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NATIONAL CENTER FOR EARTHQUAKEENGINEERING RESEARCH

State University of New York at Buffalo

/PB95-"--S21-7S--· 1111111111111111111111111111111

II

3D-BASIS-TABS: Version 2.0Computer Program for Nonlinear Dynamic Analysis

of Three Dimensional Base Isolated Structures

by

A.M. ReinhornDepartment of Civil Engineering

State University of New York at BuffaloBuffalo, New York 14260

~. NagarajaiahDepartment of Civil Engineering

University of Missouri. Columbia, Missouri 65221

M.C. Constantinou, P. Tsopelas and R. LiDepartment of Civil Engineering

State University of New York at BuffaloBuffalo, New York 14260

Technical Report NCEER-94-0qJ8 ~ ._ .. ~~EPFlODUCED BY 1

u;ii:;~~~MtO'CO",",."o : U.S. DEPARTMENT OF COMMERCe INOMMBITo,"M'C'! IMfolme'OM 50"11" : NATIONAL TECHN ICALSpriMgr,O". V,ri'M" 22101 i INFORMATION SERVICE I

June 22, 1994 . SPRINGFIELD, VA 22161 ., .-_.______ __ _ .J

This research was conducted at the State University of New York at Buffaloand the Univer~ity of Missouri at Columbia and was partially supported by

the National Science Foundation under Grant No. BCS 90-25010 andthe New York State Science and Technology Foundation under Grant No. NEC-91029.

DISCLAIMERThe program 3D-BASIS-TABS has been developed using computational modules in 30­BASIS-developed at the State University of New York at Buffalo, and ETABS-developed by theUniversity of California at Berkeley. The program 3D-BASIS-TABS has been developed, forresearch purposes, with financial support from National Center for Earthquake Engineer­ing Research, Center for Infrastructure Research and Development, University of Buffalo,and University of Missouri - Columbia. The following DISCLAIMER OF WARRANTY ap­plies to the use of computer program 3D-BASIS-TABS and the associated subroutines (in­cluding routines from 3D-BASIS and ETABS).

DISCLAIMER OF WARRANTYThe program 3D-BASIS-TABS, the associated subroutines, and the data files, are provided "ASIS" i.-l,Jithout warranty of any kind. The authors and the aforementioned institutions make no U!ar­ranties, express or implied, that the program is free of error or is consistent with any particularstandard of merchmltability, or that the program will meet your requirements for any particularappl1calion. The program should not be relied on for solving a problem whose incorrect solution couldrestllt in injury to a person or loss of property. If you do use the program in such a manner, itis at your own nsk. The authors and the aforementioned institutions disclaim all liability for director consequential damages resulting from your use of the program.

The ownership of the program remains with the developers. The program should not beresold or redistributed in whole or in part for direct profit. Neither the whole programnor routines of the program shall be incorporated in to the source code or the executablebinary code of other programs without prior written permission from the authors. Pro­grams containing 3D-BASIS-TABS routines must acknowledge acceptance of the aboveDISCLAIA1ER OF WARRANTY and of the fact that no business relationship is created be­tween the program's users and the authors of 3D-BASIS-TABS or the aforementioned in­stitutions. The names of the authors and the names of the aforementioned institutionsshould not be used to promote products derived from this program without specific prior\qitten permission from the authors.

NOTICEThis report was prepared by the State University of New York at Buffalo and the Universi­ty of Missouri at Columbia as a result of research sponsored by the National Center forEarthquake Engineering Research (NCEER) through grants from the National Science Foun­dation, the New York State Science and Technology Foundation, and other sponsors.Neither NCEER, associates of NCEER, its sponsors, the State University of New York atBuffalo and the University of Missouri at Columbia, nor any person acting on their behalf:

a. makes any warranty, express or implied, with respect to the use of any information,apparatus, method, or process disclosed in this report or that such use may not infringeupon privately owned rights; or

b. assumes any liabilities of whatsoever kind with respect to the use of, or the damageresulting from the use of, any information, apparatus, method or process disclosed inthi'> report.

Any opinions, findings, and conclusions or recommendations expressed in this publica­tion are those of the author(s) and do not necessarily reflect the views of the National ScienceFoundation, the New York State Science and Technology Foundation; or other sponsors.

3D-BASiS-TABS: Version 2.0 Computer Program for NonlinearDynamic Analysis of Three Dimensional Base Isolated Structures

502n-IO

- REPORT DOCUMENTATION IL REPORT NO.

PAGE ·1 NCEER-94-0018~. Title .nd Subtitle

7. Author(s) A.M. Reinhorn, S. Nagarajaiah,P. Tsopelas, R. Li

I~

M.C. Constantinou,

5. ReDOrt O.te

June 22, 1994

8. Performinc Ol'l(aniutlon RepL No;

9. Petfonnlnc Orpnlutlon H..... end Address

Dept. of Civil EngineeringState University of NY @ BuffaloBuffalo, N. Y. 14260

Dept. of Civil EngineeringUniversity of MissouriColumbia, Missouri 65221

10. ProlectIT.sllIWOftc Unit Ho.

11. C4nCnlctCC) Of' GtllnCCG) No.

(C) BCS 90-25010NEC-91029

12. SpOMOrinc Orpnlz:etloft H.....·.nd Address 13. Type of .Report & Period e-redNational Center for Earthquake Engineering ResearchState University of New York at Buffalo Technical reportRed llcket Quadrangle 1~.Buffalo, New York 14261

15. Supplernentllry Hotes This research was conducted at the State University of New York atBuffalo and the University of Missouri at Columbia and was partially supported by theNational Science Foundation under Grant No. BCS 90-25010 and the New York State Scienceand Technology Foundation under Grant No. NEC-91029.

16. AbstrKl (Umit: 200 words)

~ ?;This report describes the develop'ment of computer program 3D- BASI S- TABS Version 2.0.The new program is an enhanced version of 3D- BASI S- TABS. The report should beviewed as a continuation and addition to previous reports NCEER-93-0011 and NCEER-91­0005. The enhancements that have been made include: ~1) addition of new isolationelements; (2) models of nonlinear dampers and other hysteretic elements; (3) additionalverification; (4) addition of several new example problems;(5) new input/output format foreasier usage; and (6) updated user's manual. (§==

J;;'

17. Document ANlI~I. •• Oescriptors

b. ldentlf"...../Open~ed Terms

3D- BASI S- TABS. Non!Fnear dynamic analysis. Base isolated structures.Three dimensional analysis. Earthquake engineering. Computer program.

Co COSATI Field/Group

II. A...II.bllity St.tement

Release Unlimited

lS_ ANSI-ZJ9.18)

19. Security Class (This ReDOrt)

Unclassified20. Secu,ity Class (Thl.. Pagel

•Unclass.ifiecL~See In.ltv~lonl on RNetSe

,21. No.· of-Pages - .

16822. Price

OPTIONAL FORM 272 C4-771(Formerly NTIS-3S1

..

·../

111 1 -------

3D-BASIS-TABS: Version 2.0Computer Program for Nonlinear Dynamic

Analysis of Three Dimensional Base Isolated Structures

by

A.M. Reinhom', S. Nagarajaiah2, M.C. Constantinou', P. Tsopelas3

, and R. Li4

June 22, 1994 .

Technical Report NCEER.;94-0018

NCEER Task Number 93-5003

NSF Master Contract Number BCS 90-25010and

NYSSTF Grant Number NEC-91029

1 Professor, Department of Civil Engineering, State University ofNew York at Buffalo2 Assistant Professor, Department of Civil Engineering, University of Missouri at Columbia;

formerly Research Assistant Professor, Department of Civil Engineering, State University ofNew York at Buffalo

3 Research Associate, Department of Civil Engineering, State University ofNew York atBuffalo

4 Research Engineer, Department of Civil Engineering, State University ofNew York atBuffalo

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

PREFACE

The National Center for Earthquake Engineering Research (NCEER) was established to expand anddisseminate knowledge about earthquakes, improve earthquake-resistant design, and implementseismic hazard mitigation procedures to minimize loss of lives and property. The emphasis is onstructures in the eastern and central United States and lifelines throughout the country that are foundin zones oflow, moderate, and high seismicity.

NCEER's research and implementation plan in years six through ten (1991-1996) comprises fourinterlocked elements, as shown in the figure below. Element I, Basic Research, is carried out tosupport projects in the Applied Research area. Element II, Applied Research, is the major focus ofwork for years six through ten. Element III, Demonstration Projects, have been planned to supportApplied Research projects, and will be either case studies or regional studies. Element IV,Implementation, will result from activity in the four Applied Research projects, and from Demon­stration Projects.

ELEMENT IBASIC RESEARCH

• Seismic hazard andground motion

• Soils and geotechnicalengineering

• Structures and systems

• Risk and reliability

• Protective and intelligentsystems

ELEMENT IIAPPLIED RESEARCH

• The Building Project

• The NonstructuralComponents Project

• The Lifelines Project

The Highway Project

ELEMENT IIIDEMONSTRATION PROJECTS

Case Studies• Active and hybrid control• Hospital and data processing

facilities• Short and medium span bridges• Water supply systems in

Memphis and San FranciscoRegional Studies

• New York City• Mississippi Valley• San Francisco Bay Area

• Societal and economicstudies

ELEMENT IVIMPLEMENTATION

• ConferenceslWorkshops• EducationfTraining courses• Publications• Public Awareness

Research in the Building Project focuses on the evaluation and retrofit of buildings in regions ofmoderate seismicity. Emphasis is on lightly reinforced concrete buildings, steel semi-rigid frames,and masonry walls or infills. The research involves small- and medium-scale shake table tests andfull-scale component tests at several institutions. In a parallel effort, analytical models and computerprograms are being developed to aid in the prediction of the response of these buildings to varioustypes of ground motion.

111 I

!!I'e_~d;n~ page blank I---

Two ofthe short-tenn products of the Building Project will be a monograph on the evaluation oflightly reinforced concrete buildings and a state-of-the-art report on unreinforced masonry.

The protective and intelligent systems program constitutes one ofthe important areas ofresearchin the Building Project. Current tasks include the following:

1. Evaluate the perfonnance of full-scale active bracing and active mass dampers already inplace in tenns ofperfonnance, power requirements, maintenance, reliability and cost.

2. Compare passive and active control strategies in tenns of structural type, degree ofeffectiveness, cost and long-tenn reliability.

3. Perfonn fundamental studies ofhybrid control.4. Develop and test hybrid control systems.

The new computerprogram documented in this report, 3D-BASiS-TABS, Version 2. 0, is an enhancedversion of 3D-BASiS-TABS and 3D-BASiS which are special purpose programs developed byNCEERfor nonlinear dynamic analysis ofthree-dimensional base isolated structure (see reportsNCEER-93-0011 andNCEER-91-0005). One limitation associated with the use of3D-BASiS is thatthe superstructure memberforces cannot be computed - since no data regarding individual membersis specified by the user in this version. 3D-BASiS-TABS overcomes this limitation by computingsuperstructure memberforces, after the completion ofthe nonlinear time history analysis, followedby output ofpeak member forces, which can be usedfor the design ofmembers. This report brieflydescribes the development of3D-BASiS-TABS and the enhancements from Version 1.0 (NCEERReport 93-0011), which include addition ofnew isolation elementsfor modeling nonlinear dampers,special slidingfriction bearings, improvement ofother hysteretic elements, additional verification,several new example problems, new input/output format, and updated user's manual.

IV

ABSTRACf

The computer program 3D-BASIS-TABS is a special purpose program developed for

nonlinear dynamic analysis of three-dimensional base isolated structures. The program can

analyze base isolated structures with linear superstructure and nonlinear isolation system.

3D-BASIS-TABS has three options for modeling the linear superstructure (i) option 1 -­

three-dimensional shear building representati~n, in which case the global stiffness matrix of

the superstructure is assembled internally by the program using story stiffnesses, specified by

the user, followed by the dynamic analysis; (ii) option 2 -- full three-dimensional represen­

tation, in which case beam, column, shear wall and bracing elements of the superstructure

are modeled explicitly, followed by assembly of the global stiffness matrix, condensation,

dynamic analysis, and recovery of internal forces in structural elements by backsubstitution;

(iii) option 3 -- three-dimensional representation, in which case the dynamic characteristics

of the superstructure, such as frequencies and mode shapes, specified by the user, are used

to compute the superstructure stiffness matrix, followed by dynamic analysis. The isolation

system is modeled by representing the force-displacement relationship of each individual

isolator explicitly. The aforementioned approach for options 1 and 3 yields accurate global

response results; however, the disadvantage is that superstructure member forces cannot be

computed, since no data is available for individual members (this is the principle disadvantage

of the previous version 3D-BASIS). Option 2 in 3D-BASIS-TABS overcomes the afore­

mentioned shortcoming by computing superstructure member forces, after the completion of

the nonlinear time history analysis, followed by output of peak member forces, which can be

used for the design of members.

This report describes the development of computer program 3D-BASIS-TABS

Version 2.0. The new program is an enhanced version of30-BASIS-TABS. The report should

be viewed as a continuation and addition to previous reports NCEER-93-0011 and

NCEER-91-0005. The enhancements that have been made include (i) addition ofnew isolation

v

elements; (ii) models of nonlinear dampers and other hysteretic elements; (iii) additional

verification; (iv) addition of severalnew example problems; (v) new input/output format for

easier usage; (vi) updated user's manual.

VI

SEC. TITLE

TABLE OF CONTENTS

PAGE

1 INTRODUCTION I-I

2 3D-BASIS-TABS 2-1

2.1 Input Data 2-12.2 Superstructure Stiffness Assembly 2-12.3 Eigenvalue Analysis 2-42.4 Isolation System Modeling 2-4

2.4.12.4.22.4.32.4.3.12.4.3.2

2.4.4

2.4.5

tinear Elastic Element 2-4tinear Viscous Element. 2-5Model for Biaxial Isolation Elements 2-5

Biaxial Model for Sliding Bearings 2-6Biaxial Model for ElastomericBearings and Steel Dampers 2-7

Model for Uniaxial IsolationElements 2-7Nonlinear Damping Element.. 2-7

2.5 Element For Friction Pendulum (FPS) Bearing 2-92.6 New Biaxial Element For Sliding Bearings 2-112.7 Global System Assembly.............. 2-112.8 wading Conditions 2-142.9 Solution of Global System Response , 2-142.10 Backsubstitution 2-152.11 Output Data 2-152.12 Users - Supplied Routines in Program 3D-BASIS-TABS 2-15

2.12.1 Routine for Additional Axial wad Due to OverturningMoment Effects 2-15

2.12.2 Routine for Describing the Dependency of Parameter f m a x

on Bearing Pressure 2-17

Vll

SEC. TITLE PAGE

3 VERFICATION AND EXAMPLE PROBLEMS 3-1

3.1 Three Story Reinforced Concrete Buildingwith Sliding Isolation System 3-2

3.1.1 Verification of Member Force Computations 3-7

3.2 Single Story Structure with Lead-rubber Bearing Isolation System.......... 3-73.3 Six Story Reinforced Concrete Structure

with Lead-rubber Bearing Isolation System 3-113.4 Six Story Structure with Lead-Rubber Bearings and Supplemental

Nonlinear Damper.... 3-14

4 CONCLUDING REMARKS 4-1

5 REFERENCES 5-1

APPENDIX A - 3D-BASIS-TABS PROGRAM USER'S MANUAL A-I

APPENDIX B - EXAMPLE 1 , B-1

APPENDIX C - EXA.MPLE 2 C-1

APPENDIX D - EXAMPLE 3 : D-1

APPENDIX E - EXA.MPLE 4 E-1

APPENDIX F· EXAMPLE 5 F-1

APPENDIX G - EXAMPLE 6 G-1

Vlll

FIGURE TITLE

LIST OF FIGURES

PAGE

2.0 Force-Velocity Function for Nonlinear Viscous Damper 2-8

2.1 Displacement Coordinates of the Base Isolated Structure 2-9

2.2 Displacement Coordinates of the Base Isolated Structure 2-12

2.3 Definition of Overturning Moments OVMX and OVMY, and OVMY,and Additional Force FOVM , 2-16

2.4 Variation of Friction Parameter fmax with Pressure 2-18

3.1 Superstructure Member configuration and Isolation SystemConfiguration of the Three-Story Reinforced Concrete Sliding IsolatedBuilding. Note the Location of the Structure Axis at the Center ofMass of the Base and the Location of the Column Lines 1,4, 13 and 16(Refer to the Input File Given in Appendix B) 3-3

3.2 Cross Section of the Three-Story Reinforced Concrete Sliding IsolatedBuilding (Left Extreme Column Line is 16 and Right Extreme ColumnLine is 13). Note the Details of the Sliding Bearing and RecenteringSpring Shown in the Inset and Plan Location Shown in Fig.3.3 3-4

3.3 Plan of the Sliding Isolation System with Teflon - Steel Disc SlidingBearings and Recenter ing Springs 3-5

3.4 Cross Sectional Plan of the Three-Story Reinforced Concrete SlidingIsolated Building Between Levels 2 and 3. Note the Location of theColumn Lines and bay Numbers (Refer to the Input File GivenjnAppendix B) ~ 3-6

3.5 Comparison of Response Computed Using 3D-BASIS-TABSand ANSR of Single-Story Structure on Lead-rubber Isolation SystemSubjected to EI Control earthquake with Component SOOE in XDirection and Component S90W in Y direction (PGD =108.9 mm ........ 3-10

3.6 Six-Story Reinforced Concrete Base Isolated Structure: (a) Section;(b) Plan 3-12

3.7 Comparison of Response Computed Using 3D-BASIS-TABS andDRAIN-2D of the Six-Story Base Isolated Structure to SimulatedEarthquake.. 3-13

IX

FIGURE TITLE PAGE

3.8 Comparison of Response of Six-Story Base Isolated Structure toSimulated Earthquake with (a) Supplemental Linear Viscous Dampersand (b) Supplemental Nonlinear Viscous Damper 3-15

LIST OF TABLES

TABLE TITLE PAGE

3-1 Comparison of Column Forces 3-8

3-2 Comparison of Beam Moments 3-8

x

SECI10N 1

INTRODUcnON

A class of computer programs have been developed by the authors to provide com­

prehensive analysis capabilities for nonlinear dynamic analysis of three-dimensional base

isolated structures, which are, 3D-BASIS (Nagarajaiah et al. 1991a;1991b), 3D-BASIS-M

(Tsopelas et al. 1991;1994), and 3D-BASIS-TABS (Nagarajaiah et al. 1993c). The newest of

the class is computer program 3D-BASIS-TABS Version 2.0 described in this report.

Computer programs 3D-BASIS have b7en specifically developed for analysis of base

isolated structures with linear superstructure and nonlinear elastomeric and/or sliding iso­

lation systems. Salient features of 3D-BASIS programs which make them specially suitable

for analysis of base isolated structures with different isolation systems are as follows:

(1) Capability to analyze isolation systems that are a combination ofelastomeric and sliding

isolation systems;

(2) Unified model capable of representing the biaxial behavior of either elastomeric or

sliding bearings and other isolation devices;

(3) Capability to capture the highly nonlinear behavior of sliding isolation systems in plane

motion;

(4) Pseudo-force solution algorithm for accurate and efficient solution of stiff differential

equations that arise in sliding systems due to stick-slip behavior;

(5) Solution algorithm with the accuracy of predictor-corrector methods and efficiency

suitable for analyzing large base isolated structures;

(6) Capability to model multistory base isolated buildings and capture the lateral-torsional

behavior under bidirectional earthquake motion;

(7) Simplicity of input requirements and execution on both main and microcomputers.

I-I

With the above mentioned capabilities 3D-BASIS programs have become increasingly

popular amongstboth researchers and practising engineers leading to several applications (i)

preliminary studies in preparation for shake table tests at SUNY-Buffalo and UC-Berkeley;

(ii) evaluation of the important effects of nonlinear biaxial interaction between orthogonal

lateral forces in isolation bearings, on the response of base isolated-structures, by Nagarajaiah

et al. (1990) and by Mokha et al. (1993); (iii) simulation of shake table test results using

measured properties of the structure and the isolation system (Nagarajaiah et al. 1992); (iv)

study oflateral torsional response ofbase isolated structures (Nagarajaiah et al. 1993a;1993b);

(v) evaluation of SEAOC code provisions for base isolated structures (Constantinou et al.

1993, Theodossiou et al. 1991, Winters et al. 1993); (vi) analysis of new base isolated buildings

and existing buildings to be retrofitted using base isolation (Amin et al. 1993, Asher et al.

1993, Button et al. 1993, Cho et al. 1993); (vi) post-earthquake evaluation studies of existing

base isolated buildings in seismically active areas such as the region of San-Andreas fault

(Clark et al. 1993).

The computer program 3D-BASIS-TABS is a special purpose program developed for

nonlinear dynamic analysis of three-dimensional base isolated structures. The program can

analyze base isolated structures with linear superstructure and nonlinear isolation system.

