthquake Commission’s Research Foundation, from



(v)

which he retired at the end of 2005.



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FREQUENTLY USED SYMBOLS AND ABBREVIATIONS(Chapters 1, 2, 3 and 8)

β : tuning parameter for combined primary-secondary system, namely (ω p-ωs)/ ωa

βij : analogue to β, for multimode primary-secondary systems

Ґe,rn : elastic-phase participation factor at position r in mode n

Ґn(z) : mode-n participation fac tor at position z

Ґ Nn : mode-n participation factor at top floor of structure (position N)

Ґn : weighting fac tor for the nth mode of vibration

Ґn(I) : isolated mode weight factor

Ґn(U) : unisolated mode weight factor

Ґrn : participation fac tor for response to ground excitation for a mass at level r of a

structure vibrating in the nth mode

Ґy,rn : yielding-phase participation factor at position r in mode n

γxz : shear strain of rubber disc

γ : interac tion parameter of combined primary-secondary system, given by ms/mp

γ : ‘engineering’ shear strain

γij : interaction parameter, analogue to γ, for multimode primary-secondary systems

γn : wave number of mode n, possibly complex

γy : shear-strain coordinate of yield point

∆n : difference between nth root of equation (4.17) and (n-1)π

δd : nonclassical damping parameter in combined primary-secondary system

δij : analogue to δd , for multimode primary-secondary systems

ε : ω b/ωFB1 = ratio of frequenc ies of rigid-mass isolated structure and first-mode

unisolated structure, used for expressing orders of perturbation

ε : strain = (increment in length)/(original length)

εm : maximum amplitude of cyclic strain

εy : strain coordinate of yield point

Θn : variation of spatial phase of mode-n displacement down shear beam



(vi)

T

T

ζs : damping of secondary structure

ζ p : damping of primary structure

ζa : average damping of combined primary-secondary system, given by

ζa = (ζ p+ζs)/2

ζd

: damping difference of combined primary-secondary system, given by ζd= ζ

p -ζ

s

ζFBn : fraction of critical viscous damping of (unisolated) fixed-base mode n

ζ : velocity- (viscous-) ‘damping fac tor’ or ‘fraction of critical damping’ for single-mass

oscillator

ζ b : velocity-damping fac tor for isolator

ζB : ‘effective’ damping factor of bilinear isolator, given by sum of velocity- and

hysteretic-damping factors

ζ b1 : velocity-damping fac tor in ‘elastic’ region of bilinear isolator

ζ b2 : velocity-damping fac tor in ‘plastic’ or ‘yielded-phase’ region of bilinear isolator

ζh : hysteretic damping factor of bilinear isolator

ζn : fraction of critical viscous damping of mode n; also called mode-n damping fac tor

μ j0 : modal mass of free-free mode j

: u j0[M]u j0

μsj : jth modal mass of secondary system =Φsj [Ms] Φsj

ξn(t) : modal (relative displacement) coordinate for mode n at time t

ρ : uniform density of shear beam representing a uniform shear structure

σ : nominal stress, as used in ‘scaled’ (σ-ε) curves for steel dampers in Chapter 3

σ : stress = force/ area (Pascals)

σy : stress coordinate of yield point

τ : nominal shear stress, as used in ‘sca led’ (σ-ε) curves for steel dampers in Chapter 3

τ : shear stress = (shear force)/area (Pascals)

τy : shear-stress coordinate of yield point

Φ : [Φ1, … Φ2, … Φ3], the mode shape matrix, a function of space, not time

Φn,Φm : mode shape in the nth or mth mode of vibration



(vii)

Φrn : mode shape at the rth level of the structure during the nth mode of vibration

Φe,rn : elastic-phase modal shape at position r in mode n

Φy,rn : yielding-phase modal shape at position r in mode n

Φn(z,t) : shape of mode n, used interchangeably with un(z,t); normalized to unity at the top

level

Ψn : phase angle of participation factor vectorΓn

ωs : (circular) frequency of secondary structure

ω p : (circular) frequency of primary structure

ωa : average frequency of combined primary-secondary system, given by

ωa = (ω p + ωs) /2

ω pi : analogue to ω p, for multimode primary-secondary system

ωsj : analogue to ωs, for multimode primary-secondary system

ω1 (U) : unisolated undamped first-mode natural (circular) frequency, the same asωFBi

ωFFn : mode-n natural (circular) frequency with ‘free-free’ boundary conditions

ω b : isolator frequency =√(K b/M) for a rigid mass M

ωFB1 : natural (circular) frequency of (unisolated) fixed-base made 1, equivalent to ω1 (U)

ωFBn : natural (circular) frequency of (unisolated) fixed base mode n

ωn : undamped natural (circular) frequency of mode n, related to frequency f n by

ωn = 2πf n

ωd : damped natural (circular) frequency of single-mass oscillator

ωn : undamped natural (circular) frequency of single-mass oscillator, or nth-mode

natural frequency of multi-degree-of-freedom linear oscillator

A : area of rubber bearing in Chapter 3

A : cross-sec tiona l area of shear beam representing a uniform shear structure

Ah : area of bilinear hysteresis loop

an(t) : absolute acceleration of mode n

A′ : overlap area of rubber bearing in Chapter 3

b : subscript denoting base isolator

ůb, ůb(t) : relative veloc ity of base mass with respect to ground



(viii)

B : subscript denoting bilinear isolator

BF : ‘bulge fac tor’ describing the ratio Sr/Sr,1 of total shear to first-mode shear at level r in

a structure, particularly at mid-height

c(r,s) : interlevel veloc ity-damping coefficient, defined only for r≥ s

Cb : coefficient of veloc ity-damping for a base isolator, with units such as Nm-1s = kgs s-1

C F : correction factor linking displacement of bilinear isolator to equivalent spectral

displacement

ck : stiffness-proportiona l damping coefficient of shear beam representing a uniformshear structure

CK : overall stiffness-proportional damping coefficient C kA/L of uniform shear structure

cm : mass-proportional damping coefficient of shear beam representing a uniform shear

structure

CM : overall mass-proportional damping coefficient CmAL of uniform shear structure

c rs : element of damping coefficient matrix

[C] : damping coefficient matrix, with elements c rs related to c (r,s)

e : subscript used to denote ‘elastic-phase’

e : subscript used to denote ‘experimental model’ in ‘scaled’ (σ-ε) or ( τ- γ) curves for

steel dampers in Chapter 3

E : Young’s modulus =σ/ε in elastic region

f : force-scaling fac tor, as used in ‘scaled’ (σ-ε) or ( τ- γ) curves for steel dampers in

Chapter 3

F : force or shear-force as obtained from ‘scaled’ (σ-ε) or ( τ- γ) curves for steel

dampers in Chapter 3

FAr(T,ξ) : floor ac celeration spectrum at rth level of a structure

Fb : isolator force arising from bilinear resistance to displacement

Fe′ : residual force in elastic phase of bilinear isolator

FF : subscript denoting ‘free-free’ boundary condition corresponding to perfect

isolation

FFn : subscript denoting mode-n ‘free-free’ vibration

Fn(z) : maximum seismic force per unit height, at height z of mode n

Fr : maximum inertia load on the masss mr at level r

Frn : maximum seismic force of mode n at the rth point of a structure

Fy′ : residual force in yielding phase of bilinear isolator



(ix)

G : shear modulus = τ/γ in elastic region

G : constant shear modulus of shear beam representing a uniform shear structure

G0 : white noise power spec trum

hr : height of rth level of a structure

I : ‘degree of isolation’ or ‘isolation ratio’ given by ωFB1/ωb=Tb/TFB1=Tb/T1(U)

k : stiffness of single-mass oscillator

K : overall stiffness GA/L of uniform shear structure

k(r,s) : interlevel stiffness, such that k(r,r-1) = KN for a N-mass uniform structure and k(1,o) =

K b it if is isolated

K b : stiffness of linear isolator

K B : ‘effective’ or ‘secant’ stiffness of bilinear isolator

K b(r) : stiffness of rubber component of lead rubber bearing

K b1 : ‘initial’ or ‘elastic’ stiffness of bilinear isolator

K b2 : ‘post-yield’ or ‘plastic’ stiffness of bilinear isolator

K c : stiffness of spring introduced to isolator to reduce higher-mode responses (Figure

2.2c)

K n : stiffness of nth ‘spring’ in discrete linear cha in system

krs : element of stiffness matrix

[K] : stiffness matrix, with elements krs related to k(r,s)

ℓ : length-scaling fac tor, as used in ‘scaled’ (σ-ε) or ( τ- γ) curves for steel dampers in

Chapter 3

L : length of shear beam representing a uniform shear structure

m : mass of single-mass oscillator

M : mass pAL of uniform shear structure

M : total mass of structure; together with the mass of the isolator this gives M T

Mb : isolator (base) mass

mp : mass of primary structure

mr : mass at rth level

: M/ N for a uniform structure with N levels

ms : mass of secondary structure

M T : total mass of structure plus isolator



(xi)

Sn max : maximum shear at any position, in mode n

Sn (z) : maximum seismic shear at height z of mode n

Srn : maximum shear force at the rth point of a structure oscillating in mode n

Sv(T,ζ) : spectral relative velocity for period T and damping ζ

t : time

T : superscript indicating ‘transpose’

T : natural period

T1(U) : unisolated undamped first-mode period, the same as TFB1

Tb : natural period of linear base isolator = 2π/ω b

TB : ‘effective’ period for bilinear isolator

Tb1 : period assoc iated with K b1, in ‘elastic’ region of bilinear isolator

Tb2 : period assoc iated with K b2, in ‘plastic’ region of bilinear isolator

Tn(1) : isolated nth period

Tn(U) : unisolated nth period

u : vector containing the displacements ur

u(z,t) : relative displacement, at position z in the structure, in the horizontal x direc tion, with

respect to the ground at time t; often written as u, without arguments, in the

differential form of the equation of motion

ü(z,t) : relative acceleration with respect to ground of position z at time t

u1 : displacement of bilinear isolator

ub, ub(t) : relative displacement of base mass with respect to ground

üb, üb(t) : acceleration of base mass with respect to ground

ubj0 : base displac ement in free-free mode j

ubn(t) : nth-mode relative displacement, with respect to ground, at base of structure

at time t

ue,rn : elastic-phase displac ement at position r in mode n

üe,rn : elastic-phase relative acceleration at position r in mode n

uFBn(z,t) : fixed-base mode-n relative displacement with respect to ground at position z at

time t

uFFN(z,t) : ‘free-free’ mode-n relative displacement with respect to ground, at position z and

time t



(xii)

üg, üg(t) : ground acceleration

ULn, UNn : amplitude of nth-mode displacement at position z=L (top of shear beam) (possibly

complex); amplitude at top of discrete N-component structure

un(z) : nth mode shape, used interchangeably with Φn(z); usually normalisation is not

defined

un(z,t) : mode-n relative displacement, with respect to ground, of position z at time t

un0 : zeroth-order term in the perturbation expression for the mode shape

ups : displacement of secondary structure mounted on the primary structure

üps : acceleration of secondary structure mounted on the primary structure

urn(t) : Φrnξn(t) = displacement of mode-n at rth level of structure, where Φrn is the spatial

variation and ξn is the time variation

us : displacement of secondary structure mounted on the ground

üs : ac celeration of secondary structure mounted on the ground

uy,rn : yielding-phase displac ement at position r in mode n

üy,rn : yielding-phase relative acceleration at position r in mode n

un : displacement vector for discrete linear system in nth mode

v : vector comprising the relative velocity and relative displacement vectors

vn : vectorv for mode n

W : total weight of structure

X : displacement, as obtained from ‘scaled’ (σ-ε) or ( τ- γ) curves for steel dampers in

Chapter 3

Xb : maximum relative displacement of isolator or of base of isolated structure

XNn : maximum mode-n relative displacement at top floor of structure (position N)

Xp : peak response of primary structure when mounted on the ground

Xp(RMS) : RMS response of primary structure when mounted on the ground

Xps : peak response of secondary structure when mounted on primary structure

Xr : maximum relative displacement with respect to ground at any level r

Xrn : peak value of mode-n relative displacement at the rth point of a structure

Xs : peak response of secondary structure when mounted on the ground

Xs(RMS) : RMS response of secondary structure when mounted on the ground



(xiii)

Xy : yield displacement of bilinear isolator

Xy : displacement coordinate of yield point

..

Xrn : peak value of mode-n absolute acceleration at the rth point of a structure

.

Xrn : peak value of mode-n relative velocity at the rth point of a structure

z : vertical coordinate; height of a point of a structure

Zn(t) : relative displacement response, of one-degree-of-freedom oscillator of undamped

natural frequencyωn and damping ζn, to ground acceleration üg(t)

LIST OF COMMONLY USED ABBREVIATIONS

CQC : abbreviation for ‘Complete Quadratic Combination’, a method of adding

responses of several modes

DSIR : Department of Scientific and Industrial Research, New Zea land

LRB : Lead rubber bearing

MDOF : abbreviation for multiple-degree-of-freedom

MWD : Ministry of Works and Development, New Zealand

PEL : Physics and Engineering Laboratory of the DSIR, later DSIR Physica l Sciences

PTFE : polytetrafluoroethylene

SRSS : abbreviation for ‘Square Root of the Sum of the Squares’, a method of adding

responses of several modes

1DOF : abbreviation for one-degrees-of-freedom

2DOF : abbreviation for two-degrees-of-freedom



1

Chapter 1 INTRODUCTION

1.1 SEISMIC ISOLATION IN CONTEXT

A large proportion of the world's population lives in regions of seismic hazard, at risk fromearthquakes of varying severity and varying frequency of occurrence. Earthquakes causesignificant loss of life and damage to property every year.

Various a seismic construction designs and technologies have been developed over the yearsin attempts to mitigate the effects of earthquakes on buildings, bridges and potentiallyvulnerable contents. Seismic isolation is a relatively recent, and evolving, technology of this kind.

Seismic isolation consists essentially of the installation of mechanisms which decouple thestructure, or its contents, from potentially damaging earthquake-induced ground, or support,motions. This decoupling is achieved by increasing the flexibility of the system, together with

providing appropriate damping. In many, but not all, applications the seismic isolation system ismounted beneath the structure and is referred to as 'base isolation'.

Although it is a relatively recent technology, seismic isolation has been well evaluated andreviewed (e.g. Lee & Medland, 1978; Kelly, 1986; May 1990 issue of "Earthquake Spectra" ); andhas been the subjec t of international workshops (e.g., NZ-Japan Workshop, 1987; US-JapanWorkshop, 1990; Assisi Workshop, 1989; Tokyo Workshop, 1992); is included in the programmes ofinternational, regional and national conferences on Earthquake Engineering (e.g., 9th WCEEWorld Conference on Earthquake Engineering, Tokyo, 1988; Pacific Conferences, 1987, 1991;Fourth US Conference, 1990); and has been proposed for specialised applications (e.g., SMIRT11, Tokyo, 1991).

Seismic isolation may be used to provide effective solutions for a wide range of seismic designproblems. For example, when a large multi-storey structure has a critical Civil Defence rolewhich calls for it to be operational immediately after a very severe earthquake, as in the case ofthe Wellington Central Police Station (see Chapter 8), the required low levels of structural andnon-structural damage may be achieved by using an isolating system which limits structuraldeformations and ductility demands to low values. Again, when a structure or sub-structure isinherently non-ductile and has only moderate strength, as in the case of the newspaper printingpress at Petone (see Chapter 8), isolation may provide a required level of earthquake resistancewhich cannot be provided practically by earlier seismic techniques. Careful studies have beenmade of c lasses of structure for which seismic isolation may find widespread application. This hasbeen found to include common forms of highway bridges.

The increasing acceptance of seismic isolation as a technique is shown by the number of

retrofitted seismic isolation systems which have been installed. Examples in New Zealand are theretrofitting of seismic isolation to existing bridges and to the electrical capacitor banks atHaywards (see Chapter 8), while the retrofit of isolators under the old New ZealandParliamentary Buildings was completed in 1993. Many old monumental structures of highcultural value have little earthquake resistance.

The completed isolation retrofit of the Salt Lake City and County Building in Utah is described insome detail in Chapter 8.

Isolation may often reduce the cost of providing a given level of earthquake resistance. TheNew Zealand approach has been to design for some increase in earthquake resistance,together with some cost reduction, a typical target being a reduction by 5% of the structural

cost.



2

Reduced costs arise largely from reduced seismic loads, from reduced ductility demand andthe consequent simplified load-resisting members, and from lower structural deformations whichcan be accommodated with lower-cost detailing of the external cladding and glazing.

Seismic isolation thus has a number of distinctive beneficial features not provided by otheraseismic techniques. We believe that seismic isolation will increasingly become one of the many

options routinely considered and utilised by engineers, architects and their clients. Theincreasing role of seismic isolation will be reflected, for example, in widespread further inclusionof the technique in the seismic provisions of structural design codes.

When seismic isolation is used, the overall structure is considerably more flexible and provisionmust be made for substantial horizontal displacement. It is of interest that, despite the widelyvarying methods of computation used by different designers, a consensus is beginning toemerge that a reasonable design displacement should be of the order of 50 to 400 mm, andpossibly up to twice this amount if 'extreme' earthquake motions are considered. A 'seismic gap'must be provided for all seismically isolated structures, to allow this displacement duringearthquakes.

It is imperative that present and future owners and occupiers of seismically isolated structuresare aware of the functional importance of the seismic gap and the need for this space to beleft clear. For example, when a road or approach to a bridge is resealed or re-surfaced,extreme care must be taken to ensure that sealing material, stones etc, do not fall into theseismic gap.

In a similar way, the seismic gap around buildings must be kept secure from rubbish, and neverused as a convenient storage space.

All the systems presented in this book are passive, requiring no energy input or interaction withan outside source. Active seismic isolation is a different field, which confers different aseismicfeatures in the face of a different set of problems. As it develops, it will occupy a niche amongaseismic structures which is different from that occupied by structures with passive isolation. In a

typical case, a mass which is a fraction of a percent of the structural mass is driven with largeaccelerations so that the reaction to its inertia forces tend to cancel the effects of inertia forcesarising in the structure as a result of earthquake accelerations. Such a system may be apractical, but expensive, means of reducing the effective seismic loads during moderate, and insome locations frequent, earthquakes. Practical limitations on the size and displacements of theactive mass would normally render the system much less effective during major earthquakes.Moreover, it is difficult to ensure the provision of the increasing driving power required duringearthquakes of increased severity. In principle, such an active isolation system might be used tocomplement a passive isolation system in certain special cases. For example, a structure withpassive seismic isolation may be satisfactory in all respects, except that it may containcomponents which are particularly vulnerable to high-frequency floor-acceleration spectra. The active-mass power and displacement requirements for the substantial cancellation of these

short-period low-acceleration floor spectra may be moderate, even when the earthquake isvery severe. Moreover, such moderate power might be supplied by an in-house source, with itsdependability increased by the reduced seismic attack resulting from isolation.

A number of factors need to be considered by an engineer, architect or client wishing todecide whether a proposed structure should incorporate seismic isolation.

The first of these is the seismic hazard, which depends on local geology (proximity to faults, soilsubstructure), recorded history of earthquakes in the region, and any known factors about theprobable characteristics of an earthquake (severity, period, etc). Various proposed solutions tothe design problem can then be put forward, with a variety of possible structural forms andmaterials, and with some designs incorporating seismic isolation, some not. The probable level

of seismic damage can then be evaluated for each design, where the degree of seismicdamage can be broadly categorised as:



3

(1) minor

(2) repairable (up to about 30% of the construction cost)

(3) not repairable, resulting in the building being condemned.

The whole thrust of seismic isolation is to shift the probable damage level from (3) or (2) towards(1) above, and thereby to reduce the damage costs, and probably also the insurance costs.Maintenance costs should be low for passive systems, though they may be higher for activeseismic isolation. As discussed above, the construction costs including seismic isolation usuallyvary by + 5 to 10% from unisolated options.

The total 'costs' and 'benefits' of the various solutions can then be evaluated, where the analysishas to include the 'value' of having the structure or its contents in as good as possible acondition after an earthquake, and the reduced risk of casualties with reduced damage. Inmany cases such additional benefits may well follow the adoption of the seismic isolation option.

1.2 FLEXIBILITY, DAMPING AND PERIOD SHIFT

The 'design earthquake' is spec ified on the basis of the seismicity of a region, the site conditions,and the level of hazard accepted (for example, a '400-year return period' earthquake for agiven location would be expected to be less severe than one which occurred on averageonce every 1000 years).

Design earthquake motions for more seismic areas of the world are often similar to thatexperienced and recorded at El Centro, California, in 1940, or scalings of this motion, such as '1.5El Centro'. The spectrum of the El Centro accelerogram has large accelerations at periods of 0.1to 1 second. Other earthquake records, such as that at Pacoima Dam in 1971 or 'artificial'earthquakes A1 or A2 are also used in specifying the design level.

It must also be recognised that occasionally earthquakes give their strongest excitation at longperiods. The likelihood of these types of motions occurring at a particular site can sometimes beforeseen, such as with deep deposits of soft soil which may amplify low-frequency earthquakemotions, the old lake-bed zone of Mexico City being the best-known example. With this type ofmotion, flexible mountings with moderate damping may increase rather than decrease thestructural response. The provision of high damping as part of the isolation system gives animportant defence against the unexpected occurrence of such motions.

Typical earthquake accelerations have dominant periods of about 0.1 to 1 seconds as shown inFigure 2.1 in the next Chapter, with maximum severity often in the range 0.2 to 0.6 s. Structureswhose natural periods of vibration lie within the range 0.1 to 1 seconds are, therefore, particularlyvulnerable to seismic attack because they may resonate. The most important feature of seismicisolation is that its increased flexibility increases the natural period of the structure. Because theperiod is increased beyond that of the earthquake, resonance and near-resonance areavoided and the seismic acceleration response is reduced.

This period shift is shown schematically in Figure 1.1(a) and in more detail in Figure 2.1 inChapter 2.



4

Figure 1.1: Effect of increasing the flexibility of a structure:

(a) The increased period and damping lower the seismic acceleration response;(b) The increased period increases the total displacement of the isolated system,

but this is offset to a large extent by the damping. (After Buckle & Mayes, 1990.)

The increased period, and consequent increased flexibility, also affects the horizontal seismicdisplacement of the structure, as shown in Figure 1.1(b) for the simplest case of a single-massrigid structure and as shown in more detail in Figure 2.1 in Chapter 2. Figure 1.1(b) shows howexcessive displacements are counterac ted by the introduction of increased damping. Realvalues of the maximum undamped displacement for isolated structures could be as large as1 m in typical strong earthquakes; damping typically reduces this to 50 to 400 mm, and this is thedisplacement which has to be accommodated by the 'seismic gap.' The actual motion of partsof the structure depends on the mass distribution, the parameters of the isolating system, andthe 'participation' of various modes of vibration. This is discussed in detail in Chapters 2 and 6.

Seismic isolation is thus an innovative aseismic design approach aimed at protecting structures

against damage from earthquakes by limiting the earthquake attack rather than resisting it.Conventional approaches to aseismic design provide a structure with sufficient strength,deformability and energy-dissipating capacity to withstand the forces generated by anearthquake, and the peak acceleration response of the structure is often greater than the peakacceleration of the driving ground motion. On the other hand, seismic isolation limits the effectsof the earthquake attack, since a flexible base largely decouples the structure from thehorizontal motion of the ground, and the structural response accelerations are usually less thanthe ground accelerations. The forces transmitted to the isolated structure are further reducedby damping devices which dissipate the energy of the earthquake-induced motions.

Figure 1.2(a) illustrates the seismic isolation concept schematically. The building on the left isconventionally protected against seismic attack and that on the right has been mounted on aseismic isolation system. The performance of a pair of real test buildings of this kind, at Tohoku

University, Sendai, J apan, is described in Chapter 8. Similar schematic diagrams can be drawnto illustrate the seismic isolation of bridges and of parts of buildings which contain delicate orpotentially hazardous contents.



5

Figure 1.2: (a) Schematic seismic response of two buildings; that on the left is conventionallyprotected against earthquake, and that on the right has been mounted on aseismic isolation system.

(b) Maximum base shear for a single-mass structure, represented as a linear resonator,with and without seismic isolation. The structure is subjected to P a times the El CentroNS 1940 accelerogram. (From Skinner & McVerry, 1975).

In Figure 1.2(a) it can be seen that large seismic forces act on the unisolated, conventionalstructure on the left, causing considerable deformation and cracking in the structure. In theisolated structure on the right, the forces are much reduced, and most of the displacementoccurs across the isolation system, with little deformation of the structure itself, which movesalmost as a rigid unit. Energy dissipation in the isolated system is provided by hysteretic or viscousdamping. For the unisolated system, energy dissipation results mainly from structural damage.

Figure 1.2(b) illustrates the reduction of earthquake induced shear forces which can be

achieved by seismic isolation. The maximum responses of seismically isolated structures, as afunction of unisolated fundamental period are shown by a solid line and those of the unisolatedstructures as a dotted line, with results shown for three scalings of the El Centro NS 1940earthquake motion. It is seen that seismic isolation markedly reduces the base shear in all cases.

1.3 COMPARISON OF CONVENTIONAL & SEISMIC ISOLATION APPROACHES

Many of the concepts of seismic isolation using hysteretic isolators are similar to the conventionalfailure-mode-control approach ('capacity design') which is used in New Zealand for providingearthquake resistance in reinforced concrete and steel structures.

In both the seismic isolation and failure-mode-control approaches, specially selected ductilecomponents are designed to withstand several cycles well beyond yield under reversedloading, the yield levels being chosen so that the forces transmitted to other components of thestructure are limited to their elastic or low ductility, range. The yielding lengthens thefundamental period of the structure, detuning the response away from the energetic periodrange of most of the earthquake ground motion. The hysteretic behaviour of the ductilecomponents provides energy dissipation to damp the response motions. The ductile behaviourof the selected components ensures sufficient deformation capacity, over a number of cyclesof motion, for the structure as a whole to ride out the earthquake attack.

However, seismic isolation differs fundamentally from conventional seismic design approaches inthe method by which the period lengthening (detuning) and hysteretic energy dissipating

mechanisms are provided, as well as in the philosophy of how the earthquake attack iswithstood.

(a) (b)



6

In well-designed conventional structures, the yielding action is designed to occur within thestructural members at specially selected locations ('plastic hinge zones'), e.g. mostly in thebeams adjacent to beam-column joints in moment-resisting frame structures. Yielding ofstructural members is an inherently damaging mechanism, even though appropriate selectionof the hinge locations and careful detailing can ensure structural integrity. Large deformations

within the structure itself are required to withstand strong earthquake motions. Thesedeformations cause problems for the design of components not intended to provide seismicresistance, because it is difficult to ensure that unintended loads are not transmitted to themwhen the structure is deformed considerably from its rest position. Further problems occur in thedetailing of such items as windows and partitions, and for the seismic design of building services.

In the conventional approach, it is accepted that considerable earthquake forces and energywill be transmitted to the structure from the ground. The design problem is to provide thestructure with the capacity to withstand these substantial forces.

In seismic isolation, the fundamental aim is to reduce substantially the transmission of theearthquake forces and energy into the structure. This is achieved by mounting the structure on

an isolating layer (isolator) with considerable horizontal flexibility, so that during an earthquake,when the ground vibrates strongly under the structure, only moderate motions are inducedwithin the structure itself. Practical isolation systems must trade-off between the extent of forceisolation and acceptable relative displacements across the isolation system during theearthquake motion. As the isolator flexibility increases, movements of the structure relative tothe ground may become a problem under other vibrational loads applied above the level ofthe isolation system, particularly wind loads. Acceptable displacements in conjunction with alarge degree of force isolation can be obtained by providing damping, as well as flexibility in theisolator. A seismic isolation system with hysteretic force-displacement characteristics canprovide the desired properties of isolator flexibility, high damping and force-limitation underhorizontal earthquake loads, together with high stiffness under smaller horizontal loads to limitwind-induced motions. A further trade-off is involved if it is necessary to provide a high level ofseismic protection for potentially resonant contents and substructures, where increased isolator

displacements and/or structural loads are incurred when providing this additional protection.

1.4 COMPONENTS IN AN ISOLATION SYSTEM

The components in a seismic isolation system are spec ially designed, distinct from the structuralmembers, installed generally at or near the base of the structure. However, in bridges, where theaim is to protect relatively low-mass piers and their foundations, they are more commonlybetween the top of the piers and the superstructure. The isolator's viscous damping andhysteretic properties can be selected to maintain all components of the superstructure withinthe elastic range, or at worst so as to require only limited duc tile action. The bulk of the overall

displacement of the structure can be concentrated in the isolator components, with relativelylittle deformation within the structure itself, which moves largely as a rigid body mounted on theisolation system. The performance can be further improved by brac ing the structure to achievehigh stiffness, which increases the detuning between the fundamental period of thesuperstructure and the effective period of the isolated system and also limits deformations withinthe structure itself. Both the forces transmitted to the structure and the deformation within thestructure are reduced, and this simplifies considerably the seismic design of the superstructure, itscontents and services, apart from the need for the service connections to accommodate thelarge displacements across the isolating layer.



7

Figure 1.3: Schematic representation of the force-displacement hysteresis loops produced by:(a) a linear damped isolator;(b) a bilinear isolator with a Coulomb damper.

Figure 1.3 is a schematic representation of the two major models encountered in the practicaldesign of seismic isolating systems. Figure 1.3(a) represents a linear damped isolator by means ofa linear spring and 'viscous damper'. The resultant force-displacement loop has an effectiveslope (dashed line) which is the 'stiffness', or inverse flexibility, of the isolator. Figure 1.3(b)represents a 'bilinear' isolator as two linear springs, one of which has a 'Coulomb damper' inseries with it.

The resultant hysteresis loop is bilinear, characterised by two slopes which are the 'initial' and'yielded' stiffnesses respectively, corresponding to the elastic and plastic deformation of theisolator.

A variety of seismic isolation and energy dissipation devices has been developed over the years,all over the world. The most successful of these devices also satisfy an additional criterion,namely, they have a simplicity and effectiveness of design which makes them reliable andeconomic to produce and install, and which incorporates low maintenance, so that a passivelyisolated system will perform satisfactorily, without notice or forewarning, for 5 to 10 seconds of

earthquake activity at any stage during the 30- to 100-year life of a typical structure. In order toensure that the system is operative at all times, we suggest that zero or low maintenance bepart of good design.

Detailed discussion of the material and design parameters of seismic isolation devices is given inChapter 3.

1.5 PRACTICAL APPLICATION OF THE SEISMIC ISOLATION CONCEPT

The seismic isolation concept for the protection of structures from earthquakes has beenproposed in various forms numerous times this century. Many systems have been put forward,involving features such as roller or rocker bearings, sliding on sand or talc, or compliant first-storeycolumns, but these have generally not been implemented.



8

The practical application of seismic isolation is a new development pioneered by a feworganisations around the world in recent years. The efforts of these pioneers are nowblossoming, with seismic isolation becoming increasingly recognised as a viable designalternative in the major seismic regions of the world.

The authors' group at DSIR Physical Sciences, previously the Physics and Engineering Laboratory

of the Department of Scientific and Industrial Research (PEL, DSIR) in New Zealand, haspioneered seismic isolation, with research starting in 1967. Several practical techniques forachieving seismic isolation and a variety of energy-dissipating devices have been developedand implemented in over 40 structures in New Zealand, largely through the innovativeapproach and cooperation of engineers of the Ministry of Works and Development (MWD), aswell as private structural engineering consultants in New Zealand.

All the techniques developed at DSIR Physical Sciences have had a common element, in thatdamping has been achieved by the hysteretic working of steel or lead (see Chapter 3).Flexibility has been provided by a variety of means: transverse rocking action with base uplift(South Rangitikei railway bridge, and chimney at Christchurch airport), horizontally flexiblelead-rubber isolators (William Clayton Building, Wellington Press Building, Petone, and numerous

road bridges), and flexible sleeved-pile foundations (Union House in Auckland and WellingtonCentral Police Station). Hysteretic energy dissipation has been provided by various steelbending-beam and torsional-beam devices (South Rangitikei Viaduct, Christchurch airportchimney, Union House, Cromwell bridge and Hikuwai retrofitted bridges), lead plugs inlaminated steel and rubber bearings (William Clayton Building and numerous road bridges); andlead-extrusion dampers (Aurora Terrace and Bolton Street motorway overpasses in Wellingtonand Wellington Central Police Station). More details of these structures are given in Chapter 8.

Before their use in structures, all these types of devices have been thoroughly tested at full scaleat DSIR Physical Sciences, in dynamic test machines under both sinusoidal and earthquake-likeloadings. Other tests have been performed at the Universities of Auckland and Canterbury.

Shaking-table tests of elastomeric and lead rubber bearings and steel dampers have beenperformed at the University of California, Berkeley, and in Japan on large-scale model structures.Quick-release tests on actual structures containing these types of bearings and dampingdevices have been performed in New Zealand and J apan. Some seismically isolated structureshave performed successfully during real, but so far, minor, earthquake motions.

A number of organisations around the world have developed isolation systems different fromthose at DSIR Physical Sciences. Most have used means other than the hysteretic action ofductile metal components to obtain energy dissipation, force limitation and base flexibility.Various systems have used elastomeric bearings without lead-plugs, damping being providedeither by the use of high-loss rubber or neoprene materials in the construction of the bearings orby auxiliary viscous dampers. There have been a number of applications of frictional slidingsystems, both with and without provision of elastic centring action. There has been substantial

work recently on devices providing energy-dissipation alone, without isolation, in systems notrequiring period shifting, either because of the substantial force reduction from large damping orbecause the devices were applied in inherently long-period structures, such as suspensionbridges or tall buildings, where isolation itself produces little benefit. There has also been work onvery expensive mechanical linkage systems for obtaining three-dimensional isolation.

Seismic isolation has often been considered as a technique only for 'problem' structures or forequipment which requires a spec ial seismic design approach. This may arise because of theirfunction (sensitive or high-risk industrial or commercial fac ilities such as computer systems,semiconductor manufacturing plant, biotechnology facilities and nuclear power plants); theirspecial importance after an earthquake (e.g., hospitals, disaster-control centres such as policestations, bridges providing vital communication links); poor ground conditions; proximity to a

major fault; or other special problems (e.g., increasing the seismic resistance of existingstructures).



9

Seismic isolation does indeed have particular advantages over other approaches in thesespecial circumstances, usually being able to provide much better protection under extremeearthquake motions. However, its economic use is by no means limited to such cases.

In New Zealand, the most common use of seismic isolation has been in ordinary two-lane roadbridges of only moderate span, which are by no means special structures, although admittedly

the implementation of seismic isolation required little modification of the standard design whichalready used vulcanised laminated rubber bearings to accommodate thermal and othermovements.

1.6 TOPICS COVERED IN THIS BOOK

In this book we seek to present a parallel development of theoretical and practical aspects ofseismic isolation, as well as presenting information about buildings and bridges that have beenbuilt using this technique all over the world, and how they have performed in real earthquakes.

Mathematical rigour is achieved by retaining Chapters 2 of “An Introduction to Seismic Isolation”which presents mathematical concepts derived from the basic equations of damped simpleharmonic motion.

In Chapter 2 the principal seismic response features conferred by isolation are outlined, withdescriptions and brief explanations. Seismic response spectra are introduced as the maximumseismic displacements and accelerations of linear 1.mass damped vibrators. It is later shownthat these spectra give good approximations to the maximum displacements, accelerationsand loads of structures mounted on linear isolation systems, which respond approximately asrigid masses with little deformation and little higher-mode response.

The spectra vary depending on the accelerogram used to excite the seismic response, with ElCentro NS 1940, or appropriately scaled versions of this design earthquake, being used most

commonly throughout this book.

When the single mass is mounted on a bilinear isolation system, the maximum seismicdisplacement and acceleration responses can be represented in terms of 'effective' periodsand dampings. This concept is an oversimplification but is valid for a wide range of bilinearparameters. It is convenient to introduce an 'isolator nonlinearity factor' NL, which is defined interms of the force-displacement hysteresis loop. However, unlike the case with linear isolation,many bilinear isolation systems result in large higher-mode effects which may make large oreven dominant contributions to the maximum seismic loads throughout the isolated structure. They may also result in relatively severe appendage responses, as given by floor accelerationspectra, for periods below 1.0 seconds.

The above and other features of the maximum seismic responses of isolated structures areillustrated at the end of Chapter 2 by seven case studies, as summarised in Table 2.1 andFigure 2.7 and further by Table 2.2. Features examined include the maximum seismicresponses of a simple uniform shear structure and of 1.mass top-mounted appendages,when the structure is unisolated and when it is supported on each of six isolation systems.

Chapter 3, which is also carried over from “An Introduction to Seismic Isolation”, presents detailsof seismic isolation devices, with particular reference to those developed in our laboratory overthe past 25 years, including steel-beam dampers, lead extrusion dampers and lead rubberbearings. The treatment discusses the material properties on which the devices are based, andoutlines the principal features which influence the design of these devices.



10

Chapters 4 and 5 of the original manuscript “an Introduction to Seismic isolation” have not beencarried over into this new book.

Chapters 4, 5, 6 and 7 of this book contain new material written by Trevor Kelly. Chapter 4continues from Chapter 3, giving engineering properties of the devices described in the previouschapter. Chapter 5 presents detailed procedures for isolation system design. Chapter 6 is a

detailed analysis of the seismic responses of various prototype buildings each of which isprovided with different isolating systems. Chapter 7 continues this work with examples of seismicisolation of a building and a bridge.

Chapter 8 of this new book carries over Chapter 6 of “An Introduction to Seismic Isolation” andgives some details of seismically isolated structures worldwide. The original Chapter 6 has beenvirtually unchanged in being transposed to Chapter 8 of the new book, and it presentsinformation on the world-wide use of seismic isolation in buildings, bridges and spec ial structureswhich are particularly vulnerable to earthquakes. The information was compiled in 1992 with thehelp of colleagues world-wide, who have enabled us to build up a picture of the isolationapproaches which have been adopted in response to a wide range of seismic designproblems. We should like to thank these colleagues for their contributions.

Chapter 9 discusses implementation issues which arise in seismic isolation projects and providesguidance for dealing with these issues.

It is clear that engineers, architects and their clients world-wide are building up extensiveexperience in the development, design and potential uses of isolation systems. In time, theseisolated structures will also provide a steadily increasing body of information on the performanceof seismically isolated systems during actual earthquakes. In this way the evolving technology ofseismic isolation may contribute to the mitigation of earthquake hazard worldwide. Chapter 10presents ideas as to where seismic isolation could go in the new millennium, when it is widelyrecognised as a practical means of reducing death, injury, property damage in the event ofan earthquake. Chapter 10 also presents additional devices that have been developed orare under development, such as in-structure damping and the RoBall seismic isolator.



11

Chapter 2 GENERAL FEATURES OF STRUCTURES WITHSEISMIC ISOLATION

2.1 INTRODUCTION

For many structures the severity of an earthquake attack may be lowered dramatically byintroducing a flexible isolator as indicated by Figure 1.1. The isolator increases the natural periodof the overall structure and hence decreases its acceleration response toearthquake-generated vibrations. A further decrease in response occurs with the addition ofdamping. This increase in period, together with damping, can markedly reduce the effect ofthe earthquake, so that less-damaging loads and deformations are imposed on the structureand its contents.

This chapter examines the general changes in vibrational character which different types ofseismic isolation confer on a structure, and the consequent changes in seismic loads anddeformations. The study is greatly assisted by considering structural modes of vibration andearthquake response spectra, an approach which has proved very effective in the study anddesign of non-isolated aseismic structures (Newmark & Rosenblueth, 1971; Clough & Penzien,1975).

The seismic responses of general linear structures are introduced early to provide the conceptsused throughout this Chapter and later in the book. Attention is also given to seismic responsemechanisms since they assist in understanding the seismic responses of isolated structures andhow they are related to the responses of similar structures which are not isolated. The generalconsequences of seismic isolation are illustrated using 6 different isolation systems.

This chapter leads to some useful approaches for the study of seismic isolation, gives a greaterunderstanding of the mechanisms involved, and indicates some useful design approaches.

The discussions throughout this chapter assume simple torsionally-balanced structures in whichthe structural masses at rest are centred on a vertical line, as illustrated in the figures 2.1 to 2.7.

2.2 ROLE OF EARTHQUAKE RESPONSE SPECTRA AND VIBRATIONAL MODES INTHE PERFORMANCE OF ISOLATED STRUCTURES

2.2.1 Earthquake Response Spectra

The horizontal forces generated by typical design-level earthquakes are greatest on structureswith low flexibility and low vibration damping. The seismic forces on such structures can bereduced greatly by supporting the structure on mounts which provide high horizontal flexibilityand high vibration damping. This is the essential basis of seismic isolation. It can be illustratedmost clearly in terms of the response spectra of design earthquakes.

The main seismic attack on most structures is the set of horizontal inertia forces on the structuralmasses, these forces being generated as a result of horizontal ground accelerations. For moststructures, vertical seismic loads are relatively unimportant in comparison with horizontal seismicloads. For typical design earthquakes, the horizontal accelerations of the masses of simpleshorter-period structures are controlled primarily by the period and damping of the firstvibrational mode, i.e., that form in which the system resonates at the lowest frequency.



12

The dominance of the first mode occurs in isolated structures, and in unisolated structures withfirst-mode periods up to about 1.0 seconds, a period range which includes most structures forwhich isolation may be appropriate.

Neglecting the less important factors of mode shape and the contribution of higher modes of

vibration, the seismic acceleration responses of the isolated and unisolated structures may becompared broadly by representing them as single-mass oscillators which have the periods anddampings of the first vibrational modes of the isolated and unisolated structures respectively.

The natural (fundamental) period T, natural frequency and damping factor of such asingle-mass oscillator, of mass m, are obtained by considering its equation of motion:

where u is the displacement of the single-mass oscillator relative to the ground, ug is the grounddisplacement, k is the 'spring stiffness' and c is the 'damping coefficient'.

The natural (fundamental) frequency of undamped, unforced oscillations (c=0 and üg=0) is

or

The solution for damped, unforced oscillations is

where

and where A and are constants representing the initial displacement amplitude and initialphase of the motion.

The damped, unforced oscillation has thus a lower frequency d than the natural frequency,and d decreases as the value of the damping coefficient c is increased. If c is increased to a'critical value' ccr such that d=0, the system will not oscillate. The critical damping is given by

A 'damping factor' can then be defined which expresses the damping as a fraction of criticaldamping:

The equation of motion can then be divided by m to give

or

Åm-=ku+uc+mÅ g (2.1)

k/m=2 (2.2)

m/k 2=T (2.3)

) +t( cos eA=u dtm)2-(c/

)m2(c/ - (k/m)= 22d

mk 2=ccr

m4cT/ = m2c/=)mk c/(2=cc/= cr (2.4)

u-=um

k +u

m

c +u g

u-=u+u2+u g2

(2.5)



13

For this (damped, forced) dynamic system, the displacement response to ground accelerationsmay be given in closed form as a Duhamel integral, obtained by expressing ü g(t) as a series ofimpulses and summing the impulse responses of the system. When the system starts from rest attime t = 0, this gives the relative displacement response as:

By successive differentiation, similar expressions may be obtained for the relative velocityresponse u and the total acceleration response ü + üg. For particular values of and , theresponses to the ground accelerations of a given earthquake may be obtained from step-by-step evaluation of equation (2.6) or from other evaluation procedures.

Since structural designs are normally based on maximum responses, a convenient summary ofthe seismic responses of single-mass oscillators is obtained by recording only the maximumresponses for a set of values of the oscillator parameters (or T) and . These maximumresponses are the earthquake response spectra. They may be defined as follows:

Such spectra are routinely calculated and published for important accelerograms, e.g. EERLReports (1972.5).

Figure 2.1 shows response spectra for various damping factors (0, 2, 5, 10 and 20 percent ofcritical) for a range of earthquakes.

d)-(tsin)]-(texp[- )(Å)/(1-=u(t) dgt0d (2.6)

)u(t =) ,(T S ;)(t u=) ,(T S ;))(t Å + (Å=) ,(T S DV g A maxmaxmax (2.7)

(a)



14

Figure 2.1: Response spectra for various damping factors. In each figure, the curvewith the largest values has 0% damping and successively lower curves are for

damping factors of 2, 5, 10 and 20% of c ritica l.(a) Acceleration response spectrum for El Centro NS 1940(b) Acceleration response spectrum for the weighted average of eight

accelerograms (El Centro 1934, El Centro 1940, Olympia 1949, Taft 1952). Thesymbols U and I refer to unisolated and isolated structures respectively.

(c) Displacement spectra corresponding to Figure 2.1(b).

Figure 2.1(a) shows acceleration response spectra for the accelerogram recorded in the S0oEdirection at El Centro, California, during the 18 May 1940 earthquake (often referred to as'El Centro NS 1940'). This accelerogram is typical of those to be expected on ground ofmoderate flexibility during a major earthquake. The El Centro accelerogram is used extensivelyin the following discussions because it is typical of a wide range of design accelerograms, andbecause it is used widely in the literature as a sample design accelerogram.

Seismic structural designs are frequently based on a set of weighted accelerograms, which areselected because they are typical of site accelerations to be expected during design-levelearthquakes.

(b)

(c)



15

The average acceleration response spectra for such a set of 8 weighted horizontal accelerationcomponents are given in Figure 2.1(b). Each of the 8 accelerograms has been weighted togive the same area under the acceleration spectral curve, for 2% damping over the periodrange from 0.1 to 2.5 seconds, as the area for the El Centro NS 1940 accelerogram (Skinner,1964).

Corresponding response spectra can be presented for maximum displacements relative to theground, as given in Figure 2.1(c). These displacement spectra show that, for this type ofearthquake, displacement responses increase steadily with period for values up to about3.0 seconds. As in the case of acceleration spectra, the displacement spectral values decreaseas the damping increases from zero. The spec tra shown in Figures 2.1(b) and 2.1(c) are moreexact presentations of the concept illustrated in Figure 1.1.

While the overall seismic responses of a structure can be described well in terms of groundresponse spectra, the seismic responses of a light-weight sub-structure can be described moreeasily in terms of the response spectra of its supporting floor. Floor response spectra are derivedfrom the accelerations of a point or 'floor' in the structure, in the same way that earthquakeresponse spectra are derived from ground accelerations. Thus they give the maximum responseof light-weight single-degree-of-freedom oscillators located at a particular position in thestructure, assuming that the presence of the oscillator does not change the floor motion. It isalso possible to derive floor spectra which include interaction effects. Floor response spectratend to have peaks in the vicinity of the periods of modes which contribute substantialacceleration to that floor.

The response spectrum approach is used throughout this book to increase understanding of thefactors which influence the seismic responses of isolated structures. The response spec trumapproach also assists in the seismic design of isolated structures, since it allows separateconsideration of the character of design earthquakes and of earthquake-resistant structures. Atechnique which is given some emphasis is the extension of the usual response spectrumapproach for linear isolators to the case of bilinear isolators.

2.2.2 General Effects of Isolation on the Seismic Responses of Structures

The first mode of a simple isolated structure is very different from all its other modes, which havefeatures similar to each other. We treat the first mode separately from all the other modes,which are usually referred to herein as 'higher modes'. The first-mode period and damping of anisolated structure, and hence its seismic responses, are determined primarily by thecharacteristics of the isolation system and are virtually independent of the period and dampingof the structure.

In the first isolated mode the vertical profiles of the horizontal displacements and accelerationsare approximately rectangular, with approximately equal motions for all masses (see later,Figure 2.5). Hence an isolated structure may be approximated by a rigid mass when assessingthe seismic responses of its first vibrational mode.

Except for special applications, the seismic responses of structures with linear isolation can bedescribed in terms of earthquake response spectra, and the simple first mode of vibration.When the isolation is strongly nonlinear, many important seismic responses can still be describedin terms of mode 1, but higher modes can be of importance.

Figures 2.1(a) and (b) show acceleration response spectra for typical design earthquakes. It isseen that these maximum accelerations, and hence the general inertia attacks on structures,

are most severe when the first vibrational period of the structure is in the period range fromabout 0.1 to 0.6 seconds and when the structural damping is low. This period range is typical ofbuildings which have from 1 to 10 storeys.



16

The shaded area marked (U) in Figure 2.1(b) gives the linear acceleration spectral responses forthe range of first natural periods (up to about 1.0 second) and structural dampings (up to about10% of critical) to be expected for structures which are promising candidates for seismicisolation. Similarly, the shaded area marked (I) in Figure 2.1(b) gives the acceleration spectralresponses for the range of first-mode periods and dampings which may be conferred on a

structure by isolation systems of the types described in Chapter 3.

A comparison of the shaded areas for unisolated and isolated structures in Figure 2.1(b) showsthat the acceleration spectral responses, and hence the primary inertia loads, may well bereduced by a factor of 5 to 10 or more by introducing isolation. While higher modes of vibrationmay contribute substantially to the seismic accelerations of unisolated structures, and ofstructures with non-linear isolation, this does not seriously alter the response comparison basedon the shaded areas of Figure 2.1(b). This figure therefore illustrates the primary basis for seismic

isolation.

The contributions of higher modes to the responses of isolated structures are described ingeneral terms below, and in more detail later in this chapter.

Almost all the horizontal seismic displacements, relative to the ground, are due to the firstvibrational mode, for both unisolated and isolated structures. The seismic displacementresponses for unisolated and isolated structures are shown in Figure 2.1(c) by the shaded areas(U) and (I) respectively. These shaded areas have the same period and damping ranges as thecorresponding areas in Figure 2.1(b). As noted above, the first-mode period and damping ofeach isolated structure depend almost exclusively on the isolator stiffness and damping. Figure2.1(c) shows a considerable overlap in the displacements which may occur with and withoutisolation. This may arise when high isolator damping more than offsets the increase indisplacement which would otherwise occur because the isolator has increased the overallsystem flexibility.

Moreover, while displacements without isolation normally increase steadily over the height of astructure, the displacements of isolated structures arise very largely from isolator displacements,with little deformation of the structure above the isolator, giving the approximately rectangularprofile of mode 1. Figure 2.1(c) shows that isolator displacements may be quite large. The largerdisplacements may contribute substantially to the costs of the isolators and to the costs ofaccommodating the displacements of the structures, and therefore isolator displacements areusually important design considerations.

A convenient feature of the large isolator displacements is that the isolator location provides aneffective and convenient location for dampers designed to confer high damping on thedominant first vibrational mode. Moreover, some dampers require large strokes to be effective.Such damping reduces both the accelerations which attack the structure and the isolatordisplacements for which provision must be made.

2.2.3 Parameters of Linear and Bilinear Isolation Systems

A typical isolated structure is supported on mounts which are considerably more flexible underhorizontal loads than the structure itself. It is assumed here that the isolator is at the base of thestructure and that it does not contribute to rocking motions. As a first approximation, thestructure is assumed to be rigid, swaying sideways with approximately constant displacementalong its height, corresponding to the first isolated mode of vibration.

Some isolation systems used in practice are 'damped linear' systems such as presented in

equations (2.1) and (2.5). However, an alternative approach, for the provision of high isolatorflexibility and damping, is to use nonlinear hysteretic isolation systems, which also inhibitwind-sway.



17

Such nonlinearity is frequently introduced by hysteretic dampers, or by the introduction of slidingcomponents to increase horizontal flexibility, as discussed in Chapter 3. These isolation systemscan usually be modelled approximately by including a component which slides with friction,and gives a bilinear force-displacement loop when the model is cycled at constant amplitude.Models of linear and bilinear isolation systems, with the structure modelled by its total mass M,

are shown in Figures 2.2(a) and 2.3(a).

Figure 2.2: Schematic representation of a damped linear isolation system.(a) Structure of mass M supported by linear isolator of shear stiffness K b, with

velocity damper (viscous damper) of coefficient Cb.

(b) Shear force S versus displacement X showing the hysteresis loop and definingthe secant stiffness of the linear isolator: K b =Sb/Xb.

(c) Linear isolator with high damping coefficient and higher-mode attenuator K c.

(a)

(b)

(c)



18

Figure 2.3: Schematic representation of a bilinear isolation system.(a) Structure of mass M supported by bilinear isolator which has linear 'spring'

components of stiffnesses K b1 and K b2, together with a sliding (Coulomb)damper component.

(b) Shear force versus displacement showing the bilinear hysteresis loop anddefining the secant stiffness of the bilinear isolator: K B =Sb/Xb. Theindividual stiffnesses K b1 and K b2 are the slopes (gradients) of the hysteresis

loop as shown, and (Xy, Qy) is the yield point.(c) Comparison of linear hysteresis loop with a circumscribed rectangle, to

enable definition of the nonlinearity factor NL.

The linear isolation system (Figure 2.2) has shear stiffness K b and its coefficient of (viscous-)velocity-damping is Cb, where the subscript b is used to denote parameters of the linear isolator. These parameters may be related to the mass M or the weight W of the isolated structure using

equations (2.3) and (2.4). This gives the natural period Tb and the velocity damping factorb:

and

Figure 2.2(b) shows the 'shear force' versus 'displacement' hysteresis loop of such a dampedlinear isolator, which is traversed in the clockwise direction as the shear force and displacementcycle between maximum values +Sb and +Xb respectively. The 'effective stiffness' of the isolatoris then defined as

The design values chosen for Tb and b will usually be based on a compromise between seismic

)K M/(2=T b b (2.8a)

M) /(4 T C = bbb (2.8b)

X /S=K b b b (2.9)

(a)

(c)

(b)



19

forces, isolator displacements, their effec ts on seismic resistance and the overall costs of theisolated structure.

When the isolator velocity-damping is quite high, say b greater than 20%, higher-modeacceleration responses may become important, especially regarding floor acceleration

spectra. Such an increase in higher-mode responses may be largely avoided by anchoring thevelocity dampers by means of components of appropriate stiffness K c, as modelled inFigure 2.2(c).

The bilinear isolator model (Figure 2.3(a)) has a stiffness K b1 without sliding, (the 'elastic-phasestiffness'), and a lower stiffness K b2 during sliding or yielding, (the 'plastic-phase stiffness'). Byanalogy with the linear case, these stiffnesses can be related to corresponding periods ofvibration of the system:

Corresponding damping factors can also be defined:

An additional parameter required to define a bilinear isolator is the yield ratio Qy/W, relating theyield force Qy of the isolator, Figure 2.3(b), to the weight W of the structure. Yielding occurs at adisplacement Xy given by Qy/K b1. When the design earthquake has the severity and characterof the El Centro NS 1940 accelerogram it has been found that a yield ratio Q y/W ofapproximately 5% usually gives suitable values for the isolator forces and displacements. In orderto achieve corresponding results with a design accelerogram which is a scaled version of anEl Centro-like accelerogram, it is necessary to scale Qy/W by the same factor, as described inChapters 4 and 5.

It is found useful to describe the bilinear system using 'effective' values, namely an appropriatelydefined 'effective' period TB and 'effective' damping factor B. The subscript B is used for theseeffec tive values of a bilinear isolator.

The effective bilinear values TB and B are obtained with reference to the 'shear force' versus'displacement' hysteresis loop shown in Figure 2.3(b). This balanced-displacement bilinear loop isa simplification used to define these parameters of bilinear isolators. In practice, the reversedisplacements, immediately before and after the maximum displacement Xb will have lowervalues. In general, the concept of these 'effective' values is a gross approximation, but it workssurprisingly well. Note also that the simplified bilinear loop shown does not include the effects ofveloc ity-damping forces. The damping shown is 'hysteretic', depending on the area of thehysteresis loop.

The 'effective' stiffness K B (also known as the 'secant' stiffness) is defined as the diagonal slope ofthe simplified maximum response loop shown in Figure 2.3(b):

This gives the effective period

)K M/ (2 ,)K M/ (2=T ,T b2b1b2b1 (2.10a)

M) /(4TCM), /(4TC=, 2 b b1 b b2 b1 b (2.10b)

X /S=K b bB (2.11a)

K M/ 2=T BB (2.11b)



20

An equivalent viscous-damping factor h can be defined to account for the hysteretic dampingof the base. Any actual viscous damping b of the base must be added to h to obtain theeffective viscous-damping factor B for the bilinear system. In practice h is usually larger than b,i.e. the damping of a bilinear hysteretic isolator is usually dominated by the hysteretic energydissipation rather than by the viscous damping b.

Thus

where, from equation (2.4),

and where h is obtained by relating the maximum bilinear loop area to the loop area of avelocity-damped linear isolator vibrating at the period TB with the same amplitude Xb, to give

where Ah = area of the hysteresis loop.

For nonlinear isolators, it is convenient to have a quantitative definition of nonlinearity. We havefound it useful to define a nonlinearity factor, NL, in terms of Figures 2.3(b) and 2.3(c), as the ratioof the maximum loop off-set, from the secant line joining the points (Xb,Sb) and (-Xb,-Sb), to themaximum off-set of the axis-parallel rectangle through these points, i.e., P1/P2. Hence thenonlinearity factor increases from 0 to 1 as the loop changes from a zero-area shape to arectangular shape. For a bilinear isolator this is equivalent to the ratio of the loop area Ah to thatof the rectangle.

The nonlinearity factor NL is thus given by

From equations (2.13) and (2.14) it is seen that the hysteretic damping factor h is proportional tothe non-linearity factor NL for bilinear hysteretic loops. However, re-entrant bilinear loops mayhave a much lower ratio of damping to nonlinearity.

2.2.4 Calculation of Seismic Responses

When the isolator is linear and the base flexibility sufficient for the first mode to dominate theresponse, the maximum seismic responses of the system may be approximated bydesign-earthquake spectral values, as given for example in Figure 2.1, for the isolator period Tb and damping b. For the approximately rigid-structure motions of the first isolated mode, themaximum displacement Xr at any level r in the structure is given by

The maximum inertia load Fr, on the r-th mass mr, is given by

The inertia forces are approximately in phase and may be summed to give the shear at eachlevel. In particular the base-level shear is given by

h bB += (2.11c)

M) /(4TC B b b (2.12)

) X S /(4 A )(2/ = bbhh (2.13)

X /X-S /Q=)XS(4 /A= NL by by b bh (2.14)

) ,T (S X bb Dr (2.15a)

) ,T (S mF bb Ar r (2.15b)



21

When the isolator is bilinear, seismic responses may still be obtained from design-earthquakespectral values, but the solutions are less exact than in the linear case. The results of a separateanalysis, not given here, allow the seismic responses of a range of isolators to be compared in

section 2.5 below. These results were obtained by calculating the responses of 81 differentisolator-structure systems and analysing the patterns which emerged.

It was found that the effective period TB and effective damping B of equations (2.11) to (2.13)may be used with earthquake spectra to obtain rough approximations for the seismic responsesof the first mode. The maximum base displacement Xb and the maximum base shear Sb (neglecting velocity-damping forces) may be derived from the isolator parameters and 'bilinear'spectral displacement SD(TB,B) as follows:

Here CF is a correction factor which was found empirically. For the El Centro NS 1940accelerogram, the correction factor CF lies approximately in the range 0.85 to 1.15 for a widerange of the bilinear isolator parameters Tb1, Tb2 and Qy/W. This gives an idea of the uncertaintiesassoc iated with this method. Note that the method is also iterative, as TB and B are functions ofXb and Sb.

2.2.5 Contributions of Higher Modes to the Seismic Responses of Isolated Structures

The contributions of higher modes of vibration to the seismic responses of isolated structures canbe described briefly in general terms.

A linear isolation system with a high degree of linear isolation and moderate isolator damping,(i.e. b < 20%) or with high isolator damping which includes a higher-mode attenuator as inFigure 2.2(c), gives small higher-mode acceleration responses. Hence all the seismic responsesof a structure with such linear isolation are approximated reasonably well by first-moderesponses and by a rigid-structure model. Without higher-mode attenuation, high isolatordamping may seriously distort mode shapes, and complicate their analysis. Also, higher-moderesponses may increase as the damping increases, because greater base impedances causedby the base damping result in larger effective participation factors.

When a bilinear isolator has a high degree of nonlinearity, there are usually relatively largehigher-mode acceleration responses. These usually give substantial increases in the seismicinertia forces, compared to those produced by the first mode. Shear forces at various levels of

the structure are typically increased by somewhat smaller amounts, the exception being near-base shears which remain close to their mode-1 values because shears arising from higherisolated modes have a near-zero value at the isolator level.

Increased floor acceleration spectra may result from increased higher-mode accelerationresponses and may be of concern when the seismic loads on light-weight substructures, or onthe contents of the structure, are an important design consideration.

The higher-mode acceleration responses are generally reduced by reducing the nonlinearity ofthe isolator, but other isolator parameters may modify the effects of nonlinearity. When theisolator is bilinear the degree of nonlinearity can usually be reduced by reducing the period ratio Tb2/Tb1 and the yield ratio Qy/W, since these changes usually give a less rectangular loop.However, the nonlinearity should normally be left at the highest acceptable value, since the

hysteretic damping of a bilinear isolator is proportional to the degree of nonlinearity, and thefirst-mode response generally decreases as the damping increases.

) ,T ( MS S bb Ab (2.15c)

) ,T (S C X B B DF b (2.16a)

)X - X( K +QS y b2 by b (2.16b)



22

For a given degree of nonlinearity, the higher-mode acceleration responses can generally bereduced by making the elastic period Tb1 considerably greater than the first unisolated period T1(U). This approach becomes more practical and effective for structures whose period T1(U) isrelatively low.

2.3 NATURAL PERIODS AND MODE SHAPES OF LINEAR STRUCTURES -UNISOLATED AND ISOLATED

2.3.1 Introduction

It has been stated above that most or all of the important seismic responses of a structure withlinear isolation, and many of the seismic responses with nonlinear isolation, can beapproximated using a rigid-structure model.

However, more detailed information is often sought, such as the effects of higher modes of

vibration on floor spectra, especially for spec ial-purpose structures for which seismic isolation isoften the most appropriate design approach. Such higher-mode effects are convenientlystudied by modelling the superstructure as a linear multi-mass system mounted on the isolators.

Linear models and linear analysis can be used for unisolated structures and also when thestructure is provided with linear isolation, except that high isolator damping may complicateresponses. Simplified system models may be adopted to approximate the isolated naturalperiods and mode shapes when there is a high degree of modal isolation, namely when theeffective isolator flexibility is high in comparison with the effective structural flexibility. The'degree of modal isolation' is a useful concept.

When a structure is provided with a bilinear isolator, it is found that the distribution of the

maximum seismic responses of higher modes can be interpreted conveniently in terms of thenatural periods and mode shapes which prevail during plastic motions of the isolator. Thisapproach is effective for the usual case in which the yield displacement is much less than themaximum displacement. These mode shapes and periods are given by a linear isolator modelwhich has an elastic stiffness equal to the plastic stiffness K b2 of the bilinear isolator. These modeshapes explain the distribution of maximum responses through the structure, but in general theamplitudes of the responses will be different to those of a linear system with base stiffness K b2. The elastic-phase isolation factor I(K b1)=Tb1/T1(U) and the nonlinearity factor NL are importantparameters affecting the strengths of the higher-mode responses.

2.3.2 Structural Model and Controlling Equations

The earthquake-generated motions and loads throughout non-yielding structures has beenstudied extensively, e.g., Newmark & Rosenblueth, (1971); Clough & Penzien, (1975). Thestructures are usually approximated by linear models with a moderate number N of point massesmr, as illustrated in Figure 2.4(a) for a simple 1-dimensional model.



23

Figure 2.4: (a) Linear shear structure with concentrated masses. The seismic displacementsof the ground and of the r-th mass mr are ug and (ur+ug) respectively. The relativedisplacement of the r-th mass is ur. Here k(r,s) and c(r,s) are, respectively, the stiffness

and the velocity-damping coefficient of the connection between massesr and s.

(b) Uniform shear structure with total mass M and overall unisolated shear stiffness K,such that the level mass mr=M/N and the intermass shear stiffness kr=KN. If N tends

to infinity, the overall height l=hN, the mass per unit height m=M/l and the stiffnessper unit height k=Kl.

In general, each pair of masses mr, ms is interconnected by a component with a stiffness k(r,s)and a velocity damping coefficient c(r,s). In Figure 2.4(a), each mass mr has a single horizontaldegree of freedom, ur with respect to the supporting ground, or ur + ug with respect to the pre-earthquake ground position, where the horizontal displacement of the ground is ug.

At each point r, the mass exerts an inertia force -(ür+üg)mr, while each interconnection exerts anelastic force -(ur - us)k(r,s) and a damping force -(ur -u s)c(r,s). The N equations which give thebalance of forces at each mass can be expressed in matrix form:

where [M], [C] and [K ] are the mass, damping and stiffness matrices, and where the matrixelements crs and krs are simply related to the damping coefficients and the stiffnesses, c(r,s) andk(r,s) respectively.

Here [M], [C] and [K ] are N x N matrices since the model has N degrees of freedom, and u is anN-element displacement vector.

The model in Figure 2.4(a) and the force-balance equation (2.17) can be extended readily to a3-dimensional model with 3N translational degrees of freedom (and 3N rotational degrees of

freedom if the masses have significant angular momenta).

However, Figure 2.4 and equation (2.17) are sufficiently general for most of the discussions here.

u[M]1-=u[K]+uC][+ÅM][g (2.17)



25

2.3.4 Example - Modal Periods and Shapes

Natural periods and mode shapes for unisolated and well-isolated structures may be illustratedusing a continuous uniform shear structure, hereafter referred to as the standard structure. If a

frame building has equal-mass rigid floors, and if the columns at each level are inextensible andhave the same shear stiffness, the building can be approximated as a uniform shear structure. This may be modelled as shown in Figure 2.4(b) with mr = M/N and k(r, r-1) = KN for r = 1 to N, andwith all other stiffnesses removed. The model is given linear isolation by letting k(1,0) = K b, whereK b is typically considerably less than the overall shear stiffness K. It is given base velocitydamping by letting c(1,0) = Cb.

The structural model is made continuous by letting N .

From the partial differential form of equations (2.17) which arises in the limit of N , or

otherwise, it may be shown that the mode shapes n 39 have a sinusoidal profile, and that the

modal frequenciesn are proportional to the number of quarter-wavelengths in the modal

profile. Unisolated modes have (2n-1) quarter-wavelengths and isolated modes have just over(2n-2) quarter-wavelengths, as shown in Figure 2.5. If the stiffnesses K and K b are chosen to givefirst unisolated and isolated periods of 0.6 and 2.0 seconds respectively, the periods of othermodes follow from the number of quarter-wavelengths as shown in Figure 2.5. Moreover, thereare 0.6/2.1 quarter-wavelengths in isolated mode 1, so that the first-mode shape value b1 at thebase of the structure, above the isolator, is given by b1 = cos (0.29 x 90o) = 0.90, as shown. Higherisolated modes rapidly converge towards (2n-2) quarter-wavelengths with increasing n, andcorresponding periods occur.

Figure 2.5: Variation, with height hr, of rn, which is the approximate shape of the n-th mode

at the r-th level of the continuous uniform shear structure obtained by letting Ntend to infinity in the structural model of Figure 2.4(b), when T1(U)=0.6 s and Tb=2.0 s. The modal shapes and periods are shown when the structure is unisolated (U) andisolated (I). Note that the responses interleave, with periods Tn(I) and Tn(U)alternating between 2.09, 0.6, 0.29, 0.2, 0.15 and 0.12 seconds respectively.



26

Modal acceleration profiles have the same shapes as the corresponding displacement profilesbut are of opposite sign, and hence, for a uniform mass distribution, the modal force profiles alsohave the same shapes as the displacement profiles. The shear at a given level may beobtained by summing the forces above that level, so it is evident from Figure 2.5 that the shearprofiles for the higher modes (n > 1) of the isolated structures have small near-nodal values at

the base level, because of the cancelling effects of the positive and negative half-cycles of theprofile.

The unisolated and isolated natural periods and modal profiles of Figure 2.5 may be expressedas follows:

For structures which are non-shear and non-uniform, and have inter-mass stiffnesses in additionto k(r, r-1), period ratios are less simple but retain the general features given by Figure 2.5. For awell-isolated structure, the first-mode period is controlled by the isolator stiffness. All otherisolated and unisolated periods are controlled by the structure and are interleaved in the ordergiven by Figure 2.5. The isolated mode-1 profile is still approximately rectangular. Higher-modeprofiles are no longer sinusoidal but have the same sequences of nodes and antinodes.Moreover the shear profiles of higher isolated modes still have small near-nodal values at theisolator level.

For all well-isolated structures, the damping of mode 1 is controlled by the isolator damping. Thedamping of all higher modes is controlled by structural damping, provided the velocity dampingof the isolator is not much greater than that of the structure. It is commonly assumed that thestructural damping is approximately equal for all significant modes.

2.3.5 Natural Periods and Mode Shapes with Bilinear Isolation

When a structure is provided with a bilinear isolator there are two sets of natural periods and twocorresponding sets of mode shapes; one set is given by a system model which includes a linearisolator which has the elastic stiffness K b1 of Figure 2.3, while the other set is given when the linearisolator has the plastic stiffness K b2.

The yield level of a bilinear isolator is normally chosen to ensure that the maximum seismicdisplacement response, for a design-level excitation, is much larger than the isolator yielddisplacement. With such isolators the distribution of the maximum seismic motions and loads,and the floor spectra, can be expressed effectively in terms of the set of modes for which theshapes, and the higher-mode periods, are those of the normal modes which arise when thestructure has a linear isolator of stiffness K b2. An approximate effective period for mode 1 isderived from the secant stiffness K B at maximum displacement, as given by equation (2.11a)

and illustrated in Figure 2.3(b). The relevance of the normal modes arising with stiffness K b2 is tobe expected, since maximum or near-maximum seismic responses should normally occur whenthe isolator is moving in its plastic phase, with an incremental stiffness K b2.

seconds- 1)n-/(20.6=(U)T n (2.23a)

seconds- 1>nfor,2) -n/(20.6(I)T ;2.1=(I)T n1 (2.23b)

)]h /h2)(/1)( -n[(2sin=(U) Nr rn (2.23c)

2))]/)(h/h-(1 cos[(0.3(I) Nr 1r (2.23d)

)]h /h2)(/2)( -n[(2cos(I) Nr rn (2.23e)



27

2.4 MODAL AND TOTAL SEISMIC RESPONSES

2.4.1 Seismic Responses Important for Seismic Design

This section considers the seismic response quantities which are commonly important for thedesign of non-isolated or isolated structures.

Important seismic responses normally include structural loads and deformations and mayinclude appendage loads and deformations. Appendage responses indicate the level ofseismic attack on light-weight substructures, and on plant and fac ilities within the structures. Foran isolator, seismic displacement is likely to be the most important and limiting design fac tor.

The contributions of structural modes and response spectra to the important seismic responsesare indicated on the left of Figure 2.6. The earthquake accelerations give accelerationresponse spectra which combine with structural modes to give mass accelerations and hencestructural seismic forces. Similarly floor (or structural-mass) acceleration response spectra givethe appendage seismic forces.

Figure 2.6: Schematic representation of the responses which dominate seismic design. The floor

spectra have the same role in the response of the appendage as the earthquake spectrahave in the response of the structure.



28

2.4.2 Modal Seismic Responses

The modal seismic responses of linear multi-mass structures can be expressed in a simple formwhen the shapes of all pairs of modes are orthogonal with respect to the stiffness, mass and

damping matrices. It may be shown that undamped free-vibration mode shapes areorthogonal with respect to the mass and stiffness matrices. Moreover structural damping canusually be represented well by a matrix which gives classical in-phase mode shapes. Such adamping matrix does not couple or change the shape of the undamped modes. Particularexceptions to orthogonal damping may arise with highly-damped isolators or with dampedappendages, but this is beyond the scope of this book.

The orthogonality of the mode shapes, with respect to the mass and stiffness matrices, may beobtained from equation (2.21) by noting that the mass and stiffness matrices are unaltered bytransposition; the mass matrix because it is diagonal, and the stiffness matrix because it issymmetric.

If equation (2.21), for mode n, is pre-multiplied by m

T

, and again the transpose of equation (2.21),for mode m, is post-multiplied by n, this gives:

Since [M] T = [M] and [K ] T = [K ], subtraction of equation (2.24b) from equation (2.24a) gives, forthe usual case when m2 n2, the orthogonality condition:

Similarly

For the special case where two or more modes share the same frequencym, the mode shapesfor modes m and n with the common frequency can be chosen such that equations (2.25a)and (2.25b) hold.

It is found that the responses of damped linear structures can also be described in terms of thesame classical (in-phase) normal modes if the damping coefficients are also constrained by asimilar orthogonality condition. That is, provided

It can be shown that equations (2.25) imply that the inertia forces, the spring forces and thedamping forces of any mode (n) do no work on the motions of any other mode (m).

The displacements u(t) of equation (2.17) may be expressed as the sum of factored modeshapes:

Substituting from equation (2.26) into equation (2.17), then pre-multiplying each term by n T andeliminating all terms given as zero by equations (2.25) produces:

nm

T

nm

Tn2 K][=M][ (2.24a)

n

T

m

T

n

T

m

Tm2 K][= M][ (2.24b)

m _ nwhen,0=M][ nm

T (2.25a)

m _ nwhen,0=K][ nT

m (2.25b)

m _ nwhen,0=C][ n

T

m (2.25c)

(t) =(t)u nn N1 (2.26)



29

When compared with equation (2.5), equation (2.27a) is seen to describe a single-degree-of-freedom damped oscillator with damping factor n and frequencyn given by:

Here equations (2.27) are the N-degree-of-freedom counterparts of equations (2.2), (2.4) and(2.5).

Since u=u

n

N

1=n54

it follows from equation (2.26) that the displacement at level r of the n-thmode is given by:

Substituting from equation (2.28) into equation (2.27) gives:

where

Hence, since [M] is a diagonal matrix,

The factorr n may be called a participation factor since it is the degree to which point r ofmode n is coupled to the ground accelerations. Equation (2.30c) defines a mode weight factor

n. It is here convenient to define Nn as unity.

For simple tower-like structures, when Nn = (-1)n-1 then n is positive.

When equations (2.5) and (2.7) are compared with equation (2.29) and (2.30c) it is seen that:

Å]M[

1]M[ -=

]M[

]K [ +

]M[

]C[ + g

nn

T

n

T

n

nn

T

nn

T

n

nn

T

nn

T

n

(2.27a)

nn

Tnn

T

nn]M[

]C[ =2 (2.27b)

nn

Tnn

T

n2

]M[

]K [ = (2.27c)

nnrnr =u (2.28)

Å-=u+u2+Å gnrnrn2

nrnnnr (2.29)

nn

Tn

T

nrnr]M[

1]M[ = (2.30a)

(2.30b)

(2.30c)

),T(S=X nnVnnrnr (2.31b)

),T(S=X nnDnnrnr (2.31a)

),T(S=X nnAnnrnr (2.31c)

nnr

2

nii N1=i

nii N1=i

nrnr

=

m

m =



30

where the peak values Xrn, X rn and X rn are defined as urn max, u rn max, and (ürn +r nüg)max respectively. Note that these maximum seismic responses do not occur simultaneously, so, for

instance the maximum accelerationX is NOT the derivative of the maximum velocity X .

The maximum seismic displacements of mode n are given by equation (2.31a). The maximum

seismic forces Frn follow directly from equation (2.31c). Moreover, since all the massaccelerations for these classical normal modes are in phase, and therefore reach maximumvalues simultaneously,

maximum shear forces Srn and overturning moments OM rn, at level r, may be obtained bysuccessive summation of maximum forces. This gives:

where hr = height to mass mr.

2.4.3 Structural Responses from Modal Responses

Usually the maximum structural responses cannot be obtained from the maximum responses ofa set of modes by direct addition, since modal maxima occur at different times.

The response levels of a mode, when plotted against time, vary in a somewhat noise-like way

and the probable maximum combined response of several modes may usually beapproximated by the square root of the sum of squares (SRSS) method (Der Kiureghian, 1980).For example, the probable force at level r, may be expressed as:

where the mode i ranges over the significant modes.

However, if near-maximum responses of 2 or more modes are correlated in time by close modalperiods (often arising with torsional unbalance or with near-resonant appendages), or by veryshort periods or very long periods, then the complete quadratic combination (CQC) methodmay need to be used. Strongly nonlinear isolators may well provide a further mechanism which

correlates modal responses, so that the SRSS combination is not accurate.

2.4.4 Example - Seismic Displacements and Forces

Important features of equations (2.30), (2.31) and (2.32) can be illustrated for the unisolated andthe linearly isolated continuous uniform shear structure. Top mass participation fac tors forsuccessive modes are

where T1(U)/Tb = 0.3.

Xm=F nrr nr (2.32a)

F =S ni

N

r =i

nr (2.32b)

S)h-h(=OM ni1i-i

N

1r+=inr (2.32c)

F =F2irir (2.33)

1)]n-(2/[4,... 0.25, 0.42,1.27,=(U) Nn

,]0.3/2)n-/[(22,...0.011,0.045, 1.0,(I) 2 Nn



31

Higher isolated modes are seen to have much lower participation factors than correspondingunisolated modes.

