REPORT NO.

UCB/EERC-80/16

JUNE 1980

EARTHQUAKE ENGINEERING RESEARCH CENTER

CYCLIC INELASTIC BUCKLINGOF TUBULAR STEEL BRACES

byVICTOR A. ZAYAS

EGOR P. POPOV

STEPHEN A. MAHIN

Report to the National Science Foundation

COLLEGE OF ENGINEERING

UNIVERSITY OF CALIFORNIA • Berkeley, CaliforniaREPRODUCED BY.NATIONAL TECHNICALINFORMAnON SERVICE

u.s. DEPARTMENT OF COMMERCESPRIlIGfIHD, VA 22161

(Formerly NTIS-aS).... _-,.---~_ .... - .. ......._- ..._.

- i _ta

ABSTRACT

Experimental results are presented from tests on six individual brace members subjected

to severe inelastic cyclic loading. The tubular brace specimens considered are one-sixth scale

models of braces of the type used for offshore platforms. Each brace specimen is alternatively

subjected to cycles of compressive inelastic buckling followed by tensile stretching. Examined

are the effects resulting from different end fixity conditions (pinned vs. fixed), and from

different diameter-to-wall thickness ratios (33 vs. 48). Also, the behaviors of heat treated

braces are compared to the behavior of braces made from tubing as received from the manufac­

turer. The inelastic responses of the braces are presented and interpreted, including axial load­

axial displacement hysteretic loops; axial load-midspan lateral deflection hysteretic loops; brace

deflected shapes; brace energy dissipation; and inelastic axial strains, curvatures and rotations in

plastic regions.

Special attention is directed to the deterioration of buckling load with inelastic cycling.

Design code buckling formulas are for columns or braces that have not been previously yielded

and have initial cambers within the code allowances. Cyclic inelastic loadings cause changes in

the mechanical material properties of the braces which subsequently reduces the buckling load.

A method of predicting the reduction in buckling load is presented. The changes in material

properties are identified for a "critical section" within the plastic hinge of a brace and the

reduced buckling loads under repeated cyclic loadings are calculated. The results are examined

with respect to design procedures prescribed by the American Institute of Steel Construction

and the American Petroleum Institute.

- ii -

ACKNOWLEDGEMENTS

The work reported in this paper is a part of general investigation of Braced Steel Struc­

tures which is one of the sub-projects supported by the National Science Foundation under

Grants ENV-76-04263 and PFR-79-08984. The authors are most grateful for the support which

made this work possible, and to Dr. S. C. Liu, the Project Manager for NSF.

A large staff was required for the completion of the experimental work, data reduction,

and report preparation. The authors are indebted to the several graduate students who assisted.

In particular the authors would like to thank Benson Shing, Keith Hjelmstad, Willy Yau, R.

Gary Black, Bruce Fong and Lawrence Oeth who contributed with personal effort and

enthusiasm to the project. Don Clyde of the technical staff set up and operated the test equip­

ment. Leona Rambeau and Amy Pertschuk prepared the illustrations. Joy Kono typed the

report drafts, and Linda Garbesi did the Unix text preparation. The help of these people is

greatly appreciated.

Any opinions, findings, and conclusions or recommendations expressed in this report are

those of the authors and do not necessarily reflect the views of the National Science Founda­

tion.

