evaluation of seaoc design requirements for sliding
TRANSCRIPT
'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
TABLE OF CONTENTS (cont'd.)
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~
TABLE OF CONTENTS (cont'd.)
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
4-4 Comparisons of Base Displacement Time Histories Obtained by
Programs 3D-BASIS, DRAIN-2D and a Rigorous Analysis Program
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
4-5 Comparisons of Base Displacement Time Histories Obtained by
Programs 3D-BASIS, DRAIN-2D and a Rigorous Analysis Program
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
4-6 Comparisons of Base Displacement Time Histories Obtained by
Programs 3D-BASIS, DRAIN-2D and a Rigorous Analysis Program
for 8 - 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 4-21
4-7 Comparisons of Base Displacement Time Histories Obtained by
Programs 3D-BASIS, DRAIN-2D and a Rigorous Analysis Program
for 1 - Story Structure Subjected to Eureka (023) N44E
Earthquake Component in the Longitudinal Direction.
Scaling of the Record is Based on PGV According to Table 7.4 4-22
4-8 Comparisons of Base Displacement Time Histories Obtained by
Programs 3D-BASIS, DRAIN-2D and a Rigorous Analysis Program
for 8 - Story Structure Subjected to Eureka (023) N44E
Earthquake Component in the Longitudinal Direction.
Scaling of the Record is Based on PGV According to Table 7.4 4-23
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
and Comparison of its Spectrum with the Target Spectrum............................... 6-4
xiv
FIGURE TITLE
LIST OF ILLUSTRATIONS (cont'd.)
PAGE
6-3 Artificial Record No#3 Compatible with OAg Sl Design Spectrum
and Comparison of its Spectrum with the Target Spectrum 6-5
6-4 Artificial Record No#4 Compatible with OAg S2 Design Spectrum
and Comparison of its Spectrum with the Target Spectrum............................... 6-6
6-5 Artificial Record No#5 Compatible with OAg S2 Design Spectrum
and Comparison of its Spectrum with the Target Spectrum............................... 6-7
6-6 Artificial Record No#6 Compatible with OAg S2 Design Spectrum
and Comparison of its Spectrum with the Target Spectrum............................... 6-8
6-7 Artificial Record No#7 Compatible with OAg S3 Design Spectrum
and Comparison of its Spectrum with the Target Spectrum............................... 6-9
6-8 Artificial Record No#8 Compatible with OAg S3 Design Spectrum
and Comparison of its Spectrum with the Target Spectrum 6-10
6-9 Artificial Record No#9 Compatible with OAg S3 Design Spectrum
and Comparison of its Spectrum with the Target Spectrum............................... 6-11
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
7-2 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 Stiff Soil Sites 7-10
xv
FIGURE TITLE
LIST OF ILLUSTRATIONS (cont'd.)
PAGE
7-3 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 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
6.4 Analysis Results for 1 - story Isolated Structure with R =88.048 in
(Tb = 3 sec), fmax = 0.05, Excited in Transverse (T) Direction by
Artificial Record Compatible with Design Spectra. 6-15
6.5 Analysis Results for 1 - story Isolated Structure with R =88.048 in
(Tb = 3 sec), fmax = 0.10, Excited in Transverse (T) Direction by
Artificial Record Compatible with Design Spectra 6-16
6.6 Analysis Results for 8 - story Isolated Structure with R=39.132 in
(Tb = 2 sec), fmax = 0.10, Excited in Transverse (T) Direction by
Artificial Record Compatible with Design Spectra. 6-17
6.7 Analysis Results for 8 - story Isolated Structure with R=88.048 in
(Tb = 3 sec), fmax = 0.05, Excited in Transverse (T) Direction by
Artificial Record Compatible with Design Spectra. 6-18
6.8 Analysis Results for 8 - story Isolated Structure with R=88.048 in
(Tb = 3 sec), fmax = 0.10, Excited in Transverse (T) Direction by
Artificial Record Compatible with Design Spectra 6-19
6.9 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
6.10 Analysis Results for 8 - story Isolated Structure with R =88.048 in
(Tb = 3 sec), fmax = 0.05, 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 6-25
xix
TABLE TITLE
LIST OF TABLES (cont'd.)
PAGE
6.11 Analysis Results for 8 - story Isolated Structure with R=88.048 in
(Tb =3 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. 6-26
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
7.5 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 Rock Sites (Representative
of Soil Type Sl). Weight is Total Weight of Structure Including
Base. Height is 12ft 7-16
7.6 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
xx
TABLE TITLE
LIST OF TABLES (cont'd.)
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
Structure Including Base. Height is 12f1. 7-18
7.8 Analysis Results for 1 - story Isolated Structure with R =88.048 in
(Tb = 3 sec), fmax = 0.05. 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. 7-19
7.9 Analysis Results for 1- story Isolated Structure with R=88.048 in
(Tb = 3 sec), fmax = 0.05. Excitation Represented by a Set of Pairs
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.. 7-20
7.10 Analysis Results for 1 - story Isolated Structure with R =88.048 in
(Tb = 3 sec), fmax = 0.05. 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 12f1. 7-21
xxi
TABLE TITLE
LIST OF TABLES (cont'd.)
PAGE
7.11 Analysis Results for 1 - story Isolated Structure with R=88.048 in
(Tb = 3 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. 7-22
7.12 Analysis Results for 1 - story Isolated Structure with R=88.048 in
(Tb = 3 sec), fmax = 0.10. Excitation Represented by a Set of Pairs
of Scaled Earthquake Motions Recorded on Stiff Soil Sites
(Representative of Soil Type Sl). Weight is Total Weight of
Structure Including Base. Height is 12ft. 7-23
7.13 Analysis Results for 1 - story Isolated Structure with R=88.048 in
(Tb = 3 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. 7-24
7.14 Analysis Results 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. Height is 12ft. 7-25
7.15 Analysis results for 8 - story Isolated Structure with R=39.132 in
(Tb = 2 sec), fmax = 0.10. Excitation Represented by a Set of Pairs
xxii
TABLE TITLE
LIST OF TABLES (cont'd.)
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 12ft. 7-26
7.16 Analysis Results 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 Medium Soil Sites
(Representative of Soil Type S2). Weight is Total Weight of
Structure Including Base. Height is 12ft , 7-27
7.17 Analysis Results for 8 - story Isolated Structure with R =88.048 in
(Tb = 3 sec), fmax = 0.05. 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. 7-28
7.18 Analysis Results for 8 - story Isolated Structure with R =88.048 in
(Tb = 3 sec), fmax = 0.05. Excitation Represented by a Set of Pairs
of Scaled Earthquake Motions Recorded on Stiff Soil Sites
(Representative of Soil Type Sl). Weight is Total Weight of
Structure Including Base. Height is 12ft. 7-29
7.19 Analysis Results for 8 -story Isolated Structure With R=88.048 in
(Tb = 3 sec), fmax = 0.05. 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. 7-30
xxiii
TABLE TITLE
LIST OF TABLES (cont'd.)
PAGE
7.20 Analysis Results for 8 - story Isolated Structure With R =88.048 in
(Tb = 3 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. 7-31
7.21 Analysis Results for 8 - story Isolated Structure With R=88.048 in
(Tb = 3 sec), fmax = 0.10. Excitation Represented by a Set of Pairs
of Scaled Earthquake Motions Recorded on Stiff Soil Sites
(Representative of Soil Type Sl). Weight is Total Weight of
structure Including Base. Height is 12ft.. 7-32
7.22 Analysis Results for 8 - story Isolated Structure With R =88.048 in
(Tb = 3 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. 7-33
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
7.24 Summary of Results of the Mean and the Mean Plus One Standard
Deviation Values of the Base Displacement for 8 - story Isolated
xxiv
TABLE TITLE
LIST OF TABLES (cont'd.)
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
7.25 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
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
7.26 Summary of Results of the Mean and the Mean Plus One Standard
Deviation Values of the Base Displacement for 8 - story Isolated
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
LIST OF TABLES (cont'd.)
PAGE
8.2 Analysis Results for 1 - 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. Height is 12ft 8-7
8.3 Analysis Results for 1 - story Isolated Structure with R=88.048 in
(Tb = 3 sec), fmax = 0.05, 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. 8-8
8.4 Analysis Results for 1 - story Isolated Structure with R=88.048 in
(Tb = 3 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. 8-9
8.5 Analysis Results 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. Height is 12ft. 8-10
8.6 Analysis Results for 8 - story Isolated Structure with R =88.048 in
(Tb = 3 sec), fmax = 0.05, 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. 8-11
xxvi
TABLE TITLE
LIST OF TABLES (cant'd.)
PAGE
8.7 Analysis Results for 8 - story Isolated Structure with R=88.048 in
(Tb = 3 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. 8-12
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
Structure with R=39.132 in (Tb = 2 sec.), fmax = 0.10.
Excitation Represented by Artificial Records Compatible with
Design Spectra. Height is 12 ft. A-2
xxvii
TABLE TITLE
LIST OF TABLES (cont'd.)
PAGE
A,3 Analysis Results of Maximum Story Shear for 8 - story Isolated
Structure with R=88.048 in (Tb = 3 sec.), fmax = 0.05.
Excitation Represented by Artificial Records Compatible with
Design Spectra. Weight is Total Weight of Structure Including Base A-3
AA Analysis Results of Maximum Interstory Drift for 8 - story Isolated
Structure with R=88.048 in (Tb = 3 sec.), fmax = 0.05.
Excitation Represented by Artificial Records Compatible with
Design Spectra. Height is 12 ft. A-4
A.5 Analysis Results of Maximum Story Shear for 8 - story Isolated
Structure with R=88.048 in (Tb = 3 sec.), fmax = 0.10.