The above mode-participation factors, together with the periods from equation (2.23) and the

spectra of Figures 2.1(b) and (c), can now be used to find important seismic motions and loadsfor modes 1 and 2 from equations (2.31) and (2.32).

For simplicity, a low damping factor of 5% is assumed for all modes. With practical isolatedstructures a higher damping would normally be provided for mode 1.

Since modal displacements may be represented by top displacements, consider

Notice that displacements are completely dominated by mode 1 for both unisolated andisolated structures. Moreover, for any well-isolated structure, the base displacement is almost aslarge as the top displacement:

Since modal loads may be represented by the force per unit height at the top of the structure

FNn, consider ,5),T(S=/F nA Nn Nn 72 where : hM/= N 73

Note that the force for isolated mode 1 is relatively small because it has a low responsespectrum factor, while the forces for higher isolated modes are relatively small because theyhave small participation factors.

2.4.5 Seismic Responses with Bilinear Isolators

When the isolator is bilinear, there are a number of possible ways of defining the modes. For anyof the definitions we consider, the total response of a linear structure with bilinear isolation canbe expressed exactly as the sum of the modal responses, as for a linear system. However, themodal equations of motion will be coupled, unlike those for classically damped linear systems.

Several of the possible definitions of the mode shapes with bilinear isolation are useful forinterpreting the response or estimating the maximum response quantities.

In section 2.2c, we discussed the responses of a first mode defined by a rigid structure mountedon an 'equivalent' linear isolator with 'effective stiffness' K B, 'effective period' TB and 'effectivedamping' B. This model gives good approximations to the displacements and base shear of a

structure on a bilinear isolator.

:5),T(S=X nD Nn Nn

m ,0.0037=2(U)X 0.085;=1(U)X N N

m ,0.00092(I)X ;0.181(I)X N N

)1(IXX N b

sm/ ,3.60=/2(U)F ;9.31=/1(U)F2

N N

sm/ ,0.37 _ /2(I)F ;1.80/1(I)F2

N N



32

A useful set of modes for systems with bilinear isolation are those obtained by using the post-yieldstiffness of the isolator. Then the higher-mode periods and all mode shapes are given byequations (2.20) and (2.21) for a linear system with K b = K b2. Hence, as with moderately dampedlinear isolators, the bilinear modes are classical and normal. These modes are relevant for themaximum responses because they relate to the post-yield phase, when the maximum

displacements and shears occur.

When the bilinear isolator has a high degree of nonlinearity, the seismic responses of highermodes are often much greater than the responses which occur with the above 'equivalent'linear modes. Bilinearity usually gives greater higher-mode accelerations and loads, andparticularly it usually gives greater values for floor acceleration spectra over the period rangecovered by significant higher modes. The reasons for the larger seismic responses of the highermodes are summarised briefly here.

With bilinear isolation, the inputs of seismic energy, and the energy level of the overall system,are given roughly by a rigid-structure model with a linear isolator of effective period TB andeffective damping factorB.

When the structure is sufficiently flexible to give a substantial contrast between the mode-1shapes for the first and second isolator stiffnesses, then there is usually significant energy in thehigher modes, where relatively small fractions of the structural energy can result in relatively highmodal accelerations and forces.

In terms of the modes for the plastic-phase stiffness K b2, each isolator transition through theelastic phase redistributes the energy between the modes. This should result in a net transfer ofenergy from the large-energy mode 1 to the small-energy higher modes. The effects of therelatively large seismic responses of higher modes, with many bilinear isolators, are seen in thecase studies below.

The mode-shapes corresponding to the post-yield stiffness K b2 are usually very similar in shape to

the free-free mode shapes, obtained when the isolator stiffness is zero. It is sometimes moreconvenient to interpret the responses in terms of the free-free modes rather than those based onK b2, because of the symmetry of the free-free modes and because there is no need to calculatenew mode shapes for different values of K b2.

Decomposition of the response in terms of the free-free mode shapes also has the usefulproperties that the base shear is contributed entirely by the first mode, and that the first-modedisplacements are uniform within the structure. Also, the base shear scaled by appropriateparticipation factors provides the driving forces for the higher modes.

The seismic responses of isolated structures can be decomposed into the contributions fromsuitably defined modes by a mode-sweeping technique. Either the modes based on

base-stiffness K b2 or the free-free modes can be used with this technique. The free-free modeshapes have been used to obtain the results given in Section 2.5 below.



33

Table 2.1: Responses to the El Centro NX 1940 Accelerogram of an Unisolated

Uniform Shear Structure, and of Six Isolated Structures



34

2.5 COMPARISONS OF SEISMIC RESPONSES OF LINEAR AND BILINEARISOLATION SYSTEMS

2.5.1 Comparative Study of Seven Cases

This section demonstrates many of the key features of seismic isolation, through seven exampleswhich show the seismic responses of structures and appendages for various ranges of isolationsystem parameter values and structural flexibility. The examples are summarised in Table 2.1 interms of the physical parameters of the systems, the maximum overall and modal responsequantities, and the values of the nonlinearity factor and elastic-phase isolation factor which areimportant parameters governing the isolated response.

Figure 2.7: Responses to the El Centro NS 1940 accelerogram of a uniform shear structurewhen unisolated, when linearly isolated (2 cases) and when bilinearly isolated (3cases). The information in this figure complements that in Table 2.1. The floor spectra

are for the low-damping case of 2%. The solid lines are the total response, whiledotted and chain-dotted lines are the seismic responses of modes 1 and 2respectively. Note the 5-fold differences in scale of the unisolated and isolated cases.

The scale changes are along the abscissae for X,X /g and S/W, and along theordinate for the floor spectra. Note also that the shear-force/displacement hysteresis

loops have been drawn for cyclic displacements of +0.4 Xb in order to show thevarious stiffnesses clearly.

Figure 2.7 shows the maximum values of the displacements, accelerations and shears and the2% damped top floor spectra calculated for an unisolated structure and six isolated structures inresponse to the El Centro 1940 NS ground acceleration. The solid lines represent maximum totalresponses, with the maximum values obtained from response history analysis. The dotted linesand chain-dotted lines where given, represent, respectively, the maximum first- and second-mode responses at the various levels. In some cases the first-mode responses dominate to theextent that dotted and solid lines coincide (e.g., parts of the floor spectra, particularly at longerperiods). In other cases, the difference between the solid and dotted lines indicates the higher-mode contribution to the response.



35

The modal responses were obtained from the overall response histories at all masses in thestructures by sweeping with the free-free mode shapes, except for the unisolated structure,where the modal responses are in terms of the true unisolated modes.

The 'un-isolated' structure (case (i)) is a uniform linear chain system, with 4 equal masses and 4

springs of equal stiffness, the lowest being anchored to the ground. It has a first-modeundamped natural period of 0.5s, and 5% damping in all its modes.

Most of the 'isolated' cases represent systems obtained simply by adding below this structure anisolation system modelled as a base mass, a linear or bilinear-hysteretic base spring and a linearviscous base damper. However, two of the 'isolated' cases involve stiffer structures, withunisolated periods of 0.25 seconds, in order to show the effects of high elastic-phase isolationfac tors. In all the isolated cases, the added base mass is of the same value as the other masses,comprising 0.2 of the total isolated mass.

The viscous damping of the isolated structures is 5% of critical for all the free-free modes, with thenonlinear isolation systems having linear viscous base dampings b2 which are 5% of critical in thepost-yield phases, as well as hysteretic damping. The table shows values of b for the linearisolators, and values of b, b1 and b2 for the bilinear isolators, where b =b2 TB/Tb2.

The cases were chosen to represent a wide variety of isolation systems, with various degrees ofnonlinearity and pre- and post-yield isolation ratios. In calculating the isolation factors, I=Tb/T1(U)and I(K b1)=Tb1/T1(U), the unisolated period T1(U) corresponds to that of the structure when theisolator is rigid, while the isolator periods Tb and Tb1 are calculated for the 5 masses, from thestructure and the isolator, with all their interconnecting springs treated as rigid, mounted on theisolator spring.

Cases (ii) and (iii) represent medium-period structures with a high degree of linear isolation(T1(U)=0.5s, Tb=2.0s, I=4), and with low (b=5%) and high (b=20%) values for the viscous dampingof the isolator, respectively.

Case (iv) is a bilinear hysteretic system with similar characteristics to that of the William ClaytonBuilding (Section 6.2(d)), which was the first building isolated on lead rubber bearings. Theparameter values are typical for structures with this type of isolation system.

The unisolated period of the structure is 0.25s (the William Clayton Building has a nominalunisolated period of 0.3s), with a pre-yield isolator period Tb1 of 0.8s and a post-yield isolatorperiod Tb2=2.0s. The yield force ratio Qy/W is 0.05, less than the William C layton Building's value of0.07. However, the latter value was chosen to give a near-optimal base shear response (seesection 4.3.2) in 1.5 El Centro, so scaling down the yield-force/weight ratio by approximately 2/3is appropriate for a system with El Centro as the design motion. The post-yield isolator period isequal to the isolator period of the linear systems of cases (ii) and (iii). The equivalent viscous

damping from the combined hysteretic and viscous base damping at the amplitude of itsmaximum response to El Centro is 24% (Table 2.1), comparable with the viscous damping of 20%for the linear system (iii).

Case (v) represents bilinear systems with elastic- and yielding-phase isolation fac tors towards thelow ends of their practical ranges. The unisolated period is 0.5s, with the isolator periods Tb1=0.3sand Tb2=1.5s, giving isolation factors of 0.6 and 3 in the two phases. The yield force ratio Qy/W is0.05, as for all the nonlinear cases. This system has a moderate nonlinearity factor which isvirtually identical to that of case (iv) (0.33 compared to 0.32), but considerably reduced isolationfactors, most importantly in the elastic phase where it is 0.6. The low elastic-phase isolation givesresponse characteristics similar to those for a system with an isolator which is rigid before it yields.

In case (vi), the post-yield period of the isolator has been doubled from that of case (v), to Tb2=3.0s, but the other parameter values are the same. This change produces a considerablyhigher nonlinearity factor of 0.60, but still a low elastic-phase isolation fac tor of only 0.6.



36

The response characteristics are similar to those for what is sometimes referred to as a 'resilient-friction base isolator' (Fan & Ahmadi (1990, 1992); Mostaghel & Khodaverdian (1987)).

The final example, case (vii), is a strongly nonlinear system, with a nonlinearity factor of 0.71, butunlike case (vi) it has high isolation factors in both phases of the response. The force-

displacement characteristics of the isolator are almost elasto-plastic, with a post-yield period of6.0s. The unisolated period of the structure (T1 (U)=0.25s) and the yield-force ratio (Qy/W=0.05)are identical to case (iv), and the pre-yield isolator period (Tb1=0.8s) and hence the elastic-phaseisolation factor are very similar to those in case (iv). This represents a system with high hystereticdamping, high isolation in both phases of the response, and a maximum base shear closelycontrolled by the isolator yield force because of the nearly perfectly plastic characteristic in theyielding phase.

The response characteristics of this wide range of examples are illustrated in Figure 2.7, anddemonstrate many of the key features of the response characteristics of base-isolatedstructures.

Comparisons can be made between features of the responses of unisolated and isolatedstructures, and between those of various isolated structures. Systematic variations in responsequantities can be seen as the equivalent viscous damping, the nonlinearity factor and theelastic-phase isolation factor are varied.

The first point to note in Figure 2.7 is that the response scales for the unisolated structure of case(i), as emphasised by heavy axis lines, are five times larger than those for all the isolated casesshown in the other parts of the figure.

The next general comment regarding Figure 2.7 is that the force-displacement hysteresis loopshave been drawn for cyclic displacements of +0.4 Xb. This has been done in order to show therelative slopes.

Direct comparisons of various response quantities can be made for the unisolated structure andthe four cases (ii), (iii), (v) and (vi) involving the same structure on various isolation systems. Cases(iv) and (vii) involve shorter-period structures on the isolators, so direct comparisons of these withcase (i) are not appropriate. The base shears of the isolated systems with the 0.5s structure arereduced by factors of 4.6 (for the lightly damped linear isolator of case (ii)) to over 10 (for case(vi) with high hysteretic damping). Base displacements, which contribute most of the totaldisplacement at the top of the isolated structures, range from 0.7 to 2.5 times the topdisplacement of the unisolated structure. Inter-storey deformations in the isolated structures aremuch reduced from those in the unisolated structures, since they are proportional to the shears.Since large deformations are responsible for some types of damage, the reduction in structuraldeformation is a beneficial consequence of isolation. First-mode contributions to the top-massaccelerations in the isolated structures are reduced by factors of about 6 to 14 compared to the

values in the unisolated structure. The linear isolation systems show marked reductions in thehigher-frequency responses as well, but the second-mode responses for the systems with thegreatest nonlinearities are only slightly reduced from those in the unisolated structure. Theseeffects are most evident in the top-floor response spectra.

Figure 2.7 shows several important characteristics of the response of isolated structures ingeneral. In isolated systems, increased damping reduces the first-mode responses, but generallyincreases the ratio of higher-mode to first-mode responses, particularly where the dampingresults from nonlinearity. The elastic-phase isolation fac tor I(K b1) has a marked effect on higher-mode responses, which increase strongly as I(K b1) reduces from about 1.0 towards zero. Theeffects of these parameters are demonstrated by considering each of the isolated cases in turn.

The lightly damped linear isolation system of case (ii) reduces the base shear by a factor of 4.6from the unisolated value, but requires an isolator displacement of 180mm.



37

The response is concentrated almost entirely in the first mode, as shown by the comparison ofthe first-mode and total acceleration and shear distributions and by the top floor spectra. Thedifferences between the first-mode and total distributions largely arise from the differencebetween the free-free first-mode shape which was used in the sweeping procedure and theactual first-mode shape with base stiffness K b. The maximum second-mode acceleration

calculated by sweeping with the second free-free mode shape is only about 1/6th that foundby sweeping with the first free-free mode shape.

By increasing the base viscous damping from b=5% to 20% of critical, as in case (iii), themaximum base displacement is reduced from 180mm to 124mm, with less percentagereduction in the base shear. The mode-2 acceleration more than doubles, showing the effectsof increased base impedance from the increased base damping and modal coupling from thenonc lassical nature of the true damped modes. The first-mode response still dominates,however. The floor response spectra reflect the reduction in first-mode response, but showincreases in the second- and third-mode responses compared to case (ii).

Case (iv) has an effective base damping similar to case (iii), but with the main contributioncoming from hysteretic damping. All first-mode response quantities, and those dominated bythe first-mode contribution, including the base shear and the base displacement, are reducedfrom the values for the linear isolation systems. The nonlinearity of this system is only moderate(0.32), and there is a high elastic-phase isolation factor of 3.2, but the second-mode response ismuch more evident than for the linear isolation systems, particularly in the floor responsespectrum.

Case (v) has the same degree of nonlinearity as the previous case, but a much reducedelastic-phase isolation factor of 0.6. The low elastic-phase isolation factor has produced a muchincreased second-mode acceleration response, which is 50% greater than the first-moderesponse on the top floor.

The distribution of maximum accelerations is much different from the uniform distribution

obtained for a structure with a large linear isolation factor. The accelerations are muchincreased from the first-mode values near the top and near the base, while the shear distributionshows a marked bulge away from the triangular first-mode distribution at mid-height. Stronghigh-frequency components are evident in the top floor acceleration response spectrum, withprominent peaks corresponding to the second and third post-yield isolated periods.

Case (vi) is an exaggerated version of case (v). The post-yield isolator period has beenincreased to 3.0s, giving a high nonlinearity factor as well as a low elastic-phase isolation factor,both conditions contributing to strong higher-mode response. The nearly plastic behaviour ofthe isolator in its yielding phase produces a more than 40% reduction in the base shear fromcase (v), at the expense of a 33% increase in the base displacement. The maximum second-mode acceleration response at the top floor is 2.5 times the first-mode response, being the

highest value of this ratio for any of the seven cases. The acceleration at the peak of the top-floor response spectrum at the second-mode post-yield period has the greatest value of any ofthe isolated cases, almost identical to the second-mode value in the unisolated structure, which,however, occurs at a shorter period.

Case (vii) demonstrates that high elastic-phase isolation can much reduce the relativecontribution of the higher modes for highly nonlinear systems. The nonlinearity factor of 0.71 isthe highest of any of the cases, but the second-mode response is less than 40% that of cases (v)and (vi), which have poor elastic-phase isolation. The high nonlinearity has reduced the baseshear to 70% of that of case (iv). The mode-2 acceleration response has been reduced by 13%from that of case (iv), but its ratio with respect to mode 1 has increased from 0.85 to 1.25.



38

Maximum base shears and displacements of isolated structures are dominated by first-moderesponses. Maximum first-mode responses of bilinear hysteretic isolation systems can in turn beapproximated by the maximum responses of equivalent linear systems, as discussed earlier in thischapter. The final section of Table 2.1 demonstrates the degree of validity of the equivalentlinearisation approach. It gives effective dampings and periods calculated for the equivalent

linearisation of the bilinear isolators, using equation (2.11b) for TB and equations (2.11c) to (2.13)for B. The response spectrum accelerations and displacements for these values of period anddamping are listed. The spectral values for the base displacements give reasonableapproximations to the actual values, with correction factors C F of approximately unity, exceptfor case (vii), with the nearly plastic post-yield stiffness, for which the correc tion factor is 1.6.However, the spectral accelerations SA(TB,B) provide much poorer estimates of either the first-mode or overall base-mass accelerationX b. Much improved estimates of the base shear Sb canbe obtained from K BXb, which has a smaller relative error than the estimate of Xb from SD(TB,B). This is the procedure we recommend when using the equivalent linearisation approach (Section2.2).

2.6 GUIDE TO ASSIST THE SELECTION OF ISOLATION SYSTEMS

The examples summarised in Figure 2.7 and Table 2.1 show the effects of various ranges ofisolation system parameters. In particular, the effec ts of base damping, nonlinearity fac tor andelastic-phase isolation factor have been demonstrated. Table 2.2 generalises the results foundfor these examples and presents them in a more qualitative way, providing guidance to the setsof parameter values appropriate for particular purposes, and giving examples of practicalisolation systems which can provide the desired parameter values.

In Table 2.2, we are considering c lasses of systems, rather than examples with specific parametervalues. The examples (i) to (vii) considered in Figure 2.7 and Table 2.1 fit into the correspondingcategories in Table 2.2. However, the qualitative descriptions of the nature of various response

quantities show minor deviations from those which would be obtained solely by consideration ofthese examples. Use has been made of results of other cases considered by the authors orreported in the literature in order to generalise the results from the spec ific ones given above.



39

Table 2.2: Guide to the behaviour of isolation systems, showing seven classescorresponding broadly to the cases in Figure 2.7.



40

Thus, class (vi) has been extended to include rectangular hysteresis loops (K b1=, K b2=0), whilethe example of case (vi) has 'high' and 'low' values of these stiffnesses respectively. The responsecharacteristics of simple sliding friction systems included by this generalisation are similar to thoseof the example of case (vi). The ways in which the various cases of Table 2.1 have beengeneralised to the classes of Table 2.2 are discussed below.

Class (i) represents unisolated linear structures with periods up to about 1 second and dampingup to about 10%. This class is provided only for purposes of comparison. Most short- tomoderate-period unisolated structures will be designed to respond nonlinearly, so theiracceleration- and force-related responses may be considerably less than those of the linearelastic cases considered here. Isolation still provides benefits in that nonlinear response in suchunisolated structures requires ductile behaviour of the structural members, with the considerableenergy dissipation within the structure itself often assoc iated with significant damage.

Class (ii) represents lightly-damped, linear isolation systems, with the isolator damping less than10%. Only systems providing a high degree of isolation are considered, with an isolation factor Tb/T1(U) of at least 2 and a period Tb of at least 1.5 s for El Centro-type earthquakes.

The response of such systems is almost purely in the first mode, with very little higher-frequencyresponse, so they virtually eliminate high-frequency attack on contents of the structure. This typeof isolation can be readily obtained with laminated rubber bearings, with the low isolatordamping provided by the inherent damping of the rubber. Higher-damping rubbers may benecessary to achieve the 10% damping end of the range without the provision of additionaldamping devices. The higher-damping rubbers may not behave as linear isolators since theyare often amplitude dependent and history dependent. Various mechanical spring systemswith viscous dampers fall into this category.

Class (iii) corresponds to linear isolation with heavier viscous damping, ranging between about10% and 25% of critical. Increased damping reduces the isolator displacement and base shear,but generally at the expense of increased high-frequency response. The high-frequency

response results from increased isolator impedance at higher frequencies. These systems stillprovide a high degree of protection for subsystems and contents vulnerable to motions of a fewHz or greater, but with reduced isolator displacements compared to more lightly dampedsystems.

We consider class (iv), bilinear hysteretic systems with good elastic-phase isolation (Tb1/T1(U) > 2)and moderate nonlinearity (corresponding to equivalent viscous base damping of 20-30% ofcritical), as a reference class. For many applications, this represents a reasonable designcompromise to achieve low base shears and low isolator displacements together with low tomoderate floor response spectra. This type of isolation can often be provided by lead rubberbearings.

Class (v) represents bilinear isolators with poor elastic-phase isolation (Tb1/T1(U) < 1) and relativelyshort post-yield periods (~ 1.5s). The relatively high stiffnesses of these isolation systems producevery low isolator displacements, but strong high-frequency motions and stronger base shearsthan the reference bilinear-hysteretic isolator class.

Class (vi) is similar in many respects to c lass (v), but with a long post-yield period (Tb2 > ~ 3s),which gives nearly elasto-plastic characteristics and thus high hysteretic damping and a highnonlinearity factor. Rigid-plastic systems, such as given by simple sliding friction without anyresilience, are extreme examples of this class. Low base shears can be achieved because ofthe low post-yield stiffness and high hysteretic damping, but at the expense of strong high-frequency response. Even this advantage is lost with high yield levels. This class of bilinearisolator is not appropriate when protection of subsystems or contents vulnerable to attack atfrequencies less than 1 Hz is important, but some systems in this class can provide low baseshears and moderate isolation-level displacements very cheaply. Displacements can becomevery large in greater than anticipated earthquake ground motions.



41

Class (vi) consists of nonlinear hysteretic isolation systems with a high degree of elastic-phaseisolation (Tb1/T1(U) > 3) and a long post-yield period (Tb2 > ~ 3s), producing high hystereticdamping. The low post-yield stiffness means that the base shear is largely controlled by the yieldforce, is insensitive to the strength of the earthquake, and can be very low. The high degree ofelastic-phase isolation largely overcomes the problem of strong high-frequency response usually

assoc iated with high nonlinearity factors. Systems of this type are particularly useful for obtaininglow base shears in very strong earthquakes when provision can be made for large isolatordisplacements. One application of this class of system was the long flexible pile system used inthe Wellington Central Police Station (Chapter 8.2 (f)), with the elastoplastic hysteretic dampingcharacteristics provided by lead-extrusion energy dissipators mounted on resilient supports.

As indicated by the preceding descriptions of the isolator systems and the discussion of theresponse characteristics of the various examples in the last section, the selection of isolationsystems involves 'trade-offs' between a number of factors.

Decreased base shears can often be achieved at the cost of increased base displacementsand/or stronger high-frequency accelerations. High-frequency accelerations affect the

distribution of forces in the structure and produce stronger floor response spectra. If strong high-frequency responses are unimportant, acceptable base shears and displacements may beachieved by relatively crude but cheap isolation systems, such as those involving simple sliding.In some cases, limitations on acceptable base displacements and shears and the range ofavailable or economically acceptable isolation systems may mean that strong high-frequencyaccelerations are unavoidable, but these may be acceptable in some applications. Somesystems may be required to provide control over base shears in ground motions more severethan those expected, requiring nearly elasto-plastic isolator characteristics and provision forlarge base displacements.

The selection of appropriate isolation systems for a particular application depends on whichresponse quantities are most critical to the design. These usually can be spec ified in terms ofone or more of the following factors:

i) base shearii) base displacementiii) high-frequency (i.e., > ~ 2Hz) floor response spectral accelerationsiv) control of base shears or displacements in greater than design-level earthquake

ground motionsv) cost

Isolation systems are easily subdivided on the basis of those for which high-frequency (> 2Hz)responses can be ignored and those where they make significant contributions to theacceleration distributions and floor spectra. Floor spectral accelerations are important when animportant design criterion is the protec tion of low-strength high-frequency subsystems or

contents.

In well-isolated linear systems, high-frequency components, which correspond to higher-modecontributions, can generally be ignored, although they become more significant as the basedamping increases (Figure 2.7, cases (ii) and (iii)). In nonlinear systems, there will generally bemoderate to strong high-frequency components when there is a low elastic-phase isolationfactor, less than about 1.5. This generally eliminates systems with rigid-sliding type characteristicswhen strong high-frequency response is to be avoided. For a given elastic-phase isolationfactor, high-frequency effects have been found to generally increase with the nonlinearityfac tor. These considerations suggest that the selection of isolation systems for the protec tion ofhigh-frequency subsystems is limited to linear systems, or nonlinear systems with high elastic-phase isolation factors and moderate nonlinearity factors (i.e., corresponding to cases (ii), (iii) or(iv) in Figure 2.7). Some systems with high nonlinearity factors but also with high elastic-phaseisolation factors may also produce acceptably low high-frequency response.



42

For example, case (vii) in Figure 2.7 with a high nonlinearity factor has a similar top-floor responsespectrum to case (iv) for which the nonlinearity factor is moderate, and has a spectrum notmuch stronger than that of the linearly-isolated case (iii) with high viscous damping. The linearsystems usually give better performance strictly in terms of high-frequency floor-responsespectral accelerations, but the introduction of nonlinearity can reduce the base shear and

isolator displacement, which may give a better overall performance when the structure,subsystems and contents are considered together.

For situations where a need for small floor-response spectral accelerations is not a major designcriterion, the range of acceptable nonlinear isolation systems is likely to be much greater. Themain performance c riteria are then usually related to base shear and base displacement. Boththese quantities depend primarily on the first-mode response.

Except for nearly elasto-plastic systems, the base shear decreases as Qy/W increases from zero,passes through a minimum value at an optimal yield force, and then increases as Q y/Wcontinues to increase. Thus the base shear of most linear isolation systems can be reduced byselecting a nonlinear isolation system with Tb2=Tb of the linear system and an appropriate yield

force ratio and elastic-phase period. For a given yield force, the base shear generallydecreases as Tb2 increases, i.e., the system becomes more elasto-plastic in character. This isillustrated by the examples in Figure 2.7. This is generally at the expense of greater basedisplacement, as for case (vii), or strong high-frequency response when the elastic-phaseisolation is poor, as in case (vi). When base shear and base displacements are the controllingdesign criteria, systems with rigid-plastic type characteristics, such as simple pure friction systems,which are not appropriate when the protection of high-frequency subsystems or contents is aconcern, may give cheap, effective solutions provided the coefficient of friction remains lessthan the maximum acceptable base shear. However, some centring force is usually a desirableisolator characteristic. For protection against greater than design-level excitations, systems witha nearly plastic yielding-phase characteristic have the advantage that the base shear is onlyweakly dependent on the strength of excitation, but the disadvantage that their isolatordisplacements may become excessive. A system similar to our reference case with

characteristics of moderate nonlinearity and good elastic-phase isolation is often a good designcompromise when minimisation of high-frequency floor-response spectral accelerations is not anoverriding design criterion.



44

In the simplest case a linear isolation system is produced by using components with linearflexibility and linear damping. In other cases the isolation system may be nonlinear.

A special case of nonlinearity, the bilinear system, occurs when the shear-force/displacement

loop is a parallelogram, as shown in Figure 2.3 and discussed in the assoc iated text. Differentseismic responses result from linear, bilinear and other nonlinear isolation systems.

In the simplest case, a system which has both a linear flexibility component and a lineardamping component can be modelled in terms of the differential equation (2.1), i.e.

where the flexibility is the inverse of the stiffness constant 'k' and the velocity-damping isdescribed by a constant 'c'. Figure 2.2 and the assoc iated text define this kind of system andshow the elliptical velocity-damped shear-force/displacement hysteresis loop which results.

However, the components may not be linear. The most common source of nonlinearity in acomponent is amplitude-dependence. For example, in the typical bilinear isolation system thestiffness is amplitude-dependent, changing from K b1 to K b2 at the yield displacement. Thedamping in this case is also nonlinear because the hysteretic contribution to the damping,which usually dominates, depends on the area of the hysteresis loop and therefore alsodepends on the maximum amplitude Xb.

Table 3.1 analyses the flexibility and damping of some common isolator components, examiningeach to see if it is linear or nonlinear. The analysis is somewhat idealised and over-simplified,since material properties can vary. Also, it is worthwhile checking to see if a particular system israte- or history-dependent. For example, types of high-damping rubber depend both on theamplitude and on the number of cycles which the sample has undergone.

PROPERTY LINEAR NONLINEAR

Restoring Force(providing spring constantand flexibility)

*Laminated rubber bearing*Flexible piles or columns*Springs*Rollers between curvedsurfaces (gravity)

*High-damping rubberbearing

*Lead rubber bearing*Buffers*Stepping (gravity)

Damping *Laminated rubber bearing*Viscous damper

*High-damping rubberbearing

*Lead rubber bearing

*Lead extrusion damper*Steel dampers*Friction (e.g. PTFE)

Table 3.1: Flexibility and Damping of Common Isolator Components

u m - =ku+ uc + u m g



45

As seen in Table 3.1, the laminated rubber (elastomeric) bearing is the only single-unit isolationsystem, among those considered, which has both linear restoring force and linear damping. Inthe commercially used form, this comprises layers of rubber vulcanised to steel plates.Considerable experience exists for the design and use of the elastomeric bearing, since its initialmajor application was to accommodate thermal expansion in bridges and it was only later

adopted as a solution to seismic isolation problems. However, for seismic isolation, this systemhas the disadvantage that the maximum achievable damping is very low, approximately 5% ofcritical. Attempts to overcome this disadvantage by increasing the inherent damping of therubber have not yet produced an ideal system with linear stiffness and linear damping.

Flexible piles or columns provide a simple, effective linear restoring force but dampers need tobe added to control the displacements during earthquakes and on other occasions. If thedampers are linear, e.g., viscous dampers, then a linear system results. Viscous dampers areexcellent candidates for linear dampers, but may be difficult to obtain at the required size, maybe strongly temperature-dependent and may require maintenance, given that the requiredlifetime may be 30 to 80 years.

Springs with the required stiffness are likely to be difficult to produce, but do provide a linearrestoring force. The German GERB system achieves this, mainly intended for industrial plant, suchas large silos. Rollers or spheres between curved (parabolic) surfaces can provide linearrestoring forces. Since they have 'line' or 'point' contact it is difficult to provide for high loads.Again, damping will usually need to be added in practice and linear damping will produce alinear system.

Gravity in the form of a 'stepping' behaviour (see, for example the Rangitikei viaduct, Chapter 6)can provide an excellent nonlinear restoring force. Such systems need additional damping foreffective isolation. The resultant isolation systems are nonlinear.

High-capacity hysteretic dampers may be based on the plastic deformation of solids, usuallylead or steel. The damper must ensure adequate plastic deformation of the metal whenactuated by large earthquakes. It must be detailed to avoid excessive strain concentrations; forexample these may cause premature fatigue failure of a steel damper at a weld. Excessiveplastic cycling of steel dampers, for example by wind gusts, must be avoided since this givesprogressive fatigue deterioration.

Steel damping devices, often in the form of bending beams of various cross-sections, have ahigh initial stiffness and are effective dampers but care must be taken in their manufacture toensure a satisfac tory lifetime. They are strongly amplitude-dependent. Combined withcomponents to provide flexibility, they can result in bilinear or nonlinear isolation systems. Elasto-plastic steel dampers have been used in New Zealand and other countries, including the seismicisolation of many bridges in Italy (see Chapter 8).

The lead extrusion damper behaves as a plastic device operating at a constant force with verylittle rate- or amplitude-dependence at earthquake frequencies. It creeps at low loads (seeFigure 3.10), enabling thermal expansion to be accommodated.

When combined with a linear component for flexible support, e.g., flexible piles, then a bilinearsystem can result, as was used in the Wellington Central Police Station (see Chapter 8).

The lead rubber bearing, which comprises an elastomeric bearing with a central lead plug,gives structural support, horizontal flexibility, damping and a centring force in a single easilyinstalled unit. It has high initial stiffness, followed by a lower stiffness after yielding of the lead,and is for many situations the most appropriate isolation system. The hysteretic damping of thisdevice is via the plastic deformation of the lead. The device is nonlinear but can be well

described as bilinear, i.e., it has a parallelogram-shaped hysteresis loop as shown in Figure 2.3and discussed in the associated text.



46

Friction devices behave in a similar way to the extrusion damper, are simple but may requiremaintenance. Changes may occur in the friction coefficient due to age, environmental attack,temperature or wear during use. A further problem is that of 'stick-slip', where after a long timeunder a vertical load the device requires a very large force to initiate slipping. A dramaticexample of a system isolated by this means is the Buddha at Kamakura; a stainless steel plate

was welded to the base of the statue and it was rested on a polished granite base withoutanchoring.

3.2 PLASTICITY OF METALS

The damping devices which have been found to be most economic and suitable for use inisolators are usually those which rely on the plastic deformation of metals. To understand thebehaviour of these devices and to gain some knowledge of their limitations it is necessary toexamine the mechanisms enabling plastic deformation to occur.

Figure 3.1(a) shows the stress-strain curve for a metal in simple tension. Initially the stress isproportional to the strain, and the constant of proportionality is the Young's modulus E.

This elastic region of the stress-strain curve is reproduced on loading and unloading and has theequation of state

so that the slope of the (-) graph is E.

The corresponding relationship between shear stress and engineering strain (where is twicethe tensor strain) is given by

where G = shear modulus.

If the strain is continually increased, it reaches a value (point B, the yield point, in Figure 3.1(a)) atwhich the material yields plastically. The yield point is of particular importance in the design ofisolator components. It has coordinates (y, y), (y, y) and (Xy, Qy) on the stress-strain, shearstress-strain and force-displacement curves respectively.

Further increase in the stress results in a 'plastic-region' curve which is nearly horizontal, in thecase of lead, or which rises moderately in the case of mild steel. If the stress is reduced to zerofrom a very large value of strain, then the curve follows the line CD in Figure 3.1(a). Onunloading, the metal no longer returns to its initial state but has a 'set', i.e. an added plasticdeformation. The unloading curve has the same gradient as that in the elastic region, namelythe Young's modulus or shear modulus (Van Vlack, 1985).

E_ = (3.1a)

G= (3.1b)



47

Figure 3.1: (a) Stress-strain curves for a typical metal which changes from elastic to plastic behaviourat the yield point (B).

(b) Stress-strain curves for a typical mild steel under cyclic loading.

It should be noted that the area ABCE in Figure 3.1(a) represents input work while the area DCErepresents elastic energy stored in the metal at point C and released on unloading to point D. The difference area ABCD represents the hysteretic energy absorbed in the metal.

In the case of lead, the absorbed energy is rapidly converted into heat, while in the case of mildsteel it is dominantly converted to heat, but a small fraction is absorbed during the changes of

state associated with work hardening and fatigue.

Since metal-hysteresis dampers involve cyclic plastic deformation of the metal components, it isappropriate to consider the stress-strain relationship for a metal cycled plastically in various strainranges, as shown in Figure 3.1(b) for a metal with the features typical of mild steel. Included inFigure 3.1(b) is the initial stress-strain curve of Figure 3.1(a). Notice the increasing stress levels withincreasing strain range, and the lower yield levels during plastic cycling. With lead, the hystereticloops are almost elastic-plastic, i.e., an elastic portion is followed by yield at a constant stress(zero slope in the plastic region). Typical operating strains are much greater than the yield strain,the loop tops are almost level, and the loop height is not significantly influenced by strain range.

To understand the behaviour of a metal as it is plastically deformed, it is necessary to look at it on

an atomic scale. Previous to the 1930's, the plastic deformation of a metal was not understood,and theoretical calculations predicted yield stresses and strains very different from thoseobserved in prac tice. It was calculated that a perfect crystal, with its atoms in well-definedpositions, should have a shearing yield stress y of the order of 1010 Pa, and should break in abrittle fashion, like a piece of chalk, at a shear strain y of the order of 0.1. In practice, metalsingle crystals start to yield at a stress of 106 to 107 Pa (a strain of 10-4 to 10-3) and continue to yieldplastically up to strains of 0.01 to 0.1 or more. The weakness of real metal crystals could in partbe attributed to minute cracks within the crystal, but the model failed in that it did not indicatehow the crystal could be deformed plastically (Van Vlack (1985); Read (1953); Cottrell (1961)).

The dislocation model was then devised and overcame these difficulties. Since its inception thedislocation model has been extremely successful in explaining the strength, deformability and

related properties of metal single crystals and polycrystals.

(b)(a)



48

The plastic deformation in a crystalline solid occurs by planes of atoms sliding over one anotherlike cards in a pack. In a dislocation-free solid it would be necessary for this slip to occuruniformly in one movement, with all the bonds between atoms on one slip plane stretchingequally and finally breaking at the same instant, where the bond density is of the order of 1016 bonds per square centimetre. In most crystals, however, this slip, or deformation, is not uniform

over the whole slip plane but is concentrated at dislocations. Figure 3.2(a) is a schematicdrawing of the simplest of many types of dislocation, namely an edge dislocation with the solidspheres representing atoms. The edge dislocation itself is along the line AD and it is in the regionof this line that most of the crystal distortion occurs. Under the application of the shear stress thisdislocation line will move across the slip plane ADCB, allowing the crystal to deform plastically. The bonds, which must be broken as the dislocation moves, are of the order of 108 percentimetre, and are concentrated at the dislocation core, thus enabling the dislocation tomove under a relatively low shear stress. As the dislocation moves from the left-hand edge ofthe crystal (Figure 3.2a) it leaves a step in the crystal surface, which is finally transmitted to theright-hand side. Figure 3.2(b) shows the other major type of dislocation, namely a simple screwdislocation, which may also transmit plastic deformation by moving across the crystal.

Figure 3.2: Atomic arrangements corresponding to:(a) an edge dislocation,(b) a screw dislocation.Here b is the Bergers vector, a measure of the local distortion and AD is the dislocation line.

The dislocations in crystals may be observed using electron microscopy, while the ends ofdislocations are readily seen with the optical microscope after the surface of the crystal hasbeen suitably etched. Typical dislocation densities are 108 dislocations per square centimetre ina deformed metal and about 105 per square centimetre in an annealed metal, namely one

which has been heated and cooled slowly to produce softening. Dislocations are heldimmobile at points where a number of them meet, and also at points where impurity atoms areclustered.

The three main regions of a typical stress-strain curve are interpreted on the dislocation model asfollows:

(1) Initial elastic behaviour is due to the motion of atoms in their respective potential wells;existing dislocations are able to bend a little, causing microplasticity.

(2) A sharp reduction in gradient at the yield stress is due to the movement of dislocations.

(b) (a)



49

(3) An extended plastic region, whose gradient is the plastic modulus or strain-hardeningcoefficient, occurs when further dislocations are being generated and proceed tomove. As they tangle with one another, and interact with impurity atoms, they causework hardening.

It is also possible to model a polycrystalline metal as a set of interconnected domains, each with(different) hysteretic features of the type conferred by dislocations, which give the generalstress-strain features displayed by the hysteresis loops of Figure 3.1(b).

Since dislocations are not in thermal equilibrium in a metal, but are a result of the metal's history,there is no equation of state which can be used to predict accurately the stress-strain behaviourof the metal. However, the behaviour of a metal may be approximately predicted in particularsituations, if the history and deformation are reasonably well characterised.

3.3 STEEL HYSTERETIC DAMPERS

3.3.1 Introduction

General

By the late 1960's a number of damping mechanisms and devices were being used to increasethe seismic resistance of a range of structures. At that time the logical approach to developinghigh-capacity dampers for structures was to utilise the plastic deformation of steel beams.During that decade the plastic deformation of steel structural beams had been increasinglyused to provide damping and flexibility for aseismic steel beam-and-column (frame) buildings. The cyclic ductile capacity of structural members was limited by material properties, localbuckling and the effects of welding (Popov, 1966).

Early steel-beam dampers developed in the Engineering Seismology Section of the Physics andEngineering Laboratory, DSIR, were given a much greater fatigue resistance than typical steelstructural members by adopting suitable steels and beam shapes, and attachments with weldsremote from regions of plastic deformation. Descriptions of the principal steel-beam dampersdeveloped are given by Kelly, Skinner & Heine (1972) (including possible uses within aseismicbuildings, proposed by Skinner); Skinner, Kelly & Heine (1974 and 1975); Tyler & Skinner (1977); Tyler (1978); Cousins, Robinson and McVerry (1991). The principal developers of the three mainclasses of steel-beam dampers which emerged from the Physics and Engineering Laboratoryprogramme which started in 1968 were Kelly: Twisting-beam dampers (Type E); Tyler: Tapered-beam dampers (Type T); and Skinner & Heine: Uniform-moment dampers (Type U).

The earliest bridge structure provided with seismic isolation in New Zealand was a bridge atMotu, rebuilt in 1973, (McKay et al, 1990). The superstructure was provided with seismic isolationto protect the existing slab-wall reinforced concrete piers, which had only moderate strength toresist seismic forces. Isolator flexibility was provided by sliding bearings. Hysteretic damping wasprovided by plastic deformations near the bases of vertical cantilevers, in the form ofstructural-type steel columns. Seismic isolation systems using steel-beam dampers developed atthe Physics and Engineering Laboratory in New Zealand structures are outlined or listed inChapter 8.

An early New Zealand application of steel-beam dampers was in the stepping seismic isolationsystem for the tall piers of the South Rangitikei Viaduct. The seismic responses of the proposedstepping bridge, with the inclusion of hysteretic dampers, were studied by Beck and Skinner(1972, 1974). Steel twisting-beam dampers were selected for the isolation system andprototypes were developed. Construction of the bridge commenced in 1974 and it wasopened in 1981 (Cormack, 1988).



50

Structures with steel tapered-slab dampers in their isolation systems included a stepping chimneyin Christchurch (Sharpe & Skinner, 1983), and Union House, isolated by mounting on flexible piles,in Auckland (Boardman, Wood & Carr, 1983), while conically-tapered steel dampers were usedin the isolation systems for the Capacitor Banks at Haywards. Uniform-moment steel dampers

were used in the superstructure isolation system for the Cromwell Bridge (Park & Blakeley, 1979).

Steel-beam dampers have also been adopted and developed, and used to provide hystereticdamping for seismic isolation in other countries, as outlined in Chapter 8. In Italy, they havebeen used extensively in seismic isolation systems for bridge superstructures. In J apan, steeldampers have been used in the seismic isolation systems of a range of structures.

Features of Steel Hysteretic Dampers

Steel was initially chosen as the damper material since it is commonly used in structures andshould therefore pose no very unusual design, construction or maintenance problems, apartfrom possible fatigue failure at welds and stress concentrations.

Moreover, it was hoped that the development of these dampers would throw additional light onthe performance of steel in ductile aseismic structures.

The performance of steel-beam hysteretic dampers during earthquakes is closely related to theperformance of high-ductility steel-frame structures. However, the dampers are designed tohave a much higher fatigue resistance and to operate at higher levels of plastic strain. This isachieved by using high-ductility mild steels, by using damper forms with nominally equal strainranges over each plastic-beam cross-section, by using plastic beams of compact section(usually rectangular or circular), and by detailing the connections between the plastic beamsand the loading members so as to limit stress concentrations, particularly at welds.

In this section, the results of many years of experience with different shapes and designs of steeldamper are summarised in terms of a 'scaling' procedure, which generalises all the differentfindings and also makes it possible to arrive at initial parameters for the design of steel-beamdampers with the desired properties. However, it must be noted that the following discussion isbased on a large number of tests on many models and a few full-scale dampers, using in themain one kind of steel (BS4360/43A) after stress relieving. Other steels and heat treatments areexpected to give similar, but not necessarily identical, results, particularly for the life of thedamper. The procedures suggested here, particularly for 'scaling', are approximations which areincluded in order to enable a designer to obtain starting parameters for a given design. Inpractice, the full-scale device should be tested.

For a given strain range, the load-displacement loop changes only moderately with repeatedcycling, with a moderate reduction in damping capacity, until the yielding beams are near the

end of their low-cycle fatigue life. The damper loop parameters and their fatigue life can beestimated adequately, on the basis of cyclic tests on damper prototypes or on small-scalemodels.

Since steel-beam dampers have a strictly limited low-cycle fatigue life, controlled by fatigue-lifecurves of the type shown in Figure 3.6 below, it is necessary to design the dampers so as to limitthe cyclic strain ranges during earthquakes, and to ensure a capacity to resist severaldesign-level earthquakes as well as at least one extreme-level earthquake. For a typicalwell-designed isolator and for El Centro-type earthquakes, this might call for a nominal maximumstrain range of + 3% during design earthquakes and + 5% during extreme earthquakes. Again, toavoid premature failure the isolator installation should ensure that wind loads do not imposemore than a few tens of cycles of plastic deformation on damper beams during the design life

of the isolated structure. The fatigue life of well-designed steel-beam dampers is discussedfurther in Section 3.3(e) below.



51

3.3.2 Types of Steel Damper

While steel beams may be subject to shape instability during cyclic deformations into the plasticrange, each of the damper geometries described below is stable for a very wide range ofmember proportions.

The three types of steel hysteretic damper to be discussed are shown in Figure 3.3:

(i) A 'uniform'-moment bending-beam damper with transverse loading arms, sloped at anangle as shown in Figure 3.3(a) (Type-U damper).

(ii) A tapered-cantilever bending-beam damper (Type-T damper). The apex of thetapered slab is at the loading level, while the apex of the tapered cone is substantiallyabove the loading level. The c ircular-section cantilevered beam in Figure 3.3(b) may beloaded in any direction perpendicular to the beam axis. Figure 3.3(c) shows theload-displacement curves for this cantilever damper, as used in retrofitting HaywardsPower Station with seismic isolation (see Chapter 8).

(iii) A torsional-beam damper with transverse loading arms (Type-E damper). Figure 3.3(d)shows the E-type damper used in the South Rangitikei Viaduct (see Chapter 8).

Note, as shown in Figures 3.3(a) and 3.3(d) that the welds are placed at low-stress regions of thedamper.

Figure 3.3: (a) Full-scale steel 'U-type' bending-beam damper prototype (100 kN, +50 mm). Shaft

diameter 100 mm. Note position of welds in low-stress region.(b) Steel cantilever 'T-type' damper (10 kN, + 200 mm), as retrofitted in order to isolate the

capacitor banks at Haywards Power Station (see Chapter 6). Shaft diameter 50 mm.

(a)

(c)

(b)

(d)



53

Table 3.2:Scaling Factors for Steel Beam Dampers

Figure 3.4 shows scaled stress-strain loops for a Type Tr steel-beam damper made of hot-rolledsteel complying with BS4360/43A. Table 3.2 shows the force- and displacement-scaling factors, fand l respectively, for 7 types of damper.

The scaling factors f and l of Table 3.2 and Figure 3.4 are based on a greatly simplified but

effec tive model of the yielding beam. The extreme-fibre strains (or ) are based on the shapewhich the beam would assume if it remained fully elastic. The nominal stresses or^ are relatedto the force scaling factor f on the assumption that they remain constant over a beam section(as they would for a rigid-plastic beam material.) The c ircumflex ( ) is introduced to emphasisethe nominal nature of the stresses and moduli derived using the uniform-stress assumption.

It can be shown that premultiplication of the scaling factor f by about 0.6 will correct to someextent for the approximation's nonvalidity. However, if such refinement is required, it ispreferable to scale using the method of c(iii) and d(iii) below.

The force F and displacement X can then be obtained

where ˆ , 6 are given by Figure 3.4, ˆ , 7 are given approximately by Figure 3.4, by letting = and /2, and where 'a' is a small correction factor for large-displacement shape changes.

For dampers of Type U, T and E respectively, values of the correction factor 'a' are:

where R and L are defined in Table 3.2.

)or (,X (3.2a)

))Xa + (1 ˆ f (or),Xa + (1 ˆf F 22 (3.2b)

),R /(21a;)R /(L+2a);R /(81 -a2

E2

T2

U (3.2c)



54

Figure 3.3(c) is an example of the effect of a positive 'a' value on the loop shapes of Figure3.1(b). The positive a T and aE values of equation (3.2c) cause an increase in the slope of theforce-displacement loop for large yield displacements of T-type and E-type dampers, inaccordance with equation (3.2b). Similarly, the negative aU value causes a reduction in theloop slope for large yield displacements of U-type dampers.

The stress-strain loops of Figure 3.4 were derived from force-displacement loops for a Tr-typedamper, using equations (3.2) and f(Tr) and l(Tr) values from Table 3.2. The force-displacementloops in Figure 3.4 were not corrected for beam-end effects, since these were consideredtypical for bending-beam dampers. Hence damper designs based on Figure 3.4 and Table 3.2already includes typical beam-end effects. The initial stiffness of the damper is somewhatuncertain, owing to variations in end-effects and the stiffness of beam-loading arms.

When equations (3.2) are used to generate the stress-strain loops from the force-displacementloops of a Tr damper, they eliminate the large-displacement increases in nominal stresses, as isevident from a comparison of Figures 3.3(c) and 3.4. When dampers are then designed usingFigure 3.4, equations (3.2) reintroduce appropriate large-displacement changes in force and

stiffness.

By introducing the very rough approximation ˆˆ 2 9 and using =, Figure 3.4 and Table 3.2can be used to obtain a rough estimate of the force-displacement loops for E-type (torsional)

dampers. However, it would be more accurate to generate a separate set of -ˆ 10 loopsbased on force-displacement loops for an E-type damper and equations (3.2). A representativebeam section should be used, say a rectangle with B=2t, where B and t are defined in Table 3.2.Alternatively, the method of c(iii) should be used if more accuracy is required.

Errors in Approximate Damper Loops

There are four main sources of error in the damper loops and parameters derived by the

method described in c(i) above.

(1) Differences between the material properties of the hysteretic beam used to generatethe stress-strain loops of Figure 3.4 and the material properties of the hysteretic beam inthe prototype.

(2) End-effects and non-beam deformations. End-effects usually reduce the initial stiffnessby about 50% and are particularly important for rectangular-beam type-E dampers.

(3) Alteration of loop loads, for a given displacement, by changes in the shape of thedamper under large deflections. Shape changes reduce K b2 for type-U dampers andincrease K b2 for type-T and type-E dampers. First-order corrections have been derived

for the load changes due to damper shape changes. These have been used to removelarge-deflection effects from the loops in Figure 3.4.

(4) Small changes in the damper loops caused by secondary forces. For example, the E-type damper is deformed by bending as well as by twisting forces. These effects havebeen small or moderate for all the damper proportions tested.

The inelastic interaction of primary and secondary beam strains results in a gradual progressivecycle-by-cycle change in beam shape. The beam of a U-type damper deforms progressivelyaway from a line through the loading pins. The beams of an E-type damper deformprogressively towards the axis of the loading pin. These effec ts were not serious in any of thedampers tested.

The method given below in c(iii) gives a more accurate procedure for generatingforce-displacement loops for steel-beam dampers.



56

The yield stiffness K b2 is approximated by the slope of the parallel lines AC, A'C', where CC' is theline through O with slope K b1. Xy and Qy, the coordinates of point C, are the yield displacementand the yield force respectively for the bilinear approximation to the curved hysteresis loop. Thestress-strain loops of Figure 3.4 can also be approximated by bilinear loops with an initial modulus

Ê1 (or _ 1), a yielded modulus Ê2 (or _ 2) and a yield stress ).ˆ(or ˆ yy 14

The bilinear loop parameters change rapidly with strain amplitude m at low strains, but moreslowly with maximum strain for larger strains. In practice, these parameter changes do notintroduce large errors to seismic designs based on bilinear loops, since seismic responses aredominated by relatively large strains, with slowly varying parameters. With fixed values of K b1, K b2 and Qy, the bilinear loops nest on a two-slope generating curve with a fixed starting point.

Bilinear Damper Parameters from the Bilinear Parameters of Stress-Strain Loops

Bilinear approximations to the stress-strain loops of Figure 3.4 have been used to generate themoduli and the yield stresses and strains listed in Table 3.3.

These moduli and stresses may be scaled by the factors f and l of Table 3.2 to give the bilinearstiffness and yield parameters for particular dampers, as follows:

where

where m is the maximum amplitude of cyclic strain and 'a', the large-deflection correctionfactor, is defined in equation 3.2.

For a (torsional) E-type damper, Ê1, Ê2 and y 19 of Table 3.3 and equations (3.4) are replaced

by _ 1, _ 2 and ,ˆy 20 which are, very approximately, half as large.

m

%

Ê1

102 MPa

Ê2

102 MPa

y

102 MPa

y

%

1 700 122 2.70 0.36

2 " 25.6 3.70 0.55

3 " 12.2 4.06 0.59

4 " 7.58 4.24 0.61

5 " 5.34 4.42 0.63

6 " 4.79 4.52 0.65

7 " 4.65 4.58 0.66

Table 3.3: Approximated Moduli, Stresses and Strains, up to a Strain Amplitude m of 7%

E )/f (K 11 b (3.4a)

) / + (1 XQa+E ) /f (K mymy22 b (3.4b)

f Q yy (3.4c)

mm =X



57

Stiffness and Yield Parameters from Models of Similar Proportions

The modelling procedure described in c(iii) can be used to give the parameters of a proposed

damper. Again, subscripts pand e refer to the 'prototype' and 'experimental' dampersrespectively, and f and l values are obtained from Table 3.2.

If the correction factor involving 'a' is neglected, then equations (3.4) give

and

For the Uc damper, for example, Table 3.2 gives either stiffness ratio of the form:

and

The above approach is equivalent to generating a loop or loops of the type shown inFigure 3.4, based on an approximate model of a proposed damper, and then using values from Tables 3.2 without end-corrections or large-deflection corrections, to find the parameters of theproposed damper.

3.3.5 Fatigue Life of Steel-Beam Dampers

While the load-deflection parameters of a steel-beam damper may be achieved readily, usingthe above design parameters, some sophistication is required in design detailing and inmanufacturing techniques which will assure a maximum in the potential fatigue life. Thepotential fatigue life may be estimated from cyclic tests on simple specimens and from thenominal maximum cyclic strains as derived from simple beam theory.

The 'life', or number of cycles a steel hysteretic damper can be expected to survive, isdependent upon the behaviour of the steel under cyclic loading as well as on the design of thedamper. The stresses which a material can survive under cyclic loading are far less than forstatic loading. As the stress amplitude increases, the number of cycles to failure reduces rapidly.

These results are normally summarised in 'S-N' curves, in which the cyclic stress amplitude isplotted against the number of cycles to failure. For steel hysteretic dampers to operate, thestress level needs to exceed the yield strength while remaining below the ultimate strength.Fortunately for most seismic isolation solutions, it is the displacement amplitude, and thus thestrain, which is the controlling factor. Therefore, for the problem of seismic isolation the importantcurve is the stra in amplitude versus the number of cycles to failure (Figure 3.6). Note thelogarithmic scale on the abscissa.

)f ( /)f ((e)K /(p)K (e)K /(p)K pee p2 b2 b1 b1 b (3.5a)

f /f (e)Q /(p)Q e pyy (3.5b)

L R d L R d (e)K /(p)K p2 p

4ee

2e

4 p1 b1 b

R d R d (e)Q / p)(Q p3ee

3 pyy



58

Figure 3.6: Fatigue-life curve for a steel-beam damper. (The strain amplitude versus the number ofcycles to failure.) (Based on Tyler, 1978.)

By contrast, the lead devices do not fatigue readily at normal operating temperatures, becausethe melting point of lead is so low. During and after deformation, the deformed lead undergoesthe interrelated processes of recovery, rec rystallisation and grain growth. This behaviour is similarto that which occurs for steel above about 400C.

When assessing low-cycle fatigue capacity, the cyclic displacements of an earthquake may becharacterised by various strain ranges, say 2 cycles at ±5% strain, 6 cycles of ±4% strain and 12cycles at ±3% strain, as is commonly done when assessing the fatigue capacity of ductilereinforced-concrete structural members. The total fatigue capacity of a well-designed steel-beam damper, for any fixed strain range, may be estimated from Figure 3.6. A roughapproximation to the reduction in fatigue resistance caused by given earthquakedisplacements may be obtained as follows. When a strain range of ±x% gives a damper fatiguelife of nx cycles, as indicated by Figure 3.6, assume that m cycles consume m/nx of the totalfatigue capac ity of the damper. Hence the above earthquake displacement consumes 2/45 +6/77 + 12/108 = 0.23 of the total damper fatigue capacity, and the damper is estimated to justsurvive the cyclic deflections of 4 such earthquakes.

As suggested by the above example, the fatigue capacity of damper-beam materials may becompared effectively on the basis of the cyclic fatigue capacity of simple standard specimenssubject to a single nominal strain range, say ±5%.

The beam and its end fixings must be detailed to avoid severe stress concentrations at locationsof high plastic strain. In particular, yielding-beam welds should be confined to lower-strainlocations. Again it is appropriate to adopt a damper geometry which gives a decrease in thenominal plastic strain towards the ends of the yielding beams. Large-deformation effec ts give

this end-strain reduction for type-U dampers with prismic yielding beams. It also occurs for type- Tc dampers, with circular cones loaded at the level given at the bottom of Table 3.2. For somedampers, such as type-Tr, it is appropriate to use curved transitions between yielding and non-yielding parts of the beam.

Rises in the plastic-beam temperature, during design earthquakes or extreme earthquakes,should cause little change in the damper parameters or in the damper fatigue resistance.

The plastic-deformation damper beam should be of mild steel, for example BS4360/43A. It maybe an advantage to select for low levels of those constituents known to reduce low-cyclefatigue. The damping beam material should not be more than moderately cold-worked. Theas-rolled condition is usually appropriate for damper beams. With higher cold-working during

manufacture, partial annealing is appropriate. Full annealing will considerably increase fatiguelife while reducing damping forces, which will then increase moderately during the first severalcycles of damper operation.



59

3.3.6 Summary of Steel Dampers

Steel-beam dampers are characterised by hysteretic force-displacement (stress-strain) loopswhich can be analysed using a scaling method or approximated by bilinear loops. The 'life' ofsteel dampers is limited by their fatigue characteristics on cycling.

3.4 LEAD EXTRUSION DAMPERS

3.4.1 General

Another type of damper utilising the hysteretic energy dissipation properties of metals is the LeadExtrusion Damper, developed at PEL (DSIR) (the Physics and Engineering Laboratory of the NZDepartment of Scientific and Industrial Research). The cyclic extrusion damper was invented inApril 1971 by Bill Robinson, immediately after he had a morning-tea discussion with Ivan Skinneron the problems associated with the use of steel in devices to absorb the energy of motion of astructure during an earthquake.

The process of extrusion consists of forcing or extruding a material through a hole or orifice,thereby changing its shape (Figure 3.7). The process is an old one. Possibly the first design of anextrusion press was that of J oseph Bramah who in 1797 was granted a patent for a press "formaking pipes of lead or other soft metals of all dimensions and of any given length without joints", (Pearson, 1944).

Figure 3.7: A representation of the extrusion of a metal, showing the changes inmicrostructure. (Robinson, 1976.)

A lower bound for the extrusion pressure p may be derived from the yield stressy of the materialunder simple axial load, following J ohnson & Mellor (1975). Simple extrusion involves a reductionin the cross-sectional area of a solid prism from A1 to A2 by plastic deformation, with an increasein length corresponding to little volume change. The process may be idealised as the frictionlessextrusion of an incompressible elastic-plastic solid which has a constant yield stressy. Theminimum work W, required to change the section from A1 to A2, or the equal minimum work tochange the section from A2 to A1, arises when A1 and A2 have the same shape and when the

deformation involves plane strain. Such plane strain occurs when plane sections prior todeformation remain plane throughout the deformation process.



60

The work W of plane-strain deformation can be derived by considering a prism of section A2 which is compressed between frictionless parallel anvils to form a prism of section A1. The yieldforce increases with the increasing sectional area to give the work W as

where L1 is the length when the prism area is A1. Indeed, equation (3.6a) can be used as a basisfor the experimental determination of the simple-strain yield stress y for lead, since a suitablylubricated lead cylinder, compressed between smooth anvils, deforms in almost true planestrain.

The work required to cause the reverse change in area by simple frictionless extrusion would begreater than W by an amount which depends on the departures from plane-strain, which shouldnot be great with a gradually-tapered extrusion orifice.

For this almost plane-strain case, a result which appears to have been first put forward in 1931 bySiebel and Fangmeier, the extrusion pressure p follows simply from equation (3.6a), giving

where the extrusion ratio ER = A1/A2

and exceeds 1.0 by a small amount which arises from the departure from plane-straindeformation.

A practical extrusion process will involve significant surface friction which will give a furtherdeparture from plane-strain and hence an increase in , beyond the zero-friction value. Afurther increase in pressure occurs in reaction to the axial component of the surface frictionforces.

If there are significant changes in y over sections of the extruded material, as may well arisewhen hysteretic heating causes temperature differences, this may change the pattern ofextrusion strains substantially, a factor which may be significant with cyclic extrusion.

When a back-pressure and a re-expansion throat are included to return a lead plug to itsoriginal sectional area A1, as shown in the schematic sketch of an extrusion damper in Figure 3.8,the theoretical frictionless pressure of equation (3.6b) is doubled. For a prac tical system witheffective lubrication, the extrusion pressure, as given by equation (3.6b), should also be roughlydoubled when the contraction from area A1 to A2 is followed by an expansion from area A2 toA1.

A /AnLA =W 21y11 (3.6a)

ER n= p y (3.6b)

(a)



62

Since the recrystallisation temperature of lead is below room temperature, any deformation oflead at or above room temperature is in fact 'hot work' in which the processes of recovery,recrystallisation and grain growth occur simultaneously. Working lead at room temperature isequivalent to working a piece of iron or steel at a temperature of more than 400oC. Indeed,lead is the only common metal which need not suffer progressive fatigue when cycled

plastically at room temperature.

A device which acts as a hysteretic damper by utilizing this property of lead (Robinson &Greenbank (1976); Robinson & Cousins (1987, 1988), is shown in Figure 3.8(a). It consists of athick-walled tube co-axial with a shaft which carries two pistons. There is constriction on thetube between the pistons, and the space between the pistons is filled with lead. The lead isseparated from the tube by a thin layer of lubricant kept in place by hydraulic seals around thepistons. The central shaft extends beyond one end of the tube. During operation, axial loadsare applied with one attachment point at the protruding end of the central shaft and the otherat the far end of the tube. The hysteretic damper is fixed between a point on the structure anda point on the earth, which move relative to one another during an earthquake. As theattachment points move to and fro, the pistons move along the tube and the captive lead isforced to extrude back and forth through the orifice formed by the constriction in the tube.Since extrusion is a process of plastic deformation, work is done, while very little energy is storedelastically, as the lead is forced through the orifice during structural deformation. Thus during anearthquake such a device, by absorbing energy, limits the build-up of destructive oscillations ina typical structure.

The successful operation of this hysteretic damper depends on the use of a material, in this caselead, which recovers and recrystallised rapidly at the operating temperature, so that the forcerequired to extrude it is prac tically the same on each successive cycle. If the extruded materialhad a recrystallisation temperature much above the operating temperature, it would work-harden and be subject to low-cycle fatigue. Moreover, such materials typically have muchhigher stresses which would present very severe problems for containment, piston sealing andlubrication in a cyclic extrusion device.

A hysteretic damper which operates on this same principle but has different construction detailsis shown in Figure 3.8(b). Here the extrusion orifice is formed by a bulge on the central shaftrather than by a constriction in the outer tube. The central shaft is located by bearings whichalso serve to hold the lead in place. As the shaft moves relative to the tube, the lead mustextrude through the orifice formed by the bulge and the tube.

3.4.2 Properties of the Extrusion Damper

One of the most important properties of a hysteretic damper is its force-displacement loop. Ifthe device acts as a 'plastic solid' or 'Coulomb damper' then over one cycle the force-

displacement hysteresis loop will be rectangular and the energy absorbed will be a maximumfor the particular force and stroke. Figure 3.9(a) shows hysteresis loops typical of constrictedtube and bulged-shaft dampers. For both types, the force rises almost immediately on loadingwhile there is no detectable recoverable elasticity on unloading. Note the plastic force is theforce Qy for the extrusion damper. The performance fac tor, defined as the ratio of the workabsorbed by the damper to that contained by the rectangle c ircumscribing the hysteresis loop,is 0.90 to 0.95.



63

Figure 3.9: (a) Typical load-displacement hysteresis loops for lead extrusion dampers.(b) Comparison of hysteresis loops obtained for a constricted-tube lead-extrusion damper

tested in 1976 (solid line) and again in 1986 (dashed line). (Cousins & Robinson, 1987.)

The force to operate one of the extrusion hysteretic dampers has also been found to be almostindependent of both the stroke and the position from which displacement starts. The hysteresisloops in Figure 3.9(b), which shows the behaviour of the same damper at an interval of 10 years(1976 and 1986), confirm the stability of the extrusion dampers (Robinson & Cousins (1987, 1988)).

The extrusion force is rate-dependent, as can be understood on the dislocation model byconsidering the speeds of dislocation motion and grain boundary sliding. To examine the ratedependence of the extrusion force, for the extrusion energy absorbers, a number of them weretested at speeds ranging from 3x10-10 to 1 m/sec.

(a)

(b)



64

Figure 3.10 Rate dependence of lead extrusion hysteretic damper. The force is compared with thatcorresponding to a speed of 1 m/s, and this load ratio is plotted as a function of speed.

The experimental results for the rate dependence of the energy absorbers are shown in Figure

3.10, in which the ordinate is the 'load ratio' relating the force to that which will cause thedamper to yield at a speed of 1 m/s. The damper's performance has two differentcharacteristics, with the change occurring at a speed of 10-4 m/sec . Below this speed, theexponential equation (3.7b) is given by b=0.14. Hence if the rate of cycling is increased by afactor of ten, the load increases by 38 per cent, or the rate must be increased 140 times for theload to be doubled. Above a speed of 10-4 m/s, b = 0.03. In this case a 7% increase in loadincreases the rate by a factor of ten, while a 40% increase in the load requires the rate to beincreased 105 times. The value of 0.14 for b, for rates below 10-4 m/s, agrees well with the figureof 0.13 obtained by Pearson (1944) for lead at 17oC. Loads which cause creep may also becompared with the load at an earthquake-like speed of 10-1 m/sec. At a load ratio F/F(10-

1 m/sec) = 0.2, the creep rate becomes ~10 mm/yr. The results above 10-4 m/sec indicate that at these speeds the extrusion energy absorbers are

nearly rate-independent; for example, at a rate of ~102

m/sec the extrusion force is expected tobe 1.15 times that for an earthquake-like speed of 10-1 m/sec.

Above a rate of 2 x 10-2 m/sec, tests on large energy-absorbing devices become difficultbecause of the large power required. For example, for a 200 kN hysteretic damper operating at1 Hz with a total stroke of 250 mm, a power of 100 kW must be supplied.

The effect of temperature on the extrusion energy absorber is complex, in that an increase intemperature, due either to ambient changes, or to the absorption of energy during anearthquake, has a twofold effect:

- As the temperature increases the extrusion force decreases.

- The higher the temperature, the more rapidly the lead will undergo recovery,recrystallisation and grain growth, thereby eliminating work hardening andregaining its plasticity.

These factors ensure that the extrusion damper is a stable device which cannot destroy itself bybuilding up excessive forces. A 15 kN constricted-tube extrusion damper was operatedcontinuously at 1 Hz for 1,800 cycles and during this test the temperature on the outside of theorifice reached an equilibrium value of 210oC. The effect of lowering the temperature waschecked by cooling an energy absorber to -20oC but no noticeable change in extrusion force,compared to that at 25oC, was observed.

The lifetime of an extrusion energy absorber has been tested by operating a 15 kN constricted-

tube device continuously at frequencies of 0.5, 1 and 2 Hz for a total of 3,400 cycles (Robinsonand Greenbank (1976)).



65

After this test, which provided conditions far more severe than those to be expected in service,(during an earthquake the device would be expected to undergo ~10 cycles), the extrusionenergy absorber was found to operate as initially at 1.7 x 10-3 m/sec. This result is not surprisingsince 'hot worked' lead is forever recovering its original mechanical properties. Therefore theextrusion damper should be able to cope with a very large number of earthquakes.

The maximum energy an extrusion damper can absorb in a short time is limited by the heatcapacity of the lead and the surrounding steel. To increase the temperature of lead from 20oCto its melting point of 327oC, but without melting it, requires 3.8 x 104 joules/kg of lead. Thesurrounding steel raises the heat capacity of the device by a factor of ~4 so that the totalenergy capacity of the extrusion device is ~1.6 x 105 joules/kg (total weight).

An extrusion damper with a 30 mm outside diameter had an extrusion force of ~15 kN while adevice with a 150 mm outside diameter required a force of ~150 kN to operate it. The stroke ofthe extrusion energy absorber is not limited in any way by the basic properties of the device. Todate the largest extrusion dampers made had a total stroke of 800 mm (±400 mm) andoperated at a force of 250 kN. The total length of a device when at its maximum extension is

three to four times the length of its stroke.3.4.3 Summary and Discussion of Lead Extrusion Dampers

The extrusion damper, in which mechanical energy is converted to heat by the extrusion of leadwithin a tube, is a device that is suitable for absorbing the energy of motion of a structure duringan earthquake. The principle is simple but the design is not necessarily so.

The extrusion damper has the following properties:

(1) It is almost a pure 'Coulomb damper' in that its force-displacement hysteresisloop is nearly rectangular and is practically rate-independent at earthquake-likefrequencies.

(2) Because the interrelated processes of recovery, recrystallisation and graingrowth occur during and after the extrusion of the lead, the energy absorber isnot affected by work hardening or fatigue, but instead the lead is foreverreturning to its original undeformed state. The extrusion damper therefore has avery long life and does not have to be replaced after an earthquake.

(3) The extrusion damper is stable in its operation and cannot destroy itself bybuilding up excessive forces. As the temperature rises during its operation, then- the extrusion force decreases and therefore the energy absorbed and

heat generated decrease, and- the higher the temperature, the more rapidly the lead will recover and

recrystallised, thereby regaining its plasticity.

(4) The length of stroke of the extrusion energy absorber is limited only by theproblem of buckling of the shaft during compression. The dimensions of a 150 kNenergy absorber with a stroke of ±200 mm are:

Outside diameter ~150 mm Total length ~1.5 m Total mass ~100 kg

These dimensions ensure simple installation in many isolator applications. The lead extrusiondamper has, to date, been used in New Zealand in three bridges and to provide damping forone ten-storey building mounted on flexible piles (see Chapter 6). It has also been installed in

the walls to increase the damping of two buildings in J apan. In addition to providing damping,the extrusion damper 'locks' the structure in place against wind loading in the case of buildings,and against the braking of motor vehicles in the case of sloping bridges.



66

3.5 LAMINATED-RUBBER BEARINGS FOR SEISMIC ISOLATORS

3.5.1 Rubber Bearings for Bridges and Isolators

Another method of seismically isolating structures is by mounting them on laminated rubberbearings (elastomeric bearings). These bearings are a fully developed commercial productwhose main application has been for bridge superstructures, which often undergo substantialdimensional and shape changes due to changes in temperature. More recently their use hasbeen extended to the seismic isolation of buildings and other structures (Chapter 6).

These bearings are designed to support large weights while providing only small resistance tolarge horizontal displacements, and to moderate tilts, of the upper surfaces of the bearings. Atypical bridge bearing consists of a stack of horizontal rubber layers vulcanised to interleavedsteel plates, as shown schematically in Figure 3.11 for a cylindrical bearing.

Figure 3.11: Sketch of laminated elastomeric bearing, of area A and circumference C,in which rubber layers, of thickness t, are bonded to thin steel plates.

For a given bearing area and rubber composition, the load capacity is increased by reducingthe thickness of each rubber layer, while the resistance to horizontal and tilting movements isreduced by increasing the total height of the rubber.

Rubber bearings, of the types used for bridges, can be dimensioned to provide the supportcapacity and the horizontal flexibility required for seismic isolation mounts. Of particularimportance is the ratio of bearing weight capacity to horizontal flexibility, which determines themaximum achievable value for the rigid-structure period Tb. Of equal importance is themaximum acceptable horizontal displacement Xb, which is set either by the allowable rubberstrain or by the allowable offset between the plan areas of the top and bottom of the bearing.Rubber bearings also provide adequate isolator centring forces during large seismicdisplacements.

Rubber bearings have a considerable range of applications in seismic isolators, as describedlater in this chapter. In their basic form, rubber bearings may be used to provide support,horizontal flexibility and centring forces. Isolator damping may then be increased by separatecomponents. Alternatively, lead plugs may be inserted in rubber bearings to add high hystereticdamping to the features of the basic bearings, as described in 3.6 below. Again, rubberbearings may be surmounted by horizontal slides which provide increased horizontal flexibilityand frictional damping. Additional isolation roles for rubber bearings include tilting supports forrocking structures and elastic components in displacement-limiting buffers.

The detailed design and the manufacture of rubber bearings call for some technicalsophistication. However, the approximate features of rubber bearings may be derived using

simple well-known approaches, as described below. An understanding of the factorsinfluencing the features of elastomeric bearings is useful when developing isolation systems, andmay assist during preliminary design studies.



67

3.5.2 Rubber Bearing, Weight Capacity Wmax

The principal features of rubber bearings can be seen from the behaviour of a thin rubber disc,with rigid plates bonded (vulcanised) to its plane surfaces, when subjected to normal (axial) andto parallel (or shearing) loads. The relationship between the load W and the maximum

engineering shear strain in the disc has been derived by Gent & Lindley (1959) as outlinedbelow in modified form. (Following Borg (1962), =xz =w/x +u/z = 2xz where xz is the tensorshear strain.)

When the rubber is assumed incompressible, a vertical compressive strainz causes the rubber tobulge by an amount proportional to its distance from the centre of the disk. When the bulgeprofile at any radius r is approximated by a parabola, constant rubber volume gives themaximum shear strain xz as:

where the vertical strain z =t/t, the thickness of the rubber layers is denoted t, and the shapefactor S = (loaded area)/(force-free area). For example, for a circular disc of unstraineddiameter D and thickness t, S = D/4t.

The rubber shear forces cause a pressure gradient within the disc which is proportional to thedistance from the centre. This gives a parabolic pressure distribution, as shown in Figure 3.12.

Figure 3.12: Sketch of circular layer of rubber, diameter D, thickness t,and of the parabolic pressure distribution p.

The maximum pressure po is given by:

where G = shear modulus of rubber.

The corresponding load W may be obtained by summing the pressure over a disc area A togive:

Now consider a basic rubber bearing consisting of n equal rubber layers of any compact shape.Also let the top of the bearing be displaced by Xb to give an overlap area A between the topand bottom of the bearing, as shown in Figure 3.13.

zxzS6 = (3.8a)

xzo

GS2 = p (3.8b)

xzAGS =W (3.8c)



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Figure 3.13: Sketch of rubber cylinder of diameter D, with a shear displacement Xb and overlap A'.

Then experiment and analysis show that equation (3.8c) may be generalised approximately asfollows:

whereWmax = allowable weightw = allowable shear strain due to weightA = overlap of bearing top and bottom

The use of A in equation (3.8d) is a somewhat arbitrary simplification and is probablyconservative.

3.5.3 Rubber-Bearing Isolation: Stiffness, Period and Damping

If an isolator consists of a set of equal rubber bearings, each supporting an equal weight, thenthe isolator period can be calculated directly from the weight and stiffness for a single bearing.In practice the average weight per bearing may be reduced because the weight on somebearings has been reduced to offset vertical seismic loads, or for structural or architecturalconvenience. However, such weight reductions are neglected here and the isolatorparameters are expressed in terms of those for a single bearing.

Bearing Horizontal Stiffness K b

A rubber bearing may be approximated as a vertical shear beam, since the steel laminationsseverely inhibit flexural deformations while providing no impediment to shear deformations. Theapproximate horizontal stiffness K b is therefore given by

whereA = rubber layer areah = total rubber height.

There will be some reduction in bearing height with large displacements, partly due to flexuralbeam action and partly due to increased compression of the reduced overlap area A.

wmax GSA = W (3.8d)

GA/h = K b (3.9)



69

The resulting inverted pendulum action, under structural weight, reduces the horizontal stiffnessK b and in extreme cases might cause serious reductions in the centring forces. However, theinverted pendulum forces are reduced by increasing the layer shape factor S, and these forcesare unlikely to be serious for S values in the range from 10 to 20, a range appropriate for isolatormounts.

