Evaluation of SEAOC Design Requirements for Sliding ...

'I IIIIIENGINEERING RESEARCH

State University of New York at Buffalo

June 10, 1991

Evaluation of SEAOC Design Requirementsfor Sliding Isolated Structures

by

D. Theodossiou and M. C. ConstantinouDepartment of Civil Engineering

State University of New York at BuffaloBuffalo, New York 14260

Technical Report NCEER-91-0015

REPRODUCED BYU.s. DEPARTMENT OF COMMERCE

NATIONAL TECHNICALINFORMATION SERVICESPRINGFIELD, VA 22161

This research was conducted at the State University of New York at Buffalo and was partiallysupported by the National Science Foundation under Grant No. EeE 86-07591.

NOTICEThis report 'was prepared by the State University of New Yorkat Buffalo as a result of research sponsored by the NationalCenter for Earthquake Engineering Research (NCEER). NeitherNCEER, associates of NCEER, its sponsors, State University ofNew York at Buffalo, nor any person acting on their behalf:

a. makes any warranty, express or implied, with respect to theuse of any information, apparatus, method, or processdisclosed in this report or that such use may not infringe uponprivately owned rights; or

b. assumes any liabilities of whatsoever kind with respect to theuse of, or the damage resulting from the use of, any information, apparatus, method or process disclosed in this report.

50272-101

REPORT DOCUMENTATION /1. REPORT NO.

PAGE ·1 NCEER-91-0015 I~3. PB92-11~602

4. Title and Subtitle

Evaluation of SEAOC Design Requirements for SlidingIsolated Structures

5. Report Date

June 10, 1991

7. Aothor(s)

D. Theodossiou and M. C. Constantinou8. Performing Organization Rept. No;

9. Perfonnlng Organization Name and Address

Department of Civil ·EngineeringState University of New York at BuffaloBuffalo, New York 14260

10. Projec:t/Task/Worlc Unit No.

11. ContracteC) or GranteG) No.

(C) ECE 86-07591

eG) BCS-8857080

12. Sponwring Organization Hame·and Address ".. National Center for Earthquake Engmeermg Research

State University of New York at Buffalo.Red Jacket QuadrangleBuffalo, New York 14261

13. Type of~eport & Period Covered

Technical Report

14.

15. Supplementary Notes • •This research was conducted at the State University of New York at Buffalo and waspartially supported by the National Science Foundation under Grant No. ECE 86-07591.

16. Abstract (Umit: 200 words)

The Structural Engineers Association of California (SEAOC) developed in 1990 thedocument IITentative General Requirements for the Design and Construction of SeismicIsolated Structures ll

• The SEAOC document specifies analysis procedures for seismicallyisolated structures, including a static and dynamic analysis procedure. Described in thisreport is a study that concentrated on verifying these procedures for sliding seismicallyisolated structures. The study involved the following: 1) evaluation of the response ofsliding seismically isolated structures with stiff and flexible superstructure; 2) comparison of dynamic analysis results with the results of th~ static analysis procedure ofSEAOC. The main conclusion reached is that a degree of conservatism exists in theSEAOC static analysis procedures. Specific cases are studied and the differencesquantified.

17. Document Analysis a. Descriptors

b. Identlf"t<trs/Open·Ended Terms

EARTHQUAKE ENGINEERING.SLIDING ISOLATION SYSTEMS.FRICTION PENDULUM SYSTEMSSEISMIC ISOLATION SYSTEMS.

PROTECTIVE SYSTEMS. SECONDARY SYSTEMS.BASE ISOLATION SYSTEMS. BUILDING CODES.

(FPS). NONLINEAR ISOLATION SYSTEMS.STATIC ANALYSIS. DYNAMIC ANALYSIS.

c. COSATI FIeld/Group

19. Security Class (This Report) 21. No. of Pages

Unclassified 2/f/~1--='~---------+--":-':'jO-_._--

22. Price

18. Availability Statement

Release Unlimited20. Security Class (This Page)

L.~:::-::::,:,,"=- -:---:-_--:-_--::~_...:U~~nc~la:,::s:,::s:.:.i~fi~e~d:..- ~~:;;;;:;-;;;;;;;;V2"(4=m(~~'ANSI-:L~Q.1Rl c __ •__•••.••.•_. __ D ..._.__ OPTIONAL FORM 272 (4-77)

11111111111,---Evaluation of SEAOC Design Requirements

for Sliding Isolated Structures

by

D. Theodossiou1 and M.C. Constantinou2

June 10, 1991

Technical Report NCEER-91-00l5

NCEER Project Numbers 89-2101 and 90-2101

NSF Master Contract Number ECE 86-07591

and

NSF Grant Number BCS-8857080

1 Research Assistant, Department of Civil Engineering, State University of New York atBuffalo

2 Associate Professor, Department of Civil Engineering, State University of New York atBuffalo

NATIONAL CENTER FOR EARTHQUAKE ENGINEERING RESEARCHState University of New York at BuffaloRed Jacket Quadrangle, Buffalo, NY 14261

"II

PREFACE

The National Center for Earthquake Engineering Research (NCEER) is devoted to the expansionand dissemination of knowledge about earthquakes, the improvement of earthquake-resistantdesign, and the implementation of seismic hazard mitigation procedures to minimize loss of livesand property. The emphasis is on structures and lifelines that are found in zones of moderate tohigh seismicity throughout the United States.

NCEER's research is being carried out in an integrated and coordinated manner following astructured program. The current research program comprises four main areas:

• Existing and New Structures• Secondary and Protective Systems• Lifeline Systems• Disaster Research and Planning

This technical report pertains to Program 2, Secondary and Protective Systems, and more specifically, to protective systems. Protective Systems are devices or systems which, when incorporated into a structure, help to improve the structure's ability to withstand seismic or other environmentalloads. These systems can be passive, such as base isolators or viscoelastic dampers;or active, such as active tendons or active mass dampers; or combined passive-active systems.

Passive protective systems constitute one of the important areas of research. Current researchactivities, as shown schematically in the figure below, include the following:

1. Compilation and evaluation of available data.2. Development of comprehensive analytical models.3. Development of performance criteria and standardized testing procedures.4. Development of simplified, code-type methods for analysis and design.

Base Isolation Systems... -------1 Program 1

Analytical Modeling and Data Compilation 1Experimental Verification and Evaluation ... I - Seismicity and

~ /I Ground Motion1 ______ -

Performance Criteria andTesting Procedures

t--------11Program 2 I

- 1 II - Secondary 1

Methods for Analysis 1 Systems 1and Design

1 ______ --

iii

This report addresses a recently published SEAOC document entitled Tentative General Requirementsfor the Design and Construction ofSeismic Isolated Structures, in which static anddynamic analysis procedures are specified for seismically isolated structures. Specifically,analysis procedures for sliding systems are evaluated based on either test results or dynamicnonlinear time history analysis. The main conclusion reached is that a degree of conservatismexists in the SEAOC static analysis procedures. Specific cases are studied and the differencesquantified.

iv

ABSTRACT

The Structural Engineers Association of California (SEAOC) developed a document

in 1990 entitled 'Tentative General Requirements for the Design and Constmction of Seismic

Isolated Stmctures': The document specifies analysis procedures for seismically isolated

structures, including a static and a dynamic analysis procedure.

This study concentrates on verifiying these procedures for sliding seismically isolated

structures. The study involves the following:

(1) Evaluation of the response of sliding seismically isolated structures with stiff and

flexible superstructure, and

(2) Comparison of dynamic analysis results to results of the static analysis procedure of

SEAOC.

v

ACKNOWLEDGMENTS

Financial support for thiswork has beenprovided by the National Center for Earthquake

Research (Contract Nos. 89-2101 and 90-2101) and the National Science Foundation (Grant

BCS-8857080). This work represents a product of accumulated knowledge on the behavior

of sliding isolation systems at SUNYjBuffalo which has been the result of research funded

by the National Science Foundation (Grant BCS-8857080), the National Center for Earth

quake Engineering Research (Contract Nos. 87-2002, 88-2002A, 89-2101 and 90-2101) and

various industrial sponsors (Watson Bowman Acme Corp., MTS Systems Corp., GERB

Vibration Control and Earthquake Protection Systems, Inc.).

Dr. Charles Kircher, president of Charles Kircher and Accociates, Inc. of Mountain

View, California and chairman of the Base Isolation Subcommittee of the Seismology

Committee of the Structural Engineers Association of Northern California, supplied the

earthquake records used in this study and provided interpretation on details of the SEAOC

Seismic Isolation Requirements. Dr. Kircher and Dr. Bahman Laskari, of Jack Benjamin and

Associates, Inc. of Mountain View, California, reviewed the technical content of the report

and performed confirmatory analysis of selected results.

Preceding page blank

TABLE OF CONTENTS

SECTION TITLE PAGE

1

2

2.1

2.2

2.2.1

2.2.1.1

2.2.1.2

2.2.2

2.2.2.1

2.2.2.2

2.2.2.3

2.2.2.4

2.2.3

2.2.3.1

2.2.3.2

2.3

INTRODUCTION .

SEAOC DESIGN PROCEDURE FOR ISOLATED STRUCTURES ..

General Requirements. . .

Design Methods. . .

Equivalent Static Method .

Conditions for Use ..

Design Formulae .

Dynamic Lateral Response Procedure .

Conditions for Use .

Ground Motion Design Spectra .

Time Histories .

Response Spectrum Analysis .

Lower Bound Limits on Applying the Results of a Dynamic

Analysis Procedure .

Isolation System and Structural Elements Below the

Isolation Interface ..

Structural Elements Above the Isolation Interface .

Application to Sliding Systems .

1-1

2-1

2-1

2-4

2-4

2-4

2-5

2-11

2-11

2-12

2-12

2-13

2-13

2-13

2-14

2-14

Preceding page blank

SECTION TITLE

TABLE OF CONTENTS (cont'd.)

PAGE

3

4

4.1

4.2

4.2.1

4.2.2

4.2.3

4.3

4.4

4.4.1

4.4.1.1

4.4.1.2

4.4.2

TECHNICAL APPROACH . OVERVIEW.................................................... 3-1

STRUCTURE AND ISOLATION SYSTEM MODELS. 4-1

Superstructure Configuration ,....... 4-1

Isolation System. 4-2

DeScrIptlOn. ............................................................................................•........... 4-2

Isolation System Properties. 4-10

SEAOC Design Values for the Isolation System Properties. 4-13

Program 3D-BASIS........................................................................................... 4-13

Comparison of Results Obtained by 3D-BASIS to Other Computer

Programs. 4-15

Comparison with Rigorous Mathematical Solution. 4-15

Presentation of the Analytical Method.......................................................... 4-15

Comparison. 4-17

Comparison with the DRAIN - 2D Program................................................ 4-17

5 COMPARISON OF SEAOC STATIC PROCEDURE TO SHAKE

5.1

5.1.1

5.1.2

5.1.3

TABLE TESTS .

Experimental Setup .

Superstructure .

Isolation System .

Test Program .

x

5-1

5-1

5-1

5-3

5-3


SECTION TITLE PAGE

5.2 SEAOC Static Analysis Procedure. 5-5

5.3 Comparison of Experimental Results and Design Values

According to SEAOC Static Analysis Procedure. 5-10

6 EVALUATION OF RESPONSE FOR ARTIFICIAL EARTHQUAKES

COMPATIBLE TO DESIGN SPECTRA...................................................... 6-1

6.1 Comparison of the Time History Analysis Resutls for One

Excitation to SEAOC Design Formulae 6-2

6.2 Comparison of the Time History Analysis Resutls for

Bi-directional Excitation to SEAOC Design Formulae.............................. 6-22

7 STATISTICAL EVALUATION OF RESPONSE FOR A SET OF

RECORDED PAIRS OF HORIZONTAL EARTHQUAKE

COMPONENTS 7-1

7.1 Earthquake Time Histories. 7-1

7.2 Scaling Factors................................................................................................... 7-3

7.3 Comparison of Time History Analysis Results to SEAOC

Design Formulae. 7-12

8 TIME HISTORY ANALYSIS ON THE BASIS OF SEAOC

DYNAMIC ANALYSIS REQUIREMENTS 8-1

8.1 Comparison of Time History Analysis Results to SEAOC

Design Formulae............................................................................................... 8-6

9 CONCLUSIONS tJ..... 9-1

10 REFERENCES 10-1

X~


SECTION TITLE PAGE

APPENDIX A Results of Maximum Story Shear and Interstory Drift for 8-

Story Isolated Structure. Excitation Represented by Artificial

Records Compatible with Design Spectra. Excitation Only in the

Transverse (T) Direction. A-I

APPENDIX B Response Spectra for 5% Damping of Components of PGV Scaled

Motions Used In Dynamic Analyses and Comparison to Design

Spectra......................................................................................................... B-1

APPENDIX C Results of Maximum Story Shear and Interstory Drift for 8 - Story

Isolated Structure. Excitation Represented by a Set of Pairs of

Scaled Earthquake Motions (Scaling Based on PGV)........................ C-1

APPENDIX D Results of Maximum Story Shear and Interstory Drift for 8

Story Isolated Structure. Excitation Represented by Scaled Pairs

of Real Records According to the Dynamic Analysis Procedure of

SEAOC....................................................................................................... D-1

APPENDIX E Conversion to SI Units. E-1

Xll

LIST OF ILLUSTRATIONS

FIGURE TITLE PAGE

2-1 Normalized ATC-3 Design Spectra 2-3

2-2 Ideal Force-Displacement Loop for the Friction Pendulum

System.......................................................................................................................... 2-16

4-1 Typical Section of a FPS Bearing........................................................... 4-8

4-2 Plan View of the Base of the Building Models Used in the

Analyses and Numbering of the Bearings.............................................................. 4-12

4-3 Comparisons of Base Displacement Time Histories Obtained by

Programs 3D-BASIS, DRAIN-2D and a Rigorous Analysis Program

for 1 - Story Structure Subjected to San Fernando (220) S90W

Earthquake Component in the Longitudinal Direction. Scaling of

the Record is Based on PGV According to Table 7.4 4-18



for 8 - Story Structure Subjected to San Fernando (220) S90W

Earthquake Component in the Longitudinal Direction. Scaling of

the Record is Based on PGV According to Table 7.4 4-19



for 1 - Story Structure Subjected to Imperial Valley EI Centro

(117) S90W Earthquake Component in the Longitudinal Direction.

Scaling of the Record is Based on PGV According to Table 7.4 4-20

xiii

FIGURE TITLE

LIST OF ILLUSTRATIONS (cont'd.)

PAGE



for 8 - Story Structure Subjected to Imperial Valley EI Centro

(117) S90W Earthquake Component in the Longitudinal Direction.




for 1 - Story Structure Subjected to Eureka (023) N44E

Earthquake Component in the Longitudinal Direction.




for 8 - Story Structure Subjected to Eureka (023) N44E

Earthquake Component in the Longitudinal Direction.


5-1 Model Used for Shake Table Testing 5-2

5-2 Displacement Spectra for 5% Damping of Records Used in Shake

Table Testing (in Prototype Scale) and Corresponding ZNS Values 5-6

6-1 Artificial Record No#1 Compatible with O.4g S1 Design Spectrum

and Comparison of its Spectrum with the Target Spectrum............................... 6-3

6-2 Artificial Record No#2 Compatible with OAg S1 Design Spectrum


xiv

FIGURE TITLE


PAGE

6-3 Artificial Record No#3 Compatible with OAg Sl Design Spectrum

and Comparison of its Spectrum with the Target Spectrum 6-5










and Comparison of its Spectrum with the Target Spectrum 6-10



7-1 5% Average Spectra of Components T,L and Square Root of Sum

of Square of Components T and L of PGV and PGA Scaled

Motions used in Dynamic Analyses and Comparison with the Design

Spectrum. Earthquake Records Recorded at Rock Sites 7-9



Motions Used in Dynamic Analyses and Comparison with the·Design

Spectrum. Earthquake Records Recorded at Stiff Soil Sites 7-10

xv

FIGURE TITLE


PAGE



Motions Used in Dynamic Analyses and Comparison with the Design

Spectrum. Earthquake Records Recorded at Medium Soil Sites 7-11

7-4 Comparison of Circular and Square Interaction Models of Isolation Bear-

ings 7-38

8-1 5% Damping Spectra of Components T, L and Square Root of Sum of

Squares of Components T and L of Scaled Earthquake Motions Selected

for Dynamic Analyses According to SEAOC Time History Analysis

Procedure and Comparison with 1.3 Times OAg S1 Design Spectrum. 8-3

8-2 5% Damping Spectra of Components T, L and Square Root of Sum of

Squares of Components T and L of Scaled Earthquake Motions Selected

for Dynamic Analyses According to SEAOC Time History Analysis

Procedure and Comparison with 1.3 Times OAg S2 Design Spectrum. 8-3

B-1 Response Spectra for 5% Damping of Components of PGV Scaled. Motions

Used in Dynamic Analyses and Comparison to Design Spectra. B-1

xvi

LIST OF TABLES

TABLE TITLE PAGE

2.1 Seismic Zone Coefficient Z 2-7

2.2 Near Field Response Coefficient N 2-7

2.3 Site Coefficient S 2-7

2.4 Damping Coefficient B 2-7

4.1 Properties for 1 - story Isolated Structure 4-3

4.2 Properties for 8 - story Isolated Structure 4-3

4.3 Dynamic Characteristics of 1 - story Superstructure (Including

5% Mass Eccentricity) 4-4

4.4 Dynamic Characteristics of 8 - story Superstructure (Including

5% Mass Eccentricity). Modes Higher than the 9th are not Presented 4~5

4.5 Isolation System Properties 4~11

4.6 Axial Load Carried by Each One of the Bearings, for 1 - story

and 8 - story Isolated Structure, as a Proportion of the Total

Weight WT of the Structure 4-11

4.7 Displacement and Base Shear Over Weight Ratio Values According

to SEAOC Static Analysis Procedure for Use in Comparison

with the Results of Nonlinear Dynamic Analyses Performed

in this Study 4-14

5.1 Earthquake Records Used in Test Program 5-4

xvii

TABLE TITLE

LIST OF TABLES (cant'd.)

PAGE

5.2 Comparison of the Peak Acceleration and ZNS Values Used by

Chalhoub and Kelly, 1990 and Griffith et aI, 1988 with the

Ones Used in this Study 5-12

5.3 Shake Table Testing Results (Extrapolated to Prototype) for the

Higher Friction Material (fmax = 0.095) and Comparison to

SEAOC Design Values 5-13

5.4 Shake Table Testing Results (Extrapolated to Prototype) for the

Higher Friction Material (fmax = 0.075) and Comparison to

SEAOC Design Values 5-14

6.1 Summary of Results of Maximum Base Displacement at Geometric Center

of 1 - story Isolated Structure Excited in the Transverse (T)

Direction by Artificial Records Compatible to Design Spectra and

Comparison of these Displacements with the Design Displacements

According to SEAOC Static Analysis Procedure 6-12

6.2 Summary of Results of Maximum Base Displacement at Geometric Center

of 8 - story Isolated Structure Excited in the Transverse (T)

Direction by Artificial Records Compatible to Design Spectra and

Comparison of These Displacements with the Design Displacements

According to SEAOC Static Analysis Procedure. 6-13

6.3 Analysis Results for 1 - story Isolated Structure with R =39.132 in

(Tb = 2 sec), fmax = O.lO, Excited in Transverse (T) Direction by

Artificial Record Compatible with Design Spectra 6-14

xviii

TABLE TITLE

LIST OF TABLES (cont'd.)

PAGE


(Tb = 3 sec), fmax = 0.05, Excited in Transverse (T) Direction by

Artificial Record Compatible with Design Spectra. 6-15




6.6 Analysis Results for 8 - story Isolated Structure with R=39.132 in










(Tb = 2 sec), fmax = 0.10, Excited by Bi-directional Artificial

Record Compatible with Design Spectra. 100% in the Transverse (T)

and 83% of Artificial Record in the Longitudinal (L) Direction 6-24


(Tb = 3 sec), fmax = 0.05, Excited by Bi-directional Artificial


and 83% of Artificial Record in the Longitudinal (L) Direction 6-25

xix

TABLE TITLE


PAGE


(Tb =3 sec), fmax = 0.10, Excited by Bi-directional Artificial


and 83% of Artificial Record in the Longitudinal (L) Direction. 6-26

6.12 Summary of Results of Maximum Base Displacement at Geometric Center of

8 - story Isolated Structure Excited by Bi-directional Artificial Records Com

patible to Design Spectra (100% of Artificial Records in Transverse (T)and

83% of Artificial Records in Longitudinal (L) Direction) and Comparison of

these Displacements with the Design Displacements According to SEAOC

Static Analysis Procedure 6-27

7.1 Horizontal Earthquake Components Recorded at Rock Sites 7-4

7.2 Horizontal Earthquake Components Recorded at Stiff Soil Sites 7-5

7.3 Horizontal Earthquake Components Recorded at Medium Soil Sites 7-6

7.4 Scaling Factors of the Earthquake Components 7-8


(Tb = 2 sec), fmax ::: 0.10. Excitation Represented by a Set of Pairs

of Scaled Earthquake Motions Recorded on Rock Sites (Representative

of Soil Type Sl). Weight is Total Weight of Structure Including

Base. Height is 12ft 7-16


(Tb :;:; 2 sec), fmax :::: 0.10. Excitation Represented by a Set of Pairs

xx

TABLE TITLE


PAGE

of Scaled Earthquake Motions Recorded on Stiff Soil Sites

(Representative of Soil Type Sl). Weight is Total Weight of

Structure Including Base. Height is 12f1. 7-17

7.7 Analysis Results for 1- story Isolated Structure with R=39.132 in

(Tb = 2 sec), fmax = 0.10. Excitation Eepresented by a Set of Pairs

of Scaled Earthquake Motions Recorded on Medium Soil Sites

(Representative of Soil Type S2). Weight is Total Weight of



(Tb = 3 sec), fmax = 0.05. Excitation Represented by a Set of Pairs



Base. Height is 12ft. 7-19

7.9 Analysis Results for 1- story Isolated Structure with R=88.048 in




Structure Including Base. Height is 12f1.. 7-20






xxi

TABLE TITLE


PAGE










Structure Including Base. Height is 12ft. 7-23











7.15 Analysis results for 8 - story Isolated Structure with R=39.132 in


xxii

TABLE TITLE


PAGE








Structure Including Base. Height is 12ft , 7-27




of Soil type Sl). Weight is Total Weight of Structure Including







7.19 Analysis Results for 8 -story Isolated Structure With R=88.048 in





xxiii

TABLE TITLE


PAGE

7.20 Analysis Results for 8 - story Isolated Structure With R =88.048 in





7.21 Analysis Results for 8 - story Isolated Structure With R=88.048 in




structure Including Base. Height is 12ft.. 7-32

7.22 Analysis Results for 8 - story Isolated Structure With R =88.048 in





7.23 Summary of Results of the Mean and the Mean Plus One Standard

Deviation Values of the Base Displacement for 1 - story Isolated

Structure Excited by PGV Scaled Earthquake Time Histories and

Comparison of These Results With the Design Values According to

SEAOC Static Analysis Procedure. Units are Inches 7-34



xxiv

TABLE TITLE


PAGE

Structure Excited by PGV Scaled Earthquake Time Histories and

Comparison of these Results With the Design Values According to

SEAOC Static Analysis Procedure. Units are Inches 7-35



Structure Excited by PGV Scaled Earthquake Time Histories

Considered in this Study Representative of the Soil Sites they were

Recorded and Comparison of These Results with the Design Values

According to SEAOC Static Analysis Procedure. Units are Inches.

Certain Records were Removed as Indicated in Tables 7.5 to 7.22 7-36



Structure Excited by PGV Scaled Earthquake Time Histories

Considered in this Study Representative of the Soil Sites they were

Recorded and Comparison of these Results with the Design Values

According to SEAOC Static Analysis Procedure. Units are Inches.

Certain Records were Removed as Indicated in Tables 7.5 to 7.22 7-37

7.27 Analysis Results for 1- story Isolated Structure with R=39.132 in(Tb = 2 sec),

fmax = 0.10. Excitation Represented by a Set of Pairs of Scaled Earthquake

Motions Recorded on Medium Soil Sites (Representative of Soil Type S2).

Weight is Total Weight of Structure Including Base. Height is 12ft. Square

Interaction Model for Isolation Bearings 7-39

8.1 Selected Time Histories and Their Scaling Factors 8-5

xxv

TABLE TITLE


PAGE


(Tb = 2 sec), fmax = 0.10, Excited by Scaled Pairs of Real

Records According to the Dynamic Analysis Procedure of SEAOC.

Weight is Total Weight of Structure Including Base. Height is 12ft 8-7




Weight is Total Weight of Structure Including Base. Height is 12ft. 8-8








Weight is Total weight of Structure Including Base. Height is 12ft. 8-10





xxvi

TABLE TITLE

LIST OF TABLES (cant'd.)

PAGE





8.8 Summary of Analysis Results of Maximum Base Displacement at

Geometric Center of I - story Isolated Structure Excited by Scaled

Pairs of Real Records According to the Dynamic Analysis

Procedure of SEAOC and Comparison of these Displacements with the

Design Displacements According to SEAOC Static Analysis Procedure. ......... 8-13

8.9 Summary of Analysis Results of Maximum Base Displacement at

Geometric Center of 8 - story Isolated Structure Excited by Scaled

Pairs of Real Records According to the Dynamic Analysis

Procedure of SEAOC and Comparison of these Displacements with the

Design Displacements According to SEAOC Static Analysis Procedure. ......... 8-14

A.l Analysis Results of Maximum Story Shear for 8 - story Isolated

Structure with R=39.132 in (Tb = 2 sec.), fmax = 0.10.

Excitation Represented by Artificial Records Compatible with

Design Spectra. Weight is Total Weight of Structure Including Base A-I

A.2 Analysis Results of Maximum Interstory Drift for 8 - story Isolated



Design Spectra. Height is 12 ft. A-2

xxvii

TABLE TITLE


PAGE

A,3 Analysis Results of Maximum Story Shear for 8 - story Isolated



Design Spectra. Weight is Total Weight of Structure Including Base A-3

AA Analysis Results of Maximum Interstory Drift for 8 - story Isolated




A.5 Analysis Results of Maximum Story Shear for 8 - story Isolated



Design Spectra. Weight is Total Weight of Structure Including Base A-5

A.6 Analysis Results of Maximum Interstory Drift for 8 - story Isolated




C.l Analysis Results of Maximum Story Shear for 8 - story Isolated

Structure with R=39.132 in (Tb = 2 sec), fmax = 0.10.

Excitation Represented by a Set of Pairs of Scaled Earthquake

Motions Recorded on Rock Sites (Representative of Soil

Type Sl). Weight is Total Weight of Structure Including Base C-l

xxviii

TABLE TITLE


PAGE

C.2 Analysis Results of Maximum Interstory Drift for 8 - story Isolated




Type Sl). Height is 12ft. C-2

C.3 Analysis Results of Maximum Story Shear for 8 - story Isolated



Motions Recorded on Stiff Soil Sites (Representative of Soil

Type Sl). Weight is Total Weight of Structure Including Base C-3

CA Analysis Results of Maximum Interstory Drift for 8 - story Isolated




Type S1). Height is 12ft. C-4




Motions Recorded on Medium Soil Sites (Representative of Soil

Type S2). Weight is Total Weight of Structure Including Base C-5



xxix

TABLE TITLE


PAGE




e.7 Analysis Results of Maximum story shear for 8 - story Isolated




type Sl). Weight is Total Weight of Structure Including Base C-7

e.8 Analysis Results of Maximum Interstory Drift for 8 - story Isolated





e.9 Analysis Results of Maximum Story Shear for 8 - story Isolated




Type S1). Weight is Total Weight of Structure Including Base C.9

e.10 Analysis Results of Maximum Interstory Drift for 8 - story Isolated





xxx

TABLE TITLE


PAGE

c.n Analysis Results of Maximum Story Shear for 8 - story Isolated

Structure with R =88.048 in (Tb = 3 sec), fmax = 0.05.



Type S2). Weight is Total Weight of Structure Including Base C-ll

C.12 Analysis Results of Maximum interstory Drift for 8 - story Isolated




Type S2). Height is 12f1. C-12










Type S1). Height is 12f1. C-14

C.15 Analysis Results of Maximum story shear for 8 - story Isolated


xxxi

TABLE TITLE

LIST OF TABLES (coot'd.)

PAGE




C16 Analysis Results of Maximum Interstory Drift for 8 - story Isolated





C17 Analysis Results of Maximum Story Shear for 8 - story Isolated




Type S2). Weight is Total Weight of Structure Including Base C-17

Ci8 Analysis Results of Maximum Interstory Drift for 8 - story Isolated




Type S2). Height is 2ft C-18

D.l Analysis Results of Maximum Story Shear for 8 - story Isolated

Structure with R = 39.132 in (Tb = 2 sec), fmax = 0.10, Excited by

Scaled Pairs of Real Records According to the Dynamic Analysis

Procedure of SEAOC Weight is Total Weight of Structure Including

Base D-1

xxxii

TABLE TITLE


PAGE

D.2 Analysis Results of Maximum Interstory Drift for 8 - story Isolated



Procedure of SEAOC. Height is 12ft. D-2

D.3 Analysis Results of Maximum Story Shear for 8 - story Isolated



Procedure of SEAOC. Weight is Total Weight of Structure Including

Base D-3

D.4 Analysis Results of Maximum Interstory Drift for 8 - story Isolated




D.5 Analysis Results of Maximum Story Shear for 8 - story Isolated



Procedure of SEAOC. Weight is Total Weight of Structure Including

Base D-5

D.6 Analysis Results of Maximum interstory drift for 8 - story Isolated




xxxiii

SECTION 1

INTRODUCTION

The seismic isolation concept is based on the premise that a structure can be sub

stantially decoupled from potentially damaging earthquake motions. By decoupling the

structure from ground vibration, a reduction occurs in the level of response of a structure,

from the level that would otherwise occur in a conventional fixed-base building.

It is intended that decoupling will be accomplished using an isolation scheme which

makes the fundamental period of the isolated structure several times greater than the period

of the elastic fixed-base structure above the isolation system. In this way, the fundamental

period of the isolated structure shifts to a period range, where the response accelerations are

much less than those at the fixed-base period.

A reduction of the acceleration response is associated, however, with an increase in

the displacement of the isolation system. Control of this displacement within acceptable limits

is achieved by the introduction of an energy dissipating mechanism. In this respect, isolation

systems consisting primarily of elastomeric bearings have been developed.

Alternatively, isolation systems have been proposed which do not shift the fundamental

period of the system but rather limit the transmission of force to the superstructure by utilizing

only sliding supports. However, the lack of recentering capability in such systems may result

in excessively large permanent displacements. Accordingly, sliding isolation systems with

various forms of recentering devices have been developed.

Fixed-base (conventional) buildings absorb earthquake forces by inelastic response of

the strutural system which lengthens the period of the system and increases its energy dissi

pation capacity. Inelastic response may cause building damage, both to the structural system

I-I

and nonstructural components. Earthquake damage can have significant cost impacts such as

repair and post earthquake disruption costs, increased earthquake insurance premiums and

potential liability for losses and injuries.

The base isolation alternative reduces the forces transmitted to the structure, limiting

inelastic response of the structural system and damage to the building and its contents.

Isolation can provide a level of performance well beyond that of conventional buildings with

potential for substantiallife-cyc1e cost reduction.

The benefits offered by the new technology of seismic isolation, have become evident

and widely accepted. Currently, several buildings and bridges in California and other countries

such as Japan, New Zealand, Italy, U.S.S.R., and others have been constructed by applying

the seismic isolation technology.

The familiarity and general recognition of the appealing seismic isolation advantages

from the professional community and the public has led to the need to extend the imple

mentation of this concept into a wider area of construction. Accordingly, the Seismology

Committee of the Structural Engineers Association of California (SEAOC) felt that the

existing provisions for the design of conventional buildings should be supplemented with

design requirements developed especially for seismically isolated structures. This effort was

considered necessary for the following reasons:

(1) Conventional building code were not adequate for isolated building design, and

(2) Design engineers and building officials needed special code provisions for preparing,

reviewing and regulating isolated building design.

On the basis of the above, the seismic isolation concept and the criteria that would be

appropriate for design aQ.d construction ofseismically isolated structures have beenconsidered

by various Structural Engineers Associations of California (SEAOC) groups, since the early

1980's. Specifically, in the mid-1980's, members of the southern section of SEAOC published

several papers that provide guidelines for the design of buildings with seismic isolators. In

1986, the northern section of SEAOC published "Tentative Seismic Isolation Design Require-

1-2

ments" (SEAONC, 1986), the first collection of design provisions for seismic isolated struc

tures. In 1990, SEAOC recognized the need for a document that would represent a consensus

opinionofall its sections. The SeismologyCommittee ofSEAOC developed 'Tentative General

Requirements for the Design and Construction ofSeismic Isolated Structures" (SEAOC, 1990a)

as an appendix to supplement the 1990 "SEAOC Recommended Lateral Force Requirements",

also known as Blue Book (SEAOC,1990b). This appendix has been adopted by the Inter

national Conference of Building Officials and has been incorporated in the 1991 Edition of

the Uniform Building Code (UBC, 1991).