Excitation Represented by Artificial Records Compatible with
Design Spectra. Weight is Total Weight of Structure Including Base A-5
A.6 Analysis Results of Maximum Interstory Drift for 8 - story Isolated
Structure with R=88.048 in (Tb = 3 sec.), fmax = 0.10.
Excitation Represented by Artificial Records Compatible with
Design Spectra. Height is 12 ft. A-6
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
LIST OF TABLES (cont'd.)
PAGE
C.2 Analysis Results of Maximum Interstory Drift 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). Height is 12ft. C-2
C.3 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 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
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 Stiff Soil Sites (Representative of Soil
Type S1). Height is 12ft. C-4
C.5 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 Medium Soil Sites (Representative of Soil
Type S2). Weight is Total Weight of Structure Including Base C-5
C.6 Analysis Results of Maximum Interstory Drift for 8 - story Isolated
Structure with R=39.132 in (Tb = 2 sec), fmax = 0.10.
xxix
TABLE TITLE
LIST OF TABLES (cont'd.)
PAGE
Excitation Represented by a Set of Pairs of Scaled Earthquake
Motions Recorded on Medium Soil Sites (Representative of Soil
Type S2). Height is 12ft. C-6
e.7 Analysis Results of Maximum story shear for 8 - story Isolated
Structure with R=88.048 in (Tb = 3 sec), fmax = 0.05.
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-7
e.8 Analysis Results of Maximum Interstory Drift for 8 - story Isolated
Structure with R=88.048 in (Tb = 3 sec), fmax = 0.05.
Excitation Represented by a Set of Pairs of Scaled Earthquake
Motions Recorded on Rock Sites (Representative of Soil
Type S1). Height is 12ft. C-8
e.9 Analysis Results of Maximum Story Shear for 8 - story Isolated
Structure with R=88.048 in (Tb = 3 sec), fmax = 0.05.
Excitation Represented by a Set of Pairs of Scaled Earthquake
Motions Recorded on Stiff Soil Sites (Representative of Soil
Type S1). Weight is Total Weight of Structure Including Base C.9
e.10 Analysis Results of Maximum Interstory Drift for 8 - story Isolated
Structure with R=88.048 in (Tb = 3 sec), fmax = 0.05.
Excitation Represented by a Set of Pairs of Scaled Earthquake
Motions Recorded on Stiff Soil Sites (Representative of Soil
Type Sl). Height is 12ft. C-10
xxx
TABLE TITLE
LIST OF TABLES (cont'd.)
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.
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 C-ll
C.12 Analysis Results of Maximum interstory Drift for 8 - story Isolated
Structure with R=88.048 in (Tb = 3 sec), fmax = 0.05.
Excitation Represented by a Set of Pairs of Scaled Earthquake
Motions Recorded on Medium Soil Sites (Representative of Soil
Type S2). Height is 12f1. C-12
C.13 Analysis Results of Maximum Story Shear for 8 - story Isolated
Structure with R=88.048 in (Tb = 3 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-13
C.14 Analysis Results of Maximum Interstory Drift for 8 - story Isolated
Structure with R=88.048 in (Tb = 3 sec), fmax = 0.10.
Excitation Represented by a Set of Pairs of Scaled Earthquake
Motions Recorded on Rock Sites (Representative of Soil
Type S1). Height is 12f1. C-14
C.15 Analysis Results of Maximum story shear for 8 - story Isolated
Structure with R=88.048 in (Tb = 3 sec), fmax = 0.10.
xxxi
TABLE TITLE
LIST OF TABLES (coot'd.)
PAGE
Excitation Represented by a Set of Pairs of Scaled Earthquake
Motions Recorded on Stiff Soil Sites (Representative of Soil
Type Sl). Weight is Total Weight of Structure Including Base C-15
C16 Analysis Results of Maximum Interstory Drift for 8 - story Isolated
Structure with R=88.048 in (Tb = 3 sec), fmax = 0.10.
Excitation Represented by a Set of Pairs of Scaled Earthquake
Motions Recorded on Stiff Soil Sites (Representative of Soil
Type Sl). Height is 12ft. C-16
C17 Analysis Results of Maximum Story Shear for 8 - story Isolated
Structure with R=88.048 in (Tb = 3 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 C-17
Ci8 Analysis Results of Maximum Interstory Drift for 8 - story Isolated
Structure with R=88.048 in (Tb = 3 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). 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
LIST OF TABLES (cont'd.)
PAGE
D.2 Analysis Results of Maximum Interstory Drift 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. Height is 12ft. D-2
D.3 Analysis Results of Maximum Story Shear for 8 - story Isolated
Structure with R = 88.048 in (Tb = 3 sec), fmax = 0.05, Excited by
Scaled Pairs of Real Records According to the Dynamic Analysis
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
Structure with R = 88.048 in (Tb = 3 sec), fmax = 0.10, Excited by
Scaled Pairs of Real Records According to the Dynamic Analysis
Procedure of SEAOC. Height is 12ft. D-4
D.5 Analysis Results of Maximum Story Shear for 8 - story Isolated
Structure with R = 88.048 in (Tb = 3 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-5
D.6 Analysis Results of Maximum interstory drift for 8 - story Isolated
Structure with R = 88.048 in (Tb = 3 sec), fmax = 0.05, Excited by
Scaled Pairs of Real Records According to the Dynamic Analysis
Procedure of SEAOC. Height is 12ft. D-6
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
Component Component Component Component Component Component Component Component Component
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
Modal damping ratio assumed in analyses
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
Component Component Component Component Component Component Component Component Component
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
Modal damping ratio assumed in analyses
0.03 0.03 0.03
4-7
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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........
FIGURE 5-2 Continued.
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.
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)
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
• SEAOClAnalysis
6-13
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TA
BL
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cite
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30
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
tibl
ew
ith
desi
gnsp
ectr
a.10
0%of
arti
fici
alre
cord
inth
etr
ansv
erse
(T)
and
83%
ofar
tifi
cial
reco
rdin
the
long
itud
inal
(L)
dire
ctio
n.
BA
SE
CE
NT
ER
CO
RN
ER
BE
AR
ING
CO
RN
ER
TO
BA
SESH
EA
R1s
tST
OR
YSH
EA
R1s
tST
OR
YD
RIF
TS
OIL
EX
CIT
AT
ION
DlS
PL
(IN
CH
)D
lSP
L(I
NC
H)
CE
NlE
RD
lSP
LW
EIG
HT
WE
IGH
TH
EIG
HT
(%)
TY
PE
RA
TIO
LT
LT
LT
LT
LT
SI
AR
TIF
ICIA
L#1
1.79
2.16
1.87
2.30
1.06
0.10
50.
128
0.10
40.
125
0.24
770.
3009
SI
AR
TIF
ICIA
L#2
1.49
1.80
1.59
1.98
1.10
0.09
90.
122
0.10
30.
119
0.24
030.
2818
SI
AR
TIF
ICIA
L#3
2.12
2.54
2.26
2.80
1.10
0.11
60.
141
0.09
80.
119
0.22
610.
2781
S2
AR
TIF
ICIA
L#4
2.43
2.94
2.47
3.00
1.02
0.12
10.
146
0.10
80.
129
0.25
180.
3030
S2
AR
TIF
ICIA
L#5
2.18
2.56
2.44
3.03
1.18
0.11
60.
140
0.09
9.0.
120
0.23
040.
2814
S2
AR
TlA
CIA
L#6
2.13
2.57
2.17
2.65
1.03
0.11
20.
139
0.10
90.
130
0.25
570.
3072
S3A
RT
IFIC
IAL
#76.
087.
316.
107.
351.
000.
216
0.26
40.
179
0.21
90.
4115
0.50
67
S3A
RT
lAC
IAL
#85.
416.
505.
516.
681.
030.
198
0.21
40.
172
0.20
80.
3942
0.48
05
S3A
RT
IFIC
IAL
#96.
237.
506.
307.
621.
020.
218
0.26
60.
194
10
. 232
0.45
860.
5510
~
TA
BL
E6.
10A
naly
sis
resu
lts
for
8•
stor
yis
olat
edst
ruct
ure
wit
hR
=88
.048
in(T
b=
3se
c),
f max
=0.
05,e
xcit
edby
bi-d
irec
tion
alar
tifi
cial
reco
rdco
mpa
tibl
ew
ith
desi
gnsp
ectr
a.10
0%of
arti
fici
alre
cord
inth
etr
ansv
erse
(T)
and
83%
ofar
tifi
cial
reco
rdin
the
long
itud
inal
(L)
dire
ctio
n.
BA
SE
CE
NT
ER
CO
RN
ER
BE
AR
ING
CO
RN
ER
TO
BA
SESH
EA
R1s
tsrO
RY
SHE
AR
1sts
rOR
YD
RIF
TS
OIL
EX
CIT
AT
ION
DlS
PL
(IN
CH
)D
lSP
L(I
NC
H)
CE
NT
ER
DlS
PL
WE
IGH
TW
EIG
HT
HE
IGH
T(%
)T
YP
ER
AT
IO
LT
LT
LT
LT
LT
51A
RT
IFIC
IAL
#1
3.46
4.20
3.54
4.34
1.03
0.07
00.
085
0.06
80.
082
0.16
340.
1972
51A
RT
IFIC
IAL
#22.
653.
182.
693.
261.
030.
060
0.07
20.
059
0.07
10.
1392
0.16
91
51A
RT
IFIC
IAL
#33.
694.
443.
724.
501.
010.
074
0.08
90.
065
0.Q
780.
1517
0.18
41
52
AR
TIF
ICIA
L#4
7.10
8.54
7.13
8.58
1.01
0.11
20.
134
0.10
80.
130
0.25
490.