Bearing Period Tb

The bearing weight capacity, Wmax, from equation (3.8d), and the horizontal stiffness, K b, fromequation (3.9), can be combined to give the bearing and isolator period Tb, when the bearing issupporting its maximum weight, as

where w is the allowable shear strain due to the weight W.

For example let S = 16, h = 0.15 m, A/A = 0.6, and w,max = 0.2L/L, where the breaking tensilestrainL/L = 5, (typically 4.5 to 7.0). Then Tb = 2.4 seconds.

Bearing Damping zb

Energy losses in the deforming rubber layers provide damping which is predominantlyvelocity-dependent. Typical bridge bearings provide bearing and isolator damping factors inthe range from 5% to 10% of critical. However, acceptable bearing rubbers have beenmanufactured which increase the bearing and isolator damping to about 15%, anddevelopment aimed at higher damping values continues.

Bearing Vertical Stiffness K z

Some isolator applications of rubber bearings are influenced by their vertical stiffness, and someby their related bending stiffness.

The vertical deflection of a bearing is the sum of the deflections due to rubber shear strain andto rubber volume change, and these two respective stiffnesses are added in series. Thus theoverall vertical stiffness is

where K z(), the vertical stiffness of the bearing without volume change, is given by equations(3.8a) and (3.8c) as

and where K z(V), the vertical stiffness due to volume change without shear strain, is simply

where = rubber compression modulus.

Thus

)/AgA (Sh2 = T‰

w b (3.10)

VK + K /(V)K K = K zzzzz (3.11a)

,hA /SG6 = K 2z (3.11b)

,hA /= VK z (3.11c)

h) + SG/(6A GS6=K 22

z (3.11d)



70

Equations (3.11) show that a small shape factor S gives a moderate vertical stiffness which iscontrolled by shear strain, while a sufficiently large value of S gives a very high vertical stiffnesswhich is controlled by volume change. For a typical bridge-bearing rubber, with G = 1 MPa and = 2000 MPa, shear strain and volume change make equal contributions to vertical stiffnesswhen S 18. The above discussion neglec ts the usually small reduction in K z() which occurs, due

to a pressure redistribution in the layers, when rubber compressibility is introduced. When theS-value is high, rubber compressibility reduces considerably the bearing vertical stiffness and therelated bending stiffness. However, rubber compressibility causes little change in the otherbearing parameters described.

3.5.4 Allowable Seismic Displacement Xb

Displacement Limited by Seismic Shear Strain gs

When the rubber shear strain w, due to the vertical load W, is below its maximum allowable

value there is a reserve shear strain capacity, say s, to accommodate a horizontaldisplacement Xb, which is given by

where s = allowable shear strain due to horizontal seismic displacement.

If this displacement is inadequate it may be increased by increasing the rubber height h. Inaddition, or alternatively,s may be increased if the strain due to weight w is reduced.

Displacement Limited by Overlap Factor A¢/A

For an isolator bearing, a lower limit to the overlap factor A /A is set by the reducing weightcapacity, equation (3.8d), and sometimes by the increasing end moments. Typical lower limitsfor the overlap factor may be 0.8 for a sustained horizontal displacement and 0.6 for designearthquake displacements. Where possible, such overlap limits should be based on laboratorytests and field experience. The relationship between the overlap factor A/A, the bearingdisplacement Xb and the bearing dimensions depends somewhat on the shape of the horizontalsection of the bearing.

For a cylindrical bearing with rubber discs of area A and diameter D:

where sin = Xb/D .Hence for moderate values of Xb/D

Similarly, for a rectangular bearing

where Xb(B) and Xb(C) are the bearing displacements parallel to the sides of lengths B and Crespectively. Hence, for displacements parallel to side B,

s b h = X (3.12)

cossin+ /2 - 1 =/AA (3.13a)

/AA - 1D0.8 X b (3.13b)

C /CX-B /BX-1 /AA b b (3.13c)

/AA - 1B (B)X b (3.13d)



71

When the displacement Xb may be in any direction, a more appropriate displacement limit is

where B is the shorter side of the bearing.

From equations (3.13b) and (3.13e) it is seen that, for a seismic overlap factor A /A = 0.6, theallowable values of Xb are D/3 and B/3 respectively.

When the weight per bearing is low, the bearing diameter D or side B may be too short toaccommodate the required seismic displacement Xb. If the discrepancy is not great it might bemet by increasing the bearing area A and/or by reducing the design-earthquake displacementXb. The bearing area may be increased, without changing the bearing stiffness ratio K b/W, ifthere is a compensating reduction in the rubber shear modulus G and/or an increase in therubber height h, as required by equation (3.9). Again, the bearing area may be increased if it ispossible to design the isolator with fewer bearings and hence with a greater weight W per

bearing. Alternatively, the design earthquake displacement Xb may be reduced by increasingthe effective isolator damping.

If the weight per bearing is so low that the allowable displacement falls well short of the designearthquake displacement, then the allowable displacement may be increased as required, bysegmenting the bearing and introducing stabilising plates, as described below.

Segmented Bearing for a Low Weight/Displacement Ratio W/Xb

When a rubber bearing supports a small weight W it has a small area A, and hence itsdisplacement capacity, as given by equation (3.13b) or (3.13e), is also small. Such a simplebearing may be replaced by an equivalent segmented bearing, as shown in Figure 3.14, which

increases the displacement capacity.

Figure 3.14: Segmented bearing formed by rubber segments placed at the corners ofcommon stabilising plates, illustrated by 6 stabilising plates and 20 (multilayer) segments.

Consider the replacement of a simple bearing by an equivalent segmented bearing in whichsets of 4 segments are located near the corners of rectangular stabilisation platforms or plates,as shown in Figure 3.14 and illustrated by Skinner (1976).

/AA - 1B0.8 X b (3.13e)



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If all the linear dimensions (including the thickness) of the segment rubber layers are half those ofthe simple bearing layers, and if the number of layers is increased so that the rubber height isunaltered, then both bearings have the same values for the rubber area A and the rubberheight h, and the same shape factor S, resulting in the same load capacity and the samehorizontal stiffness K b. For a given rubber and operating conditions, a shape factor which is

suitable for a non-segmented bearing is also suitable for the equivalent segmented bearing. Typically each of the cylindrical segments shown in Figure 3.14 will be multilayer, to give the smalllayer thickness required without the use of more stabilising plates than are necessary to retainthe overlap factor required for overall bearing stability.

When, as here, the segments have half the horizontal dimensions of the correspondingnon-segmented bearing, and there are n segments in each vertical stack (eg, n=5 in Figure3.14), then a required overlap factor is retained with an increased allowable displacementgiven by

Where

Xb(1) = allowable displacement for the corresponding non-segmented bearing.

3.5.5 Allowable Maximum Rubber Strains

Allowable Shear Strains gw and gs

The allowable rubber shear strains for various loads and displacements are important factors inthe performance of rubber bearings, as discussed above. When bearings are used as isolationmounts for compact structures, they must withstand the combined rubber shear strains due tostructural weight and seismic displacements. When bearings isolate bridge superstructures,some provision must be made for additional shear strains due to traffic loads and to thermaldisplacements. In addition to their seismic design, rubber bearing mounts must be checked fortheir capacity to withstand the more sustained non-seismic loads and displacements.

The damaging effect of a given rubber strain increases with its total duration and with thenumber of times it is reduced or reversed. In particular, rubber strains due to frequent andfluctuating traffic loads are found to be more severe than a corresponding steady strain appliedfor the life of a bearing. On the other hand, laboratory tests show that the cyclic strains due toseismic displacements are much less severe than corresponding long-duration steady strains,evidently because they involve so few cycles and have such a short duration.

The sustainable steady shear strain in a rubber bearing is sometimes given as (Bridge EngineeringStandards, 1976)

where t = short-duration failure strain in simple tension.

Experiments suggest that corresponding factors for shear strain during earthquakes are 0.4 ormore for design earthquakes and say 0.7 for extreme earthquakes.

Allowable Negative Pressure

Under the combined action of uplift forces and end moments the rubber within isolator bearingsmay be subjected to large negative pressures. Consider a rubber bearing subject to an upliftforce of -Wmax. From equation (3.8) it is found that this gives a small increase in bearing height ofh = hw/(6S), and a large central negative pressure of po = -2GSw. For a typical bridge bearing,with G = 1 MPa, h = 0.15 m, S = 10, and -w = -1.0, it follows that h = 2.5 mm and po = -20 MPa.

2/(1)Xn = (n)X b b (3.14)

tw 0.2 = (3.15)



74

It is normal practice to design bridge bearing installations so that negative pressures do notoccur in the rubber under the combined action of non-seismic loads and motions. It is alsoappropriate to design isolated structures so that non-seismic actions do not cause negativepressures.

However, when seismic actions cause negative pressures in isolator mounts, their duration andfrequency are so low that considerable negative pressures might be tolerated (Tyler, 1991). Ingeneral, an isolator design should be adopted which avoids very high negative pressures duringseismic action. In the particular case of high uplift forces under the corner columns of two-wayframe structures, high negative pressures in corner rubber bearings may be avoided byattaching the bearing tops to the bottom beams of the frames designed to allow corner uplift,for example as described by Huckelbridge (1977).

3.5.6 Other Factors in Rubber Bearing Design

In practice the application of laminated-rubber bearings to seismic isolation calls forsophisticated design and specialised manufacturing technology. The rubber must be

formulated for long-term stability and resistance to environmental factors, particularlydeterioration due to ozone and ultraviolet light. The bonds (vulcanising) between the rubberand the interleaved metal plates must resist the large and varying operating stresses. Bearingsmust be provided with end and side rubber cover to inhibit corrosion of the metal plates and toremove rubber-surface deterioration from regions of high operating strains. The rubber coverand additional surface materials may be used to increase fire resistance. Interleaved steelplates must have adequate strength to resist rubber shear forces. However, some platebending may reduce the build-up of rubber tension when large displacements give high endmoments. Bearing end-plates must provide for dowels or for other means of preventing end slipunder high shear forces. Such shear connections must operate despite end moments and insome cases when uplift occurs.

The effect of a fire on the performance of rubber elastomeric bearings and lead rubberbearings has been checked by Miyazaki (1991) in J apan, by heating the outside of bearings togreater than 800oC for more than 100 minutes while carrying a vertical load.

After this heating the rubber elastomeric bearings and the lead rubber bearings performed in asatisfactory way without any appreciable change in their force-displacement loops or loadbearing capac ities.

3.5.7 Summary of Laminated Rubber Bearings

Laminated rubber bearings are already in use in bridges, in order to accommodate thermalexpansion. Their modification for the seismic isolation of buildings and bridges is a fairly simpleengineering concept, but in practice it requires sophisticated design and specialised

manufacturing technology.

3.6 LEAD RUBBER BEARINGS

3.6.1 Introduction

Laminated rubber bearings are able to supply the required displacements for seismic isolation.By combining these with a lead plug insert which provides hysteretic energy dissipation, thedamping required for a successful seismic isolation system can be incorporated in a singlecompact component. Thus one device is able to support the structure vertically, provide the

horizontal flexibility together with the restoring force, and provide the required hystereticdamping.



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Figure 3.16: (a) Lead rubber bearing which consists of a lead plug inserted into a vulcanised laminatedrubber bearing. The form shown here is suitable for applications where there is noapplied tension.

(b) Lead rubber bearing for William Clayton Building (see Chapter 6). Note the 300 mm ruleplaced on the bearing. Load capacity 3 MN, stroke +100 mm. (Robinson, 1982.)

(c) Lead rubber bearing under static test. (Robinson, 1982.)(d) Lead rubber bearing for William Clayton Building under dynamic test (1979). The motive

force was supplied from the drive of a converted caterpillar trac tor: vertical load up to 4MN, frequency 0.9 Hz, maximum power 100 kW, maximum shear force 400 kN, stroke+90 mm. (Robinson, 1982.)

(e) Lead rubber bearing with top and bottom plates vulcanised to the rubber, suitable forapplications requiring applied vertical tension. (Robinson, 1982.)

(a)(b)

(d)

(c)

(e)



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3.6.2 Properties of the Lead Rubber Bearing

Test procedures were designed to measure the load-deflection loops of lead rubber bearingsduring the horizontal displacements of design earthquakes and extreme earthquakes, while anaxial load representing structural weight was applied. These tests were performed at seismic

velocities to ensure that the lead strain rates and temperature rises represented those whichwould apply during the simulated earthquakes. Further load measurements were made at verylow velocities to find the reactions to structural dimension changes arising from dailytemperature cycling, and also the reactions to the even slower motions associated with thedecay of residual isolator displacements after an earthquake (Robinson & Tucker (1977, 1981);Robinson (1982)).

The force-displacement hysteresis loop of an elastomeric bearing without a lead plug is shownas the dotted curve in Figure 3.17. This loop, which is for a bearing 650 mm in diameter, is mainlyelastic with a rubber shear stiffness, K b(r) = 1.75 MN/m and a small amount of hysteresis. Also inthe figure, is the loop for the same bearing when it contains a lead insert with a diameter of170 mm. The dashed lines are at the slope of 1.75 MN/m and are a good approximation to the

post-yield stiffness. In this case the lead is behaving as a plastic solid which adds ~235 kN to theelastic force required to shear the bearing.

Another factor of interest is the initial elastic part of the force-displacement curve for smallforces.

Thus a reasonable description of the hysteresis loop is a bilinear solid with an initial elastic stiffnessof K b1 followed by a post yield stiffness of K b2 where

where K b(r) is given by equation (3.9).

Figure 3.17: Dynamic force-displacement hysteretic loop, for a 650 mm diameter bearing,obtained using equipment shown in Figure 3.16(d), with vertical compression force

F(vert) =3.15 MN, frequency 0.9 Hz, stroke +90 mm. The dotted line is for the bearing without a lead plug. The solid line is for a lead plug of 170 mm diameter. The slope of the dashed line is K(r) (Robinson, 1982.)

Dependence on the Diameter of the Lead Insert

The horizontal force, F, required to cause the bearing to be horizontally sheared can beconsidered as two forces acting in parallel, the first due to the rubber elasticity and the seconddue to the plasticity of the lead. The rubber elasticity results in a force which is proportional tothe displacement while the plasticity requires a force which is independent of displacement.

(r)K 10~K b1 b (3.16a)

(r)K K b2 b (3.16b)



78

Thus to a very good approximation

where the shear stress at which the lead yields (Pb) = 10.5 MPa, A(Pb) is the c ross-sectional area

of the lead, K(r) is the stiffness of the rubber in a horizontal plane, and X is the displacement ofthe top of the bearing with respect to its base. This fact is illustrated in Figure 3.18 where themaximum shearing force, minus the force due to the elastic stiffness of the rubber, is plottedagainst the cross-sec tional area of the lead insert. The slope of this line is the yield stress of lead,10.5 MPa (Robinson (1982). Note Qy of a hysteretic damper is given approximately by(Pb)A(Pb).

Figure 3.18: Force due to the lead, F(b) - F(r), as a function of the cross-sectionalarea of the lead insert. (Robinson, 1982.)

Figure 3.19: (a) Force-displacement hysteresis loops for a lead rubber bearing used in the William ClaytonBuilding, at 45 and 110mm strokes, with a vertical force of 3.15MN at 0.8Hz. (FromRobinson, 1982.).

(b) Force-displacement curves for the bearings used in the Wellington Press Building (Chapter8). (From Robinson & Cousins, 1987 & 1988).

Figure 3.19 contains the force-displacement hysteresis loops for two recent examples, namelythe lead rubber bearings for the seismic isolation for (a) the William Clayton Building and (b) theWellington Press Building. For both of these examples the initial stiffness K b1~10K(r) while thepost-yield stiffness is approximately K(r).

XK(r) + A(Pb) (Pb)=F (3.17)



79

Rate Dependence

For a number of applications it is necessary to know the behaviour of the lead rubber bearingunder creep conditions. For example, if a bridge deck is mounted on the bearings then, duringthe normal 24 hour cycle of temperature, the bearings will have to accommodate several

displacements of ~+3 mm without producing large forces. In order to determine the effect ofcreep rates of ~1 mm/h, the second lead rubber bearing made, (that is, one with dimensions of356 x 356 x 140 mm with a 100 mm lead plug) was mounted in the back-to-back reaction framein the Instron testing machine. The first result was obtained at 6 mm/h, with the force due to thelead alone reaching a maximum after 2.5 h before decreasing slowly.

After 6 hours the displacement was held constant and the force due to the lead decreased toone half in about one hour, and continued to fall with time, giving a relaxation time of 1 to 2 h.Another creep test was carried out at 1 mm/h for six hours, when the direction was reversed,giving the hysteresis shown in Figure 3.20. For completeness the force F(R), due to the rubber, isincluded with its +20 per cent error bar. The shear stress in the lead plug reached a maximum of3.2 MPa, which is ~30 per cent of the stress of 10.5 MPa for the dynamic tests. The force due tothe rubber is great enough to drive the deformed lead, and the structure, back to its originalposition.

Figure 3.20: Force due to lead during creep of 356 mm2 bearing with 100 mm lead plug,at vertical force of 400 kN. Open points are 6 mm/h, filled points are 1 mm/h

and dashed line is F(r). (Robinson, 1982.)

Because of the large errors caused by F(r), it was not possible to determine accurately therate-dependence of the lead in the lead rubber bearing. To overcome this problem three leadhysteretic dampers, which had been developed earlier to operate in shear without a rubberbearing (Robinson (1982), were tested at various strain rates. These dampers consisted of leadcylinders whose diameters varied parabolically as shown in the insert to Figure 3.21, and whoseends were soldered to two brass plates. The parabolic variation was designed to minimise theeffect of bending stresses, which occur away from the neutral axis of the lead, during theapplication of shearing displacements: in fact, the shear stress near the parabolic surface of thelead remained constant to a first approximation. The rate-dependence of these dampers, withtheir shear stress normalised to that at = 1 s-1, is shown in Figure .21, by the circled points. Thisfigure also denotes, with the symbol (x), the values obtained for the second lead rubber bearingmade, at rates of =10-5 and 3 x 10-1 s-1. These results have a rate-dependence

where below = 3 x 10-4 s-1, b = 0.15 and above, b = 0.035. For the lead extrusion damper(Figure 3.10) it was found that, for the two regions, b = 0.14 and 0.03. For slow creep otherauthors conclude that b = 0.13 (Birchenall (1959), Pugh (1970)). When the experimental errors

are taken into account, all of these results are in reasonable agreement.

b

a=(Pb) (3.18)



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Figure 3.21: Rate dependence of lead cylinders of parabolic section (see insert) in shear,as indicated by the circled points. The crosses indicate the rate dependence of the lead

plug in a lead rubber bearing. (Robinson, 1982.)

These results indicate that the lead rubber bearing has little rate-dependence at strain rates of3 x 10-4 s-1 to 10 s-1, which includes typical earthquake frequencies of 10-1 to 1 s-1. For this range ofstrain rates, an increase in rate by a factor of ten causes an increase in force of only 8 per cent.Below strain rates of 3 x 10-4 s-1, the dependence of the shear stress on creep rate is greater, witha 40 per cent change in force for each decade change in rate. However, this means that atcreep displacements of ~1 mm/h for a typical bearing 100 mm high (that is, at ~ 3 x 10-6 s-1), theshear stress has dropped to 35 per cent of its value at typical earthquake rates, ~ 1 s-1.

Fatigue and Temperature

The lead rubber bearing can be expected to survive a large number of earthquakes, each withan energy input corresponding to 3 to 5 strokes of +100 mm. For example, the results for a series

of dynamic tests on the 650 mm diameter bearing with a 140 mm diameter lead plug are shownin Figure 3.22. The symbols F(a) and F(b) correspond to points such as a and b on Figure 3.17.F(a) and F(b) decreased by 10 and 25 per cent over the first five cycles but recovered some ofthis decrease in the five-minute breaks between tests.

Figure 3.22: Dynamic tests on lead rubber bearing over seven simulated earthquakes. (Robinson, 1982.)



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Bilinear Parameters for Small Earthquakes

When the isolator motions arise from small earthquakes, with displacement spectra reduced bya factor of 2 or more, the bilinear loop parameters change in the same general way as thebilinear loop parameters for an isolator consisting of laminated rubber bearings mounted beside

steel-beam dampers, with the same beneficial results. Reduced displacements causeconsiderable reductions in Qy and considerable increases in K b2, as shown in Figure 3.24. As anet result, the effective (secant) period, and sometimes the hysteretic damping, falls moreslowly, with decreasing earthquake severity, than they would with a fixed-parameter bilinearloop.

Figure 3.24: (a) Difference in bilinearloop parameters corresponding to small and large displacements.

(b) Load-displacement loops for various strokes of lead rubber bearing used inPress Hall, Petone (see Chapter 6). (Robinson & C ousins, 1987, 1988.)

Summary of Lead Rubber Bearings

For strain rates of ~1 s-1, the lead-rubber hysteretic bearing can be treated as a bilinear solid withan initial shear stiffness of ~10 K b(r) and a post-yield shear stiffness of K b(r). The yield force of thelead insert can be readily determined from the yield stress of the lead in the bearing, i.e.y(Pb) ~10.5 MPa. Thus the maximum shear force for a given displacement is the sum of theelastic force of the elastomeric bearing and the plastic force required to deform the lead. Theactual post-yield stiffness is likely to vary by up to + 40 per cent from K b(r) but will probably bewithin + 20 percent of this value. The initial elastic stiffness has only been estimated from theexperimental results and may in fact be in the range of 9 K b(r) to 16 K b(r). The prediction for themaximum force, F(b), is more accurate and has instead an uncertainty of + 20 percent which isthe same as expected for the uncertainty in the shear stiffness of manufactured elastomericbearings. The actual area of the hysteresis loop formed by this bilinear model is approximately

20 per cent greater than the area of the measured hysteresis loop. The lead-rubber hysteretic bearing provides an economic solution to the problem of seismicallyisolating structures, in that the one unit incorporates the three functions of vertical support andhorizontal flexibility (via the rubber) and hysteretic damping (by the plastic deformation of thelead). Further discussion on lead rubber bearings is contained in Robinson & Cousins (1987,1988); Skinner et al (1980); Skinner, Robinson & McVerry (1991); Cousins, Robinson & McVerry(1991).



83

3.7 FURTHER ISOLATOR COMPONENTS AND SYSTEMS

A wide range of further isolator components, to provide flexibility and/or damping, have beenused or proposed. Some of these isolator components are based on material properties,

particularly those which provide flexibility and hysteretic damping forces, as in the cases of theisolator components described above.

A second class of isolator components depends on sliding supports and on frictional dampingforces. A third class of isolator components depends on geometrical fac tors such as rockingwith uplift, or rolling surfaces, or pendulum action under gravity forces. Representative examplesfrom each class of isolator component are described briefly below.

3.7.1 Isolator Damping Proportional to Velocity

In Chapter 2 it was found that linear isolators, with damping forces proportional to the velocity ofisolator deformation, greatly attenuated the higher-mode seismic responses and floor spectra ofthe isolated structures. In contrast, it was found that high isolator damping, which departsseverely from linear velocity dependence, gives smaller reductions in the seismic responses ofhigher modes. When small higher-mode seismic responses, or low floor spectra, are a designrequirement then the benefits of high isolator damping can still be obtained by increasing thevelocity-dependent damping.

Bearings with High-Loss Rubber

Velocity-dependent damping may be obtained using high-loss elastomers, or pitch-likesubstances, or hydraulic dampers with viscous liquids.

The rubber bearings, which may be required for horizontally flexible supports, may use speciallyformulated and manufactured rubbers which give an effective isolator damping of about 15%of critical. These high damping rubbers are both very amplitude dependent and historydependent, for example, at a strain amplitude of 50% in the rubber during the first cycle ofoperation, the 'unscragged' state, the modulus is approximately 1.5 times that for the third andsubsequent cycles, when 'scragged'. The original unscragged properties return in a few hours to days. The reduction of modulusbetween the unscragged and scragged state decreases as the strain amplitude increases.

Future improvements in the energy absorption of rubbers are to be expected, but at presentproblems arise with creep under sustained loads, with non-linearity and temperaturedependence of the damping forces, and with change of shape of the bearing at large

displacements, giving rise to amplitude-dependent damping.

Hydraulic Dampers

It should be possible to develop effective velocity dampers, of adequate linearity, for a widerange of seismic isolator applications by utilising the properties of existing high-viscosity siliconeliquids.

In principle, the development of a velocity-dependent silicone-based hydraulic damper isstraightforward. A double-ac ting piston might be used to drive the silicone liquid cyclicallythrough a parallel set of tubular orifices, designed to give high fluid shears and hence therequired veloc ity damping forces. By using a sufficient working volume of silicone fluid to limitthe temperature rise to 40oC, during a design-level earthquake, the corresponding reduction indamper force is limited to about 25%. For comparison the thermal capacity, per unit volume, forsilicone fluid is comparable to that for lead, or about 40% of that for iron.



84

The development of practical linear hydraulic dampers is complicated by a number of factorsincluding the increase in silicone liquid volume with temperature, about 10% for a 100oCtemperature rise, and also the tendency of the silicone liquid to cavitate under negativepressure.

3.7.2 PTFE Sliding Bearings

Non Lubricated PTFE Bearings

The weight of a structure may be supported on horizontally moving bearings consisting of blocksof PTFE (polytetrafluoroethylene) sliding on plane horizontal stainless-steel plates. Starting about1965, such bearings were used to provide low-friction supports for parts of many bridgesuperstructures. The coefficient of friction of a PTFE bridge bearing is typically of the order of0.03, when operating at the very low rates arising from temperature cycling of the bridgesuperstructure. However, it is found that the coefficient of friction is very much higher, and is

dependent on pressure and sliding velocity, when the operating velocity is typical of that whichoccurs in an isolator during a design-level earthquake, and when the operating pressure istypical of that adopted for PTFE bridge bearings (Tyler, 1977). For operating conditions typical ofseismic isolator actions during design-level earthquakes, the frictional coefficients ranged fromabout 0.10 to 0.15 or more.

Consider a set of the above PTFE bearings used as a seismic isolator. The first isolator period Tb1 arises from foundation flexibility only, and is typically very short. The second isolator period Tb2 tends to infinity and therefore provides no centring force to resist displacement drift. The yieldratio Qy/W is given by the bearing coefficient of friction and is therefore rather large andvariable. The approximately-rectangular force-displacement loop gives very high hystereticdamping. However, absence of a centring force may result in large displacement drift if seismicinertia forces are substantially greater than the bearing frictional forces. Also high initial stiffnessleads energy into higher modes, providing strong floor spectra of high frequencies.

An isolator with a wider range of applications is obtained if part of the weight of the structurerests on PTFE bearings, while the remainder of the weight rests on rubber bearings. The reducedsliding weight reduces the yield ratio Qy/W, while the rubber bearings can be used to give anappropriate value for the centring force, as indicated by the second isolator period Tb2, whichshould usually be in the range between 2.0 and 4.0 seconds.

Problems arising from a very short first period Tb1 may be removed by mounting the PTFE bearingson rubber bearings, as described below.

Lubricated PTFE Bearings

Lubricated PTFE bearings have quite small coefficients of friction, usually less than 0.02 (Tyler,1977), for the pressures and velocities which they would encounter as seismic isolator mounts.When an isolator has low-friction load-support bearings, then components to provide centringand damping forces need not support weights. For example, approximately linear centring anddamping forces could be provided by blocks of high-loss elastomer, for which creep is not aproblem without sustained loads. If higher linear damping is required, hydraulic dampers couldbe added. However, since almost every isolator application is tolerant of at least a moderatedegree of non-linearity, it should usually be possible to provide some of the centring anddamping forces by non-linear components, such as weight-supporting lead rubber bearings.

For high reliability, lubricated PTFE bearings should be serviced regularly. However, for

high-technology applications, for example nuclear power plant isolation, maintenance shouldnot present a serious problem.



85

3.7.3 PTFE Bearings Mounted on Rubber Bearings

In Chapter 2 it was found that a bilinear isolator with a short first period Tb1 results in relativelylarge higher-mode seismic accelerations and floor spectra. In Chapter 4 it is shown that thesehigher-mode seismic responses may be substantially reduced by increasing the first bilinear

period Tb1 to exceed the first period of the unisolated structure T1(U).

A compound isolator component developed in France (Plichon, et al, 1980) consisted of asliding bearing mounted on top of a rubber bearing. Initially the bearings were made oflead-bronze blocks sliding on stainless steel, while later designs replaced the lead-bronze blocksby PTFE blocks.

The flexibility of the laminated rubber components of the compound bearing can be chosen togive a first bilinear period Tb1 which exceeds T1(U), the first structural period. As in the previoussection, the second bilinear period Tb2 may be limited to a value which prevents excessivedisplacement drift by supporting part of the structural weight directly on rubber bearings. Thisalso reduces the value of Qy/W for the isolator.

3.7.4 Tall Slender Structures Rocking with Uplift

The seismic design loads and deformations of tall slender structures are normally associated withhigh overturning moments at the base level. If the narrow base of such a structure is allowed torock with uplift, then the base moment is limited to that required to produce uplift against therestraining forces due to gravity. This base moment limitation will usually reduce substantially theseismic loads and deformations throughout the structure.

The feet of a stepping structure are supported by pads which allow some rotation of the weight-supporting feet, while the overall structure rocks with uplift of other feet. Laminated rubber orlead slabs have been used to allow this rotation. These feet pads also accommodate small

irregularities and slope mismatches between the feet and the supporting foundations. Thestepping feet move in vertical guides which prevent 'walking', which would give horizontal orrotational displacements of the base of the structure.

Rocking with stepping is particularly effective in reducing the seismic loads and deformations oftop-heavy slender structures such as tower-supported water tanks (where the tanks should beslender or contain baffles to prevent large long-period sloshing forces during majorearthquakes). Another top-heavy structure is a bridge with tall slender piers. The piers may bepermitted to rock in a direction transverse to the axis of the superstructure, providing thesuperstructure can accommodate the resulting deformations.

The seismic responses of a slender rocking structure are related in some ways to the responses ofa structure with an approximately rigid-plastic horizontally-deforming isolator, but there are alsomajor differences.

For mode-1 seismic responses a rigid rocking structure may be assumed, with forces anddisplacements expressed as horizontal actions at the height of the centre of gravity. The cyclicforce-displacement curve is then almost vertical for all forces below the uplift force (whichcorresponds to Qy with bilinear hysteresis) and almost horizontal for all displacements duringuplift. The force-displacement curve is essentially bilinear elastic. An effective period may bederived using the secant stiffness for maximum seismic displacement. The effective damping willarise from any energy losses during structural and foundation deformations together with thecontribution of any added dampers. The effective period and damping may then be used torelate the maximum seismic displacement to the earthquake displacement spectra, as in thecase of any other non-linear isolator.



86

Since stepping isolation is a very non-linear constraint, and since the equivalent first isolatorperiod Tb, is substantially less than the first period of the unisolated structure, the maximumseismic acceleration responses of the higher isolated modes are expected to be relatively large.With stepping the higher mode periods and shapes may be derived by assuming a zero basemoment, instead of the zero base shear force assumed when the isolator acts horizontally.

With rocking isolation there is always a substantial centring force, which is given by the upliftforce. This centring force ensures that there is little drift displacement to add to the spectraldisplacement. The substantial centring force, and the high first stiffness, of the rocking isolatoralso ensure that there is very little residual displacement after an earthquake, even whensubstantial hysteretic dampers have been introduced.

An early application of rocking with uplift, to increase the seismic resistance of a tall slenderstructure, is contained in a design study by Savage (1939). The 105 meter piers of the proposedPit River road-rail bridge were designed with their bases free to rock with uplift under severealong-stream seismic loads. A New Zealand railway bridge at Mangaweka, over the RangitikeiRiver, with 69 meter piers, was designed and built with the pier feet free to uplift during severe

along-stream seismic loads (see Chapter 8). A tall rocking chimney structure, built atChristchurch New Zealand, is described by Sharpe & Skinner (1983).

3.7.5 Further Components for Isolator Flexibility

Tall Columns and Free Piles

Horizontal flexibility can be provided by tall first-storey columns or by free-standing piles. Suchflexible columns must have adequate length to avoid Euler instability under combined gravityearthquake loads, while providing adequate horizontal flexibility. With tall columns, the endmoments may be severe despite relatively low horizontal shears.

With deep free-standing piles it is usually convenient to provide dampers and stops or buffers atthe pile tops since it is usually practical to anchor them at this level. This approach has beenused in Union House, Auckland, which uses steel cantilever dampers, and the Wellington CentralPolice Station, which uses lead-extrusion dampers (see Chapter 8). If tall columns are used toisolate a tower block it would be possible to anchor dampers to a surrounding high stiffness high-strength mezzanine structure.

In both the above cases where isolation was provided by tall free-standing piles, the tall pileswere required to support the structure on a high-strength soil which underlay a low-strength soillayer. The tall piles were made free-standing by surrounding them with clearance tubes.Basement boxes, supported on shorter piles and embedded in the surface layer, were used toprovide anchors for the hysteretic dampers and the buffers.

Hanging Links and Cables

It is possible to provide horizontal flexibility by supporting a structure with hanging hinged links orwith hanging flexible cables (Newmark & Rosenblueth, 1971). Effective pendulum lengths of 1.0and 2.25 meters would give isolator periods of 2.0 and 3.0 seconds respectively. The necessaryoverlap of the supports and the structure can certainly be provided but in most cases this wouldbe somewhat inconvenient and probably expensive, particularly for the longer links required forthe longer isolator periods.

When isolation is required for a relatively small item within a structure it would sometimes beappropriate to suspend it from anchors at a higher structural level.



88

Omni Directional Buffers using Tapered Steel Beams

Steel-beam buffers can be made omni directional in the same way as rubber buffers can. Theymay be designed to yield at a level which limits the base shear on the structure to anacceptable level. They may be of lower cost but more costly to install than equivalent-

capacity rubber buffers. Operationally they are superior because of their yield-limited resistanceforce and because of the capacity to absorb most of the energy put into them.

Buffer Anchors

For many structures it will be difficult to provide buffer anchors of the desired strength. If thebuffer anchors deform in a controlled way with an appropriate level of resistance, they maythemselves function as buffers and greatly reduce the demands on a buffer device or evenremove the need for added buffers.

The basement box which provides stops for base displacement of the New Zealand CentralPolice Station has a level of soil and of pile resistance which allows it to provide considerable

buffer action. Because the basement box is comparable in mass to a building storey, it isnecessary to have a base-to-basement deformable interaction which has lower stiffness thanthe interstorey members, to attenuate impact shear pulses. Such a deformable interaction isprovided by lead collars, around the columns near their tops, which may impact basementstops during extreme earthquakes.

3.7.7 Active Isolation Systems

Active Control of Isolator Parameters

When it is necessary to control the floor accelerations accurately during frequent moderateearthquakes, it should be possible to exercise a large measure of control over isolatorparameters by including a set of double-acting hydraulic dampers with their coefficient ofvelocity damping force under the direct control of electrical signals, which are a function of themeasured floor accelerations and base displacements. In the event of control system failure orfor large earthquakes, the isolator should revert to an essentially passive system, effective forsevere earthquakes.

It should be possible to check on the performance of this system by applying an artificial flooracceleration signal or by monitoring the response of the isolator by measuring its effect onground micro tremors.

Active Forces on Isolated Structures

Where a very low level of vibration is important it would be possible, in principle, to use an active

system to ensure a very low level of building horizontal vibrations. For example, the buildingcould be supported on lubricated PTFE mounts and the ac tive drive would only have to providethe low frictional losses in the mounts. In prac tice some additional power would be necessary toprovide some centring action. The displacements required to accommodate such an isolatorwould be large during a major earthquake. The system would be most practical if it was onlyrequired to provide a high degree of isolation during frequent moderate earthquakes.

To resist wind loads it would be necessary to provide some clamping system whenever windloads exceed the force capacity of the isolator actuators. Alternatively the structure could beenclosed by wind shields, in special cases.

A more practical system for many applications is likely to be a linear isolator which provides

sufficient attenuation of the first mode(s) and an active system to further attenuate some of thesmall higher-mode responses, if necessary.



89

CHAPTER 4: ENGINEERING PROPERTIES OF ISOLATORS

4.1 SOURCES OF INFORMATION

The plain rubber, high damping rubber and lead rubber isolators are all based on

elastomeric bearings. The following sec tions describe the properties of these types of

bearing manufactured from natural rubber with industry standard compounding. High

damping rubber bearings are manufactured using proprietary compounds and vary from

manufacturer to manufacturer. Some examples are provided of high damping rubber but if

you wish to use this type of device you should contact manufacturers for stiffness and

damping data.

Examples of properties of devices in this chapter are from specific manufacturers and mayvary with manufac turer. The properties show general characteristics but manufac turers

literature should be consulted for specific values.

4.2 ENGINEERING PROPERTIES OF LEAD RUBBER BEARINGS

Lead rubber bearings under lateral displacements produce a hysteresis curve which is acombination of the linear-elastic force-displacement relationship of the rubber bearing plus

the elastic-perfectly plastic hysteresis of a lead core in shear. The lead core does not

produce a perfectly rectangular hysteresis as there is a “shear lag” depending on the

effec tiveness of the confinement provided by the internal steel shims. This is discussed further

in the chapter on design procedures.

Figure 4.1: Lead Rubber Bearing Hysteresis

The resultant hysteresis curve, as shown in Figure 4.1, has a curved transition on unloading

and reloading. For design and ana lysis an equivalent bi-linear approximation is defined such

that the area under the hysteresis curve, which defines the damping, is equal to the

measured area. It is possible to model the bearing with a continuously softening element but

this is not often used.

SHEAR DISPLACEMENT

S H E A R F O R C E

Actual Hysteresis

Bi-Linear Approximation



91

Most lead rubber bearings use a medium- to low-modulus natural rubber which is not

compounded to provide significant viscous damping by hysteresis of the rubber material. All

damping is assumed to be provided by the lead cores.

4.2.3 Cyclic Change in Properties

For lead rubber bearings the effective stiffness and damping are a function of both the

vertical load and the number of cycles. There is a more pronounced effect on these

quantities during the first few cycles compared to elastomeric bearings without lead cores.

Test results from dynamic tests with varying load levels and shear strains to quantify these

effects. Figures 4.3 and 4.4 show the variation in hysteresis and loop area versus cycle

number for 380 mm (15") diameter lead rubber bearings. The test results plotted are for 100%

shear strain and a vertical load of 950 KN (211 kips), corresponding to a stress of 9 MPa (1.3

ksi).

Figure 4.3: Variation In Hysteresis Loop Area

Figure 4.4: Variation in Effective Stiffness

At slow loading rates there is a relatively small drop in loop area, A h, and effective stiffness,

K eff , with increasing cycles. For faster loading rates, the values at the first cycles are higher

but there is a larger drop off. The net effect is that the average values over all cycles are

similar for the different loading rates.

0

20

40

60

80

100

120

140

160

180

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

CYCLE NUMBER

H Y S T E R E S I S L O O P A R E A ( k i p - i n )

Test Frequency 0.01 hz



0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

CYCLE NUMBER

E F F E C T I V E S

T I F F N E S S ( k i p / i n c h )

Test Frequency 0.01 hz Test Frequency 0.10 hz Test Frequency 0.40 hz



92

The design procedures and prototype test requirements are such that the design hysteresis

loop area and effective stiffness are required to be matched by the average of three cycle

tests at the design displacement. This test is considered to best match the likely earthquake

demand on the bearings. The maximum reduction in loop area will be about 1% per cycle

for the first 10 cycles but then the hysteresis loop stabilizes. The actual maximum reduction in

loop area is a function of the dimensions of the isolator and lead core and the properties of

the elastomer.

There appears to be a size dependence on the variation in effective stiffness and hysteresis

loop area with increasing number of cycles when bearings are tested at the actual

expected frequency of response. For practical reasons, there are few test results of large

isolation bearings which have been subjected to multiple cycles of the design displacement

at the actual expected frequency of loading. One example is tests of large isolators with

very large lead cores, approaching the maximum size likely to be used for LRBs. As such, the

measured changes with increasing cycles are probably the extreme which might be

experienced with this type of isolator.

Diameter(mm)

Height(mm)

CoreSize

(mm)

AppliedDisplacement

(mm)

ShearStrain

Type 1 820 332 168 254 139%

Type 2 870 332 184 305 167%

Type 2M 1020 332 188 305 167%

Type 3 1020 349 241 280 163%

Table 4.1: Isolator Dimensions

Figure 4.5 plots the ratio of hysteresis loop area (EDC = Energy Dissipated per Cycle)measured from each cycle to the requirement minimum loop area in the specification.

Values are plotted for each of 15 cycles, which were applied at a frequency of 0.5 hz

(corresponding to the isolation period of 2 seconds).

40%

60%

80%

100%

120%

140%

160%

180%

200%

220%

240%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

CYCLE

E D C /

E D C M i n i m u m

Type 1 0 Deg

Type 2 0 Deg

Type 2M 0 Deg

Type 3 0 Deg

Figure 4.3: Cyclic Change in Loop Area



93

Figure 4.5 shows that the initial loop area is well above the specified minimum and remains

higher for between 6 and 8 cycles. By the end of the 15 cycles the EDC has reduced to

about 60% of the specified value. Figure 4.5 plots the ratios from the 1st and 15th cycles and

the mean ratios over all cycles. This shows that the mean value is quite c lose to the specified

minimum.

The reduction in loop area is apparently caused by heat build up in the lead core and is a

transient effect. This is demonstrated by the results in Figure 4.6 as each isolator was tested

twice, once at zero degrees and the bearing was then rotated by 90 degrees and the test

repeated. As the figure shows, the initial EDC for the Cycle 1 of the second test was similar tothe 1st cycle of the preceding test, not the 15th cycle. This indicates that most of the original

properties were recovered and it is likely than total recovery would have occurred with a

longer interval between tests.

0%

50%

100%

150%

200%

250%

T y p e 1 0 D

e g

T y p e 1 9 0 D

e g

T y p e 2 0 D

e g

T y p e 2 9 0 D

e g

T y p e 2 M 0 D

e g

T y p e 2 M 9 0 D

e g

T y p e 3 0 D

e g

T y p e 3 9 0 D

e g

T E S T E D C / E D C M i n

Cycle 1

Cycle 15

Average

Figure 4.4: Mean C yclic Change in Loop Area

Actual earthquakes would rarely impose anything like 15 cycles at the design displacements.Most time history analyses show from 1 to 3 cycles at peak displacements and then a larger

number of cycles at smaller displacements. If there are near fault effects there is often only a

single cycle at the peak displacement. Figure 4.5 shows that the LRBs will provide at least the

design level of damping for this number of cycles.

4.2.4 Age Change in Properties

The rubber tests on compounds used for LRBs show an increase in hardness by up to 3 Shore

A after heat aging. This increase in hardness is equivalent to an increase in shear modulus of

10%. The increase in shear modulus would have a lesser effec t on the total bearing stiffness

as the lead core yield force is stable with time.

In service, the change in hardness for bearings would be limited to the outside surface since

the cover layer prevents diffusion of degradants such as oxygen into the interior. Therefore,

average effects would be less than the 10% value. For unprotected natural rubber in serviceover 100 years (for example, Rail Viaduct in Melbourne, Australia) the deterioration was

limited to approximately 1.5 mm (0.06 inches) from the exposed surface.



94

There is not much information on direct measurement of the change in stiffness properties

with time of loaded elastomeric bearings. One example was machine mountings

manufactured in 1953 and in service continuously in England. In 1983, after 30 years, two

test bearings which had been stored with the machine were tested again and were found to

have increased in stiffness by 15.5% and 4.5%.

A natural rubber bearing removed from a freeway bridge in Kent showed an increase inshear stiffness of about 10% after 20 years service.

Since the time that the bearings above were manufactured, considerable advances have

been made in environmental protection of the bearings. It is predicted that changes in

stiffness of the elastomer will be no more than 10% over the design life of the isolators. The

net effect on isolator effective stiffness at seismic displacements would be about one-half this

value. Damping would not be effected by aging of LRBs as the rubber damping is negligible

compared to that provided by the lead core.

4.2.5 Design Compressive Stress

The design procedures used to calculate vertical load capac ity are based on a rated load(limiting strain) approach, as incorporated in codes such as AASHTO and BS5400. The

effective allowable compressive stress is a func tion of (1) the ultimate elongation of the

rubber (2) the safety factor applied to the ultimate elongation (3) the bearing plan size (4)the bearing shape factor and (5) the applied shear strain.

For long term gravity loads (displacement = 0) a fac tor of 1/3 is applied to the elongation at

break. For short term seismic loads (displacement > 0) a factor of 0.75 is applied to the

elongation for DBE loads and 1.0 for MCE loads.

Additional rules are used based on experience to ensure that the bearings will perform

satisfac torily. For example, it is generally required that the effective bearing area (area ofoverlap between top and bottom plates) be at least 20% of the gross area at maximum

displacement.

The result of this procedure is that the allowable compressive stress is a function of the

bearing size and the applied displacement.

Ultimate compressive stresses are calculated by the same procedure as for allowable stresses

except that a factor of 1.0 is applied to the elongation at break to obtain the load c apac ity.

4.2.6 Design Tension Stress

Elastomeric based bearings such as LRBs and HDR bearings have in the past been designed

such that tension does not occur. This is because there is little design information for rubberbearings under this type of load. As successive code revisions have increased seismic loads,

it has provided very difficult to complete isolation designs such that no tension occurs andsome designs do permit tension on the isolators.

Provided high quality control is exercised during manufac ture, elastomeric bearings can resista high tension without failure. Bearings (without lead cores) have been tested to a tensile

strain of 150% at failure, as shown in Figure 4.7. The tension stiffness is approximately elastic

to a stress of 4 MPa at a strain of approximately 15%. The stiffness then reduces as cavitation

occurs and remains at a low stiffness to a strain of 150%.



95

The rubber used for the bearing in Figure 4.7 has a shear modulus G = 1.0 MPa. The isolator

design procedures permit an ultimate compression stress of 3G, which would permit a tensile

stress of 3 MPa (30 kgf/cm2) for this bearing. As shown in Figure 4.7, this level of stress provides

an adequate factor of safety before cavitation oc curs.

Figure 4.5: Tension Test on Elastomeric Bearing

The tests above were for plain bearings under pure tension. Lead rubber bearings for the

have also been tested under combined shear and tension at close to the design limit (2.4G

versus 3G limit) to a shear strain of 225% (Table 8-2). The bearings were undamaged under

these conditions. The maximum uplift displacement was approximately 12 mm ( ½”).

Type A Type B

Diameter (mm)

Tension Force (KN)

Tension Stress (MPa)

Displacement (mm)

Shear Strain

920

549

0.89 (2.4G)

686

225%

970

608

0.88 (2.4G)

686

225%

Table 4.2: Combined Shear and Tension Tests

4.2.7 Maximum Shear Strain

As discussed above for allowable vertical compressive stresses, the load capacity is

calculated based on a total strain formulation where the strain due to compression and the

applied shear strain are combined and required to be less than a specified fraction of the

elongation at break.



96

The converse applies for ultimate shear strain, where the maximum shear strain that can be

applied depends on the concurrent vertical strain. Although the formulas produce a

maximum shear strain based on concurrent vertical loads, empirical limits are also applied to

the shear strain based on experimental evidence. Generally, the limiting shear strain is taken

as 150% for DBE loads and 250% for MC E loads, unless the design formulas provide a lower

limit.

Testing of lead rubber bearings at high shear strain levels have shown that failure in lead

rubber bearings occurs between 300% and 350% shear strain. The bearings without lead

cores can survive imposed shear strains of 400%.

Table 4.3 summarizes test results for lead rubber bearings (LRB), high damping rubber

bearings (HDR) and LRBs without the lead core (R).

BEARING Type Diam.D0

(mm)

VertStress(MPa)

Max.Disp(mm)

ShearStrain

Effect.Area

TotalStrain

HITEC 150 kip

HITEC 500 kip

HITEC 750 kip

LRB

LRB

LRB

450

620

620

4.7

8.0

12.0

335

434

381

320%

339%

190%

0.11

0.16

0.24

925%

795%

614%

(1)

(1)

(2)

PEL HDR 450 8.8 305 340% 0.22 762% (2)

J QT Tension J QT Shear/Tens

J QT Shear/Comp.

RR

RR

R

R

R

350350

500500

500

500

500

-5.5-2.7

2.57.5

10.0

15.0

20.0

84140

250250

400

250

250

155%250%

250%250%

400%

250%

250%

Vert0.61

0.400.40

0.11

0.40

0.40

Strain363%

282%347%

854%

444%

509%

(3)(4)

(5)

Table 4.3: High Shear Test Results

Notes to Table 4.1:

1. The 150 kip and 500 kip HITEC specimens were tested to failure.

2. The 500 kip HITEC bearing was cycled to 15” displacement but the equipmentwas not sufficient to perform the failure test. The 18” bearing in the PEL test

was cycled to 340% strain without failure.

3. The J apanese Tension test was to failure under pure tension at an ultimate

tensile strain of 155%.

4. The J apanese combined shear/tension test was for 5 cycles at 150% and 5

cycles at 250% shear strain. Failure did not occur.

5. Failure did not occur in any of the J apanese combined shear/compression

tests

6. LRB indicates Lead Rubber Bearing, HDR indicates high damping rubber

bearings, R indicates LRB without lead core.



97

4.2.8 Bond Strength

The bond strength defines the adhesion between the rubber layers and the internal steel

shims. Spec ifications typically require that the adhesive strength between the rubber andsteel plates be at least 40 lb/inch when measured in the 90 peel test specified by ASTM

D429, Method B. Failure is required to be 100% rubber tear. All compounds used for LRBsshould meet this requirement.

4.2.9 Vertical Deflections

The initial vertical deflections under gravity loads are calculated from standard design

procedures for elastomeric bearings. For bearings with a large shape fac tor the effects of

bulk modulus are important and are included in the calculation of the vertical stiffness on

which deflection calculations are based.

Elastomeric bearings are stiff under vertical loads and typical deflections under dead plus

live load are usually of the order of 1 mm to 3 mm (0.04 to 0.10 inches).

Long Term Vertical Deflection

Creep is defined as the increase in deformation with time under a constant force and so is

the difference between short term and long term deflection. In rubber, creep consists of

both physical creep (due to molecular chain slippage) and chemical creep (due to

molecular chain breakage). For structural bearings the physical deformation is dominant.

Chemical effects, for example oxidation, are minimal since the bulk of the bearing prevents

easy diffusion of chemicals into the interior. Therefore, chemical effects can be ignored.

Natural rubber generally offers the greatest resistance to creep compared to all other

rubbers. The actual values depend on the type and amount of filler as well as thevulcanization system used.

Creep usually does not exceed more than 20% of the initial deformation in the first few weeksunder load and at most a further 10% increase in deformation after a period of many years.

The maximum long term deflections for design purposes are conservatively taken to be 1.5times the short term values.

A detailed case study has been made of a set of bearings over a 15 year period. Thebuilding, Albany Court in London, was supported on 13 bearings of capacity from 540 KN to

1800 KN (120 kips to 400 kips). Creep was less than 20% of the original deflection after 15

years.

Vertical Deflection Under Lateral Load

Under lateral loads there will be some additional vertical deflections as the bearing displaceslaterally. Generally, this deformation is relatively small. Figure 4.8 is an example of a

combined compression shear test in which vertical deformations were measured.



98

The bearing is displaced to a shear displacement of 508 mm (20”) under a vertical load of

2500 KN (550 kips). The initial vertical deflection when the load is applied is 2.5 mm (0.1”)

which increases to a maximum of approximately 4.6 mm (0.18”) at the 508 mm lateral

displacement. The most severe total vertical deflec tion measured was 12.4 mm (0.49”) at a

lateral displacement of 686 mm (27”).

Based on these results, allowance in design should be made for about 15 mm (0.6”) vertical

downward movement at maximum displacements.

-30.00 -20.00 -10.00 0.00 10.00 20.00 30.00

inch

Displacement

-150

-100

-50

0

50

100

150

k i p

F o r c e

Act ual

Theoretical

SHEAR FORCE v s DISPLACEMENT (per Bearing)

A2h10

-30.00 -20.00 -10.00 0.00 10.00 20.00 30.00

inch

Shear Displacement

490

500

510

520

530

540

550

560

570

k i p

A x i a l L o a d

-0.200

-0.150

-0.100

-0.050

0.000

0.050

i n c h

D i s p l a c e m e n t

Load

Displacement

COMPRESSION LO AD an d DISPLACEMENT A2h10

Figure 4.6: Combined Compression and Shear Test

Wind Displacement

For LRBs, resistance to wind loads is provided by the elastic stiffness of the lead cores. Typical

wind displac ements for projects have ranged from 3.5 mm (0.14”) under a wind load of

0.01W to 11 mm (0.43”) under a load of 0.03W. The cores are usually sized to have a yieldlevel at least 50% higher than the maximum design wind force.

Comparison of Test Properties with Theory

The discussions above, and the design procedures in Chapter 5, are based on theoretical

formulations for LRB design. A summary of test results from nine projects in Table 4.4

compares the theoretical values with what can be achieved in prac tice:



99

Project PlanSizemm

MmDesign

K EFF KN/mm

DesignEDC

KN-mm

TestK EFF

KN/mm

TestEDC

KN-mm

K TEST/K DESIGN

EDCTEST /EDC DESIGN

1. 662 264 1.42 115720 1.41 143425 99% 124%

2. 875 58.2 11.51 640 12.02 741 104% 116%

3.

420

365

11001000

158

104

113125

0.91

0.91

9.5111

220

90

12401790

0.922

1.008

10.33611.406

286

117

17122381

101%

111%

109%104%

130%

130%

138%133%

4.686

686

76

76

6.00

6.85

511

407

5.04

6.00

542

397

84%

88%

106%

98%

5.

686

686686

206

185261

12.69

15.0912.57

127102

136246202082

14.17

14.6512.11

184823

167792266662

112%

97%96%

145%

123%132%

6. 500 169 1.27 81870 1.20 97425 94% 119%

7.

813

864

1016

1016

254

305

305

279

13.28

14.14

19.63

28.76

166764

233058

240030

369989

13.97

14.32

20.44

29.44

201625

303581

346672

554355

105%

101%

104%

102%

121%

130%

144%

150%

8. 1219 406 13.95 500748 13.43 482803 96% 96%

9.914

965

508

508

6.81

7.45

240259

241059

7.16

7.89

294894

307124

105%

106%

123%

127%

Table 4.1: LRB Test Results

Of the 19 isolators tested in Table 4.4, the effective stiffness in 13 was within 5% of the design

value and a further 3 were within 10%. One test produced a stiffness 12% above the design

value and two were respectively –12% and –16% lower than the design values. These last two

were for the same project (Project 4) and were the result of a rubber shear modulus lower

than specified. Spec ifications generally require the stiffness to be within 10% for the total

system and allow 15% variation for individual bearings.

The hysteresis loop area (EDC) exceeded the design value for 17 of the 19 tests. Three tests

were lower than the design value, by a maximum of 4%. Spec ifications generally require theEDC to be at least 90% of the design value, with no upper limit.



100

4.3 ENGINEERING PROPERTIES OF HIGH DAMPING RUBBER ISOLATORS

High damping rubber bearings are made of specially compounded elastomers which

provide equivalent damping in the range of 10% to 20%. The elastomer provides hysteretic

behavior as shown in Figure 4.9.

Figure 4.9: High Damping Rubber Hysteresis

Whereas the properties of lead rubber bearings have remained relatively constant over thelast few years, there have been continuous advances in the development of high damping

rubber compounds. These compounds are specific to manufacturers as they are a function

of both the rubber compounding and the curing process.

Although the technical literature contains much general information on HDR, there is not alot of technical data specific enough to enable a design to be completed. The information

in these sec tions relates to a spec ific compound developed for a building projec t. This can

be used for a preliminary design. In terms of currently available compounds it is not a

particularly high damping formulation, so design using these properties should be easily

attainable. If you wish to use HDR, the best approach is probably to issue performance

based specifications to qualified manufacturers to get final analysis properties.

4.3.1 Shear Modulus

The shear modulus of a HDR bearing is a function of the applied shear strain as shown in

Figure 4.10. At low strain levels, less than 10%, the shear modulus is 1.2 MPa or more. As theshear strain increases the shear modulus reduces, in this case reaching a minimum value of0.4 MPa for shear strains between 150% and 200%. As the shear strain continues to increase

the shear modulus increases again, for this compound increasing by 50% to 0.6 MPa at astrain of 340%.

The initial high shear modulus is a characteristic of HDR and allows the bearings to resistservice loads such as wind without excessive movement.

The increase in shear stiffness as strains increases beyond about 200% can be helpful in

controlling displacements at the MCE level of load, which may cause strains of this

magnitude. However, they have the disadvantage of increasing force levels and

complicating the analysis of an isolated structure on HDR bearings.

SHEAR DISPLACEMENT

S H E A R F O R C E



101

Figure 4.10: HDR Shear Modulus and Damping

4.3.2 Damping

Although the majority of the damping provided by HDR bearings is hysteretic in nature there

is also a viscous component which is frequency dependent. These viscous effects may

increase the total damping by up to 20% and, if quantified, can be used in design.

Viscous damping is difficult to measure across a full range of displacements as the power

requirements increase as the displacements increase for a constant loading frequency. For

this reason, viscous damping effects are usually quantified up to moderate displacement

levels and the results used to develop a formula to extrapolate to higher displacements.

Figure 4.11 shows the equivalent viscous damping for a load frequency of 0.1 hz, a slow

loading rate at which viscous effects can be assumed to be negligible. For strains up to

100%, the tests used to develop these results were also performed at a loading rate of 0.4 hz(period 2.5 seconds), an average frequency at which an isolation system is designed to

operate.

The damping at 0.4 hz was higher than that at 0.1 hz by a fac tor which increased with strain.

At 25% the factor was 1.05 and at 100% the factor was 1.23. The frequency dependency

indicates the presence of viscous (velocity dependent) damping in the elastomer. The

velocity increases proportionately to the frequency and so the high frequency test gives rise

to higher viscous damping forces. The tests at various strain levels are performed at the

same frequenc ies and so the velocity increases with strain. The veloc ities are four times as

high at 100% strain as at 25%. This is why the factor between the 0.4 hz and 0.1 hz damping

increases.

The added viscous damping adds approximately 20% to the total damping for strains of 100%

or greater, for this compound increasing the damping from 8% to 9.6%.

0

2

4

6

8

10

12

14

0 50 100 150 200 250 300 350

Shear Strain %

E q u i v a l e n t V i s c o u s D a m p i n g %

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

S h e a r M o d u l u s M P a

DampingShear Modulus



102

Figure 4.11: Viscous Damping Effects in HDR

4.3.3 Cyclic Change in Properties

The properties of a HDR bearing will change under the first few cycles of loading because of

a process known as “scragging”. When a HDR bearing is subjected to one or more cycles of

large amplitude displacement the molecular structure is changed. This results in more stable

hysteresis curves at strain levels lower to that at which the elastomer was scragged. Partial

recovery of unscragged properties is likely. The extent of this recovery is dependent on the

compound.

Figure 4.12: Cyclic Change in Properties for Scragged HDR

When HDR bearings are specified the specifications should required one to three scragging

cycles at a displacement equal to the maximum test displacement. You should request

information from each manufacturer as to scragging effects on a particular compound to

enable you to dec ide on just how many scragging cycles are needed.

Once a HDR bearing has been scragged the properties are very stable with increasednumber of cycles, as shown in Figure 4.12.

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

0 20 40 60 80 100 120 140 160 180 200

Shear Strain %

E q u i v a l e n t V i s c o u s

D a m p i n g %

0.1 hz Damping

0.4 hz Damping

1.2 x 0.10 hz Damping

Extrapolated Data

VARIATION WITH REPEATED CYCLES STRAIN = 100%

0

0.1

0.2

0.3

0.4

0.5

0.6

1 2 3 4 5 6 7 8 9 10

LOADING CYCLE NUMBER

S H E A R M O D U L U S ( p s i )

0

2

4

6

8

10

12

E Q U I V A L E N T D A M P I N G %

Shear Modulus

Equivalent Damping



103


Although most HDR compounds have a more limited service record than other natural

rubber formulations the same additives to resist environmental degradation are used as for

other elastomers and there is no reason to suspect that they will have a shorter design life.However, as the compounds are so specific to particular manufacturers you should request

data from potential suppliers. The specifications will require the same accelerated (heat)

aging tests as for lead rubber bearings.

4.3.5 Design Compressive Stress

HDR bearings are generally designed using the same formulas as for LRBs and so the

comments in the sec tions on LRBs also apply.

4.3.6 Maximum Shear Strain

The maximum shear strains for LRBs usually have an empirical limit which may restrict theshear strain to a lesser value than permitted by the design formulas. These limits are related

to performance of the lead core and so do not apply to HDR bearings. The maximum shear

strain is based on the limiting strain formulas and may approach 300% for MC E loads,

compared to a 250% limit for LRBs.

The higher shear strain limits for HDR bearings may result in a smaller plan size and lower

profile than a LRB, for a smaller total volume. However, this also depends on the levels of

damping as the displacements may differ between the two systems.

4.3.7 Bond Strength

The bond strength requirements are the same as for LRBs previously.

4.3.8 Vertical Deflections

The vertical stiffness, and so deflections under vertical loads, is governed by the same

formulas as for LRBs and so will provide similar deflections for similar construction although the

specific elastomer properties may cause more differences.

Long Term Vertical Deflections

HDR bearings are cured differently from LRBs and have higher creep displacements. The

compression set (after 22 hours at 158F) may be as high as 50%, compared to less than 20%

for low damping rubber compounds. This may cause an increase in long term deflections

and you should seek advice from the supplier on this design aspect.



104

4.3.9 Wind Displacements

HDR bearings generally rely on the initially high shear modulus to resist wind loads and do not

require a supplemental wind restraint. The wind displacement can be calculated usingcompound-spec ific plots of shear modulus versus shear strain. This may require an iterative

procedure to solve for a particular lateral wind load. There have been no reported instancesof undue wind movements in buildings isolated with HDR bearings.

4.4 ENGINEERING PROPERTIES OF SLIDING TYPE ISOLATORS

Most specifications for sliding bearings require that the sliding surface be a self-lubricating

polytetrafluoroethylene (PTFE) surface sliding across a smooth, hard, non-corrosive matingsurface such as stainless steel.

There are two types of sliding isolators commonly used:

1. Curved slider bearings (the Friction Pendulum System) providing the total

isolation system.

2. Sliding bearings in parallel with other devices, usually with HDR or LRB.

The former application uses proprietary products and the detailed information on the sliding

surfaces, construction etc. will be provided by the supplier. The information supplied should

provide the information described here for other sliding devices.

Most applications which have used sliding bearings to provide part of the isolation system

have been based on “pot” bearings, a commercially available bearing type which has longbeen used for non-seismic bridge bearings. For light loads, such as under stairs, a simpler

sliding bearing can be constructed by bonding the PTFE to an elastomeric layer.

Pot-type bearings have a layer of PTFE bonded to the base of the "pot" sliding on a stainless

steel surface. The "pot" portion of the bearing consists of a steel piston, inside a steel

cylinder, bearing on a confined rubber layer. The pot allows rotations of typically up to at

least 0.20 radians. Figure 4.13 shows a schematic sec tion of the bearing.

Slide Plate

Stainless Steel

Sliding Surface

Recessed PTFE

Cylinder

Pot

Confined

Elastomer

Figure 4.7: Section through Pot Bearings



105

The pot bearing in Figure 4.13 is oriented with the slide plate on top. The bearing can also be

oriented with a reversed orientation and the slide plate at the bottom. The option of the

slide plate on the top has the advantage that debris will not settle on the stainless steel slide

surface but the disadvantage that under lateral displacements the eccentricity will cause

secondary moments in the structure above the isolation plane. With the slide plate on the

bottom the moments due to eccentricity will be induced in the foundation below the isolator

which will often be better able to resist these moments. In this case, either wipers or aprotective skirt may be required to prevent debris settling on the slide plate.

The reason for selecting pot bearings rather than simply PTFE bonded to a steel plate is that in

many locations some rotational capability is required to ensure that during earthquake

displacements the load is evenly distributed to the PTFE surface. This may be achieved by

bonding the PTFE to a layer of rubber or other elastomer. However, the advantage of a pot

bearing is that the elastomer is confined and so will not bulge or extrude under high vertical

pressures. In this condition, the allowable pressure on the rubber is at least equal to that on

the PTFE and so more compact bearings can be used than would otherwise be required.

Methods of protecting the sliding surface should be considered as part of supply. Pot

bearings which have been installed on isolation projects previously have used wipers to c leardebris from the sliding surface before it can damage the PTFE/stainless steel interface.

4.4.1 Dynamic Friction Coefficient

The coefficient of friction of PTFE depends on a number of factors, of which the most

important are the sliding surface, the pressure on the PTFE and the velocity of movement.

Data reported here is that developed for pot bearings based on tests of bearings used for a

building projec t. For this projec t tests showed that the minimum dynamic coefficient for a

veloc ity < 25 mm/sec (1 in/sec ) ranged from 2.5% to 8% depending on pressure. These

results were from a wide range of bearing sizes and pressures. The mean coefficient offriction at low speeds was 5% at pressures less than 13.8 MPa (2 ksi) decreasing to 2% at

pressures exceeding 69 MPa (10 ksi).

The high load capac ity test equipment used for the full scale bearings was not suitable for

high velocity tests and so the maximum dynamic friction coefficient was obtained from two

sources:

1. A series of tests were performed at the University of Auckland, New Zealand (UA), using

bearing sizes of 10 mm, 25 mm and 50 mm (3/8”, 1” and 2”) diameter. The effect of

dynamic coefficient friction versus size was determined from these tests.

2. Additional data was obtained from State University of Buffalo tests performed on 254 mm(10”) bearings using the same materials (Technical Report NCEER-88-0038). This dataconfirmed the results from the UA tests.



106

Figure 4.14: Coefficient of Friction for Slider Bearings

Figure 4.14 plots the coefficient of friction for 254 mm (10") bearings. The test results from the

UA series of tests showed some size dependence, as the maximum dynamic coefficient of

friction for veloc ities greater than 500 mm/sec (20 inch/sec ) was approximately 40% higher

for 50 mm (2 inch) diameter bearings compared to 254 mm (10 inch) bearings.

4.4.2 Static Friction Coefficient

On initiation of motion, the coefficient of friction exhibits a static or breakaway value, B,

which is typically greater than the minimum coefficient of sliding friction. This is sometimes

termed sta t ic frict ion or stic tion . Table 4.5 lists measured values of the maximum andminimum static friction coeffic ient for bearing tests from 1000 KN (220 kips) to 36,500 KN (8,100

kips). These values are plotted in Figure 4.15 with a power "best fit" curve. As for the

dynamic coefficient, the friction is a function of the vertical stress on the bearing.

At low stresses (10 MPa) the static coefficient of friction is about 5% and the maximum

sticking coefficient almost two times as high (9%). At high pressures (70 MPa) the static

coefficient is approximately 2% and the sticking coefficient up to 3%.

The ratio of the maximum to minimum depends on the loading history. A test to ultimate limit

state overload invariably causes a high friction result immediately after.

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0 100 200 300 400 500 600

VELOCITY (mm/sec)

C O E F F I C I E N T O F F R I C

T I O N

p = 7 Mpa (1 ksi)

p = 14 Mpa (2 ksi)

p = 21 Mpa (3 ksi)

p = 45 Mpa (6.5 ksi)



107

Type VerticalLoad(kips)

VerticalStress(ksi)

StickingFriction

Coefficient%

MinimumSpeedFriction

Coefficient%

36500KN

8100 kip

2028

4056

8111

11333

1.51

3.01

6.03

8.42

4.92

3.40

3.00

2.70

4.30

2.96

2.60

2.44

23500KN

5200 kip

1306

2611

5222

7833

1.51

3.03

6.06

9.09

5.48

3.90

3.00

2.22

4.58

3.40

2.68

1.94

7800KN

3900 kip

989

1978

39565933

1.48

2.96

5.918.86

6.28

4.36

2.622.34

5.10

3.50

2.422.04

15400KN3400 kip

8561711

3422

5133

1.462.94

5.87

8.81

7.004.54

2.90

2.22

5.743.94

2.52

1.96

9100KN

2000 kip

506

1011

2022

3033

1.70

3.39

6.78

10.17

6.38

4.98

3.32

2.66

5.54

3.96

2.92

2.40

3000KN

670 kip

167

333

667

1067

1.48

2.96

5.91

9.46

7.18

3.90

2.88

2.30

5.52

3.02

2.50

1.92

1000KN

220 kip

56

111222

356

1.49

3.005.99

9.58

7.16

4.743.22

2.80

6.04

4.242.72

2.26

Table 4.2 : Minimum/Maximum Static Friction



108

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30 40 50 60 70 80

Vertical Stress (MPa)

C o e f f i c i e n t o f F r i c t i o n %

Sticking Friction

Slow Speed FrictionBest Fit (Slow Speed)

Best Fit (Sticking)

Figure 4.8: Static and Sticking Friction

4.4.3 Effect of Static Friction on Performance

An isolation system which was formed of a hybrid of flat sliding and high damping rubber

bearings was studied extensively to assess the effect of static friction on the forcestransmitted into the superstructure.

The sliding friction element used for the study has a sliding force which is a function of the

velocity and pressure on the element. The coefficient of friction is continually updated

during the time history analysis as either of these parameters change.

The element also has a sticking fac tor where the initial coefficient of friction is factored by a

sticking factor which reduces exponentially over a specified travel distance. For this project

the response with a sticking fac tor of 2.0 was assessed.

Figure 4.9: Time History with Sticking

-80,000

-60,000

-40,000

-20,000

0

20,000

40,000

60,000

0 1 2 3 4 5 6

TIME (seconds)

F R I C T I O N F O R C E ( K N )

No Sticking

Sticking Factor 2.0



109

Figure 4.16 shows the effect of the sticking factor on the time history of friction force. The

structure has a weight of 400,000 KN on the sliding bearings, a static coefficient of friction of

4% and a maximum coefficient of friction of 10%. The maximum coefficient of friction

produces a sliding force of 40,000 KN. Because the sticking initially occurred at the lower

coefficient of friction, the sticking factor of 2.0 increased the maximum force by a lesser

factor, increasing the force by 50% to 60,000 KN.

Figure 4.17 shows the force-displacement function over the same time period shown in Figure

4.16.

Figure 4.10: Hysteresis with Sticking

The isolation system comprises sliding bearings supporting 35% of the seismic weight and high

damping rubber bearings supporting the remaining 65%. Figure 4.18 plots the hysteresis

curves for each of these isolator components and the total hysteresis for the combined

system.

Figure 4.11 Combined Hysteresis with Sticking

The effects of the static breakaway friction are dissipated over relatively small displacements

and after displacements of 50 mm or more the effects are negligible. The HDR bearingsprovide a force which increases with increasing displacement and so the sticking force is not

as high as the force which occurs at maximum displacement when the maximum HDR force

is added to the friction force at maximum velocity.

-80,000

-60,000

-40,000

-20,000

0

20,000

40,000

60,000

-100 -50 0 50 100 150 200 25

DISPLACEMENT (mm)


No Sticking

Sticking Factor 2.0

-100,000

-50,000

0

50,000

100,000

150,000

-150 -100 -50 0 50 100 150 200 250 30

DISPLACEMENT (mm)


TFE Bearings

HDR Bearings

Total Force



110

This type of evaluation can be used on projects which contain sliding bearings as one

component to determine the maximum weight which can be supported on sliders such that

the breakaway friction does not govern maximum forces.

4.4.4 Check on Restoring Force

The UBC requires systems without a restoring force to be designed for a displacement equal

to three times the design displacement. This has a large impact on P- forces, the size of the

separation gap and the cost of separating services and components. Wherever possible,

systems should be designed to provide a restoring force.

The definition of a restoring force is that the force at the design displacement is at least

0.025W greater then the force at one-half the design displacement.

Calculations for the restoring force for the example described above are listed in Table 8-6.

This design just achieves the UBC definition of a system containing a restoring force. As this

system had 35% of the weight on sliders, an upper limit of 30% should be used for preliminary

design to ensure that the restoring force definition is achieved.

Design DisplacementForce at Design Displacement, FDD

½ Design Displacement

Force at ½ Design Displacement,

F0.5DD

FDD – F0.5DD =0.107W – 0.082W

245 mm121,915 KN = 0.107W

122 mm93,859 KN = 0.082W

0.025W 0.025 W Ok

Table 4.3: Calculation of Restoring Force

The restoring force requirement is absolute, not earthquake specific, and so may causeproblems in low seismic zone when total forces, as a fraction of seismic weight, are low. For

such zones it may not be possible to use sliders as part of the isolation system and still complywith the UBC requirement for a restoring force. However, in low seismic zones it may be

practical to design and detail for three times the computed seismic displacement anyway.


PTFE is about the best material known to man for corrosion resistance, which is why there is

difficulty in etching and bonding it.

For base isolation use, the PTFE is dry/non lubricated and any changes over the design life willbe minor. Tests confirm little change in friction over several thousand cycles such as occurs in

a bridge with daily and seasonal movements due to thermal stresses.



112

4.7 EFFECTS OF TEMPERATURE ON PERFORMANCE

Elastomeric bearings are usually compounded from natural rubber and so are subjected to

temperature constraints typical to this material. The upper operating range of servicetemperature for natural rubber, without special compounding, is 60C (140F) and so the

upper limit of the design temperatures for most projects will not cause any problems.

The stiffness of natural rubber is a function of temperature but within the range of -20C to

60C (-5F to 140F) the effect is slight and not significant in terms of isolation performance.Below -20C the stiffness gradually increases as the temperature is lowered until at about –

40C (-40F) it is double the value at 20C (68F). The variation in stiffness is reversible as

temperature is increased.

As an example of the assessment of the effect of extreme low temperatures, the base

isolation properties for a bridge project in a cold region were calculated assuming the shear

modulus was increased by a fac tor of 2. Figure 4.19 illustrates the effect on maximum pier

and bent forces in the longitudinal direc tion.

Figure 4.19: Effect of Low Temperatures

The Pier 3 longitudinal force increased by 25%. The transverse Pier 3 force increased by 18%.

Bent 2 and 4 forces were essentially unchanged as the force was determined by the elastic

stiffness which is only a weak function of rubber shear modulus.

For this project, if a design earthquake occurred at temperatures below -20C the pier forces

could increase, with a maximum increase of about 25% at the extreme low temperature.

The probability of a design level earthquake occurring while temperatures are below -20C isprobably low, although this depends on the temperature distribution at the bridge site. If the

probability was considered significant, and the increased forces could lead to substructuredamage, the isolators could be modified to ensure that the forces at minimum temperature

did not exceed target values.

4.8 TEMPERATURE RANGE FOR INSTALLATION

For bridge isolation projects, base isolators are designed to resist the maximum seismic

displacements plus the total R+S+T (creep, shrinkage and thermal) displacements. Therefore,

the temperature of installation does not matter from a technical perspective.

For aesthetic reasons it is desirable to install the bearings at as close to mean temperature as

possible so that the bearings are not in a deformed configuration for most of their service life.

0

100

200

300

400

500

600

700

800

900

1000

Bent 2 Pier 3 Bent 4

L O N G I T U D I N A L B E N T F O R C E ( K N )

No Base Isolators

With Base Isolators at 20F

With Base Isolators at -40C



113

CHAPTER 5: ISOLATION SYSTEM DESIGN

5.1 INTRODUCTION

This Chapter describes a design procedure for seismic isolation systems. Many isolation

systems use a combination of elastomeric bearings types (lead-rubber, high damping rubber

and plain rubber) which are designed specifically for the applied loads and displacements.

Other isolation solutions, such as sliding systems and the friction pendulum system, are based

on devices which are designed by the supplier for the particular application.

The design procedures here are used to design elastomeric bearing types and perform a

preliminary assessment of the performance of an isolation system which incorporates one or

more types of device. The procedure is suitable for design office use to select the types andproperties of devices which will achieve the desired performance. The design characteristics

developed by the procedure are used as input to a detailed analysis and evaluation of theisolated structure.

Because of the complexity of hardware design, and empirical aspects of design for most

types of isolators, it is usual to obtain assistance from manufacturers. As base isolationtechnology has evolved, manufacturers have realized that structural engineers do not have

the skills to design hardware and so will provide this assistance.

There are codes available (U.S, British and Australian) which provide design rules for devices

used in isolation, such as elastomeric bearings and Teflon sliding bearings. However, most of

these codes are for non-seismic bridge applications and need to be adapted to use forseismic isolation applications.