It is implied that these successive efforts had a common motive, arising from the fact

that seismic isolation is a relative new technology. As experience with many design-related

issues increases and the results of related research become available, the design requirements

for seismic isolated structures can be refined accordingly. Based on this thought, the 1990

appendixofSEAOC is considered to be prepared in keeping with the most current information

and the present state of the practice of seismic isolation.

However, a lack of precise knowledge of the behavior of structures supported by all of

the existing types of seismic isolation systems still exists. In anticipating the arising uncer

tainties, the SEAOC document, rather than addressing a specific method, provides require

ments that are generally applicable to a wide range of possible isolation systems. It requires

rigorous dynamic analysis for all, or virtually all the isolated buildings, but also, by providing

simple formulae, it accomplishes the anticipation of the uncertainties by defining.lower bound

limits for the predicted response values.

In this study, an attempt is made to create a set of nonlinear dynamic analysis results

which examine the behavior of structures supported by a certain type of sliding isolation

system. Those results are further compared to the key design requirements provided by

SEAOC and in this way, provide a basis for judging the validity and applicability of those

requirements.

]-3

A certain type of isolation system, the Friction Pendulum System (Zayas et aI, 1987,

Mokha et aI, 1990b and 1991) was used in the analyses. By introducing a highly nonlinear

isolation system, the comparison is of peculiar interest, since the formulas that confine the

design values provided by SEAOC are based on the assumption of a linear isolation system.

The selection of the Friction Pendulum System for this study is based on the belief that it

represents the best sliding isolation system. Shake table tests performed at SUNYjBuffalo

have provided evidence for this (Mokha et aI, 1990b and 1991, Constantinou et al 1990a and

1991). However, the obtained results are representative of the behavior of other isolation

systems with similar characteristics.

1-4

SECTION 2

SEAOC DESIGN PROCEDURE FOR ISOLATED STRUCTURES

The seismic isolation concept and the criteria that would be appropriate for design and

construction of isolated buildings has been considered by various Structural Engineers

Association of California (SEAOC) groups, since the early 1980's. These successive efforts

arise from the fact that seismic isolation is a relative new technology and as experience with

many design-related issues increases and the results of related research become available, the

design requirements for seismically isolated structures can be refined accordingly.

On this basis, SEAOC developed a document entitled "Tentative GeneralRequirements

for the Design and Constmction ofSeismic Isolated Stmctures" (SEAOC, 1990a). This document

specifies design procedures for seismically isolated structures.

2.1 General Requirements

Rather than addressing a specific method on seismic isolation, the SEAOC document

provides requirements that are applicable to a wide range ofpossible seismic isolation systems.

In general, it requires that an isolation system has the following basic properties: (1) remain

stable for the design displacement, (2) provides increasing resistance with increasing dis

placement, (3) does not degrade under repeated cyclic loading, and (4) has quantifiable

engineering parameters.

Furthermore, the design requirements permit the use of either one of two different

procedures for determining the design-basis seismic loads. The first procedure is intended for

use on stiff buildings of regular configuration located on rock or stiff soil sites, away from

active faults. This procedure uses a-simple formula (similar to the seismic coefficient formula

now used in conventional building design) to describe peak lateral displacement and force as

2-]

a function of seismic zone, soil profile, proximity to active faults and isolated building period

and damping. The second approach, which is required for all the other situations, relies on

dynamic analysis procedures to determine maximum force and displacement response of the

isolated building. Dynamic analysis procedures include both response spectrum (linear)

analysis and time history (nonlinear) analysis. The latter is required for the design ofbuildings

with significantly nonlinear isolation systems and/or superstructure elements.

Both the static and dynamic analysis procedures are based on the same level of seismic

input and require the same level of performance from the building. The Design-Basis

Earthquake load corresponds to a level of ground motion that has a 10% probability of being

exceeded in a 50 year time period. For buildings not requiring a site-specific hazard analysis,

the Design-Basis Earthquake spectra are defined by the ground motion spectra recommended

by ATC 3-06 (ATC, 1978) and are essentially the same as those specified by the Blue Book

(SEAOC, 1990b) for dynamic analysis of conventional fixed-base buildings. Those design

spectra are shown in Figure 2-1. As an additional requirement, the isolation system stability

must be verified by test of the maximum level of the earthquake motion that can be expected

at the site. This earthquake intensity is defined as the level of ground motion that has a 10

percent probability of being exceeded in a 250 year time period.

When the first procedure is implemented according to SEAOC, limits arise which are

associated with certain existing conditions, such as the soil profile type, the proximity of the

structure to active faults, the seismic zone, the complexity of the configuration of the structure,

etc. In those cases, a dynamic analysis approach is required by using the second procedure. If

dynamic analysis is to be made, the response values must be subjected to limitations for the

design. The lower bound limits are determined by applying the equations prescribed in the

first procedure, where the static analysis approach exists.

2-2

3.02.52.0

------ ---.... -

1.5

' ....

1.0

//

SOIL PROFILE TYPE 53

ffSO'L PROFILE TYPE S2

_ _ _ SOIL PROFILE TYPE 51

""", ,

4

z0I-

Z «30 a:t= w

..J« wa:: uw U..J <WU c 2u« z

::>0

..J a:< C)

a::I- :Eu ::>w :iQ.en x

<:i

00 0.5

PERIOD .. SECONDS

FIGURE 2-1 Normalized ATC-3 Design Spectra

2-3

Therefore, we can observe that current 5EAOC thinking requires rigorous dynamic

analysis for all, or virtually all, isolated buildings, but to also prescribes , by introducing a

formula, a minimum design displacement of the isolation system. This approach ensures that

complex or nonlinear structures will be evaluated using the appropriate dynamic analysis

method and also provides a simple formula for validating the final design. The concept for

using simple formula to define a lower-bound limit for isolation system displacement is

analogous to the UBC's (Uniform Building Code, 1991) use of a prescriptive formula to define

a minimum base shear for design of conventional fixed-base buildings. It is a process which

ensures a measure of uniformity in buildings of common construction and guards against gross

underdesign of key elements.

2.2 Design Methods

According to 5EAOC, a seismically isolated structure may be analyzed either by the

static analysis method or by a dynamic analysis method. The latter may be either a response

spectrum or a time-history analysis. The conditions for use of these analysis methods are

presented in the sequel.

2.2.1 Equivalent Static Method

2.2.1.1 Conditions for Use

According to SEAOC, a static lateral response procedure may be used for design

provided:

(1) The structure is located at least 15 km from all active faults.

(2) The structure is located on a soil profile with a site factor of S1 or 52.

(3) The structure is located in Seismic Zone 3 or 4.

(4)The structure above the isolation interface is equal or less than four stories, or 65 feet, in

height.

(5)The isolated period of the structure, T, is equal or less than 3.0 seconds.

2-4

(6)The isolated period of the structure, T, is greater than 3 times the elastic, fixed-base period

of the structure above the Isolation Interface, as determined by the Blue Book (SEAOC,

1990b).

(7) The structure above the isolation interface is of regular configuration.

(8)The isolation system does not limit the Total Maximum Displacement to less than 1.5

times the Total Design Displacement.

(9) The isolation system is defined by all of the following attributes:

(a) The effective stiffness of the isolation system at the Design Displacement is

greater than one-third of the Effective Stiffness at 20% of the Design Dis

placement.

(b) The isolation system is capable of producing a restoring force, such that the

lateral force at the Total Design Displacement is at least 0.025W greater than

the lateral force at 50 percent of the Total Design Displacement.

(c) The isolation system has force deflection properties which are independent of

the rate of loading.

(d) The isolation system has force deflection properties which are independent of

vertical load and bilateral load.

2.2.1.2 Design Formulae

The isolation system shall be designed and constructed to withstand minimum lateral

displacements which act in the direction of each of the main horizontal axes of the structure

in accordance with the formula:

D = 10ZNSTB

where,

2-5

(2.1 )

D =Design Displacement of the isolation system at the center of the building in the direction

under consideration.

Z = Seismic Zone coefficient (Table 2.1).

N =Near field coefficient related to the proximity of the structure to active faults. (Table

2.2)

S = Soil type coefficient (Table 2.3).

T = Isolated building period, provided by equation 2.4.

B =Coefficient related to the effective damping of the isolation system (Table 2.4).

The above mentioned formula is based directly on the shape of the ATC-3 spectra for

periods greater than 1.0 second, with two additional factors: (1) the near-field coefficient, N,

to account for the possibility of increased displacement at sites near faults and (2) the damping

coefficient, B, to account for damping in the isolation system other than 5% of critical. The

relationship between this formula and the ATC-3 spectra may be seen by first setting both

the damping and the near-field terms to 1.0 (i.e. 5% damped response for sites not near an

active fault). Equation 2.1 becomes:

D = lOZST (2.2)

(2.3)

Design displacement, D, may then be converted to spectral acceleration, SA, by multiplying

by(2;r, where g is the gravity constant (386.22 in.jsec2):

SA=lOZST(2~r ~ZS386.22 T

At periods greater than 1.0 second, the above expression of spectral acceleration is

seen to be consistent with the 5% design spectra recommended by the ATC-3 study for use

in building codes (Figure 2-1). To use the design displacement formula (equation 2.1), an

effective period of the isolated building is defined as follows:

2-6

TABLE 2.1 Seismic Zone Coefficient Z

Zone 0 1 2a 2b 3 4

Z 0.05 0.1 0.15 0.2 0.3 0.4

TABLE 2.2 Near-Field Response Coefficient N

Closest Distance, dF, to an dF > 15 krn dF =10 krn dF < 5 krnActive Fault

N 1.0 1.2 1.5

TABLE 2.3 Site Coefficient S

Soil Profile Type Sl S2 S3 S4

S 1.0 1.5 2.0 2.7

TABLE 2.4 Damping Coefficient B

Effective Dampin~ <2% 5% 10% 20% 30% 40% >50%(Percent of Critic

B 0.8 1.0 1.2 1.5 1.7 1.9 2.0

2-7

l6T= 2nKming

where,

(2.4)

W =building weight,

g = acceleration of gravity, and

Kmin =effective stiffness of the isolation system, determined by cyclic-load test as the slope

of a line between the origin and the minimum test value of force at the design dis

placement.

By basing the effective period, T, on the minimum effective stiffness of the isolation

system, determined by test, the above formula approximates the longest period of the isolated

building at peak response. In this manner the design displacement, which is proportional to

the period, is intended to prescribe the maximum excursion of the isolated structure due to

the design-basis event.

The relationship between the damping coefficient, B, and the value of effective

damping, [3, is given in Table 2.4. The effective damping, [3, is prescribed on the basis of the

hysteretic behavior of the isolation system, as follows:

f3 = A2nK maxD2

where,

(2.5)

A = area of the hysterisis loop determined from test results at an amplitude

equal to the design displacement,

Kmax =the maximum effective stiffness of the isolation system, determined by cyclic-load

tests.

By basing the damping coefficient, B, on the force-deflection behavior of the isolation system,

the above formula estimates the reduction in displacement response for systems which have

damping values greater than 5% of critical.

2-8

The provisions also prescribe Total Design Displacement, DT (Design Displacement

including torsional effects), on the basis of structure configuration and eccentricity as follows:

D = D[ 1 + l2ye ]T b 2 + d 2

where,

(2.6)

DT =Total Design Displacement of the isolation system, including both the translational

displacement D, at the center of rigidity and the component of torsional displacement

in the direction under consideration.

y = distance between the center of isolation system rigidity and the point of interest, measured

perpendicular to the direction under consideration.

e =actual eccentricity between the center of mass of the structure and the center of rigidity

of the isolation system, plus accidental eccentricity taken as 5% of d.

d = longest plan dimension of the structure.

b = shortest plan dimension of the structure, measured perpendicular to d.

The additional component of displacement due to torsion, as prescribed by equation 2.6,

increases the Design Displacement at the corner of the structure by about 15% (for a perfectly

square building in plan) to about 30% ( for a very long rectangular building for an eccentricity

of 5 percent). Values less than those of equation 2.6 can be used with justification, but DT

cannot be less than 1.1 D.

The Total Maximum Displacement, DTM required for verification of the isolation

system stability in the most critical direction of horizontal response is calculated as follows:

(2.7)

The Total Maximum Displacement, according to SEAOC, is used to verify adequate

clearances and separations, verification of isolator stability and load testing of the isolator

prototypes.

2-9

The peak force below and at the isolation system, Vb, corresponding to the peak dis

placement D, is given by the following expression:

KmaxDV =---

b l.S (2.8a)

In defining this equation, SEAOC introduces a reduction factor of the order of 1.5, as

to adjust the peak shear to a level compatible with the working-stress allowables specified in

other sections of the Blue Book (SEAOC, 1990b).

The value of Vb shall not be taken as less than the following:

(1) The lateral seismic force required for a fixed-base structure 'Of the same

weight and a period equal to the isolated period, T.

(2) The lateral seismic force required to fully activate the isolation system (e.g.

the yield level of a softening system, the ultimate capacity of a sacrificial

Wind-Restraint System or the static friction level of a sliding system).

Furthermore, SEAOC specifies a minimum design force for the structure above the

isolation system which is in the same form as equation 2.8a but with a reduction factor RWI,

other than 1.5

KmaxDV =---

S RW1

(2.8b)

This reduction factor depends on the lateral force resisting system of the superstructure

and is about four times less than the Rw factor used in the calculation of the lateral force for

the design of conventional non-isolated structures (SEAOC, 1990b). In this respect, it is

required by SEAOC that base isolated structures remain essentially elastic for the Design

Basis Earthquake.

The distribution of force Vs with height is based on an assumed uniform distribution

of seismic acceleration over the height of the structure above the isolation interface.

2-10

2.2.2 Dynamic Lateral Response Procedure

2.2.2.1 Conditions for Use

According to SEAOC, a dynamic analysis, interpreted either as a response spectrum

analysis or a time history analysis, is required for design of the following isolated structures:

(1) Structures with a seismic isolated period T, which is less than 3 times the

elastic, fixed-base period of the structure above the isolation interface.

(2)Structures (above the isolation interface) having a" stiffness, weight or

geometrical vertical irregularity or other irregularity, for which the 1990

Blue Book requires dynamic analysis.

(3)Structures located within 15 km of an active fault.

(4)Structures located at a soil profile with a site factor of S3 or S4 (soft and

very soft soil types).

(5) The structure is located in Seismic Zone 0,1,2A or 2B.

(6)The structure above the isolation system is greater than 4 stories or greater

than 65 feet in height.

(7)The isolated period of the structure, T, is greater than 3.0 seconds.

Additionally, time history analysis is required to determine the design displacement of

the isolation system and the peak floor displacements of the structure above the isolation

system for the following isolated structures:

(1) The structure is located on a soil profile with a site factor S4.

(2)The isolation system limits the Maximum Credible Earthquake displace

ment to less than 1.5 times the Design-Basis Earthquake displacement.

(3)The isolation system has one or more of the following attributes:

(a)The Effective Stiffness at the Design Displacement is less than

one-third of the Effective Stiffness at 20% of the Design Dis

placement.

(b)The isolation systemis not capable ofproducing a restoring force

2-11

specified in the detailed requirements.

(c)The isolation system has force deflection properties which are

dependent of the rate of loading.

(d)The isolation system has force deflection properties which are

dependent of vertical load and bilateral load.

2.2.2.2 Ground Motion Design Spectra

Properly substantiated, site specific spectra are required for design ofall structures with

an isolated period, T, greater than 3.0 seconds, or located on a soil type profile of S3, or S4,

or located within 15 km of an active fault or located in Seismic Zones 1, 2A or 2B. Structures

not requiring site-specific spectra shall be designed by using the spectra of Figure 2-1.

A design spectrum shall be constructed for the Design-Basis Earthquake. This design

spectrum shall not be taken as less than the normalized response spectrum given in Figure

2-1 for the appropriate soil type, scaled by the seismic zone coefficient.

Exception: If a site-specific spectrum is calculated for the Design-Basis Earthquake, then the

spectrum may be taken as less than 100 percent, but not less than 80 percent of the normalized

response spectrum given in Figure 2-1 for the appropriate soil type, scaled by the seismic zone

coefficient.

Also, a design spectrum shall be constructed for the Maximum Credible Earthquake. This

design spectrum shall not be taken as less than 1.25 times the Design-Basis Earthquake

spectrum. This design spectrum shall be used to determine the Total Maximum Displacement

for testing of the stability of the base-isolation system.

2.2.2.3 Time Histories

Pairs of horizontal ground motion time history components shall be selected from not

less than three recorded events. Each pair of time histories shall be applied simultaneously

to the structure, considering the least advantageous location of the mass center. These

motions shall be scaled such that the square root of the sum of the squares (SRSS) of the 5%

2-12

damped-spectrum of the scaled horizontal components does not fall below 1.3 times the

5%-damped spectrum of the Design-Basis Earthquake by more than 10% in the period range

T, as described by formula 2.1, for periods from T, minus 1.0 seconds to T plus 2.0 seconds.

The maximum response of the parameter of interest as calculated by the three time history

analyses shall be used for design.

The duration of the time histories shall be consistent with the magnitude and source

characteristics of the Design-Basis Earthquake. Time histories developed for sites 15 km of

a major active fault shall incorporate near fault phenomena.

2.2.2.4 Response Spectrum Analysis

Response spectrum analysis shall be performed using a damping value equal to the effective

damping of the isolation system or 30 percent of critical, whichever is less. Response spectrum

analysis used to determine the Total Design Displacement and the Total Maximum Dis

placement shall include simultaneous excitation of the model by 100 percent of the most

critical excitation of ground motion and 30 percent of the ground motion on the orthogonal

axIS.

2.2.3 Lower Bound Limits on Applying the Results of a Dynamic Analysis Procedure

As previously stated, certain limits confine the implementation of response values for

design, if they are predicted according to a dynamic analysis procedure. These limits are

described below.

2.2.3.1 Isolation System and Structural Elements Below the Isolation Interface

(l)The Total Design Displacement of the isolation system shall not be taken

as less than 90 percent of DT' as specified in the equation 2.6.

(2)The Total Maximum Displacement ofthe isolation system shall not be taken

as less than 80% of DTM, prescribed by equation 2.7.

2-13

(3)The design lateral shear force on the isolation system and structural ele

ments below the isolation interface shall not be taken as less than 90 percent

of Vb, prescribed by equation 2.8a.

2.2.3.2 Structural Elements Above the Isolation Interface

(1)The design lateral shear force on the structure above the isolation interface, if

regular in configuration, shall not be taken as less than 80 percent of Vs(equation

2.8b), nor less than the limits imposed to Vs as prescribed in the Equivalent Static

Method.

Exception : The design lateral shear force on the structure above the isolation

interface, if regular in configuration, may be taken as less than 80 percent of Vs,

but not less than 60% of Vs, provided time history analysis is used for design of the

structure.

(2)The design lateral shear force on the structure above the isolation interface, if

irregular in configuration, shall not be taken as less than Vs (equation 2.8b).

2.3 Application to Sliding Systems

The design methods of SEAOC, as described in Section 2.2, refer generally to all iso

lation systems. In interpreting the design formulae for a certain isolation system, one has to

account for those parameters that configure the relation between the displacement and the

developed force, for the specific isolation system.

In the case of sliding isolation systems, complications occur between the displacement

of the system and the developed forces. They are attributed to the variation of the coefficient

of friction with respect to the velocity of sliding. For the Friction Pendulum System (FPS),

the force developed is equal to the combination of the mobilized frictional force and the

restoring force which develops as a result of the induced rising of the structure along the

2-14

spherical surface. (For further details on the FPS, see Section 4.1.) Figure 2-2 shows the ideal

force-displacement loop for the Friction Pendulum System. The dotted extended lines describe

the behavior ofthe FPS when the coefficient offriction has a constant value, fmax, independent

of the velocity of sliding. The effective stiffness of the isolation system is then defined as

follows:

w WK =f -+-

elf max D R

where,

fmax =maximum value of the coefficient of friction at high velocity of sliding.

W = weight of the structure.

D = maximum displacement of the isolation system.

R = radius'of curvature of the FPS bearings.

The effective damping, [3, is evaluated from equation 2.5 with the area A being:

A = 4DfmaxW

(2.9)

(2.10)

By substituting equation 2.10 to 2.5 and setting the value of Kerr equal to Kmax, we have:

2( f max )f3 = - D

n f max + Ii(2.11)

The period T of the isolation system is provided by equation 2.4, which for Keff equal to Kmin

and after using equation 2.9 yields:

T= 2n1

f g+gmaxi) R

(2.12)

The design displacement for the Friction Pendulum System is then calculated by equation

2.1, where the terms Band T are estimated by an iteration procedure through equations 2.11

and 2.12 and Table 2.4. The base shear is finally estimated by combining equations 2.8a and

2.9 (1.5 reduction factor is omitted):

2-15

DISPL.

wfmax W + liD

t

FORCE

f max W L_-==:::::::rC'

D-DL ~:::::....---=----+_----.-

FIGURE 2-2 Ideal force-displacement loop for the Friction Pendulum System.

2-16

Vb DW = f max + R (2.13)

The structure shear, V s is again given by equation 2.13 (without the RWI factor). It

should be noted that in developing the above equations, it has been assumed that the effective

stiffness, Kerr, does not change between a minimum, Kmin' and a maxirimm, K max, value. In

fact, this behavior has been observed in tests (Mokha et aI, 199Gb and 1991), in which the

stiffness properties of FPS bearings remained unchanged under repeated testing.

2-17

SECTION 3

TECHNICAL APPROACH· OVERVIEW

In the previous section, the requirements specified by SEAOC to estimate the design

values for an isolation system were introduced. According to SEAOC, a rigorous dynamic

analysis is required for all, or virtually all the isolated buildings, but the predicted response

values should be subjected to certain limitations, also specified by SEAOC.

The lack of response data have prompted analyses to verify the SEAOC design

requirements. Specifically, the work by Kircher and Lashkari, 1989, has been reported. In

their report, an evaluation of SEAOC requirements was attempted through a series of non

linear dynamic analyses of isolated structures. These analyses examined the behavior of a

rigid structure supported by bearings which exhibited bilinear hysteretic behavior and was

excited by various earthquake motions. Statistical quantities, such as the mean and the

standard deviation values, provided a measure of the level and inherent variation of response

parameters as a function of the variation in the ground motion. In this way, a basis for judging

the validity and applicability of SEAOC design requirements was provided.

A similar approach is attempted in this report. By concentrating on a class of sliding

seismically isolated structures, and performing dynamic analyses undervarious considerations,

a set ofnonlinear response data was obtained. This data enabled comparisons and conclusions

to be developed for the SEAOC procedures.

The adopted isolation system for this study is the Friction Pendulum System (Zayas et

aI, 1987, Mokha et aI, 1990b and 1991). This is a sliding isolation system where nonlinearity

betweenthe displacements and the developed forces exists. The performed analyses accounted

for the nonlinear behavior ofthis isolation system. The dependence ofthe coefficient offriction

at the frictional interface to the velocity of sliding and the bi-directional interaction of the

3-1

forces at each isolation bearing, all properties of sliding isolation systems, were also taken

into account. In this way, it was indicated that the performed analyses were accurate enough

for the prediction of response of the examined cases.

In this study, two isolated structure models were used, which were considered to rep

resent buildings exhibiting stiff and flexible superstructure behavior. Two structures were

selected: 1 - story and an 8 - story. A mass eccentricity of the order of 5% was decided. These

also provide the investigation of the potential of torsional response of the base ofthe isolated

structure, as a function of the floors that the structure carries. Further, the increased values

of the displacements due to torsional effects are compared to equation 2.6 that SEAOC

introduces for defining the Total Design Displacement, accounting for torsion.

A total of three different designs of the isolation system was examined in this study

and the differentiation between them is based on their properties such as the maximum

coefficient of friction, fmax, and the radius of curvature, R, of the concave sliding surface. An

analytical description of the FPS system and the values for the above properties selected for

this study is made in Section 4. The combining of different values for fmax and R (see Section

4.2.2) was done to create a group of designs (a total of three) with combined strong or weak

frictional force and restoring force. In this way, two different FPS systems always had a common

value, which could be either their maximum coefficient of friction or their radius of curvature.

This provides the reader with the ability to further compare the dynamic analysis results with

the SEAOC procedures, and also the dynamic analysis results between them.

Four different approaches were adopted in this study for the evaluation of SEAOC

design code requirements. The first one, which is developed in Section 5, proceeds to the

comparison of SEAOC static procedure to response values recorded during shake table tests

(extrapolated to prototype scale). In this way, the basis for judging SEAOC requirements is

provided through directly recorded response values of structures as if they were excited with

real earthquake motions.

3-2

All the following approaches rely on a dynamic analysis procedure, which accounts for

the properties of the FPS, as described above. The earthquake motions were all generated or

scaled (from real records) to correspond to Seismic Zone 4. This zone was selected since it

is the zone of highest seismicity and is where most isolated structures have been or will be

constructed.

The second approach (see Section 6) utilizes artificially generated earthquake motions

and examines the behavior of the structures under this excitation. The records were generated

to be compatible with the design spectra specified in SEAOC. In this way, earthquake motions

were also obtained to correspond to soil type S3 (soft soil sites), since no real records for those

sites were currently available. For every one of the site conditions under interest (Sl, S2, S3

soil types), three corresponding earthquake motions were generated. In this way, for every

combination of isolation system, superstructure and soil site, three identical analyses were

performed which examine the behavior of the structure under excitation.

The third approach is based on the work done by Kircher and Lashkari, 1989 described

in the beginning of this section. The basis for providing a statistical evaluation analysis was

to examine the same structure - isolation system model under excitation with different

earthquake motions that all corresponded to the same soil site. Under these conditions, sta

tistical quantities like the mean and the standard deviation values were calculated and

reported. The scaling of the records was initially based on both Peak Ground Acceleration

(PGA) and Peak Ground Velocity (PGV). As explained in Section 7, the study showed that

scaling according to PGAwas not appropriate and reliable for use in the analyses. Accordingly,

the effort was concentrated only in the case of scaling based on PGV.

The fourth approach (Section 8) implements SEAOC procedures when dynamic

analysis is to be made. The earthquake motions are selected and scaled among those used in

the statistical evaluation approach. A total of six pairs of scaled earthquake motions was

applied and examined.

3-3

The intent of this study is to create a set ofdata from which comparisons and evaluations

can be made for SEAOC requirements for sliding isolated structures. By selecting four dif

ferent, and all acceptable approaches to the problem, the predicted results, comparisons and

conclusions contain a desirable and sufficient level of reliability and validity.

3-4

SECTION 4

STRUCTURE AND ISOLATION SYSTEM MODELS

The major intent of this study is to create, using a series of nonlinear analyses, a col

lection of results upon which comparisons and evaluations can be made on the response of

sliding isolated structures with rigid and flexible superstructure. In this work, a certain type

of sliding isolation system, the Friction Pendulum System (FPS) is examined in correlation

with two different types of superstructure models. These models were configured appropri

ately, and represent isolated buildings that exhibit a relatively rigid and flexible superstructure

behavior.

The nonlinear analyses were performed using the 3D-BASIS program (Nagarajaiah

et aI, 1989). This program utilizes special modeling options that account for the behavior of

sliding isolation systems.

4.1 Superstructure Configuration

The structure - isolation system models used in this study were representative of one

and eight story moment resisting frames of rectangular configuration. In both cases, the

superstructure consisted in plan of four bays by eight bays with each bay measuring 20 feet

by 20 feet. One FPS isolator was placed at the intersection of the bays, for a total of45 isolators.

Floor height was 12 feet.

The one - story superstructure had a fundamental period of 0.2 seconds, whereas the

eight - story superstructure had a period of 1.14 seconds. These values are representative of

moment resisting frames. The weight of each floor was 1280 kips (based on a combined dead

and seismic live load of 100 psf). The distribution of mass on each floor was assumed to be

asymmetric so that an eccentricity of the order of5%of the longest plan dimension was created

4-1

in the longitudinal direction. Each story had identical stiffnesses in the two orthogonal

directions. In the eight - story building, the first three stories had the same stiffness, the next

three had 0.75 times the stiffness of the first three stories, and the last two had half the stiffness

of the first three stories. The distribution of stiffnesses to the various story elements was

selected in such way as to result in a torsional period in the absence of eccentricities of 0.58

times the translational period. The superstructure stiffness matrix was constructed in a shear

type representation with a diagonal mass matrix.

The properties of each structural system are summarized in Tables 4.1 and 4.2. The

dynamic characteristics, frequencies and mode shapes of the two systems are presented in

Tables 4.3 and 4.4. It should be noted that the fundamental period of the two structures is

slightly different than 0.2 and 1.14 sees, respectively. This is caused by the mass eccentricity.

In the dynamic analysis of the 8 - story structure, twelve out of twenty four modes were

accounted for. The other twelve modes corresponded to periods less than 0.16 seconds and

their contribution was assumed insignificant.

4.2 Isolation System

4.2.1 Description

Sliding isolation systems utilize sliding interfaces (usually Teflon - steel interfaces) to

support the weight of the structure. These interfaces provide little resistance to lateral loading

by virtue of their low friction. Recentering capability is provided by a separate mechanism.

In the case of the FPS, the isolated structure is supported by bearings, each one con

sisting of an articulated slider on a spherical concave surface. A typical section of an FPS

bearing is shown in Figure 4-1. The slider is faced with a bearing material which, when in

contact with the polished metal spherical surface results in a maximum coefficient on friction

on the order of 0.1 or less at high velocity of sliding and a minimum friction coefficient of the

order of 0.05 or less at very slow velocity of sliding. This dependency of the coefficient of

4-2

TABLE 4.1 Properties for 1 . story isolated structure.

Story Weight Rotational Stiffness Rotational Eccentricity/ (kips) Inertia (kipsfm) Stiffness (ft)

Floor (kips-in-s~) (kips-inch)xlOOO Longitudinal Transverse

1 1280 1272642.5 3270.958 3733792.62 8 0

Base 1280 1272642.5 8 0

TABLE 4.2 Properties for 8 . story isolated structure.

Story Weight Rotational Stiffness Rotational EccentricityI (kips) Inertia (kipsfm) Stiffness (ft)

Floor (kips-in-sec2) (kips-inch)

xlOOO Longitudinal Transverse

8 1280 1272642.5 1700.898 1997933.76 8 0

7 1280 1272642.5 1700.898 1997933.76 8 0

6 1280 1272642.5 2551.347 2996900.64 8 0

5 1280 1272642.5 2551.347 2996900.64 8 0

4 1280 1272642.5 2551.347 2996900.64 8 0

3 1280 1272642.5 3401.796 3995867.52 8 0

2 1280 1272642.5 3401.796 3995867.52 8 0

1 1280 1272642.5 3401.796 3995867.52 8 0

Base 1280 1272642.5 8 0

4-3

TABLE 4.3 Dynamic characteristics of 1- story superstructure (including 5% mass eccentricity).

Mode

Floor 1 2 I 3 IL T Rotational L T Rotational L T Rotational

Component Component Component Component Component Component Component Component Component

1 0.000 0.547 6.898E~5 0.549 0.000 0.000 0.000 -0.0427 8.837E-04

Period (sees)

0.201 0.200 0.116

Frequency (Hz)

4.970 4.998 I 8.637 IModal damping ratio assumed in analyses

0.03 0.03 I 0.03 I

4-4

TABLE 4.4 Dynamic characteristics of 8 • story superstructure (including 5% masseccentricity). Modes higher than the 9th are not presented.

Mode

Floor 1 2 3L T Rotational L T Rolational L T Rotatiooal


8 0.000 0.285 3.440E-05 0.286 0.000 0.000 0.000 -0.0213 4.598E-04

7 0.000 0.268 3.237E-05 0.269 0.000 0.000 0.000 -0.0200 4.326E-04

6 0.000 0.235 2.842E-05 0.236 0.000 0.000 0.000 -0.0176 3.798E-04

5 0.000 0.204 2.466E-05 0.205 0.000 0.000 0.000 -0.0153 3.296E-04

4 0.000 0.165 1.993 E-05 0.166 0.000 0.000 0.000 -0.0124 2.664E-04

3 0.000 0.119 1.442E-05 0.120 0.000 0.000 0.000 -0.0089 1.927 E-04

2 0.000 0.082 0.986E-oS 0.082 0.000 0.000 0.000 -0.0061 1.317 E-04

1 0.000 0.041 O.SooE-oS 0.042 0.000 0.000 0.000 -0.0031 0.668E-04

Period (sees)

1.147 1.140 II 0.651

Frequency (Hz)

0.872 0.877 1.537

Modal damping ratio assumed in analyses

0.03 0.03 0.03

4-5

TABLE 4.4 Continued.

Mode

Floor 4 5 6L T ROlatiooal L T ROlatiooal L T ROlatiooal

Cootponem Cootponent Cootponent Cootponent Cootponent Cootponent Component Cootponent Component

8 0.000 -0.290 -3.505 E-05 -0.291 0.000 0.000 0.000 0.236 2.850E-05

7 0.000 -0.165 -1.989 E-05 -0.166 0.000 0.000 0.000 -0.023 -0.279E-05

6 0.000 0.032 0.386E-05 0.032 0.000 0.000 0.000 -0.257 -3.101 E-05

5 0.000 0.154 1.858 E-05 0.154 0.000 0.000 0.000 -0.225 -2.713 E-05

4 0.000 0.231 2.795E-05 0.232 0.000 0.000 0.000 -0.028 -0.034E-05

3 0.000 0.242 2.926E-05 0.243 0.000 0.000 0.000 0.189 2.283 E-05

2 0.000 0.198 2.392E-05 0.199 0.000 0.000 0.000 0.248 2.996E-05

1 0.000 0.111 1.341 E-05 0.111 0.000 0.000 0.000 0.171 2.065 E-05

Period (sees)

0.424 H 0.422 0.266

Frequency (Hz)

2.357 H 2.371 3.756


0.03 H 0.03 0.03

4-6

TABLE 4.4 Continued.

