EXPERIMENTAL STUDY OF REINFORCED CONCRETE COLUMNS SUBJECTED TO MULTI-AXIAL CYCLIC LOADING · PDF file · 2009-12-03Experimental Study of Reinforced Concrete Columns subjected to...

REPORT NO.

UCB/EERC.87/14

SEPTEMBER 1987

REPRODUCED BYU.S. DEPARTMENT OF COMMERCE

NATIONAL TECHNICALINFORMATION SERVICESPRINGFIELD, VA. 22161

PB88-1T4347

EARTHQUAKE ENGINEERING RESEARCH CENTER

EXPERIMENTAL STUDY OFREINFORCED CONCRETE COLUMNSSUBJECTED TO MULTI-AXIALCYCLIC LOADING

by

STANLEY S. LOW

JACK P. MOEHLE

Report to the National Science Foundation

COllEGE OF ENGINEERING

UNIVERSITY OF CALIFORNIA • Berkeley, California

For sale by the National Technical Information Service, U.S. Department of Commerce,Springfield, Virginia 22161.

See back of report for up to date listing ofEERC reports.

DISCLAIMERAny opinions, findings, and conclusions orrecommendations expressed in this pUblication are those of the authors and do notnecessarily reflect the views of the Sponsorsor the Earthquake Engineering ResearchCenter, University of California, Berkeley

I~!f0171 '10

REPORT DOCUMENTATION 11. REPORT NO.

I PAGE NSF/ENG-87039•• Title and Subtitle

Experimental Study of Reinforced Concrete Columnssubjected to Multi-Axial Cyclic Loading

3. Recipient'. Aceeaslon No. I

PB3 8 1 1 4: 3 4 ? I~5. Raport Date

September 1987

1--------------------'----------------.. ---------------17. Author(s)

Stanley S. Low and Jack P. Moehle9. Performing Organization Name and Addres.

Earthquake Engineering Research CenterUniversity of California1301 South 46th StreetRi chmond, Cal iforni a 94804

12. Sponsorlne Organization Name and Address

National Science Foundation1800 G. Street, N.W.Washington, D.C. 20550

15. Supplementary Notes

16. Abstract (Limit: 200 words)

8. Performlne Organization Rept. No.

UCS/ EERC -87/1410. Project/Task/Work Unit No.

11. Contract(C) or Grant(G) No.

(C)

(G) CEE-831666213. Type at Report & Period Covered

14.

between:

!,

~Five nominally identical quarter-scale reinforced concrete columns were constructed andtested using multiaxial cyclic loading histories. The columns were detailed to satisfyrequirements of current North American building codes for reinforced concrete structures inregions of high seismic risk. The columns were loaded as cantilevers attached to stifffoundation blocks. The primary variable was the load history. Load histories included (1)uniaxial cyclic lateral loads with constant axial load, (2) biaxial cyclic lateral loads with~onstant axial load, and (3) biaxial cyclic lateral loads with cyclicly-varying axial loads.

Measured responses indicate that inelastic deformations in these tests were due primarilyto effects of flexure and reinforcement slip from the foundation blacks. Visible damage,stiffness, and resistance were markedly affected by the load history. Existing procedures forcomputing stiffness and strength under biaxial loading correlated reasonably well with the·measured behavior ••

This report documents the experiments and measured data, and presents comparisonsmeasured and calculated responses.

17. Document Analysis •• Descriptors

concrete columnsstiffnessinelastic deformationflexure

b. Identifiers/Open·Ended Terms

c. CaSATl Field/Group

18. Availability Statemen:

Release unlimited

.(See ANS1-Z39.1B)

reinforcement slipuniaxial cyclic loadbiaxial cyclic load

19. Security Cia•• (This Report)

Unclassified20. Security Class (This Paee)

Unclassifieds.. '".truct/one on Rever.e

21. No. of Pages

13S-

OPTIONAL FORM 272 (4-77)(Formerly NTlS-35)Department of Commerce

EXPERIMENTAL STUDY OF REINFORCED CONCREjTE COLUMNS

SUBJECTED TO MULTI-AXIAL CYCLIC LOADING

by

Stanley S. LowResearch Assistant

and

Jack P. MoehleAssoc. Professor of Civil Engineering

A Report to Sponsor:

National Science Foundation

Report No. UCB/EERC-87/14

Earthquake Engineering Research Center

College of Engineering

University of California

Berkeley, California

September 1987

ABSTRACT

Five nominally identical quarter-scale reinforced concrete

columns were constructed and tested using multiaxial cyclic

loading histories. The columns were detailed to satisfy

requirements of current North American building codes for

reinforced concrete structures in regions of high seismic risk.

The columns were loaded as cantilevers attached to stiff

foundation blocks. The primary variable was the load history.

Load histories included (1) uniaxial cyclic lateral loads with

constant axial load, (2) biaxial cyclic lateral loads with

constant axial load, and (3) biaxial cyclic lateral loads with

cyclicly-varying axial loads.

Measured responses indicate that inelastic deformations in

these tests were due primarily to effects of flexure and

reinforcement slip from the foundation blocks. Visible damage,

stiffness, and resistance were markedly affected by the load

history. Existing procedures for computing stiffness and

strength under biaxial loading correlated reasonably well with

the measured behavior.

This report documents the experiments and measured data, and

presents comparisons between measured and calculated responses.

i

ACKNOWLEDGMENTS

The research reported herein was funded by the National

Science Foundation under Grant No. CEE-8316662 and by the

generous contributions from individuals of the Industrial Liaison

Program of the College of Engineering of the University of

California at Berkeley. (The views presented in this report are

those of the authors, and do not necessarily represent the view

of the sponsors.)

The authors thank the support staff of the Department of

civil Engineering for their expert assistance in fabricating the

test specimens, conducting the tests, and reducing the

experimental data. The authors also acknowledge the following

for their advice and encouragement: Professors F. Filippou and

S. Mahin, and graduate research assistants xiaoxuan Qi and Shyh

Jiann Hwang, all of the Department of civil Engineering at the

University of California at Berkeley.

The research described in this report is based primarily on

work conducted by the first author in partial fulfillment of

requirements for the degree of Master of Engineering under the

supervision of the second author.

ii

Abstract

Acknowledgments

Table of Contents

List of Tables

TABLE OF CONTENTS

i

ii

iii

v

List of Figures vi

1 . Introduct ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1. 1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1. 2 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Relevance of Experiment to Current Research ........• 3

2. Description of the Experiment .........................•. 4

2 . 1 Text Specimens . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . 4

2.2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3 Loading Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . 5

2.4 Instrumentation and Data Acquisition •................• 6

2. 5 Test Procedure . . . . • . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . 8

3. Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . .. 11

3. 1 Summary of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11

3.2 Visible Damage . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . •. 11

3.3 Lateral Load-Displacement Relations .....•........•.. 13

3.4 Base Moment-Base Rotation Relations 14

3.5 Strain Histories 15

4. Discussion of Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . • .. 16

4.1 Introductory Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 16

iii

4.2 Computed Monotonic Behavior .•.•..•....•............. 16a.) Moment-Curvature Relations 16b.) Biaxial Moment-Axial Load Interaction Diagrams 18c.) Shear strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 18d.) Bar Slip Relations • . . . . . . . . . • . . . . . . . . . . . . . . . . .. 19e.) Calculated Monotonic Load-Displacement Relations. 20

4.3 Comparison Between Computed and Measured Quantities 21a.) Failure Mode •..................•..•.........•.. 21b. ) strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 21c.) Load-Displacement Relations ....•............... 23

4.4 Source of Deformation at Final Loading Stage . . . . . . .. 23

4.5 Effect of Load History~on Load-Displacement Response . 25

4.6 Effect of Load History on Damage • • • • • • . • • • • • • • • • • • •• 29

5. Summary and Conclusions • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• 32

References • • • • • • • • • • • • • • • • • • • • • • • • . . • • • • • • • . • • • • • • • • • • • • • • •• 35

Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 37

Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 42

iv

LIST OF TABLES

Tables

2.1 Chronology of the Experiments

2.2 Concrete Batch Quantities for One Cubic Yard, SaturatedSurface-Dry Aggregates

2.3 Concrete Compressive Strengths

2.4 Concrete Splitting Tensile Strengths

2.5 Reinforcement properties

3.1 Summary of Selected Experimental Results

4.1 Calculated Effect of Bar Slip on Column End Displacements

v

Figures

LIST OF FIGURES

2.1 Test Specimen Configuration

2.2 Test Specimens Ready for casting

2.3 Test Specimens After casting

2.4 Concrete Stress-strain Relation

2.5 Longitudinal Steel Stress-Strain Relations

2.6 Loading Apparatus and Instrumentation

2.7 Photograph of Experimental Setup

2.8 Base Moment Determination

2.9 Intended Displacement and Load Histories

3.1 Photographs of Test Specimens at Conclusion of Testing

3.2 Crack Patterns at Conclusion of Testing

3.3 Measured Load History for Specimen 1

3.4 Measured Load History for specimen 2




3.8 Lateral Load Versus Lateral Displacement for Specimen 1





3.13 Base Moment Versus Lower Column Rotation for Specimen 1




vi


3.18 Strain Histories for Specimen 1




3.22 strain Histories for Specimen 5

4.1 Concrete Stress-Strain Relations Assumed forMoment-Curvature Calculations

4.2 Steel Stress-Strain Relations Assumed forMoment-Curvature Calculations

4.3 Computed Moment-Curvature Relations

4.4 Computed Uniaxial Moment-Axial Load Interaction Diagrams

4.5 Computed Biaxial Moment-Axial Load Interaction Diagrams

4.6 Computed Monotonic Load-Displacement Relations

4.7 Comparison Between Measured and Computed Base-Moment Strengths

4.8 contribution of Base Rotation to Total Column Deflection

4.9 Idealized Biaxial Hysteresis Relations for Load Steps "a"through "c"

4.10 Idealized Biaxial Hysteresis Relations for Load steps "a"through "f"

4.11 Idealized Biaxial Hysteresis Relations for Load Steps "a"through "i"

4.12 Idealized Biaxial Hysteresis Relations for Load steps "a"through "m"

4.13 Load Resistance Envelopes for Specimens 1, 2, and 3

4.14 Comparison of Loading stiffnesses

vii

CHAPTER 1

INTRODUCTION

1.1 General

Conventional seismic design of reinforced concrete buildings

is carried out considering one direction of seismic loading at a

time. Usually, the analysis model assumes elastic behavior and

monotonically appl ied loads. However, during an actual severe

earthquake, a building is loaded simultaneously along both axes

and may be sUbj ect to inelastic deformations with many load

reversals. Thus, the capacity of columns in the building to

absorb and dissipate energy during multi-axial loading becomes an

important factor in the design of the structure.

In conventional design practice, a column is designed

explicitly for an ultimate flexural moment, Mu ' shear, Vu ' and

axial load, Pu ' The required ductility of a column is assured

implicitly by establishing an upper and lower limit on the

longitudinal reinforcement ratio and by requiring a minimum

amount and spacing of transverse reinforcing. Adequacy of the

current design method in providing the required strength and

ductility under uniaxial loading reversals has been demonstrated

in previous experimental studies [7). Although behavior of

columns under biaxial loading has been studied previously [5),

adequacy of the design method for columns sUbjected to multi

axial loadings has not been fully investigated.

1.2 Scope

To further investigate behavior under mUlti-axial cyclic

loading, an experimental study was carried out in which five one

quarter scale reinforced concrete columns were sUbjected to

inelastic load histories with reversals. The columns were

nominally identical, and satisfied major requirements of current

codes for design of lateral load resisting columns in regions of

high seismic risk [8].

approximately 5000 psi.

Concrete had compressive strength of

Reinforcement was typical of Grade 60.

The longitudinal reinforcement ratio was 0.0226. Average axial

load was approximately O. 06f I cAg, in which f I c = concrete

compressive strength at time of test and Ag = gross area of

column cross section.

The columns were tested as cantilevers projecting from stiff

foundation blocks. cyclic lateral load histories were either

uniaxial along a principal axis of the column, uniaxial along a

skewed axis of the column, or a "cloverleaf" biaxial loading.

Axial loads were either constant or varied as a function of the

lateral load history.

The experiments and measured data are described in later

sections of this report. Existing analysis methods are used to

compute expected behaviors of the columns, including stiffness,

rebar slip effects, monotonic loading curves, and strength under

biaxial loading. computed and measured responses are compared.

2

1.3 Relevance of Experiment to Current Research

In addition to the importance (as described above) of

studying biaxial loading effects in general, it is noted that the

columns described in this report are nominally identical to

first-story columns of a six-story shake-table model tested in

the Earthquake Simulator Laboratory at the Earthquake Engineering

Research Center of the Berkeley campus [3]. The shake-table

model wassubj ected to "biaxial" excitations on the earthquake

simulator. Column data presented in this report will supplement

the study of the shake-table model.

3

CHAPTER 2

DESCRIPTION OF THE EXPERIMENT

2.1 TEST SPECIMENS

The columns are approximately one-quarter scale models of

columns considered representative of those occurring in modern,

moderately-tall, ductile concrete frames located in regions of

high seismic risk. The columns had the configuration depicted in

Fig. 2.1.

Each column was a 21. 5 in. long cantilever, having gross

cross section of 5 in. by 6.5 in. LongitUdinal reinforcement

comprised #3 deformed bars at each corner, two #2 deformed bars

(0.049 in. 2 cross section) along each long face, and one #2 bar

deformed bar along each short face (Fig. 2.1). The longitudinal

reinforcement ratio, defined as the ratio between total

longitudinal steel area and gross column cross-sectional area,

was 0.0226. All longitudinal bars were anchored with 90-degree

hooks embedded 7-in. into a 13 -in. by 14-in. by 18-in.

reinforced concrete footing. Plain, gage No.9 wire (0.0123 in. 2

cross section) was used as transverse reinforcement in the

columns. starting from the top of footing, tie spacing was 1 in.

for the first nine inches followed by ties at 1.5 in. on centers.

According to prevailing codes [1 J, the first tie spacing above

the top of footing should have been 0.5 in. rather than 1 in.

Apart from this deviation, the columns satisfy current code

requirements for columns in ductile moment resisting frames

located in regions of high seismic risk [8J.

4

The test specimens will be designated as specimens 1 through

5, corresponding to chronology of the individual test dates. As

described in Sections 2.2 and 2.5, the designation also indicates

variations in concrete materials and test load histories. A

chronology of. construction and testing is in Table 2.1.

2.2 Materials

The test specimens were cast in a horizontal position in two

batches, specimens 1 through 3 in the first batch, and 4 and 5 in

the second. Photographs of the reinforcing cages and forms

before and after casting are in Fig. 2.2 and 2.3, respectively.

Details of the materials are given in the following tables

and figures: Concrete mix proportions (Table 2.2), concrete and

steel mechanical properties (Tables 2.3 through 2.5), and stress

strain curves (Fig. 2.4 and 2.5). It is noted that mechanical

properties of the longitudinal reinforcement were characteristic

of those usually obtained for Grade 60 reinforcement, with mean

yield stresses ranging from 60 to 73 ksi. Mean concrete

compressive strengths were approximately 5300 psi for specimens 1

through 3, and 4600 psi for specimens 4 and 5 at time of testing.