5.1.1 Assessing Suitability

Not all structures are suited for seismic isolation and the first stage in the design procedure is

to check suitability. The checks should examine the need for isolation, the suitability of the

site and the suitability of the particular structure. Table 5.1 lists some of the items which should

be assessed prior to commencing any detailed design.

Some structures are more suited than others to isolation, as listed in Table 5.2. Most examples

of isolated buildings fall into one or more of these categories. This does not exclude other

building types, but most projects will have one or more of (1) requirements for continuing

operation (2) low ductility (3) historic merit or (4) valuable contents.



115

5.1.2 Design Development for an Isolation Project

If a project appears to be a suitable candidate for isolation, the level of design of the

isolation system depends on the procurement strategy to be adopted for the isolationsystem. Specifications will be either prescriptive or performance based on some combination

of the two, as listed in Table 5.3.

A prescriptive specifications provides details of the devices to be supplied (materials,

dimensions etc.) as for other structural components such as steel frames, concrete walls etc.

A performance specification states the performance to be achieved and requires the

suppliers to design devices to meet this performance (such as for a design-and-build

contrac t). Each of these approaches has advantages and disadvantages and in most cases

a combined specification is most effective. In this case, the engineer would supply properties

of a complying system (e.g. effective stiffness and damping for HDR devices) but also supply

the expected performance of this system to allow vendors of other systems to design and bid

systems with at least equal performance.

Description Advantages Disadvantages

Prescriptive Specification.

Specify detailed device

characteristics, including

stiffness and damping.

May spec ify sizes.

Structural engineer retains

control.

Simple to evaluate bids.

Requires the structural

engineer to be expert in

isolation design.

Limits potential bidders.May not be optimal

system.

Performance Based SpecificationSpecify performance

requirements of the

isolation system (period,

displacement, and

damping).

Vendors design devices.

Does not require expertise

in device design.

Wider range of bidders.

Less engineering effort at

design stage.

Difficult to evaluate bids.

May need to check

analysis of a large numberof systems.

Combined Prescriptive / Performance Specification

Specify a complying

system as for prescriptive

approach.

List performance of this

system and allow other

devices that can match

this.

Widest range of bidders.

Most likely to attract

optimal design.

Requires design expertise.

Difficult to evaluate bids.

May need to check

analysis of a large number

of systems.

Table 5.3: Procurement Strategies



116

5.2 DESIGN EQUATIONS FOR ELASTOMERIC BEARING TYPES

5.2.1 Codes

The vertical load capac ity of elastomeric isolation bearings has traditionally been based on

a limiting strain formulation as implemented in the British codes BS 5400 and BE 1/76. Thesecodes were intended for non-seismic applications where lateral forces are from sources such

as traffic loads and thermal movements in bridges.

The U.S. AASHTO bridge code provides rules for vertical load capac ity of elastomeric

bearings subjected to earthquake induced displacements. This code adjusts the factors of

safety from the British codes to be more appropriate for short duration, infrequently occurringloads.

5.2.2 Empirical Data

For lead rubber bearings some of the procedures are based on empirical data, in particularthe effective yield stress of the lead core and the elastic (unloading) stiffness. The values

reported here are typical of those used by manufacturers, based on a database of test

results for this type of bearing assembled from projects from 1978 to the present. The values

used have been shown to give an accurate estimate of force levels and hysteresis loop

areas. However, specific manufacturers may recommend different data for their bearings.

5.2.3 Definitions

The symbols and definitions used in engineering design and in codes sometimes differ from

the scientific terminology used in earlier chapters of this book. In this chapter, the symbols

have the meaning defined below.

Ab = Bonded area of rubber

Ag = Gross area of bearing, including side cover

Ah = Area of hysteresis loop (Also termed EDC = energy dissipated per

cycle)Apl = Area of Lead core

Ar = Reduced rubber area

B = Overall plan dimension of bearing

Bb = Bonded plan dimension of bearing

E = Elastic modulus of rubber

= 3.3 to 4.0 G depending on hardnessEb = Buckling Modulus

Ec = Effec tive Compressive Modulus

E = Bulk Modulus

f = Fac tor applied to elongation for load capac ity

= 1 / (Factor of Safety)

Fm = Force in bearing at specified displacement

g = Acceleration due to gravity

G = Shear modulus of rubber (at shear strain )Hr = Height free to buckleI = Moment of Inertia of Bearing

k = Material constant (0.65 to 0.85 depending on hardness)

K d = Yielded stiffness of lead rubber bearing = K r



117

K eff = Effec tive Stiffness

K r = Lateral stiffness after yield

K u = Elastic Lateral stiffness

K v = Vertical stiffness of bearing

K vi = Vertical stiffness of layer i

n = Number of rubber layers

p = Bonded perimeterP = Applied vertical load

Pcr = Buckling Load

P = Maximum rated vertical load

Qd = Characteristic strength

(Force intercept at zero displacement)

Si = Shape factor for layer i

ti = Rubber layer thickness

tsc = Thickness of side cover

tsh = Thickness of internal shims

Tpl = Thickness of mounting plates

Tr = Total rubber thickness

W = Total seismic weight

= Applied lateral displacement

m = Maximum applied displacement

y = Yield displacement of lead rubber bearing

= Equivalent viscous damping

c = Compressive Strain

sc = Shear strain from applied vertical loads

sh = Shear strain from applied lateral displacement

sr = Shear strain from applied rotationu = Minimum elongation at break of rubber

= Applied rotation

y = Lead yield stress

5.2.4 Range of Rubber Properties

Rubber compounds used for isolation are generally in the hardness range of 37 to 60, with

properties as listed in Table 5.4. As compounding is a continuous process intermediate values

from those listed are available. As seismic demands have increased over the last 10 years the

softer rubbers tend to be used more often. The lowest stiffness rubber has a shear modulus G

of about 0.40 MPa although some manufacturers may be able to supply rubber with G aslow as 0.30 MPa.

There is uncertainty about the appropriate value to use for the bulk modulus, K , with quotedvalues ranging from 1000 to 2000 MPa. The 1999 AASHTO Guide Specifications provide a

value of 1500 MPa and this is recommended for design.



118

HardnessIRHD2

Young’sModulus

E(MPa)

ShearModulus

G(MPa)

MaterialConstant

k

Elongationat

BreakMin, %

37

404550

55

60

1.35

1.501.80

2.203.25

4.45

0.40

0.450.54

0.640.81

1.06

0.87

0.850.80

0.73

0.64

0.57

650

600600

500

500

400

Table 5.4: Vulcanized Natural Rubber Compounds

5.2.5 Vertical Stiffness and Load Capacity

The dominant parameter influencing the vertical stiffness, and the vertical load capac ity, of

an elastomeric bearing is the shape factor. The shape factor of an internal layer, Si, is defined

as the loaded surface area divided by the total free to bulge area:

i

i4t

BS for square and circular bearings

(5.1a)for lead rubber bearings, which have a hole for the lead core,

ib

plb

itπB

A AS

(5.1b)

5.2.6 Vertical Stiffness

The vertical stiffness of an internal layer is calculated as:

i

rc vi

t

AEK (5.2)

where the compressive modulus, Ec, is a function of the shape factor and material constantas follows:

2

ic 2kS1EE (5.3)

In the equation for vertical stiffness, a reduced area of rubber, Ar, is calculated based on the

overlapping areas between the top and bottom of the bearing at a displacement, , as

follows (see Figure 5.1):

b

brB

A A 1 for square bearings (5.4a)



119

22

12 sin

b

b

r

B

where

BB0.5 A

for circular bearings (5.4b)

When the effective compressive modulus, Ec, is large compared to the bulk modulus E then

the vertical deformation due to the bulk modulus is included by dividing Ec by 1 + (E c /E) to

calculate the vertical stiffness.

Bulk modulus effects are included when the vertical stiffness is used to calculate verticaldeformations in the bearing but not the shear strains due to vertical load. The 1999 AASHTOGuide Specifications are an exception to this – see below.

5.2.7 Compressive Rated Load Capacity

The vertical load capac ity is calculated by summing the total shear strain in the elastomer

from all sources. The total strain is then limited to the ultimate elongation at break of the

elastomer divided by the factor of safety appropriate to the load condition.

The shear strain from vertical loads, sc

, is calculated as

ELEVATION

RECTANGULAR

CIRCULAR

Shaded = Overlap Area

Figure 5.1:Effective Compression Area



120

cisc S 6 (5.5)

where

i vi

ctK

P (5.6)

If the bearing is subjected to applied rotations the shear strain due to this is

ri

2

bsr

T2t

B (5.7)

The shear strain due to lateral loads is

r

sh T

(5.8)

For service loads such as dead and live load the limiting strain criteria are based on AASHTO14.5.1P

scuf where f = 1/3 (Factor of safety 3) (5.9a)

And for ultimate loads which include earthquake displacements

shscu f where f = 0.75 (Factor of safety 1.33) (5.9b)

Combining these equations, the maximum vertical load, P, at displacement can be

calculated from:

i

shui vi

S

f tK

6

P (5.10)

Codes used for buildings and other non-bridge structures (e.g. UBC) do not provide specific

requirements for calculating elastomeric bearing load capacity. Generally, the total strain

formulation from AASHTO is used with the exception that the Maximum Considered

Earthquake (MCE) displacement is designed using f = 1.0.

5.2.8 AASHTO 1999 Requirements

The 1999 AASHTO Guide Specifications generally follow these same formulations but maketwo adjustments:

1. The total strain is a constant value for each load combination, rather than a function ofultimate elongation. Using the notation of this section, AASHTO defines a strain due to

non-seismic deformations, s,s and a strain due to seismic displacements, s,eq. The limits

are then:

5.2sc (5.11a)

0.5, sr sssc (5.11b)

5.55.0, sr eqssc (5.11c)



121

2. The shear strain due to compression, sc, is a function of the maximum shape factor:

)21(2

32

kS G A

SP

r

sc For S 15, or (5.12a)

r

scGkSA

E GkS P

4

)/81(3 2

For S > 15. (5.12b)

Equation (5.12a) for S 15 is a re-arranged form of the Equation (5.5) with the approximation

that E = 4G. The formula for S > 15 has approximated (1+2kS2) 2kS 2 and adjusted the vertical

stiffness for the bulk modulus effects.

There is no universal agreement regarding the inclusion of bulk modulus effects in load

capacity calculations and it is recommended that the 1999 AASHTO formulas be used only if

the spec ifications spec ifica lly require this (see Sec tion 4.3 for discussion).

5.2.9 Tensile Rated Load Capacity

For bearings under tension loads, the stiffness in tension depends upon the shape of the unit,

as in compression, but limited available data suggests that the stiffness under tension is much

less than the compression stiffness. Due to lack of definitive data, the same equations are

used as for compressive loads as tension except that the strains are the sum of absolute

values.

When rubber is subjected to a hydrostatic tension of the order of 3G, cavitation may occur.

This will drastically reduce the stiffness. Although rubbers with very poor tear strength may

rupture catastrophically once cavitation occurs, immediate failure does not generally takeplace. However, the subsequent strength of the component and its stiffness may be

affected. Therefore, the isolator design should ensure that tensile stresses do not exceed 3G

under any load conditions.

Because of the low tension strength relative to compressive strength, and the uncertainty

about tensile stiffness, elastomeric based bearings should not be used in locations where

there may be significant tensions. In practice, design should be such as to avoid all tension

loads under the design basis earthquake but permit limited tensions, up to 3G, for the

maximum earthquake.

5.2.10 Bucking Load Capacity

For bearings with a high rubber thickness relative to the plan dimension the elastic buckling

load may become critical. The buckling load is calculated using the Haringx formula as

follows:

The moment of inertia, I is calculated as

12

BI

4

b for square bearings (5.13a)

64

4

bBI

for circular bearings (5.13b)



122

The height of the bearing free to buckle, that is the distance between mounting plates, is

shir 1)t(n )(nt H (5.14)

An effective buckling modulus of elasticity is defined as a function of the elastic modulus andthe shape factor of the inner layers:

)0.742SE(1E 2

ib (5.15)

Constants T, R and Q are calculated as:

r

rb

T

HIE T (5.16)

rr HK R (5.17)

rHQ

(5.18)

From which the buckling load at zero displacement is:

10

R

4TQ1

2

R P

2

cr (5.19)

For an applied shear displacement the critical buckling load at zero displacement is reduced

according to the effective "footprint" of the bearing in a similar fashion to the strain limited

load:

g

r0

crcr A

APP

(5.20)

The allowable vertical load on the bearing is the smaller of the rated load, P, or the buckling

load.

5.2.11 Lateral Stiffness and Hysteresis Parameters for Bearing

Lead rubber bearings, and elastomeric bearings constructed of high damping rubber, have

a nonlinear force deflection relationship. This relationship, termed the hysteresis loop, defines

the effective stiffness (average stiffness at a specified displacement) and the hysteretic

damping provided by the system. A typical hysteresis for a lead rubber bearing is as shown in

Figure 5.2.



123

Figure 5.2: Lead Rubber Bearing Hysteresis

For design and analysis this shape is usually represented as a bilinear curve with an elastic (or

unloading) stiffness of K u and a yielded (or post-elastic) stiffness of K d. The post-elastic

stiffness K d is equal to the stiffness of the elastomeric bearing alone, K r. The force intercept at

zero displacement is termed Qd, the characteristic strength, where:

ply d AQ (5.21)

The theoretical yield level of lead, y, is 10.5 MPa (1.5 ksi) but the apparent yield level is

generally assumed to be 7 MPa to 8.5 MPa (1.0 to 1.22 ksi), depending on the vertical load

and lead core confinement.

The post-elastic stiffness, K d, is equal to the shear stiffness of the elastomeric bearing alone:

r

r

r T

AGK

(5.22)

The shear modulus, G, for a high damping rubber bearing is a function of the shear strain ,but is assumed independent of strain for a lead rubber bearing manufactured from natural

rubber and with standard cure.

The elastic (or unloading) stiffness is defined as:

ru K K for elastomeric bearings (5.23a)

r

pl

ru A

AK K

1215.6 (5.23b)

or for lead rubber bearings

ru 25K K (5.23c)

For lead rubber bearings, the first formula for K u was developed empirically in the 1980’s to

provide approximately the correct stiffness for the initial portion of the unloading cycle andto provide a calculated hysteresis loop area which corresponded to the measured areas.

The bearings used to develop the original equations generally used 12.7 mm (½”) rubber

layers and doweled connections. By the standard of bearings now used, they were poorly

confined. Test results from more recent projects have shown that the latter formula for K u

provides a more rea listic estimate for many configurations of LRBs.



124

The shear force in the bearing at a specified displacement is:

r K dm QF (5.24)

from which an average, or effective, stiffness can be calculated as:

m

eff

FK (5.25)

The sum of the effective stiffness of all bearings allows the period of response to be

calculated as:

eff

eK g

W T

2 (5.26)

Seismic response is a function of period and damping. High damping and lead rubber

bearings provide hysteretic damping. For high damping rubber bearings, the hysteresis loop

area is measured from tests for strain levels, , and the equivalent viscous damping

calculated as given below. For lead rubber bearings the hysteresis area is calculated at

displacement level m as:

y mdh 4Q A (5.27)

from which the equivalent viscous damping is calculated as:

2

2

1

eff

h

K

A

(5.28)

The isolator displacement can be calculated from the effective period, equivalent viscous

damping and spectral acceleration as:

B

T S ea

m 2

2

4 (5.29)

where Sa is the spectral acceleration at the effective period Te and B is the damping factor, a

function of which is obtained from the appropriate code. The Eurocode EC8 provides a

formula for the acceleration at damping relative to the acceleration at 5% damping as:

2

7)5,(),( t T (5.30)

Where is expressed as a percent of critical damping. UBC and AASHTO provide tabulated Bcoefficients, as listed in Table 5.5. FEMA-356 provides a different fac tor for short and long

periods but generally the factor Bl would apply for all isolated structures. This has the same

values as the UBC and AASHTO.

In Table 5.5 the reciprocal of the EC8 value is listed alongside the equivalent factors from

FEMA-356. EC8 provides for a greater reduction due to damping than the other codes and

seem to relate to the short period values, Bs, from FEMA-356.



125

Effective Damping% of Critical

B FactorFEMA 356 (Periods > To)

AASHTOUBC

EurocodeEC8

< 2

5

102030

40

> 50

0.8

1.0

1.21.5

1.71.9

2.0

0.75

1.00

1.311.77

2.14

2.45

2.73

Table 5.5: Damping Coefficients

The formula for m includes Te and B, both of which are themselves a function of m. Therefore, the solution for maximum displacement includes an iterative procedure.

5.2.12 Lead Core Confinement

The effect of inserting a lead core into an elastomeric bearing is to add an elastic-perfectly

plastic component to the hysteresis loop as measured for the elastomeric bearings. The lead

core will have an apparent yield level which is a function of the theoretical yield level of

lead, 10.5 MPa, (1.58 ksi) and the degree of confinement of the lead. As the confinement of

the lead increases the hysteresis of the lead core will move more towards an elasto-plasticsystem as shown in Figure 5.3.

Confinement is provided to the lead core by three mechanisms:

1 The internal shims restraining the lead from bulging into the rubber layers.

2 Confining plates at the top and bottom of the lead core.

3 Vertical compressive loads on the bearings.

The confinement provided by internal shims is increased by decreasing the layer thickness,

which increases the number of shims providing confinement. Earlier lead rubber bearings

used doweled and then bolted top and bottom mounting plates. Current practice is to use

bonded mounting plates, which provides more effective confinement than either of the two

earlier methods.

Figure 5.3:Effect of Lead Confinement



126

The degree of confinement required also increases as the size of the lead core increases.

Smaller diameter cores, approximately B/6, tend to have a higher apparent yield level than

cores near the maximum diameter of B/3.

The effective stiffness and loop area both reduce with the number of cycles. The effective

stiffness is essentially independent of axial load level but the loop area varies proportional to

vertical load. During an earthquake some bearings will have decreased loop area whenearthquake induced loads act upwards. However, at the same time instant other bearings

will have increased compressive loads due to earthquake effects and so an increased loop

area. The net effect will be little change in total hysteresis area based on an average dead

load.

Lead core confinement is a complex mechanism as the lead is flowing plastically during

seismic deformations and the elastomer must be considered to be a compressible solid.

These features preclude explicit calculations of confinement forces. Manufacturers generally

rely on their databases of prototype and test results plus manufacturing experience to ensure

that the isolators have adequate confinement for each particular application. This is then

demonstrated by prototype tests.

For long term loads, lead will creep and the maximum force in the core will be less than the

yield force under suddenly applied loads. For structures such as bridges where non-seismic

displacements are applied to the bearings this property will affect the maximum forcetransmitted due to c reep, shrinkage and temperature effects.

Tests at slow loading rates have shown that for loads applied over hours or days rather than

seconds the stress relaxation in the lead is such that the maximum force in the lead will be

about one-quarter the force for rapid loading rates. Therefore, for slowly applied loads the

maximum lead core force is assumed to be F = 0.25 Qd.

5.3 BASIS OF AN ISOLATION SYSTEM DESIGN PROCEDURE

Most isolation systems produce hysteretic damping. Both the effective period and damping

are a function of displacement, as shown in Figure 5.4 for a lead rubber bearing. Similar

curves can be developed for other types of device.

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0 50 100 150 200 250 300 350 400

ISOLATOR DISPLACEMENT (mm)

E F F E C T I V E P E R I O D ( S e

c o n d s )

15%

20%

25%

30%

35%

40%

45%

E Q U I V A L E N T V I S C O U S D A M P I N G

Effective Period

Equivalent Damping

Figure 5.4: Isolator Performance



127

Because of this displacement dependence, the design process is iterative. A further

complication arises for elastomeric types of bearing in that, as well as period and damping,

the minimum plan size of the bearing is also a function of displacement.

5.3.1 Elastomeric Based Systems

For elastomeric based systems, the iterative process involves the size and properties of the

devices. Initial bearing plan sizes are determined, based on maintaining a fac tor of safety ofat least 3 under maximum vertical loads in the undeformed configuration.

The number of rubber layers, and the lead core sizes if any, is then set by a trial-and-error

procedure to achieve the required seismic performance. As the damping is a function of

displacement, this requires an iterative procedure which can be implemented using

standard design office tools.

The iterative procedure can be automated, for example, by using spreadsheet macros, but

there is no guarantee that convergence will be achieved as there are limits on effective

periods and damping using practical isolators. Generally, the higher the vertical load on an

elastomeric bearing the easier it will be to achieve long effective periods.

5.3.2 Sliding and Pendulum Systems

Both flat and curved sliding systems can be designed using the same procedure as outlined

above but is generally simpler in that the device properties are not a function of dimensions.

The isolation system properties are defined by two parameters:

1. The characteristic strength, defined as W where is the coefficient of friction for the

sliding surface and W is the total seismic weight.

2. The post-yielded stiffness is defined as zero for a flat slider or W/R for a spherical slider.

The steps above are then used to iterate to solve for the isolated displacement.

5.3.3 Other Systems

The design procedure can be used for any type of isolation system which can be

approximated with a softening bi-linear hysteresis loop, that is, the yielded stiffness is less than

the elastic stiffness, or for which tabulated values of damping and stiffness versus

displacement are available.

For devices that do not have these characteristics, special design procedures may need to

be developed.

5.4 STEP-BY-STEP IMPLEMENTATION OF A DESIGN PROCEDURE

This section describes the step-by-step implementation of a design procedure, which can be

performed manually but is best automated using design tools such as Excel or MathCad. The

procedure is based on the manual selection of, and adjustment to, isolator sizes. It is difficult

to develop an automatic optimization routine because of constraints imposed by practical

bearing sizes and properties. Example spreadsheets with this procedure implemented for

bridges and buildings are supplied with this book. These spreadsheets are described later

with the bridge and building isolation design examples.



128

Figure 5.5 illustrates the steps in implementing the isolation system design procedure. Many of

the steps relate to calculations involving the properties and capacities of elastomeric

devices and so the procedure is simplified for sliding and FPS types of isolators.

1. Define Seismic Input (e.g. UBC,NZS 1170, AASHTO)

2. Define bearing types (e.g. LRB,

HDR, PTFE), material properties and

load data

3. Set assumed bearingdimensions

(plan size, height, core size)

Elastomericbased systems

only

4. Calculate bearing properties for

assumed sizes

Elastomeric

based systems

only

5. Calculate seismic performance

for DBE and MCE

6. Calculate load capac ity under

maximum displacements for

a. Gravity

b. DBE

c. MCE

Elastomeric

based systems

only

7. Assess factors of safety and

performance at DBE and MCE

levels.

8. If necessary, adjust bearing sizes

in Step 3. above.

Elastomeric

based systemsonly

Figure 5.5: Design Procedure Flow Chart

5.4.1 Example to Illustrate Calculations

The design procedure is illustrated using numerical values for a simplified design of a healthfacility as shown in Figure 5.6. This building has a lateral load system comprising perimeter

concrete moment frames and internal steel chevron braces. The internal steel columns have

high axial loads, and the potential for uplift.

The isolation system selected for this building is a combination of 27 lead rubber bearings atthe perimeter and 4 flat slider bearings, one under each internal steel column. The flat sliding

bearings are PTFE on stainless steel. To permit rotations due to possible uplift, pot type

bearings would be used at these internal locations.



129

Figure 5.6: Example Building

5.4.2 Design Code

The example provided in this section is based on design to 1997 UBC requirements. Designs

based on other codes follow the same general principles. The main differences between

different codes are in specification of the seismic input. UBC, in common with most codes,

has a constant velocity for isolation periods (periods, T, greater than 1 second).

A constant spectral velocity simplifies design as the acceleration is inversely proportional to T

and the displacement is directly proportional to T. However, the procedure can be adjustedif necessary to calculate response for design spectra which are not based on constant

spectral veloc ity.

The design procedures used for elastomeric based bearings such as lead rubber and high

damping rubber are derived from the AASHTO 1991 Guide Specifications. These could be

relatively simply modified to incorporate changes in the AASHTO 1999 Guide Specifications

although these seem to be conservative relative to other codes. Building codes do not

specify the design methods for individua l bearings but rather require prototype tests which

are in the nature of proof tests. Experience has shown that design to 1991 AASHTO, rather

than the more conservative 1999 AASHTO, produces designs which can demonstrate stabilityin proof tests.

5.4.3 Units

The example calculations here are in the SI units of kN and mm. The procedure will work with

any consistent set of units. Care must be taken to ensure that parameters such as the

gravitational constant, g, are in the correct units. Also, properties generally expressed as

MPa, such as E and G , must be converted to kN, mm.



130

5.4.4 Seismic and Building Definition

The project definition parameters for the example building are listed in Table 5.6. The

information provided defines the seismic loads and the structural data required in terms of

the UBC requirements for evaluating performance. Other codes define the seismic inputdifferently and may have differing requirements for torsion.

1. The seismic information is extrac ted from UBC tables for the particular site. This requires

the zone, soil type and fault information.

For UBC design, the parameters are used to derive coefficients C V and C VM which define

the spectral acceleration for a given period. These are for the two levels of load defined

in the UBC, respectively DBE (Design Basis Earthquake) and MCE (Maximum Capable or

Maximum Considered Earthquake). For other codes, equivalent formulations of these

coefficients will be defined.

2. The isolated lateral force coefficient, RI is the factor by which isolated elastic design

forces are reduced. For UBC design, the response modification coefficient, R, andimportance factor, I, for an equivalent fixed base building are required as they form a

limitation on base shear. Note that, for base isolated structures, the importance factor isassumed to be unity for all structures in the UBC.

As for the seismic coefficients, other codes may specify different response modification

factors and the procedure for developing design forces from the elastic response may

need to be adjusted.

3. Building dimensions are required to estimate the torsional contribution to the totalisolation system displacement. The formula listed in Table 5.6 is that provided by the UBC.

The project definition information is specific to a project and, once set, does not need to bechanged as different isolation systems are assessed and design progresses.



131

Seismic Zone Fac tor, Z 0.4 Table 16-I

Soil Profile Type SB Table 16-J

Seismic Coefficient, CA 0.400 Table 16-Q

Seismic Coefficient, CV 0.480 Table 16-RNear-Source Factor Na 1.000 Table 16-S

Near-Source Factor Nv 1.200 Table 16-T

MCE Shaking Intensity MMZNa 0.484 Calculated

MCE Shaking Intensity MMZNv 0.581 Calculated

Seismic Source Type A Table 16-U

Distance to Known Source (km) 10.0 From site seismology

MC E Response Coefficient, MM 1.21 Table A-16-D

Lateral Force Coefficient, RI 2.0 Table A-16-E

Fixed Base Lateral Force Coefficient, R 5.5 Table 16-NImportance Factor, I 1.0 Table 16-K

Seismic Coefficient, CAM 0.484 Table A-16-F

Seismic Coefficient, CVM 0.581 Table A-16-G

Eccentricity, e 3.50 5% of d or d

Shortest Building Dimension, b 32.00 Building size

Longest Building Dimension, d 70.00

Dimension to Extreme Isolator, y 35.0 From geometry

D TD/DD = D TM/DM 1.24822

121

d b

e y

Table 5.6: Seismic and Building Definition

5.4.5 Material Definition

Material definition requirements for design are device specific. The parameters required forvarious devices are listed in Table 5.7. This is the basic information used for the design process

and includes parameters for lead rubber bearings and sliding bearings.

The range of properties available for rubber is restricted and some properties are related toothers, for example, the ultimate elongation, material constant and elastic modulus are a ll afunction of the shear modulus (see Table 5.4 earlier in this Chapter). Designers should check

with manufacturers for values outside the range given in Table 5.4.

As for the rubber, the PTFE properties used for sliding bearings are supplier-specific. Values

listed in Table 5.7 are suited for evaluating alternative designs but manufacturers will need to

be consulted for final specification.



132

Parameter Symbol Value Comment

Shear Modulus G 0.0004 Shear modulus of rubber. See Table 5.1.(Note units are kN, mm)

Ultimate Elongation u 6.5 From Table 5.1 for shear modulus used.

Material Constant k 0.87 From Table 5.1 for shear modulus used.Elastic Modulus E 0.00135 From Table 5.1 for shear modulus used.

Bulk Modulus E 1.5 Typical value for natural rubber.

Damping 0.05 5% used for plain rubber bearings

Lead Yield Strength Y 0.008 Consult manufac turer, usually 7 to 8.5 MPa.

Teflon Coefficient

of Friction 0.10 Use high veloc ity value for design

Gravity g 9810 Set gravitation constant in current units

TFE Properties These are required for analysis only (e.g. ETABS)

Vertical Stiffness 5000 Generally, use a high value

Lateral Stiffness 2000 High initial lateral stiffness for sliding bearings

Low Velocity 0.04

High Veloc ity 0.10

Coefficient a 0.90

These are typical values,

consult manufacturer

Table 5.7: Material Properties Used For Design

High damping rubber is the most variable of the common isolator materials as each

manufacturer has specific properties for both stiffness and damping. The design procedure

can be adapted to interpolate from tabulated values of the shear modulus and equivalent

damping. The damping values tabulated may include viscous damping effects if

appropriate.

An example of HDR stiffness and damping properties versus shear strain is listed in Table 5.8.

These are for a relatively low damping rubber formulation and so any design based on these

properties should be easily achievable from a number of manufacturers. As such, they shouldbe conservative for preliminary design.

Shear Strain

%

Shear ModulusG

MPa

Equivalent Damping

%

10 1.21 12.7225 0.79 11.28

50 0.57 10.00

75 0.48 8.96

100 0.43 8.48

125 0.40 8.56

150 0.38 8.88

175 0.37 9.36

200 0.35 9.36

Table 5.8: High Damping Rubber



133

5.4.6 Isolator Types and Load Data

The isolator types and load data are defined as shown in Table 5.9. See Chapter 7 for

assistance on selecting the device types and the number of variations in type. For mostprojects, there will be some iteration as the performance of different types and layouts is

assessed.

1. The procedure here is based on equivalent viscous damping in linear or bi-linear systems.

As such, the types of isolators which can be included in this procedure are lead rubber

bearings (LRB), high damping rubber bearings (HDR), elastomeric bearings (ELAST,

equivalent to an LRB with no lead core), flat sliding bearings (TFE) and curved sliding

bearings (FPS).

2. For each isolator type, vertica l load conditions must be defined. The average DL + SLL is

used to assess seismic performance. The maximum and minimum load combinations are

used to assess the isolator capacity.

The latter values are generally available only after analysis has been performed. For

preliminary design, a conservative estimate is generally to assume a maximum verticalload of two times the maximum dead load and a minimum load of zero. These can be

adjusted as more accurate loads become available. If minimum loads are tensile, youwill have to consult manufacturers to ensure that the tension stresses are not excessive.

Tension loads cannot be resisted by sliding bearings and uplift may occur at these

locations if a tension is indicated. Nonlinear analysis can quantify uplift, if any.

3. The total wind load on the isolators may form a lower limit on the design shear forces.

This does not govern for most buildings.

4. Most building projec ts will not have a non-seismic displacement or rotation; these are

more common on bridge projects. High rotations (greater than about 0.003 radians) will

severely limit the capacity of the elastomeric types of isolator (LRB, HDR and ELAST). If

there are high rotations in particular locations, the pot-bearing type of slider may be a

better solution.

For most projects, the data in this section will be changed as variations of isolation system are

examined. Often, the isolator type will be varied and sometimes variations in the number of

each type of isolator will be considered, for example, to vary the seismic weight ratio

between LRB and TFE bearings.



135

LRB TFE Comment

Plan Dimension, B 870 500 Use nominal dimension for sliders, not used

in design

Depth (optional), D Rectangular bearings may be used for

bridges

Layer Thickness, ti 10 Usually, use same for all elastomeric types

Number of Layers, N 21 Vary as part of design process

Lead C ore Size, dpl 175 Vary as part of design process

Shape C May include equations for square (S),

circular (C) or rec tangular isolators (R).

Side Cover, tsc 10 Typically 10 mm

Internal Shim Thickness, tsh 3.0 Typically 3 mm

Load Plate Thickness, Tpl 40.0 Required to get total height

Total Rubber Thickness, Tr 210 N t I

Total Height, H 350 = Nti+ (N-1)tsh + 2Tpl Radius of Curvature, R Required for FPS isolators only

2

2

4

gT R

Total Yield Level of System

(summed over all types)

5.89% Calculated using Qd from Table 5.7 as:

W

earings xNumberofBQ

W

Q d d

Table 5.10: Isolator Dimensions

1. The minimum plan dimensions for the elastomeric isolators are those required for the

maximum gravity loads. The gravity factor of safety (F.S.), at zero displacement, should

be at least 3 for both the strain and buckling limit states.

The design procedure requires a plan dimension such that this factor of safety is

achieved. In practice, the seismic demands are usually such that the gravity F.S. is larger

than 3. A good starting point for high seismic regions is a strain factor of safety of 5 under

maximum DL + LL.

For metric dimensions, an increment of 50 mm in plan sizes is generally used with sizes in

the sequence of 570 mm, 620 mm etc. This is based on mold sizes in 50 mm increments

plus 20 mm side cover rubber. Manufacturers may have spec ific recommendations.

2. The rubber layer thickness is generally a constant at 10 mm. This thickness provides goodconfinement for the lead core and is sufficiently thin to provide a high load capacity. If

vertical loads are critical the load thickness may be reduced to 8 mm or even 6 mm

although you should check with manufacturers for these thin layers. Thinner layers add tothe isolator height, and also cost, as more internal shims are required. The layer thickness

should not usually exceed 10 mm for LRBs but thicker layers may be used for elastomeric

or HDR bearings (up to 15 mm). The load capacity drops off rapidly as the layer thickness

increases.



136

3. The number of layers defines the flexibility of the system. This needs to be set so that the

isolated period is within the desired range and so that the maximum shear strain is not

excessive. This is set by trial and error. The aim is generally to keep strain below 150%

under maximum displacements (200% for HDR) and so the total rubber thickness should

be in the range of estimated total displacement divided by 1.5 or 2.

An increase in the number of layers will decrease the buckling load and so as thenumber of layers is increased an increase in plan size may be needed. As for the strain

F.S, it is recommended that the buckling Factor of Safety under maximum gravity loads

be in the range of 4 to 5.

4. The size of the lead core for LRBs defines the amount of damping in the system. The ratio

of QD/W is calculated for guidance. This ratio usually ranges from 3% in low seismic zones

to 10% or more in high seismic zones. Usually the softer the soil the higher the yield level for

a given seismic zone. As for the number of rubber layers, the lead core is sized by trial and

error.

5. Plan shapes are usually circular but may be square (plus rec tangular for bridges). Most

building projec ts use c ircular bearings as it is considered that these are more suitable forloading from all horizontal directions. Square and rectangular bearings are more oftenused for bridges as these shapes may be more space efficient.

The procedure for fine tuning dimensions is to set initial values, solve for the isolation

performance and change the configuration to achieve the improvements you need. At

each step, the effect of the change is evaluated by assessing the isolation system

performance.

5.4.8

Calculate Bearing Properties

The device dimensions defined in the preceding section are used to calculate the bearing

properties listed in Table 5.11. For elastomeric based bearings many of the properties are afunction of plan shape and formulas are listed for both c ircular and square bearings.

The stiffness and strength properties are a function of the type of device. Formulas are listed

in Table 5.11 for LRB, TFE and FPS devices. HDR bearing design is based on tables of shear

modulus and effective damping versus applied shear strain and so a design procedure

requires a method to lookup the appropriate values, for example, the Excel LOOKUP

function.



137

LRB TFE Equation

Gross Area, Ag 594468 B 2 (Square)

B2/4 (Circular)

Bonded Dimension, Bb 850 B – 2t sc

Bonded Depth (R only), Db D – 2t sc

Bonded Area, Ab 567450 B b2 (Square)

Bb2/4 (Circular)

Plug Area, Apl 24053 dpl2/4

Net Bonded Area, Abn 543397 A b - A pl

Total Rubber Thickness, Tr 210 N t I

Bonded Perimeter, p 2670 Bb (C ircular)

4Bb (Square)

Shape Factor, SI 20.3 A bn / ( t I p)

Characteristic Strength, Qd 192.4 498.6 yApl (LRB)

Pd (TFE or FPS)0.0 (HDR)

Shear Modulus (50%) 50 0.0004 G (LRB)

Need to LOOKUP from table of

G vs Strain for HDR

Yielded Stiffness K r 1.09 0.00 G(Ag-Apl)/Tr (LRB, HDR)0 (TFE)

Pd/R (FPS)

For LRB

c1, Coefficient on K r

c2, Coefficient on Apl/Ab

6.50

12.00

Typical values, see discussion in

Section 4.2.11

Elastic Stiffness K u 10.81 0.00 c 1K r (1 – c 2Apl/Abn) (LRB)

0 (TFE or FPS)

= K r (HDR)

Yield Force, Fy 213.9 498.6 Q d/(1 – K r/K u) (LRB)

Qd (TFE or FPS)

Yield Displacement,y 19.78 0.00 F y / K u (LRB)

0 (TFE or FPS)

Moment of Inertia, I 2.56e10 Bb4 / 64 (Circular)Bb4/ 12 (Square)

Buckling Factors Elastomeric Types only

Height Free to Buckle, Hr 270.0 T r + t sh (N – 1)

Buckling Modulus, Eb 0.416 E (1 + 0.742 S i2

)Constant T 1.37e10 EbIHr / T r

Constant R 293.4 K r Tr

Constant Q 0.0116 / H r

Table 5.11: Bearing Properties



138

5.4.9 Gravity Load Capacity

For elastomeric bearing types the gravity load capacity is calculated prior to assessing

earthquake performance. If necessary, plan sizes and layer configurations are adjusted to

ensure that the bearings have adequate factors of safety under maximum dead plus liveloads. The vertical stiffness is also calculated. Table 5.12 lists the calculations required for this

phase of the design procedure.

As discussed above, for high seismic zones it is recommended that the starting point of the

design be such that there are factors of safety of 4 to 5 at zero displacement undermaximum dead plus live loads. This is achieved by limiting to the range of 0.2 u to 0.25 u

and ensuring Pcr > 4 or 5 P DL+LL. These factors can be adjusted by changing the plan size, layer

thickness and / or number of layers.

The design procedure in Table 5.12 includes an empirical adjustment to the yielded stiffness,

K r, as a function of the ratio of applied load to the buckling load. This has been incorporated

as a result of observed stiffness from prototype tests as the vertical load is varied.

Manufacturers may be able to provide alternate functions to account for vertical loads onthe bearings.

The vertical stiffness is not used directly as part of the design and evaluation procedure but is

required for analysis. It can also be used to calculate vertical deflections in the bearings atthe time of installation.



139

LRB TFE Comment / Equations

Factor f on u 0.33 Fac tor of safety 3 for gravity

Applied Vertical Load, PDL+LL 4948 Maximum DL + LL

Applied Displacement 0.000 Non-Seismic Displacement NS

Applied Rotation 0.000 Non-Seismic Rotation, NS Shape Factor, Si 20.35 From properties

Constant k 0.87 From material properties

Elastic Modulus, E 0.0014 From material properties

Compressive Modulus, Ec 0.974 E (1 + 2kS i2)

Reduced Area, Ar 567450

b b

B1A NS (Square)

22 b

b

12

B

where

BsinB0.5

NS

(C ircular)

Vertical Stiffness, K vi 55273 E cAr/ tI (per layer)

Compressive Strain, c 0.009 P / K viti

Compressive Shear Strain, sc 1.09 6S ic

Displacement Shear Strain, sh 0.00 NS / T r

Rotational Shear Strain, sr 0.00 B b2NS/ (2 ti Tr)

Total Strain, 1.09 c + sc + sr

Allowable Strain 2.17 u / f

Buckling Load, Pcr 23188

G

r

A

A

1

R

4TQ1

2

R

2

Status OK Satisfactory if u/f

and Pcr > P DL +LL Adjusted Shear Modulus 0.00033 G (1 – PD / P cr)

Adjusted Stiffness K r* 0.91 K r (1 – P D / P cr)

Vertical Stiffness Calculation

K vi 55273 calculated above

K v 2632 K vi / N

Bulk Modulus E 1.5 From material properties

Vertical Stiffness, K v 1596 K v / (1 + E c/E)

Table 5.12: Gravity Load Capacity

5.4.10 Calculate Seismic Performance

For design to UBC, the seismic performance must be assessed for two levels of earthquake

load, termed DBE and MCE. Tables 5.13 and 5.14 detail the procedure to assess maximum

response for these two levels of load. The steps involved are:

1. A displacement, , is assumed (the total rubber thickness provides a convenient

starting point).

2. The maximum force in each bearing, F, is calculated at this displacement.



140

3. The effective stiffness of each bearing at this displacement is calculated as F/. The

total system effec tive stiffness is the summation of the individual device stiffness times

the number of each type.

4. The effective period is calculated using the total seismic mass and the effective

stiffness.

5. The equivalent viscous damping is calculated from the area of the hysteresis loop. For

HDR, the damping and shear modulus are interpolated from tabulated values of these

quantities versus shear strain.

6. The damping factor, B, is calculated for the calculated level of equivalent viscous

damping.

7. The spectral displacement is calculated from the acceleration response spectrum at

the effective period, modified by the damping factor B.

8. This displacement is compared with the displacement assumed in Step 1. above. If the

difference exceeds a preset tolerance, the calculated displacement defines a newstarting displacement and the procedure is repeated until convergence is achieved.

The seismic performance is evaluated for both the design level and the maximum seismic

events.

For UBC design the spectral acceleration is calculated as SA = E

V

BT

C and the spectral

displacement as SD = B

T C

g E V 24

(which is equivalent to2

2

4

e A

gT S ). For other codes, there will

be different formulas for SA (often defined as the seismic coefficient, C). Provided S A can be

defined, SD can be calculated directly from this.

The procedure in Tables 5.13 and 5.14 is developed for LRB, TFE and FPS bearings. For HDR

bearings the properties are extracted from tabulated properties of shear modulus and

damping versus shear strain as follows:

1. Shear strain is calculated as = / T r.

2. The effective stiffness is calculated as K e = G Ab/Tr where G is the shear modulus atstrain .

3. The damping, , at strain is used to calculate the equivalent hysteresis loop area as:

Ah = 2 K e2. (5.31)

NOTE: The equivalent hysteresis area is only required if HDR bearings are used with

other bearing types. If all bearings are HDR then can be used to calculate the B

factor directly.

The iteration procedure can be automated using design office tools such as spreadsheets.Figure 5.7 provides an example of a subroutine written in VBA which can be used in Excel

spreadsheets. This relies on named ranges in the spreadsheet:

1. The cell containing total rubber thickness is named, in this example as Trma x, which is

the maximum rubber thickness in any bearing.



141

2. The assumed displacement is named as d b e 1 and mc e 1 for the two levels of

earthquake load respectively.

3. The calculated spectral displacement is named as d b e 2 and m c e 2 for the two levels

of earthquake load respectively.

A button can be added to the spreadsheet to run the subroutine as a macro. (Named

ranges are shown bolded in Tables 5.13 and 5.14).

DBEPerformance

LRB TFE Total Comment

Number of Isolators 27 4 31 Number of each type of

isolator

Elastic Stiffness, K u 10.81 0.00

Yielded Stiffness, K r* 0.91 0.00

Yield Displacement, y 19.78 0.00Characteristic Strength, Qd 192.4 498.6

Bearing parameters

calculated from

bearing propertiesabove

Seismic Displacement, DD 181.3

“dbe1”Assume a displacement,

adjust until SD/DD = 1.0

Bearing Force, F 357.2 498.6 Qd+DDK r*

Effec tive Stiffness, K e 1.97 2.75 64.22 F/D D

Seismic Weight, W 122058 Sum of dead loads

Seismic Mass, M 12.44 W/g

Effective Period, TE 2.77

eK

M 2

Loop Area, Ah 124286 361500 4801722 4Q D(DD- y)

Damping, 30.55% 63.66% 36.22%22

1

De

h

DK

A

Damping Factor, B 1.82 UBC Table A-16-C

Spectral Acceleration, SA 0.095

E

V

BT

C

Spectral Displacement, SD 181.25

“dbe2” B

T C

g E V 24

Check Convergence 1.00 SD/ m

Table 5.13: Seismic Performance for DBE



142

MCEPerformance

LRB TFE Total Comment

Number of Isolators 27 4 31

Elastic Stiffness, K u 10.81 0.00

Yielded Stiffness, K r* 0.91 0.00 Yield Displacement, y 19.78 0.00

Characteristic Strength, Qd 192.4 498.6

Seismic Displacement, Dm 252.42

“mce1”

Bearing Force, F 421.9 498.6

Effec tive Stiffness, K e 1.672 1.975 53.035

Seismic Weight, W 122058

Seismic Mass, M 12.442

Effective Period, TE 3.04

Loop Area, Ah 179058 503423 6848245

Damping, 26.76% 63.66% 32.26%

Damping Factor, B 1.74

Spectral Acceleration, SA 0.110

Spectral Displacement, SD 252.43

“mce2”

Check Convergence 1.00

See

Table 5.9

for

Formulas

Table 5.14: Seismic Performance for MCE

Sub SolveDisp()

tol = 0.0001ds = Range("Trmax")

i = 0

Range("dbe1") = dsDo Until Abs(1 - (Range("dbe1") / Range("dbe2"))) < tol

i = i + 1

ds = Range("dbe2")Range("dbe1") = ds

If i > 200 ThenCall MsgBox("Cannot Solve DBE")

Exit Sub

End IfLoop

ds = Range("Trmax")

i = 0

Range("mce1") = dsDo Until Abs(1 - (Range("mce1") / Range("mce2"))) < tol

i = i + 1ds = Range("mce2")

Range("mce1") = dsIf i > 200 Then

Call MsgBox("Cannot Solve MCE")

Exit SubEnd If

Loop

End Sub

Figure 5.7: Subroutine to Solve for Displacement



143

5.4.11 Seismic Load Capacity

For elastomeric based bearings the vertical load carrying capacity is a function of applied

shear displacement and so the capacity must be checked using the same procedures aswere used for gravity loads (Table 5.12) with adjustments to acceptance criteria to reflect

the lower frequency of seismic loads.

Table 5.15 lists the calculations for maximum DBE displacements. The center of mass

displacements calculated above are factored by the torsional factor (in this example, by

1.248). The equivalent calculations for MC E are listed in Table 5.16. As the MCE seismic load

has a long return period the minimum factor of safety is reduced to 1.0 for these

displacements.

LRB TFE Comment / Equations

Fac tor f on Eu 0.75 Fac tor of safety 1.33 for DBEApplied Vertical Load, PDL+SLL+E 8358 Maximum DL + SLL + E

DBE Displacement 181.3 DBE Displacement DD

Factor on Displacement 1.248 D TD/DD

Applied Displacement 226.2 D TD

Applied Rotation 0.000 Seismic Rotation, E

Shape Factor, SI 20.35 From properties

Constant k 0.87 From material properties

Elastic Modulus, E 0.0014 From material properties

Compressive Modulus, Ec 0.974 E (1 + 2kS i2)


b

b

B

1A TD D (Square)

22 b

b

12

B

where

BsinB0.5

TD D

(C ircular)

Vertical Stiffness, K vi 36766 E cAr / tI (per layer)

Compressive Strain, c 0.023 P / K viti

Compressive Shear Strain, sc 2.78 6S ic

Displacement Shear Strain, sh 1.08 NS / T r

Rotational Shear Strain, sr 0.00 B b2NS/ (2 ti Tr)

Total Strain, 3.85 c

+ sc

+ sr

Allowable Strain 4.88 u / f


G

r

A

A

1

R

4TQ1

2

R

2

Status OK Satisfactory if u/fand Pcr > P DL +LL

Table 5.15: Load Capac ity at DBE



144

LRB TFE Comment/Equations

Factor f on Eu 1.00 Factor of safety 1.0 for MCE

Applied Vertical Load, PDL+SLL+E 8358 Maximum DL + SLL + E

MC E Displacement 252.4 MC E Displacement DM

Factor on Displacement 1.248 D TM/DM

Applied Displacement 315.1 D TM

Applied Rotation 0 Seismic Rotation, E

Shape Factor, SI 20.35

Constant k 0.87

Elastic Modulus, E 0.0014

Compressive Modulus, Ec 0.974


Vertical Stiffness, K vi 29797

Compressive Strain, c 0.028

Compressive Shear Strain, sc 3.42

Displacement Shear Strain, sh 1.50

Rotational Shear Strain, sr 0.00

Total Strain, 4.93

Allowable Strain 6.50


See Table 5.12

Status OK Satisfactory if u/f

and Pcr > P DL +LL

Table 5.16: Load Capacity at MCE

5.4.12 Assess Factors of Safety and Performance

Tables 5.9 to 5.16 have developed bearing properties, isolation system performance and

load capacities. Key response parameters are extracted from these tables to provide a

summary list for evaluation of fac tors of safety and seismic performance.

Factors of Safety

The values in Table 5.17 are used to ensure that the demands on the bearings are withinacceptable limits:

1. The gravity factor of safety should exceed 3.0 for both strain and buckling. For high

seismic zones it will generally be higher as performance is governed by seismic limit

states.

2. The DBE factor of safety should be at least 1.5 and preferably 2.0 for both strain and

buckling.

3. The MC E factor of safety should be at least 1.25 and preferably 1.5 for both strain and

buckling.

4. The ratio of reduced area to gross area should not go below 25% and should

preferably be at least 30%.



145

5. The maximum shear strain for LRBs should not exceed 200% and preferably be less than

150%. For HDR bearings higher strains are acceptable, up to 250% but preferably less

than 200%.

The limit states are governed by both the plan size and the number of rubber layers. An

adjustment to either of both these parameters may be required to achieve a design within

the limitations above. At each change, a check will also be required to ensure that theseismic performance is ac hieved.

LRB TFE Comment

Gravity Strain F.S. 5.95 u/ = 6.50 / 1.09

Buckling F.S 4.69 Pcr/P = 23188/4948

DBE Strain F.S 1.69 u/ = 6.50 / 3.85

Buckling F.S 1.85 Pcr/P = 15424/8358

MCE Strain F.S 1.32 u/ = 6.50 / 4.93

Buckling F.S 1.50 Pcr/P = 12501/8358

Reduced Area / Gross Area 53.9% at MC E = Ar / A b Maximum Shear Strain 150% at MCE =sh

Table 5.17: Summary of Demand on Elastomeric Bearings

Seismic Performance

The performance of the isolated structure is summarized for the DBE and MCE levels in Table

5.18. These are extracted from earlier stages of the design process. Performance indicators to

assess are:

1. The isolated period. Most isolation systems have an effective period in the range of 1.50

to 2.50 seconds for DBE, with the longer periods tending to be used for high seismic zones.

It may not be possible to achieve a period near the upper limit if the isolators have light

loads.

2. The displacements and total displacements. The displacements are estimated values at

the center of mass and the total displacements, which include an allowance for torsion.

The latter values, at MCE loads, define the separation required around the building.

3. The force coefficient Vb/W is the maximum base shear force that will be transmitted

through the isolation system to the structure above. This is the base shear for elasticperformance but is necessarily the design base shear.

4. The design base shear coefficient is defined by UBC as the maximum of four cases:

a). The elastic base shear reduced by the isolated response modification factor VS =

VB/RI.

b). The yield force of the isolation system factored by 1.5.

c). The base shear corresponding to the wind load.



146

d). The coefficient required for a fixed base structure with a period equal to the isolated

period.

For this example, the second condition governs, 1.5 times the isolation yield level.

5. The performance summary also lists the equivalent viscous damping of the total isolation

system and the assoc iated damping reduction factor, B. Design should always aim for atleast 10% damping at both levels of earthquake and preferably 15%.

DBE MCE Comment

Effective Period TD TM 2.77 3.04

Displacement DD D M 181.2 252.4

Total Displacements D TD D TM 226.2 315.1

From

Seismic

Performance

Force C oefficient Vb / W 0.095 0.110 SA

Force C oefficient Vs/ W 0.048 SA / R I

1.5 x Yield Force / W 0.088 F Y/ W

Wind Force / W 0.013 Fw / W

Fixed Base V at TD 0.070 From UBC

Base Shear Force 10,785 MAX(Vs,Vy, Vw, VF)

x W (at DBE)

Damping eff 36.2% 32.3%

Damping Coefficients BD B M 1.82 1.74

From Seismic

Performance

Table 5.17: Summary of Seismic Performance

There is quite an art to the selection of final isolation design parameters. For example, in this

case damping is very high and could be decreased by reducing the lead core sizes in theLRBs. If the cores are reduced from 175 mm to 150 mm then the design shear force is

reduced from 0.088 to 0.071, approximately equal to the fixed base limit of 0.070. However,

the maximum MCE displacement is increased from 315 mm to 363 mm. The designer must

assess whether the decrease in design shear justifies the increased seismic displacement,

with assoc iated increases in separation gap and connection design forces.

5.4.13 Properties for Analysis

The properties developed as part of the design procedure are used to derive the stiffness

properties for analysis. Table 5.19 shows the calculations to provide properties as defined bythe ETABS computer program. Values are calculated for both the effective stiffness and non-

linear methods of analysis.



147

LRB TFE

First Data Line:

ID 1 2 Identification Number

ITYPE Isolator1 Isolator2 Biaxial Hysteretic/Linear/Friction

KE2 1.67 1.98

KE3 1.67 1.98

Spring Effective Stiffness

= K r* + Qd / D D

DE2 0.218 0.587

DE3 0.218 0.587

Spring Effective Damping Ratio

= - 0.05

Second Data Line:

K1 1595.8 5000.0 Spring Stiffness along Axis 1 (Axial)

K2 10.64 2000.00

K3 10.64 2000.00

Initial Spring Stiffness

= K u

FY2/K11/CFF2 210.41 0.10

FY3/K22/CFF3 210.41 0.10

Yield Force

= Fy for LRB = High Velocity for TFE

RK2/K33/CFS2 0.09 0.04

RK3/CFS3 0.09 0.04

Post-Yield Stiffness Ratio

= K r*/K u for LRB = Low Velocity for TFE

A2 0.90A3 0.90

Coefficient controlling friction= Coefficient a

R2 0.000

R3 0.000

Radius of Contact

= R for FPS devices

Table 5.19: Analysis Properties for ETABS

5.4.14 Hysteresis Properties

The design properties can also be used to develop the bi-linear hysteresis curve for eachtype of device. Table 5.20 lists the calculations for each point on the hysteresis curves, which

are plotted in Figure 5.8.

Disp Force Disp Force Comment

Yield Displacement, Y 19.78 0.00 Bearing Properties

Design Displacement, DD 252.4 252.4 DBE Performance

Yield Force, F Y 210.4 498.6 Bearing Properties

Origin 0 0 0 0 Start of Plot

Point A 19.8 213.9 0.0 498.6 = Y

F = F Y

Point B 252.4 421.9 252.4 498.6 = D D

F = QD + D DK r*Point C 212.9 -5.88 252.4 -498.6 = D D – 2 Y

F = QD + D DK r* - 2F Y

Point D -252.4 -421.9 -252.4 -498.6 = - D D

F = - QD - D DK r*

Point E -212.9 5.88 -252.4 498.6 = - D D + 2 Y

F = - QD - D DK r* + 2F Y

Point A 19.8 213.9 0.00 498.6 = Y

F = F Y

Table 5.20: Points on Hysteresis



148

-600

-400

-200

0

200

400

600

-300 -200 -100 0 100 200 300

SHEAR DISPLACEMENT (mm)

S H E A R F O R C E ( K N )

Lead Rubber

SliderA

E

C

B

Figure 5.8: Hysteresis Curves



150

The eight storey building was modeled with periods of 0.50 and 1.00 seconds,

corresponding respectively to a stiff URM type building and a stiff moment frame, bracedframe or structural wall building.

The height and period range of the prototypes have been restricted to low to mid-rise

buildings with relatively short periods for their height. This is the type of building that is most

likely to be a candidate for base isolation.

6.1.2 Design of Isolators

A total of 32 variations of five types of isolation system were used for the evaluation. The

designs were completed using the Holmes UBC Template.xls spreadsheet which implements

the design procedures described later in these guidelines. For most systems the solution

procedure is iterative; a displacement is assumed, the effective period and damping iscalculated at this displacement and the spectral displacement at this period and damping

extracted. The displacement is then adjusted until the spec tral displacement equals the trial

displacement.

Each system was designed to the point of defining the required stiffness and strength

properties required for evaluation, as shown in Figure 6.2.

3A T = 0.20 Seconds

3B T = 0.50 Seconds

5A T = 0.20 Seconds

5B T = 0.50 Seconds

5C T = 1.00 Seconds

8A T = 0.50 Seconds

8B T = 1.00 Seconds

Figure 6.1: Prototype Buildings

F o r c e

Deformation

K1

K2

f y

Figure 6.2: System Definition



151

The design basis for the isolation system design was a UBC seismic load using the factors listed

in Table 6.1. The site was assumed to be in the highest seismic zone, Z = 0.4, within 10 kms of a

Type A fault. This produced the design spectrum shown in Figure 6.3. The UBC requires two

levels of load, the Design Basis Earthquake (DBE) which is used to evaluate the structure and

the Maximum Capable Earthquake (MCE, formerly the Maximum Credible Earthquake)

which is used to obtain maximum isolator displacements.

Each system, other than the sliding bearings, was defined with effective periods of 1.5, 2.0,

2.5 and 3.0 seconds, which covers the usual range of isolation system period. Generally, thelonger period isolation systems will be used with flexible structures. The sliding system was

designed for a range of coefficients of friction.

Seismic Zone Factor, Z

Soil Profile Type

Seismic Coefficient, CA

Seismic Coefficient, CV

Near-Source Factor Na

Near-Source Factor Nv

0.4

SC

0.4000.672

1.000

1.200

Table 16.I

Table 16.J

Table 16.Q Table 16.R

Table 16.S

Table 16.T

MCE Shaking Intensity MMZNa

MCE Shaking Intensity MMZNv

0.484

0.581

Seismic Source Type

Distance to Known Source (km)

A

10.0

Table 16.U

MC E Response Coefficient, MM

Lateral Force Coefficient, RI

1.21

2.0

Table A-16.D

Table A-16.E

Fixed Base Lateral Force

Coefficient, RImportance Factor, I

3.0

1.0

Table 16.N

Table 16.K

Seismic Coefficient, CAM

Seismic Coefficient, CVM

0.484

0.813

Table A-16.F

Table A-16.G

Table 6.1: UBC Design Factors

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0.00 1.00 2.00 3.00 4.00

PERIOD (Seconds)

A c c e l e r a t i o n ( g )

UBC MCE

UBC DBE

Figure 6.3: UBC Design Spec trum



152

1. The ELASTIC system is an elastic spring with no damping. This type of system is not

practical unless used in parallel with supplemental dampers as displacements will be

large and the structure will move under service loads. However, it serves as a benchmark

analysis to evaluate the effect of the damping in the other systems. This is modeled as a

linear elastic spring with the yield level set very high.

2. The LRB is a lead rubber bearing. Variations were designed with three values of Qd,

corresponding to 0.05W, 0.075W and 0.010W. Qd is the force intercept at zero

displacement and defines the yield level of the isolator. For this type of bearing the

effective damping is a function of period and Qd and ranges from 8% to 37% for the

devices considered here.

3. HDR is a high damping rubber system. There are a large number of high damping

formulations available and each manufacturer typically provides a range of elastomers

with varying hardness and damping values. The properties are a function of the applied

shear strain. The properties used for this design were as plotted in Figure 6.4.

These properties represent a mid-range elastomer with a shear modulus of approximately

3 MPa at very low strains reducing to 0.75 MPa for a strain of 250%. The damping has a

maximum value of 19% at low strains, reducing to 14% at 250% strain. Most elastomeric

materials have strain-stiffening characteristics with the shear modulus increasing for strains

exceeding about 250%. If the bearings are to work within this range then this stiffening

has to be included in the design and evaluation.

The strain-dependent damping as plotted in Figure 6.4 is used to design the bearing. Foranalysis this is converted to an equivalent hysteresis shape. Although complex shapes

may be required for final design, the analyses here used a simple bi-linear representation

based on the approximations from FEMA-273. A yield displacement, y, is assumed at

0.05 to 0.10 times the rubber thickness and the intercept, Q, calculated from the

maximum displacement and effective stiffness as:

)(2

2

y

eff Q

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

4.0

0 50 100 150 200 250

SHEAR STRAIN (%)

S H E A R M O D U L U S ( M P a )

0

2

4

6

8

10

12

14

16

18

20

E Q U I V A L E N T D A M P I N G ( % )

Shear Modulus

Damping

Figure 6.4: HDR Elastomer Properties



153

The damping for these bearings varies over a narrow range of 15% to 19% for the isolator

periods included here.

4. PTFE is a sliding bearing system. Sliding bearings generally comprise a sliding surface of a

self-lubricating polytetrafluoroethylene (PTFE) surface sliding across a smooth, hard,

noncorrosive mating surface such as stainless steel. (Teflon ©is a trade name for a brandof PTFE). These bearings are modeled as rigid-perfectly plastic elements (k1 =, K 2 = 0).A range of coefficients of friction, m, was evaluated. The values of = 0.06, 0.09, 0.12

and 0.15 encompass the normal range of sliding coefficients. Ac tual sliding bearing

coefficients of friction are a func tion of normal pressure and the veloc ity of sliding. Forfinal analysis, use the spec ial purpose ANSR-L element that includes this variability.

For this type of isolator the coefficient of friction is the only variable and so design cannot

target a specific period. The periods as designed are calculated based on the secant

stiffness at the calculated seismic displacement. The hysteresis is a rectangle thatprovides optimum equivalent damping of 2/ = 63.7%.

5. FPS is a patented friction pendulum system, which is similar to the PTFE bearing but whichhas a spherical rather than flat sliding surface. The properties of this type of isolator are

defined by the radius of curvature of the bowl, which defines the period, and the

coefficient of friction. Two configurations were evaluated, using respectively, coefficients

of friction of 0.06 and 0.12. Bowl radii were set to provide the same range of periods as

for the other isolator types. Equivalent viscous damping ranged from 9% to 40%, a similar

range to the LRBs considered.

These bearings are modeled as rigid-strain hardening elements (k1 =, K 2 > 0). As for the

PTFE bearings, the evaluation procedure was approximate and did not consider

variations in the coefficient of friction with pressure and veloc ity. A final design and

evaluation would need to account for this.

Table 6.2 lists the variations considered in the evaluation and the hysteresis shape parametersused for modeling.



154

System Variation IsolatedPeriod

(Seconds)

(%) (mm)C k 1

(KN/mm)k 2

(KN/mm)f y

NONE 0.0 0% 0 100000 0 100000ELASTIC

ELASTIC

ELASTIC

ELASTIC

1.5

2.0

2.5

3.0

5%

5%

5%

5%

250

334

417

501

0.447

0.336

0.269

0.234

8.94

5.03

3.22

2.34

8.94

5.03

3.22

2.34

100000

100000

100000

100000

LRB

LRB

LRB

LRB

Qd=0.050 1.5

2.0

2.5

3.0

8%

11%

15%

20%

230

272

310

342

0.417

0.273

0.199

0.153

62.83

32.82

19.87

12.82

7.98

4.10

2.40

1.49

287

287

287

287

LRBLRB

LRBLRB

Qd=0.075 1.52.0

2.53.0

13%20%

26%31%

194229

262295

0.3490.227

0.1680.134

60.5228.94

15.969.81

7.053.30

1.770.96

426426

426426

LRBLRB

LRB

LRB

Qd=0.100 1.52.0

2.5

3.0

20%28%

33%

37%

167203

240

276

0.2990.206

0.156

0.128

55.1024.72

11.56

6.83

5.962.60

1.14

0.41

562562

562

562

HDR

HDR

HDR

HDR

1.5

2.0

2.5

3.0

15%

16%

17%

19%

186

242

303

348

0.184

0.140

0.110

0.094

45.28

20.06

10.34

9.02

7.62

4.28

2.60

1.74

514

462

414

414

PTFE

PTFE

PTFEPTFE

=0.06

=0.09

=0.12=0.15

5.6

3.7

2.82.2

64%

64%

64%64%

467

312

234187

0.060

0.090

0.1200.150

500

500

500500

0

0

00

300

450

600750

FPS

FPS

FPS

FPS

=0.06 1.5

2.0

2.5

3.0

9%

13%

17%

21%

200

231

253

269

0.417

0.292

0.223

0.180

500

500

500

500

8.94

5.03

3.22

2.24

300

300

300

300

FPS

FPS

FPS

FPS

=0.12 1.5

2.0

2.5

3.0

21%

28%

34%

40%

135

150

159

164

0.359

0.270

0.222

0.193

500

500

500

500

8.94

5.03

3.22

2.24

600

600

600

600

Table 6.2: Isolation System Variations



155

Figure 6.5 plots the hysteresis curves for all isolator types and variations included in this

evaluation. The elastic isolators are the only type which have zero area under the hysteresis

curve, and so zero equivalent viscous damping. The LRB and HDR isolators produce a bi-

linear force displacement function with an elastic stiffness and a yielded stiffness. The PTFE

and FPS bearings are rigid until the slip force is reached and the stiffness then reduces to zero

(PTFE) or a positive value (FPS).

It is important to note that these designs are not necessarily optimum designs for a particular

isolation system type and in fact almost surely are not optimal. In particular, the HDR and FPS

bearings have proprietary and/or patented features that need to be taken into account in

final design. You should get technical advice from the manufac turer for these types of

bearing.

The UBC requires that isolators without a restoring force be designed for a displacement

three times the calculated displacement. A system with a restoring force is defined as one in

which the force at the design displacement is at least 0.025W greater than the force at 0.5

times the design displacement. This can be checked from the values in Table 6.2 as R = (k2 x

0.5)/W. The only isolators which do not have a restoring force are the LRB with Qd = 0.100

and an isolated period of 3 seconds and all the sliding (PTFE) isolation systems.

ELASTIC ISOLATORS

-3000

-2000

-1000

0

1000

2000

3000

-600 -400 -200 0 200 400 600

DISPLACEMENT (mm)

F O R C E ( K N )

T=1.5 T=2.0

T=2.5 T=3.0

LEAD RUBBER BEARINGS Qd = 0.05

-3000

-2000

-1000

0

1000

2000

3000

-400 -200 0 200 400

DISPLACEMENT (mm)

F O R C E ( K N )

T=1.5 T=2.0

T=2.5 T=3.0


-2000

-1500

-1000

-500

0

500

1000

1500

2000

-400 -300 -200 -100 0 100 200 300 400

DISPLACEMENT (mm)

F

O R C E ( K N )

T=1.5 T=2.0

T=2.5 T=3.0


-2000

-1500

-1000

-500

0

500

1000

1500

2000

-400 -300 -200 -100 0 100 200 300 400

DISPLACEMENT (mm)

F

O R C E ( K N )

T=1.5 T=2.0

T=2.5 T=3.0



156

Figure 6.5: Isolation System Hysteresis

6.1.3 Evaluation Procedure

As discussed later, the procedures for evaluating isolated structures are, in increasing order of

complexity, (1) static analysis, (2) response spectrum analysis and (3) time-history analysis.

The static procedure is permitted for only a very limited range of buildings and isolationsystems and so the response spec trum and time-history analyses are the most commonly

used methods. There are some restrictions on the response spec trum method of analysis thatmay preclude some buildings and/or systems although this is unusual. The time-history

method can be used without restriction. As the same model can be used for both types of

analysis it is often preferable to do both so as to provide a check on response predictions.

In theory, the response spectrum analysis is simpler to evaluate as it provides a single set ofresults for a single spec trum for each earthquake level and eccentricity. The time-history

method produces a set of results at every time step for at least three earthquake records,

and often for seven earthquake records. In practice, our output processing spreadsheetsproduce results in the same format for the two procedures and so this is not an issue. Also,

the response spectrum procedure is based on an effective stiffness formulation and so is

usually an iterative process. The effective stiffness must be estimated, based on estimated

displacements, and then adjusted depending on the results of the analysis.

HIGH DAMPING RUBBER BEARINGS

-2500

-2000

-1500

-1000

-500

0

500

10001500

2000

2500

-400 -200 0 200 400

DISPLACEMENT (mm)

F O R C E ( K N )

T=1.5 T=2.0

T=2.5 T=3.0

PTFE SLIDING BEARINGS

-1000

-800

-600

-400

-200

0

200

400600

800

1000

-600 -400 -200 0 200 400 600

DISPLACEMENT (mm)

F O R C E ( K N )

m=0.06 m=0.09

m=0.12 m=0.15

FRICTION PENDULUM BEARINGS m = 0.06

-3000

-2000

-1000

0

1000

2000

3000

-300 -200 -100 0 100 200 300

DISPLACEMENT (mm)

F O R C E ( K N )

T=1.5 T=2.0

T=2.5 T=3.0

FRICTION PENDULUM BEARINGS m = 0.12

-2000

-1500

-1000

-500

0

500

1000

1500

2000

-200 -100 0 100 200

DISPLACEMENT (mm)

F O R C E ( K N )

T=1.5 T=2.0

T=2.5 T=3.0



157

The evaluations here are based on both the response spectrum and the time-history method

of analysis, respectively termed the Linear Dynamic Procedure (LDP) and the Non-Linear

Dynamic Procedure (NDP) in FEMA-273.

Response Spectrum Analysis

The response spectrum analysis follows the usual procedure for this method of analysis withtwo modifications to account for the isolation system:

1. Springs are modeled to connect the base level of the structure to the ground. These

springs have the effective stiffness of the isolators. For most isolator systems, this stiffness is

a function of displacement – see Figure 6.6.

2. The response spectrum is modified to account for the damping provided in the isolated

modes. Some analysis programs (for example, ETABS) allow spectra for varying damping

to be provided, otherwise the 5% damped spectrum can be modified to use acomposite spectra which is reduced by the B factor in the isolated modes – see Figure

6.7.

SHEAR DISPLACEMENT

S H E A R F O R C E

Isolator Hysteresis

Effective Stiffness

Figure 6.6: Effec tive Stiffness

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 1.0 2.0 3.0 4.0

PERIOD (Seconds)

A C C E L E R A T I O N ( g ) 5%

Damped

Sa

Sa

B

Isolated

Period

Figure 6.7: Composite Response Spectrum



158

More detail for the response spectrum analysis based on effective stiffness and equivalent

viscous damping is provided in Chapter 10 of these guidelines.

Time History Analysis

Each building and isolation system combination was evaluated for three earthquake records,

the minimum number required by most codes. The record selec tion was not fully codecompliant in that only a single component was applied to a two-dimensional model and the

records selected were frequency scaled to match the design spectrum, as shown in Figure

6.8.

The frequency scaled records were chosen as these analyses are intended to compare

isolation systems and analysis methods rather than obtain design values. The time history

selection procedure specified by most codes results in seismic input which exceeds theresponse spectrum values and so would produce higher results than those reported here.

Figure 6.8: 5% Damped Spectra of 3 Earthquake Records

Each building model and damping system configuration was analyzed for the 20 second

duration of each record at a time step of 0.01 seconds. At each time step the accelerations

and displacements at each level were saved as were the shear forces in each storey. These

values were then processed to provide isolator displacements and shear forces, structural

drifts and total overturning moments.

6.1.4 Comparison with Design Procedure

The isolator performance parameters are the shear force coefficient, C, (the maximum

isolator force normalized by the weight of the structure) and the isolator displacement, .

The design procedure estimates these quantities based on a single mass assumption – see

Table 6.2.

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

0.000 1.000 2.000 3.000 4.000

PERIOD (Seconds)

A C C E L E R A T I O N ( g ) El Centro Seed

Olympia Seed

Taft Seed

Design Spectrum

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

0.000 1.000 2.000 3.000 4.000

PERIOD (Seconds)

A C C E L E R A T I O N ( g )

Envelope

Design Spectrum



159


The response spectrum results divided by the design estimates are plotted in Figure 6.9.

These values are the average over all buildings. Numerical results are listed in Table 6.3. A

value of 100% in Figure 6.9 indicates that the analysis matched the design procedure, avalue higher than 100% indicates that the time history provided a higher value than the

design procedure.

The response spectrum analysis displacements and shear coefficients were consistently lower

than the design procedure results with one exception. The results were lower by a relativelysmall amount. Both the shear coefficients and the displacements were generally from 0% to

10% lower than the predicted values. An exception was type H (High Damping Rubber)

where the differences ranged from +10% to –20%. This is because the design for these typeswas based on tabulated viscous damping whereas the analysis was based on an equivalent

hysteresis shape.

0%

20%

40%

60%

80%

100%

120%

E

T = 1 . 5

E

T = 2 . 5

L 1 T = 2 . 0

L 1 T = 3 . 0

L 2 T = 1 . 5

L 2 T = 2 . 5

L 3 T = 2 . 0

L 3 T = 3 . 0

H

T = 1 . 5

H

T = 2 . 5

P T = 2 . 8

P T = 5 . 6

F 1 T = 1 . 5

F 1 T = 2 . 5

F 2 T = 2 . 0

F 2 T = 3 . 0

Average Response Spectrum Displacement/ Design Value

Average Response Spectrum Shear Coefficient/Design Value

Figure 6.8: Isolator Results from Response Spectrum Analysis Compared to Design



160

DesignProcedure

ResponseSpectrumAnalysis

Time HistoryMaximum of

3 Earthquakes

System Variation Period(Seconds) (mm)

C(mm)

C(mm)

C

NONE 0 0.678 1.551

ELAST

ELAST

ELAST

ELAST

1.5

2.0

2.5

3.0

250

334

417

501

0.447

0.336

0.269

0.234

236

323

409

483

0.423

0.325

0.263

0.225

309

369

434

528

0.552

0.371

0.279

0.247

LRB

LRB

LRB

LRB

Qd=0.050 1.5

2.0

2.5

3.0

230

272

310

342

0.417

0.273

0.199

0.153

206

256

295

325

0.379

0.260

0.192

0.148

144

213

269

344

0.280

0.225

0.180

0.153

LRBLRB

LRB

LRB

Qd=0.075 1.52.0

2.5

3.0

194229

262

295

0.3490.227

0.168

0.134

175212

248

278

0.3220.216

0.164

0.130

140195

258

332

0.2720.204

0.167

0.141

LRB

LRB

LRB

LRB

Qd=0.100 1.5

2.0

2.5

3.0

167

203

240

276

0.299

0.206

0.156

0.128

152

190

226

258

0.282

0.199

0.153

0.127

140

197

269

384

0.267

0.203

0.163

0.137

HDR

HDRHDR

HDR

1.5

2.02.5

3.0

186

242303

348

0.184

0.1400.110

0.094

206

212270

279

0.366

0.2540.202

0.165

148

177269

320

0.277

0.2250.202

0.179

PTFE

PTFE

PTFE

PTFE

=0.15

=0.12

=0.09

=0.06

2.2

2.8

3.7

5.6

187

234

312

467

0.150

0.120

0.090

0.060

177

225

305

0.149

0.120

0.090

204

223

309

430

0.150

0.120

0.090

0.060

FPS

FPS

FPS

FPS

=0.06 1.5

2.0

2.5

3.0

200

231

253

269

0.359

0.270

0.222

0.193

179

216

239

259

0.328

0.255

0.213

0.188

124

160

199

228

0.280

0.221

0.188

0.162

FPSFPS

FPSFPS

=0.12 1.52.0

2.53.0

135150

159164

0.3280.255

0.2130.188

117135

145152

0.3810.277

0.2140.176

103111

122130

0.3010.231

0.1980.178

Table 6.3: Isolation System Performance (Maximum of All Buildings, All Earthquakes)



161

The c lose correlation between the two methods is not surprising as they are both based on

the same concepts of effective stiffness and equivalent viscous damping. The main

difference is that the design procedure assumes a rigid structure above the isolators whereas

the response spec trum analysis includes the effect of building flexibility.

The effect of building flexibility is illustrated by Figure 6.10, which plots the ratio of response

spectrum results to design procedure values for the lead rubber bearing (LRB 1) with a period

of 1.5 seconds. Figure 6.9 shows that the average ratio for this system is 90% of the design

values. However, Figure 6.10 shows that the ratio actually ranges from 97% for buildings with

a period of 0.2 seconds to 77% for the building with a 1.0 second period.

As the building period increases the effects of building flexibility become more important and

so the response spec trum values diverge from the design procedure results. The effects

shown in Figure 6.10 tend to be consistent in that for all systems the base displacement and

base shear coefficient was lower for the buildings with longer periods. The only exception

was for the sliding systems (PTFE) where the shear coefficient remained constant, at a value

equal to the coefficient of friction of the isolators.


The ratios of the displacements and shear coefficients from the time history analysis to the

values predicted by the design procedure are plotted in Figure 6.11. Two cases are plotted

(a) the maximum values from the three time histories and (b) the average values from the

three time histories. In each case, the values are averaged over the 7 building

configurations.