Mode

Floor 7 8 9L T Rolalional L T RowiOllal L T Rotational


8 0.237 0.000 0.000 0.000 0.022 4.684E-04 0.000 -0.223 -2.692E-05

7 -0.023 0.000 p.OOO 0.000 0.012 -2.659 E-04 0.000 0.254 3.063 E-05

6 -0.258 0.000 0.000 0.000 -0.002 -O.516E-04 0.000 0.188 2.270E-05

5 -0.225 0.000 0.000 0.000 -0.012 2.483 E-04 0.000 -0.124 -1.493 E-05

4 -0.028 0.000 0.000 0.000 -0.017 3.735 E-04 0.000 -0.259 -3.129 E-05

3 0.189 0.000 0.000 0.000 -0.018 3.911 E-04 0.000 -0.025 -0.305 E-05

2 0.249 0.000 0.000 0.000 -O.Q15 3.197 E-04 0.000 0.177 2.138 E-05

1 0.171 0.000 0.000 0.000 -0.008 1.792 E-04 0.000 0.190 2.297E-05

Period (sees)

0.265 D 0.241 0.191

Frequency (Hz)

3.778 4.154 5.241


0.03 0.03 0.03

4-7

i'" 00

AR

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IDE

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ING

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AV

EC

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UR

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1T

ypic

alse

ctio

no

faF

PS

bear

ing.

friction on velocity is a characteristic of Teflon based materials as described by Mokha et aI,

1988 and 1990a. The FPS bearing acts like a fuse which is activated only when the earthquake

forces overcome the minimum value of friction. When set in motion, the bearing develops a

lateral force equal to the combination of the mobilized frictional force and the restoring force

which develops as a result of the induced rising of the structure along the spherical surface.

This restoring force is proportional to the displacement and the weight carried by the bearing

and is inversely proportional to the radius of curvature of the spherical surface. Accordingly,

the system has the following important properties:

(1)Rigidity for forces up to 0.05 times the weight.

(2)Lateral force which is proportional to the weight carried by the bearing. As

a result of this significant property, the lateral force develops at the center

of the mass, thus eliminating eccentricities at the isolation system level.

(3)Period of vibration in the sliding mode which is independent of the mass of

the structure and related only to the radius of curvature of the spherical

surface.

In addition to these properties, the Friction Pendulum System has other properties

common to sliding isolation systems, such as low sensitivity to the frequency content of

excitation and high degree of stability (Mokha et al 1988, Constantinou et al 1990b).

The lateral force that develops at an FPS bearing follows with excellent accuracy the

following relationship:

(4.1 )

in which W is the weight carried by the bearing, R is the radius of curvature of the bearing,1-L

is the coefficient of friction mobilized during sliding and Vb is the bearing displacement. The

first term in equation 4.1 corresponds to the stabilizing tendency of pendulum action of the

4-9

FPS bearing with the quantity W/R representing the slope of the force-displacement rela

tionship (see also Fig. 2-2). Accordingly, the period of vibration of the structure in its rigid

body condition and with friction neglected is:

(R) 1/2

T b = 2n g (4.2)

From experimental measurements, it was found that the coefficient of friction follows the

relation below, which was proposed by Constantinou et aI, 1990b:

(4.3)

in which fmax and (fmax - Df) are the maximum and minimum mobilized coefficients of friction

respectively, and a is a parameter that controls the variation of the coefficient with the velocity

of sliding.

It should be noted that Tb represents the period of free vibration of an isolated rigid

structure. This is not the same as period T, equations 2.4 and 2.12 which is a ficticious quantity.

4.2.2 Isolation System Properties.

Each of the 45 isolators had identical properties of coefficient of friction and radius of

curvature. The combinations used in this study are summarized in Table 4.5.

The axial load on each bearing was different due to the 5% mass eccentricity. Table

4.6 presents the portion of total weight WT carried by each of the 45 bearings. For numbering

of the bearings, refer to Figure 4-2. WT equals 2560 kips for the 1 - story structure and 11520

kips for the 8 - story '5tructure.

Each of the 45 FPS bearings was modeled by a bi-directional sliding element which

conforms to the law of equation 4.3 and by a spring element of stiffness equal to W/R where

W is the axial load carried by the bearing (see Table 4.6).

4-10

TABLE 4.5 Isolation System Properties.

Frictional properties GeometricalIsolation Properties

SystemNo# fmax fmin=fmax-Df(se~/in)

R Tb(in) (sec)

1 0.10 0.05 0.9 39.132 2

2 0.05 0.025 0.9 88.048 3

3 0.10 0.05 0.9 88.048 3

TABLE 4.6 Axial load carried by each one of the bearings, for 1 • story and 8 • story isolatedstructure, as a proportion of the total weight WT of the structure.

Bearing Load/WTNo#

1 0.00625

2 0.0125

3 0.0125

4 0.0125

5 0.015625

6 0.01875

7 0.01875

8 0.01875

9 0.009375

10 0.0125

11 0.025

12 0.025

13 0.025

14 0.03125

15 0.0375

16 0.0375

17 0.0375

Bearing Load/WTNo#

18 0.01875

19 0.0125

20 0.025

21 0.025

22 0.025

23 0.03125

24 0.0375

25 0.0375

26 0.0375

27 0.01875

28 0.0125

29 0.025

30 0.025

31 0.025

32 0.03125

,33 0.0375

34 0.0375

Bearing Load/WTNo#

35 0.0375

36 0.01875

37 0.00625

38 0.0125

39 0.0125

40 0.0125

41 0.015625

42 0.01875

43 0.01875

44 0.01875

45 0.009375

4-11

9 18 27 _36 45-I I I L

8 117 126 135 44 LTn---,- -~ - -, --I

1 I I7 -Jl~ _ ~5_ ~3!. - 1

43t- -

I I I

6 115 124 I 42,-,3~ _ t~--,--r co

I ~9. I ~t~ __~14-_ .13_ ~3!. _ 41

TI I I

4 113 122 I40-,3!.. _ tn---,--r-

0

I I I(!)....

~ _ -Jl!. _ .u1 _ ~3!L _ tII

39 '0N

I I I l<

coI I I 38.~ _ ...,1!.. _ ~O _ ...,22... _ t

I I I1 110 119 128 37

14

4 X 20'= 80' -I

FIGURE 4-2 Plan view of the base of the building models used in the analyses andnumbering of the bearings.

4-12

4.2.3 SEAOC Design Values for the Isolation System Properties

The intent ofthis study is to perform a series ofnonlinear dynamic analyses and evaluate

the response of isolated structures located in Seismic Zone 4 (Z =0.4), 15km or greater from

an active fault (N =1), with various soil types (coefficient S) and supported by the Friction

Pendulum System. These response values are compared with the design values that SEAOC

specifies through a static analysis procedure. For this comparison, the SEAOC static analysis

procedure was applied and the calculated isolation system displacements and base shear force

values are listed in Table 4.7. The response quantities are presented as function of the soil

type and isolation system properties (radius of curvature, R, and maximum coefficient of

friction, fmax).

4.3 Program 3D·BASIS

The nonlinear analysis program 3D-BASIS (Nagarajaiah et aI, 1989) was used in all

the analyses made in this study. This program was developed as an efficient tool for analysis

of base-isolated structures, in which the superstructure remains elastic during the earthquake

and any nonlinear behavior is restricted to the isolation system. This program offers special

options for the mathematical modeling of isolation systems, such as linear elastic, viscous,

hysteretic and frictional elements with uni-directional and bi-directional behavior. All these

elements are located at the base of the structure. The analysis methodology is based on the

following assumptions:

(1) Superstructure remains elastic.

(2)Each floor has three degrees of freedom, X and Y translations and rotation

about the center of mass of the floor.

(3)There exists a rigid slab at the base level that connects all isolation elements.

The three degrees of freedom at the base are attached to the center of mass

of the base.

4-13

TABLE 4.7 Displacement and base shear over weight ratio values according to SEAOC staticanalysis procedure for use in comparison with the results of nonlinear dynamic analysesperformed in this study.

Sliding Isolation System Properties

SoilR=39.132 in R=88.048 in R=88.048 in(Tb=2 sec.) (Tb= 3 sec.) (Tb= 3 sec.) Type

fmax=O.10 fmax=O.05 fmax=O.lO

D (in) VJW D (in) VJW D (in) VJWSI

2.809 0.172 5.277 0.110 3.113 0.135 Rock/Stiff Soil TypesCoefficient S = 1.0

S25.717 0.246 10.189 0.166 6.320 0.172 Medium Soil Sites

Coefficient S =1.5

S39.057 0.331 16.307 0.235 10.553 0.220 Soft Soil Sites

Coefficient S = 2.0

4-14

(4)Since three degrees of freedom per floor are required in the three

dimensional representation of the superstructure, the number of modes

required for modal reduction is always a multiple of three. The minimum

number of modes required is three.

(S)The isolation system is rigid in the vertical direction and torque resistance

of individual isolation pads is neglected.

4.4 Comparison of Results Obtained by 3D-BASIS to Other Computer Programs.

Verifications were performed to compare the results from the 3D-BASIS program to

a rigorous mathematical solution and to the DRAIN-2D program (Powell, 1973), to ensure

the accuracy of the predicted results. For this reason, the response of the structural systems

developed in Section 4.1 is evaluated for three different earthquake components by the three

procedures. It should be noted that in order to comply to the limitations imposed by the

programDRAIN-2D (2-Dimensional consideration only), the selected isolated buildingswere

subjected to only one horizontal earthquake component. By applying this component in the

longitudinal direction (L-Direction) only, no mass-eccentricity effects could be considered.

Accordingly, the accidental eccentricity in the longitudinal (L) direction was set equal to zero

(see Section 4.1). Therefore, the verification analyses were confined to only a 2-Dimensional

consideration. A total of 18 analyses were performed. The motions used in the comparison

study are scaled records of earthquakes, as explained in Section 7.1

4.4.1 Comparison with Rigorous Mathematical Solution

4.4.1.1 Presentation of the Analytical Method

The response of the structures is analyzed using a lumped mass model. The equations

of motion of the superstructure are:

4-15

[M] {U} + [C] {V} + [K] {U} = -[M] {l} (V 9 + U b) (4.4)

in which {U} is the vector of floor displacements with respect to the base, Ub is the base

displacement with respect to the ground, and Ug is the ground displacement. A dot denotes

differentiation with respect to time. Furthermore, [M], [C], and [K] are the mass, damping

and stiffness matrices of the superstructure, respectively.

The equation of dynamic equilibrium of the entire system in the horizontal direction

is:

N

I mi(U i + Ub + Ug) + mb(U b+ U g) + F b= 0i- 1

( 4.5)

in which mi, i=1,...,N are the floor masses, mb is the base mass and Fb is the force mobilized

at the isolation interface. This force is given by:

(4.6)

in which ~ is described by equation 4.3, W is the weight of the structure and Z is a variable

governed by the following differential equation (Constantinou et aI, 1990b):

(4.7)

in which Y is the "yield" displacement (0.01 inches) and ~ + Y = 1. Z replaces the signum

function in equation 4.1 and is used to account for the conditions of separation and reat

tachment. Equations 4.4 to 4.7 are reduced to a system of first order differential equations

and numerically integrated using an adaptive integration technique with truncation error

control which is appropriate for stiff differential equations (Gear, 1971). This approach has

been described by Mokha et al 1990b.

4-16

4.4.1.2 Comparison

As shown in Figures 4-3 to 4-8, there is virtually no difference in the response that was

computed from the two methods. Program 3D-BASIS is capable of reproducing thoroughly

and capturing every detail of the response of the base displacement of the models used, as it

was predicted by the rigorous mathematical solution.

4.4.2 Comparison with the DRAlN-2D Program

Program DRAIN-2D represents a standard nonlinear dynamic analysis computer

program used by many structural engineers. It has been extensively tested and verified. The

behavior of the FPS bearings could not be accurately modeled by DRAIN-2D, however, it

was compared to 3D-BASIS because of its wide acceptance.

In modeling the frictional behavior with program DRAIN-2D, the bilinear hysteretic

element was used. In this respect, the velocity dependence of the coefficient of friction was

not accounted for. In the bilinear hysteretic element, the yield force was selected to be equal

to fmaxWand the yield displacement to be 0.01 inches. The post yielding stiffness was selected

to be equal to WfR. All bearings were lumped into a single element. The extremely small

yield displacement required an accordinglyvery small time step of integration. Stable solutions

were achieved with a time step of 0.002 seconds.

Figures 4-3 to 4-8 compare the base displacement time histories calculated from the

two programs. The results demonstrate that 3D-BASIS and DRAIN-2D yield the same or

almost the same displacement time histories. Some small differences in the details of the

time histories are attributed to the velocity dependence of the coefficient of friction which

was not accounted for in the DRAIN-2D solution.

Based on the above observation it may be concluded that:

(1)The velocity-dependent behavior ofTeflon-based sliders is of secondary importance

4-17

(a)

(i) 2.0 .....----------------:--------SC-L-E'OW SAN FERNANOO (220) S90W PGV AI 1-STORY STRUCTURE / Tiso = 2 SEC / Fmax = 0.10U 1.5Z PGV = 13.1 IN/SEC

'-' 1.0I-r5 0.5Lt5 0.0 r-J..¥\:1'r~:-:--_:~~:;:::====::;::::::::::=:::;;:::::::::;:::.4

~ -0.5U10-1.0

WU1 -1.5 -- 3D-BASIS<{ - - - 20 RIGOROUS ANALYSISm _2.0 +-,r-r-"T'"'"T~--.-T"T..,._,_,_r_r_"'T"""'T_.__r_r_r_r....,r_r,....,...,.,_,_IT"..,.-,_,_".."'T"""'T--r-I

o 5 10TIME (SEeS)

(b)

15 20

--.U1 2.0 -r-------------------------.,W SAN FERNANDO (220) S90W PGV SCALEDI 1 51-STORY STRUCTURE I Tiso = 2 SEC I Fmox = 0.10U .Z PGV = 13.1 IN/SEC'-J 1.0I-~ 0.5Lt5 0.0 r--~~~-~-=--~J=:~~:==::;;::;;::;;;::;;:::;;;:::;~.,..S-9-

~.·-0.5U10-1.0

wU1 -1.5 -- 3D-BASIS«m _2.0 -h-r-r--"T-r-""T0......R_A.-INT"T-....--.2......Dr-r-.,.-,....--.......r-T"""'T"""T...,....,r-r-"T'"'"T-.-.-r-r-r-,...,.~r-r-,....,--i

a 5 10TIME (SEeS)

15 20

FIGURE 4-3 Comparisons of base displacement time histories obtained by programs3D-BASIS, DRAIN-2D and a rigorous analysis program for 1 . story structure subjected toSan Fernando (220) S90W earthquake component in the longitudinal direction. Scaling ofthe record is based on PGV according to Table 7.4

4-18

(a)

U1 2.0 ...,------------------------,W SAN FERNANDO (220) S90W PGV SCALEDI 5 a-STORY STRUCTURE / Tise = 2 SEC / Fmox = 0.10U 1.Z PGV = 13.1 IN/SEC"--/ 1.0I-

~ 0.5~t3 0.0

«0= -0.5U10-1.0

WU1 -1.5 -- 3D-BASIS

(ij _2.0 +-,-r-r--r--r2-,0;-r-R,1G-r0,R-,O_U,S,A,N,A-yL,YS,'"ST""'T"-r--;r-r-r-r....-r'O.",...,.-,-r-r""""""'rlo 5 10

TIME (SECS)15 20

(b)

U1 2.0 ...,--------)---------------E-O'w SAN FERNANDO (220 S90W PGV SCALI a-STORY STRUCTURE / rise = 2 SEC / Fmax = 0.10U 1.5Z PGV = 13.1 IN/SEC

201510TIME (SECS)

I-~ 0.5~t5 0.0

~ -0.5U10-1.0

I~ -1.5 -_ 30-BASI~« - - -DRAIN - 20m _2.a +-................-r"""T""'"'"1"'"'""T"""r-r-""T"""T-r-T""'"'T'""'T"'"'T-r--;,.,r-r.,.-,,,.,,,...,.-,-r-rT""'T"-r--;r-r-r-r..,.--j

o 5

......., 1.0

FIGURE 4-4 Comparisons of base displacement time histories· obtained by programs3D-BASIS, DRAIN.2D and a rigorous analysis program for 8 - story structure subjected toSan Fernando (220) S90W earthquake component in the longitudinal direction. Scaling ofthe record is based on PGV according to Table 7.4

4-19

(a),,-...

4.0(f)W IMPERIAL VALLEY EL CENTRO (117) S90W PGV SCALEDI l-STORY STRUCTURE / Tise = 3 SEC / Fmax 0.10U

PGV = 18.9 IN/SECZ........" 2.0f-Zw2w 0.0u~0..(f)

0-2.0

W(f) --3D-BASIS« - - - 20 RIGOROUS ANALYSISco

-4.00 5 10 15 20

TIME (SECS)

(b),,-...(f) 4.0 ~ ----------------------,W IMPERIAL VALLEY EL CENTRO (117) S90W PGV SCALEDG 1-STORY STRUCTURE / Tise = 3 SEC / Fmox = 0.10Z PGV = 18.9 IN/SEC

20

-,. -

10 15TIME (SECS)

5

fZw2~ 0.0 -j-..............L--r.~rt-='\1----1::T""d,;::=jf-\------------I

~0..(f)

0-2.0

w(f)«III -4.0 -t--,...,...,rr-rrr-rTT"T"T..,.-,.,.,...,...,rr-rrr-rTT"T"T,....,.,.,.,...,rr-rrT""'T"T'"'r'"T""T-rl

o

........" 2.0

FIGURE 4-5 Comparisons of base displacement time histories obtained by programs3D-BASIS, DRAIN-2D and a rigorous analysis program for 1 - story structure subjected toImperial Valley EI Centro (117) S90W earthquake component in the longitudinal direction.Scaling of the record is based on PGV according to Table 7.4

4-20

(a)

2015

IZW~W 0.0 -t-------+------.~~:O-+---_+----------__jU«--I0...(f)

0-2.0

w(f) -- 3 -BASIS«en _4.0 -+-r-.."---y-;-,2rD,,R,IG,O,R,O,U,S.....,A...,N.....,A,LY,Sr'S"T-r",...,...""rr""""-'''''''''-'---ri

o 5 10TIME (SEeS)

,--...(f) 4.0 ~-------------------------,w IMPERIAL VALLEY EL CENTRO (117) S90W PGV SCALEDG 8-STORY STRUCTURE / Tise = 3 SEC / Fmax = 0.10Z PGV = 18.9 IN/SEC......., 2.0

(b)

205 10 15TIME (SEeS)

IZW~W 0.0 -+--'---+--~.......,.--/..-.::.~f__--_+_-----------1U

:50...(f)

0-2.0

W(f)

«OJ -4.0 -+-T.....,...,--r-"lr-T"".-r--r-r-......-r-r-r-r-r.............,....,r-r-..-.-...-r.,....,--r-T-r-T-.-.r-r-r-r-r-r-T""T"......-r....-l

o

,--...(f) 4.0 ...,..--------------------------,W IMPERIAL VALLEY EL CENTRO (117) S90W PGV SCALEDG 8-STORY STRUCTURE / lise = 3 SEC / Fmax = 0.10Z PGV = 18.9 IN/SEC , .... - \......., 2.0 \ __ ,

FIGURE 4-6 Comparisons of base displacement time histories obtained by programs3D-BASIS, DRAIN-2D and a rigorous analysis program for 8· storystructure subjected toImperial Valley EI Centro (117) S90W earthquake component in the longitudinal direction.Scaling of the record is based on PGV according to Table 7.4

4-21

-.. ...---------------------:--::~~~ 12.0 EUREKA (023) N44E PGV SCALEDI 1-STORY STRUCTURE / Tiso = 3 SEC / Fmox = 0.10~ 8.0 PGV = 26.0 IN/SEC

~ 4.0W:2w 0.0 -!---------'-~-l~--------~---___ju:5B1 -4.0

oW -8.0(/) -- 3D-BASIS<r: _ - -20 RIGOROUS ANALYSISm -1 2.0 -h--r"1.,...,"':""'...,.-,....,-,....,-r-rTl'-r-r..."....,.,.--rT--rT..,..-,-,..,rrr-r--r-r,....,-r-rrr""""

o 5 10 '5 20TIME (SEeS)

(b)-..

12.0(/)EUREKA (023) N44E PGV SCALEDw

I 1-STORY STRUCTURE / Tiso = 3 SEC / Fmox = 0.10(.) 8.0 PGV = 26.0 IN/SEC:z'--'

I- 4.0Zw::::E - - - --W 0.0u:sCl -4.0f./)

0

W -8.0f./) --3D-BASIS« - - -DRAIN - 20CD

-12.0200 5 10 15

TIME (SEeS)

FIGURE 4-7 Comparisons of base displacement time histories obtained by programs3D-BASIS, DRAIN-2D and a rigorous analysis program for 1- story structure subjected toEureka (023) N44Eearthquake component in the longitudinal direction. Scaling of therecord is based on PGV according to Table 7.4

4-22

§' 12.0 --r-"E-U-RE-K-A-(0-2-3-)-N-4-4-E------------=P~GV~S:-:C-:-A:-::LE::lD

I 8-STORY STRUCTURE / Tiso = 3 SEC / Fmax = 0.10~ 8.0 PGV = 26.0 IN/SEC

155 10TIME (SECS)

o

~ 4.0W::::2w 0.0 +------.L-T-+-----\::~'c::I_--=~---:r==~;::::::jU

:50... -4.0(f)

ow -8.0(f) --3D-BASIS<t: _ - -20 RIGOROUS ANALYSISm -1 2.0 -h.....,.....,.........rT""T""'T"T"T-r-r.,-,,..,-r-rr-rT"TT"T-r-r.,-,,..,-rrr-rT"T-rr--r-r...,,.....,rrl

20

(b)

§' 12.0 -r-"E-U-R-EK-A-(0-2-3-)-N-4-4-E------------=p:':GV-:-:S:::C":":AL-:E::'lD

I 8-STORY STRUCTURE / TIso = 3 SEC / Fmax = 0.10~ 8.0 PGV = 26.0 IN/SEC

o 5

~ 4.0W~W 0.0 +-------.L...-1f-+-----t:;i.~=i_-;=;___t--,=~::::::::lU

:551 -4.0

ow -8.0(f) 3D-BASIS<t: - - -DRAIN - 20m -12.0 -h~r-rT'"T"'T"TT"T""T""T_"....,,~T""T"TI"'T"TT"T""T""T-,,"""'T"'~T""T"JT".,..,.""T"T""T""T-r1

10 15 20TIME (SECS)

FIGURE 4-8 Comparisons of base displacement time histories obtained by programs3D-BASIS, DRAIN-2D and a rigotous analysis program for 8· story structure subjected toEureka . (023) N44E earthquake component in the longitudinal direction. Scaling of therecor«i ~ based on PGV according to Table 7.4

4-23

to the calculation of peak isolator displacements, and

(2)Bilinear (non-velocity dependent) elements can be used to accurately calculate the

displacement response of sliding isolation systems.

4-24

SECTION 5

COMPARISON OF SEAOC STATIC PROCEDURE TO SHAKE TABLE TESTS

Experimental data are essential for the verification of simplified design procedures

like the SEAOC static procedure. In this regard, the experimental results from shake table

testing ofsliding isolation systems are utilized (Mokha et aI, 1990b and 1991). Similar attempts

for elastomeric and combined elastomeric - sliding systems have been reported by Chalhoub

and Kelly, 1990 and Griffith et aI, 1988.

5.1 Experimental Setup

5.1.1 Superstructure

The main purpose of the shake table tests carried by Mokha et al 1990b, was to

investigate the feasibility of the Friction Pendulum System in isolating taller buildings with a

large aspect ratio. Shake table tests were performed on a 1/4-scale artificial mass simulation

model ofa six-story steel moment resisting frame. In this model, the ratio ofheight to maximum

distance between bearings was 2.25. The three bay model (Figure 5-1) had a weight of 51.4

kips. The fundamental frequency of the scaled model was 2.34 Hz or 1.17 Hz in prototype

scale. This value is consistent with the behavior of a typical 6 - story moment resisting frame.

The columns of the model were bolted to two heavy W14X90 sections and four bearings were

placed between these beams and the shake table.

5-1

3@

4'=1

2'I"

,I4'

'"'"..

I

FP

SB

EA

RIN

G

L1Y2

x1V2

.X'4

TYR

SH

AK

ET

AB

LE

I....

ItoI

8

... ,7rI

II

I~S3x5.7

~/"

...

/"-.

.TY

R\f

l

<0V

Iw

II~

I/"-I~'2Kips

• NTY

R

FIG

UR

E5-

1M

odel

used

for

shak

eta

ble

test

ing.

5.1.2 Isolation System

The isolation system consisted of four FPS bearings which were placed under the base

of the model at 8 feet distance as shown in Figure 5-1. In this configuration, the aspect ratio

of the height of the model to distance between bearings is 2.25. The radius of curvature R,

was equal to 9.75 inches (39 in. in prototype scale). This radius resulted in a period of 1seconds

( 2 seconds in the prototype scale). Two different bearing materials were used:

(1)A form of woven Teflon under bearing pressure of about 20 ksi. The

frictional properties of this material, when in contact with the polished

metal surface, followed the law of equation 4.3 with fmax = 0.075, Df =

0.035 and a = 1.1 sec/inch.

(2)A material which carries the trade name Techmet B (product of Oiles

Industry Co., Japan). Average pressure at the sliding interface was about

7 ksi. Under these conditions, this material exhibited a higher coefficient

of friction than the other bearing material. The frictional properties of this

material werefmax = 0.095, Df = 0.045 and a = 0.9 sec/inch.

5.1.3 Test Program

The isolated model was tested with six different earthquake motions. The character

istics of these earthquake motions are listed in Table 5.1. The records have significantly dif

ferent frequency content, with Hachinohe and Mexico City being long period motions. The

records were time scaled by a factor of two to satisfy similitude requirements of the quarter

scale model. The time scaled Mexico City motion has a frequency content almost entirely at

1 Hz, which coincides with the rigid body mode frequency of the isolated model.

The earthquake tests were performed at varying peak acceleration levels for each of

the signals. Each earthquake signal was run at increasing levels of peak table acceleration

5-3

TABLE 5.1 Earthquake records used in test program.

PREDOMINANTNOTATION RECORD PEAK ACCEL. FREQ.RANGE MAGNITUDE

(g) (Hz)

El Centro Imperial Valley 0.34 1- 4 6.7SOOE May 18, 1940

Component SOOE

Taft KemCounty 0.16 0.5 - 5 7.2N21E July 21, 1952

ComponentN21E

Pacoima San Fernando 1.08 0.25 - 2 6.4S74W February 9,1971

Component S74W

Pacoima San Fernando 1.17 0.25 - 6 6.4SI6E February 9, 1971

Component S16E

Miyagi- Tohoku Univ. 0.16 0.5 - 5 7.4Ken-Oki Sendai, Japan

EW June 12, 1978Component EW

Hachinohe Tokachi-Oki 0.23 0.25 - 1.5 7.9NS Earthq., Japan

May 161968Component NS

Mexico SCT Building 0.17 0.5 8.1City Seppt. 19, 1985

Component N90W

5-4

until the peak interstory drift reached approximately the value of 0.18 inches or 0.005 times

the story height. This value has been analytically determined to be the limit of the elastic

behavior of the structure.

5.2 SEAOC Static Analysis Procedure

As stated in Section 2, the design displacement formula prescribed by SEAOC is:

D = IOZNSTB

(5.1 )

where T is the effective period of the system and B is a damping related term. Both depend

on the isolation system properties and the displacement of the system. Parameters Z, Nand

S are dependent on the earthquake motion. For comparison of the predictions of equation

5.1 to the experimental results, parameters Z, Nand S must be properly selected.

In the studies of Chalhoub and Kelly, 1990 and Griffith et aI, 1988, parameter S was

selected according to the frequency content of the motion. Product ZN was interpreted as the

velocity related coefficient Av in accordance to ATC 3-06 (ATC, 1978).

The interpretation of product ZNS is different in this study. It is based on equation 5.1

and the 5% spectraof the earthquake motions. For 5% damping, parameter B =1. Accordingly,

the term 10ZNS is the ratio between D and T. Thus, in the displacement spectrum of an

earthquake motion, this ratio is expressed as the tangent of a straight line starting from the

origin of the axes and trying to approximate an ideal spectrum, where proportionality between

the period (T) and the displacement (D) exists.

Accordingly, for the evaluation of the displacements of the model used in the shake

table tests according to the SEAOC equivalent static method, an estimation of the factor ZNS

for the respective earthquake excitations was preceded by applying the above mentioned

concept. Figure 5-2 shows the 5% damping elastic displacement spectra of the earthquake

motions (not scaled in time) that were used in the experiments and the proposed linear ones.

5-5

(a)

EL CENTRO SOOE :100% 150~ 200~

5~ ELASTIC SPECTRA30

ZNS=O.603ZNS=O.804Vi'

~ 25o~

~ 20 ZNS=0.402w::2wo:5 15n..~a<i 10e:t:IoW

~ 5

o " I I Ii' I i II I Ii' II r II' i I I I II I I I i I I I I r I j iii I I Iii' I i II I I i I

o 1 2 J 4 5PERIOD (SEeS)

(b)

TAFT NZ1E :100% 300%5~ ELASTIC SPECTRA

25

IZ

~ 15wo:5n..510go~ 5Vl

2 3PERIOD (SEeS)

4 5

ZNS=O.465

ZNS=O.155

FIGURE 5-2 Displacement spectra for 5% Damping of records used in shake table testing(in prototype scale) and corresponding ZNS values.

5-6

(c)

PACOIMA DAM S74W :100lll511I ELASTIC SPECTRUM

2 3 4 5PERIOD (SEeS)

(d)

PACOIMA DAM S16E :5~

511I ELASTIC SPECTRUM15

Vi' ZNS=O.613wJ:UZ.::::-

!z 10w~wu:5n.V10...J 5<l:a::'-uwn.V1

2 3 4 5PERIOD (SECS)

12

!z 8w~wu:5n.V1o;i 4a::Iuwn.V1

UlWJ:UZ.::::-

FIGURE 5-2 Continued.

5-7

(e)

MIYAGI-KEN-OKI EW :10~ 30~5111 ELASTIC SPECTRA

10

,..... ZNS=0.464Vlwr 8uzc-I-Zw 6:::i!wu:5 ZNS=O.155Q..VlB 4

.J«~I-Uw 2Q..Vl

00 2 3 4 5

PERIOD (SEeS)

(f)

HACHINOHE NS :1O~ 15~

5lII ELASTIC SPECTRA25 ZNS=O.901

,.....VllJJ

G20

2-I-Z~ 15lJJu:5Q..Vlis 10.J«~I-UlJJ 5Q..Vl

2 3 4 5PERIOD (SECS)

FIGURE 5·2 Continued.

5-8

(g)

MEXICO CITY N90W :70l\15~ ELASTIC SPECTRUM

40

54

ZNS=1.162

2 3PERIOD (SECS)

o4CT.......'I"'M;...,..,."T""T'"........-r-r~.....-r-r-r- .........'""T"T""T""T'"............,...,.....,......,,.....,.."T""T'",..,...,...,...,.....,......,M-T"'l""T"".....o

IZW~Wu::s 20a..(/l

15....J«0::t10w0(/l

r--(/lw:x:u~ 30........


5-9

The spectra were constructed from the recorded table motions. The percentage figure in

Figure 5-2 represents the acceleration scaling of the original earthquake record. For example,

the figure 200% implies an increase of the peak ground acceleration of the actual record by

approximately a factor of 2.

The linear spectra were selected so that they give equivalent or conservative results

when compared to the actual spectra in the period range from 1.0 to 2.0 seconds. This range

contains the effective period ofthe tested sliding isloated structure. One should note, however,

that the selection of the ZNS values is rather arbitrary and that several different values could

fit the jagged shape of the test spectra at long periods. In some cases, the ZNS values in this

study compare well with the ZNS values used by Chalhoub and Kelly, 1990 and Griffith et aI,

1988. Table 5.2 compares ZNS values used in those studies and in this study.

The greatest uncertainty in the selected ZNS values occurs in the cases of long period

motions like the Hachinohe and Mexico City motions. The spectra of these motions have a

predominant peak which resembles the spectra of harmonic motions. An appropriate value

of ZNS in these cases could be the one corresponding to a linear spectrum which matches the

actual spectral displacement at the effective period of the isolation system.

