Drc.-at- - NISTR.E Lobo, 1.M. Bracci, K.L. Shen, A.M. Reinhorn and T.T. Soong Stale University of...

Isun'lftll II III1II1IIII1 -REPORT DOCUMENTATION II. 1t[~RT NO. II.

PAGE NCEER-93-0006 PB 9 3 - 2 274 8 6 -4. Tit..........lIClt.. 5. 11.-'0...Inelastic Response of Reinforced Concrete Structures with April 5, 1993Viscoelastic Braces

6-

7. Aut_") L ...~ 0 ............. II..,.. No.

R. F. Lobo, J.M. Bracci, K.L. Shen, A.M. Rein'horn, T.T.Soongto __.... O"'..i ....... N_ ..... AcIcI.... 10- ~1T.all~ \1M ....State University of New York at BuffaloDepartment of Civil Engineering n. e-.-cC) or Gr_IGI ....Buffalo, New York 14260 lel BCS 90-25010

NEC-91029IGl

'2. ,--ri,.. Drc.-at- N......nd~I IJ. T_ of ......... _ e:-_National Center for 'Earthquake Engineering Research Technical reportState University of New York at BuffaloRed Jacket Quadrangle •••Buffalo, New York 111261

.s. ........._ ....". _ ••This research was conducted at the State University of New York at Buffalo and waspartially 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 .

.... _tract lUonlt: lOCI _I

The addition of viscoelastic braces in structures for vibration reduction was proposed andimplemented in the past decade in metal models or full-scale structures. Viscoelasticbraces provide energy dissipation, while the structures remains by-and-large elastic. Inreinforced concrete structures, the seismic response is by-and-large inelastic, which isoften accompanied by permanent deformations and damage. The addition of viscoelasticdampers can dissipate energy at the early stages of cracking of the concrete elements andreduce the development of damage. However the addition of viscoelastic dampers maystiffen the structure unnecessarily producing increased inertial forces and base shearswhen subjected to seismic motion. The quantification of the influence of viscous andelastic stiffness properties of dampers during the inelastic response of reinforced concretestructures is thus the subject of this investigation. Models for analysis of inelastic re-sponse with damage indexing for reinforced concrete structures that include viscoelasticbraces are developed and calibrated using experimental data produced by shaking tabletests. These models are then used to determine the variation of expected damage in thepresence of damping and quantify the hysteretic energy dissipation along with thedamping energy.

17. o.c- _.,.,••. Oono:ript....

• 0 '''-lfIan'~Me4 T.,ma

Bracing systems. Energy dissipation. Damage mechanisms. Stiffness.Reinforced concrete structures. Viscoelastic dampers. Damping devices.Inelastic response. S.cale models. Shaking table tests. System identification.Mathematical models. Dynamic response analysis. Input energy.E!~W\t~st!....~valuatlon• Earthquake Engineering.

1.. Aw....lIlIIty su- I'. 1h~ ea-H: .....-0Zl. .... ., ......

nc assl ed 112Release Unlimited --

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0PnIltNAL POIIM zn (4-77)CF-"r fffl$-JIt........._.... ""',.....--....,..

1111111111111111111111111111111

NATIONAL CENTER FOR EARTHQUAKEENGINEERING RESEARCH

State University of New York at Buffalo

Inelastic Response of Reinforced Concrete Structureswith Viscoelastic Braces

by

R.E Lobo, 1.M. Bracci, K.L. Shen, A.M. Reinhorn and T.T. SoongStale University of New York at Buffalo

Department of Civil EngireeringBuffalo, New York 14260

Technical Report NCEER-93-0006

Aprj] 5, 1993

This research \\',1" conducted at the State University of New York at Buffalo and was partially supportedby the National Sl.:ience Foundation under Grant No. BCS 90-25010

and the New York State Science and Technology Foundation under Grant No. NEC-91029."1·,..k"Nt·~"".Il~'lWllt>, .....alIIIf ..." ....". 'W........,l .. 1.,_llIr" "' (',.,.,,,,~1'

"l4'1I1'.'''''Io.\' ,"'" ~:lf,l

NOTICEThis Tl'port was prepaTl'd by the State University of New Yorkat Buffalo as a result of research sponsored by the NationalCenter for Earthquake E.1gineering Research (NCEER) thn'ughgrants fmm the Nation.ll Science fuundation, the New York StateScience and Technology fuundation, and other sponsors. NeitherNCEER, associates of NCEER, its sponsors, the State University of New York at Buffalo, nor any person acting on their behalf:

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

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

Any opinions, findings, and conclusions or recommendationsexpressed in this publication are those of the author(s) and donot necessarily reflect the views of the National Science Foundation, the New York State Science and Technology fuundation,or other sponsors.

Inelastic Response of Reinforced Concrete Structureswith Visooelastic Braces

by

R.F. Lobo l, J.M. Bracciz, K.L. Shen\ A.M. Reinhorn4 and T.T. Soong~

April 5, 1993

Technical Report NCEER-93-O<106

NCEER Projttt Number 91-3111B and 91-5131B

NSF Master Contract Number BCS 90-25010and

NYSSTF Grant Number NEC-91029

Graduate Research Assistant, Department of Civil Engineering, State University of New Yorkat Buffalo

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

3 Graduate Rest~~ch Assistant, Department of Civil Engineering, State U'1iversity of New Yorkat Buffalo

4 Professor, Department of Civil Engineering, State University of New York at Buffalo5 Samuel P. Capen Professor, Department of Civil Engineering. State University of New York

at Buffalo

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

PREFACE

The NatiOl\al Center for Earthquake Engineering Research (NCEER) was establi'ihed to expand anddisseminate knowledge about earthquakes, improve earthquake-resistant d~sign. 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 (199 1 1996) comprises fourinterlocked elements, as shown in the figure below. Element I, Basic Research, is carried out to supportprojects in the Applied Research area Element II, Applied Research, is the major focus of work foryears six through ten. Element III, Demonstration Projects, have been planned to support AppliedResearch project!>, and will be either case studies or regional studies Element IV, Implementation, willresult from activity in the four Applied Research projects, and from Demonstration Pro~ects

ELEMENT IBASIC RESEARCH

• seismic haurd andground motion

• Solis and geotechniCalengineering

• Structures and systems

• Risk and reliability

• Protective and intelligentsystems

• SOCietal and economicstudies

ELEMENT IIAPPLIED RESEARCH

• The Building Project

• The Nonstruc:turalComponents Project

• The Lifelines Project

• The Highway Project

ELEMENT IIIDEMONSTRATION PROJECTS

C... Studiea• Ac:tive and hybrid control• ~pn.1 and data ptoeeasing

fM:1l1t1es• Short and medium span bridges• Wner suppl~ systems in

Memphis and San Franc:illCORegiona' Studies

• New York City• Mlululppl Valley• San Franc:lsco Bay Are.

ELEMENT IVIMPLEMENTATION

• Con~hope• EduestIonITralnlllGl coursee• PUblications• Public: Awa,..,...

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, andmasonry wallsor infills. The research involves small- andmedium-~e shake table tests and full-scalecomponent tests at several institutions. In a parallel effort, analytical models and computer programsarebeing developed to aid inthe prediction ofthe response ofthese buildingstovarious typesofgroundmotion.

III

Preceding page blank

Two of the short-term 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 protntivt and inttlligtnt systtms program constitutes one ofthe important areas ofresearchin the Building Projtct Current tasks include the following

Evaluate the performance offull-scale active bracing and active mass dampers already in placein terms of performance. power requirements, maintenance, reliability and wst

2. Compare passive and aelive control stralegies in terms of structural lype, degree ofeffectiveness, cost and long-term reliability

3 Perform fundamental studies of hybrid control.4. Develop and test hybrid control systems

Re.w:arch al N( 'r.ER on Sf!ismic applicalions ofVlscoelaslic damptrs 10 relrofit nonduclile concreleframes I.'i bemg (:arried oul as a collaboralive effort among researchers at the (Iniver.'iity ofl//illOis,1I. S. Army Corps of f.'ngineers, the 3M CompaJlY. and the Stale University ofNew York al Buffalo,Presented in Ih,s reptJrt are rp.fUlts relaled 10 VISCOUS and stiffness effecls due 10 addIllOn of lhedampers on lhe inelaslic response ofreinforced concrele frames. Verificalion ofthese resulls wasperformedba"edon shakmg lable lestscvnductedana one-IhirdscaledmOtkIofa Ihree-story lighllyreinforced con(:rete frame.

IV

ABSTRACT

The additIOn of viscoelastic hraces in structures for vihration reduction was proposed and

irnplememed 10 the past lIt'cade in metal models or full-scale structures Viscoelastic hraces provide

energy diSSipatIOn. while the strul'turcs remains hy-and-Iarge clastic In reinforced concrete

structures, the seismic response IS hy-and-large inelastic. which is often accompanied hy permanent

defnrmations and damage. The addition of viscoelastic dampers can diSSIpate energy at the early

stages of cracking of the concrete clements and reduce the development of damage With proper

selection of dampers. thiS damage can he suhstantially reduced or nell chmina:··d. However the

addition of viscoelastic dampers may stiffen the structure unnece!o>sarily producing increased inertial

forces and ha!o>e shears when suhjected to seismic motion. The quantification of the influence of

VISCOUS and clastiC stiffnes!o> propertIes of dampers during the inelastil' response of reinl(1[ced

concrete stru..:ture... i ... the ...uhject of thi ... investigation. Models lor analysi ... of inelastic response

with damage indexing for reinforced concrete structures that include viscoc lastic hraces arc

developed and cahhratcd using experimental data produced hy shaking tahle tests. These models

arc then used to determine the v;.:natlOn ofexpected damage in th~ presence ofdamping and quantify

the hystt'retic energy dissipatIon along with the damping energy.

v

ACKNOWLEDGEMENTS

Fmam: iat !'lU pport ha!'l been provided by the Nationat Center of Earthquake Engineering Research

under Grant Nos. NCEER-91-3Itl B. NCEER-91-5131 Band NCEER92-5202A. The authors

are grateful to Dr. EJ. Nielsen and Dr. M.L. Lai of the 3M Company for technical and financial

!'lUPpl>rt. and for supplying the viscoelastic dampers used in the experiments.

The authors would like to thank Mr. M. Pitman. Mr Dan Walch and Mr. Richard C'izd7.iel of

the Sei!'lmic Simulation Laboratory for their dedicated assistance during the experiments and

data processing. The authors want tothank Mr. Mike Riley for his support with the computational

facilities.

vii


SECTION TITLE

TABLE OF CONTENTS

PAGE

INTRODUCTION 1-1

2 INELASTIC DAMAGE ANALYSIS OF REINFORCED CON-

CRETE STRUCTURES WITH VISCOELASTIC BRACES 2-1

2.\ Numerical Solution for Dynamic Analysis 2-2

2.2 Determination of Damper Properties 2-4

2.3 Innuen(~e of the Individual Dampers Properties on the Structure Properties

..................................................................................................................... 2-7

2.4 Determination of Damping Ratios 2-8

2.4.1 E4uivalent Damping Ratio for an Undamped System 2-8

2.4.2 Complex Formulation for Damping Ratio 2-9

3 PERFORMANCE VERIFICAnON OF ANALYTICAL MODEL IN

1:3 SCALE STRUCTURE TESTING 3-1

3.\ Experimental Program 3- I

3.2 Stiffness Identification 3-10

3.2.1 Experimental Identification of Stiffness 3-10

3.2.2 Analytical Identification of Stiffness 3-12

3.3 Identification of Natural Frequencies and Damping Ratios 3-13

3.4 Memory Dependency in RIC Members 3-15

3.5 Comparison of Displacement and Acceleration Time Histories 3-17

3.6 Damper Forces 3-17

ix


SECTION TITLE

TABLE OF CONTENTS (cont.)

PAGE

l .. /

4

4.1

4.2

4.3

Base Shears and Damper Stiffnesses 3-30

Ef'FECTS OF VISCOELASTIC BRACES ON STRUCTURAL 4-)

RESP()NSE .

Natural Frequency I Period 4-1

Story forces and Drifts 4-4

Column Axial Forces 4-4

Energy Input ..... . 4-9

4.5 Damage Mechanism 4-10

5 INFLUENCE OF VISCOELASTIC PROPERTIES ON SEISMIC

RESPONSE OF RIC STRUCTURES 5·)

6 CONCLUDING REMARKS 6·)

7 REFERENCES 7-1

APPENDIX A·)

x

FIGURE TITI.E

LIST OF ILLUSTRATIONS

PAGE

2-) StructUial Model With Viscoelastic Braces 2-5

2-2 Typical Force Deformation Loop at 3Hz (Experimental) 2-5

3-1 I: 3 Sc:.tle RIC Frame Structure 3-2

a, Before Conventional Retrofit

b. After Conventional Retrofit of Columns

3-2 Front Elevation of TeM Structure Before Conventional RetrofIt 3-3

3-3 Side Elevation of Test Structure 3-4

3-4 Conventional Retrofit by Jacketing of Interior Columns 3-5

3-5 Details of Conventional Retrofit 3-6

3-6 RIC Frame with Viscoelastic Brace Dampers 3-8

a. Elevation

b. Viscoelastic Brace Damper

c. Details of Viscoelastic Damper

3-7 Top Story Displacement During Taft Earthquake. PGA=O.2g (Test #5) ....... 3-16

a. Hysteretic Properties not Updated - Single Analysis

b. Hysteretic Properties Updated - Following Sequential Analysis

3-8 Displacement Time History with Damper A for Taft. PGA 0.05g 3-18

3-Y Displacement Time History with Dampers B for Taft. PGA 0.05g 3-19

xi

LIST OF ILLUSTRATIONS (coot.)

FIGt:RE TITLE

3-10

3-11

3-12

Displacement Time History with Damper A for Taft, PGA 0.2g

Displacement Time History with Damper B for Taft, PGA O.2g

Acceleration Time History w;th Damper A for Taft, PGA O.05g

PAGE

3-20

3-21

3-22

3-13 Acceleration Time History with Damper B for Taft, PGA 0.05g 3-23

3-14 Acceleration Time History with Damper A for Taft, PGA O.2g 3-24

3-15 Acceleration Time History with Damper B for Taft, PGA 0.2g 3-25

3-16 Force Displacement (I Dampers A for Taft, PGA O.05g 3-26

3-17 Force Displacement of Dampers B for Taft, PGA O.05g 3-27

3-18 Force Displacement of Dampers A for Taft, PGA O.2g 3-28

3-19 Force Displacement of Dampers B for Taft, PGA O.2g 3-29

3-20 Base Shear in Columns with Dampers A for Taft, PGA 0.05g 3-31

3-21 Base Shear in Columns with Dampers B for Taft, PGA O.05g 3-32

3-22 Base Shear in Columns with Dampers A for Taft, PGA 0.2gA 3-33

3-23 Base Shear in Columns with Dampers B for Taft, PGA O.2g 3-34

xii

FIGURE TITLE

LIST OF ILLUSTRATIONS (cont.)

PAGE

4-1 Acceleration Transfer Function with Dampers A (for White Noise

PGA O.025g) 4-2

4-2 Acceleration Transfer Function with Dampers B (for White Noise

PGA O.025gl 4-3

4-3 Forces-Deformation at First Floor with Dampers A for (PGA O.2g) 4-5

4-4 Forces-Deformation at First Floor with Dampers B for (PGA O.2g) 4-6

4-5 Capacity Diagrams versus Force Demands in Interior Columns with

Dampers A...................................................................................................... 4-7

4-6 Capacity Diagrams versus Force Demands in Interior Columns with

Dampers B 4-8

4-7 Energy Input in the Test Structure 4-11

4-8 Mechanism Formed in the Building 4-13

4-9 Story Damage Evaluation 4-13

a. Ela.,tic Superstructure

b. Inelastic Superstructure

5-1 Pseudo Acceleration Transfer Functions for Added Damping 5-2

a. Elastic Superstructure

b. Inelastic Superstructure

5-2 Pseudo Acceleration Transfer Functions for High Levels of Additional

Damping 5-2

xiii

LIST OF ILLUSTRATIONS (cont.)

FI<;URE TITLE PAGE

5-~ Variation of First Mode hequencies 5-~


h. Inelastic Superstructure

5-4 Influence of Earthquake on Structural Response with ViscoelastIC Braces ... 5-5

a. Base Shear Response

b. Displacement Response

5-5 Apparent Equivalent Damping with Viscoelastic Braces with Added Stiffness

(Percent of First Story) 5-5

A-I Layout of Slah Steel Reinforcement A-2

A-2a Details of Beam Steel Reinforcement A-3

A-2b Details of Beam Steel Reinforcement (Continued) A-4

A-3 Details of the Column Steel Reinforcement A-5

A-4 Gradation Analysis of the Concrete Mix A-6

A-5 Average Concrete Specimen Strength Versus Time A-6

A-6 Measured Representative Stress-Strain Relationships of the Reinforcing Steel

........................................................................................................................ A-8

xiv

TABLE TITLE

LIST OF TABLES

PAGE

3-1 Properties of Dampers in Retrofitted Structure 3-9

3-2 Testing Program for the Retrofitted Model with Viscoela..tic Braces 3-10

3-3 Dynamic Characteristics History of the Retrofitted Model from Low Level

Vibrations (White Noise PGAO.025g) 3-11

3-4 Analytical Versus Experimental ~tiffness Matrices Without Dampers 3-13

3-5 Structure's Properties with Viscoelao;tic Dampers From Strong Vibrations

3-14

3-6 Analytical Versus Experimental Damping and Stiffness 3-15

4-1 First Mode Dynamic Characteristics During Low Level Vibration Tests ...... 4-2

4-2 Maximum Measured Story Response 4-9

xv

SECTION 1

INTRODUCTION

The addition of viscoelastic braces in structures for vibration reduction was thoroughly investigated

in the past decade using metal scaled models or full-scaled structures. While the viscoelastic braces

provide energy dissipation through non-load bearing elements. the load bearing structure remains

hy-and-Iargc clastic. Reinforced concrete structures are designed to resist earthquakes by dissipating

the input energy transmitted to the structure through inelastic deformations of the load bearing

components. Thc sClsmic response is therefore accompanied hy permanent inelastic deformations

and damage. Proper selection of additional viscoelastic dampers can contribute to the energy

dissipation in the early stages of cracking and limit the development of damage or completely

eliminate it.

Various damping devices were suggested for use in structurcs to limit damage to the load bearing

structural clements. Of these devices the two more popularly used are: (i) the direct shear seismic

damper (DSSD) (Mahmoodi. 1969) and (ii) the steel plate added damping and stiffness (ADAS)

damper SchoU ,1990). Mahmoodi (1969) showed that viscoelastic dampers al appropriate locations

within the structure are effective in reducing the vibrations in tall buildings. These dampers have

proved successful as adequate damping devices with stable engineering properties with regards to

aging in the World Trade Center Buildin~s (New York) and the Columbia Center Building (Seattle),

(Keel ct al. 1986). A number of experimental studies have also been conducted to show the

effectiveness of these dampers in reducing the story displacements. accelerations. shear forces, and

damage to structures. Lin et al. ( 1991 ) tested a 1/4-scale three story steel framed model building.

Chang ct at. (1992) tested a 2/S-scale five story steel framed model building, to name a few. These

studies show conclusive evidence that mechanical dampers, acting as non-load bearing elements,

effectively damp the vibrations in buildings caused by wind, seismic. or other forms of transient

lateral loadings. These dampers effectively dissipate the input energy to the structure by increasing

1-\

SECTION 2

INELASTIC DAMAGE ANALYSIS OF REINFORCED CONCRETE

STRUCTURES WITH VISCOELASTIC BRACES

Inelastic analysis of rClnforced concrcte structures to seismic or wind loadings has been the subject

of several prcvious devcloprncnh fur planar systems, ~:uch as DRAIN-2D (Kanaan and Powell.

1Y73), SARCF (Rodriguez-Gomel et aI., 1990) and a family of analytical developments, IDARC

(Park et al.. 1987 and Kunnath et al.. 1992). A recent development of the two dimensional version

of IDARC (Kunnath et at.. 1992) was extended to a full three dimensional analysis of reinforced

concrete structures including space torsional behavior and biaxial bending interaction in the

structural elements, IDARC-3D (Lobo et aJ '. 1992), The salient features of the above analytical

model for reinforced concrete structures are:

(i) An extensive hysteretic model governed by several parameters to simulate inelastic behavior

of beams, columns, shear-walls, and braces.

(ii) A distributed flexibility model that accounts for the nonsymmetric distribution of plasticity

along the members.

(iii) A variety of loading conditions including simultaneous action of static, cyclic. and random

forces and base excitations.

(iv) Evaluation of damage progression and energy balances, The hysteretic model has the

capability of reproducing a variety of hysteretic curves by selection of three independent

parameters which control stiffness degradation. strength deterioration and pinching usually

generated by bond slip of the reinforcement during cracking (Kunnath et aI .• 1992).