3D-BASIS-TABS has three options for modeling the linear superstructure (i) option 1 -­

three-dimensional shear building representation, in which case the global stiffness matrix of

the superstructure is assembled internally by the program using story stiffnesses, specified by

the user, followed by the dynamic analysis; (ii) option 2 -- full three dimensional representation,

in which case beam, column, shear wall and bracing elements of the superstructure are

modeled explicitly, followed by assembly of the global stiffness matrix, condensation, dynamic

analysis, and recovery of internal forces in structural elements by backsubstitution; (iii) option

3 -- three-dimensional representation, in which case the dynamic charact~ristics of the

superstructure, such as frequencies and mode shapes, specified by the user, are used to

1-2

compute the superstructure stiffness matrix, followed by dynamic analysis. The isolation system

is modeled by representing the force-displacement relationship of each individual isolator

explicitly. The aforementioned approach for options 1 and 3 yields accurate global response

results; however, the disadvantage is that superstructure member forces cannot be computed,

since no data is available for individual members (this is the principal disadvantage of the

previous version 3D-BASIS). Option 2 in 3D-BASIS-TABS overcomes the aforementioned

shortcoming by computing superstructure member forces, after the completion of the non­

linear time history analysis, followed by output of peak member forces, which can be used for

the design of members.

This report describes the development of computer program 3D-BASIS-TABS

Version 2.0. The new program is an enhanced version of3D-BASIS-TABS. The enhancements

that have been made include (i) addition of new isolation elements and models for nonlinear

dampers and nonlinear bearings; (ii) additional verifications; (iii) several new example

problems; (iv) new input/output format for easier usage; (v) updated user's manual.

The input format for the superstructure in 3D-BASIS-TABS has been retained in the

same format as in ETABS to facilitate usage. It is to be noted that the aforementioned beam,

column, shear wall and bracing elements, substructure condensation, global assembly, and

backsubstitution procedures are adopted from the computer program ETABS (Wilson et al.

1975).

1-3

SECflON2

3D·BASIS·TABS

A complete description of computer program 3D-BASIS-TABS has been presented

by Nagarajaiah et al. (1993c); however, for the sake completeness a brief description of the

structural model and the solution algorithm is presented in this section. The major steps

involved in the assembly of the structural model and the solution algorithm are presented in

the Flowchart 2.1. The detailed description of each step is described in the following sub­

sections.

2.1 INPUT DATA

The input format has been retained in the same format as in ETABS to facilitate usage

(since many designers are familiar with the superstructure input requirements for ETABS).

The data in the form ofbeam, column, shearwall, and bracing member properties, conneetivity,

etc., need to be input. In addition the isolation system data in the form of isolator properties,

connectivity, etc., need to be input. The data needed for the dynamic analysis also has to be

input. The user's manual in APPENDIX A specifies the data input requirements.

2.2 SUPERSTRUCfURE STIFFNESS ASSEMBLY

The superstructure is assumed to be remain elastic at all times. Coupled lateral­

torsional response is accounted for by'maintaining three degrees of freedom per floor, i.e.,

two translational and one rotational degree of freedom attached to the center of mass. The

base and floors are assumed to be rigid diaphragms.

3D·BASIS·TABS is designed to include three options for modeling the superstructure;

option 1 for 3D-shear building, in which case story stiffnesses are to be input; option 2 for full

3D-building, in which case member properties for beam, column, etc., are to be input, for

detailed member by member representation of the superstructure; option 3 for full 3D­

building, in which case eigenvalues/eigenvectors are to be input. If option 1 or 3 is used,

member forces are not output, as no data for representing individual members is available.

2-1

INPUT DATA

STlFFNESS ASSEMBLYBEAM, COLUMN, WALL ELEMENT STIFFNESSES

CONDENSATION TO 3 DOF/FLOOR

EIGENVALUE ANALYSISFlXED BASE MODE SHAPES AND FREQUENCIES

GLOBAL SYSTEM ASSEMBLYGLOBAL SYSTEM· COMBINED SUPERSTRUCTURE AND ISOLATION

SYSTEM

SOLUTION FOR GLOBAL SYSTEM RESPONSESOLUTION USING PSEUDOFORCE SOLUTION ALGORITHM

BACKSUBSTlTUTlONBACKSUBST1TUT10N TO COMPUTE MEMBER FORCES

OUTPUTSUPERSTRUCTURE RESPONSE· MEMBER FORCES

ISOLATION SYSTEM RESPONSE

FLOW CHART OF MAJOR STEPS IN 3D·BASIS·TABS

2-2

In option 1, the superstructure of the three-dimensional shear building is represented

by a global stiffness matrix assembled using story stiffnesses specified by the user. The global

displacement coordinate system consists of three degrees of freedom at the center of mass of

the floors. It is assumed that the center of mass of all the floors lie on a common vertical axis;

floors and beams are rigid; walls and columns are inextensible.

In option 2, the procedure for assembly of the global stiffness matrix from ETABS

(Wilson et al. 1975) is adopted. The procedure involves (i) formulation of the lateral stiffness

matrix of each frame, which is treated as separate substructure with an associated frame

displacement coordinate system; (ii) assembly of the global stiffness matrix, using the frame

substructure stiffness transformed to the global displacement coordinate system, with the

assumption that all frame substructures are c,onnected at each floor level by a diaphragm

which is rigid in its own plane. Each joint in the structure is modeled with six degrees of

freedom. Within each frame joint three degrees offreedom (two translations and one rotation

in the floor plane) are transformed, using the rigid floor diaphragm assumption, to the frame

displacement coordinate system at that floor level. The remaining three frame joint degrees

of freedom are eliminated by static condensation. The condensed frame substructure stiffness

is transfonned to the global displacement coordinate system and added to the global structural

stiffness. The global displacement coordinate system consists of three degrees of freedom at

the center of mass of the floors. The position of the center of mass may vary from floor to

floor; hence, the mass matrix, required for dynamic analysis, will be a diagonal matrix --which

simplifies the eigenvalue' analysis. The global stiffness matrix of the superstructure, in the

fixed base condition, is used for eigenvalue analysis.

In option 3, the superstructure of the three-dimensional building is represented by a

global stiffness matrix, assembled using the dynamic characteristics, such as frequencies and

mode shapes specified by the user (minimum of three modes of vibration, with the global

displacement coordinate system of three degrees of freedom at the center of mass of the floors,

2-3

to be specified). Implicit in this approach is that the axial deformation of columns, bending

and shear deformation of column and beam members, and arbitrary location of the center of

mass, are accounted for by the condensed dynamic characteristics.

2.3 EIGENVALUE ANALYSIS

The eigenvalue analysis is performed to determine the eigenvalues and eigenvectors,

Le., frequencies and mode shapes in the fixed base condition using the global stiffness matrix.

The frequencies and mode shapes are used in the global system assembly of the superstructure

and the isolation syst~m. The frequencies and mode shapes obtained correspond to the global

coordinate system with three degrees of freedom at the center of mass of the floors.

2.4 ISOLATION SYSTEM MODELING

The isolation system is modeled with spatial distribution and explicit nonlinear

force-displacement characteristics of individual isolation devices. The isolation devices are

considered rigid in the vertical direction and individual devices are assumed to have negligible

resistance to torsion.

The following are the elements available for modeling the behavior of an isolation

system (i) linear elastic element --spring; (ii) linear viscous element --damper; (iii) hysteretic

element for elastomeric bearings and steel dampers; (iv) hysteretic element for sliding

bearings; (v) nonlinear damper element --a new element for modeling damping devices;

(vi friction pendulum (FPS) element; (vii) new biaxial element for sliding.

2.4.1 Linear Elastic Element

The linear elastic element can be used to approximately simulate the behavior of

elastomeric bearings along with the viscous element. All linear elastic devices of the isolation

system specified are combined, internally by the program, in global elements at the center of

mass ofthe base, having the combined properties ofall the elastic devices, with the translational

stiffnesses, Kx and Ky and the rotational stiffness, Kr.

2-4

(2.1 )

2.4.2 Linear Viscous Element

The linear viscous element can be used to simulate theviscous properties ofthe isolation

devices. All linear viscous devices are combined, internally by the program, in global viscous

elements at the center of mass of the base, having the combined properties of all the viscous

devices, with the translational damping coefficients ex and Cy and rotational damping coef­

ficient Cr.

2.4.3 Model for Biaxial Isolation Elementsi

iI

At a bearing undergoing plane motion with displacement components /U x and U y

and velocity components (j x and (j y in the x: and Y directions, lateral forces develop and

these forces exhibit biaxial interaction. In addition a torsional moment develops at the bearing.

The contribution of this torsional moment to the total torque exerted to the structure supported

by several bearings is insignificant.

The direction of the resultant force at the bearing opposes the direction of the motion

given by:

e =tan-I(~:)

The model presented herein accounts for the direction and magnitude of the resultant

hysteretic force.

The model for biaxial interaction is based on the following set of equations proposed

by Park, Wen and Ang (1986):

(2.2)

2-5

in which, Zx and Zy are hysteretic dimensionless quantities, Y is the yield displacement, A, Y

and f3 are dimensionless quantities that control the shape of the hysteresis loop. The values

of A = 1, Y = 0.9 and f3 = O. 1 are used in this report. When yielding commences, Eq. 2.2

has the following solution, provided that A / (f3 + y) = 1:

Z y = cos e, Z y = sin e (2.3)

Zx and Zy are bounded by values.±.l and account for the direction and biaxial interaction of

hysteretic forces. The interaction curve given by Eq. 2.2 is circular.

2.4.3.1 Biaxial Model for Sliding Bearings

For a sliding bearing, the mobilized forces are described by the equations (Constantinou

et al. 1990):

(2.4 )

in which, W is the vertical load carried by the bearing and I-l s is the coefficient of sliding

friction which depends on the value ofbearing pressure, anglee and the instantaneous velocity

of sliding (;:

0= (0 2 + ( 2 )1/2y Y (2.5)

Zx and Zy, given by Eq. 2.2, are bounded by the values .±.1, account for the conditions of

separation and reattachment (instead of a signum function) and also account for the direction

and biaxial interaction of frictional forces.

The coefficient of sliding friction is modeled by the following equation (Constantinou

et al. 1990):

I-l s = f max - (f max - f min) exp (- a IV I) (2.6)

in which, f max is the maximum value of the coefficient offriction and f min is the minimum

(at 0 - 0) value of the coefficient of friction. f max' f min and a may be, in general,

functions of bearing pressure and angle e.

2-6

2.4.3.2 Biaxial Model for Elastomeric Bearings and Steel Dampers

For a elastomeric bearing, the mobilized forces are described by the equations:

FYF =a-U +(I-a)FYZ

x y x x'

FYF =a-U +(l-a)FYZ

Y y Y Y(2.7)

in which, a is the postyielding to preyielding stiffness ratio, F Y is the yield force and Y is the

yield displacement. Zx and Zy, given by Eq. 2.2 account for the direction and biaxial interaction

of hysteretic forces.

2.4.4 Model for Uniaxial Isolation Elements

The biaxial interaction can be neglected' when the off-diagonal elements of the matrix

in Eq 2.2 are replaced by zeros. This results in a uniaxial model with two either frictional or

bilinear independent elements in the two orthogonal directions. Eq.2.2 collapses to the

uniaxial model governed by the following equation (Wen 1976):

Zy = AU-lzl'"'(ySgn(UZ)+ P-»U (2.8)

where 11 = 2 in the biaxial case and this parameter controls the transition from elastic range

to the post yielding range. The value ofthis parameter can be increased to achieve near-bilinear

behavior rather than smooth bilinear behavior. The interaction curve in the uniaxial case is

effectively square. In the case of uniaxial sliding element the velocity used for calculation of

the coefficient of friction from Eq. 2.6 is either Ux or Uy'

2.4.5 Nonlinear Damping Element

Many physical systems exhibit nonlinear damping mechanisms such as Coulomb

damping, viscous damping, orifice damping, and velocity raised to power p damping. Several

fluid viscous damping and friction damping devices have been proposed. The nonlinear

damping force of such devices can be described as being proportional to the the power p of

relative velocity across the damper:

(2.9)

2-7

F

-_.-------F ----------------------~----~~~~:~--~-~-~-----------------ma. ",,"" __,.-

rqel

u

Fig. 2.0 Force-Velocity Function for Nonlinear Viscous Damper

where F 01 is an offset constant for stage i, the damping coefficient C i and the exponent

Pi may have any positive value. The- signum function S 9 n ( U) accounts for the phase

between the damping force F d and the relative velocity· V, and n is the number of stages

(maximum 2). The applications of such generalized formulation of the damping force are

demonstrated as foHows:

Coulomb damping ( P 1 = 0)

F d = CiSgn(U)

Linear viscous damping (p 1 = I)

F d = CiIUISgn(U)

Nonlinear viscous damping (p i = 2)

F d = c I IUI 2 Sgn(V)

(2.10)

(2.11)

(2.12)

where C 1 for Pi = 0 is the magnitude of the Coulomb damping force, C i for Pi = I is

the coefficient of viscous damping, and C i for Pi = 2 is the coefficient of nonlinear

visc6us damping. Devices with values of exponent Pi in the range of 0.4 to 2 have been

produced.

2-8

2.5 ELEMENT FOR FRICTION PENDULUM (FPS) BEARING

The principles of operation of the FPS Bearing have been established by Zayas et al.

1987, Mokha et al. 1990 and Constantinou et al. 1993. These principles are, of course, valid

for all types of spherical sliding bearings. A cross-section view of an FPS bearing is shown in

Fig. 2.1. The bearing consists of a spherical sliding surface and an articulated slider which is

faced with a high pressure capacity bearing material. The bearing may be installed as shown

in Fig. 2.1 or upside-down with the spherical surface down rather than up. In both installation

methods the behavior is identical.

BEARING WATERIAL-~

SEAL

ARTICULATED SUDER

ENCLOSINCCYUNDER

SPHERICAL SURFACE

Fig. 2.1 FPS Bearing Section.

The force-displacement relation of an FPS bearing in any direction is given by:

F =W

Ru + (2.13)

in which R is the radius of curvature of the spherical sliding surface, W is the normal load and

~l s is the coefficient of the sliding friction. In cases in which the normal load may be assumed

to be constant and equal to the carried weight W j, modeling of an FPS bearings may be

accomplished by combining the linear elastic element of Section 2.4.1, using stiffness

K xi = K yl = I-v' II R, and the biaxial element for sliding bearing of Section 2.4.3, using

W = W /. To reduce computational effort, all the linear elastic elements may be combined in

a global element described by translational stiffnesses K x = K y = LWi I R (L W / =total

weight) and corresponding rotational stiffness K r and associated eccentricities e~ and e ~

(see Section 2.4.1 and Nagarajaiah et al. 1989 and 1991).

2-9

In general, the vertical load on an isolation bearing does not remain constant but rather

varies as a result of the vertical ground motion and the effect of overturning moment. For

vertically rigid structures, the normal load on an FPS bearing is:

+ +g

(2.14)

where Iv i is the weight (j v is the vertical ground acceleration (positive when the direction is

upwards) and N OM is the additional axial force due to the overturning moment effects (N OM

is positive when compressive - see requirements for subroutine in Section 2.10.1.)

The direct effects of vanations in the normal load on the behavior of the FPS bearing

are to instantaneously change the stiffness and friction force. Another indirect effect is to

change the coefficient of frietion which is pressure dependent. Modeling of the behavior of

FPS bearings to this detail is important in the accurate estimation of the forces in individual

bearings. However, use of W = h/ I rather than Eq. (2.14) results in nearly the same global

isolation system response and superstructure, response. This has been demonstrated by

comparison of analytical results to shake table results of a seven-story model in which the

axial forces on individual bearings varied from 0 to 2 W" Wi being the gravity load (AI­

Hussaini et al. 1994).

The forces in the FPS element are described by (Tsopelas et al. 1994):

r,,"

F -. U, + ~s • N Z.,'RW

F -. U + II • W ZY R y rs y (2.15)

whichZ, andZ yare described by Eq. 2.2 and W is described by Eq. 2.14. The current program

requires user-supplied routines to:

a) Calculate the additional force on individual bearings from overturning moments about

the two horizontal axes, and

b) Describe the variation of coefficient! max in Eq. 2.6 with bearing pressure.

Details of these routines are given in Section 2.12.

2-10

2.6 NEW BIAXIAL ELEMENT FOR SLIDING BEARINGS

The new biaxial element for flat sliding bearings is described by equations (2.4-2.6 and

2.2) with the exception that W is not constant but rather described by Eq. 2.14. The element

requires the user-supplied routines (Tsopelas et al. 1994) described in Sections 2.5 and 2.10.

It should be noted that when Uu is not given and when the user-supplied routine returns zero

for the additional axial load NOM (Eq. 2.14), the model collapses to the original constant

normal load (W = W J model.

2.7 GWBAL SYSTEM ASSEMBLY

The formulation for global system assembly of the combined superstructure and the

isolation has been presented in detail by Nagarajaiah et al. (1993c); hence, it is presented only

. briefly herein.

A typical base isolated multistory building and the displacement coordinates that will

be used in the formulation are shown in Fig. 2.2 ( U i , U b , U g may be in X or Y

direction). The superstructure is modeled as an elastic frame-wall structure with three degrees

of freedom per floor, as described earlier. The three degrees of freedom are attached to the

center of mass of each floor and base. The floors and the base are assumed to be infinitely

rigid inplane. The isolation system may consist ofelastomeric and/or sliding isolation bearings, .

linear springs, viscous elements, and nonlinear damping elements.

The equations of motion for the elastic superstructure are expressed in the following

form:

(2.16)

in which, n is three times the number of floors, M is the diagonal superstructure mass

matrix, C is the superstructure damping matrix, I< is the superstructure stiffness matrix

2-11

FIXEDREFERENCE

U.1

Jm

11

]

Fig. 2.2 Displacement Coordinates of the Base Isolated Structure

2-12

and R is the matrix of earthquake influence coefficients Le., the matrix of displacements

and rotation at the center of mass of the floors resulting from a unit translation in the X and

Y directions and unit rotation at the center of mass of the base (with respect to global structure

reference axis). Furthermore, ii, U and u represent the floor acceleration, velocity and dis­

placement vectors relative to the base, ii b is the vector of base acceleration relative to the

ground and ii 9 is the vector of ground acceleration.

The equations of motion for the base are as follows:

(2.17)

in which, M b is the diagonal mass matrix of the rigid base, C b is the resultant damping

matrix of viscous isolation elements, I< b is the resultant stiffness matrix of elastic isolation

elements and f is the vector containing the forces mobilized in the nonlinear elements of the

isolation system such as the presented elements for sliding, elastomeric bearings, etc.

Employing modal reduction:

Un = <t> nxm U :x/ (2.18)

in which, <P is the modal matrix normalized with respect to the mass matrix and u ,. is the

modal displacement vector relative to the base and m is the number of eigenvectors retained

in the analysis, and combining Eqs. 2.16 to 2.18 the following equation is derived:

(2.19)

in which, ~/ = the modal damping ratio, andw/ = the natural frequency, of the fixed base

structure in the mode i. In Eq. 2.19 matrices[2~/wi] and [w~] are diagonal.

2-13

Eq. 2.16 can be written as follows:

MO, + CO, + RU I + f , = P,

At timet + 6t

Written in incremental form

(2.20)

(2.21 )

(2.22)

in which,M , C, RandP represent the reduced mass, damping, stiffness and load matrices

(see Eq. 2.19). Furthermore, the state of motion of modal superstructure and base is repre­

sented by vectors fi ,, ii I and fi I (see Eq. 2.19).

2.8 WADING CONDITIONS

Vertical static loading conditions for representing dead loads, and earthquake loads

--representing seismic excitation, can be,specified. The vertical loading conditions can include

up to three independent vertical load distributions (1,11,111) and these distributions are

combmed to form load cases for the complete building. For earthquake loading conditions,

biclirectionallateral ground motions can be specified.

2.9 SOLUTION FOR GWBAL SYSTEM RESPONSE

The incremental nonlinear force vector (j, f 1+ 6.1 in Eq. 2.22 is unknown. This vector is

brought on to the right hand side of Eq. 2.22 and treated as a pseudo-force vector. The two

steps in the solution algorithm are (i) The solution ofequations ofmotion usingunconditionally

stable Newmark's constant-average-acceleration method (Newmark 1959); (ii) The solution

of differential equations governing the behavior of the nonlinear isolation elements using

unconditionally stable semi-implicit Runge-Kutta method (Rosenbrock 1964) suitable for

solution of stiff differential equations. Furthermore, a iterative procedure consisting of cor­

rective pseudo-forces is employedwithin each time step until equilibrium is achieved. Detailed

explanation of the solution algorithm can be found in Nagarajaiah et al. (1991a;1991b).

2-14

2.10 BACKSUBSTITUTION

The time history of member forces are computed by backsubstitution, after the non­

linear time history analysis is completed. The peak member forces are output to facilitate the

design of members. The backsubstitution procedure from ETABS is adopted.