5.3 Comparison of Experimental Results and Design Values According to SEAOC Static

Analysis Procedure

Tables 5.3 and 5.4 provide information on the experimental results (extrapolated to

prototype) of the displacement and the base shear coefficient of the tested model. The

respective values according to SEAOC design formulae are also listed. For the calculation of

the SEAOC design values, the procedure described in Section 2.3 was employed. The base

shear over weight ratio was calculated without the 1.5 reduction factor to be consistent with

the experimental value.

5-10

A direct observation can be made on the fact that SEAOC formulae consistently

overestimate the displacement of the isolation system and the base shear coefficient, as they

were recorded during the experiments. This observation is more intent in the case were the

model was excited with long period motions. The ratio of SEAOC displacement to the

experimental value for various earthquakes appears to be larger than those reported by

Chalhoub and Kelly, 1990 and Griffith et aI, 1988 for elastomeric and combined elastomer

ie/sliding isolation systems.

In the case of long period motions, like the Mexico City earthquake, the calculated

SEAOC displacements are considerably larger than the experimental ones. Concentrating

on the case of Mexico City 70% motion (Figure 5-2g), we repeat the calculations with a

different interpretation of the ZNS value. We interpret this value as the one which results in

a linear spectrum that intersects the actual displacement spectrum at the effective period of

the isolation system. For the case of the system with fmax = 0.075 and R = 39 in., several

iterations were needed before arriving at the modified ZNS value of 0.6, effective period T

= 1.67 sees and displacement D = 6.89 in. The linear spectrum for ZNS = 0.6 is shown with

dashed line in Figure 5-2g. The calculated displacement is considerably less than the one

calculated with ZNS equal to 1.162 (Table 5.4). It is still, however, about 1.86 times the

experimental one.

In the case of the base shear coefficient, SEAOC design values are also consistently

conservative to the ones during the experiments. The ratio between the two values is lower

than the ratio of the displacement values and this is attributed to the fact that the displacement

and the base shear coefficient are not straightproportional, but they are rather related through

equation 2.13, where the constant value of fmax mediates. It should be noted, however, that

equation 2.13 (SEAOC formula for base shear in sliding isolation systems) predicts accurately

the experimental results, provided that the experimental value of displacement is used. For

example, if the experimental displacement of 4.92 in. for the El Centro 200% motion (see

Table 5.3) is used in equation 2.13, the result is Vb = 0.22W which is almost exact (0.218W).

5-11

TABLE 5.2 Comparison of the peak acceleration and ZNS values used by Cbalhoub andKelly, 1990 and Griffith et ai, 1988 with the ones used in this study.

This study Other studies

Motion Peak ZNS Peak ZNSAcceleration Acceleration

(g) (g)

ElCentro 0.68 0.804 0.65 0.971SOOE

Pacoima Dam 0.56 0.613 0.50 0.578S16E

TaftN21E 0.53 0.465 0.74 0.825

5-12

TABLE 5.3 Shake table testing results (extrapolated to prototype) for the higher frictionmaterial (fmax =0.095) and comparison to SEAOC design values.

Ratio betweenPeak SEAOC design Experimental SEAOC

Excitation Ground ZNS values (extrapolated to design values andAcceleration prototype) experimental

results

(g) D Vb/W* D Vb/W D IVb/W I(inch) (inch)

EI Centro 0.34 0.402 3.01 0.172 1.58 0.126 1.91 1.37SOOE 100%

EI Centro 0.51 0.603 6.00 0.249 3.05 0.157 1.97 1.59SOOE 150%

EI Centro 0.68 0.804 9.46 0.338 4.92 0.218 1.92 1.55SOOE200%

Taft 0.17 0.155 0.63 0.111 0.45 0.101 1.40 1.10N21E 100%

Taft 0.53 0.465 3.92 0.196 3.57 0.173 1.10 1.13N21E 300%

Miyagiken 0.19 0.155 0.60 0.110 0.30 0.096 2.00 1.15OkiEW100%

Miyagiken 0.57 0.464 3.85 0.194 2.10 0.138 1.83 1.41OkiEW300%

Hachinohe 0.22 0.601 5.89 0.246 2.27 0.152 2.59 1.62NS 100%

Hachinohe 0.36 0.900 11.40 0.387 4.48 0.199 2.54 1.94NS 150%

Pacoima 0.92 0.687 7.25 0.281 5.60 0.203 1.29 1.38S74W 100%

Pacoima 0.57 0.613 6.12 0.252 4.44 0.198 1.38 1.27S16E 50%

* Without 1.5 reduction factor.

5-13

TABLE 5.4 Shake table testing results (extrapolated to prototype) for the lower frictionmaterial (fmax = 0.075) and comparison to SEAOC design values.

Ratio betweenPeak SEAOC design Experimental SEAOC

Excitation Ground ZNS values (extrapolated to design values andAcceleration prototype) experimental

results

(g) D Vb/W * D Vb/W ~I Vb/WI(inch) (inch)

El Centro 0.34 0.402 3.56 0.167 1.73 0.114 2.06 1.46SOOE 100%

El Centro 0.68 0.804 10.94 0.356 7.04 0.243 1.55 1.47SOOE2oo%

Taft 0.17 0.155 0.79 0.095 0.54 0.090 1.46 1.06N21E 100%

Taft 0.55 0.465 4.48 0.190 4.16 0.173 1.08 1.10N21E 300%

Miyagiken 0.19 0.155 0.79 0.095 0.36 0.088 2.19 1.08OkiEW1oo%

Miyagiken 0.56 0.464 4.48 0.190 2.24 0.123 2.00 1.54Oki EW 300%

Hachinohe 0.22 0.601 6.74 0.248 2.35 0.126 2.87 1.97NS 100%

Hachinohe 0.35 0.901 12.84 0.404 5.44 0.201 2.36 2.01NS 150%

Pacoima 0.92 0.687 8.50 0.293 6.08 0.198 1.40 1.48S74W 100%

Pacoima 0.56 0.613 7.00 0.254 5.12 0.195 1.37 1.30S16E 50%

Mexico N90W 0.07 0.664 8.08 0.282 0.18 0.087 .44.89 3.2440%

MexicoN90W 0.11 0.996 15.06 0.461 1.05 0.116 14.34 3.9760%

Mexico N90W/ 0.12 1.162 18.96 0.561 3.70 0.176 5.12 3.1970%

* Without 1.5 reduction factor.

5-14

In this respect, the SEAOC formula for the base shear in sliding isolation systems

(equation 2.13) is exact provided that the design displacement, D, is accurately estimated.

Accordingly, for the evaluation of SEAOC design procedure, we shall concentrate only on

comparisons of the design displacement (equation 2.1) to the dynamic analysis results.

Concluding this section, we note that the SEAOC static procedure overpredicts uni

directional test displacements. The amount of overprediction is difficult to quantify because

of the difficulty in selecting ZNS values to represent a single earthquake motion history.

5-15

SECTION 6

EVALUATION OF RESPONSE FOR ARTIFICIAL EARTHQUAKES COMPATIBLE TO

DESIGN SPECTRA

An alternate approach for the evaluation of the response of sliding seismically isolated

structures under earthquake excitations is examined in this section. Specifically, a series of

analyses was made where the two building models discused in Section 4 were subjected to

artificially generated earthquake motions. The intent of this methodology is to create

appropriate simulated time histories, which are compatible with specified response spectra,

and, using these simulated motions, to perform nonlinear dynamic analyses. With this concept

in mind, a collection of response data was created from structures that are subjected to

earthquake excitations, whose response spectra closely match the shape of the recommended

spectra for use in building codes, according to the ATC 3-06.

The two building models were subjected to excitation only in their transverse (T)

direction. This way, the effects of mass eccentricity were taken into full account, since in both

models a 5% mass eccentricity existed only in the transverse direction. This assumption

allowed investigation of the potential for rotation of the isolation system and the calculation

of corner bearing displacements.

Recognizing that the above approach is limited to one - directional excitation, analyses

were also performed for the case of the 8 - story structure with bi-directional simulated

excitation. This excitation consisted of 100% of the simulated motion in the transverse (T)

direction and a portion (83%) of the same simulated motion in the longitudinal (L) direction,

acting simultaneously. The 100%-83% combination is consistentwith the dynamic time history.

analysis approach ofSEAOC as described in Section2.2.2.3 «L2+ T2)1/2= (~+ 0.832)1/2= 1.3).

6-1

A total of 9 earthquake motions was generated. Grouped by three, their spectra suf

ficiently approximated the spectra prescribed by ATe 3-06 for soil types Sl,S2 and S3. All of

the· records had a peak ground acceleration of OAg, which is the effective PGA for Seismic

Zone 4. This zone, as referred to the introduction of this study, was the zone of interest for

all the series of analyses that were made within this work, since it is both the zone of highest

seismicity, and the zone where most isolated structures have been and will be constructed.

The duration of the generated accelerograms was 20 seconds for those that corresponded to

soil types S1 and S2, and 30 seconds for the ones that were created according to the S3 design

spectrum. This. selection was made with the assumption that those values of time intervals

could be considered representative of the duration of main intensity intervals of real earth

quakes, as recorded in soil types 51, 52 and 53.

The time histories of acceleration of the simulated motions and their 5% damping

elastic spectra are presented in Figures 6-1 to 6-9. The target spectra are also included in

these figures. It may be seen that the response spectra of the simulated motions closely match

the target spectra over the entire range of periods of interest in this study. The simulation of

the earthquake motions was based on the approach of Gasparini and Vanmarke, 1976.

6.1 Comparison ofTime History Analysis Results for One-directional Excitation to SEAOC

Design Formulae

In the analyses that were performed, the two building models discussed in Section 4

were combined with the three different isolation system models and excited by 9 artificial

earthquake motions, grouped by three to represent site conditions 51, 52 and 53. A total of

54 analyses was performed.

Tables 6.1 and 6.2 summarize the results of the maximum displacements for the i-story

and the 8-story structure, respectively. Tables 6.3 to 6.8 present results of the analyses in more

detail. It should be noted that for every combination of isolation system, superstructure and

6-2

0.4--.--------------------------,

r--..

~ 0.2

zoI-« -0.0n::::w~

wu~ -0.2

o 5 10TIME (SECS)

15 20

(b)

~ DAMPING SPECTRAARTIFICIAL RECORD NO# 1--- SIMULATION- - - TARGET SPECTRUM

O.4g S1r

zo 1.0

~0:::~

WUu«-1 0.5

«0:::IUW0...(f)

0.0 -rl-"--'-r-,.-,..-,--"1-"--'-r--r-,..-,--"1-"--,-,"'-",-..--,-.-,--",--r,-,..-,"--"-,-"r-T-r,,-rl"r-r-'-"-;j0.0 0.5 1.0 1.5 2.0 2.5 3.0

PERIOD (SECS)

FIGURE 6-1 Artificial recordNo#l compatible with O.4gSl Design Spectrum and comparisonof its spectrum with the target spectrum.

6-3

ARTIFICIAL RECORD. NOf/2 0.4g ::)1

~ DAMPING SPECTRAARTIFICIAL RECORD NO#2--- SIMULATION- - - TARGET SPECTRUM

O.4g Sl

0.4 ....------------,----------,

,,-...~ 0.2

zo~~-O.O

W-.JWU~ -0.2

-0.4 .:to""T"-'1rr-r-r-r-r.,.....,~5rrT"T-r-T-,-rr,...lTO"'TI.,...,rT""T"T-r-T-"5-rrr."...,,-rrj20

TIME (SECS)

(b)

z01.0

~0:::-.JWUU«-.J 0.5«0:::.-UWa..(f')

0.0 " ...........-,....--.--.,-'j.....,...,......--.---r,-'I...--r,~, """I,...........- •.......,.,-..-,'.....,...'~I"""Ii--'-'-"...--ri-'j""-""--"""""-;10.0 0.5 1.0 1.5 2.0 2.5 3.0

PERIOD (SECS)

FIGURE6-2 Artificial record N0#2 compatiblewith O.4g81 Design Spectrumand comparisonof its spectrum with the target spectrum.

6-4

0.4 -----------------.-------------.

.........~ 0.2

zo~~-O.O

W-lWU~-0.2

201510TIME (SEeS)

5-0.4- -4-r-T'-r-.......-r-T""T"'"'I~"r""T''"T"'"'"1r-r-.-r ...........-,.............,.-.-..---................................,....,.....,....~-.- ............-l

o

(b)

5" DAMPING SPECTRAARTIFICIAL RECORD NO#3--_. SIMULATION- - - TARGET SPECTRUM

0.49 51

------

z01.0!;(et:-1WUU«...J 0.5«OCr-uwa...(()

0.0 "I,--r,""""""""T"-""",-...-.-.,--r-,---.,--.-,-,,-,--.,---'-.-,-,--',"""""-..-,--.(--r(--.-,--.,---.--.---.,r---TI-r-,"""",r---T,""""T'"j~I0.0 0.5 1.0 1.5 2.0 2.5 3.0

PERIOD (SEes)

FIGURE6-3 Artificial recordNo#3 compatiblewith O.4gSI Design Spectrumand comparisonof its spectrum with the target spectrum.

6-5

ARTIFICIAL RECORD NO#4 O.4g S20.4 -r--------------y-------.-----~

,.......~ 0.2

zof~ -0.0 ~1VH1l-

W-lWU~ -0.2

201510TIME (SECS)

5- 0.4 -i-rT"TI-.-r-r-r-t-,-",....,,,...,..-L,-""T-.--r......,--.--r-r--.--r-r-r-r-.--.r-r-..........-.-.-.-........J

o

(b)

511S DAMPING SPECTRAARTIFICIAL RECORD NO#4--- SIMULATION- - - TARGET SPECTRUM

0.4g S2

z01.0

~a::::-lWUU«-l0.5«a::::f-UW0...en

O.a -',--r,-'--Y--T'",-'1-""',-r--r-T",...,•..--.-,r-r-,-'j--r,- •..--.-,-'-,-0,---", I ...,--r-.-....,-'-1-.,--.-.....-.....,~I0.0 0.5 1.0 1.5 2.0 2.5 3.0

PERIOD (SECS)

FIGURE 6-4 Artificial record No#4 compatible with O.4g 82 Design 8pectrumand comparisonof its spectrum with the target spectrum.

6-6

0.4 ....---------------~--------,

-~ 0.2

zoI~ -0.0 -"'tl~-Ha-

W..JWU~-0.2

o 5 10TIME (SEeS)

15 20

(b)

- --

~ DAMPING SPECTRAARTIFICIAL RECORD NO#5--- SIMULATION- - - TARGET SPECTRUM

0.49 S2

z01.0

~ct:--IWUU«--1 0.5«ct:IUWQ..(J)

0.0 ,,-..,..,-.---.-.,-,-,""'-"""""""'r--Tj-r,-;,r--TI--r,-jr--T,--r,--,-,oj""""l--r-.-r--r-r,'1--'-'--.--.-T'-110.0 0.5 1.0 1.5 2.0 2.5 3.0

PERIOD (SEeS)

FIGURE 6-5 Artificial record No#5 compatible with O.4g S2 Design Spectrumand comparisonof its spectrum with the target spectrum.

6-7

ARTIFICIAL RECORD NONS 0.49 S2

201510TIME (SEeS)

5-0.4 +-.r-r-.,....,............-.-..-...-r-r-r-r-r-"'T'"'"'"T--r-"1.-.--r'-r'..,....,r-r-...-r......-r-r-r-r-"'T'"'"'"T.....-r-r-...-r.......-1

o

0.4 -r------~----------------___.,

zo~<t: -0 0 -f'I;ftH-0:::: •W-1WU~-0.2

.--..~ 0.2

(b)

- -

~ DAMPING SPECTRAARTIFIC/At RECORD NoNs-- SIMULATION- - - TARGET SPECTRUM

0.49 S2

z01.0

~0::::--lWoo<t:--l0.5<t:0::::IUW0..U1

0.0 'I--r',.....-"'-',r--YI-r-,~T""O,--rl-"O'"'r,-.,"Tj-'-1-r,--r',...,,--r.-'rO'"'r,-r..,.-rr'I--r.-,-..,.-"r-i.0.0 0.5 1.0 1.5 2.0 2.5 3.0

PERIOD (SEeS)

FIGURE 6-6 Artificial record N0#6 compatiblewith O.4g 82 Design 8pectrumand comparisonof its spectrum with the target spectrum.

6-8

ARTIFICIAL RECORD NO#7 O.4g S30.4 .,--------,---------------~

zoI~ - o.a -H-11H-J.-H-

w--lWU~ -0.2

,,--..

.!?] 0.2

15 20TIME (SECS)

25 30

(b)

5. DAMPING SPECTRAARTIFICIAL RECORD NO#7-- SIMULATION- - - TARGET SPECTRUM

O.4g S3

z01.0

~--lWUU«--1 0•5«a:::IuWQ..(f)

0.0 -rl--'-I..,.-..-rl-"'--'1""'T"""--TI-jr-T'-.-'-"'--"""'T"j,.--.-,-.•....--.-,~I-.,--r--r-....,........., -"--"-"-""'-:10.0 0.5 1.0 1.5 2.0 '2.5 3.0

PERIOD (SECS)

FIGURE 6-7 Artificial record N0#7 compatible with OAg S3 Design Spectrum and comparisonof its spectrum with the target spectrum.

511 DAMPING SPECTRAARTIFICIAL RECORD NoNs-- SIMULATION- - - TARGET SPECTRUM

O.4g S3

~I"'I' ,_,,-,,_ ." ."_ .. _,,-

0.4 ....-----------:-;-------1"""----,

---S 0.2

zo~<t: -000:: •W-lWU~ -0.2

-0.4 ~0-.-rrr-r.,......TT"T5*rTTTrn,,.0-rnn-rT'T"l'lT5T'T"T-rrrrr"'T2TOrrTTrrTTT2T'5n"TTT1n-r1j30

TIME (SECS)

(b)

z01.0

~0::-lWUU«-l0.5«0::IUW0..(/)

0.0 II........' -'-'-T"''jr-T'-'-....-T'-r-I11-",'........' -'-.,,--,-,',r-TI-'-',,-r-r-,,--,-,"r-T-,-,'-;j0.0 0.5 '.0 '.5 2.0 2.5 3.0

PERIOD (SECS)

FIGURE 6·8 Artificial record N0#8 compatiblewith O.4g S3 Design Spectrumand comparisonof its spectrum with the target spectrum.

6-10

ARTIFICIAL RECORD NO#9 O.4g S30.4----------------,.------------,

zoI-~ -0.0 ~W-I-II-Vk-

W-1WU~ -0.2

,,-....3 0.2

- 0.4 .40....-T'".,....,..,.-r-r-T""T""T5...........T""T""T~ .....1-r0T"T""'1r-r-rT"T'"1""T1.,...5TT'T-rrrrr.,...2T"OrrT,.,...,rrrT"2n5..".rn.,.,rl.30

TIME (SECS)

(b)

---

5~ DAMPING SPECTRAARTIFICIAL RECORD NON9--- SIMULATION- - - TARGET SPECTRUM

O.4g S3

z01.0

~:J IW IUU«-1 0.5«a:::IUW0...(f)

0.0 "1,---r",-r--r-r,-'j---r,-'-"""T"'"""",""""""""'-'-'-"---r"'-'--1""T,--r-"j-"i-r'-'-1""T,--r...-.,-r-,,,--r...-.,-110.0 0.5 1.0 1.5 2.0 2.5 3.0

PERIOD (SECS)

FIGURE 6-9 Artificial record N0#9 compatible with O.4g S3 Design Spectrum and comparisonof its spectrum with the target spectrum.

6-11

TABLE 6.1 Summary of results of maximum base displacement at geometric center of 1 story isolated structure excited in the transverse (T) direction by artificial records compatibleto design spectra and comparison of these displacememts with the design displacementsaccording to SEAOC static analysis procedure.

Sliding Isolation System Properties.

R=39.132 in R=88.048 in R=88.048 inSoil (Tb= 2 sec.) (Tb= 3 sec.) (Tb= 3 sec.)

Typefmax=O.10 fmax=O.05 fmax=O.10

Analysis SEAOC Ratio * Analysis SEAOC Ratio * Analysis SEAOC Ratio *(inch) (inch) (inch) (inch) (inch) (inch)

SI 1.43 2.81 1.97 3.44 5.28 1.53 1.96 3.11 1.59

S2 3.85 5.72 1.49 8.31 10.19 1.23 4.14 6.32 1.53

S3 6.92 9.06 1.31 9.73 16.31 1.68 6.53 10.55 1.62

* SEAOC/Analysis

6-12

TABLE 6.2 Summary of results of maximum base displacement at geometric center of 8 •story isolated structure excited in the transverse (T) direction by artificial recordscompatible to design spectra and comparison of these displacememts with the designdisplacements according to SEAOC static analysis procedure.



Typefmax=O.10 fmax=O.05 fmax=O.10


51 2.27 2.81 1.24 3.48 5.28 1.52 2.64 3.11 1.18

S2 2.36 5.72 2.42 7.14 10.19 1.43 3.44 6.32 1.84

S3 7.97 9.06 1.14 13.63 16.31 1.20 8.69 10.55 1.21

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soil site, three identical analyses were performed corresponding to the three artificial records

whose spectra match the design spectrum. The maximum value of the displacement of the

isolation system calculated by those three analyses was the one of interest and is shown in

Tables 6.1 and 6.2. Also listed in these tables are the corresponding design displacements

according to SEAOC static analysis procedure, and the ratio between them and those esti

mated from the time history analyses of this study.

The SEAOC design formulae consistently overestimate the time history analysis results

by an average factor of about 1.5. There is no special trend for a magnification or a reduction

of the ratios of the displacements evaluated from the two approaches as a function of the soil

type or isolation system properties. Rather, a random distribution of the ratio values is

observed with respect to the soil type and the isolation system properties. It is interesting to

note (see Tables 6.3 to 6.8) that the isolation system displacements in the 8 - story structure

are either larger or smaller than the corresponding displacements of the 1 - story structure.

Clearly, the flexibility of the superstructure has important effects on the response of the

isolation system, particularly in the case of sliding isolation systems in which higher mode

response occurs (Constantinou et aI, 1990a and Mokha et aI, 1990b).

Another important observation is that, essentially, the rotation of the base ofthe I-story

structure due to mass eccentricity is negligible. Tables 6.3 through 6.5 provide supplementary

information for the I-story structure where it can be seen that the ratio of the displacement

between the corner bearing and the displacement at the center of mass of the base did not

exceed the value of 1.02. At this point, it is interesting to refer to the results of the work done

by Kircher and Lashkari, 1989, where for bilinear hysteretic behavior in the isolation system

and for a 5% mass eccentricity and a rigid superstructure, corner bearing displacements up

to 1.66 times the displacement at the center ofmasswere calculated. For the FrictionPendulum

System, this behavior (which will also be discussed in other comparison approaches in Sections

7 and 8) indicates that, essentially, the resultant lateral force of the FPS bearings develops at

the center of mass of the structure, thus no rotation occurs during an earthquake excitation.

6-20

This significantproperty is attributed to the fact that for each individual bearing, the developed

lateral force is proportional to the weight carried by the bearing. (See equations 2.9, 4.6).

Zayas et al 1987, has confirmed this behavior in shake table tests. The ratio of the corner

bearing displacement to the displacement at the center of mass of the base is, according to

SEAOC, given by equation 2.6. For the analyzed structure, this ratio is 1.24. When a more

rational analysis is used, SEAOC allows the use of a smaller ratio which is not less than 1.1.

The property of the Friction Pendulum System to resist torsion becomes less apparent

in the case of the 8-story structure (see Tables 6.6 through 6.8). A maximum ratio between

the corner bearing displacement and the displacement at the center of mass of the base of

1.22 is observed. In the 1 - story structure, this ratio was only 1.02. An explanation for this

difference is provided by the statement that in the 8 - story structure, an eccentricity between

the mass center and the rigidity center existed in eight out of nine levels of the structure (at

the isolation level there was no eccentricity since the lateral force developed at the FPS

bearings was proportional to the axial load on the bearing). In the 1 - story structure, this

eccentricity existed for the one out of two levels of the structure. In general, the eccentric

inertia forces in the flexible superstructure result in torsional motion of the superstructure

which "drives" the isolation system in similar motion. The SEAOC static design procedure

does not account for the property of sliding isolation systems, and in particular the Friction

Pendulum System, to reduce torsional effects due to mass eccentricity, especially for rigid or

very stiff superstructures.

Finally, it is evident by observing Tables 6.3 through 6.8 that the excitation of both the

structures in the transverse (T) direction resulted in the development of forces only in that

direction. The occurrence of small values of displacements of the corner bearings in the

longitudinal (L) direction (up to 0.04 inches for the I-story structure and 0.39 inches for the

8-story structure) is due to the rotation of the base of the structure, whereas the displacement

in the L direction at the center of mass of the two models and the respective developed shear

forces were found in all cases to be zero.

6-21

Appendix A provides supplementary information for the results of the maximum

calculated story shear force and interstory drift of all the floors, in the case of the 8 - story

structure excited by the artificial earthquake motions. The interstory drift is divided by the

story height (12ft). These results are particularly useful in studying the distribution of story

shear with height of the structure, which is not attempted in this study. However, one could

not avoid observing that the maximum story shear remains essentially the same in all stories

except for the top two stories. This indicates higher mode response, a characte!istic of sliding

isolation systems which has been confirmed in experiments (Constantinou et aI, 1990a and

Mokha et aI, 1990b). Furthermore, the interstory drift ratio is restricted to values less than

0.006, which satisfies the limits imposed by SEAOC.

6.2 Comparison of Time History Analysis to Bi-directional Excitation to SEAOC Design

Formulae

To study the effect of bi-directional excitation on the response of isolated structures,

the analyses reported in Section 6.1 are repeated with an additional excitation component in

the longitudinal direction. The full simulated motion is applied in the transverse (T) direction

and 83% of the same motion is applied in the longitudinal (L) direction. Detailed results are

presented in Tables 6.9 to 6.11. Analyses were performed only for the 8-story structure.

As expected, the bi-directional excitation results in larger bearing displacements in

both directions except in a single case, in which the opposite occurs. For comparison to the

SEAOC design displacement, Table 6.12 was prepared. In this table, the maximum dis

placement among the three artificial records for each soil type is presented together with the

SEAOC displacement and the ratio of this displacement to the calculated one. Evidently, for

the considered bi-directional excitation, the time history results on the displacement are very

close to the SEAOC values, which are on the conservative side within 25% of overestimation

on the average.

6-22

The above results indicate that the SEAOC design formula can predict displacements

within an acceptable range of overestimation provided that the earthquake excitation is

interpreted as having bi-directional components. The two orthogonal components have the

square root of the sum of the squares (SRSS) of their 5%-damped spectra matching the 1.3

times the 5% damped design spectrum (~ I 2 + 0.83 2 = 1.3). This is consistent with the

dynamic time history analysis approach of SEAOC.

It is interesting to note that under the bi-directional artificial excitation, the ratio of

corner bearing displacement to center point displacement is less than in the case of the

one-directional excitation. In the considered bi-directional excitation, the two components

are in phase, resulting in ground motion in a single direction at a 40 degree angle with respect

to the longitudinal axis. With respect to this axis of excitation, the mass eccentricity is less

than 8ft and equal to 6.13ft. This amounts to 3.8% rather than 5% mass eccentricity. This

explains the reduction in torsion.

Concluding this section we note the following:

(l)The SEAOC displacement values are about 1.5 larger than those calculated in

urn-directional artificial time history analyses.

(2)The SEAOC displacement values are about 1.25 larger than those calcuiated in

bi-directional artificial time history analyses.

(3)The effect of bi-directional excitation appears to be significant. On the average,

bi-directional excitation results in 20% larger response than uni-directional exci

tation. This difference is larger than the one observed in the study of Kircher and

Lashkari, 1989. Responsible for this difference is the modeling of the isolation

elements. In the Kircher and Lashkari, 1989 study, each isolator was modeled by

two bilinear hysteretic elements placed at right angle. The interaction curve in this

model is effectively square. In contrast, the model used in the present study has

6-23

9' ~

TA

BL

E6.

9A

naly

sis

resu

lts

for

8-s

tory

isol

ated

stru

ctur

ew

ith

R=3

9.13

2in

(Tb

=2

sec)

,fm

u:=

0.10

,ex

cite

dby

bi-d

irec

tion

alar

tifi

cial

reco

rdco

mpa

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ith

desi

gnsp

ectr

a.10

0%of

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fici

alre

cord

inth

etr

ansv

erse

(T)

and

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ofar

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the

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itud

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(L)

dire

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SE

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tST

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TABLE 6.12 Summary of results of maximum base displacement at geometriccenter of 8-story isolated structure excited by bi-directional artificial records compatible to design spectra (100% of artificial records in transverse (T) and 83% ofartificial records in longitudinal (L) direction) and comparison of thesedisplacements with the design displacements according to SEAOC static analysisprocedure.


R=39.132 in R=88.048 in R=88.048 inSoil (Tb= 2 sec.) (Tb= 3 sec.) (Tb=3 sec.)Type

fmax=O.lO fmax=O.05 fmax=O.lO


SI 2.54 2.81 1.11 4.44 5.28 1.19 2.86 3.11 1.09

S2 2.94 5.72 1.95 8.54 10.19 1.19 4.16 6.32 1.52

53 7.50 9.06 1.21 17.35 16.31 0.94 10.00 10.55 1.06

* 5EAOClAnalysis

6-27

circular interaction curve which closely resembles reality (Constantinou et aI,

199Gb). For bi-directional excitation the circular interaction curve results in larger

displacement response than the square interaction curve.

6-28

SECTION 7

STATISTICAL EVALUATION OF RESPONSE FOR A SET OF RECORDED PAIRS OF

HORIZONTAL EARTHQUAKE COMPONENTS.

In this section, a statistical approach for the evaluation of the nonlinear response of

the structure-isolation models described in Section 4 is developed. This approach uses sets of

time histories that are consistent in amplitude and frequency content with the design spectra

currently required by the seismic codes, and calculates statistical quantities like mean values

and standard deviations of the response parameters which are under consideration. In this

way, a measure of the level of the inherent variation of the response parameters as a function

of the variation in the ground motion is provided.

The idea of a statistical consideration and estimation of the results of a performed

series of nonlinear analyses, for the prediction of response of sliding seismic isolated systems,

is, as stated in Section 3, based on the work done by Kircher and Lashkari, 1989. In this work,

a collection of nonlinear response data was created from where a basis for judging the validity

and applicability ofSEAOC design requirements was provided through a statistical processing.

In the study examined in this section, all the major principles and assumptions that were

included in the work of Kircher and Lashkari, 1989 are adopted.

7.1 Earthquake Time Histories.

The ground motions that were selected for this work are the same as those used by

Kircher and Lashkari, 1989. According to them, appropriate earthquake time histories should

be the ones that are consistent in amplitude and frequency content with the design spectra,

currently required by seismic codes, i.e. the ATC-3 spectra. For this reason, the time histories

7-]

were selected from the records that were used by Seed et aI, 1974 to develop those site

depended spectra. It is interesting to note that Seed's study yielded results that have been

used as the primary basis for the ATC-3 design spectra, and also for the seismic criterk of

the Blue Book (SEAOC 1990b) and the Uniform Building Code (UBC, 1991).

The Seed study developed site-dependent spectra by calculating mean and mean

plus-one-standard-deviation spectra of normalized acceleration time history records. The

earthquake records were grouped by one of four different site conditions, listed below with

the corresponding ATC-3 soil type:

(1) Rock sites - Soil type Sl.

(2)Stiff soils with depths less than about 150 ft. - Soil type Sl.

(3)Deep cohesionless soils with depths greater than about 250 ft. - soil type

S2.

(4)Soil deposits consisting of soft to medium stiff clays with associated strata

of sands or gravels. - Soil type S3.

Horizontal earthquake records with peak ground acceleration (PGA) values of 0.05g/'

or greater were selected by the Seed study from available data up to and including the San

Fernando earthquake of 1971. The Seed study treated the two horizontal components as

independent records and collected about 30 records each for rock, stiff soil and medium soil

sites, and 15 records for soft soil sites.

In this study, only records with both horizontal components exceeding 0.10g PGAwere

considered appropriate for the nonlinear analyses. After elimination of the less significant

records, the following number of records remained in each group:

(1) Rock sites - 10 pairs (20 records), representative of soil type Sl.

(2) Stiff soil sites - 10 pairs ( 20 records), representative of soil type Sl.

(3) Medium soil sites - 9 pairs (18 records), representative of soil type S2.

7-2

Since there were no records greater than O.lOg PGAfor soft soil sites, this site condition

was not evaluated during the series of the statistical evaluation analyses. Pertinent information

for each pair of horizontal earthquake time histories is provided in Table 7.1 for records at

rock sites, in Table 7.2 for records at stiff soil sites and in Table 7.3 for records at medium

soil sites.

Values of the PGA and the peak ground velocity (PGV) given in these tables were

taken directly from the California Institute of Technology data (CIT, 1974). In certain cases,

it was noted that the PGA values reported in the Seed study differed from the CIT data. No

explanation for these discrepancies could be found, except that some values reported in the

Seed study may have been for "uncorrected" records. Each set of earthquake records has a

large proportion from the San Fernando earthquake of 1971. The Seed study investigated the

potential biasing of results that can occur if the spectra are dominated by the San Fernando

earthquake, and concluded that the results were not unduly influenced. On the basis of the

findings of Seed's study, Kircher and Lashkari, 1989 treated those earthquake records as

representative of the ATC-3 design spectra for soil types Sl (rock and stiff soil types) and for

soil types S2 (medium soil sites), respectively.