The above analytical platform was verified using extensive simulations and comparisons with

experimental data from laboratory tests of components and structures (Kunnath et aI., 1992, Bracci

et aI., I992a, 1992b. 1992c. and EI-Attar et aI,. 1991). The simulations obtained are suitable to

2-1

either duplicate or predict actual measured behavior. Thus the analytical modeIIDARC'-3D was

chosen as a nase to develop the new models for analysis of reinforced concrete huildings with

viscoelastic dampers.

2.1 Numerical Solution for Dynamic Analysis

Thl' inelastic analysis of structures with viscoelastic hraces is done using numerical models and

direct integration techniljucs. The fundamental cquation of motion for numeril'al integration is

l'xpressed in matrix form as:

Mii + Cil + Ku = -MIu. + F14 (2.1 )

where M = mass matrix.. C = mass proJX)rtional damping matrix.. K = instantaneous overall stiffness

matnx., I = vector of ones or zeros indicating excitation in any degree of freedom. u. ii, and ii =

displacemcnt. velocity. and acceleration vectors, respectively. iiK=ground acceleration vector. and

1'14 = wind forces. Equation (2.1) can be solved by a linear step-by-step dynamic analysis

procedure using the Newmark Beta constant average acceleration method. which gives an uncon

ditionally stahle solution. It can hy ex.pressed in a generalized form in terms of the incremental

forces and displacements after the inclusion of the additional stiffness and damping from the

viscoelastic hraces as:

where

M'- = K-~u

L\F- =-MIMK

+ L\Fw + M(~ ... + 2ii] + 2(C + ~C]iI

. [4 2 ]K = -,M + -(C + ~C) +(K + AK]61' At

" .. = ··;11 _ "('-\). AV = ~I) _ For- I)u~ ~ ~ .~w II' II'

2-2

(2.2)

where .1.u = t;le vector of incremental displacements. .1.ii. = the increment of ground acceleration .

.1.F\4 = the vel:lor of innemental wind forces. iJ and ii = the velocity and acceleration at the heginning

of the time step. and .1.K and .1.C = the matrices corresponding to the additional stiffness and

additional damping provided hy the viscoelastic oraces. These matrices can he ohtained hy line-

ari/ation of frequenq dependent viscoelastic models models of complex formulation as shown in

the following.

The glohal cljllivalent visLous damping in reinforced concrete huildings seems to play an imponant

role for the clastic hehavi(\r. usually in the non-damaged state. When structures cnter the inelastic

range mUl:h energy is dissipated hy hysteretic hehavior and therefore the influence of this viscous

damping effects to the total apparent damping diminishes. A proportional damping representation

used in IDARC -~D. (Loho. 1()9~ l, accounts for the glooal viscous damping and produces acceptahle

results hoth in the elastic as well as the inelastic range. When more control on the damping in the

various modes is required. in the clastic range. the proponional damping matrix can he expressed

as:

(2.3)

where a".al.a~ arc proportionally factors that lead to real modes and frequencies. The first two

terms correspond to the mass and stiffness proportional damping respectively. Using an effective

critical d;lmping ratio. 1;., corresponding to mass or stiffness proportional damping matrix, could

yield adequate results if the numher of dampers were located uniformly throughout the structure.

This procedure provides. however, only an approximation of the damping produced by addition of

supplemental damping such as provided by viscoelastic braces. which is non proportional. III the

further modeling it is assumed that, only the lateral degrees of freedom are affected, without

influencing the damping to the rotational degrees of freedom. Non proportional viscous damping

for multi degree of freedom systems. produces free vibration response of the structure, that is

2-3

exponentially damped at the same freqUl:ncy, but at different phase angles, resulting in non stationary

modes. This is well represented hy complex eigcn values and eigen vectors. Thus the use of an

equivalent critical damping ratio ~ to rt'prcsent damping is only an approximation limited to

structures with evenly distributed supplemental damping.

Various attempts were made to emphasize more realistically the influence ofadded damping. Instead

of the equivalent damping approach, Caravani and Thomson ( 1974) suggested to define a damping

matrix that included the intluenl:e of story damping in an implicit way. Modeling of viscoelastic

hraces was successfully attempted by Hanson et a!., (1987). Su and Hanson (1990) modeled the

structural and hysteretic damping of ADAS devices using the Ramberg - Osgood hysteresis model

in DRAIN-2D (Kanaan and Powell, 1973). Pall elal (1982) modelled the response of structures

with diagonal cross friction bracing using a non symmetric bilinear model, also using DRAIN-2D.

Recently Liang and Lee ( 1991 ) have expressed the damping matrix similar to the previous authors,

however the influence of modal frequencies and structural brace configurations was also included.

The m"del of viscoelastic braces used in IDARC- 3D and detailed in the next section is an extension

of the models proposed by Ashour et al. ( 1987) and Liang et al. ( 1991).

2.2 Determination of Damper Properties

Viscoelastic damping material as the name implies, has two components, the viscous part or energy

absorbing pan, and the elastic part or energy restoring part. Figure 2.1 shows a typical structural

model with supplemental viscoelastic braces which serves as a test case for modeling and analysis

using IDARC-3D. For a single viscoelastic damper (see fig. 2-2) subjected to a steady state har

monic excitation. the damping force can be described by the complex relation:

(2.4)

2-4

Floor 3

Floor 2

Floor 1

Column(typical)

ShearWall

Seismic Excitation

FIGURE 2-1 Structural Model With Viscoelastic Braces

1.5 ---~-- ---.-----------,-~----~----------------

1.0 - - - - - - - - - - - - - - - - - - - - - - - ~ - - - - - - - - - . - - - '- - - - - - - - - - - - -

0.0

I0.5 I- - - - - - - - - -

Via..~woc:rf2 -0.5

-1.0 ------I

~

-1.5 i-0.06 -0.03 o

DISPLACEMENT (IN)

--~I

Fa iI

:11 = Fe IFa

:k l = 11 ks: ,-.--J

0.03 0.06

FIGURE 2-2 Typical Force Deformation Loop at 3Hz (Experimental)

2-5

where I." =the force in the brace. k,(w)= the shear storage stiffness, k,(w) =the shear loss stiffness,

and x =the displacement in the damper. Since the damping coefficient force formulation is

dependent on frequency (Liang, 1991), Eg. (2.4) can be generalized as:

(2.5)

where 11(W) =the loss factor and defined as the ratio of k,(O»)/k,(oo). for a process governed hy a

narrow hand excitation the coefficients k,(w) and 11<(0) may be considered constant.

With this assumption and after some, manipulations of Eq. (2.5), using the definition of viscous

damping coefficient. c, as:

11k,£' =

(t)

The force in the damper can be defined:

An inverse Fourier transform applied to (2.7) produces

(2.6)

(2.7)

Fd(f)=k,.x(l)+ci(t) (2.8)

which indicates that the shear storage stiffness (k, = 11k,) influences the stiffness of the brace and

the shear loss stiffness (k,) influences the damping of the brace. Although the stmcture shows

vibrations in various modes. the first mode of vibration is dominant and therefore the properties of

the damper k,(w) and 11(00) can be selected based on the significant mode without appreciable loss

of accuracy.

If the shear storage modulus (G') is known. the stiffness k, can be obtained directly according to

the relation

2-6

k, =G'AI/ (2.9)

where A IS the total shear area of the viscoelastic material and r is the thi.:kness of the viscoelastic

material. Similarly kl can he ohtained as

k, =G"Alt (2.10)

when the shear 10\\ modulus (Goo) is known. The same stiffnesscs k, and k: can also be ohtained

from the cyclic test hysteresi ... results as shown in Fig. 2-2.

2.3 Influence of Individual Damper's Properties on the Structure Properties

The properties of each hrace using identIcal damping devices arc incorporated in the structural

mod-:I a~ lnncmcnts of the stiffness, !1K, and of the damping. ~C. matrices:

.1.K = k,R and ~C = cR

where B is a nl.lll dimensional hracc location matrix that takes the following form:

- ,\'/Ul",:S J

(2.11 )

N,co~' 6, + N, co~' 6: - N:cos'6]

-N,cos'a, N,CllS'9, +N,cns'9,

(2.12)

where Nk =the number of dampers at the k-th story such that Nt£" is the total damping coefficient

of all the dampers at k-th story and cos8 =the indination of each brace from the horizontal. For

unequal dampers. the value of Nk may be a noninteger B can be therefore suitably modified to

reflect a variable number of braces at each floor. the variable damper properties. and the indination

of the dampers.

2-7

The incremental matrices ~ and ~C are added to the dynamic equations of motion, Eq. (2.2),

within IDARC-3D. The validity of the above formulation is verified with experimental data and

used for further parametric analysis as described in the subsequent sections.

2.4 Determination of Damping Ratios

2.4.1 Equivalent Formulation of Damping Ratio

The contribution of identical viscoelastic devices to the critical damping in each mode can be

obtained using modal characteristics as :

I <J)~(~C)<J)J C <J)~IWlJ

~.\J - 2w, «I>;M«I>, - 200, «1J;M«I>,(2.13)

where «1>, is the i-th modal Shllpe and w, is the i-th modal frequency. For very simple structures

such as in Fig. 2- I the i-th modal damping ratio can be obtained from Eq. (2.13) or as:

(2.14)

where mJ

is the j-th story mass and J is the total number of stories. Eq. (2.13) or (2.14) ~an be used

in design process for estimating the required damping property, c, of a typical brace such that a

desired supplemental modal damping ratio ~ can be obtained. The total damping can be further

obtained including the contribution from the inherent viscous damping already existing in the

structure as:

0), <J)~(C + ~C)cI> i

l;mr, = 2 <J)~(K + M)cI>,(2.IS)

Equation (2.15) can be expressed in terms of the individual damping ratio contributions as:

2-8

(2.16)

Where ~, is the original structural modal damping ratio 0), (4);CeJ),)f2(<IJ;KCI>,) and a., is

<I»~dK<IJ,IcI>;K<I>,. Note that for a small stiffness increase M\. the resultant damping is the sum of

the added damping and the original one.

2.4.2 Complex Formulation for Damping Ratio

The STilT, computed by this process is only an approximate value of the critical damping ratio.

because of the non proportional characteristics of the damping matrix. The natural frequencies 00,

and corresponding damping ratios ~TOTI for each mode can be computed more accurately from the

set of homogeneous equations (Frazeret. al. 1946) using the total complex damping C· , and stiffness

K· matrices based on the state equation:

or:

AS' + By =0

where

The eign solution can therefore be obtained from:

y = -'Ay

or:

2-9

(2.17a)

(2.17b)

(2.17b)

(2.18)

IAy = -By

A

Equation (2.19) has complex roots that can be obtained as:

A, = Jf, + iv,

where Jumdu, are calculated from the characteristic equation;

A.~ + 2~,ro,A., + ro~ =0

that yields the characteristic values:

Jf, = ~,(j),

v, = ro,~1 -~~

The free vibration response is obtained from:

(2.19)

(2.20)

(2.21 J

(2.22a)

(2.22b)

(2.23)

with the natural frequencies and the equivalent damping ratios for the respective modes computed

as:

(2.24)

(2.25)

(2.26)

2-10

A comparison of the analytical predictions of equivalent damping ratio!> and of complex ratios to

the values obtained in experiments are given in the next section.

2-11

SECTION 3

PERFORMANCE VERIHCATION OF ANALYTICAL MODEL IN

1:3 SCALE STRUCTURE TESTING

An experimental study of a 1:3 scale RiC frame structure retrofiued with viscoelastic braces using

3MTH materials was carried out at NCEER IShen. Soong. Bracci/1993). The purpose of this

experimental study is

(i) To observe the performance of viscoelastic dampers

(Ii) To validate the analytical (computational) model that make use of several simplified

assumptions.

(Iii) To determine the influence of dampers on the structural components and overall structural

system.

The results of this study are used here to validate the analytical model described in the proceeding

section.

3.1 Experimental Program

A one-third scale mooel of C\ three story lightly reinfarced concrete frame building (Figs. 3.1, 3.2.

and 3.3) was previously tested under simulated base motions using the shaking table in the Seismic

Simulation Laboratory at the Sta,e University of New York at Buffalo (Bracci et aI .• 1992a and

1992b). The structure was tested using a series of simulated motions obtained from the scaled 1952

Taft earthquake. N21E component. nonnalized for peak ground accelerations (PGA) of O.05g.

O.20g, and O.30g representing minor, moderate, and severe ground motions. The structure was also

tested with a uniform random noise (w~ite noise) after each episode for identification purposes.

The severe base motions induced large inter-story drifts and internal damage to the columns such

that an incipient column-sidesway mec~lanismwas apparent and leading towards a collapse situation

3-1

12'-0" 2· Slab (tyg

le 4· '00»

~ ~M (of)

S'-O"

le

i. 2-314" PL T&B (TYP) 2'-51/2·

~ Y LOAD CELL (TYP)7"(of)

4"-0" 2'-51/2"

le

2'-5 1/2·

~(of)

Co

k" ;V ~ v v v v v7::::>l >1 >1 >1 7\

4" S'-S" 4" 5'-8" 4· 5'-8· 4·

FIGURE 3-2 Front Elevation of Test Structure Before Conventional Retrofit

3-3

2" Slab (typ)-,I--

: I4"(typ)

~

\c3'-6"I iI~

1'-5 1/2"

"-5 1/2"

~__ I.'---------1-: 2-.3/4" PL T&8 (TYP)I 1'-5 1/2",I'~ LOAD CEl.l. (TYP) 7"

i I;I

~-- .._------.....~I

1

I( v v If II' V/I

" 10" ;;r /J "" 7171

- 4" 5'-8" 4" 1'-10"

CD (2)FlGURE 3-3 Side Elevalioa of Test Structure

3-4

PlcteI I Stee'i ~

"'>.-- ~I_.-_-_·=tt:t::=::::z1~t·IH·IH·:j;=7J _·--.---.-...ll ~_=~~~_=J_?I

•

~r_.----------~L--~~L4+--~~~--~~~~~--

Transverse HoopReinforCt:ment

- .........~-il

SleevecThrecdbws (Typ)

Unsleeved iThreadDcrs (T~

I

Elevation

FIGURE 3-4 Conventional Retront by Jacketing of Interior Columns

3-5

L')'--/---

C~'-': c~tC" i.>J;~

ere __ '-:'C",f..:C (~y;;<._

~/~. c"r- S:CC'w'€C

~rreCC~G"s (~y;::)

7/E CO it--ce'r: 5esm (""y;::)',

3/8' ~;c Ihrecc~crs

(Le'lC;:r:~12')

Section 1

Section 2

4"--- ---1' j'

• ,~ / f! ., C I C ~\ '--" • S J :: •

l_CC'I'" cf':c:..- ~:res~re~:~:""'G

2/8 Cc __ r-e"- (-y::'(C'l(W'-"-~/4)

~" CC'is~r-.Jc~icf', r-o':e B:J'"eC''1 SIC:;; (ly;:;)

Be'ld ,n?:cce (lyD)

./ ,

~.3

D4 Re~ar

Reproduced frombest available copy

FIGURE 3-5 Details of Conventional Retrofit

3-0

(BralTi et al.. 1992h). Suhsequently the damaged hUilding was retrofitted conventionally (See

fig. 3.1) hy strengthenmg the interior columns of the building using conuete Jacketing. strength

ening the hcam-column joints wllh a reinforced connell' fillel. and post-tensioning the repaired

I:olumns to 20rlr of their ultimate axial strength as shown in Figs. 3.4. and 3.5.

(Bral:l:1 et al.. IYY2c l. The syslem was subsequently lested using :he same motions as for the original

huilding. The pel formance of the repaired structure was suhstantially improved producing only

IIKal damage in Ileams and slahs. However the complete hcam-sidesway mechanism was not ncar

full development. thus reducing the overall damage and collapse risk.

This damaged hullding served the ohJective for further experimental studies of retrofit using vis

coelastic dampers of the direct shear type.

The huilding was retrofitted again by adding viscoelastic diagonal braces in the interior bay of each

frame (sec Fig. 3.6) and tested by Shen. Bracci. Soong and Reinhorn. For sake of completion the

descnptiqn of the test is repeated in here. The viscoelastic dampers made hy 3M™ Company

Minneapolis. MN. conSIsted of two pads of 3M™ manufactured viscoelastic material honded

hctween three steel plates and emhcdded in steel braces connected by steel brackets to the story

slabs (sel' Fig. 3.7). The brackets were located above and hclow the horizontal hcams strengthening

somewhat the hcam-column joint over a 2" distance at each end.

Two sets of OS' thick viscoelastic dampers of differl"nt sizes (type A with total shear area of 35

in." and type B with total area of 17.5 in.z) were alternatively tested for the retrofit of the structure.

The dampers were tested under cyclic loading prior to the shaking table tests. As shown in Fig.

2.2. the storage stiffness and the loss stiffness for each test are determined. from which the other

relevant properties of the damper at a particular frequency can be calculated. The relevant properties

required for the analysis predictions ofthe response of the structure with viscoelastic dampers were

obtained from tests done by Shen. Soong. et al.. and are listed in Table 3.1. The viscoelastic dampers

display a lx:havior dependent on frequency. strain amplitude, and temperature. Although this

3-7

,'.- ........._-~ - ---------- .... ~~

FUilJRF. 3-6 RIC Frame with Viscoelastic Brace Dam~rs

TABLE ~-l Properties of Dampers in Retrofitted Structure

Shear Shear Shear Shear Damping

Storage Lo~~ Storage Lm~ Loss Coefficient

Frc4ucncy Modulus Modulus Stiffness Stiffness Factor c

f (HI) G,fhil G,(ksil I.: J (kiplin) 1.:, (kiplin) '1 (kipstin/sec)

( II (2) (3) (4) (5) (6) (7)

(a) Properties of Damper A

10 O.llQ O.24S 12.74 17.~6 1.36 2.76

1.5 D.244 0.305 17.0R 21.35 1.25 2.27

2.0 O.2\)4 (UOO 20.5K 25.02 1.24 2.04

2.5 (U~5 (U% 23.45 27.72 I.IH \.76

3.0 (U45 O.4~ 1 24.15 30.17 1.25 l.bO

(h) Properties of Damper B

10 0.1 \)9 0.25\) 6.97 907 1.30 144

1.5 0.265 O.32b 9.28 I 1041 \.23 1.21

2.0 (U(X) 0.395 10.50 LU3 1.32 1.10

2.5 0.365 0.463 12.78 16.21 1.27 1.03

3.0 0.385 0.487 13.48 17.05 1.26 0.90

temperature dependency is the most significant. the variations in the damper properties can be

neglected in a temperature controlled environment (such as room temperature in most office

buildings and laboratories).

The frame structure was subjected to a shaking table testing schedule as shown in Table 3-2. Wide

banded (0 - 50 Hz.) white noise excitations were used for identification of the dynamic characteristics

of the structure before and after every earthquake shaking table motion. Since testing was conducted

3-9

TABLE ~-2 Testing Program for the Retrofitted Model with Yiscoela~tjl' Braces

Te ...t Tnt Dt'Script ion YE Damper Test Lahcl PurposeType

(I \ (21 (3) (4) (51

O. Taft N21 E. PGA O.20g None TF20- WO Comparison Responseno Taft N21 E. PGA (UOg THO- WO Comparison Response

I. Whitl' NOIse. PGA O.025g WNB-YEA Identification,

Whill' NOIse. PGA 0.025g WNC YEA Identification-

J. Jaft N21E. PGA O.OS E A It'OS YEA Minor Eadhquake4. White Noise. PGA 0.025g WND- YEA Identification

s.. Jaft N21E. PGA 0.20 I: It'2O YEA Moderate Earthquaken. White Noise. PGA (U}2~g WNE- YEA Identification

7 White Noise. PGA O.025g WNA- YES Identification

3.. JaD NUE. PGA 0.05 E It'OS YEB Minor Earthquakel). White Noisl', P(,A (U)2~g S WNB- YES IdentificatIOn10. White Noise. I'(JA(H)2~g WNC - YES Identification

11. Iaft N21E. P<jA 0.20 I It'20 YEB Moderate Earthquake12. White Noise. PGAO.025g WND- YES Identification

Note: _WO indicates no dampers and _YEx mdicates viscoclastic dampers of type x.

over several days. consecutive white noise I?xcitations were used to validate the current dynamic

characteristics of the huilding. Fncus on the analytical performance evaluation is drawn to tests

#3. #5. #K and # II. as they are indicative of the rcsponse of the building to the representative base

motions tix minor and moderate e.uthquakes with additional stiffness and damping.