2.3 Loading Apparatus

The columns were tested in a horizontal position with the

weak direction (short column cross-sectional dimension) parallel

to the laboratory floor as shown in Fig. 2.6 and 2.7. The

footing block was shimmed and prestressed to a massive reinforced

concrete block before testing. Two 40-kip hydraulic actuators

5

(for lateral loads) and a hydraulic jack (for axial load) were

then attached to the "free" end of the column through a

specially-fabricated universal joint. The joint allowed forces

to be applied at the column end with negligible rotational

restraint.

The hydraulic pressure for the actuators and jack was

provided by three portable Haskel hydraulic pumps. The pumps

were controlled manually, with applied loads varied to follow

approximately the prescribed displacement or force histories.

2.4 Instrumentation and Data Acquisition

Instrumentation measured lateral column displacements,

column loads, deformations of the column near the base, and

strain of longitudinal reinforcement. The instrument locations

are shown schematically in Fig. 2.6, with a photograph of the

test setup in Fig. 2.7.

Displacements of the column were measured near the free end

of the column using LVDTs (linear voltage displacement

transducers). The LVDTs were mounted to a stiff reference frame

attached to the footing blocks, so that recorded displacements

are relative to the footing. Thus, any movement of the footing

blocks during testing does not influence the recorded

displacements.

Deformations of the column near the base were measured with

clip gages attached between the top of the foundation block and

an aluminum yoke that was fixed to the column concrete a distance

6

of 5 in. from the top of the foundation block. Three clip gages

were used, one at each of three corners of the yoke. Average

rotations about each axis along this length were calculated by

dividing the differences in relative displacements by the

distance between clip gages. It is noted that these rotations

include both the rotations due to slippage of the longitudinal

reinforcement in the footing and the flexural curvature in the

lower 5 in. of the column.

The hydraulic actuators and jack were mounted to strain

gaged load cells that were calibrated to obtain the applied

column load. Column base moments (at the top of footing) were

computed as the sum of (1) the primary moment due to lateral load

and (2) the secondary moment due to the axial load acting through

lateral deflections. The primary moment was calculated as the

product between lateral load and loading height. The secondary

moment (P-delta moment) was calculated according to the procedure

outlined in Fig. 2.8. As noted in the equation given in that

figure, the P-delta moment includes both the effect of the axial

load acting through lateral displacement of the column and the

effect of the horizontal component of the "axial" load acting

through column height.

Weldable strain gages having I-in. gage length were

installed on two longitudinal bars located along a diagonal of

the column cross section (Fig. 2.1 and 2.6). The gages were

centered 0.5 in. from the face of the footing block.

signals from all electronic instruments were scanned at

7

discrete intervals using a low-speed scanner box. The signals

were stored digitally on a computer disk. In addition, signals

from displacement and load gages were recorded in analog form on

X-Y and X-Y-Y' plotters. The test program was controlled

manually by monitoring the plotted signals.

All specimens were whitewashed to make cracks in the

concrete more visible. Cracks were marked when the peak

displacement in each direction of a given cycle was reached.

Maximum crack width was also recorded at this time.

2.5 Test Procedure

The footing block of a specimen was shimmed and then

prestressed to a massive concrete block prior to testing.

Instrumentation was then installed and zero values set, followed

by attachment of the loading jack and actuators. Testing began

within an hour of setting zero values for the instruments and

attaching the jack and actuators. The load history was different

for the different test specimens. The target load/deformation

histories for the specimens are shown in Fig. 2.9.

descriptions of the load history of each specimen follow.

Brief

SPECIMEN 1: Uniaxial lateral loading about the weak axis, withconstant axial load of 10 kips

SPECIMEN 2: Biaxial lateral loading with column tipdisplacements along an axis at 45 degrees relativeto the principal axes of the column cross section,with constant axial load of 10 kips.

SPECIMEN 3: Biaxial lateral loading with column tipdisplacements following a "cloverleaf" pattern,with constant axial load of 10 kips.

8

SPECIMEN 4: Biaxial lateral loading with column tipdisplacements along an axis at 45 degrees relativeto the principal axes of the column cross section,with axial load varying from 0.5 to 20 kips.

SPECIMEN 5: Biaxial lateral loading with column tipdisplacements following a "cloverleaf" pattern, withaxial load varying from 0.5 to 20 kips.

The axial loads for specimens 4 and 5 varied with the tip

displacement in the weak direction. For a given displacement

cycle, the axial load varied approximately linearly from 10 kips

at zero displacement to 20 kips at the maximum positive

displacement for that cycle. For loading in the negative

direction, the axial load varied approximately linearly from 10

kips at zero displacement to 0.5 kips at the most negative

displacement for that cycle.

In the early stages of loading before reinforcement yielded,

loading was controlled by the applied lateral load. For all

specimens, the first cycles were at forces corresponding

approximately to first cracking, followed by loading to

approximately 40% of yielding, followed by loading approximately

to initial yielding of reinforcement, as determined for specimen

1. After reinforcement yielded, loading was controlled by the

magnitude of the measured tip displacement.

Two complete cycles were carried out at each level of

loading (Fig. 2.9). The tip displacement was increased

progressively until lateral displacement reached 0.96 in. (5.3%

of specimen height measured from top of footing). After reaching

the maximum displacement for each cycle, the hydraUlic equipment

was not manually adjusted for the period of time (approximately

9

ten minutes) that damage was observed and recorded. Some drop in

hydraulic pressure typically was observed during this time.

10

CHAPTER 3

EXPERIMENTAL RESULTS

3.1 summary of Data

Observed damage is summarized in photographs and crack

diagrams in Fig. 3.1 and 3.2, respectively. Measured load

histories are presented in Fig. 3.3 through Fig. 3.7 (in these

figures, one unit of "time" is defined to pass whenever data

readings are taken). Lateral load versus lateral displacement

along each principal axis is presented in Fig. 3.8 through Fig.

3.12. Similarly, relations between base moment (corrected to

account for second-order effects) and base rotation along the

lower five inches of the column are presented in Fig. 3.13

through Fig. 3.17. Reinforcement strain gage readings are

plotted versus time in Fig. 3.18 through Fig. 3.22. A summary of

selected experimental results is in Table 3.1.

3.2 Visible Damage

Several observations are made regarding crack patterns,

and apparent failure modes (Fig. 3.1 and 3.2).

(1) Primary cracks were generally perpendicular to the

longitudinal axis of the columns, and were apparently due to

flexural effects.

(2) As the load increased to yield in either direction, minor

diagonal tension cracks were observed. For specimen 1, the

diagonal cracks formed only on the two faces parallel to the

direction of lateral load. For the other specimens, the diagonal

cracks formed on all faces. Although flexural cracks

11

predominated, the diagonal tension cracks indicate that shear was

a contributing factor in behavior of the test specimens.

(3) Cracks generally closed when the loading fell below

approximately the load that first caused cracking. This is

probably attributable to the presence of axial load on the

column.

(4) Between column end displacements of 0.32 in. and 0.64 in.,

and thereafter, development of new cracks slowed. As larger

displacements were applied in this range of loading, crack width

in existing cracks became larger.

(5) The widest crack in all specimens was at the intersection

between the column and the footing block, indicating the

occurrence of slip of longitudinal bars from the footing.

However, the width of these cracks could not be determined

because the crack grew partially below the footing surface.

(6) For specimens 2 through 5, spalling of concrete cover

initiated at the corners of the column near the footing during

displacement cycles of 0.32 in. or 0.64 in. Specimen 1 did not

begin spalling until the displacement cycle to 0.96 in.

(7) For specimens 2 through 5, total spalling of concrete cover

near the corners occurred for displacements in the range between

0.64 in. 0.96 in. In specimens 2 and 4, only two diagonal

corners spalled, whereas in specimens 3 and 5, all four corners

spalled and small portions of cover adjacent to diagonal tension

cracks showed minor spalling.

(8) The primary failure mode of all specimens was by flexure.

As gaged by the amount and distribution of diagonal cracks, shear

12

also played a minor role in the failure of specimens 3 and 5.

Examination of the specimens revealed that longitudinal

reinforcement did not buckle.

3.3 Lateral Load-Displacement Relations

Relations between lateral load and displacement are plotted

in Fig. 3.8 through 3.12. Lateral loads reported in those

figures are readings obtained directly from load cells in the

lateral-load actuators, without a correction for the lateral

component of the force in the axial load jack. Lateral

displacements were determined directly from readings of LVDTs

(Fig. 2.6), and reflect displacement of the column tip relative

to a rigid reference frame mounted to the footing block. Twist

of the column end about the column longitudinal axis could be

determined from the available LVDT readings, and was observed to

be negligible.

Based on the envelope of load-displacement responses in Fig.

3.8 through 3.12, three distinctly different ranges of stiffness

can be observed, the first corresponding roughly to loading

before flexural cracking, the second corresponding to the range

between cracking and yield of longitudinal bars, and the third

after yield. After the column longitudinal bars had yielded, and

for displacement cycles that did not significantly exceed prior

displacement maxima, a reduction in both stiffness and resistance

were noticeable. When sUbj ected to increased displacements,

resistance was mostly regained.

13

Hysteretic responses for specimens 1, 2, and 4 are similar

to those commonly observed for reinforced concrete elements

sUbjected to axial loads and not having significant shear or

anchorage deterioration [7]. Hysteretic relations for specimens

3 and 5 show loads "relaxing" for lateral displacements near the

maximum and near zero, without significant change in

displacement. The relaxation is attributed to the nature of the

biaxial loading history, as follows. As shown in Fig. 2.9, drift

was first imposed in one direction while ideally fixing

displacement in the transverse direction, and then the axes of

loading were switched. The relaxation shown in Fig. 3.10 and

3.12 is concurrent with commencement of loading in the

perpendicular direction. section 4. 5 of this report discusses

this phenomenon further.

3.4 Base Moment-Base Rotation Relations

Measured relations between base moment and base rotation are

in Fig. 3.13 through 3.17. As noted in Section 2.4 and

illustrated in Fig. 2.8, base moment includes second-order

effects of the axial load acting through lateral displacements.

Base rotations are the total rotation of the column cross-section

at 5 in. from the top of the footing relative to the top of the

footing (Section 2.4 and Fig. 2.6). Thus, the reported rotations

include effects both of column flexure and reinforcement slip

from the footing.

In general, the shape of the moment-rotation relation for

each specimen (Fig. 3.13 through 3.17) appears similar to the

14

corresponding lateral load-displacement relation (Fig. 3.8

through 3.12). The similarity supports a hypothesis that

flexural and bond slip deformations in the "plastic-hinge" region

of the column were the predominant actions contributing to

overall specimen deformation. Section 4.4 of this report

examines the contribution quantitatively.

3.5 strain Histories

strain histories (Fig. 3.18 through 3.22) indicate that

corner longitudinal bars experienced greater inelastic

compression and tension strains in specimens subj ected to the

biaxial cloverleaf lateral loading than in the single specimen

(specimen 1) subj ected to uniaxial lateral loading. The high

strain in the corner portion of the column is consistent with the

observed damage (Fig. 3.1 and 3.2). The observation that the

longitudinal bars did not buckle, despite having undergone many

cycles of high inelastic compression and tension, supports a

conclusion that current detailing procedures are effective in

controlling buckling of reinforcement. The strains developed in

the columns loaded along an axis skewed to the principal axes

(specimens 2 and 4) were less than in the other specimens because

the gaged bars were located (by oversight) on the diagonal axis

of the column transverse to the diagonal of lateral loading.

15

CHAPTER 4

DISCUSSION OF TEST RESULTS

4.1 Introductory Remarks

Data present in Chapter 3 are analyzed and discussed in this

chapter. Computed responses are presented and compared with

measured responses. Sources of deformation in the columns are

analyzed. A summary of the effects of load history on behavior

concludes the chapter.

4.2 Computed Monotonic Behavior

Responses of the columns to monotonically-increasing loads

were computed for comparison with measured responses. Included

in the computed responses are uniaxial and biaxial moment

curvature relations, biaxial moment-axial load interaction

diagrams, shear strengths, bar slip relations, and uniaxial load

deflection relations. These are described in the following

subsections.

(a) Moment-Curvature Relations

Moment-curvature relations were computed for monotonic

loading using conventional assumptions that plane sections remain

plane (including perfect bonding between steel and concrete),

stresseS are related directly to strain, and relations of statics

are valid. A computer program was written to facilitate

computation of the relations. The computational scheme is as

follows:

(1) The cross section is sUbdivided into a grid of small

16

rectangular elements (fiber approach (15]). A material property

is assigned to each of these small elements. Additional elements

on the cross section are defined for the reinforcement.

(2) A strain field is imposed on the cross section, defined by a

maximum concrete strain, depth of neutral axis, and inclination

of neutral axis. The strain at the center of each element

(fiber) of the cross section is computed from geometry

considerations.

(3) Given the strain at the center of each element, stress at

the center of each element is determined from a predefined

stress-strain relation. An average force in each element is

defined as the product between the stress at the center of the

element and cross-sectional area of the element.

(4) Axial load and moment about each axis are determined by

summing effects of averages forces acting on each element of the

cross section. A correction is made for concrete displaced by

reinforcement. Axial load is defined to be acting at the

geometric centroid of the gross concrete cross section. Moments

are defined relative to that centroid.

For the columns in this study, unconfined and confined

concretes were defined using properties measured from test

cylinders, and analytical relations defined by Scott and Park

[13] . The assumed curves are plotted in Fig. 4.1. Assumed

stress-strain relations for reinforcement are in Fig. 4.2.

Computed moment-curvature relations, for the range of axial

loads experienced during the experiments, are in Fig. 4.3. The

17

relations indicate that strength and ductility are affected by

the level of axial load and the orientation of loading. However,

as would be expected for well-confined concrete columns with

axial loads below the balanced point, the columns exhibit

"adequate" ductility for all plotted axial loads.

(b) Biaxial Moment-Axial Load Interaction Diagrams

Interaction diagrams were constructed using the same

computer program described in Section 4.2 (a) . Families of

uniaxial interaction diagrams are plotted in Fig. 4.4 for various

assumed maximum concrete compressive strains. Biaxial moment

interaction diagrams for various assumed maximum concrete

compressive strains and for various axial loads are plotted in

Fig. 4.5.

(c) Shear strength

To check if shear could limit the strength of the columns,

shear strengths were computed using the beam shear strength

equations of the ACI Building Code [lJ. Accordingly, a concrete

shear strength of Vc = 2~ bd = 2 /4900 (S) (S. 8) = 4.1 kips is

computed parallel the long cross-sectional dimension, and Vc = 2

14900 (6.S) (4.3) = 3.9 kips is computed parallel the short

dimension. Using a limiting steel yield stress of 60 ksi,

strength of steel in the long direction is Vs = Ayfyd/s =

(0.0369) (60) (S. 8) /1 = 12.8 kips, and in the short direction is

(0.0492) (60) (4.3)/1 = 12.7 kip. Adding the steel and concrete

strengths in each direction, the total nominal shear strengths

are 16.9 kips and 16.6 kips in the long and short directions,

18

respectively. Wi th a moment arm of 21.5 in. used in the

experiments, the base moments corresponding to shear failure are

363 kip-in. and 357 kip-in. in the long and short directions,

respectively. These strengths are approximately double the

computed flexural strengths (Fig. 4.5). Thus, shear failures are

not anticipated.