3082
52
AR
TIF
ICIA
L#5
5.93
7.11
6.04
7.30
1.03
0.09
80.
119
0.09
00.
108
0.21
040.
2533
52
AR
TIF
ICIA
L#6
6.52
7.84
6.57
7.93
1.01
0.10
50.
126
0.10
10.
121
0.23
730.
2877
53A
RT
IFIC
IAL
#78.
5710
.32
8.62
10.4
11.
010.
128
0.15
40.
116
0.14
00.
2701
0.32
81
53A
RT
IFIC
IAL
#88.
7310
.49
8.81
10.6
21.
010.
130
0.15
70.
120
0.14
40.
2802
0.33
93
53A
RT
IFIC
IAL
#914
.41
17.3
514
.42
17.3
71.
000.
195
0.23
40.
182
0.21
80.
4246
0.51
29
~
TA
BL
E6.
11A
naly
sis
resu
lts
for8
-sto
ryis
olat
edst
ruct
ure
wit
hR
=88
.048
in(T
b=
3se
c),f
ma
=0.
10,
exci
ted
bybi
-dir
ecti
onal
arti
fici
alre
cord
com
pati
ble
wit
hde
sign
spec
tra.
100%
of
arti
fici
alre
cord
inth
etr
ansv
erse
(T)
and
83%
ofar
tifi
cial
reco
rdin
the
long
itud
inal
(L)
dire
ctio
n.
BA
SE
CE
NT
ER
CO
RN
ER
BE
AR
ING
CO
RN
ER
TO
BA
SESH
EA
R1s
tST
OR
YSH
EA
R1s
tST
OR
YD
RIF
Tso
n.E
XC
ITA
TIO
ND
lSP
L(I
NC
H)
DlS
PL
(IN
CH
)C
EN
lER
DlS
PL
WE
IGH
TW
EIG
IfT
HE
IGIf
T(%
)T
YP
ER
AT
IO
LT
LT
LT
LT
LT
51A
RT
IFIC
IAL
#12.
312.
782.
422.
981.
070.
088
0.10
60.
094
0.11
30.
2246
0.27
23
51A
RT
IFIC
IAL
#21.
551.
861.
682.
091.
120.
079
0.09
80.
092
0.10
60.
2179
0.25
35
51A
RT
IFIC
IAL
#32.
392.
862.
583.
201.
120.
089
0.10
90.
089
0.10
40.
2124
0.25
25
52A
RT
IFIC
IAL
#43.
444.
163.
484.
221.
010.
100
0.12
10.
102
0.12
20.
2387
0.28
61
52A
RT
IFIC
IAL
#52.
663.
142.
883.
551.
130.
087
0·W
70.
099
0.11
70.
2376
0.27
43
52A
RT
IFIC
IAL
#62.
903.
503.
013.
711.
060.
094
0.11
60.
096
0.11
40.
2218
0.26
66
53A
RT
IFIC
IAL
#76.
788.
18.6
.80
8.21
1.00
0.13
80.
171
0.12
00.
145
0.28
420.
3456
53A
RT
IFIC
IAL
#86.
007.
316.
157.
481.
020.
130
0.15
90.
122
0.14
50.
2863
0.34
45
53A
RT
IFIC
IAL
#98.
3010
.00
8.36
10.1
11.
010.
158
0.18
7/0.
164
0.19
50.
3830
0.45
98
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.
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.)Type
fmax=O.lO fmax=O.05 fmax=O.lO
Analysis SEAOC Ratio * Analysis SEAOC Ratio * Analysis SEAOC Ratio *(inch) (inch) (inch) (inch) (inch) (inch)
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
oriz
onta
lear
thqu
ake
com
pone
nts
reco
rded
atro
cksi
tes.
CO
MP
OE
AR
TH
QU
AK
ED
IST
AN
CE
LO
CA
LP
GA
PG
VP
GD
No#
NE
NT
ST
AT
ION
No#
DA
TE
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
.269
-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
oriz
onta
lear
thqu
ake
com
pone
nts
reco
rded
atst
iffs
oils
ites
.
CO
MP
OE
AR
TH
QU
AK
ED
IST
AN
CE
LO
CA
LP
GA
PG
VP
GD
NoH
NE
NT
ST
AT
ION
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
oriz
onta
ler
thq
uak
eco
mpo
nent
sre
cord
edat
med
ium
soil
site
s.
CO
MP
OE
AR
TII
QU
AK
ED
IST
AN
CE
LO
CA
LP
GA
PG
VP
GD
No#
NE
NT
ST
AT
ION
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
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(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.
7-15
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'-l
I ~ ~
TA
BL
E7.
22A
naly
sis
resu
ltsfo
r8
.sto
ryis
olat
edst
ruct
ure
with
R=
88.0
48in
(Tb
=3
sec.
),f m
u=
0.10
.Exc
itatio
nre
pres
ente
dby
ase
tofp
airs
ofsc
aled
eart
hqua
kem
otio
nsre
cord
edon
Med
ium
Soil
Site
s(re
pres
enta
tive
ofso
ilty
peS2
).W
eigh
tist
otal
wei
ghto
fstr
uctu
rein
clud
ing
base
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ght
is12
ft.
IIB
AS
EC
EN
TE
RC
OR
NE
RB
EA
RIN
GC
OR
NE
RT
OB
AS
ESH
EA
RIs
/ST
OR
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EA
Rls
tST
OR
YD
RIF
T(~)
EX
CIT
AT
ION
DIS
PL
(IN
CH
)D
ISP
L(I
NC
H)
CE
NT
ER
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PL
RA
TIO
WE
IGH
TW
EIG
HT
HE
IGH
T()
LT
LT
LT
LT
LT
21W
EST
ER
NW
ASH
(325
)3.
644.
403.
684.
691.
070.
123
0.14
50.
137
0.14
20.
3358
0.34
49
22E
UR
EK
A(0
22)
4.53
4.03
4.56
4.06
1.01
0.12
70.
129
0.12
40.
148
0.28
350.
3620
23E
UR
EK
A(0
23)
12.3
45.
0112
.39
5.12
1.00
0.19
30.
150
0.17
10.
128
0.39
300.
2963
24FE
RN
DA
LE
(023
)2.
481.
322.
571.
391.
040.
105
0.11
40.
116
0.11
60.
2730
0.28
71
25SA
NFE
RN
AN
DO
(241
)8.
177.
518.
277.
581.
010.
153
0.17
10.
141
0.15
10.
3335
0.35
19
26SA
NFE
RN
AN
DO
(458
)5.
786.
735.
976.
931.
030.
155
0.16
70.
130
0.16
30.
2963
0.38
22
27SA
NFE
RN
AN
DO
(264
)6.
373.
586.
383.
691.
000.
156
0.11
70.
161
0.12
70.
3848
0.31
00
28SA
NFE
RN
AN
DO
(267
)5.
134.
205.
184.
281.
010.
145
0.13
50.
130
0.15
80.
3080
0.38
43
29P
UG
ET
SOU
ND
(325
)3.
606.
463.
686.
511.
010.
102
0.16
80.
117
0.16
50.
2742
0.40
07
ME
AN
5.78
4.80
5.85
4.92
1.02
0.14
00.
144
0.13
60.
144
0.32
020.
3466
(J2.
811.
782.
811.
790.
020.
027
0.02
00.
018
0.01
60.
0426
0.03
84
ME
AN
OF
MA
X(L
,T)
6.29
(5.5
4)•
6.39
(5.6
4)•
I0.
154
i0.
153
i0.
3657
I(J
OF
MA
X(L
,n2.
64(1
.65)
•2.
63(1
.64)
•0.
023
0.01
60.
0032
9
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.
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.)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
S1
Stiff Soil 2.52 3.59 2.81 6.90 10.10 5.28 2.91 4.14 3.11
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.
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.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)
Sl
Rock 1.59 2.51 2.81 2.34 3.25 5.28 1.69 2.70 3.11
Sites
Sl
Stiff Soil 2.88 3.86 2.81 7.38 11.06 5.28 3.32 4.53 3.11
Sites
S2
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).
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.)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)
S1
Rock 1.77 2.23 2.81 2.72 3.54 5.28 1.84 2.38 3.11
Sites
S1
Stiff Soil 2.52 3.59 2.81 4.98 6.52 5.28 2.91 4.14 3.11
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).
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.1O 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 1.59 2.51 2.81 2.34 3.25 5.28 1.69 2.70 3.11
Sites
Sl
Stiff Soil 2.88 3.86 2.81 5.18 6.99 5.28 3.32 4.53 3.11
Sites
S2
Medium 5.22 7.16 5.72 7.52 10.02 10.19 5.54 7.19 6.32Soil
Sites
7-37
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27A
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),f m
ax=
0.10
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xcit
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(rep
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ofs
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SH(3
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81
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50
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60
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30
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98
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(02
2)
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00
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70
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70.
121
0.1
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(023
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01
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25SA
NFE
RNAN
DO(2
41
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5.4
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5.4
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0.1
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0.2
37
0.1
39
0.16
10
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56
0.0
89
3
26SA
NFE
RNAN
DO(4
58
)3
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2.2
83
.32
2.2
91
.00
0.18
10
.15
30
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30
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90
.06
67
0.0
65
7
27SA
NFE
RNAN
DO(2
64
)6
.27
2.6
56
.27
2.6
71
.00
0.2
56
0.1
66
0.1
72
0.1
49
0.09
340
.08
27
28SA
NfE
RNA
ND
O(2
67
)3
.86
3.8
23
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3.8
21
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0.1
96
0.1
96
0.1
60
0.1
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0.0
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90
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D(3
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6.9
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210.