- iii -

TABLE OF CONTENTS

Abstract

Acknowledgements

Table of Contents

List of Symbols

Chapter 1. Introduction

Objectives and Scope

Chapter 2. Experimental Program

Experimental Setup

Instrumentation

Loading Procedure

Material Properties

Chapter 3. Overall Behavior of Strut Specimens Under Cyclic Loading

Hysteretic Behavior

Normalized Load vs. Axial Displacement

Deterioration of Buckling Loads

Deflected Shapes

Energy Dissipation

Chapter 4. Inelastic Behavior at Plastic Hinges - Annealed Struts

Basic Considerations of Brace Inelastic Buckling

Curvature in Plastic Hinge Regions

Inelastic Rotations

Cumulative Curvature and Centroidal Axial Strain

Occurrence of Local Buckling

Chapter 5. Prediction of Buckling Loads - Annealed Structs

A Generalized Tangent Modulus Procedure

Page

ii

iii

vi

3

5

6

7

8

8

11

11

15

16

16

18

21

22

23

26

27

28

32

34

- iv -

Prediction of First Buckling Load

Deterioration of Buckling Load

Chapter 6. Inelastic Behavior of the Unannealed Struts

Characteristics of the Material Properties

Prediction of Buckling Loads

Chapter 7. Conclusions

Recommendations for Future Research

References

Tables

Figures

Appendix

36

36

40

40

41

43

44

46

48

61

156

A

B

C

CIS

CY

D

E

EtF

G3

kLir

LB

LP

LVDT

MpP

PyST

I>

I>y

d

€

- v -

LIST OF SYMBOLS

Load Point - Zero Load Before Compression

Load Point - Maximum Compressive Load

Load Point -Maximum Compressive Displacement

Cumulative Inelastic Strain (Centroidal)

Cycle

Load Point - Zero Load After Compression

Load Point - Maximum Tensile Load

Tangent Modulus of Elasticity

Load Point- Zero Load After Tension

Strain Gage Number 3 (Typical)

Effective Slenderness Ratio

Local Buckling

Designation of Load Point

Linear Variable Differential Transformer

Plastic Moment

Axial Load

Yield Load

Designation for Strut

Axial Displacement

Axial Yield Displacement

Midspan Lateral Displacement

Strain

Stress

Yield Stress

Tube Section

CHAPTER 1

INTRODUCTION

The level of seismic forces that buildings located in regions of high seismic risk would be

required to resist, if designed on an elastic basis alone, would generally raise the cost of con­

struction to nearly prohibitive levels. Fortunately, it is not necessary to design for these large

elastic forces, if ductile inelastic deformations can be permitted. Stresses beyond the elastic

limit will cause permanent deformations and localized damage, but a properly designed struc­

ture will not collapse.

The concept of using braced frames in seismic-resistant design has received little attention

until very recently due to the belief that such framing is not sufficiently ductile to withstand

severe seismic disturbances. Consequently, the majority of large structural steel buildings in

seismically active regions are designed as moment-resisting frames. For buildings having wide

facades, such a structural system is economical and has been shown to be very satisfactory for

resisting lateral forces caused by earthquakes. However, in some instances moment-resisting

frames tend to be somewhat flexible, and although safe from collapse, during a severe earth­

quake, can develop costly non-structural damage. Moreover, by using moment-resisting frames

alone, along a narrow width of a building, it may be very difficult, and economically impractical,

to develop the required stiffness and strength to resist the lateral forces. Recent experience has

shown that stiff buildings can behave well during major earthquakes [I]. For these reasons

increasing attention is being given to the possibility of employing a variety of bracing schemes

[2-8]. In these designs the braces can become subjected to severe cyclic axial loadings causing

the braces to sequentially buckle and stretch inelastically.

To supplement the scant data available on the behavior of braces subjected to cyclic ine­

lastic loadings, an extensive experimental program is being carried out at the University of Cali­

fornia, Berkeley. Some twenty-four hot rolled steel sections commonly used in the building

industry have already been tested [9]. All of these members conformed to the American Insti­

tute of Steel Construction (AISC) requirements for compact sections [IO]. In order to

broaden the scope of these studies, tubular steel models representative of those employed in

offshore construction were also included in the investigation. This report presents the findings

from experimental tests on six tubular steel braces subjected to severe cyclic axial loadings.

Because of the stiffness and strength required to resist lateral forces due to the actions of

wind, waves and currents, offshore construction has traditionally employed braced frames as

standard design practice. Recent emphasis on seismic considerations in offshore construction

has brought attention to the inelastic cyclic behavior of these types of braced frames. Applica­

ble offshore design criteria specify a strength design requirement based on an elastic approach,

and the levels, of seismic design forces considered are comparable to those used for onshore

structures. In addition, the 1977 and 1979 editions of the American Petroleum Institute (API)

Recommended Practice for Planning, Designing, and Constructing Fixed Offshore Platforms

each have stipulated ductility design requirements. The 1977 recommendations require

offshore braced frames to remain stable under rare and intense earthquake motions capable of

imposing displacements twice those of the strength design requirement. The 1979 recommen­

dations require offshore platforms to be capable of absorbing at least four times the amount of

energy absorbed at the strength design requirement with the structure remaining stable. Very

little information is presently available regarding the inelastic cyclic behavior of tubular steel

braced frames, their ductility capabilities, and their ability to absorb energy.