3.2 Stiffnes.1i Identification

3.2.1 Experimental Identincation of Stiffness

The stillness matrix is computed from the experimentally determined frequencies, mode shapes

and the mass at each story level (Bracci. 1992) ao;

3-10

(3.1 )

TABLE 3-3 Dynamic Characteristics History of the Retrofitted Model

From Low Level Vibrations (While Noise PGA 0.025g1

Test Frc4ucncy Modal Shapes Stiffness Matri,.; Story EquivalentName Stiffnesses Viscous

Damping

f «1>'1 K'I k, ~,(Hz.) (kip/in) (kip/in) (~)

(a) Helme Earthquake Test Taft N21EPGA O.20g

WhiTI' r 2.7S ) f IC~) - 0. Ko- "" ] 20S2 - 23K.ft 7Ih ( 23&.0 3.0

fUII'.\t'll)·3S j O.7l/ OAK I.m - 2.~Xh 4214 - 27K2 l27~.2 1.9

WIfNR H 16.7'\ \OA2 I.<KI - (l.X4 71.h - 27K2 4.U7154.5 1.3

W/IIT" ' 2.M [ I.'"-(Uib -II."] 14XlJ - 23H2

",2 1 238.2 4.7111 '1,\l' 1).1 X 0.7'l 0.45 100 - 2.'X. 2 4.'X5 - 274 I 279.1 1.8

WHNR C Ih 7fl 0-+4 I.IKI - OX' (,<'2 - 2741 404.0I?'\ '\ Ih

(b) After Earthquake Tesl Tiift N21E PGA O.20g

WIINN f)

I/;'W( I

" "",·tlII'It'

l.lJX \

lUI

\S.1~

1.00 - 0.X6

I, X2 0.42

O.4h 1.IKI

- O.5h] ( IX2. 7UX) ·21K2

-(Ull 71lJ

- 21X2

~5hlj

-22'U

71.4 I- 22'i.~

., IX., )

21~.2

229.3IN.O

( 6.6

2.6

1.4

"liNN j)

("".'1)\~'hlr"n()i,,'

1.93

7.9~

1'\4X[

1,00

OX?

04X

- O.XX

lUX

I.(KI

- 22h4

356.5

- 2UX

XO.h ]-2HX311.4

226.91233.87R I j

8.\

2.8UR

(c) After Earthquake Test Taft N21E PGA 0.30g

WIfNN j.. I.SH[ 1.("

-(un -f15.] [ 1"1-2(J'U ... ] 205.3 5.5

(t.'U.ll ) 7.5 \J.x:! 0,36 1.00 - 205.) 3427 - 215.X 2\5.8 1.9","'T"tllII.'"

14.84 0.45 I.(X) - 0.76 6'/.6 - 215N 277.561.7 1.5

WHNRJ.· 1.73[ l.CXl

- O.M -0"] ( "5.0 - 203.X .75 ] 203.8 6.7(",,",I·t) 7.50 O.H) 0.36 I.(K) - 203.l! 344.0 -217.X 217.8 1.9

WhiTenOlSt'14 ~4 0.4'/ l.lK) - 0.76 h75 - 217.X 277.8

f.fIO 1 '2

3-1\

where

U = dill.': (W;. w;. .....w: )

~ = mass normalized mode shape matrix (c\>'Mc\> = I)

Tahle 3-3 shows the history of dynamic characteristics of the huilding pnor to the retrofit with the

viscoelastic hraces ( from Bracci et al.. I(}(}2c).

3.2.2 Analytical Identification of StitTness

The analytical stiffness matrix was computed hy a standard matrix condensation of the massless

degree" of freedom of the structure. Expressing the overall stiffness matrix K without addition of

dampers in (2.1) as

K =[~: ~] (3.2)

where suhscripts a and ~ correspond to mass and massless degrees of freedom respectively. The

reduced stiffness matrix is determined as

(3.3)

Reinforced concrete has a nonlinear hysteretic behavior in which the force depends on the past

history of deformations and the current state of deformation. The stiffness variations are also

memory dependent and are defined hy the past as well a.. current state of defomlation dictated by

the hysteretic activity it undergoes. In order to predict the response of buildings which have

pn~viously experienced inelastic deformations. the hysteretic properties for all the components

would need to be updated before proceeding any new analyses. As the modr! was subjected to a

number of damaging base motions prior to retrofitting with concrete jacketing, the response pre

dictions for suhsequent tests became questionable. To overcome this hurdle, a simplifying

3-12

TABLE :'-4 Analytical Versus Experimental Damping and Stiffness

Analytical Stiffness Matrix

(kip/in)

(I)

Experimental Stiffness Matrix

(kip/in)

(2)

(a) White Noise, PGA 0.025 Before Earthquake Test #0

[ 1836-239.6 70.0 ] [ 2052 -238.6

71.6 JK= -239.6 421.4 - 278.5 K = -238.6 421.4 - 278.2

70.0 -278.5 430.0 71.6 - 278.2 432.7

(h) White Noise. PGA 0.025 during Test #1

[ 152.5 -IR4.8 396 ] [ 16R.l - 205.369.6]

K = -184.8 315.0 -166.8 K = -205.3 342.7 -215.8

39.6 -166.8 222.0 69.6 -215.8 277.5

assumption was made by which the member structural properties were determined from engineering

data by slightly modifying the gross moments of inertia such that the overall dynamic characteristics

of the building were in agreement with those obtained experimentally from the first low level

vibrations under earthquake excitation test. The identification of the stiffness matrix using this

procedure insured that the influence of the viscoelastic braces can be suitably incorporated. The

analytical stiffness matrix is compared in Table 3-4, with the one identified from experiments using

the measured properties.

3.3 Identification of Natural Frequencies and Damping Ratios

The cxperirr.ental damping ratios are estimated by the half-power method. from the story transfer

functions. The analytical damping ratios are computed from Eqs. (2.13), (2.16) and (2.26). The

identified properties using the two sets of dampers are listed in Table 3-5. Adding the inherent

viscous damping properties of the structure without the additional braces. the total damping ratio

3-13

TABLE 3-5 Structure\, Properties with Viscoelastic Dampers From Strong Vihrations

Identified Dynamic

Characteristic(1)

Retrofitted Structure with Dampers

A(2)

(al Experimental Properties

1.00 -0.72 n55 ] 1.00 -0.72 n56]Modal Matrix (<1» 0.X7 026 - 1.00 O.XX 0.24 -1.00

O.4t> - I.CXl O.M 0.50 1.00 0.64

First Mode Frequency. f IHI.] 2.62 2.13

Total Damping IExp.] E,( lk) 22.0 IX.O

(h) Analytical Properties from Equivalent Dynamic Analysis

1st. mode Freq. IIRad] /IHIII 15.38/2.45 13.07 / 2.0X

Added Damping' ~«(7r) 19.7 15.3

Total Damping ~((7c) 21.2 16.8

(c) Analytical Properties from ClJmplex Eigenvalue Analysis..

I,t. Mode Rotational Frcq. [Rad] 2.96 ± i 14.96 1.98 ± i 12.94

I st. Mode Freq. [(Rad) / [HzII 14.96/2.38 12.94/2.06

Added DampingC~ (7(") 19.4 15.1

Total Damping ~ 20.9 16.6

obtaIned is dose to that identified from the experiment. It is ohserved that the damping ratios

computed analytically arc slightly lower than that obtained from experiment. This could he hecause

the energy dissipated by hysteretic dampers is not included in the analytical computations of

equivalent damping. Also for the range of damping in consideration. the response is not very

sensitive to the additional damping. either inherent viscous, or the inaccuracies ir. the determination

of the appropriate supplemental damping.

lfrom Eq. (2.13)2from Eq. (2.26)

3-14

TABLE 3-6 Analytical Ver~u~ Experimental Damping and Stiffness

Structures Properties Retrofittcd Structure with Dampers

A B( I ) (2) 0)

Story Damping. c Experimental 2.10 1.55

(kiplin/sec) Analylical (total) 2.07 1.60

Experimcntal 49.0 27.5

Story Stiffnes~. Analytical (dampers only) 34.0 15.0

k (kiplin) Analytical (lo:al) 50.0 2X.O

The damping properties and the stiffness of c.:ach Hoor. shown in Tahle 3-6. were cakulated from

data in Tahlc ~-I and Eq. (2.7) and compared with those measured in the identification tests. The

properties corrt:~ponding to frequencies of 2.5 Hz and 2.0 Hz. closet to the actual 2.6Hz and 2.2Hz

for hraces with dampers A and B respectively were selected for analytical evaluation.

The stiffness properties calculated without considering the influence of the mounting brackets of

braces differ largely from those considering thc influence of the brackets influence; (see contrihution

of ~tiffness from damper alone computed from Table 3-1 to the total stiffne~s in Tahle 3-6). The

"total" values are used in further analysis for comparison (If performances.

3.4 Memory Dependancy in RIC Members

The effect of "memory" in the inelastic properties and the sensitivity of structural response to this

memorize effect is ~~hown in Fig. 3.1. The analysis for Test episode #5. subsequent to various other

tests (see Table 3-7). was done in two ways: (i) independently without precise k.nowledge of the

modified hysteretic properties of reinforced concrete members [see Fig. 3-7(a) J and (ii) in a

sequential consecuti.e fashion (ie. analyzing all prior episodes of testing and the current one

consecutively), such that the hysteretic properties are automatically updated (see Fig. 3-7 (b)]. It

is evident that the" memorization" of hysteretic properties is important and the sequential analysis

3-15

-- EXPERIMENT jANALYTICAL

0.41

Z 0.2 ~~ ~~ Ir---J{~ 1.1~ ~~ I

-0.4 IL.-~_-LJ~,---------.A _____0.0 5.0 10.0 15.0 20.0

TIME (SEC)

a. Hysteretic Properties not Updated· Single Analysis

__ EXPERIMENT 1ANALYTICAL 1

-0.4 L-.--_--'__--L-----L._--'-__.....A-__'"'---__L-.--_---'-__--'

0.0 5.0 10.0 15.0 20.0TIME (SEC)

b. Hysteretic Properties Updated. Following Sequential Analysis

"'IGURE 3-7 Top Story Displacement During Taft Earthquake, PGA=O.2g (Test IS)

3-16

duplicates the experimental results suitably.

3.5 Comparison of Displacement and Acceleration Time Histories

A comparison of story displacement. and acceleration. time histuries for tests #3 #5 #8 and # II are

shown in figs. figures 3.8 through 3.15 The analytical response is in good agreement with the

experimental response. Due lo the high level of damping the melastlc response is reduced sub-

stantially a,ld with It many of the possihle errors usually involved in nonlinear dynamic analysis.

3.6 Damper Forces

For two dampers placed at an angle e with the horizontal. the component of damping in the lateral

direction is

(3.4)

and the component of additional stiffness in the lateral direction is

(3.5)

The lateral force in the damper was computed as a combination ofelastic and dampmg components.

The force in each damper (assuming two dampers per floor) is therefore:

(3.6a)

(3.6b )

where i =the story level.

A comparison of the forces obtained in the dampers from Eq. (3.6a) and Eq. (3.6b) to those obtained

from the experiment are shown in Figs. 3-16 through 3-19. The differences are minimal.

3-17

TOP STORY0.8

- EXPERIMENT

~ 0.4 ~- - - ANAlYSIS

%~ 0.0 . • • ••• . , ~

w ., 0' •• .,~, ..~ .0.4 ~en0

.0.8 I I

0.0 10.0 20.0 30.0

SECOND STORY0.8 T

- EXPERIMENT~ 0.4 ~

- - - ANALYSIS

~~ 0.0 • • • ...W ., of •• -'f '.,0

~ .0.4 ~

0

.0.8 .0.0 10.0 20.0 30.0

FIRST STORY0.8

- EXPERIMENT~ 0.4 - - . ANAlYSIS

!z! 0.0 ..~ '. '. 'Y'

i -0.4

-0.80.0 10.0 20.0 30.0

TIME (SEC)

FIGURE 3-8 Displacement Time History with Dampers Afor Taft, PGA 0.051

3-18

TOP STORY0.8

~-- EXPERIMENT

0.4 - - - ANAl'iSIS

~~ 0.0w

i -0.40

-0.80.0 10.0 20.0 30.0

SECOND STORY0.8 I

~- EXPERIMENT

0.4 I-- - - ANAL'iSIS -

!Z~ 0.0 " L l. .l. .

~v' 'vr vv ·w, 'vyv 'y

-0.4 I-fI) -C5

-0.8,

0.0 10.0 20.0 30.0

FIRST STORY0.8 I

~-- EXPERIMENT

0.4 - - - ANAl'iSIS -~~ 0.0 A ••• . ..W V "'. ... . ...~ -0.4Q

-0.8 I

0.0 10.0 20.0 30.0TIME (SEC)

FIGURE 3-9 Displacement Time History with Dampers B for Tan. PGA G.OSg

3-19

TOP STORY0.8 t----.------....,-----.....-----r-----~---_,

- EXPERIMENT~ - - - ANAlYSIS0.4!Z~w 0.0 l----.."rWII

~ -0.4i5

30.020.010.0-0.8 L.- ~ .....l_ __'_ ___L '"-__---J

0.0

SECOND STORY0.8 .----~---__r_---_.__---__._---____r---__,

~ 0.4

- EXPERIMENT- - - ANAlYSIS

~

Z

~W 0.0 l------.rWoJU

~ -0."15

30.020.010.0

-0.8 L- -'-- ...J- -'- -L.. --'- --l

0.0

FIRST STORY0.8 r----~----__r_---_.__---__._---__._---__.

~ 0.4

- EXPERIMENT- - - ANAlYSIS

!Z~W 0.0 ~--.-.r\ll

i -0."Q

30.020.0-0.8 7----"'------L--__"'--- L-__--''--__--.J

0.0 10.0TIME (seC)

FIGURE 3-10 Displacement Time History with Dampers A for Taft, PGA 0.2g

3-20

TOP STORY0.30.. - EXPERIMENT

~ 0.15 - - - ANAlYSIS -~

.~~~~~•. '1.' ...~ •~ 0.00 .... l • f ,""'WYVw~

w0 -0.15 -0~

-0.30 I I

0.0 10.0 20.0 30.0

SECOND STORY0.30 I

.- -- EXPERIMENT

~ 0.15 ANALYSIS -zQ

~~\r.w.v'~~~~--~

~ 0.00LC~

W0 -0.15 -0~

-0.30 I

0.0 10.0 20.0 30.0

FIRST STORY0.30 ,-.. - EXPERIMENT

g 0.15 . . ANAlYSIS -

I 0.00 ".~..~-'-T"'~

~

~ -0.15 ~ -

-0.300.0 10.0 20.0 30.0

TIME (SEC)

FIGURE 3-12 Acceleration Time History with Dampers A for Taft, P<,A O.OSg

3-22

TOP STORY0.30 I I

:;- EXPERIMENT

0.15 - - . ANAlYSIS

~~N,~V'.NtWwJN~N~N~~.tyi 0.00 '."

W...J

~ -0.15 f-

~

-0.30 I I

0.0 10.0 20.0 30.0

SECOND STORY0.30

.- - EXPERIMENT

S 0.15 ANAlYSISzQ

}~/1f'ItA4~~~""'~~~-....~ 0.00W...JW

8 -0.15

<

.a.3O0.0 10,0 20.0 30.0

FIRST STORY0.30

:; -- EXPERIMENT

0.15 f-" ANALYSIS -

~~UA~~~

< 0.00II: -'~·f ~ -~~ .a.15 ~ -~

.a.3O I

0.0 10.0 20,0 30.0TIME (SEC)

FIGURE 3-13 Acceleratioo Time History with Dampers B for Taft, PGA 0.05g

3-23

TOP STORY0.30 r------...--------,--------.--------,----r------,..

~ 0.15 I I-EXPERIMENTI II ... ANAly~S

30.0-0.30 '::-__~ I...___I__....I.....-_____lI'_____..o......____1

0.0 10,0 20.0

SECOND STORY0.30 ,.------r----r-------'-,-----r-------.

FIRST STORY0.30 .------...-----,-------.--------,r-----....------,

.. - EXPERIMENT

I:: ~,~;t~ ~~~\~I~;~~I~IkN,w~~~:::· .. ·~ -0.15 I ,

30.020.0-0.30 '::---....I.....------J.-----'------l---"'-----~

0.0 10.0TIME (SEC)

FIGURE 3-14 Acceleration Time History with Dampers A for Taft, PGA O.2g

3-24

TOP STORY0.30 r----~----,-I--~~---~I---~.---~

.. - EXPERIMENT

~ 0.15 ~ . ~ I l . --.ANAlYSIS

~ 0.00 I---~~wo -0.15~

30.020.010.0-0.30 L-.-__--"-__~ ~ _L______'______J

0.0

SECOND STORY0.30 .-----.------,-I---.-------rl---~--........

30.020.010.0-0.30 L--__--'--__---I... ""----__J.--__---'-__----l

0.0

FIRST STORY0.30 .-----r-----,----..-----.----,-------,

30.0-0.30 L:------"--_~I L._____L..I -'---_____.J

0.0 10.0 20.0TIME (SEC)

FIGURE 3·15 Acceleration Time History with Dampers B for Taft. PGA 0.21

3-25

TOP STORY TOP STORY8.0 8.0

1 I 1 1

EXP~RIMENt 1 ANAlYTICALI 1

f 4.0,.. __ ..J ___ J.. ___ 1___

f 4.0,.. __ ..J ___ J.. __ -1___

1 I 1 1 1 1

g 1 1 I~

I I I

W 0.0,.. __ ..J ___~ ___ 1___

w 0.0,.. __ ..J ___ , __ -1___

(.) 1 I 1 (.) 1 I I

~1 I 1 ~ I I 1

....0,.. __ ..J ___ 1. ___ 1___

l&. ....0 f- - - ..J ___ 1. - - _1- __1 I 1 I 1I I 1 I I

-8.0 -8.0-0.3 -0.15 0 0.15 0.3 -0.3 -0.15 0 0.15 0.3

DISPlACEMENT (IN) DISPLACEMENT (IN)

SECOND STORY SECOND STORY8.0 8.0

I 1 1 1 I

,.. _E~J1~I~~N! ___:___ ANALYTICAL! 1

Ui 4.0 Ui 4.0__ ..J ___ J.. ___ 1___

Q.. 1 I 1 9: 1 I I

g 1 I 1~

I 1 I

W 0.0 --~---I---:- -- W 0.0 --~ ---1- --:- --(.) (.)a:: 1 I I a:: 1 I I

~ ....0_ _ ..J ___ J.. ___ 1___ ~ ....0

__ ..J ___ J.. ___ 1___

1 1 1 I I 11 1 I 1 1 I

-8.0 -8.0 I I I

-0.3 -0.15 0 0.15 0.3 -0.3 -0.15 0 0.15 0.3DISPlACEMENT (IN) DISPLACEMENT (IN)

FIRST STORY FIRST STORY8.0 8.0

1 I 1 1 1

EXP~RIMENt 1 ANALYTICAl! 1

U; 4.0_ _ _ __ J.. ___ 1___

6i 4.0_ _ ..J ___ J.. ___ 1___

Q.. I I I 9: 1 1 Ig.