Cd) Bar Slip Relations

The presence of "wide" cracks at the base of the columns

suggests that slip of longitudinal reinforcement may have

contributed significantly to deformations of the columns. To

estimate the contribution, slip of reinforcement from the

footings was calculated assuming a uniform bond stress acting

over the stressed lead-in length of the reinforcement anchorages.

For No. 3 deformed bars, anchored in confined concrete similar to

that occurring in the footings, and sUbjected to monotonic

tension loading, an average uniform bond stress of 1300 psi was

estimated to be effective [6]. For this bond-stress model, the

length, 1, of rebar required to develop the tension T in the

loaded end of the bar is given by Eq. 4.1.

T1 = ----- (4 1).. ... .. ......... ............................ .

Ubdb'tT

in which ub = average uniform bond stress and db = nominal bar

diameter. The elongation, 0, of the bar over the length 1 is

given by Eq. 4.2.

T2

D = ---------- ••••••••••••••••••••••••••••.•••••••••• (4.2)

19

in which Ab = cross-sectional area of the bar and Es = Young's

modulus for the bar.

Values for 1 and D are tabulated in Table 4.1 for different

values of the steel stress, f s ' and with T in Eq. 4.1 and 4.2

taken equal to the product between f s and Ab . Even when stressed

to yield (approximately 70 ksi in Table 4.1), the length 1 does

not exceed the available lead-in length for the bars in the

footing (Fig. 2.1). Thus, deformations along the bent portion of

the hook and beyond need not be considered according to the

analytical model. Accordingly, total slip of the bar from the

footing is equal to the value of D.

Displacement at the end of the column due to bar slip is

computed as the product between column height and rotation due to

bar slip. Rotation due to bar slip is computed as the ratio

between bar slip, D, and the distance between the bar and the

neutral axis for bending. The distances are taken equal to 3.1

in. and 4.1 in. for bending about the weak and strong axes,

respectively. Computed column end displacements, Dx and Dy , for

bending about the weak and strong axes , respectively, are

tabulated in Table 4.1.

(d) Calculated Monotonic Load-Displacement Relations

Relations between load and displacement at the column end

were computed by numerically integrating calculated curvatures

over height and adding calculated displacements due to bar slip

from the foundation (Table 4.1).

20

The relations are plotted in

Fig. 4.6. It is noted that the computed displacement due to bar

slip effects is approximately 10 to 20 percent of the total

computed displacement before yield.

4.3 comparison Between Computed and Measured Quantities

(a) Failure Mode

According to computed responses, each specimen is

anticipated to fail in flexure after developing deformations well

in excess of yield. The measured results support this

expectation. Cracks were primarily flexural (Fig. 3.1 and 3.2).

Longitudinal reinforcement showed strain histories consistent

with inelastic flexural response (Fig. 3.18 through 3.22). Load

deformation relations (Fig. 3.8 through 3.12) are characteristic

of flexural response, and shear distortions were at no time

visible during testing. At the final load stages, concrete cover

spalled near the base only, with patterns of spalling consistent

with expected compression forces from flexural effects.

Shear, although apparently reSUlting in some inclined cracks

(Fig. 3.1 and 3.2), did not appear to be a prime contributor.

Slip of reinforcement from the footing, although contributing to

deformations, did not limit the strength.

(b) strength

Figure 4.7 compares measured biaxial base moment histories

(corrected for second-order effects) and computed biaxial moment

envelopes. The computed envelopes were obtained using the

computer program described in Section 4.2(a), with maximum

21

concrete compression strain of 0.01. For specimens 4 and 5, for

which axial load during testing varied between 0.5 and 20 kips

compression, three computed biaxial moment envelopes are shown,·

one each for axial compression of 0.0 kip, 10 kips, and 20 kips.

The data in Fig. 4.7 indicate that measured biaxial moment

strengths compare well with computed strengths. In general,

measured moment strengths exceed computed values. Although no

detailed analysis of the overstrengths will be presented in this

report, it is possible to attribute the overstrength to a

combination of several effects. For one, measured compression

strains in reinforcement exceeded the value of 0.01 assumed for

concrete in the analysis. As shown in Fig. 4.4, flexural

strengths are higher for the range of axial loads under

consideration if larger compression strains are assumed. In

addition, Bauschinger effects due to inelastic load reversals

generally result in higher reinforcement stresses for a given

strain than recognized in the scheme used to calculate member

strengths under monotonic loading. Reinforcement is also likely

to reach higher stresses in the columns than in coupon tension

tests because the smaller length under maximum tension in a

column is not likely to contain a weak "link" that limits

strength in a coupon tension test. Column strength is also

increased due to increases in concrete strength and maximum

strain capacity that result from high strain gradients and

confinement of concrete by the large footing block at the column

base. All of these effects are likely to increase the column

22

strength to values exceeding calculated strength.

(c) Load-Displacement Relations

Measured and calculated load-displacement relations are

compared in Fig. 3.9 through 3.12, with calculated relations

shown by broken curves. The calculated relations are identical

to those described in Section 4.2(d) and Fig. 4.6, and include

effects of reinforcement slip from the footings as described in

section 4.2(d). For columns loaded biaxially, computed relations

are shown for lateral load assumed to be uniaxial and parallel to

the direction for which the response is shown, and for lateral

loads resulting in displacement response at 45 degrees to the

direction being shown.

Calculated responses assuming uniaxial load for specimen 1

or biaxial load for the remaining four specimens compare well

with measured responses, suggesting that existing analytical

models are adequate for this purpose. For the biaxially-loaded

columns, it is apparent by comparison with computed uniaxial

load-displacement relations that the biaxial loading results in

reduced effective moment resistance along the principal axes of

the column.

4.4 Source of Deformation at Final Loading stage

The appearance of the columns following testing (Fig. 3.1)

suggests that the majority of column tip displacement was due to

23

inelastic rotations occurring at the base of the columns. In

support of this observation, column tip displacements about both

principal axes due to rotations measured by clip gages at the

base of the column were computed for comparison with measured

displacements. For this purpose, the rotation measured over a

five-in. gage length by the clip gages was assumed to be

concentrated at the center of the five-in. length as shown at the

top of Fig. 4.8. Computed displacements due to base rotations

are compared with actual measured maximum displacements at the

bottom of Fig. 4.8. According to this calculation, base

rotations along the bottom five in. of the column contributed

between 82 and 92 percent of the total maximum tip displacement.

A conventional design practice [11] is to assume that all

inelastic action is attributable to uniform flexural curvature

within a plastic hinge region at the end of an element. For the

columns of this study, a plastic hinge length equal to

approximately five in. is appropriate. Hence, rotations inferred

from the clip-gage readings at the base of the column are

effectively the equivalent plastic hinge rotations.

If the measured base rotations are assumed to be

attributable to uniform flexural curvature over the plastic hinge

length, then for specimen 1, for example, the computed curvature

is equal to (0.06 rad)/(5 in.) = 0.012 rad/in. In addition, if

the distance from the neutral axis to the tension reinforcement

is taken equal to the distance between extreme layers of

24

longitudinal reinforcement, that is, 3.0 in., then the expected

strain in longitudinal reinforcement is equal to (0.012

rad/in.)(3 in.) = 0.036 in./in. Actual maximum measured strain

for specimen 1 was 0.029 in./in. Thus, the method for estimating

strain produces fairly good estimates of maximum expected strain.

It is noted in relation to the preceding paragraph that the

calculated strain exceeds the measured strain, even though the

measured strain is likely to be a maximum value whereas the

calculated strain is an average. A plausible reason for this

apparent inversion of magnitudes is that the calculation method

does not consider the effect of rebar slip from the footing

blocks. Because of slip of the reinforcement, the column base

rotation is developed by reinforcement strains over a longer

length, thereby reducing the actual required reinforcement strain

over that length.

4.5 Effect of Load History on Load-Displacement Response

As described in Chapter 2, the columns were loaded to effect

displacement histories that followed prescribed patterns (Fig.

2.8 and 3.3 through 3.7). Under uniaxial lateral loading, either

along one principal axis as for specimen 1 or along an inclined

axis as for specimens 2 and 4, the resulting hysteretic relations

between lateral load and displacement (Fig. 3.8, 3.9, and 3.11)

show familiar patterns of slightly spindle-shaped loops. For

specimens 3 and 5, which were loaded in a cloverleaf pattern of

displacements, the hysteretic loops (Fig. 3.10 and 3.12) and

25

biaxial moment interactions (Fig. 4.7c and 4.7e) follow

unfamiliar patterns. The hysteretic responses of specimens 3 and

5 are explained qualitatively in the following paragraphs.

Figure 4.9 through 4.12 present an idealized chronological

sequence of displacement paths, load-deformation loops, and

biaxial moment interaction diagrams. The diagrams are considered

representative of specimen 3, with constant axial load, and for

lateral loads inducing inelastic response. Similar diagrams can

be plotted for specimen 5, but these would be complicated

somewhat by the simultaneous variations of axial loads during the

loading sequence. To clarify the presentation, the diagrams are

plotted successively on several sheets.

The diagram at the upper left of each sheet of Fig. 4.9

through 4.12 represents the displacement path during a selected

portion of one complete cloverleaf loading cycle. Points "a"

through "m" denoted on the displacement path occur successively.

The second pair of diagrams at the bottom of each sheet

represents the load-deformation relation along "X" and "Y" axes

of the column, with points "a" through "m" from the displacement

history designated at appropriate points. The diagram at the

upper right of each sheet represents the relation between base

moments about each axis, again with points "a" through "m"

designated at appropriate points. There is no attempt to present

the diagrams to any prescribed scale.

Figure 4.9 plots idealized responses for roughly the first

26

quarter cycle (points "a" through "c"). At first loading, the

displacement is increased in the "X" direction to point "a" (Fig.

4.9a). The load-deformation relation in the "X" direction loads

to point "a" (Fig. 4.9c), whereas no loading is noted in the "Y"

direction (Fig. 4.9d). The moment interaction diagram (Fig.

4.9b) shows moment only about the "Y" axis (that is, in the "X"

direction) •

As the displacement progresses to point "b" (Fig. 4.9a), the

load in the "Y" direction increases (Fig. 4.9d). As the moment

Mx increases for loading in the "Y" direction, flexural strength

considerations require that the moment My, developed during

loading to point "a", must decrease (Fig. 4.9b). The decrease in

moment My is noted also in the load-deformation relation in the

"X" direction (Fig. 4.9c). In addition, the displacement in the

"X" direction increases slightly as the load in that direction

relaxes (Fig. 4.9c). The magnitude of this increase in

displacement is partly a function of the test specimen and partly

a function of the loading system used in the experiments.

Similarly, moving from point "b" to point "c", the displacement

in the "X" direction is decreased, which simultaneously results

in an inelastic relaxation of load and displacement in the "Y"

direction.

As the loading is continued into the second quarter cycle

(points "d" through "f" in Fig. 4.10), similar behavior occurs.

Moving from point "c" to point lid", the column is loaded from a

27

positive "Y" displacement to an equally large negative "Y"

displacement (Fig. 4.10a). There is a simultaneous drop in load

in the "X" direction (Fig. 4.10c) as the cross section realigns

to the newly-imposed strain distribution. Moving to point "e",

displacement is applied in the positive "X" direction, as in the

first quarter cycle, with the characteristic relaxation of load

in the "Y" direction (Fig. 4.10d) as moments follow the biaxial

moment interaction diagram (Fig. 4.10b). A familiar pattern is

repeated in moving to point "f".

The diagrams in Fig. 4.11 and 4.12 continue the pattern

described in the preceding paragraphs. The completed idealized

hysteretic loops of Fig. 4.12 are qualitatively similar to those

measured for specimens 3 and 5 (Fig. 3.5 and 3.7, 3.10 and 3.12,

and 4.7).

The influence of biaxial lateral loading on the load

displacement envelopes is illustrated by Fig. 4.13. Figure 4.13a

is an envelope relation of lateral load in the weak direction for

various loading points for specimens 1, 2, and 3, with loading

points illustrated in Fig. 4.13c. As would be expected from

well-known principles for columns under uniaxial and biaxial load

[llJ, specimen 2 (with loading applied approximately along a

diagonal) has less lateral-load resistance than specimen 1 (with

load along the principal axis). For specimen 3, two different

points are plotted. Points "3a" correspond to first loading to

maximum displacement in the weak ("X") direction (Fig. 4.13c).

The envelope for these points is lower than those for specimen 1,

indicating that prior biaxial loading has reduced the effective

28

resistance of specimen 3. Points II 3b" , occurring after the

column has subsequently been loaded in the strong (IIY") direction

(Fig. 4 .13c), reveal even lower resistance (Fig. 4. 13a) ,

indicating that if transverse loads are applied while strength is

being maintained in one direction, a further reduction in load

resistance will occur. Fig. 4.13b presents similar data for the

strong ("yn) direction of loading.

The loading history also influences the loading stiffness.

Figure 4.14 plots loading paths (base moment about the llyn axis

versus base rotation in the same direction) in the positive

loading direction for all specimens. In those figures, different

loading paths are designated with a number. The number

corresponds to a specific displacement cycle of the loading

program, so that, for example, the number "6" for all specimens

corresponds nominally to the same loading cycle "6" for all

specimens. It is concluded from the data in Fig. 4.14 that

loading stiffness in a given principal direction is reduced

significantly by biaxial lateral loading, the biaxial loading

either having been applied previous to or simultaneous with the

current loading.

4.6 Effect of Load History on Damage

The different load histories resulted in markedly different

amounts of damage in the different columns. Photographs of the

five specimens at the conclusion of testing are shown in Fig.

3.1. The photographs were taken after loose concrete was removed

by hand. Even though the columns were each loaded with the same

29

number of cycles in the weak direction, and to the same lateral

displacement, differences in visible damage are clear. The

uniaxially-loaded column, specimen 1, shows very little concrete

spalling. The columns loaded along the diagonal, specimens 2 and

4, show significantly greater damage in the corners along the

loading diagonal. Once the damage began in the corners for those

columns, it spread more readily to other parts of the column

perimeter. The columns with cloverleaf displacement histories,

specimens 3 and 5, show the most severe damage, with major

spalling around the entire perimeter at the base of the column.

In addition to effects of the displacement history,

examination of the photographs in Fig. 3.1 reveals that the

columns with varying axial load, specimens 4 and 5, had more

severe damage than corresponding specimens 2 and 3, respectively,

which underwent the same lateral displacement histories with

constant axial load.

The greater extent of damage in columns with cloverleaf

loading histories (specimens 3 and 5) relative to the uniaxially

loaded column (specimen 1) is also apparent in longitudinal

reinforcement strain histories (Fig. 3.18, 3.20, and 3.22).

(strain-history data for specimens 2 and 4 are not indicative of

the severity of loading, as the measured strains are for bars not

located in the most-severely strained corners of those columns.)

The extensive variation in apparent damage, despite

similarities in maximum lateral drift, is an indicator that

response levels in real structures cannot be closely approximated

30

based on visible damage following an earthquake. A biaxially

loaded column, as might be found in a real structure following an

earthquake, reveals damage significantly different from a similar

column subjected in the laboratory to uniaxial loading.