7.2 Scaling Factors

As referred in Section 2, for this study, Seismic Zone 4 was the only zone considered.

The effective PGA for Seismic Zone 4 is 0.4 g, the value ofacceleration specified by the ATC-3

study for scaling of the normalized response spectra. As summarized in Tables 7.1 through

7.3, the unsealed records have a variety of PGA values, most of which are considerably less

than 0.4 g. Thus, scaling the records was required to insure that the response spectra be

consistent with Seismic Zone 4 design spectra.

7-3

-..J~

TA

BL

E7.

1H

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thqu

ake

com

pone

nts

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LP

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PG

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No#

NE

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ST

AT

ION

No#

DA

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MA

GN

ITU

DE

FR

OM

MM

ID

IRE

CT

ION

(g)

(in.

/sec

)(i

n.)

SO

UR

CE

(KIn

)

1T

HE

LE

NA

10/3

1/35

6.0

8-

SOO

W0.

146

2.89

0.56

L(3

23)

S90

W0.

145

-5.2

4-1

.47

2T

KE

RN

CO

UN

TY

07/2

1/52

7.6

56V

IIS

69E

0.17

9-6

.97

-3.6

0L

(095

)N

21E

0.15

6-6

.18

-2.6

4

3T

LY

TL

EC

RE

EK

09/1

2nO

5.4

15V

IS

25W

0.19

8-3

.79

0.41

L(2

90)

S65

E0.

142

-3.4

9-0

.87

4T

PA

RK

FIE

LD

(097

)06

/27/

665.

67

VII

S25

W-0

.347

8.87

-2.1

6L

N65

W-0

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-5.7

11.

83

5T

SA

NF

ER

NA

ND

O0

2/0

9n

l6.

630

VII

S08

E0.

217

3.89

2.76

L(2

84)

S82

W0.

202

2.46

-1.8

1

6T

SA

NF

ER

NA

ND

O0

2/0

9n

l6.

626

VII

S69

E0.

171

-2.2

60.

49L

(126

)S

21W

-0.1

46-3

.38

0.69

7T

SA

NF

ER

NA

ND

O02

!09n

l6.

63

IXS

16E

-1.1

70-4

4.57

14.8

3L

(279

)S

74W

1.07

5-2

2.72

-4.2

6

8T

SA

NF

ER

NA

ND

O0

2/0

9n

l6.

640

VII

N87

W-0

.169

-2.6

2-2

.33

L(1

04)

N03

E-0

.140

2.08

-1.2

4

9T

SA

NF

ER

NA

ND

O0

2/0

9n

l6.

621

VIn

N21

E-0

.353

5.81

0.70

L(1

28)

N69

W0.

283

-5.0

23.

4910

TS

AN

FE

RN

AN

DO

02

/09

nl

6.6

24V

IIN

OO

E-0

.167

4.88

-1.9

1L

(220

)S

90W

0.15

05.

91-2

.14

..,J v.

TA

BL

E7.

2H

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thqu

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com

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oils

ites

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CO

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NoH

NE

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ST

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NoH

DA

TE

MA

GN

ITU

DE

FR

OM

MM

ID

IRE

CT

ION

(g)

(in.

/sec

)(i

n.)

SO

UR

CE

(Km

)

11T

LO

WE

RC

A12

/30/

346.

558

-S

90W

-0.1

834.

55-1

.44

L(1

17)

SOO

W-0

.160

-8.2

1-1

.65

12T

IMP

ER

IAL

VA

LE

Y05

/18/

406.

68

VII

ISO

OE

0.34

813

.17

4.28

LE

LC

EN

TR

O(1

17)

S90

W0.

214

-14.

53-7

.79

13T

PA

RK

FIE

LD

(014

)06

/27/

665.

65

VII

IN

85E

-0.4

34-1

0.02

-2.8

0L

N05

W-0

.355

-9.1

2-2

.09

14T

SA

NF

ER

NA

ND

O02

/09n

l6.

621

VIn

N21

E-0

.315

-6.7

61.

67L

(110

)N

69W

-0.2

70-1

0.94

3.73

15T

SA

NF

ER

NA

ND

O02

/09n

l6.

635

VII

N90

E-0

.211

-8.3

2-5

.79

L(1

35)

SOO

W0.

170

-6.5

03.

17

16T

SA

NF

ER

NA

ND

O02

/09n

l6.

639

VII

NO

OE

-0.1

368.

794.

50L

(208

)S

90W

0.14

47.

30-4

.57

17T

SA

NF

ER

NA

ND

O02

/09n

l6.

639

VII

NO

RT

H0.

157

-6.9

03.

17L

(211

)W

ES

T-0

.132

8.45

-4.5

7

18T

SA

NF

ER

NA

ND

O02

/09n

l6.

628

VII

Nll

E0.

225

-11.

12-5

.30

L(4

66)

N79

W-0

.149

-9.2

3-4

.06

19T

SA

NF

ER

NA

ND

O02

/09n

l6.

628

VII

S12

W-0

.248

12.4

37.

21L

(253

)N

78W

0.20

1-7

.01

3.73

20T

SA

NF

ER

NA

ND

O02

/09n

l6.

639

VII

N90

E-0

.165

-6.5

4-4

.08

L(1

99)

SO

OW

-0.1

617.

243.

56

....,J ~

TA

BL

E7.

3H

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onta

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site

s.

CO

MP

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AR

TII

QU

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No#

NE

NT

ST

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No

#'

DA

TE

MA

GN

ITU

DE

FR

OM

MM

ID

IRE

CT

ION

(g)

(in.

/sec

)(i

n.)

SO

UR

CE

(Krn

)

21T

WE

ST

ER

N04

/13/

497.

120

VII

IN

86E

-0.2

80-6

.72

4.08

LW

AS

H(3

25)

N04

W0.

165

8.43

-3.3

8

22T

EU

RE

KA

12/2

1/54

6.5

25V

III

N79

E-0

.258

11.5

65.

53L

(022

)N

llW

0.16

8-1

2.44

4.88

23T

EU

RE

KA

12/2

1/54

6.5

30V

IIN

46W

0.20

1-1

0.24

-3.7

9L

(023

)N

44E

0.15

914

.03

-5.5

8

24T

FE

RN

DA

LE

12/1

0/67

5.6

25V

IIS

44W

-0.2

374.

700.

65L

(023

)N

46W

0.10

54.

65-0

.67

25T

SA

NF

ER

NA

ND

O0

2/0

9n

l6.

616

VII

NO

OW

-0.2

55-1

1.81

-5.8

7L

(241

)S

90W

-0.1

349.

425.

45

26T

SA

NF

ER

NA

ND

O0

2/0

9n

l6.

619

VII

SO

OW

0.11

612

.46

-6.9

3L

(458

)S

90W

0.10

5-1

1.33

6.02

27T

SA

NF

ER

NA

ND

O0

2/0

9n

l6.

630

VII

NO

OE

-0.2

01-3

.87

-1.0

7L

(264

)N

90E

-0.1

85-6

.47

2.72

28T

SA

NF

ER

NA

ND

O0

2/0

9n

l6.

630

VII

S82

E0.

212

5.48

-1.9

5L

(267

)S

08W

0.14

23.

62-1

.14

29T

PU

GE

TS

OU

ND

04/2

9/65

6.5

58V

IIS

86W

-0.1

985.

14-1

.51

L(3

25)

S04

E0.

137

3.21

-1.0

7

Two methods were used to scale time histories: scaling by peak ground acceleration

(PGA) and scaling by peak ground velocity (PGV). The first method, which parallels the

approach taken by the Seed study, scaled each pair of earthquake components by a common

factor such that the average PGA of the two components is equal to O.4g. This method is

consistent with the approach used by the Seed study except that the Seed study scaled (i.e.

normalized) each component individually, rather than in pairs.

The advantage of using PGA to scale the records is that it is the same method used

implicitly in the Seed study to develop site-dependent design spectra. The shortcoming of

scaling the time histories by PGA is that the response of an isolated structure is primarily

influenced by the amplitude and frequency content of the velocity domain of the design

spectrum. As a second method for scaling, each pair of earthquake components was scaled

by a common factor such that the average PGV of the two components was equal to either

12 in./sec for rock site, 18 in.fsec for stiff soil sites or 22.5 in./sec for medium soil sites. The

same values were adopted in the work done by Kircher and Lashkari, 1989. Scaling the records

by PGV, rather than by PGA was considered a more appropriate method of representing the

amplitude and frequency content of ground motion at periods greater than 1.0 second. The

scaling factors used in the series of the statistical evaluation analyses are listed in Table 7.4.

Figures 7-1 to 7-3, show, grouped by the three soil types, the average spectra of

PGV-scaled and PGA-scaled time histori~s in the longitudinal (L), transverse (T) directions

and the spectra that are created by averaging the square root of the sum of the squares of the

spectra of the two horizontal components of every earthquake, individually «L2+ 'f2)1/2).

Also, each figure shows (with solid line) the respective design spectrum, which is one of the

three ATe-3 Design Spectra (see Figure 2-1). An observation can be made to the fact that

the average spectra of the time histories match the design spectra reasonably well for stiff soil

and medium soil sites. For rock sjtes, however, the average acceleration spectra are lower

than the ATC-3 design criteria for long periods. The reason for this large discrepancy between

the design criteria of the ATC-3 study and the average spectrum for rock sites is not known.

7-7

TABLE 7.4 Scaling factors of the earthquake components.

No# EARTHQUAKE PGA PGVSTATIONNo# SCALED SCALED

1 HELENA (323) 2.749 2.952

2 KERN COUNTY (095) 2.388 1.825

3 LYTLE CREEK (290) 2.353 3.297

4 PARKFIELD (097) 1.299 1.646

5 SAN FERNANDO (284) 1.909 3.780

6 SAN FERNANDO (126) 2.524 4.255

7 SAN FERNANDO (279) 0.356 0.357

8 SAN FERNANDO (104) 2.589 5.106

9 SAN FERNANDO (128) 1.258 2.216

10 SAN FERNANDO (220) 2.524 2.224

11 LOWER CA (117) 2.332 2.821

12 IMP. VALLEY EL CENTRO (117) 1.423 1.300

13 PARKFIELD (014) 1.014 1.881

14 SAN FERNANDO (110) 1.368 2.034

15 SAN FERNANDO (135) 2.100 2.429

16 SAN FERNANDO (208) 2.857 2.237

17 SAN FERNANDO (211) 2.768 2.345

18 SAN FERNANDO (466) 2.139 1.769

19 SAN FERNANDO (253) 1.782 1.852

20 SAN FERNANDO (199) 2.454 2.612

21 WESTERN WASH (325) 1.798 2.970

22.

EUREKA (022) 1.878 1.875

23 EUREKA (023) 2.222 1.854

24 FERNDALE (023) 2.339 4.813

25 SAN FERNANDO (241) 2.057 2.120

26 SAN FERNANDO (458) 3.620 1.892

27 SAN FERNANDO (264) 2.073 4.352

28 SAN FERNANDO (267) 2.260 4.945

29 PUGET SOUND (325) 2.388 5.389

7-8

.-..0.50 5!1 DAMPING SPECTRA-...;

ROCK SITE OAGZ ATC-3 PGA-SCALED 6---6--60 0.4

~PGV-SCALED ~MEAN OF COMPONENTS T

0::~0.3WUU<: 0.2-l<:0::t; 0.1WQ.Ul

0.00.5 1.0 1.5 2.0 2.5 3.0 3.5

PERIOD (SECS)

.-..0.50 5!1 DAMPING SPECTRA-...;

ROCK SITE OAGZ ATC-3 PGA-SCALED 6---6--60 0.4

~PGV-SCALED ~

0::MEAN OF COMPONENTS L

~0.3WUU<: 0.2-l<:0::t; 0.1Wn.Ul

0.00.5 1.0 1.5 2.0 2.5 3.0 3.5

PERIOD (SECS)

3.5

5!1 DAMPING SPECTRAROCK SITE 0.4GPGA-SCALED ..........--..PGV-SCALED ~MEAN OF (r+T 2)'/2

~0.5

~D:: 0.4 ATC-3W-lWU 0.3U<:~0.2

0::.....t] 0.1

n.Ul

O.0 ,"t""r-T"T"'r-T"T"'~"TT'T......._r:r:~T'TTT'TTrn-r-T"T"',....,..,-rrr ..............."...T'TT,....,...,...-rl0.5 1.0 1.5 2.0 2.5 3.0

PERIOD (SECS)

.-..0.6 r-------------------....,S

FIGURE 7-1 5% average spectra of components T,L and square root of sum of square ofcomponents T and L of PGV and PGA scaled motions used in dynamic analyses andcomparison with the Design Spectrum. Earthquake records recorded at Rock Sites.

7-9

5llI DA!.APING SPECTRASTIFF SOIL SITE 0.4GPGA-SCALED ~PGV-SCALED l>-B---€l

MEAN OF CO!.APONENTS T

........0.6 .,.-----------------

.8ZO.5o~a::: 0.4 ATC-3w.JwUO.3U«.J 0.2«a:::f-~0.1

n..Ul

0.0 "'!-rrrrTTTTT"TTT"lTT"1"'-"'"IT'"n',rrlT"'nl'TI"nlJCTIT"I,niTI n,1'T'"nO,rr'T"'n,",-TTTTT"lTT"1rr-r,.,..,..l0.5 1.0 1.5 2.0 2.5. 3.0 3.5

PERIOD (SEeS)

3.5

5llI DA!.APINC SPECTRASTIFF SOIL SITE 0.4GPGA-SCALED~PGV- SCALED l>-B---€l

MEAN OF CO!.APONENTS L

1.5 2.0 2.5 3.0PERIOD (SEeS)

ZO.5o~eJ 0.4 ATC-3.JwUO.3U«.J 0.2«a:::f-~O.,

n..Ul

0.0 "I-rrrrTTT.,..,..,TT"lTT"1rr-rTTTTTT-rrrTT"lTT"1rrrTTTT_rr-rrr~"T"T"rr_r.....,..T_rr....l0.5 1.0

........0.6 .,.----------------------.,t.:l'-"

3.53.01.0

Zoi= 0.6

~W.JWUO.4U«.J«a::: 0.2fUwn..Ul 0.0 +rTTTTTT"""""""TT"1rrrTTTTTTTTT"""".,.,.,rrrrrrTTTTTT-rrr"""TT"1rrr~

0.5

8°·8 -;r-------------5llI--DA-!.A-P-IN-C-SP-E-C-TRA----,

'-" STIFF SOIL SITE 0.4GPGA-SCALED ..----..PGV-SCALED ~MEAN OF (~+T2)'/2

FIGURE 7-2 5% average spectra of components T,L and square root of sum of squares ofcomponents T and L of PGV and PGA scaled motions used in dynamic analyses andcomparison with the Design Spectrum. Earthquake records recorded at Stiff Soil Sites.

7-10

3.51.5 2.0 2.5 3.0PERIOD (SECS)

1.0

ZO.5of=C2 0.4w-.lW00.3

~-.l 0.2<t:D:::I~0.1

0-Ul

0.0 .q.,...rrrrrrTTTTTTTTTTT"TTM....,..,....,..,rrnrrrrrrrrrrrrTTTTTTTT"TTMTM-rrJ0.5

SO.6 -;:r-------------511-D-AM-P-IN-G-S-PE-C-TR-A--.

........ ATC-3 MEDIUM SOIL SITE 0.4GPGA-SCALED .........--.PGV- SCALED I!--&-El

MEAN OF COMPONENTS T

3.53.0

5ll DAMPING SPECTRAMEDIUM SOIL SITE 0.4GPGA-SCALED .........--.PGV-SCALED l>---&-<J

MEAN OF COMPONENTS L

1.0

ATC-3

-.li'i 0.2I-

~0.10-Ul

0.0 "'\-r1nT1n-rrrrrrrrrrrrrTTTTTTTTT'TTTTTTTTTnT1rrT'1n-rrrrr-rrrrr.........,-,.i0.5

,...,0.7.,,-------------------------,SZ 0.6o~0.5D:::wd 0.4o~0.3

ATC-3

60.8~D:::~0.6Woo<t: 0.4-J<t:D:::0 0.2w0-

Ul 0.0 .:h-.n-rrrrrrrrrrrrr.........rrrTTTTTT'TTTTT"TTTT.....,TMnT1,....,..,rrrrrrrrr,.,.;0.5 1.0 1.5 2.0 2.5 3.0 3.5

PERIOD (SECS)

S 1.0 ~------------511-D-AM-P-IN-:G--SP-:E-:CT=RA:------,

........ MEDIUM SOIL SITE 0.4GPGA-SCALED .........--.PGV-SCALED ..........-.,MEAN OF (L~T2)'/2

FIGURE 7-3 5% average spectra of components T,L and square root of sum of squares ofcomponents T and L of PGV and PGA scaled motions used in dynamic analyses andcomparison with the Design Spectrum. Earthquake records recorded at Medium Soil Sites.

7-11

Apparently, the ATC-3 study felt that the time histories used by the Seed study to develop

rock spectra do not contain a level of ground motion appropriate for design of long-period

structures. Regardless of the motive, the ATC-3 study defined rock and stiff soil as a single

site condition (soil type Sl) and based the design criteria for this site condition ofthe average

spectrum of stiff soil time histories.

Note that in Figures 7-1 to 7-3, the mean of the square root of the sum of the squares

of the spectra values of the two horizontal components «L2+ T2)1/2) of the cases of stiff soil

and medium soil sites is substantially larger than the design spectrum. Even when the mean

of (L2+T2)1/2 spectra is compared to 1.3 times the design spectrum (doted line), still the

(L2+ T2)1/2 spectra indicate a stronger motion particularly for stiff soil (Figure 7-2). The

response spectra for each of the components of the PGV scaled motions are presented in

Appendix B. It may be observed that the response spectra of some of these motions exhibit

strong distinct peaks in the range of periods of 1.4 to 1.7 seconds (motions No. 15,18,19,23

and 25). One would expect that such peaks are characteristics of motions recorded on soil

types other than Sl or S2. Actually, these motions resulted in bearing displacements which

are considerably larger than those for other motions within each soil group. When these

motions are removed from the sample, their mean (L2+ T2)1/2 spectra appear to be consistent

with the 1.3 times the design spectrum for stiff and medium soil sites.

7.3 Comparison of Time History Analysis Results to SEAOC Design Formulae

In the previous section, two methods were used in this study to scale time histories:

scaling by peak ground acceleration (PGA) and scaling by peak ground velocity (PGV). The

analysis results have shown that the estimated meanvalues for the displacement ofthe isolation

system according to the two methods were predicted to be almost the same whereas the

standard deviation values differed thoroughly. When scaling by PGA, the standard deviations

7-12

were as much as two times greater than the standard deviations estimated through the PGY

scaling. It was concluded that the results based on PGA scaling were less representative of

the behavior of isolated structures. Accordingly, they are not reported in this study.

Tables 7.5 to 7.22 present the results of analyses of the six structure/isolation systems

(1- story and 8 - story with three different isolation system properties) to the 29 pairs of PGY

scaled motions. The tables include the peak displacement in the longitudinal (L) and trans

verse (T) directions at the base center and at the corner bearing, the peak base shear and first

story shear (normalized by the total weight of the structure) and the peak first story drift ratio

(for story height of 12 ft). Results on the story shear and the interstory drift ratio for the other

stories of the 8 - story structure are presented in Appendix C. Furthermore, the tables present

values of the ratio of peak corner displacement to peak base center displacement, as well as

means and standard deviations (CY) of the calculated response quantities. For the comparison

to the SEAOC design procedure for the displacement of the isolation system, the quantities

of interest are the mean and standard deviation of the maximum displacement between

components Land T for each of the three groups of the soil conditions. These values are listed

in the last two lines of each table. For soil conditions of stiff and medium soils, certain motions

have been excluded in the calculation of the mean and standard deviation (value in parenthesis

and identified by an asterisk). These motions were those having in their spectra distinct peaks

at high values of period. As discussed earlier, these motions may not be representative of

stiff and medium soil conditions, but rather representative of soils with deeper profiles.

The first observation to be made in the results of Tables 7.5 to 7.22 is that the corner

to center displacement ratio is equal to unity for the 1 - story structure, (mean = 1, CY = 0).

This is significantly different than the value of 1.24 (by use of equation 2.6) required by the

SEAOCstaticprocedure or the minimum 1.1 value allowedwhenproper analysis isperformed.

In the case of the 8 - story structure, the corner displacement is larger than in the case of the

7-13

1 - story structure. Evidently, the torsional response is affected more by the flexibility of the

superstructure and the properties of the isolation system than by the plan dimensions of the

building.

An other observation to be made is the fact that the peak displacements of the isolated

structure are significantly influenced by local site conditions. In general, peak response differs

between rock, stiff soil and medium soil sites in a manner consistent with the differences in

the mean spectra of the time histories of the different sites ( see Figures 7-1 through 7-3).

For comparison of the calculated values of the isolation system displacement to the

SEAOC static procedure, Tables 7.23 and 7.24 are presented. They include the mean and

the mean plus one standard deviation values of the maximum displacement which occur in

either the longitudinal (L) or transverse (T) direction. The tables also include the SEAOC

minimum design values. Furthermore, Tables 7.25 and 7.26 present the same information but

with certain records removed from the sample as not being representative of the assumed soil

conditions. The reported values in Tables 7.25 and 7.26 are those in Tables 7.5 to 7.22 which

are included in parenthesis and identified by an asterisk.

From the results of Tables 7.23 and 7.24, it maybe observed that the SEAOC formula

for the design displacement can predict well or accurately well the mean estimated values

when the excitation is referring to stiff or medium soil sites. In general, the design values for

those site conditions are between the mean and the mean plus one standard deviation of the

estimated values or slightly lower than the mean values. However, for rock sites, the design

displacements of SEAOC are consistently higher than the ones predicted through the dynamic

analyses. Of course, this is primarily attributed to the fact that SEAOC specifies the same

design displacement for rock and stiff soil sites since both of them are corresponding to soil

type Sl.

From the results of Tables 7.25 and 7.26 it may be observed that the mean values are

slightly lower than the ones described in Tables 7.23 and 7.24. However, the standard deviation

7-14

values are significantly lower than the originally estimated. Both sets of results are presented

because together they provide a better picture of the variation in response due to the inherent

variability of ground motion.

Based on the results of Tables 7.23 to 7.26 it may concluded that the SEAOC dis

placements are in good agreement with the mean of the peak displacements as calculated in

the nonlinear dynamic analysis. A key point to be made is that the above conclusion is based

on the results of analyses with bi-directional excitation and with circular interaction curve for

the isolation bearing model. As explained in Section 6, the combination of these two factors

results in larger bearing displacements than when a square interaction curve model is used.

To quantify the effect of the isolation bearing model, the analysis of the 1-story isolated

structure with R =39.132 in (Tb = 2 sec), fmax = 0.10 and excited by PGV scaled earthquake

motions recorded on medium soil sites was repeated. Each isolation bearing was modeled

by two bilinear hysteretic elements placed along the T and L directions of the structure. Each

element had force-displacement characteristics described by equations 4.6 and 4.7. Effec

tively, the interaction curve between the forces in the two orthogonal directions was square.

A comparison of this model to the previously used circular interaction model is presented in

Figure 7-4. As seen in this figure the square interaction model results in force-displacement

relation which is dependent on the direction of motion. The force is always larger than that

in the circular interaction model.

The results of the analysis of the 1-story structure are summarized in Table 7.27. This

table should be compared to Table 7.7 which contains results for the same structure but with

circular interaction model for the bearings. The results clearly demonstrate that the square

interaction model predicts bearing displacements which are about 17% less than those pre

dicted by the circular interaction model.

When comparing to the SEAOC static procedure, SEAOC predicts 5.72 in. displace

ment (see Table 7.23) as compared to the meanof4.95 in. ofthe analysis with square interaction

model.

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TABLE 7.23 Summaryofresults ofthe mean and the mean plus onestandard deviation valuesof the base displacement for 1 • story isolated structure excited by PGV scaled earthquaketime histories and comparison of these results with design values according to SEAOC staticanalysis procedure. Units are inches.


R=39.132 in R=88.048 in R=88.048 inSoil (Tb =2 sec.) (Tb=3 sec.) (Tb =3 sec.)Type

fmax=O.lO fmax=O.05 fmax=O.10

Mean of Mean Mean of Mean Mean of Meanmax plus 10 SEAOC max plus 10 SEAOC max plus 10 SEAOC(L,T) of max (L,T) of max (L,T) of max

(L,T) (L,T) (L,T)

S1

Rock 1.77 2.23 2.81 2.72 3.54 5.28 1.84 2.38 3.11

Sites

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Sites

S2

Medium 5.94 8.53 5.72 11.14 16.10 10.19 5.78 8.08 6.32Soil

Sites

TABLE 7.24 Summary ofresults of the mean and the mean plus onestandard deviation valuesof base displacement for 8· story isolated structure excited by PGV scaled earthquake timehistories and comparison of these results with the design values according to SEAOC staticanalysis procedure. Units are inches.


R=39.132 in R=88.048 in R=88.048 inSoil (Tb = 2 sec.) (Tb = 3 sec.) (Tb = 3 sec.)

Typefmax=O.lO fmax=O.05 fmax=O.10


(L,T) (L,T) (L,T)

Sl

Rock 1.59 2.51 2.81 2.34 3.25 5.28 1.69 2.70 3.11

Sites

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Sites

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Medium 5.81 8.28 5.72 10.50 15.33 10.19 6.29 8.93 6.32Soil

Sites

7-35

TABLE 7.25 Summary ofresults ofthe mean and the mean plus onestandard deviation valuesof the base displacement for 1 • story isolated structure excited by PGV scaled earthquaketime histories considered in this study representative of the soil sites they were recorded andcompa~sonof these results with the design values according to SEAOC static analysis procedure. Units are inches. Certain records were removed as indicated in Tables (7.5) to (7.22).


R=39.132 in R=88.048 in R=88.048 inSoil (Tb= 2 sec.) (Tb = 3 sec.) (Tb= 3 sec.)Type

fmax=O.10 fmax=O.05 fmax=O.lO

Mean of Mean Mean of Mean Mean of Meanmax plus lCf SEAOC max plus 1Cf SEAOC max plus 1Cf SEAOC(L,T) of max (L,T) of max (L,T) of max

(L,T) (L,T) (L,T)

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Rock 1.77 2.23 2.81 2.72 3.54 5.28 1.84 2.38 3.11

Sites

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Sites

S2

Medium 5.25 7.07 5.72 8.11 10.31 10.19 5.04 6.01 6.32Soil

Sites

7-36

TABLE 7.26 Summary ofresults ofthe mean and the mean plus one standard deviation valuesof the base displacement for 8 • story isolated structure excited by PGV scaled earthquaketime histories considered in this study representative of the soil sites they were recorded andcomparison of these results with the design values according to SEAOC static analysis procedure. Units are inches. Certain records were removed as indicated in Tables (7.5) to (7.22).


R=39.132 in R=88.048 in R=88.048 inSoil (Tb = 2 sec.) (Tb = 3 sec.) (Tb = 3 sec.)

Typefmax=O.1O fmax=O.05 fmax=O.10


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7-37

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0.1

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0.0

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90

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86

29PU

GET

SOUN

D(3

25

)1

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24

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210.

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MEA

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00

a2

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00

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"0

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0.0

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II0

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0183

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NOF

MAX

(L,1

)4

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~0

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OF"l

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(L,T

)1

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10

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60

SECTIONS

TIME HISTORY ANALYSES ON THE BASIS OF SEAOC DYNAMIC ANALYSIS

REQUIREMENTS

In this section, a different approach is used for the evaluation of the code requirements

related to seismic isolation. The methodology that follows is based on the SEAOC specifi

cations for time history analysis. Thus, comparisons can be made between the results of the

dynamic analysis approach according to the SEAOC specifications and the static analysis

procedure, as prescribed by the design formula of SEAOC.

According to SEAOC requirements, referring to time history analysis, pairs of hori

zontal ground motion time history components shall be selected from at least three recorded

events. These motions shall be scaled appropriately, so that the square root of the sum of the

squares (SRSS) of the 5% damped spectrum of the horizontal scaled components does not

fall below 1.3 times the 5% damped spectrum of the Design-Basis Earthquake by more than

10% in the period range of T minus 1.0 seconds to T plus 2.0 seconds, where T is the period

as determined by equation 2.4.

In order to comply with the above requirements, 6 pairs of earthquake records were

selected from the total of 29 that were used in the series of statistical evaluation analyses, as

discussed in Section 7. Three of those records were recorded on rock or stiff soil sites (soil

type Sl) and three of them on medium soil sites (soil type S2). The horizontal components of

each record were scaled in amplitude separately, by contrast with the methodology followed

in the series of the statistical evaluation analyses, (i.e. scaling both components by a common

factor). The scaling factors were estimated appropriately after performing trials, so that the

square root of the sum of the squares of the 5% damped spectrum of the scaled horizontal

components will be as consistent as possible with the desired one, according to the SEAOC

specifications. No time scaling of the records was employed.

8-1

This scaling approach was followed by an effort to make the SRSS spectrum of the

scaled horizontal components have a lower bound not more than 10% less of the 1.3 times

of the 5% damped spectrum of the Design-Basis Earthquake, as specified by SEAOC, and

also be smooth and comparable in shape with the one of the Design-Basis Earthquake.

In fact, almost all of the 5% damping spectra of the horizontal components of the

selected earthquake records included certain peaks in the period range under consideration,

and they were not attenuating smoothly as the period increased the way that the design

spectrum does. Thus, an effort was made as to predict the best combination of scaling factors,

so that the shape of the SRSS spectra approximated the Design-Basis spectra. The lower

bound limit criteria for the SRSS 5% damped spectra of the selected motions were satisfied

almost everywhere in the period range under consideration (0.5 seconds to 3.5 seconds).

Furthermore, the average of the three SRSS spectra in each case of soil type was above the

1.3 times the Design-Basis spectrum.

The 5% damping spectra of the selected earthquake motions and their respective SRSS

spectra are shown in Figures 8-1 to 8-2. Table 8.1 is a list of the motions selected, the factors

that scaled their components and the resulting PGA and PGV values of those components.

One can observe that the resulted peak ground accelerations are generally higher than OAg,

having a maximum value of 1.313g. Likewise, the peak ground velocity values had a maximum

of23.66 in/sec for S1soil types and 27.37 in/sec for S2 soil types. Those values can be compared

to the values that were determined to be the basis for scaling according to PGA (PGA=OAg)

or PGV (PGV=12in/sec for rock sites, 18in/sec for stiff soil sites and 22.5 in/sec for medium

soil sites) applied in the series of the statistical evaluation analyses.

Finally, it should be noted that in all the selected motions, the component that yielded

the most intense 5% damping spectrum was the one applied in the transverse (T) direction

of the structure. In this way, the strongest earthquake component was coupled with the mass

eccentricity to create torsional motion.

8-2

(a)......... 1.0

CJl 5ll DAUPING SPECTRA.......lAOTlON 1 (SAN FERNANDO 284)

Z - -- 1.3 TllAES 0.49 S10

~-T....-.-.., L

ll:: -- (L2+T 2)'/2W-.JWUO.5U«-.J«ll::I-UWQ..(J)

0.00.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

PERIOD (SEeS)

(b),.....1.00' \ 5ll DAlAPING SPECTRA.......,

\ lAOTION 2 (SAN FERNANDO 208)Z

\ - - - 1.3 TllAES 0.49 510

~-T...--..-... L

a::: __ (L2+T 2)'/2W-.JWUO.5t)«-.J«a:::......t)W0-(J)

0.00.0 0.5 1.0 1.5 2.0 2.5 3.0 :3.5 4.0

PERIOD (SECS)

(c)......... 1.00' 5ll DAMPING SPECTRA

'-"' lAOTION 3 (EL CENTRO 117)Z - -- 1.3 TllAES 0.49 S10 -T~ -----.. La::: -- (L'+T 2)'/2W...Jw(.)0.5(.)«...J<{a:::......(.)W0-(/l

0.00.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

PERIOD (SECS)

FIGURE 8-1 5% damping spectra of components T,L and square root of sum of squares ofcomponents T and L of scaled earthquake motions selected for dynamic analyses accordingto SEAOC time history analysis procedure and comparison with 1.3 times O.4g SI DesignSpectrum.

8-3

(a)r--.l.00>

\ 5lI DAMPING SPECTRA~

\ MOTION .. (WESTERN WASH. 325Z - - - 1.3 TIMES 0.49 520i= -T« ............... L0:: __ (L2+T 2)'/2W...JwUO.5U«...J«0::I-UW0-If)

0.00.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

PERIOD (SECS)

(b)r--.l.0

CJl 5lI DAMPING SPECTRA~

MOTION 5 (SAN FERNANDO 264)Z - - - 1.3 TIMES 0.49 520

~-T...........--.. L

0:: __ (~+T2)'/2W...JWUO.5U«...J«0::I-UW0-If)

0.00.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

PERIOD (SECS)

(c)r--.l.0

CJl 5lI DAMPING SPECTRA~

ZMOTION 6 (EUREKA 022)

0- - - 1.3 TIMES 0.49 52

i= -T« ...........--.. L0:: __ (L2+T 2)'/2W...JwUO.5U«...J«0::I-UWCl.If)

0.00.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 ".0

PERIOD (SECS)

FIGURE 8-2 5% damping spectra of components T,L and square root of sum ofsquares ofcomponents T and L of scaled earthquake motions selected for dynamic analyses accordingto SEAOC time history analysis procedure and comparison with 1.3 times O.4g S2 DesignSpectrum.