--~-_._,---:--- ~1 I 1

~0.0

~0.0 - - ~ - - ,- - -:- - -

a:: I I 1 a: 1 I 1f2 ~.O__ ...J ___ 1. ___1___ f! --4.0

_ _ ...J ___ .L. ___ 1___

I I I I 1 I1 I I 1 1 I

-8.0 -8.0-0.3 -0.15 0 0.15 O.:i -0.3 -0.15 0 0.15 0.3

DISPLACEMENT (IN) DISPLACEMENT (IN)

FIGURE 3-16 Force Displacement of Dampers A for Tan, PGA 0.051

3-26

TOPSTORV TOP STORY

-8.0 L,.,---L----"-~--'-_1_.L-.L-L-J..........__'

-0.3 -0.15 0 0.15 0.3DISPLACEMENT (IN)

8.0 [' , i I • ; • , i ' t Jiii 1,.0 ~:f.~ ~ - - _:- --a. I I Ig I I ,

W 0.0 - - ..J - - - • - - - ,- - -o 1 1 1a:: I I If2 -4.0 - - ...J 1. - _ - '- _ -

I I 1I I I

0.3

0.0

1,.0

1 I I

_E~rj~I~~N! : _1 I II I I

__ ..J _. _ -i1 - - _1- - -

1 I I, I I

__ ..J 1. 1 _

I I II , ,

-8.0 '---'---L----"---'-~.J--'--~.l__IL._..I__'-0.3 -0.15 0 0.15

DISPlACEMENT (IN)

SECOND STORY SECOND STORY

I 1

(j) 4.0 r- _E~'1~I~~Ni : _a. I I 1g I I I

~ 0.0 r- - - ~ - - #- - -:- - -a:: I' I

f2 -4.0 t-- - - ...J - - - 1. - - _1- - _I I 11 I I

I

ANAL'iTICAl I ,__ ..J 1. 1 _

I I I1 I ,

- - ~ - -~ - -:- --I I ,

_ _ ...J .L 1 _

I I II I I

0.3-8.0 '---'---L----"---'-~_'__'__-I....-.l__L--I.....J

-0.3 -0.15 0 0.15 0.3DISPlACEMENT (IN)

-8.0 L-t.~.....l.......-.L..J--'----'-.....L.--'--.Io--J

-0.3 -0.15 0 0.15DISPLACEMENT (IN)

FIRSTSTORV FIRSTSTORV

I I I

iii ".0 r- ~~Pj~I~~t - - _:- - -e: I I~ I I I

~ 0.0 t-- - - ~ - - ,. - -:- - -

a:: 1 I I

~ ".0 r- - - ..J - - - 1. - - _1- __I I I1 I 1

-8.0 I I

-0.3 -0.15 0 0.15 0.3DISPlACEMENT (IN)

I I

ANALV'rICAL 1 IVi 4.0 - - ....J - - - 1. - - -1- - -a. I I I~ I I I

~ 0.0 - - ~ - -~ - -:- - -

a:: I I I~ .....0 - - ...J J. 1 _

I I II I 1

-8.0 I I

-0.3 -0.15 0 0.15 0.3DISPLACEMENT (IN)

FIGURE )-17 Force Displacement of Dampers B for 1'aft, PGA 0.051

3-27


1 1 I 1

_E~j~I~~N! ___:___ ANALTTICAL I 1

f •.0~

4.0__ .J _ - _!. ___ 1__ -

1 1 1 1 I 1

~- - ~ - -, - -:- - -

& --~--*--:- --w 0.0 w 0.00 00: I 1 I ~ 1 I 10u.. ......0

__ ..J ___ L ___1___ u.. ....0_ _ .J ___ !. ___ 1___

1 I 1 1 I 1I I 1 1 I 1

-8.0 I -8.0-0.3 -0.15 0 0.15 0.3 -0.3 -0.15 a 0.15 0.3



1 I 1 1

_E~~I_:___ ANALYTICAL 1 I

Vi •.0 fi) •.0 --:/1-:---a.. a..g I I g.W 0.0 __ ..J _ _1___

w 0.0 __.J_ _1 ___

0 I 1 0 1 10: I 1 a: 1 1l( ......0

__ ..J ___1___ f2 ....0_ _ .J L ___ 1___

1 I 1 I I 11 I 1 I 1 1

-8.0 -8.0-0.3 -0.15 0 0.15 0.3 -0.3 -0.15 0 0.15 0.3



I 1 I 1

_E~j~I~_Nt ANALYTICAL 1

fi) 4.0 f •.0__ .J ___ !.

a.. I 1 I

i I ~ 1 1

~0.0

__ ..J 1_- _W 0.0

__ ..J_ _1- __

1 0 I Ia: 1 0: I I~ ......0 - - _1- __ ~ ......0 - - _1- __

1 I1 1

-8.0 -8.0-0.3 -0.15 a 0.15 0.3 -0.3 -0.15 0 0.15 0.3


FIGURE 3-18 Force Displacement of Dampers A for Taft, PGA 0.21

3-28


I I I I

_E~~I~E!4! ___:___ ANAL'/TICAL I I

f 4.0 f 4.0_ _ ..J ___ 4. ___1___

I I I I I I

~

- -~- -,--:--- ~I I 1

W 0.0 W 0.0 - - ~- -~ - -:- --() 0

~I I 1 !5 I I 1

"'.0__ ..J ___ L ___1___

~ "'.0_ _ ...J ___ 1. ___ 1___

I I 1 I I 1I I 1 I I 1

-8.0 I I -8.0 I

-0.3 -0.15 0 0.15 0.3 -0.3 -0.15 0 0.15 0.3DISPlACEMENT (IN) DISPlACEMENT (IN)


I I I 1

... _E~~~I~~Nt ___:___ ANAL"TICAL I 1.- 4.0 en 4.0

__ ...J ___ 1. ___ 1____

en .__J(#1--- __JI)__Q. Q.

g gw 0.0

~0.0

() I 1 I 1a: I 1 II: I 1

~ "'.0... __ ...J ___ L ___L __ ~ "'.0

_ _ ...J ___ 1. ___ 1___

I I 1 I I 1I I I I I 1

-8.0 -8.0-0.3 -0.15 0 0.15 0.3 -0.3 -0.15 0 0.15 0.3

DISPlACEMENT (IN) DISPlACEMENT (IN)


I I 1 I

E~RIMENt ANAL.Y'rICAL I

f 4.0 -- --- -- f 4.0__ ..J ___ 4. __

I 1

g, I ~ I

~0.0 __ ..J

~0.0

__ ..J

II: II:f[ "'.0 ~ "'.0

-8.0 -8.0-0.3 -0.15 0 0.15 0.3 -0.3 -0.15 0 0.15 0.3

DISPlACEMENT (IN) DISPLACEMENT (IN)

FIGURE 3-19 Force Displ8ftment 01 Dampen B for Taft, PGA 0.11

3-29

3.7 Base Shears and Damper Stift'nesses

The hase shear developed in the columns is compared with this obtained from the experiment in

Figs. 3-20through 3-23. Only a limited inelastic response occurs in columns while energy is mostly

dissipated by the viscoela:o.tic hraces. The braces also display substantial stiffness as shown by the

sloped hysterias ill Figs. 3-16 through 3-19. The stiffness calculated without considering the

influcncc of mounting hrackets is largely different from this considering the brackets influences.

(sec contrihution of stiffness from damper alone computed from Table 3-1 to the total stiffness in

Table 3-4). The "total" values are used in further analysis for comparison of performances.

3-30

I I I

I I I

EXPERIMENT I I II I I

--------,---------r--------,---------I I I

- - - - - - - - ~ - - - - - --/-- - - - - ~ - - - - - - - - -I I II I I

--------~---------~--------~---------I I II I II I I

10

U)5~

52CE:<~ 0U)

i::>g -5

-10-0.3 -0.15 o

FIRST STORY DRIFT (IN)0.15 0.3

5

o

-5

10 r--'--~-'-'I---r----,--"",,·-.......,r----r--"""T"""---"--""'--"'"

IANALYTICAL I

I I I

--------,---------r--------,---------I I I

--------~------~------~---------I I II I I

--------l---------r--------l---------j.10 I • Itt I I , •

-0.3 -0.15 0 0.15 0.3FIRST STORY DRIFT (IN)

FIGURE 3-20 Base Shear in Columns with Dampen A. for Taft, PGA. 0.051

3-31

10 ,..---r--"""T""--....--,-"""'T""---.-----.,--....---r---,r--......--........---.I I I

EXPERIMENT I I II I I

5~--------,---------r--------,---------I I I

O"--------~-----~-----~---------I I I

~~--------~---------~--------~---------I I II I II I I

I I T, I I

ANALYTICAL I I I

I I I--------,---------r--------,---------I I I

--------~------~----~---------I I II I I

--------~---------~--------~---------I I II I I

I I I

10

~ 5~

~

*0

~S -5

·'0-0.3

-0.'5

-0.'5

oFIRST STORY DRIFT (IN)


0.15

0.15

0.3

0.3

FIGURE 3-21 Base Shear in Columns with Dampen B for Taft, PGA O.05e

3-32

0.30.15

III

--------~---------II

I I

-----~--------~---------I II II I


-0.15

I

EXPERIMENT II I

--------i---------r------I II II I

--------~--------III

--------~--

10

~ 5:.c

a:c~ 0en!:Jg -5

-10-0.3

0.30.15oFIRST STORY DRIFT (IN)

,---------III

-------~---------II

I I

-------~--------~---------I II II I

-0.15

IANAlYTICAl I

I I--------,---------r------

I II II I

--------~--------III

--------~

10

en 5~

~

I 0

i:)

g -5

-10-0.3

FIGURE 3-22 Base Shear in Columns with Dampers A for Taft, PGA 0.2.

3-33

0.30.15

III

-------~---------I

II I

----~--------~---------I II II I


-0.15

IEXPERIMENT I

I I--------,---------,------

I II II

--------~--------III

----------l--

10

en5~

i2IX:C

~ 0en!=>g -5

-10-0.3

0.30.15oFIRST STORY DRIFT (IN)

III

-------~---------II

I I

------~--------~---------I II II I

-0.15

IANAlYTICAL I

I I--------,---------r------I II II

--------~--------III

----------l

10

en5~

i2IX:C

!t! 0en!=>S -5

-10-0.3

FIGURE 3-23 Ba~ Shear in Columns with Dampers B for Taft, PGA O.2g

3-34

SECTION 4

EFFECTS (W VISl'OELASTIC BRACI':S ON STRUCTlJRAL RK~P()NSE

The interpn:tatilln III thc expenmental data rClJuire~ a good analytical model that is capahlc of

providing internal mformatinnnf forcc~.I()caldcformatiom.and(hange~in ~tructuralcharacteristic~.

The analytical model ~pe(ifled and vcrilled in the previous sections is used in conjunction with the

eXj'l<:rin\l:ntal rl'~lIlts to identIfy the ml1uem:e nl the dampers <m the modifil:atioo of stiffness.

redistrihutlOn Ill' internal forces and redistrihution of energy dissipation hclwccn e1emenh. The

intlucnu: of viscoelastic dampers is summaril.cd as follows:

4.1 Natural FrequendesIPeriod

The structure with visCllClasti( hraces suhjected to low level (white noisel displays simultaneous

inaeasl'1Il frequencies and l'quivalent viscous damping in all modes as shqwn in Figs. 4-1 and 4-2

and numcllCally III Tahle 4-1. The apparent damping increased 4 times in the structure with dampers

A and 3 time., in the structure with dampers B. Both types of dampers contrihute to an increase in

structural stiffness and therefore a redm.:tion ufthe natural period that might contrihute to an increase

of the overall hase shear.

TABLE 4-1 FIrst Mode Dynamic Characteristics During Low Level Vibration Tests

Natural Frequency (Hz) Period Equivalent Viscous Damping %

( I ) (2) (sec) (3) (4 )

No dampers 1.88 0.53 5.5

With damper A 2.93 0.34 22.0

With damper B 2.54 0.39 18.0

4-1

TOP STORY

20.015.010.0FREOUENCY.HZ

5.0

I

WIT~ DAMPERS I :

--.---------r--------,---------WitH DAMPER A I :

--~-~---- ----~--------~---------.• I I I

... - J ..

1!».0

~ 10.0~

~IL.::::i

! 5.0

0.00.0

SECOND STORY

5.0

810.00(()

ir~::Ic:

I

WI~HOUT DAMPERS I :

--.---------r--------,---------I I I

1 WITH DAMPER A : :

-~~---------:--------~---------I'" I I I

FIRST STORY15.0 r--.....--__,_---.-.,...--.-__,_-~~___._--,-or__r___,_-~._--,----.--r---r-_,

10.0

I IWITHOUT DAMPERS I

I I I--.---------r--------,---------I I II I WITH DAMPER A II I I

-----~---- -~--------~---------I I II I

I • '. ' .. ,,,.0.0 L:~.::s..~~~::.:.~~~~...~ed~~~~~~~2O0

0.0 5.0 10.0 .FREQUENCY, HZ

~~Qi 5.0

FIGURE 4-1 Acceleratioo Transfer Functioo with Dampers A(for White Noise PGA 0.0251)

4-2

TOPSTORV

10.0~

§i 5.0

~~_~=~~~~=-~:.::.~~"'=,.~.L~'?l!"'~'~~~~~~~l!!:!!Il!~__~0.0 L

0.0 5.0 10.0 15.0 20.0FREQUENCY. HZ

SECOND STORY

~ ::: r--~~--.---_.--,"-I~~~~~~-T_-D""~-_-P.,....~-~-~..._-_-rl-_"""'_-_...,_-_-r,-_-_'T'-_-,r1-_...,~...-_ -r~-_--'-~-_---'-~-_""1

!< I I Is.2U. I WITH DAMPER B : :

~ So. ~.74---------: --------~---------I I

0.0 ~~---,-"::=::~~....~~~~~~~~~~~~~~~~....."j0.0 5.0 10.0 15.0 20.0

FREQUENCY. HZ

FIRST STORY15.0 r---'--~-"'---'--"""""'-""---'----'--""--~---'----'-""-""""'--r-""--""""'----"-"--""

10.0

I IWITHOUT DAMPERS I

I I I--,---------r--------,---------I I I

I WITH DAMPER B II I I

-----~---- -~--------~---------I , I

I II

0.0 ~=-~~~~~~~~~:.::&~~~~~~5~y0.0 5.0 10.0 15.0 20.0

FREQUENCY, HZ

~

5i 5.0

FIGURE 4-2 Accderation Transfer Function with Dampen B(for White Noise PGA 0.0251)

4-3

The frequencie.. identified from lhe while noi ..e tests ..how a higher natural frequency for hoth

dampcr"lypcs A and B than that delermined during earthquake (Tesl .. #5 and #11. Tahle 3-2) from

Ihe lran.. fer rUnt'tlon.. for lhe lop ..lory acceleration, The rcason for these differences is in lhe

nonlineanty of the nacked relllforced concrete section... At very low vihratinn... pre-exisling cracks

do not opcn and the ..ection .. hchave almosl like ideal "gro......ections', At larger vihrations. such

a.. tho..e created dunng earthquake... the nack.. open lhu.. rcduclllg the ..liffne.... and their "natural

frl'quency", Small variation.. are oh..erved also for the equivalent damping.

4.2 Stor)' .'orces and Drifl..

The inler· .. tory drifts and ..tory shears in the columns are suhstantlally reduced at all floors as

mdiciJlcd III TiJhlc 4-2, While the defnrmations arc reduced approximately 3 times. the shear forces

arc reduced only twice. These forces arc much smaller than lhe ultimate strength of the columns.

moreover smaller than their yielding strength (see also Bracci et. al.. 1992a and 1992c). A sct of

force-deformations ,It the first floor for Taft earthquake motion (PGA O.20g) (sce Figs. 4-3 and

4-4) indIcate.. that the column forces and deformations are substantially reduced. while most of the

energy dIssipation (arc.! of hysteretic loops) is transferred from the columns to the viscoelastic

dampers, Although some inelastic deformations are experienced by the columns. their response is

sub.. tantially improved in the presence of the viscoelastic braces.

4.3 Columns Axial Forces

The addition of hraces changes the load transfer pattern in the structure, Additional axial forces

will he generated in the columns by the added brace stiffness which are in pha"e with the other

forces from the structural stiffening system,

The axial force variation in the columns in the presence of dampers is shown in Figs. 4-5 and 4-6.

The trajectory of variation of the axial forces and moments are plotted in comparison to the failure

envelopes on a P-M interaction curve. The reduction in the moment demand (horizontal fluctuation)

4-4

25.0 .----.-----.--.-----.-----.--..---.--,

0.8

I 1 I, 1 ,

15.0 ~ - - -,- - - i - - -,- - -I 1 I

5.0 ----4--X+--1---, 1

, 1 1-5.0 - - -I - - I - - - 1- - -

I 1 1-15.0 ... - - .., - - - l' - - -1- - -

, I 1

.25.0 L-....l.-.....L.--'-_'---'--.....L.--'----'

-0.8 -0.4 0 0.4INTER-STORY DRIFT, IN

IiiCl.S2a:oe(w::r(/)

enz~::>

5u

0.8

, I

I I---,---r--I I

---4---I

___I_II

5.0

-5.0

15.0

-25.0 ~....l.--I---L. ~_L...-....L-----'---.J

-0.8 -0." 0 0."INTER-STORY DRIFT, IN

-15.0

enCl.g,a:oe(w::r(/)

(/)z~:::l~ou

enCl.ga:~::r(/)

(/)a:wCl.:Eoe(Cl

25.0 ,---.,....--r-.........-.----.,....-.....,..............--,I

I 1 115.0 - - -, - - - T - - -1- - -

5.0 --~--.-:----5.0 ~ - - -: - • - -:- - -

I , 1-15.0 ... - - .., - - - T' - - -1- - -

I I ,

-25.0 I I I

-0.8 -0.4 0 0.4 0.8INTER·STORYDRIFT, IN

I I, , I

- - -1- - - T - - -,- - -I I I

- - --l - - - - -1- - -I ,

- - _1- _ _ __ 1 _I II I

- - .., - T - - -1- - -, I I

5.0

-5.0

15.0

25.0 .--.,....-.....,..............-.----.,....--r---,.-

-25.0 L.-....L---'----''--..L--I-----'_-'--..J

-0.8 -0.4 0 0.4 0.8INTER-STORY DRIFT. IN

-15.0

-,- --I

- - _1- __I

1 ,- l' - - -,- - -

I I

,, ,---,---,--, ,---4._--,---'--I

I

5.0

-5.0

15.0

-15.0

-25.0 L...-"""'-........--"_"--..........~----''-----'

-0.8 -0.4 0 O.~ 0.8ImER·STORY DRIFT. IN

WITHOUT DAMPERS (TEST' 0) WITH DAMPERS A (TEST' 5)

FIGURE 4-3 Forces-Deformations at First Floor with Dampers A for (PGA O.2g)

4-5

Ii) 25.0(i) 25.0

I IQ. Q. I I Ig 15.0

I I~ 15.0---,---r-- - - -1- - - r - - -1- --

II. , I a:

"--~--£-:---« 4(UJ 5.0 -- .... --- UJ 5.0~ I ~ , Il/l (/J

l/l -5.0 - - -'-- (/J -5.0 ---'-- !. ___ I__ -Z I Z I 1 1~ , ~ 1 1 1::> -15.0 :J ·15.0 r- - - ..., - - - ,. - - -,- - -..J ..J0 0 I 1 1(,) u

-25.0 ·25.0-0.8 -0.4 0 0.4 0.8 -0.8 -0.4 0 0.4 0.8

INTER-STORY DRIFT, IN INTER-STORY DRIFT. IN

25.0Ii) I I IQ. tilg 15.0 ~ - - -I - - - r - - -1- - -a: 1 I 14( 5.0

r---~-.-:---wJ:(/J ___1- ___ 1___(/J ·5.0a: I I IW , I IQ. ·15.0~

- - .., - - - r - - -1- - -

"" I 1 I0

-25.0 I I I

-C.8 -C.4 0 0.4 0.8INTER·STORY DRIFT. IN

25.0 25.0

fI 1

15.01 I f 15.0

1 1 1---I---r-- ---:-1-:---~ I I ~IX: 5.0 -- .... --- -1- -- IX: 5.0 - - .... - - - -1- - -

i I 1 ~ , I

-5.0 ---'-- - - _1- __ i -5.0 - - -' - - - - -'- - -~

I I~

I I, I I I 1 I

~-15.0 - r - - -1- -- ~

-15.0 - - .., - - - r - - -1- - -I I , I I

-25.0 ·25.0I I

-0.8 -0.4 0 0.4 0.8 -0.8 -C.4 0 0.4 0.8INTER-STORY DRIFT,IN INTER·STORY DRIFT. IN

WITHOUT DAMPERS (TEST It 0) WITH DAMPERS a (TEST' 11)

FIGURE 4-4 Forces·Deformations at First Floor with Dampers B (or (PGA O.2g)

4-6

~-"--.-.....l-I._~~-------'-200 ·100 0 100 200 300

MOMENT. KIP·IN

SECOND FLOOR BOTTOM

200 ~I

100 ~

·1 00 ~---L.--------'-----__

-300 -200 .100 0 100 200 300

FIRST FLOOR BOTTOM

200 ~- -- ........... __

100 ~ (/// "~~ \

o ~-~, __< ./d-//~, --~--------

.100 I__~_- _L.-:r=---'----......_~~_·300 ·200 ·100 0 100 200 300

FIRST FLOOR TOP300 ----.----~ ---r----~- -"-~-·l

SECOND FLOOR BOTTOM300 ;. -~-----r--~- r---.----T--~ -T---~-~-

~ !

~ r ///~~--"100 ~ ( /~ ,~ "

ol-~~ i\JLl "-<::::< ~~

-100~ -l--..--.~_-L_---'-300 ·200 -100 0 100 200 300

FIRST FLOOR TOP

FIRST FLOOR BOTTOM300 ~- i 1 300

en -~ : UlQ. 200 SUHF DYNAMIC lL 200 ,g Ulnw.rE g

\0 SURFACE, 0.: 100 .: 100 ~0 0

f..J ..J...J ...J.: D~- .: 0'X X r<

tSURFACE < i

-100 ·100·300 ·200 ·100 0 100 200 300 -300

MOMENT. KIP·IN

WITHOU r DAMPERS (TEST -a) WITH DAMPERS A (TEST '5)

FIGURE 4-5 Capacity Diagrams versus Force Demands in Interior Columnswith Dampers A

4-7

SECOND FLOOR TOP SECOND FLOOR TOP

SECOND FLOOR BOnOM300 :--.------------~-r__------,---.-----,---..----

l i200 ~ --------T~ ~

\ /-----,/ ~/ ~100 r ~

o ~, --..J ~j ~

,100 __-"--_-'--_.J...-..-_-'--__-----J

-300 -200 -100 0 100 200 300

FIRST FLOOR TOP FIRST FLOOR TOP300 ---~--.--

300100 200o

200

-1 00 '---_'--_'---_'--._~_.L

·300 ·200 -100

100

ViQ.

go

~g

,~r-"'!l, ~ ~-300 ·200 ·100 0 100 200 300

FIRST FLOOR BOTTOM FIRST FLOOR BOTTOM

Ol-----~..~-------i

.1 00 L~_'__~__.L__......_ _"__-'-_ ___J

-300 ·200 ·100 0 100 200 300MOMENT, KIP-IN

200 300

'00

300 rl----r---r------r--~~-,t NOMINAL ULTIMAn: I PROJECTED 1 Vi

200 SURFA , K DYNAMIC 1 Q.

1g

Ul:--:~E 09~

o r--- - CRACKING :!f SURFACE j ~

•100 '---~---'-'---,-, ~~~'-"~----'-~--.J-300 ·200 -100 0 100

MOMENT. KIP·IN

WITHOUT DAMPERS (TEST '0) WITH DAMPERS B (TEST 1111)

FIGURE 4·6 Capacity Diagrams versus Force Demands in Interior Columnswith Dampers B

4-8

TABLE 4-2 Maximum Measured Story Response

Inter-Story Drifts, (in.) Column Story Shears, (kips)

first Second Third First Second Third

(1 ) (2) (3) (4) (5) (6) (7)

(a) For White Noise Excitation

No Dampers n.047 0.034 O.OIR 238 1.53 1.33

Damper A 0.016 0.013 0.008 0.97 0.65 0.46

Damper B O.ll\9 0.017 0.008 1.25 0.84 0.52

(0) For Taft 0.2g Excitation

No Dampers 0.656 0.388 0.167 20.63 16.20 10.71

Dam(X'r A O. )94 0.147 0.066 7.68 5.71 4.19

Damper B 0.297 0.196 0.097 9.47 8.25 4.67

is quite significant with the addition of dampers. However some inclination of the trajectory is

noticed, more signifi(;antly in the first story columns. This indicate some variation of the axial load.