The main element required to maintain the overall structural integrity of a braced frame

subjected to lateral forces is the brace. A typical load-deformation relationship of a brace sub­

jected to a cycle of inelastic loading is schematically shown in Fig. 1.1. In stage A-B a plastic

hinge is formed in the brace while loading in compression. In stages C-F, the brace is com­

pletely straightened by tensile stretching. Several simple macroscopic computer models hav~

been developed to account for this type of hysteretic behavior [2,3,5,12,13]. One such model,

implemented by Roeder and Popov [3], is illustrated in Fig. 1.2. The model approximates the

behavior of a brace by defining a sequence of linear segments. The stiffness of the model in

each segment must be selected on the basis of experimental results, or mathematical

2

formulations. At this time, accurate mathematical or numerical procedures for determining the

form of the hysteretic loops are not fully developed. Consequently, experimental data are

necessary, not only to assess current design procedures, but to obtain data with which analytical

models can be developed and verified.

Unfortunately, only little experimental information is currently available regarding the

hysteretic behavior of tubular brace members. An experimental investigation of brace

members was carried out by Jain, Goel and Hanson at the University of Michigan in 1978 [81.

Small square tube (and angle) specimens were subjected to large cyclic static and dynamic dis­

placements. Experimental investigations of tubular beam-column and brace members made

from small diameter pipe are in progress at the University of Wisconsin-Milwaukee under the

direction of D. R. Sherman. Preliminary results of this investigation are reported in Ref 14.

Objectives and Scope

In this report, experimental results from tests on six tubular braces subjected to cyclic ine­

lastic loading are presented and evaluated. The objectives are to present the experimental data

in a form which can later be utilized in analytical studies, and to interpret the experimental

observations.

The brace specimens are one-sixth scale models of bracing members used in offshore

structures. The dimensions of the test specimens were based on a representative X-braced

offshore platform designed according to wave and earthquake criteria applicable to Southern

California [15]. The response of specimens designed as semi-compact tubular braces, with a

diameter-to-thickness (D/t) ratio of 48, are compared to the response of specimens considered

fully compact with a diameter-to-thickness ratio of 33 [11]. The effects resulting from different

end fixity conditions are examined. Also, the behavior of heat treated braces is compared to

the behavior of braces made from tubing as received from the manufacturer. Experimental data

presented and interpreted for the brace specimens include: axial force vs. axial displacement

hysteretic loops; axial force vs. midspan lateral deflection hysteretic loops; brace deflected

3

shapes; brace energy dissipation; inelastic axial strains; and inelastic curvatures and rotations

within plastic hinges. The deterioration of buckling load capacity with cycles of loading is

accorded special attention and a method of predicting such deterioration is developed. The

results of the research reported herein are examined with respect to design procedures

prescribed by the AISCand API for axially loaded members.

4

CHAPTER 2

EXPERIMENTAL PROGRAM

The bracing member specimens were one-sixth scale models of braces· found in a

representative Southern California offshore platform (Fig. 2.1 a). At this scale the cross braces

were represented by 4-inch 002 mm) diameter steel tubing. Specimens of two dimensions

were fabricated: a first group with a diameter-to-thickness ratio of 33 and a second group with a

ratio of 48. The first group simulated fully compact A36 steel members able to maintain their

capacity through large inelastic deformations [I 1], whereas the second group modeled A36 steel

members capable of developing their full plastic load capacity without being able to withstand

large inelastic deformations.

To assess the effect of end restraint on brace behavior, two bounds on the possible end

conditions were considered: both ends pinned and both ends fixed. The ends of the first four

specimens were pinned and those of the remaining two specimens were fixed. The actual end

restraint of braces in a braced frame would depend on a variety of factors -- such as frame

configuration and loading, connection detailing, member slenderness and initial camber, joint

flexibility, and inelastic behavior of adjacent members -- and would ordinarily fall in the range

of restraint between the two bounds.