2.11 OUTPUT DATA

The output data consists of three sets (i) input data for the structure and isolation

system; (ii) dynamic characteristics of the structure; (iii) peak response results in the fonn of

maximum response quantities; (iv) time history of response. The dynamic characteristics of

the structure output are periods and mode shapes. The peak response results of member

response and isolator response is output. A full range of options for output are available, the

details of which can be found in the user's manual in APPENDIX A

2.U USERS - SUPPLIED ROUTINES IN PROGRAM 3D-BASIS-TABS

2.12.1 Routine for Additional Axial Load Due to Overturning Moment Effects

The routine (a function) has the fonn:

FOVM(OVMX,OVMY,XP,YF,I)

in which I is the bearing number, XP and YF are arrays containing the bearing coordinated

(XP(I) =X coordinate ofbearing I etc.), and OVMX and OVMY are the overturning moments

about the X and Y axes, as illustrated in Fig. 2.3. Function FOVM is called by the main

program at all time steps: The function returns to the main program the additional axial load

FOVM on bearing I. FOVM is positive when-compressive.

2-15

z

CENTER OFMASS OF BASE

FOVM

XP(I) 1ISOLAnONBEARING................. " I

YP(I)

xOVMY

Fig. 2.3 Definition of Overturning Moments OVMX and OVMY,

and Additional Force FOVM.

It should be noted that we have assumed a unique relation between overturning

moments and additional axial load on bearings. The user is cautioned that this is a simplifi­

cation ofa complex phenomenon. However, it is a commonly used engineering approximation.

The report of AI Hussaini et al. 1994 provides valuable insight into the behavior of slender

isolated structures with FPS bearings which are subjected to strong overturning moments.

To exclude the effect of the overturning moment on the additional axial force, function FOVM

should be as follows:

FUNCTION FOVM(OVMX,OVMY,SP,YP,I)IMPUCITREAL '8COMMON/MAIN1/NB,NP,MNF,MNE,NFE,MXFDIMENSION XP(NP), YP(I)FOVM=O.DORETURNEND

This default version of function FOVM in 3DBASIS-TABS.

2-16

2.12.2 Routine for Describing the Dependency of Parameter f max on Bearing Pressure

Constantinou et al. 1990 and 1993 described the dependency on bearing pressure of

the parameters in the model offriction in Eq. 2.6. Specifically, the coefficient ofsliding friction

is given by:

Il s = fmax~(fmax- fmln)eXp(-allil) (2.23)

where a is nearly independent of pressure, whereas f min is dependent on pressure for

unfilled and glass-filled PTFE but nearly independent of pressure for the PTFE-composites

used in the FPS bearings. Parameter f max is generally dependent on bearing pressure.

Since parameter f max describes the maximum friction force that is transmitted through the

bearing, its dependency on pressure is explicitly modeled in this program. However, the much

less significant dependency on pressure of parameters a and f min is neglected.

The user-supplied routine (function) has the form:

FFMAX(FRMAX,FRMIN,FNOR,I)

in which I is the bearing number, FNOR is the normal load on bearing I, which includes the

gravity, vertical ground motion and overturning moment effects, normalized by the weight

Wi on the bearing. Furthermore, FRMAX and FRMIN are, respectively, the supplied,

through the INPUT, parameters f ma xO and f minO under almost zero static pressure of

bearing I. Function FFMAX returns the value of f m a x at the bearing pressure resulting

from the instantaneous normal load. Note that parameter f min is assumed independent of

pressure, that is f minO = f min'

For example, consider the case iIi which the dependency on pressure of parameter

f m a x is neglected.

Function FFMAX should be:

FUNCTION FFMAX(FRMAX,FRMIN,FNOR,I)IMPliCIT REAL *8COMMON/MAIN1/NB,NP,MNF,MNE,NFE,MXFFFMAX=FRMAXRETURNEND

2-17

This is the default version of function FFMAX.

Consider now the case of pressure dependent parameter f max' Figure 2.4 shows the

assumed dependency on pressure of parameter f ma x' It is typical of the behavior of sliding

bearings (Soong and Constantinou 1994). An accurate representation of the variation of

parameter f Ill'" with pressure can be accounted for by using the following expression:

f In a" = f m a yO - (f ma xO - f ma x p ) tan h ( E P) ( 2 .24 )

where P is the instantaneous bearing pressure, ! maxp is the maximum coefficient of

friction at very high pressures, ! ma ,0 is the value of the coefficient at zero pressure, E is

a constant that controls the transition of f ma:l' between very low and very high pressure.

fmax

(fmaxp

PRESSURE

Fig. 2.4 Variation of Friction Parameter! Ifl~ ~ with Pressure

2-18

As an example, Constantinou et a1. 1993 gave the following values for the parameters

of a bearing at pressure of 17.2 MPa: f max :;= O. 12, f maxp = 0.05, E = 0.0 12 (P the

bearing pressure is in the units of MPa). For this case function FFMAX should be of the

fonn:

FUNCTION FFMAX(FRMAX,FRMIN,FNOR,I)IMPLICIT REAL *8COMMON/MAIN1/NB,NP,MNF,MNE,NFE,MXFDIMENSION P(SOO)DATA/P(J) = 17.2,J = 1,.. /

etc. etc.

PRES=FNOR*P(I)FFMAX =FRMAX-O.07*DTANH(O.012*PRES)END

Note that P(J) contains the bearing pressure under static conditions of bearing J.

Quantity PRES is the instantaneous bearing pressure in units of MN/m2 or MPa.

2-19

SECTION 3

VERIFICATION AND EXAMPLE PROBLEMS

3D-BASIS-TABS has been verified by the authors (Nagarajaiah et a!. 1993c). This

section describes the previous verification briefly, for completeness sake, and also describes

additional verification of 3D-BASIS-TABS.

The verification is performed using three example problems. The first example problem

consists of a three story reinforced concrete building with sliding isolation system. The second

example considered is a single story structure on lead-rubber isolation system. The third

example problem -consists of a six story reinforced concrete building with lead-rubber bearing

isolation system.

The verification using the three story reinforced concrete building with sliding isolation

system is accomplished by comparing the dynamic analysis results of program 3D-BASIS­

TABS, in the form of peak member forces at a chosen instant oftime during the time history,

with the pseudo-static analysis results offinite element program STAAD; thus, validating the

member force computations in the program 3D-BASIS-TABS. The pseudo-static analysis,

performed using commercially available finite element program STAAD, consists of appli­

cation of lateral forces or inertial forces, at the same instant of time as chosen in 3D­

BASIS-TABS time history analysis, at the center of mass of the three floors. The lateral forces

or inertial forces are extracted from the dynamic analysis using 3D-BASIS-TABS.

The verfication using the single story structure with lead-rubber bearing isolation system

is accomplished by comparing the results at the center of mass from program 3D-BASIS-TABS

with the results of program-ANSR (Mondkar and Powell 1975); thus, validating the global

results.

The verification using the six story reinforced concrete buildingwith lead-rubber bearing

isolation system is accomplished by comparing the results of3D-BASIS-TABS with the results

of a two dimensional analysis performed using DRAIN-2D (Kannan and Powell 1975). Also,

3-1

results, at the center of mass, from program 3D-BASIS-TABS --modeling the superstructure

explicitly element-by-element-- are compared with the results of program 3D-BASIS (Na­

garajaiah et a1. 1991b) using the dynamic characteristics of the superstructure, i.e., eigenvalues

and eigenvectors; thus, validating the global results.

3.1 THREE STORY REINFORCED CONCRETE BUILDING

WITH SLIDING ISOLATION SYSTEM

The three story reinforced concrete building considered has three bays in each direction

and has a square plan with dimensions 12 x 12 meters as shown in Fig. 3.1. The dimensions

of the various members shown in Fig. 3.1 are (i) beams 300 x 400 mm; (ii) interior columns

300 x 400 mm; (iii) exterior columns 300 x 300 mm; (iv) RIC bracing members 300 x 300 mm;

(v) shear wall or panel of 100 mm thickness. The floor slab is 150 mm thick. The floor masses

are (i) translational mass of 119.4 kN-sec2/m; and (ii) mass moment of inertia of 2985.6

kN-m-s2. The modulus of elasticity of the concrete is assumed to be Ee = 29862560 kN/m2.

The damping ratio in the superstructure is assumed to be 5% of critical.

The building is base isolated using a sli~ing isolation system as shown in Fig. 3.2 and

Fig. 3.3. The sliding isolation system consists of 16 sliding bearings placed concentrically under

each column and 4 recentering springs placed at the four corners of the building as shown in

Fig. 3.3. Design of the isolation system is based on appropriate code provisions. The sliding

isolation bearings are made of unfilled Teflon and polished stainless steel plates. The sliding

bearings have a coefficient offrictionf max = O. 1 andf min = 0.07. The recentering helical

springs are designed to provide an isolation period Tb = 3 sec. The sliding bearings and helical

springs are shown in Fig. 3.2 in greater detail (see the enlarged detail Fig. 3.2).

3D-BASIS-TABS is used to analyze the base isolated building excited by El Centro NS

earthquake. The input and output files for this building are given in APPENDIX B.

3-2

REC::NIE~ING

SPRING

SLAB

\~__ Y SLIDING BEARING

X . CENTER OF' MASS OF" BASE<STRUCTURE AND FRAME 1 REFE~ENCE AXES)

BRACe: PANEL" ,~~~~~~~-+__~....~'-__....$4 -LEvEL 3

® ID NUMBER OF" COLUMN LINE

FIG. 3.1. Superstructure Member configuration and Isolation System Configuration of the Three­Story Reinforced Concrete Sliding Isolated Building. Note the Location of the Structure A..x.is atthe Center of Mass of the Base and the Location of the Co Iurnn Lines 1, 4, 13 and 16 (Refer to

the Input File Given in Appendix B)

3-3

3.5m

3.5m

RECENTERING SPRI

TEFLON-STEEL DISC SLIDING BEARING

fIG. 3.2. Cross Section of the Three-Story Reinforced Concrete Sliding Isolated Building (LeftExtreme Column Line is 16 and Right Exlreme Column Line is 13). Note the Details of theSliding Bearing and Recentering Spring Shown in the Inset and Plan Location Shown in rIO 3.3

3-4

TEFLON-STEEL DISC SLIDING BEARING, \

RECENTERING SPRING'" \e-- ---e e-- " ~

"-jI· I I

I I -Je-- ---e e--CENTER OF MASS OF BASE

I (GLO~TRlcTURE I, REFERENCE AXIS) ,

e- • e-- II I I

I. I I .1e-- ---e e-- ---e

tE

-.;:T

~tE

-.;:T

t

tE~

x

- 4m-- 4m-'- 4m­I I I I

FIG. 3.3. Plan of the Sliding Isolation System with Teflon - Steel Disc Sliding Bearings andRecentering Springs

3-5

Y

xI,!I

E~

tE~

I,!I

E~

wU<l::~

CD

®

® ©® 7 B= Q11. @ 15.

BRACE nCENTER OF MASS

@ ~ ~

~ 6 @:,10oll @14J.BRACE

1

2

4

3

1- 4m ~I- 4m -1- 4m -I

BAY NUMBER

10 NUMBER OF COLUMN LINEFIG. 3.4. Cross Sectional Plan of the Three-Story Reinforced Concrete Sliding Isolated BuildingBetv.'een Levels 2 and 3. Note the Location of the Column Lines and Bay Nwnbers (Refer to theInput Fil~ Given in Appendix B)

3-6

3.1.1 Verification of Member Force Computations

The local response results, in the form of peak member forces at a chosen instant of

time (t = 3.05 sec) during the time history analysis, are verified by comparing the results of

3D-BASIS-TABS with the results of a pseudo-static analysis -- performed using commercially

available finite element program STAAD. The pseudo-static analysis using STAAD consists

of-application of lateral forces or inertial forces, at the same instant of time as chosen in

3D-BASIS-TABS time history analysis, at the center of mass of the three floors. The lateral

forces or inertial forces are extracted from the dynamic analysis using 3D-BASIS-TABS. A

comparison between the member forces computed in 3D-BASIS-TABS and STAAD is shown

in Table 3-1 and 3-2. Table 3-1 shows the column moments and forces. Table 3-2 shows the

beam moments. It is evident from the comparison in Tables 3-1 and 3-2 that member force

computation in 3D-BASIS-TABS is accurate.

3.2 SINGLE STORY STRUCTURE WITH LEAD-RUBBER BEARING ISOLATION

SYSTEM

The single story shear building has equal base dimensions L=480 inch (12192 mm); it

is supported on four corner columns; it has a height of 180 inch (4572 mm) and a total weight

of 480 Kips (2135 kN). Equal floor and base weight is considered. The center of mass of both

the floor and the base are assumed to be on the same vertical axis. The vertical axis of centers

of mass is offset from the geometric center of the building for inducing a mass eccentricity of

0.083L in the Y direction. Eccentricities ex = ey = O.lL, of the center of resistance of the

superstructure from the center of mass, are considered. The uncoupled translational period

of the superstructure Ts is 0.3 sec in both X and Y directions. The uncoupled torsional period

of the superstructure T 8 is equal to 0.58 Ts. Viscous damping of 2 percent of critical is used

for the superstructure in all the three modes.

An isolation system consisting of four lead-rubber bearings placed below the columns

is considered. The design of the isolation system is based on a ground motion with

3-7

vJ , oc

Tab

le3-

1C

om

par

iso

no

fC

olu

mn

For

ces

Flo

orM

embe

r3D

-BA

SIS

-TA

OS

ST

AD

DII

IID

MO

M-X

MO

M-Y

SH

-XS

H-Y

AX

IAL

MO

M-X

MO

M-Y

SH

-XS

H-Y

AX

IAL

(kN

-m)

(kN

-m)

(kN

)(k

N)

(kN

)(k

N-m

)(k

N-m

)(k

N)

(kN

)(k

N)

CO

L.

III

9.75

0.06

7.43

0.03

23.4

39.

730.

067.

420.

0323

.41

(TO

P)

lsI

CO

L.

#113

.29

0.03

7.43

0.03

23.4

313

.28

0.03

7.42

0.03

23.4

1(B

OT

.)

CO

L.

III

9.63

0.11

6.19

0.07

14.3

39.

620.

106.

180.

0614

.30

(TO

P)

2nd

CO

L.

#19.

610.

106.

190.

0714

.33

9.61

0.09

6.18

0.06

14.3

0(B

OT

.)

CO

L.

#110

.26

0.21

6.15

0.12

5.Q

610

.24

0.20

6.14

0.11

5.03

(TO

P)

3rd

CO

L.

III

8.82

0.16

6.15

0.12

5.06

8.81

0.15

6.14

0.11

5.03

(BO

T.)

Tab

le3-

2C

om

par

iso

no

fB

eam

Mom

ents

Flo

orM

embe

rID

3D-B

AS

IS-T

AB

SS

TA

DD

III

I-M

OM

J-M

OM

I-M

OM

J-M

OM

(kN

-m)

(kN

-m)

(kN

-m)

(kN

-m)

lsi

BE

AM

AT

BA

Y11

418

.95

15.6

918

.94

15.6

8

2n

dB

EA

MA

TB

AY

114

18.5

015

.58

18.4

815

.56

3rd

BE

AM

AT

BA

Y11

410

.29

8.26

10.2

88.

25

the characteristics of the ATC OAg S2 spectrum and on the procedure developed by Dynamic

Isolation Systems (1983). A design live load of 200 Kips (889.6 kN) is considered in addition

to the total dead load of 480 Kips (2135 kN). The bearings chosen are of 13 inch (330.2 mm)

diameter and with 18 layers of natural rubber (hardness 50) of 0.375 inch (9.53 mm) thickness.

Lead plugs of 2.5 inch (63.5 mm) diameter are present in all four bearings. The average

properties of bearings determined are the initial elastic stiffness of 17.8 K/in (3.12 kN jmm),

the postyielding stiffness of 2.74 K/in (0048 kN/mm) and the yield strength FY of 6.6 Kip (29.36

kN). The total yield strength of the isolation system is 5.5% the structural weight. The rigid

body mode period is:

(W ) 1/2

T b =2n Kb9 (3. I )

in which, W is the total weight and Kb is the total post yielding stiffness of four Lead-rubber

bearings. Tb in the present case is 2.12 sec.

The single story base isolated building excited by 1940 El Centro is analyzed using

3D-BASIS-TABS. The SOOE component is input in the X direction and S90W is input in the

Y direction. The input and output files for the single story base isolated building are given in

APPENDIX C.

Fig. 3.5 shows the bearing displacement response at corner bearing No.1 (see the

input/output files in APPENDIX C for details). The peak ground displacement (PGD) of

4.29 inch (108.96 mm) is used for normalizing the displacement response. The same base

isolated building is analyzed using ANSR (Mondkar and Powell 1975). The comparison

between the response computed using 3D-BASIS-TABS and ANSR --with completely dif­

ferent modeling and solution procedures-- is shown in Fig. 3.5, from which, it is evident that

the results of 3D-BASIS-TABS are accurate. Also, the results of 3D-BASIS-TABS (see

APPENDIX C) and the results of 3D-BASIS (refer to section 7.3 of NCEER 91-0005;

Nagarajaiah et al. 1991b) are identical.

3-9

-- 3D-BASJS-TABS ----- ANSR

, 5

, 5

, 2

12

9

(SEC)6

TIME

6 9

TIME (SEC):3o

z~ 0.2u~ 0.0o)- -0.2

-0.4

-0.6

-0.8 ~-1.a -+1-.,...----r--...,_---r-"""T"""'-,....----r---r---r--r- ~_r_-r___r___f

o

z§ 0.2u~ 0.0ox -0.2

-0.4

-0.6

-O.B

-1.0 -4--..,-----r---,-- -~--r------r-...,___r-"""T"""'-,....___r_-~__:_____.,

0.4

1.0

0.8

0.6

0.4

oc....?0..."-...I­Zw2wu:50­enoc...? 1.0 ~---------------------,ZCC 0.84:W 0.6rIl

FIG. 3.5. Comparison of Response Computed Using 3D-BASIS-TABS and ANSR of Single­Story Structure on Lead-rubber Isolation System Subjected to E1 Centro Earthquake withComponent SOOE in X Direction and Component S90W in Y Direction (POD = 108.9 mm)

3-10

3.3 SIX STORY REINFORCED CONCRETE STRUCTURE WITH LEAD-RUBBER

BEARING ISOLATION SYSTEM

The analysis of a six story reinforced concrete base isolated structure with the lead­

rubber bearing isolation system is considered. The plan and section of the building are shown

in Fig. 3.6. The reinforced concrete superstructure is designed to resist lateral loads equivalent

to a seismic base shear coefficient of 0.15 g using shear walls. Damping of 5% of critical is

used for the superstructure in all the modes. 3D-BASIS-TABS is used to model the super­

structure (i) using option 2 -- with member-by-member modeling; (ii) using option 3 -- with

eigenvalues and eigenvectors.

The lead-rubber bearing isolation system designed based on the procedure developed

by Dynamic Isolation Systems (1983) consists of 22 lead-rubber bearings (see Fig. 3.6(b)). A

site specific response spectrum is used in the design of the structure/isolation system. The

average isolation yield level Qd is set to 0.045W, where W is the total weight of the structure

= 25143 kN. The rigid body isolation period Tb (see Eq. 3.1) is 1.65 sec. The dynamic response

is computed for a artificial accelerogram of 20 sec duration. The artificial accelerogram is

realized from the site specific response spectrum. For more details about the isolation system

parameters and the artificial accelerogram refer to Nagarajaiah et al. (1991b). The 3D­

BASIS-TABS input and output files, for option 2 are given in APPENDIX D, and for option

3 in APPENDIX E.

To verify the response the structural stiffness properties are condensed to six degrees

of freedom (one per floor in the Y direction) and used for a two dimensional analysis using

DRAlN-2D (Kannan and Powell 1975). The properties of the isolation system are lumped

with F Y= 1328 kN, Y = 0.00525 meters, a = 0.148, and Q d = 0.045W in a single isolation

element, resulting in Tb =1.6 sec. The artificial accelerogram used in 3D-BASIS-TABS analysis

is used as the excitation. The base displacement response (Y direction) is shown in Fig. 3.7.

The comparison between the results of 3D-BASIS-TABS and DRAIN-2D, shown in Fig. 3.7.

3-11

ROOF

(a) SECTION

7m

2m

8m

am

2m

2m

t. 6.65 m + 6.85 m-+

~D c:JrO Tm,

0 c::J T3.

I I I 3rd Fh I

- ~3.

D I 2nd FL.I- -

3.

- ~

D c:J 3.

LEAD-R;:LD c:J-, 3.

-LBEARINGS --

• 815-9-2.75LEADRUBBER • 818-9-4.0BEARING

• 821-9-3.59.15 m

3.6 ID...,;.,3.45 m

! -- I -- , ! CEJnR::-' -1----I-l---...i l-°~¥.~1~~_ ~_ :~:__m".1

II I I I I I

I 'I ~ ~m ~

6.85 m i j f~' ~ I' i I

J

3.6 m .I 3.6 m .:. 3.6 m .1

I

I6.65 m

(b) PLAJ.'i

FIG. 3.6. Six-Story Reinforced Concrete Base Isolated Structure: (a) Section; (b) Plan

3-12

100-E 80E-w 60

CI'l< 40I-ID

Zww_20::: .....wI-

Uu..0::So

c-CI'l~CI'l -200<l.I.J:::

-40V1u..<00

Ct: -60LUI-z -80LUu

-'00a

-3D-BASIS-TABS ---DRAIN-2D

LEAD-RUBBER BEARINGISOLA.TION SYSTEM

20

FIG. 3.7. Comparison of Response Computed Using 3D-BASIS-TABS and DRAIN-2D of theSix-Story Base Isolated Structure to Simulated Earthquake

3-13

indicates good agreement. Also, the results of 3D-BASIS-TABS (see APPENDIX D and E)

and the results of 3D-BASIS (refer to section 8 and APPENDIX B of NCEER 91-0005;

Nagarajaiah et al. 1991b) are identical.