31

CHAPTER 5

SUMMARY AND CONCLUSIONS

An experimental program was conducted to study the behavior

of reinforced concrete columns sUbjected to inelastic multiaxial

loads with reversals. Five nominally-identical, one-quarter

scale columns were tested in the program. The test specimens

represented columns considered typical of those occurring in

moderately tall buildings designed to satisfy current code

requirements for reinforced concrete construction in regions of

high seismic risk.

The columns were tested as cantilevers projecting from stiff

foundation blocks, with lateral and axial loads applied at the

end of the cantilever. The main variable in the experiments was

the load history. Three columns were tested with constant axial

load, one with uniaxial lateral load directed along a principal

axis of the column, one with uniaxial lateral load directed along

a skew axis of the column, and one with biaxial lateral loads

resulting in a "cloverleaf" displacement pattern. Two remaining

columns were tested under varying axial loads, with lateral load

either applied uniaxially along a skewed axis or applied

biaxially to achieve a cloverleaf displacement pattern.

Experimental measurements include applied lateral loads, column

end displacements, longitudinal reinforcement strains, and column

base deformations.

This report documents the experiments and discusses observed

behavior both qualitatively and by comparison with analytically

32

computed responses. Major conclusions include the following.

(1) Lateral deformations of the columns were predominated by

rotations occurring within a length equal to approximately one

column width measured from the top of the footing. These

rotations are attributed to flexural curvature over this length

and to slip of reinforcement from the footing.

(2) Based on observed damage, and as supported by calculations,

lateral-load strength of the columns was limited by flexural

strength.

(3) Reinforcement details, which satisfied current codes for

ductile concrete frames in regions of high seismic risk, resulted

in satisfactory behavior. strength under load reversals was

sustained through displacements equal to approximately five

percent of column height (displacement ductility of approximately

six), and could probably have been sustained through larger

deformations had the test apparatus permitted further loading.

Buckling of reinforcement did not occur, despite spalling of

concrete cover and measured reinforcement compressive strains as

large as 0.04.

(4) Biaxial lateral loading influenced observed behavior.

Visible damage (concrete cracking and crushing) was notably more

extensive in the biaxially-Ioaded columns. Measured strains in

reinforcement, particularly in compression, were larger than for

the uniaxially-loaded columns. Measured strengths and

stiffnesses under biaxial loading were less than under monotonic

loading. Even columns loaded uniaxially at a given stage of

testing did not reach the uniaxially-measured strengths and

33

stiffnesses if those columns had been previously sUbjected to

transverse loading. In general, the state of damage worsened for

columns also sUbjected to axial load variations, even though the

maximum axial load in these experiments was less than half the

balanced axial load.

(5) Hysteretic relations under biaxial loading were strikingly

different from those measured for uniaxial loading.

(6) Measured strengths and load-deflection envelopes could be

reproduced reasonably well using existing analytical concepts for

reinforced concrete sections sUbjected to monotonic loading. The

analytical correlations were better for the columns loaded

uniaxially along the principle axis or along a skew axis than for

the columns loaded in the cloverleaf pattern.

(6) For columns loaded in the cloverleaf pattern, measured base

moments were closely bounded by biaxial moment envelopes

calculated assuming monotonically applied loads.

34

REFERENCES

1. American Concrete Institute, "Building Code Requirements forReinforced Concrete," (ACI 318M-83), Detroit, Michigan, 1984

2. American Concrete Institute, "CoIDIDentary on Building CodeRequirements for Reinforced Concrete," (ACI 318-83), Detroit,Michigan, 1983

3. Shahrooz, B. M., "Experimental Study of Seismic Response ofRIC Setback Buildings," Ph.D. Dissertation Submitted to theUniversity of California, Berkeley, September 1987.

4. Bertero, V.i Popov, E. and Wang, T., "Hysteretic Behavior ofReinforced Concrete Flexural Members with Special WebReinforcement," Report No. UCB/EERC-7 4/09, EarthquakeEngineering Research Center, University of California,Berkeley, California, 1974.

5. Desai, J. A. and Furlong, R. W., "Strength and stiffness ofReinforced Concrete Rectangular Columns Under BiaxiallyEccentric Thrust," University of Texas, Austin, Texas,January 1976.

6. Filippou, F. C. i Popov, E. and Bertero, V., "Effects of BondDeterioration on Hysteretic Behavior of Reinforced ConcreteJoints," Report No. UCB/EERC-83/19, Earthquake EngineeringResearch Center, University of California, Berkeley,California, August 1983.

7. Gill, W. D.; Park, R., and Priestley, M. J. N., "Ductilityof Rectangular Reinforced Concrete Columns With Axial Load,"Department of Civil Engineering, university of Canterbury,Christchurch, New Zealand, February 1979.

8. International Conference of Building Officials, uniformBuilding Code, Whittier, Ca., 1982.

9. Lai, S. i Will, G. and Otani, S., "Model For InelasticBiaxial Bending of Concrete Members," JOURNAL OF STRUCTURALENGINEERING, Vol. 110 No. 11, November 1984, pg. 2563 2584.

10. Maruyama, K. i Ramirez, H. and Jirsa J., "Short RC ColumnsUnder Bilateral Load Histories,: JOURNAL OF STRUCTURALENGINEERING, Vol. 110 No.1, January 1984, pg. 120 - 137.

11. Park, R. and Paulay, ., "Reinforced Concrete Structures,"John Wiley & Sons, New York, 1975.

35

12. Popov, E.~ Bertero, V. and Krawinkler, H., "Cyclic Behaviorof Three Reinforced Concrete Flexural Members With HighShear," Report No. UCB/EERC-72/05, Earthquake EngineeringResearch Center, university of California, Berkeley,California, 1972.

13. Scott, B. D. ~ Park R., and Priestley, M. J. N., "Stress Strain Relationships For Confined Concrete: RectangularSections," Department of civil Engineering, University ofCanterbury, Christchurch, New Zealand, February 1980.

14. Umehara, H. and Jirsa, J., "Short Rectangular RC ColumnsUnder Bidirectional Loading," JOURNAL OF STRUCTURALENGINEERING, Vol. 110 No.3, March 1984, PG. 605 - 618.

15. Zeris, C. A. , "Three Dimensional Nonl inear Response ofResponse of Reinforced Concrete Buildings," Ph.D.Dissertation Submitted to the University of California~

Berkeley, November 1986.

36

Table 2.1 Chronology of Experiments

1. Construction of Reinforcing Cage for Specimens 1 to 5

a.) Reinforcing Cagesb.) Attaching Strain Gages

2. Casting of Specimens 1 to 3 (2/7/86)

3. Casting of Specimens 4 and 5 (3/7/86)

4. Setup of Testing Apparatus

a.) Loading Apparatusb.) Instrumentations

5. Testing of Specimen 1 (4/17/86)

a.) Uniaxial Lateral Loading with Constant Axial Load


a.) Biaxial Lateral Loading at 45 Degrees with Constant Axial Load


a.) Biaxial "Cloverleaf" Lateral Loading with Constant Axial Load


a.) Biaxial Lateral Loading at 45 Degrees with Varying Axial Load

Q. Testing of Specimen 5 (5/30/86)

a.) Biaxial "Cloverleaf" Lateral Loading with Varying Axial Load

10. Reduction of Experimental Data and Analytical Analysis

37

To.lole 2.2 Concrete Bo.tch QUo.ntltles forOne CulolC Yo.rd" So. turo.ted Surfo.ce-Dry

Bo.tch #1 (llo) Bo.tch #2 (llo)Me. terle.ls

SpeciMens 1-3 SpeciMens 4-5

Type II CeMent611 641

PerMo.nente CI028

'vi 0. ter 342 342

Fine So.nol 325 325Tiolewo.ter BlendCourse So.nol 1300 1300Ro.duM TopFine Gro.vel

1315 1315Ro.duM 3/8' Pea.

Toto.l 3893 3923

To.lole 2.3 Concrete COMpressive strengths

Cycllnder Age of Cycltnoler Avero.geSize Concrete Strength Strength

(Do.vs) (051.) (051.)

28 5459 516948793 x 6 5120Bo.tch #1

63 551b 5318

28 501~ 520153526 x 12 532063 5550 5435

284Rn?

493350643 x 6 5000

Bo.tch #270 5143 5071

28 4500 447044406 x 12 455670 4562 4559

38

TOoble 2.4 Concrete Splitting Tensile Strengths

6 x 12 Age of LoOocl Tensile Avg. TensileCycllncler Concrete strength strength

(DOovs) (lb) (osl.) (osl.)

67000 592BOotch #1 63 592

67100 593

60700 536Ba.tch #2 50 493

50700 449

TOoble 2.5 ReinforceMent Properties

Properties 13 DeforJ'led 12 DeforJ'led 12 DeforJ'led GuOoge 19800r BOor BOor TrOonsverse

(shlpJ'lent 11> (shlpJ'lent 12) RelnforceJ'lent

f y(ksl.) 64.9 64.4 73.1 60.0

f (ksl.) 95.7 86.0 96.5 85.5u

ff (ksl.) 95.7 86.0 96.5 85.5

E (ksl.) 29000.0 29000.0 29000.0 29000.0

Esh

(ksl.) 1690.0 1200.0 1250.0 2500.0

e (In/In) 0.0022 0.0022 0.0025 0.0021Y

e sh(In/In) 0.0120 0.0300 0.0252 0.0025

e (In/In) 0.1310 0.1740 0.1300 0.1000u

e f (In/In) 0.1600 0.2000 0.1640 0.1200

39

Table 3.1 Summary of Selected Experimental Results

Specimens:11=1 #2 #3 :11=4 #5

YIELDMy (kip-in) 116.0 81.0 62.0

Mx 137.0 85.0

Vx (kips) 5.2 3.4

I2.9

Vy i 5.9 4.5! I

dx (inches) I,

0.19 0.14 0.15

dv I 0.15 0.15ULTIMATE IIMy (kip-in) I 136.0 95.0

I

123.0 142.0 146.0

Mx I 161.0 175.0 151.0 168.0I!

Vx (kips) I 5.9 3.8 5.1 4.0 4.8!

Vv I 6.7 7.6 6.2 7.0MAXIMUM Idx (inches) I 1.12 1.01 1.01 0.99 1.01

Idv I 0.99 1.01 0.97 1.01

40

Table 4.1. Calcula ted Effect of Bar Slipon ColuMn End Displa.ceMents

r n

H

SLIP

J

-I il

... - '---

=ARM -I I-

D=[SLIPIARMJ*H j DXJ Dy

H=20 in,

ARMx =3.1 in, 'Wea.k Direction

ARMy =4.1 in, Strong Direction

ARM: Denotes the ApproxlMa. teDlsta.nce Between theNeutra.l Axis a.nd the Ba.r'Where Slip Is Occurring

Steel Bond Refoa.r Hook TotOol End D/splo.ceMentStress stress Slip Slip Pull-out

(ksl) ufo (ks/) (In.) (In,) (In,) Dx (In,) Dy (In,)

70 1.30 0,0061 0 0.0061 0.040 0.030

60 1.30 0.0045 0 0,0045 0,029 0.022

SO 1.30 0,0031 0 0.0031 0.020 0.015

40 1.30 0.0020 0 0.0020 0.013 0,010

30 1.30 0.0011 a 0.0011 0,007 0.005

20 1.30 0.0005 0 0,0005 0,003 0,002

10 1.30 0.0001 a 0,0001 0,001 0,000

a 0.00 0.00000 0 0.00000 0.000 0,000

41

Y

STRONG DIRECTION

STRAIN GAGE #1------------~

X\lEAK DIRECTION

GUAGE 19 TIE

12 DEfORMED BARTYPICAL

0.5' CLEAR TOLONGITUDINAL BARTYPICAL

~-'3 DEfORMED BARSAT EACH CORNER

~+-+--- STRAIN GAGE 12

J5.00'

6.50' -----+-t+---..,.&:~:--

CROSS SECTION

NOTE: #2 DEFORMED BARS ALONG THE "Y" AXISARE TYPE "SHIPMENT #1" IN TABLE 2.5.ALL OTHER #2 DEFORMED BARS ARE TYPE"SHIPMENT #2"

FIG. 2.1 Test Specimen Configuration

42

ANCHOR ROD

5/8' STEEL PLATEFILLET 'YIELDEDTO REBAR

TEST COLUMN SEECROSS-SECTION

REINFORCED CONCRETEFOOTING

r'"...--

- ...

V@ 1.5'

@ l'

rL::J., r'c.:J,rL--.J., ,i.--~

I I I II I I I rI I I IIV0' I I

I II II I

~ ~I II II II II II II I

i iI I

TIES

9 TIES

5.00'LDADING HEIGHT l

21.50'

7.0

13.00' !

L' ~II I I ,I I I II I I I

14.00'

COLUMN ELEVATION "yN DIRECTION

FIG. 2.1 Continued

43

HOR ROD

NFORCED CONCRETETING

ST COLUMN SEEOSS-SECTION

8' STEEL PLATE

r6,50'lA ~

---.-5/

~ '-

1.25' ]

~TECR

REIFOO

L~ L~_I I I II

V- ANCI II

IvIIII I

c :s IIIIIIIII

21.50'

13.00'

LOADING HEIGHT

'----- 18,00' ------

COLUMN ELEVATION 'XII DIRECTION

FIG. 2.1 Continued

44

FIG. 2.2 Test Specimens Ready for Casting

FIG. 2.3 Testing Specimens After Casting

45

65

43

21

3020

10

7000

"-

6000

2500

V1,...

Q.

V1'-

/Q

.

5000

'-/

V1 V1V1

2000

Qj

V1

LQ

j

",

+'

4000

L

'"+

'a.

(I)

Qj

1500

>Q

j

V130

00>

V1V1

Qj

V1

LQ

j10

00~

2000

L Q.

0E:

(..J

0 (..J

1000

500

Str

uln

(x1

0-4

In/I

n)

Str

uln

(xlO

-4In

/In

)

FIG

.2.

4C

on

cre

teS

tress

-Str

ain

Rel

atio

ns

100

'" 80lI\

.Y'-/

lI\ 60lI\QI!...+'

"" 40 #3 DeforMed Bur~

QIQI+'

"" 20

4 8 12 16

Steel Stro.ln (x10 -2 In/In)

100

'"lI\ 80.Y'-/

lI\lI\ 60QI!...+'

"" 40 #2 DeforMed BurQIQI+'

"" 20

4 8

Steel Stro.ln

12

(x10-2 In/In)

16

FIG. 2.5 Longitudinal Steel Stress-Strain Relation.

47

LVD

TAT

CEN

TER

OFCO

LUM

NI

20

,0'------i

""(XlHY

DRAU

LIC

JACK

AXIA

LLO

ADRA

M

LOAD

CELL

I

SPEC

IALL

Y-F

AB

RIC

ATE

DU

NIV

ERSA

LI

JOIN

T

TYPI

CAL C

LIP

GAGE

SPEC

IMEN

LOAD

CELL

HYDR

AULI

CAC

TUAT

OR

"II/F

LO

OR

EL

EV

AT

ION

VIE

'w'

FIG

,2

,6L

oad

ing

Ap

para

tus

an

dIn

stru

men

tati

on

HY

DR

AU

LIC

AC

TUA

TOR

LOA

DC

ELL

~S

,O'

2-

LV

DT

AT

1.7

5'

LwI

FRO

MC

ENTE

RO

FCO

LUM

N-j

S,O

'EA

CH

DIR

ECTI

ON

20.0

'

.... \D

SPE

CIM

EN

CL

IPG

AG

ET

YPC

IAL

TOP

VIE

'"

FIG

,2

,6C

on

tin

ued

)

FIG. 2.7

f,." '

•~

;r,

•.:

;

)

Photographs of Experimental Setup

50

A

PAXIAL LOAD

I\II\IIII\IIt

II\III

l'

Hr

F r ~?JJ_~'1LATERAL LOAD / /

h SPECIMEN !!I II II II I

FIG. 2.8 Bnse Moment Determination

51

0.96SPECIMEN #1

Y STRONGDIRE lION

0.64

X 'WEAKDIRECTION

Y STRONG

2a.