The pinned-end struts (Struts 1-4) were 74-3/8 in. 0.89 m) long, the distance between

the center of the intersection of the cross braces and the face of the jacket leg (Fig. 2.1 b) The

specimen length, from pin to pin, included heavy end support clevises that contained roller

bearings and attachment plates (Fig. 2.2). The effect of the heavy end sections on the buckling

load of the struts was calculated to be less than 3%. The fixed-end specimens (Struts 5 and 6)

were 70-114 in. 0.78 m) long between points of fixity, the distance between the face of the

jacket leg and a point within the thick-walled insert of the cross joint (Fig. 2.1b). The effective

slenderness ratios, kL/r, were 54 and 25 for the pinned-end and fixed-end specimens, respec­

tively.

5

The test specimens were made of AISI 1020 mild steel tubing. (AISI 1020 is a mild steel

similar in carbon content and properties to A36.) Because of the drawing process used in its

manufacture, the material properties of this tubing in the as-received condition are considerably

different from the A36 steel welded pipe used in full scale construction. To achieve properties

in the test specimens closer to those encountered in full scale braces and to assess the effect of

material properties on test specimen behavior, four of the tubes used in the test specimens

were annealed by heating to 1600 0 F (870 0 C) and oven-cooling to 1000 0 F (538 0 C).

Full scale construction pipe will have initial residual stresses that differ from the annealed test

tubing; however, the effect of these initial residual stresses on cyclic inelastic buckling should

not be significant after the first inelastic cycle. Two specimens were not annealed in order that

the effect of the as received material properties on the structural response could be assessed.

The geometric properties, end restraint condition, heat treatment, and initial horizontal

and vertical cambers of individual specimens are summarized in Table 2.1.

Experimental Setup

The experimental apparatus used for the tests on the strut specimens is illustrated in Figs.

2.3 through 2.6. One end of the strut was either pinned or rigidly connected to a stiff braced

steel foot frame attached to a concrete reaction block. The other end of the strut was attached

to a double-acting hydraulic jack that was pin-connected to another concrete reaction block.

For the pinned-end specimens, the jack and specimen were connected by a head pin assembly

which was restrained horizontally by a single side arm. For the fixed-end specimens, the strut

was rigidly bolted to a head unit that was restrained against rotation and translation normal to

the axis of the specimen by means of two parallel side arms. Bolts in slotted holes were used to

restrain translation or rotation of the head unit in the vertical plane (Fig. 2.5a). Photogram­

metric records verified to within .0016 rad. that in the fixed-end condition, the specimens

achieved full fixity.

6

The initial cambers present in the tubular specimens were carefully measured, and the

specimens were oriented so that initial buckling would be expected to occur in a horizontal

plane. The small frictional forces present in the test setup were measured so that they could be

accounted for when the data were reduced. The friction forces were found to be 0.4 kips 0.78

kN) and 0.8 kips 0.56 kN) for the pinned and fixed test setups, respectively.

Instrumentation

Linear variable differential transformers (LVDT's) were used to measure axial displace­

ment and linear potentiometers were used to measure midspan horizontal lateral displacement

of the strut specimens (Fig. 2.2 and 2.7). Linear potentiometers were also used to measure

midspan vertical lateral displacement of the fixed-end specimens where a component of buck­

ling could occur in the vertical plane. The axial load on the specimens was measured by a load

cell attached to the loading ram.

Photogrammetric instrumentation was used to determine the deflected shape of the struts.

Aluminum foil targets were evenly spaced longitudinally along the centerline of the members,

and the camera was stationed on an overhead crane approximately twenty feet above the speci­

men. Glass plate film was used; pictures were taken at predetermined points in the loading

cycles. The plates were read on an X-Y comparator and the actual and normalized deflected

shapes were plotted by a CDC 6400 Cal Comp Plotter.

SR-4 strain gages were placed at strategic locations along each member. Strain gages were

concentrated where plastic hinges were expected to form. Reduced strain gage data provided

strain histories at specified points, cross-section curvature histories, and plastic hinge rotations.

Data from the load cell, LVDT's, linear potentiometers, and strain gages were recorded

on a Data General Nova Computer high speed data acquisition system. During the tests load

and displacement response parameters were also monitored on X-Y recorders and visual obser­

vation records of local buckling phenomena and tearing were kept. (Fig. 2.8).