The time history results varied from the design procedure predictions by a much greater

amount than the response spectrum results, with discrepancies ranging from +40% to -40% for

the maximum results and from +20% to –42% for the mean results. For the elastic systems the

time history analysis results tended to be closer to the design procedure results as the period

increased but this trend was reversed for all the other isolation system types. As the elastic

system is the only one which does not use equivalent viscous damping this suggests that

there are differences in response between hysteretic damping and a model using the

viscous equivalent.

0%

20%

40%

60%

80%

100%

120%

3

STORY

T=0.2

3

STORY

T=0.5

5

STORY

T=0.2

5

STORY

T=0.5

5

STORY

T=1.0

8

STORY

T=0.5

8

STORY

T=1.0

Response Spectrum Displacement/ Design Value

Response Spectrum Shear Coefficient/ Design Value

Figure 6.9: Spectrum Results for LRB1 T=1.5 Seconds



162

As the period increases for the hysteretic systems, the displacement also increases and the

equivalent viscous damping dec reases. The results in Figure 6.11 suggest that the viscous

damping formulation is more accurate for large displacements than for small displacements.

0%

20%

40%

60%

80%

100%

120%

140%

160%

E

T = 1 . 5

E

T = 2 . 5

L 1 T = 2 . 0

L 1 T = 3 . 0

L 2 T = 1 . 5

L 2 T = 2 . 5

L 3 T = 2 . 0

L 3 T = 3 . 0

H

T = 1 . 5

H

T = 2 . 5

P T = 2 . 8

P T = 5 . 6

F 1 T = 1 . 5

F 1 T = 2 . 5

F 2 T = 2 . 0

F 2 T = 3 . 0

Maximum Time History Displacement/Design Value

Maximum Time History Shear Coefficient/Design Value

Figure 6.10: Isolator Results from Time History Analysis Compared to Design

(A) Maximum From Time History Analysis

0%

20%

40%

60%

80%

100%

120%

140%

E

T = 1 . 5

E

T = 2 . 5

L 1 T = 2 . 0

L 1 T = 3 . 0

L 2 T = 1 . 5

L 2 T = 2 . 5

L 3 T = 2 . 0

L 3 T = 3 . 0

H

T = 1 . 5

H

T = 2 . 5

P T = 2 . 8

P T = 5 . 6

F 1 T = 1 . 5

F 1 T = 2 . 5

F 2 T = 2 . 0

F 2 T = 3 . 0

Average Time History Displacement/Design Value

Average Time History Shear Coefficient/Design Value

(B) Mean From Time History Analysis



163

Figure 6.12 plots the ratios based on the maximum values from the three earthquakes

compared to the design procedure values for the lead rubber bearing (LRB 1) with a period

of 1.5 seconds (compare this figure with Figure 6.10 which provides the similar results from the

response spectrum analysis). Figure 6.12 suggests that results are relatively insensitive to the

period of the structure above the isolators. However, Figure 6.12, which plots the results for

the individual earthquakes, shows that for EQ 1 and EQ 3 the results for the 1.0 second period

structures are less than for the stiffer buildings, as occurred for the response spectrum analysis.However, this effect is masked by EQ 2 which produces a response for the 1.0 second period

structures which is much higher than for the other buildings. This illustrates that time history

response can vary considerably even for earthquake records which apparently provide very

similar response spec tra.

The mean time history results show that the design procedure generally provided a

conservative estimate of isolation system performance except for the elastic isolation system,

where the design procedure under-estimated displacements and shear forces, especially for

short period isolation systems.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

3

STORY

T=0.2

3

STORY

T=0.5

5

STORY

T=0.2

5

STORY

T=0.5

5

STORY

T=1.0

8

STORY

T=0.5

8

STORY

T=1.0

Time History Displacement/Design Value

Time History Shear Coefficient/Design Value

Figure 6.11: Time History Results for LRB1 T=1.5 Sec

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

3

STORY

T=0.2

3

STORY

T=0.5

5

STORY

T=0.2

5

STORY

T=0.5

5

STORY

T=1.0

8

STORY

T=0.5

8

STORY

T=1.0

EQ 1 Displacement Ratio



Figure 6.12: Variation Between Earthquakes



164

6.1.5 Isolation System Performance

The mean and maximum results from the three time histories were used above to compare

displacements and base shear coefficients with the design procedure and the response

spectrum procedure. For design, if three time histories are used then the maximum ratherthan the mean values are used. (Some codes permit mean values to be used for design if at

least 7 earthquakes are used).

Table 6.3 listed the average isolation response over the 7 building configurations for each

system. These results are plotted in Figures 6.14 and 6.15, which compare respectively theshear coefficients and displacements for each isolation system for both the response

spectrum method and the time history method.

The plots show that although both methods of analysis follow similar trends for mostisolation systems, the response spectrum results are higher in many cases. This is

consistent with the comparisons with the design proc edure discussed earlier, where the

time history tended to produce ratios that were lower than the response spectrum.

For all isolation systems, the base shear coefficient decreases with increasing period and

the displacement increases. This is the basic tradeoff for all isolation system design.

The PTFE (sliding) bearings produce the smallest shear coefficients and the smallest

displacements of all systems except the FPS. However, as these bearings do not have a

restoring force the design displacements are required to be increased by a factor of 3.

With this multiplier the PTFE displacements are higher than for all other isolator types.

There are relatively small variations between the three types of Lead Rubber Bearings

(LRB). For these systems the yield force is increased from 5% W to 7.5% W to 10% W for

systems 1, 2 and 3 respec tively. The LRB systems produce the smallest shear coeffic ientsafter the PTFE sliders.

The two Friction Pendulum Systems (FPS) variations are the values of the coefficient of

friction, 0.06 for Type 1 and 0.12 for Type 2. The increased coefficient of friction has little

effect on the base shear coefficients but reduces displacements. The FPS with = 0.12

produces the smallest displacements of any system.

There is no one optimum system, or isolated period, in terms of minimizing both base shear

coefficient and displacement. This isolator performance in only one aspect in selecting a

system, the performance of the structure above is usually of at least equal performance. This

is examined in the following sections and then well-performing systems are identified in terms

of parameters that may be important depending on project objectives.



165

0.00

0.10

0.20

0.30

0.40

0.50

0.60

E L A S T = 1 . 5

E L A S T = 2 . 5

L R B 1 T = 2 . 0

L R B 1 T = 3 . 0

L R B 2 T = 1 . 5

L R B 2 T = 2 . 5

L R B 3 T = 2 . 0

L R B 3 T = 3 . 0

H D R

T = 1 . 5

H D R

T = 2 . 5

P T F E

T = 2 . 8

P T F E

T = 5 . 6

F P S 1 T = 1 . 5

F P S 1 T = 2 . 5

F P S 2 T = 2 . 0

F P S 2 T = 3 . 0

B A S E S H E A R C O E F F I C I E

N T Response Spectrum

Time History

Figure 6.13: Isolator Performance: Base Shear Coefficients

0

100

200

300

400

500

600

E L A S T = 1 . 5

E L A S T = 2 . 5

L R B 1 T = 2 . 0

L R B 1 T = 3 . 0

L R B 2 T = 1 . 5

L R B 2 T = 2 . 5

L R B 3 T = 2 . 0

L R B 3 T = 3 . 0

H D R

T = 1 . 5

H D R

T = 2 . 5

P T F E

T = 2 . 8

P T F E

T = 5 . 6

F P S 1 T = 1 . 5

F P S 1 T = 2 . 5

F P S 2 T = 2 . 0

F P S 2 T = 3 . 0

I S O L A T O R D I S P L A C E M E N T ( m m

)

Response Spectrum

Time History

Figure 6.14: Isolator Performance : Isolator Displacements



166

6.1.6 Building Inertia Loads

The isolation system response provides the maximum base shear coefficient that is the

maximum simultaneous summation of the inertia forces from all levels above the isolator

plane. The distribution of these inertia forces within the height of the structure defines thedesign shears at each level and the total overturning moments on the structure.


The inertia forces are obtained from the response spectrum analyses as the CQC of theindividual modal responses, where modal inertia forces are the product of the spectral

acceleration in that mode times the participation factor times the mass. Figure 6.16 plots

these distributions for three building configurations, each for one isolator effective period.

The combinations of building period and isolator period have been selected as typical

values that would be used in practice.

Figure 6.16 shows that the inertia force distributions for the buildings without isolation

demonstrate an approximately linear increase with height, compared to the triangular

distribution assumed by most codes for a uniform building with no devices. Note that the

fixed base buildings have an inertia force at the base level. This is because a rigid spring was

used in place of the isolation system for these models and the base mass was included. As

all modes were extracted this spring mode has acceleration equal to the ground

acceleration and so generates an inertia force.

All isolation systems exhibit different distributions from the non-isolated building in that the

inertia forces are almost constant with the height of the building for all buildings. Some

systems show a slight increase in inertia force with height but this effec t is small and so for all

systems the response spectrum results suggest that a uniform distribution would best representthe inertia forces. As the following sec tion describes, the results from the time history analysis

were at variance with this assumption.



167

3 Story Building T = 0.2 Seconds Ti = 2.0 Seconds

0 500 1000 1500 2000

F0

F1

F2

F3

INERTIA FORCE (KN)

FPS 2

FPS 1

PTFE

HDR

LRB 2

LRB 1

Elastic

No Devices


0 200 400 600 800 1000 1200

F0

F1

F2

F3

F4

F5

INERTIA FORCE (KN)

FPS 2FPS 1

PTFE

HDR

LRB 2

LRB 1

Elastic

No Devices


0 100 200 300 400 500 600

F0

F1

F2

F3

F4

F5

F6

F7

F8

INERTIA FORCE (KN)

FPS 2

FPS 1

PTFE

HDR

LRB 2

LRB 1

Elastic

No Devices

Figure 6.15: Response Spectrum Inertia Forces


As discussed above, for a fixed base regular building most codes assumed that the

distribution of inertia load is linear with height, a triangular distribution based on the

assumption that first mode effects will dominate response. This distribution has an effectiveheight at the centroid of the triangle, that is, two-thirds the building height above the base

for structures with constant floor weights. A uniform distribution of inertia loads would have a

centroid at one-half the height.

The effective height was calculated for each configuration analyzed by selecting the

earthquake which produced the highest overturning moment about the base and

calculating the effective height of application of inertia loads as Hc = M/VH, where M is the

moment, V the base shear and H the height of the building. Figure 6.17 plots Hc for the fixed

base configuration of each of the building models.



168

Although there were some variations between buildings, these results show that the

assumption of a triangular distribution is a reasonable approximation and produces a

conservative overturning moment for most of the structures considered in this study.

An isolation system produces fundamental modes comprising almost entirely of deformationsin the isolators with the structure above moving effectively as a rigid body with small

deformations. With this type of mode shape it would be expected that the distribution of

inertia load with height would be essentially linear with an effective height of application ofone-half the total height, as was shown above for the response spectrum analysis results.

Figure 6.18 plots the effective heights of inertia loads, Hc, for the 8 isolation system variationsconsidered in this study. Each plot contains the effec tive period variations for a particular

device. Each plot has three horizontal lines

1. Hc = 0.50, a uniform distribution

2. Hc = 0.67, a triangular distribution

3. Hc = 1.00, a distribution with all inertia load concentrated at roof level.

0.00

0.10

0.20

0.30

0.40

0.50

0.600.70

0.80

3 T = 0 . 2

3 T = 0 . 5

5 T = 0 . 2

5 T = 0 . 5

5 T = 1 . 0

8 T = 0 . 5

8 T = 1 . 0

H E I G H T O F I N T E R I A L O A

D / H

No Devices

Triangular

Figure 6.16: Height of Inertia Loads



169

Figure 6.17: Effective Height of Inertia Loads for Isolation Systems

0.00

0.20

0.40

0.60

0.80

1.00

1.20

3 T = 0 . 2

3 T = 0 . 5

5 T = 0 . 2

5 T = 0 . 5

5 T = 1 . 0

8 T = 0 . 5

8 T = 1 . 0

H E I G H T O F I N E R T I A L

O A D / H

ELAST T=1.5 ELAST T=2.0ELAST T=2.5 ELAST T=3.0Uniform Triangular

0.00

0.20

0.40

0.60

0.80

1.00

1.20

3 T = 0 . 2

3 T = 0 . 5

5 T = 0 . 2

5 T = 0 . 5

5 T = 1 . 0

8 T = 0 . 5

8 T = 1 . 0

H E I G H T O F I N E R T I A

L O A D / H

LRB 2 T=1.5 LRB 2 T=2.0 LRB 2 T=2.5LRB 2 T=3.0 Uniform Triangular Top

0.00

0.20

0.40

0.60

0.80

1.00

1.20

3 T = 0 . 2

3 T = 0 . 5

5 T = 0 . 2

5 T = 0 . 5

5 T = 1 . 0

8 T = 0 . 5

8 T = 1 . 0

H E I G H T O F I N E R T I A L O A D / H

HDR T=1.5 HDR T=2.0 HDR T=2.5HDR T=3.0 Uniform Triangular Top

0.00

0.50

1.00

1.50

2.00

2.50

3 T = 0 . 2

3 T = 0 . 5

5 T = 0 . 2

5 T = 0 . 5

5 T = 1 . 0

8 T = 0 . 5

8 T = 1 . 0

H E I G H T O F I N E R T I A L O A D / H

PTFE T=2.2 PTFE T=2.8 PTFE T=3.7PTFE T=5.6 Uniform Triangular Top

0.00

0.20

0.40

0.60

0.80

1.00

1.20

3 T = 0 . 2

3 T = 0 . 5

5 T = 0 . 2

5 T = 0 . 5

5 T = 1 . 0

8 T = 0 . 5

8 T = 1 . 0


L O A D / H


0.00

0.20

0.40

0.60

0.80

1.00

1.20

3 T = 0 . 2

3 T = 0 . 5

5 T = 0 . 2

5 T = 0 . 5

5 T = 1 . 0

8 T = 0 . 5

8 T =

1 . 0

H E I G H T O F I N E R

T I A

L O A D /

H

FPS 1 T=1.5 FPS 1 T=2.0 FPS 1 T=2.5FPS 1 T=3.0 Uniform Triangular Top

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

3 T = 0 . 2

3 T = 0 . 5

5 T = 0 . 2

5 T = 0 . 5

5 T = 1 . 0

8 T = 0 . 5

8 T =

1 . 0


L O A D /

H

FPS 2 T=1.5 FPS 2 T=2.0 FPS 2 T=2.5FPS 2 T=3.0 Uniform Triangular Top

0.00

0.20

0.40

0.60

0.80

1.00

1.20

3 T = 0 . 2

3 T = 0 . 5

5 T = 0 . 2

5 T = 0 . 5

5 T = 1 . 0

8 T = 0 . 5

8 T =

1 . 0


L O

A D /

H




171

The FPS 2 isolators (higher coefficient of friction) produce a shear distribution that has the

shape of an inverted triangle, with maximum inertia forces at the base and then reducing

with height. The distribution producing the maximum moment has a similar form to the PTFE

plots, exhibiting reversed signs on the inertia loads near the base. The FSP 1 isolators (lower

coefficient of friction) also show this reversed sign for the moment distribution.

5 Storey Building (Figure 6.20)

The distributions for the 5 storey building follow the trends in the 3 storey building but tend to

be more exaggerated. The elastic isolators still produce uniform distributions but all others

have distributions for moment which are weighted toward the top of the building, extremely

so for the sliding bearings.

8 Storey Building (Figure 6.21)

The 8 storey buildings also follow the same trends but in this case even the elastic isolator

moment distribution is tending toward a triangular distribution.

These results emphasize the limited application of a static force procedure for the analysis

and design of base isolated buildings as the distributions vary widely from the assumed

distributions. A static procedure based on a triangular distribution of inertia loads would benon-conservative for all systems in Figure 6.18 in which the height ratio exceeded 0.67. This

applies to about 25% of the systems considered, including all the flat sliding systems (PTFE).



172

NO DEVICES 1 T=0.0

0 500 1000 1500 2000 2500 3000 3500

L0

L1

L2

L3

Inertia Force (KN)

Max Shear

Max Moment

Elastic 1 T=2.0

0 500 1000 1500 2000 2500 3000 3500

L0

L1

L2

L3

Inertia Force (KN)

Max Shear

Max Moment

LRB 1 T=2.0

0 500 1000 1500 2000 2500 3000 3500

L0

L1

L2

L3

Inertia Force (KN)

Max Shear

Max Moment

LRB 2 T=2.0

0 500 1000 1500 2000 2500 3000 3500

L0

L1

L2

L3

Inertia Force (KN)

Max Shear

Max Moment

HDR 1 T=2.0

0 500 1000 1500 2000 2500 3000 3500

L0

L1

L2

L3

Inertia Force (KN)

Max Shear

Max Moment

PTFE 1 T=2.8

-100

0

-500 0 500 1000 1500 2000 2500 3000 3500

L0

L1

L2

L3

Inertia Force (KN)

Max Shear

Max Moment

FPS 1 T=2.0

-500 0 500 1000 1500 2000 2500 3000 3500

L0

L1

L2

L3

Inertia Force (KN)

Max Shear

Max Moment

FPS 2 T=2.0

-500 0 500 1000 1500 2000 2500 3000 3500

L0

L1

L2

L3

Inertia Force (KN)

Max Shear

Max Moment

Figure 6.17: Time History Inertia Forces: 3 storey Building T = 0.2 Seconds



173

NO DEVICES 1 T=0.0

0 500 1000 1500 2000 2500

L0

L2

L4

Inertia Force (KN)

Max Shear

Max Moment

Elastic 1 T=2.5

0 500 1000 1500 2000 2500

L0

L2

L4

Inertia Force (KN)

Max Shear

Max Moment

LRB 1 T=2.5

0 500 1000 1500 2000 2500

L0

L2

L4

Inertia Force (KN)

Max ShearMax Moment

LRB 2 T=2.5

-500 0 500 1000 1500 2000 2500

L0

L2

L4

Inertia Force (KN)

Max ShearMax Moment

HDR 1 T=2.5

0 500 1000 1500 2000 2500

L0

L2

L4

Inertia Force (KN)

Max Shear

Max Moment

PTFE 1 T=3.7

-500 0 500 1000 1500 2000 2500

L0

L2

L4

Inertia Force (KN)

Max Shear

Max Moment

FPS 1 T=2.5

-500 0 500 1000 1500 2000 2500

L0

L2

L4

Inertia Force (KN)

Max Shear

Max Moment

FPS 2 T=2.5

-500 0 500 1000 1500 2000 2500

L0

L2

L4

Inertia Force (KN)

Max Shear

Max Moment

Figure 6.18: Time History Inertia Forces 5 Storey Building T = 0.5 Seconds



174

NO DEVICES 1 T=0.0

-200 0 200 400 600 800 1000

L0

L2

L4

L6

L8

Inertia Force (KN)

Max Shear

Max Moment

Elastic 1 T=3.0

0 200 400 600 800 1000

L0

L2

L4

L6

L8

Inertia Force (KN)

Max Shear

Max Moment

LRB 1 T=3.0

0 200 400 600 800 1000

L0

L2

L4

L6

L8

Inertia Force (KN)

Max Shear

Max Moment

LRB 2 T=3.0

-200 0 200 400 600 800 1000

L0

L2

L4

L6

L8

Inertia Force (KN)

Max Shear

Max Moment

HDR 1 T=3.0

-200 0 200 400 600 800 1000

L0

L2

L4

L6

L8

Inertia Force (KN)

Max Shear

Max Moment

PTFE 1 T=5.6

-400 -200 0 200 400 600 800 1000

L0

L2

L4

L6

L8

Inertia Force (KN)

Max Shear

Max Moment

FPS 1 T=3.0

-200 0 200 400 600 800 1000

L0

L2

L4

L6

L8

Inertia Force (KN)

Max Shear

Max Moment

FPS 2 T=3.0

-200 0 200 400 600 800 1000

L0

L2

L4

L6

L8

Inertia Force (KN)

Max Shear

Max Moment

Figure 6.19: Time History Inertia Forces 8 storey Building T = 1.0 Seconds



175

6.1.7 Floor Accelerations

The objective of seismic isolation is to reduce earthquake damage, which includes not only

the structural system but also non-structural items such as building parts, components andcontents. Of prime importance in attenuating non-structural damage is the reduction of

floor accelerations.


The floor accelerations from the response spectrum analysis are proportional to the floor

inertia forces, as shown in Figure 6.22. The accelerations for the building without devicesincrease approximately linear with height, from a base level equal to the maximum ground

acceleration (0.4g) to values from 2.5 to 3 times this value at the roof (1.0g to 1.2g). The

isolated displacements in all cases are lower than the 0.4g ground acceleration and exhibitalmost no increase with height.


0.000 0.200 0.400 0.600 0.800 1.000 1.200 1.400

F0

F1

F2

F3

ACCELERATION (g)

FPS 2

FPS 1

PTFE

HDR

LRB 2

LRB 1

Elastic

No Devices


0.000 0.500 1.000 1.500

F0

F1

F2

F3

F4

F5

ACCELERATION (g)

FPS 2

FPS 1

PTFE

HDR

LRB 2

LRB 1

ElasticNo Devices


0.000 0.200 0.400 0.600 0.800 1.000 1.200

F0

F1

F2

F3

F4

F5

F6

F7

F8

ACCELERATION (g)

FPS 2

FPS 1

PTFE

HDR

LRB 2

LRB 1

Elastic

No Devices

Figure 6.20: Response Spectrum Floor Accelerations



176


Plots of maximum floor accelerations for three building configurations, one of each height,

are provided in Figures 6.23, 6.24 and 6.25. These are the same building and isolation system

configurations for which the inertia forces are plotted in Figures 6.19 to 6.21. All plots are the

maximum values from any of the three earthquakes. They include the accelerations in the

building with no isolation as a benchmark. The acceleration at Elevation 0.0, ground level, is

the peak ground acceleration from the three earthquakes, which is constant at 0.56g.

The most obvious feature of the plots is that most isolation systems do not provide theessentially constant floor accelerations developed from the response spectrum analysis in

Figure 6.22. There are differences between isolation systems but the trends for each system

tend to be similar for each building.

The elastic (E) isolation bearings provide the most uniform distribution of acceleration. Asthe period of the isolators increases, the accelerations decrease. The longest period, 3.0

seconds, produces accelerations in the structure equal to about one-half the ground

ac celeration and as the period reduces to 1.5 seconds, the accelerations in the structure

are about equal to the ground acceleration. As the building period increases the shortperiod isolators show some amplification with height but this is slight.

The lead rubber bearings (L) produce distributions which are generally similar to those for

the elastic bearings but tend to produce higher amplifications at upper levels. The

amplification increases as the yield level of the isolation system increases (L1 to L2 to L3

have yield levels increasing from 5% to 7.5% to 10% of W). Again as for the elastic

bearings, the accelerations are highest for the shortest isolated periods.

The PTFE sliding bearings (T) tend to increase the ground accelerations from base level

with some amplification with height. Accelerations increase as the coefficient of friction

increases, that is, as the effective isolated period reduces.

The friction pendulum bearings (F) produce an acceleration profile which, unlike the

other types, is relatively independent of the isolated period. This type of isolator is more

effective in reducing accelerations for the coefficient of friction of 0.06 (F 1) compared to

the 0.12 coefficient (F 2). The accelerations are generally higher than for the elastic or

lead rubber systems.

Although some systems produce amplification with height and may increase acceleration

over the ground value, all isolation systems drastically reduce accelerations compared to the

building without isolators by a large margin although, as the plots show, the system type andparameters must be selected to be appropriate for the building type.



177

Figure 6.21: Floor Accelerations 3 Storey Building T = 0.2 Seconds

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0.00 0.50 1.00 1.50 2.00 2.50 3.00

ACCELERATION (g)

E L E V A T I O N

( m )

No Isolators

E 1 T=1.5

E 1 T=2.0

E 1 T=2.5

E 1 T=3.0 0.0

2.0

4.0

6.0

8.0

10.0

12.0

0.00 0.50 1.00 1.50 2.00 2.50 3.00

ACCELERATION (g)

E L E V A T I O

N ( m )

No Isolators

L 1 T=1.5

L 1 T=2.0

L 1 T=2.5

L 1 T=3.0

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0.00 0.50 1.00 1.50 2.00 2.50 3.00

ACCELERATION (g)

E L E V A

T I O N ( m )

No Isolators

L 2 T=1.5

L 2 T=2.0

L 2 T=2.5

L 2 T=3.0 0.0

2.0

4.0

6.0

8.0

10.0

12.0

0.00 0.50 1.00 1.50 2.00 2.50 3.00

ACCELERATION (g)

E L E V A T I O N ( m )

No Isolators

L 3 T=1.5L 3 T=2.0

L 3 T=2.5

L 3 T=3.0

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0.00 0.50 1.00 1.50 2.00 2.50 3.00

ACCELERATION (g)

E L E V

A T I O N ( m )

No Isolators

H 1 T=1.5H 1 T=2.0

H 1 T=2.5

H 1 T=3.0 0.0

2.0

4.0

6.0

8.0

10.0

12.0

0.00 0.50 1.00 1.50 2.00 2.50 3.00

ACCELERATION (g)

E L

E V A T I O N ( m )

No Isolators

T 1 T=2.2

T 1 T=2.8 T 1 T=3.7

T 1 T=5.6

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0.00 0.50 1.00 1.50 2.00 2.50 3.00

ACCELERATION (g)

E L E V A T

I O N ( m )

No IsolatorsF 2 T=1.5

F 2 T=2.0

F 2 T=2.5

F 2 T=3.00.0

2.0

4.0

6.0

8.0

10.0

12.0

0.00 0.50 1.00 1.50 2.00 2.50 3.00

ACCELERATION (g)


No Isolators

F 1 T=1.5F 1 T=2.0

F 1 T=2.5

F 1 T=3.0



178


0.0

5.0

10.0

15.0

20.0

0.00 0.50 1.00 1.50 2.00 2.50 3.00

ACCELERATION (g)


No Isolators

E 1 T=1.5

E 1 T=2.0

E 1 T=2.5

E 1 T=3.00.0

5.0

10.0

15.0

20.0

0.00 0.50 1.00 1.50 2.00 2.50 3.00

ACCELERATION (g)


No Isolators

L 1 T=1.5

L 1 T=2.0

L 1 T=2.5

L 1 T=3.0

0.0

5.0

10.0

15.0

20.0

0.00 0.50 1.00 1.50 2.00 2.50 3.00

ACCELERATION (g)


No Isolators

L 2 T=1.5

L 2 T=2.0

L 2 T=2.5

L 2 T=3.0

0.0

5.0

10.0

15.0

20.0

0.00 0.50 1.00 1.50 2.00 2.50 3.00

ACCELERATION (g)

E L E V A T

I O N ( m )


F 1 T=2.0

F 1 T=2.5

F 1 T=3.00.0

5.0

10.0

15.0

20.0

0.00 0.50 1.00 1.50 2.00 2.50 3.00

ACCELERATION (g)

E L E V A T

I O N ( m )


F 2 T=2.0

F 2 T=2.5

F 2 T=3.0

0.0

5.0

10.0

15.0

20.0

0.00 0.50 1.00 1.50 2.00 2.50 3.00

ACCELERATION (g)

E L E V A T

I O N ( m )

No Isolators T 1 T=2.2

T 1 T=2.8

T 1 T=3.7

T 1 T=5.6

0.0

5.0

10.0

15.0

20.0

0.00 0.50 1.00 1.50 2.00 2.50 3.00

ACCELERATION (g)


No Isolators

L 3 T=1.5

L 3 T=2.0

L 3 T=2.5

L 3 T=3.0

0.0

5.0

10.0

15.0

20.0

0.00 0.50 1.00 1.50 2.00 2.50 3.00

ACCELERATION (g)


No IsolatorsH 1 T=1.5

H 1 T=2.0

H 1 T=2.5

H 1 T=3.0



179


0.0

5.0

10.0

15.0

20.0

25.0

30.0

0.00 0.50 1.00 1.50 2.00

ACCELERATION (g)


No IsolatorsE 1 T=1.5

E 1 T=2.0

E 1 T=2.5

E 1 T=3.00.0

5.0

10.0

15.0

20.0

25.0

30.0

0.00 0.50 1.00 1.50 2.00

ACCELERATION (g)


No IsolatorsL 1 T=1.5

L 1 T=2.0

L 1 T=2.5

L 1 T=3.0

0.0

5.0

10.0

15.0

20.0

25.0

30.0

0.00 0.50 1.00 1.50 2.00

ACCELERATION (g)

E L E V A T

I O N ( m )


L 2 T=2.0

L 2 T=2.5

L 2 T=3.00.0

5.0

10.0

15.0

20.0

25.0

30.0

0.00 0.50 1.00 1.50 2.00

ACCELERATION (g)

E L E V A T

I O N ( m )


L 3 T=2.0

L 3 T=2.5

L 3 T=3.0

0.0

5.0

10.0

15.0

20.0

25.0

30.0

0.00 0.50 1.00 1.50 2.00

ACCELERATION (g)

E L E V A

T I O N ( m )

No Isolators

H 1 T=1.5

H 1 T=2.0

H 1 T=2.5

H 1 T=3.00.0

5.0

10.0

15.0

20.0

25.0

30.0

0.00 0.50 1.00 1.50 2.00

ACCELERATION (g)

E L E V A

T I O N ( m )

No Isolators

T 1 T=2.2

T 1 T=2.8

T 1 T=3.7

T 1 T=5.6

0.0

5.0

10.0

15.0

20.0

25.0

30.0

0.00 0.50 1.00 1.50 2.00

ACCELERATION (g)

E

L E V A T I O N ( m )

No Isolators

F 2 T=1.5

F 2 T=2.0

F 2 T=2.5

F 2 T=3.0

0.0

5.0

10.0

15.0

20.0

25.0

30.0

0.00 0.50 1.00 1.50 2.00

ACCELERATION (g)

E L E V

A T I O N ( m )

No Isolators

F 1 T=1.5F 1 T=2.0

F 1 T=2.5

F 1 T=3.0



180

6.1.8 Optimum Isolation Systems

The results presented in the previous sections illustrate the wide differences in performance

between systems and between different properties of the same system. Different systems

have different effects on isolation system displacement, shear coefficient and flooraccelerations and no one device is optimum in terms of all possible objectives.

Table 6.4 lists the top 15 systems (of the 32 considered) arranged in ascending order of

efficiency for each of three potential performance objectives:

1. Minimum Base Shear Coefficient. The PTFE sliding systems provide the smallest base shear

coefficients, equal to the coefficient of friction. These are followed by the LRB with a high

yield level (Qd = 0.10) and 3 second period. However, none of these 4 systems provide a

restoring force and so the design displacement is three times the calculated value (UBCprovisions). After these four systems, the optimum systems in terms of minimum base

shear coeffic ient are variations of the LRB and FPS systems.

2. Minimum Isolation System Displacement. The FPS systems with a coefficient of friction of

0.12 and relatively short isolated periods are the most efficient at controlling isolationsystem displacements and the lowest five displacements are all produced by FPS

variations. After these are 3 LRB variations and then HDR and FPS. Most of the systems

that have minimum displacements have relatively high base shear coefficients and

accelerations.

3. Minimum Floor Accelerations. Accelerations are listed for three different building periods

and are ordered in Table 6.4 according to the maximum from the three buildings. Some

systems will have a higher rank for a particular building period. The elastic isolation

systems produce the smallest floor accelerations, followed by variations of LRB and HDR

systems. The FPS and PTFE systems do not appear in the optimum 15 systems for flooraccelerations.

No system appears within the top 15 of a ll three categories but some appear in two of three:

1. The FPS systems with a coefficient of friction of 0.12 and a period of 2.5 or 3.0 provide

minimum base shear coefficients and displacements. However, floor accelerations are

quite high.

2. The LRB with a period of 2 seconds and Q d = 0.05, 0.075 or 0.10 appear on the list for both

minimum displacements and minimum accelerations. The base shear coefficients for

these systems are not within the top 15 but are moderate, with a minimum value of 0.203

(compared to 0.06 to 0.198 for the top 15).

3. Five LRB variations and two HDR variations appear in the top 15 for both base shear

coefficients and floor accelerations. Of these, the minimum isolated displacement is 258

mm, compared to the range of 103 mm to 213 mm for the top 15 displacements.

These results show that isolation system selection needs to take account of the objectives of

isolating and the characteristics of the structure in which the system is to be installed. Formost projects a series of parameter studies will need to be performed to select the optimum

system.



181

Table 6.4: Optimum Isolation Systems

Maximum FloorAcceleration (g)

System Variation Period(mm)

C T = 0.2 s T = 0.5 s T = 1.0 s

Minimum Base Shear Coefficient, C

PTFE

PTFE

PTFELRB

LRB

PTFE

LRB

FPS

LRB

LRBFPS

HDRLRB

FPS

FPS

=0.06

=0.09

=0.12Qd=0.1

Qd=0.075

=0.15

Qd=0.05

=0.06

Qd=0.1

Qd=0.075

=0.12

Qd=0.05

=0.06

=0.12

5.6

3.7

2.83.0

3.0

2.2

3.0

3.0

2.5

2.53.0

3.02.5

2.5

2.5

1291

926

6691152

332

613

344

228

269

258130

320269

199

122

0.0600.090

0.1200.1370.1410.1500.1530.1620.1630.1670.178

0.1790.1800.188

0.198

0.58

0.65

0.750.15

0.15

0.83

0.16

0.50

0.18

0.190.77

0.190.20

0.46

0.77

0.89

0.99

1.020.25

0.27

1.07

0.31

0.83

0.33

0.331.03

0.250.34

0.80

1.05

1.09

1.45

1.480.42

0.43

1.32

0.39

1.08

0.58

0.551.38

0.410.62

1.13

1.33

Minimum Isolation System Displacement,

FPS

FPSFPS

FPSFPS

LRB

LRB

LRB

HDR

FPS

HDR

LRB

LRB

FPSLRB

=0.12

=0.12

=0.12

=0.06

=0.12

Qd=0.075

Qd=0.1

Qd=0.05

=0.06

Qd=0.075

Qd=0.1

=0.06Qd=0.05

1.5

2.02.5

1.53.0

1.5

1.5

1.5

1.5

2.0

2.0

2.0

2.0

2.52.0

103111122

124130140140144148160177195197199213

0.301

0.2310.198

0.2800.178

0.272

0.267

0.280

0.277

0.221

0.225

0.204

0.203

0.1880.225

0.75

0.750.77

0.530.77

0.35

0.33

0.35

0.33

0.49

0.26

0.27

0.28

0.460.24

1.01

1.071.05

0.861.03

0.70

0.74

0.53

0.50

0.83

0.38

0.41

0.51

0.800.36

1.11

1.231.33

0.941.38

0.85

1.01

0.77

0.79

1.14

0.70

0.68

0.76

1.130.56

Minimum Floor Accelerations, A

ELASTIC

ELASTIC

LRB

HDR

LRB

LRBELASTIC

HDR

LRB

LRB

LRBLRB

LRBHDR

LRB

Qd=0.05

Qd=0.1

Qd=0.075

Qd=0.075

Qd=0.05

Qd=0.1Qd=0.05

Qd=0.075

Qd=0.1

3.0

2.5

3.0

3.0

3.0

3.02.0

2.5

2.5

2.0

2.52.5

2.02.0

2.0

528

434

344

320

1152

332369

269

258

213

269269

195177

197

0.247

0.279

0.153

0.179

0.137

0.1410.371

0.202

0.167

0.225

0.1630.180

0.2040.225

0.203

0.250.290.160.190.15

0.150.400.200.190.240.180.20

0.270.260.28

0.260.300.310.250.25

0.270.420.270.330.360.330.34

0.410.380.51

0.290.340.390.410.42

0.430.490.510.550.560.580.62

0.680.700.76



182

6.2 EXAMPLE ASSESSMENT OF ISOLATOR PROPERTIES

The limited studies discussed above have shown that there is no one isolation system type, or

set of system parameters, which provides optimum performance in all aspects. For projects,it is recommended that a series of studies by performed to tune the system to the structure.

Following is an example of how this has been applied to a building project.

For this project a lead rubber system was selected as the isolation type based on a need for

relatively high amounts of damping. The LRB properties were selec ted by assessing

performance for a wide range of properties. For this type of bearing the plan size is set by

the vertical loads. The stiffness, and so effective period, is varied by changing the height of

the bearing, which is accomplished by changing the number of rubber layers. The yield level

of the system is varied by modifying the size of the lead cores in the bearing.

For this project the performance was assessed by varying the number of layers from 40 to 60

(changing stiffness by 50%) and by varying the lead core diameter from 115 mm (4.5”) to 165

mm (6.5”), changing the yield level by 100%.

A program was set up to cycle through a series of 3D-BASIS analyses. For each variation, theprogram adjusted the input file properties for stiffness and yield level, performed the analysis

and extracted the output response quantities from the output file. From these results the

plots in Figures 6.25 and 6.26 were generated. The isolator naming convention is, forexample, L40-6, which indicates 40 layers with a 6” lead core.

These plots are used to determine trends in isolator displacements, shear forces and

maximum floor accelerations. For this particular structure and seismic input, both the isolator

displacement and the base shear coefficient dec rease as either the stiffness is decreased or

the yield level is increased. However, the maximum floor accelerations increase as the

displacements and coefficients decrease and there is a point, in this case when the lead

core is increased beyond 6”, where the accelerations increase dramatically.

From the result of this type of analysis, isolators can be selected to minimize respective floor

accelerations, drifts, and base shears of isolator coefficients. As listed in Table 6.5, in this case

the minimum accelerations and drifts occur for a tall bearing (60 layers) with a small lead

core (4.5”). The isolator displacement can be reduced from 420 mm (16.5”) to 350 mm

(13.8”) and the base shear coefficient from 0.121 to 0.113 by increasing the lead core from

4.5” to 5” (a 23% increase in yield level). This only increases the floor accelerations and drifts

by 10% so is probably a worthwhile trade-off.

Minimum isolator displacements are provided by a stiff bearing (44 layers) with a large core

(6.5”) but there is a small penalty in base shear coefficient and a very large penalty in flooraccelerations assoc iated with his. For this projec t, design should accept isolator

displacements of 350 mm to ensure the best performance of the isolated structure.



183

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0

L 4 0 - C 4 . 5

L 4 6 - C 4 . 5

L 5 2 - C 4 . 5

L 5 8 - C 4 . 5

L 4 2 -

C 5

L 4 8 -

C 5

L 5 4 -

C 5

L 6 0 -

C 5

L 4 4 - C 5 . 5

L 5 0 - C 5 . 5

L 5 6 - C 5 . 5

L 4 0 -

C 6

L 4 6 -

C 6

L 5 2 -

C 6

L 5 8 -

C 6

L 4 2 - C 6 . 5

L 4 8 - C 6 . 5

L 5 4 - C 6 . 5

L 6 0 - C 6 . 5

ISOLATOR TYPE

D I S P L A C E M E N T ( i n c h e s )

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

B A S E S H E A R C O E F F I C I E N T

Isolator Displacement

Base shear Coefficient

INCREASING YIELD LEVEL

DECREASINGSTIFFNESS

Figure 6.25: Displacement versus Base Shear

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0

L 4 0 - C

4 . 5

L 4 6 - C

4 . 5

L 5 2 - C

4 . 5

L 5 8 - C

4 . 5

L 4 2 - C 5

L 4 8 - C 5

L 5 4 - C 5

L 6 0 - C 5

L 4 4 - C

5 . 5

L 5 0 - C

5 . 5

L 5 6 - C

5 . 5

L 4 0 - C 6

L 4 6 - C 6

L 5 2 - C 6

L 5 8 - C 6

L 4 2 - C

6 . 5

L 4 8 - C

6 . 5

L 5 4 - C

6 . 5

L 6 0 - C

6 . 5

ISOLATOR TYPE

D I S P L A C E M E N T ( i n c h e s )

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

F L O O R A C C E L E R A T I O N ( g )

Isolator Displacement

Maximum Floor Acceleration

INCREASING YIELD LEVEL

DECREASINGSTIFFNESS

Figure 6.26: Displacement versus Floor Acceleration



184

Isolator

Displacementmm

(Inches)

Base

ShearCoefficient

(g)

Maximum

FloorAcceleration

(g)

Maximum

Drift

Minimum Floor AccelerationL60-C4.5 420 (16.5) 0.121 0.420 0.0032

Minimum DriftL60-C4.5 420 (16.5) 0.121 0.420 0.0032

Minimum Base Shear

Coefficient

L60-C5

350 (13.8) 0.113 0.460 0.0035

Minimum Isolator

Displacement

L44-C6.5

260 (10.2) 0.132 1.590 0.0071

Table 6.5: Optimum Isolator Configuration

These analyses also illustrate the discussion earlier about the non-uniform nature of the

acceleration distribution when determined from the time history method of analysis. Figure

6.27 plots the acceleration profiles for the systems which provide the minimum floor

accelerations and minimum isolator displacements, respectively. Even though these systems

provide a similar base shear coefficient, the stiff system with high damping provides floor

accelerations over three times as high. The shape of the acceleration profile for the lattersystem exhibits the characteristics of very strong higher mode participation. An analysis

which used only effective stiffness would not reflect this effect.

0

1

2

3

4

5

6

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

MAXIMUM ACCELERATION (g)

F L O O R L E V E L

L60-C4.5

L44-C6.5Base Shear Coefficient 0.121Base Shear Coefficient 0.132

Figure 6.27: Floor Acceleration Profiles



185

CHAPTER 7: SEISMIC ISOLATION OF BUILDINGS AND

BRIDGES

7.1 INTRODUCTION TO ISOLATION OF BUILDINGS

As discussed in previous chapters, the ideal of base isolation is to install flexible devices toincrease the period beyond 2.0 seconds. The preferred site conditions are a stiff subsoil

profile and the building preference is for a relatively heavy building so as to achieve the

target isolated period within the range of stiffness provided by the usual type of device.

The reality is often different and this example is intended to illustrate how benefits can be

achieved even when these idea l conditions are not met. The example structure is relatively

light and it is located on a soft soil site close to a major fault. Favoring isolation was thebuilding type, an essential medical facility which was required to remain operational during

and after an earthquake. This required essentially elastic response of the structure.

Following the design of the isolated building, a description of a spreadsheet based

procedure which can be used to implement base isolation for buildings is described.

7.2 SCOPE OF BUILDING EXAMPLE

This example design is based on the submittal for a small health care fac ility located in New

Zealand. The contract documents for supply of isolation bearings specified that design

calculations were to be provided for the isolators and the results of dynamic analysis of the

structure modeled using the assumed isolator properties.

The Structural Engineer had set performance criteria for the isolation system based on

considerations of seismic loads, building weights and performance requirements and theisolation system had to meet the following requirements:

1. Total design displacement not to exceed 350 mm for DBE.

2. Total maximum displacement not to exceed 400 mm for MC E

3. Elastic base shear for DBE not to exceed 0.65.

4. Inter-storey drift ratio of the structure above the isolation system not to exceed 0.0100.

The building was a low-rise structure located in a high seismic zone with relatively light

column loads. As will be seen in the design of the isolation system, this limits the extent of the

period shift and so the degree of isolation which can be achieved.



186

7.3 SEISMIC INPUT

A site-specific seismic assessment of the site developed a suite of time histories to define

each of the DBE and MCE levels of load. Five time histories defined the lower levelearthquake and four the upper level. For each level, one modified (frequency scaled) and

four or three as-recorded time histories were used. The records are listed in Table 7.1.

Figure 7.1 plots the envelopes of the 5% damped response spectra of the records used to

define the DBE and MCE levels of load respectively. Also plotted on Figure 7.1 is the code

response spectrum for a hospital building on this site without a site specific study.

The seismic definition has an unusual characteristic in that the MCE level of load is

approximately the same as the DBE level of load whereas usually it would be expected to be

from 25% to 50% higher. This is because the earthquake probability at this location is

dominated by the Wellington Fault which has a relatively short return period and is expected

to generate an earthquake of high magnitude.

The elastic base shear coefficient on this site for a non-isolated building with a period of 0.42

seconds is approximately 2.5, based on the envelope of the scaled time histories. Thespecification requires a maximum base shear of 0.65, which is a reduction by a factor of

almost 4.

Level Filename Record ScaleFactor

EQ1

EQ2

EQ3EQ4EQ5

DBE EL40N00E

EL40N90W

HOLSE000GZ76N00EHMEL40NE

El Centro 1940 NS

El Centro 1940 EW

Hollister and Pine0 deg, 1989 Loma PrietaGazli, 1976 NSModified El Centro 1940 NS

3.25

3.90

1.691.171.30

EQ6

EQ7

EQ8

EQ9

MCE GZ76N00E

SYL360

EL79723

MEL79723

Gazli 1976 NS

Sylmar Hospital 360 deg, 1994 Northridge

El Centro Array No. 7 230 deg, 1979

Modified El Centro Array No. 7, 1979

1.20

1.00

1.70

1.00

Table 7.1: Input Time Histories



187

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

PERIOD (Seconds)


DBE Envelope

MCE Envelope

NZS4203 Soft Z 1.2 Sp 1 R 1.3

Figure 7.1: 5% Damped Envelope Spectra

7.4 DESIGN OF ISOLATION SYSTEM

The isolation system was designed using a spreadsheet developed following the procedures

described in Chapter 4. A series of design studies was performed using the spreadsheet to

optimize the isolator dimensions, shear modulus and lead core diameter for the level ofseismic load as determined from envelope spec tra of the time histories. These studies

resulted in an isolator size of 675 mm diameter x 380 mm high (total rubber thickness 210 mm)a 130 mm diameter lead core. Design was based on a moderately soft rubber (G = 0.60

MPa).

Figure 7.2 summarizes the performance of the isolation system as designed. This isolation

system configuration provided an effective period of approximately 1.5 seconds. The lead

cores provided displac ement-dependent hysteretic damping. The equivalent viscous

damping ranged from 32% at 50 mm displacement to 13% at 400 mm displacement. Figure

7.3 shows the theoretical hysteresis of this isolator.

The factors of safety listed for each limit case are close to the ac ceptable limit for leadrubber bearings under MC E, where the strain fac tor of safety is less than 2. An acceptable

lower limit for the ratio of reduced area to gross area is 25% and an acceptable upper limit

on strain is 200%. This design is very close to these limits for this type of device.



188

PERFORMANCE SUMMARY

Type 1 Pad B DBE MCE

Gravity Strain F.S. 16.34

Buckling F.S 12.25

DBE Strain F.S 2.14 Buckling F.S 3.71

MCE Strain F.S 1.76

Buckling F.S 2.81

Reduced Area / Gross Area 25.6%

Maximum Shear Strain 196%


Displacement DD DM 313 358

Total Displacements DTD DTM 360 412

Force Coefficient Vb / W 0.596 0.659

Force Coefficient Vs / W 0.298

1.5 x Yield Force / W 0.229Wind Force / W 0.000

Fixed Base V at TD 0.348

Governing Design Coefficient 0.348

Base Shear Force 8730


Damping Coefficients BD BM 1.35 1.32

Figure 7.2: Summary of Isolation Design



189

-600

-400

-200

0

200

400

600

-400 -300 -200 -100 0 100 200 300 400



Type 1 LRB

Figure 7.3:Hysteresis to Maximum Displacement

7.5 ANALYSIS MODELS

The performance was quantified using time history analysis of a matrix of 18 ETABS models

(Figure 7.4). The models included the 9 earthquake records, one mass eccentricity location

(+5% X and Y) and earthquakes applied along the X and Y axes of the structure respectively.

As the structure is doubly symmetric only the positive eccentricity case was evaluated.

Spring properties for the isolators were as listed in Figure 7.5. These were calculated using the

equations given in the design procedure in Chapter 5.



190

Figure 7.4: ETABS Model

Type 1LRB

First Data Line:

ID 1 Identification Number

ITYPE ISOLATOR1 Biaxial Hysteretic/Linear/Friction

KE2 1.28 Spring Effective Stiffness along Axis 2

KE3 1.28 Spring Effective Stiffness along Axis 3

DE2 0.092 Spring Effective Damping Ratio along Axis 2

DE3 0.092 Spring Effective Damping Ratio along Axis 3

Second Data Line:

K1 895.7 Spring Stiffness along Axis 1 (Axial)

K2 9.55 Initial Spring Stiffness along Axis 2

K3 9.55 Initial Spring Stiffness along Axis 3

FY2/K11/CFF2 118.39 Yield Force Along Axis 2

FY3/K22/CFF3 118.39 Yield Force Along Axis 3

RK2/K33/CFS2 0.103 Post-Yield stiffness ratio along Axis 2

RK3/CFS3 0.103 Post-Yield stiffness ratio along Axis 3

A2 Coefficient controlling fric tion Ax is 2

A3 Coefficient controlling fric tion Ax is 3

R2 Radius of Contact 2 direction

R3 Radius of Contact 3 direction

Figure 7.5: ETABS Properties



191

7.6 ANALYSIS RESULTS

Figures 7.6 to 7.8 show histograms of maximum response quantities for each of the scaled

earthquakes used to evaluate performance (refer to Table 7.1 for earthquake names and

scale factors).

1. The maximum response to DBE motions is dominated by EQ3, which is the Hollister Sth and

Pine Drive 0 degree record from the 1989 Loma Prieta earthquake, scaled by 1.69. Thisrecord produced maximum displacements about 20% higher than the next highest

records, the 1940 El Centro NW record scaled by 3.90 and the 1976 Gazli record scaled by1.17.

2. A similar dominant record appears for MCE response, the El Centro Array No. 7 230

degree component from the 1979 Imperial Valley earthquake, which produced results

higher than the other two records for all response quantities.

Figure 7.9 shows the input acceleration record for the dominant DBE earthquake, EQ3. This

record has peak ground ac celerations of approximately 0.6g. The trace is distinguished by alarge amplitude cycle at approximately 8 seconds, a characteristic of records measured

close to the fault.

The maximum bearing displacement trace, Figure 7.10, shows a one and one-half cycle high

amplitude displacement pulse between 8 and 10 seconds, with amplitudes exceeding 300mm. The remainder of the record produces displacements not exceeding 150 mm. This is

typical of the response of isolation systems to near fault records.

Figure 7.11 plots the time history of storey shear forces. The bi-linear model used to represent

the isolators has calculated periods of 0.54 seconds (elastic) and 1.69 seconds (yielded).

The fixed base building has a period of 0.42 seconds. The periodicity of response would be

expected to reflect these dynamic charac teristics and Figure 7.11 does show shorter periodresponse imposed on the longer period of the isolation system.



192

0

50

100

150

200

250

300

350400

450

E Q 1

E Q 2

E Q 3

E Q 4

E Q 5

E Q 6

E Q 7

E Q 8

E Q 9

D i s p l a c e m e n t ( m m ) X Direction

Y Direction

Figure 7.6: Total Design Displacement

0.00

0.10

0.20

0.30

0.40

0.500.60

0.70

E Q 1

E Q 2

E Q 3

E Q 4

E Q 5

E Q 6

E Q 7

E Q 8

E Q 9

B a s e S h e a r C o e f f i c i e n t X Direction

Y Direction

Figure 7.7: Base Shear Coefficient



193

0.0%

0.1%

0.2%

0.3%

0.4%

0.5%

0.6%

0.7%

0.8%

E Q

1

E Q

2

E Q

3

E Q

4

E Q

5

E Q

6

E Q

7

E Q

8

E Q

9

D r i f t ( % )

X Direction

Y Direction

Figure 7.8: Maximum Drift Ratios

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00

TIME (Seconds)

I N P U T A C C E L E R A T I O N ( g )

Figure 7.9: DBE Earthquake 3 Input



194

-400

-300

-200

-100

0

100

200

300

400

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00

TIME (Seconds)

B E A R I N G D I S P L A C E M E N T

( m m )

Figure 7.10:DBE Earthquake 3 : Bearing Displacement

-15000

-10000

-5000

0

5000

10000

15000

5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00

TIME (Seconds)

S T O R E Y S H E A R F O R C E

( k N )

Roof First FloorGround Floor

Figure 7.11: DBE Earthquake 3: Storey Shear Forces



195

7.6.1 Summary of Results

Table 7.2 lists the maximum values of the critical response parameters identified in the

specifications:

Maximum bearing displacements of 323 mm (DBE) and 397 mm (MC E) were within the

spec ification limits of 350 mm and 400 mm respectively.

A maximum bearing force of 423 kN at DBE levels, less than the maximum specified value

of 450 kN.

A maximum drift ratio of 0.0067 (MCE), within the specification limits of 0.0100.

DBE LIMIT MCE LIMIT

Base Shear Coefficient

Center of Mass Displacement

Maximum Bearing DisplacementMaximum Bearing ForceMaximum Drift

0.549

290

323423

0.0061

350450

0.650

364

397497

0.0067

400

0.0100

Table 7.2:Summary of Results

7.7 TEST CONDITIONS

The results of the ETABS analysis were used to derive the prototype and production test

conditions, as listed in Table 7.3. The displacements and vertical loads define the test

conditions. The shear force and the hysteresis loop area define the performance required of

the prototype and production tests.

Test Parameter Prototype

Test

Production

Test

Total Design Displacement (mm)

Total Maximum Displacement (mm)

Average DL (kN)

Average 1.2D + 0.5LL + E (kN)

Average 0.8D - E (kN)

Maximum 1.2D + LL + E (kN)

Shear Force (kN)

Hysteresis Loop Area (kN-mm)

323

397

950

795

369

1224

424

131,925

260

1100

375.4

117,520

Table 7.3: Prototype Test Conditions

The acceptance criteria for prototype and production tests are set out in codes such as the

UBC and AASHTO. Some obvious criteria relate to the requirements that the bearings remainstable and that there be no signs of damage in the test. Other UBC requirements relate to

the change in properties over multiple cycles. However, the UBC does not provide guidanceas to the comparison between test properties and design properties. AASHTO provides

some guidance in this respect, requiring that the effective stiffness be within 10% of the

design value and that the hysteresis loop area be at least 70% of the design value for the

lowest cycle.



196

For building projects, specifications generally require that the average effective stiffness (or

shear force, which is proportional) be within 10% of the design value and that the average

loop area be at least 80% of the design value (no upper limit). These were the limits for this

project.

7.8 PRODUCTION TEST RESULTS

A total of 38 isolation bearings were tested under combined compression and shear to the

center of mass DBE displacement of 260 mm. The isolators were tested in pairs and so 19

individual results were obtained.

Table 7.4 provides a summary of the production tests results. The measured shear forces

ranged from –2.5% to +3.2% of the design value, with a mean value –0.8% lower than the

design value. The measured hysteresis loop areas exceeded the design value by at least

17.8%, with a mean value 22% higher than the design value.

Measured DeviationFrom

Specification

DeviationFromMean

Shear Force (kN)

Maximum

Mean

Minimum

387.4

372.5

365.9

3.2%

-0.8%

-2.5%

4.0%

0.0%

-1.8%

Loop Area (kN-mm)

Maximum

Mean

Minimum

148,757

143,425

138,456

26.5%

22.0%

17.8%

3.7%0.0%

-3.5%

Table 7.4: Summary of 3 Cycle Production Test Results

Figure 7.12 provides an example of one production test of a pair of isolation bearings. As istypical of LRBs, the first loading cycles produces a much higher shear force than subsequent

unloading and loading cycles. Although the reasons for this are not fully understood, theincrease is believed to be a function of both lead core characteristics and the effect of the

initial loading pulse from zero displacement and velocity.

For most LRB tests it is common to test for one cycle additional to the test requirements and

exclude the first cycle from the evaluation of results. This is shown in Figure 7.12. The

production tests specify 3 cycles at a 260 mm displacement and the test is performed for 4

cycles with the results processed from Cycles 2 to 4.

Loop MinLoadkN

MaxLoadkN

MinDispmm

MaxDispmm

LoopArea

kN.mm

Strain%

K eff kN

Qd kN

Damping%

1 -390.6 480.5 -264.7 266.2 173081 126% 1.641 154.3 23.8%

2 -359.4 416.0 -264.7 265.7 149232 126% 1.462 132.8 23.1%

3 -349.6 400.4 -264.7 265.7 140849 126% 1.414 125.0 22.5%

4 -345.7 392.6 -264.7 265.7 136797 126% 1.392 121.1 22.2%

Avg -351.6 403.0 -264.7 265.7 142293 126% 1.423 126.3 22.6%



197

Figure 7.12: Example Production Test

7.9 SUMMARY

In terms of suitability for isolation this building would be termed marginal in terms of site

suitability (soft soils) and building suitability (a light building with relatively low total seismic

mass). However, in terms of need for isolation it scored highly as the site-spec ific earthquake

records indicated a maximum elastic coefficient of over 2.5g at the fixed base period.

The low mass necessitated a short isolated period (approximately 1.5 seconds) and a highyield level to provide damping to control displacements due to the soft soil (yield level equal

to 15% of the weight). This resulted in a high base shear coefficient at the MCE level of

0.65g. However, in spite of these restrictions on isolation system performance the force levels

in the structure were still reduced by a factor of almost 4 (from 2.5g to 0.65g) and floor

motions would be reduced proportionately.

Standard design office software (ETABS) was used to evaluate the performance of thestructure and isolation system using the non-linear time history method of analysis. The results

from this analysis provided the displacements, vertical loads and required performancecharacteristics to define the prototype and production test requirements.

The prototype and production test results demonstrated that the design performance could

be achieved. In this example, the production test results produced a mean shear force

within 1% of the design values and hysteresis loop areas exceeding the design values by at

least 15%.



198

7.10 IMPLEMENTATION IN SPREADSHEET

Included with this book is a spreadsheet which can be used to evaluate system performance

and factors of safety based on user selec ted isolator details. The spreadsheet is not intendedfor final design or to substitute for the calculations by the structural engineer of record. It is atool provided to assist users in developing their own isolation design procedures.

The example provided in this section is based on design to 1997 UBC requirements. Designs

based on other codes follow the same general principles. In the spreadsheet, cells colored

red indicate user-specified input. The workbook contains a number of sheets with the design

performed within the sheet Design .

The spreadsheet is set up for up to three types of isolator mixed in a project. This can be

extended by inserting additional columns and copying formulas ac ross the sheet.

7.10.1 Material Definition

The material definitions are contained on the sheet Desig n Da ta , as shown in Figure 7.13. This

is the basic information used for the design process. The range of properties available forrubber is restricted and some properties are related to others, for example, the ultimate

elongation, material constant and elastic modulus are all a function of the shear modulus.

Information on available rubbers is provided elsewhere in this book. Users should a lso check

with manufacturers, especially for high damping rubber formulations.

As for the rubber, the PTFE properties used for sliding bearings are supplier-spec ific. The values

listed in Figure 7.13 are typical of the material but other properties are available.

High damping rubber is the most variable of the isolator materials as each manufacturer has

specific properties for both stiffness and damping. The design procedure is based ontabulated values of the shear modulus and equivalent damping, as listed in Figure 7.13. The

damping values tabulated may include viscous damping effects if appropriate.

Default HDR properties listed are for a relatively low damping rubber formulation and so any

design based on these properties should be easily achievable from a number of

manufacturers. As such, they should be conservative for preliminary design.



200

PROJECT: UBC Design Example

Units: KN,mm

Seismic Zone Factor, Z 0.4 Table 16-I

Soil Profile Type SC Table 16-J

Seismic Coefficient, C A 0.400 Table 16-QSeismic Coefficient, CV 0.672 Table 16-R

Near-Source Factor Na 1.000 Table 16-S

Near-Source Factor Nv 1.200 Table 16-T

MCE Shaking Intensity MMZNa 0.484

MCE Shaking Intensity MMZNv 0.581

Seismic Source Type A Table 16-U

Distance to Known Source (km) 10.0

MCE Response Coefficient, MM 1.21 Table A-16-D

Lateral Force Coefficient, RI 2.0 Table A-16-E

Fixed Base Lateral Force Coefficient, R 5.5 Table 16-N

Importance Factor, I 1.0 Table 16-K

Seismic Coefficient, C AM 0.484 Table A-16-F

Seismic Coefficient, CVM 0.813 Table A-16-G

Eccentricity, e 0.31

Shortest Building Dimension, b 5.03

Longest Building Dimension, d 6.23

Dimension to Extreme Isolator, y 3.1

DTD/DD = DTM/DM 1.182

Figure 7.14: Project Definition

7.10.3 Isolator Types and Load Data

The isolator types and load data are defined as shown in Figure 7.14. This stage assumes thatthe user has decided on the type of isolator at each location. See elsewhere in this book for

assistance on selec ting the device types and the number of variations in type. For mostprojects, there will be some iteration as the performance of different types and layouts is

assessed.

1. The types of isolators which can be included in this spreadsheet are lead rubber bearings

(LRB), high damping rubber bearings (HDR), elastomeric bearings (ELAST, equivalent to

an LRB with no lead core), flat sliding bearings (TFE) and curved sliding bearings (FPS).

2. For each isolator type, vertical load conditions are defined. The average DL + SLL is used

to assess seismic performance. The maximum and minimum load combinations are usedto assess the isolator capacity.

3. The total wind load on the isolators may be provided if it applied a lower limit to the

design shear forces.



201

4. Most building projec ts will not have a non-seismic displacement or rotation; these are

more common on bridge projects. If they do apply, they are entered on this sheet. High

rotations will severely limit the capacity of the elastomeric types of isolator (LRB, HDR and

ELAST). Other types of bearing may be more suited for high rotations, for example, pot

type sliding bearings.

For most projects, the data in this section will be changed as variations of isolation systemsare assessed. Often, the isolator type will be varied and sometimes variation of the number

of each type of isolator will be considered.

BEARING TYPES AND LOAD DATA

LRB-A LRB-B TFE-C Total

Location

Type (LRB, HDR, ELAST,TFE,FPS) LRB LRB TFE

Number of Bearings 12 12 6 30

Number of Prototypes 2 2 2

Average DL + SLL 800 1200 500

Maximum DL + LL 1100 1600 250

Maximum DL + SLL + EQ 1600 2400 500

Minimum DL - EQ 0 0 0

Seismic Weight 9600 14400 3000 27000

Total Wind Load 620

Non-Seismic Displacement

Non-Seismic Rotation (rad)

Seismic Rotation (rad)

Figure 7.15: Isolator Types & Load Data

7.10.4 Isolator Dimensions

The spreadsheet provides specific design for the elastomeric types of isolator (LRB, HDR and

ELAST). For other types (TFE and FPS) the design procedure uses the properties spec ified on

this sheet and the Desig n Da ta sheet but does not provide design details. For these types of

bearings the load and design conditions will need to be supplied to manufacturers for

detailed design.

The isolators are defined by the plan size and rubber layer configuration (elastomeric based

isolators) plus lead core size (lead rubber bearings) or radius of curvature (curved slider

bearings). For curved slider bearings the radius defines the post-yielded slope of the isolation

system and the period of response. Appropriate starting values are selec ted from the

project performance spec ifications and fine tuned by trial and error.

1. The minimum plan dimensions for the elastomeric isolators are those required for the

maximum gravity loads. The gravity factor of safety (F.S.), at zero displacement, should

be at least 3 for both the strain and buckling limit states. A starting point for the design

procedure is to set a plan dimension such that this factor of safety is achieved.

2. The design process is iterative because the plan dimension is also a function of the

maximum displacement. For moderate to high seismic zones the plan size based on a

F.S. of 3 will likely need to be increased as the design progresses.



202

3. The rubber layer thickness is generally a constant at 10 mm. This thickness provides good

confinement for the lead core and is sufficiently thin to provide a high load capacity. If

vertical loads are critical the load thickness may be reduced to 8 mm or even 6 mm

although manufacturers should be consulted for these thin layers. Thinner layers add to

the isolator height, and also c ost, as more internal shims are required. The layer thickness

should not usually exceed 10 mm for LRBs but thicker layers may be used for elastomericor HDR bearings. The load capacity drops off rapidly as the layer thickness increases.


isolated period is in the range required and so that the maximum shear strain is notexcessive. This is set by trial and error.


of QD/W is displayed for guidance. This ratio usually ranges from 3% in low seismic zones

to 10% or more in high seismic zones. Usually the softer the soil the higher the yield level

for a given seismic zone. As for the number of rubber layers, the core is sized by trial and

error.

6. Available plan shapes are circular and square (plus rectangular for bridges). Most

building projec ts use c ircular bearings as it is considered that these are more suitable for

loading from all horizontal directions. Square and rectangular bearings are more often

used for bridges as these shapes may be more space efficient.

BEARING DIMENSIONS

LRB-A LRB-B TFE-C

Plan Dimension (Radius for FPS) 670 770

Depth (R only)Layer Thickness 10 10

Number of Layers 20 20 Qd/W

Lead Core Size 90 110 6.75%

Shape (S = Square, C = Circ) C C

Side Cover 10 10

Internal Shim Thickness 2.7 2.7

Load Plate Thickness 25.4 25.4

Load Plate Dimension 670 770

Load Plate Shape (S or C) S S

Total Height 301 301

Figure 7.16: Isolator Dimensions

The procedure for fine tuning dimensions is to set initial values, activate the macro to solve for

the isolation performance and change the configuration to achieve the target

performance. At each step, the effect of the change is evaluated by assessing the isolation

system performance, as described below.



203

7.10.5 Isolator Performance

The workbook contains a macro which solves for isolation performance once all dimensions

and properties have been set. This is not automatic, and must be activated once changesare made. If changes affect the performance of the isolation system a message DBE (or

MC E) NOT CONVERGED will be displayed. Running the macro will update the performance

summary.

As changes are made, two parameters are checked, (1) the status of the isolation bearings

to safely support the loads and (2) the performance of the isolation system.

The isolation bearing status for all elastomeric based isolators is summarized by the fac tors of

safety, as shown in Figure 7.17. Although generally factors of safety exceeding 1.0 indicate

satisfac tory performance, experience has shown that some more severe restrictions should

be imposed during the design process. This conservatism in design is recommended as it will

increase the probability of successful prototype tests.

PERFORMANCE SUMMARY

LRB-A LRB-B TFE-C DBE MCE

Gravity Strain F.S. 12.26 12.91

Buckling F.S 7.88 9.54

DBE Strain F.S 2.10 2.28


MCE Strain F.S 1.38 1.62


Reduced Area / Gross Area 28.2% 36.6%

Maximum Shear Strain 196% 196%


Displacement DD DM 240.8 331.8

Total Displacements DTD DTM 284.5 392.1

Force Coefficient Vb / W 0.225 0.284

Force Coefficient Vs / W 0.112

1.5 x Yield Force / W 0.101

Wind Force / W 0.023

Fixed Base V at TD 0.070

Design Base ShearCoefficient 0.112


Damping Coefficients BD BM 1.44 1.32

Figure 7.17: Performance Summary

1. The gravity factor of safety should exceed 3.0 for both strain and buckling. For high

seismic zones it will generally be at least 6.0 as performance is governed by seismic limit

states.

2. The DBE factor of safety should be at least 1.5 and preferably 2.0 for both strain andbuckling.



204

3. The MBE fac tor of safety should be at least 1.25 and preferably 1.5 for both strain and

buckling.

4. The ratio of reduced area to gross area should not go below 25% and shouldpreferably be at least 30%.

5. The maximum shear strain should not exceed 250% and preferably be less than 200%.

The limit states are governed by both the plan size and the number of rubber layers. Both

these parameters may need to be adjusted to achieve a design within the limitations above.

At each change, a check is also required to assess whether the seismic performance is

achieved.

The performance of the isolated structure is summarized for the DBE and MCE in the final two

columns in Figure 7.17. Performance indicators to assess are:

1. The isolated period. Most isolation systems have an effective period in the range of

1.50 to 2.50 seconds for DBE, with the longer periods tending to be used for high seismic

zones. It may not be possible to achieve a period near the upper limit if isolators have

light loads.

2. The displacements and total displacements. The displacements are estimated values

at the center of mass and also total displacements, which include an allowance for

torsion. The latter values, at MCE loads, define the separation required around the

building.

3. The force coefficient Vb/W is the maximum base shear force that will be transmittedthrough the isolation system to the structure above. This is the base shear for elastic

performance but is not necessarily the design base shear.

4. The design base shear coefficient is defined by UBC as the maximum of four cases:

a) The elastic base shear reduced by the isolated response modification factor VS =

VB/RI.

b) The yield force of the isolation system factored by 1.5.

c) The base shear corresponding to the wind load.

d) The coefficient required for a fixed base structure with a period equal to the

isolated period.

For this example, the first condition governs. The designer should generally aim for this

situation as the isolation system will be used most efficiently if this limit applies.

The performance summary also lists the equivalent viscous damping of the total isolation

system and the assoc iated damping reduction factor, B. Design should always aim for at

least 10% damping at both levels of earthquake and preferably 15%.



205

The design worksheet also provides details of the calculations used to obtain this

performance summary. Figure 7.18 shows the calculations for the MCE level. In this example,

the TFE slider bearing provides much higher damping than the LRBs on an individual bearing

basis. However, as only about 10% of the total seismic weight is supported on sliders thecontribution to total system damping of the sliders is not large.

Seismic Performance : Maximum Capable Earthquake

LRB-A LRB-B TFE-C MCE

Number of Isolators 12 12 6 30

Elastic Stiffness, Ku 5.56 7.49 0.00

Yielded Stiffness, Kr* 0.63 0.84 0.00

Yield Displacement, Dy 10.46 11.55 0.00

Characteristic Strength, Qd 50.89 76.03 50.00

Seismic Displacement, Dm 331.80

Bearing Force = Qd+DmKr* 259.4 354.9 50.000

Effective Stiffness = F/Dm 0.782 1.070 0.151 23.124

Seismic Weight 27000

Seismic Mass = W/9810 2.752

Effective Period = 2(M/K) 2.17

Ah = 4QD(m-y) 65415 97388 66359 2351797

= (1/2)(Ah/Ke2) 12.10% 13.16% 63.66% 14.70%

B Factor 1.32

SA = Cvd/BT 0.28

SD = (g/42)*CvdTd/Bd 331.81

Check Convergence = Sd/m 1.00

Figure 7.18:Performance at MCE Level

There is quite an art to the selection of final isolation design parameters. For example, in this

case damping could be increased by increasing lead core sizes in the LRBs. The core sizescannot be increased much, however, as the yield force will increase. As shown in Figure

7.17, the design base shear force will be governed by the 1.5F Y condition if core sizes are

increased. Therefore, the extra damping may actually result in an increase in structural

design forces.

7.10.6 Properties for Analysis

The workbook provides a plot of the hysteresis curves for each of the isolator types as

designed for displacements up to the MCE total displacement level. These plots (Figure

7.19) show the bi-linear properties to be used for system evaluation.

The properties used to develop the hysteresis loop are also listed in a format suitable for the

ETABS program, as shown in Figure 7.20. The use of these properties is discussed elsewhere in

this book.



206

-400

-300

-200

-100

0

100

200

300

400

-400 -300 -200 -100 0 100 200 300 400



LRB-A LRB

LRB-B LRB

TFE-C TFE

Figure 7.19: Hysteresis of Isolators

ETABS Spring Properties

LRB-A LRB-B TFE-C

LRB LRB TFE

First Data Line:

ID 1 2 3 Identification Number ITYPE ISOLATOR1 ISOLATOR1 ISOLATOR2 Biaxial Hysteretic/Linear/Friction

KE2 0.78 1.07 0.15 Spring Effective Stiffness along Axis 2

KE3 0.78 1.07 0.15 Spring Effective Stiffness along Axis 3

DE2 0.071 0.081 0.587 Spring Effective Damping Ratio along Axis 2

DE3 0.071 0.081 0.587 Spring Effective Damping Ratio along Axis 3

Second Data Line:

K1 709.4 1145.0 5000.0 Spring Stiffness along Axis 1 (Axial)

K2 5.49 7.41 2000.00 Initial Spring Stiffness along Axis 2

K3 5.49 7.41 2000.00 Initial Spring Stiffness along Axis 3

FY2/K11/CFF2 57.47 85.59 0.10 Yield Force Along Axis 2

FY3/K22/CFF3 57.47 85.59 0.10 Yield Force Along Axis 3

RK2/K33/CFS2 0.11 0.11 0.04 Post-Yield stiffness ratio along Axis 2

RK3/CFS3 0.11 0.11 0.04 Post-Yield stiffness ratio along Axis 3

A2 0.90 Coefficient controlling friction Axis 2

A3 0.90 Coefficient controlling friction Axis 3

R2 0.000 Radius of Contact 2 directionR3 0.000 Radius of Contact 3 direction

Figure 7.20: Analysis Properties for ETABS



208

Bridge isolation does not have the objective of reducing floor accelerations which is

common for most building structures. For this reason, there is no imposed upper limit on

damping provided by the isolation system. Many isolation systems for bridge are designed to

maximize energy dissipation rather than providing a significant period shift.

7.12 SEISMIC SEPARATION OF BRIDGES

It is often difficult to provide separation for bridges, especially in the longitudinal direction.

However, the consequences of lack of separation may not be severe. For any isolated

structure, if there is insufficient clearance for the displacement to occur then impact will

occur.

For buildings, impact almost always has very undesirable consequences. The impact will

send a high frequency shock wave up the building, damaging the contents that the isolation

system is intended to protect.

For bridges, the most common impact will be the superstructure hitting the abutment backwall. Generally, the high accelerations will not in themselves be damaging and so theconsequences of impact may not be high. The consequences may be minimized by

building in a failure sequence at the location of impact. For example, a slab and “knock off”detail as shown in Figure 7.22.

Thermal Separation

Seismic Separation

Friction Slab on Grade

Frictionoint

Figure 7.22: Example "Knock-Off" Detail

An example of the seismic separation reality is the Sierra Point Bridge, on US Highway 101

between San Francisco and the airport. This bridge was retrofitted with lead rubber bearings

on top of existing columns that had insufficient strength and ductility. The bearings were

sized such that the force transmitted into the columns at maximum displacement would not

exceed the moment capacity of the columns. The existing superstructure is on a skew and

has a separation of only about 50 mm (2”) at the abutments. In an earthquake, it is likelythat the deck will impact the abutment. However, regardless of whether this occurs, or the

superstructure moves transversely along the direction of skew, the columns will be protectedas the bearings cannot transmit a level of shear sufficient to damage them.



209

There may well be local damage at the abutments but the functionality of the bridge is

unlikely to be impaired. This type of solution may not achieve “pure” isolation, and may be

incomplete from a structural engineer’s perspective, but nevertheless it achieves the project

objectives.

7.13 DESIGN SPECIFICATIONS FOR BRIDGES

Design of seismic isolations systems for bridges often follow the AASHTO Guide Specifications,

published by the American Assoc iation of State Highway and Transportation Officials. The

initial specifications were published in 1991, with a major revision in 1999.

These bridge design specifications have in some ways followed the evolution of the UBC

code revisions. The original 1991 edition was relatively straightforward and simple to apply

but the 1999 revision added layers of complexity. Additionally, the 1999 revision changed

the calculations of the seismic limit state to severely restrict the use of elastomeric type

isolators under high seismic demands.

7.13.1 The 1991 AASHTO Guide Specifications

The 1991 AASHTO seismic isolation provisions permitted isolated structures to be designed forthe same ductility factors (as implemented through the R factor) as for non-isolated bridges.

This differed from buildings where the UBC at this time recommended an R value for isolated

structures of one-half the value for non-isolated structures. However, AASHTO

recommended a value of R = 1.5 for essentially elastic response as a damage avoidance

design strategy.

AASHTO defined two response spectrum analysis procedures, the single-mode and multi-

mode methods. The former was similar to a static procedure and the latter to aconventiona l response spectrum analysis. Time history analysis was permitted for all isolated

bridges and required for systems without a self-centering capability (sliding systems).

Prototype tests were required for all isolation systems, following generally similar requirements

to the UBC both for test procedures and system adequacy criteria.

In addition to the seismic design provisions, the 1991 AASHTO specifications provided

additions to the existing AASHTO design provisions for Elastomeric Bearings when these typesof bearings were used in implementing seismic isolation design. This section provided

procedures for designing elastomeric bearings using a limiting strain criterion. As this codewas the only source providing elastomeric design conditions for seismic isolation the

formulations provided here were also used in design of this type of isolator for buildings (seeChapter 9 of these Guidelines).



211

Prior to this edition, the bulk modulus was used to calculate vertical stiffness but not to

calculate the shear strain due to compression. Its inclusion in AASHTO for calculating vertical

load capacity is controversial as other codes (for example, AustRoads) explicitly state that

the bulk modulus effect does not reduce the load capac ity.

Figure 7.23 shows the difference in load capacity at earthquake displacements for

elastomeric bearings designed using the 1991 and 1999 AASHTO load spec ifications. The plot

is for typical isolators (10 mm layer thickness, area reduction factor of 0.5 and seismic shear

strain of 150%). The load capacity is similar for smaller isolators (600 mm plan size or less) but

the 1999 requirements reduce the load capacity for larger isolators such that for 1000 mm

isolators the load capacity is only one-half that permitted by the earlier revision. Isolators of

1.0 m diameter or more are now common for high seismic zones as near fault displacements

cause high deformations.