Y STRONGDIRE TION

21:>

X 'WEAK----~&-<----- DIRECTION

DIRE nON3h 31 3c 31:>

3g 3a.

3l 3f

3k 3J 3d 3..

II:> Ia. X 'WEAK:=c===ct===~:::"DIREcnON

SPECIMEN #3

SPECIMEN #2

0.32 A A0.16 V\ A I II

V V 1/ I ~

ll", me<

-0.64

0.320.16

0.320.16

-0.16-0.32

-0.16-0.32

"-CIl -0.64w:I:U~ -0.96v 0.96~zW:I: 0.64wu<l:-JQ..CIl....I:l

!!:. -0.16~ -0.32zCJt:: -0.64uwe:; -0.96I:l 0.96~<l:W~ 0.64

-0.96AXIAL LOAD = 10 KIPS ONE CYCLE

FIG. 2.9 Intended Displacement and Load Histories

52

0.96SPECIMEN #4

Y STRONGDIRE TION

0.644Q

X 'WEAKDIRECTION

Y STRONG

4b

DIRE nON5h 51 5c 5b

59 5Q

Sf'

5k 5J 5d 5"

X 'WEAK------,.i;L-----DIRECnON

SPECIMEN #5

z 0.64Cl.....~

~. 0.32lk: 0.16.....~

~ -0,16~ -0.32

-0.64

"III~ 0.32 A

~ 0.16li\ A f\....~ -0.16 V V \/ V ~Q -0,32 II::EW

~ -0,64if. ONE CYCLEIIIS -0.96c.. 0.96....~

-0.96AXIAL LOAD (KIPS) ONE CYCLE

-0.96 -0.64 -0.32-0,16 0.16 0,32 0,64 0.96

'WEAK DIRECTION TIP DISPLACEMENT <INCHES)

FIG. 2.11 Continued

53

\

FIG. 3.1 Photograph of Test Specimens at Conclusion of Testing

FIG.3.1a Photograph of Test Specimen 1 at Conclusion of Testing

54

\

.'1(

--,#z-

,~ $,o. 'f{,

FIG.3.1b Photograph of Test Specimen 2 at Conclusion of Testing

FIG.3.1c Photograph of Test Specimen 3 at Conclusion of Testing

55

FIG.3.1d Photograph of Test Specimen 4 at Conclusion of Testing

\

FIG.3.1e Photograph of Test Specimen 5 at Conclusion of Testing

56

Left View

Top View

Ay

B

+ X

C DBottol'l View

Right View

AT----------~-..,__-___:"-~

\

B~-----......--..L..--...I-----___=r

Top View

B

D

V

\,V·v

\;

l~I (

IG

\ ~'///

Right View

A

CLeft View

C

~-----..--.L-.--....;......-~~r__------I. DBottom View

FIG. 3.2 Crack Patterns at Conclusion of Testing - Specimen 1

57

~Ight VIew

Top VIew

AY

B

+ -X

C D

Left VIew

BottofW\ View

A..----------r------,,--~__;__r-_y

\

BTop View

B

DRight View

A--~--___;:--__;~------__,A

Left View

Bottom View

FIG. 3.2a Crack Patterns at Conclusion of Testing _ Specimen 2

58

Right View

Top View

AY

B

+ X

C D

Left View

D

Bottofl'l ViewA

"\\~

BTop View

Bi\

Right View

l-----------,---,------,A

cLeft View

Bottom View

FIG. 3.2b Crack Patterns at Conclusion of Testing - Specimen 3

59

RIQht View

Top View

AY

B

+ X

C D

Left VIew

Bottol"l ViewA.-------:~~--~.,.__----.,_-__:___;_-_:_V

Top View

B

nL-----------------..:..--''-tRight View

Left View

C

nBottom View

FIG. 3.2c Crack Patterns at Conclusion of Testing - Specimen 4

60

Right VIew

Top View

AY

B

+ X

C D

L4Pft VIew

A

B

BottOM View

Top View

B

DRight View

A

cLeft View

Bottom View

FIG. 3.2d Crack Patterns at Conclusion of Testing - Specimen 6

61

1.2

88

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FIG. 3.4 Measured Load History for Specimen 263

1.218

t.~

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66

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"-enz-e:~ "l:l< (l.)

~ ::s"- s::.-x +-'

(S> s::CP t- oell) ;:) uCI) ~ an

<Z C""l

0 dHt- -< u..t-o~

I.CI)I

CI) ICI)CI). .CI) CI)

Cll)-I

82

t80

.00

0

H 0 H E N T Y0

.00

0

I()

:)f(

wI p - I N I

-f8

0.0

00

-0.0

60

9.9

00

ROTA

TION

ABOU

TY

IRA

DIA

NS/

FIG

.3.

16B

ase

Mom

ent

Ver

sus

Low

erC

olum

nR

otat

ion

for

Spe

cim

en4

9.0

60

=C5)

mGO-I

'"(I)z<H0 "'0< Cl.)0: ::i

'" ~.-X -C5) ~

CS) t- OCS) ::J UGIl 0

en \0< -Z M

00H

t- -< I:,I..t-o0:

GIlCDmmI

%O%I&IZf- x

t88

.98

8

H 0 H E N T V0

.00

0I

00K

U1

I p - I N I

-t8

0.0

00

-8.8

80

0.9

98

ROTA

TION

ABOU

TY

/RA

DIA

NS/

FIG

.3.

17B

ase

Mom

ent

Ver

sus

Low

erC

olum

nR

otat

ion

for

Spe

cim

en5

8.0

60

CD

II-

.....enzc(I-tQ ~c( 0« =...... t::.-X

....m t::CS> ... 0m :;:) UCS> 0

l"-mc(

z M

0 c.:JI-tt- -c l.l..t-o«

CDCDCD.CDI

I ICD. .

CD mCD-I

86

"o"ENT

y

IICIp

INI

I~OOOO

•••

-180.000

-te.... ..... ,..... st....

y

•

Strain Gage Location

......

"o"ENT

y

IKIp-INI

180.000

.....

-I~OOOO

-II.'" ..... ...... 21.... .....

y

•


......

FIG. 3.18 Strain Histories for Specimen 1

87

"o"ENT

y

IIeIp

INI

I ~().()()O

....

-I~O.OOO

-..... ..... ...... 28.... SI.I8e

y

•

Strain Gar.e Loc:ation

48....

STEEL STRAIN' I tm.-INIIN I

"o"ENT

y

IIeIp

INI

180.000

....

-180.000

-II.... ..... I ..... 28.... SI....

y

•


48....

FIG. 3.19

STEEL STRAIN I KtL-:Dl1IN I

Strain Histories for Specimen 2

88

"o"ENT

X

IIeIp

INI

II'lO.OOO

....

-180.(}(}()

-te.... ..... II. tee 2t.tee ••••

•

Strain Gage location

......STEEl. STRAIN I MIL-INIIN I

"o"ENT

X

IIeIp

INI

180.000

....

-180.000

-II.... ..... II.... 28._ .....

y

•


48.888

STEEL STRAINS I IfIl.-INIIN I

Fig. 3.19

89

Continue

180.000

"0"£"TY I."IIeIp

INI

-l~O.()OO

-.... -28.888 -II.... 1.888 18.888 28.888

STRAIN GAGE nRST WENTOUT OF RANGE

v

•x


• .•88

J~O.OOO

STEEL STRAIN I HIL-INIIN I

"o"ENT

y

IItIp

1NI

I."

t==========~... -----...:yo...~~:-....~.,::: ~:,~~/~' ------ "OUT OF RANGE

y

Sll'llin Gale loc:Ilion

-180.000......... -..... -28.... -II.'" ..... te.'" 28."

FIG. 3.20

STEEL STRAIN I HIL-INIIN I


90

i ~().()()()

"0"ENT

X ....IItIp

INI

-180,000

-,.... -28." -te.888 '.888 1'.888 28.888

STRAI~ CACE rJRST WENT

OI.:T OF RANCE

y

•)(


3CU~"

180.000

STEEL STRAIN I Pm.-INIIN I

STRA"" CAGE rJRST WE~TOI.:TOF RANGE

"0"ENT

X ....IItIp

INI

-180.000........ -,..... -28.... -II.... ..... II....

y

x

Strain Gap: Location

28.881

STEEL STRAIN I Pm.-INIIN I

Fig. 3.20

91

Continue

"o"ENT

y

IItIP

INI

l~().OO()

....

•1~().000

-II." ..... II.... 28.... .....

y

•

Strain Gage Loc:ation

.....STEEl. STRAIN I MIL-INIIN I

"o"EHT

y

IIt:rp

IHI

l~().()()O

....

- I~O.OOll

-II.• ..... I ..... 28.... .....

y

Strain G. Loc:ation

.......

FIG. 3.21

STEEl. STRAIN I MIL-INIIN I


92

180.000

"0"ENT

lC ....,IItIP

INI

-180.000

-II.... '.888 II.'" 28.'" 38."

y

•x

Strain Gagt Location

48.'"

STEEL STRAIN I tal- INIIN I

180.000

"0"ENTS

lC '.888IItIP

INI

-180.000

-'8.'" 8.888 '1.888 28." 38.819

y

+x

•

Strain Gagt Location

48....

STEEL STRAINS I tlIl-INIIN I

Fig. 3.21

93

Continue

"o"ENT

y

IIeIp

INI

1~(1.000

•••

- H~O.O(lO

•

Strain Ga~t Localion

-,... -21.• -,... ..... ...... 2..... ,.....STEEL. STRAIN I ItIl-IN/IN I

"o"E"Ty

IIeIp

INI

11<0000

•••

• \ RO.OO(l....... -,... -21.• -f..... ..... ,.....


21....

FIG. 3.22

STEEl. STRAIN I MIL-INII" I


94

I>lO.OOO

"0"["TX 1.18CiIIKIp

IN/

-180.000

-•. 18CiI -28.18Ci1 -It.... ..... 18.888 28....

y

x

Strain Ga~e Location

.....STEEL STRAIN / NIL-IN/IN /

"o"ENT

X

IKIp

IN/

180.000

1.18CiI

-I ~O.()O()

-<lI.18CiI -..... -28.... -1•.888 •. 18CiI 1.....

y

\

•

Strain Ga~e Location

28 ....

Fig. 3.22

95

Continue

8

'.

'.

",

"

..........

....... .."

.....

UN

CO

NF

INE

DC

ON

CR

ET

E

..........

.........CO

NF

INE

DC

ON

CR

ET

E

..........

........

.....-

..../

,~.

.t'

c 0 n6

c r e

\0t

(j\

e S t r4

e s s k s i2

/

0_ 0.0

0.0

02

0.0

04

0.0

06

0.0

08

0.0

10

0.0

12

0.0

14

Ccr

1cr

ete

Str

ain

FIG

.4

.1C

on

cret

eS

tres

s-S

trai

nR

elat

ion

sA

ssu

med

for

Mo

men

t-C

urv

atu

reC

alcu

lati

ons

12

01

Tn

:----------------------------------'"

--1

10

0

S t e e8

01

~S

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t r e6

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40

i ir

20Ii

oII

!I

III

0.0

0.0

50

.10

Ste

el

Str

ain

0.1

50

.20

FIG

.4

.2S

teel

Str

ess-

Str

ain

Rel

atio

ns

Ass

um

edfo

r:M

om

ent-

Cu

rvat

ure

Cal

cula

tio

ns

20

0.0

00

H'6

0.0

00

0P

=2

0k

ips

P-1

5k

ips

H----

==P

=1

0k

ips

P=

5k

ips

E N T'2

8.8

88L/~~~~

P=

Ok

ips

y

\D/

(Xl

K Isa

.000

P - I N I4

9.0

00

8.8

88

8.0

08

8.0

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0.0

10

8.0

15

8.0

28

8.0

25

8.0

30

0.0

35

8.0

48

8.8

4S

8.8

S8

CURV

ATUR

EAB

OUT

Y/

t/IN

/

FIG

.4.

3C

ompu

ted

Mom

ent-

Cur

vatu

reR

elat

ions

20

0.0

00

P=

15

kipl

IP

=1

0ki

plI

P=

5ki

plI

I(}ij/~~

p=

ok

ips

H1

60

.00

0

0 H E N T1

20

.00

0

X

~I

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80

.00

0P - I N I

40

.00

0

0.0

00

0.0

00

0.0

05

0.0

10

0.0

15

0.0

20

0.0

25

0.0

30

0.0

35

0.0

40

0.0

45

0.0

50

CURV

ATUR

EAB

OUT

X/

t/IN

/

FIG

.4.

3C

onti

nued

24

0.0

00

22

0.0

00

20

0.0

00

A1

80

.00

0X I A

le0

.00

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14

0.0

00

0 A1

20

.00

00

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10

0.0

00

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80

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60

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0

40

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0

20

.00

0

0.9

00

0.0

00

40

.00

08

0.0

00

12

0.0

00

16

0.0

00

20

0.9

00

24

0.0

00

MOME

NTY

IKIP

-IN

I

FIG

.4.

4Co~puted

Uni

axia

lM

omen

t-A

xial

Loa

dIn

tera

ctio

nD

iagr

ams

24

9.9

99

22

9.9

99

29

9.9

90

A1

89

.88

8X I A

te8

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8L L

1-49

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9.99

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9.00

0Ie I

89

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00

/

48

.09

0

29

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8

0.0

00

0.0

80

40

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08

0.0

00

120.

900

160.

000

20

9.9

00

24

0.0

00

MOME

NTX

/KIP

-IN

/

FIG

.4.

4C

onti

nued

t60

.00

0ec=

O.0

03

14

0.0

00

M 01

20

.00

0M E N

10

0.0

00

T Y8

0.0

00

r~~

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..........

.......

/""

P=

15

kip

s~

I0

Kl\

)

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0.0

00

P - IP

=5

kip

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40

.00

0l-

I

l2

0.0

00

P=

10

kip

s

0.0

00

0.0

00

40

.00

08

0.C

00

12

0.0

00

160.

00C

20

0.0

00

MOM

ENT

XIK

IP-I

NI

FIG

.4.

5C

ompu

ted

Bia

xial

Mom

ent-

Axi

alL

oad

Inte

ract

ion

Dia

gram

s

16

0.0

00

ec=

O.O

l

14

0.0

00

M 01

20

.00

0M E N

10

0.0

00

T y8

0.0

00

....I

0

~w

KP

=O

kip

s

I6

0.0

00

X'\.