7

Loading Procedure

All specimens were subjected to quasi-static cycles of reversing axial displacement. These

cycles generally included compressive inelastic buckling followed by tensile stretching. The

prescribed displacement sequence was designed to represent ductility levels expected in braces

within the Southern California example structure subjected to severe seismic loading [I2]. The

same displacement history was designed for the early cycles of all six test struts. The history

prescribed for the first seven loading cycles was as follows. Axial displacement was uniformly

incremented 0.07 in. per cycle during cycles I through 5. On reaching ± 0.35 in. during the

fifth cycle, the imposed displacement was held constant until cycle 7. The loading for subse­

quent cycles varied depending on the behavior of the individual struts.

The displacement pattern applied to each strut is illustrated in Figs. 2.9 through 2.14.

Struts 3 and 4, fabricated from the unannealed tubing, were unable to follow the prescribed dis­

placement history. Both fractured during the tensile phase of cycle 3. These struts were

repaired and testing resumed with the tensile displacements limited to prevent fracture.

Load points within a cycle have been identified by a letter code system as illustrated for a

typical hysteretic loop in Fig. 2.l5a and from a loading schematic in Fig. 2.15b. This system of

identification is used throughout the report.

Material Properties

The material properties influence the brace behavior through the fundamental characteris­

tics of yield point stress level, stress-strain curve shape, and elongation capacity. Differences in

yield points, if the yield points are in fact discernible, can, in part, be accounted for by normal­

izing brace response parameters. This normalization is accomplished by dividing load (or dis­

placement) levels in each strut by its respective yield load (or yield displacement). Neverthe­

less, a similar yield point for the model and full scale brace is desirable in order to retain the

correct relationship between brace displacement ductility and frame displacements of the exam­

ple structure. Also, to model inelastic behavior correctly it is important to have similar stress-

8

strain curve shape and elongation capacities.

Two material types were used to fabricate the specimens: annealed and unannealed (as

received) steel tubing. The effect of annealing is clearly indicated in the tensile stress-strain

curves plotted in Figs. 2.16 through 2.18 for coupons taken from each type of material. The

stress-strain curve for the annealed material is elastic-plastic, similar to that for A36 steel. The

average yield strength of the annealed material as measured from the coupon tests was 35 ksi

(242 MPa). Ultimate strengths of approximately 52 ksi (359 MPa) were typically obtained at

strains of about 14% and fractures occurred at strains of about 28%.

The yield strength of the unannealed material, based on a 0.2% strain offset, was consid­

erably higher; equal to 92 ksi (635 MPa) for the tubing with an 0.083 in. (2.1 mm) wall thick­

ness, and 74 ksi (511 MPa) for the tubing with an 0.120 in. (3.0 mm) wall thickness. No dis­

cernible yield point and no plastic plateau appear in the unannealed material stress-strain

curves. The unannealed material coupons fractured at strains of less than 8%.

Material tests were also performed on full cross-sections of pipe. The tests were of two

types: compression stub test (Figs. 2.19 and 2.20) and cyclic tests (Figs. 2.21 and 2.22).

Stress-strain curves from compression stub tests were generally used for predicting first buck­

ling loads of struts. The cyclic tests were used to quantify the extent of the Bauschinger effect

that results from inelastic yield and strain reversals. In all the material tests the unannealed

material behaved differently for specimens with 0.083 in. (2.1 mm) wall thickness and 0.120 in.

(3.0 mm) wall thickness, whereas there was no apparent wall thickness effect for the annealed

material. The average yield stress of the annealed material from the full cross-section material

tests was 31 ksi (214 MPa).

A summary of the initial yield stresses for the six test struts is presented in Table 2.2.

The initial yield stress for the unannealed struts is based on a 0.2% strain offset from the

coupon tests. The reported initial yield stress for the annealed struts is based on the first dis­

cernible yield plateau, as averaged from the cyclic and compression stub tests. In general, the

coupon tests showed 4-5 ksi (31 MPa) higher yield stresses than the full section cyclic and

9

compression stub tests. The yield stresses observed in the test struts (reported in Chapter 3)

agree with the stresses observed in the cyclic and compression stub tests. The higher stresses

observed in the coupon tests could be a result of cutting out and machining the coupon speci­

mens.

Based on the initial yield stress, initial axial yield loads (Py) and yield displacements (I)y)

were computed and are also listed in Table 2.2. These computed yield loads and yield displace­

ments are used to normalize the brace hysteretic plots and energy dissipation data presented in

the following chapter.