Although insignificant in this test case. increase in axial forces might lead to exceedence of capacity

envelope. C~re should he taken in the design of columns with dampers such that the axial load!

mument demand do not intersect with the failure envelope. This could be of serious concern

especaJly in the design of taller structures, where the axial load gets accumulated at the base.

4.4 Energy Input

The effect of the viscoelastic dampers is more evident in the distribution of the energy input

throughout the structural system. Assuming that the energy balance (Uang and Bertero. 1990) at

each time step in any structure is:

(4.1)

4-9

where /:', I~ the kinetic energy. Ep is the clastic/potential energy. EH is the hysteretic energy dissipated

hy the structural system. I:'~ is the viscou, damped energy. and £, is the total energy input. The

hy,teretic energy (f' 1 l' usually associated with the permanent damage in the structural system.

A reduction of this energ) can result in a reduction of damage.

The addition of dampers adds another term to the energy halance:

(4.2)

where 1:'1/ is the energy dissipated hy the added viscoelastic dampers and E1. is the elastic-kinetic

energy (/:', + /:'/,).

The viscoelastic dampers alter thc overall energy input halance as shown in Fig, 4-7. For the

earthq uake used in the experiment (Taft 1952), shown in Figs. 4-7a.h the total input energy is

increased primarily due to stiffness increase. However the added viscoelastic dampers dissipate

the majority of this energy. leaving only a small amount of hysteretic energy to be dissipated by

the structure. In th~ structure without dampers. the majority of input energy is dissipated in form

of hysteretic ~nergy hy the structural components, that are actually damaged. Similar pictures are

obtained analytically for other earthquakes (see Fig. 4-9). although the overall energy input may

vary depending on the match between the structural frequelicies and the earthquake frequf'ncy

content.

4.5 Damage Mechanism

The amount of damage to the individual members, story levels, and overall structure from seismic

excitations can be described analytically in terms of damage indicators defined as damage indicies.

These damage indicies are used to evaluate the extent of damage on a scale representing minor.

moderate. or severe damage. Damage index models have been developed to incorporate effects of

ductility demand and low cycle fatigue or strength deterioration by Park et aI. ( 1985). Chung et at.

4-10

NO ADDED VISCOELASTIC BRACES ADDED VISCOELASTIC BRACES

30.0 r---.--,.--""'---T""--"""""--'

TAFTt952

f• 20.0

~

i~ 10.0w

[

TEAETI:

KINETlC VISCOUS

'/,~...::- ==-= I-: -.: =-=.: -.=0.0 .....c..~ _, ._.~..... .c...",-....0.0 10.0 20.0 30.0

TIME (SEC)

TAFT 1952

~ ,,'--,~AET:-.;,.J

.{ ~1(1NET1: _.I.~~. ..V __ -""~..... ,._I-- .. ~. .1_ .••• _ ..•.

10.0 20.0 30.0TIUE(SEC)

5.0

0.0 .0.0

25.0

~• 20.0

e.~> 15.0

"a:~ 100UJ

(a) (b)

40.0 r--'---r--'--,,--'--,,--'---, 40.0 ,.---,-.-.---r--.--.......- ,----,-..,

MEXICO 1985

K

0.0- -,,-_0L::00.0

f 30.0

e.x;:- 20.0

~

~ 10.0

..PUT

MEXICO 1985

I(

~.," \/ISCOUS

0.0 -- -~-<,:,- ~,::.l-_'"-,,0.0 20.0 40.0 60.0 80.0

TIME (SEC)

g 30.0

0-i';- 20.0

Ifffi 10.0

(e) (d)

eo.OELCENTAQ 11140 ELCENTAO 1940

f---~o:e:-1/.1

.~--::j:"'::'::7~:::=1. .-.;.7.::1.:. . ...... . ,r:

10.0 20.0 30.0TIME (SEC)

Cf)

100.0

80.0i"~ 60.0~

1;010.0a:

~w

20.0

0.00.030.0

0.0 ,' •.._"-'4_••. ;;...••.•. 1 •.0.0 10.0 20.0

TIME (SEC)

(e)

20.0

100.0 ,.---.---.--,...-.-.......-r----,

!l:: 60.0~

~ 010.0

ffi

FIGURE 4-7 EneraY Input in the T_ Strudure

4-11

( IlJ~7), Powell et al. ( 1988), and Bracci ct al. (I {)89). It h4ls been shown, that a combination of

deformation and strength deterioration damages provide an accurate assessment of the member

damage and of the remaining reserve capacity. Such a damage model is used here to verify the

slructure performance and dampers. This model is a modificd version of the Park and Ang's model

[Kunnath et al. I t)l)()] expres ...ed in terms of momenls and curvatures of structural members. The

expression for this damage index IS given by:

where Q>n"" = maximum observed curvature, Q>U/f = ultimate curvature. ~ = strength deterioration

fador, jdE = ab.,orbed hysterctic energy. M, = yield moment. A procedure for determining the

ultimate curvature in both columns and beams was proposcd by Bracci et 411. (1989), with the damage

index formulated to vary between 0 and I. The extent of damage 10 the structure is determined

fmm the following damage index table.

DI =1.0

0.06 ~ DI < I

0.33 ~ DI < 0.66

0.0 < DI < 0.33

Collapse

Severe - "Irrcpairable" Damage

Moderate - "Repairable" Damage

Minor - "Serviceable" Damage

The structure with viscoelastic dampers experiences a reduced number of plastic hinges and cracks

when subjected to the same earthquake motions (see Fig. 4-8). In fact. only minor cracks and some

unavoidable base column hinging can be noticed. The damage configuration (hinging) does not

indicate development of either the column-sidesway or beam-sidesway collapse mechanisms. The

actual story damage evaluated using the above model is shown in Fig 4-9. It indicates the efficiency

of the added braces to limit the damage to less than half ofthat developed in the original unretrofitted

structure.

4-12

WIT

HO

UT

DA

MP

ER

S

LEGE

ND

3n·

,i

'I

'I

FIG

UR

E4·

9S

tory

Dam

age

Eva

luat

ion

oI

II!

~,

II

I

o0.

10.

20.

3S

TOR

YD

AM

AG

EIN

DE

X

-1.

....,-

----

.

3n

f'"

I--

TAFT

ME

XIC

O-

--

ELC

EN

TRO

oI

III

"I:!

,

o0.

10.

20.

3S

TOR

YD

AM

AG

EIN

DE

X

WIT

HD

AM

PE

RS

...J w2

~ > a: °1 ~...J w2

> ~ >- :x:._

_~

~1

r!I

-\en

(b)

Bui

ldin

gw

ithad

ded

dam

pers

FIG

UR

E4-

8M

echa

nism

form

edin

the

Bui

ldin

g

(a)

Bui

ldin

gw

ithou

tadd

edda

mpe

rs

'\---

------

1tf-

------

-m---

---r

I I I

----

----

----

----

--, , , I ,

----

----

----

----

--I I , I I

----

----

---

----

----

----

----

I,

/I

I

I,

I,

I,

I,

II

II

----

----

-~

----

----

---

----

----

--I

I

~,

I

II

II

II

II

II

II

II

II

----

----

---

----

----

----

----

I

'V'

I

II

,I

II

,I

II

,I

II

II

I~

~I

Yie

IdlId

CtII

dled

w ~

~f" -

SECTION 5

INt'LUENC}: OF VISCOELASTIC PROPERTIES ON SEISMIC RESPONSE OF RIC

STRUCTURES

The I:~ scale model structure described in the previous section is further used as the subject in an

analytical evaluation for stIJdying the effects of increasing either the viscous propenies, or clastic

stiffness properties, or both of the ahove, for seismic retrofit of reinforced concrete structures using

viscoelastic materials.

It is well known that increased viscous properties in an elastic structure (ie. increase in the equivalent

critical damping ratio) contributes to a reduction in the dynamic response amplification as shown

in Fig. 5-1 a. It is also known that a structure responding inelastically ex.periences a softening effect

or a reduction in its fundamental frequency (see Fig. 5- Ib). The effect of increasing the viscous

properties is more drastic in an inelastic system, since it limits the decrease of the fundamental

frequency to a stable level not far below its elastic value (see Fig. 5-2).

Viscoelastic dampers have also a substantial contribution to the initial stiffness of the structure.

The added stiffness supplied by viscoelastic braces increases the first mode natural frequency in an

elastic lo.uperstructure as shown in Fig. 5-3a, while the viscous properties have a small effect. In

reinforced concrete structures experiencing inelastic deformations, the additional stiffness increase

the natural frequency, only if substantial damping is added to the structure. Otherwise the tendency

of stiffness softening during inela·;tic response will almost compensate for the increased stiffness

due to addition of dampers. It should be noted that while the stiffening effect may lelld to bener

control of lateral deformations, the same stiffening may lead to largerforces produced during various

ground motions. In such cases, the positive effect of added damping might be diminished by the

stiffening effect.

5-1

-

-

-

-

-

-

1.0 ~

~.- 0.5 .....

~ :::L_----------------p~ 2.5~o~ 2.0~

~ 1.5

~

L ---'-- .l-I __...L-__.J.I__-..L__~l_=_-----'--__::

0.0 30 0 .. ,. 00.0 10.0 20.0 . 4\1.

ADDITIONAL STIFFNESS ( % 1st STORY)


40.010.0 20.0 30.0ADDITIONAL STIFFNESS ( % 1st STORY)

...../~~"'.~-~ •.:-:~~~~~"'"__ ~ 0.0%

- - - - ~ 3.0%~ 6.0%

-- ~ 9.0%- _ ~t2.0% ............ ~ 15.0% -j

~..•. ~ 18.0%

~1.5

1.0t;~

0.5

0.00.0

4.0 r---~------.----r------.------._-,_-~--___.

_ 3.5

~- 3.0>u~ 2.5~

~ 2.0~

b.lnelastic Superstrudure

F1GURE 5·3 Variation ofFint Mode Frequencies

5-3

The effect of viscoelastic properties is hest summarizcd in Fig. 5-4 which shows the influence of

incrcasing viscous properties and stiffness on the base shear and story displacement response of

the structure, For the test type cM:it,ltion. ie Taft 1952. thc hase shear inuease ... almost -' time... due

to ·HIII( additional stiffne ...s in the hraces. if no viscous damping is added. However with the addition

of more than 12(!c damping. the hase shear is reduced independently of thc stiffness inaease (sec

Fig 5-4al. It is worthwhile noting that the displacements are reduced somewhat hy the stiffness

incrl'ase. hut the major reduction comes from the viscous properties of the hraces. that increase the

damping. The variation of response characteristics was obtained for the 1952 Taft ground motion.

This particular ground motion produced substantial changes in the inelastic response. more than

any other motion used in the study and therefore is being thought as representative.

11 is also worthwhile noting that the change in the initial stiffness alters the overall apparent critIcal

damping ratio (ohtained from the free vibration "tail" of an earthquake analysis). In an inelastic

response. the hysteretic behavior generally adds to the apparent damping. However in certain cases.

the overall critical damping is slightly decreased (see Fig. 5-5). This is due to the more erratic

response and possibly due to inaccuracies in determining the equivalent damping during the inelastic

response.

5-4

-~ 0.0""- - - ~ u""- - ~ '.0""- - ~ '.0""- • ~ 12.0""- ~ 1S.o""- - ~ 1•.11 ..

0.20

0.00 L..-"""--.....L..~---'~...o.--...J---'--J

0.0 10.0 20.0 30.0 40.0ADDITIONAL STIFFNESS~ 1ST STORY)

a. Base Shear Response

'.0 r-.....,......-,.-r--r---'--r-"""""""",

...... - ... ,.- , , ,,- ........ ...'.. _-......... "' "------ , ........ '........... --. -.... ......... ... "-- -':.-.. -... -........ '" --

0.0 ~--'----'--~--'----'-_.........--'---'0.0 10.0 20.0 30.0 40.0ADOlTIONAL SnFFNESS ~ 1ST STORY)