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3.8
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68
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2I
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0183
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(L,1
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4.9
5
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8
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43
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OF"l
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(L,T
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1.9
60
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70
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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
RII
PG
A(g
)I
PG
V(i
n/se
c).
nO
NT
YP
ER
EC
OR
DT
LT
LT
LT
L
MO
TIO
N#1
SI
SA
NF
ER
NA
ND
OS
82W
S08
E6.
503.
701.
313
0.80
315
.990
14.3
93(2
84)
Mo
nO
N#
2S
IS
AN
FE
RN
AN
DO
NO
OE
S90
W2.
401.
800.
326
0.25
921
.096
13.1
40(2
08)
MO
TIO
N#3
SI
EL
CE
NT
RO
SOO
ES
90W
1.30
1.00
0.45
20.
214
17.1
2114
.530
(117
)
MO
TIO
N#4
S2
WE
ST
ER
NW
AS
HN
04W
N86
E2.
982.
100.
492
0.58
825
.121
14.1
12(3
25)
MO
TIO
N#5
S2
SA
NF
ER
NA
ND
ON
90E
NO
OE
3.85
3.85
0.71
20.
774
24.9
1014
.900
(264
).
MO
TIO
N#6
S2
EU
RE
KA
N79
EN
11W
2.35
2.20
0.60
60.
370
27.1
6627
.368
(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
wit
hR
=39
.132
in(T
b=
2se
c),f
mllS
=0.
10,e
xcit
edby
scal
edpa
irs
ofre
alre
cord
sac
cord
ing
toth
eD
ynam
icA
naly
sis
Pro
cedu
reo
fSE
AO
C.W
eigh
tis
tota
lw
eigh
to
fstr
uctu
rein
clud
ing
base
.H
eigh
tis
12ft
.
BA
SEC
EN
TE
RC
OR
NE
RB
EA
RIN
GC
OR
NE
RTO
BA
SESH
EA
R1s
tST
OR
YSH
EA
R1s
tST
OR
YD
RIF
TE
XC
ITA
TIO
ND
1SPL
(IN
CH
)D
1SPL
(IN
CH
)C
EN
lER
D1S
PLW
EIG
HT
WE
IGH
TH
EIG
HT
(%)
RA
TIO
LT
LT
LT
LT
LT
MO
TIO
N#1
1.01
1.78
1.02
1.78
1.00
0.10
60.
143
0.19
10.
223
0.10
380.
1225
MO
TIO
N#2
0.99
2.11
0.99
2.11
1.00
0.09
80.
139
0.10
20.
129
0.05
510.
0707
MO
TIO
N#3
1.50
2.16
1.51
2.16
1.00
0.13
50.
143
0.08
40.
119
0.04
530.
0652
MO
TIO
N#4
1.97
3.31
1.97
3.31
1.00
0.13
30.
171
0.11
80.
155
0.06
430.
0851
MO
TIO
N#5
2.17
5.69
2.17
5.69
1.00
0.11
60.
210
0.11
50.
142
0.06
270.
0782
MO
TIO
N#6
3.75
4.52
3.75
4.52
1.00
0.16
50.
202
0.12
30.
136
0.06
700.
0745
co I co
TA
BL
E8.
3A
naly
sis
resu
lts
for
1•
stor
yis
olat
edst
ruct
ure
wit
hR
=88
.048
in(T
b=
3se
c),f
mas
=0.
05,e
xcit
edby
scal
edpa
irs
ofre
alre
cord
sac
cord
ing
toth
eD
ynam
icA
naly
sis
Pro
cedu
reof
SE
AO
C.W
eigh
tis
tota
lw
eigh
tofs
truc
ture
incl
udin
gba
se.
Hei
ghti
s12
ft.
BA
SEC
EN
TE
RC
OR
NE
RB
EA
RIN
GC
OR
NE
RlU
BA
SESH
EA
R1s
tST
OR
YSH
EA
R1s
tST
OR
YD
RIF
TE
XC
ITA
TIO
ND
ISPL
(IN
CH
)D
ISPL
(IN
CH
)C
EN
TE
RD
ISPL
WE
IGH
TW
EIG
HT
HE
IGH
T(%
)R
AT
IO
LT
LT
LT
LT
LT
MO
TIO
N#1
2.27
3.60
2.27
3.60
1.00
0.06
80.
089
0.09
50.
101
0.05
130.
0557
MO
TIO
N#2
2.86
5.88
2.86
5.88
1.00
0.07
70.
112
0.05
40.
065
0.02
920.
0357
MO
TIO
N#3
5.18
4.81
5.18
4.81
1.00
0.10
40.
103
0.05
90.
077
0.03
180.
0421
MO
TIO
N#4
4.12
6.92
4.12
6.92
1.00
0.08
90.
113
0.08
80.
111
0.04
790.
0606
MO
TIO
N#5
3.85
8.06
3.8
5·
8.07
1.00
0.08
70.
127
0.06
40.
079
0.03
790.
0430
MO
TIO
N1t
69.
4911
.17
.9.4
911
.17
1.00
0.14
90.
152
0.07
70.
086
0.04
190.
0470
00 .0
TA
BL
E8.
4A
naly
sis
resu
lts
for
1•s
tory
isol
ated
stru
ctur
ew
ith
R=
88.0
48in
(Tb
=3
sec)
,fm
a
=0.
10,e
xcit
edby
scal
edpa
irs
ofr
eal
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
.Hei
ghti
s12
ft.
BA
SEC
EN
TE
RC
OR
NE
RB
EA
RIN
GC
OR
NE
RT
OB
ASE
SHE
AR
1stS
TO
RY
SHE
AR
1st S
TO
RY
DR
IFT
EX
CIT
AT
ION
DlS
PL(I
NC
H)
DlS
PL(I
NC
H)
CE
NT
ER
DlS
PLW
EIG
HT
WE
IGH
TH
EIG
HT
(%)
RA
TIO
LT
LT
LT
LT
LT
MO
TIO
N#1
1.14
1.97
1.14
1.97
1.00
0.10
30.
120
0.19
10.
232
0.10
350.
1277
MO
TIO
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
TIO
N#5
2.12
5.39
2.73
5.40
LOO
0.11
60.
152
0.12
10.
136
0.06
540.
0745
MO
TIO
N#
65.
056.
235.
076.
251.
000.
134
0.15
20.
081
0.14
40.
0438
0.07
85
00 I -o
TA
BL
E8.
5A
naly
sis
resu
lts
for
8-s
tory
isol
ated
stru
ctur
ew
ith
R=
39.1
32in
(Tb
=2
sec)
,fm
u
=0.1
0,ex
cite
dby
scal
edpa
irs
ofr
eal
reco
rds
acco
rdin
gto
the
Dyn
amic
Ana
lysi
sP
roce
dure
'o
fSE
AO
C.W
eigh
tis
tota
lw
eigh
tofs
truc
ture
incl
udin
gba
se.
Hei
ghti
s12
ft.
BA
SEC
EN
TE
RC
OR
NE
RB
EA
RIN
GC
OR
NE
RTO
BA
SESH
EA
R1s
tST
OR
YSH
EA
R1s
tST
OR
YD
RIF
TE
XC
ITA
TIO
ND
1SPL
(IN
CH
)D
1SPL
(IN
CH
)C
EN
TE
RD
1SPL
WE
IGH
TW
EIG
HT
HE
IGH
T(%
)R
AT
IO
LT
LT
LT
LT
LT
MO
TIO
NHI
1.22
2.51
1.44
2.64
1.05
0.11
60.
158
0.11
10.
152
0.26
300.
3606
MO
TIO
NH
21.
412.
131.
482.
311.
080.
121
0.13
40.
113
0.12
50.
2652
0.29
33
MO
TIO
NH
32.
062.
612.
212.
761.
060.
133
0.13
90.
125
0.13
20.
2896
0.31
80
MO
TIO
N#4
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
Pro
cedu
reof
SE
AO
C.W
eigh
tis
tota
lw
eigh
tofs
truc
ture
incl
udin
gba
se.H
eigh
tis
12ft
.
BA
SE
CE
NT
ER
CO
RN
ER
BE
AR
ING
CO
RN
ER
TO
BA
SESH
EA
R1s
tST
OR
YSH
EA
R1s
tST
OR
YD
RIF
TE
XC
ITA
TIO
ND
ISP
L(I
NC
H)
DlS
PL
(IN
CH
)C
EN
lER
DlS
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
.22
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
,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.H
eigh
tis
12ft
.
BA
SEC
EN
TE
RC
OR
NE
RB
EA
RIN
GC
OR
NE
RTO
BA
SESH
EA
R1s
tSTO
RY
SHE
AR
1stS
TOR
YD
RIF
TE
XC
ITA
TIO
ND
ISPL
(IN
CH
)D
lSPL
(IN
CH
)C
EN
lER
DIS
PLW
EIG
HT
WE
IGH
TH
EIG
HT
(%)
RA
TIO
LT
LT
LT
LT
LT
MO
TIO
NH
I1.
433.
681.
504.
011.
090.
106
0.13
90.
112
0.12
80.
2618
0.30
45
MO
TIO
NH
21.
532.
621.
662.
761.
050.
112
0.11
90.
102
0.12
30.
2389
0.29
35
MO
TIO
NH
32.
533.
112.
613.
131.
010.
112
0.12
60.
109
0.12
50.
2540
0.30
15
MO
TIO
N#4
2.63
3.21
2.77
3.41
1.06
0.11
70.
128
0.12
00.
143
0.28
740.
3538
MO
TIO
NH
52.
695.
642.
895.
661.
000.
104
0.15
10.
129
0.15
20.
3046
0.36
51
MO
TIO
NH
65.
866.
325.
906.
.34
1.00
0.13
80.
156
0.13
30.
153
0.30
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.