8-4

00 c:,.

·TA

BL

E8.

1S

elec

ted

time

hist

orie

san

dth

eirs

cali

ngfa

ctor

s.

EX

CIT

AS

OIL

OR

IGIN

AL

CO

MP

ON

EN

TS

IS

C.F

AC

TO

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A(g

)I

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V(i

n/se

c).

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NT

YP

ER

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OR

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LT

LT

LT

L

MO

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SA

NF

ER

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82W

S08

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503.

701.

313

0.80

315

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14.3

93(2

84)

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40(2

08)

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EL

CE

NT

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SOO

ES

90W

1.30

1.00

0.45

20.

214

17.1

2114

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(117

)

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ST

ER

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AS

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25)

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90E

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.900

(264

).

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KA

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60.

370

27.1

6627

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(022

)

8.1 Comparison of Time History Analysis Results to SEAOC Design Formulae.

The analysis results are presented in Tables 8.2 to 8.7. Additional results for the story

shear and the interstory drift ratios are presented in Appendix D. These results show that the

corner to center ratio of the isolation system displacement is equal to unity in the case of the

1 - story structure. Furthermore, this ratio is larger than unity in the 8 - story structure. These

results are consistent with those obtained in the dynamic analyses of Section 7.

Tables 8.8 and 8.9 compare the SEAOC design procedure to the results of the time

history analysis. The tables include the maximum displacement at the geometric center of

the base (maximum among T and L components of all three records) and the value of the

displacement according to the SEAOC static procedure. It may be observed that for soil type

S2, the analysis results are in good agreement with the SEAOC displacement. The SEAOC

formula predicts displacements with error of less than 10% of the calculated value. In the

case of soil type S1, the SEAOC formula underestimates the calculated displacement (by as

much as 25%) for the system with Tb = 3 seconds. For this system, the effective period T

(equation 2.4) is about 2.5 seconds. From the spectra of Figure 8-1, it can be observed that at

this period, the spectra for motions of soil type S1 overestimate the target spectrum by as

much as 30%. This should explain the difference.

It may be concluded that the procedure employed in this section produces results that

are in agreement with those obtained in Section7. Bothprocedures (the one based on statistical

evaluation of the response and the one based on scaled records according to the dynamic

analysis procedure of SEAOC) are consistent with the results of SEAOC static analysis

procedure.

8-6

00~

TA

BL

E8.

2A

naly

sis

resu

lts

for

1•

stor

yis

olat

edst

ruct

ure

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=39

.132

in(T

b=

2se

c),f

mllS

=0.

10,e

xcit

edby

scal

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irs

ofre

alre

cord

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cord

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toth

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ynam

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cedu

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to

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clud

ing

base

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eigh

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12ft

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SEC

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OR

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OR

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(IN

CH

)D

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(IN

CH

)C

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HT

WE

IGH

TH

EIG

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(%)

RA

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LT

LT

LT

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TIO

N#1

1.01

1.78

1.02

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60.

143

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10.

223

0.10

380.

1225

MO

TIO

N#2

0.99

2.11

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80.

139

0.10

20.

129

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510.

0707

MO

TIO

N#3

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119

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530.

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T(%

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LT

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LT

LT

LT

MO

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N#1

2.27

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2.27

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1.00

0.06

80.

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0.09

50.

101

0.05

130.

0557

MO

TIO

N#2

2.86

5.88

2.86

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0.07

70.

112

0.05

40.

065

0.02

920.

0357

MO

TIO

N#3

5.18

4.81

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4.81

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0.10

40.

103

0.05

90.

077

0.03

180.

0421

MO

TIO

N#4

4.12

6.92

4.12

6.92

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0.08

80.

111

0.04

790.

0606

MO

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N#5

3.85

8.06

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5·

8.07

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790.

0430

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190.

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00 .0

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4A

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48in

(Tb

=3

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a

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EIG

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(%)

RA

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MO

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1.14

1.97

1.14

1.97

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120

0.19

10.

232

0.10

350.

1277

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N#

21.

432.

681.

432.

691.

000.

107

0.11

90.

101

0.11

50.

0546

0.06

33

MO

TIO

N#3

1.92

2.35

1.92

2.36

1.00

0.12

00.

119

0.09

00.

114

0.04

890.

0628

MO

TIO

N#4

1.84

4.01

1.84

4.02

LOO

0.11

40.

134

0.11

80.

155

0.06

420.

0853

MO

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N#5

2.12

5.39

2.73

5.40

LOO

0.11

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152

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136

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540.

0745

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N#

65.

056.

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076.

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134

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081

0.14

40.

0438

0.07

85

00 I -o

TA

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5A

naly

sis

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lts

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8-s

tory

isol

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stru

ctur

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R=

39.1

32in

(Tb

=2

sec)

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u

=0.1

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1.22

2.51

1.44

2.64

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0.11

60.

158

0.11

10.

152

0.26

300.

3606

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21.

412.

131.

482.

311.

080.

121

0.13

40.

113

0.12

50.

2652

0.29

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NH

32.

062.

612.

212.

761.

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133

0.13

90.

125

0.13

20.

2896

0.31

80

MO

TIO

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2.12

2.85

2.23

2.86

1.00

0.14

20.

160

0.12

90.

174

0.30

480.

4256

MO

TI0

NH

52.

535.

522.

605.

581.

010.

126

0.22

90.

126

0.22

30.

3015

0.52

92

MO

TI0

NH

64.

144.

714.

174.

741.

010.

170

0.20

00.

152

0.19

50.

3537

0.47

01

~ - -

TA

BL

E8.

6A

naly

sis

resu

lts

for

8•s

tory

isol

ated

stru

ctu

rew

ith

R=

88.0

48in

(Tb

=3

sec)

,fm

u:=

0.05

,exc

ited

bysc

aled

pair

so

frea

lre

cord

sac

cord

ing

toth

eD

ynam

icA

naly

sis

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cedu

reof

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AO

C.W

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12ft

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ISP

L(I

NC

H)

DlS

PL

(IN

CH

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EN

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PL

WE

IGH

TW

EIG

HT

HE

IGH

T(%

)R

AT

IO

LT

LT

LT

LT

LT

MO

TIO

N#1

2.75

3.66

2.76

3.70

1.01

0.07

90.

089

0.06

90.

085

0.16

150.

2020

MO

TIO

N#2

3.25

6.84

3.27

6.92

1.01

0.07

30.

118

0.06

40.

111

0.14

940.

2583

MO

TIO

N#3

5.39

4.75

5.50

4.84

1.02

0.10

90.

094

0.09

40.

088

0.22

310.

2121

MO

TIO

N#4

4.87

6.88

4.89

6.89

1.00

0.10

10.

110

0.09

80.

124

0.23

070.

2986

MO

TIO

N#5

4.16

6.56

4.17

6.68

1.02

0.09

20.

109

0.08

20.

108

0.18

810.

2567

MO

TIO

N#6

9.75

11.1

79.

8511

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1.00

0.14

50.

152

0.13

40.

142

0.31

000.

3385

00 • -t-.J

TA

BL

E8.

7A

naly

sis

resu

lts

for

8•s

tory

isol

ated

stru

ctur

ew

ith

R=

88.0

48in

(Tb=3

sec)

,fm

u=

0.10

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156

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153

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750.

3762

TABLE 8.8 Summary of analysis results of maximum base displacement at geometriccenter of 1 • story isolated structure excited by scaled pairs of real records according to theDynamic Analysis Procedure of SEAOC and comparison of these displacements with thedesign displacements according to SEAOC static analysis procedure.

Sliding Isolation System Pyroperties.

R=39.l32 in R=88.048 in R=88.048 inSoil (Tb= 2 sec.) (Tb= 3 sec.) (Tb= 3 sec.)

Typefmax=O.1O fmax=O.05 fmax=O.1O

Analysis SEAOC Ratio * Analysis SEAOC Ratio * IAnalysis SEAOC Ratio *(inch) (inch) (inch) (inch) (inch) (inch)

SI 2.16 2.81 1.30 5.88 5.28 0.90 2.68 3.11 1.16

S2 5.69 5.72 1.01 11.17 10.19 0.91 6.23 6.32 1.01

* SEAOClAnalysis

8-13

TABLE 8.9 Summary of analysis results of maximum base displacement at geometriccenter of 8 • story isolated structure excited by scaled pairs of real records according to theDynamic Analysis Procedure of SEAOC and comparison of these displacements with thedesign displacements according to SEAOC static analysis procedure.



Typefmax=O.lO fmax=O.05 fmax=O.10


Sl 2.61 2.81 1.08 6.84 5.28 0.77 3.68 3.11 0.85

S2 5.52 5.72 1.04 11.17 10.19 0.91 6.32 6.32 1.00

* SEAOC/Analysis

8-14

SECTION 9

CONCLUSIONS AND DISCUSSION

In this study, a comparison has been made between SEAOC design requirements and

sliding isolated structure results obtained either by tests or by dynamic nonlinear time history

analysis. In the dynamic analysis, six different combinations of structural systems and prop

erties of isolation system were considered. The structural systems consisted of either a 1

story stiff structure or an 8 - story flexible structure. The isolation system consisted of 45

Friction Pendulum System (FPS) isolators with stiffness and frictional properties covering a

wide range of values. The isolators were modeled as elements having linear stiffness and

friction with circular interaction. In this way, the force-displacement relation of each isolator

was identical in all directions.

Each isolated structure was analyzed by three different procedures. In the first, a small

set of artificial motions was used. These motions were comparable with design spectra for

Seismic Zone 4. In the second, another small set of actual but scaled records was used. These

records were also compatible with design spectra for Seismic Zone 4. The scaling of these

records followed the procedure required by the SEAOC for time history analysis. In the third,

a large set of actual earthquake records was used. The records were scaled so that the peak

ground velocity (PGV) of each record had a value compatible with spectra for Seismic Zone

4. In this case, the variation in the response due to the variability of ground motion was

evaluated by calculating mean and standard deviation values.

This study concentrated on the evaluation of the SEAOC static analysis formula that

prescribes peak displacements of the isolation system. However, additional results like base

9-1

shear force, story shear forces and interstory drifts are presented for all analyzed structures.

This collection of nonlinear response data could be further used to evaluate design require

ments for sliding isolated structures.

The conclusions of this study are:

(l)Friction pendulum bearings can be accurately modeled with bilinear (non-velocity

dependent) hysteretic elements. In this respect, standard computer programs like

DRAIN-2D may be used provided that care is exercised in selecting the proper "yield

displacement" and time step for integration.

(2)The SEAOC formula for the design displacement (equation 2.1) overpredicts uni

directional test displacements. However, the amount of overprediction is difficult

to quantify because of the difficulty in establishing ZNS values which are

representative of a single earthquake motion history.

(3)The SEAOC formula (equation 2.1) overpredicts uni-directional artificial time his

tory displacements by an average of about 50%. For the calculation of the time

history displacements, three artificial (spectrum compatible) earthquake motions

were used for each set of analyses. Furthermore, the SEAOC formula overpredicts

bi-directional artificial time history displacements by an average of 25%. The bi

directional excitation consisted of one artificial, spectrum compatible earthquake

motion applied in one building direction and 83% of the same motion applied in the

other direction. In this way, the square root of the sum of squares of the spectra of

the two artificial components was compatible with 1.3 times the Design-Basis spectra.

(4)The SEAOC formula (equation 2.1) predicts accurately the mean peak displacement

response of several bi-directional real earthquakes scaled to have a common PGV

and whose average spectrum equals the SEAOC design spectrum. Furthermore, the

scaled earthquakes have the average of their SRSS combined spectra (square root

of sum of squares of the Land T spectra) above the 1.3 times the SEAOC design

spectrum (Design-Basis spectrum).

9-2

(5)The SEAOC formula (equation 2.1) predicts accurately the peak displacement

response as calculated by the time history analysis method specified by SEAOC for

dynamic analysis.

(6)The additional displacement due to torsion is significantly lower in sliding isolation

systems than in other isolation systems. In particular, a 5% mass eccentricity in a

stiff 1 - story structure was found to generate, in all analyzed cases, an insignificant

additional displacement in sliding isolation systems. The maximum calculated ratio

of corner bearing displacement to geometric center displacement was only 1.02,

whereas the SEAOC static procedure prescribes a value of 1.24 for the analyzed plan

configuration. In the case of a flexible 8 - story structure, the additional displacement

due to torsion is considerably larger than that in the stiff 1- story structure. In general,

torsion in sliding isolation systems is primarily affected by the combination of mass

eccentricity and superstructure flexibility and not by the mass eccentricity alone. In

this respect, the minimum factor of 1.1 specified in SEAOC for the amplification of

the design displacement (D) to account for torsion should be modified so that it

reflects the effect of the superstructure flexibility.

The main conclusion of this study is that the SEAOC static analysis procedure predicts

displacements of the isolation system which compare well with displacements calculated in

time history dynamic analysis. In this analysis, the earthquake motions consisted of two ort

hogonal components whose spectra, when combined by the SRSS rule, matched or were above

the 1.3 times the SEAOC design spectra (Design-Basis spectra).

In the cases in which the earthquake motions matched the 1.3 times the Design-Basis

spectra (artificial records), the SEAOC formula overpredicted the time history displacements

by about 25%.

In the cases in which the earthquake motions had combined spectra above the 1.3 times

the Design-Basis spectra (PGV scaled, Figures 7-2 and 7-3), the SEAOC formula predicted

well the mean peak displacement of these earthquake motions. When a square interaction

9-3

model was used for the isolation bearings (as done in the study ofKircher and Lashkari, 1989),

the SEAOC formula overpredicted the mean peak displacement by less than 20%. In this

respect, the degree of conservatism in the SEAOC static analysis procedure appears to be

about the same for the studied sliding isolation systems and the bilinear isolation systems

studied by Kircher and Lashkari, 1989.

9-4

SECTION 10

REFERENCES

[1] Applied Technology Council, (1978). Tentative Provisions for theDevelopmentofSeismic

Regulations for Buildings, ATC 3-06, NBS 510, NSF 78-8, Washington, D. C., June.

[2] California Institute of Technology (1975). Analyses of Strong Motion Earthquake

Accelerograms. Report No. EERL 75-80, Vol III, Part T, Earthquake Engineering

Laboratory, Pasadena, CA.

[3] Chalhoub, M.S. and Kelly, J.M. (1990). Comparison of SEAONC Base Isolation Ten

tative Code to Shake Table Results. Journal of Structural Engineering, ASCE, Vol. 116,

No.4, pp.925-938.

[4] Constantinou, M.C., Mokha, A. and Reinhorn, A.M. (1990a). Experimental and Ana

lytical Study ofa Combined SlidingDisc Bearing and Helical Steel Spring Isolation System.

Report No. NCEER-90-0019, National Center for Earthquake Engineering Research,

Buffalo, N.Y.

[5] Constantinou, M.C., Mokha, A. and Reinhorn, A.M. (1990b). Teflon Bearings in Base

Isolation. Part 2: Modeling. Journal of Structural Engineering, ASCE, Vol. 116, No.2,

pp.455-474.

[6] Constantinou, M.C., Mokha,A. and Reinhorn, A.M. (1991).Study ofa Sliding Bearing

and Helical Steel Spring Isolation System. Journal of Structural Engineering, ASCE,

Vol. 117, No.4, pp.1257-1275.

[7] Gasparini, D.A. and Vanmarke, E.H. (1976). Simulated Earthquake Motions Com

patible with Prescribed Response Spectra. Report No.2, Department of Civil Engi

neering,Massachusetts Institute of Technology, Boston, Massachussetts.

[8] Gear, C.W. (1971). The Automatic Integration of Ordinary Differential Equations.

Numerical Mathematics, Communications of ACM, Vol. 14(3), pp.176-190.

10-1

[9] Griffith, M.e., Aiken, I.D. and Kelly, J.M. (1988). Experimental Evaluation ofSeismic

Isolation ofa 9 - Story Braced Steel Frame Subject to Uplift. Report No. UBC/EERC

88/05. Earthquake Engineering Research Center, University of California, Berkeley,

CA.

[10] Kircher, e.A And Lashkari, B. (1989). Statistical Evaluation ofNonlinear Response of

Seismic Isolation Systems. Report No. JBA 109-070, Jack R. Benjamin and Associates,

Inc. Mountain View, CA.

[11] Mokha, A., Constantinou, M.e. and Reinhorn, AM. (1988). Teflon Bearings inAseismic.

Base Isolation. Experimental Studies and Mathematical Modeling. Report No.

NCEER-88-0038, National Center for Earthquake Engineering Research, State

University of New York, Buffalo, N.Y.

[12] Mokha, A., Constantinou, M.e. and Reinhorn, A.M. (1990a). Teflon Bearings in Base

Isolation. Part 1: Testing. Journal of Structural Engineering, ASCE, Vol. 116, No.2,

pp.438-454.

[13] Mokha, A., Constantinou, M.C. and Reinhorn, A.M. (1990b). Experimental and Ana

lytical Study of a Sliding Isolation System with a Spherical Surface.. Report No.

NCEER-900020, National Center for Earthquake EngineeringResearch, Buffalo, N.Y.

[14] Mokha, A., Constantinou M.C., Reinhorn A.M. and Zayas V. (1991). Experimental

Study ofFriction Pendulum Isolation System. Journal of Structural Engineering, ASCE,

Vol. 117, No.4, pp.1201-1217.

[15] Nagarajaiah, S., Reinhorn, A.M. and Constantinou, M.e. (1989). Nonlinear Dynamic

Analysis of Three - Dimensional Base Isolated Structures - Program 3D-BASIS. Report

No. NCEER-89-0019, National Center for Earthquake Engineering Research, State

University of New York, Buffalo, N.Y.

[16] Powell, G.H. (1973). DRAIN 2D User Guide. Report No. EERC 73-22. Earthquake

Engineering Research Center, University of California, Berkeley, CA.

10-2

[17] Structural Engineers Association ofCalifornia (1990a). Tentative GeneralRequirements

for the Design and Construction of Seismic Isolated Sructures. Appendix IL of Recom

mended Lateral Force Requirements and Commentary. San Francisco, CA.

[18] Structural Engineers Association of California (1990b). Recommended Lateral Force

Requirements and Commentary (Blue Book). Seismology Committee.San Francisco,

CA.

[19] Structural Engineers Association of Northern California (1986).Tentative Seismic

Isolation Design Requirements, San Francisco, CA.

[20] Seed, H.B., Ugas, C. And Lysmer, J. (1974). Site - Dependent Spectra for Earthquake

Resistant Design, Report No. EERC 74-12, Earthquake Engineering Research Center,

University of California, Berkeley, CA.

[21] Uniform Building Code (1991). International Congress ofBuilding Officials, Whittier,

CA.

[22] Zayas, V., Low, S.S. and Mahin, S.A. (1987). The FPS Earthquake Resisting System,

Experimental Report. Report No. UBC/EERC-87/01, Earthquake Engineering

Research Center, University of California, Berkeley, CA.

10-3

fJ-/

APPENDIX A

RESULTS OF MAXIMUM STORY SHEAR AND INTERSTORY DRIFT FOR 8· STORY

ISOLATED STRUCTURE. EXCITATION REPRESENTED BY ARTIFICIAL RECORDS

COMPATIBLE WITH DESIGN SPECTRA. EXCITATION ONLY IN THE TRANSVERSE

(T) DIRECTION.

TA

BL

EA

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R=3

9.13

2in

(Tb=

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:f)-I

APPENDIXB

RESPONSE SPECTRA FOR 5% DAMPING OF COMPONENTS OF PGV SCALED

MOTIONS USED IN DYNAMIC ANALYSES AND COMPARISON TO DESIGN SPEC·

TRA.

....--.0.6CJl

L 5~ DAMPING SPECTRA'-"

Z ROCK SITE0 NO# 1 HELENA (323)~<{ PGV SCALEDn::: 0.4 0.4g S1 "W-l "W "-U .....U .....<{ ..... -<i 0.2n:::~ TUW0..(J)

0.00.5 1.0 1.5 2.0 2.5 3.0 3.5

PERIOD (SEeS)

3.5

(095)

- -L

5~ DAMPING SPECTRA

ROCK SITE

NO#2 KERN COUNTRYPGV SCALED

T

1.5 2.0 2.5 3.0PERIOD (SEeS)

1.0

0.49 S1z00.4

~n:::w--.J 0.3WUU<{ 0.2--.J<{n:::t:; 0.1W0..(J)

0.0 -+r.,.,....,rTTTT1rTT.,.,....,rTT-.r1rTT-.r1rTTTT1rTT-.r1rrr.,.,rrrrn-rrrnrrr.,.,..,..,..rrri0.5

....--.0.5 ...-------------------------,CJl

'-"

FIGURE B-1 Response spectra for 5% damping of components ofPGV scaled motions usedin dynamic analyses and comparison to Design Spectra.

B-1

3.53.0

5l'l DAMPING SPECTRA

ROCK SITE

NO#3 LYTLE CREEK (290)PGV SCALED

--

1.5 2.0 2.5PERIOD (SEeS)

1.0

T

L

S1 \ , , ," "

O.4gz00.4

~n:::w---I 0.3WUU« 0.2---I«n:::b 0.1W

BJ 0.0 irn-rrrrr-rrrrr"TT""TT"T"TT""TT"T~::~=~~~~~:;:;~"TT""rrTJ0.5

..---0.5 -r--------------------------,01.........

3.5

- -

5l'l DAMPING SPECTRA

ROCK SITENO#4 PARKFIELD (097)PGV SCALED

-

1.5 2.0 2.5 3.0PERIOD (SECS)

1.0

L

S1 \ ,T ,

" "

0.4gz00.4

~n:::w---I 0.3WUU« 0.2---I«n:::0 0.1W(L(f1

0.0 -+-rrn-rrrrr-rr"""'"TT""rrTTT1rr.-rn-rrrrr"TT""TT"T..-rrr.-TT1-rrrTI"TT""TT"T..-rrri0.5'

..---0.5 ~------------------------,01.........

FIGURE B:.1 Continued.

B-2

3.53.0

5l1S DAMPING SPECTRAROCK SITENO#5 SAN FERNANDO (284)PGV SCALED

-

1.5 2.0 2.5PERIOD (SECS)

1.0

T

zor- 0.6<{0:::W-lWU 0.4U<{

-l<{

g: 0.2UWQ..(f)

0.°+rTT1"'TTTTl"TT"TT1"TTTT1'T"rrrr"""-;rTTTT1rTTTT1"'TTTT1"TT"TT1'T"rTTT'T"rrrrTT"'!

0.5

,,",0.8 .,..--------------~--------__,01..........

,,",0.601

5,.. DAMPING SPECTRA..........

Z L ROCK SITE0 NO#6 SAN FERNANDO (126)~ PGV SCALED0::: 0.4 O.4gW-lWU TU<{

<i 0.2 -0::: - -r- ---uWQ..(f)

0.00.5 1.0 1.5 2.0 2.5 3.0 3.5

PERIOD (SECS)

FIGURE B-1 Continued.

B-3

3.53.0

~ DAMPING SPECTRAROCK SITENO#7 SAN FERNANDO (279)PGV SCALED


1.0

L

O.4gz00.4

~n:::w-l0.3WUU<{ 0.2-l<{n:::t> 0.1W0...(J)

o.0 +-r-T""r"T"'T""T""r-rT"rT"""I--r-r-T""T"T""""""!"""T"T""T""1'""'T"'T""T""r-rT"rT"""I--r-r-T""T"T""""""!"""T"T".,..,..,.......,....,r-rT.,........,...,...,...1"'"T"'T""'!

0.5

--.0.5 -r--------------------------,0"1

'--'

--.0.50"1

'--' 5'" DAMPING SPECTRAZ ROCK SITE00.4 O.4g S1 \ NO#S SAN FERNANDO (104)~ , PGV SCALEDn::: ,w .....-l0.3 .....W .....U .....U .....<{0.2

.....

-l T<{n::: L - -t> 0.1W0...(J)

0.00.5 1.0 1.5 2.0 2.5 3.0 3.5

PERIOD (SECS)


B-4

,.......0.5Ol

5ss DAMPING SPECTRA..........

Z ROCK SITE00.4

0.49 S1 \ NO#9 SAN FERNANDO (128)

~ T " PGV SCALED0::: "W ,-.J 0.3 ,w .....U ......U ...... .....c< 0.2 ..... ..... .....-1c< --0::: LG0.1W0...Cf)

0.00.5 1.0 1.5 2.0 2.5 3.0 3.5

PERIOD (SEeS)

0.5 -:r--------------------------,

3.53.0

5ss DAMPING SPECTRA

ROCK SITENO#10 SAN FERNANDO (220)PGV SCALED


L

1.0

0.49

0.0 -+rTT1rTTTT1rTTrrr.....-rrTTTT""rrTTT1rTTrrr.....-rrTTTT""rTTTr1rTTTT1rTTrrT,...,r-rl

0.5

.......'"...... 0.4zo

~w 0.3...Jw()

~...J 0.2c(

g:()

~ 0.1(J)


B-5

3.5

~ DAMPING SPECTRA

STIFF SOIL SITE

NO#11 LOWER CA (117)

PGV SCALED

1.5 2.0 2.5 3.0PERIOD (SEeS)

T

1.0

0.49 S1 ,

___ 0.6 ...,--------------------------,0'1

"--'

3.53.0

~ DAMPING SPECTRASTIFF SOIL SITENO#12 ELCENTRO (117)PGV SCALED

1.5 2.0 2.5PERIOD (SEeS)

T

1.0

0.49 S1 "

zoI- 0.6«n:::w-lW00.4o«-l«g: 0.2ow0..U1

0.0 -+rT"T'"T"'T""T""r-rT"T'"'r1"'T""T""r-rT"TT""1"'TT"""""TT""1"'TT",...,.,.TT1rrrT"T'"TTT1rTTT"T'"T-rT"1r-rT"T"T'"T""';

0.5

___ 0.8 ...,------------------------,Ol

"--'


B-6

3.5

~ DAMPING SPECTRA

STIFF SOIL SITENO#13 PARKFIELD (014)PGV SCALED

1.5 2.0 2.5 3.0PERIOD (SECS)

L

1.0

O.4gz00.4

~0:::W--l0.3wUU« 0.2--l«0:::G0.1W0..(/)

0.0 -+rrrr-rrrrr-ro-....,..,..-rrrTT1rrrrrr-rrrrrTT1,.,...rrr'TT1r-rrrrrTT1rrrTTT-rr"""""-/0.5

..-0.5 ..,-------------------------,O"l---

3.53.0

~ DAMPING SPECTRASTIFF SOIL SITENO#14 SAN FERNANDO (110)PGV SCALED


L

1.0

zoI- 0.6«0:::W--lWUO.4U«--l«g: 0.2UW0..(/)

0.0 -+rTTT-rrrrrTT1-n-rrrTT1""1"'T"rrrTT1r-rrrrrTT1r-rrrrrTT1r-rrrrrTT1r-rr,..,...,."'T""T-!0.5

..-0.8 ..,--------------------------,O"l---


B-7

.-..0.8O'l

~ DAMPING SPECTRA'-'

Z STIFF SOIL SITE0 NO#15 SAN FERNANDO (135)I- 0.6

PGV SCALED<{~W-oJWU 0.4 0.4gU<{

-oJ<{

g: 0.2 - -U - --w LD-C/)

0.00.5 1.0 1.5 2.0 2.5 3.0 3.5

PERIOD (SEes)

3.53.0

--- - --

5. DAMPING SPECTRASTIFF SOIL SITENO#16 SAN FERNANDO (208)PGV SCALED

'.5 2.0 2.5PERIOD (SEeS)

T

1.0

0.4g S1

zoI- 0.6<{~W-oJWU 0.4U<{

-oJ<{

~0.2

UwD-C/)

o.0 -M-T""T""'T""T"T'"T""T"T"T"T"r-T""T"T""T""'lr-r-T""T""T""'lr-T"T"T""T""'T""T"T'"T""T"T"'T"T""r-T""T"T""T""'lr-r-T"T""T""'T""T"T'"T""T"T"'T"T""r-T""T.,.,..,r-r-l

0.5

.-..0.8 ...,.--------------------------,O'l'-'

FIGURE B·l Continued.

B-8

3.5

---

5~ DAMPING SPECTRASTIFF SOIL SITE

NOH17 SAN FERNANDO (211)PGV SCALED

T

1.5 2.0, 2.5PERIOD (SECS)

L50.5

~ffi 0.4 0.49 S1 ,.....JW00.3o«<i! 0.2a:::I-~ 0.10...U1

0.0 -=h-rn"""'T"TT"T'T"'1rr1TTTTT"rTTTTl"""'T"TT"T'T"'1rr1TTTTnrrlTTTTT"rTTTn.."...rrrl

0.5 1.0

--.0.6 ....,..------------------------,0'1..........

.3.5.3.0

~ DAMPING SPECTRASTIFF SOIL SITENOH18 SAN FERNANDO (466)PGV SCALED

--- --- - --L


1.0

0.49 S1 ,

zo~a::: 0.4W.....JWoo«<i! 0.2a:::IoW0...U1

O.0 -h-T"T"T""T"'T"1n-T"..-.-r"""'n-T"..-.-r"'TT'r-r-r..-.-r"'TT'T"'T"T"T'T"1"'TT'T"'T"T"T'T"1"'TT'T'T""T"T'T"1r-T""T"T'T""T~

0.5

--.0.6 .....------------------------,0'1..........


B-9

3.53.0

- -- -

5. DAMPING SPECTRA

STIFF SOIL SITE

NO#19 SAN FERNANDO (253)

PGV SCALED

---


1.0

L

T

O.4gz00.4

~~W-1 0.3WUU« 0.2....J«~

b 0.1Wa..(/)

0.0 -+-rTT"1"'T""T'"I""T"T-rnr-rrrr-r-rr""""'TT"1"'T""T'"I""T"T-rnr-rrrr-r"T"T"1rTT"TTT"'T""T'"rrrTTl""TT"T"TT"'t

0.5

.-..0.5 -,--------------------------,0'1

'-"

3.53.0

5lS DAMPING SPECTRA

STIFF SOIL SITENO#20 SAN FERNANDO (199)PGV SCALED


L

1.0

O.4g

zoI- 0.6«~w....JWUO.4U«....J«~ 0.2UWa..(/)

0.0 -h-T"TI'TT1rTT"'TTT"T"T"1rTT"TT'T'"TTrrrTT'T'"TTI""T"TTT"l""TT"rTTTT"l""TT"rTT-rnr-rrrTT"T'T"'!

0.5

.-..0.8 -,-------------------------,Ol

'-"


B-10

.3.5.3.0

5" DAMPING SPECTRAMEDIUM SOIL SITE

NO#21 WESTERN WASH.(325)PGV SCALED


L

T

1.0

0.49 S2 l\..

zoI-- 0.6«e:::w-JWU 0.4U«-J«g: 0.2UW0...(f)

o.0 +r-TT""'I""TT"T""T"T"T'T""1~TT'T"T"T'"r_r_r"T""T""1""TT"T""T"T"T'T""1r_T"T",..,..,."T"T'"r_r_rTT""'l""TT"T""T"T"T'T""1r_T""T"",...,...,...1

0.5

......... 0.8 -r--------------------------,01

'--"

.3.5

5~ DAMPING SPECTRAMEDIUM SOIL SITE

NO#22 EUREKA (022)PGV SCALED

1.5 2.0 2.5 .3.0PERIOD (SECS)

1.0

T

0.49

6 0.5

~e::: 0.4w-JWUO.3U«<i! 0.20:::I--~ 0.1n..(f)

O.0 ~"T'"r1-rrT"TT"T'"r1n_r~.,.....,I'"TT"T'T"I'..,..,..I'"TT""T""T""1.,..,...r_r_r"T""T""1""TT"r_r_r"T""T""1""TT"T""T"T"T""T""1~

0.5

......... 0.6 -:r------------------------,01

'--"


B-ll

......-.-.0.80'1 L......... ~ DAMPING SPECTRA

ZT MEDIUM SOIL SITE

0 NO#23 EUREKA (023)....... 0.6« PGV SCALED0:: 0.49 S2 'W-JWUO.4U ......

« .....

-J«~0.2UWa..(f)

0.00.5 1.0 1.5 2.0 2.5 3.0 3.5

PERIOD (SECS)

3.5

- -

S. DAMPING SPECTRAMEDIUM SOIL SITE

NO#24 FERNDALE (023)PGV SCALED

----

1.5 2.0 2.5 3.0PERIOD (SECS)

1,0

T

0.49 S2 \

zot;(0::: 0.4W-JWUU«<i. 0.20::.......UWa..(f)

0.0 -+r-TT"T"T"T"'I"'TT"""'"T"T'"I"'TTT"T""1-rT"T'TTT"T""1-rT"T'TTT"T""1M"T'TT"T"1"T'"1M"T'TT"T"1"T'"1M"T'TT"T"'T"T""i

0.5

......-.-.0.6 ....,....---..,.....---------------------,0'1.........