b. Displacement Response

FIGURE 54 Innuen(e or Earthquake on Structural Response with Viscoelastic Braces

30.0 ~----..------,----...,.-----.----:O--~'O'"""7'--.....,

~~~.... 20.0zW..J

~

~~ 10.0wa:~~

/

-- 6K1Ke.0%-- 6K1Ki_0%

6 KlKi .6%- - 6K/Ki - 12%

1\K/K1.19%- - - - A '(1tC! • 25%

6 KlKi .31%- - - 6KJKi. 31%

0.0 L.-. .......... -J".. ----" -::-:"-:- -'--__~:_:

0.0 10.0 20.0 30.0ADDITIONAL. DAMPING RATIO

FIGURE 5·5 Apparent Equivalent Dampinl with ViIcoelutk Braces with Added Stift'nels(Percent ofFint Story)

5-5

SECTION 6

CONCLUDING REMARK...~

The resronse of reinforced concrete structures, in general. and those that already suffered previous

damage can benefit from the strengthening using viscous or viscoelastic dampers. The addition of

suhstantial damping in many cases offsets the negative effect that might he caused from the stiffening

of the systt:m.

The analytical studies of reinforced concrete structures under variOllS earthquake motions indicates

th.lt an increase of damping to an overall ratio of ISlJf or larger will produc~ effects that ..... ill outweigh

the stiffness increase associated with viscoelastic dampers. These studies show an excellent benefit

of increasing only the viscous damping. which can be obtained using other types of dampers such

as liquid silicon dampers (Constantinou et al.. 1992, Reinhorn et al.. 1993).

Tht: scaled model experiments and this analytical study indicate that retrofit using viscoe1aslIc

dampers can reduce the overall response, but more importantly, can reduce the risk. of developing

a damaging mechanism ncar collapse. In particular, the hysteretic energy dissipation is transferred

from the load hearing elements, such as the columns or beams, to non-load bearing devices that can

dissipate energy without damage.

This paper presents a simplified analytical model of viscoelastic braces that can be used in con

junction with a step-by-step dynamic analysis used for reinforced concrete structures. The model

was veritied by shaking table tests that emphasize the adequacy of the simplitied modeling.

Finally, the analytical platform for evaluation ofdamage in RIC structures with viscoelastic dampers

presented herein can also a'lalyze more complicated damping devices that can be represented by

alternative viscoelastic or hysteretic models. Due to its step-by-step solution characteristics. variable

damping characteristics can also he considered. Dampers with such characteristics were proposed

for further improvement and control of seismic response in structures (Reinhorn et aI., 1993).

6-1

SECTION 7

REFERENCES

Aiken. 1.0 and Kelly. J.M. (1990). "Earthquake Simulator Testing and Analytical Studies of Two

Energy - Ahsorhing Systems for Multistory Structures". Report No. UCBIEERC - S·OI03, Unil'erSl1y

of California at Berke/ev.

Ashour. S.A. and Hanson. R.D. (1987). "Elastic Seismic Response of Buildings with Supplemental

Damping". Univ. of Michigan/Ann Arbor. Repon UMCE 87-1.

Bergman. D.M. and Hanson. R.D. (1990). "Viscoelastic Versus Steel Plate Mechanical Damping

Devices: an Experimental Comparison". Pmaedin!?s of Fourth U.S. NlI1ional Conferena on

EarthlJuake I:·n~ineerin~. May 20-24. Palm Springs. California. Vol. 3. pp. 469-477.

Bracci. J.M. Reinhom. A.M .. and Mander. lB. (1992a). "Seismic Resistance of Reinforced

Connete Frame Structures Designed only for Gravity Loads: Part I - Design and Properties of a

One-Third Scale Model Structure". Technical Report NCEER-92-0027, National Center for

Earthquake Engineering Research, SUNYlBuffalo. (in print)

Bracci, J.M .. Rcinhom. A.M .. and Mander, lB. (1992b). "Seismic Res!stance of Reinforced

Connete Frame Structures Designed only for Gravity Loads: ~art III - Experimental Performance

and Analytical Study of Structural Model". Technical Repon NCEER-92-0029, National Center

for Earthquake Engineering Research. SUNYlBuffalo. (in print)

Bracci. J.M.. Reinhom. A.M .. and Mander. lB. (1992c). "Evaluation of Seismic Retrofit of

Reinforced Concrete Frame Structures: Part II - Experimental Performance and Analytical Study

of Retrofitted Structural Model Structure". Technical Repon NCEER-92-0031. National Center for

Earthquake Engineering Research. SUNYlBuffalo. (in print)

Caravani. P. and Thomson, W.T. (1974). "Identification of Damping Coefficient in Multidimen

sional Linear Systems". Journal ofApplied Mechanics. V41. pp. 379-382.

Chang. K.C.. Soong. T.T.. Oh. SoT. and Lai, M.L. (1991). "Seismic Response of a 2/5 Scale Steel

Structure with Added Viscoelastic Dampers". Report No. NCEER· 91-00/2. National Center for

Earthquake EnRineerin!? Research. Buffalo. N. Y.

7-1

Kunnath. S. K . Reinhorn, A.M .. and Looo. R.F. (; 4(2). "IDARC - Version 3.0: Inelastit: Damage

Analysi<, 01 Remfon.:ed Connctc Strut:turcs". Tcchnical Report NCEER-92-IX}22. National Center

for Earthquake Engineering Re<,carl:h, Slir-; Y/Buffalo. (in print)

Liang. Z. and Lee, G.e (lYYI). "Damping of Structure ...: Part 1 - Theory of Complex Damping",

Tcchnical Report NCEER-91-(}()04. NatIOnal Center for Earthquake Engineering Rc...eaKh.

Sl:;-";Y/Butlalo,OctoOcr.

Lin. R.c., Liang. Z. Soong. T.T., Zhang. R.H., and Mahmoodi, P. (1991). "An Experimental Study

on Sei<,mil: Behavior of Viscoclastically Damped Structures", f;n~. Srmc/., Vol. 13, 1'1'.75-84.

Lin, R.C.. Liang, Z., Soong. T.T,. and Zhang. R.H. (19RRj. "An Experimental Study of Seismic

Strul:tural Rc<,p<msc with Added Vbcoclastic Dampers", Technical Report NCEER-83-0018.

National Ccnter for Earthquake EngInccnng Research. SUNY/Buffalo. June.

Looo. R.F., Kunnath. S.K., and Reinhorn. A.M. (1992a) "3D Irl"lastic Dynamic An.tlysis of RC

Structures". Computin}{ itt Civil Ettl{illeerin~ (lnd Gt'of{raphic Information Systems SYmposium,

B.G. Goodno and lR. Wright, cds., ASCE, NY.

Mahmoodi, P. (1969). "Structural Dampers", ASCE Journal of the Structural f);v;fion, Vol. 95.

August. PI'. 1661-1672,.

Pall. A.S. and Marsh. C. (1982). "Response of Friction Damped Braced "'rames". Journal of

SrrtKtl4mll:nf{;neerinf{. ASCE. 108(6}. 1313 - 1323.

Park, YJ., Reinhorn. A.M., and Kunnath. S.K. (1987). "IDARC: Inelastic Damage Analysis of

Reinforced Concrete Frame -- Shear-Wall Structures", Technical Report NCEER-87-0008. National

Center for Earthquake Engineering Research. SUNYlBuffalo.

RodrigueZ-Gomez, S .. Chung, Y.S., and Meyer. C (1990). "SARCF-II User's Guide - Seismic

Analysisof Reinforced Concrete Frames", Technical Report NCEER-90-0027, National Center for

Earthquake Engineering Research, SUNY!Buffalo.

Scholl, R.E. (1990), "Improve the Earthquake Performance of Structures with Added Damping

and Stiffness Elements". Proceedinfl.J of Fourth u.s. National Confereflce on Earthquake EnKi

neerinfl., May 20-24, Palm Springs. California.

7-3

Scholl. R.E. and Martinez-Romero. E. (1986). "Earthquake Retrofit Design of a 12 - story Building

using Structural Dampers", Proceedinxs of the Second International En}(ineeriilR and Technolo}()'

Conference. Mexico City. Mexico. August.

Scholl, R.E. (1990). "Improve the Earthquake Performance of Structures with Added Damping

and Stiffness Elements", ProceedinKs of Fourth U.S. National Conference on Earthquake EnKi-

1lf't'rinK. May 20-24. Palm Springs. California.

Soong. T.T.. and Lai. M.L. ( 19911. " Correlation of experimental results with predictions of vis

coelastic damping for a model structure." Proc. Damping '91, Air Force Systems Command.

Wright-Patterson Air force Base. Ohio, FCB 1-7

Suo Y.F. and Hanson. R.D. (1990). 'Comparison of Effective Supplemental Damping Equivalent

Viscous and Hysteretic", Proceedi,,!?.\' (~f Fourth lIS. National Conference on Larthquake I:nRi

nt'ain/.:. May 20-24, Palm Springs. California, Vol. 3. pp. 507-516.

Uang. C-M. and Bertcro. V.V. (1990). "Evaluation ufSeismic Energy in Structures", Earthquake

EnKineerillR lind Structural lJvnamio, Vol. 19, 77-90.

Xia, C and Hanson. R.D. (1992). "Influence of ADAS Element Parameters on Building Seismic

Response", Journal of Structural EnxineerinK, Vol. 118. No.7, July, pp. 1903-1918.

Whittaker. A.S., Bertero. V. V., Alonso. J.L. and Thompson, C.L. (1989). "Earthquake Simulator

Testing of Steel Plate Added Damping and Stiffness Elements", Report No. UCBIEERC - 89102.

University of California. Berkeley.

Wu, J. and Hanson, R. ( 1989). "Study oflnela..tic Spectra with High Damping" ,JournalofStructural

EnRineerin}(, ASCE, 115(6),1412-1431

7-4

APPENDIX A

A I-I Reinforcement Details

The following provides details of the rcinfercing steel used in the model based on scale factor of 3

for geometric length sImilitude. Detailed information is presented by Bracci et al., ( 1992a). but is

repeated here for sakc of completion of this report.

The slab stccl in the prototype structure was designed by the direct design method of the ACI 318/83.

The design required #3 rebars at 6 in. spacing in different sections of the slab. To avoid ex.cess

:abor in the construction of the 3-stol) model, a 2 in. square mesh composed of gauge 12 galvanized

wires is chosen for acceptable similitudes of strength and geometric spacing length. Since the slab

strengtl. is not the main enlphasis for this study, the slight disparities of slab steel placement due

to the mesh are considered satisfactory for the experiment. Figure A-I shows the layout details for

the top and bottom reinforc;tlg steel mesh in the slab. The longitudinal (direction of motion) and

transverse (perpendicular to the direction of motion) beam reinforcement details for the model are

shown in Fig. A-2. Figure A-3 shows the reinforcement details for the columns in the model based

on the prototype design.

A 1.2 Model Materials

The following outlines the materials used in the construction of the model. It is to be noted that

the materials used in the model are identical to materials in assumed prototype structure (Bracci et

al .• 1992 a). Therefore the scale factors were appropriately developed ba..ed on the principles of

modeling the same acceleration and material.

A 1.2.1 Concrete properties

The concrete mix analysis and design was based on trial mixes from various recipes and a design

mix was establis~ed for a 28 day target strength ('f 3500 psi. slump of4 in.• and maximum 4'ggregate

size of 1/2 in (#1 crushed stone). Table A-1 shows the mix fOffilUla for a one cubic yard batch of

concrete.

The mix formulation is based on a saturated. surface dry concrete sand. lbe water: cement (: sand

: stone) ratio is 0.5 : 1.0 (: 3.0: 3.6). The full gradation analysis of the aggregates in the concrete

mIX is shown in Fig. A-4.

A-l

Reproduced frombest available copy

5' everlap

gc.·2 r""1esr #2'SQuCreS, tyc

2'-C"f,r6'-0"

'C'-o"

I Bottom S,ob Steel(Typical in each boy)

!liiliiiIl!il!i~iI!IIilIliIi!il~/©

1"I 2'-0'v )<

-:i"---- gI : II,,': II,v' I I, I "I 4' overic:::

c0

• I

~

'l )I

T-

I

0I

L~x 2' SQuor~ hole

@I

CD (2)FIGURE A-I Layout of Slab Steel Reinforcement

A-2

~ 10W-gc1'02-2/.3"\... ..

6'-0"

11 VI' - 90' 102- 2!3" k .I-.r__1_~_Wc-_9:...:0,---'-c-'O~2-.....:2:.:./...::3_"-+)

_~__-=3:....:'~OL." ......--,J""

Longitudinal BeaIns (Nonh-South)

.l'-,I,_-=.gW.:.:..-.....:9z.:0::...;.1....;.1=O=-2--:2:.L/~...._"---.t,l ot'~__1_1W_--'9'-O_.1_1...:..• .::;.2-_2~/...:..J-,I.. lt

Transverse BeaJDs (East-West)

FlGURE A·2a Details of the Beam Steel ReinfOlUment

A-3

\ ~r ~I

l i'lW-go.11(typ) •2 04

3" -? ,..,L 1 3'

A A 8 B

J~t ,Vi 'tIO j

l W-'lgo(typ)n 4 2 04

Ii 3'

, t 3"'1"-

C C 0 0

3/4"~-I

5" W-qo,11 (typ) 5'~ W-\I0.1 1 (typ)

~ ~

BcUll Sections

FIGURE A·2b DetaIls of the Beam Steel ReiDforcemeDt ( Continued )

A-4

L= 1'-6 1/4"

L=i'-61/4"

L=2'-6 1/4"

L=2'-6 1/4'

L:=j'-11"

,.12'-0'

ror. 8'-0"'[5" q---

f"7

4 W- gc, 11 C 2~"._.',.1iiiiii4 iii'-~O"1 '1

y

W-go.1 i 04"

4 W-go,11 02"

W-go 11 @4"

4 W-go11 @2"

3 W-c:;a 11 @2'

10 W-gc,1 1 04"

0"

CELLp)

12'-0"8'f-.---,

4r,.

I

2" ~6" e'-

2" ,.

II

4"

,

2' 4'-0"~-

2 -# R fI

} ~y

V LOAD4" (TY

2,7

rn

Vv-gcli@

y

4 W-go.11 @

W-gO.l1 @

4 W-gc11 @

L '·'-C;C.1', @

4 W-gc 11 @

2 W--go.11 @

10 W-<;;a1i @

:3 W-gc 11 @2

(a) Exterior Section (b) Interior Section

Jfr1t41D4BAA~S~..

llUJw-gc." 3"

2 1/2"~ ~ ,,,

4" J

~ ~

(c) Section Y-Y

FIGURE .4..) DetaIls of the Column Steel Reinforcement

A-S

100.1DIAMETER, IN

0.010.001

--- IIN

II / ---Stone--V ......,...,

Sand--""*uv

If Aggregater

lJ~v

/ov V V 1./--

II~ [7/~.-

"'OV

/8~

I

~ V I I~ I

~~i 1/ I 1/lvj

kt~~1 i0+- --

nGt:RE A-4 Gradation Analysis of the Concrete Mix

1000100TIME, DAYS

10

•• , , , " I I I , • ""

: ' : : : : : : :... :-~:'" . . .: :: : : ; : •• , I H: I •• "

....... ,.... ,... i··;·· i· i ·;·i~··· _..+. ' .. , .. i~· i· i .;.~ .....':".~.....;... ~ .. ~...:.~, , ... , . ... ,... "...... , ""

, ••••• I I ,. I I

• , • • I I • , I ,; Eq. (S. i): : : : i::: : :_.•.. ~-;_. --;-_.: ~.~ .. t~:·6 ...... - .. : ..... -;'" ; .. : __::_!":";" __ ..... ; ; :" "; ;_:

· , , , .. , . '" "I I , , • I. I... • I

• , •• " • I. •· , ..... " .I •• I I I '" I I I • "1 I' •••• ••

--_ •• _-~- ••• ~-_ •• - -1 _ ~ " J •• ~ 6,.~ _ •• ro. ~ _J._ L 1_"

· ~:~i!~~~ ~ !!~1~~i! . !~1 ~i' • I •• "" • I I 1'1 I I , " • t

- •• " II •••• ""

I • • • , • '" I •• I I "" ••. __ ._ - _- - - -.. ---- .. - _ _.· , , . , . ;" ..' I I •• I.. • ••• , • "• I • • •••• • , I , I • ", I •••• I' •• , • , • '.· .... '" . , . , , . " ..

• , I I , I I I I I • , • , I.. , " I I' . . . , . , .. . . . .. "" ..

• • - - - y • - ~ - , - , .,. ,. , - - - - r- - - •• r Oo • "'I ••,.. "'I ,. r - •• - , "' ,. •• r _ • .,.,.• •• '. I , •••••• ,. , ,. .,

" , .. , "'"· , .... , . .. ".,' • I I., I • I I •• " • "· . . . , .. , '. '". . . , . , . '. . ,. "

1.2

1.0

0.8CO

~ 0.6to-

0.4

0.2

0.01

HGURE A-5 Average Connete Specimen Strength Versus Time

A-6

rahlc A-I Mix De.,ign Formula for the :\~odcl ronnete

Ingredient Weight

Type I Cement 490lh

Concrete Sand 14R71h

# I Cru.,hed Stone 17R5 In

Water 2421h

Supcrpla.,tiCilcr 39.201.

Micro-Air 2.90z

A suhstantial variatIOn can he ohservcJ in the mix strengths for the different components. even

though ail mixes had the same target strength (see Tanlc A-2). The final strengths were very sensitive

to moislUre variations in the materiab and the widely varying amhient temperatures at the time of

cOIl:·.truction. The vanation of streng.h versus time :s shown in Fig. 3-5. which indicates asymptotic

stahili/ation of coneret.: strength.

Tahlc A-2 Concrete Properties of the Model Structure

Pour Number and Location r, E, EIII £,,,,,/1

(ksi) (ksi) (strains) (strains)

I. Lower Ist Story Columns 3.J8 2920 0.0020 0.011

2. Upper 2nd Story Columns 4.34 3900 0.0020 0.017

3. I st Story Columns 4.96 3900 0.0021 0.009

4. Lower 2nd Story Column 4.36 3900 0.0026 0.014

5. Uppcr 2nd Story Column 3.82 3360 0.0022 0.020

6. 2nd Story Slah 2.92 2930 0.0015 0.020

7. 3rd Story Columns 3.37 3800 0.0019 0.020

8. 3rd Story Slah 4.03 3370 0.0021 0.012

A-7

The rcinfon:ing steel uses a mix of # II & # 12 gage wires and 04, 05 annealed deformed hars. The

summary of their properties is given in Tahle A-3

Tahle A-3 Reinforcing Steel Properties of the Model Structure

Bar d,. A" f, E, .t;lId"A £.(inl (in: ) (bil (ksil (ksil

#12 gao 0.109 O.(Xl93 5H 29900 64 013

0.120 o.ot n 5() 29HlXl 70 -

0.225 0.04(x) 6H 31050 73 D.15

0.252 O.05(x) 3R 31050 54 -

The D4 rehar was also :mnealed at different temperatures between 900" F and 1140() F to produce

a yield strength between 49 and 73 ksi for yield foree similitude with a #6 rebar. At a temperature

of 1140() F. the average yield strength consistently reached was 68 ksi. Based on yield force

similitude. the D4 rehar represented a #6 rebar with a yield strength of 55.6 ksi. Since a grade 40

steel has yield strengths between 40 and 60 ksi. the D4 rebar satisfied similitude with a #6 rehar.

Hoth the original and annealeJ stress-strain relationships for the D4 and 05 rebars are shown in

Fig. A-6.

. - -_ .

...... ---_ - --_ .