'\.'\

."~

P=

20

kip

s

PP

=5

kip

s

- I N4

0.0

00

to/

P=

10

kip

s

20

.Q0

0

0.9

00

0.0

00

40

.00

08

0.0

00

12

9.0

00

16

9.0

00

20

0.0

90

MOM

ENT

X/K

IP-I

N/

FIG

.4.

5C

onti

nued

16

0.0

00

ec=

O.0

2

14

0.0

00

MI~

IP

=1

5k

ips

01

20

.00

0M E

I----

-------.....~~

"'-

rP

=2

0k

ips

N1

00

.00

0T

IP

=O

kip

s

y8

0.0

00

......

rP

=5

kip

s0

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KI

P=

lOk

ips

I6

0.0

00

P - I N4

0.0

00

/

20

.00

0

0.0

00

0.9

00

40

.00

08

0.0

00

12

0.0

00

16

0.0

00

20

0.0

00

MOME

NTX

/KIP

-IN

/

FIG

.4.

5C

onti

nued

f0.0

00

8.0

00

L 0 A

p8

D6

.00

0

IX

....I

0 01K

4.0

00

I P S I

2.0

00

0.0

00

0.0

00

0.2

50

0.5

00

0.7

50

1.0

00

1.2

50

1.5

00

f.7

50

2.0

00

DISP

LACE

MEN

TX

IIN

CH

ES/

FIG

.4

.6C

om

pu

ted

Mo

no

ton

icL

oad

-Dis

pla

cem

ent

Rel

atio

ns

1121.1

211211

21

8.1211

21121

L 0 A D6.1

211211

21

Y

.....I

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4.9

99

0'\

I P S I

2.9

99

9.91

219

.P

=2

0k

ips

P=

15

kip

sP

=lO

kip

sP

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kip

s

-P

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kip

s

9.0

00

0.2

50

0.51

210

0.75

121

t.01

21121

t.25

121

t.51

21121

1.7

50

2.01

210

DISP

LACE

MEN

TY

IINC

HES

/

FIG

.4

.6C

on

tin

ued

'ea.

aaa

H 0 H E N T Y9

.99

9I

~K

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P - I N I

..,.

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,--"",,"

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// I , , ,

, ".....

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I/

///

//

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-----

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--

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nal

yti

cal

bia

xia

lm

on

oto

nic

mo

men

ten

vel

op

eat

ec=

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Ian

dP

=IO

kip

s

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9.g

e9

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aae

e.aa

a

HOHE

NTX

/KIP

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/

FIG

.4

.7C

om

pari

son

Bet

wee

nM

easu

red

an

dC

om

pu

ted

Bas

e-M

om

ent

Str

en

gth

s-

Sp

ecim

en2

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ea

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.98

9

M 0 M E N T Y9

.90

8/

I-'

K0

I(X

)

P - I N /

--

--

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aly

tical

bia

xia

lm

on

oto

nic

mo

men

ten

velo

pe

at

ec=

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lan

dP

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kip

s

-f8

9.8

08 -1

80

.88

00

.00

0

MOM

ENT

X/K

IP-I

N/

FIG

.4.7

aC

om

par

iso

nB

etw

een

Mea

sure

dan

dC

om

pu

ted

Bas

e-M

om

ent

Str

en

gth

s-

Sp

ecim

en3

188.

808

tse.

eae

H 0 H E N T Y9.

9ge

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0 \0I P - I N /

.....,.

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----

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nal

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cal

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oto

nic

mo

men

ten

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lan

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=2

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9 -IS

9.98

9e.

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MOM

ENT

X/K

IP-I

N/

FIG

.4.7

bC

om

par

iso

nB

etw

een

Mea

sure

dan

dC

om

pu

ted

Bas

e-M

om

ent

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en

gth

s-

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f80

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8

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I

M 0 M E N T Y8

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--

--

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naly

tical

bia

xia

lm

on

oto

nic

mo

men

ten

vel

op

eat

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lan

dP

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ips

-f8

8.8

98 -1

80

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88

.00

018

0.00

0

MOM

ENT

XIK

IP-I

N/

FIG

.4.7

cC

om

par

iso

nB

etw

een

Mea

sure

dan

dC

om

pu

ted

Bas

e-M

om

ent

Str

en

gth

s-

Sp

ecim

en5

~ DISPLACEMENT DUE TOI PLASTIC HINGE ROTATION

/117.5'

_L2.5' T

SPECIMEN DIRECTIONMAXIMUM DISPLACEMENT MAXIMUM

ROTATION DUE TO MAX, DISPLACEMENT(rOod.) ROTATION (In.) L.V.D.T, (In.)

1 'WEAK 0,060 1.02 1.12

'WEAK 0.053 0.93 1.012

STRONG 0.046 0.81 0.99

'WEAK 0.051 0.90 1.013

STRONG 0.051 0.90 1.01

\lEAK 0.049 0,86 0.994

STRONG 0,049 0.86 0.99

'WEAK 0.049 0,86 1.015

STRONG 0.049 0.86 1.01

FIG. 4.8 Contribution of Base Rotation to Total Column Deflection

111

My

hI

Lly

bc

90.

lP'

If

l:1

kJ

de

x

---/..

..-//

" "-....

........

...

-- --

/c/

//

---M

x

0..

)Lo

o.d

His

tory

-O

neC

ycle

bJ

MO

Men

tV

ers

us

MO

Men

t

I-'

I-'

t-J

My

Mx

b

0.

c

c.)

Lo

o.d

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forM

o.t

lon

In'X

'D

ire

cti

on

By

d.)

Lo

o.c

l-D

efo

rMo

.tlo

nIn

'Y'

Dir

ecti

on

ex

FIG

.4

.9Id

eali

zed

Bia

xia

lH

yst

eres

isR

elat

ion

sfo

rL

oad

Ste

ps

"a"

thro

ug

h"e

"

hI

b.y

bc

90.

l1"1

fb

.

kJ

de

x

e

" ", '--

My

/c,/

//

---M

x

b,>

MO

Men

tV

ers

us

MO

Men

t

.... .... w

0..>

Lo

o.d

HIs

tory

-O

neC

ycle

My

0.

f

d

c

0y

e

Mx

b

ex

c.)

Lo

o.d

-De

forl

"'lo

.tlo

nIn

'X'

Dir

ectI

on

d.)

Lo

o.d

-De

forl

"lo

.tlo

nIn

'y'

DIr

ecti

on

FIG

.4

.10

Idea

lize

dB

iax

ial

Hy

ster

esis

Rel

atio

ns

for

Lo

adS

tep

sIIa"

thro

ug

h"r

'

9

My

"'-

..........

.. ---M

x

-e

x

hI

6.y

bc

90.

lr'l

f6.

kJ

01e

0..

)Lo

o.oI

His

tory

-D

neC

ycle

b.)

MO

r'len

tV

ers

us

MO

r'len

t

f-O f-O "'"M

y

0.

f

9

By

Mx

e

ex

c.)

Loo.

oI-D

efo

rMo

.tlo

nIn

'X'

Dir

ecti

on

01.)

Loo.

oI-D

efo

rr'lo

.tlo

nIn

'Y'

Dir

ecti

on

FIG

.4

.11

Idea

lize

dB

iax

ial

Hy

ster

esis

Rel

atio

ns

for

Lo

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20::: _..------------- SPECIMEN 1~ 2 ------« -- 3b--J Y 2

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DISPLACEMENT X (INCHES)X

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SPECIMEN 2en 10a.C, 8

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FIG. 4.13 Load Resistance Envelopes for Specimens 1, 2, and 3

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FIG. 4.14 Comparison of loading Stiffnesses

117

EARTHQUAKE ENGINEERING RESEARCH CENTER REPORT SERIES

EERC repons are available from the National Information Service for Eanhquake Engineering(NISEE) and from the National Tecbnical InformationService(NTIS). Numbers in parentheses are Accession Numbers assigned by the National Technical Information Service; these are followed by a price code.Contact NTIS. 5285 Pon Royal Road, Springfield Virginia, 22161 for more information. Repons without Accession Numbers were not available from NTISat the time of printing. For a current complete list of EERC repons (from EERC 67-1) and availablity information, please contact Univenity of California,EERC. NISEE, 1301 South 46th Street, Richmond, California 94804.

UCBIEERC,80101 'Eanhquake Response of Concrete Gravity Dams Including Hydrodynamic and Foundation Interaction Effects: by Chopra, A.K.,Chakrabani. P. and Gupta, S.• January 1980. (AD-A087297)AIO.

UCB/EERC,80/02 'Rocking Response of Rigid Blocks to Eanbquakes; by Yim. e.S., Chopra, A.K. and Penzien, 1.. January 1980, (PB80 166 (02)A04.

UCB/EERC,80/03 'Optimum Inelastic Design of Seismic·Resistant Reinforced Concrete Frame Structures: by Zagajeski. S.W. and Benero, V.V.• January1980. (PB80 164 635)A06.

UCB/EERC·80/04 'Effects of Amount and Arrangement of Wall·Panel Reinforcement on Hysteretic Behavior of Reinforced Concrete Walls," by lIiya, R.and Benero. V.V.• February 1980. (PB81 122 525)A09. ,

UCB/EERC·80/05 'Shaking Table Research on Concrete Dam Models,' by Niwa, A. and Gough. R.W., September 1980. (PBSI 122 368)A06.

UCB/EERC·80/06 'The Design of Steel Energy-Absorbing Restrainers and their Incorporation into Nuclear Power Plants for Enhanced Safety (Voila):Piping with Energy Absorbing Restrainers: Parameter Study on Small Systems,' by Powell. G.H.. Oughourlian. e. and Simons, J.• June1980.

UCB/EERC-80/07 'Inelastic Torsional Response of Structures Subjected to Eanhquake Ground Motions: by Yamazaki. Y., April 1980. (PB81 122327)A08.

UCB/EERC-80/08 'Study of X-Braced Steel Frame Structures under Eanhquake Simulation: by Ghanaat, Y.• April 1980, (PB81 122 335)AII.

UCB/EERC-80/09 'Hybrid Modelling of Soil-Structure Interaction; by Gupta, S., Lin. T.W. and Penzien. J.• May 1980. (PB81 122 319)A07.

UCB/EERC-80/1O 'General Applicability of a Nonlinear Model of a One Story Steel Frame; by Sveinsson. B.l. and McNiven, H.D.• May 1980. (PB81124877)A06.

UCBIEERC-801 II •A Green-Function Method for Wave Interaction with a Submerged Body,' by Kiok&, W.• April 1980. (PB81 122 269)A07.

UCBIEERC-80/12 'Hydrodynamic Pressure and Added Mass for Axisymmetric Bodies.; by Nilrat. F.• May 1980. (PB81 122 343)A08.·

UCBIEERC·80/13 'Treatment of Non-Linear Drag Forces Acting on Offshore Platforms,' by Dao. B.V. and Penzien.l.• May 1980, (PB81 153413)A07.

UCBIEERC-80/14 '2D Plane/Axisymmetric Solid Element (Type 3-E1astic or Elastic-Perfectly Plastic) for the ANSR·II Program: by Mondkar. D.P. andPowell. G.H.• July 1980. (PB81 122 350)A03.

UCBIEERC·80115 •A Response Spectrum Method for Random Vibrations,' by Der Kiuregbian. A.• lune 1981. (PB81 122301)A03.

UCB/EERC·80116 "Cyclic Inelastic Buckling of Tubular Steel Braces; by Zayas, VA, Popov, E.P. and Manin. SA. June 1981, (PB81 124885)AIO.

UCB/EERC-SOI17 'Dynamic Response of Simple Arch Dams Including Hydrodynamic Interaction; by Poner. C.S. and Chopra, A.K.. July 1981. (PB81124000)AI3.

UCB/EERC-80118 "Experimental Testing of a Friction Damped Aseismic Base Isolation System with Fail-Safe Characteristics,' by Kelly. J.M.• Beucke.K.E. and Skinner. M.S., July 1980, (PB81 148 595)A04.

UCB/EERC-80/19 "The Design of Steel Emergy-Absorbing Restrainers and their Incorporation into Nuclear Power Plants for Enhanced Safety (VoUB):Stochastic Seismic Analyses of Nuclear Power Plant Structures and Piping Systems Subjected to Multiple Supponed Excitations,' byLee, M.C. and Penzien. J•• June 1980, (PB82 201 872)A08.

UCB/EERC·80/20 "The Design of Steel Energy·Absorbing Restrainers and their Incorporation into Nuclear Power Plants for Enhanced Safety (Vol 10:Numerical Method for Dynamic Substructure Analysis,' by Dickens, J.M. and Wilson. E.L. June 1980.

UCB/EERC-80/21 'The Design of Steel Energy-Absorbing Restrainers and their Incorporation into Nuclear Power Plants for Enhanced Safety (Vol 2):Development and Testing of Restraints for Nuclear Piping Systems,' by Kelly, J.M. and Skinner. M.S., June 1980.

UCB/EERC·80/22 '3D Solid Element (Type 4-Elastic or Elastic-Perfectly-Plastic) for the ANSR·II Program; by Mondkar. D.P. and PoweD, G.H., July1980. (PB81 123 242lA03.

UCB/EERC·80/23 'Gap-Friction Element (Type 5) for tbe Ansr-II Program; by Mondkar. D.P. and Powell. G.H.• July 1980. (PB81 122285)A03.

UCB/EERC·80/24 'U-Bar Restraint Element (Type II) for the ANSR-II Program; by Oughourlian, e. and Powell. G.H.• July 1980. (PB81 122293)A03.

UCB/EERC-80/25 'Testing of a Natural Rubber Base Isolation System by an Explosively Simulated Eanhquake.· by Kelly, J.M., August 1980. (PB81 201360)A04.

UCB/EERC-80/26 'Input Identification from Structural Vibrational Response; by Hu, Y., August 1980. (PB81 152 308)A05.

UCB/EERC-80/27 "Cyclic Inelastic Behavior of Steel Offshore Structures; by Zayas, VA. Mahin. SA and Popov, E.P.• August 1980. (PB8I 196180lA15.

UCBlEERC-80/28 "Shaking Table Testing ofa Reinforced Concrete Frame with Biaxial Response; by Oliva, M.G., October 1980. (PB81 154304)AIO.

UCB/EERC·80/29 "Dynamic Properties of a Twelve-Story Prefabricated Panel Building,· by Bouwkamp, J.G., Kollegger. J.P. and Stephen. R.M.• October1980, (PB82 138 777)A07.

UCBlEERC-80130 'Dynamic propenies of an Eight-Story Prefabricated Panel Building,' by Bouwkamp, J.G., Kollegger, J.P. and Stephen. R.M., October1980, (PBSI 200 313)A05.

UCB/EERC-80/31 'Predictive Dynamic Response of Panel Type Structures under Eanhquakes; by Kollegger. 1.P. and Bouwkamp. J.G.• October 1980.(PB81 152316)A04.

119

Preceding page blank

UCBlEERC-80/32 -The Design of Steel Energy-Absorbing Restrainers and their Incorporation into Nuclear Power Plants for Enhanced Safety (Vol 3):Testing of Commercial Steels in Low-Cycle Torsional Fatique,- by Spanner, P., Parker, E.R., IongeWlW'd, E. and Dory, M., 1980.

UCB/EERC-80133 "The Design of Steel Energy-Absorbina Restrainers and their Incorporation into Nuclear Power Plants for Enhanced Safety (Vol 4):Shaking Table Tests of Piping Systems with Ene!'llY-Absorbing Restrainers: by Stiemer, S.F. and Godden, W.G., September 1980,(PB82 201 880)A05.