B-12

3.53.0

5lS DAMPING SPECTRAMEDIUM SOIL SITENO#25 SAN FERNANDO (241)PGV SCALED

- ----


T

1.0

0.4g S2

Z00.8

~n:::w-.J 0.6wUU<t: 0.4-.J<t:n:::t3 0.2wQ..(J)

0.0 +rTTl-rrrr-rTTlrn-n-r"'-rrTrn-rrrr-rTTl",.-n-rTTlrrr,.,...,.,.,-rr-rTTl-rrrr-r-l0.5

---.1.0 ...,.--------------------------,0'1..........

3.53.0

---

5lS DAMPING SPECTRAMEDIUM SOIL SITENO#26 SAN FERNANDO (458)PGV ·SCALED


T

1.0

Z00.8

~n:::wd O.4gUU<t: 0.4-.J<t:n::IUWQ..(J)

0.0 -I-r-,.,...,.,.,-rr-rrn-rrrr-rrn-rrrr-rTTl-rrrr-rTTlrn-n-rTTlrn-n-r-rnrrrn-r-,-rj0.5


B-13

3.5

(264)

5~ DAMPING SPECTRA

MEDIUM SOIL SITE

NO#27 SAN FERNANDO

PGV SCALED

1.5 2.0 2.5 3.0PERIOD (SECS)

LZ00.8

~0::Wcd O.4g S2UU« 0.4-l«0::rUWa..(f)

o.0 -!-r-.....,...,........................"T"T""'I...,....,...T'"T"T"'T""r1,..,.......-rr-r......................."T""T""1-rrT"T"T"'T""r11"""T""T'"-rr-r"T'"T""I'""TT"T"T""'I-rrrrrl

0.5 1.0

3.5

(267)

- --

5~ DAMPING SPECTRAMEDIUM SOIL SITE

NO#28 SAN FERNANDO

PGV SCALED

1.5 2.0 2.5 3.0PERIOD (SECS)

1.0

L

T

Z00.8

~0::W-l

~ O.4gU« 0.4-l«0::r-UWa..(f)

0.0 -!-r-T""rT""'T""r1.................,...,........................"T"T""'I...,....,...I'""TT"T""T""1...,....,...T"T"T"'T""T'"'I-rrT""rT"'T""T'"'II"""T""T'"T"T'T"'T"T"'1r-rT'T-rT"'T'T"'f

0.5


B-14

3.5

(325)

511 DAMPING SPECTRAMEDIUM SOIL SITENO#29 PUGET SOUNDPGV SCALED

1.5 2.0 2.5 3.0PERIOD (SEeS)

1.0

O.4g S2

Z00.8

~0::W-.JWUU« 0.4-.J«0::fUW0...(f)

O.a +r-rrT""-'r-rT"T"T'T"'T'T""rrr"""""'T'T"",...,..,........,,..,,...,..,.""-',..,rrT.,.,-,r-r-rrrTTT"1r-rT"TT'"T-rrl

0.5


B-15

c-r'

APPENDIXC

RESULTS OF MAXIMUM STORY SHEAR AND INTERSTORY DRIFT FOR 8 • STORY

ISOLATED STRUCTURE. EXCITATION REPRESENTED BY A SET OF PAIRS OF

SCALED EARTHQUAKE MOTIONS (SCALING BASED ON PGV).

Q -

TA

BL

EC

.lA

naly

sis

resu

lts

ofm

axim

umst

ory

shea

rfo

r8

-sto

ryis

olat

edst

ruct

ure

wit

hR

=39.

132

in(T

b=2

sec.

),f m

u=0

.10.

Exc

itat

ion

repr

esen

ted

bya

seto

fpai

rso

fsca

led

eart

hqua

kem

otio

nsre

cord

edon

Roc

kS

ites

(rep

rese

ntat

ive

of

soil

type

SI)

.W

eigh

tis

tota

lw

eigh

to

fst

ruct

ure

incl

udin

gba

se.

II:1MST

OR

YSH

EA

R"d

STO

RYS

HE

AR

~'STORY

SHE

AR

'"ST

OR

YSH

EA

R'"

STO

RY

SHE

AR

1~ST

OR

YSH

EA

R'"

STO

RY

SHE

AR

EX

CIT

AT

ION

WE

IGH

TW

EIG

HT

WE

IGH

TW

EIG

HT

WE

IGH

TW

EIG

HT

WE

IGH

T

LT

LT

LT

LT

LT

LT

LT

1H

EL

EN

A(3

23)

0.15

40.

057

0.13

50.

054

0.12

40.

043

0.12

20.

042

0.11

50.

055

0.10

20.

054

0.06

40.

040

2K

ER

NC

OU

NT

Y(0

95)

0.11

00.

100

0.10

80

.10

10

.09

30

.10

70

.09

70

.11

60

.09

50

.10

90.

077

0.09

10

.05

20

.06

23

LY

TL

EC

RE

EK

(290

)0.

102

0.09

60.

081

0.08

00.

112

0.10

20.

135

0.10

30.

121

0.08

80.

126

0.11

50.

082

0.09

34

PA

RK

FIE

LD

(097

)0.

083

0.11

00.

082

0.10

10.

079

0.09

40.

079

0.09

10.

067

0.09

20.

080

0.09

80.

059

0.06

85

SA

NF

ER

NA

ND

O(2

84)

0.10

70.

118

0.10

20.

116

0.09

40.

114

0.08

20.

102

0.06

90.

095

0.06

30.

081

0.04

30.

050

6S

AN

FE

RN

AN

DO

(126

)0.

149

0.09

40.

141

0.09

30.

118

0.08

00.

113

0.08

30.

081

0.07

10.

083

0.08

00.

063

0.07

77

SA

NF

ER

NA

ND

O(2

79)

0.09

60.

114

0.Q

920.

100

0.08

30.

092

0.08

30.

087

0.07

90.

078

0.07

30.

079

0.05

60.

056

8S

AN

FE

RN

AN

DO

(104

)0.

076

0.10

90.

080

0.11

80.

080

0.10

80.

073

0.08

90.

061

0.09

20.

055

0.06

50.

063

0.06

69

SA

NF

ER

NA

ND

O(1

28)

0.09

40.

119

0.08

90.

111

0.08

40.

105

0.10

60.

101

0.09

00.

097

0.08

30.

096

0.09

20.

095

10S

AN

FE

RN

AN

DO

(220

)0.

111

0.10

10.

103

0.09

70.

095

0.08

60.

091

0.07

30.

078

0.06

40.

074

0.06

30.

051

0.05

1

ME

AN

0.10

80.

102

0.10

10.

097

0.09

60.

093

0.09

80.

089

0.08

60.

084

0.08

20.

082

0.06

30.

066

(J0.

024

0.01

70.

021

0.01

80.

Ql5

0.02

00.

019

0.01

90.

019

0.01

60.

019

0.Q

l80.

014

0.01

7M

EA

NO

FM

AX

(L,n

0.12

00.

111

0.10

70.

105

0.09

60.

089

0.06

8(J

OF

MA

X(L

,n0.

017

0.01

70.

010

0.Q

l50.

014

0.01

60.

Ql5

Q N

TA

BL

EC

.2A

naly

sis

resu

lts

of

max

imum

inte

rsto

rydr

ift

for

8-

stor

yis

olat

edst

ruct

ure

wit

hR

=39.

132

in(T

b=2

sec.

),f m

u=0

.10.

Exc

itat

ion

repr

esen

ted

bya

set

ofp

airs

ofs

cale

dea

rthq

uake

mot

ions

reco

rded

onR

ock

Site

s(r

epre

sent

ativ

eo

fsoi

ltyp

eS

l).H

eigh

tis

12ft

.

EX

CIT

AT

ION

2nd

srO

RY

DRI

FT(%

)3r

dsr

OR

YD

RIF7

('1o)

4th

srO

RY

DRI

FT('1

t.)5t

hsr

OR

YD

RIFT

('1o)

6th

srO

RY

DRI

FT('1

t.)7t

hsr

OR

YD

RIFT

('1t.

8th

srO

RY

DRI

FT('1

t.)H

EIG

HT

HE

IGII

TH

EIG

HT

0H

EIG

IIT

HE

IGH

T0

HE

lGil

l0

HE

lGil

l0

LT

LT

LT

LT

LT

LT

LT

1H

EL

EN

A(3

23)

0.36

350.

1325

0.30

950.

1294

0.38

640.

1406

0.37

970.

1344

0.35

730.

1767

0.47

740.

2563

0.29

920.

1909

2K

ER

NC

OU

NT

Y(0

95)

0.25

920.

2397

0.24

820.

2446

0.29

930.

3408

0.30

490.

3674

0.29

910.

3449

0.36

620.

4264

0.24

610.

2934

3L

Y1l

..EC

RE

EK

(290

)0.

2404

0.21

680.

1808

0.18

370.

3485

0.33

290.

4148

0.33

090.

3706

0.27

730.

6003

0.54

130.

3824

0.43

89

4P

AR

KF

IEL

D(0

97)

0.19

820.

2477

0.19

250.

2297

0.24

490.

2918

0.24

870.

2837

0.21

050.

2945

0.37

910.

4628

0.27

430.

3302

5S

AN

FE

RN

AN

DO

(284

)0.

2506

0.27

380.

2394

0.27

130.

2954

0.35

760.

2589

0.32

270.

2145

0.30

120.

2966

0.38

990.

2009

0.24

08

6S

AN

FE

RN

AN

DO

(126

)0.

3309

0.22

070.

3282

0.22

140.

3721

0.25

850.

3584

0.25

370.

2586

0.23

110.

3895

0.37

630.

2967

0.36

28

7S

AN

FE

RN

AN

DO

(279

)0.

2312

0.27

790.

2171

0.23

840.

2625

0.28

930.

2597

0.28

450.

2491

0.24

440.

3393

0.37

260.

2581

0.26

43

8S

AN

FE

RN

AN

DO

(104

)0.

1748

0.22

530.

1885

0.28

370.

2503

0.34

410.

2273

0.28

000.

1922

0.29

100.

2588

0.29

580.

2925

0.31

30

9S

AN

FE

RN

AN

DO

(128

)0.

1969

0.27

560.

2099

0.26

240.

2681

0.31

680.

3252

0.31

980.

2857

0.30

400.

3861

0.45

780.

4278

0.45

96

10S

AN

FE

RN

AN

DO

(220

)0.

2593

0.23

900.

2432

0.22

950.

2948

0.27

120.

2930

0.23

170.

2489

0.20

170.

3477

0.29

780.

2400

0.24

28

ME

AN

0.25

050.

2349

0.23

570.

2294

0.30

220.

2944

0.30

710.

2809

0.28

870.

2667

0.38

410.

3877

0.29

180.

3137

(J0.

0559

0.04

040.

0473

0.04

270.

0479

0.06

010.

0586

0.06

150.

0570

0.04

930.

0908

0.08

350.

0642

0.08

24

ME

AN

OF

MA

X(L

,T)

0.27

540.

2598

0.33

420.

3309

0.30

200.

4220

0.32

45

(JO

FM

AX

(L,T

)0.

0398

0.03

930.

0327

0.04

470.

0416

0.07

990.

0720

Q ~

TA

BL

EC

.3A

naly

sis

resu

lts

ofm

axim

umst

ory

shea

rfo

r8

-st

ory

isol

ated

stru

ctu

rew

ith

R=3

9.13

2in

(Tb=2

sec.

),fm

u:=0

.10.

Exc

itat

ion

repr

esen

ted

by

ase

tofp

airs

ofs

cale

dea

rtb

qu

ake

mot

ions

reco

rded

onS

tiff

Soil

Sit

es(r

epre

sent

ativ

eo

fsoi

lty

peS

I).W

eigh

tis

tota

lw

eigh

tof

stru

ctur

ein

clud

ing

base

.'

Utd

srO

RY

SHE

AR

3rd

srO

RY

SHE

AR

4th

srO

RY

SHE

AR

5th

srO

RY

SHeA

R6t

hST

OR

YSH

eAR

7th

STO

RY

SHE

AR

8th

STO

RY

SHE

AR

EX

CIT

AT

ION

WE

IGH

TW

EIG

lIT

WE

IGlI

TW

EIG

HT

WE

IGH

TW

EIG

HT

WE

IGH

T

LT

LT

LT

LT

LT

LT

LT

11L

OW

ER

CA

(117

)0.

132

0.11

30.

116

0.09

60.

101

0.13

70.

092

0.14

10.

099

0.1

l80.

096

0.10

60.

069

0.08

0

12E

LC

EN

TR

O(1

17)

0.13

20.

126

0.13

40.

122

0.13

60.

126

0.12

20.

126

0.11

40.

124

0.10

00.

124

0.06

00.

074

13P

AR

KF

IELD

(014

)0.

084

0.13

30.

082

0.12

10.

101

0.1l

10.

098

0.09

70.

105

0.09

90.

113

0.12

00.

075

0.07

8

14S

AN

FE

RN

AN

DO

(110

)0.

150

0.l

l20.

143

O.ll

O0.

131

0.10

00.

117

0.09

10.

1II

0.09

50.

107

0.09

40.

065

0.07

3

15S

AN

FE

RN

AN

DO

(135

)0.

099

0.16

50.

091

0.15

10.

072

0.12

90.

084

0.10

30.

089

0.10

80.

079

0.10

50.

058

0.08

516

SA

NF

ER

NA

ND

O(2

08)

0.l

l90.

122

0.11

60.

116

0.10

60.

109

0.09

80.

108

0.08

30.

091

0.Q

750.

Q75

0.05

20.

054

17S

AN

FE

RN

AN

DO

(211

)0.

121

0.12

70.

116

0.11

90.

109

0.10

80.

100

0.09

30.

087

0.08

20.

076

0.Q

750.

050

0.05

218

SA

NF

ER

NA

ND

O(4

66)

0.17

40.

149

0.16

30.

145

0.14

80.

142

0.12

60.

128

0.09

80.

105

0.08

70.

097

0.05

80.

070

19S

AN

FE

RN

AN

DO

(253

)0.

100

0.12

90.

096

0.11

70.

083

0.10

20.

095

0.10

00.

080

0.09

"50.

064

0.10

40.

058

0.08

020

SA

NF

ER

NA

ND

O(1

99)

0.12

50.

115

0.12

50.

111

0.11

00.

106

0.10

50.

105

0.09

50.

090

0.08

90.

076

0.05

80.

059

ME

AN

0.12

40.

129

0.11

80.

121

'0.1

100.

117

0.10

40.

109

0.09

60.

101

0.08

90.

098

0.06

00.

071

cr0.

Q25

0.01

60.

023

O.D1

S0.

022

0.01

40.

013

0.01

60.

D11

0.01

20.

D15

0.01

70.

007

0.01

1

ME

AN

OF

MA

X(L

,T)

0.13

90.

131

0.12

20.

113

0.10

40.

100

0.07

0

crO

FM

AX

(L,1

)0.

017

0.01

6O

.otS

0.01

40.

01l

0.01

60.

011

~

TA

BL

EC

.4A

naly

sis

resu

lts

ofm

axim

umin

ters

tory

drif

tfo

r8

-st

ory

isol

ated

stru

ctur

ew

ithR

=39.

132

in(T

b=2

sec.

),f m

ax=0

.10.

Exc

itat

ion

repr

esen

ted

bya

set

ofp

airs

ofs

cale

dea

rthq

uake

mot

ions

reco

rded

onSt

iff

Soil

Site

s(r

epre

sent

ativ

eo

fso

ilty

peS

l).

Hei

ght

is12

ft.

EX

CIT

AT

ION

2nd

STO

RY

DRI

F1('1

t.)3r

dST

OR

YD

RIF1

(lft.)

4th

STO

RY

DR

IFT(

lft.)

5th

STO

RY

DRI

FT(lf

t.)6t

hST

OR

YD

RIFT

(lft.)

7th

STO

RY

DRI

FT(lf

t.8t

hST

OR

YD

RIF

T(lft

.)H

EIG

HT

0H

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,T)

0.28

510.

2764

0.36

160.

3405

0.31

880.

4731

0.32

69

(JO

FM

AX

(L,T

)0.

0164

0.02

670.

0371

0.04

920.

0416

0.08

230.

0536

<;J .... -..J

TA

BL

EC

.17

Ana

lysi

sre

sult

so

fmax

imum

stor

ysh

ear

for

8·

stor

yis

olat

edst

ruct

ure

wit

hR

=88

.048

in(T

b=

3se

c.),

f mu

=0.

10.

Exc

itat

ion

repr

esen

ted

bya

set

of

pair

so

fsc

aled

eart

hqua

kem

otio

nsre

cord

edon

Med

ium

Soil

Site

s(r

epre

sent

ativ

eof

soil

type

S2).

2nd

STO

RY

SHE

AR

3rd

STO

RY

SHE

AR

4th

STO

RY

SHE

AR

5th

STO

RY

SHE

AR

6th

STO

RY

SHE

AR

7th

STO

RY

SHE

AR

8th

STO

RY

SHE

AR

EX

CIT

AT

ION

WE

/GIf

TW

E/G

IfT

WE

/GIf

TW

E/G

IfT

WE

/GIf

TW

E/G

IfT

WE

/GH

T

LT

LT

LT

LT

LT

LT

LT

21W

Esr

nR

NW

AS

H(3

25)

0.14

80.

134

0.15

60.

123

0.15

00.

115

0.12

40.

123

0.11

90.

118

0.11

80.

104

0.08

200

75

22E

UR

EK

A(0

22)

0.13

20.

146

0.14

00.

121

0.13

70.

113

0.11

60.

108

0.09

90.

103

0.08

90.

103

0.05

00.

074

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UR

EK

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23)

0.15

40.

108

0.14

10.

097

0.13

00.

100

0.11

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097

0.09

10.

091

0.07

40.

073

0.05

10.

045

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ER

ND

AL

E(0

23)

0.12

50.

126

0.13

10.

122

0.12

90.

121

0.13

30.

109

0.12

50.

093

0.10

60.

081

0.06

80.

076

25S

AN

FE

RN

AN

DO

(241

)0.

140

0.14

60.

135

0.13

90.

124

0.12

70.

107

0.12

30.

088

0.11

10.

073

0.10

80.

050

0.08

126

SA

NF

ER

NA

ND

O(4

58)

0.12

50.

156

0.12

10.

146

0.12

00.

136

0.11

60.

120

0.09

60.

099

0.07

40.

081

0.04

80.

056

27S

AN

FE

RN

AN

DO

(264

)0.

162

0.13

20.

163

0.1

l60.

157

0.10

90.

150

0.12

20.

139

0.11

00.

122

0.10

60.

079

0.08

728

SA

NF

ER

NA

ND

O(2

67)

0.12

00.

174

0.12

00.

140

0.12

40

.1l4

0.12

50.

107

0.09

70.

105

0.08

60.

125

0.07

40.

094

29P

UG

ET

SO

UN

D(3

25)

0.12

60.

164

0.13

20.

160

0.13

40.

152

0.13

50.

134

0.12

20.

131

0.1

l00.

131

0.07

40.

113

ME

AN

0.13

70.

143

0.13

80.

129

0.13

40.

121

0.12

40

.1l6

0.10

80.

101

0.09

50.

101

0.06

40.

078

<10.

014

0.01

90.

014

0.01

80.

012

0.01

50.

012

0.01

l0.

017

·-e.0

120.

019

0.01

90.

013

0.01

9

ME

AN

OF

MA

X(L

.n0.

153

0.14

60.

138

0.12

70.

114

0.10

80.

079

<1O

FM

AX

(L.n

0.01

30.

010

0.01

l0.

01l

O.o

I50.

Ql8

0.01

8

(')

I ... 00

TA

BL

EC

.18

Ana

lysi

sre

sults

ofm

axim

umin

ters

tory

drift

for

8·s

tory

isol

ated

stru

ctur

ew

ithR

=88

.048

in(T

b=

3se

c.),

f mu

=0.

10.

Exc

itatio

nre

pres

ente

dby

ase

tof

pair

sof

scal

edea

rthq

uake

mot

ions

reco

rded

onM

ediu

mSo

ilSi

tes

(rep

rese

ntat

ive

ofso

ilty

peS2

).H

eigh

tis

12ft

.

EX

CIT

AT

ION

2nd

STO

RY

DR/

FT(iT

<)3r

dST

OR

YD

R/F

l(",

)4t

hST

OR

YD

R/F

T(",

5th

STO

RY

DR

/FT

(",)

6th

STO

RY

DR

/FTC

"')

7th

STO

RY

DR

/FT(

%8t

hST

OR

YD

R/F

T("

,)H

E/G

HT

0H

E/G

HT

0H

E/G

HT

0)

HE

/GH

T0

HE

/GH

T0

HE

/GH

TH

E/G

HT

0

LT

LT

LT

LT

LT

LT

LT

21W

ES

TE

RN

WA

SH

(325

)0.

3429

0.31

760.

3663

0.28

840.

4703

0.37

090.

3885

0.39

150.

3721

0.37

490.

5415

0.49

190.

3833

0.35

57

22E

UR

EK

A(0

22)

0.30

250.

3381

0.32

530.

2859

0.42

890.

3620

0.36

130.

3388

0.31

560.

3210

0.42

250.

4801

0.23

650.

3569

23E

UR

EK

A(0

23)

0.36

210.

2516

0.33

270.

2290

0.41

940.

3145

0.35

970.

3046

0.28

560.

2805

0.34

840.

3567

0.23

650.

2125

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ER

ND

AL

E(0

23)

0.27

940.

2751

0.29

630.

2893

0.39

600.

3844

0.41

080.

3432

0.38

900.

2949

0.50

160.

3708

0.32

160.

3589

25S

AN

FE

RN

AN

DO

(241

)0.

3241

0.33

510.

3133

0.32

580.

3854

0.40

310.

3363

0.38

960.

2788

0.35

260.

3457

0.50

950.

2353

0.38

5626

SA

NF

ER

NA

DO

(458

)0.

2832

0.36

750.

2826

0.34

510.

3778

0.42

670.

3604

0.37

890.

3024

0.31

580.

3545

0.38

200.

2245

0.26

4027

SA

NF

ER

NA

ND

O(2

64)

0.37

520.

2936

0.37

600.

2655

0.48

680.

3412

0.47

390.

3693

0.43

530.

3352

0.57

390.

5024

0.37

030.

4113

28S

AN

FE

RN

AN

DO

(267

)0.

2844

·0.3

952

0.28

170.

3320

0.37

750.

3644

0.38

470.

3351

0.29

710.

3369

0.41

270.

5978

0.34

990.

4591

29P

UG

ET

SO

UN

D(3

25)

0.28

200.

3859

0.31

250.

3779

0.42

020.

4806

0.42

000.

4201

0.37

730.

4071

0.50

550.

6099

0.34

430.

5373

ME

AN

0.31

510.

3289

0.32

070.

3043

0.41

800.

3831

0.38

840.

3635

0.33

920.

3354

0.44

510.

4779

0.30

020.

3713

(J0.

0352

0.04

350.

0316

0.04

260.

0371

0.04

620.

0392

0.03

370.

0521

0.03

690.

0828

0.08

750.

0621

0.09

09

ME

AN

OF

MA

X(L

,n0.

3535

0.34

190.

4321

0.39

670.

3576

0.50

590.

3770

(JO

FM

AX

(L,n

0.03

280.

0255

0.03

670.

0331

0.04

530.

0840

0.08

63

APPENDIXD

RESULTS OF MAXIMUM STORY SHEAR AND INTERSTORY DRIFT FOR 8· STORY

ISOLATED STRUCTURE. EXCITATION REPRESENTED BY SCALED PAffiS OF

REAL RECORDS ACCORDING TO THE DYNAMIC ANALYSIS PROCEDURE OF

SEAOC.

9 ....

TA

BL

ED

.lA

naly

sis

resu

lts

ofm

axim

umst

ory

shea

rfo

r8

•st

ory

isol

ated

stru

ctur

ew

ith

R=3

9.13

2in

(Tb

=2

sec)

,fm

u=

0.10

,exc

ited

bysc

aled

pair

sof

real

reco

rds

acco

rdin

gto

the

Dyn

amic

Ana

lysi

sP

roce

dure

ofS

EA

OC

.Wei

ghti

sto

tal

wei

ghto

fstr

uctu

rein

clud

ing

base

.

2NJ

STO

RY

SHE

AR

3rd

STO

RY

SHE

AR

4th

STO

RY

SHE

AR

Sth

STO

RY

SHE

AR

6th

STO

RY

SHE

AR

7th

STO

RY

SHE

AR

8th

STO

RY

SHE

AR

EX

CIT

AT

ION

WE

1GIf

fW

E1G

Iff

WE

1GIf

fW

ElG

lff

WE

1GIf

fW

EIG

Iff

WE

lGlf

f

LT

LT

LT

LT

LT

LT

LT

MO

TIO

NfH

0.11

30.

142

0.11

50.

129

0.11

30.

112

0.10

30.

109

0.09

70.

092

0.08

20.

088

0.05

00.

066

MO

TIO

N#1

20.

109

0.12

50.

106

0.12

00.

095

0.11

30.

086

0.11

20.

074

0.09

80.

067

0.08

20.

044

0.05

8M

OT

ION

#13

0.10

90.

129

0.10

90.

126

0.11

10.

128

0.10

00.

130

0.09

30.

126

0.Q

780.

124

0.04

50.

074

MO

TIO

N#1

40.

126

0.18

30.

120

0.18

40.

108

0.16

30.

101

0.13

00.

090

0.12

50.

087

0.12

10.

061

0.08

6M

OT

ION

#IS0.

124

0.21

10.

108

0.18

90.

102

0.15

90.

107

0.14

20.

098

0.12

90.

107

0.11

20.

083

0.08

2M

OT

ION

#16

0.14

30.

193

0.15

80.

171

0.15

90.

160

0.13

90.

140

0.12

90.

116

0.11

80.

099

0.06

50.

087

~

TA

BL

ED

.2A

naly

sis

resu

lts

ofm

axim

umin

ters

tory

drif

tfor

8•s

tory

isol

ated

stru

ctu

rew

ith

R=

39.1

32in

(Tb

=2

sec)

,fm

all

=0.

10,e

xcit

edby

scal

edpa

irs

of

real

reco

rds

acco

rdin

gto

the

Dyn

amic

Ana

lysi

sP

roce

dure

ofS

EA

OC

.Hei

ghti

s12

ft.

EX

CIT

AT

ION

2IId

STO

RY

DR

IFT

(%)

3rd

STO

RY

DR

IFT

(%)

4tlt

STO

RY

DR

IFT

(%SI

ltST

OR

YD

RIF

T(%

)6t

1tST

OR

YD

RIF

T(%

)71

1tST

OR

YD

RIF

T(%

8t1t

STO

RY

DR

IFT

(%)

HE

IGJr

fH

E/G

Jrf

HE

/GJr

fH

E/G

Jrf

HE

/GJr

fH

E/G

Jrf

HE

/GJr

f

MO

TIO

NII

I0.

2571

0.34

220.

2642

0.30

870.

3504

0.36

260.

3207

0.34

690.

3025

0.28

830.

3887

0.46

400.

2388

0.30

97

MO

TIO

N11

20.

2563

0.28

010.

2492

0.27

890.

2972

0.35

140.

2637

0.35

340.

2348

0.31

010.

3143

0.39

020.

2054

0.27

53

MO

TIO

N"3

0.25

430.

3022

0.25

710.

3007

0.35

120.

4238

0.31

660.

4059

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3909

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750.

5920

0.20

920.

3546

MO

TIO

N11

40.

2986

0.42

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2846

0.43

500.

3374

0.51

950.

3126

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140.

2843

0.39

120.

4041

0.56

090.

2833

0.40

89M

OT

ION

"50.

2812

0.50

550.

2620

0.45

290.

3277

0.50

310.

3235

0.45

100.

2965

0.40

980.

5047

0.53

030.

3916

0.38

84M

OT

lON

II6

0.32

060.

4430

0.36

290.

4034

0.49

270.

5114

0.43

300.

4358

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520.

3568

0.55

850.

4576

0.31

230.

4142

~ ~

TA

BL

ED

.3A

naly

sis

resu

lts

ofm

axim

umst

ory

shea

rfo

r8

•st

ory

isol

ated

stru

ctur

ew

ith

R=8

8.04

8in

(Tb

=3

sec)

,fm

u=

0.05

,exc

ited

bysc

aled

pair

so

frea

lre

cord

sac

cord

ing

toth

eD

ynam

icA

naly

sis

Pro

cedu

reo

fSE

AO

C.W

eigh

tis

tota

lw

eigh

tofs

truc

ture

incl

udin

gba

se.

2nd

STO

RY

SHEA

R3r

dST

OR

YSH

EAR

4111

STO

RY

SHEA

RSI

ltST

OR

YSH

EAR

6111

STO

RY

SHE

AR

711t

STO

RY

SHE

AR

8t1t

STO

RY

SHE

AR

EX

OT

AT

ION

WE

IGIf

fW

EIG

Iff

WE

IGIf

fW

EIG

Iff

WE

IGIf

fW

EIG

Iff

WE

IGIf

f

LT

LT

LT

LT

LT

LT

LT

MO

TIO

NIf

I0.

064

0.08

00.

062

0.08

20.

057

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053

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70.

053

0.06

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051

0.06

60.

036

0.03

9

MO

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057

0.10

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056

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058

0.08

80.

055

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80.

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60.

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7

MO

TIO

Nlf3

0.08

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091

0.08

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081

0.07

20.

093

0.06

60.

082

0.05

70.

085

0.03

60.

054

MO

TIO

Nlf4

0.09

60.

123

0.08

90.

111

0.08

00.

0102

0.06

80.

082

0.06

00.

059

0.05

10.

065

0.04

00.

045

MO

TIO

NIf

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079

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076

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20.

068

0.09

10.

067

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40.

063

0.06

70.

065

0.07

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058

0.04

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OT

ION

lf60.

120

0.13

00.

106

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084

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0.07

70.

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0.06

80.

030

0.04

8

~

TA

BL

ED

.4A

naly

sis

resu

lts

ofm

axim

umin

ters

tory

drif

tfor

8•s

tory

isol

ated

stru

ctur

ew

ith

R=8

8.04

8in

(Tb

=3

sec)

,fm

u=

0.05

,exc

ited

bysc

aled

pair

so

frea

lre

cord

sac

cord

ing

toth

eD

ynam

icA

naly

sis

Pro

cedu

reo

fSE

AO

C.H

eigh

tis

12ft

.

EX

CIT

AT

ION

2N1

STO

RY

DRI

FT'

(%)

3rd

STO

RY

DRI

FT'

(%)

41ft

STO

RY

DRI

FT'

(%S

IftST

OR

YD

RIFT

'(%

)61

ftST

OR

YD

RIFT

'(%

)71

ftST

OR

YD

RIF

T'(%

)S

lftST

OR

YD

RIF

T'(%

)

HE

IGH

TH

EIG

HT

HE

IGH

TH

EIG

HT

HE

/GH

TH

E/G

lff

HE

lGlf

f

MO

TlO

N*

l0.

1411

0.19

150.

1446

0.19

090.

1801

0.24

390.

1634

0.24

360.

1679

0.19

030.

2389

0.30

870.

1713

0.18

02

MO

TlO

N*2

0.13

490.

2443

0.13

350.

2253

0.18

540.

2744

0.17

270.

2455

0.15

230.

2088

0.18

160.

2466

0.12

150.

1772

MO

TIO

N*3

0.20

120.

1903

0.20

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2108

0.25

520.

2495

0.22

550.

2867

0.20

250.

2597

0.26

640.

4028

0.16

880.

2568

MO

TlO

N*4

0.22

3602

856

0.20

930.

2610

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040.

3150

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640.

2549

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960.

1934

0.24

120.

3089

0.18

670.

2124

MO

TlO

N*S

0.17

960.

2421

0.17

600.

2418

0.21

090.

2877

0.20

280.

2668

0.19

220.

2168

0.30

500.

3611

0.27

180.

2168

MO

TIO

N*6

0.28

370.

3111

0.24

760.

2702

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720.

3237

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2743

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2460

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910.

3207

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APPENDIXE

CONVERSION TO SI UNITS

To convert To Multiply by

in. nun 25.4

ft nun 304.8

kip kN 4.459

psf Pa 47.88

ksi MPa 6.895

E-l

NATIONAL CENTER FOR EARTHQUAKE ENGINEERING RESEARCHLIST OF TECHNICAL REPORTS

The National Center for Earthquake Engineering Research (NCEER) publishes technical reports on a variety of subjects relatedto earthquake engineering written by authors funded through NCEER. These reports are available from both NCEER'sPublications Department and the National Technical Information Service (NTIS). Requests for reports should be directed to thePublications Department, National Center for Earthquake Engineering Research, State University of New York at Buffalo, RedJacket Quadrangle, Buffalo, New York 14261. Reports can also be requested through NTIS, 5285 Port Royal Road, Springfield,Virginia 22161. NTIS accession numbers are shown in parenthesis, if available.