0

5000

10000

15000

20000

25000

200 400 600 800 1000

ISOLATOR PLAN SIZE (mm)

L O A D C A P A C I T Y ( K N

)

1991 AASHTO1999 AASHTO

Figure 7.23: Elastomeric Bearing Load Capacity

This change in load capac ities has little effect on most projects but has a major impac t on

design for conditions of high vertical loads and high seismic displacements.

For example, on a California building project bearings were 970 mm diameter, designed to

the 1991 AASHTO requirements. If design had been based on the 1999 provisions the

diameter would have needed to be increased to 1175 mm. This 48% increase in plan areawould require a corresponding increase in height to achieve the same flexibility. This would

have made base isolation using LRBs impossible for this retrofit project as there were space

restrictions.

These bearings were successfully tested beyond the design displacement to a point close tothe design limit of the 1991 code. This implies a factor of safety of at least 2 for vertical loads

relative to the 1999 AASHTO. This fac tor of safety is beyond what would normally be

required for displacements based on an extreme MC E event.



212

If project specifications require compliance with 1999 AASHTO then if will be required to use

the formulation for total shear strain that includes the bulk modulus. However, there does not

seem enough evidence that designs excluding the bulk modulus are non-conservative, to

change procedures for other projects for which compliance with this code is not mandatory.

7.15 DESIGN OF ISOLATION SYSTEMS

Isolation systems for bridges are designed using the same principles as outlined in Chapter 5.

For design according to AASHTO, the seismic input is defined by the acceleration coefficient,

A, and the coefficient for site-soil profile, Si, which ranges from 1.0 to 2.7. These coefficients,

together with the isolation period and damping coefficient (Teff and B respectively) definethe maximum spectral acceleration as:

g BT

AS S

eff

i A (in units of acceleration) (7.1)

and the spectral displacement as

B

T AS T S S S

eff ieff A A D 22

2

2 4)2( (7.2)

The damping coefficient is derived from the hysteresis loop area ymdh 4QA , the

effec tive stiffness, K eff , and the displacement, , which gives the equivalent viscous damping

as:

22

1

eff

h

K

A

(7.3)

The B factor is then interpolated from the values in Table 7.5 for the calculated value of .

Percentage of Critical Damping, 2 5 10 20 30 40 50

B 0.8 1.0 1.2 1.5 1.7 1.9 2.0

Table 7.5: Damping Coefficient, B

These equations provide the maximum force coefficient, SA, and the maximum

displacement, SD, for a rigid mass on a spec ified isolation system. However, practical

isolation systems for bridges also need to provide resistance to non-seismic loads and for

most bridges the seismic response will be modified by flexibility of the structure below the

isolation plane. The following sec tions discuss the influence of these factors on design of theisolation system.

7.15.1 Non-Seismic Loads

Bridges are required to resist a number of load types in service. Table 7.6 lists the three

categories of non-seismic loads which may apply for a particular bridges:

1. Vertical loads, which arise from the self-weight of the bridge plus surfacing and the live

loads from traffic. The bearings are sized to resist the maximum combinations of these

loads with a minimum factor of safety of 3.



213

2. Service horizontal loads, which may arise from wind load, wind on live load,

longitudinal breaking forces and centrifugal forces for bridges on a curved alignment.

The lead cores are sized to resist the maximum combinations of these loads.

3. Service horizontal displacements are applied from creep and shrinkage and from

thermal movements. These are typically slowly applied loads. These displacementswill deform the bearings and transmit a force into the substructure. For slowly applied

loads the lead will creep and the maximum force transmitted will be less than for

rapidly applied loads.

Vertical Loads

D

L

Dead load

Live load

Select plan size and layer configuration to resist

maximum vertical load combinations.

Short Term Service Horizontal Loads

WWL

LF

CF

Wind load

Wind on live load

Longitudinal force

Centrifugal Force

Size lead cores to resist each combination of short

term service loads using short term force in lead core

d ST QF

Long Term Service Horizontal Displacements

R

S T

Rib Shortening

Shrinkage Temperature

Calculate maximum force in bearing using long term

force in lead core (equal to 0.25 x short term yield

force)

LT r d

LT K Q

F 4

Table 7.6: Bearing Non-Seismic Design Actions

7.15.2 Effect of Bent Flexibility

The most common location of the isolation plane for bridges is immediately below thesuperstructure, on top of the bents (piers or abutments). The seismic mass is concentrated in

the superstructure and so maximum inertia loads are transmitted from the deck through thebearings. The bearing forces will deform the bents below, modifying the dynamics of the

response.

Figure 7.24 shows schematically the usual configuration of an isolated bridge. The total deck

displacement is a combination of bearing displacement plus bent displacement. The

relative proportions of each are a function of the relative stiffness of each, taking into

account the nonlinearity of the bearings. AASHTO 1999 provides guidance in incorporating

the effect of substructure flexibility on response and the equations in this section are

extracted from this source.



214

K eff

K sub

Superstructure

isub

Bearing(s)

Substructure

y i

k d

k eff

Qd

Figure 7.24: Effect of Substructure Flexibility

For calculating the effective stiffness of an isolator, the effects of substructure flexibility must

be included where appropriate. The isolator and the substructure act as a pair of springs inseries and the total stiffness, K eff , is a function of the effective stiffness of the individualbearings, keff , and the stiffness of the substructure, ksub

j

jeff

j eff sub

eff subeff K

k k

k k K , (7.4)

Similarly, the effective damping must also account for substructure flexibility

j

jeff eff K

y patedEnergTotalDissi

K

ipated EnergyDiss

)(22 2,

2

(7.5)

For lead rubber bearings, the hysteresis loop area of each bearing is 4Qd(i – y) and so the

effective damping can be calculated as:

j

subi jeff

j

yid

eff subi

yid

K

Q

K

Q

2,

)

2

)

)(

(2

)(

(2

(7.6)

Once the effective stiffness is defined the effective period can be calculated. The effective

period and damping can then be used to calculate the force coefficient and spectral

displacement as described earlier. However, both the period and damping are each a

function of the spectral displacement and so an iterative solution is required.



215

7.16 ANALYSIS OF ISOLATED BRIDGES

AASHTO specifies four analysis procedures, in increasing order of complexity (1) uniform load,

(2) single mode spectral method, (3) multimode spectral method or (4) time history methodsof analysis.

For isolated bridges, the uniform load and single mode spectral method are essentially the

same as the method described in this chapter and implemented in the sample workbook.

This method includes the effect of bent flexibility but does not account for flexure of the

bridge deck or the self-weight of the bents.

The multimode spectral method is often difficult to implement for isolated bridges. This is

because of the displacement dependent nature of both the effective stiffness and the

damping. Some form of iteration needs to be incorporated to solve for a compatible

displacement, stiffness and damping at each bearing location. This will require a large

number of changes to the computer input and will generally not be practical unless anautomated procedure is developed.

The time history method can be based on either the maximum response from three timehistories or the mean results of 7 time histories. Two dimension analyses are permitted for

normal bridges without skews or curves and this simplifies the procedure, allowing programssuch as DRAIN-2D to be used with separate longitudinal and transverse models.

Figure 7.25 shows the form of the longitudinal model for an isolated bridge. Each bent is

modeled with two truss elements in series, one representing the bent and the second

representing the sum of the bearings at the top of the bent. Usually, one-half the bent

weight is lumped as a seismic mass at the top of the bent. For substructures which are heavy

relative to the substructure, multiple mass points may be used within the height of the bent,each with tributary mass derived from the bent weight.

Mass Point of Superstructure

Fixed Nodes

Truss Elements in series

A: Substructure EA/ L = K sub

B: Bi-linear Bearing EA1/ L = K u

EA2 / K = K r

Beam Element EA = EAdeck

Earthquake Loads Applied Along X

A B

Mass Point of Bent

Figure 7.25:DRAIN-2D Longitudinal Model



216

The transverse model uses similar elements to those of the longitudinal model but is oriented

as shown in Figure 7.26. This orientation allows for the effects of deck flexural deformations

and rotations to be incorporated into the results.

Earthquake Loads Applied Along X

Mass Point of Superstructure

Fixed Nodes

Truss Elements in series

A: Substructure EA/ L = K sub

B: Bi-linear Bearing EA1/ L = K u

EA2 / K = K r

Beam Element EA = EAdeck

A B

Mass Point of Bent

Figure 7.26:DRAIN-2D Transverse Model

7.17 DESIGN PROCEDURE FOR BRIDGE ISOLATION

This section develops a procedure for design of isolation systems for bridges, using anexample bridge to develop the methodology. The procedure requires an iterative solution

for damping and displacement. This has been incorporated into an automatedspreadsheet procedure, an example of which is provided on the C D supplied with this book.

7.17.1 Example Bridge

This example is the design of lead-rubber isolators for a 4 span continuous bridge. The bridge

configuration is a superstructure of 4 steel plate girders with a conc rete deck. The

substructure is hollow concrete pier walls (see Figures 7.27 and 7.28).



217

Figure 7.27: Longitudinal Section of Bridge

Figure 7.28: Transverse Section of Bridge



218

Two isolation options, both using lead rubber bearings, are examined:

1. Full base isolation (period approximately 2 seconds). (This option is contained on the

example spreadsheet provided on the CD with this book).

2. Energy dissipation (period approximately 1 second).

For the base isolation design the aim is to minimize forces and distribute them approximately

uniformly over all abutments and piers. The objective of the energy dissipation design is to

minimize displacements and attempt to resist more of the earthquake forces at the

abutments than at the piers. These represent different design strategies which may beadopted for bridge design.

The response predicted by the design procedure was checked using nonlinear analysis. The

designs were based on an AASHTO design spectrum with an acceleration level, A, of 0.32and a soil fac tor, S, of 1.5. All calculation are performed using metric units (kN, mm).

7.17.2 Design of Isolators

The bearing design was based on a natural rubber formulation with a shear modulus G of

0.71 MPa, a medium hardness rubber which has been used widely for bridge isolation

systems. Table 7.7 lists the material properties for this rubber. The lead yield strength was 9

MPa, which represents the mid-point of measured effective yield strengths for LRBs.

Rubber Shear Modulus 0.00071 KPa

Lead Yield Strength 0.00900 KPa

Elongation at Break 6.00

Material Constant, k 0.65

Elastic Modulus, E 0.00284 KPaBulk Modulus 287 KPa

Table 7.7: Material Properties

Base Isolation Design

Designed was performed using a trial and error method. Original sizes were selec ted based

on the maximum vertical loads, with a starting point of setting the strain under vertical loads

approximately one-half the strain limit. The lead cores were sized so as to provide a total

Qd/W of about 5%, a typical value for moderate seismic zones. The number of rubber layers

was successively increased to produce the target period of 2.0 seconds.

The base isolation design used 500 mm square lead rubber bearings with 100 mm diameter

lead cores at each abutment. At the piers, the size was increased to 600 mm and the lead

core to 110 mm diameter. All bearings had 19 rubber layers each 10 mm thick, providing a

total bearing height of 324 mm, slightly above one-half the plan dimension. These isolators

met all AASHTO requirements for lead rubber bearings.



219

Table 7.8 summarizes the configuration and properties of these bearings, based on the

formulas provided in Chapter 5. Note that the total isolator yield strength is 283 kN at the

abutments and 342 kN at the piers. The designer must ensure that this value exceeds the

maximum combination of non-seismic loads at each of these locations. These non-seismic

loads may define the minimum lead core size.

(Units mm) Abut 1 Pier 2 Pier 3 Pier 4 Abut 5

Number of Bearings 4 4 4 4 4

Type LR LR LR LR LR All lead rubber

Plan Dimension 500 600 600 600 500

Number of Layers, N 19 19 19 19 19

Rubber Thickness, Tr 190 190 190 190 190

Lead C ore Size, dpl 100 110 110 110 100

K r 3.3 4.7 4.6 4.6 3.1 G(Ag-Apl)/Tr

K u 30.4 41.4 40.5 40.2 29.0

r

pl

ruA

AK K

1215.6

Qd 283 342 342 342 283 yApl

y 10.44 9.34 9.53 9.60 10.92

)1(u

r u

d

u

y

K

K K

Q

K

F

Table 7.8: Isolator Properties – Base Isolation

Energy Dissipation Design

For the energy dissipation option the abutment bearings were increased in size to 750 mm

square lead rubber bearings and the lead cores increased to 250 mm diameter. At the piers,the plan size of 600 mm square was retained but the lead cores were reduced from 110m to

100mm diameter. The abutment bearings had 8 rubber layers 10 mm thick, providing a total

bearing height of 181 mm, about one-quarter the plan dimension. The pier bearings had 12

layers and a total height of 233 mm. Table 7.9 provides the properties for this option.

(Units mm) Abut 1 Pier 2 Pier 3 Pier 4 Abut 5


Type LR LR LR LR LR All lead rubber

Plan Dimension 750 600 600 600 750

Number of Layers, N 8 12 12 12 8

Rubber Thickness, Tr 80 120 120 120 80

Lead C ore Size, dpl 250.0 100.0 100.0 100.0 250.0K r 18.1 7.8 7.7 7.7 18.0 G(Ag-Apl)/Tr

K u 260.6 65.4 64.6 64.3 259.8

r

pl

ruA

AK K

1215.6

Qd 1767 283 283 283 1767 yApl

y 7.29 4.91 4.97 5.00 7.31

)1(u

r u

d

u

y

K

K K

Q

K

F

Table 7.9: Isolator Properties – Base Isolation



220

7.17.3 Accounting for Bent Flexibility in Design

The bearing properties listed in Tables 7.8 and 7.9 can be used directly to solve for the

isolation performance if they are mounted on rigid substructures. Most bridges have flexible

substructures, at least at the pier locations, and the stiffness of these elements must beincluded.

For cantilever bents, the stiffness under lateral loads can be calculated as:

3

3

H

I E K

colcol

sub

(7.7a)

If the columns are in double curvature, such as under transverse loads on a multi-column

bent with a stiff cross beam:

3

12

H

I E K

colcol

sub (7.7b)

For more complex bent configurations, a model of the bent may be required to define the

stiffness. For example, this can be obtained by using a computer model of the bridge; apply

a load at deck level, obtain the displacement, sub at the top of each substructure and

record the total force in the substructure, Fsub. The stiffness is thensub

subsub

F K

. This method

also permits the effect of sub-soil flexibility to be included.

For the example bridge, the bent data required for the design are listed in Table 7.10. Thestiffness is based on gross dimensions of the conc rete section. For final design, more refined

calculations would be warranted.

Bent 1 Bent 2 Bent 3 Bent 4 Bent 5 Total

Span 35 45 50 50 180

Weight, Wi 2880 6560 7800 8200 4120 29560Longitudinal Stiffness 8.9E+08 1.5E+05 1.1E+05 2.6E+05 8.9E+08 1.8E+09

Transverse Stiffness 5.7E+10 9.8E+06 7.1E+06 1.7E+07 5.7E+10 1.1E+11

Table 7.10: Data for Bent Calculations

Calculation of the seismic performance is based on the bearing properties and bent

properties listed in Tables 7.9 and 7.10. The procedure is iterative to obtain isolation

deformations and damping which is consistent with the spec tral displacement and hysteresis

area. The steps, tabulated in Table 7.11, are:

1. Assume a deck displacement.

2. Assume a damping factor.

3. Calculate the bearing displacement at each bent for this deck displacement.

4. Calculate the hysteresis loop area and effective stiffness at each bent for this bearing

displacement.

5. Calculate the bent effec tive stiffness.



223

a. The location of the center of mass is calculated by taking moments about the left hand

abutment.

b. The location of the center of rotation is calculated by taking the first moment of the

bent stiffness.c. The torsional stiffness of the bridge is calculated as keff x2.

d. The applied torque is the total seismic force times the eccentricity between the center

of mass and the center of rotation.

e. Total shear at each bent is then calculated as the sum of the direct shear plus the

shear due to torsion.

The procedure then continues as for the longitudinal direction from Step 9 above. The

additional variables complicate the iterations on displacement and damping and it may be

more difficult to obtain convergence in this direc tion. Often, a higher tolerance is used.

For Each Bent Total Bridge

Total Shear Force W S V Atotal

Distance from Left Hand Bent, L from geometryWeight x Lever Arm, WiL

bents

i LW

Center of Mass, LCM

W

LW

bents

i

Stiffness x Distance to C entroid Lk sub bents

sub Lk

Distance to C enter of Rotation, LCR

eff

bents

bents

sub

K

Lk

Distance to C enter of Rotation, lcr L - LCR

Torsional Inertia, I T 2)( CReff L Lk bents

CReff L Lk 2)(

Eccentricity, e LCM – LCR

Torque, T eVtotal

Direc t Bent Shear, Vd

eff

eff total

k

k V

Torsional Bent Shear, Vt

T

CReff

I

Tlk

Total Bent Shear, Vb Vd + Vt

Total Bent Displacement

eff

b

k

V

Table 7.12:Additional Calculations for Deck Rotation



224

7.17.4 Evaluation of Performance

The iterative procedure described above was used to solve for longitudinal and transverse

seismic performance for each isolation option for the example bridge, base isolation andenergy dissipation. Implementation used an Excel spreadsheet, supplied with this book.

Base Isolation Design

Tables 7.13 and 7.14 list the seismic performance calculations for the longitudinal and

transverse direc tions respec tively

For longitudinal loads, the isolation system provided an effective period of 2.00 seconds and

equivalent viscous damping of 19%. The design spec trum gives a displacement of 162 mm

and a force coefficient of 0.162 for this period and damping. The 162 mm displacement was

the total displac ement at deck level. Displacements in the bearings ranged from amaximum of 162 mm at the abutments to a minimum of 152 mm at the central pier, the most

flexible bent.

In the transverse direction the piers are stiffer and so the effec tive period is slightly less, 1.94

seconds, and damping the same at 19%. Corresponding displacements and force

coefficient were 159 mm and 0.164. In the transverse direc tion the deck rotated as the spans

are not symmetrical about the center of the bridge. Bearing displacements increased from

126 mm at Abutment 1 to 200 mm at the opposite end of the bridge.


Deck Displacement 161.6


Bearing Displacement 162 155 152 158 162

Solvedby

IterationIsolator Loop Area 170995 198835 195322 202543 170448 938143

Bearing Effec tive Stiffness 5.0 6.9 6.9 6.8 4.9

Bent Stiffness 892721 153 112 265 892721

Bent Effec tive Stiffness 5.0 6.6 6.5 6.6 4.9 29.6

Period 2.004

Acceleration 0.162

Displacement 161.62

Total Shear Force 4786

Bent Shear Force 813 1072 1046 1065 790 4786

Bent Displacement 162 162 162 162 162

Elastic Energy 131457 173242 169013 172194 127661 773567

Equivalent Damping 0.193

B Factor 1.479

Table 7.13: Seismic Performance Calculations – Longitudinal



225


Deck Displacement 159.3


Bearing Displacement 125.9 140.4 159.1 179.8 200.6

Solved

by

Iteration

Isolator Loop Area 130552 179216 204435 232854 214493 961550

Bearing Effec tive Stiffness 5.5 7.2 6.8 6.5 4.5

Bent Stiffness 57134128 9797 7142 16929 57134128

Bent Effec tive Stiffness 5.5 7.2 6.8 6.5 4.5 30.5

Period 1.976

Acceleration 0.164

Displacement 159.3

Total Shear Force 4855

Distance to Center of Mass 0 35 80 130 180

Mass x Distance to

Centroid

0 229600 624000 1066000 741600 2661200

Center of Mass 90.03

Stiffness x Distance to

Centroid

0 250 541 844 818 2453

Center of Rotation 80.49

Distance to Center of

Rotation

-80 -45 0 50 100

Stiffness x Distance 2 35817 14800 2 15904 45017 111540

Eccentricity 9.54

Torque 46294

Direct Bent Shear 881 1139 1078 1034 724 4855

Torsional Bent Shear -185 -135 -1 133 188 0 Total Bent Shear 696 1004 1076 1167 912 4855

Total Bent Displacement 126 140 159 180 201

Elastic Energy = F x D 87592 140975 171222 209841 182914 792544

Equivalent Damping 0.193

B Factor 1.479

Table 7.14: Seismic Performance Calculations - Transverse

Energy Dissipation Design

The evaluation was repeated with bearing plan sizes and lead core sizes adjusted as

described earlier. For seismic loads, the energy dissipation system provided an effectiveperiod of 1.00 seconds and equivalent viscous damping of 29%. Table 7.15 compares the

seismic response of the base isolation and energy dissipation options.

The energy dissipation design produces displacements less than one-half that of the base

isolation design but the force coefficient is almost twice as high. This is a result of lesser

benefits from the period shift effect but higher levels of damping for the energy dissipation

option.



226

Longitudinal Direction Transverse Direction

BaseIsolation

EnergyDissipation

BaseIsolation

EnergyDissipation

Effective Period (seconds) 2.00 1.00 1.98 0.99

Deck Displacement (mm) 162 70 159 70Equivalent Viscous Damping 19% 29% 19% 29%

Base Shear Coefficient 0.162 0.286 0.164 0.288

Bearing Displacement (mm)

Maximum

Minimum

162

152

70

64

201

126

76

64

Bent Shear (kN)

Maximum

Minimum

1072

790

3040

772

1167

695

3135

800

Table 7.15: Summary of Results

Comparison with Time History Analysis

A time history analysis was performed of the base isolation option using the mean results from

7 time histories, each frequency scaled to be compatible for the AASHTO design spectrum.

To be equivalent with the design procedure, bent weights were excluded from the timehistory analysis. The effect of this is discussed later.

Figures 7.29 and 7.30 compare the results from the single mode method (termed Design

Procedure) with the minimum, maximum and mean results from the 7 time histories for the

base isolation and the energy dissipation option respectively.

In the longitudinal direction, the bent displacements are equal at each location as the deck

does not deform axially. Figures 7.29 and 7.30 show that the design procedure estimate of

longitudinal displacements lies approximately midway between the mean and the maximum

time history values for the base isolation option and close to maximum time history values for

the energy dissipation option.

The transverse response of the bridge includes a rotational component because of the

unequal height of the piers and non-symmetrical span lengths, as shown in Figure 7.29 for the

base isolation option. The energy dissipation option is designed to distribute a higher

proportion of superstructure inertia loads to the abutments which requires the deck to

function as a deep beam. Figure 7.30 shows the influence of deck flexural deformations on

transverse displacements for this option.

As for longitudinal displacements, the transverse displacements estimated from the design

procedure are between the mean and maximum values from the time history analysis. The

design procedure shows similar levels of rotation to the time history results but does not

include the deck flexural deformations which are important for the energy dissipation option.



227

Longitudinal

0

50

100

150

200

250

BENT 1 BENT 2 BENT 3 BENT 4 BENT 5

D e c k D i s p l a c e m e n t ( m

m )

Time History Minimum

Time History Average

Time History Maximum

Design Procedure

Transverse

0

50

100

150

200

250


D e c k D i s p l a c e m e n t ( m m )

Time History Minimum Time History Average Time History MaximumDesign Procedure

Figure 7.29:Base Isolation Displacements

Longitudinal

0

20

40

60

80

100

120



Time History Minimum

Time History Average

Time History Maximum

Design Procedure

Transverse

0

20

40

60

80

100

120



Time History Minimum Time History Average Time History MaximumDesign Procedure

Figure 7.30: Energy Dissipation Displacements

These results show that the simplified design procedure, including bent flexibility, provides a

good approximation to the more accurate response calculated from the time history. The

design procedure results are higher than the mean from the 7 time history results but lowerthan the maximum results. However, the results also show that when a system incorporates

significant force distribution between bents, as for the energy dissipation option, moredetailed analysis of deck deformations may be required.

These results imply that, depending on whether the mea n o f 7 or ma ximum o f 3 time history

method were chosen, the design procedure would be either slightly conservative or slightlynon-conservative. Given the uncertainties implicit in the selection of the time histories, this

suggests that an isolation system based on the simplified design procedure would provide a

system with satisfactory performance.



228

7.17.5 Effect of Isolation System on Displacements

The design of an isolation system for the example bridge has considered two options, a base

isolation system (large period shift, moderate damping) and an energy dissipation system(moderate period shift, high damping). A range of systems between these two could also

be designed.

The type of system selected depends on the objectives as there are significant differences in

displacements and force distributions. Figures 7.31 and 7.32 compare respectively the

longitudinal and transverse deck displacements for the base isolation system and the energy

dissipation system.

In the longitudinal direction the displacements at deck level are enforced to be equal by the

axial stiffness of the deck. The base isolation displacements of 162 mm are 2.3 times as high

as the maximum energy dissipation displacements of 70 mm. In the transverse direction the

large lead cores at the abutments restrain rotation and there is some deformation due to

flexure of the deck. The maximum isolated displacement of 201 mm at Abutment B is 2.6

times the displacement with with the energy dissipation bearings, 76 mm. Therefore, theenergy dissipation option requires much smaller expansion joints at the abutments.

0

20

40

60

80

100

120

140

160

180

Bent 1 Bent 2 Bent 3 Bent 4 Bent 5


Base Isolated

Energy Dissipation

Figure 7.31:Longitudinal Displacements



230

0

2000

4000

6000

8000

10000

12000


Force (kN)

Base Isolated

Energy DissipationFixed

Figure 7.33:Longitudinal Forces

Transverse

In the transverse direction, the fixed bearings distribute seismic forces to the piers in

approximate proportion to their stiffness as shown in Figure 7.34. The maximum abutment

force is 5244kN and the maximum pier force is 5,447kN at Pier 3, the shortest pier.

With isolation bearings, the forces are distributed relatively uniformly between all abutments

and piers. The maximum abutment force is 912kN, the maximum pier force is 1167kN. As for

the longitudinal direction, peak forces are reduced by a fac tor of over 5. The energy

dissipation bearings produce a force distribution which differs from both the fixed bearingsand isolation bearings. Most force is resisted at the abutments, which have a maximumforce of 3134kN and a small proportion at the piers, where the maximum force is 840kN.

0

1000

2000

3000

4000

5000

6000


Force (kN)

Base Isolated

Energy Dissipation

Fixed

Figure 7.34: Transverse Forces



231

7.17.7 Summary

This bridge example has illustrated how bearings can be used in bridge structures both to

reduce overall seismic forces on the bridge and to a lter the distribution of these forces to thedifferent substructure elements.

In this example, a typical seismic isolation design is based on a 2 second isolated period and

similar isolators at all abutments and piers. This reduces total seismic forces by a factor of

almost 5 in both the longitudinal and transverse directions. Because the forces are

approximately equally distributed, the isolation bearings reduce local forces by a greater

factor. The longitudinal abutment forces are reduced by a factor of 10, the transverse pier

forces are reduced by a factor of almost 5. However, the force reductions were assoc iated

with maximum deck displacements of over 160 mm and so a substantial expansion joint willbe required to permit this amount of free movement.

The energy dissipation design used stiffer bearings with large lead cores at the abutments toreduce the isolated period to 1 second and concentrate forces in the abutments. This

reduced the displacements compared to the isolated design, with longitudinal

displacements of 70 mm, 40% of the isolated displacements. This provides savings in the

provision of expansion joints at the abutments. As the period shift was less, the seismic force

reductions compared to the fixed bearing design were smaller.

This example provides two examples of achieving different objectives using lead rubber

bearings and there are numerous other possible permutations. The aim of a designprocedure is to enable rapid evaluation of alternative isolator configurations, as

implemented in the spreadsheet provided with this book.

7.18 IMPLEMENTATION IN SPREADSHEET

Included with this book is a spreadsheet which can be used to evaluate system performance

and fac tors of safety based on user selec ted isolator details. The spreadsheet is not

intended for final design or to substitute for the calculations by the engineer of record. It is atool provided to assist users in developing their own isolation design procedures.

The example provided in this section is based on design to 1991 AASHTO requirements.

Designs based on other codes follow the same general principles. In the spreadsheet, cells

colored red indicate user-spec ified input. The workbook contains a number of sheets with

the design performed within the sheet CONTROL.

The spreadsheet is set up for up to 8 substructures. This can be extended by inserting

additional columns and copying formulas ac ross the sheet.



232

7.18.1 Material Properties

The material definitions are contained on the sheet ISOLATORS , as shown in Figure 7.35. This is

the basic information used for the design process. The range of properties available forrubber is restricted and some properties are related to others, for example, the ultimate

elongation, material constant and elastic modulus are all a function of the shear modulus.

Information on available rubbers is provided elsewhere in this book.

MATERIAL PROPERTIES

Rubber Shear Modulus 0.00071 KPa

Lead Yield Strength 0.009 KPa

Elongation at Break 6.00

Material Constant, k 0.65

Elastic Modulus, E 0.00284 KPa

Bulk Modulus 287 KPa

Figure 7.35: Material Properties

7.18.2 Dimensional Properties

Dimensional properties are also set on the ISO LATORS sheet (Figure 7.36). These are

properties which are constant for the type of bearing and which do not change as plan size

changes:

1. Rubber layer, usually 10 mm (or 3/8”) but may be changed depending on load

conditions.

2. Isolator shape, usually square for bridge bearings.

3. Internal shim thickness, typically 3 mm (1/8”).

4. Load plate thickness, usually at least 25 mm (1”).

Other dimensional parameters (plan size, number of layers) are not set on this sheet as they

are a ltered from the CONTROL sheet as design progresses.



233

BEARING DIMENSIONS

Plan Dimension 500 600 600 600 500

Layer Thickness 10 10 10 10 10

Number of Layers 19 19 19 19 19

Lead Core Size 100.00 110.00 110.00 110.00 100.00

Shape (S = Square, C = Circ) S S S S S

Total Height 294.00 294.00 294.00 294.00 294.00

BEARING PROPERTIES

Gross Area 250000 360000 360000 360000 250000

Side Cover 10 10 10 10 10

Bonded Dimension 480 580 580 580 480

Bonded Area 230400 336400 336400 336400 230400

Plug Area 7854 9503 9503 9503 7854

Net Bonded Area 222546 326897 326897 326897 222546

Total Rubber Thickness 190.00 190.00 190.00 190.00 190.00

Bonded Perimeter 1920 2320 2320 2320 1920

Shape Factor 11.6 14.1 14.1 14.1 11.6

Internal Shim Thickness 3.00 3.00 3.00 3.00 3.00

Load Plate Thickness 25.00 25.00 25.00 25.00 25.00

Lead Yield Strength (KPa) 0.01 0.01 0.01 0.01 0.01

Characteristic Strength, Qd 70.7 85.5 85.5 85.5 70.7Shear Modulus (50%) 0.0006 0.0006 0.0006 0.0006 0.0006

Yielded Stiffness Kr (50%) 0.82 1.18 1.15 1.15 0.78

Elastic Stiffness Ku (50%) 7.59 10.34 10.13 10.06 7.26

Yield Force 79.3 96.5 96.5 96.5 79.3

Yield Displacement 10.44 9.34 9.53 9.60 10.92

Figure 7.36: Dimensions and Properties

7.18.3 Load and Design Data

The required load and design conditions are entered on the DESIGN sheet, as shown in Figure

7.37. Required data from this sheet is:

1. Superstructure seismic weight at each bent, usually dead load alone. This is divided by

the number of bearings to get the seismic vertical load per bearing.

2. Total dead plus live load at each bent. This is divided by the number of bearings to get

the maximum gravity load per bearing.

3. Calculated stiffness of each bent in the longitudinal and transverse direc tions. Note

that the spreadsheet contains formulas for cantilever piers. These can be replaced by

other formulas, or stiffness values can be entered direc tly. For stiffness properties, onlythe rows for Lon g itud ina l K and Transve rse K are used for the design.



234

Abut 1 Pier 2 Pier 3 Pier 4 Abut 5

DESIGN DATA (KN, m)

Span 35 45 50 50

Superstructure Weight (Longl) 2880 6560 7800 8200 4120

Superstructure Weight (Trans) 2880 6560 7800 8200 4120

Total D + L at Bent 6080 12960 14200 14600 7320

Pier Dimensions

Dimension Longitudinal 2.0 2.0 2.0 2.0 2.0

Dimension Transverse 16.0 16.0 16.0 16.0 16.0

Pier Height (Longl) 1.0 18.0 20.0 15.0 1.0

Pier Height (Trans) 1.0 18.0 20.0 15.0 1.0

Elastic Modulus 2.8E+07 2.8E+07 2.8E+07 2.8E+07 2.8E+07

Calculated Stiffnesses

Longitudinal I 10.7 10.7 10.7 10.7 10.7

Longitudinal K 8.9E+08 1.5E+05 1.1E+05 2.6E+05 8.9E+08

Transverse I 683 683 683 683 683

Transverse K 5.7E+10 9.8E+06 7.1E+06 1.7E+07 5.7E+10

Transverse Breakaway Force

Thermal Span 90 55 10 -40 -90

Temperature Change,oF 54

Thermal Movement 31.6 19.3 3.5 14.0 31.6

Figure 7.37: Load and Design Data

7.18.4 Isolation Solution

Once material, dimensional and design data have been entered the isolation system is

designed by entering values on the CONTROL worksheet. This is an iterative process,

controlled by the portion of the spreadsheet shown in Figure 7.38. The procedure is to enter

dimensional values in the cells and then active the macro to Solve Disp la c em ent for thisconfiguration. As part of the design process, changes are made to the following

parameters:

1. Plan dimensions. These must be set so that the isolator status (at the bottom of Figure 5-19) is “OK” for each AASHTO condition.


isolated period is in the range required and so that the maximum shear strain is not

excessive. This is set by trial and error.


of QD/W is displayed for guidance. This ratio usually ranges from 3% in low seismic zones

to 10% or more in high seismic zones. Usually the softer the soil the higher the yield level

for a given seismic zone. As for the number of rubber layers, the core is sized by trial and

error.

The user must ensure that the total yield strength of the lead cores at each substructure is

sufficient to resist all combinations of short term non-seismic lateral loads, as discussed earlier.



235

Job title Test Bridge

Bridge Number: 1

Units M (US (kip,ft) or Met

Gravity 9.81 9810 1000

AASHTO

G 0.32

S 1.50

ISOLATORS (Units mm) Abut 1 Pier 2 Pier 3 Pier 4 Abut 5


Type (LR or F (fixed)) LR LR LR LR LR

Isolator Plan Dimension 500 600 600 600 500

Number of Layers 19 19 19 19 19

Isolator Rubber Thickness 190 190 190 190 190

Isolator Lead Core Size 100.0 110.0 110.0 110.0 100.0

Kr 3.3 4.7 4.6 4.6 3.1

Ku 30.4 41.4 40.5 40.2 29.0

Qd 283 342 342 342 283

Dy 10.44 9.34 9.53 9.60 10.92

Abut 1 Pier 2 Pier 3 Pier 4 Abut 5

PERFORMANCE

Longitudinal Displacement 161.6 161.6 161.6 161.6 161.6

Longitudinal Force 813.3 1071.8 1045.6 1065.3 789.8

Transverse Displacement 125.9 140.4 159.1 179.8 200.6

Transverse Force 695.9 1004.1 1076.3 1166.9 911.9

ISOLATOR STATUS Abut 1 Pier 2 Pier 3 Pier 4 Abut 5

Maximum Displacement 161.6 161.6 161.6 179.8 200.6

AASHTO Condition 1 OK OK OK OK OK



Buckling OK OK OK OK OK

Reduced Area

Solve Displacement

Figure 7.38: Control of Design Process



237

CHAPTER 8 APPLICATIONS OF SEISMIC ISOLATION

8.1 INTRODUCTION

This chapter presents details of seismically isolated buildings, bridges and other structures all overthe world, up to the time it was written, in 1992. The information, photographs and tables werecompiled with input from the authors’ colleagues worldwide and this enabled compilation of awide-ranging and objective overview of applications of seismic isolation to that date.

In order to retain the information as a complete unit, it is reproduced here as it was written in1992. Chapter 10 will present results that have been achieved in the twelve years since then, upto the time of writing this new book, in 2004.

The authors began by noting that, since beginning their studies of seismic isolation, some 25years before, (1967), they had been in more or less continuous contact with colleagues in J apan, the United States of America, and more recently Italy. They were thus well aware of thesituation in New Zealand and in those countries and the emphasis of this chapter is placed onapplications of seismic isolation there. However, as discussed by Buckle & Mayes (1990), seismicisolation has also been applied in many other countries, as summarised in Table 8.1.

This table, together with Tables 8.2 to 8.8, gives an indication of the criteria for choosing theseismic isolation option, namely the likelihood of a seismic event occurring, multiplied by theintensity of the anticipated event, multiplied by the value or the hazard of the structure and/orcontents. In the text we have discussed seismic applications under three broad headings,namely, buildings, bridges and 'delicate' or 'hazardous' structures.

An issue of prime importance is the performance of seismically isolated structures in severeearthquakes, but none of the structures discussed below have been subjected to such a test.Of the buildings and bridges seismically isolated in New Zealand to date, only one, the Te TekoBridge over the Rangitaiki River, has undergone the effects of a large earthquake. This was theEdgecumbe earthquake in March 1987, Richter magnitude 6.3, MM9, epicentre 9 km north ofthe bridge. A strong-motion accelerograph located 11 km south of the bridge recorded a peakhorizontal ground acceleration of 0.33 g. This bridge "provides an example of goodperformance of modern earthquake resistance technology, i.e., base isolation using lead rubberbearings" (Dowrick, 1987). However, one of the standard elastomeric bearings elsewhere on thebridge was not properly restrained against sliding, and was thrown out of position, so that itceased supporting the deck (Skinner & Chapman, 1987). The behaviour of the bridge was,therefore, not perfect.

In order that seismic isolation be effective, it must be stressed that it is the responsibility of all thepeople concerned in the design, manufacture and use of a seismically isolated structure, toensure that the system is maintained operative, and particularly that the seismic gap isprotected. As mentioned in Chapter 1, this space must be uncluttered by waste material, and itmust be respected during subsequent building alterations. The seismic gap must remain free atall times, so that the structure can move by the required amount during the 5 or so seconds of amajor earthquake, which can occur at any unpredictable time in the life of the structure.

This is obviously an educational problem, which is currently severe because seismic isolation is arelatively new technology. New owners/operators are likely, through ignorance, to abuse theseismic gap and thereby render the seismic isolation system inoperative.



238

It is suggested that permanent notices or plaques be situated at or near the gap, that the stateand relevance of the seismic isolation be stressed in the 'ownership papers', and that engineersand building inspectors take particular notice of the need for security of the gap.

Country Constructed Facilities

Canada

Chile

China

England

France

Greece

Iceland

Iran/Iraq

Italy

J apan

Mexico

New Zealand

Rumania

USSR

South Africa

USA

Yugoslavia

Coal ship loader, Prince Rupert, BC

Ore ship loader, Guacolda

2 houses (1975);weigh station (1980);4-storey dormitory, Beijing (1981)

Nuclear fuel processing plant

4 houses (1977-82)3-storey school, Lambesc (1978)Nuclear waste storage fac ility (1982)2 nuclear power plants, Cruas and Le Pelliren

2 office buildings, Athens

5 bridges

Nuclear power plant, Karun River12-storey building (1968)

See text and Table 8.8

See text and Tables 8.4 and 8.5

4-storey school (Mexico City)


Apartment

3 buildings, Sevastopol3-storey building

Nuclear power plant


3-storey school, Skopje (1969)

Table 8.1: Applications of Seismic Isolation World-wide (after Buckle & Mayes, 1990)



239

8.2 STRUCTURES ISOLATED IN NEW ZEALAND

8.2.1 Introduction

In New Zealand, seismic isolation has been achieved by a variety of means: transverse rockingaction with controlled base uplift, horizontally flexible elastomeric bearings, and flexible sleeved-pile foundations. Damping has been provided through hysteretic energy dissipation arising fromthe plastic deformation of steel or lead in a variety of devices such as steel bending-beam andtorsional-beam dampers, elastomeric bearings with and without lead plugs, and lead-extrusiondampers (See Chapter 3).

The New Zealand approach to seismic isolation incorporates energy dissipation in the isolationsystem, in order to reduce the displacements required across the isolating supports, to furtherreduce seismic loads, and to safeguard against unexpectedly strong low-frequency content inthe earthquake motion. Combined yield-level forces of the hysteretic energy dissipators rangefrom about 3% to 15% of the structure's weight, with a typical value of about 5%. Displacement

demands across the isolators range from about 100-150 mm for motions of El Centro type andseverity, to about 400 mm for the Pacoima Dam record. Structural response can often belimited to the elastic range in the design-level earthquake, with limited ductility requirementsduring extreme earthquake conditions. Substantial cost savings of up to 10% of the structure'scost, together with an expected improvement in the seismic performance of the structure, haveresulted from the adoption of the isolation approach. Some New Zealand applications arediscussed by McKay e t a l (1990).

Bridges and structures which have been built in New Zealand are discussed in this section. Table8.2 shows the variety of techniques used in the seismic isolation of buildings, of which the WilliamClayton Building in Wellington, started in 1978 and completed in 1981, was the first in the world toincorporate lead rubber bearings. This and other buildings are discussed in the text. Current

work is the design of a retrofitted seismic isolation system for New Zealand Parliament Buildings(Poole & Clendon, 1991).

Table 8.3 shows that lead rubber bearing isolation is the technique favoured in bridges. Theparticular applicability of lead rubber bearings for bridge isolation arises from the fact thatelastomeric bearings, made of laminated steel and rubber as described in Chapter 3, arealready an accepted technology for the accommodation of thermal expansion in bridges.Isolation can then be added at a small additional cost by the removal of further constraints, byprovision for larger displacements, and by the incorporation of suitable lead plugs to providehigh levels of hysteretic damping.



240

Building Height/Storeys

Total FloorArea (m2)

Isolation System Date Completed

William C laytonBuilding, Wellington

4 storeys17 m

17000 Lead Rubberbearings

1981

Union House,Auckland

12 storeys49 m

7400 Flexible piles andsteel dampers

1983

Wellington CentralPolice Station

10 storeys 11000 Flexible piles andlead extrusion

dampers

1990

Press Hall, PressHouse, Petone

4 levels14 m

950 Lead rubber bearings 1991

Parliament House,Wellington

5 storeys19.5 m

26500 Retrofit ofelastomeric bearings

and lead rubber

Original building1921;

retrofit proposed

Parliament Library,Wellington

5 storeys16 m

6500 Retrofit ofelastomeric bearings

and lead rubber

Original 1883/1899;retrofit proposed

Table 8.2: Seismically Isolated Buildings in New Zealand



241

Bridge Name SuperstructureType

Length(m)

Isolation System DateBuilt

123456789101112

131415161718192021-24252627

28293031323334,3536,37383940414243

444546474849

MotuSouth Rangitikei viaductBolton StreetAurora Terrace ToetoeKing Edward StreetCromwellClydeWaiotukupunaOhaakiMaungatapuScamperdown

GulliverDonneWhangaparoaKarakatuwheroDevils CreekUpper AorereRangitaiki (Te Teko)NgaparikaHikuwai No. 1-4 (retrofit)OretiRapids Tamaki

Deep Gorge Twin Tunnels TaraweraMoonshineMakarika No. 2 (retrofit)Makatote (retrofit)Kopuaroa No. 1 & 4(retrofit)Glen Motorway & RailwayGrafton No. 4Grafton No. 5Northern WairoaRuamahanga at Te OreOreMaitai (Nelson)Bannockburn

HairiniLimeworksWaingawaMangaonePorirua State HighwayPorirua Stream

Steel TrussPSC Box

Steel I BeamSteel I BeamSteel TrussPSC Box

Steel TrussPSC U-Beam


PSC SlabSteel Box

Steel TrussSteel Truss

PSC I-BeamPSC I-BeamPSC U-Beam


Steel TrussSteel Plate G irder

PSC I-BeamPSC I & U-Beam

PSC I-Beam

Steel TrussPSC I-BeamPSC I-BeamPSC U-Beam

Steel Plate G irderSteel Plate G irderSteel Plate G irder

PSC T-BeamPSC T-BeamPSC I-BeamPSC I-BeamPSC U-BeamPSC I-BeamSteel Truss

PSC SlabSteel Truss

PSC U-BeamSteel Truss

PSC T-BeamPSC U-Beam

170315716172522725744834685

3636125105266410376

74-922206840

7290631684787

25 & 5560508049211693147

6272135523884

Steel UBs in flextureSteel torsion bar/rocking

piersLead extrusionLead extrusionLead/rubber

Steel CantileverSteel flexural beam

Lead/rubberLead/rubberLead/rubberLead/rubber

Lead/rubberLead/rubberLead/rubberLead/rubberLead/rubberLead/rubberLead/rubberLead/rubberLead/rubberLead/rubberLead/rubberLead/rubber

Lead/rubberLead/rubberLead/rubberLead/rubberLead/rubber

Steel CantileverLead/rubber

Steel CantileverLead/rubberLead/rubberLead/rubberLead/rubberLead/rubberLead/rubber

Lead/ rubber &Lead extrusionLead/rubberLead/rubberLead/rubberLead/rubberLead/rubberLead/rubber

197319741974197419781979197919811981198119811982

19831983198319831983198319831983

1983-4198419841985

198419851985198519851986

1986-71987198719871987198719871988

19891990199019921992

Key: PSC = prestressed concrete

UB = U-beam

Table 8.3: Seismically Isolated Bridges in New Zealand



242

8.2.2 Road Bridges

Since 1973 forty-eight road bridges and one rail bridge in New Zealand have been seismicallyisolated, see Table 8.3. Four examples of seismic upgrading by the retrofitting of isolation systems

are included in this list.

By far the most common form of isolation system for bridges uses lead rubber bearings, usuallyinstalled between the bridge superstructure and the supporting piers and abutments. The leadrubber bearing combines the functions of isolation and energy dissipation in a single compactunit, while also supporting the weight of the superstructure and providing an elastic restoringforce. The lead plug in the centre of the elastomeric bearing is subjected to a sheardeformation under horizontal loading, providing considerable energy dissipation when it yieldsunder severe earthquake loading. The lead rubber bearing provides an extremely economicsolution for seismically isolating bridges.

Many unisolated New Zealand bridges use elastomeric bearings between superstructures and

their supports, to accommodate thermal movements. Little modification to standard structuralforms has been necessary in order to incorporate the lead plug to produce seismic isolationbearings, apart from the removal of some constraints and provision of a seismic gap toaccommodate the increased superstructure displacements which may occur under seismicloading. As well as providing energy dissipation during large movements, the lead plug alsostiffens the bearing under slow lateral forces up to its yield point, reducing the displacementsunder wind and traffic loading (Robinson, 1982).

Further information on the seismic isolation of road bridges in New Zealand, including casestudies and design procedures, is given by Blakeley (1979), Billings & Kirkcaldie (1985), & Turkington (1987).

The first bridge to be seismically isolated in New Zealand was the Motu Bridge, built in 1973. The

light-weight replacement superstructure was a 170 m steel truss supported by the existingreinforced-concrete slab-wall piers. The superstructure was isolated using sliding bearings withthe damping provided by vertical-cantilever structural-type steel columns. An example of theuse of lead rubber bearings in bridges is illustrated in Figures 8.1 and 8.2, which show theMoonshine Bridge, a 168 m prestressed, concrete, curving bridge on a motorway in the Huttarea, New Zealand.

Figure 8.1: Moonshine Bridge, Upper Hutt, New Zealand



243

Figure 8.2: Moonshine Bridge, Upper Hutt, showing lead rubber bearing underthe beams, and restraining stops.

Figure 8.3: Aurora Terrace over bridge, Wellington C ity.

Figure 8.3 shows a bridge over the Wellington Motorway which is fitted with lead extrusiondampers at the lower abutment. It is one of a pair of sloping bridges which were seismicallyisolated by being mounted on glide bearings, the restoring force being provided by steel

columns. The advantage of the extrusion dampers is that they lock the bridges in place duringthe braking of vehicles travelling downhill, yet at earthquake loads allow the bridges to move. Thermal expansion forces can be released by the creep of the extrusion dampers. After a largeearthquake it is expected that the bridges will no longer have the seismic gaps ideallypositioned.

If necessary the bridges can then be jacked to the ideal position or allowed to creep back withthe flexible columns providing the restoring force.



244

8.2.3 South Rangitikei Viaduct with Stepping Isolation

The South Rangitikei Viaduct, which was opened in 1981, is an example of isolation throughcontrolled base-uplift in a transverse rocking action. The bridge is 70 metres tall, with six spans ofprestressed concrete hollow-box girder, and an overall length of 315 metres (Cormack, 1988).

Figure 8.4 shows the stepping isolation schematically, and Figures 8.5 and 8.6 are photographs ofthe bridge under construction, and of the first train to use it.

Figure 8.4: Schematic of base of stepping pier, South Rangitikei Viaduct.

Figure 8.5: South Rangitikei Viaduct during construction.

Figure 8.6: Inaugural train on South Rangitikei Viaduct.



245

The stresses which can be transmitted into the slender reinforced concrete H-shaped piers underearthquake loading are limited by allowing them to rock sideways, with uplift at the basealternating between the two legs of each pier. The extent of stepping, and the assoc iatedlateral movement of the bridge deck, is limited by energy dissipation provided by the hystereticworking of torsionally-yielding steel-beam devices connected between the bottom of the

stepping pier legs and the caps of the high-stiffness supporting piles. (The E-type steel damperused is shown in Figure 3.3.)

The stepping action reduces the maximum tension calculated in the tallest piers, for the 1940El Centro NS record, to about one-quarter that experienced when the legs are fixed at thebase; unlike the fixed-base case there is little increase in base-level loads for stronger seismicexcitations. The dampers reduce the displacements to about one-half those in the undampedcase, and reduce the number of large displacements to less than one-quarter. The maximumdisplacement at the deck level for the damped stepping bridge is about 50% greater than forthe fixed-leg bridge, Beck & Skinner (1974).

The twenty-four energy dissipators operate at a nominal force of 450 kN with a design stroke of

80 mm. The maximum uplift of the legs is limited to 125 mm by stops. The weight of the bridge atrest is not carried by the dampers, but is transmitted to the foundations through thin laminated-rubber bearings whose primary functions are to allow rotation of each unlifted pier foot, and todistribute loads at the pier/pile-cap interfaces.

The stepping action is very effective in reducing seismic loads on this bridge because its centreof gravity is high, so that the non-isolated design was strongly dominated by overturningmoments at the pier feet. The hysteretic damping during stepping is quite effective becausethe estimated self-damping of the stepping mechanism is quite low, owing to the relatively rigidpile caps.

A chimney structure at the Christchurch Airport was also provided with a stepping base. Theresultant cost saving was about 7% (Sharpe & Skinner, 1983).

8.2.4 William Clayton Building

The William Clayton Building in Wellington, started in 1978 by the New Zealand Ministry of Worksand Development and completed in 1981, was the first building in the world to be seismicallyisolated on lead rubber bearings. (See Chapter 3 and Figure 3.16.)

Figure 8.7: Diagram showing detail of lead rubber bearing, William Clayton Building, Wellington.



246

Details of a lead rubber bearing for this building are shown in Figure 8.7. The 80 bearings arelocated under each of the columns of the 4-storey reinforced concrete frame building, which is13 bays long by 5 bays wide with plan dimensions of 97 m x 40 m. Each bearing carries a verticalload of 1 to 2 MN and is capable of taking a horizontal displacement of + 200 mm. Detaileddescriptions of the building have been given by Meggett (1978) and Skinner (1982). It is shown,

during construction and after completion, in Figures 8.8 and 8.9.

Figure 8.8: Wellington Clayton Building during construction; note lead rubber bearing.

Figure 8.9: William Clayton Building completed and occupied.

The pioneering nature of the building and its proximity to the active Wellington fault dictatedthat a conservative design approach be taken. The design earthquake was taken as 1.5 ElCentro NS 1940, for which the calculated maximum dynamic base shear was 0.20 times thetotal building weight W, and this was selec ted as the design static base shear force. The artificialA1 record, which is intended to represent near-fault motion in a magnitude 8 earthquake, wasconsidered as the 'maximum credible' motion, producing a calculated maximum base shear of0.26 W. Even though the calculated response of the seismically isolated structure was essentiallyelastic for the design earthquake motions, a capacity design procedure was used, as requiredfor design with high ductility.



248

Although Auckland is in a region of only moderate seismic activity, there is concern that it couldbe affected by large earthquakes, up to magnitude 8.5, centred 200 km or more away in theBay of Plenty and East Cape regions near the subduction zone boundary between the Pacificand Indo-Australian plates. Such earthquakes could cause strong shaking in the flexible soils atthe site.

Isolation was achieved by making the piles laterally flexible with moment-resisting pins at eachend. The piles were surrounded by clearance steel jackets allowing ±150 mm relativemovement, thus separating the building from the potentially troublesome earthquake motionsof the upper soil layers and making provision for the large base displacements necessary forisolation. An effective isolation system was completed by installing steel tapered-cantileverdampers at the top of the piles at ground level to provide energy dissipation and deflectioncontrol. The structure was stiffened and strengthened using external steel cross-bracing, (seeFigure 8.10).

Figure 8.10: Union House, Auckland City; note the external diagonal bracing.

The increased stiffness improved the seismic responses, giving reduced inter-storeydisplacements, a reduced shear force bulge at mid-height and reduced floor spectra.Moreover, the cross-brac ing provided the required lateral strength at low cost. The reducedstructure ductility was adequate with the well-damped isolator.

The dampers are connected between the top of the piles supporting the superstructure and the

otherwise structurally separated basement and ground-floor structure, which is supporteddirec tly by the upper soil layers.

As Auckland is a region where earthquakes of only moderate magnitude are expected, theseismic design specifications for Union House are less severe than for many other seismicallyisolated structures. The maximum dissipator deflections in the 'maximum credible' El Centromotion were 150 mm, with 60 mm in the design earthquake. The effective period of the isolatedstructure was about 2 seconds. Maximum inter-storey deflections were typically 10 mm for themaximum credible earthquake and 5 mm for the design earthquake.



249

Union House is an example of the economical use of seismic isolation in an area of moderateseismicity. An appropriate structural form was chosen to take advantage of the reductions ofseismic force, ductility demands and structural deformations offered by the seismic isolationoption. The inherently stiff cross-braced frame is well-suited to the needs for a stiff superstructurein the seismically isolated approach. Isolation in turn makes the cross-brac ing feasible, because

low ductility demands are placed on the main structure. However, if very low floor spectra arerequired, it may be necessary to use more linear veloc ity dampers. An important fac tor in thedesign of such isolation systems is the need for an appropriate allowance for the displacementof the pile-sleeve tops with respect to the fixed ends of the piles.

Other structural forms were investigated during the preliminary design stages, including two-wayconcrete frames, peripheral concrete frames, and a cantilever shear core. The cross-bracedisolated structure allowed an open and light structural facade, and a maximum use of precastelements. The seismically isolated option produced an estimated cost saving of nearly7 percent in the total construction cost of NZ$6.6 million (in 1983), including a construction-timesaving of three months.

8.2.6 Wellington Central Police Station

The new Wellington Central Police Station (Charleson e t a l ., 1987), completed in 1991, is similar inconcept to Union House. The ten-storey tower block is supported on long piles founded 15 mbelow ground in weathered greywacke rock. The near-surface soil layer consists of marinesediments and fill of dubious quality.

Figure 8.11: Lead extrusion damper in basement of Wellington Central Police Station.



250

Figure 8.12: Wellington Central Police Station; note the external diagonal bracing.

Again the piles are enclosed in oversize casings, with clearances which allow considerabledisplacements relative to the ground. Energy dissipation is provided by lead-extrusion dampers,(Robinson & Greenbank, 1976), connected between the top of the piles and a structurallyseparate embedded basement (see Figure 8.11). A cross-braced reinforced concrete frameprovides a stiff superstructure (see Figure 8.12). The flexible piles and lead-extrusion dampersprovide an almost elastic-plastic force-displacement characteristic for the isolation system,which controls the forces imposed on the main structure.

The seismic design spec ifications for the Wellington Central Police Station are considerably more

severe than those for Union House in Auckland. The Police Station has an essential Civil Defencerole and is therefore required to be in operation after a major earthquake. The New ZealandLoadings Code requires a risk factor R=1.6 for essential facilities. The site is a few hundred metresfrom the major active Wellington fault, and less than 20 km from several other major faultsystems.

Functional requirements dictated that the lateral load-resisting structure should be on theperimeter of the building. Three structural options were considered: a cross-braced frame, amoment-resisting frame or a seismically isolated cross-braced frame. This last option lookedattractive from the outset because the foundation conditions required piling, but the perimetermoment-resisting frame was also considered at length.

The structure is required to respond elastically for seismic motions with a 450-year return period,

corresponding to a 1.4 times scaling of the 1940 El Centro accelerogram. The building mustremain fully functional and suffer only minor non-structural damage for these motions. This isassured by the low inter-storey deflections of approximately 10 mm. With an isolation systemwith a nearly elastic-plastic force-deflection characteristic, and a low yield level of 0.035 of thebuilding seismic weight, it was found that there was only a modest increase in maximum frameforces for the 1000-year return period motions, corresponding to 1.7 El Centro NS 1940 or the1971 Pacoima Dam record. The increase in force was almost accommodated by the increasefrom dependable to probable strengths appropriate to the design and ultimate load conditionsrespectively. It is possible that some yielding will occur under the 1000-year return periodmotions, but the ductility demand will be low and specific ductile detailing was consideredunnecessary. The Pacoima Dam record poses a severe test for a seismic isolation systembecause it contains a strong long-period pulse, thought to be a 'fault-fling' component, as well

as high maximum accelerations. The Pacoima record imposes severe ductility demands onmany conventional structures.



251

The degree of isolation required to obtain elastic structural response with these very severeearthquake motions requires provision for a large relative displacement between the top of thepiles and the ground. A c learance of 375 mm was provided between the 800 mm diameterpiles and their casings, to give a reasonable margin above the maximum calculateddisplacements; 355 mm was calculated for one of the 450-year return period accelerograms.

Consideration was also given to even larger motions, when moderately-deformable columnstops will contact the basement structure, which has been designed to absorb excess seismicenergy in a controlled manner in this situation.

The large displacement demands on the isolation system and the almost elastic-plastic responserequired from the energy dissipators led to the choice of lead-extrusion dampers rather thansteel devices as used in Union House. In total, 24 lead-extrusion dampers each with a yield forceof 250 kN and stroke of ±400 mm were required. This was a considerable scaling-up of previousversions of this type of damper used in several New Zealand bridges: the bridge dampers had ayield level of 150 kN and a stroke of ±200 mm. The new model damper was tested extensivelyto ensure the required performance.

The seismically isolated option was estimated to produce a saving of 10% in structural cost overthe moment-resisting frame option. In addition, the seismically isolated structure will have aconsiderably enhanced earthquake resistance. Moreover, the repair costs after a majorearthquake should be low. Importantly, the seismically isolated structure should be fullyoperational after a major earthquake.

8.3 STRUCTURES ISOLATED IN JAPAN

8.3.1 Introduction

The first seismically isolated structure to be completed in Japan was the Yachiyodai ResidentialDwelling, a 2-storey building, completed in 1982. This building is mounted on six laminatedrubber bearings and relies on the friction of a precast concrete panel for the damping. Since1985, more than 50 buildings have been authorised, of 1 to 14 storeys in height. They range fromdwellings to tower blocks, with floor areas from 114 m2 to 38 000 m2. Details of buildingsseismically isolated in J apan are given in Table 6.4 (Shimoda 1989-1992; Saruta, 1991, 1992; Seki,1991, 1992). Various seismic isolation and damping systems have been used, often in hybridcombinations, as indicated in Table 6.4 and its footnote. The most popular isolation systems forbuildings are laminated rubber for the isolation, with either steel or lead providing the damping. The first seismically isolated bridge in J apan was completed in 1990 and is mounted on leadrubber bearings. Details of some bridges seismically isolated in J apan are given in Table 8.5(Shimoda 1989-1992; Seki, 1991, 1992; Saruta, 1991, 1992). Except for one mounted on a high-damping rubber bearing, all of these use lead rubber bearings.



252

Type Building Name Storey TotalFloorarea(m2)

IsolationSystem

LicenceDate

DwellingInstituteInstituteLaboratoryDormitoryInstituteMuseum

Test MdlApartment

OfficeInstituteInstituteOfficeInstituteApartmentOfficeApartmentDormitoryInstituteRest houseApartmentOfficeStoreDwellingComputerOfficeClinicDwellingApartmentInstituteOfficeLaboratoryOfficeInstitute

Office

YachiyodaiResearch LabHigh-Tech. Research LabOiles Tech. Centre Tikuyu-RyoAcoustic LabElizabeth Sanders (re-design) Tohoku UniversityApt. HukumiyaSibuya Simizu Building

Research Lab No. 6 Tsukuba Muki-Zaiken Tsuchiura branchLab. J buildingKousinzuka Toranomon BuildingItoh MansionItinoe DormitoryClean Room LabAtagawa HoyojoOgawa MansionAsano BuildingKusuda BuildingIchikawa residenceComputer CentreSagamihara CentreGerontology Res. Lab.M-300 HoyosyoHarvest HillsAcoustic Lab Toshin BuildingDwell. Test LabMSB-21 OotukaWind LaboratoryCP Fukuzumi

2455322

34

5+B13144381032147

4+B1263

2+B1262

9+B13

12+B23

5

1141330162347651530656293

208681

3385306616636117347633733583770405140118632551047297

100322551615309206565675736805962555

4406

EB+FEB+SEB+SLRB+EEB+VEB+SEB+S

EBEB+S

EB+SLRBEB+SLRBSL+REB+SEB+SLRBEB+SEB+VSL+SHDRLRBHDREB

HDRHDREB+SLRBEB+SEB+SEB+SEB+SLRBHDR

EB+F

19821985198619861986198619861986

1986

1987198719871987198719871987198819881988198819881988198819881988198819881989198919891989198919891989

1989



253

Type Building Name Storey TotalFloorarea

(m2)

IsolationSystem

LicenceDate

ApartmentOfficeDormitoryDwellingApartmentComputerFactoryOfficeComputerOfficeOffice

OfficeInstituteDormitoryDormitoryComputerLaboratoryDormitoryOfficeDormitory

Apartment

Employees Buildings Toho-Gas Centre Tudanuma DormitoryM-300 Yamada'sKoganei-ApartmentOperation CentreUrawa-KogyoKanritouNoukyou CentreC-1 BuildingKeisan Kenkyusyo

Kasiwa KojyoAcoustic Laboratory Yamato-ryoKawaguchi-ryoDounen Computer CentreAndou Tech. Centre Toyo Rubber Shibamata-ryoAoki Tech. CentreDai Nippon Daboku Ichigaya-ryoDomani-Musashino

432232533

7+B13

4284437

4+B14

3

6521799202214714

104631525955542337846627

218690819216593310545352044001186

742

LRB+HDRSL+RSEB+SLRB

LRB+EBLRBHDREB+VLRBLRB

EB+V

HDREB+FEB+SLRB

EB+LDLRB

EB+S+oilLRB

EB+LD

EB+S

19891989198919891989198919891990199019901990

199019901990199019911991199119911991

1991

EB = elastomeric bearingLRB = lead rubber bearingHDR = high damping rubber bearingSL = sliding system (PTFE)S = steel damperV = viscous damperF = friction damperRS = rubber springLD = lead damperB1,B2 = basements

Table 8.4: Seismically Isolated Buildings in Japan



254

Bridge name Site Super-structure

Type

BridgeLength

(m)

IsolationSystem

Completion(Scheduled)

On-netohOh-hashi Bridge

Hokkaido 4-spancontinuous

steel girder

102 RB(12 Pcs)LRB(18 Pcs)

1991

Nagaki-gawaBridge

Akita 3-spanContinuoussteel girder

99 LRB(20 Pcs) 1991

Maruki Bridge Iwate 3-span

ContinuousPC Girder

122 LRB(8 Pcs) 1991

MiyagawaBridge

Shizuoka 3-spanContinuous

steel girder

104 LRB(10 Pcs) 1991

MetropolitanHighway BridgeNo. 12

Tokyo 6-spanContinuous

PC slab

138 LRB(10 Pcs) 1991

Hokuso Line

Viaduct(Railway)

Chiba 2-span

Continuoussteel girder

80 LRB(8 Pcs) 1990

Kanko Bridge Tochigi 6-spanContinuousPC girder

296 LRB(10 Pcs) 1991

Matsuno-hamaBridge

Osaka 4-spanContinuoussteel girder

211 LRB(12 Pcs) 1991

Uehara Bridge Aichi 2-spanContinuous

steel girder

65 LRB(18 pcs) 1991

Shirasuji Viaduct(Railway)

Chiba 2-spanContinuoussteel girder

76 RB(4 pcs)LRB(4 pcs)

1993(scheduled)

Trans-Tokyo Bay

Highway Bridge

Tokyo Bay 10-span

Continuoussteel girder

800 LRB(18 Pcs) 1994

(scheduled)

Karasu-yamaNo. 1 Bridge

Tochigi 6-spanContinuous

PC girder

245 HighDamping

Rubber(14 Pcs)

1992(scheduled)

EB = elastomeric bearing LRB = lead rubber bearingHDR = high damping rubber bearing SL = sliding system (PTFE)

S = steel damper V = viscous damperF = fric tion damper RS = rubber springLD = lead damper B1,B2 = basements

Table 8.5: Seismically Isolated Bridges in Japan



255

8.3.2 The C-1 Bui lding, Fuchu City, Tokyo

This large building is expected to be completed in 1992, with a total area of more than 45000 m2,of which the isolated parts (higher building) have an area of 37846 m2, a height of 41 m and aweight of 62800 tonne. It will be used as a computer centre; seismic isolation was chosen to

protect the equipment.

The building will consist of a 7-floor superstructure, a penthouse and a 1-floor basement, with thecomposite structure being formed of steel and steel-reinforced concrete. It is mounted on 68lead rubber bearings for seismic isolation.

The bearings are between 1.1 and 1.5 m in diameter, with lead plugs from 180 to 200 mm indiameter (Nakagawa & Kawamura, 1991). Each bearing is surrounded by a thickness of 10 mmof rubber to protect it from attack by ozone and damage due to fire.

At small displacements the natural period for the isolated building is expected to be about 1.4 s,while at large displacements, about 300 mm, the period is about 3 s. This should give an

adequate frequency shift for an earthquake of the kind expected at the site.

The maximum base shear force at the isolators due to wind is not expected to exceed 45% ofthe yield shear force of the bearings, so the building should not move appreciably during strongwinds.

8.3.3 The High-Tech R&D Centre, Obayashi Corporation

This reinforced concrete structure, 5 storeys high, was completed in August 1986 (Teramura e t a l ,1988). It is equipped with a seismic isolation system consisting of 14 laminated rubber bearings,with an axial dead load of 200 tonnes, as well as 96 steel bar dampers, of a diameter of 32 mm.

It also has friction dampers as sub-dampers for experimental purposes. The laminated rubberbearings give the seismically isolated structure a horizontal natural period of 3 s. (See Figures 8.13and 8.14.)

Figure 8.13: Isolation system used in the Obayashi High-tech R & D Centre, Tokyo

(Photograph courtesy Obayashi Corporation)



256

Figure 8.14: Obayashi High-tech R & D Centre (photograph courtesy Obayashi Corporation)

Seismic isolation has allowed a reduction of design strength and permits a large span structurewith smaller columns and beams, which in turn provides open space. Key equipment, includinga supercomputer, is installed on the top floor.

During the 1989 Ibaraki earthquake, accelerograms recorded on the roof of the isolatedbuilding, and on the roof of the unisolated main building of the institute, clearly demonstratedthe effectiveness of the seismic isolation, with a ten-fold reduction in roof acceleration in the

isolated building.

8.3.4 Comparison of Three Buildings with Different Seismic Isolation Systems

A comparative study has been carried out (Kaneko e t a l , 1990) on the effectiveness anddynamic characteristics of four types of base isolation system, namely: laminated rubberbearing with oil damper system, high-damping rubber bearing system, lead rubber bearings,and laminated rubber bearings with a steel damper system. The study was carried out byearthquake response observations of full-sized structures, as well as by numerical analyses. Thethree buildings studied were the test building at Tohoku University in Sendai, northern Japan, Tsuchiura Office building northeast of Tokyo, and the Toranomon building in Tokyo.

The test building at Tohoku University was seismically isolated in order to be used in experiment;for comparison, an identical building on the same campus was conventional, i.e. had not beenisolated. Both buildings are 3-storey reinforced concrete structures 6 m x 10 m in plan. In the firststage of the investigation, the isolated building was fitted with 6 laminated rubber bearings and12 viscous dampers (oil), (see Figures 8.15 and 8.16) and earthquake observation wasconducted for a year. After that, the devices were changed to high-damping rubber bearings,and observations continued.



257

Figure 8.15: Oil dampers and laminated rubber bearings in Test Building at Tohoku University,Sendai (photograph courtesy Shimizu Corporation)

Figure 8.16: Test Buildings at Tohoku University. On the left is the conventional building,

and on the right is the seismically isolated building (photograph courtesy Shimizu Corporation)

The natural frequencies and damping ratios of each building were obtained by forced vibrationtests. The damping ratios of the isolated building with viscous dampers were about 15% andthose with high-damping rubber about 12%, which are about 10 times and 8 times larger thanthose of the unisolated building respectively.

The Tsuchiura office building of Shimizu Corporation is a four-storey reinforced concrete structure12.5m x 12.5 m in plan. It is isolated by lead rubber bearings and the damping ratios were foundto be anisotropic, being 9.9% and 12.7% along two orthogonal directions.

The Toranomon building is 8.storey steel-framed reinforced concrete with an irregular shape andlarge eccentricity. The isolation devices have been arranged to reduce the eccentricity forearthquake loading. The building is supported by bearing piles on the Tokyo gravel layer, about22 m below the surface. The isolation devices consist of 12 laminated rubber bearings and 25steel dampers, each consisting of 24 steel bars (see Figure 8.17). Eight oil dampers (four for eachdirection) are also installed for small vibration amplitudes.



258

Figure 8.17: High damping rubber bearing, steel dampers and oil damper in basementof Bridgestone Toranomon Building, Tokyo (photograph courtesy Shimizu Corporation)

Accelerograms of the largest earthquake motions in the records of each building can besummarised as follows. In the two systems studied on the test building at Tohoku University, themaximum accelerations at the roof of the isolated building were about one-third of those on theunisolated building. For the lead rubber bearing system at Tsuchiura, the maximum accelerationat the roof was about 0.6 times that at the base. The response of the Toranomon building couldnot be clearly evaluated because only small amplitude earthquakes occurred and the steeldamper system was still in the elastic region. Torsional responses were small in all four isolatedstructures.

8.3.5 Oiles Technical Centre Bui lding

The Technical Centre Building of the Oiles Corporation (Shimoda e t a l , 1991) received specialauthorisation from the Ministry of Construction, based on the provisions under Article 38 of theBuilding Standards Law of J apan, since it was the first building in Japan to be equipped withlead rubber bearings for seismic isolation, and it was completed in February 1987.

It is a 5-storey structure of reinforced concrete, with a total floor area of approximately 4800 m2 and a total weight of 7500 tons (see Figures 8.18 and 8.19).

Figure 8.18: Diagram of Oiles Technical Centre showing seismic accelerationsas measured on 18/03/88 (courtesy Oiles Corporation)



259

Figure 8.19: Oiles Technical Centre, Tokyo (photograph courtesy Oiles Corporation)

Tests were carried out to verify the reliability of the base-isolated building under an earthquake. The tests consisted of free vibration tests, forced vibration tests and micro tremor observations. The appropriateness and accuracy of the method were also verified.

The results of dynamic analysis showed that the response acceleration of each floor of thebuilding was reduced to about 0.2g even during strong earthquakes (0.3-0.5g) at an input of50 cm/sec. The maximum response acceleration was reduced to between 0.2 and 0.3g evenunder a veloc ity of 0.75 m/s. The building remained elastic since the shearing force for eachstorey was shown to be less than the yielding force, while the maximum response displacementwas 370 mm.

8.3.6 Miyagawa Bridge

The Miyagawa Bridge, across the Keta River in Shizuoka prefecture, is the first seismically isolatedbridge constructed in Japan (Matsuo & Hara, 1991). The three-span continuous bridge with steelplate girders of length 110 m, is in an area where the ground is stiff, and is mounted on leadrubber bearings (see Figures 8.20-8.22).

In the traverse direction the bridge superstructure is restrained, allowing movements in thelongitudinal direction of +150 mm before restraints at the abutments stop further displacement. The lead rubber bearings were chosen and distributed so that 38% and 12% of the total inertiaforce was allocated to each pier and each abutment, respectively. The fundamental period ofthe unisolated bridge was computed as 0.3 seconds, while the isolated design has a natural

period of 0.8 seconds for small amplitude vibrations, and 1.2 seconds for larger. The system usedfor the design for seismic isolation is known in J apan as the "Menshin design method" (Matsuo &Hara, 1991).



260

Figure 8.20: Miyagawa Bridge, Shizuoka Prefecture, showing bridge deck, isolation system and piers.

Figure 8.21: Lead Rubber Bearing in Miyagawa Bridge showing transverse restraints(Photograph courtesy Oiles Corporation).

Figure 8.22: Miyagawa Bridge, Shizuoka Prefecture, J apan (photograph courtesy Oiles Corporation)



261

8.4 STRUCTURES ISOLATED IN THE USA

8.4.1 Introduction

The first use of seismic isolation in the USA occurred during 1979, when circuit breakers weremounted on 7% damped elastomeric bearings. Since that time a number of bridges andbuildings have been built or retrofitted with seismic isolation. The Foothill Communities Law and J ustice Centre, on elastomeric bearings, was the first new building in the USA to be mounted onseismic isolation. Tables 8.6 and 8.7 show buildings and bridges which have been seismicallyisolated in the USA.(Mayes, 1990, 1992).

Building Height/Storeys

Floor Aream2

Isolation System Date

Foothill Communities Law and J usticeCentre

4 17,000 10% dampedelastomeric bearings

1985/6

Salt Lake City and County Building(Retrofit)

5 16,000 Rubber and Leadrubber bearings

1987/8

Salt Lake City Manufacturing Facility(Evans and Sutherland Building)

4 9,300 Lead rubberbearings

1987/88

USC University Hospital 8 33,000 Rubber and Leadrubber bearings

1989

Fire Command and Control Facility 2 3,000 10% damped

elastomeric bearings

1989

Rockwell Building (Retrofit) 8 28,000 Lead rubberbearings

1989

Kaiser Computer Center 2 10,900 Lead rubberbearings

1991

Mackay School of Mines (Retrofit) 3 4,700 10% dampedelastomeric bearings

plus PTFE

1991

Hawley Apartments (Retrofit) 4 1,900 Friction-pendulum/slider

1991

Channing House Retirement Home(Retrofit)

11 19,600 Lead rubberbearings

1991

Long Beach VA Hospital (Retrofit) 12 33,000 Lead rubberbearings

1991

Table 8.6: Seismically Isolated Buildings in the United States



262

Bridge Superstructure type Bridgelength(m)

IsolationSystem

CompletionDate

Sierra Point Bridge, California(US101) (Retrofit)

Longitudinal steelplate girders

190 LRB 1984/5

Santa Ana River Bridge, California(Retrofit)

Steel trusses 310 LRB 1986/7

Main Yard Vehicle Access Bridge,California (Retrofit)

Steel plate girders 80 LRB 1987

Eel River Bridge, California (US101)

(Retrofit)

Steel through truss

simple spans

185 LRB 1987

All American Canal Bridge,California (Retrofit)

Continuous steel plategirders

125 LRB 1988

Sexton Creek Bridge, Illinois Continuous steel plategirders

120 LRB 1990

Toll Plaza Road Bridge,Pennsylvania

Simple span steel plategirder

55 LRB 1990

Lacey V. Murrow Bridge WestApproach, Washington (Retrofit)

Continuous concretebox girders

340 LRB 1991

Cache River Bridge, Illinois (Retrofit) Continuous steel plate

girders

85 LRB 1991

Route 161 Over Dutch HollowRoad, Illinois

Steel plate girder 110 LRB 1991

West Street Overpass, New York(Retrofit)

Steel beam 50 LRB 1991

US 40 Wabash River Bridge, Indiana Continuous steel plategirders

270 LRB 1991

Metrolink Light Rail, St Louis, (7 dualbridges)

Concrete box girder 65 to280

LRB 1991

Pequannock River Bridge,

New J ersey


Blackstone River Bridge,Rhode Island


Bridges, B764 E & W, Nevada(Retrofit)


Squamscott River Bridge,New Hampshire


Olympic Blvd Separation, California Steel plate girders 210 LRB 1992

Carlson Blvd Bridge, California Concrete box girder 45 LRB 1992

Clackamas Connector, Oregon Concrete box girder 305 LRB 1992

Cedar River Bridge, Washington Steel plate girders 160 LRB 1992

Table 8.7: Seismically Isolated Bridges in the United States



263

8.4.2 Foothi ll Communi ties Law and Justice Centre, San Bernardino, Californ ia

This building, the first in the USA to be seismically isolated, in 1986, is mainly of steel frameconstruction with the basement level consisting of concrete shear walls. It is a 4-storey buildingwith a total floor area of about 17 000 m2 mounted on 96 'high damping' rubber bearings (see

Figures 8.23 and 8.24) (Way, 1992). The 'high damping' of 10 to 15% is obtained by increasing theamount of carbon black in the rubber. Before the plans were finalised, estimates were made ofthe accelerations and displacements of the structure when isolated and unisolated. For anunisolated building with a structural damping of 5%, it was estimated that the resonant periodwould be 1.1 sec, the base shear 0.8 g and the rooftop would undergo accelerations anddisplacements of 1.6 g and 300 mm respectively. For the isolated case with a conservativevalue of 8% for the damping, the acceleration above the bearings was estimated to be 0.35 g,while at the rooftop the acceleration was estimated at 0.4 g with a displacement of 380 mm. The resonant period had a value of 2 sec.