UCB/EERC-80134 "The Design of Steel Energy-Absorbing Restrainers and their Incorporation into Nuclear Power Plants for Enhanced Safety (Vol 5):Summary Report," by Spencer, P., 1980.

UCB/EERC-80/35 'Experimental Testing of an Energy-Absorbing Base Isolation System: by Kelly, I.M., Skinner, M.S. and Beuclte. K.E., October 1980,(PB81 154 072)A04.

UCB/EERC-80/36 "Simulating and Analyzing Artiticial Non-Stationary Earth Ground Motions," by Nau, R.F., Oliver, R.M. and Pister, K.S., October1980. (PB81 153 397)A04.

UCB/EERC-80/37 -Earthquake Engineering at Berkeley - 1980: by, September 1980, (PB81 205674)A09.

UCB/EERC·80/38 'Inelastic Seismic Analysis of Large Panel Buildings: by Schriclter, V. and Powell, G.H., September 1980, (PB81 154 338)AI3.

UCBlEERC-80/39 "Dynamic Response of Embankment. Concrete-Gavity and Arch Dams Including Hydrodynamic Interation: "by Hall, ].F. and Chopra,A.K., October 1980, (PB81 152 324)AII.

UCB/EERC-80/40 -Inelastic Buckling of Steel Struts under Cyclic Load Reversal.: by Black, R.G.• Wenger. W.A. and Popov. E.P., October 1980. (PB81154 312)A08.

UCB/EERC-80/41 "Influence of Site Characteristics on Buildings Damage during the October 3,1974 Lima Earthquake: by Repello, P., Arango, I. andSeed, H.B.• September 1980, (PB81 161 739)A05.

UCB/EERC·80/42 "Evaluation of a Shaking Table Test Program on Response Behavior of a Two Story Reinforced Concrete Frame: by Blondet, ].M.,Clough. R.W. and Mahin. S.A.,December 1980. (PB82 196 544)AII.

UCB/EERC-80/43 "Modelling of Soil-Structure Interaction by Finite and Infinite Elements: by Medina. F., December 1980, (PB81 229 270)A04.

UCB/EERC·81/01 'Control of Seismic Response of Piping Systems and Other Structures by Base Isolation: by Kelly, I.M., January 1981, (PB81 200735)A05.

UCB/EERC-81/02 "OPTNSR- An Interactive Software System for Optimal Design of Statically and Dynamically Loaded Structures with NonlinearResponse: by Bhalti, M.A., Ciampi, V. and Pister. K.S., Ianuary 1981, (PB81 218 851)A09.

UCB/EERC-81103 "Analysis of Local Variations in Free Field Seismic Ground Motions: by Chen, ].-C., Lysmer, J. and Seed, H.B.. January 1981, (ADA099508)A13.

UCB/EERC-81/04 "Inelastic Structural Modeling of Braced Offshore Platforms for Seismic Loading. : by Zayas., V.A., Shing, P.-S.B., Mahin. S.A. andPopov, E.P.. January 1981. (PB82 138 777)A07.

UCB/EERC-81/05 'Dynamic Response of Light Equipment in Structures: by Der Kiureghian, A., Sackman, ].L and Nour-0mid, B., April 1981, (PB81218497)A04.

UCB/EERC-81/06 "Preliminary Experimental Investigation of a Broad Base Liquid Storage Tank,' by Bouwkamp, ].G., Kollegger, ].P. and Stepben, R.M.,May 1981, (PB82 140 385)A03.

UCBJEERC-81107 "The Seismic Resistant Design of Reinforced Concrete Coupled Structural Walls: by Aktan, A.E. and Bertero, V.V., Iune 1981, (PB82113358)AII.

UCB/EERC-81/08 "Unassigned: by Unassigned, 1981.

UCB/EERC·81/09 -Experimental Behavior of a Spatial Piping System with Steel Energy Absorbers Subjected to a Simulated Differential Seismic Input," byStiemer, S.F., Godden. W.G. and Kelly, I.M., Iuly 1981. (PB82 201 898)A04.

UCB/EERC-81110 "Evaluation of Seismic Design Provisions for Masonry in the Uniled Stales: by Sveinsson, B.I., Mayes, R.L and McNiven, H.D.,August 1981, (PB82 166 075)A08.

UCB/EERC"81111 "Two-Dimensional Hybrid Modelling of Soil-Structure Interaction: by Tzong, T.·I., Gupta, S. and Penzien. I., August 1981. (PB82 142I 18)A04.

UCB/EERC·81/12 'Studies on Effects of Intills in Seismic Resistant RIC Construction: by Broklten, S. and Bertero, V.V., October 1981, (PB82 166190)A09.

UCB/EERC-81/13 "Linear Models to Predict tbe Nonlinear Seismic Behavior of a One-Story Steel Frame," by Valdimarsson, H., Shah. A.H. andMcNiven, H.D., September 1981. (PB82 138 793)A07.

UCB/EERC-81/14 "TLUSH: A Computer Program for the Three-Dimensional Dynamic Analysis of Earth Dams: by Kagawa, T., Mejia. LH., Seed, H.B.and Lysmer, I., September 1981, (PB82 139 940)A06.

UCBJEERC·8IJI5 -Three Dimensional Dynamic Response Analysis ofEanh Dams: by Mejia, LH. and Seed, RB., September 1981, (PB82 137 274)AI2.

UCBlEERC-81/16 "Experimental Study of Lead and Elastomeric Dampers for Base Isolation Systems: by Kelly, I.M. and Hodder, S.B., October 1981,(PB82 166 182)A05.

UCB/EERC-81/11 "The Influence of Base Isolation on tbe Seismic Response of Light Secondary Equipment,- by Kelly, I.M., April 1981, (PB82 255266)A04.

UCB/EERC-81/18 "Studies on Evaluation of Shaking Table Response Analysis Procedures: by Blondet, 1. Marcial, November 1981, (PB82 197 278)AIO.

UCB/EERC-81/19 "DELlGHT.STRUCT: A Computer-Aided Design Environment for .Structural Engineering. : by Balling, R.J., Pister, K..S. and Polak,E., December 1981, (PB82 218 496)A07.

UCB/EERC-81/20 "Optimal Design of Seismic"Resistant Planar Steel Frames," by Balling, RJ., Ciampi, V. and Pister, K.S., December 1981, (PB82 220I79)A07.

120

UCBlEERC-8210I ·Dynamic Behavior of Ground for Seismic Analysis of Lifeline Systems," by Sato, T. and Der Kiwqhian, A.. January 1982. (PB82 218926)A05.

UCBlEERC·82102 "Sbakinc Table Tests of a Tubular Steel Frame Model: by Gbanaal, Y. and Oough, R.W., January 1982. (PB82 220 161)A07.

UCBlEERC"82103 "Behavior of a Pipinl System under Seismic Excitation: Experimental Investi8lltions of a Spatial Pipins System supported by Mechanical Shock Amston," by Schneider, S., Lee, H.-M. and Godden, W. G., May 1982, (PB83 172 S44)A09.

UCB/EERC"82104 ·New Approaches for the Dynamic Analysis of Larse Structural Systems," by Wilson, E.L, June 1982, (PB8l 148 080)AOS.

UCB/EERC"82105 "Model Study of Effects of Damage on the Vibration Properties of Steel Offshore Platforms,· by Shahrivar, F. and Bouwkamp, J.G.,June 1982, (PB83 148 742)AIO.

UCB/EERC-82106 "States of the Art and Pratice in the Optimum Seismic Design and Analytical Response Prediction of RIC Frame Wall Structures," byAktan. A.E. and Bertero, V.V., July 1982, (PB83 147 736)A05.

UCB/EERC-82107 "Further Study of the Earthquake Response of a Broad Cylindrical Liquid-Storqe Tank Model,· by Manos. G.C. and Oough. R.W.,July 1982, (PB83 147 744)AII.

UCB/EERC-82108 "An Evaluation of the Design and Analytical Seismic Response of a Seven Story Reinforced Concrete Frame," by Charney, F.A. andBenero. V.V., July 1982. (PB83 157 628)A09. I

UCBlEERC-82109 "F1uid"Structure Interactions: Added Mass Computations for Incompressible Fluid. : by Kuo, J.S."H., August 1982, (PB83 156281)A07.

UCB/EERC·82110 "Joint..()pening Nonlinear Mechanism: Interface Smeared Crack Model: by Kuo, J.S.-H., August 1982. (PB83 149 195)A05.

UCB/EERC-82111 "Dynamic Response Analysis ofTechi Dam: by Oough, R.W., Stephen, R.M. and Kuo. J.S."H., August 1982, (PB83 147 496)A06.

UCB/EERC·82112 "Prediction of the Seismic Response of RIC Frame-Coupled Wall Structures," by Aktan, A.E., Bertero, V.V. and Piazza, M., August1982. (PB83 149 203)A09.

UCB/EERC·82113 "Preliminary Report on the Smart I Strong Motion Array in Taiwan: by Boll, BA ,Loh, C.H., Penzien, J. and Tsai, Y.B., August1982. (PB83 159 4OO)AI0.

UCB/EERC·82114 "Shaking-Table Studies of an Eccentrically X"Braced Steel Structure," by Yang, M.S., September 1982, (PB83 260 778)A12.

UCB/EERC·82115 "The Performance of Stairways in Earthquakes: by Roha, C., Axley, J.W. and Benero, V.Y., September 1982. (PB83 157 693)A07.

UCB/EERC-82116 "The Behavior of Submerged Multiple Bodies in Earthquakes: by Liao, W.-G., September 1982, (PB83 158 709)A07.

UCB/EERC-82117 "Effects of Concrete Types and Loading Conditions on Local Bond·Slip Relationships: by Cowell, A.D., Popov, E.P. and Benero. V.V.•September 1982. (PB83 153 577)A04.

UCB/EERC-82118 "Mechanical Behavior of Shear Wall Venical Boundary Memben: An Experimental Investigation," by Wagner, M.T. and Benero. V.V.,October 1982, (PB83 159 764)AOS.

UCB/EERC-82119 "Experimental Studies of Multi-suppon Scismic Loading on Piping Systems: by Kelly, J.M. and Cowell, A.D.• November 1982.

UCB/EERC"82120 'Generalized Plastic Hinge Concepts for 3D Beam-Column Elements: by Chen, P. F.-S. and Powell, G.H.• November 1982, (PB83 247981)AI3.

UCB/EERC"82121 "ANSR·II: General Computer Program for Nonlinear Structural Analysis; by Oughourlian, C.V. and Powell, G.H., November 1982.(PB83 2S1 330)AI2.

UCB/EERC·82122 "Solution Strategies for Statically Loaded Nonlinear Structures," by Simons, J.W. and Powell. G.H., November 1982, (PB83 197970)A06.

UCB/EERC·82123 "Analytical Model of Deformed Bar Anchorages under Generalized Excitations: by Ciampi, V., Eligebausen, R., Bertero. V.V. andPopov. E.P., November 1982. (PB83 169 S32)A06.

UCB/EERC·82124 'A Mathematical Model for the Response of Masonry Walls to Dynamic Excitations," by. Sucuoglu. H., Menli, Y. and McNiven, H.D.,November 1982, (PB83 169 OII)A07.

UCBlEERC-82125 "Earthquake Response Considerations of Broad Liquid Storage Tanks: by Cambra, FJ., November 1982, (PB83 251 215)A09.

UCBlEERC·82126 "Computational Models for Cyclic Plasticity, Rate Dependence and Creep: by Mosaddad. B. and PoweD, G.H., November 1982, (PB8324S 829)A08.

UCBlEERC-82127 "Inelastic Analysis of Piping and Tubular Structures: by Mahasuverachai, M. and Powell, G.H., November 1982, (PB83 249 987)A07.

UCB/EERC-83/01 "The Economic Feasibility of Seismic Rehabilitation of Buildings by Base Isolation: by KeUy, J.M., January 1983, (PB83 197 988)AOS.

UCB/EERC-83/02 "Scismic Moment Connections for Moment-Resisting Steel Frames.: by Popov, E.P., January 1983, (PB83 195 412)A04.

UCB/EERC,83/03 "Design of Links and Beam·tO-Column Connections for Eccentrically Braced Steel Frames: by Popov, E.P. and Malley, J.O., January1983, (PB83 194 81I)A04.

UCB/EERC·83/04 "Numerical Tecbniques for the Evaluation of Soil-Structure Interaction Effects in the Time Domain: by Bayo, E. and Wilson, E.L,February 1983, (PB83 24S 605)A09.

UCBlEERC·83/0S 'A Transducer for Measuring the Internal Forces in the Columns of a Frame-Wall Reinforced Concrete Structure," by Sause, R. andBenero, V.V., May 1983, (PB84 119 494)A06.

UCBlEERC"83/06 'Dynamic Interactions Between Floating Ice and Offshore Structures: by Croteau. P., May 1983, (PB84 119 486)A16"

UCBlEERC,83/07 ·Dynamic Analysis of Multiply Tuned and Arbitrarily Supponed Secondary Systems. : by Igusa, T. and Der Kiureghian, A., July 1983,(PB84 118 272)A11.

UCB/EERC·83/08 •A Laboratory Study of Submerged Multi-body Systems in Earthquakes,· by Ansari, G.R., June 1983, (PB83 261 842)A17.

UCBlEERC·83/09 "Effects of Transient Foundation Uplift on Earthquake Response of Structures,' by Vim, C.-S. and Chopra, A.K., June 1983, (PB83 261396)A07.

121

UCBlEERC-83/1O 'Optimal Design of Friction·Braced Frames under Seismic Loading,' by Austin. M.A. and Pister. KS.• June 1983. {PB84 119 288)A06.

UCBlEERC-83/11 'Shaking Table Study of Sinl!e,Story Masonry Houses: Dynamic Performance under Three Component Seismic Input and Recommen,dations," by Manos, G.c.. Gough, R.W. and Mayes, R.L.. July 1983. {UCBlEERC,83111)A08.

UCBlEERC-83112 'Experimental Error Propaption in Pseudodynamic Testing,' by Shiing, P.B. and Mahin, S.A.. JUDe 1983. {PB84 119 270)A09.

UCB/EERC-83113 'Experimental and Analytical Predictions of the Mechanical Characteristics of a I/S-scale Model of a 7-stOry RIC Frame-Wall BuildilllStructure: by Ak1an. A.E.• Bertero. V.V., Chowdhury, A.A. and Napshima, T.• June 1983. {PB84 119 2l3)A07.

UCB/EERC·83/14 'Shaking Table Tests of l.arge-Panel Precast Concrete Buildilll S)'Item Assemb1a&es." by Oliva. M.G. and Gough, R.W.• June 1983.{PB86 110 210/AS)AI 1.

UCBlEERC-831IS 'Seismic Behavior of Active Beam Links in Eccentrically Braced Frames,' by Hjelmstad, K.D. and Popov, E.P.• July 1983. {PB84 119676)A09.

UCBlEERC·83/16 'System Identification of Structures with Joint Rotation: by Dimsdale. J.S.• July 1983. (PB84 192 210)A06.

UCB/EERC-83/17 "Construction of Inelastic Response Spectra for Sinl!e-Degree-of·Freedom Systems: by Mahin. S. and Lin, J .• June 1983. {PB84 208834)AOS.