3.4 SIX STORY STRUCTURE WITH LEAD-RUBBER BEARINGS AND

SUPPLEMENTAL NONLINEAR DAMPERS

The analysis of the six-stories base isolated structure presented previously in Section 3.3

is considered again with addition of nonlinear viscous dampers at the base to limit the max­

imum base movement. The plan of the building and its characteristics are described in

Section 3.3.

The base isolation is complemented in this example by the addition of four pairs of

dampers placed at the bearings S18-9-4.0 positions along the north and south lines at the

intersection with the first interior column lines (see Fig. 3.6). Each pair of dampers has

rectangularly arranged dampers co-linear with the column lines. Each nonlinear damper has

a linear range at low velocities (Col = 877kN-sec/m, p = 1, F01-= 70kN), a nonlinear range

starting at 10 em/sec (Co2 = 182.6kN-sec/m, p = 0.5, F02 = 100kN) and is limited to deliver a

maximum force of 200 kN for velocities larger than 35 cm/sec. The design was obtained

aiming to add approximately 10% of critical damping to the damping delivered by the lead

rubber bearings.

The structure was reanalyzed with the same artificial accelerogram obtained from the

site specific response spectrum. The 3D-BASIS-TABS input-output files are presented in

Appendix G.

The response of the isolation base without supplemental damping and with the additional

dampers, with linear characteristics only, is presented in Fig. 3.8(a). The response of the same

structure with the supplemental nonlinear dampers is shown in Fig. 3.8(b). The effect of the

nonlinear dampers is particularly strong in reducing the peak base movement from 8 to 5.2

em. Although the forces in the superstructure may increase somewhat, this increase is not

substaT'tial to require a change in the design.

3-14

- LEAD RUBBER & LINEAR VISCOUS ELEMENT....... LEAD RUBBER ELEMENT ONLY

0.10

.- 0.08Ew 0.06(J)«CD 0.04u.0~ 0.02()

u. 0.000f-

-0.02zw~w -0.04()

:5 -0.060-(J)

0 -0.08

-0.100 5 10

TIME (sees)15 20

2015

- LEAD BUBBER & NONLINEAR VISCOUS ELEMENT......., LEAD RUBBER ELEMENT ONLY

5

0.10

.- 0.08E-w 0.06(J)«CD 0.04LL.0~ 0.02()

u. 0.000f-

-0.02zw~w -0.04()

:5 -0.060-C/)

Cl -0.08

-0.100 10

TIME (sees)

Fig. 3.8 Comparison of Response of Six-Story Base Isolated Structure To Simulated

Earthquake with (a) Supplemental Linear

Viscous Dampers and (b) Supplemental Nonlinear Damper

3-15

SECTION 4

CONCLUDING REMARKS

3D-BASIS-TABS Version 2.0 has been described in this report. 3D-BASIS-TABS

integrates the special features of ETABS, such as the efficient modeling approach for the

3D-superstructure, and the special features of 3D-BASIS, such as the modeling approach for

sliding isolation systems in plane motion and accurate solution algorithm; this enhanced

program will help engineers to analyze and design base isolated structures with accuracy and

efficiency.

Addition of new isolation elements for modeling nonlinear dampers has been

descrihed. Addition of frictional bearings (FPS) with variable pressure resu Iting from vertical

earthquake components and from overturning has been described. The verification of 3D­

BASIS-TABS has also been described by means of several useful examples (the input and

output files of which are included in the APPENDICES). Microcomputer PC version, and

main frame VAX and SUN versions oDD-BASIS-TABS have been developed. The versatility

of 3D-BASTS-TABS stems from the fact that it can analyze base isolated structures, like sliding

isolated structures, with great accuracy and yet complete the analysis in a reasonable CPU

time on a microcomputer.

Extensions to 3D-BASTS-TABS to incorporate hybrid control capabilities are envis­

aged. Hyhrid control involves augmentation of the passive isolation system with active

hydraulic devices (Reinhorn et a1. 1993, Yang et a1. 1992, Feng et a1. 1993, Nagarajaiah et al.

1993d;1993e, Riley et a1. 1993, Subramaniam et al. 1993).

4-1

SECTION 5

REFERENCES

Al-Hussaini, T., Zayas, V. and Constantinou, M.C. (1994). "Seismic isolation of multi-story framestructures using spherical sliding isolation systems." Report No. NCEER-94-0007, Nat. Ctr. forEarthquake Engrg. Res., State University of New York, Buffalo, N.Y.

Aiken, I. D., Clark, P. W., Kelly, 1. M., Kikuchi, M., Saruta, M. and Tamura, K. (1993). "Design- and ultimate-level earthquake tests of a 1/2.5-scale base-isolated reinforced concrete building"Proceedings A TC-17-1 Seminar on Seismic Isolation, Passive Energy Dissipation, and ActiveControl, Vol. 1, 281-292.

Arnin, N., Mokha, A and Fatehi, H. (1993). "Seismic isolation retrofit of the U.S. court of appealsbuilding." Proceedings A TC-17-1 Seminar on Seismic Isolation, Passive Energy Dissipation, andActive Control, Vol. 1, 185-196.

Asher, 1. W. and Hussain, S. M. (1993). "Structural engineering perspective on the design andconstruction of base isolated buildings." Proceedings ATC-17-1 Seminar on Seismic Isolation,Passive Energy Dissipation, and Active Control, Vol. 1, 95-104.

Buckle, I. G. and Mayes, R. L. (1990). "Seismic isolation: history, application and performance ­A world overview." Earthquake Spectra, 6(2), 161-202.

Buckle, I. G. and Liu, H. (1993)"Stability of elastomeric seismic isolation systems," ProceedingsATC-l 7-1 Seminar on Seismic Isolation, Passive Energy Dissipation, and Active Control, Vol. 1,293-306.

Buckle, I. G. (1993). "Future Directions in Seismic Isolation, Passive Energy Dissipation andActive Control." Proceedings ATC-J7- J Seminar on Seismic Isolation, Passive EnergyDissipation, and Active Control, Vol. 2, 825-830.

Button, M. R. (1993). "Story shear distributions in seismically isolated structures." ProceedingsA TC-17-J Seminar on Seismic Isolation, Passive Energy Dissipation, and Active Control, Vol. I,307-318.

Cho, D. M. and Retamal, E. (1993). "The Los Angeles County Emergency Operations Center onhigh damping rubber bearings to withstand an earthquake bigger than the big one." ProceedingsA TC-J 7-J Seminar on Seismic Isolation, Passive Energy Dissipation, and Active Control, Vol. 1,209-220.

Clark, P. W., Whittaker, A. S., Aiken, I. D. and Egan, 1. A. (1993). "Performance considerationsfor isolation systems in regions of high seismicity." Proceedings A TC-17-1 Seminar on SeismicIsolation, Passive Energy Dissipation, and Active Control, Vol. 1,29-40.

5-1

Constantinou, M. C., Mokha, A. and Reinhom, A. M. (1990). "Teflon bearings in base isolation II:Modeling." J Strnct. Engrg. ASCE, 116(2),445-474.

Constantinou, M. c., Winters, C. W. and Theodossiou, D. (1993). "Evaluation of SEAOC &UBC analysis procedures, Part 2: Flexible superstructure." Proc. ATC-J 7-J Seminar on SeismicIsolation, Passive Energy Dissipation, and Active Control, Vol. 1, 161-172.

Dynamic Isolation Systems, Inc. (1983). Seismic Base Isolation Using Lead-robber Bearings,Berkeley, Calif.

Feng, M. Q., Shinozuka, M. and Fujii, S. (1993). "A friction controllable sliding isolation system."J Engrg. Mech.., ASCE, 119(6), 569-578.

Kannan, A. M. and Powell, G. H. (1975). DRAIN-2D: a general purpose computer program fordynamic analysis of inelastic plane structures with users guide." Report No. UCB/EERC-73/22,Earthquake Engrg. Res. Ctr., University of California, Berkeley, Calif.

Kelly, 1. M. (1993) "State-of-the-art and state-of-the-practice in base isolation." ProceedingsA TC-J 7-1 Seminar on Seismic Isolation, Passive Energy Dissipation, and Active Control, Vol. 1,9-28.

Mokha, A., Constantinou, M. C. and Reinhorn, A. M. (1993). "Verification of friction model ofTeflon bearings under triaxial load. " J Struct. Engrg. ASCE, 119(1), 240-261.

Mondkar, D. P. and Powell, G. H. (1975). "ANSR-general purpose program for analysis ofnonlinear structural response." Report No. UCB/EERC-75/37, Earthquake Engrg. Res. Ctr"University of California, Berkeley, Calif.

Nagarajaiah, S., Reinhom, A. M. and Constantinou, M. C. (1990). "Analytical modeling of threedimensional behavior of base isolation devices." Proc. Fourth Us. Nat. Con! on EarthquakeEngrg., Earthquake Engrg. Res. Inst., 3, 579-588.

Nagarajaiah, S., Reinhom, A. M. and Constantinou, M. C. (1991a). "Nonlinear dynamic analysisof 3D-Base isolated structures," J Struct.Engrg., ASCE, 117(7), 2035-2054.

Nagarajaiah, S. Reinhom, A. M. and Constantinou, M. C. (1991b). "3D-BASIS: Non-lineardynamic analysis of three-dimensional base isolated structures - Part II" Report No. NCEER-9 J­0005, Nat. Ctr. for Earthquake Engrg. Res., State University of New York, Buffalo, N.Y.

Nagarajaiah, S., Reinhom, A. M. and Constantinou, M. C. (1992). "Experimental study of slidingisolated structures with uplift restraint." J Struct. Engrg., ASCE, 118(6), 1666-1682,

Nagarajaiah, S., Reinhom, A. M. and Constantinou, M. C. (1993a). "Torsional coupling in slidingbase isolated structures." J Struct. Engrg., ASCE, 119( 1), 130-149.

5-2

Nagarajaiah, S, Reinhorn, A M. and Constantinou, M. C. (1993b). "Torsion in base isolatedstructures with elastomeric systems," J Struct. EtIgrg.,ASCE, 119(10),2932-2951.

Nagarajaiah, S., Li, c., Reinhorn, A M. and Constantinou, M, C. (1993c). "3D-BASIS-TABSComputer program for nonlinear dynamic analysis of three dimensional base isolated structures,"Report No. NCEER-93-0011, Nat. Ctr. for Earthquake Engrg. Res., State University of NewYork, Buffalo, N.Y.

Nagarajaiah, S., Riley, M. A and Reinhorn, A M. (1993d). "Control of sliding isolated bridgeswith absolute acceleration feedback" J Engrg. Mech., ASCE, 119(11), 2317-2332.

Nagarajaiah, S., Feng, M. Q. and Shinozuka, M. (1993e). "Active control of structures withfriction controllable isolation bearings." J Soil Dyn. and Earthquake Engrg., 12(2), 103-112.

Nagarajaiah, S., Tsopelas, P.S., Li, c., Reinhorn, A M. and Constantinou, M. C. "3D-BASIS: Aclass of computer programs for nonlinear dynamic analysis of base isolated structures," Proc­A. TC-17-1 - Seminar on Base Isolation. Passive Energy Dissipation and Active Control, SanFrancisco, CA, March 11-12,1,173-184.

Newmark, N, M, (1959). "A method of computation for structural dynamics" J Engrg. Mech.Div., ASCE, 85 (3), 67-94.

Park, Y. 1., Wen, Y. K. and Ang, A H S. (1986), "Random vibration of hysteretic systems underbidirectional ground motions," Earthquake Engrg. Struct. Dyn., 14(4),543-557,

Reinhorn, AM., Nagarajaiah, S., Subramaniam, R. S. and Riley, M. A (1993). "Study of hybridcontrol for structural and nonstructural systems." Proceedings International Workshop onStmctural C01llrol, Hawaii, 405-416

Riley, M. A, Subramaniam, R. S., Nagarajaiah, S. and Reinhorn, A M. (1993). "Hybrid controlof sliding base isolated structures" Proceedings A TC-17-1 Seminar on Seismic Isolation, PassiveEnelgy Dissipation, and Active Control, Vol. 2, 799-810.

Rosenbrock, H H (1964). "Some general implicit processes for the numerical solution ofdifferential equations." Computer J, 18, 50-64.

Subramaniam, R. S., Reinhorn, A M. and Nagarajaiah, S. (1993). "Application of fuzzy settheory to the active control of base isolated structures." Proceedings Second IEEE InternationalConference on Fuzzy Systems, San Francisco, CA, 223-231,

Theodossiou. D. and Constantinou, M. C. (1991). "Evaluation of SEAOC design requirementsfor sliding isolated structures" Report No. NCEER-91-0015, Nat. Ctr. for Earthquake Engrg.Res" State University of New York, Buffalo, N.Y.

5-3

Tsopelas, P. c., Nagarajaiah, S., Constantinou, M. C. and Reinhom, A. M. (1991). "Nonlineardynamic analysis of multiple building base isolated structures program 3D-BASIS-M." Report No.NCEER-91-001-l, Nat. Ctr, for Earthquake Engrg. Res., State University of New 'York, Buffalo,N,y'

Tsopelas, P. c., Constantinou, M. C. and Reinhom, A. M. (1994). "3D-BASIS-ME: Computerprogram for nonlinear dynamic analysis of seismically isolated single and multiple structures andliquid storage tanks," Report No. NCEER-94-0010, Nat. Ctr. for Earthquake Engrg. Res., StateUniversity of New York, Buffalo, N.Y.

Tsopelas, P. c., Nagarajaiah, S. Constantinou, M. C. and Reinhom, A. M. (1994). "Nonlineardynamic analysis of multiple building base isolated structures." 1. Computers and Structures, 50(1),47-57.

Wen, Y. K. (1976) "Method of random vibration of hysteric systems." J Engrg. Mech Div.ASCE, 102(2), 249-263.

Wilson, E. L., Hollings, 1. P. and Dovey, H. H. (1975). "ETABS-Three dimensional analysis ofbuilding systems." Report No. UCB/EERC-75/13, Earthquake Engrg. Res, Ctr., University ofCalifornia, Berkeley, Calif.

Winters, C. and Constantinou, M. C. (1993) "Evaluation of static and response spectrum analysisprocedures of SEOACIUBC for seismic isolated structures." NCEER Report No. 93-0004,National Center for Earthquake Engrg, Research, State University of New York, Buffalo, N.Y.

Yang, 1. N., Li, Z., Danielians, A., and Liu, S. C. (1992). "Aseismic hybrid control of nonlinearhysteretic structures." 1. Engrg. Mech., ASCE, 118(7), 1423-1440.

5-4

APPENDIX A

3D·BASIS·TABS PROGRAM

USER'S MANUAL

A.I INPUT FORMAT

The program 3D-BASIS-TABS prompts for the input file name, the output file name

and the earthquake excitation file names; the choice of file names (e.g., EXAMPLl.DAT,

EXAMPL1.0UT, WAVEX.OAT, WAVEYDAT and WAVEZ.DAT) rests with the user.

Instructions of use of the program, input information and short cuts for various operating

systems (DOS, VAX, UNIX) are included in the distribution computer diskettes. In the

program dynamic arrays are used; also, double precision is used for accuracy. Common block

size has been set to 100,000 and should be changed if the need arises.

A free format is used to read all input data. Hence, conventional delimiters (commas,

blanks) may be used to separate data items. Standard FORTRAN variable format is used to

distinguish integers and floating point numbers. Input data must therefore, conform to the

specified variable type. All values are to be input unless mentioned otherwise. No blank lines

are to be specified.

Note: Provision is made for a line of user defined descriptive text between each set of data

items (refer to variable USER TXT in sections A.2 to A.9 and to the example data files- .

accompanying this manual).

A.2 PROBLEM TITLE

TITLE

A.3 UNITS

UNITS

TITLE upto 80 characters.

UNITS upto 80 characters.

A-I

A.4 CONTROL PARAMETERS

A.4.1 General Control Information

USER TEXT Reference information: upto 80 characters of text.

ISEV,NST,NFQ,NP,LOR, G, IEXE

(1)*

(1)

(1)

(2)

(3)

ISEV = 1 for option 1 - Data for 3D-shear building (story

shear stiffnesses to be specified in the input file).

ISEV = 2 for option 2 - Data for full 3D-building

(member properties for beams, columns etc. to be

specified in the input file).

ISEV = 3 for option 3 - Data for 3D-building

(Eigenvalues/Eigenvectors to be specified

in the input file).

NST = Number of stories in the complete building

excluding the base (If NST< 1 then NST set = 1)

NFQ = Number of eigenvectors/eigenvalues to be retained

in the analysis (If NFQ <3 then NFQ set = 3)

NP = Number of isolators such as bearings, dampers etc.

(if NP<4 then NP set = 4)

LOR = Length of earthquake records (number of data points;

the X, Y, and Z direction records must have the same length).

G = Gravitational acceleration

IEXE = Flag (integer) for data check

= 1 for data check only

= 0 data check and complete execution of analysis.

A-2

*Notes: 1. For explanation of the option 1, option 2 and option 3 refer to section 3.2 (of NCEER93-0011). If option 1 or 3 are used then member forces are not needed as output.

2. Number of eigenvectors/eigenvalues retained in the analysis should be in groups of

three - the minimum being one set of three modes.

3. Number of bearings refers to the total number of bearings which could be a combination

of linear elastic elements, viscous elements, elastomeric bearings, steel dampers, and

sliding bearings.

A.4.2 Superstructure Control Information (for ISEV =2 only; skip this section and go to

Section A.4.3 if ISEV = 1 OR 3)

USER TXT

NDF,NTF,NLD

(1)*

(1)

(2)

Reference information; upto 80 characters of text.

NDF = Number of frames with different properties

or different vertical loading

NTF = Total number of frame or shear wall elements

in the structure

NLD = Total number of load conditions

*Notes: 1. Input data for frames with identical properties and vertical loading are given onlyonce - see also section A5.1.3 on Frame Location.

2. Load conditions are defined as combinations of the four load cases - see section A8 on

Load Case Definition.

A-3

A.4.3 Integration Control Parameters

USER TXT Reference information; upto 80 characters of text.

TSI,TOL,FMNORM,MAXMI,KVSTEP

(1)*

(2)

(3)

(4)

TSI = Time step of integration.

(If TSI >TSR then TSI set = TSR;

refer to A.4.5 for details about TSR)

TOL = Tolerance for the nonlinear force

vector computation.

FMNORM = Reference moment at

the center of mass of the base

used for computing convergence.

MAXMI = Maximum number of iterations within

a time step.

KVSTEP = Index for time step variation.

KVSTEP = 1 for constant time step.

KVSTEP = 2 for variable time step.

"'Note: 1. The time step of integration cannot exceed the time step of earthquake record givenin A.4.5.

2. Tolerance for force computation may be 0.001.

3. The reference moment at the center of mass of the base can be calculated approximately

by multiplying the base shear by one half the maximum dimension at the base.

4. If MAXMI is exceeded the program is terminated with an error message.

A.4.4 Newmark's Method Control Parameters

USER TXT

GAM,BET

Reference information; upto 80 characters of text.

GAM = Parameter which produces numerical

damping within a time step.

(if GAM = 0.0 tqen GAM set = 0.5)

BET = Parameter which controls the

variation of acceleration within a

time step.

(if GAM = 0.0 then GAM set = 0.25)

A.4.5 Earthquake Control Parameters

USER TXT Reference information; upto 80 characters of text.

INDGACC,TSR,XTH,ULF

(l)a"

(l)b

(l)c

(l)d

(2)

INDGACC = 1 for a single lateral earthquake record

at an angle of incidence XTH.

INDGACC = 2 for two independent lateral earthquake

records along the X and Y axes.

INDGACC = 3 for tw~ independent lateral earthquake records

along the X and Z axes.

INDGACC = 4 for three independent lateral earthquake

records along the X, Y, and Z axes.

TSR = Time step of the earthquake

record(s).

A-5

(3)

XTH = Angle of incidence of the earthquake

with respect to the X axis in anticlockwise

direction in degrees (for INDGACC = 1).

ULF = Load factor.

*Notes: 1. Two options are available for the earthquake reGord input:

a) INDGACC = 1 refers to a single earthquake record input at any angle of incidence

XTH with respect to the X axis. Input only one earthquake record (read through a single

file e.g., WAVEX.DAT). Refer to A.9.1 for wave input information.

b) INDGACC = 2 refers to two independent earthquake records input in the X and Y

directions, e.g., EI Centro N-S along the X direction and El Centro E-W along the Y

direction. Input two independent earthquake records in the X and Y directions (read

through two files e.g., WAVEXP1.DAT and WAVEYP1.DAT). Refer to A.9.1 and A.9.2

for wave input information.

c) INDGACC = 3 refers to two independent earthquake records in X and Z directions.