Figure 8.23: End elevation of Foothill Communities Law and J ustice Centre, San Bernardino, California(courtesy Base Isolation Consultants, Incorporated)

Figure 8.24: Foothill Communities Law and J ustice Centre (photograph courtesyBase Isolation Consultants, Incorporated)



264

8.4.3 Salt Lake City and County Buil ding: Retrofit

This historic building, a massive 5-storey unreinforced masonry and stone structure with a 76 mhigh central clock tower, completed in 1894, is highly susceptible to earthquake damage, being

3 km from the Wasatch fault. It was retrofitted with seismic isolation, using a combination of leadrubber bearings and elastomeric bearings (Bailey & Allen, 1989)

Figure 8.25 shows the façade of the building. The retrofitting project began with an analysis ofpossible seismic isolation systems, each of these to be carried out in conjunction with otherstructural changes such as a steel space truss within the clock tower, various plywooddiaphragms, and anchorage of seismic hazards, such as chimneys, statues, gargoyles andbalustrades, around the exterior of the building. The option of seismic isolation by means of acombination of elastomeric bearings and lead rubber bearings at the base of the building waschosen because it would be least disruptive to the interior of the building; other options requiredconsiderable demolition. Calculations indicated that this system would be adequate towithstand the design earthquake.

Figure 8.25: Salt Lake City and County Building, Utah; an historic building retrofittedwith seismic isolation (photograph courtesy Dynamic Isolation Systems, Incorporated)

The task of retrofitting was complex, and was made more difficult by inaccurate detailing of thefoundations on the original building plans, by variations in the level of the building foundation,and by the requirement that the building be damaged as little as possible, so that impact toolscould not be used for cutting through the stone. The original plan had placed 500 isolatorsbelow existing foundations, but it was found that a massive concrete mat extended underneath

the four main tower piers. Isolators were therefore installed on top of the existing footings, butthe new first floor had to be raised 36 cm, and hundreds of slots had to be cut through existingwalls above the footings in order to install the isolators. A major concern of the constructionengineers was that an earthquake might occur during retrofit, when part of the building wasisolated and part not, and when some walls had been removed.

It was suggested (Bailey & Allen, 1989) that, in future, isolator locking mechanisms be employedduring isolator installation in areas of high seismicity.

A total of 443 isolators were used. All isolators were of the same size, approximately 43 cmsquare by 38 cm tall, to cut down on fabrication costs and to simplify installation. Not all theisolators had lead plugs, since computer analyses had indicated unacceptably high tower

shear for certain earthquake records. The isolators with lead plugs, approximately half of thetotal, were located around the perimeter of the building to give high damping for rotationalvibrations, and hence cut down on torsional response.



265

A retaining wall was constructed round the building's exterior to ensure a 400 mm seismic gap,this including a large safety factor as computer analysis had predicted only 12 cm lateraldisplacement of the building during the design earthquake. A bumper restraint system was alsoinstalled as a backup safety device.

The project clearly demonstrated the feasibility of retrofitted isolation for a building of this kind,where:

- short periods result in high seismic forces- the ratio of horizontal strength to weight is low- ductility is low- the risk of seismic collapse or cost of seismic repairs is unacceptable- preservation has high cultural value- the need to preserve exteriors and interiors limits scope for increasing strength

and ductility- it is practical to modify for inclusion of isolators- the structural form and proportions do not give uplift for isolator-attenuated

seismic forces- adequate clearances for isolator and structure may be provided- a practical isolation system gives an adequate reduction in seismic loads and

deformations.

8.4.4 USC Universit y Hospital, Los Angeles

This is an 8.storey, 35000 square-metre, steel-braced frame structure, with an asymmetric floorplan, scheduled for occupation in 1991 (Asher e t a l , 1990). It is a 275-bed teaching hospital, andis the first seismically isolated hospital in the world. The owner had been made aware of thepotential benefits of seismic isolation and requested that it be considered as an alternativeduring the schematic design phase.

As no consensus document for isolation design procedures existed, the structural engineersubmitted proposed criteria for approval by the California Office of the State Architect. Issuesaddressed by the criteria were: seismic input, design force levels and essentially elasticbehaviour, design displacement limits, and spec ific analysis requirements. The scope of theanalysis was set by the approved criteria and extensive computation followed.

The seismic isolation solution arrived at is shown schematically in Figure 6.26, namely acombination of lead rubber bearings at the exterior braced-frame columns, and elastomericbearings at the interior vertical load-bearing columns. The completed hospital is seen inFigure 8.27.

Figure 8.26: Plan of USC Hospital, Los Angeles, showing positions of lead rubber bearingsand elastomeric bearings (courtesy Dynamic Isolation Systems, Incorporated)



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Figure 8.27: Completed USC Hospital, Los Angeles, California (photograph courtesyDynamic Isolation Systems, Incorporated)

The Design Displacement arrived at was about 260 mm, a value in good accordance with thoseobtained by seismic isolation engineers in similar projects. All joints were detailed to allow aseismic gap 75 mm larger than the Design Displacement.

Provision was made for inspection and replacement of the bearings if necessary. This is currentlycommon practice throughout the world, although in the future, as experience with elastomericbearings is gained, it will probably be found that these bearings do not need replacementduring the life of a building.

It was concluded (Asher e t a l , 1990) that, although the analysis procedures for a seismicallyisolated structure are more complex than for a conventional fixed-base structure, the actualdesign problems are no more complex than for an ordinary building.

8.4.5 Sierra Point Overhead Bridge, San Francisco

The Sierra Point Bridge was the first bridge in North America to be retrofitted using seismicisolation (Mayes, 1992). Originally built in 1956, it is 200 m long and 40 m wide on slight horizontalcurvature (see Figure 6.28). Dynamic analysis indicated the bridge would sustain damageduring a large design earthquake with horizontal acceleration of 0.6 g. The solution was to

seismically isolate the bridge by replacing the existing steel spherical pin type bearings with leadrubber bearings. It was calculated that, in an earthquake of magnitude Richter 8.3 on theSan Andreas Fault 7 km from the site, these bearings would lengthen the natural period ofvibration of the structure so as to produce a six-fold reduction in real elastic forces to a levelwithin the elastic capacity of the columns. Restraining bars were added to prevent the stringersfrom falling off their connections to the transverse girders. All work was done with no interruptionof traffic on or under the bridge. The bridge is expected to remain in service during andimmediately after the design event. (It did not receive a good test in the 1989 Loma Prietaearthquake, since the maximum ground acceleration was 0.09g.)



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Figure 8.28: Sierra Point Overhead Bridge, San Francisco, seismically isolated by retrofittingwith lead rubber bearings (photograph courtesy Dynamic Isolation Systems, Incorporated)

8.4.6 Sexton Creek Bridge, Illino is

This structure, carrying Illinois Route 3 over Sexton Creek near the town of Gale in AlexanderCounty, is the first new bridge in North America to be seismically isolated (1988). It was designedby the Illinois Department of Transportation Office of Bridges and Structures. It is a 3-spancontinuous composite steel plate girder superstructure on slightly curved alignment, supportedon wall piers and seat type abutments. There are five 1.4 m deep girders in the 13 m widecross-section, and the spans are 40-50-40 m. The piers and abutments are founded on piledfootings (see Figure 8.29) (Mayes, 1992).

Figure 8.29: Sexton Creek Bridge, Illinois, fitted with lead rubber bearings(Photograph courtesy Dynamic Isolation Systems, Incorporated)

Feasibility studies were conducted, leading to alternative solutions. The solution selectedachieved the objective of reducing the seismic and non-seismic loads on the piers as much aspossible, because of the poor foundation conditions. Seismic criteria for Sexton Creek includedan acceleration coefficient of 0.2g and a Soil Profile Type III, in accordance with the AASHTOGuide Specifications for Seismic Design of Highway Bridges. The scheme chosen distributed theseismic load demands to the abutments using twenty lead rubber bearings, with twentyelastomeric bearings at the piers ("Force Control Bearings"). Seismic and wind forces at the pierswere minimised through adjustments in bearing stiffness at the piers and abutments. The realelastic base shear was reduced to 0.13 W.



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8.5 STRUCTURES ISOLATED IN ITALY

8.5.1 Introduction

The concept of seismic isolation has been enthusiastically applied to bridges in Italy, but thereare far fewer examples of seismically isolated buildings.

Available information (Parducci, 1992) on housing constructions is given in (b) below, while (c)describes the Mortaiolo Bridge, a new 9.6 km two-way bridge in Livorno-Cecina.

The earliest records of bridges built in Italy go back two thousand years or more. A woodenbridge is described in Caesar's Gallic Wars, Book 4, but bridges spanning powerful rivers wereusually built with stone piers and wooden superstructures, such as the Flavian Rhine Bridge atMoguntiacum, or Trajan's Danube Bridge, some 1120 m long (Cary, 1949). The moderntechnology of seismic isolation has been incorporated into the Italian bridge-building tradition

since 1974, as shown in Table 8.8 (Parducci, 1992), in which details are given of over 150 bridgesseismically isolated in Italy. A wide variety of isolating systems has been used, as seen in Table 8.8, although the earliest applications were designed without modern isolation criteria,certainly without official guidelines; a preliminary design guideline was published by AutostradeCompany in 1991. Generally, elastic-plastic systems based on flexural deformations of steelelements of various shapes ('EP' in Table 6.8) were chosen. One such device is seen in Figure8.30, while a device used in the Mortaiolo Bridge is described in detail below. Table 8.8 showsthat, even when 2-way bridges are regarded as single structures, over 100 km of bridge in Italyhas been seismically isolated in some way.

Figure 8.30: An elastic-plastic device used in the seismic isolation of bridges in Italy

(Photograph courtesy A Parducc i).

8.5.2 Seismically isolated buildings

To date, only few seismically isolated housing constructions have been designed or built in Italy(Parducci, 1992). These are detailed below. Vulcanised rubber-steel multi-layer pads are theseismic isolation system used.



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(i) SIP Regional Administration Centre, AnconaFive seven-storey seismically isolated buildings Type 'A': Isolated mass = 7.0 x 106 kg, 61 isolators Type 'B': Isolated mass = 3.7 x 106 kg, 36 isolatorsElastomeric bearing = 600 mm, H = 190 mm

Horizontal stiffness = 114, 65 MN/mNatural periods = 1.5, 1.6 sDesign viscous damping = 0.06 (experimental 0.12)Maximum response spectrum acceleration= 0.5 gMaximum design displacement = 145 mm

A full scale test was carried out on a type 'A' building; imposed displacements were up to107 mm, before instant release.

(ii) Nuovo Nucleo Arruolamento Volontari, Ancona

Isolated mass = 0.5 x 106 kgNatural period = 1.6 sEquivalent damping = 10%Maximum ground acceleration = 0.5 g ('single shock' quake)Maximum design displacement = 85 mm

(iii) Centro Medico Legale Della Marina Militare, Augusta, (designed)

Isolated mass = 0.2 x 106 kgNatural period = 2.0 sEquivalent damping = 10%Maximum ground acceleration = 0.25 gMaximum design displacement = 180 mm

(iv) Buildings Della Marina Militare, Augusta, (designed)

Isolated mass = 0.4 x 106 kgNatural period = 2.0 sEquivalent damping = 13%Maximum ground acceleration = 0.25 gMaximum design displacement = 180 mm

8.5.3 The Mortaiolo Bridge

The Mortaiolo Bridge, a major 2-way bridge in the Livorno-Cecina section of theLivorno-Civitavecchia highway, was completed in 1992. The bridge crosses the large plaincomposed of deep soft clay stratifications lying near Livorno, in a region of seismic risk.

The bridge is 9.6 km long, with typical spans of 45 m (see Figure 8.31(a)), made of pre-stressedreinforced concrete slab, with elastic-plastic devices on all the piers, shock-transmitter systems inthe longitudinal direction, and a designed peak ground acceleration of 0.25 g. The elasticstiffness of the isolating device, in a typical section, is 135 MN/m, the yield/weight ratio is 0.11 andthe maximum seismic displacement of the isolating system is + 80 mm (Parducci & Mezzi, 1991;Parducci, 1992).



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Figure 8.31: (a) Schematic of Mortaiolo Bridge(b) Schematic of one of the isolation devices used in the

Mortaiolo Bridge (courtesy A Parducc i)

Two equivalent isolating systems, manufactured by Italian firms, have been utilised in the bridge.Although they are based on different mechanical systems, they respond in the sameelastic-plastic way. In both the devices the dissipating behaviour is based on the hystereticflexural deformations of steel elements. Figure 8.31(b) illustrates the principle of operation of oneof these devices. Provision for relative tilting between the piers and superstructure is provided bya spherical bearing. Damping is provided elasto-plastically by the deflection of numerous steelcantilevers arranged in a ring. A shock transmitter, a highly viscous device based on anoil-piston system, is in series with the isolator. The device is shown under test in Figure 8.32.

Figure 8.32: One of the isolation devices used in the Mortaiolo Bridge, under test(Photograph courtesy A Parducci)

(b)

(a)



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Figure 8.33 shows the Mortaiolo Bridge during construction; further details are given by Parducci& Mezzi (1991), where it is also shown that the real incremental cost of the isolating systems wasonly 4.8% of the bridge cost. Figure 8.34 shows the nearly completed bridge.

Figure 8.33: Mortaiolo Bridge near completion (photograph courtesy A Parducci).



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Table 8.8: Bridges Seismically Isolated in Italy

KEY EP = Elastic-plastic behaviourEL = Elastic

OL = Oleodynamic system (EP equivalent)SL = Sliding supportST = Shock transmitter system associated with SL

RB = Rubber bearingsLRB = Lead rubber bearingsRC = Reinforced concretePCB = Prestressed concrete beams



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NOTES Where bridges are two-way, they have been regarded as a single bridge in estimating thelength. The total length of isolated bridges is thus greater than 100 km.

Of the more recent bridges (1985-1992), typical design values of the parameters are:• Yield/weight ratio: 5 to 28%, with a representative value of 10%• Maximum seismic displacement: +30 to +150 mm, with a representative value of

+ 60 mm

• Peak ground acceleration: 0.15 to 0.40 g, with a representative value of 0.25 g.Known retrofits are indicated with an asterisk (*).

8.6 ISOLATION OF DELICATE OR POTENTIALLY HAZARDOUSSTRUCTURES OR SUBSTRUCTURES

8.6.1 Introduction

Seismic problems arise with light-weight, delicate or potentially hazardous structures andsubstructures, such as life-support equipment in hospitals, important works of artistic or religioussignificance, e.g. the big statue of Buddha at Kamakura, Japan, equipment sensitive tovibration, and the radioactive components and associated support systems of nuclear reactors.

An example of such a structure, where seismic isolation was installed because the cost of thecontents far exceeds that of the building, is the Evans and Sutherland Building in Utah, whichmanufactures computerised flight simulator equipment (Mayes, 1992). Another example is theMark II detector for the Stanford Linear collider at Stanford University, Palo Alto, California, whichwas provided with seismic isolation in 1987 (Mayes, 1992). Four lead rubber bearings wereinstalled under the detector, also supporting the 1500 tonne mass of the collider. The isolationsystem was designed to reduce seismic forces by a factor of 10 and provide seismic protection

of this sensitive and expensive equipment at less than 0.4% of its cost. The detector was notdamaged during the 1989 Loma Prieta earthquake (Richter magnitude 7.1).

Approximately bilinear isolators, which usually provide most of the mode-1 damping, have beenfound to be practical and convenient for the large-scale isolation of buildings and bridges assuch. However, when an aseismic design is critically controlled by the responses of relativelylight-weight substructures it is often appropriate to restrict the isolators to moderate or low levelsof non-linearity. For such isolators it will sometimes be appropriate to provide a substantial partof the mode-1 damping by approximately-linear velocity dampers. These restrictions would notpreclude the use of moderate levels of bilinear damping by means of metal yielding or by lowsliding-friction forces. For example, the weight of an isolated structure might be carried onlubricated PTFE bearings. However, to minimize resonant-appendage effects during relatively-

frequent moderate earthquakes, such PTFE bearings should be supported by flexible mounts, asin the laminated-rubber/lead-bronze bearings pioneered by J olivet & Richli (1977). Furtherisolator components should include flexible elastic components to provide centring forces, andsometimes substantial velocity damping. Both the latter components reduce the maximumextreme-earthquake base movements for which provision must be made.

Nuclear power plants contain critical light-weight substructures essential for their safe operationand shut-down, including control rods, fuel rods and essential piping. These can be given a highlevel of protection by appropriate seismic isolation systems, designed to give low levels ofseismic response for higher vibrational modes of major parts of the power plants. Further seriousseismic problems arise with fast-breeder reactors in which critical components are given lowstrength by measures designed to give high rates of heat transfer. For some breeder-reactordesigns it may be desirable to attenuate vertical as well as horizontal seismic forces. In this caseit may be practical to provide horizontal attenuation for the overall plant and verticalattenuation for the reaction vessel only.



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Since the dominant vertical earthquake accelerations have considerably shorter periods thanthe associated horizontal accelerations, displacements associated with vertical attenuationshould be much smaller than those for horizontal attenuation.

Early papers on nuclear power plant isolation, (Skinner e t a l , 1976a, 1976b), concentrated on the

protection of the overall power plant structure but did not treat the problems with light-weightsubstructures, which arise from the seismic responses of higher modes of structural vibration.Structural protection may now be achieved with simpler alternative isolator components; forexample the use of lead rubber bearings may remove the need for installing steel-beamdampers.

8.6.2 Seismically Isolated Nuclear Power Stations

Seismic isolation of nuc lear structures is seen as a way to simplify design, to facilitatestandardisation, to enhance safety margins and possibly to reduce cost (Tajirian e t a l , 1990); forexample, it has been demonstrated that the weight of a pool-type Fast Breeder Reactor can be

reduced by half if horizontal isolation is used.

By 1990 it was reported (Tajirian et al, 1990) that six large Pressurised Water Reactor units hadbeen installed, with seismic isolation, in France and South Africa and that several advancednuclear concepts in the USA, J apan and Europe had also incorporated this approach.

The design concepts for seismic isolation of two Liquid Metal Reactors, with the acronyms PRISMand SAFR, have been carried out in the USA. For the PRISM design, horizontal protection, for thereactor module only, is provided by 20 high-damping elastomeric bearings, while the SAFRdesign is unique in providing vertical as well as horizontal isolation, by using bearings which areflexible, both horizontally and vertically, the entire SAFR building being supported on100 isolators.

The seismic design basis for both plants is expected to cover over 80% of potential nuclear sitesin the USA, and options for higher seismic zones have also been investigated.

8.6.3 Protection of Capacitor Banks, Haywards, New Zealand.

The AC Filter Capac itor Banks at the Haywards HVDC Converter Station in the Hutt Valley,New Zealand were built in 1965. Their earthquake resistance was increased in 1988 to thecurrent seismic design requirement using a base isolation method employing rubber bearingsand hysteretic steel dampers (Pham, 1991). (See Figures 8.34 and 8.35).

Figure 8.34: Capacitor banks at Haywards HVDC converter station in the Hutt Valley,New Zealand, seismically isolated by retrofitting with segmented rubber bearings and steel dampers.



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Figure 8.35: Detail of retrofitted seismic isolation system for Haywards, as seen on the left ofFigure 8.34. Note the low-stiffness elastomeric bearing, the steel cantilever damper and

the original concrete support.

Figure 8.36: End elevation of Press Hall for Wellington Newspapers, Petone.

Due to the light mass involved, lead rubber bearings were found to be inappropriate andspec ially-designed segmented rubber bearings were used. These bearings have rubber layersbonded alternatively with steel plates in the conventional manner. However the rubber layersare not continuous but divided into four discs at 110 mm diameter each, as shown in Figure 3.14. This is to reduce the rubber shear area, while maintaining stability, and hence to reduce theshear stiffness sufficiently to shift the natural periods of the relatively light AC Filter CapacitorBanks from 0.2-0.5 sec to 1.8 sec.

Dynamic shaking tests were done on 1 tonne bearings and static shear tests were done on 5tonne bearings of this design. Test results have indicated that the bearings met the designspec ifications. To limit the displacements during large earthquakes and provide lateral restraintsduring minor earthquakes and for wind loads, hysteretic steel dampers were provided (seeFigure 3.3(b)).

Even with the base isolation, it was found that the insulators supporting the capacitor stackwould not have adequate seismic strength. To reduce the bending moment at the supportinsulators, the stacks are split into two halves, thus effectively reducing the bending moment atthe support insulators by a factor of two.



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The specifications are as follows:

AC Filter Capacitor Banks: a total of 18 banks of three different types with individual massesvarying from 20 000 kg to 32 000 kg. The heights of the banks vary from 6.6 m to 9.6 m.

Rubber Bearings: each bank has four to six bearings rated at 5000 kg each. Each bearing has 19layers with a total height of 254 mm and a plan dimension of 400 x 400 mm. The shear stiffness israted at 0.06 kN/mm.

Dampers: each bank is provided with two circular tapered steel dampers with a base diameterof 45 mm, a height of 500 mm and was designed for a yield force Q y of 10.6 kN.

8.6.4 Seismic Isolation of a Printing Press in Wellington, New Zealand

In 1988 Wellington Newspapers Ltd approached the DSIR seeking advice on earthquake

protection for a proposed new printing press establishment to be built in the Wellington region atPetone (Dowrick e t a l , 1991). The need for special protection of brittle cast-iron press machineshad been demonstrated by the vulnerability of paper machines in the 1987 Edgecumbeearthquake. The site for this project was chosen because of its ready access to rail and roadtransport, but turned out to be traversed by the Wellington fault.

To give the printing presses maximum protection from earthquakes, the building required aseismic isolation system, and in addition the building had to be as stiff as possible up to the top ofthe presses to limit the horizontal deflections of the presses in all direc tions. The originallyproposed concrete walls were therefore extended in height and length around the ends of thepress hall, and the mezzanine floor was stiffened.

Creating enough horizontal stiffness in the direction lateral to the presses at the top platformlevel proved to be particularly difficult because visibility required for operations necessitated theuse of a horizontal steel truss at this level (rather than using an opaque concrete slab). It was notpracticable to create a truss with the optimum desired stiffness, but a workable solution wasfound. (See Figure 8.37.)

Figure 8.37: Lead Rubber Bearings for Press Hall under test

The dynamic analyses were carried out using a computer program for analysing seismically

isolated structures incorporating the non-linear behaviour of the special isolating and dampingsystem introduced below the ground floor.



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From the results of the first trial analysis, it was found that the horizontal accelerations applied tothe isolated structure, due to the very strong shaking caused by a rupture on the Wellingtonfault, would be in the range approximately 0.4g to 0.6g. It would have been both expensiveand physically very difficult to give a high level of protection to the press against damagingdeflections under such accelerations, particularly at the upper platform level.

An additional disadvantage arose from the fact that it was not feasible operationally to applyany lateral restraint to the press at a level midway between the top platform and the mezzaninefloor.

It was found practicable to provide protection against earthquake-generated accelerations,transmitted through the structure, of about 0.3g at the top of the press and 0.25g at the lowerlevels. The specially designed building housing the press was mounted on lead rubber bearings460 mm thick. This reduced the estimated loads and deflections on the press by a fac tor of 8 to10 compared with the non-isolated case. (See Figure 8.38). As a result, the press should sufferonly modest damage in earthquake shaking somewhat stronger than that required by theNew Zealand earthquake code for the design of buildings.

Figure 8.38: Lead Rubber Bearing in place in Press Hall.



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CHAPTER 9: IMPLEMENTATION ISSUES

9.1 INTRODUCTION

Preceding chapters have described the theory and design procedures for seismic isolationsystems. A number of practical issues arise in implementing seismic isolation for a specificproject and this chapter discusses these issues. Guidance is supplied to help decide on theisolation plane, the isolator locations and the types of device used. Seismic input is a criticaldesign parameter for isolation and this is discussed in some detail. The remainder of thechapter discusses other aspec ts of the design process – structural analysis, connectiondesign, structure design and specifications.

9.2 ISOLATOR LOCATIONS AND TYPES

9.2.1 Selection of Isolation Plane

Buildings

The paramount requirement for installation of a base isolation system is that the building beable to move horizontally relative to the ground, usually at least 100 mm and in someinstances up to 1 meter. A plane of separation must be selected to permit this movement.Final selection of the location of this plane depends on the structure but there are a fewitems to consider in the process. See discussion later in this chapter on Structural Design, asthere are design consequences of decisions made in the selection of the location of theisolation plane.

The most common configuration is to install a diaphragm immediately above the isolators. This permits earthquake loads to be distributed to the isolators according to their stiffness. Fora building without a basement, the isolators are mounted on foundation pads and thestructure constructed above them, as shown in Figure 9.1. The crawl space is usually highenough to allow for inspection and possible replacement of the isolators, typically at least 1.2m to 1.5 m.

Ground Floor

Crawl SpaceIsolator

Figure 9.1 Building with No Basement



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If the building has a basement then the options are to install the isolators at the top, bottomor mid-height of the basements columns and walls, as shown in Figure 9.2. For the options atthe top or bottom of the column/wall then the element will need to be designed for thecantilever moment developed from the maximum isolator shear force. This will often requiresubstantial column sizes and may require pilasters in the walls to resist the face loading.

Figure 9.2 Installation in Basement

The mid-height location has the advantage of splitting the total moment to the top andbottom of the component. However, as discussed later in Connection Design there will be P- moments in the column/wall immediately above and below the isolator.

The demands on basement structural members can be minimized by careful selection of

isolator types and by varying the isolator stiffness. For example, if a LRB system is used thenlarge lead cores may be used in isolators at locations such as wall intersections where there isa high resistance to lateral loads. More vulnerable elements such as interior columns mayhave isolators with small cores or no cores. As the diaphragm will enforce equaldisplacements at all isolators this will reduce the forces on the interior columns.

If structural elements below the isolation interface are flexible then they may modify theperformance of the isolation system as some displacement will occur in the structuralelement rather than the isolator. They should be included in the structural model. (Seediscussion on bridge isolation where flexible substructures are common).

Selection of the isolation plane for the retrofit of existing buildings follows the same process asfor new buildings but usually there are more constraints. Also, many of the issues which areresolved during design for a new installation, such as secondary moments, diaphragm actionabove the isolators and the capacity of the substructure to resist to maximum isolator forces,must be incorporated into the existing building.

Figure 9.3 shows conceptually some of the issues that may be faced in a retrofit installation ofany isolation system. These are schematic only as most retrofit projec ts have uniqueconditions. Each project may encounter some of all of these and will most likely also need todeal with other issues.



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Isolators loaded

with flatjacksWalls strengthened

locally with pilasters

Portion of wall between isolators removed after

isolators installed and pre-loaded with flatjacks

ELEVATION SECTION

Figure 9.3 Conceptual Retrofit Installation

1. The isolators must be installed into the existing structure. The existing structure must becut away to permit installation. For column installation this will require temporary supportfor the column loads. For wall structures, it may be possible to cut openings in the wallfor the isolators to be installed while the non-separated portion of the wall supports theload. The wall between isolators is removed after installation of the isolators.

2. The gravity load must be distributed to the isolators. Usually this is accomplished with flatjacks, which are hydraulic capsules in the form of a flat double saucer. Thrust plates areplaced top and bottom, as shown in Figure 9.4 (adapted from a PSC Freyssinetcatalogue). When the jack is inflated hydraulically the upper and lower plates areforced apart. The jacks can be inflated with hydraulic oil but for most isolation projectsan epoxy grout is used and the jacks are left in place permanently.

Inlet

Before Pressurizing

After Pressurizing

PLAN

Figure 9.4Flat J ack



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3. For installation in wall structures, the walls will be needed to be strengthened above andbelow the isolators to resist primary and secondary moments. Often, precast concretehorizontal needle beams are clamped to each side of the existing wall above andbelow the isolators. These needle beams are connected using stressed rods.

4. The existing wall will usually need strengthening to transfer the bending moment arisingfrom the isolator force to the foundation elements. This may require pilasters.

5. The structure above the isolators must be able to move freely by the maximumdisplacements, usually in the range of 150 mm to 500 mm or more. This will requireconstruction of a moat around the building and may influence selection of the isolationplane as installation at the bottom of the basement will require deep retaining walls toallow movement.

Architectural Features and Services

Apart from the structural aspects, base isolation requires modifications to architecturalfeatures and services to accommodate the movements. Especially important are itemswhich cross the isolation plane, which will include stairs, elevators, water, communications,waste water and power. Provision will also need to be made to ensure that the separationspace does not get blocked at some future time.

There are devices available to provide flexible service connections and these can generallybe dealt with by the services engineers, who must be advised of the location of the isolationplane and the maximum movements.

Elevators usually cantilever below the isolation plane. The portion below the isolation system

will need to have separation all round so that the movement can occur. Stairs maycantilever from above the isolation plane or may be on sliding bearings.

Most isolation projects will have some items such as stairs; shaft walls etc, which requirevertical support but must move with the isolators. The most common support for thesesituations is small sliding bearings. As the vertical reaction is usually small the frictionresistance will be negligible compared to the total isolation force.

With sliding bearings, no matter how small the load the displacement will still be equal to themaximum displacements and so even though a small bearing pad is used the size of the slideplate will be as large as for a heavy load.

Most of the problems you encountered will have been solved on previous isolation projects.It will be helpful to consult some of the published case studies from isolation projects worldwide.

Bridges

As noted in Chapter 7 of these guidelines, the most common location for the isolation planefor bridges is at the top of bents, isolating the superstructure. If the bents are single columnbents then the pier will function as a cantilever. Multi-column bents will function ascantilevers under longitudinal loads but will act as frames transversely if the isolators areplaced above the top transverse beam.



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The weight of the bents themselves is often a high proportion of the total bridge weight and itmay be preferable to isolate this portion of the mass as well as the superstructure mass. Thiscould be achieved by placing the isolators at the base rather than at the top of the bentcolumns. In practice, this is likely to be a problem as there will be large moments, which mustbe resisted by the bridge superstructure. There may be some bridge configurations wherethis is practical.

An unusual form of isolation which has been used on the South Rangitikei Viaduct in NewZealand is a rocking isolation system. The 70 m tall twin column piers have a horizontalseparation plane near the bottom of each column. When the bridge moves undertransverse earthquake loads the piers will rock on one column. Steel torsion bar energyabsorbers are used to control the upward displacements and absorb energy under eachuplift cycle.

Other Structures

Selection of the isolation plane for other types of structures will follow the same generalprinciples as for buildings and bridges. Isolation reduces the inertia forces in all mass abovethe isolators and so the general aim is to isolate as much of the weight as possible, whichusually means placing the isolators as close to the base as possible.

Exceptions may be where a large mass is supported on a light frame, such as an elevatedwater tank. It may be possible to install the isolators under the tank at the top of the frame. This will isolate the majority of the mass and will minimize the overturning moments on theisolators, avoiding tension loads in the isolators. However, the frame base must be able toresist the overturning moments from the maximum isolator shear forces applied at the top ofthe frame.

Buildings and bridges are all relatively heavy and most isolation devices are best suited tolarge loads. This is because for a given isolation period the displacement is the sameregardless of mass and it is difficult to retain stability of small isolators under largedisplacements. Sliding devices work well under light loads and there has been somedevelopment work performed on other low mass devices. Systems based on elastomericbearings are suitable for loads per device of at least 50 kN and preferably 200 kN. This mayrestrict options available for structures other than buildings and bridges.

9.2.2 Selection of Device Type

No one type of device is perfect. If it were, all projects would use the same type of device.Of the types available, following is a summary of their characteristics and advantages anddisadvantages. Each project will have specific objec tives and constraints and so devices willneed to be selected as those best fitting specific project criteria.

Mixing Isolator Types and Sizes

Most projects use a single type of isolator although sliding bearings in particular are oftenused with lead rubber or high damping rubber bearings. As discussed below, sliding bearingsprovide good energy dissipation, can resist high compression loads and permit uplift shouldtension occur but have the disadvantages of sticking friction and not providing a restoringforce. If used in parallel with bearing types that do provide a restoring force the advantages

of sliding bearings can be gained without the disadvantages.



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The UBC procedures can be used to determine the ratios of the two types of bearing. A ruleof thumb is that the sliding bearings should support no more than 30% of the seismic massand LRBs or HDR bearings the remainder. The most common use of sliding bearings is whereshear walls provide high overturning forces. A sliding bearing can efficiently resist the highcompression and the tension end of the wall can be permitted to uplift.

For most bearing types the plan size required increases as vertical load increases but theheight (of LRB and HDR bearings) or radius (of FPS bearings) is constant regardless of verticalload as all bearings will be subjected to the same displacement. Therefore, the bearings canbe sized according to the vertical load they support. In practice, usually only a single size ortwo sizes are used for a particular project. This is for two reasons:

1. For most applications, each different size of bearing requires two prototypes, which areextra bearings used for testing and not used in the finished structure. If the plan size isreduced for some locations with lower loads then the cost savings are often not enoughto offset the extra prototype supply and testing costs. If there are less than 20 isolators ofa particular size then it is probably more economical to increase them to the next sizeused.

2. For high seismic zones, a minimum plan size of LRB or HDR isolators is required to ensurestability under maximum lateral displacements. As all bearings have the samedisplacement, a reduced vertical load may not translate into much reduction, if any, inplan size.

The design procedures can be used to decide whether several sizes of isolator areeconomically justified. Sort the isolator locations according to maximum vertical loads andthen split them into perhaps 2, 3 or more groups, depending on the total number of isolators.Design them using first the same size for all groups and then according to minimum plan size.Check the total volume required for each option, including prototype volume. Price isgenerally proportional to total volume so this will identify the most economical grouping.

Elastomeric Bearings

An elastomeric bearing consists of alternating layers of rubber and steel shims bondedtogether to form a unit. Rubber layers are typically 8 mm to 20 mm thick, separated by 2 mmor 3 mm thick steel shims. The steel shims prevent the rubber layers from bulging and so theunit can support high vertical loads with small vertical deflections (typically 1 mm to 3 mmunder full gravity load). The internal shims do not restrict horizontal deformations of therubber layers in shear and so the bearing is much more flexible under lateral loads thanvertical loads, typically by at least two orders of magnitude.

Elastomeric bearings have been used extensively for many years, especially in bridges, andsamples have been shown to be functioning well after over 50 years of service. They providea good means of providing the flexibility required for base isolation.

Elastomeric bearings use either natural rubber or synthetic rubber (such as neoprene), whichhave little inherent damping, usually 2% to 3% of critical viscous damping. They are alsoflexible at all strain levels and so do not provide resistance to movement under service loads. Therefore, for isolation they are generally used with special elastomer compounds (highdamping rubber bearings) or in combination with other devices (lead rubber bearings).



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As discussed later, the load capacity of an elastomeric bearing in an undeformed state is afunction of the plan dimension and layer thickness. When shear displacements are appliedto the bearing the load capacity reduces due to the shear strain applied to the elastomerand to the reduction of effective “footprint” of the bearing. Figure 9.5 provides an exampleof the load capacity of elastomeric bearings with a medium soft rubber and 10 mm layers.

0

5000

10000

15000

20000

25000

30000

400 500 600 700 800 900 1000

BEARING DIAMETER (mm)

V E R T I C A L L O A D ( K N )

Gravity

Moderate Seismic

High Seismic

Figure 9.5 Load Capacity of Elastomeric Bearings

The load capac ity is plotted for gravity loads (assuming zero lateral displacements) and fortwo seismic conditions, the first a moderate displacement producing a shear strain of 150%and an effec tive area of 0.50 times the gross area. The second is for a very severe seismicdisplacement, producing a shear strain of 250% and an effective area of only 0.25 times thegross area. This latter case represents the extreme design limits for this type of bearing.

As shown in Figure 9.5, the allowable vertical load reduces rapidly as the seismicdisplacement increases. This makes the sizing of these isolators complicated in high seismic

zones. This is further complicated by the fac t that vertica l loads on the bearings mayincrease with increasing displacements, for example, under exterior columns or under shearwalls.

High Damping Rubber Bearings

The term high damping rubber bearing is applied to elastomeric bearings where theelastomer used (either natural or synthetic rubber) provides a significant amount of damping,usually from 8% to 15% of critical. This compares to the more "usual" rubber compounds,which provide around 2% damping.



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The additional damping is produced by modifying the compounding of the rubber andaltering the cross link density of the molecules to provide a hysteresis curve in the rubber. Therefore, the damping provided is hysteretic in nature (displacement dependent). For mostHDR compounds the viscous component of damping (velocity dependent) remains relativelysmall (about 2% to 5% of critical).

The damping provided by the rubber hysteresis can be used in design by adopting theconcept of "equivalent viscous damping" calculated from the measured hysteresis area, asin done for LRBs. As for LRBs, the effective damping is a function of strain. For most HDR usedto date the effective damping is around 15% at low (25% to 50%) strains reducing to 8%-12%for strains above 100%, although some synthetic compounds can provide 15% or moredamping at higher strains.

For design, the amount of damping is obtained from tabulated equivalent viscous dampingratios for particular elastomer compounds. The load capacity for these bearings is based onthe same formulas used for elastomeric bearings.

Lead Rubber Bearings

A lead rubber bearing is formed of a lead plug force-fitted into a pre-formed hole in anelastomeric bearing. The lead core provides rigidity under service loads and energydissipation under high lateral loads. Top and bottom steel plates, thicker than the internalshims, are used to accommodate mounting hardware (Figure 9.6). The entire bearing isencased in cover rubber to provide environmental protection.

When subjected to low lateral loads (such as minor earthquake, wind or traffic loads) thelead rubber bearing is stiff both laterally and vertically. The lateral stiffness results from thehigh elastic stiffness of the lead plug and the vertical rigidity (which remains at all load levels)results from the steel-rubber construction of the bearing.

Rubber Layers

Lead

Core

Internal Steel Shims

Figure 9.6 Lead Rubber Bearing Section

At higher load levels the lead yields and the lateral stiffness of the bearing is significantlyreduced. This produces the period shift effect characteristic of base isolation. As thebearing is cycled at large displacements, such as during moderate and large earthquakes,the plastic deformation of the lead absorbs energy as hysteretic damping. The equivalentviscous damping produced by this hysteresis is a function of displacement and usually ranges

from 15% to 35%.



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A major advantage of the lead rubber bearing is that it combines the functions of rigidity atservice load levels, flexibility at earthquake load levels and damping into a single compactunit. These properties make the lead rubber bearing the most common type of isolatorused where high levels of damping are required (in high seismic zones) or for structures whererigidity under services loads is important (for example, bridges). As for HDR bearings, the

elastomeric bearing formulas are also applicable for the design of LRBs.

Flat Slider Bearings

Sliding bearings provide an elastic-perfectly plastic hysteresis shape with no strain hardeningafter the applied force exceeds the coefficient of friction times the applied vertical load. This is attrac tive from a structural design perspec tive as the total base shear on the structureis limited to the sliding force.

An ideal friction bearing provides a rectangular hysteresis loop, which provides equivalentviscous damping of 2/ = 63.7% of c ritica l damping, much higher than achieved with LRBs or

HDR bearings.

In practice, sliding bearings are not used as the sole isolation component for two reasons:

1. Displacements are unconstrained because of the lack of any centring force. Theresponse will tend to have a bias in one direction and a structure on a sliding systemwould continue to move in the same direc tion as earthquake a ftershocks occur.

2. A friction bearing will be likely to require a larger force to initiate sliding than the forcerequired to maintain sliding. This is termed static friction, or “sticktion”. If the sliders arethe only component then this initial static friction at zero displacement will produce thegoverning design force.

The UBC and AASHTO codes require that isolation systems either have a specified restoringforce or be configured so as to be capable of accommodating three times the earthquakedisplacement otherwise required. As maximum design earthquake displacements may be ofthe order of 400-500 mm this would require sliding systems to be designed for perhaps 1.5m ofmovement. This may be impractical for detailing movement joints, services, elevators etc.

A hybrid system with elastomeric bearings providing a restoring force in parallel with slidingbearings may often be an economica l system. Sliding bearings such as pot bearings using Teflon as a sliding surface can take much higher compressive stresses than elastomericbearings (60 MPa or more versus 15 MPa or so for elastomeric). Also, the bearings can upliftwithout disengagement of dowels. Therefore, they are especially suitable at the ends of

shear walls and were used at these locations for the Museum of New Zealand.

The most common sliding surface is Teflon on stainless steel. This has a low static coefficientof friction, around 3%. However, the coefficient is a function of both pressure and velocity ofsliding. With increasing pressure the coefficient of friction decreases. With increasing velocitythe coefficient increases significantly and at earthquake velocities (0.2 to 1 m/sec) thecoefficient is generally about 8% to 12%.

For preliminary design a constant coefficient of friction of about 10% is usually assumed. Fordetailed analysis, the element model should include the variation with pressure and velocity.



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Curved Slider (Friction Pendulum) Bearings

Although a number of curved shapes are possible, the only curved sliding bearing which hasbeen extensively used is a patented device in which the sliding surface is spherical in shaperather than flat, termed the Friction Pendulum System. The schematic characteristics of thisdevice are shown in Figure 9.7.

R

W

Spherical Surface

Articulated Slider

W/ R

W

Force

Dis lacement

Figure 9.7 Curved Slider Bearing

The isolator provides a resistance to service load by the coefficient of friction, as for a flatslider. Once the coefficient of friction is overcome the articulated slider moves and becauseof the spherical shape a lateral movement is accompanied with a vertical movement of themass. This provides a restoring force, as shown in the hysteresis shape in Figure 9.7.

The bearing properties are defined by the coefficient of friction, the radius of the sphere and

the supported weight. The post-sliding stiffness is defined by the geometry and supportedweight, as W/R.

The total force resisted by a spherical slider bearing is directly proportional to the supportedweight. If all isolators in a project are of the same geometry and friction properties and aresubjected to the same displacement then the total force in each individual bearing is aconstant times the supported weight. Because of this, the center of stiffness and center ofmass of the isolation system will coincide and there will be no torsion moment. Note that thisdoes not mean that there will be no torsion movements at all as there will likely still beeccentricity of mass and stiffness in the building above the isolators.



289

Ball and Roller Bearings

Although roller bearings are attractive in theory as a simple means of providing flexibilitythere do not seem to be any practical systems based on ball or roller bearings available. Aball system is under development using a compressible material, which deforms as it rollsproviding some resistance to service loads and energy dissipation (the Robinson RoBall).Preliminary results have been presented at conferences and the device appears to havepromise, especially for low mass applications. More detail should become available in thenear future.

Solid ball and roller bearings constructed of steel or alloys usually have the problem offlattening of the contact surface under time if they are subjected to a high stress, as theywould be under buildings and bridges. This appears to have restricted their use. Also, theydo not provide either resistance to service loads or damping so would need to be used inparallel with other devices.

Supplemental Dampers

Systems which do not have an inherent restoring force and/or damping, such as elasticbearings, sleeved piles or sliding bearings, may be installed in parallel with dampers. Thesedevices are in the same categories used for in-structure damping, a different form of passiveearthquake protection. Supplemental damping may also be used in parallel with dampeddevices such as LRBs or HDR bearings to control displacements in near fault locations.

External dampers are c lassified as either hysteretic or viscous. For hysteretic dampers theforce is a function of displacement, for example, a yielding steel cantilever. For viscousdampers the force is a function of veloc ity, for example, shock absorbers in an automobile.

For an oscillating system the velocity is out of phase with the displacement and the peakveloc ity occurs at the zero displacement crossing. Therefore, viscous damping forces areout of phase with the elastic forces in the system and do not add to the total force at themaximum displacement. Conceptually, this is a more attractive form of damping thanhysteretic damping.

In practice, if a viscous damper is used in parallel with a hysteretic isolator then there is alarge degree of coupling between the two systems, as shown in Figure 9.8. The maximumforce in the combined system is higher than it would be for the hysteretic isolator alone. Ifthe viscous damper has a veloc ity cut-off (a constant force for velocities exceeding a pre-setvalue) then the coupling is even more pronounced.



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DISPLACEMENT

D A M P I N G F O R C

E

Total

Viscous

Hysteretic

Figure 9.8 Viscous Damper in Parallel with Yielding System

Practically, it is difficult to achieve high levels of viscous damping in a structure responding toearthquakes. The damping energy is converted to heat and materials exhibiting highlyviscous behavior, such as oil, tend to become more viscous with increasing temperature. Therefore, the dampers lose effectiveness as the earthquake amplitude and durationincreases unless a large volume of material is used.

These factors have restricted the number of suppliers of viscous dampers suited for

earthquake type loads. Hardware tends to be dec lassified military devices and is expensive.

For either viscous or hysteretic dampers, the damping contributed to the total isolationsystem is calculated from the total area of the hysteretic loop at a specified displacementlevel. This loop area is then added to the area from other devices such as lead rubberbearings. These concepts are the same as used for in-structure damping and energydissipation.

Advantages and Disadvantages of Devices

Table 9.1 summarizes the advantages and disadvantages of the most commonly used

device types. Note that although disadvantages may apply to a generic type, somemanufacturers may have specific procedures to alleviate the disadvantage. For example,static friction is a potential disadvantage of sliding bearings in general but manufactures ofdevices such as the Friction Pendulum System may be able to produce sliding surfaces thatare not subject to this effect.

Some factors listed in Table 9.1 are not disadvantages of the device itself but may be adesign disadvantage for some projects. For example, the LRBs and HDR bearings produceprimary and secondary (P-) moments which are distributed equally to the top and bottomof the bearing and so these moments will need to be designed for in both the foundationand structure above the isolators. For sliding systems the total P- moment is the same butthe sliding surface can be oriented so that the full moment is resisted by the foundation and

none by the structure above (or vice versa).



291

The advantages and disadvantages listed in Table 9.1 are general and may not becomprehensive. On each project, some charac teristics will be more important than others.For these reasons, it is not advisable to rule out specific devices too early in the designdevelopment phase. It is usually worthwhile to consider at least a preliminary design forseveral type of isolation system until it is obvious which system(s) appear to be optimum. It

may be advisable to contact manufacturers of devices at the early stage to get assistanceand ensure that the most up-to-date information is used.

Advantages Disadvantages

Elastomeric Low in-structure accelerationsLow cost

High displacementsLow dampingNo resistance to serviceloadsP- moments top andbottom

High DampingRubber

Moderate in-structure accelerationsResistance to service loads

Moderate to high damping

Strain dependent stiffnessand

dampingComplex analysisLimited choice of stiffnessanddampingChange in properties withscraggingP- moments top andbottom

Lead Rubber Moderate in-structure accelerationsWide choice of stiffness / damping

Cyclic change in propertiesP- moments top andbottom

Flat Sliders Low profileResistance to service loadsHigh dampingP- moments can be top or bottom

High in-structureaccelerationsProperties a function ofpressure and velocityStickingNo restoring force

Curved Sliders Low profileResistance to service loadsModerate to high dampingP- moments can be top or bottomReduced torsion response

High in-structureaccelerationsProperties a function ofpressure and velocitySticking

Roller Bearings No commercial isolators available.

Sleeved Piles May be low costEffective at providing flexibility

Require suitable applicationLow dampingNo resistance to serviceloads

HystereticDampers

Control displacementsInexpensive

Add force to system

ViscousDampers

Control displacementsAdd less force than hystereticdampers

ExpensiveLimited availability

Table 9.1 Device Advantages and Disadvantages



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9.3 SEISMIC INPUT

9.3.1 Form of Seismic Input

Earthquake loads are a dynamic phenomenon in that the ground movements that give rise

to loads change with time. They are a lso indeterminate in that every earthquake event willgenerate different ground motions and these motions will then be modified by the propertiesof the ground through which they travel. Efficient structural design requires a small numberof defined loads so codes represent earthquake loads in a format more suited to designconditions. The codes generally spec ify seismic loads in three forms, in increasing order ofcomplexity:

Equivalent Static Loads

These are intended to represent an envelope of the storey shears that will be generated byan earthquake with a given probability of occurrence. Most codes now derive these loadsas a function of the structure (defined by period), the soil type on which it is founded and theseismic risk (defined by a zone factor). The static load is applied in a specified distribution,usually based on an assumption of inertia loads increasing linearly with height. Thisdistribution is based on first mode response and may be modified to account for structuralcharacteristics (for example, an additional load at the top level or use of a power functionwith height).

Base isolation modifies the dynamic characteristics of the structure and usually also addsdamping. These effects are difficult to accommodate within the limitations of the static loadprocedure and so most codes impose severe limitations on the structures for which thisprocedure is permitted for isolated structures.

Response Spectrum

A response spectrum is a curve that plots the response of a single degree of freedomoscillator of varying period to a specific earthquake motion. Response spectra may plot theacceleration, veloc ity or displacement response. Spectra may be generated assumingvarious levels of viscous damping in the oscillator.

Codes specify response spectra which are a composite, or envelope, spectrum of allearthquakes that may contribute to the response at a spec ific site, where the site is definedby soil type, and zone fac tor. The code spectra are smooth and do not represent any singleevent.

A response spectrum analysis assumes that the response of the structure may be uncoupledinto the individual modes. The response of each mode can be calculated by using the

spectral acceleration at the period of the mode times a participation factor which definesthe extent to which a particular mode contributes to the total response. The maximumresponse of a ll modes does not occur at the same time instant and so probabilistic methodsare used to combine them, usually the Square Root of the Sum of the Square (SRSS) or, morerecently, the Complete Quadratic Combination (CQC). The latter procedure takes accountof the manner in which the response of closely spaced modes may be partially coupled andis considered more accurate than the SRSS method.

The uncoupling of modes is applicable only for linear elastic structures and so the responsespectrum method of analysis cannot be used direc tly for most base isolated structures,although this restriction also applies in theory for yielding non-isolated structures. Most codespermit response spectrum analysis for a much wider range of isolated structures than the

static load procedure.



293

In practice, the isolation system is modeled as an equivalent elastic system and the dampingis implemented by using the appropriately damped spectrum for the isolated modes.

The analyses described in Chapter 6 suggest that this procedure may underestimate flooracceleration and overturning effects for non-linear systems.

Time History

Earthquake loads are generated in a building by the accelerations in the ground and so intheory a load specified as a time history of ground accelerations is the most accurate meansof representing earthquake actions. Analysis procedures are available to compute theresponse of a structure to this type of load. The difficulty with implementing this procedure isthat the form of the acceleration time history is unknown.

Recorded motions from past earthquakes provide information on the possible form of theground acceleration records but every record is unique and so does not provide knowledgeof the motion which may occur at the site from future earthquakes.

The time history analysis procedure cannot be applied by using composite, envelopemotions, as can be done for the response spectrum procedure. Rather, multiple timehistories that together provide a response that envelopes the expected motion must beused. Seismology is unlikely ever to be able to predict with prec ision what motions will occurat a particular site and so multiple time histories are likely to be a feature of this procedure inthe foreseeable future.

Codes provide some guidance in selecting and scaling earthquake motions but none as yetprovide specific lists of earthquakes with scaling factors for a particular soil condition andseismic zone. The following sec tions discuss aspects of earthquake motions but each projectwill require individual selection of appropriate records.

9.3.2 Recorded Earthquake Motions

Pre-1971 Motions

The major developments in practical base isolation systems occurred in the late 1960’s andearly 1970’s and used the ground motions that had been recorded up to that date. Anexample of the data set available to those researchers is the Caltech SMARTS suite ofmotions (Strong Motion Accelerogram Record Transfer System) which contained 39 sets ofthree recorded components (two horizontal plus vertical) from earthquakes between the1933 Long Beach event and the 1971 San Fernando earthquake.

A set of these records was selected for processing, excluding records from upper floors ofbuildings and the Pacoima Dam record from San Fernando, which included specific siteeffects. Response spectra were generated from the remaining 27 records, using each of thetwo horizontal components, and the average values over all 54 components calculated. The envelope and mean 5% damped acceleration spectra are shown in Figure 9.9 and theequivalent 5% damped displacement spectra in Figure 9.10.



294

A curve proportional to 1/T fits both the acceleration and the displacement spectra forperiods of 0.5 seconds and longer quite well, as listed in Table 9.2. This shows that:

1. If it is assumed that the acceleration is inversely proportional to T for periods of 0.5seconds and longer, the equation for the acceleration coefficient is Sa = C0/T. Thecoefficient C0 can be calculated from the acceleration at 0.5 seconds as C 0 = 0.5 x

0.278 = 0.139. The accelerations at periods of 2.0, 2.5 and 3.0 seconds calculated as Sa = 0.139/T match the ac tual average spec trum accelerations very well.

2. The spectral displacements is related to the spec tral acceleration as Sd = SagT2/42. Formm units, g = 9810 mm/sec2 and so Sd = 248.5Sa T2. Substituting Sa = 0.139/T provides foran equation for the spectral displacement Sd = 34.5 T, in mm units. The values are listedin Table 9.2 and again provide a very close match to the calculated averagedisplacements.

These results show that the code seismic load coefficients, defined as inversely proportionalto the period, had a sound basis in terms of reflecting the characteristics of actual recordedearthquakes. Figures 9.11 and 9.12, from the 1940 El Centro and 1952 Taft earthquake

respectively, are typical of the form of the spectra of the earlier earthquakes. For medium tolong periods (1 second to 4 seconds) the accelerations reduced with increased period andthe displacement increased with increasing period. However, as discussed in the followingsections later earthquake records have not shown this same trend.

Period0.5

Seconds

Period2.0

Seconds

Period2.5

Seconds

Period3.0

Seconds

Acceleration (g)Average ValuesCalculated as 0.139/T

0.2780.278

0.0740.070

0.0570.056

0.0480.046

Displacement (mm)

Average ValuesCalculated as 34.5T

1717

7369

8986

106104

Table 9.2: Average 5% Damped Spec trum Values

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

PERIOD (Seconds)


Envelope

Average

Figure 9.9:SMARTS 5% Damped Acceleration Spectra



295

0

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700

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900

1000

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

PERIOD (Seconds)

D I S P L A C E M E N T ( m m

) Envelope

Average

Figure 9.10:SMARTS 5% Damped Displacement Spectra

EL CENTRO SITE IMPERIAL VALLEY IRRIGATION

DISTRICT S90W IMPERIAL VALLEY MAY 18 1940

0.00

0.20

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1.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

PERIOD (Seconds)


0

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500

D I S P L A C E M E N T ( m

m )

ACCELERATION

DISPLACEMENT

EL CENTRO SITE IMPERIAL VALLEY IRRIGATION

DISTRICT S00E IMPERIAL VALLEY MAY 18 1940

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500

D I S P L A C E M E N T ( m m )

ACCELERATION

DISPLACEMENT

Figure 9.11: 1940 El Centro Earthquake



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TAFT LINCOLN SCHOOL TUNNEL S69E KERN

COUNTY 1952

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PERIOD (Seconds)


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ACCELERATION

DISPLACEMENT

TAFT LINCOLN SCHOOL TUNNEL N21E KERN

COUNTY 1952

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PERIOD (Seconds)


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DISPLACEMENT

Figure 9.12: 1952 Kern County Earthquake

Post-1971 Motions

Since 1971 the number of seismic arrays for recording ground motions has greatly increasedand so there is an ever increasing database of earthquake records. As more records areobtained it has become apparent that there are far more variations in earthquake recordsthan previously assumed. In particular, ground accelerations are much higher and near fault

effects have modified the form of the spectra for long period motions.

The following Figures 9.13 to 9.18, each of which are 5% damped spectra of the twohorizontal components for a particular earthquake, illustrate some of these effects:

1. The 1979 El Centro event was recorded by a series of accelerographs that straddled thefault. Figure 9.13 shows the spectra of Array 6, less than 2 km from the fault. This showsnear fault effects in the form of a spectral peak between 2 seconds and 3 seconds anda spectral displacement that exceeded 1 m for a period of 3.5 seconds. For this record,an isolation system would perform best with a period of 2 seconds or less. If the periodincreased beyond two seconds, both the acceleration and the displacement wouldincrease.



297

1979 Imperial Valley CA E l Centro Arr #6 230

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PERIOD (Seconds)

A C C E L E R A T I O N

( g )

0

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800

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1200

1400


Acceleration

Displacement

1979 Imperial Valley CA E l Centro Arr #6 140

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0.00 1.00 2.00 3.00 4.00 5.00 6.00

PERIOD (Seconds)

A C C E L E R A T I O N

( g )

0

200

400

600

800

1000

1200

1400


Acceleration

Displacement

Figure 9.13: 1979 El Centro Earthquake: Bonds Corner Record

2. The 1985 Mexico C ity earthquake caused resonance at the characteristic site period of2 seconds, as shown clearly in the spectra in Figure 9.14. An isolated structure on thistype of site would be counter-effective and cause damaging motions in the structure.

1985 MEXICO CITY SCT1850919BL.T S00E

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m )

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Displacement

1985 MEXICO CITY SCT1850919BT.T N90W

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0

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1250


m )

Acceleration

Displacement

Figure 9.14: 1985 Mexico City Earthquake

3. The 1989 Loma Prieta earthquake produced a number of records on both stiff and softsites. Figure 9.15 shows a stiff site record. This record shows the characteristics ofdecreasing acceleration with period but the stronger component has a constantdisplacement for periods between 2 seconds and 4 seconds. Within this range, isolationsystem flexibility could be increased to reduce accelerations four-fold (from 0.4 to 0.1)with no penalty of increased displacements.



298

Loma Prieta 1989 Hollister South & Pine Component

090 Deg

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D I S P L A C E M E N T

( m m )

Acceleration

Displacement

Loma Prieta 1989 Hollister South & Pine Component

000 Deg

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0

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( m m )

Acceleration

Displacement

Figure 9.15: 1989 Loma Prieta Earthquake

4. The 1992 Landers earthquake produced records with extreme short period spectralaccelerations (Figure 9.16), exceeding 3g for the 5% damped spectra, and constantacceleration in the 2 second to 4 second range for the 270 component. For this typeof record isolation would be very effective for short period buildings but the optimumisolation period would not exceed 2 seconds. For longer periods the displacementwould increase for no benefit of reduced accelerations.

1992 Landers Earthquake Lucerene Valley 000 Degree

Component

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Displacement

1992 Landers Earthquake Lucerene Valley 270 Degree

Component

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Acceleration

Displacement

Figure 9.16: 1992 Landers Earthquake

5. The Sepulveda VA record of the 1994 Northridge earthquake, Figure 9.17, produced veryhigh short period spectral accelerations, exceeding 2.5g, but the 360 component alsohad a secondary peak at about 2 seconds. For this component, the displacementwould increase extremely rapidly for an isolated period exceeding 2 seconds.



299

1994 Northridge st=LA Sepulveda V.A. 360 corrected

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2.50

3.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

PERIOD (Seconds)


0

100

200

300

400

500

600


( m m )

Acceleration

Displacement

1994 Northridge st=LA Sepulveda V.A. 270 corrected

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

PERIOD (Seconds)


0

100

200

300

400

500

600


( m m )

Acceleration

Displacement

Figure 9.17: 1994 Northridge Earthquake

6. The Sylmar C ounty Hospital record, also from the 1994 Northridge earthquake (Figure9.18) also produced short period spectral accelerations exceeding 2.5g for onecomponent. This record was unusual in that both components produced very highspectral accelerations at longer periods, exceeding 0.5g for 2 second periods. Anisolation system tailored for this earthquake would use an isolated period exceeding 3seconds as beyond this point both displacements and accelerations decrease withincreasing period.

1994 NORTHRIDGE SYLMAR-COUNTY HOSP.

PARKING LOT 90 Deg

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

PERIOD (Seconds)


0

150

300

450

600

750

900


Acceleration

Displacement

1994 NORTHRIDGE SYLMAR-COUNTY HOSP.

PARKING LOT 360 deg

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

PERIOD (Seconds)


0

150

300

450

600

750

900


Acceleration

Displacement

Figure 9.18: 1994 Northridge Earthquake

One common factor to all these earthquakes is that the particular characteristics of eachearthquake suggest an optimum isolation system for that earthquake. However, an optimumsystem selected on the basis of one earthquake would almost certainly not be optimal for all,or any, of the other earthquakes.



300

Code requirements for time history selec tion require use of records appropriate to faultproximity and so often one or more records similar to those shown in Figure 9.13 to 9.18 will beused for a project. The manner of scaling specified by codes such as UBC and FEMA-356also result in relatively large scaling factors. Naeim & Kelly [1999] discuss this in some detail.

9.3.3 Near Fault Effects

Near fault effects cause large velocity pulses close to the fault rupture. Effects are greatestwithin 1 km of the rupture but extend out to 10 km. The UBC requires that near fault effectsbe included by increasing the seismic loads by factors of up to 1.5, depending on thedistance to the nearest active fault and the magnitude of earthquake the fault is capable ofproducing. The current edition of the UBC does not require that this effect be included inthe design of non-isolated buildings.

There has been some research in New Zealand on this effect and recent projects for essentialbuildings have included time histories reflec ting near fault effects. Figure 9.19 shows onesuch record used for the Parliament project. Between 6 and 9 seconds relatively largeaccelerations are sustained for long periods of time, causing high velocities and

displacements in structures in the medium period range of 1.5 to 3.0 seconds. This type ofaccelerogram will affect a wide range of structures, not just isolated buildings.

-0.50

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0 2 4 6 8 10 12 14 16

TIME (Seconds)


El Centro, 1979 Earthquake: Bonds Corner 230 deg.

Figure 9.19: Ac celeration Record With Near Fault Charac teristics

9.3.4 Variations in Displacements

Figure 9.20 shows the variation in maximum displacements from 7 earthquakes each scaledaccording to UBC requirements for a site in California. Displacements range from 392 mm to968 mm, with a mean of 692 mm. If at least 7 records are used, the UBC permits the meanvalue to be used to define the design quantities. The mean design displacement, 692 mm, isexceeded by 4 of the 7 earthquake records. These records, from Southern California, wereselected because each contained near fault effects. Each has been scaled to the sameamplitude at the isolated period. The scatter from these earthquakes is probably greaterthan would be obtained from similarly scaled records that do not include near fault effects.



301

Available options to the designer are:

1. Use the mean of 7 records, a displacement of 692 mm.

2. Selec t the three highest records and use the maximum response of these, 968 mm.

3. Selec t the three lowest records and use the maximum response of these, 585 mm.

811

968

585

407

846

392

839

692

0

200

400

600

800

1000

1200

Hollister Lucerene Sylmar El Centro NewHall Supulveda Yermo

D I S P L A C E M E N T (

m m )

Maximum Displacement

Mean Displacement

Figure 9.10: Variation between Earthquakes

It is difficult to rationalize a design decision where the majority of earthquakes will producedisplacements greater than the design values. However, the requirements of any codewhich requires a minimum of 3 time histories could also be satisfied using the 3rd, 4th and 6th records from Figure 9.20, resulting in a design displacement of 585 mm as in option 3. above.

There is c learly a need to develop specific requirements for time histories to ensure thatanomalies do not occur and that the probability of maximum displacements beingexceeded is not too high.

One procedure, which has been used on several projects, is to use at least one frequencyscaled earthquake in addition to the scaled, actual earthquakes. A frequency scaledrecord has the frequency content of the record altered so that it produces a spectrum whichis a close match (usually within 5%) of the design spectrum at all periods. This ensures thatthe full frequency range of response is included in the analysis.



302

9.3.5 Time History Seismic Input

A major impediment to the implementation of seismic isolation is that the time history methodis the only reliable method of accurately assessing performance but code requirements for

selecting time histories result in much higher levels of input than alternative methods such asthe response spectrum procedure.

Overly conservative seismic design input for base isolation not only results in added costs butalso degrades the performance at the more likely, lower levels of earthquake. All practicalisolation systems must be targeted for optimum performance at a spec ified level ofearthquake. This is almost always for the maximum considered earthquake as thedisplacements at this level must be controlled. This results in a non-optimum system for alllower levels of earthquake.

Regardless of this, it is mandatory to use records scaled in accordance with the applicablecode requirements. Wherever possible, a site specific seismic study by a seismologica l

consultant should be used to define near fault effects and both the return period forearthquake magnitude and the probability of the site being subjected to near fault effects.It is also preferable that the seismologist provide appropriate time histories, with scalingfactors, to use to represent both the DBE and MC E events.

9.3.6 Selecting and Scaling Records for Time History Analysis

As noted above, the best method of selecting time histories is to have the seismologist supplythem. However, this option is not always available and, if not, some guidance can beobtained from codes as to means of selecting and scaling records.

The UBC and FEMA-356 Guidelines are explicit and generally follow the same requirements. These sources require a minimum of three pairs of time history components. If seven or morepairs are used then the average results can be used for design else maximum values must beused. The records are required to have appropriate magnitudes, fault distances and sourcemechanisms for the site. Simulated time histories are permitted.

The UBC provides an explicit method of scaling records:

For ea c h p a ir of ho rizonta l co m p on ents, the sq ua re roo t o f the sum of th e sq ua res (SRSS)

of the 5% d am pe d spe c t rum sha ll b e c onst ruc ted . The m ot ions sha ll be sc a led suc h tha t

the a verag e va lue o f the SRSS sp ec tra d oe s not fa ll b elow 1.3 t im es the 5% d am p ed

sp ec trum of the d esig n b a sis ea rthq ua ke b y m ore tha n 10% for pe riod s from 0.5T D to

1.25T M .

In this definition, TD is the period at the design displacement (DBE) and TM the period at themaximum displacement (MCE).

It is generally interpreted that a verag e v a lue of the SRSS is the average at each period overall records. In this case, the scaling factor for any particular record depends on the otherrecords selected for the data set.

The ATC-40 document provides 10 records identified as suitable candidates for sites distantfrom faults (Table 9.3) and 10 records for sites near to the fault (Table 9.4). In the absence ofother records, these may be useful.



303

No. M Year Earthquake Station File

12345678910

7.16.56.66.67.17.17.57.56.76.7

1949195419711971198919891992199219941994

WesternWashingtonEureka, CASan Fernando, CASan Fernando, CALoma Prieta, CALoma Prieta, CALanders, CALanders, CANorthridge, CANorthridge, CA

Station 325Station 022Station 241Station 241Hollister, Sth & PineGilroy #2 Yermo J oshua TreeMoorparkCentury City LAC C N

wwash.1eureka.9sf241.2sf458.10holliste.5gilroy#2.3yermo.4 joshua.6moorpark.8lacc_nor.7

Table 9.3: Records at Soil Sites > 10 km From Sources

No. M Year Earthquake Station File

12345678910

6.56.57.17.16.96.76.76.76.76.7

1949195419711971198919891992199219941994

Imperial Valley, CAImperial Valley, CALoma Prieta, CALoma Prieta, CACape Mendocino,CANorthridge, CANorthridge, CANorthridge, CANorthridge, CANorthridge, CA

El Centro Array 6El Centro Array 7CorralitosCapitolaPetroliaNewhall Fire StationSylmar HospitalSylmar Converter Stat.Sylmar Converter St ERinaldi TreatmentPlant

ecarr6.8ecarr7.9corralit.5capitola.6petrolia.10newhall.7sylmarh.4sylmarc.2sylmare.1rinaldi.3

Table 9.4: Records at Soil Sites Near Sources

9.3.7 Selecting Records from a Set

Although the UBC and FEMA documents specify the end product of the scaling ofearthquake records, they do not provide guidance in selecting particular records from a setof calculating scaling factors for the individual records. The recent revision to the NewZealand Loadings Code, NZS 1170, provides a procedure which can be adopted for other

codes.

In this procedure, there are two steps, scaling of individual records and then scaling of thefamily of records:

1. Determine the record scale factor, k 1, for each of the horizontal ground motioncomponents where k 1 = scale value which minimises in a least mean square sense thefunction log(k 1SA component/SA target) over the period range of interest. This can beimplemented using design tools such as spreadsheets by computing the factor D1 as:

TSA

SAk (

T4.05.1

1D 2

T5.1

T4.0

1

11 d ])log[

)( target

component

(9.1)



304

A solver is then used to select k1 so as to minimise D1. This is the scale fac tor for theparticular record.

2. The second step of is to ensure that the envelope of the scaled records exceeds thetarget spectrum. The procedure is to determine the record family scale factor, k 2,

which such that for every period in the period range of interest, the principalcomponent of at least one record spectrum scaled by its record scale factor k 1,exceeds the target spectrum.

When selecting a subset of records from a larger set, the value of D1 is calculated for allrecords and those producing the smallest values are used as the subset.

The New Zealand code scales on the principal component of the record and applies the

scaling factor to both components. For UBC or FEMA scaling, 22

21 SASASAcomponent where

SA1 and SA2 are the two components of the individual earthquake record. SAtarget is then setat 1.3 times the design spectrum.

9.3.8 Comparison of Earthquake Scaling Factors

The FEMA and UBC documents specify a procedure for selecting scale factors for timehistories which differs in two main respects from the procedure of NZS1170:

1. The individual UBC scaling factors are based on the ratio of the SRSS of the twocomponents to 1.3 C(T), rather then the ratio of the primary component to C(T) as forNZS1170.

2. The UBC family scaling factor is calculated so that the average of the three records

exceeds the target spectrum at each period point. The NZS1170 family scaling factor ifselected so that at least one record exceeds the target.

The net effect of these two differences is that the UBC scaling factors resulting in a 15% higherspec tral response than the NZS1170 fac tors, as shown in Table 9.5 for an isolated building witha 2 second period. The spectral displacement at the two second period is 469 mm, and thisis approximately the isolation system displacement which would be determined from aresponse spectrum analysis. The time history analysis would produce displacements 12%higher (NZS 1170) or 29% higher (UBC).

As the response spectrum and time history methods have the same acceptance criteria inthe UBC, it is unlikely that the time history procedure would be used for projec ts evaluated to

these guidelines.

Record NZS 1170 UBC

Mexico, UNIO, La Union Michoacan (Mexico) 1985 S00E 4.01 5.42

Iran, Tabas Tabas (Iran) 1978 N74E 0.96 1.03

Iran, Tabas Tabas (Iran) 1978 N90E 1.01 0.96

Spectral Acceleration at 2.0 seconds (C(T) = 0.48) 0.54 0.62

Spectral Displacement at 2.0 seconds (C(T) = 469 mm) 526 605

Table 9.5: Comparison of Scaling Factors



305

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 1.0 2.0 3.0 4.0

Period (Seconds)


C(T)

NZ Scaling

UBC Scaling

Isolated Period

2 seconds

Figure 9.21: 5% Damped Acceleration Spectra

0

200

400

600

800

1000

1200

0.00 1.00 2.00 3.00 4.00

Period (Seconds)


C(T)

NZ Scaling

UBC Scalin

Isolated Period

2 seconds

Figure 9.22: 5% Damped Displac ement Spectra



306

9.4 DETAILED SYSTEM ANALYSIS

The design procedure described elsewhere in this book is based on the response of theisolation system alone, without accounting for the flexibility of the structure itself. The

flexibility of the structure above the bearings (or the substructure below bridge bearings) willmodify the response because some of the displacement will take place in the structure. The extent of this variation from the assumed response will depend on the flexibility of thestructure or substructure relative to the isolation system.

It is possible to modify the design procedure to take account of substructure flexibility, as forbridge structures. In this modification, the stiffness of the bearings is calculated as thecombined stiffness of the isolators and the bent acting in series. However, most designoffices have computers with structural analysis programs and it is generally more efficient toinclude structural flexibility at the analysis phase rather than as part of the design process.

There is a hierarchy of analysis procedures, as listed in Table 9.6 in order of complexity. Each

procedure has its role in the design and evaluation process. The analysis options are notmutually exclusive and in fact all methods are usually performed in sequence up to the mostcomplex procedure appropriate for a project. In this way, each procedure providesbenchmark results to assess the reasonableness of the results from the next, more complexprocedure.

1. SINGLE DEGREE OF FREEDOMNONLINEAR

Isolation System Design

2. PLANE FRAME / PLANE WALL

2D BRIDGE MODELS

NONLINEAR Design Level vs. Damage Studies

Effec t of Bent Flexibility

3. THREE DIMENSIONAL

LINEAR Member Design Forces

4. THREE DIMENSIONAL

LINEAR SUPERSTRUCTURE

NONLINEAR ISOLATORS Isolation System Properties

5. THREE DIMENSIONALNONLINEAR SUPERSTRUCTURE

NONLINEAR ISOLATORS Isolation System and Structure Performanc e

Table 9.6: Analysis of Isolated Structures



307

9.4.1 Single Degree-of-Freedom Model

A simple model is often used at the preliminary design phase, especially for hybrid systems. The superstructure is assumed rigid and the total weight modeled as a single mass. Anumber of elements in parallel are then used to model the isolators. For example, all

elastomeric bearings are represented as a single elastic element, the lead cores as anelasto-plastic element and the sliding bearings as a single friction element. Viscous dampingwould be included in the elastic element but not the yielding elements. This model providesmaximum isolator displacements and forces and acts as a check on the design procedureused.

This model will produce results equivalent to those produced by the design procedure butwith more accuracy in two areas:

1. The input for this model is a series of time histories and so this procedure quantifies thedifference in results that will be produced by time history analysis compared to theresponse spectrum analysis method used in the design procedure.

2. The mass can be excited by two components of earthquake simultaneously, which willprovide displacements and base shear forces which incorporate the interaction ofisolator yield in the two directions.

A number of programs are available for this type of analysis, including NONLIN or DRAIN-2Dfor single component analysis and 3D-BASIS, SAP2000, ETABS or ANSR for concurrent analyses.

9.4.2 Two Dimensional Nonlinear Model

Two-dimensional models of a single representative frame or shear wall from the building are

an effective way of assessing the effects of superstructure / substructure response andyielding. The structural elements are represented as bilinear yielding elements and theisolators as for the single degree of freedom model.

For bridge structures, two separate 2D models are usually developed, one to modellongitudinal response and the other to model transverse response.

The DRAIN2D2 program is typica l of the type used for these analyses. This type of analysis israrely used for buildings as computer hardware is such that three-dimensional non-linearanalyses are practical in almost all cases. It is still used for bridges as the final analyses forbridges can be performed separately for the longitudinal and transverse direc tions.

9.4.3 Three dimensional Equivalent Linear Model

A linear elastic model using a building analysis program such as ETABS (or STRUDL for bridges)is sufficient for final design for some structures. A response spectrum analysis is performed toobtain earthquake response. In this type of analysis the isolators are represented as shortcolumn or bearing elements with properties selected to provide the effective stiffness of theisolators. Damping is incorporated by reducing the response spectrum in the range ofisolated periods by the B Factor.

As described earlier, there are some doubts about a possible under-estimation of theoverturning moments for most non-linear isolation systems if this procedure is used.



308

Pending resolution of this issue, it seems advisable that a time history analysis always beperformed on this model. Note that in ETABS and other programs the same model can beused for both response spectrum and time history analyses.

9.4.4 Three Dimensional Model - Elastic Superstructure, Yielding Isolators

This type of model is appropriate where little yielding is expected above or below theisolators. Some programs, for example 3D-BASIS, represent the building as a "super-element"where the full linear elastic model of the fixed base structure is used to reduce thesuperstructure to an element with three degrees of freedom per floor. This type of analysisprovides isolator displacements direc tly and load vectors of superstructure forces. Thecritical load vectors are applied back to the linear elastic model to obtain design forces forthe superstructure.

As the isolators are modeled as yielding elements the response spectrum method cannot beused and so a time history analysis must be performed. ETABS has non-linear isolatorelements and it is recommended that this option be used for all structures.

9.4.5 Fully Nonlinear Three Dimensional Model

Full non-linear structural models have become more practical as computer hardware indesign offices has improved although they remain time consuming and are generally onlypractical for special structures. The Museum of New Zealand nonlinear model with 2250degrees of freedom and over 1500 yielding elements was analyzed on MS-DOS 486computers and provided full details of isolator forces and deformations, structural plasticrotations, drifts, floor accelerations and in-structure response spectra. Current desktopcomputers are capable of analyzing models in excess of 20,000 degrees of freedom.