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.lO fmax=O.05 fmax=O.10
Analysis SEAOC Ratio * Analysis SEAOC Ratio * Analysis SEAOC Ratio *(inch) (inch) (inch) (inch) (inch) (inch)
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
.lA
naly
sis
resu
lts
ofm
axim
um
stor
ysh
ear
for
8.s
tory
isol
ated
stru
ctu
rew
ith
R=3
9.13
2in
(Tb=
2se
c.),
f mu=0
.10.
Exc
itat
ion
repr
esen
ted
by
arti
fici
alre
cord
sco
mp
atib
lew
ith
Des
ign
Spec
tra.
Wei
ght
isto
talw
eigh
to
fstr
uctu
rein
clu
din
gb
ase.
2nd
STO
RY
SHE
AR
3rd
STO
RY
SHE
AR
II4/h
STO
RY
SHE
AR
II5/h
STO
RY
SHE
AR
II6th
STO
RY
SHE
AR
II7th
STO
RY
SHE
AR
II8th
STO
RY
SHE
AR
l::JE
XC
ITA
TIO
NW
EIG
IIT
WE
IGH
TW
EIG
IIT
WE
IGH
TW
EIG
HT
WE
IGH
TW
EIG
HT
>T
YP
EI
LT
LT
LT
LT
LT
LT
LT
-51
AR
TIF
ICIA
L#1
0.00
00.
119
0.00
00.
111
0.00
00.
103
0.00
00.
097
0.00
00.
079
0.00
00.
091
0.00
00.
064
51A
RT
IFIC
IAL
#20.
000
0.14
10.
000
0.12
40.
000
0.11
70.
000
0.12
00.
000
0.10
60.
000
0.09
10.
000
0.06
7
51A
RT
IFIC
IAL
#30.
000
0.12
70.
000
0.11
20.
000
0.09
20.
000
0.08
40.
000
0.09
00.
000
0.09
40.
000
0.07
0
52A
RT
IFIC
IAL
#40.
000
0.13
40.
000
0.12
70.
000
0.11
90.
000
0.11
40.
000
0.09
10.
000
0.08
30.
000
0.06
2
52A
RT
IFIC
IAL
#50.
000
0.13
90.
000
0.14
50.
000
0.14
10.
000
0.13
60.
000
0.11
70.
000
0.09
70.
000
0.06
5
52A
RT
IFIC
IAL
#60.
000
0.13
70.
000
0.13
30.
000
0.12
70.
000
0.11
00.
000
0.10
60.
000
0.09
80.
000
0.06
3
53A
RT
IFIC
IAL
#70.
000
0.22
50.
000
0.20
20.
000
0.18
60.
000
0.14
60.
000
0.14
10.
000
0.12
10.
000
0.08
253
AR
TIF
ICIA
L#8
0.00
00.
180
0.00
00.
166
0.00
00.
153
0.00
00.
125
0.00
00.
120
0.00
00.
112
0.00
00.
076
53A
RT
IFIC
IAL
#90.
000
0.19
80.
000
0.18
00.
000
0.15
90.
000
0.14
30.
000
0.13
70.
000
0.12
20.
000
0.08
0
TA
BL
EA
.2A
naly
sis
resu
ltsof
max
imum
inte
rsto
rydr
iftfo
r8
.sto
ryis
olat
edst
ruct
ure
with
R=
39.1
32in
(Tb
=2
sec.
),f m
u=
0.10
.Exc
itatio
nre
pres
ente
dby
artif
icia
lrec
ords
com
pati
ble
with
Des
ign
Spec
tra.
Hei
ght
is12
ft.
SOIL
IEXC
ITA
TIO
N2n
dST
OR
YD
RIF
1(",
)3r
dST
OR
YD
RIF
T(",
4th
STO
RY
DR
IFT
('1t.)
5th
STO
RY
DR
IFT
('1t.)
6th
STO
RY
DR
IFT
'1t.~rth
STO
RY
HE
IGII
T0
HE
IGH
T0
HE
IGH
T0
HE
IGH
T0
HE
IGH
T(
0H
EIG
l
>~
TY
PEI
,L
TL
TL
TL
TL
TL
TL
TN
51A
RT
IFIC
IAL
#10.ססOO
0.28
600.ססOO
0.26
690.ססOO
0.33
010.
0000
0.30
950.ססOO
0.25
540.ססOO
0.43
230.ססOO
0.30
68
51A
RT
IFIC
IAL
#20.ססOO
0.32
430.ססOO
0.29
100.ססOO
0.36
730.ססOO
0.37
050.ססOO
0.32
420.ססOO
0.43
240.ססOO
0.31
76
51A
RT
IFIC
IAL
#30.ססOO
0.29
770.ססOO
0.26
860.ססOO
0.29
320.ססOO
0.27
260.ססOO
0.28
700.ססOO
0.45
170.ססOO
0.33
00
52
AR
TIF
ICIA
L#4
0.ססOO
0.31
690.ססOO
0.29
930.ססOO
0.38
340.ססOO
0.35
420.ססOO
0.28
230.ססOO
0.39
700.ססOO
0.29
315
2A
RT
IAC
IAL
#50.ססOO
0.31
670.ססOO
0.33
780.ססOO
0.44
730.ססOO
0.43
070.ססOO
0.37
220.ססOO
0.46
150.ססOO
0.31
25
52
AR
TIF
ICIA
L#6
0.ססOO
0.31
890.ססOO
0.31
840.ססOO
0.40
430.ססOO
0.34
940.ססOO
0.33
570.ססOO
0.46
690.ססOO
0.30
00
53
AR
TIF
ICIA
L#7
0.ססOO
0.53
770.ססOO
0.48
900.ססOO
0.60
400.
0000
0.45
990.ססOO
0.43
840.ססOO
0.58
340.ססOO
0.39
135
3A
RT
IFIC
IAL
#80.ססOO
0.43
640.ססOO
0.39
710.ססOO
0.50
270.ססOO
0.39
730.ססOO
0.37
820.ססOO
0.52
990.ססOO
0.36
155
3A
RT
IFIC
IAL
#90.ססOO
0.48
000.ססOO
0.42
690.
0000
0.50
320.ססOO
0.44
560.ססOO
0.42
860.ססOO
0.57
890.ססOO
0.38
07
> , ~
TA
BL
EA
.3A
naly
sis
resu
ltsof
max
imum
stor
ysh
ear
for
8.s
tory
isol
ated
stru
ctur
ew
ithR
=88
.048
in(T
b=
3se
c.),
fmu
=O.
OS.E
xcita
tion
repr
esen
ted
byar
tific
ial
reco
rds
com
pati
ble
with
Des
ign
Spec
tra.
Wei
ght
isto
talw
eigh
tof
stru
ctur
ein
clud
ing
base
.
2nd
STO
RY
SHE
AR
3rd
STO
RY
SHE
AR
4th
STO
RY
SHE
AR
5th
STO
RY
SHE
AR
61hS
TOR
YSH
EA
R7t
hST
OR
YSH
EA
R8t
hST
OR
YSH
EA
R5
0IL
EX
CIT
AT
ION
WE
IGH
TW
EIG
HT
WE
IGH
TW
EIG
HT
WE
IGH
TW
EIG
Iff
WE
IGH
TI
TY
PE
LT
LT
LT
LT
LT
LT
LT
51A
RT
IFIC
IAL
#10.
000
0.08
60.
000
0.08
80.
000
0.07
80.
000
0.06
90.
000
0.07
40.
000
0.06
90.
000
0.04
851
AR
TIF
ICIA
L#2
0.00
00.
081
0.00
00.
072
0.00
00.
062
0.00
00.
061
0.00
00.
053
0.00
00.
053
0.00
00.
041
51A
RT
IFIC
IAL
#30.
000
0.08
60.
000
0.07
40.
000
0.07
20.
000
0.06
80.
000
0.06
80.
000
0.05
90.
000
0.05
1
52A
RT
IFIC
IAL
#40.
000
0.12
20.
000
0.11
70.
000
0.1I
00.
000
0.09
60.
000
0.07
80.
000
0.06
30.
000
0.04
152
AR
TIF
ICIA
L#5
0.00
00.
113
0.00
00.
116
0.00
00.
1I9
0.00
00.
104
0.00
00.
098
0.00
00.
073
0.00
00.
055
52A
RT
IFIC
IAL
#60.
000
0.1I
40.
000
0.1I
20.
000
0.10
70.
000
0.09
50.
000
0.08
00.
000
0.06
00.
000
0.04
7
53A
RT
IFIC
IAL
#70.
000
0.12
30.
000
0.12
00.
000
0.1I
00.
000
0.09
60.
000
0.09
30.
000
0.08
50.
000
0.05
253
AR
TIF
ICIA
L#8
0.00
00.
138
0.00
00.
118
0.00
00.
103
0.00
00.
096
0.00
00.
082
0.00
00.
070
0.00
00.
054
53A
RT
IFIC
IAL
#90.
000
0.17
90.
000
0.16
30.
000
0.14
60.
000
0.12
20.
000
0.09
70.
000
0.08
50.
000
0.05
5
TA
BL
EA
.4A
naly
sis
resu
ltsof
max
imum
inte
rsto
rydr
iftfo
r8
.sto
ryis
olat
edst
ruct
ure
with
R=
88.0
48in
(Tb=
3se
c.),
f mu
=0.
05.E
xcita
tion
repr
esen
ted
byar
tific
ialr
ecor
dsco
mpa
tibl
ew
ithD
esig
nSp
ectr
a.H
eigh
tis
12ft
.
2nd
STO
RYD
RIF
T3r
dST
OR
YD
RIF
T(%
4th
STO
RY
DR
IFT
(%)1
15th
STO
RY
DR
IFT
('1.}
116th
STO
RY
DR
IFT
('1.J
I1th
STO
RY
DR
IFT
('1.}~8th
STO
RY
DR
IFT
('1.)