1 .

0.02 0.04 0.06 O.oe 0.10 0.12 o.1~ 0.16STRAIN

FIGURE A-6 Measured Representative Stress-Strain Relationships of theReinforcing Steel

A-8

' ..\TIO'''!. Cfo:,n:R fo'oR EARTHQlAKfo: plim:"liU:RI:"Ii(j RESEARCHLIST Ofo' n:CH!'IiICA!. Rf:I'()RTS

The Nallonal Cenll" 'or Earth'luake En~mccfln~ Research (NCEER) put-I"hes leLhnlcalrep"rt., on a "anely 01 sut-,.,,,,, lelalc,110 eanh'luilke cn~UlL..,r",~ 'HIllen h) aUlh",s funJcd thmu~h NCEER These leports iIle a.a,lat-1c from t-oth NCEEI< ,Put-I"al .. "" IJcranrnl'nt and th" Nat,onal T""hnrcallnlolmaIK.n Scrnu: (NTIS) Rcqu."ls fnr rep',rts should he: dueLled to IhePut-lIcal,on' lJcl'artmenl. Nat,onal ('enlel 10, Eartlkjuue En~lIl""nnll Research. Slale UnwefSlty 01 New York at Buffalo. RedJ.... ket Vuadran~le. Rulla]I'. New York 1411\1 KCp'lrt, can also he: IC<.j ...eslnllhrou~h NTIS. 51115 1'011 Royal Road. Spnnllllcid.

V"~'IlI" 111(,1 NTIS .... ce'''on numhe:rs ale sh<Jwn ,n parenlhc,lS. If a.arlahlc

NCEER 1<7-IUII "hlst Year I'lo~ram rn I(esl'arch. EJuLaUon and TeLhnology Transfer." ~/5/11,7. (\'BIlIlU417SiAS)

NCEER IIi IHI2 "bpcrunel1lal E.·aIuallon ,.1 Inslantan.,..us Opt,mal AI~onthm, lor StrucluraI Control," hy R CLan. TTSl~,nf and AM I< elllh..rn. 4/20iK7. (l'BIlII-U434I/AS)

N('EER 117 tUII "E.pcnrnentatl<Jn LJ"n~ th.· Earth..juue S,mulatlOn FaClhtles .11 Un,ve",ly at Ruffal..... hy A.M Relllhom andK L Ketler. II' he: puhhshed

NCEEKK7IU14 "Th., S.,'tem Characlerlstlcs and I'erf."mance 01 a Shurnll Tahle," hy JS. Hwan~. K.C. Chanlot and G C L"".I\iI/1I7. (I'RIlIlD425WAS) Th,s report IS a.allahIe only thmullh NTIS Is"" address Iotlven ahove).

NCEEI< 117 IUI~ "A Frnlte Element Fonnulatloll lor NOI,lInear VI~opla.sta: Matenal U,rn~ a (J Model," hy 0 Gye'" and GOasgupla. 11/2/117. (1'81l1121 HM,AS)

NCEER K7(UJ6 "Sylllt'oll~ MallIpulatron I'r,,~ram (SMI') AI~ehral" Codes for Two and Three O,mensl<'nal F'OIle ElementFonnulatlons." t-y X Lee and G. Oas~upta. I 1NiK7, (I'RII8-21~<j22fAS).

NCEER K7(H17 "I",tanlanellus Optimal ConlroI Laws lor Tall RUlldm~s Under Se.sm'L EX"llaIIORS." hy LN. Yan~, AAkharpoul and P. Ghaemmaghaml, 6/lOjK7. (I'RIIIl-I.'4D3iAS)

NCEER ·K7 ·(HIIl "'UAKC Inelasllc lJamage AnalySIS o[ Kemlorced C"n<:lelc F,ame· SlJeaJ Wall Struclules," by YJ. Parl.,A.M Kernholll and SK KlInnath. 7f201B7. (pRIlIl13432S/AS)

NCEEI( K7-(Hl'J "L'4ucla.:tllln I'otentlai IIlr New YOll State A Preltmmal)' Report on S'lcs III Manhanan and Buffalo," byM Budhu, V VIJayuumar. R.F. GlCse and L Baumgras. 8131/ll7. (PB8S-163704iAS). This report .saVaJIahle only lhrough NTIS (see address given above).

NCEERK7-lKllO "Verl,,,al and Tnrsl<mal Vlhrahon 01 Foundabons m InhomoFeneous MedIa." by A.S. VeIetsos and K.W.lJotson, h/1/1l7. (I'BIlIl. B42<JI/AS)

NCEER·K7·1l1l1 "SclSmiC I'rnhab.hsllc R,-k Assessment and Selsm,,- Margms Sludtes fOI Nudear Powel Plants." hy HowardI1.M. Hwan~, ilIl <;/87. (I'BIlII-I34267/AS).

NCEEK-1l7-1l1l2 "Paramelm Studies of Frequcnc.:y Response of Secondary Systems Under Ground-AccelerauOIl Exc.lauons,"by Y YIln~ and YK. Lan, 6/10/87, (pB88-134309iAS).

NCEEK87-1l1l3 "FrC\lucncy Kcs(X,,'se 01 Secondary Syslcms Under ScumII'; EXClllllion," by I.A. HoLung. I. ClII and Y.K Lm,713I/ll7. (I>B88-n4317/AS).

NCEER-87-111l4 "Modelhng Earth'iuu.e Ground Mouons m SeISlllI<:llUy AclIVe RegIOns Usmg ParametrK: Tune SenesMelhods," by G.W. Elias and AS CUmak, 8/2.<;/87, (PB88-134283/AS)

NCEEK 1l7-(oI<; "1)etoctlnn and Assessment of SeISmIC Struclural Damage," by E. DIPasquale and A.S. Cakmak, 8/'lj187.(PBllllln3712/AS).

B-1

NCEEI<1<7 IMIII> "1'lrdlO~ bpeflfn~nt all'arl/leld. Call1omlll.'' hy J lsenllerl( and E K,dard"m. WI~/K7, (l'RKl! 1I>H20/AS)

Th" r~r"rl " avallah'" only throul(h NTIS (see adJr...,,, !lIVen ahov!:1

N,EEI< 1<71M>l7 'l)'~'lal SimulatIOn "I SCISm ... Gruund MotIOn." hy M Shmo/ula. G. \)eodatlS and T HaJada. 1l~ljI<7,

(I'HKK 1~~1'I7/AS, Th" rep"rt IS an,lahle only Ihrou~h NTIS (""c: adJrc:" ~,vcn ahovc)

NCEEK 1<71.1111 "I'!alllla! C"'l"dclalll'IlS 101 Slrudural C"ntrol System Un..c:r1amly, System Tlm~ lJelay MId Trunlallon 01Sm.1I C"nlIol FOlce,," J N Yanl! and A Akharpour, 1l/ICljl<7. <l'RKll tt,H1K/AS)

Nl'EEI< 1<7 1M II <,' "M,,,lal Analy'" LIt NOllda"llally IJaJllped SuoctUlai Systems Usml( C,monl.. a1 Translormat.on." hy J N

YanJ:, S Sarblll and F X L"nl(, Y/27f11,7,lI'RllK·11l711'iI/AS)

NCLLK 1<7 (M120 "" N"'ISlall""ary S"lul,on III Kandom Vlhratlon Th",.fY," hy J K Ked Horse and I'lJ Sran"" 11/ljI<7,(I'RKK If,H41>/AS,

NCEEI< 1<7 'l121 "H,,"/onlal Irnpc,tanll"s 10' Kadlally Inh..m0l!~n~ou.s V....oelasl!l S•• ,l Layers," ~y AS Velels", and K W[)ot~on. 111/1 VIO. (I'RKX l'iOII'i'l/AS)

NCTEI< 1<7 1M12.:! '~"11l1l [)ama~l' As....."ment 01 I(ellll"r...,d ('onaete Memht·rs." hy Y S Chunl(. C Meyer and MShlllo/uk-,. \11:WK7. i1'RllK 1";OK,.,7/AS, This rep"rt IS ava.lahk "nly throulth NTIS hlX addre" ~lVcn

~t~.V\·)

NCEEK 1<71MI21 'AllIVc StruduJal C"ntrol III Clv,l Enj(ll1eellnj(," hy TT S'M.nl(. 111I1/K7, (l'RKKIK7T'K/AS,

NCEEK 1<7 (.124 "Verll..al and TOlS,onal ImpeJan...,s tor K...... a1ly Inhomogeneous VIS....c1astl.. So,1 Lay..rs," hy K W. Dot.,,,n

aild AS Vckt"". 1~/lI7. II'BK>I IK77Kfl/A'i,

NCFFI< 1<7 (U2', "l"r'MLCe,lInp lrom I~ SympoSIum on SCISm,.. Ha/Mds, Ground M"tlllns, So,IL'4uclad".n and Englnccnn~

1'1 ... I'c~' "' E.,krn N..rth Arnerrca," ()<,t..hcr 2i1~22, i~ln, ed,t",1 hy KH J3Oll>. 12/l17, (I"RKKlll>lII~/AS)

NCEFI< K7(U~1> 'Kepnel on I~ Whlll,cl Narrows, California. Earthquake 0/ (ktuhcr I. I'IX7," hy JI'anlehc and A, KClllhonJ, IIfII,7, (I'RllllIK77~2JAS) Th,~ repunlS ava,lahlc ..nly thr"ul(h NTIS (SIX adoJressgiven ahl\'c)

NCEEKK7mn "L>c~lltn 01 a ModulaJ l'roj(ram lor TranSient Nonlinear AnalySiS III Larj(e ~·lJ Rulldlng StrULtures," hy 'iSIIVa.SlaV and JF Aile!. 12t10fll,7, (I'RlIKIK7Y~O/ASI

NCEEK~K7·m~K "Sc... >nd·Ycar l'c0ltram In Kc""arch, Educallon and Te.;hnology Tran.rer," 3/8/KK, (PRIl8·21'}4110/AS)

NCEEKKII (Ull "Worksh"p on SCISm... C"mputer AnalySiS and lk..gn or Ru,ldlOg. WIth Inter....1lvc Graphl...... h)' WML{'ulfe. JF Allel and CH Conley, 1/llIfII,lI. (I'8l1K IK77tJO/ASj

NCEEI<·l!K·IUI2 "( )pt,mal Control 01 Nonlinear Aellble SIJULture5," by J,N. Yang, FX ulIlg and lJ. Wong. 1/22/llll, (PHKH·

2D772/AS)

NCEEK·l!K·UIlH "Suhslru..tunng T""hn"'llJel> m lhe Tune Domalll ror Prunary-Se"undary Struuural Systcm.... by G.lJ, Manoll.and G Juhn. 2JI0/Kll, (1'811111D7110IASj

NCEEKl!K-IX)()4 "Iterallve SCism... Analys.s 01 Pnmary-Seu>ndary Systems," by A, SIOShaJ. L.lJ, LUleIl and P.D. SparIOI.2f2lfll,H (l'RKK·2 D7YK/AS)

NCEEK-Kll-(UJ~ "Sto"halih.. FlIlltc Element ExpanSIon for Random MedIa," by PD. Spanos and R. Ghanem. 3/14/88. (PRSS21 11l116/AS).

B-2

NCEEI< XX CU)() "Cornhln,nj: SlJudural IlplJmllallon IIlld Strudwal ControL" hy F '; ("hen~ dnd ('I' Pantchdes. l/l0illX.

(PRXI< ~llXI4iAS)

NCEEI< XX·cUI7 ",e"rm, Performa,,,e Assessment oj C,l<k [)cSlj:ncJ StrUdW~"'." h~ H.H·M Hwang. J W Ja'4 .100 H J 'hau.I/.:!II!XX. "'RXX 21'14~I!ASJ

NCEFI< XI< IHIX "Kellaholll) Analy'" 01 (',,,Ie [)cSlj:ned Struclure' Under Nalural Halard,." hy H.H M Hwan~. H lI,h,haand M Shlll"/uk... 2i:'lJIllX. (I'RXII2N47IiAS)

NCEEI< XX IH14Sc,,,mc Fra~lhty Analy", 01 Shear Wall Slrudures." hy J·W Jaw and HH M. Hwan~. 4f'II!XX. (I'AXlJIIl~Xh7!AS)

NCEEK XX IK))1l "Raw I-"Iat.on "I a Mull' Slof) RUlldlnj: UnJcr a Harmon" GrounJ Mollon A C"mpan,on Ii Pcrl",rnancc,01 Varl"u, Sy,lell1\." hy F G bn. G AhmaJI and IG Tad)hakh'h. 'iIlX!XX. (I'RXlJ·122.:!IK/ASI

NCE[K IIX IX)) I Sn'lTlIc Fit .., Ke,pon", Specua lor a ('ornl,lned Sv,tern hy Green', Fun~lI11n,." hy FM Las·elle. LARel!,lTlilll and I'D Spano,. 'i!l/XI( II'AllI:IIO.:!K7'i/AS,

NCEEK I<X 11112 A New ,,,Iut,,,n Te~hnl'iuc I"r Kandomly Exclled Hy'lerehc SlruclUres,' by G () Cal and YK Lin. 'ill (,!XII.il'RIN II I.:! 1111 liAS)

NCEEK IlIIO)) l "A SluJy of I<ad.allun Uampln~ and SOII·Struclure Inlcrachon Elfe"ts In lhe Centr.luge."hy K Weissman. supervIsed hy J H Prevost. 'i/24/1l1l. (I'RlIlJ·I447m/AS)

NCEEKIIIlIOl4 "I'arameler Idenllhcal,,,n and ImplemenlatJun "f a KlIlemallc l'IaslI"ly Mood lor Fncllunal SOils," hy LHI'rcvo,t allll O.V GIIlillhs. 10 he puhllShcd.

NCEEK 1111 lIli 'i "Two and Three Unnen'lonal Dynarmc Finite Element Analyses of the L"n~ Valley Dam." hy DV Gnfflthsand J H I'rev"'t. hil7ll!lt. (I'AltlJ·I44711/AS)

NCEEK Kllllllt. "Dama~c Assessmenl "I Kelllforc:ed Concrelc Struclures In Eastern UOIlcd Stat;:s," by A.M. R;:lOhom, M.JSeidel. SK Kunnalh arld Yl Park. h/15illll. (l'Rf19·I22220/ASj.

NCEEK~Il·(l'17 "DynamIC ('omphan"" o' Vert"ally u'aJcd Strip Foundahons III Muh.laycrcJ V,sc;oela.sllc S...ls,'· hy SAhmad and A.S.M Israll. 6117/KS. (pRll~·102f19I/AS)

NCEEKKIl.lllllI "All Expcnmenlal Sludy 01 Selsm,c SIClIciuraI Response With AJded V••,;oelasllc: Dampers." by K.C. Lm.

I. LIIII\~. TT S(K'n~ and K.H. Zhang. 6/30/811, (PRllY·1222121AS). 1111. report .. aV&llable "nly throughNTIS (set: address f,lwn ahove).

NCEEK·I!Il-OlIY "Expenmenlal In~esllgalJonof Pnmary - Secondary System Ir,teracllon," by GD. MiUlOhs. G. Juhn and A.M.Relllhom. S/27/KK. (l'RIN-122204/AS).

NCEER·KS lKl.:!O "A Response Spectru,n ApprollCh For Arualysl5 of NondusKally Damped Str&x;tures," by J.N Yang. S.Sarkam and F.X Long. 4122/81l. (pRIIY-IO:N!lY/AS)

NCEEK-lIll·ll)21 "SeismIC; IntenM:t,on of Structures and Sods: Stochasta.; Approa.;h." by A.S. Veleoos and A.M. Prasad.7121!X1l. (1'8I1YI221%/AS).

NCEEK·IlK·1lI22 "ldenhf.... a1lon or the SeI'VK:eablhly Llmll Stale and Dete<;lIon of SeISmiC; SllUl.:tural Damage," by E.U'P8S<.juale and AS CamlOk. 6/IS/88. (PR89·122188/AS). This report is available uRly through NTIS (seeaddrc" given ahove)

NCEERKKlXl23 "Mulu-Huard Risk Arualysl5: Case of a Simple Offshore Slruclure." by RX. Bhartla and E.H. V&l'II1IlIIdte.7121/811, (PBIl9145213/AS).

B-3

NCEEK·Kll·UI24 "Aulomal<J SelSrnK lJeSign of Kemfor.:cd CoIK.T.:le BUlldlOgs," h~ YS Ch<lng, C M~er and M Shmo/uka.7/'i/llll. II'BIN 122170/AS) ThIS repon IS avallabl.: only through NTIS (see address given ahovc)

NCEEK Kll·(WI2'i "Experlmenl.ll Sludy of A,llve Contrlll of MIJ()F Stru,lurcs Under SeiSmk: Ex"tahons." by LL Chung. KCLm. TT S'M'n~ and AM Kcmhorn. 7/IO/llK. (l>8K."I22f>lKI/AS)

NCEEK KKIll2r- "Earlh4uaitc SUllulahon Tests or a Low·Klse Metal SlIUdure." hy JS Hwang. K~ Chang. GC Lee and ~LKellet. KI I/ilK. (I'8S.,,· 102'J 171AS)

NCEEK 88·111n "Syslcms SlUdy 01 Urhan Response and Kf.X;onslIUl:IKIO L>uc 10 CatastrophlL Earth<.juaites," by F KOLin andH K Zhou. 'J/22JKK, (1'8~) 11l234K/AS)

NCEEK·8Km2K "SelSrn" Fraglllly AnalysIs of Plane Frame Stru,lures," by H.HM Hwan~ al'd Y K L\lw. 7~1/llK. (I'BK4Dl44'i/AS)

NCEEK·KK·m2'J "Ke'I~lnse AnalySIs 01 Slll,hashL StrUl:lures:' by A Kardara. C 8udler and M Shmo/uka. W22/llK. O'8K4.1744 2'11AS)

NCEEKKKm~o "Nonnonnlll A,.:clcrahons Oue 10 Yleldmg m a l'nmary Stru,lure: by D CK Chen and L.L> LUles, lJ/1"'/IlK.,,'BINnI4,7/AS)

NCEEK·8K·m~l·lJeSignArpwilLhes for S,,,I·S!Ju<;lure Intera<;l1on," by AS. Veletso5, A.M. l'Ta.sad and Y. Tang. 121"'/llK,(1'8K<,I·1744'7/AS) ThIS report IS anllahle only INougb NTIS (see address 1(1ven ahove).

NCEEK·KK·(Xt12 "A Kc·evaluallon of lJeslgn SJ'C"tra for SelSml, L>amage Control," by CJ Turkstra and AG Tailln. I I{7/llK,(f'BKY·14'i221/ASj

NCEEK·!lJ(·m:n "The BehaVior and Design of Noll<;ullla;1 Lap Spb,;cs Subjet:led 10 Kepealed lnelastk: Tensile Loadmg," byV.E Sagan. I' Gergely and K.N While. 12/8/1lX. (pRIN-Ib3737/AS)

NCEEKKll·Il'34 "Selsm.- Response llf Pile Foundaltons," by S.M. MarrK)(lfl. P.K. 8anerJee and S. Ahmad. 11/11ll1!. (PBIlY·1452W/AS)

NCEEK·8Il-OJ3'i "M,><khnj/. of R/C BUlldmg Struo.:tures With Flexible ROOf I.>taphragms \IUAKC2)," by A.M. Rcmoom, S.KKunnath and N Panahshahl, yntss, (PB89207153IAS)

NCEEK·!lJ(·(ll.\6 "S"lulton o( lhe L>am·Reservolr InlerlKuon !'n.blcm USPlII a Comblnlbon ot FEM, BEM with l'artK:ularIntegrals. Mudal AnaIy.as, and Subslrlll:turPlg," by C-S. TSIl, G.c. Lee and R.L Keller. 12(3IIllI!, (PBS'}.2071 46/AS).

NCEER-88-<XJ37 "Optimal Pla.;ement of ActuatoB for Structural Cootrol," by F.Y. Cheng and C.P. PlllIelides, 8/15188, (PB89Ifl2846/AS).

NCEER-88-lxns "Teflon Beannlls an AKlsmac Bue lsol.bon: Ellpenmental Studaes aM Mathematical ModehOJl:' by AMok.ha. M.C ConslanbllOU .00 A.M. Relnhom, 12lS188, (PB89-2184~7/AS). This report IS aVlllable onlythrough NTIS (see address given ahove).

NCEER·S8-ll13<,1 "Selsmll; BehaVior of Flat Slab Hip-RISe 8ulldlngs in the New York City Are," by P. Weldlmger and M.Euouney, 10/151118. (PB90-14S68l1AS).

NCEER-88-0040 "EvaluauOll of the EMthquakc Rcaaalancc of UlslllJI Buddmlls PI New York City," by P. Weidlm,er and M.Euouney. 10/15188, to be published.

NCEER-88-0041 "Small-Scale Modellll' Technique. for Remforced Conaetc Stnx:tura Sub,ectcd 10 Seaamic Loa." by W.Kim, A. El·AIlU and R.N. While. 11122188, (1'889-189625/1.5).

8-4

NCEER·IIIl·(X)42 ··MoJelln¥. Strong Ground Molu.n trom Multiple Event Earthljuakes," hy G.W. Ellis and A.S Cakmak.III/I "iIKK. (PRK'I17444"i/AS)

NCEER KX·(.)4 \ "Nonslahonary Model, of Se"ml~ Ground AIXek:rahon," t>y M Gngonu, 5.E Ihlll and E. Rosenhlueth.

7f\~IKK. (PRKY IK%17/AS)

NCEERKXHl44 "SAKeF User', GUide SelSm,c An"lysl' of Reln""",,,1 C"n.:relc Fra,,:.es," "y Y5 Chunjl. (' ;.Acyer ~nd MShmo,ull.a, IIN/KK, II'RIN.1744"i2/A5)

NCEER·IIK(X)4"i "FIr,' Expert Panel Meetlnj: lin Ulsasler Kescar~h and Planmng," edited hy J ",,"kill ,,"d I Stoyk, Wl"i/llK.(PRIN I74460iAS)

NCEER ·IIK·(X)41> "1'rehmmiITY' Siudies 01 the Efl,,~t of U.::;raJ.ng Inhll Walls on the Nonlln"ar Sc"ml~ K",pon", 01 51",,1harne'," hy Cl Chrysostomou. " Gcr¥.e1y and IF. Ahcl. I2IIYlKII, (l'RII'I 201l'tIJ/AS)

NCEEK III! 1"47 "Re'nlorccd Conaele Frame Cllmponcnt TcstlOg FJk:lhty Lk....lgn. Conslru,tIOIl. Instrumentatloll andOperation," hy S I' I'e",ll, C Conley, T Rond. I' Gergely and R.N. WhIle, I 21 II>/KX, (I'Rll'J 17447K/AS)

NCEER -K'I(X'O I "Et,,"~t, of Protatlve Cushion and SUlI Cllmplla,cy on the Response III Equ.pment W •• hlll a Selsmllally

E~"lled RUlldll1g," hy JA HoLung, 2111>j8Y, (PBKY·211717Y/ASj

NCEERK'I.(U)2 "Stahs\t~al Evaluation 01 Kesponse MuJllilatlOIo Fa.:IOTS lor RCll1lor~ed COI1lTete Slru~tun:s," hy H.H·MHwang and JW Jaw. 2117/KY, (PBllY-207IK7/ASJ

NCEER·II'1·(Un "Hy'terell~ C,lumn, Under Raoollm EX~ltatJ()Il," try G<]. Cat ~nd Y.K. LIIl, 1/':1/11'1, (I'BKYIYh"iD/AS)

NCEER·KY-(U)4 "Exp,mmcnlal Study III 'Eler:larJt Foot Bulge' Instahltily o[ThIn-Walled Metal Tanks," hy Z-H Jla and R.L.

Kelter, 2122/KY, (I'Bll'J·207IYS/AS).

NCEEK·KY·llOlJ"i "Expcnment Iln I'erftlrmance of Burled PIpelines Across San AnJreas Fault," try J Isenberg, E. Ib;hardsonand TU. O'Kourkc, .'/1 ()/89, (PBII92111440/AS).

NCEEK-KY·UIOI> "A Knowledge-Based Apprn'iCh to Slruetural1)eslgn uf Earthquake-Resistant BUlldlllgs," by M. Subramam,

P Gergely, C.H. Conley, J.F. Abel and A,H. Zaghw, 1115/89, WB89-218465/AS).

NCEEK-IIY-lXlO7 "LI'Iucf""\tUT1 Hazards and Their Effects on Burled Pipelines," by T.O. O'Rourke and P.A. Lane, 211/8"),(PB8'I-21 R4lII)

NCEER-8"J-UlO8 "Fundamentals nf System Identification 111 SlnK;lUral [)ynllTllcs," by H. Imal. CoB. Yun, 0 Maruyama and

M. Shtnuzuka, 1/26/8"), (PB1I9-207211/AS).

NCEER-8"J-UJ(JlJ "Efleds of the 1,,)8"i Mt<;hoal,;&/l Euthquate 011 Wiler Systems and Other Burled Lllelll1Cs III Mexioo," byA.G. Ayala and MJ. O'Rourke, ~/8189, (PB89-207229/"'S).

NCEER-8'l·KOlll "NCEEK Bibliography of Earthquake Education Maleflals," try K.E.K. Ross, Second ReVISIon, 911 IllY. (PB9<)

125352/AS)_

NCEER-IlY-(JIII "Inelastu: Tbree-UlmenslOnal Response AnalySIS of Rell1lorced Concrde BUilding

SlnK;lurcs (IDARC·3i). Put I . Modebng," by S,K. Kunnath and AM. Remhorn, 4/17/89, (PB9<J

1146121A5).

NCEER·89-<OI2 "Recommended ModifICatIOns to ATC·14," by C.D. Poland and 1.0. Milley. 4/12189, (PB90-I08648/.A.S),

NCEER·8"J-CX1I3 "Repaar and Slrenglhcnmg of Bearn-to-Column COlIJICCuonl Subjected to Earthquake Loading," by M.

Coralau and A.J Durram. 2f18/89, (PB90 1098115/AS).

8-S