10

CHAPTER 3

OVERALL BEHAVIOR OF STRUT SPECIMENS UNDER CYCLIC LOADING

The test struts were subjected to cyclic inelastic axial displacements. The principal param­

eters monitored during the tests have been plotted in the form of hysteretic loops. These plots

are not only a valuable means of viewing the overall response history of the tested struts, but

they also lay the ground work for additional data reduction and subsequent development of

information related to deterioration of buckling loads, energy dissipation, and plastic hinge for­

mation. Details of inelastic behavior within plastic hinge regions are discussed in Chapter 4.

Hysteretic Behavior

The axial load vs. axial displacement curves for the six strut specimens are shown in Figs.

3.1 through 3.14; the lateral deflections that correspond to the early loading cycles are shown in

Figs. 3.15 through 3.20. Maximum compressive and tensile loads attained in each cycle of

loading are reported in Table 3.1; maximum compressive and tensile displacements are reported

in Table 3.2.

Strut 1 was subjected to a preliminary compressive pulse when the load control system

was activated. Residual strains ranging from 0.006 in.lin. in compression to 0.004 in.lin. in

tension were recorded following the pulse. The initial camber of the strut, 0.12 in. (3.0 mm),

increased to 0.25 in. (6.4 mm) as a result of this preliminary loading. Thus, Strut 1 started

cycle 1 with previous inelastic straining and an initial camber larger than the other struts. As a

result, the cycle 1 buckling load attained was 25% lower than that predicted by AISC formulae

[to]. (The factor of safety has been removed from the AISI formulae for all AISC buckling

predictions made in this report.)

The buckling load of Strut 1 decreased significantly in each loading cycle subsequent to

cycle 1 (Fig. 3.1). The post-buckling compressive load of the strut decreased rapidly with

increasing displacement during each cycle. The axial stiffness for tension loading deteriorated

significantly with each cycle. Full tensile load is attained when all fibers within a cross-section

11

have yielded in tension. The greater the compressive displacement within a given cycle, the

greater are the resulting strains within the plastic hinge due to inelastic rotation. After unload­

ing in compression, a residual inelastic rotation remains in the strut. When the .direction of

loading is reversed and the strut is loaded in tension, the tensile displacement required to

develop full tensile yielding depends on the prior compressive displacement and on the magni­

tude of the residual inelastic rotation. While the full tensile capacity of Strut I was developed

during the first six cycles, the capacity was achieved at tensile displacements approximately

equal to the preceding compressive displacement applied.

Local buckling was observed at the middle of Strut I during cycle 3. Local buckles tended

to straighten out under tensile load, but reformed when compressive load was again applied.

Tears developed in the steel during cycle 5 owing to the large local strain reversals associated

with this behavior. Both strength and stiffness rapidly deteriorated during subsequent cycles

(Fig. 3.2).

The hysteretic curves for Strut 2 during cycles 1 through 5 (Fig. 3.3) are generally similar

to those for Strut 1. Since the diameter-to-thickness ratio of Strut 2 was smaller and the cross­

sectional area 44% greater, the tensile and compressive load capacities of Strut 2 were greater.

A slight ovaling of the cross-section at the midspan of Strut 2 occurred during the fourth cycle.

Local buckling developed in this region during the fifth cycle and tearing of the steel initiated

during the tension portion of cycle 8 (Fig. 3.4). As a consequence of the smaller diameter-to­

thickness ratio of Strut 2, local buckling was delayed and the strength of Strut 2 deteriorated

less than the strength of Strut 1 during later cycles.

The axial load vs. midspan lateral deflection curves for Struts 1 and 2 are given in Figs

3.15 and 3.16. These indicate that the initial camber in the two pinned-end specimens existing

prior to cycle 1 was nearly eliminated by tension yielding during the first cycle of loading.