Refer to A.9.1 and A.9.3 for wave input information.

d) INDGACC = 4 refers to three independent earthquake records in X, Y, and Z direc­

tions. Refer to A.9.3. for wave input information.

2. The time step of earthquake record and the length of earthquake record has to be the

same in X, Y and Z directions for INDGACC = 1, 2, 3 and 4.

3. Load factor is applied to the earthquake records in X,Y and Z directions.

A.S SUPERSTRUCTURE DATA

Go to A.5.1 for ISEV = 2 (refer to A.4.1) and specify beam, column, panel and bracing

properties for full three dimensional representation of the superstructure.

Go to A.5.2 for ISEV = 1 (refer to A.4.1) and specify story stiffness for three dimensional

shear building representation of the superstructure.

A-6

Go to A.5.3 for ISEV = 3 (refer to A.4.1) and specify eigenvalues and eigenvectors for

three dimensional representation of the superstructure.

A.5.1 THREE DIMENSIONAL BUILDING (for ISEV = 2 only; Skip this section if ISEV =lOR 3)

USR TXT Reference information; upto 80 characters of text

Note: The sections A.5.1.1 to A.5.1.3 are based on the input requirements of ETABS.

A.5.l.I Story Data

USR TXT Reference information; upto 80 ch£..rar~~-,"s of text.

[(SD(N,I),I =2,6), N = 1,NST]

SD(N,2) "' .ory height [distance from the floor (or roof)

level to the floor (or base) level below].

SD(N,3) = Translational mass.

SD(N,4) = Rotational mass moment of inertia about a

vertical axis through the center of mass.

(1)

(1)

SD(N,5) = X-distance to the center of mass measured from

the STRUCTURE REFERENCE AXIS.

SD(N,6) = Y-distance to the center of mass measured from

the STRUCTURE REFERENCE AXIS.

Note: Input one set per story from the top story to the bottom story of the superstructure.

(1) The GLOBAL STRUCTURE REFERENCE AXIS has to be a yertical axis at the

center of mass of the base.

A-7

A.5.1.2 Frame Data

Repeat the following block of data for each different frame (upto the total number of

different frames = NDF).

USR TXT Reference information; upto 80 characters of text.

A.5.1.2.1 Frame Control Parameters

USR TXT Reference information; upto 80 characters of text.

M,NS,NC,NB,NCP,NBP,NFEF,NPAN,NTRU

(1)*

(2)

(3)

(4)

(5)

(6)

(7)

(8)

M = Frame identification number.

NS = Number of story levels above the base.

NC = Number of vertical column lines in the frame.

NB = Number of bays in the frame.

NCP = Number of sets of different column properties.

NBP = Number of sets of different beam properties.

NFEF = Number of sets of different fixed end moments

and shears to be applied as vertical loads to beams

NPAN = Number of infill shear panels in the frame.

NTRU = Number of bracing elements in the frame.

*Note: One set of data must be entered for each different frame. Frames with differentlocations but identical properties and vertical loading need be entered only once (see also

section A.5.1.3 on Frame location cards).

A-8

1. Frame identification numbers must be entered in numerical sequence beginning with

number one (1). This frame may be located (repeated) at different positions in the

structure.

2. If a frame does not extend the full height of the building, then only those story levels

actually existing in the frame are to be input.

3. An isolated shear wall is a single column line frame. For this case all data pertaining to

beams is meaningless and must be omitted in the data input section to follow.

4. Column properties may be referenced to any number of columns in the frame. The

number of column property sets control A.5.1.2.3.

5. The number of beam property sets control the number sets of data to be read in section

A,5.1.2.4.

6. If no vertical static loads act on the structure, then input zero, and skip section A.5 .1.2.5.

7. Ifno panel elements are included in this frame, then input zero, and skip section A.5.1.2.8.

8. If no bracing elements are included in this frame, then input zero, and skip section

A.5.1.2.9.

A.5.1.2.2 Vertical Column Line Coordinates

USR TXT Reference information; upto 80 characters of text.

(M,(CLN(J,I),I =1,2),J =1,NC)

(1) *

(2)

M = Column line identification number

CLN(J,l) =X-distance to Jth column line from frame reference point.

CLN(J,2) = Y-distance to Jth column line from frame reference point.

A-9

*Note: 1. One set of vertical column line coordinates have to be input for each column linein the frame. For frames with a single column line a second column should be specified

to define the major axis for column properties entered in section A.5.1.2.7.

2. Coordinates of column lines are measured from the frame (local) axis.

A.5.1.2.3 Column Property

USR TXT Reference information; upto 80 characters of text.

(M,(CP(J,I),J =1,9),1 =1,NCP)

~ = Identification nUJ'!lber for this column property set

CP(1,1) = Modulus of Elasticity, E.

CP(2,1) = Axial Area A.

(2)

(2)

(3)

(4)

CP(3,I) = Shear area associated with shear forces

in major axis direction.

CP(4,1) = Shear area associated with shear forces

in minor axis direction.

CP(5,1) = Torsional inertia.

CP(6,1) = Flexural inertia for bending in the major axis direction.

CP(7,1) = Flexural inertia for bending in the minor axis direction.

CP(8,1) = Rigid zone depth at the top of column (for both axis). DT.

CP(9,1) = Rigid zone depth at the bottom of column. DB.

A-10

*Note: One set of data must be supplied for each different column in this frame.

1. Property set identification numbers mustbe in increasing numerical sequence beginning

with one (1).

2. Shearing deformations are ignored if shear areas are zero.

3. The rigid zone depth is used to reduce the effective length of the column about both

axIS.

4. Usually zero unless beam extends above the floor level.

/~jor.· ../CX1S ,/ - I......

. ,. ~ column./

.,/

II ..__ j ~r-ror. r2=lS.

Fig. A-I - Typical Column Model.

A-II

A.5.1.2.4 Beam Property

USR TXT Reference information; upto 80 characters of text.

(M,(BP(J,I),J =1,9),1 =1,NBP)

(1)*

(2)

(3 )

M = Identification number for this beam property set

BP(1,1) = Modulus of Elasticity, E.

BP(2,1) = Shear Area A.

BP(3,I) = Torsional inertia.

BP(4,1) = Flexural inertia, I.

BP(5,1) = Kn - stiffness factor (e.g., 4)

BP(6,1) = KJJ - stiffness factor (e.g., 4)

BP(?,I) = KTJ - stiffness factor (e.g., 2)

BP(R,l) = Rigid zone length at end I of the beam.

BP(9,1) = Rigid zone length at end J of the beam.

"'Note: One set of data must be supplied for each different beam in the frame; skip this inputif the frame has only one column line.

1. Property set identification numbers muSt be input in increasing numerical sequence

beginning with one (1).

2. Shearing deformations are ignored if shear areas are zero.

3. The beam rigid zone lengths are used to reduce the effective length of the beam.

A-12

I 2I I

[ Cr. JJI

LI2 4. LI2 1•

IEI. KL IJ

Fig. A·2 • Typical Notation of Beam Stiffness Coefficients

A.5.1.2.5 Fixed-End Beam Loads

(if NFEF = 0 in section A.5.1.2.1 skip this section)

USR TXT Reference information; upto 80 characters of text.

(M,IFEF(I),(FEF(J,I),J =1,5),1 =1,NFEF)

(1)* M = Identification number for this vertical loading set

IFEF(I) = Index:

EQ. 0; Fixed-end forces are applied at the column faces

EQ. 1; Fixed-end forces are applied at the column centerlines

A-13

(2)

(3)

FEF(l,l) = Fixed-end reaction, M1

FEF(2,I) = Fixed-end reaction, VI

FEF(3,1) = Fixed-end reaction, M2

FEF(4,1) = Fixed-end reaction, V2

FEF(5,1) = Uniform force per unit length, w, acting

downward to be added to fixed-end reactions

*Note: One set of data must be supplied for each different type of vertical beam loading; omitthis data set if this is a single column line frame

1. Load set numbers must be input in sequence.

2. Reactions act on the beam ends and are positive as shown in the Fig. A-3.

3. Additional fixed-end forces due to the uniform load, w, are calculated using:

M = w*12/12; V = w*lj2

and are added to any specified fixed-end reactions. The forces due to uniform load, w, are

exact only for prismatic beams.

Fig. A-3 - Typical Beam Loading

A-14

A.S.l.2.6 Beam Location, Properties and Loads

USR TXT Reference information; upto 80 characters of text.

[ { I,(LB(N,M,L),L= 1,3),K,(LDB(N,M,L),L= 1,3) },N = I,NS ],M = I,NB

I = Bay identification number for this beam.

(1)*

(2)

(3)

(4)

LB(N,M,I) = Column line number at end I.

LB(N,M,2) = Column line number at end J.

LB(N,M,3) = Beam property set identification number for this beam.

K = Number of beams in sequence below to be generated

having the same properties and vertical loading as this beam.

LDB(N,M,I) = Vertical loading set identification number

for vertical load case I.

LDB(N,M,2) = Vertical loading set identification number

for vertical load case II.

LDB(N,M,3) = Vertical loading set identification number

for vertical load case III.

*Note: One set of data must be input from top to bottom and from bay to bay in the frame(unless the data generation option is used)

1. Position of I and J ends defines local coordinate .axis with local "y" positive from I to J

and local "z" positive vertically upwards. A right hand screw rule sign convention applies.

2. Beams with zero stiffness (missing beams) may be input as having a property set number

of zero; if the beam has finite stiffness, the set number must reference an existing property

set defined previously is section A.5.1.2.4.

A-15

3. The generation option can only be used to define girders within the current bay; a new

bay must be started with a new beam card.

4. The vertical loading sets defined in section A.5.1.2.5, are applied to the beams defined

herein. Three independent vertical load distributions (1,11,111) are allowed, and these

distributions are combined to form load cases for the complete building; see section A.B.

A.5.1.2.7 Column Location and properties

USR TXT Reference information; upto 80 characters of text.

[ { KK,(LC(N,M,I),I =1,2),K } ,N =I,NS l,M =I,NC

KK = Column line identification number for this column.

(1)*

(2)

(3)

LC(N,M,I) = Column property set identification number.

LC(N,M,2) = Column line number defining direction of major axis.

K = Number of columns in sequence below to be generated

having the same properties as this column member.

·Note: One card per column must be input from top to bottom and from column line to columnline of the frame (unless the data generation option is used).

1. Missing columns may be input as having a property set number of zero (0); if the column

has finite stiffness, then the set number referenced must correspond to one of the property

sets defined previously in section A.5.1.2.3.

2. Defines direction on local "y" axis; local "z" axis is in the vertical plane .with positive

upwards. A right hand screw rule convention applies.

3. Generation is allowed only within the current column line; begin a new column line

with a new column card.

A-16

A.5.1.2.8 Panel Properties

USR TXT Reference information; upto 80 characters of text.

(LP(1,I),LP(2,I),LP(3,I),(PP(J,I),J =1,5),1 = I,NPAN)

LP(l,l) =Level identification number at the top of this panel.

LP(2,1) = Column line number at the I side of this panel.

LP(3,1) = Column line number at the J side of this panel.

PP(l,l) = Modulus of elasticity, E.

PP(2,1) = Gross sectional area, A.

(2) PP(3,1) = Moment of inertia, I.

PP(4,1) = Effective shear area, Ay

PP(5,1) = Shear modulus, G.

*Note: Input one set of data per panel in any order; no generation is allowed.

1. Base is defined as level zero, and the roof level number is equal to the total number of

stories in the building.

2. A zero (0) value for the moment of inertia selects the pure shear deformation panel

model. The pure shear panel uses the gross sectional area, not the effective area, tocal­

culate stiffness and stress values.

A-I?

A.S.l.2.9 Bracing Properties

USR TXT Reference information; upto 80 characters of text.

(LT(1,I),LT(2,I),LT(3,I),TP(1,I),TP(2,I),I =1,NTRU)

LT(l,I) = Level identification number at the top of this brace.

LT(2,I) = Column line number at the upper end of this brace.

LT(3,I) = Column line number at the lower end of this brace.

TP(l,I) = Modulus of elasticity, E.

TP(2,I) = Cross sectional area, A.

*Note: Input one set of data per brace in any order; no generation is allowed.

A.S.l.3 Frame location cards

USR TXT Reference information; upto 80 characters of text.

IF,IFC,Xl,Yl,ANG

(1)*

(2)

(3)

IF = Frame identification number

IFC = Force calculation code;

EO. 0; Frame forces will be calculated and printed.

EO. I; Frame forces will not be calculated.

Xl = Distance, Xl'

Y1 = Distance, Yl'

A-I8

(4) ANG = Angle between the frame x axis and the structure

(global) X axis (anti-clockwise from X to x).

*Note: One set of data must be entered in this section for each frame (or single column) inthe building; the total number of frame locations to be read is controlled by the entry in

section AA.2.

1. Frame identification numbers may be repeated, but location data set must be input in

frame identification number sequence.

2. A frame force calculation code of one (1) will suppress output of member forces.

3. Distance from Structure (Global) axis to the origin of the frame (Local) axis. Structure

reference axis has to be at the center of mass of the base.

4. Angle is input in degrees and decimal fractions e.g., 15°30' input as 15.5.

y

XI --411~frame re ferene I

pcint

&- 001------XS't'n.Icture rite rlne'

point

Fig. A-4 - Typical Coordinate Systems.

A-19

A.5.2 Shear Stiffness Data for Three Dimensional Shear Building

(for ISEV =1 only; skip this section if ISEV =2 or 3)

USR TXT Reference information; upto 80 char<:l.-cters of text

A.5.2.! Shear Stiffness· X, Y and Torsional Stiffness in 0 Direction

USR TXT

SX(I),I =1,NF

SY(I),I =1,NF

ST(I),I =1,NF

Reference information; upto 80 characters of text.

SX(I) = Shear stiffness of story I

in the X direction.

SY(I) = Shear stiffness of story I

in the Y direction.

ST(I) = Torsional stiffness of story I

in the adirection about

the center of mass of the floor.

Note: Input shear stiffness in the X and Y direction and torsional stiffness in the adirection

of each individual story starting from the top story to the first story.

A.5.2.2 Eccentricity Data· X and Y Direction'

USR TXT

EX(I),I =1,NF

EY(I),! =1,NF

Reference information; upto 80 characters of text.

EX(I) = Eccentricity of center of resistance

from the center of mass of the floor l.

EY(I) = Eccentricity of center of resistance

from the center of mass of the floor I.

Note: Input eccentricity at each individual story in the X and Y direction starting from the

top story to the first story. If both the eccentricities are zero, a default value of 0.0001 is

used to facilitate eigensolution.

A-20

A.5.3 Eigenvalues and Eigenvectors for Three Dimensional Building

(for ISEV = 3 only; skip this section if ISEV = 1 or 2)

USR TXT

A.5.3.! Eigenvalues

USR TXT

W(I),I =1,NFQ

Reference information; upto 80 characters of text

Reference information; llpto 80 characters of text.

W(I) = Eigenvalue of mode I

Note: Input from the first mode to the NFQ Il'l;ode given in section A.4.1.

A.5.3.2 Eigenvectors

USR TXT Reference information; upto 80 characters of text.

E(3*NF,I),l =1,NFQ

E(3 *NF,I) = Eigenvector of mode I.

Note: Input from the first mode to the NFQ mode given in section AA.1.

A.5,4 Superstructure Translational Mass and Rotational Mass moment ofInertia (Skip this

section if ISEV =2)

USR TXT Reference information; upto 80 characters of text.

CMX(I),I = 1,NF CMX(I) = Translational mass at floor 1.

CMR(I).I =l.NF CMR(I) = Mass moment of inertia offloor I ahout the center of mass.

Note: Input from the top floor to the first floor.

A-21

A.5.5 Superstructure Damping

USR TXT

DR(I),I =1,NE

Reference information; upto 80 characters of text.

DR(I) = Damping ratio corresponding to mode 1.

Note: Input from the first mode to the NE mode.

A.5.6 Eccentricities of center of mass

USR TXT Reference information; upto 80 characters of text.

XN(I),YN(I),I =1,NF

XN (1) = Distance of the center of mass of

the floor I from the center of mass of

the base in the X direction.

YN(1) = Distance of the center of mass of

the floor I from the center of mass of

the base in the Y direction.

(If ISEV = 1 then XN(I) and YN(1) set = a)

Note: Input from the top floor to the first floor.

A.5.7 Height of Difl'erent Floors and the Base

USR TXT

H(I),I =1,NF+ 1

Reference information; upto 80 characters of text.

H(I) = Height from the ground to the floor 1.

Note: Input heights from the top floor to the base.

A-22

A.6 ISOLATION SYSTEM DATA

USR TXT Reference information; upto 80 characters of text.

A.6.1 Stiffness Data for Linear Elastic Isolation System

t

USR TXT Reference information; upto 80 characters of text.

SXE,SYE,STE,EXE,EYE

SXE = Resultant stiffness of

the linear elastic isolation system

ill the X direction.

SYE = Resultant stiffness of

the linear elastic isolation system

in the Y direction.

STE = Resultant torsional stiffness of

the linear elastic isolation system

in the adirection

about the center of mass of the base.

EXE = Eccentricity of the center

of resistance of the linear elastic

isolation system in the X direction from

the center or Illass ur the baSt:.

A-23

EYE = Eccentricity of the center

of resistance of the linear elastic

isolation system in the Y direction from

the center of mass of the base.

Note: Data for linear elastic elements can also be input individually (refer to A,6.4.1).

A.6.2 Mass Data of the Base

USR TXT

CMXB,CMTB

Reference information; upto 80 characters of text.

CMXB = Mass of the base in the

translational direction.

CMTB = Mass moment of Inertia of the base

about the center of mass of the base.

A.6.3 Global Damping Data of the Base

USR TXT Reference information; upto 80 characters of text.

CBX,CBY,CBT,ECX,ECY

CBX = Resultant global damping coefficient

in the X direction.

CBY = Resultant global damping coefficient

in the Y direction.

CBT = Resultant global damping coefficient

in the adirection about the

center of mass of the base.

A-24

ECX = Eccentricity of the center of

global·damping of the isolation

system in the X direction from the

center of mass of the base.

ECY = Eccentricity of the center of

global damping of the isolation

system in the Y direction from the

center of mass of the base.

Note: 1. Data for viscous elements can also be input individually (refer to A.6.4.2).

A.6.4 Isolation Element Data

USR TXT Reference information; upto 80 characters of text.

Notes for sections A.6.4.1 to A.6.4.4:

(i). K= 1,NP •• Data for NP isolation elements to be given using the elements in A.6.4.1,

A6.4.2, A.6.4.3, A.6.4.4, A.6.4.5, A.6.4.6, A.6.4.7, and A.6.4.8.

(ii). The indices INELEM(NP,2) are used in the subsequent sections A.6.4.1 to A.6.4.8 to

identify the element types in the isolation system. Index INELEM(NP,2) is defined as

follows:

INELEM(K,1:2) = Indices for the isolation element K

indicating its type and whether it is a

uniaxial or biaxial element.

INELEM(K,l) = 1 for a uniaxial element

in the X direction, (or A direction)

INELEM(K,1) = 2 for a uniaxial element

in the Y direction, (or B'direction)

INELEM(K, 1) = 3 for a biaxial element

A-25

INELEM(K,2) = 1 for linear elastic element.

INELEM(K,2) = 2 for linear viscous element.

INELEM(K,2) = 3 for hysteretic element

for elastomeric bearing steel damper.

INELEM(K,2) = 4 for element for flat sliding bearing

(friction force and fmax independent of instant changes in

!,lormal force)

INELEM(K,2) = 5 for hysteretic element for flat sliding

bearing (friction force and fmax depend on instant change

in normal force)

INELEM(K,2) = 6 for FPS bearing element

INELEM(K,2) = 7 for hysteretic nonlinear stiffening element

(not available in the current Version)

INELEM(K,2) = 8 for nonlinear viscous element

A.6.4.1 Linear Elastic Element

INELEM(K,1:2) INELEM(K,l) can be either 1,2 or 3

INELEM(K,2) = 1

(Refer to A.6.4 for further details).

PS(K, 1),PS(K,2)

PS(K,1) = Shear stiffness in the X

direction for biaxial element or uniaxial

element in the X direction

(leave blank if the uniaxial element

is in the Y direction only).

PS(K,2) = Shear stiffness in the Y

direction for biaxial element or uniaxial

element in the Y direction

(leave blank if the uniaxial element

is in the X direction only).

A-26

Note: Biaxial element means elastic stiffness in both X and Y directions (no interaction

between forces in the X and Y direction).

A.6.4.2 Linear Viscous Elements

Fig. AS • Position of Viscous Elements Cluster

INELEM(K,1:2) INELEM(K,l) can be either 1,2 or 3

INELEM(K,2) = 2

(Refer to A.6.4 for further details).

CA, CB, THETAA, THETAB

CA = C(K,3) = Damping coefficient in the A direction for

biaxial element or uniaxial element in the A direction

(leave blank if the unia,xial element is in the B direction

only).