SOILIEXC
ITA
TIO
N/l
ElG
/iT
(%)
>~
TY
PE
HE
IGH
TH
EIG
HT
HE
IGH
T0
HE
IGH
T011
HE
IGH
T0
HE
IGH
T0
~L
TL
TL
TL
TL
TL
TL
T51
AR
TIA
CIA
L1/1
0.00
000.
2033
0.00
000.
2019
0.00
000.
2445
0.00
000.
2213
0.00
000.
2395
0.00
000.
3342
0.00
000.
0226
3
51A
RT
IAC
IAL
1/2
0.00
000.
1896
0.00
000.
1696
0.00
000.
2029
0.00
000.
1940
0.00
000.
1646
0.00
000.
2478
0.00
000.
0199
5
51A
RT
IAC
IAL
1/30.
0000
0.20
110.
0000
0.17
650.
0000
0.22
630.
0000
0.20
770.
0000
0.21
490.
0000
0.27
780.
0000
0.02
426
52
AR
TIF
ICIA
L1/
40.
0000
0.28
840.
0000
0.27
790.
0000
0.34
500.
0000
0.30
360.
0000
0.24
940.
0000
0.29
940.
0000
0.01
937
52
AR
TIA
CIA
L1/
50.
0000
0.26
570.
0000
0.27
250.
0000
0.37
010.
0000
0.32
910.
0000
0.30
750.
0000
0.34
600.
0000
0.02
571
52
AR
TIA
CIA
L11
60.
0000
0.27
140.
0000
0.26
360.
0000
0.33
500.
0000
0.30
070.
0000
0.25
470.
0000
0.28
650.
0000
0.02
247
53A
RT
IAC
IAL
1/1
0.00
000.
2992
0.00
000.
2779
0.00
000.
3475
0.00
000.
3059
0.00
000.
2892
0.00
000.
4066
0.00
000.
0253
553
AR
TIA
CIA
L1/
80.
0000
0.31
890.
0000
0.27
570.
0000
0.32
870.
0000
0.29
910.
0000
0.25
650.
0000
0.33
530.
0000
0.02
562
53A
RT
IAC
IAL
119
0.00
000.
4239
0.00
000.
3865
0.00
000.
4624
0.00
000.
3887
0.00
000.
3071
0.00
000.
4048
0.00
000.
0265
4
> I til
TA
BL
EA
.SA
naly
sis
resu
lts
ofm
axim
um
stor
ysh
ear
for
8•s
tory
isol
ated
stru
ctu
rew
ith
R=
88.1
48in
(Tb
=3
sec.
),f m
u=
0.10
.Exc
itat
ion
rep
rese
nte
db
yar
tifi
cial
reco
rds
com
pat
ible
wit
hD
esig
nSp
ectr
a.W
eigh
tis
tota
lwei
ght
ofst
ruct
ure
incl
ud
ing
base
.
IEXmA
TIONI
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
ST
OR
YSH
EA
R8t
hST
OR
YSH
EA
RSO
ILW
EIG
IIT
WE
IGII
TW
EIG
HT
WE
IGH
TW
EIG
HT
WE
IGH
TW
EIG
HT
TYPE
LT
LT
LT
LT
LT
LT
LT
51A
RT
IRC
IAL
#10.
000
0.10
90.
000
0.10
00.
000
0.10
10.
000
0.10
10.
000
0.09
00.
000
0.09
90.
000
0.06
7
51A
RT
IRC
IAL
#20.
000
0.13
90.
000
0.12
40.
000
0.11
80.
000
0.12
20.
000
0.10
10.
000
0.08
80.
000
0.06
4
51A
RT
IRC
IAL
#30.
000
0.12
70.
000
0.11
10.
000
0.09
00.
000
0.09
80.
000
0.08
50.
000
0.09
20.
000
0.06
9
52A
RT
IRC
IAL
#40.
000
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40.
000
0.11
30.
000
0.12
20.
000
0.12
00.
000
0.09
70.
000
0.08
90.
000
0.06
152
AR
TIR
CIA
L#5
0.00
00.
153
0.00
00.
161
0.00
00.
153
0.00
00.
141
0.00
00.
122
0.00
00.
101
0.00
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069
52A
RT
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IAL
#60.
000
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20.
000
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90.
000
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20.
000
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00.
000
0.10
30.
000
0.09
90.
000
0.06
3
83A
RT
IRC
IAL
#70.
000
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00.
000
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60.
000
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60.
000
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80.
000
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000
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20.
000
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7S3
AR
TIR
CIA
L#8
0.00
00.
167
0.00
00.
159
0.00
00.
140
0.00
00.
128
0.00
00.
120
0.00
00.
110
0.00
00.
076
S3A
RT
IRC
IAL
#90.
000
0.17
70.
000
0.15
90.
000
0.14
00.
000
0.13
20.
000
0.12
80.
000
0.11
60.
000
0.08
1
~
TA
BL
EA
.6A
nal
ysis
resu
lts
ofm
axim
um
inte
rsto
rydr
iftf
or8
-sto
ryis
olat
edst
ruct
ure
wit
hR
=88.
148
in(T
b=3
sec.
),f m
ax=0
.10.
Exc
itat
ion
rep
rese
nte
db
yar
tifi
cial
reco
rds
com
pat
ible
wit
hD
esig
nS
pec
tra.
Hei
ght
is12
ft.
SOIL
EX
CIT
AT
ION
2nd
STO
RY
DR
IFI(
"d3r
dST
OR
YD
RIF
TIf<
4th
STO
RY
DR
IFT(
'ft.)
5th
STO
RY
DRI
FT(I
f<)
6th
STO
RY
DR
IFT
('ft
7th
STO
RY
DR
IFT
('ft)
8th
STO
RY
DR
IFT(
If<)
TY
PE
HE
IGH
T0
HE
IGH
T(0
HE
IGH
T0
HE
IGH
T0
HE
IGH
T0)
HE
IGH
T0
HE
IGH
T0
LT
LT
LT
LT
LT
LT
LT
51A
RT
IFIC
IAL
#10.ססOO
0.25
460.ססOO
0.23
760.ססOO
0.31
400.ססOO
0.31
170.
0000
0.28
140.
0000
0.46
970.ססOO
0.32
17
51A
RT
IHC
IAL
#20.ססOO
0.31
820.ססOO
0.29
310.ססOO
0.36
790.
0000
0.37
660.
0000
0.31
220.
0000
0.41
030.
0000
0.30
3751
AR
TIF
ICIA
L#3
0.ססOO
0.29
520.ססOO
0.26
810.ססOO
0.28
800.ססOO
0.30
140.
0000
0.26
530.ססOO
0.44
310.ססOO
0.32
79
52
AR
TIF
ICIA
L#4
0.ססOO
0.26
920.ססOO
0.27
080.ססOO
0.38
110.ססOO
0.37
650.
0000
0.30
420.ססOO
0.42
620.ססOO
0.29
215
2A
RT
IHC
IAL
#50.ססOO
0.34
990.ססOO
0.37
460.ססOO
0.48
310.ססOO
0.44
900.ססOO
0.38
600.ססOO
0.47
790.ססOO
0.32
615
2A
RT
IFIC
IAL
#60.ססOO
0.29
420.ססOO
0.28
600.ססOO
0.38
020.ססOO
0.34
330.
0000
0.32
670.ססOO
0.47
250.ססOO
0.29
80
53
AR
TIF
ICIA
L#7
0.ססOO
0.36
620.ססOO
0.38
800.ססOO
0.49
850.
0000
0.43
860.ססOO
0.40
130.ססOO
0.53
220.ססOO
0.36
645
3A
RT
IFIC
IAL
#80.ססOO
0.39
470.ססOO
0.37
990.ססOO
0.44
490.
0000
0.39
720.ססOO
0.37
780.ססOO
0.51
960.ססOO
0.36
355
3A
RT
IHC
IAL
H9
0.ססOO
0.40
890.ססOO
0.37
580.ססOO
0.44
820.ססOO
0.4I
l70.ססOO
0.39
810.ססOO
0.55
230.ססOO
0.38
55
: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
1.5 2.0 2.5PERIOD (SECS)
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)
FIGURE B-1 Continued.
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
1.5 2.0 2.5PERIOD (SECS)
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)
FIGURE 8-1 Continued.
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
"--'
FIGURE B-1 Continued.
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
1.5 2.0 2.5PERIOD (SECS)
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---
FIGURE B-1 Continued.
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
1.5 2.0 2.5PERIOD (SECS)
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..........
FIGURE B-1 Continued.
B-9
3.53.0
- -- -
5. DAMPING SPECTRA
STIFF SOIL SITE
NO#19 SAN FERNANDO (253)
PGV SCALED
---
1.5 2.0 2.5PERIOD (SECS)
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
1.5 2.0 2.5PERIOD (SECS)
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
'-"
FIGURE 8-1 Continued.
B-10
.3.5.3.0
5" DAMPING SPECTRAMEDIUM SOIL SITE
NO#21 WESTERN WASH.(325)PGV SCALED
1.5 2.0 2.5PERIOD (SECS)
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
'--"
FIGURE 8-1 Continued.
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.........
FIGURE 8-1 Continued.
B-12
3.53.0
5lS DAMPING SPECTRAMEDIUM SOIL SITENO#25 SAN FERNANDO (241)PGV SCALED
- ----
1.5 2.0 2.5PERIOD (SECS)
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
1.5 2.0 2.5PERIOD (SECS)
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
FIGURE B-1 Continued.
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
FIGURE B-1 Continued.
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
FIGURE B-1 Continued.
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
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naly
sis
resu
lts
ofm
axim
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edst
ruct
ure
wit
hR
=39.