NCEERlN-11114 "Program EXKAL2 lor Id"nl1ll(;lhon of Slrudural [)Ynarnll; ~y,'err.,,' hy O. w.a~yama, C·R. YUiI. M.H",hlya and M Shlllo/Uu. ~ilYlIN. WB~l-I(J'l1l77/AS).

NCEER·IN-(ll1~ "Resp'.n,,, of Frames WIth Bolted S"ml-RIgKl Cunn<X:tlons. Part I Expe:ru"':ntal ~tudy and Analytlc~1

1.......JI.. lJllns ... hy P.J. L>,Cllr,'I. A.M. Remh,.rn. J.R L>1~erson. J.B. RaJ'lmm,kt a:ld W.L. i-Iarper. b/I/1N, 10

he: puhhsh-d

NCEER-IN-lll1 h "ARMA Monte Carlo SlmulalJon III \'robab,llsllc Structural AnalySIS," hy 1'.:1. Sp~no, and MP Mlgnolet.7/1 II/IN, (I'RIjCI J(l'Jll'J.~/AS)

NCEER·ll'J I~JI7 "Prclllnmary Pro.:ccdln~s lmm the Lonlerenu'on L>"a.stcr Prcparedne" - The Plan' o'-Earth'juak" EducallonIII ()ur S"hools,' E.hkd hy /(EK R..... h/n/ll'J.

NCEEK-K'J-111l7 "1'r'IUC'dll1gs fr"m Ihe Conferem;e on l>tsasler Preparedness - The PllICe of Earthquakl' Educahlln m OurSdl<.ols,'· Ed.led hy K E.K. Ross. I2I31/IN. (l'RY()-20711Y~l ThIS report IS avallahle nn!y th:oligh N ns ('iCc

addrc's given ahove).

NCEER-IN-II'lll "MulhdlmensIl'nal Modd, (If HY'krellc Malenal RehavlOr fm VlhI'allon AnalySIS IIf Shape: Memo')' EnergyAhsllrhm~ l>t:vICCS. hy E.J. Gra""er and F.A CouaIelh. tl/7/IN. (I'R'JO-I64146/AS)

NCEERIN·IIII'J "Nonlmcal [)ynam,.. Analy"sofThree-L>lmensumal Ra'iC Isolated Structures (3L>.BASIS)," hy S. NagaraJalah.AM !<elllhom and M.C' Consiantlllou. ll/31ll9. (I'B9()·161\)~b/AS). This rep"rt IS avallahle only throu~h

NTIS [see address given above).

NCEER·IN·/ll20 "Structural Control Consldenr.g T.mc·Rak of Conlrol Forces and Control Rare ConstraInts," by F.Y Chengand c.p Pantchdes. Kf3/K'J. (I'B\)()-120445/AS).

NCEER-KY·/Xl21 "Suhsurfacc Cnndlt.ons nf McmphlS and Shelby County," hy K.W. Ng. T-S. Chang and H-H.M. Hwang.i /26/1'.'1, (l'RIjC)-12()4~7/AS).

NCEER-IN-mn "Scl,m,c Y,Iave l'ropagal1on Effecls nn Stralghl ]olllkd Buncd Plpehnes," by K. Elhmadl and M.J. O·Rourle.K/24/K'J. (I'RYll-1 tl21221AS)

NCEEK·IIY-/I)2~ "Workshnp nn Servlceah,hty AnalySIS of Wakr Delivery Syskms." edlled by M. Gngonu. 3/b/'tJ'j. (I'B9()I 27424/ASj

NCEER-lN-(ll24 "Shaklllg Table Study of a 1/5 Scale Sleel Frame Composed of Tapered Members," byK.C Chang. 1.S. Hwang and G.C. Lee. 9/18/89. (PB90-160169/AS).

NCEER-lW-m2~ "DYNA 1L>: A Cnmpurer Program fnr Nonlinear SeismIC S,1e Response AnalySIS - Technical Docurnentalion,"hy Jean H 1'1_,\,nsl, 9/l4/ll9. (pB90·lbl944/AS). ThIS ceponIS AVllllable only through rTIS (see 8ddrcssgiven ahove).

NCEER-lW-m2to "1:4 Scale Mndel Studies of Active Tendon Syskms and Af.:tive Mass Dampers for Aseismic Protection." byA.M Relllhorn, T.1 Soong. R.C. Lin. Y,P. Yang. Y. Fubo. H. Abe and M. Nakai. 9/15/89. (1'89017'l146/AS).

NCEER-89-0027 "Scattering of Waves by IndulHons in a Nonhomogeneous Elastic HalfS~ Solved by Boundary ElementMcthods," by PK. Hadley. A. Askar and A.S. Cakmak. 6/15/89. (PB90-l4S699/AS).

NCEER-lN-m28 "Stallstrcal EvaluatIOn of Deflection Amplrficabon Fa;lors for Reirfon:ed Corx;rele StnJcturcs." by H.H.M.Hwan~. J-W. Jaw and A.L Ch'ng, 8131/89. (pB90-I64633/AS).

NCEER-lN·OO29 "Bcdrod. AcceleratIOns In t.4emphis Ma Due to t.ge New Maid Eanhquaka:' by H.H.M. HW&ng. C.H.S.Chen and G. Yu. 11{1/89. (PB90-162330/AS).

8-6

NCEERYCI-(lKIK "1'1101 Sludy on Sel,ml~ Vulnerablltty of Crude 011 TranSlnlSSllIn Syslcms:' by 1. Anman, R. J.)obry, M.Gngonu. F. KOlin, M O·Rourke. 1. O'Rourke and M. ShI1lO7Uk.a.. Sn.SN<l. (PR91-10811J7/AS)

NCEER·YCI-(lKN "A Pr0t/.raJTI 10 Generale SlIe Uependenl TIme Hlslones EQGEN," by G.W. Eilts. M Snmva..an and A.SCakmak, IfllWO, (1'891-IOK1l2WAS)

NCEEK·'JO-lXlIO "A~llvc I-olallon ror Selsml~ l''''lecllon of Operating R'M,ms," by M,E. Tail-Oil, Superv""d by M. ShllltUuk.a..6111/4. (PR91110205IAS)

NCEER·YCl-llll I "f>rogram L1NEARIU fm IdenltflCahon of Lrnear Struclural [)ynarnlc Syslems:' by C-R. Vun and M.Shlll",uka. fI/2"",l. (pR91-IIlHI2/AS).

NCEER·YCl-0l12 "Two-DImensional Two-['ha.<e Elaslo-Plaslt<: SeismIC Response of Earth Uams:' by A,N.VIal-lOS. SupervIsed by J.H. f>revosl, 6n.O!9O. (pB91-110197/AS).

NCEER·YCl·lXl]J "Secundary Syslcms In Base-Isolaled SUUclures: Expenmental Invesllgahon. Slochaslic Response andSllJcha.sllc Sen"IIVtly," hy GD. Manolts. G Juhn. M.C. Conslanllllou :md AM. Relllhum 7f\N<1. (I'R91IlOJ20/ASl

NCEER-'·IO-lXlI4 "SclSmlc Behavlur of Lightly-Reinforced CO",-Tele Column and Bearn-Column Joml u..-tails." hy S.P. Pess.lu.C.H. ClInley, P. Gergely and R.N. White. 8122190. (PB91-108795/AS).

NCEER·YCl-OOl" "Two Hyhnd Control Syslems for Building Structures Under Strong Eanhquakes," by J.N. Vang and A.lJamcltam. 6/29/'/0, (PB91-125393/AS).

NCEER·\~O·OOI6 "Inslantaneous Opltmal Contn.1 WIth AU'e1erallon and Veloclly Feedback:' by J.N. Yang and Z. Li, 6129N<>,(1'891 12..401/AS)

NCEER-YCI-lXlI7 "Reconnalssan.:e Repllll on the Northern Iran Earthquake of June 21. I~)," by M. Mehralll, 1O/4N<>, (PB9112S377/AS)

NCEEK-YCHXJI K "Evaluallon of L"luefacllon Polenl1a1 in MemphiS and Shelby County," by T.S. Chang, P.S. Tang. C.S. Leeand H. Hwang, 8/1O~l. (PB91-125427/AS).

NCEER-'X.l-OOI9 "Expefllnenlal and AnalytICal Sludy of a Combined Shding DiiC Bearing and Helical Sleel Spnng IsolationSyslem," hy M,C. Conslanlll1ou, A.S. Mokha and A.M. Reinhom, 1014~, (PB91-12538'i/AS).

NCEER-90-0020 "Ellpenmenlal Study and Analytical PredIction or Eanhquake Response 01 a Sbdrng Isolation System Witha Sphencal Surface:' by AS. Mokha. M.C, ConstanblIOU and A.M. Relllhorn. IOlIl~·O. (PB91-1254I9/AS).

NCEER-90·lXI21 "lJynaml<: Interaction Factors for Floalil18 Pile Groups," by G, Gazetu. K. Fan, A. Kaynia and E. Kause!.9/IO~. (pB91-1703811AS)

NCEER-90-OO22 "Evaluatioo of SeISmIC Damage lndices for Reinforced Concrete S\nJCtures: by S. Rodriguez-Gomez VtdA.S Cakmak, 9(30f9{J, PB91· '71322/AS).

NCEER-90-0023 "Sludy of Sile Response II L ,.elected Memphis Site." by H. Desai. S. Ahmad, E.S Guetas and M.R. OIl,1O/1I1'Xl. (PB91-l968'i7/AS),

NCEF.R·YO-OO24 "A User'. Gwde to Stron':I" Version 1.0 of NCEER's Strong-Motion Data AcceIa Tool for PCs andTenninals:' by P.A Friberg a..Jd CAT. Susch. 1l/1'iI9O, (PB91·1712721AS).

NCEER-YC-0025 "A Three-Dimensional Analytical Study of SpaIia1 Vwbibty of Sei5llli" Ground Motions," by L-L. HOI18and A.H.-S. Allg. JO(30f9{J, (pB91-l70399/AS),

8-8

NCEEI(.',)I)-11l2h "MUMOIU Us~r's Gu..le - A Program fur the l<lentlflUltlOn of M"dal Paramekn.,'· hy S. Rodr I guez-Gorneland E lAl'aS/.luaie. lJlJOMJ. (PRYI-17lNll/AS)

NCEEKIIlI.(XI27 "SAKCFII User's GUld~ - SelsmK AnalysIs of K~mfor"edC"n"rete Frames," hy S. Kudr I j:Ue1 Gomel. YSChunj: and C Meyer. '1{lOMI. (I1R41-1712lto/A.S).

NCEEKIIlI<X1211 'VI'U'U' lJ"mp<". Te,II0It. M,>dchoil and Apph"all"n to VIN-au"n and Selsml" ts"latllm." hy N. Miokn' andM C C"n,tantlllou. 12/20/40 (PRY 1-lljIl'ifll/AS)

NCEER-40-IXl24 "S",l Efte<:ts on Eanhquak.c Ground Mollons m the MemphIS Area," hy H Hwang. CS Lee. K W. N~ andTS Chang. "/2MI. IPR'}l l'}07.~I/AS).

NCEERYI-IUli "I'rowedtn~sIrom the llmd Japan-'!S Workshop on Earthquake ReSistant [)eSlgn 01 Lllellne Fa",lIltJes andCountermeasures for S",I L'qucl""bon. Oe<:emhel f 7 -14, 1'N(1." edited hy T.ll. O'Rourke and M. Hamada.211m. (PR') 1-1142: '1/AS)

NCEER-'!I-\UI2 "1'I1y""al Spa.:e S"lullon, 01 Noo-Pn'p"1110nally Uamred Syst~ms," hy M. Tong. Z LIang and GC' L"".III'iNl.II'A4117lJ242/AS)

NCEEIl.-'H ·mln "Sclsmr.: RespJIIsc of Smgle l'lles and I'lle Grou~," by K. Fan and G. Gazetas. I/HWI. (I'B92-174'JIM/AS).

NCEER-41-IH14 "Uamprog of Stru"tur~s ParI I - Tneory of Complex Vamping." by Z LIang and G. Lee, !0/1 ON I , (PR'}2·1'J72J'i/AS)

NCEER-'JI-IU)'i "~V·AASIS· Nunhnear ()ynamlc AnalysIS 01 Three Vlmenslonal Base lsulateJ SlrlJl.;tures Pan II," by S.Na~araJalah. A.M. Remhorn and MC Conslanltnou. 21211NI. (PB91-14055J/AS).

NCEEk-'II-IK)(lt, "A MulllduneRSlonal HyslerdJ" Model for ~lasllclly Vel"nmng Metals III Energy Absorhmg [)eVIl;es," l>yEJ. Gracsser and FA. Cozzardh, 4NNI. (l'B92·108364/AS).

NCEER-41·IXX17 "A Framework for Cu,tomllallle Knowledge-Based Ellpert Systems WIth an ApphcatKlfI to a KBES for

Evaluallll~ ll>e Sc"ml" ReslstanJ.'C of ElIasllng BUildings," by E.G. Ibarra-Anaya and SJ. hnves. 4NNI.(l'B91·210lJ:l(1/AS)

NCEER-YI-lXlOH "Nonlinear AnalySIS of S~I Frames WIIh Semi-Rigid Connecltons USIllIl the Capa.;ily Spectrum Method,""y GG. [)el~rleln. S-H. Hsieh, Y-J. Shen and IF. Abel, 7r~1. (PB92·113828/AS).

NCEER-IJI-LUl'J "Earlh'luak~ Edu<:alJon Malenals for Grades K-12," by K.E.K. Ros~. 4f30191. (pB91-212142/AS)

NCEER-YI-(X)1O "Phase Wave Veloc.ues and Dtsplao;cmenl Ph_ Wfei'l:n"es in • Harmonially OsciUBMg Pile," by N.MWrs and G. Gliletas. 718m. (PB92-108356/AS).

NCEER-91-0011 "Dynamic CharactenslJi:S of B Full-Size Five-Story Steel Structure and • '215 s..ale Model," by K.C. Chlllg,G.C. Yeo. G.C. Lee. D.S. Hao and Y.C. Yeti," 7(2/'H.

NCEER·IJI-OOI2 "Seismic Response of a 2/5 xale Steel Slructure with Added Viscoelastic Dampen," by K.C. Chang. TT.Soong. S-T. Oh and ML La., 5/11191 (PB92-11OS16/AS).

NCEER-91-OJ13 ..Earthquake Response (If Retalnina Walls; Full-SuIe TCSb"llrld Compulalional Modeh".... by S. Alampalh

and A-W.M. Elgamal. 6/20191. lD be publishod.

NCEER-<; i -0014 "3D-BASIS·M: Nonline. DynamIC Ana\yail of Mulbple Buildill& 8_boWed SlrUl;tura." by P.C. Tsopel••S. NagaraJaiah, M.e. Constantinou and A.M. Relnhorn. 5/2Sm. (PB92·1I388~/AS).

8-9

NCEEK ~~ IH,7 "En):lfleerll1~ EsaJuallon of I'ermant'nl Ground Oelonnall.•ns OUt" to SelSlnI"ally-lndlKcJ L'4udadl"n." hyM.H RaIla!. K J)"tory and AW.M. EI~amal. V24N2, (I'8YL'22421/AS)

NCEEK Y~ iHll\ "A Pro,:edure 101 Ihe S"lsmK Evaluallon nl RUlldlnp In It-.e Cenlnl and Easkrn Unrled Stales:' to~' CO.Poland and J () Malley. 4/~N2, (P8Y2·2224W/AS)

NCEEK ·Y~·I n IY "Expenmenlal and AnalYll\al Study of a Hytond Isnlallon Syslem USIn): Fnd,nn COnllllllatol" Shdln~

8eannp.' hy MV Fen~. S FUJII and M Shlnn/uka. 5/15!Y2. (I'RY3-1'\(1282/AS)

NCEEK ~2·U)I() "SelSlnl' K"'rslan,e 01 Slah·Colwnn Connedlo"s In EXlsllnl!l Nnn·OU"lIle RBI·Plale 8utldmp." toy AJDunalll and Y Du. 'iii K!Y2

NCEEK~2lklil "The Hysl",e,1S and Llynaml' Rehavlor nr Rnd Ma.snnry Walls UpgradcJ hy Fernl<OCmenl ('oatmp UnderCy,h, Lnadlfl~ and Sunn): S,mulated Ground Mnllnn.· hy H. Lee and SP l'rawel. 'i/ll!Y2. In hoe puhhsheJ

NCEEKY2IX)I~ "Sludy nr W,re Rope Syslems Inr SelsmK l'roles:lIon nf EqUIpment III RUlldllll!ls," toy G.F lJemcU.adc:.. M.CConslanllnnu and AM R"lnhorn. V20N2

NCEEK·Y2-UlB "Shap<' Memory Slrudural DamrefS MalenaJ l'rnperlJes. lJeslgn and SClsml, Teslrng." hy I'.R Wlllrng andF.A. C,<.I/ardh, ~/2"!Y2

NCEEK~2·(X1I4 "u'n~'luJlI1al ""nnanem Grnund lJefonnallon EHeS:ls nn RWled Cnnunuous Pipelines," toy MJ O·Rourkc.anJ C NOldhcrg. /l1I5N2

NCEER·~2-1X1l5 "A Simulalllln Mclhod fnr Stallnnal)' Gaussian Random Funs:unns Based nn Ihe Sampling Thcl'rem." toy M,Gngnnu and S. Ralopoulou. 6/ll!Y2. (I'R93-1274%/AS).

NCEER-Y2-(Xlill "Gra\'lty·LoadlJeSll1ncd Remlnrs:ed Co""rele Bu.lilings: Selsml" Evaluauon 01 EXlstlnl1 Conslrocllnn andlJcla"ln~ Slrat"glcs for Improved S"lsml' Rcsistan""." hy C.W. Hoffmann. S.K. Kunnath. J.8 Mander anJA.M R"lnhnrn. 7115!Y'2. 10 he puhhshed

NCEER ·1l2-IXII7 "Ot>sel\'allo"s nn Waler Systcm and I'tpellnc Perfonnans:c rn the Lllnlln Area nl Cosla RI"a Due 10 Ihe Apnl2:2. IWI Eartlkjuakc." hy M. O'Row-kc and D Ballanlyne. 6/30192. (I'B93-116811/AS)

NCEER·Y2·/X1I8 "Founh Edition of Earlhquake Edu<:allon Malenals for Grades K·12." Edited hy K,E,K. Ross, 8/10192,

NCEER-Yl-<Xl19 "Prou:cdlOgs from the Fourlh Japan-U,S, Workshop on Earthquake ReSISlan1 L>eslgn of Lifeline Fauhbes and

Counlermeasures for 5011 Liqueflll:tion:' Edited by M, Hamada and TD, O'Rourke. 8/12~2. (I'B93163YW/AS)

NCEER-Y2-11120 "Adlve Bras:1011 Syslcm: A Full Scale Implementation 01 Active Control." by A.M, Remhom. T.T. Soong.R.C'. Lm. MA RIley. Y,P. Wang. S. Aizawa and M, HlgllShlOO. 8114~2. (I'B93-127512/AS),

NCEER-Y2-lXl21 "Ernptn<:d AnalySIS 01 Honwntal Ground DtsjJlacemena Generated by Llqueflll:lIon-lnduced Laleral Spreads."by SF Banlcll and TL Ynoo, 8/17!Y2

NCEER-92-0022 "IL>ARC Versl...n 3.0: lnelllSlIc L>amage Analysl~ 01 Reinlor~ Concrele Structures." by S.K, KUMath, A,M.RelOhom and RF. Lobo. 8/3I!Yl. 10 be pubhshed

NCEER-92-lXJ23 "A Seml-EmpUical AnalYSIS of Strong·Mobon Peals 10 Tenns 01 SelSmK: Source, Propagalll1l1 Path and LocalSIIe COndItIlIflS. hy M. Kamiyama, MJ, O'Row-ke and R, Aores-Rerrones. 9~!Y2. (PB93-IS0266/AS).

NCEER-92-0024 "SeISmiC BehaVIOr 01 Reinforced Concrete Frame SlI\Icturrs wllh Nonductile Dewls. Part I: Summary 01Expenmental Flndmgs of Full Scale Beam-Column ~oml Tests." by A. Beres. R_N. Wlule and P. Gergely.9OO!Y2. to be pubhshcd.

NCEER-92-0025 "Expenmental Results 01 Repured and Reuofillcd Beam-Column 1011I1 TellS in Liahdy Relllforced ConcreteFrame Buildings." by A. Beres. S. El-BorJi. R.N. While and P GcrJCly, 10I29~2, to be published.

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NCEEIV,l:!-nl2t> "A GCn<,rallratll>n of <)ptImal Conlr,,1 Th.",..y: Lmear and Nonlinear Structures." hy IN Yang. Z L, anJ S

Von~<:havahlkul. 11(2./92

NCEER<,l2-IMI27 "SclSmlC Resisun..., of Remfnr<:ed Cun<:rele Frame Stru.:tures OeSl~ned Only for Gravity L..ads: Part I

l>c"gn and l'r"pert.." "f a One Thlld S"ak Modd Stru<:lure," 1»' J.M Bra.:.:" A.M. Remhonl and 18Mand<:r. 12flN:!

NCEEK·',l2-1.12K ··SclSmll ReSISlan.:c ul Rel11fnrced Com;rek Frame SUu.:tures lkslgned Only fur Gravity Loads: Part II Exp<"rnncnlall'ertnrrT,ance of Suhassemhlage,,'· hy L.E Aycard .. lB. Mand..."I' and A.M. Remhum. 12/11'-12.

NCEER-<,l2-IMI2',l ·'ScISmlC Rcsislanle of Rel11fol\;ed Conc:rele Frame Structures l>cslgned Onl .. for GravIty Loads: I'ltI1 III Ex!",rnncntall'erfllrmanu: and AnalylJ<:al Study Ilf a SUUdural Model.·· hy J.M Brac:",. AM Rel11hum al1<l

JB Mander. 12/1H:!. to ho: puhhsh<:d.

NCEER-',l2IMI\() '·Evaluatlllll 01 SelSmll Retrolll 01 Remlor<:ed COI1<:rele Frame StrUltures: Part I - Expenmentall'erfonnanc:elit Retrntotled Suha,o;emhlages.'· hy LJ Choudhurl. J.8. Mander and A.M Relllhom. 12/KI92.

NCEEK',l2IH\J ··Evaluatllln lIf SClSmlC: R"trllf,lllf RCl11forced COIlc:ret" Frame Slruc:tUln Parr II Exp<.."I'lmenta! PerfN:nanleand AnalylJsal Study of a Rerwfilled Stru<:tural Modd,'· hy J.M. Broc':l. A.M Rel11hom and lA Mander.

l2.'l!I'-I~

NCEEK-',l2-iH\2 ··Expenmental and Anillyllc:al Invesllgahon uf SeISmIC Respllnsc of Srru"rur", With Supplt:mcnral FlUid

VIS<.UUS Damper,,'· hy M.C'. Conslantmuu and M.O. Symans. 12121/92.

NCEER<,l2-IMIH '·Rocllnnalssanu: Report Iln the Caml. Egypt Earthquake III (),;tllher 12. 1'N2," hy M Khat"r, 12/2~/92

NCEEK ',l2 1MI.\4 ··Low Level L>ynaml': Charocll."fISUC:s of Four Tall Flat-Plate RUlldl11gs 111 New Yorlr. Cny,'· hy H Gavin. S

Yuan. J Grossman. E P~Ir.~lIs and K Jllwh, 12(2.11/92.

NCEEK-',l3-{Ull ·'An Expenmcntal Srudy on the Setsml': l'erformanu: of Bn<:lr.-Infilled Steel Frames Wllh and WIthoutRetrofit,'· "'y J.R Mander. B. Nail, K. W~ljlr.owslu and 1. Mil, 1(2.9193

NCEER-<,l3-IUI2 ··5.""al AcwunlIng tor lJlsaster IJreparedl1t'ss and Kec:overy PlannUlg," by S. Cole. E. PanlllJa and V. Ra..r.ak.

2(2.2/9~. lLJ ho: puhhshed.

NCEER-H-lun ·'Assessment of 19',11 NEHRP PnlVlslOns fur NonstrU<:turaJ Compolll:nlS and Rewllum:nued RevISIOns," ~T.T. Soong. G. Ch<:n, Z. Wu. R-H. Zhang and M. Gngoriu. 3/1/93.

NCEER~93tU14 "Evaluauon of Slatlc and Response Spectrum AnalySIS Procedures of SEAOC/UBC for Selsmll; Isolated

Struclures," by CW. WlRlers and M.C. Coostanllllou, 3/23/93

NCEER·93-0005 "Earthquakes In the Northeast· Are We [goonng the Hazard" A WOllsho-.p on Elllthquake SCIenu: and Safetyfor Eduntors"· edited by K.E.K. Ross. 4(2./93.10 be publisht;d.

NCEER-93-0006 "inelastIC Response of Reinforced Concrele StruclUJes with VUlcooiastK Braces," by R.F. Lobo. J.M. BrllC(;l.

K.L Shen. A.M. Reinhorn and T.T. Soong. 415/93.

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Drc.-at- - NISTR.E Lobo, 1.M. Bracci, K.L. Shen, A.M. Reinhorn and T.T. Soong Stale University of...

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Transcript of Drc.-at- - NISTR.E Lobo, 1.M. Bracci, K.L. Shen, A.M. Reinhorn and T.T. Soong Stale University of...