CB = PC(K,6) = Damping coefficient in the B direction for

biaxial element or uniaxial element in the B direction

(leave blank if the uniaxial element is in the A direction

only).

A-27

THETAA = PC(K,13) = Orientation angle e for damper A with X

axis in degrees (-18CF ~ e ~ 180=') (leave blank if the uniaxial element

is in the B direction only)

THETAB = PC(K,14) = Orientation angle e for damper B with X

axis in degrees (-18CF ~ e ~ 180=') (leave blank if the uniaxial element

is in the A direction only)

Note: Biaxial element means damping in both A and B directions (no interaction between

forces in two directions).

A.6.4.3 Hysteretic Element for Elastomeric Bearings/Steel Dampers

INELEM(K,1:2) INELEM(K,I) can be either 1,2 or 3

INELEM(K,2) = 3

(Refer to A,6.4 for further details).

ALP(K,I),YF(K,I),YD(K,I),I =1,2

ALP(K,l) = Post-to-preyielding stiffness ratio;

YF(K,l) = Yield force;

YD(K,l) = Yield displacement;

in the X direction for biaxial element or uniaxial

element in the X direction

(leave blank if the uniaxial element

is in the Y direction only).

ALP(K,2) = Post-to-preyielding stiffness ratio;

YF(K,2) = Yield force;

YD(K,2) = Yield displacement;

in the Y direction for biaxial element or uniaxial

element in the Y direction

(leave blank if the uniaxial element

is in the X direction only).

A-28

A.6.4.4 Biaxial Element for Sliding Bearings with (Friction Independent of

Instantaneous Change of Normal Load)

INELEM(K,1:2) INELEM(K,1) can be either 1,2 or 3

INELEM(K,2) = 4 (Refer to C.6 for further details).

(FMAX(K,I),FMIN(K,I),PA(K,I),YD(K,1),1 =1,2),FN(K)

FMAX(K, 1) = Maximum coefficient of sliding friction (leave

blank if the uniaxial element is in the Y direction only);

FMAX(K,2) = Maximum coefficient of sliding friction (leave

blank if the uniaxial element is in the X direction only);

FMIN(K, 1) = Minimum coefficient of sliding friction (leave

blank if the uniaxial element is in the Y direction only);

FMIN(K,2) = Minimum coefficient of sliding friction (leave

blank if the uniaxial element is in the X direction only);

PA(K, 1) = Constant which controls the transition of

coefficient of sliding friction from maximum to minimum

value (leave blank if the uniaxial element is in the Y

direction only);

PA(K,2) = Constant which controls the transition of

coefficient of sliding friction from maximum to minimum

value (leave blank if the uniaxial element is in the X

direction only);

YD(K,1) = Yield displacement; in the X direction for

biaxial element or uniaxial element in the X direction

(leave blank if the uniaxial element is in the Y direction

only);

A-29

YD(K,2) = Yield displacement; in the Y direction for

biaxial element or uniaxial element in the Y direction

(leave blank if the uniaxial element is in the X direction

only);

FN(K) = Initial normal force at the sliding interface.

A.6.4.5 Biaxial Element for Sliding Bearings (with Friction Dependent on

Instantaneous Change of Normal Load)

INELEM(K,1:2 INELEM(K,l) can be either 1,2, or 3

INELEM(K,2) = 5 (Refer to C.6 for further details).

(FMAX(K,I),FMIN(K,I),PA(K,I),YD(K,I),I =1,2),FN(K)

FMAX(K,l) = Maximum coefficient of sliding friction at

almost zero pressure (fmaxO in Equation 2.24) (leave blank

if the uniaxial element is in the Y direction only);

FMAX(K,2) = Maximum coefficient of sliding friction at

almost zero pressure fmaxO in Equation 2.24) (leave blank

if the uniaxial element is in the X direction only);

FMIN(K,l) = Minimum coefficient of sliding friction

(independent of pressure) (leave blank if the uniaxial

element is in the Y direction only);

FMIN(K,2) = Minimum coefficient of sliding friction

(independent of pressure) (leave blank if the uniaxial

element is in the X direction only);

PA(K,1) =Constant which controls the transition of

coefficient of sliding friction from maximum (fmax) to

minimum (fmin) value (leave blank if the uniaxial element

is in the Y direction only);

A-3D

PA(K,2) =Constant which controls the transition of

coefficient of sliding friction from maximum (fmax) to

minimum (fmin) value (leave blank if the uniaxial element

is in the X direction only);

YD(K,l) = Yield displacement; in the X direction for

biaxial element or uniaxial element in the X direction

(leave blank if the uniaxial element is in the Y direction

only);

YD(K,2) = Yield displacement; in the Y direction for

biaxial element or uniaxial element in the Y direction

(leave blank if the uniaxial element is in the X direction

only);

FN(K) = Initial normal force at the sliding interface.

A.6.4.6 Element for Friction Pendulum Bearings (FPS)

INELEM(K,1:2) INELEM(K,l) can be either 1,2 or 3

INELEM(K,2) = 6 (Refer to C.6 for further details).

ALP(K3),(FMAX(K,I),FMIN(K,I),PA(K,I),YD(K,I),I = 1,2),FN(K)

ALP(K,3) =Radius of curvature of the concave surface of

the bearing.

FMAX(K,l) = Maximum coefficient of sliding friction at

almost zero pressure (fmaxO in Equation 2.24) (leave blank

if the uniaxial element is in the Y direction only);

FMAX(K,2) = Maximum coefficient of sliding friction at

almost zero pressure fmaxO in Equation 2.24) (leave blank

if the uniaxial element is in the X direction only);

A-31

FMIN(K, 1) = Minimum coefficient of sliding friction

(independent of pressure) (leave blank if the uniaxial

. element is in the Y direction only);

FMIN(K,2) = Minimum coefficient of sliding friction

(independent of pressure) (leave blank if the uniaxial

element is in the X direction only);

PA(K, 1) =Constantwhich controls the transition of

coefficient of sliding friction from maximum (fmax> to

minimum (fmin) value (leave blank if the uniaxial element

is in the Y direction only);

PA(K,2) =Constant which controls the transition of

coefficient of sliding fr~ction from maximum (fmax) to

minimum (fmin) value (leave blank if the uniaxial element

is in the X direction only);

YD(K,l) = Yield displacement; in the X direction for

biaxial element or uniaxial element in the X direction

(leave blank if the uniaxial element is in the Y direction

only);

YD(K,2) = Yield displacement; in the Y direction for

biaxial element or uniaxial element in the Y direction

(leave blank if the uniaxial element is in the X direction

only);

FN(K) = Initial normal force at the sliding interface.

A.6.4.7 Hysteretic Nonlinear Stiffening Elements (Not available in this version)

A.6.4.8 Nonlinear Viscous Element·

(see Fig. AS for positioning definition)

INELEM(K,1:2) INELEM (K,1) can be either 1,2 or 3

INELEM(K,2) = 8 (Refer to A.6.4 for further details).

A-32

(PC(K,I), 1= 1,14)

PC(K,l) =Force offset for dampersAorBin range 1 (Fol in Eq. (2.9».

(To be determined from operation data of damper. Leave blank: if the

uniaxial element is in the B direction only);

PC(K,2) =Force offset for dampersAorB in range 2 (Fo2 in Eq. (2.9».

(To be determined from operation data of damper. Leave blank if

the uniaxial element is in the A direction only);

PC(K,3) = Nonlinear viscous constant for damper A in range 1 (ClA

in Eq. (2.9». (Leave blank: if the uniaxial element is in the B direction

only);

PC(K,4) = Nonlinear viscous constant for damper A in rallge 2 (C2A

in Eq. (2.9». (Leave blank if the uniaxial element is in the B direction

only);

PC(K,5) = Limit velocity for transition from range 1 to 2 in A direction

(V 12)A- (Leave blank ifthe uniaxial element is in the B direction only);

PC(K,6) = Nonlinear viscous constant for damper B in range 1 (ClB

in (Eq. 2.9». (Leave blank if the uniaxial element is in the A direction

only);

PC(K,7) = Nonlinear viscous constant for damper B in range 2 (C2B

in (Eq. 2.9». (Leave blank if the uniaxial element is in the A direction

only);

PC(K,S) =Limit velocity for transition from range 1 to 2 in B direction

(V12)B' (Leave blank if the uniaxial element is in the A direction only);

PC(K,9) = Power (integer or fractional) for the velocity in range 1

for either dampers A or B (PI in Eq. (2.9»);

PC(K,10) = Power (integer or fractional) for the velocity in range 2

for either dampers A or B (P2 in Eq. (2.9»;

A-33

PC(K,ll) = Maximum damper force (operational limitation) for

either one of dampers A or B (Fdmax in Eq. (2.9».

PC(K,12) = Displacement limit for damper operation start at low

velocities and displacements for either A or B.

PC(K,13) = Orientation angle 8 for damper A with x axis in degrees

(-180° ~ 8 ~ 180°)

PC(K,14) = Orientation angle 8 for damper B with x axis in degrees

(-180° ~ e ~ 180°)

*Note: This model is suitable for a cluster of two (horizontal) dampers A and B oriented

at an arbitrary angle to each other and to the building. The dampers have different nonlinear

properties, but same maximum and same offset constants).

A.6.5 Coordinates of Isolation Elements

USR TXT Reference information; upto 80 characters of text.

XP(I),YP(I),I =1,NP

XP(I) = X Coordinate of isolation

element I from the center of mass

of the base.

YP(I) = Y Coordinate of isolation

element I from the center of mass

of the base.

A-34

A.7 OUTPUT INFORMATION DATA

A.7.1 Output Parameters

USR TXT Reference information; upto 80 characters of text.

LTMH,KPD,IP1,IP2,IP3,IP4,

LTMH = afor both the time history and peak

response output.

LTMH = 1 for only peak response output.

KPD = No. of time steps before the next

response quantity is output.

IP1,IP2, IP3, IP4 = Bearing numbers of four

bearings at which the peak response values

and the force - displacement time history

response is desired.

A.7.2 Interstory drift output

USR TXT Reference information; upto 80 characters of text.

CORDX(K), CORDY(K),K= 1,6

CORDX(K) = X coordinate of the column line

K at which the interstory drift is desired.

CORDY(K) = Y coordinate of the column line

K at which the interstory drift is desired.

Note: 1. The coordinates of the column lines are with respect to the reference axis at the

center of mass of the base. Six column lines can be specified.

A-35

A.S LOAD CASE DEFINITION:

USR TXT Reference information; upto 80 characters of text.

[XM(1,L),XM(2,L),XM(3,L),XM(4,L), L= 1,NLD]

XM(l,L) = Multiplier for vertical load case I

XM(2,L) = Multiplier for vertical load case II

XM(3,L) = Multiplier for vertical load case III

XM(4,L) = Multiplier for earthquake resporise

Note: Load cases for the complete building are defined as a combination of vertical load

conditions (1,11,111), and earthquake loading. One card must be entered in this section for

each different building load case; the total number of building load cases is controlled by

the control information in section A.4.2.

A.9 EARTHQUAKE DATA

This information has to be specified in additional tiles outside the main input data tile

(e.g., WAVEXPl.DAT and WAVEVPl.DAT).

A.9.1 Unidirectional or Bidirectional Earthquake Record

Note: the following data has to be specified in the file which the user defined at the start

of the user manual in section Al e.g., in the file WAVEX.DAT

XCI),! = 1,LOR X(I) = Unidirectional acceleration component.

Note: l.If INDGACC as specified in A.4.5 is 1, then the input will be assumed at an angle

XTH specified in A4.5. If INDGACC as ~pecified in A4.5 is 2,3, or 4 then X(LOR) is

considered to be the X component of the bidirectional or tridirectional earthquake.

A-36

A.9.2 Earthquake Record in the Y Direction f«;lr the Bidirectional

Earthquake (Input only if INDGACC = 2 or 4)

Note: the following data has to be specified in the file which the user defined at the start

of the user manual in section Al e.g., in the file WAVEY.DAT

Y(1,1),1 =I,LOR Y(1,1) = Acceleration component in the Y direction.

A.9.3 Earthquake Record in the Z Direction for the Bidirectional or tridirectional Earthquake

(Input only if INDGACC=3 or 4)

Note: The following data has to be specified in the file which the user defined at the start

of the user manual in section A.I e.g., in the file

WAVEZ.DAT

Y(I,2), 1= I,LOR Y(I,2) = Acceleration component in the Z direction.

A.tO Execution Instructions

Check the README file in the distribution disk for details on execution of program.

A-37

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-27

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 tothe Publications Department, National Center for Earthquake Engineering Research, State University of New York at Buffalo,Red Jacket 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 "First-Year Program in Research, Education and Technology Transfer," 3/5/87, (PB88-134275).

NCEER-87-0002 "Experimental Evaluation of Instantaneous Optimal Algorithms for Structural Control," by R.C. Lin, T.T.Soong and A.M. Reinhorn, 4/20/87, (PB88-134341).

NCEER-87-0003 "Experimentation Using the Earthquake Simulation Facilities at University at Buffalo," by A.M. Reinhornand R.L. Ketter, to be published.

NCEER-87-0004 "The System Characteristics and Performance of a Shaking Table," by J.S. Hwang, K.C. Chang and G.C.Lee, 6/1/87, (PB88-134259). This report is available only through NTIS (see address given above).

NCEER-87-0005 "A Finite Element Formulation for Nonlinear Viscoplastic Material Using a Q Model," by O. Gyebi andG. Dasgupta, 11/2/87, (PB88-213764).

NCEER-87-0006 "Symbolic Manipulation Program (SMP) - Algebraic Codes for Two and Three Dimensional FiniteElement Formulations," by X. Lee and G. Dasgupta, 11/9/87, (PB88-218522).

NCEER-87-0007 "Instantaneous Optimal Control Laws for Tall Buildings Under Seismic Excitations," by J.N. Yang, A.Akbarpour and P. Ghaemmaghami, 6/10/87, (PB88-134333). This report is only available through NTIS(see address given above).

NCEER-87-0008 "IDARC: Inelastic Damage Analysis of Reinforced Concrete Frame - Shear-Wall Structures," by Y.J.Park, A.M. Reinhorn and S.K. Kunnath, 7/20/87, (PB88-134325).

NCEER-87-0009 "Liquefaction Potential for New York State: A Preliminary Report on Sites in Manhattan and Buffalo," byM. Budhu, V. Vijayakumar, R.F. Giese and L. Baumgras, 8/31/87, (PB88-163704). This report isavailable only through NTIS (see address given above).

NCEER-87-001O"Vertica1 and Torsional Vibration of Foundations in Inhomogeneous Media," by A.S. Veletsos and K.W.Dotson, 6/1/87, (pB88-134291).

NCEER-87-0011 "Seismic Probabilistic Risk Assessment and Seismic Margins Studies for Nuclear Power Plants," byHoward H.M. Hwang, 6/15/87, (PB88-134267).

NCEER-87-0012 "Parametric Studies of Frequency Response of Secondary Systems Under Ground-AccelerationExcitations," by Y. Yong and Y.K. Lin, 6/10/87, (PB88-134309).

NCEER-87-0013 "Frequency Response of Secondary Systems Under Seismic Excitation," by J.A. HoLung, 1. Cai and Y.K.Lin, 7/31/87, (PB88-134317).

NCEER-87-00l4 "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).

NCEER-87-0015 "Detection and Assessment of Seismic Structural Damage," by E. DiPasquale and A.S. Cakmak, 8/25/87,(PB88-163712).

H-l

NCEER-87-0016 "Pipeline Experiment at Parkfield, California," by J. Isenberg and E. Richardson, 9/15/87, (PB88-163720).This report is available only through NTIS (see address given above).

NCEER-87-0017 "Digital Simulation of Seismic Ground Motion," by M. Shinozuka, G. Deodatis and T. Harada, 8/31/87,(PB88-155197). This report is available only through NTIS (see address given above).

NCEER-87-0018 "Practical Considerations for Structural Control: System Uncertainty, System Time Delay and Truncationof Small Control Forces," J.N. Yang and A...Akbarpour, 8/10/87, (PB88-163738).

NCEER-87-0019 "Modal Analysis of Nonclassically Damped Structural Systems Using Canonical Transformation," by J.N.Yang, S. Sarkani and F.X. Long, 9/27/87, (PB88-187851).

NCEER-87-0020 "A Nonstationary Solution in Random Vibration Theory," by J.R. Red-Horse and P.D. Spanos, 11/3/87,(PB88-163746).

NCEER-87-0021 "Horizontal Impedances for Radially Inhomogeneous Viscoelastic Soil Layers," by A.S. Veletsos andK.W. Dotson, 10/15/87, (PB88-150859).

NCEER-87-0022 "Seismic Damage Assessment of Reinforced Concrete Members," by Y.S. Chung, C. Meyer and M.Shinozuka, 10/9/87, (PB88-150867). This report is available only through NTIS (see address given above).

NCEER-87-0023 "Active Structural Control in Civil Engineering," by T.T. Soong, 11/11/87, (PB88-187778).

NCEER-87-0024 "Vertical and Torsional Impedances for Radially Inhomogeneous Viscoelastic Soil Layers," by K.W.Dotson and A.S. Veletsos, 12/87, (PB88-187786).

NCEER-87-0025 "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).

NCEER-87-0026 "Report on the Whittier-Narrows, California, Earthquake of October 1, 1987," by J. Pantelic and A.Reinhorn, 11/87, (PB88-187752). This report is available only through NTIS (see address given above).

NCEER-87-0027 "Design of a Modular Program for Transient Nonlinear Analysis of Large 3-D Building Structures," by S.Srivastav and J.F. Abel, 12/30/87. (PB88-187950).

NCEER-87-0028 "Second-Year Program in Research, Education and Technology Transfer," 3/8/88, (PB88-219480).

NCEER-88-0001 "Workshop on Seismic Computer Analysis and Design of Buildings With Interactive Graphics," by W.McGuire, J.F. Abel and C.H. Conley, 1/18/88, (PB88-187760).

NCEER-88-0002 "Optimal Control of Nonlinear Flexible Structures," by J.N. Yang, F.X. Long and D. Wong, 1/22/88,(PB88-213772).

NCEER-88-0003 "Substructuring Techniques in the Time Domain for Primary-Secondary Structural Systems," by G.D.Manolis and G. JOOn, 2/10/88, (PB88-213780).

NCEER-88-0004 "Iterative Seismic Analysis of Primary-Secondary Systems," by A. Singhal, L.D. Lutes and P.D. Spanos,2/23/88, (PB88-213798).

NCEER-88-0005 "Stochastic Finite Element Expansion for Random Media," by P.D. Spanos and R. Ghanem, 3/14/88,(PB88-213806).

NCEER-88-0006 "Combining Structural Optimization and Structural Control," by F.Y. Cheng and C.P. Pantelides, 1/10/88,(PB88-213814).

H-2

NCEER-88-0007 "Seismic Perfonnance Assessment of Code-Designed Structures," by H.H-M. Hwang, J-W. Jaw and H-J.Shau, 3/20/88, (PB88-219423).

NCEER-88-0008 "Reliability Analysis of Code-Designed Structures Under Natural Hazards," by H.H-M. Hwang, H. Ushibaand M. Shinozuka, 2/29/88, (PB88-229471).

NCEER-88-0009 "Seismic Fragility Analysis of Shear Wall Structures," by J-W Jaw and H.H-M. Hwang, 4/30/88, (PB89­102867).

NCEER-88-001O "Base Isolation of a Multi-Story Building Under a Hannonic Ground Motion - A Comparison ofPerformances of Various Systems," by F-G Fan, G. Ahmadi and I.G. Tadjbakhsh, 5118/88, (PB89­122238).

NCEER-88-0011 "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, (PB89-102875).

NCEER-88-0012 "A New Solution Technique for Randomly Excited Hysteretic Structures," by G.Q. Cai and Y.K. Lin,5/16/88, (PB89-102883).

NCEER-88-0013 "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).

NCEER-88-0014 "Parameter Identification and Implementation of a Kinematic Plasticity Model for Frictional Soils," by J.H.Prevost and D. V. Griffiths, to be published.

NCEER-88-0015 "Two- and Three- Dimensional Dynamic Finite Element Analyses of the Long Valley Dam," by D.V.Griffiths and J.H. Prevost, 6/17/88, (PB89-144711).

NCEER-88-0016 "Damage Assessment of Reinforced Concrete Structures in Eastern United States," by A.M. Reinhorn,M.J. Seidel, S.K. Kunnath and Y.I. Park, 6/15/88, (PB89-122220).

NCEER-88-0017 "Dynamic Compliance of Vertically Loaded Strip Foundations in Multilayered Viscoelastic Soils," by S.Ahmad and A.S.M. Israil, 6117/88, (PB89-102891).

NCEER-88-0018 "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). This report is available only throughNTIS (see address given above).

NCEER-88-0019 "Experimental Investigation of Primary - Secondary System Interaction," by G.D. Manolis, G. Juhn andA.M. Reinhorn, 5/27/88, (PB89-122204).

NCEER-88-0020 "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).

NCEER-88-0021 "Seismic Interaction of Structures and Soils: Stochastic Approach," by A.S. Veletsos and A.M. Prasad,7/21/88, (PB89-122196).