132
in(T
b=2
sec.
),f m
u=0
.10.
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itat
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repr
esen
ted
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(rep
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of
soil
type
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eigh
tis
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to
fst
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incl
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WE
IGH
TW
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TW
EIG
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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.
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0.06
40.
040
2K
ER
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95)
0.11
00.
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0.10
80
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10
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30
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70
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70
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60
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50
.10
90.
077
0.09
10
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20
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23
LY
TL
EC
RE
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(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.
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0.09
40.
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0.09
10.
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0.09
20.
080
0.09
80.
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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.
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0.04
30.
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6S
AN
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(126
)0.
149
0.09
40.
141
0.09
30.
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0.08
00.
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0.08
30.
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0.07
10.
083
0.08
00.
063
0.07
77
SA
NF
ER
NA
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O(2
79)
0.09
60.
114
0.Q
920.
100
0.08
30.
092
0.08
30.
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0.07
90.
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0.07
30.
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AN
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(104
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90.
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69
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NA
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(220
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TA
BL
EC
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naly
sis
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of
max
imum
inte
rsto
rydr
ift
for
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stor
yis
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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
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rded
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sent
ativ
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tis
12ft
.
EX
CIT
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2nd
srO
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DRI
FT(%
)3r
dsr
OR
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('1o)
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t.)5t
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OR
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RIFT
('1o)
6th
srO
RY
DRI
FT('1
t.)7t
hsr
OR
YD
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('1t.
8th
srO
RY
DRI
FT('1
t.)H
EIG
HT
HE
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TH
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IGH
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LT
LT
LT
LT
LT
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1H
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EN
A(3
23)
0.36
350.
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0.30
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0.38
640.
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0.47
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95)
0.25
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0.21
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0.54
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3824
0.43
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AR
KF
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D(0
97)
0.19
820.
2477
0.19
250.
2297
0.24
490.
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0.24
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FE
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0.35
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0.32
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0.38
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0.24
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AN
FE
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(126
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0.22
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0.25
850.
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0.23
110.
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0.37
630.
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AN
FE
RN
AN
DO
(279
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0.27
790.
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840.
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0.28
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0.28
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0.37
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AN
FE
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DO
(104
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0.22
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0.28
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0.34
410.
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0.28
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1922
0.29
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0.29
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30
9S
AN
FE
RN
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DO
(128
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0.27
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0.26
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0.31
680.
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0.30
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0.45
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AN
FE
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(220
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0.23
900.
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0.22
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0.27
120.
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0.20
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sis
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ated
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rew
ith
R=3
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2in
(Tb=2
sec.
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u:=0
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esen
ted
by
ase
tofp
airs
ofs
cale
dea
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ake
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ions
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rded
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tiff
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ativ
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ctur
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ing
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AR
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(117
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116
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0
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EN
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TA
BL
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naly
sis
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umin
ters
tory
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r8
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ory
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ated
stru
ctur
ew
ithR
=39.
132
in(T
b=2
sec.
),f m
ax=0
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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).
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ght
is12
ft.
EX
CIT
AT
ION
2nd
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RY
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F1('1
t.)3r
dST
OR
YD
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RY
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lft.)
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740.
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4480
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3219
0.38
07
12E
LC
EN
TR
O(1
17)
0.30
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0.18
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0.33
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0.53
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0.35
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AN
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DO
(110
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0.25
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0.28
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DO
(135
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0.39
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(208
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0.28
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0.35
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17S
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(211
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0.28
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(253
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0.30
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0.28
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OF
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TA
BL
EC
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naly
sis
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ltsof
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imum
stor
ysh
ear
for
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tory
isol
ated
stru
ctur
ew
ithR
=39
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in(T
b=
2se
c.),
f mu
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10.E
xcita
tion
repr
esen
ted
bya
seto
fpai
rso
fsca
led
eart
hqua
kem
otio
nsre
cord
edon
Med
ium
Soil
Site
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epre
sent
ativ
eof
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type
S2).
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ghti
sto
talw
eigh
tof
stru
ctur
ein
clud
ing
base
.
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RY
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EA
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2
22E
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0.29
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185
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168
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137
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RN
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DO
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217
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181
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ER
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175
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20.
167
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153
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135
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110
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AN
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RN
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DO
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232
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212
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NF
ER
NA
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O(2
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0.16
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173
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146
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ET
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020.
1819
0.34
860.
3277
.0.
4142
0.32
700.
3694
0.27
500.
6003
0.54
000.
3820
0.43
38
4P
AR
KF
IEL
D(0
97)
0.19
640.
2723
0.19
580.
2389
0.24
730.
3018
0.22
6'7
0.29
050.
1913
0.30
880.
3629
0.46
630.
2670
0.31
70
5SA
NF
ER
NA
ND
O(2
84)
0.24
360.
2776
0.23
320.
2814
0.28
760.
3653
0.25
180.
3208
0.21
460.
2955
0.29
640.
3812
0.20
050.
2382
6S
AN
FE
RN
AN
DO
(126
)0.
3359
0.20
780.
3296
0.21
230.
3713
0.24
680.
3676
0.27
970.
2598
0.23
500.
3889
0.38
010.
3066
0.36
74
7S
AN
FE
RN
AN
DO
(279
)0.
2164
0.22
790.
1727
0.22
290.
2223
0.28
470.
2667
0.26
030.
2475
0.23
900.
3375
0.34
960.
2557
0.26
25
8S
AN
FE
RN
AN
DO
(104
)0.
1743
2244
0.18
870.
2822
0.25
080.
3455
0.22
650.
2920
0.18
460.
2911
0.25
560.
2979
0.29
050.
3140
9SA
NF
ER
NA
ND
O(1
28)
0.20
160.
2686
0.20
470.
2608
0.26
560.
3205
0.32
950.
3191
0.28
380.
3018
0.38
350.
4479
0.43
120.
4564
10S
AN
FE
RN
AN
DO
(220
)0.
2457
0.23
270.
2293
0.22
210.
2948
0.25
740.
2912
0.22
800.
2490
0.19
950.
3510
0.30
560.
2399
0.24
51
ME
AN
0.23
940.
2279
0.22
970.
2260
0.29
660.
2922
0.30
590.
2796
0.26
490.
2650
0.38
290.
3852
0.29
120.
3126
cr0.
0459
0.03
980.
0517
0.04
360.
0518
0.05
930.
0621
0.05
950.
0587
0.04
820.
0908
0.08
280.
0654
0.08
07
ME
AN
OF
MA
X(L
,T)
0.26
320.
2590
0.33
390.
3297
0.30
010.
4184
0.32
24
crO
FM
AX
(L,T
)0.
0333
0.04
220.
0324
0.04
440.
0389
0.08
080.
0712
() .... VI
TA
BL
EC
.IS
Ana
lysi
sre
sult
sof
max
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
by
ase
to
fpa
irs
of
scal
edea
rthq
uake
mot
ions
reco
rded
onS
tiff
Soil
Site
s(re
pres
enta
tive
ofs
oilt
ype
SI)
.Wei
ghti
stot
alw
eigh
to
fstr
uctu
rein
clud
ing
base
.
II2ndST
OR
YS
IIIW
/"d
STO
RY
SllE
AR
.,
STO
RY
SllE
AR
,,'S
TOR
YSl
lEA
R~,
STO
RY
SHE
AR
7"ST
OR
YS
IIIW
/&,
STO
RY
SllE
AR
EX
CIT
An
ON
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
11L
OW
ER
CA
(117
)0
.11
40
.11
50
.10
30
.10
00.
092
0.13
90.
095
0.14
10
.09
30
.11
70
.08
40
.10
70
.06
20
.07
912
EL
CE
NT
RO
(117
)0.
116
0.12
60.
127
0.11
40.
126
0.11
90.
113
0.13
50.
111
0.12
80.
097
0.12
40.
058
0.07
413
PAR
KFI
EL
D(0
14)
0.08
10
.14
00
.07
80
.12
60
.10
50
.11
30
.10
10
.09
90
.10
20
.10
30
.10
90
.12
70
.08
00
.07
914
SAN
fER
NA
ND
O(1
10)
0.12
10.
094
0.11
60.
094
0.10
50.
098
0.09
70.
097
0.09
70.
100
0.09
00.
088
0.06
00.
064
15SA
NfE
RN
AN
DO
(135
)0.
110
0.13
10.
101
0.13
30.
080
0.12
20.
086
0.11
30.
093
0.10
70.
081
0.10
40.
059
0.07
716
SAN
fER
NA
ND
O(2
08)
0.11
10.
122
0.10
80.
117
0.10
30.
110
0.09
40.
109
0.08
20.
090
0.07
50.
074
0.05
20.
050
17SA
NfE
RN
AN
DO
(211
)0.
120
0.12
30.
116
0.11
60.
108
0.10
60.
097
0.09
10.
084
0.08
00.
073
0.07
20.
051
0.05
118
SAN
fER
NA
ND
O(4
66)
0.11
00.
118
0.10
80.
111
0.10
20.
102
0.08
90.
090
0.07
90.
084
0.08
70.
097
0.05
80.
069
19SA
NfE
RN
AN
DO
(253
)0.
098
0.11
40.
096
0.09
80.
083
0.10
30.
096
0.10
10.
080
0.09
40.
064
0.10
40.
057
0.08
0
20SA
NfE
RN
AN
DO
(199
)0.
133
0.11
60.
135
0.11
40.
117
0.10
50.
102
0.10
50.
103
0.09
00.
095
0.07
50.
057
0.05
8
ME
AN
0.11
10.
120
0.10
90.
112
0.10
20.
112
0.09
70.
108
0.09
20.
099
0.08
60.
097
0.05
90.
068
0'
0.01
30.