NCEER-87-0001

NCEER-87-0002

NCEER-87-0003

NCEER-87-0004

NCEER-87-0005

NCEER-87-0006

NCEER-87-0007

NCEER-87-0008

NCEER-87-0009

NCEER-87-0010

NCEER-87-0011

NCEERc87-0012

NCEER-87-0013

NCEER-87-0014

NCEER-87-0015

NCEER-87-0016

"First-Year Program in Research, Education and Technology Transfer," 3/5/87, (PB88-134275/AS).

"Experimental Evaluation of Instantaneous Optimal Algorithms for Structural Control," by R.C. Lin,T.T. Soong and AM. Reinhom, 4/20/87, (PB88-134341/AS).

"Experimentation Using the Earthquake Simulation Facilities at University at Buffalo," by AM.Reinhom and R.L. Ketter, to be published.

"The System Characteristics and Performance of a Shaking Table," by lS. Hwang, K.C. Chang andG.C. Lee, 6/1/87, (PB88-134259/AS). This report is available only through NTIS (see address givenabove).

"A Finite Element Formulation for Nonlinear Viscoplastic Material Using a Q Model," by O. Gyebi andG. Dasgupta, 11/2/87, (PB88-213764/AS).

"Symbolic Manipulation Program (SMP) - Algebraic Codes for Two and Three Dimensional FiniteElement Formulations," by X. Lee and G. Dasgupta, 11/9/87, (PB88-219522/AS).

"Instantaneous Optimal Control Laws for Tall Buildings Under Seismic Excitations," by IN. Yang, A.Akbarpour and P. Ghaemmaghami, 6/10/87, (PB88-134333/AS).

"IDARC: Inelastic Damage Analysis of Reinforced Concrete Frame - Shear-Wall Structures," by Y.J.Park, AM. Reinhom and S.K. Kunnath, 7/20/87, (PB88-134325/AS).

"Liquefaction Potential for New York State: A Preliminary Report on Sites in Manhattan and Buffalo,"by M. Budhu, V. Vijayakumar, R.F. Giese and L. Baumgras, 8/31/87, (PB88-163704/AS). This reportis available only through NTIS (see address given above).

"Vertical and Torsional Vibration of Foundations in Inhomogeneous Media," by AS. Ve1etsos andKW. Dotson, 6/1/87, (PB88-134291/AS).

"Seismic Probabilistic Risk Assessment and Seismic Margins Studies for Nuclear Power Plants," byHoward H.M. Hwang, 6/15/87, (PB88-134267/AS).

"Parametric Studies of Frequency Response of Secondary Systems Under Ground-AccelerationExcitations," by Y. Yong and Y.K. Lin, 6/10/87, (PB88-134309/AS).

"Frequency Response of Secondary Systems Under Seismic Excitation," by J.A. HoLung, 1. Cai andY.K. Lin, 7/31/87, (PB88-134317/AS).

"Modelling Earthquake Ground Motions in Seismically Active Regions Using Parametric Time SeriesMethods," by G.W. Ellis and A.S. Cakmak, 8/25/87, (PB88-134283/AS).

"Detection and Assessment of Seismic Structural Damage," by E. DiPasquale and A.S. Cakmak,8/25/87, (PB88-163712/AS).

"Pipeline Experiment at Parkfield, Califomia," by J. Isenberg and E. Richardson, 9/15/87, (PB88163720/AS). This report is available only through NTIS (see address given above).

F-l

NCEER-87-0017

NCEER-87-0018

NCEER-87-0019

NCEER-87-0020

NCEER-87-0021

NCEER-87-0022

NCEER-87-0023

NCEER-87-0024

NCEER·87-0025

NCEER-87-0026

NCEER·87-0027

NCEER-87-0028

NCEER-88-0001

NCEER-88-0002

NCEER-88-0003

NCEER-88-0004

NCEER-88-0005

NCEER-88-0006

NCEER-88-0007

"Digital Simulation of Seismic Ground Motion," by M. Shinozuka, G. Doodatis and T. Harada, 8f31/87,(PB88-155197/AS). This report is available only through NTIS (see address given above).

"Practical Considerations for Structural Control: System Uncertainty, System Time Delay and Truncation of Small Control Forces," J.N. Yang and A. Akbarpour, 8/10/87, (PB88-163738/AS).

"Modal Analysis of Nonclassically Damped Structural Systems Using Canonical Transformation," byIN. Yang, S. Sarkani and F.x. Long, 9/27/87, (PB88-l87851/AS).

"A Nonstationary Solution in Random Vibration Theory," by lR. Red-Horse and P.D. Spanos, 11f3/87,(PB88-163746/AS).

"Horizontal Impedances for Radially Inhomogeneous Viscoelastic Soil Layers," by AS. Veletsos andKW. Dotson, 10/15/87, (PB88-150859/AS).

"Seismic Damage Assessment of Reinforced Concrete Members," by Y.S. Chung, C. Meyer and M.Shinozuka, 1019/87, (PB88-150867/AS). This report is available only through NTIS (see address givenabove).

"Active Structural Control in Civil Engineering," by T.T. Soong, 11/11187, (PB88-187778/AS).

Vertical and Torsional Impedances for Radially Inhomogeneous Viscoelastic Soil Layers," by K.W.Dotson and AS. Veletsos, 12/87, (PB88-187786IAS).

"Proceedings from the Symposium on Seismic Hazards, Ground Motions, Soil-Liquefaction andEngineering Practice in Eastern North America," October 20-22, 1987, edited by K.H. Jacob, 12/87,(PB88-188115/AS).

"Report on the Whittier-Narrows, California, Earthquake of October I, 1987," by J. Pante1ic and A.Reinhorn, 11/87, (PB88-187752/AS). This report is available only through NTIS (see address givenabove).

"Design of a Modular Program for Transient Nonlinear Analysis of Large 3-D Building Structures," byS. Srivastav and J.F. Abel, 12f30/87, (PB88-187950IAS).

"Second-Year Program in Research, Education and Technology Transfer," 3/8/88, (PB88-219480IAS).

"Workshop on Seismic Computer Analysis and Design of Buildings With Interactive Graphics," by W.McGuire, J.P. Abel and C.H. Conley, 1/18/8&, (PB88-187760IAS).

"Optimal Control of Nonlinear Flexible Structures," by J.N. Yang, F.x. Long and D. Wong, 1/22/88,(PB88-213772/AS).

"Substructuring Teclmiques in the Time Domain for Primary-Secondary Structural Systems," by G.D.Manolis and G. Juhn, 2/10/88, (PB88-213780IAS).

"Iterative Seismic Analysis of Primary-Secondary Systems," by A Singhal, L.D. Lutes and P.D.Spanos, 2/23/88, (PB88-213798/AS).

"Stochastic Finite Element Expansion for Random Media," by P.D. Spanos and R. Ghanem, 3/14/88,(PB88-213806/AS).

"Combining Structural Optimization and Structural Control," by F.Y. Cheng and C.P. Pantelides,1/10/88, (PB88-213814/AS).

"Seismic Performance Assessment of Code-Designed Structures," by H.H-M. Hwang, J-W. Jaw andH-l Shau, 3/20/88, (PB88-219423/AS).

F-2

NCEER-88_0008

NCEER-88-0009

NCEER-88-001O

NCEER-88-0011

NCEER-88-0012

NCEER-88-0013

NCEER-88-0014

NCEER-88-0015

NCEER-88-0016

NCEER-88-0017

NCEER-88-0018

NCEER-88-0019

NCEER-88-0020

NCEER-88-0021

NCEER-88-0022

NCEER-88-0023

NCEER-88-0024

NCEER-88-0025

NCEER-88-0026

NCEER-88-0027

"Reliability Analysis of Code-Designed Structures Under Natural Hazards," by H.H-M. Hwang, H.Ushiba and M. Shinozuka, 2/29/88, (PB88-229471/AS).

"Seismic Fragility Analysis of Shear Wall Structures," by J-W Jaw and H.H-M. Hwang, 4/30/88,(PB89-102867/AS).

"Base Isolation of a Multi-Story Building Under a Harmonic Ground Motion - A Comparison ofPerformances of Various Systems," by F-G Fan, G. Ahmadi and I.G. Tadjbakhsh, 5/18/88,(PB89-122238/AS).

"Seismic Floor Response Spectra for a Combined System by Green's Functions," by F.M. Lavelle, L.A.Bergman and P.D. Spanos, 5/1/88, (PB89-10287S/AS).

"A New Solution Technique for Randomly Excited Hysteretic Structures," by G.Q. Cai and Y.K. Lin,5/16/88, (PB89-102883/AS).

"A Study of Radiation Damping and Soil-Structure Interaction Effects in the Centrifuge," by K.Weissman, supervised by J.H. Prevost, 5/24/88, (PB89-144703/AS).

"Parameter Identification and Implementation of a Kinematic Plasticity Model for Frictional Soils," byJ.H. Prevost and D.V. Griffiths, to be published.

"Two- and Three- Dimensional Dynamic Finite Element Analyses of the Long Valley Dam," by D.V.Griffiths and J.R. Prevost, 6/17/88, (PB89-l44711/AS).

"Damage Assessment of Reinforced Concrete Structures in Eastern United States," by A.M. Reinhom,M.J. Seidel, S.K. Kunnath and Y.J. Park, 6/15/88, (PB89-l22220/AS).

"Dynamic Compliance of Vertically Loaded Strip Foundations in Multilayered Viscoelastic Soils," byS. Ahmad and A.S.M. Israil, 6/17/88, (PB89-102891/AS).

"An Experimental Study of Seismic Structural Response With Added Viscoelastic Dampers," by R.C.Lin, Z. Liang, T.T. Soong and R.H. Zhang, 6/30/88, (PB89-122212/AS).

"Experimental Investigation of Primary - Secondary System Interaction," by G.D. Manolis, G. Juhn andA.M. Reinhom, 5/27/88, (PB89-122204/AS).

"A Response Spectrum Approach For Analysis of Nonclassically Damped Structures," by J.N. Yang, S.Sarkani and F,X, Long, 4/22/88, (PB89-102909/AS).

"Seismic Interaction of Structures and Soils: Stochastic Approach," by A.S. Veletsos and A.M. Prasad,7/21/88, (PB89-l22l96/AS).

"Identification of the Serviceability Limit State and Detection of Seismic Structural Damage," by E.DiPasquale and A.S. Cakmak, 6/15/88, (PB89-122188/AS).

"Multi-Hazard Risk Analysis: Case of a Simple Offshore Structure," by B.K. Bhartia and E.H.Vanmarcke, 7/21/88, (PB89-145213/AS).

"Automated Seismic Design of Reinforced Concrete Buildings," by Y.S. Chung, C. Meyer and M.Shinozuka, 7/5/88, (PB89-l22170/AS).

"Experimental Study of Active Control of MOOF Structures Under Seismic Excitations," by L.L.Chung, R.C. Lin, T.T. Soong and A.M. Reinhorn, 7/10/88, (PB89-122600/AS).

"Earthquake Simulation Tests of a Low-Rise Metal Structure," by J.S. Hwang, K.C. Chang, G.C. Leeand R.L. Ketter, 8/1/88, (PB89-102917/AS).

"Systems Study of Urban Response and Reconstruction Due to Catastrophic Earthquakes," by F. Kozinand H.K. Zhou, 9/22/88, (PB90-162348/AS).

F-3

NCEER-88-0028

NCEER-88-0029

NCEER-88-0030

NCEER-88-0031

NCEER-88-0032

NCEER-88-0033

NCEER-88-0034

NCEER-88-0035

NCEER-88-0036

NCEER-88-0037

NCEER-88-0038

NCEER-88-0039

NCEER-88-0040

NCEER-88-0041

NCEER-88-0042

NCEER-88-0043

NCEER-88-0044

NCEER-88-0045

NCEER-88-0046

"Seismic Fragility Analysis of Plane Frame Structures," by H.H-M. Hwang and Y.K. Low, 7/31/88,(PB89-131445/AS).

"Response Analysis of Stochastic Structures," by A. Kardara, C. Bucher and M. Shinozuka, 9/22/88,(PB89-174429/AS).

"Nonnormal Accelerations Due to Yielding in a Primary Structure," by D.C.K. Chen and L.D. Lutes,9/19/88, (PB89-131437/AS).

"Design Approaches for Soil-Structure Interaction," by AS. Veletsos, AM. Prasad and Y. Tang,12/30/88, (PB89-174437/AS).

"A Re-evaluation of Design Spectra for Seismic Damage Control," by C.J. Turkstra and AG. Tallin,11/7/88, (PB89-145221/AS).

"The Behavior and Design of Noncontact Lap Splices Subjected to Repeated Inelastic Tensile Loading,"by V.E. Sagan, P. Gergely and R.N. White, 12/8/88, (PB89-163737/AS).

"Seismic Response of Pile Foundations," by S.M. Mamoon, P.K. Banerjee and S. Ahmad, 11/1/88,(PB89-145239/AS).

"Modeling of R/C Building Structures With Flexible Floor Diaphragms (IDARC2)," by AM. Reinhom,S.K. Kunnath andN. Panahshahi, 9/7/88, (PB89-207153/AS).

"Solution of the Dam-Reservoir Interaction Problem Using a Combination of FEM, BEM withParticular Integrals, Modal Analysis, and Substructuring," by C-S. Tsai, G.C. Lee and R.L. Ketter,12/31/88, (PB89-207146/AS).

"Optimal Placement of Actuators for Structural Control," by F.Y. Cheng and C.P. Pantelides, 8/15/88,(PB89-162846/AS).

"Teflon Bearings in Aseismic Base Isolation: Experimental Studies and Mathematical Modeling," by A.Mokha, M.C. Constantinou and AM. Reinhom, 12/5/88, (PB89-218457/AS).

"Seismic Behavior of Flat Slab High-Rise Buildings in the New York City Area," by P. Weidlinger andM. Ettouney, 10/15/88, (PB90-145681/AS).

"Evaluation of the Earthquake Resistance of Existing Buildings in New York City," by P. Weidlingerand M. Ettouney, 10/15/88, to be published.

"Small-Scale Modeling Techniques for Reinforced Concrete Structures Subjected to Seismic Loads," byW. Kim, A. EI-Attar and R.N. White, 11/22/88, (PB89-189625/AS).

"Modeling Strong Ground Motion from MUltiple Event Earthquakes," by G.W. Ellis and A.S. Cakmak,10/15/88, (PB89-174445/AS).

"Nonstationary Models of Seismic Ground Acceleration," by M. Grigoriu, S.E. Ruiz and E.Rosenblueth, 7/15/88, (PB89-189617/AS).

"SARCF User's Guide: Seismic Analysis of Reinforced Concrete Frames," by Y.S. Chung, C. Meyerand M. Shinozuka, 11/9/88, (PB89-174452/AS).

"First Expert Panel Meeting on Disaster Research and Planning," edited by J. Pantelic and J. Stoyle,9/15/88, (PB89-174460/AS).

"Preliminary Studies of the Effect of Degrading Infill Walls on the Nonlinear Seismic Response of SteelFrames," by C.Z. Chrysostomou, P. Gergely and J.F. Abel, 12/19/88, (PB89-208383/AS).

F-4

NCEER-88-0047

NCEER-89-0001

NCEER-89-0002

NCEER-89-0003

NCEER-89-0004

NCEER-89-0005

NCEER-89-0006

NCEER-89-0007

NCEER-89-0008

NCEER-89-0009

NCEER-89-R010

NCEER-89-0011

NCEER-89-0012

NCEER-89-0013

NCEER-89-0014

NCEER-89-0015

NCEER-89-0016

NCEER-89-P017

NCEER-89-0017

"Reinforced Concrete Frame Component Testing Facility - Design, Construction, Instrumentation andOperation," by S.P. Pessiki, C. Conley, T. Bond, P. Gergely and R.N. White, 12/16/88,(PB89-174478/AS).

"Effects of Protective Cushion and Soil Compliancy on the Response of Equipment Within a Seismically Excited Building," by J.A. HoLung, 2/16/89, (PB89-207179/AS).

"Statistical Evaluation of Response Modification Factors for Reinforced Concrete Structures," byH.H-M. Hwang and J-W. Jaw, 2/17/89, (PB89-207187/AS).

"Hysteretic Columns Under Random Excitation," by G-Q. Cai and Y.K. Lin, 1/9/89, (PB89-196513/AS):

"Experimental Study of 'Elephant Foot Bulge' Instability of Thin-Walled Metal Tanks," by Z-H. Jia andR.L. Ketter, 2/22/89, (PB89-207195/AS).

"Experiment on Performance of Buried Pipelines Across San Andreas Fault," by J. Isenberg, E.Richardson and T.D. O'Rourke, 3/10/89, (PB89-218440/AS).

"A Knowledge-Based Approach to Structural Design of Earthquake-Resistant Buildings," by M.Subramani, P. Gergely, C.H. Conley, J.F. Abel and A.H. Zaghw, 1/15/89, (PB89-218465/AS).

"Liquefaction Hazards and Their Effects on Buried Pipelines," by T.D. O'Rourke and P.A. Lane,2/1/89, (PB89-218481).

"Fundamentals of System Identification in Structural Dynamics," by H. Imai, C-B. Yun, O. Maruyamaand M. Shinozuka, 1/26/89, (PB89-207211/AS).

"Effects of the 1985 Michoacan Earthquake on Water Systems and Other Buried Lifelines in Mexico,"by A.G. Ayala and M.I. O'Rourke, 3/8/89, (PB89-207229/AS).

"NCEER Bibliography of Earthquake Education Materials," by K.E.K. Ross, Second Revision, 9/1/89,(PB90-125352/AS).

"Inelastic Three-Dimensional Response Analysis of Reinforced Concrete Building Structures (IDARC3D), Part I - Modeling," by S.K. Kunnath and A.M. Reinhorn, 4/17/89, (PB90-114612/AS).

."Recommended Modifications to ATC-14," by C.D. Poland and J.O. Malley, 4/12/89,(PB90-108648/AS).

"Repair and Strengthening of Beam-to-Column Connections Subjected to Earthquake Loading," by M.Corazao and AJ. Durrani, 2/28/89, (PB90-109885/AS).

"Program EXKAL2 for Identification of Structural Dynamic Systems," by O. Maruyama, C-B. Yun, M.Hoshiya and M. Shinozuka, 5/19/89, (PB90-109877/AS).

"Response of Frames With Bolted Semi-Rigid Connections, Part I - Experimental Study and AnalyticalPredictions," by P.J. DiCorso, A.M. Reinhorn, I.R. Dickerson, I.B. Radziminski and W.L. Harper,6/1/89, to be published.

"ARMA Monte Carlo Simulation in Probabilistic Structural Analysis," by P.D. Spanos and M.P.Mignolet, 7/10/89, (PB90-109893/AS).

"Preliminary Proceedings from the Conference on Disaster Preparedness - The Place of EarthquakeEducation in Our Schools," Edited by K.E.K. Ross, 6/23/89.

"Proceedings from the Conference on Disaster Preparedness - The Place of Earthquake Education inOur Schools," Edited by K.E.K. Ross, 12/31/89, (PB90-207895).

F-5

NCEER-89-0018

NCEER-89-0019

NCEER-89-0020

NCEER-89-0021

NCEER-89-0022

NCEER-89-0023

NCEER-89-0024

NCEER-89-0025

NCEER-89-0026

NCEER-89-0027

NCEER-89-0028

NCEER-89-0029

NCEER-89-0030

NCEER-89-0031

NCEER-89-0032

NCEER-89-0033

NCEER-89-0034

NCEER-89-0035

NCEER-89-0036

"M.ultidimensional Models of Hysteretic Material Behavior for Vibration Analysis of Shape MemoryEnergy Absorbing Devices, by EJ. Graesser and FA Cozzarelli, 6{l/89, (PB90-164l46/AS).

"Nonlinear Dynamic Analysis of Three-Dimensional Base Isolated Structures (3D-BASIS)," by S.Nagarajaiah, A.M. Reinhom and M.C. Constantinou, 8/3/89, (PB90-161936/AS).

"Structural Control Considering Time-Rate of Control Forces and Control Rate Constraints," by F.Y.Cheng and C.P. Pantelides, 8/3/89, (PB90-l20445/AS).

"Subsurface Conditions of Memphis and Shelby County," by K.W. Ng, T-S. Chang and H-H.M.Hwang, 7/26/89, (PB90-120437/AS).

"Seismic Wave Propagation Effects on Straight Jointed Buried Pipelines," by K. Elhmadi and MJ.O'Rourke, 8/24/89, (PB90-162322/AS).

"Workshop on Serviceability Analysis of Water Delivery Systems," edited by M. Grigoriu, 3/6/89,(PB90-127424/AS). '

"Shaking Table Study of a 1/5 Scale Steel Frame Composed of Tapered Members," by K.C. Chang, lS.Hwang and G.C. Lee, 9/18/89, (PB90-160169/AS).

"DYNAlD: A Computer Program for Nonlinear Seismic Site Response Analysis - Technical Documentation," by Jean H. Prevost, 9/14/89, (PB90-161944/AS).

"1:4 Scale Model Studies of Active Tendon Systems and Active Mass Dampers for Aseismic Protection," by A.M. Reinhorn, T.T. Soong, R.C. Lin, Y.P. Yang, Y. Fukao, H. Abe and M. Nakai, 9/15/89,(PB90-173246/AS).

"Scattering of Waves by Inclusions in a Nonhomogeneous Elastic Half Space Solved by BoundaryElement Methods," by P.K. Hadley, A. Askar and A.S. Cakmak, 6/15/89, (PB90-1456991AS).

"Statistical Evaluation of Deflection Amplification Factors for Reinforced Concrete Structures," byH.H.M. Hwang, J-W. Jaw and A.L. Ch'ng, 8/31/89, (PB90-l64633/AS).

"Bedrock Accelerations in Memphis Area Due to Large New Madrid Earthquakes," by H.H.M. Hwang,C.H.S. Chen and G. Yu, 11{l/89, (PB90-162330/AS).

"Seismic Behavior and Response Sensitivity of Secondary Structural Systems," by Y.Q. Chen and T.T.Soong, 10/23/89, (PB90-164658/AS).

"Random Vibration and Reliability Analysis of Primary-Secondary Structural Systems," by Y. Ibrahim,M. Grigoriu and T.T. Soong, 11/10/89, (PB90-161951/AS).

"Proceedings from the Second U.S. - Japan Workshop on Liquefaction, Large Ground Deformation andTheir Effects on Lifelines, September 26-29, 1989," Edited by T.D. O'Rourke and M. Hamada, 12/1/89,(PB90-209388/AS).

"Deterministic Model for Seismic Damage Evaluation of Reinforced Concrete Structures," by lM.Bracci, A.M. Reinhorn, J.B. Mander and S.K. Kunnath, 9/27/89.

"On the Relation Between Local and Global Damage Indices," by E. DiPasquale and A.S. Cakmak,8/15/89, (PB90-173865).

"Cyclic Undrained Behavior of Nonplastic and Low Plasticity Silts," by A.I. Walker and H.E. Stewart,7/26/89, (PB90-183518/AS).

"Liquefaction Potential of Surficial Deposits in the City of Buffalo, New York," by M. Budhu, R. Gieseand L. Baumgrass, 1/17/89, (PB90-208455/AS).

F-6

NCEER-89-0037

NCEER-89-0038

NCEER-89-0039

NCEER-89-0040

NCEER-89-0041

NCEER-90-0001

NCEER-90-0002

NCEER-90-0003

NCEER-90-0004

NCEER-90-0005

NCEER-90-0006

NCEER-90-0007

NCEER-90-0008

NCEER-90-0009

NCEER-90-001O

NCEER-90-0011

NCEER-90-0012

NCEER-90-0013

NCEER-90-0014

NCEER-90-0015

"A Detenninstic Assessment of Effects of Ground Motion Incoherence," by A.S. Veletsos and Y. Tang,7/15/89, (PB90-164294/AS).

"Workshop on Ground Motion Parameters for Seismic Hazard Mapping," July 17-18, 1989, edited byR.V. Whitman, 12/1/89, (PB90-173923/AS).

"Seismic Effects on Elevated Transit Lines of the New York City Transit Authority," by C.L Costantino, CA Miller and E. Heymsfield, 12/26/89, (PB90-207887/AS).

"Centrifugal Modeling of Dynamic Soil-Structure Interaction," by K. Weissman, Supervised by lH.Prevost, 5/10/89, (PB90-207879/AS).

"Linearized Identification of Buildings With Cores for Seismic Vulnerability Assessment," by I-K. Hoand AE. Aktan, 11/1/89, (PB90-251943/AS).

"Geotechnical and Lifeline Aspects of the October 17, 1989 Lorna Prieta Earthquake in San Francisco,"by T.D. O'Rourke, H.E. Stewart, F.T. Blackburn and T.S. Dickerman, 1/90, (PB90-208596/AS).

"Nonnormal Secondary Response Due to Yielding in a Primary Structure," by D.C.K. Chen and L.D.Lutes, 2/28/90, (PB90-251976/AS).

"Earthquake Education Materials for Grades K-12," by K.E.K. Ross, 4/16/90, (PB91-113415/AS).

"Catalog of Strong Motion Stations in Eastern North America," by R.W. Busby, 4/3/90,(PB90-251984)/AS.

"NCEER Strong-Motion Data Base: A User Manuel for the GeoBase Release (Version 1.0 for theSun3)," by P. Friberg and K. Jacob, 3/31/90 (PB90-258062/AS).

"Seismic Hazard Along a Crude Oil Pipeline in the Event of an 1811-1812 Type New MadridEarthquake," by H.H.M. Hwang and C-H.S. Chen, 4/16/90(PB90-258054).

"Site-Specific Response Spectra for Memphis Sheahan Pumping Station," by H.H.M. Hwang and C.S.Lee, 5/15/90, (PB91-108811/AS).

"Pilot Study on Seismic Vulnerability of Crude Oil Transmission Systems," by T. Ariman, R. Dobry, M.Grigoriu, F. Kozin, M. O'Rourke, T. O'Rourke andM. Shinozuka, 5/25/90, (PB91-108837/AS).

"A Program to Generate Site Dependent Time Histories: EQGEN," by G.W. Ellis, M. Srinivasan andAS. Cakmak, 1/30/90, (PB91-1108829/AS).

"Active Isolation for Seismic Protection of Operating Rooms," by M.E. Talbott, Supervised by M.Shinozuka, 6/8/9, (PB91-110205/AS).

"Program UNEARID for Identification of Linear Structural Dynamic Systems," by C-B. Yun and M.Shinozuka, 6/25/90, (PB91-110312/AS).

"Two-Dimensional Two-Phase Elasto-P1astic Seismic Response of Earth Darns," by AN. Yiagos,Supervised by J.H. Prevost, 6/20/90, (PB91-110197/AS).

"Secondary Systems in Base-Isolated Structures: Experimental Investigation, Stochastic Response andStochastic Sensitivity," by G.D. Manolis, G. Juhn, M.C. Constantinou and A.M. Reinhorn, 7/1/90,(PB91-110320/AS).

"Seismic Behavior of Lightly-Reinforced Concrete Column and Beam-Column Joint Details," by S.P.Pessiki, C.H. Conley, P. Gergely and R.N. White, 8/22/90, (PB91-108795/AS).

"Two Hybrid Control Systems for Building Structures Under Strong Earthquakes," by IN. Yang and A.Danielians, 6/29/90, (PB91-125393/AS).

F-7

NCEER-90-0016

NCEER-90-0017

NCEER-90-0018

NCEER-90-0019

NCEER-90-0020

NCEER-90-0021

NCEER-90-0022

NCEER-90-0023

NCEER-90-0024

NCEER-90-0025

NCEER-90-0026

NCEER-90-0027

NCEER-90-0028

NCEER-90-0029

NCEER-91-0001

NCEER-91-0002

NCEER-91-0003

NCEER-91-0004

NCEER-91-0005

"Instantaneous Optimal Control with Acceleration and Velocity Feedback," by J.N. Yang and Z. Li,6/29/90, (PB91-12540l/AS).

"Reconnaissance Report on the Northern Iran Earthquake of June 21, 1990," by M. Mehrain, 10/4/90,(PB91-125377/AS).

"Evaluation of Liquefaction Potential in Memphis and Shelby County," by T.S. Chang, P.S. Tang, C.S.Lee and H. Hwang, 8/10/90, (PB91-125427/AS).

"Experimental and Analytical Study of a Combined Sliding Disc Bearing and Helical Steel SpringIsolation System," by M.C. Constantinou, AS. Mokha and AM. Reinhorn, 10/4/90,(PB91-125385/AS).

"Experimental Study and Analytical Prediction of Earthquake Response of a Sliding Isolation Systemwith a Spherical Surface," by AS. Mokha, M.C. Consta,ntinou and AM. Reinhorn, 10/11/90,(PB91-125419/AS).

"Dynamic Interaction Factors for Floating Pile Groups," by G. Gazetas, K. Fan, A. Kaynia and E.Kausel, 9/10/90, (PB91-170381/AS).

"Evaluation of Seismic Damage Indices for Reinforced Concrete Structures," by S. Rodriguez-Gtinezand AS. Cakmak, 9/30/90, PB91-171322/AS).

"Study of Site Response at a Selected Memphis Site," by H. Desai, S. Ahmad, E.S. Gazetas and M.R.Oh,10/11/90.

"A User's Guide to Strongmo: Version 1.0 of NCEER's Strong-Motion Data Access Tool for PCs andTerminals," by PA Friberg and CAT. Susch, 11/15/90, (PB91-171272/AS).

"A Three-Dimensional Analytical Study of Spatial Variability of Seismic Ground Motions," by L-L.Hong and AH.-S. Ang, 10/30/90, (PB91-170399/AS).

"MUMOID User's Guide - A Program for the Identification of Modal Parameters," by S.Rodrlguez-Gtinez and E. DiPasquale, 9/30/90, (PB91-l71298/AS).

"SARCF-II User's Guide - Seismic Analysis of Reinforced Concrete Frames," by S. Rodrlguez-Gtinez,Y.S. Chung and C. Meyer, 9/30/90.

"Viscous Dampers: Testing, Modeling and Application in Vibration and Seismic Isolation," by N.Makris and M.C. Constantinou, 12/20/90 (PB91-190561/AS).

"Soil Effects on Earthquake Ground Motions in the Memphis Area," by H. Hwang, C.S. Lee, K.W. Ngand T.S. Chang, 8/2/90, (PB91-190751/AS).

"Proceedings from the Third Japan-U.S. Workshop on Earthquake Resistant Design of LifelineFacilities and Countermeasures for Soil Liquefaction, December 17-19, 1990," edited by T.D. O'RourkeandM. Hamada, 2/1m, (PB91-1792591AS).

"Physical Space Solutions of Non-Proportionally Damped Systems," by M. Tong, Z. Liang and G.C.Lee, 1/15/91, (PB91-179242/AS).

"Kinematic Seismic Response of Single Piles and Pile Groups," by K. Fan, G. Gazetas, A Kaynia, E.Kausel and S. Ahmad, 1/10/91, to be published.

"Theory of Complex Damping," by Z. Liang and G. Lee, to be published.

"3D-BASIS - Nonlinear Dynamic Analysis of Three Dimensional Base Isolated Structures: Part II," byS. Nagarajaiah, AM. Reinhorn and M.C. Constantinou, 2/28/91, (PB91-190553/AS).

F·g

NCEER-91-0006

NCEER-91-0007

NCEER-91-0008

NCEER-91-0009

NCEER-91-0010

NCEER-91-0011

NCEER-91-0012

NCEER-91-0013

NCEER-91-0014

NCEER-91-0015

"A Multidimensional Hysteretic Model for Plasticity Deforming Metals in Energy Absorbing Devices,"by E.J. Graesser and F.A. Cozzarelli, 4/9/91.

"A Framework for Customizab1e Knowledge-Based Expert Systems with an Application to a KBES forEvaluating the Seismic Resistance of Existing Buildings," by E.G. Ibarra-Anaya and SJ. Fenves,4/9/91.

"Nonlinear Analysis of Steel Frames with Semi-Rigid Connections Using the Capacity SpectrumMethod," by G.G. Deierlein, S-H. Hsieh, Y-J. Shen and J.F. Abel, 7/2/91.

"Earthquake Education Materials for Grades K-12," by K.E.K. Ross, 4/30/91.

"Phase Wave Velocities and Displacement Phase Differences in a Harmonically Oscillating Pile," by N.Makris and G. Gazetas, 7/8/91.

"Dynamic Characteristics of a Full-Sized Five-Story Steel Structure and a 2/5 Model," by K.C. Chang,G.C. Yao, G.C. Lee, D.S. Hoo and Y.C. Yeh," to be published.

"Seismic Response of a 2/5 Scale Steel Structure with Added Viscoelastic Dampers," by K.C. Chang,T.T. Soong, S-T. Oh and M.L. Lai, 5/17/91.

"Earthquake Response of Retaining Walls; Full-Scale Testing and Computational Modeling," by S.Alampa11i and A-W.M. Elgamal, 6/20/91, to be published.

"3D-BASIS-M: Nonlinear Dynamic Analysis of Multiple Building Base Isolated Structures," by P.C.Tsopelas, S. Nagarajaiah, M.C. Constantinou and A.M. Reinhom, 5/28/91.

"Evaluation of SEAOC Design Requirements for Sliding Isolated Structures," by D. Theodossiou andM.C. Constantinou, 6/10/91.

F-9

Evaluation of SEAOC Design Requirements for Sliding ...

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