NCEER-88-0022 "Identification of the Serviceability Limit State and Detection of Seismic Structural Damage," by E.DiPasquale and A.S. Cakmak, 6/15/88, (PB89-122188). This report is available only through NTIS (seeaddress given above).

NCEER-88-0023 "Multi-Hazard Risk Analysis: Case of a Simple Offshore Structure," by B.K. Bhartia and E.H.Vanmarcke, 7/21/88, (PB89-145213).

NCEER-88-0024 "Automated Seismic Design of Reinforced Concrete Buildings," by Y.S. Chung, C. Meyer and M.Shinozuka, 7/5/88, (pB89-122170). This report is available only through NTIS (see address given above).

H-3

NCEER-88-0025 "Experimental Study of Active Control of MDOF Structures Under Seismic Excitations," by L.L. Chung,R.C. Lin, T.T. Soong and A.M. Reinhorn, 7110/88, (PB89-122600).

NCEER-88-0026 "Earthquake Simulation Tests of a Low-Rise Metal Structure," by J.S.Hwang, K.C. Chang, G.C. Lee andR.L. Ketter, 8/1/88, (PB89-102917).

NCEER-88-0027 "Systems Study of Urban Response and Reconstruction Due to Catastrophic Earthquakes," by F. Kozin andH.K. Zhou, 9/22/88, (PB90-162348).

NCEER-88-0028 "Seismic Fragility Analysis of Plane Frame Structures," by H.H-M. Hwang and Y.K. Low, 7/31/88,(PB89-131445) .

NCEER-88-0029 "Response Analysis of Stochastic Structures," by A. Kardara, C. Bucher and M. Shinozuka, 9/22/88,(PB89-174429) .

NCEER-88-0030 "Nonnormal Accelerations Due to Yielding in a Primary Structure," by D.C.K. Chen and L.D. Lutes,9/19/88, (PB89-131437).

NCEER-88-0031 "Design Approaches for Soil-Structure Interaction," by A.S. Veletsos, A.M. Prasad and Y. Tang,12/30/88, (PB89-174437). This report is available only through NTIS (see address given above).

NCEER-88-0032 "A Re-evaluation of Design Spectra for Seismic Damage Control," by C.l. Turkstra and A.G. TaIlin,11/7/88, (PB89-145221).

NCEER-88-0033 "The Behavior and Design of Noncontact Lap Splices Subjected to Repeated Inelastic Tensile Loading," byV.E. Sagan, P. Gergely and R.N. White, 12/8/88, (PB89-163737).

NCEER-88-0034 "Seismic Response of Pile Foundations," by S.M. Mamoon, P.K. Banerjee and S. Ahmad, 11/1/88,(PB89-145239) .

NCEER-88-0035 "Modeling of R/C Building Structures With Flexible Floor Diaphragms (IDARC2), " by A.M. Reinhorn,S.K. Kunnath and N. Panahshahi, 9/7/88, (PB89-207153).

NCEER-88-0036 "Solution of the Dam-Reservoir Interaction Problem Using a Combination of FEM, BEM with ParticularIntegrals, Modal Analysis, and Substructuring," by C-S. Tsai, G.C. Lee and R.L. Ketter, 12/31/88,(PB89-207146).

NCEER-88-0037 "Optimal Placement of Actuators for Structural Control," by F.Y. Cheng and C.P. Pantelides, 8/15/88,(PB89-162846) .

NCEER-88-0038 "Teflon Bearings in Aseismic Base Isolation: Experimental Studies and Mathematical Modeling," by A.Mokha, M.C. Constantinou and A.M. Reinhorn, 12/5/88, (PB89-218457). This report is available onlythrough NTIS (see address given above).

NCEER-88-0039 "Seismic Behavior of Flat Slab High-Rise Buildings in the New York City Area," by P. Weidlinger and M.Ettouney, 10/15/88, (PB90-145681).

NCEER-88-0040 "Evaluation of the Earthquake Resistance of Existing Buildings in New York City," by P. Weidlinger andM. Ettouney. 10/15/88, to be published.

NCEER-88-0041 "Small-Scale Modeling Techniques for Reinforced Concrete Structures Subjected to Seismic Loads," by W.Kim, A. EI-Attar and R.N. White, 11/22/88, (PB89-189625).

NCEER-88-0042 "Modeling Strong Ground Motion from Multiple Event Earth,quakes," by G.W. Ellis and A.S. Cakmak,10/15/88, (PB89-174445).

H-4

NCEER-88-0043 "Nonstationary Models of Seismic Ground Acceleration," by M. Grigoriu, S.E. Ruiz and E. Rosenblueth,7/15/88, (PB89-189617).

NCEER-88-0044 "SARCF User's Guide: Seismic Analysis of Reinforced Concrete Frames," by Y.S. Chung, C. Meyer andM. Shinozuka, 11/9/88, (PB89-174452).

NCEER-88-0045 "First Expert Panel Meeting on Disaster Research and Planning," edited by J. Pantelic and J. Stoyle,9115/88, (PB89-174460).

NCEER-88-0046 "Preliminary Studies of the Effect of Degrading Infill Walls on the Nonlinear Seismic Response of SteelFrames," by C.Z. Chrysostomou, P. Gergely and J.P. Abel, 12/19/88, (PB89-208383).

NCEER-88-0047 "Reinforced Concrete Frame Component Testing Facility - Design, Construction, Instrumentation andOperation," by S.P. Pessiki, C. Conley, T. Bond, P. Gergely and R.N. White, 12116/88, (PB89-174478).

NCEER-89-0001 "Effects of Protective Cushion and Soil Compliancy on the Response of Equipment Within a SeismicallyExcited Building," by J.A. HoLung, 2116/89, (PB89-207179).

NCEER-89-0002 "Statistical Evaluation of Response Modification Factors for Reinforced Concrete Structures," by H.H-M.Hwang and J-W. Jaw, 2/17189, (PB89-207187).

NCEER-89-0003 "Hysteretic Columns Under Random Excitation," by G-Q. Cai and Y.K. Lin, 1/9/89, (PB89-196513).

NCEER-89-0004 "Experimental Study of 'Elephant Foot Bulge' Instability of Thin-Walled Metal Tanks," by Z-H. Jia andR.L. Ketter, 2/22/89, (PB89-207195).

NCEER-89-0005 "Experiment on Perfonnance of Buried Pipelines Across San Andreas Fault," by J. Isenberg, E.Richardson and T.D. O'Rourke, 3/10/89, (PB89-218440). This report is available only through NTIS (seeaddress given above).

NCEER-89-0006 "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).

NCEER-89-0007 "Liquefaction Hazards and Their Effects on Buried Pipelines," by T.D. O'Rourke and P.A. Lane, 2/1/89,(PB89-218481).

NCEER-89-0008 "Fundamentals of System Identification in Structural Dynamics," by H. Imai, CoB. Yun, O. Maruyama andM. Shinozuka, 1/26/89, (PB89-207211).

NCEER-89-0009 "Effects of the 1985 Michoacan Earthquake on Water Systems and Other Buried Lifelines in Mexico," byA.G. Ayala and MJ. O'Rourke, 3/8/89, (PB89-207229).

NCEER-89-ROlO "NCEER Bibliography of Earthquake Education Materials," by K.E.K. Ross, Second Revision, 9/1/89,(PB90-125352) .

NCEER-89-0011 "Inelastic Three-Dimensional Response Analysis of Reinforced Concrete Building Structures (!DARC-3D) ,Part I - Modeling," by S.K. Kunnath and A.M. Reinhorn, 4/17/89, (pB90-114612).

NCEER-89-0012 "Recommended Modifications to ATC-14," by C.D. Poland and J.O. Malley, 4/12/89, (PB90-108648).

NCEER-89-0013 "Repair and Strengthening of Beam-to-Column Connections Subjected to Earthquake Loading," by M.Corazao and AJ. Durrani, 2/28/89, (pB90-109885).

NCEER-89-Q014 "Program EXKAL2 for Identification of Structural Dynamic Systems," by O. Maruyama, CoB. Yun, M.Hoshiya and M. Shinozuka, 5119/89, (pB90-109877).

H-5

NCEER-89-0015 "Response of Frames With Bolted Semi-Rigid Connections, Part I - Experimental Study and AnalyticalPredictions," by P.J. DiCorso, A.M. Reinhorn, J.R. Dickerson, lB. Radziminski and W.L. Harper,6/1189, to be published.

NCEER-89-0016 "ARMA Monte Carlo Simulation in Probabilistic Structural Analysis," by P.D. Spanos and M.P.Mignolet, 7/10/89, (PB90-109893).

NCEER-89-POI7 "Preliminary Proceedings from the Conference on Disaster Preparedness - The Place of EarthquakeEducation in Our Schools," Edited by KE.K. Ross, 6/23/89, (PB90-108606).

NCEER-89-0017 - "Proceedings from the Conference on Disaster Preparedness - The Place of Earthquake Education in OurSchools," Edited by KE.K Ross, 12/31189, (PB90-207895). This report is available only through NTIS(see address given above).

NCEER-89-0018 "Multidimensional Models of Hysteretic Material Behavior for Vibration Analysis of Shape MemoryEnergy Absorbing Devices, by EJ. Graesser and F.A. Cozzarelli, 617/89, (PB90-164 146).

NCEER-89-0019 "Nonlinear Dynamic Analysis of Three-Dimensional Base Isolated Structures (3D-BASIS)," by S.Nagarajaiah, A.M. Reinhorn and M.C. Constantinou, 8/3/89, (PB90-16l936). This report is availableonly through NTIS (see address given above).

NCEER-89-0020 "Structural Control Considering Time"Rate of Control Forces and Control Rate Constraints," by F.Y.Cheng and C.P. Pantelides, 8/3/89, (PB90-120445).

NCEER-89-0021 "Subsurface Conditions of Memphis and Shelby County," by K.W. Ng, T-S. Chang and H-H.M. Hwang,7/26/89, (PB90-l20437).

NCEER-89-0022 "Seismic Wave Propagation Effects on Straight Jointed Buried Pipelines," by K Elhmadi and MJ.O'Rourke, 8/24/89, (PB90-l62322).

NCEER-89-0023 "Workshop on Serviceability Analysis of Water Delivery Systems," edited by M. Grigoriu, 3/6/89, (PB90­127424).

NCEER-89-0024 "Shaking Table Study of a 115 Scale Steel Frame Composed of Tapered Members," by K.C. Chang, J.S.Hwang and G.C. Lee, 9/18/89, (PB90-160169).

NCEER-89-0025 "DYNAID: A Computer Program for Nonlinear Seismic Site Response Analysis - TechnicalDocumentation," by Jean H. Prevost, 9/14/89, (PB90-161944). This report is available only through NTIS(see address given above).

NCEER-89-0026 "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, (PB90­173246).

NCEER-89-0027 "Scattering of Waves by Inclusions in a Nonhomogeneous Elastic Half Space Solved by Boundary ElementMethods," by P.K Hadley, A. Askar and A.S. Cakmak, 6/15/89, (PB90-145699).

NCEER-89-0028 "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, (PB90-164633).

NCEER-89-0029 "Bedrock Accelerations in Memphis Area Due to Large New Madrid Earthquakes," by H.H.M. Hwang,C.H.S. Chen and G. Yu, 11/7/89, (PB90-162330).

NCEER-89-0030 "Seismic Behavior and Response Sensitivity of Secondary Structural Systems," by Y.Q. Chen and T.T.Soong, 10/23/89, (PB90-164658).

H-6

NCEER-89-0031 "Random Vibration and Reliability Analysis of Primary-Secondary Structural Systems," by Y. Ibrahim, M.Grigoriu and T.T. Soong, 11/10/89, (PB90-161951).

NCEER-89-0032 "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, 1211/89,(pB90-209388).

NCEER-89-0033 "Deterministic Model for Seismic Damage Evaluation of Reinforced Concrete Structures," by J.M. Bracci,A.M. Reinhorn, J.B. Mander and S.K. Kunnath, 9/27/89.

NCEER-89-0034 "On the Relation Between Local and Global Damage Indices," by E. DiPasquale and A.S. Cakmak,8115/89, (PB90-173865).

NCEER-89-0035 "Cyclic Undrained Behavior of Nonplastic and Low Plasticity Silts," by A.J. Walker and H.E. Stewart,7/26/89, (PB90-183518).

NCEER-89-0036 "Liquefaction Potential of Surficial Deposits in the City of Buffalo, New York," by M. Budhu, R. Gieseand L. Baumgrass, 1/17/89, (PB90-208455).

NCEER-89-0037 "A Deterministic Assessment of Effects of Ground Motion Incoherence," by A.S. Veletsos and Y. Tang,7/15/89, (PB90-164294).

NCEER-89-0038 "Workshop on Ground Motion Parameters for Seismic Hazard Mapping," July 17-18, 1989, edited by R.V.Whitman, 12/1/89, (PB90-173923).

NCEER-89-0039 "Seismic Effects on Elevated Transit Lines of the New York City Transit Authority," by C.J. Costantino,C.A. Miller and E. Heymsfield, 12/26/89, (PB90-207887).

NCEER-89-0040 "Centrifugal Modeling of Dynamic Soil-Structure Interaction," by K. Weissman, Supervised by J.H.Prevost, 5/10/89, (PB90-207879).

NCEER-89-0041 "Linearized Identification of Buildings With Cores for Seismic Vulnerability Assessment," by I-K. Ho andA.E. Aktan, 11/1/89, (PB90-251943).

NCEER-90-0001 "Geotechnical and Lifeline Aspects of the October 17, 1989 Lorna Prieta Earthquake in San Francisco," byT.D. O'Rourke, H.E. Stewart, F.T. Blackburn and T.S. Dickerman, 1/90, (PB90-208596).

NCEER-90-0002 "Nonnormal Secondary Response Due to Yielding in a Primary Structure," by D.C.K. Chen and L.D.Lutes, 2/28/90, (PB90-251976).

NCEER-90-0003 ';Earthquake Education Materials for Grades K-12," by K.E.K. Ross, 4/16/90, (PB91-251984).

NCEER-90-0004 "Catalog of Strong Motion Stations in Eastern North America," by R.W. Busby, 4/3/90, (PB90-251984).

NCEER-90-0005 "NCEER Strong-Motion Data Base: A User Manual for the GeoBase Release (Version 1.0 for the Sun3),"by P. Friberg and K. Jacob, 3/31/90 (PB90-258062).

NCEER-90-0006 "Seismic Hazard Along a Crude Oil Pipeline in the Event of an 1811-1812 Type New Madrid Earthquake,"by H.H.M. Hwang and C-H.S. Chen, 4/16/90(PB90-258054).

NCEER-90-0007 "Site-Specific Response Spectra for Memphis Sheahan Pumping Station," by H.H.M. Hwang and C.S.Lee, 5115/90, (PB91-108811).

NCEER-90-0008 "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 and M. Shinozuka, 5/25/90, (pB91-108837).

H-7

NCEER-90-0009 "A Program to Generate Site Dependent Time Histories: EQGEN," by G.W. Ellis, M. Srinivasan and A.S.Cakmak, 1/30/90, (PB91-108829).

NCEER-90-00lO "Active Isolation for Seismic Protection of Operating Rooms," by M.E. Talbott, Supervised by M.Shinozuka, 6/8/9, (PB91-110205).

NCEER-90-0011 "Program LINEARID for Identification of Linear Structural Dynamic Systems," by C-B. Yun and M.Shinozuka, 6/25/90, (PB91-110312).

NCEER-90-0012 "Two-Dimensional Two-Phase Elasto-Plastic Seismic Response of Earth Dams," by A.N. Yiagos,Supervised by J.H. Prevost, 6/20/90, (PB91-110197).

NCEER-90-0013 "Secondary Systems in Base-Isolated Structures: Experimental Investigation, Stochastic Response andStochastic Sensitivity," by G.D. Manolis, G. Juhn, M.e. Constantinou and A.M. Reinhorn, 7/1/90,(PB91-110320).

NCEER-90-0014 "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).

NCEER-90-0015 "Two Hybrid Control Systems for Building Structures Under Strong Earthquakes," by J.N. Yang and A.Danielians, 6/29/90, (PB91-125393).

NCEER-90-0016 "Instantaneous Optimal Control with Acceleration and Velocity Feedback," by J.N. Yang and Z. Li,6/29/90, (PB91-125401).

NCEER-90-0017 "Reconnaissance Report on the Northern Iran Earthquake of June 21, 1990," by M. Mehrain, 10/4/90,(PB91-125377).

NCEER-90-0018 "Evaluation of Liquefaction Potential in Memphis and Shelby County," by T.S. Chang, P.S. Tang, C.S.Lee and H. Hwang, 8110/90, (PB91-125427).

NCEER-90-0019 "Experimental and Analytical Study of a Combined Sliding Disc Bearing and Helical Steel Spring IsolationSystem," by M.C. Constantinou, A.S. Mokha and A.M. Reinhorn, 10/4/90, (PB91-125385).

NCEER-90-0020 "Experimental Study and Analytical Prediction of Earthquake Response of a Sliding Isolation System with aSpherical Surface," by A.S. Mokha, M.C. Constantinou and A.M. Reinhorn, 10/11/90, (PB91-125419).

NCEER-90-0021 "Dynamic Interaction Factors for Floating Pile Groups," by G. Gazetas, K. Fan, A. Kaynia and E. Kausel,9/10/90, (PB91-170381).

NCEER-90-0022 "Evaluation of Seismic Damage Indices for Reinforced Concrete Structures," by S. Rodriguez-Gomez andA.S. Cakmak, 9/30/90, PB91-171322).

NCEER-90-0023 "Study of Site Response at a Selected Memphis Site," by H. Desai, S. Ahmad, E.S. Gazetas and M.R. Oh,10/11/90, (PB91-196857).

NCEER-90-0024 "A User's Guide to Strongmo: Version 1.0 of NCEER's Strong-Motion Data Access Tool for PCs andTerminals," by P.A. Friberg and C.A.T. Susch, 11/15/90, (PB91-171272).

NCEER-90-0025 "A Three-Dimensional Analytical Study of Spatial Variability of Seismic Ground Motions," by L-L. Hongand A.H.-S. Ang, 10/30/90, (PB91-170399).

NCEER-90-0026 "MUMOID User's Guide - A Program for the Identification of Modal Parameters," by S. Rodriguez­Gomez and E. DiPasquale, 9/30/90, (PB91-171298).

NCEER-90-0027 "SARCF-II User's Guide - Seismic Analysis of Reinforced Concrete Frames," by S. Rodriguez-Gomez,Y.S. Chung and C. Meyer, 9/30/90, (PB91-171280).

H-8

NCEER-90-0028 "Viscous Dampers: Testing, Modeling and Application in Vibration and Seismic Isolation," by N. Makrisand M.C. Constantinou, 12/20/90 (PB91-190561).

NCEER-90-0029 "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).

NCEER-91-0001 "Proceedings from the Third Japan-U.S. Workshop on Earthquake Resistant Design of Lifeline Facilitiesand Countermeasures for Soil Liquefaction, December 17-19, 1990," edited by T.D. O'Rourke and M.Hamada, 2/1/91, (PB91-179259).

NCEER-91-0002 "Physical Space Solutions of Non-Proportionally Damped Systems," by M. Tong, Z. Liang and G.C. Lee,1/15/91, (PB91-179242).

NCEER-91-0003 "Seismic Response of Single Piles and Pile Groups," by K. Fan and G. Gazetas, 1/10/91, (PB92-174994).

NCEER-91-0004 "Damping of Structures; Part 1 - Theory of Complex Damping," by Z. Liang and G. Lee, 10/10/91,(PB92-197235).

NCEER-91-0005 "3D-BASIS - Nonlinear Dynamic Analysis of Three Dimensional Base Isolated Structures: Part II," by S.Nagarajaiah, A.M. Reinhorn and M.C. Constantinou, 2/28/91, (PB91-190553).

NCEER-91-0006 "A Multidimensional Hysteretic Model for Plasticity Deforming Metals in Energy Absorbing Devices," byE.l. Graesser and F.A. Cozzarelli, 4/9/91, (PB92-108364).

NCEER-91-0007 "A Framework for Customizable 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,(PB91-210930).

NCEER-91-0008 "Nonlinear Analysis of Steel Frames with Semi-Rigid Connections Using the Capacity Spectrum Method,"by G.G. Deierlein, SoH. Hsieh, Y-!. Shen and J.F. Abel, 7/2/91, (PB92-113828).

NCEER-91-0009 "Earthquake Education Materials for Grades K-12," by K.E.K. Ross, 4/30/91, (PB91-212142).

NCEER-91-001O "Phase Wave Velocities and Displacement Phase Differences in a Harmonically Oscillating Pile," by N.Makris and G. Gazetas, 7/8/91, (PB92-108356).

NCEER-91-0011 "Dynamic Characteristics of a Full-Size Five-Story Steel Structure and a 2/5 Scale Model," by K.C.Chang, G.C. Yao, G.C. Lee, D.S. Hao and Y.C. Yeh," 7/2/91, (PB93-116648).

NCEER-91-0012 "Seismic Response of a 2/5 Scale Steel Structure with Added Viscoelastic Dampers," by K.C. Chang, T.T.Soong, SoT. Oh and M.L. Lai, 5/17/91, (PB92-110816).