UCB/EERC-83/18 'Interactive Computer Analysis Methods for Predicting the Inelastic Cyclic Behaviour of Structural Sections; by Kaba, S. and Mahin.S.• July 1983, {PB84 192 012)A06.

UCB/EERC·83/19 ' Effects of Bond Deterioration on Hysteretic Behavior of Reinforced Concrete Joints," by Filippou. F.C.• Popov. E.P. and Bertero. V.V.•August 1983. (PB84 192020)(\10.

UCB/EERC-83/20 "Analytical and Experimental Correlation of Large-Panel Precast Building System Performance.' by Oliva, M.G.• Gough, R.W.• Velkov.M. and Gavrilovic, P.• November 1983.

UCB/EERC·83/21 'Mechanical Characteristics of Materials Used in a 1/5 Scale Model of a 7·Story Reinforced Concrete Test Structure.' by Berte",. V.V.•Aktan. A.E.• Harris., H.G. and Chowdhury, A.A.. October 1983, (PB84 193 697)AOS.

UCB/EERC-83/22 'Hybrid Modelling of Soil·Structure Interaction in Layered Media: byTzong, T.-J. and Penzien. J.• October 1983. (PB84 192 178)A08.

UCB/EERC-83123 "Local Bond Stress-Slip Relationships of Deformed Bars under Generalized Excitations,' by Eligehausen. R.• Popov. E.P. and Bertero.V.V., October 1983, {PB84 192 848)A09.

UeB/EERC-83/24 'Design Considerations for Shear Links in Eccentrically Braced Frames: by Malley. J.O. and PoPOV. E.P.• November 1983. (PB84 192I86)A07.

UCB/EERC-84/01 "Pseudodynamic Test Method for Seismic Performance Evaluation: Theory and Implementation: by Shing, P.·S. B. and Mahin, S.A.•January 1984, (PB84 190 644)A08.

UCB/EERC-84/02 "Dynamic Response Behavior of Kiang Hong Dian Dam." by Gough. R.W., Chang, K.·T.• Chen. H.-Q. and Stephen. R.M.• April 1984.(PB84 209 402)A08.

UCB/EERC·84/03 "Refined Modelling of Reinforced Concrete Columns for Seismic Analysis: by Kaba, S.A. and Mahin, SA. April 1984, {PB84 234384)A06.

UCB/EERC-84/04 •A New Floor Response Spectrum Method for Seismic Analysis of Multiply Supported Secondary Systems.,' by Asfura, A. and DerKiureghian. A.• June 1984, {PB84 239 417)A06.

UCB/EERC-84/0S ·Earthquake Simulation Tests and Associated Studies of a 115th·scaIe Model of a 7·Story RIC Frame-Wall Test Structure: by 8ertero,V.V.• Aktan. A.E.• Charney. F.A. and Sause. R.• June 1984. {PB84 239 409)A09.

UCB/EERC-84/06 'RlC Structural Walls: Seismic Design for Shear: by Aktan. A.E. and Bertero. V.V.• 1984.

UCBlEERC,84/07 'Behavior of Interior and Exterior FIat-Plate Connections subjected to Inelastic Load Reversals.," by lee. H.I- and Moehle. J.P.• August1984. (PB86 117 629/AS)A07.

UCB/EERC·84/08 ·Experimental Study of the Seismic Behavior of a Tw0-8tory Flat-Plate Structure. : by Moehle. J.P. and Diebold, J.W.• August 1984.(PB86 122 553/AS)AI2.

UCB/EERC·84/09 "Phenomenological Modeling of Steel Braces under Cyclic Loading," by Ikeda, K.. Mahin. S.A. and Dermitzakis., S.N.• May 1984. (PB86132 1981AS)A08.

UCB/EERC·84/10 "Earthquake Analysis and Response of Concrete Gravity Dams: by Fenves, G. and Chopra, A.K.. August 1984. (PB8S 193902lAS)AII.

UCB/EERC-84/11 -EAGo-84: A Computer Program for Earthquake Anal)'lis of Concrete Gravity Dams." by Fenves, G. and Chopra, A.K.. August 1984.{PB8S 193 613/AS)AOS.

UCB/EERC·84/12 "A Refined Physical Theory Model for Predicting the Seismic Behavior of Braced Steel Frames," by Ikeda. K. and Mabin. S.A.• July1984, (PB8S 191 4S0/AS)A09.

UCB/EERC-84/13 "Earthquake Engineering Research at Berkeley· 1984: by. August 1984. (PB8S 197 341/AS)AI0.

UCB/EERC-84/14 'Moduli and Damping Facton for Dynamic Anal)'les ofCohesionless Soils." by Seed, H.B.• Wong, R.T.• Idriss, I.M. and Tokimatsu, K.,September 1984. (PB8S 191 468/AS)A04.

UCB/EERC-84/IS 'The Influence ofSPT Procedures in Soil Liquefaction Resistance Evaluations: by Seed, H.B.• Tokimatsu, K., Harder, L.F. and Chung,R.M.• October 1984. (PB8S 191 7321AS)A04.

UCB/EERC·84/16 'Simplified Procedures for the Evaluation of Settlements in Sands Due to Earthquake Shaking,' by Tokimatsu, K. and Seed, H.B.•October 1984. (PB8S 197 887/AS)A03.

UCB/EERC-84/17 "Evaluation of Energy Absorption Characteristics of Bridges under Seismic Conditions: by Imbsen, R.A. and Penzien. J•• November1984.

UCB/EERC-84/18 "Structure·Foundation Interactions under Dynamic Loads: by Liu. W.O. and Penzien. J•• November 1984. {PB87 124 889/AS)All.

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UCB/EERC-84119 'Seismic Modelling of Deep Foundations,' by Chen. C.-H. and Pennen, I., November 1984, (PB87 124 7981AS)A07.

UCBlEERC.84120 'Dynamic Re$ponse Behavior of Quan Shui Dam: by Gough. R.W., Chana. K.,T•• Chen. H.oO.• Slephen. R.M~ Gha.naat, Y. and Qi.J.,H., November 1984, (PB86 1I5177/AS)A07.

UCBlEERC·85/0 I

UCBlEERC-85/02

UCBlEERC·85/03

UCBlEERC-85/04

UCBlEERC·85/(15

UCBlEERC·85/06

UCBlEERC·85/07

UCBlEERC·85/08

UCBlEERC·85/09

UCB/EERC·85/10

UCBlEERC-85/11

UCB/EERC-85/12

UCB/EERC-85/13..UCB/EERC·85/14

UCB/EERC·8S/15

UCB/EERC-85/16

·Simplified Methods of Analysis for Earthquake Resistant Desiaa of Buildings,' by Cruz, E.F. and Chopra, A.K.. February 1985, (PBS6112299/AS)AI2.

'Estimation of Seismic Wave Coherency and Rupture Velocity usilll the SMART I StroDe-Motion Array Recordinp," by Abrahamson,N.A., March 1985, (PB86 214 343)A07.

'Dynamic Propenies of a Thirty Story Condominium Tower Building; by Stepbeu. R.M~ Wilson, E.L and Studer. No, April 1985.(PB86 I 1896S/AS)A06.

'Development of Substrueturing Techniques for On-Line Computer ControUed Seismic PerfOrtnaDCe Testina.· by DmBiuaJtis, s. &AdMabin. S., February 1985, (PB86 13294I1AS)A08.

'A Simple Model for Reinforcinl Bar Anchoraces under Cyclic Excitations,' by FiJippou. F.e.. March 1985. (PB86112 919/AS)A05.

'Rackina Behavior of Wood·framed Gypsum Panels under Dynamic Load,. by Oliva, M.G., June 1985.

·Earthquake Analysis and Response of Concrele Arch Dams: by Fok, K..·L and Chopra. A.I<.. June 1985, (PBI6 1396721A.S)AIO,

'Effect of Inelastic Behavior on the Analysis and Desip of Earthquake Resistant Structures; by Un. J.P. a114 Mahin, s.A. June 1985.(PB86 1353401AS)A08.

·Earthquake Simulator Testin, of a Base-Isolated Bridge Dect,' by KeUy, I.M., Buckle. I.G. and Tsai, H.-e~ January 1986. (PB81 124IS2IAS)A06.

'Simplified Analysis for Eanhquake Resistant Design of Concrete Gravity Dams," by Feaves, G. and Chopra, A.K.. June 1986. (PB87124 16OlAS)A08.

'Dynamic Interaction Elfecu in Arch Dams,' by Oouah, R.W., Chang, 1(..T.• Chen. H.oO. and Ghanaat, Y~ October 1985, (PB86135027/AS)AOS.

'Dynamic Re$ponse of Long Valley Dam in the Mammoth Lake Earthquake Series of May 25-21. 1980: by Ui. s. and Seed, H.B~November 1985, (PB86 142304/AS)A05.

•A Methodology for Computer·Aided Design of Earthquake-Resistant Steel Stttlctures," by Austin, M.~ Fister. K.S. and Mahin, s.A.December 1985, (PB86 I5948OJAS)AIO •

·Re$ponse of Tension.Leg Platfonns 10 Vertical Seismic Excitations,· by Liou. G.-5.• Penzieu. J. and Yeuar. R.W~ December 1985.(PB87 124 871/AS)A08.

"Cyclic Loading Tests of Masonry Single Piers: Volume 4 - Additional Tests with Height to Width Ratio of I: by SveiOSSOD. B.•McNiven, H.D. and Sucuoglu, H., December 1985.

•An Experimental Program for Studying the Dynamic Response of a Steel Frame with a Variety of Infill Partitions,' by YancY, B. andMcNiven. H.D., December 1985.

UCBlEERC·8611I

UCB/EERC·86/0 I

UCB/EERC·S6IIO

UCB/EERC-86/07

'A Study of Seismically Resistant Eceenlrical1y Braced Steel Frame Systems,' by Kasai. K. and Popov, E.P•• lanuary 1986. (PBS7 124178/AS)AI4.

-Design Problems in Soil Liquefaction: by Seed. H.B., February 1986, (PB87 124 186/AS)A03.

'Implications of Recent Eanhquake$ and Research on Earthquake.Resistant DesillD and CODStttleti"n of Buildings,: by Bertero. V.V.•March 1986, (PB87 124 194/AS)A05.

'The Use of Load Dependent Vectors for Dynamic and Earthquake Analyses,' by Lqer. P~ Wilsoa, E.L and CIolllllr. R.W.. March1986, (PB87 124 202lAS)AI2.

"Two Beam·To-Columa Web Connections,' by Tsai, K.-e. and Popov, E.P.• April 1986 • (PB87 124 301IAS)A04.

'Determination of Penetration Re$istance for Coarse-Grained Soils usin, the Bec:ter Hammer DrilI,' by Harder, LF. mel Seed, H.B..May 1986, (PB87 124 210/AS)A07•

•A Mathematical Model for Predicting the Nonlinear Re$ponse of Unreinfo~Masonry Walls to lD-PIane Earthquake Ucitations,' byMengi, Y. and McNiven, H.D., May 1986, (PB87 124 7801AS)A06.

'The 19 September 1985 Mexico Eanhquake: Buildin. Behavior: by Berteru. V.V.• July 1986.

'EACD-3D: A Computer Program for Three-Dimensional Earthquake Analysis of Concrete Dams,' by Folt, K.-L. Hall, J.F. aDdChopra. A.K., July 1986, (PB87 124 228/AS)A08.

'Ear!hAuake Simulation Te$u and Associated Studies of a O.3-Scale Model of a Sm-5tory ConceDUica1ly Braa:el Steel Structure,' byUaniC.·M. and Bertero. V.V.• December 1986.

'Mechanical Characteristics of Base Isolation Bearinp for a Bridge Deck Modd Test: by Kelly, J.M.. Buckle. LO. aud Kob. C-G..1987.

UCB/EERC·86112 ~ModeUin& of Dynamic Response of Elastomeric Isolation Bearings,' by Kob, e.-o. and Kelly, J.M~ 1987.

UCB/EERC·S6I08

UCB/EERC·86/09

UCB/EERC·86/0S

UCB/EERC·86/06

UCBlEERC·86/04

UCB/EERC·86/02

UCBlEERC-86/03

UCBlEERC-87/01 'FPS Eanhquake Re$istin& System: Experimental Report: by Zayas, V.A., Low, s.s. and Mahin, S.A., June 1987.

UCB/EERC·87/02 'Eanhquake Simulator Tesu and Associated Studies of a O.3-Scale Model of a Sm-5tory Ea:eatrically Braced Steel St11ll:lun:,; by Whit·taker, A.. Uang, C.·M. and Bertero, V.V., July 1987.

UCBlEERC·87103 •A Displacement Control and Uplift Restraint Device for Base-lsolated Structures,' by Kelly. J.M.. Griffitb, M.e. and Aikeu. LO~ April1987.

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lJCB/EERC-1l7/04 "Earthquake Simulator Testing of a Combined Sliding Bearing and Rubber Bearing Isolation Sys.tem," by Kelly, J.M. and Chalhllub, M.S., 19l17.

UCB/EERC-87/0S "Three-Dimensional Inelasti<.: Analysis of Reinforced Concrete Frame-Wall Structures," by Moaz·zami, S. and Bertero, V.V., MOlY 1987.

UCB/EERC·87/06 "Experiments on E<.:centrically Braced Frames With Composite Floors," by Rides, J. and Popov, E.,June 1987.

UCR/EERC-1l7/07 "Dynamic Analysis of Seismil'ally Resistant Eccentrically Rraced Frames," by Rides, J. and Popov,E., June 19M7.

UCD/EERC-87/08 "Undrained Cyclic Triaxial Tesling of Gravels· The Effect of Membrane Compliance, " by Evans,M.D. and Seed, H.B., July 19M7.

UCB/EERC-ll7/01J "Hybrid Solution Tc<.:hniques For Generalized Pseudo-Dynamic Testing," by Thewall, C. and Mahin,S. A., July 1987.

UCB/EERC-87/10 "Investigation of Ultimate Bchavior of AISC Group 4 and 5 Heavy Steel Rolled-Section Splices withFull and Partial Penetration BUll Welds," by Bruneau, M. and Mahin, S.A., July 1987.

UCB/EERC-87/11 "Residual Strength of Sand From Dam Failures in the Chilean Earthquake of March 3, 1985," by DeAlba, P., Seed, H. B., Retamal, E. and Seed, R. B., September 1987.

UCB/EERC-87/12 "Inelastic Response of Structures With Mass And/Or Stiffness Eccentricities In Plan Subjected toEarthquake Excitation." by Bruneau, M., September 1987.

UCB/EERC-87/13 "CSTRUCT: An Interactive Computer Environment For the Design and Analysis of EarthquakeResistant Steel Structures." by Austin, M.A., Mahin. S.A. and Pister, K.S., September 1987.

UCB/EERC·87/14 "Experimental Study of Reinforced Concrete Columns Subjected to Multi-Axial Loading." by Low,S.S. and Moehle, J.P., September 1987.

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EXPERIMENTAL STUDY OF REINFORCED CONCRETE COLUMNS SUBJECTED TO MULTI-AXIAL CYCLIC LOADING · PDF file · 2009-12-03Experimental Study of Reinforced Concrete Columns subjected to...

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