012
0.01
50.
012
0.01
30.
012
0.00
70.
016
0.01
00.
014
0.01
20.
019
0.00
80.
011
ME
AN
OF
MA
X(L
,T)
0.12
40.
118
0.11
50.
109
0.10
10.
100
0.06
80
'O
FM
AX
(L,T
)0.
008
0.01
20.
Q11
0.01
60.
013
0.01
70.
011
() I -0'1
TA
BL
EC
.16
Ana
lysi
sres
ults
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
=0.1
0.E
xcita
tion
repr
esen
ted
bya
set
ofpa
irs
ofsc
aled
eart
hqua
kem
otio
nsre
cord
edon
Stif
fSoi
lSite
s(r
epre
sent
ativ
eof
soil
type
SI).
Hei
ghti
s12
ft.
2nd
STO
RY
DR/
F1(.%
)3r
dST
OR
YD
R/F
1(%
)4t
hST
OR
YD
R/FT
('1<
)5t
hST
OR
YD
R/FT
('1<
)6t
hST
OR
YD
R/FT
('1<
)7t
hST
OR
YD
R/FT
('1<
8th
STO
RY
DR
/FT(
%)
EX
CIT
AT
ION
HE
IG/I
TH
E/G
lff
HE
/Gff
[0
HE
/Glf
f0
HE
/GH
T0
HE
/Gff
[0
HE
/Gff
[
LT
LT
LT
LT
LT
LT
LT
11L
OW
ER
CA
(117
)0.
2673
0.26
610.
2421
0.23
130.
2843
0.44
570.
2969
0.44
620.
2907
0.37
150.
3959
0.51
480.
2875
0.37
95
12E
LC
EN
TR
O(1
17)
0.27
140.
2865
0.29
930.
2788
0.39
960.
3866
0.35
560.
4135
0.34
120.
3977
0.45
420.
5923
0.27
250.
3529
13P
AR
KF
IEL
D(0
14)
0.18
400.
3136
0.18
150.
2973
0.32
740.
3570
0.31
430.
3108
0.32
200.
3272
0.51
680.
6036
0.37
240.
3831
14S
AN
FE
RN
AN
DO
(110
)0.
2779
0.21
850.
2712
0.22
300.
3311
0.30
870.
2994
0.30
730.
2982
0.31
410.
4227
0.42
560.
2835
0.30
53
15S
AN
FE
RN
AN
DO
(135
)0.
2536
0.30
760.
2362
0.30
870.
2529
0.38
390.
2729
0.35
780.
2879
0.34
210.
3802
0.49
280.
2810
0.36
77
16S
AN
FE
RN
AN
DO
(208
)0.
2591
0.27
620.
2541
0.27
210.
3290
0.34
550.
2912
0.34
400.
2561
0.28
670.
3504
0.35
080.
2467
0.23
57
17S
AN
FE
RN
AN
DO
(211
)0.
2751
0.27
810.
2724
0.27
070.
3437
0.33
350.
3004
0.28
960.
2637
0.25
720.
3405
0.34
650.
2370
0.24
20
18S
AN
FE
RN
AN
DO
(466
)0.
2564
0.28
460.
2530
0.26
300.
3202
0.32
300.
2804
0.28
590.
2533
0.26
770.
4084
0.46
360.
2752
0.33
07
19S
AN
FE
RN
AN
DO
(253
)0.
2338
0.25
950.
2258
0.22
670.
2668
0.32
040.
3020
0.31
720.
2526
0.28
930.
2970
0.49
380.
2710
0.38
69
20S
AN
FE
RN
AN
DO
(199
)0.
2999
0.26
060.
3114
0.25
980.
3656
0.33
460.
3184
0.33
060.
3279
0.28
490.
4476
0.34
890.
2674
0.27
45
ME
AN
0.25
790.
2751
0.25
470.
2631
0.32
210.
3539
0.30
320.
3403
0.28
940.
3138
0.40
140.
4633
0.27
940.
3258
(J0.
0297
0.02
550.
0353
0.02
750.
0422
0.03
920.
0218
0.05
000.
0312
0.04
340.
0604
0.09
030.
0345
0.05
53
ME
AN
OF
MA
X(L
,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
23E
UR
EK
A(0
23)
0.15
40.
108
0.14
10.
097
0.13
00.
100
0.11
40.
097
0.09
10.
091
0.07
40.
073
0.05
10.
045
24F
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
24F
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
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naly
sis
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lts
ofm
axim
umst
ory
shea
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r8
•st
ory
isol
ated
stru
ctur
ew
ith
R=3
9.13
2in
(Tb
=2
sec)
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u=
0.10
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ited
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pair
sof
real
reco
rds
acco
rdin
gto
the
Dyn
amic
Ana
lysi
sP
roce
dure
ofS
EA
OC
.Wei
ghti
sto
tal
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ghto
fstr
uctu
rein
clud
ing
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2NJ
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RY
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AR
3rd
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RY
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4th
STO
RY
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AR
Sth
STO
RY
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AR
6th
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RY
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7th
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RY
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8th
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AR
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NfH
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129
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112
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109
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70.
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088
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00.
066
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TIO
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109
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106
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30.
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80.
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OT
ION
#13
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129
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90.
126
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10.
128
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00.
130
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30.
126
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780.
124
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50.
074
MO
TIO
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126
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120
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108
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30.
101
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090
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087
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061
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OT
ION
#IS0.
124
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108
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102
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90.
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098
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2M
OT
ION
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193
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80.
171
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90.
160
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90.
140
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116
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099
0.06
50.
087
~
TA
BL
ED
.2A
naly
sis
resu
lts
ofm
axim
umin
ters
tory
drif
tfor
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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
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Jrf
HE
/GJr
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f
MO
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NII
I0.
2571
0.34
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3504
0.36
260.
3207
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0.28
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97
MO
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0.28
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53
MO
TIO
N"3
0.25
430.
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710.
3007
0.35
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660.
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690.
3909
0.36
750.
5920
0.20
920.
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MO
TIO
N11
40.
2986
0.42
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2846
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500.
3374
0.51
950.
3126
0.41
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
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100.
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980.
5047
0.53
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84M
OT
lON
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0.32
060.
4430
0.36
290.
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300.
4358
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0.55
850.
4576
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230.
4142
~ ~
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BL
ED
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naly
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lts
ofm
axim
umst
ory
shea
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r8
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ory
isol
ated
stru
ctur
ew
ith
R=8
8.04
8in
(Tb
=3
sec)
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u=
0.05
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ited
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pair
so
frea
lre
cord
sac
cord
ing
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eD
ynam
icA
naly
sis
Pro
cedu
reo
fSE
AO
C.W
eigh
tis
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lw
eigh
tofs
truc
ture
incl
udin
gba
se.
2nd
STO
RY
SHEA
R3r
dST
OR
YSH
EAR
4111
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RY
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ltST
OR
YSH
EAR
6111
STO
RY
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AR
711t
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RY
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AR
8t1t
STO
RY
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AR
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OT
AT
ION
WE
IGIf
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WE
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AO
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.
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CIT
AT
ION
2N1
STO
RY
DRI
FT'
(%)
3rd
STO
RY
DRI
FT'
(%)
41ft
STO
RY
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(%S
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'(%
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)
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ated
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8in
(Tb
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sec)
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CIT
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TW
E/G
lIT
WE
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lIT
WE
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TW
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MO
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0.11
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ION
ff3
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20.
132
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128
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TlO
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115
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104
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108
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00.
100
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2M
OT
ION
ffS
0.13
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150
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10.
148
0.10
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145
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135
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40.
131
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60.
118
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50.
075
MO
TIO
N#1
60.
140
0.15
30.
141
0.13
20.
129
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30.
102
0.10
20.
094
0.09
90.
077
0.11
50.
046
0.08
4
~
TA
BL
ED
.6A
naly
sis
resu
lts
ofm
axim
umin
ters
tory
drif
tfor
8•s
tory
isol
ated
stru
ctu
rew
ith
R=
88.0
48in
(Tb
=3
sec)
,fm
u=
0.10
,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
2NIS
TOR
YO
Rin
(%3r
dST
OR
YO
Rin
(%)
4'"
STO
RY
OR
in(%
S,,,
STO
RY
OR
in(%
)6t
"ST
OR
YO
RIF
T(%
)7,
,,ST
OR
YO
Rin
(%8t"
STO
RY
OR
IFT
(%)
HE
lGlf
fH
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lff
HE
lGlf
fH
ElG
lff
HE
lGlf
fH
ElG
lff
HE
lGlf
f
MO
TIO
NIII
0.26
380.
2754
0.27
110.
2845
0.35
390.
3608
0.31
660.
3433
0.29
770.
2857
0.38
170.
4636
0.23
710.
3060
MO
TIO
NliZ
0.24
050.
2867
0.23
380.
2877
0.28
900.
3682
0.26
110.
3691
0.23
260.
3123
0.31
210.
3953
0.20
380.
2661
MO
TIO
N11
30.
2517
0.29
600.
2569
0.28
550.
3326
0.39
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2991
0.41
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2784
0.39
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3550
0.58
610.
2046
0.35
04
MO
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40.
2726
0.35
560.
2428
0.37
250.
3361
0.47
450.
3071
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590.
2923
0.38
980.
4037
0.54
950.
3013
0.38
68M
OTI
ON
liS0.
2892
0.35
260.
2513
0.35
160.
3248
0.44
950.
3499
0.42
830.
3159
0.41
260.
4980
0.56
110.
3979
0.35
23M
OTI
ON
116
0.32
170.
3537
0.32
830.
3110
0.40
460.
3602
0.32
030.
3170
0.30
130.
3057
0.36
860.
5356
0.21
440.
4028
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).
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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.
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