NCEER-91-0013 "Eanhquake Response of Retaining Walls; Full-Scale Testing and Computational Modeling," by S.Alampalli and A-W.M. Elgamal, 6120/91, to be published.

NCEER-91-0014 "3D-BASIS-M: Nonlinear Dynamic Analysis of Multiple Building Base Isolated Structures," by P.C.Tsopelas, S. Nagarajaiah, M.C. Constantinou and A.M. Reinhorn, 5/28/91, (PB92-113885).

NCEER-91-0015 "Evaluation of SEAOC Design Requirements for Sliding Isolated Structures," by D. Theodossiou and M.C.Constantinou, 6110/91, (PB92-114602).

NCEER-91-0016 "Closed-Loop Modal Testing of a 27-Story Reinforced Concrete Flat Plate-Core Building," by H.R.Somaprasad, T. Toksoy, H. Yoshiyuki and A.E. Aktan, 7115/91, (PB92-129980).

NCEER-91-0017 "Shake Table Test of a 1/6 Scale Two-Story Lightly Reinforced Concrete Building," by A.G. El-Attar,R.N. White and P. Gergely, 2/28/91, (PB92-222447).

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NCEER-91-0018 "Shake Table Test of a 118 Scale Three-Story Lightly Reinforced Concrete Building," by A.G. EI-Attar,R.N. White and P. Gergely, 2/28/91, (PB93-116630).

NCEER-91-0019 "Transfer Functions for Rigid Rectangular Foundations," by A.S. Veletsos, A.M. Prasad and W.H. Wu,7/31191.

NCEER-91-0020 "Hybrid Control of Seismic-Excited Nonlinear and Inelastic Structural Systems," by LN. Yang, Z. Li andA. Danielians, 8/1/91, (PB92-143171).

NCEER-91-0021 "The NCEER-91 Earthquake Catalog: Improved Intensity-Based Magnitudes and Recurrence Relations forU.S. Earthquakes East of New Madrid," by L. Seeber and J.G. Armbruster, 8/28/91, (PB92-176742).

NCEER-91-0022 "Proceedings from the Implementation of Earthquake Planning and Education in Schools: The Need forChange - The Roles of the Changemakers, " by K.E.K. Ross and F. Winslow, 7/23/91, (PB92-129998).

NCEER-91-0023 "A Study of Reliability-Based Criteria for Seismic Design of Reinforced Concrete Frame Buildings," byH.H.M. Hwang and H-M. Hsu, 8/10/91, (PB92-140235).

NCEER-91-0024 "Experimental Verification of a Number of Structural System Identification Algorithms," by R.G.Ghanem, H. Gavin and M. Shinozuka, 9/18/91, (PB92-176577).

NCEER-91-0025 "Probabilistic Evaluation of Liquefaction Potential," by H.H.M. Hwang and C.S. Lee," 11/25/91, (PB92­143429).

NCEER-91-0026 "Instantaneous Optimal Control for Linear, Nonlinear and Hysteretic Structures - Stable Controllers," byLN. Yang and Z. Li, 11/15/91, (PB92-163807).

NCEER-91-0027 "Experimental and Theoretical Study of a Sliding Isolation System for Bridges," by M.C. Constantinou, A.Kartoum, A.M. Reinhorn and P. Bradford, 11115/91, (PB92-176973).

NCEER-92-0001 "Case Studies of Liquefaction and Lifeline Performance During Past Earthquakes, Volume 1: JapaneseCase Studies," Edited by M. Hamada and T. O'Rourke, 2/17/92, (PB92-197243).

NCEER-92-0002 "Case Studies of Liquefaction and Lifeline Performance During Past Earthquakes, Volume 2:, United StatesCase Studies," Edited by T. O'Rourke and M. Hamada, 2/17/92, (PB92-197250).

NCEER-92-0003 "Issues in Earthquake Education," Edited by K. Ross, 2/3/92, (PB92-222389).

NCEER-92-0004 "Proceedings from the First U.S. - Japan Workshop on Earthquake Protective Systems for Bridges," Editedby I.G. Buckle, 2/4/92, (PB94-142239, A99, MF-A06).

NCEER-92-0005 "Seismic Ground Motion from a Haskell-Type Source in a Multiple-Layered Half-Space," A.P. Theoharis,G. Deodatis and M. Shinozuka, 112/92, to be published.

NCEER-92-0006 "Proceedings from the Site Effects Workshop," Edited by R. Whitman, 2/29/92, (PB92-197201).

NCEER-92-0007 "Engineering Evaluation of Permanent Ground Deformations Due to Seismically-Induced Liquefaction," byM.H. Baziar, R. Dobry and A-W.M. Elgamal, 3/24/92, (PB92-222421).

NCEER-92-0008 "A Procedure for the Seismic Evaluation of Buildings in the Central and Eastern United States," by C.D.Poland and J.O. Malley, 4/2/92, (PB92-222439).

NCEER-92-0009 "Experimental and Analytical Study of a Hybrid Isolation System Using Friction Controllable SlidingBearings," by M.Q. Feng, S. Fujii and M. Shinozuka, 5/15/92, (PB93-150282).

NCEER-92-0010 "Seismic Resistance of Slab-Column Connections in Existing Non-Ductile Flat-Plate Buildings," by A.J.Durrani and Y. Du, 5/18/92.

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NCEER-92-0011 "The Hysteretic and Dynamic Behavior of Brick Masonry Walls Upgraded by Ferrocement Coatings UnderCyclic -Loading and Strong Simulated Ground Motion," by H. Lee and S.P. Prawel, 5/11/92, to bepublished.

NCEER-92-0012 "Study of Wire Rope Systems for Seismic Protection of Equipment in Buildings," by G.F. Demetriades,M.C. Constantinou and A.M. Reinhorn, 5/20/92.

NCEER-92-0013 "Shape Memory Structural Dampers: Material Properties, Design and Seismic Testing," by P.R. Wittingand F.A. Cozzarelli, 5/26/92.

NCEER-92-0014 "Longitudinal Permanent Ground Deformation Effects on Buried Continuous Pipelines," by M.J.O'Rourke, and C. Nordberg, 6/15/92.

NCEER-92-0015 "A Simulation Method for Stationary Gaussian Random Functions Based on the Sampling Theorem," byM. Grigoriu and S. Balopoulou, 6/11/92, (PB93-127496). .

NCEER-92-0016 "Gravity-Load-Designed Reinforced Concrete Buildings: Seismic Evaluation of Existing Construction andDetailing Strategies for Improved Seismic Resistance," by G. W. Hoffmann, S.K. Kunnath, A.M. Reinhornand LB. Mander, 7/15/92, (PB94-142007, A08, MF-A02).

NCEER-92-0017 "Observations on Water System and Pipeline Performance in the Limon Area of Costa Rica Due to theApril 22, 1991 Earthquake," by M. O'Rourke and D. Ballantyne, 6/30/92, (PB93-126811).

NCEER-92-0018 "Fourth Edition of Earthquake Education Materials for Grades K-12," Edited by K.E.K. Ross, 8/10/92.

NCEER-92-0019 "Proceedings from the Fourth Japan-U.S. Workshop on Earthquake Resistant Design of Lifeline Facilitiesand Countermeasures for Soil Liquefaction," Edited by M. Hamada and T.D. O'Rourke, 8/12/92, (PB93­163939).

NCEER-92-0020 "Active Bracing System: A Full Scale Implementation of Active Control," by A.M. Reinhorn, T.T. Soong,R.C. Lin, M.A. Riley, Y.P. Wang, S. Aizawa and M. Higashino, 8/14/92, (PB93-127512).

NCEER-92-0021 "Empirical Analysis of Horizontal Ground Displacement Generated by Liquefaction-Induced LateralSpreads," by S.F. Bartlett and T.L. Youd, 8/17/92, (PB93-188241).

NCEER-92-0022 "!DARC Version 3.0: Inelastic Damage Analysis of Reinforced Concrete Structures," by S.K. Kunnath,A.M. Reinhorn and R.F. Lobo, 8/31/92, (PB93-227502, A07, MF-A02).

NCEER-92-0023 "A Semi-Empirical Analysis of Strong-Motion Peaks in Terms of Seismic Source, Propagation Path andLocal Site Conditions, by M. Kamiyama, M.J. O'Rourke and R. Flores-Berrones, 9/9/92, (PB93-150266).

NCEER-92-0024 "Seismic Behavior of Reinforced Concrete Frame Structures with Nonductile Details, Part I: Summary ofExperimental Fiqdings of Full Scale Beam-Column Joint Tests," by A. Beres, R.N. White and P. Gergely,9/30/92, (PB93-227783, A05, MF-A01).

NCEER-92-0025 "Experimental Results of Repaired and Retrofitted Beam-Column Joint Tests in Lightly ReinforcedConcrete Frame Buildings," by A. Beres, S. EI-Borgi, R.N. White and P. Gergely, 10/29/92, (PB93­227791, A05, MF-A01).

NCEER-92-0026 "A Generalization of Optimal Control Theory: Linear and Nonlinear Structures," by LN. Yang, Z. Li andS. Vongchavalitkul, 11/2/92, (PB93-188621).

NCEER-92-0027 "Seismic Resistance of Reinforced Concrete Frame Structures Designed Only for Gravity Loads: Part I ­Design and Properties of a One-Third Scale Model Structure," by I.M. Bracci, A.M. Reinhorn and J.B.Mander, 12/1/92, (PB94-104502, A08, MF-A02).

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NCEER-92-0028 "Seismic Resistance of Reinforced Concrete-- Frame Structures Designed Only for Gravity Loads: Part II ­Experimental Performance of Subassemblages," by L.E. Aycardi, J.B. Mander and A.M. Reinhorn,12/1/92, (PB94-10451O, A08, MF-A02).

NCEER-92-0029 "Seismic Resistance of Reinforced Concrete Frame Structures Designed Only for Gravity Loads: Part III ­Experimental Performance and Analytical Study of a Structural Model," by J.M. Bracci, A.M. Reinhomand 1.B. Mander, 12/1/92, (PB93-227528, A09, MF-A01).

NCEER-92-0030 "Evaluation of Seismic Retrofit of Reinforced Concrete Frame Structures: Part I - ExperimentalPerformance of Retrofitted Subassemblages, " by D. Choudhuri, J.B. Mander and A.M. Reinhorn, 12/8/92,(PB93-198307, A07, MF-A02).

NCEER-92-Q031 "Evaluation of Seismic Retrofit of Reinforced Concrete Frame Structures: Part II - ExperimenulPerformance and Analytical Study of a Retrofitted Structural Model," by J.M. Bracci, A.M. Reinhorn andJ.B. Mander, 12/8/92, (PB93-198315, A09, MF-A03).

NCEER-92-0032 "Experimental and Analytical Investigation of Seismic Response of Structures with Supplemental FluidViscous Dampers," by M.C. Constantinou and M.D. Symans, 12/21/92, (PB93-191435).

NCEER-92-0033 "Reconnaissance Report on the Cairo, Egypt Earthquake of October 12, 1992," by M. Khater, 12/23/92,(PB93-188621).

NCEER-92-0034 "Low-Level Dynamic Characteristics of Four Tall Flat-Plate Buildings in New York City," by H. Gavin,S. Yuan, J. Grossman, E. Pekelis and K. Jacob, 12/28/92, (PB93-188217).

NCEER-93-0001 "An Experimental Study on the Seismic Performance of Brick-Infilled Steel Frames With and WithoutRetrofit," by 1.B. Mander, B. Nair, K. Wojtkowski and 1. Ma, 1/29/93, (PB93-22751O, A07, MF-A02).

NCEER-93-0002 "Social Accounting for Disaster Preparedness and Recovery Planning," by S. Cole, E. Pantoja and V.Razak, 2/22/93, (PB94-142114, A12, MF-A03).

NCEER-93-0003 "Assessment of 1991 NEHRP Provisions for Nonstructural Components and Recommended Revisions," byT.T. Soong, G. Chen, Z. Wu, R-H. Zhang and M. Grigoriu, 3/1/93, (PB93-188639).

NCEER-93-0004 "Evaluation of Static and Response Spectrum Analysis Procedures of SEAOC/UBC for Seismic IsolatedStructures," by C.W. Winters and M.C. Constantinou, 3/23/93, (PB93-198299).

NCEER-93-0005 "Earthquakes in the Northeast - Are We Ignoring the Hazard? A Workshop on Earthquake Science andSafety for Educators," edited by K.E.K. Ross, 4/2/93, (PB94-103066, A09, MF-A02).

NCEER-93-0006 "Inelastic Response of Reinforced Concrete Structures with Viscoelastic Braces," by R.F. Lobo, 1.M.Bracci, K.L. Shen, A.M. Reinhom and T.T. Soong, 4/5/93, (PB93-227486, A05, MF-A02).

NCEER-93-0007 "Seismic Testing of Installation Methods for Computers and Data Processing Equipment," by K. Kosar,T.T. Soong, K.L. Shen, J.A. HoLung and Y.K. Lin, 4/12/93, (PB93-198299).

NCEER-93-0008 "Retrofit of Reinforced Concrete Frames Using Added Dampers," by A. Reinhorn, M. Constantinou andC. Li, to be published.

NCEER-93-0009 "Seismic Behavior and Design Guidelines for Steel Frame Structures with Added Viscoelastic Dampers,"by K.C. Chang, M.L. Lai, T.T. Soong, D.S. Hao and Y.C. Yeh, 5/1/93, (PB94-141959, A07, MF-A02).

NCEER-93-QOlO "Seismic Performance of Shear-Critical Reinforced Concrete Bridge Piers," by 1.B. Mander, S.M.Waheed, M.T.A. Chaudhary and S.S. Chen, 5/12/93, (PB93-227494, A08, MF-A02).

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NCEER-93-0011 "3D-BASIS-TABS: Computer Program for Nonlinear Dynamic Analysis of Three Dimensional BaseIsolated Structures," by S. Nagarajaiah, C. Li, A.M. Reinhom and M.C. Constantinou, 8/2/93, (PB94­141819, A09, MF-A02).

NCEER-93-0012 "Effects of Hydrocarbon Spills from an Oil Pipeline Break on Ground Water," by OJ. Helweg andH.H.M. Hwang, 8/3/93, (PB94-141942, A06, MF-A02).

NCEER-93-0013 "Simplified Procedures for Seismic Design of Nonstructural Components and Assessment of Current CodeProvisions," by M.P. Singh, L.E. Suarez, E.E. Matheu and G.O. Maldonado, 8/4/93, (PB94-141827,A09, MF-A02).

NCEER-93-0014 "An Energy Approach to Seismic Analysis and Design of Secondary Systems," by G. Chen and T.T.Soong, 8/6/93, (PB94-142767, All, MF-A03).

NCEER-93-0015 "Proceedings from School Sites: Becoming Prepared for Earthquakes - Commemorating the ThirdAnniversary of the Lorna Prieta Earthquake," Edited by F.E. Winslow and K.E.K. Ross, 8/16/93.

NCEER-93-0016 "Reconnaissance Report of Damage to Historic Monuments in Cairo, Egypt Following the October 12,1992 Dahshur Earthquake," by D. Sykora, D. Look, G. Croci, E. Karaesmen and E. Karaesmen, 8/19/93,(PB94-142221, A08, MF-A02).

NCEER-93-0017 "The Island of Guam Earthquake of August 8, 1993," by S.W. Swan and S.K. Harris, 9/30/93, (PB94­141843, A04, MF-A01).

NCEER-93-0018 "Engineering Aspects of the October 12, 1992 Egyptian Earthquake," by A.W. Elgamal, M. Amer, K.Adalier and A. Abul-Fadl, 10/7/93, (PB94-141983, A05, MF-A01).

NCEER-93-0019 "Development of an Earthquake Motion Simulator and its Application in Dynamic Centrifuge Testing," byI. Krstelj, Supervised by J.H. Prevost, 10/23/93, (PB94-181773, A-IO, MF-A03).

NCEER-93-0020 "NCEER-Taisei Corporation Research Program on Sliding Seismic Isolation Systems for Bridges:Experimental and Analytical Study of a Friction Pendulum System (FPS)," by M.C. Constantinou, P.Tsopelas, Y-S. Kim and S. Okamoto, 11/1/93, (PB94-142775, A08, MF-A02).

NCEER-93-0021 "Finite Element Modeling of Elastomeric Seismic Isolation Bearings," by L.J. Billings, Supervised by R.Shepherd, 11/8/93, to be published.

NCEER-93-0022 "Seismic Vulnerability of Equipment in Critical Facilities: Life-Safety and Operational Consequences," byK. Porter, G.S. Johnson, M.M. Zadeh, C. Scawthorn and S. Eder, 11/24/93, (PB94-181765, A16, MF­A03).

NCEER-93-0023 "Hokkaido Nansei-oki, Japan Earthquake of July 12, 1993, by P.I. Yanev and C.R. Scawthom, 12/23/93,(PB94-181500, A07, MF-A01).

NCEER-94-0001 "An Evaluation of Seismic Serviceability of Water Supply Networks with Application to the San FranciscoAuxiliary Water Supply System," by I. Markov, Supervised by M. Grigoriu and T. O'Rourke, 1/21/94.

NCEER-94-0002 "NCEER-Taisei Corporation Research Program on Sliding Seismic Isolation Systems for Bridges:Experimental and Analytical Study of Systems Consisting of Sliding Bearings, Rubber Restoring ForceDevices and Fluid Dampers," Volumes I and II, by P. Tsopelas, S. Okamoto, M.C. Constantinou, D.Ozaki and S. Fujii, 2/4/94, (PB94-181740, A09, MF-A02 and PB94-181757, A12, MF-A03).

NCEER-94-0003 "A Markov Model for Local and Global Damage Indices in Seismic Analysis," by S. Rahman and M.Grigoriu, 2/18/94.

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NCEER-94-0004 "Proceedings from the NCEER Workshop on Seismic Response of Masonry Infills," edited by D.P.Abrams, 3/1194, (PB94-180783, A07, MF-A02).

NCEER-94-0005 "The Northridge, California Earthquake of January 17, 1994: General Reconnaissance Report," edited by1.D. Goltz, 3/11194, (PBI93943, AlO, MF-A03).

NCEER-94-0006 "Seismic Energy Based Fatigue Damage Analysis of Bridge Columns: Part I - Evaluation of SeismicCapacity," by G.A. Chang and 1.B. Mander, 3/14/94.

NCEER-94-0007 "Seismic Isolation of Multi-Story Frame Structures Using Spherical Sliding Isolation Systems," by T.M.Al-Hussaini, V.A. Zayas and M.C. Constantinou, 3/17/94, (pBI93745, A09, MF-A02).

NCEER-94-0008 "The Northridge, California Earthquake of January 17, 1994: Performance of Highway Bridges," edited byI.G. Buckle, 3/24/94, (PB94-193851, A06, MF-A02).

NCEER-94-0009 "Proceedings of the Third U.S.-Japan Workshop on Earthquake Protective Systems for Bridges," edited byI.G. Buckle and I. Friedland, 3/31/94, (PB94-195815, A99, MF-MF).

NCEER-94-0010 "3D-BASIS-ME: Computer Program for Nonlinear Dynamic Analysis of Seismically Isolated Single andMultiple Structures and Liquid Storage Tanks," by P.C. Tsopelas, M.C. Constantinou and A.M. Reinhorn,4/12/94.

NCEER-94-0011 "The Northridge, California Earthquake of January 17, 1994: Performance of Gas Transmission Pipelines,"by T.D. O'Rourke and M.C. Palmer, 5/16/94.

NCEER-94-0012 "Feasibility Study of Replacement Procedures and Earthquake Performance Related to Gas TransmissionPipelines," by T.D. O'Rourke and M.C. Palmer, 5/25/94.

NCEER-94-0013 "Seismic Energy Based Fatigue Damage Analysis of Bridge Columns: Part II - Evaluation of SeismicDemand," by G.A. Chang and J.B. Mander, 6/1194, to be published.

NCEER-94-0014 "NCEER-Taisei Corporation Research Program on Sliding Seismic Isolation Systems for Bridges:Experimental and Analytical Study of a System Consisting of Sliding Bearings and Fluid RestoringForcelDamping Devices," by P. Tsopelas and M.C. Constantinou, 6/13/94.

NCEER-94-OD15 "Generation of Hazard-Consistent Fragility Curves for Seismic Loss Estimation Studies," by H. Hwangand J-R. Huo, 6/14/94.

NCEER-94-0016 "Seismic Study of Building Frames with Added Energy-Absorbing Devices," by W.S. Pong, C.S. Tsai andG.C. Lee, 6/20/94.

NCEER-94-0017 "Sliding Mode Control for Seismic-Excited Linear and Nonlinear Civil Engineering Structures," by 1.Yang, J. Wu, A. Agrawal and Z. Li, 6/21194.

NCEER-94-0018 "3D-BASIS-TABS Version 2.0: Computer Program for Nonlinear Dynamic Analysis of Three DimensionalBase Isolated Structures," by A.M. Reinhom, S. Nagarajaiah, M.C. Constantinou, P. Tsopelas and R. Li,6/22/94.

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