9.4.6 Device Modeling

For nonlinear analysis the yield function of the devices is modeled explicitly. The form of thisfunction for a particular element depends on the device modeled:

1. HDR bearings are modeled as either a linear elastic model with viscous dampingincluded or with the hysteretic loop directly specified.

2. LRBs are modeled as either two separate components (rubber elastic, lead core elasto-plastic) or as a single bi-linear element.

3. For sliding bearings, an elastic-perfectly plastic element with a high initial stiffness and ayield level which is a func tion of vertical pressure and veloc ity. If uplift can occur this iscombined with a gap element so that the shear force is zero when uplift occurs.

The modeling must be such that damping is not included twice, with both viscous andhysteretic formulations. This is why LRBs are often better modeled as two components.Element damping is applied to the rubber component, which has some associated viscousdamping, but not to the lead component.

For the Museum of New Zealand, a series of Teflon material tests were used to develop thedependence on pressure and veloc ity of the coefficient of friction. This was used tocalibrate an ANSR-II model. The model was then used to correlate the results of shaking

table tests for a concrete block mounted on Teflon pads.



309

ETABS has a sliding element which incorporates velocity effects and can also be used forcurved sliding systems.

9.4.7 ETABS Analysis for Buildings

Versions 6 and above of the ETABS program have the capability of modeling a base isolatedbuilding supported on a variety of devices. The ETABS manual provides guidance fordeveloping an isolated model.

An isolation design spreadsheet, such as the example provided with this book, can be usedto calculate properties to use for the ETABS analysis. This sec tion describes the basis for thecalculation of these properties and procedures to analyze the isolated building using ETABS.

Isolation System Properties

The devices isolation system designs will most commonly be one or more of lead rubber

bearings (LRB), elastomeric bearings (ELAST), high damping rubber bearings (HDR) or Teflonflat or curved sliding bearings (PTFE and FPS). These are modeled as springs in ETABS. Theappropriate spring types are as follows:

Lea d Rub b e r Bea rings (LRB)

LRBs are modeled as an equivalent bi-linear hysteresis loop with properties calculated fromthe lead yield stress and the elastomeric bearing stiffness. This is modeled as type ISOLATOR1in ETABS.

Ela stom e ric Bea ring s (ELAST)

Plain elastomeric bearings are modeled as type LINEAR.

Slid ing Bea ring s (PTFE a nd FPS)

Sliding bearings are modeled as type ISOLATOR2 with properties for the coefficient of frictionat slow and fast velocities as developed from tests.

The coefficient of friction is a function of pressure on the bearing as well as veloc ity. ETABSincorporates the veloc ity dependence but not the pressure dependence. Table 9.7 lists themeasured coefficients of friction for a series of tests performed at the State University of New York, Buffalo. These are for unfilled Teflon (UF) and 15% and 25% glass filled (15GF and 25GFrespectively). Tests on the UF material were performed both parallel to the lay (P) and

perpendicular to the lay (T).



310

PressureTypeof

Teflon

SlidingDirection psi MPa

LowVelocity

Coefficient

HighVelocity

Coefficient

Exponenta

UF P 1000 7 0.027 0.119 0.60

UF P 2000 14 0.018 0.087 0.60UF P 3000 21 0.015 0.070 0.80

UF P 6500 45 0.009 0.057 0.50

15GF P 1000 7 0.040 0.146 0.60

15GF P 2000 14 0.043 0.101 0.55

15GF P 3000 21 0.043 0.085 0.60

15GF P 6500 45 0.022 0.053 0.70

25GF P 1000 7 0.055 0.132 0.65

25GF P 2000 14 0.049 0.112 0.65

25GF P 3000 21 0.044 0.096 0.32

25GF P 6500 45 0.032 0.059 0.90

UF T 1000 7 0.024 0.142 0.45UF T 2000 14 0.017 0.105 0.70

UF T 3000 21 0.029 0.082 0.55

UF T 6500 45 0.011 0.055 0.45

Table 9.7: PTFE Properties

Table 9.7 shows considerable variations with pressure, veloc ity and material. Most isolationsystems use unfilled Teflon and so only the UF values are of interest. From Table 9.7,reasonable analysis values for unfilled Teflon would be as listed in Table 9.8:

Vertical

Pressureon PTFE

FrictionCoefficient atLow Velocity

FrictionCoefficient atHigh Velocity

CoefficientControllingVariation

< 5 MPa5 - 15 MPa> 15 MPa

0.030.0250.02

0.140.100.08

0.550.650.60

Table 9.8: Analysis Values for PTFE

For curved slider bearings (FPS) the radius of curvature is also specified. To use this type of

isolator, it is recommended the supplier be consulted for appropriate friction values.

Hig h Dam p ing Rub b er Bea ring s (HDR)

Although the elastomer used for these bearings is termed "high damping" the major energydissipation mechanism of the elastomer is hysteretic rather than viscous, that is, the forcedeflec tion curves form a nonlinear hysteresis. The UBC code provides a procedure forconverting the area under the hysteresis loop to an equivalent viscous damping ratio to beused for equivalent linear analysis.

For nonlinear analysis it is more accurate to model the force deflection curve direc tly and soinclude the hysteretic damping implicitly. This avoids the approximations in converting ahysteresis area to viscous damping.



311

The second data line for the ETABS input file contains the bilinear properties for a nonlineartime history analysis. The procedure for deriving these properties is based on the followingmethodology:

1. The effective stiffness at the design displacement is known from the design procedureand the stiffness properties of the elastomer. This provides the force in the bearing at

the design displacement.

2. An equivalent "yield" strain is defined in the elastomer. This defines a "yield"displacement.

3. From the elastomer shear modulus at the assumed "yield" strain the yield force can becalculated and the hysteresis loop constructed.

4. The area of this hysteresis loop is computed and, from this and the effective stiffness, theequivalent viscous damping is calculated.

5. If necessary, the assumed "yield" strain is adjusted until the equivalent viscous damping

at maximum displacement equals the damping provided by the elastomer at that strainlevel.

Procedures for Analysis

The ETABS model can be analyzed using a number of procedures, in increasing order ofcomplexity:

1. Equivalent static loads.

2. Linear response spec trum analysis.

3. Linear Time History Analysis.

4. Nonlinear Time History Analysis.

The UBC provides requirements on the minimum level of analysis required depending onbuilding type and seismicity:

The eq uiva lent sta t ic a na lysis is limited to small, regular buildings and would almost never besufficient for isolation projec ts.

A l inear response spectrum analysis is the most common type of ana lysis used. This is

sufficient for almost all isolation systems based on LRB and/or HDR bearings.

The response spectrum analysis procedure uses the effective stiffness of the bearings, definedas the force in the bearing divided by the displacement. Therefore, it is iterative in that, ifthe analysis produces a displacement which varies from that assumed to calculate stiffnessproperties, the effective stiffness must be adjusted and the analysis repeated.



312

In practice, the single mass approximation used for system design usually gives a goodestimate of displacement and multiple analyses are not required. However, if the ETABSanalyses produce center of mass displacements above the isolators which are significantlydifferent from the design procedure values (variation more than about 10%) then theproperties should be recalculated.

The effective stiffness at a specified displacement, , can be calculated from the data onthe second line of the ISOLATOR1 input as:

KE2FY2(1 RK2)

K2.RK2

(9.2)

The effective damping can be ca lculated as:

DE22.FY2.(1 RK2)

FY2

K2KE2

( )

. .

2 (9.3)

This is the total damping - as discussed below, this must be reduced by the structuraldamping, typically 0.05, spec ified in ETABS.

Linea r tim e h isto ry a na lysis provides little more information than the response spectrumanalysis for a much greater degree of effort and so is rarely used.

No nline a r time histo ry a na lysis is required for (1) systems on very soft soil (2) systems without arestoring force (e.g. sliding systems) (3) veloc ity dependent systems and (4) systems withlimited displacement capability.

In practice, nonlinear time history has been used in many projects even where not explicitly

required by the UBC. This is largely because most isolated projects have been especiallyvaluable or complex buildings. As discussed earlier, there are some concerns about theaccuracy of equivalent stiffness analysis results.

Input Response Spectra

The response spectrum analysis calculates the response of each mode from the spectralordinate at that period. For the isolated modes the damping must include the equivalentviscous damping of LRB and HDR bearings. Therefore, a series of response spec tra must beinput covering the full range of damping values for all modes. These spectra are calculatedby dividing the spectral values by the B factor for each damping factor, as specified in the

UBC:

Equivalent Viscous Damping<2% 5% 10% 20% 30% 40% >50%

B 0.8 1.0 1.2 1.5 1.7 1.9 2.0

The time history solution applies the modal damping to the response calculated for eachmode during the explicit integration. Therefore, the input time history does not need to bemodified to reflect damping.



313

Damping

The ETABS program is relatively straightforward for modeling stiffness properties of theisolators, both for effective stiffness analysis and nonlinear time history analysis. However, themanner in which damping is applied is more complex.

The aim for most analyses is to use 5% damping for the structural modes, as is assumed in thecodes, but to use only the damping provided by the isolation system in the isolated modes. The procedure used to implement this in each type of analysis is as described below.

Respo nse Sp ec trum An a lysis

For the response spectrum analysis, a value of 0.05 is specified for DAMP in the Lateral

Dynam ic Spe c t rum Da ta sec tion. This applies damping of 5% to all modes, including theisolated modes. To avoid including this damping twice, the value of both DE2 and DE3 in theSp ring Pro p ert ies sec tion is reduced by 0.05. The example spreadsheet calculations includethis reduction.

Line a r Tim e History An a lysis

The linear time history analysis uses the effective stiffness and damping values as for theresponse spectrum analysis and so the same procedure for specifying damping as usedabove is applicable, that is, reducing DE2 and DE3 by 0.05.

An alternative method for specifying damping is available in time history analysis byproviding data lines to override the modal damping value specified. In this procedure,

NDAMP is specified as 3 in the La te ra l Dyna m ic Tim e Histo ry Da ta section and modes 1 to 3are specified to have 0.0 damping.

Nonlinea r Time History A na lysis

For nonlinear time history analysis the hysteretic damping is modeled explicitly and the valuesof DE2 and DE3 are not used. The only procedure available to avoid "doubling up" ondamping is to specify viscous damping as 0.0 in the first three modes, the second methodlisted above for linear time history analysis. This slightly underestimates total damping.

The procedures used to specify damping for the different analysis types are generally based

on an assumption of hysteretic damping only in the isolators, with no viscous damping. This isa conservative approach. From tests on these bearings at different frequencies, thedamping may be increased by about 20% by viscous effects. In some types of analysis, thisincrease can be incorporated by increasing the size of the hysteresis loop.

9.4.8 Concurrency Effects

The design procedure for isolation systems is based on a single degree of freedomapproximation which assumes a constant direction of earthquake loads. The evaluation ofthe structural system requires that earthquake motions be applied concurrently along bothhorizontal axes.



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For the response spec trum method of analysis UBC requires that the spectrum be applied100% along one direc tion and 30% of the ground motion along the orthogonal axis. The timehistory method of analysis requires that two horizontal components of each earthquakerecord be applied simultaneously.

The yield function for bi-linear systems such as lead rubber bearings is based on a circular

interaction formula:

0.1

22

y

ayax

V

V V (9.4)

where Vax and Vay are the applied shears along the two horizontal axes and Vy is the yieldstrength of the isolation system. If concurrent shear forces are being applied along eachaxis then the effective yield level along either axis will be less than the design value based onnon-concurrent seismic loads. For the case where equal shear forces are applied in both

directions simultaneously, the shear force along each axis will be equal to

2

Y V .

The reduced yield force along a particular direction will result in the equivalent viscousdamping being less than the value calculated from the design procedure. This will producea performance different from that calculated. In some c ircumstances, it may be desirable toincrease the yield level so that under concurrent action the response will closer match thatcalculated from non-concurrency.

As an example of the effects of concurrency, an isolated building was analyzed for sevennear fault earthquake records, each with two horizontal components scaled by the samefactor.

Maximum displacements and base shear coefficients were obtained for three cases:

1. The isolation system as designed, maximum vector response when both componentswere applied simultaneously.

2. The isolation system as designed, maximum vector response of the components appliedindividually.

3. The isolation system with the yield level increased by 2 , then evaluated as for 1. above,

the maximum vector response with both components applied simultaneously.

Figures 9.23 and 9.24 plot the resulting displacements and shear coefficients respectively for

the three cases for each earthquake. Also plotted are the mean results, which would beused for design if 7 earthquakes were used for analysis.



315

0

100

200

300

400

500

600700

800

900

1000

H O

L

L U

C

S Y L

E L C

N E

W

S E P

Y E

R

M E A

N

V E C T O R D I S P L A C E M E N

T ( m m )

Concurrent Unidirectional Concurrent Incr Fy

Figure 9.11: Displacements with Concurrent Loads

The results show that there is a consistent effect of concurrent versus non-concurrentapplications of the two earthquake components in that the concurrent components alwaysproduced higher displacements and higher shear forces than the non-concurrent case.However, the difference was very much a function of the earthquake records.Displacements were higher by from 2% to 57% and shears higher by from 1% to 38%. Theaverage displacement was 15% higher, the average shear 11% higher.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

H O L

L U C

S Y L

E L C

N E W

S E P

Y E R

M E A N

B A S E S H E A R C O E F F I C I E N T

Concurrent Unidirectional Concurrent Incr Fy

Figure 9.12: Shears with Concurrent Loads



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Increasing the yield strength of the isolation system generally, but not always, reducedconcurrent displacements and shears to values less than the non-concurrent values with thelower yield strength. In this example, an increase in yield level would reduce the meandisplacement to less than the non-concurrent value and reduce the base shear to onlyslightly more than the non-concurrent value.

MeanDisplacement

(mm)

MeanBase ShearCoefficient

Concurrent 706 0.320

Unidirec tional 615 0.289

Concurrent with Increased Fy 570 0.292

Although in this example an increase in yield level was effective in counteractingconcurrency effects the results were not consistent enough to demonstrate that this will

always be an effective strategy. It is recommended that the effects of concurrency beassessed on a project specific basis to check whether an increase in yield level is justified.

An increase in yield level may require higher design forces for the structure above theisolation system if design is governed by the requirement for design base shear being at least1.5 times the yield level of the system. If design is governed by this criterion then it may bepreferable to accept higher displacements and shears from concurrency effects rather thanre-design for a higher yield level.

9.5 CONNECTION DESIGN

9.5.1 Elastomeric Based Isolators

Early seismic isolation bearings used load plates bolted to a steel plate bonded internally inthe bearing. Manufacturing technology has now improved such that the majority of seismicisolation bearings are manufactured with flange plates, or load plates, bonded to thebearing top and bottom during manufacture. These plates are larger in plan dimension thanthe isolator and are used to connect the bearing to the foundation below and the structureabove.

The load plates may be c ircular, square or rectangular, depending on project requirements. The amount of overhang depends on the bolt sizes and the seismic displacement. The boltsmust be located far enough from the isolator such that they do not damage the cover

rubber during maximum seismic displacements. Square load plates allow a smaller plandimension than c ircular plates and so are often used for this reason.

The isolators are installed between the foundation and the structure, as shown conceptuallyin Figure 9.25. The connection design must ensure that the maximum forces are safelytransferred from the foundation through the bearing to the structure above.



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Top Fixing Plate with

Couplers and HD Bolts

to suit Concrete Floor Beams

Lead Rubber Bearing

Pressure Grout under

Bottom Fixing Plate to

allow for levelling

Concrete Foundation Beams

and Pads

Bottom Fixing Plate with

Couplers and HB Bolts

to suit

Figure 9.13: Typical Installation in New Building

Design Basis

The connection of the isolation bearing to a structure must transmit shear forces, verticalloads and bending moments. Bending moments are due to primary (VH) and secondary

(P) effec ts (Figure 9.26). Design for shear is relatively straightforward. Design for bendingmoments is complicated by the unknown shape of the compressive block, especially underextreme displacements.

It is recognized that the design approach used here is simplistic and not a true representationof the actual stress conditions at the connection interface. However, the procedure hasbeen shown to be conservative by prototype testing which has used less bolts, and thinnerplates, than would be required by the application of this procedure.

P

V

V

H

Figure 9.14: Forces on Bearing in Deformed Shape



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Bearing design includes the mounting plate and mounting bolts. The design basis dependson project specifications, but generally is either AASHTO allowable stress values, with a 4/3stress increase factor for seismic loads, or AISC requirements.

Design Actions

Connec tions are designed for two conditions, (1) maximum vertical load and (2) minimumvertical load, each of which is concurrent with the maximum earthquake displacement andshear force.

The bearing is bolted to the structure top and bottom and so acts as a fixed end column forobtaining design moments. Figure 9.27 shows how the actions shown in Figure 9.26 may betransformed to an equivalent column on the centerline of the bearing.

P

V

M

M

Figure 9.15: Equivalent Column Forces

The total moment due to applied shear forces, VH, plus eccentricity, P, is resisted by equalmoments at the top and bottom of the isolator. These design moments are equal to:

)(2

1 PVH M (9.5)

Connection Bolt Design

The design procedure adopted for the mounting plate connection is based on the simplifiedcondition shown in Figure 9.28, where the total axial load and moment is resisted by the boltgroup. In Figure 9.28, the area used to calculate P/ A is the total area of all bolts and thesec tion modulus used to calculate M/S is the sec tion modulus of all bolts. Figure 9.28 is for acircular load plate. A similar approach is used for other shapes.



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Load Plate Design

For a circular load plate, the assumed force distribution on which load plate calculations arebased is shown in Figure 9.29. Bending is assumed to be critica l in an outstanding segmenton the tension side of the bearing. The chord defining the segment is assumed to be tangentto the side of the bearing.

This segment is loaded by three bolts in the example displayed in Figure 9.29.Conservatively, it is assumed that a ll bolts (three in this example) have the maximum tensionforce and also that all three bolts have the lever arm of the furthest bolt.

RADIUS r

RISE

b

CHORD

c

DISTANCE TO

BOLT 1

COMPRESSION

TENSION

Figure 9.17: Circular Load Plate

The design procedure adopted for a square load plate connection is based on the conditionshown in Figure 9.30. Loading is assumed along the direction of the diagona l as this is the

most critical for the bolt layout used with this type of load plate.



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Dim 'X'

Dim 'Y'

Axis of Bending

Critical Section for Cantilever

60 Typ. (2 1/2")

150 Typ. (6")

Isolator Diameter

Load Plate Dimension

Figure 9.18 Square Load Plate

9.5.2 Sliding Isolators

For sliding isolators the eccentricity of the load at maximum displacements depends on theorientation of the bearing. If the slide plate is at the top then under maximum displacementsthe vertical load will apply a P- moment which must be resisted by the structural systemabove the isolators. If the slide plate is at the bottom then the eccentricity will load the

foundation below the isolator but will not cause moments above. For this reason, mostseismic applications of sliding isolators are more effective if the slide plate in located at thebottom.

Most sliding bearings are designed with a low coefficient of friction at the sliding interface. Intheory, they do not require any shear connection. The friction at the interface of the bearingto the structure above and to the foundation below, usually steel on concrete will have ahigher coefficient of friction and so slip will not occur. In practice, bolts are usually used ateach corner of the slide plate and the sliding component is bolted to the structure above,also usually with four bolts.

Most types of sliding bearings, such as pot bearings and friction pendulum bearings, are

proprietary items and the supplier will provide connec tion hardware as part of supply.



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9.5.3 Installation Examples

Figure 9.31 to 9.36 are example installation details which have been used on completed

isolation projec ts. These include both new and retrofit projec ts. Although these detailscannot be used directly for other projects, they provide an indication of installation methodsand the extent of strengthening associated with installation.

Figure 9.19: Example Installation: New Construction



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Figure 9.20 Example Installation: Existing Masonry Wall



324

Figure 9.21: Example Installation: Existing C olumn



325

Figure 9.22: Example Installation: Existing Masonry Wall



326

Figure 9.23: Example Installation: Steel Column



327

Figure 9.24: Example Installation: Steel Energy Dissipator

9.6 STRUCTURAL DESIGN

9.6.1 Design Concepts

The isolation system design and evaluation procedures produce the maximum base shears,displacements and structural forces for each level of earthquake, usually the DBE and MC E. These represent the maximum elastic earthquake forces that will be transmitted through theisolation system to the structure above. Even though isolated buildings have lower seismicloads than non-isolated buildings, it is still not generally cost effective to design for elasticperformance at the MC E level and sometimes yielding may be permitted at the DBE level.

Most building isolation projects have been designed elastically to the DBE level of loadingwith some ductility demand at the MCE level. This is because of the nature of buildingsisolated so far, which have been either older buildings with limited ductility or buildingsproviding essential services where a low probability of damage is required.

For new buildings in the ordinary category, design forces are usually based on the DBE levelof load reduced to account for ductility in the structural system. This is the approach takenby the UBC for new buildings. An isolated building, if designed elastically to the DBE, willlikely have higher design forces than a ductile, non-isolated building which would bedesigned for forces reduced by ductility fac tors of 6 or more. These higher forces, plus the

cost of the isolation system, will impose a significant first cost penalty on the isolated building.



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Total life cycle costs, incorporating costs of earthquake damage over the life of the building,will usually favor the isolated building in high seismic regions. However, life cycle cost analysisis rare for non-essential buildings and few owners are prepared to pay the added first cost.

The UBC addresses this issue by permitting the structural system of an isolated building to bedesigned as duc tile, although the ductility fac tor is less than one-half that specified for a non-

isolated building. This provides some added measure of protection while generally reducingdesign forces compared to an equivalent non-isolated building.

9.6.2 UBC Requirements

The UBC requirements for the design of base isolated buildings differ from those for non-isolated buildings in three main respects:

1. The importance factor I, for seismic isolated buildings is taken as 1.0 regardless ofoccupancy. For non-isolated buildings I = 1.25 for essential and hazardous fac ilities. Asdiscussed later, a limitation on structural design forces to the fixed base values doesindirectly include I in the derivation of design forces.

2. The numerical coefficient, R, which represents global ductility, is different for isolated andnon-isolated buildings.

3. For isolated buildings there are different design force levels for elements above andelements below the isolation interface.

Elements below the Isolation System

The isolation system, the foundation and all structural elements below the isolation system areto be designed for a force equal to:

D D B Dk V max (9.6)

Where kDmax is the maximum effective stiffness of the isolation system at the designdisplacement at the center of mass, DD. All provisions for non-isolated structures are used todesign for this force.

In simple terms, this requires all elements below the isolators to be designed elastically for themaximum force that is transmitted through the isolation system at the design levelearthquake.

One of the more critical elements governed by elastic design is the total moment generatedby the shear force in the isolation system plus the P- moment. As discussed previously, themoment at the top and bottom of an elastomeric type isolation bearing is:

)(2

1 D B PD H V M (9.7)

where H is the total height of the bearing and P the vertical load concurrent with V B. Thestructure below and above the bearing must be designed for this moment. For some typesof isolators, for example sliders, the moment at the loc ation of the slider plate will be PDD andthe moment at the fixed end will be VH.



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Elements Above the Isolation System

The structure above the isolators is designed for a minimum shear force, VS, using all theprovisions for non-isolated structures where:

I

D D

S

R

Dk V max (9.8)

This is the elastic force in the isolation system, as used for elements below the isolators,reduced by a factor RI that accounts for duc tility in the structure.

Table 9.9 lists values of RI for some of the structures included in UBC. For comparison theequivalent duc tility factor used for a non-isolated building, R, is also listed in Table 12-1. UBCincludes other structural types not included in this table so the code should be consulted forstructural systems not listed in Table 12-1. All systems included in Table 9.9 are permitted in allseismic zones.

The values of RI are always less than R, sometimes by a large margin. The reason for this is to

avoid high ductility in the structure above the isolation system as the period of the yieldedstructure may degrade and interact with that of the isolation system.

Structural

System

Lateral Force Resisting System Fixed

BaseR

Isolated

RI

Bearing WallSystem

Concrete Shear WallsMasonry Shear Walls

4.54.5

2.02.0

BuildingFrameSystem

Steel Eccentrically Braced Frame (EBF)Concrete Shear WallsMasonry Shear WallsOrdinary Steel Braced FrameSpecial Steel Concentric Braced Frame

7.05.55.55.66.4

2.02.02.01.62.0

MomentResistingFrameSystem

Spec ial Moment Resisting Frame (SMRF)SteelConcrete

Intermediate Moment Resisting Frame (IMRF)Concrete

Ordinary Moment Resisting Frame (OMRF)Steel

8.58.5

5.5

4.5

2.02.0

2.0

2.0

DualSystems

Shear WallsConcrete with SMRFConcrete with steel OMRFMasonry with SMRFMasonry with Steel OMRF

Steel EBF

With Steel SMRFWith Steel OMRF

Ordinary braced framesSteel with steel SMRFSteel with steel OMRF

Spec ial Concentric Brac ed FrameSteel with steel SMRFSteel with steel OMRF

8.54.25.54.2

8.44.2

6.54.2

7.54.2

2.02.02.02.0

2.02.0

2.02.0

2.02.0

CantileverColumnBuildings

Cantilevered column elements 2.2 1.4

Table 9.9: Structural Systems above the Isolation Interface



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There are design economies to be gained by selecting the appropriate structural system. Forexample, for a non-isolated building the design forces for a special moment resisting steelframe are only about 53% of the design forces for an ordinary steel moment resisting frame.However, for an isolated moment frame the design force is the same regardless of type. Inthe latter case, there is no benefit for incurring the extra costs for a special frame and so anordinary frame could be used. Care needs to be exercised with this approach because, as

discussed later, there may be some penalties in structural design forces if the ratio of R/RI islow.

Table 9.9 also shows that some types of building are more suited to isolation, in terms ofreduction in design forces, than others. For bearing wall systems the isolation system needs toreduce response by a fac tor of only 4.5 / 2 = 2.25 or more to provide a net benefit in designforces. On the other hand, for an eccentrically braced frame the isolation system needs toprovide a reduction by a factor of 7.0 / 2.0 = 3.5 before any benefits are obtained, a 55%higher reduction.

The value of VS calculated as above is not to be taken as lower than any of:

1. The lateral seismic force for a fixed base structure of the same weight, W, and a periodequal to the isolated period, TD.

2. The base shear corresponding to the design wind load.

3. The lateral force required to fully activate the isolation system fac tored by 1.5 (e.g. 1½times the yield level of a softening system or static friction level of a sliding system).

In many systems one of these lower limits on VS may apply and this will influence the design ofthe isolation system.

Fixed Base Structure Shear

In general terms, the base shear coefficient for a fixed base structure is:

RT

I C C V (9.9)

and for an isolated structure

BT R

C C

I

VD

I (9.10)

There is a change in nomenclature in the two sections and in fact CV = CVD and so to meetthe requirements of Criterion 1 above, C I C, the two equations can be combined toprovide:

I R

R B

I

(9.11)

Therefore, the limitation that forces be not lower than the fixed base shear for a building ofsimilar period effectively limits the amount of damping in the isolation system, measured by B,which can be used to reduce structure design forces.

The range of R/RI (Table 9.9) is from 1.57 to 4.25. Figure 9.37 shows the limitation on thedamping that can be used to derive structure design forces for this range of factors.



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0%

10%

20%

30%

40%

50%

60%

1.50 1.75 2.00 2.25 2.50 2.75 3.00

Ratio R / RI

M a x i m u m D a m p i n

g

I=1

I=1.25

Figure 9.25: Limitation on B

Most systems target 15% to 35% equivalent damping at the design basis earthquake level. Asseen from Figure 9.37, this damping may not be fully used to reduce design forces where theratio of R/RI is less than about 1.8, or less than 2.2 for a structure with an importance factor I =1.25.

This limitation on design base shears will generally only apply when you have a structure witha relatively non-ductile lateral load system (low R) and/or an importance factor greater than1.0.

Design Wind Load

Most isolation systems are installed in relatively heavy buildings because isolation is mosteffective for high mass structures. The yield level selec ted for optimum damping, usually 5%to 15% of the weight of a structure, is generally much higher than the wind load, which isusually less than 2% of the weight. Because the isolation system yield level is always sethigher than the wind load, then the third criterion discussed below, will govern rather thanwind.

Factored Yield Level

The requirement that the design lateral force be at least 1½ times the yield force will governin many isolation designs and will be a factor in selec tion of the isolator properties. High yieldforces are used to increase the amount of damping in a system to control displacements.Generally, the higher the seismic load and the softer the soil type the higher the optimumyield level.

Design is often a process of adjusting the yield level (for example, lead core size in LRBs) untilthe value of VS calculated from the isolation system performance is approximately equal to1.5Fy.



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The drift limitations for isolated structures may also limit the design of the structural system:

Response Spec trum Analysis 0.015 / RI

Time History Analysis 0.020 / RI

These are more restrictive than for non-isolated buildings where the limits are:

Period < 0.7 sec onds 0.025 / 0.7RPeriod 0.7 seconds 0.020 / 0.7R

Although the UBC is not specific in this respect, it can probably be assumed that the value ofRI can be lower but not greater than the values specified in Table 9.9 above. If one of thethree UBC lower limits applies to the design lateral force for the structure then the actualvalue of RI which corresponds to this force should be calculated. This will affect thecalculation of the drift limit.

9.6.3 MCE Level of Earthquake

The UBC defines a total design displacement, D TD, under the design basis earthquake (DBE)and a total maximum displacement, D TM, under the maximum capable earthquake (MCE). The vertical load-carrying elements of the isolation system are required to be stable for theMC E displacements. The MCE displacements also define the minimum separations betweenthe building and surrounding retaining walls or other fixed obstructions.

There are no requirements related to the MCE level of load for design of the structuralelements above or below the isolation interface. Presumably, it is assumed that the elasticdesign of elements below the isolation system produces sufficient over strength for MCE loadsand that the limitations on RI provide sufficient ductility above the isolation system for MCEloads.

9.6.4 Non-Structural Components

The UBC requires components to be designed to resist seismic forces equal to the maximumdynamic response of the element or component under consideration but also allows designto be based on the requirements for non-isolated structures.

For components, there are three aspects of the dynamic response which define themaximum force:

1. The maximum acceleration at the location of the component. UBC defines this for non-isolated components as a function of the ground acceleration, C a, and the height of thecomponent, hx, relative to the height of the structure, hr:

)31(r

x

ah

hC C (9.12)

2. Component amplification factor, which defines the extent of amplification when flexiblecomponents are excited by structural motion. In UBC this is defined as ap.

3. The ductility of the part can be used to reduce the design forces in a similar manner to Ris used for the structural system. UBC defines this as Rp.



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UBC requires forces to be factored by the importance factor for the part, Ip, and asimplification also allows the component to be designed for the maximum acceleration(4Ca) and ignore both ap and Rp.

For isolated structures, it is usual to replace the value of C calculated above with the peakfloor accelerations obtained from the time history analysis. Values of ap and Rp as for non-

isolated structures are then used with this value.

As time history analyses are generally used to evaluate isolated structures it is possible togenerate floor response spectra and use these to obtain values of ap, defined as the spectralacceleration at the period of the component. As this requires enveloping a large number ofspec tra, this procedure is usually only used for large projects.

9.6.5 Bridges

Although there are differences in detail, the same general principles for the structural designof bridges apply as for buildings:

1. The elastic forces transmitted through the isolation system are reduced to take accountof ductility in the sub-structure elements. The 1991 AASHTO permitted use of R valuesequal to that for non-isolated bridges but in the 1999 AASHTO this has been reduced toone-half the value for non-isolated bridges. This provides a range of RI from 1.5 to 2.5,which implies relatively low levels of ductility. RI need not be taken less than 1.5.

2. A lower limit on design forces is provided by non-seismic loads, the yield level of asoftening system or the friction level of a sliding system. AASHTO does not require the 1.5fac tor on the yield level or friction level that is spec ified in the UBC. For buildings non-seismic lateral loads are usually restricted to wind but bridges have a number of othercases which may influence design (wind, longitudinal force, centrifugal force, thermalmovements etc.).

3. Connection design forces for the isolators are based on full elastic forces, that is, R = 1.0.

Although bridges do not generally use the DBE and MC E terminology typical of buildings,design of the structure is based on a 475 year return period earthquake and the isolatorsmust be tested to displacement levels equivalent to that for a 2,400 year return periodearthquake. The 2,400 year displacement is obtained by applying a factor of 2.0 to thedesign displacements for low to moderate seismic zones (accelerations 0.19g) and 1.5 forhigh seismic zones (accelerations > 0.19g).

9.7 SPECIFICATIONS

9.7.1 General

Sample specifications reflecting current US practice are provided in Naeim and Kelly [1999].Figure 9.38 shows the major headings that are generally included in base isolationspecifications.



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1. PRELIMINARY2. SCOPE3. ALTERNATIVE BEARING DESIGNS4. SUBMITTALS

5. REFERENCES6. BEARING DESIGN PROPERTIES7. BEARING CONSTRUCTION7.1. Dimensions7.2. Fabrication7.3. Fabrication Tolerances7.4. Identification7.5. Materials8. DELIVERY, STORAGE, HANDLING AND INSTALLATION9. TESTING OF BEARINGS9.1. General9.2. Production Testing

9.2.1. Sustained Compression Tests9.2.2. Compression Stiffness Tests9.2.3. Combined Compression and Shear Tests9.3. Rubber Tests9.4. Prototype Testing9.4.1. General9.4.2. Definitions9.4.3. Prototype Test Sequence9.4.4. Determination of Force-Deflection Characteristics9.4.5. System Adequacy9.4.6. Design Properties of the Isolation System9.5. Test Documentation

10. WARRANTIES

Figure 9.26:Spec ification C ontents

Often, the specifications provide a particular bearing design which manufacturers can biddirec tly and also permit alternate systems to be submitted. Procedures need to be specifiedfor the manner in which alternate systems are designed and validated. Generally, this willrequire specification of the seismic design parameters, the form of the analysis model andthe performance requirements for the system. Performance requirements almost alwaysinclude maximum displacements and maximum base shear coefficients and may alsoinclude limits on structural drifts, floor accelerations, member forces and other factors whichmay be important on a specific project.

Care should be taken not to mix prescriptive and performance requirements. If performancerequirements of the isolation system are specified, including the evaluation method to definethis performance and the testing required to validate the properties, then the documentsshould not also spec ify design aspects such as the shear modulus of the rubber (for LRBs orHDR bearings) or the radius of curvature (for curved sliders).

Even for the complying design, the onus should be placed on the manufacturer to verify thedesign because aspects of isolation system performance are manufacturer-specific, such asdamping or lead core effective yield level. It is often useful to include a c lause such as thefollowing:



335

“The m a nufa c turer sha ll c he c k the b ea ring sizes a nd sp ec if ic a t ion s b efo re te nd er ing .

If the m a nufac turer co nsid ers tha t som e a lte ra t ion shou ld b e m a de to the b ea ring

sizes and / or prop er ties to m ee t the sta te d de sign pe rfo rm a nc e req u irem ents the

eng inee r sha ll be a d v ised of the a lte ra t ions w hic h the m a nufac turer in tend s m a king

w ith the tend er .”

9.7.2 Testing

Code requirements for base isolation require testing of prototype bearings, to ensure thatdesign parameters are achieved, and additional production testing is usually performed aspart of quality control. The UBC and AASHTO codes spec ify procedures for prototype testsand most projec ts generally follow the requirements of one of these codes. These requirethat two bearings of each type be subjected to a comprehensive sequence of tests up toMC E displacements and with maximum vertical loads.

Because of the severity of the tests, prototype bearings are not used in the structure, withsome exceptions in low seismic zones. The extra isolators can add significantly to the costs of

projects that have a small number of bearings, or a number of different types.

Production tests usually include compressive stiffness testing of every bearing plus combinedshear/compression testing of from 20% to 100% of isolators. Compression testing has beenfound difficult to use as a control parameter to ensure consistency. This is because typicalvertical deflections are in the order of 2 mm to 5 mm whereas for large bearings the out ofparallel between top and bottom surfaces will be of the same order. This distorts apparentcompressive stiffness. On recent projects, these difficulties have lead to a preference for themeasurement of shear stiffness on all production bearings to ensure consistency.

Testing requirements in the UBC have become more stringent in later editions of the code. Inparticular, the 1997 edition requires cyclic testing to the MCE displacements whereas earlier

editions required a single loading to this displacement level. This requires high capacity testequipment because MCE displacements may be 750 mm or more. Test equipment that cancycle to this magnitude of displacement is uncommon. Where a project is not required tofully comply with UBC it may be cost-effec tive to use the earlier UBC requirement of a simplestability test to the MC E displacement. This may allow manufacturers to bid who would nototherwise bid because of insufficient test capacity. This option needs to be assessed on aproject by project basis.



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Chapter 10: FEASIBILITY ASSESSMENT, EVALUATION AND

FURTHER DEVELOPMENT OF SEISMIC ISOLATION

10.1 DECISION-MAKING IN A SEISMIC ISOLATION CONTEXT

10.1.1 Seismic Isolation Decisions to be made

Chapters 1 to 9 of this book have shown that many engineers and contrac tors all over the world

have used seismic isolation, as an integral part of their designs or as a retrofit, in order to provide

a bridge or building or their contents with passive protection against a recognised natural

hazard – earthquake damage.

These chapters of this book have shown:

that seismic isolation can be installed;

that seismic isolation has been installed; that techniques are available to enable an engineer to calculate the necessary

parameters for installation of a seismic isolation system; and

that devices such as Lead Rubber Bearings can be fabricated, tested and installed to

provide seismic isolation.

However the chapters above do not address the key question:

Should seismic isolation be installed in a bridge or building in a particular case?

There are several elements to this key question:

What are the benefits and costs of installing seismic isolation in this case? (This will

depend on the geographical location of the site, the nature of the site, the probability of

an earthquake occurring and the likely magnitude and type of the earthquake).

How is the structure likely to perform in the event of an earthquake? (And how would it

compare to the likely performance of an unisolated structure).

At what stage in the design proc ess should the feasibility study be undertaken? (This

should be done as early as possible in the design process, bearing in mind that the

installation of seismic isolation can radically affect all aspects of the construction

proc ess.).

This chapter aims to provide some answers to these questions. It draws on our lifetime

experience as active practitioners in the field of seismic isolation design, assessment and

installation and indicates some of the considerations that must be taken into account in

assessing whether seismic isolation is appropriate for a given construction projec t.

The stakes (loss of human life, property damage) are so high that processes must be in place to

manage and reduce the risk that the assessment, design, installation or components are not fit

for purpose in the event of an earthquake.



338

The elements of these processes are feasibility assessment, evaluation, and response to the

results of the evaluation process by planning improvements in the system.

This chapter presents

an example of a feasibility assessment (that used prior to the installation of seismic

isolation in Te Papa Tongarewa in Wellington); a record of the known performance of seismically isolated structures in real earthquakes

to date;

a report on two new devices designed to provide large design displacements as

required in near-fault situations.

This chapter concludes with a cautionary note; decisions on seismic isolation should not be

made in isolation by an engineer or a designer, but require input from a team of interdisciplinary

experts.

10.1.2 Seismic Isolation Decisions in the Wellington Area

This chapter uses some of the seismic isolation construction projec ts that have been undertaken

in Wellington, New Zealand, to illustrate some of the issues and decisions that must be made

regarding the design, assessment and installation of seismic isolation. Some of these projects in

Wellington are included in Chapter 8 and we detail below some more work that has been done

since Chapter 8 was written. We a lso give some detail about one of the major construction

projects (completed in 1998), namely the Museum of New Zealand, Te Papa Tongarewa.

Wellington is sited in an area that is geologically active, with the fault line running along the

harbour. There is clear evidence of previous movement along the fault since this provided a

convenient site on which to build the north-south motorway into Wellington. There are also

plaques on the pavements in the city to mark the water-line before the 1840 earthquake); the

streets along the earlier waterfront are called ‘quays’; and the old cricket ground on one of the

hills is called the Basin Reserve as it was intended for ships.

Wellington residents and visitors may not be generally aware of the seismic isolation that has

been provided to bridges and buildings in the region, many of which are described in Chapter 8

and several more in the next sec tion. However, there are two seismically isolated fac ilities at

which the Lead Rubber Bearings are on display, one of these being the retrofitted Parliamentary

Buildings and the other Te Papa, the Museum of New Zealand on the waterfront, which was built

on Lead Rubber Bearings.

Te Papa is such an important icon in New Zealand that we reproduce on page 341, the

feasibility study that was carried out before the decision was made to include seismic isolation.



339

10.2 CONSTRUCTION PROJECTS IN NEW ZEALAND AND INDIA1992 TO 2005

10.2.1 Introduction

Some of the buildings and bridges built in New Zealand are detailed in Chapter 8. New Zealandcontinues to build seismically isolated structures and some of these are detailed here.

It is interesting to note that a study has been carried out (Carden, Davidson & Buckle, 2001) to

consider whether to redesign the isolation system, and if necessary to retrofit additional seismic

features on the William Clayton Building (see Chapter 8), which was completed in 1981 as the

first building to be seismically isolated on Lead Rubber Bearings. This proposal was made as a

result of two factors. First, new information is now to hand about the displacements that can

occur near an earthquake fault; in this case it might be necessary to design for two or three

times the original 300 mm displacement and seismic gap. Secondly the technology of seismic

isolation has matured over the intervening twenty years so that techniques are available for fine-

tuning the original system to provide more protection.

10.2.2 Retrofits

Since 1992 seismic isolation has been retrofitted in four historic buildings in Wellington. Two of

these were seismically vulnerable masonry buildings of historic interest, namely the adjacent

landmarks, the old Parliament Building and the Assembly Library. Seismic isolation of these

buildings was completed in 1996; using 514 individually tested Lead Rubber Bearings. The retrofit

involved re-piling the building with LRBs and rubber bearings in the supports as well as cutting a

seismic gap in the 500 mm thick concrete walls. During an earthquake the building will be able

to move in any direction on a horizontal plane up to distances of 300 mm.

Seismic isolation has also been retrofitted in the Maritime Museum, the former Head Office of the

Wellington Harbour Board, and the former BNZ building, built in 1885 and one of Wellington’soldest masonry buildings. The building has a classical Victorian style and façade and is richly

decorated with fine plasterwork. It now has been retrofitted with a Lead Rubber Bearing seismic

isolation system.

10.2.3 Te Papa Tongarewa

The Museum of New Zealand, Te Papa Tongarewa, situated on the Wellington waterfront, is a

New Zealand icon in many ways. It is a repository of New Zealand national treasures (taonga)

and a conference, exhibition, research and learning centre that attracts huge numbers of

national and international visitors every year. It is also seismically isolated.



340

Figure 10.1: Te Papa Tongarewa, Museum of NZ under Construction

Figure 10.2: Installation of Lead Rubber Bearing – Te Papa, Museum of NZ

The public is obviously interested to learn that the Museum is seismically isolated and to visit the

technical display that is on view down a set of stairs that provide access to two of the 152 Lead

Rubber Bearings on which the building is mounted. The display includes an audiovisual

presentation and other information about the Museum’s ‘base isolation’.

The display makes it clear that the seismic isolation system is there to improve safety, much in the

same way as the compaction of the ground beneath the building was carried out to reduce therisk of fluidisation of the ground beneath. None of the measures to improve safety are

guarantees of perfect safety, and this cannot be promised in any natural hazard situation (as

has been shown so recently by the tsunami and Hurricane Katrina).

We present in the next section some of the considerations and analyses that underpinned the

decision to provide seismic isolation for Te Papa.



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10.2.4 Other Seismically Isolated Buildings

Four important structures are being, or have recently been, seismically isolated in New Zealand.

These are:

a new Accident & Emergency Wing of the Wellington Hospital, the C hristchurch Women’s Hospital;

the Victoria University Rankine Brown Library Building (retrofit), and

the new Wellington Central Hospital.

These were all isolated by combinations of LRBs and sliding bearings. Both of the Wellington

buildings are close to the Wellington fault and need to be able to reduce the forces expected

from ‘near fault fling’ effects resulting in maximum displacements of the isolators of up to

600mm.

The retrofitted nine-floor Rankine Brown Library Building is of particular interest in that the library

continued to operate while the 12 columns were cut one by one, the redundant concrete piece

removed and the Lead Rubber Bearings inserted and bolted in place. This process required the

three floors above the bearings to be carefully jacked thereby redistributing the vertical loads

through the building. The customer was extremely pleased with the retrofit construction and the

lack of interference to the normal working of the library. The savings in insurance premiums were

more than enough to make this retrofit financially worthwhile.

The new Wellington Central Hospital, the main hospital for the Wellington region, is mounted on

135 lead rubber bearings and 135 sliding bearings.

The new Christchurch Women’s Hospital is mounted on a combination of 4 sliding bearings and

43 lead rubber bearings. The new patients moved in on 1 April 2005 with the first baby being

born almost immediately.

10.2.5 Bhuj Hospital

A recently completed example of seismic isolation is the 300-bed hospital at Bhuj, in the state of

Gujarat, India. The original hospital was completely destroyed in the magnitude 7.6 Bhuj

earthquake on 26 January 2001 that destroyed most of the town of Bhuj. When the hospital was

rebuilt in J anuary 2004, it was provided with seismic isolation to protec t it from earthquakes in the

future.

Immediately after the Bhuj earthquake the Prime Minister of India decided that a new hospital

should be built and that it should have the latest international earthquake-protection building

technology. The New Zealand Government was asked to respond to a request for information

on the design of the hospital. This entailed bringing two key Indian designers – an engineer and

an architect – to New Zealand for training in the practical aspects of seismic isolation. The two

designers spent several weeks visiting New Zealand engineering companies, architectural and

engineering c onsultanc ies, and building sites that used New Zealand’s seismic isolation

technologies. It was decided to use Lead Rubber Bearings plus slider bearings for the new Bhuj

Hospital.



342

The illustrations show installation of the Lead Rubber Bearings during construction of the new Bhuj

hospital, and the completed hospital in J anuary 2004. The bearings were placed on the top of

columns so that the entire building was supported by the bearings together with a number of

slider bearings. The seismically-isolated structure is designed to provide protection from damage

to the contents or structure in a 1 in 2000 year earthquake.

Figure 10.3: The completed Bhuj Hospital mounted on Lead Rubber Bearingsfor seismic isolation, J anuary 2004

Figure 10.4: Bhuj Hospital during construction.

The circles on the photograph show where the Lead Rubber Bearingsare mounted on top of the foundation columns



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10.3 A FEASIBILITY STUDY FOR SEISMIC ISOLATION

10.3.1 Te Papa Tongarewa, the Museum of New Zealand

We present here some of the considerations and analyses that underpinned the decision to

provide seismic isolation for Te Papa Tongarewa, The Museum of New Zealand. This section isbased, without modernisation, on the paper presented by Kelly & Boardman in 1993. This paper

summarises the design of the structure and the isolation system and the three-dimensional

nonlinear analyses performed to evaluate the building performance.

10.3.2 Description

The building design is monumental in nature with a total floor area of 35,000 square metres

distributed over five floor levels. The design team headed by J asmax Architects was selected in

1990 after an international competition. Seismic isolation was considered at the stage where

design development had been completed and final design and production of working

drawings was in progress.

The new building approximates a triangle in plan with maximum dimensions of 120m x 190m and

a height of 23m. Figure 1 shows the layout of the building at the isolation level. Total building

cost was estimated to be $NZ130 million.

Figure 10.5: Floor plan of Te Papa from Boardman and Kelly paper



344

A number of preliminary value engineering studies by the entire design team investigated

alternatives of reinforced concrete and structural steel and also a number of floor span

configurations. The optimum system selected was a reinforced c onc rete structure based on a

rec tangular grid of 17.4m x 8.7m with precast floor units. Ductile frames were selected in the

direc tion of the 8.7m grids and shear walls in five locations in the 17.4m span direction. The

frames are formed of pairs of columns/girders spaced 2.1m apart. The double frame system hasthe effect of reducing the span of the floor units from 17.4m to 15.3m and also providing a

system of "tunnels" for the building services.

The building site on the Wellington waterfront is on rec laimed land which has been in filled over

the last 40 years using high quality fill material which is uncompacted. Approximately 12m of this

fill material overlays up to 100m of dense sand and gravel. A number of alternate deep and

shallow foundation schemes were investigated of which the most cost effective was found to be

dynamic consolidation of the site and the use of pad footings without piles. A pilot study using

dynamic consolidation (dropping a weight of 25 tonnes a height of 25m in a fine grid pattern)

was performed over a portion of the site and demonstrated its effectiveness to a depth of 12m.

The level of the site reduces approximately a metre as a result of the consolidation.

10.3.3 Seismic Design Criteria

The site is in the most seismically active region of New Zealand and specific earthquake

performance requirements were set as part of the design brief, in particular:

1. Probability of significant damage less than 50% in 150 years, which corresponds to a 250-

year return period.

2. Probability of collapse less than 7% in 150 years, corresponding to a 2000-year return

period.

For the reinforced concrete structural system the onset of "significant damage" was defined as

(1) displacement duc tility less than 2 and (2) concrete strains less than 0.004, which correspondto plastic rotations of approximately 0.007 radians. The limit beyond which collapse could occur

was set at a strain of 0.010, a plastic rotation of 0.020 radians. The analysis procedures were

required to be such that these values could be quantified.

Site specific earthquake acceleration time histories and response spectra were generated for

each of the return periods using the SHAKE computer program to obtain surface records.

Source time histories were based on 1.8 x El Centro 1940, 0.7 x Tabas 1978 and 1.3 x Llolleo 1986.

An additional record was generated by frequency scaling the El Centro 1940 record to be

compatible with the smoothed surfac e spectrum. The 250-year and 2000-year return period

spectra were obtained by a linear scaling of the 500 year spectrum by factors of 0.8 and 1.3

respec tively.

The 250-year spec trum is about 50% higher than would be required by the loadings code for the

Wellington region. In addition, the damage criteria restrict the duc tility fac tor to 2 rather than

the 6 permitted by the code for duc tile conc rete frames. The net result of this is that elastic

design forces for the building are 4.5 times higher than would be required for a building

designed to the code.



345

This level of design load and the desire to restrict contents damage formed the basis for the

decision to investigate a base-isolated structure for the museum.

10.3.4 Feasibility Study

Seismic isolation was included in the initial concept development of the building but, as part of

the value engineering requirements of the project, its cost effectiveness was to be justified ateach stage of design. A two stage feasibility study was performed, the first investigating global

response parameters (base shear and floor accelerations) and the second evaluating and

costing various frame and shear wall designs (drifts and duc tilities).

The method used for the initial evaluation was based on a procedure developed by Ferrito

(1984) where the cost of damage to the structure and contents is estimated as a fraction of the

initial cost. Design base shear levels of 0.2g and 0.5g were assumed for both a fixed and

isolated building configuration. Maximum drifts and floor ac celerations were estimated for eac h

level of design and the cost of structural damage and damage to components assessed for

each option using Ferrito's tables. Bar charts were produced based on an assumed total

building cost of $50 m and contents value of $200 m. The procedure was approximate but did

enable some conc lusions to be drawn:

1. Total damage costs are 3 to 8 times higher for a fixed base building than for an isolated

building, the actual factor depending on the design base shear level and magnitude of

earthquake.

2. For the fixed based building damage costs actually increase if the design base shear

level is increased even though costs of structural damage are reduced. This is because

of the high value of the contents which are damaged by floor accelerations.

Accelerations increase with increasing design level.

3. Even for an isolated building significant contents damage could occur at the 250 year

earthquake level assuming a threshold of damage of 0.08g (as in the Ferrito study).

Measures must be taken in the design and operation of the structure to raise thethreshold for acceleration-related contents damage, for example by restraining exhibits.

In the second phase of the feasibility study representative frames and shear walls were designed

for base shear levels corresponding to varying levels of duc tility at the 250-year level, from fully

elastic to fully ductile. A time history analysis using the DRAIN-2D2 program was then used to

compute the response at the 250-year and 2000-year return period earthquakes for each

design. Eac h design was evaluated for acceptability in terms of the c riteria limits on damage

and for each design the quantity surveyors for the project estimated the structural construction

cost.

From a structural performance perspective both the fixed base and isolated schemes were able

to be designed to achieve the criteria objectives limiting damage at the 250-year level and

avoiding collapse for the 2000-year earthquake. This required that the frames be designed for a

minimum of 50% of the 250 year elastic forces and the walls and coupling beams for 100% of the

250 year elastic forces. The fixed base configuration required 8 shear walls versus 5 shear walls

for the isolated design and also required larger column and girder sections.



346

The effect of these increases in the structural system sizes was to counterac t the cost of the

isolation system so that the two configurations produced similar structural costs, $14.5 million for

the fixed base building and $15.1 million for the isolated building. Extra costs to accommodate

the larger drifts in the fixed base building were not quantified.

The design options had demonstrated approximately equal costs for the two systems but of

more importance for a building of this function is the cost of non-structural damage (related todrift and floor accelerations) and especially contents damage (a function of floor

accelerations). As Table 10.1 shows, the fixed base options produced drifts and accelerations

several times as high as the isolated alternative. These results led to a dec ision to proc eed with

the isolation system design.

10.3.5 Isolation System Design

As part of the feasibility studies varying isolation system parameters were studied but specific

hardware was not designed. It was assumed that the system would contain the two essential

elements of a practical isolation system in a high seismic zone, flexibility and added damping.

Both hysteretic and viscous forms of damping were evaluated. It was decided that devices to

provide hysteretic damping were more readily available than viscous dampers and so the

design was based on hysteretic damping. After evaluating a number of systems, elastomeric

bearings with lead cores to provide hysteretic damping were chosen. These bearings were not

suitable for the wall locations where high compression and tension forces occurred. At these

locations PTFE (Teflon) sliding bearings were used, the bearings uplifting when earthquake-

induced axial loads exceeded the gravity load.

Architec tural and services restrictions limited the maximum seismic gap around the building to

500 mm and so the isolation system design was required to produce displacements less than 500

mm at the 2000-year earthquake. This formed an upper bound on the flexibility of the isolation

system.

The design of the lead rubber bearings was based on procedures developed by Dynamic

Isolation Systems, Inc. (1990). Different isolator loc ation configurations were investigated and itwas found that a single, large isolator at each column location was more economical than

multiple smaller isolators because of the large displacements. The isolators as designed have a

maximum size of 950 mm diameter x 300 mm height.

10.3.6 Evaluation of Structural Performance

The final configuration of the structure and isolation system produced a very complex lateral

load resisting system. To evaluate the performance a three-dimensional model of the structure

and isolation system was developed using the ANSR-II computer program (Mondkar & Powell,

1979).

The computer model of the building was developed in successively more complex stages with

each step forming a check on the overall response produced by the succeeding step. Initial

studies on a single degree-of-freedom model were extended to planar models of the frames

and walls and then to a three-dimensional model with an elastic superstructure. The final model

was a fully yielding model which reflected all the elements of the building:



347

1. Flexural bi-linear yielding elements to model the frame girders and columns and the

shear walls and coupling beams.

2. Special purpose gap-friction elements to model the Teflon bearings. The friction force for

these elements was a function of the vertical pressure and velocity at each location at

each time step of the analysis.

3. Lead rubber bearings modelled as two components, a linear elastic element

representing the elastomer and an elastic perfectly plastic element to represent the lead

core.

4. Horizontal movement buffers at the isolation level which engaged when displacements

exceeded 500 mm.

5. A rigid diaphragm at the North and South portions of the main building linked by truss

elements to model the connection stiffness at the movement joints.

6. A West Wing "stick" model mounted on the same isolation diaphragm as the Ma in

Building but separated from it at upper levels.

As the ANSR-II model was developed, a concurrent equivalent elastic model using ETABS

(Habibullah, 1986) was used to correlate the overall performance as much as possible. This

model was used to check such effects as the distribution of shear forces between walls,

structural deformations etc.

The Teflon elements used for the program were based on a formulation of coefficient of friction

developed at NCEER, New York (Mokha, Constantinou & Reinhorn, 1988). Further static and

dynamic testing of a New Zealand produced PTFE material led to an upward adjustment of the

coefficient of friction by 25% with a maximum coefficient of friction (at high velocities) of 0.12 at

15MPa decreasing to 0.09 at 30 MPa (Davidson & Smith, 1992).

The geometry of the building is such that some frames and walls are based on a grid system

rotated approximately 30 degrees from that of the remaining elements. The large difference in

stiffness between the frames and walls coupled with this angular offset produced large opposing

walls forces when deformations were in the frame direc tion. To reduce these secondary forces

movement joints were introduced across the building between the two grid orientations. To

reflect this, the ANSR-II model used two rigid diaphragms at each floor level with the two portions

connected by truss elements with properties representing the reinforcing bars across the

movement joint.

Movement stops at the base had zero stiffness until translation exceeded 500 mm. At this point

the gap elements engaged with a large stiffness, representing impact with the surrounding

retaining wall. These elements were used to investigate the effects of designing a flexible

isolation system to reduce earthquake response of the structure for smaller earthquakes and

restrict maximum displacements by permitting impact to occur at higher earthquakes. When

this occurred it was found that the impact transmitted very large accelerations into the

diaphragm (in excess of 2g) and so the isolation system was stiffened so impact would not

occur.



348

The configuration of the building with a relatively small number of floors, a large number of

column lines and interconnected diaphragms resulted in a large model for nonlinear analysis

with a total of 2250 degrees of freedom, a maximum bandwidth of 1000 and approximately

1500 yielding elements.

10.3.7 Results of ANSR-II Analysis

The ANSR-II model was used for a basic set of 16 analyses - 4 pairs of earthquake records, 2

orientations per record and 2 return periods for each orientation. For each analysis the two

horizontal components of motions were applied simultaneously. The global results from these

analyses are summarized in Table 10.2 which lists the maximum values from the two orientations.

Maximum vec tor isolator displacements were 258 mm for the 250 year return period and 516 mm

for the 2000 year earthquake. The overall structural deformations above the isolation system

were 126 mm and 270 mm in the frame direction for the two return periods and 51 mm and 118

mm in the direc tion of the shear walls. The Teflon pads uplifted a maximum of 25 mm at the 250

year earthquake and 79 mm for the 2000 year earthquake. These uplift values were the

maximum at any of the 36 Teflon pad locations. The larger uplift values tended to oc cur at 3 or

4 locations where the end of the wall did not connect to the framing girders and so supported

very little gravity load. At other locations the uplift was much less.

The results from the 16 analyses were used to evaluate the design of the structural elements and

also to determine the most critical earthquake record and orientation for subsequent analyses.

The reinforcing was refined based on the maximum plastic rotations from the analyses. The

frequency-scaled El Centro record was used to evaluate the building with this refined strength

and also to perform further analyses to evaluate P-delta effects (less than 5%), to obtain sets of

vertical loads for foundation design and to obtain maximum inertia loads on the West Wing.

10.3.8 Conclusions

A series of feasibility and design studies performed for the Museum of New Zealand, Te Papa

Tongarewa, have demonstrated that a seismic isolation system can be installed for almost thesame first cost as a conventional, fixed base structural system. To obtain approximately similar

levels of structural damage the conventional structure requires larger columns and beams and

also a larger number of shear walls compared to the isolated structure.

The consequences of designing a fixed base structure for very high levels of earthquake load

are to increase the floor accelerations far above those of the seismically isolated scheme and so

increase the potential for damage to non-structural components and contents. For a building

such as a museum the values of the contents may be many times the value of the structure.

When this is taken into account the total damage costs in a major earthquake in a fixed base

building can be from 3 to 8 times those of an isolated building. This was the deciding factor in

the selection of an isolated configuration for the building.

The isolation system selected was a combination of elastomeric bearings with lead cores and

PTFE (Teflon) sliding bearings. The elastomeric bearings are used at column locations and the

Teflon bearings at shear walls where high overturning forces occur. A nonlinear analysis model

was used to quantify the isolator forces and displacements and the ductility demands in the

conc rete superstructure. Some adjustments to the column reinforcing were made as a result of

these analyses.



349

The design and evaluation of earthquake response has demonstrated that, even with seismic

isolation, the maximum earthquake motions to be expected in the high seismic Wellington

region will cause relatively high in-structure accelerations. These will be of a level which could

cause damage to contents and services unless mitigation measures are taken.

Consideration of earthquake effects will need to be included in the initial design of all aspects ofthe building and also of the placement and fixing of contents during the operation of the

building.

Maximum FloorAcceleration

Maximum StoreyDrift

Fixed Isolated Fixed Isolated

FRAMES250 Year

2000 Year

0.81

1.14

0.33

0.48

0.6%

1.8%

0.2%

0.7%

WALLS250 Year

2000 Year

1.02

1.69

0.27

0.38

0.5%

0.8%

0.1%

0.6%

Table 10.1: Structural Drifts and Accelerations

Figure 10.5 Museum of New Zealand, Te Papa Tongarewa



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El Centro

FrequencyScaled

El Centro

SHAKEOutput

Tabas

SHAKE Output

Llolleo

SHAKEOutput

250 - YEAR Displacements (mm)

FrameWallIsolator (Vector)

Teflon PadUplift (mm)Compression (kN)

12251247

20

34,400

8340

209

17

33,300

9347

258

21

36,400

12648

241

2535,900

2000 - YEAR Displacements (mm)

FrameWall

Isolator (Vector)

Teflon PadUplift (mm)

Compression (kN)

270118

484

79

44,800

19284

452

5544,600

199

96516

4142,000

177

84421

5641,200

Table 10.2: Results of Nonlinear Analyses

10.4 PERFORMANCE IN REAL EARTHQUAKES

Examination of the actual performanc e of isolation systems in real earthquakes should ensure

that we learn from these experiences.

One of the most frequent questions asked by potential users of isolation systems is, Has it b ee n

p roved to w ork in a c tua l ea rthquakes ? The short answer is a qualified no; no isolated building

has yet been through “The Big One” and so the concept has not been tested to the limit but

some have been subjected to earthquakes large enough to activate the system.

Our buildings in New Zealand have not been subjected to any earthquakes yet, although four

are located in Wellington so it is only a matter of time until this happens according to most

seismologists. Two bridges on lead rubber isolation systems were subjected to strong motions

during the 1987 Edgecumbe earthquake. One, Te Teko Bridge, had an abutment bearing roll

out bec ause the keeper plates were misplaced. This caused minor damage. This type of

connec tion is no longer used. The other bridge was on a privately owned forestry road and,

other than a report that there was no damage; there is no information on this.

Table 10.3 summarizes the reported performance of structures world-wide during earthquakes.

Many of the structures are not instrumented and so much evidence of performance is either

indirect or anecdotal.



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There are features of observed response that can teach us lessons as we implement base

isolation:

Some structures performed well and demonstrated the reductions in response that base

isolation is intended to achieve. The most successful is probably the USC Hospital in Los

Angeles (see C hapter 8). Occupants reported gentle shaking during the main shock and

after-shocks of the 1994 Northridge earthquake. The pharmacist reported minimal to nodamage to contents of shelves and cabinets. Other successful installations were the Tohuku

Elec tric Power building in J apan, the Stanford Linear Ac celerator and Eel River Bridge in

California and several bridges in Iceland.

At the LA C ounty Fire C ommand Centre, the contractor had poured a reinforced concrete

slab under the floor tiles at the main entrance to the buildings, preventing free movement in

the E-W direc tion. Apparently the reinforcing was added after the contrac tor had replaced

the tiles several times after minor earthquakes and did not realize that this separation was

designed to occur. This emphasizes the importance of ensuring that building operational

procedures are in place for isolated buildings.

The Seal Beach and Foothills (see Chapter 8) buildings demonstrate that accelerations will

be amplified as for a fixed-base building for accelerations which do not reach the trigger

point for the system.

The West Los Angeles residence used an owner-installed system of steel coil springs and

dashpots without a complete and adequate plane of isolation. The springs allowed vertical

movement and the building apparently responded in a pitching mode. The owner was

satisfied with the performance.

The Matsumura Gumi Laboratory building in J apan did not amplify accelerations as for a

fixed base building but also did not attenuate the motions as expected. The period of

response was shorter than expected and a possible reason for this was the temperature of

the isolators, estimated at 0C in the unheated crawl space. Potential stiffening of rubber as

temperatures are reduced needs to be accounted for in design if isolators are in locationswhere low temperatures may occur.

Bridges in Taiwan and Kobe were partially isolated, a design strategy often used for bridges

where the system provides energy dissipation but not significant period shift. The response of

these bridges shows benefits in the isolated direction compared to the non-isolated direction

but the reductions are not as great as for fully isolated structures.

The dissipators at the Bolu Viaduct in Turkey were severely damaged due to near-fault

effects when the displacement caused impact at the perimeter of the dissipator. This

appeared to be mainly due to large displacement pulses near the fault but may have been

accentuated by use of an elastic-perfectly plastic system rather than the more common

strain hardening system.

In all structural engineering, we need to learn from the lessons which earthquakes teach us.

There is discussion throughout this book on aspec ts of isolation that can degrade performance if

not properly accounted for. These earthquakes have shown the importance of attending to all

these details.



352

ACCELERATION

STRUCTURE SYSTEMTYPE

EQ FREE

FIELD(G)

STRUCTUR

E(G)

COMMENTS

USC HospitalLRB

1994

Northridge0.49 0.21

Movement estimated at up to45 mm.No damage

Continued operation

LA County FireCommand Center

HDR1994

Northridge0.22 E-W0.18 N-S

0.35 E-W0.09 N-S

Minor ceiling damage.Continued operation

Seal Beach Office LRB1994

Northridge0.08 0.15

No damage.System not activated.

Foothills Law & J ustice

CentreHDR

1994

Northridge0.05 0.10

No damage.

System not activated.

West Los AngelesResidence

Springs1994

Northridge0.44 0.63

No structural damage.

Some damage at movement joint.

Unusual isolation system.

Tohuku Electric PowerLRB

Steel

Dampers

1995Kobe

0.31 0.11No damage.Movement estimated at

120mm.

Matsumura Gumi

LaboratoryHDR

1995

Kobe0.28 0.27

Isolators at 0C, may have

stiffened.

Stanford LinearAccelerator

LRB

1989

LomaPrieta

0.29 0.14

Not instrumented, estimated

response.Movement estimated at100mm

Bai-Ho BridgeLRB

PTFE

1999

Taiwan

0.17 L

0.18 T

0.18 L

0.26 TLongitudinal isolation only.

Matsunohama Bridge LRB

1995

Kobe

0.15 L

0.14 T

0.20 L

0.36 T Longitudinal isolation only.

Bolu Viaduct

PTFECrescent

MoonEnergy

Dissipator

1999 Turkey

1.0 +Displacements exceededdevice limit of 500 mm, causing

damage

Eel River Bridge LRB

1992

CapeMendocino

0.55 L0.39 T

Not

measured

Estimated ac celeration.

Movement estimated at 200mm L and 100 mm T.Minor joint spalling.

Four bridges inIceland

LRBM6.6 and

M6.5 in June

2000.

0.84Not

measuredNo damage.

Te Teko Bridge (NZ) LRB1987

Edgecumbe0.33

Estimated ac celeration.Estimated displacement100mm.Abutment bearing dislodged

caused minor damage.

Table 10.3: Earthquake Performance of Isolated Buildings



353

10.5 NEW APPROACHES TO SEISMIC ISOLATION

10.5.1 Introduction

In the last 10 years or so, many near source records have been obtained from large

earthquakes, for example, the Lucene and J oshua Tree records from the 1992 Landers

earthquake (Mw=7.2) and the Sylmar record from the 1994 Northridge earthquake (Mw=6.7). Acommon feature of several of these records is a long period velocity pulse of very large

amplitude. Such a pulse can impose very large displacement demands on intermediate and

long period structures, including base isolated buildings (Hall et al.1995). These results have

encouraged design engineers to increase seismic gaps to 300 to 500mm. This increase in

displacement is illustrated by the example of three seismic isolation projects completed in New

Zealand during the 1990’s, viz: the new Wellington C entral Police Station with a gap of 400mm

(Charleson, et al 1987), the old NZ Parliament Buildings retrofit with a seismic gap of 300mm

(Poole & Clendon, 1991) and the new Museum of NZ (Te Papa) with a seismic gap of 450mm

(Kelly & Boardman, 1993).

The lead rubber bearing has been a very useful isolator but like all rubber bearings it is limited by

the behaviour of rubber at high strains. To satisfy the requirements of customers, isolationdesigners are now requiring strains in the rubber as high as 300 to 400%. In addition designers are

asking for non-linear restoring forces together with very large displacements (~ 1 metre).

Research and development into new approaches to seismic isolation continues with the

manufacture of prototype ‘RoBall and RoGlider. The RoBall is a device suitable for use as a

seismic isolator and the RoGlider is a sliding bearing which includes an elastic restoring force.

The two devices promise to be economic alternatives to existing seismic isolation devices.

Plans are now underway for the design and construction of a demonstration building seismically

isolated by a system based on the RoGlider approach.

10.5.2 The RoBall

A method of satisfying the demanding requirements of a very large displacement is to use a

‘friction device’ operating within an ‘inverted pendulum’ (Zayas, 1995). We have followed this

approach with the invention and development of ‘friction balls’ or ‘RoBall’ moving between

upper and lower spheroidal cavities or flat plates. The RoBall is filled with a material which is able

to provide the friction forces required to absorb the energy from numerous earthquakes while

supporting the structure.

The RoBall promises to be an ec onomical alternative to existing seismic isolation devices. It has

no inherent displacement limit, provides a constant coefficient of friction, allows greater

freedom in the choice of the restoring force and may also be used as a buffer. As a buffer the

RoBall has two very desirable characteristics: it absorbs energy, and has gently increasingstiffness at large displacement amplitudes. The buffer action may also be useful for reducing the

transmission of vertical earthquakes forces to the isolated structure. The RoBall technique is

expected to enable light and in the future possibly heavy structures to be more economically

seismically isolated.



354

The latest version of the RoBall TM includes a restoring force. The top and bottom surfaces are flat

and the sides are curved as shown in Figs. 10.5 and 10.6. Inside this version of the RoBall are

seven solid ba lls (Robinson & Gannon, 2006).

Other designs of the RoBall suitable for larger displacements could include 13, 19, 25 solid balls in

a close packed array. The sides of the RoBall may be thicker than the top and bottom surfaces

thereby contributing to a restoring force for small displacements (Figure 10.8) while for largedisplacements there is cyclic restoring with a wavelength approximately twice the diameter of

the RoBall (Figure 10.9).

The rolling action of the RoBall means that the device itself has no design displacement limit and

so the maximum displacement is limited only by installation requirements. The dynamic

behaviour of the device is independent of both frequency and ambient temperature within

ranges that are applicable to most prac tical installations. The effec tive friction coefficient, i.e.,

the ratio of the nominal yield shear force to the compression force, of the prototypes, is ~0.1.

The applications for the model of the RoBall containing solid spheres are expec ted to be for

protecting light equipment and light structures from mechanically generated or earthquake

induced vibrations.

Figure 10.6: RoBall under Vertical Load

Figure 10.7: RoBall with 7 Internal Balls being tested on C onc rete Floor in RSL Laboratory



355

-4

-3

-2

-1

0

1

2

3

4

-100 -80 -60 -40 -20 0 20 40 60 80 100

mm

k N

Figure 10.8: RoBall - Small Displacement Showing the Restoring Force Characteristic

Figure 10.9: RoBall – Large Displacement with Cyclic Shear Forces

Research and development into new approaches to seismic isolation continues with the

manufacture of prototype ‘RoBall and RoGlider. The RoBall is a device suitable for use as a

seismic isolator and the RoGlider is a sliding bearing which includes an elastic restoring force.

The two devices promise to be economic alternatives to existing seismic isolation devices.

Plans are now underway for the design and construction of a demonstration building seismically

isolated by a system based on the RoGlider approach.

-400 -300 -200 -100

0 100 200 300 400

0 50 100 150 200 250 300 350 400 450 500 550 600 mm

kg



356

10.5.3 The RoGlider

The RoGlider is a sliding bearing which includes an elastic restoring force. The RoGlider is

applicable for the seismic isolation of both light and heavy vertical loads and can be readily

designed to accommodate extreme displac ements. It is expected to perform significantly

better than rubber bearings or lead rubber bearings in providing seismic isolation at largedisplacements (Robinson et a l, 2006).

The ac tual configuration is dependent on the details of the structure being isolated and the

expected earthquake. The RoGlider presented here is a double acting unit with the restoring

force provided by two rubber membranes (Figure 10.10).

This double ac ting RoGlider consists of two stainless steel plates with a PTFE ended puck

between the plates. Two rubber membranes are attached to the puck with each being joined

to the top or bottom plates. When the top and bottom plates slide sideways with respect to

each other diagonally opposite parts of the membrane undergo tension or compression. The

tension components provide the restoring force between the plates while the compression parts

buc kle (Figures 10.10 and 10.11) and provide little or no restoring force.

The particular double ac ting RoGlider described here has a maximum displacement of +/-

600mm, maximum vertical load of 1MN, with an outside diameter of ~900mm and a coefficient

of friction of ~11%. Following this membrane approach it is expected that the elastic stiffness

can be increased by a factor of four or more using our latest designs.

The RoGlider has been chosen as the seismic isolation system for the two storey, three building

Wanganui Hospital redevelopment in Wanganui, New Zealand. Each of these light buildings will

have 30 RoG liders with eac h RoG lider able to support loads of 250 to 550kNs with a co-efficient

of friction of approximately 10% and a maximum displacement of 450mm.

Figure 10.10: RoGlider ready for Testing Figure 10.11: RoGlider during Test Displacement

Displacement 0mm – Load 850kN ±150mm – Load 850kN



357

Figure 10.12: RoGlider during Test Displacement ±575mm – Load 110kN

RoGlider

-60

-40

-20

0

20

40

60

-240 -200 -160 -120 -80 -40 0 40 80 120 160 200 240

mm

k N

μ = 0.047

Figure 10.13: RoGlider Force Displacement Curve – Vertical Load 850kN

RoGlider

-80

-60

-40

-20

0

20

40

60

80

-250 -200 -150 -100 -50 0 50 100 150 200 250

mm

k N

μ = 0.045

Figure 10.14: RoGlider Force Displacement Curve – Vertica l Load 120kN



358

10.6 PROJECT MANAGEMENT APPROACH

The importance of having a broad range of expertise in planning any seismic isolation project

cannot be overemphasized. Again it is useful to use the Te Papa example as a model of good

practice:

This is a quote from the Feasibility study presented in 10.2 above, based on the paper by Kelly &Boardman (1993):

“The adoption of a seismic isolation scheme requires the cooperation of all members of the

design team to ensure an efficient and economic solution. The architects are required to detail

for the 500 mm gap around the building and the building services engineers must ensure that all

services crossing the isolation plane have sufficient flexibility to accommodate the movement.”

The project members for this project were:

Client:

Project Manager:

Architect: Structural Engineer:

Mechanical Engineer:

Electrica l Engineer:

Geomechanical Engineer:

Peer Review.

The concept of requiring a wide range of inputs into the project at an early stage and if

necessary during its implementation is also exemplified by a New Zealand business initiative that

has been developed to provide earthquake engineering expertise to Oceania and to a number

of c ountries including India, Nepal, Taiwan, South Korea and Turkey. This is called the New

Zea land Earthquake Engineering Technology Business Cluster.

The Cluster member companies have a combined resource of some 5,000 professional and

technical personnel. All are independent consultants and have no ties to contrac tors.

Although the focus of members of this Cluster is earthquake engineering, many of the members

have a wide range of experience which allows them not only to deal with the detailed

technical issues, but to set them in context of the whole building project. Members have a wide

range of consultancy skills and experience including:

Project appraisal, including earthquake hazards

Design, including co-ordination of all disciplines

Contract administration

Construction monitoring

Manufacture, including seismic isolation devices

In particular, the engineers have relevant and ongoing experience in retrofitting seismic isolation

devices in heritage buildings.



359

By working together, the Cluster is able to provide a totally integrated service taking care of all

aspects required to identify the most appropriate structural and seismic solutions. The C luster

members are able to design the most economical and unobtrusive structural and overall

solutions, prepare contract documentation suitable for tendering (or other project delivery

methods such as design-build), and administer construction contracts.

New Zealand is fortunate to have high standards of design and construction, where fullcompliance with codes is expected by the community and delivered by the professions.

Standards are comparable to those in California and are among the best in the world.

A number of our members in the Earthquake Engineering C luster together with our colleagues in

the Natural Hazards Cluster are overseas helping in the countries devastated by the 26

December 2004 Tsunami and the more recent Indonesian earthquake.

The Earthquake Engineering and Natural Hazards Business Clusters are enabling the application

of many of the results of our engineering experience and our research and developments to real

structures in a number of countries.

10.7 FUTURE

Seismic isolation has now reached the stage where there is a range of devices suitable for

providing adequate protection for most low-to-medium height buildings in earthquake zones.

These same devices can be used to provide increased protection for bridges. The challenge

now is to design and build structures which enable the attributes of the various seismic isolation

devices to be used economically.



361

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