Strut 3 was identical to Strut 1, except that the former was not annealed. Because the

yield strength of the material in the unannealed tube was very high, this specimen did not

buckle in cycle 1 (Fig. 3.5). First buckling of Strut 3 occurred in cycle 2, and the maximum

12

compressive load then achieved was only 85% of the buckling load predicted by the AISC and

API recommended formulas [10, Ill. Failure to attain the compressive capacity predicted by

the code is attributed to the rounded stress-strain curve of the unannealed material (Figs. 2.17

and 2.20). Strut 3 fractured during the tensile phase of cycle 3. The fracture occurred in the

heat-affected zone in the tubing adjacent to the weld. The strut was repaired and tested again

with tensile displacements limited to avoid re-fracture. Hysteretic loops for the post fracture

testing (cycles 4-8) are shifted so that compression loading of cycle 4 corresponds with elastic

tensile unloading of cycle 3. Compression displacements after cycle 4 differ from the prescribed

displacement loading history by the amount of the shift. Local buckling occurred at the mid­

length during cycle 4. Tearing occurred in the region of local buckling during the sixth loading

cycle even though tensile forces were limited after the third cycle. The strength and stiffness of

the specimen decreased substantially after local buckling was initiated (Fig. 3.6).

The geometric properties and end conditions of Strut 4 were identical to those of Strut 2,

but the former differed from Strut 2 in that it was unannealed. Although this strut was fabri­

cated from a heavier tube than was Strut 3, the compressive force attained was not as high. It

can be observed from the compression stub tests (Fig. 2.20) that the 0.120 in. (3.0mm) wall

thickness material has a notably rounded stress-strain curve and this would contribute to lower­

ing the buckling load of Strut 4. In addition, the imposed displacement during cycle 2 did not

suffice to develop the full buckling capacity of Strut 4; whereas the buckling load for cycle 3

was decreased due to the Bauschinger effect resulting from tension yielding during cycle 2 (Fig.

3.7). Similar to Strut 3, Strut 4 fractured during the tensile phase of cycle 3. Again, the strut

was repaired and testing resumed with cycle 4 at limited tensile displacements. No local buck­

ling was observed during testing of Strut 4. The hysteretic loops Jor cycle 5 through 10 were

remarkably stable because no local buckling occurred (Fig. 3.8).

The ductility ratio, as defined here, is the ratio of the maximum applied axial displace­

ment to the elastic displacement at initiation of tensile yielding of the gross section. The ductil­

ity ratios for the unannealed test specimens were only 38% and 45% of those for the annealed

13

specimens. Thus, the inelastic deformations of the unannealed specimens were less severe.

Moreover, tensile forces in Struts 3 and 4 were limited to avoid fracture at the welds. Because

of the reduced inelastic tensile stretching, the lateral displacement and inelastic rotation at the

midspan were less severe for the unannealed specimens. Local buckling of these struts was

delayed because of the lesser inelastic straining and therefore the deterioration of strength

differed from that of the annealed specimens.

Strut 5 was similar to Strut 1 except that its ends were fixed. The maximum compressive

load carried by this specimen, which occurred during load cycle 3, was within 2% of the value

predicted using the AISC formulas (Fig. 3.9). The deterioration of the buckling load and the

loss of energy dissipation capacities during subsequent loading cycles (Figs. 3.10 and 3.11) was

not as severe as exhibited by Strut 1. Local buckling was observed during cycle 5, first at the

foot and then at the midspan of the specimen. With additional cycling, the center hinge

deteriorated more quickly than that at the foot and eventually tore open in tension.

A pictorial history of the local buckling phenomenon is presented in Figs. 3.21 through

3.25 for Strut 5 as an example of the general local buckling behavior exhibited by all of the

struts. The overall buckled strut, depicted in Fig. 3.21, shows concentrations of rotations at the

locally buckled regions. Figures 3.22 through 3.25 show the evolution of local buckling,

straightening after tension, and eventual tearing in tension for the center and foot sections.

The maximum compressive load developed by the other fixed-end specimen, Strut 6, was

within 1% of the value predicted using the AISC formulas. When this compressive load was

reached during cycle 3, noticeable lateral buckling occurred, accompanied by a sudden loss of

about 5 kips (22.4 kN) (Fig. 3.12). Thereafter, the strength of the specimen deteriorated little

during cycles 4 through 10. During cycle 10, the specimen buckled locally at three locations:

first at the midspan, then at the head end, and finally at the foot. Continued loading through

cycle 16 resulted in deterioration of the compressive strength (Figs. 3.13 and 3.14).

The hysteretic curves for the fixed-end specimens differ considerably from those obtained

for the pinned-end specimens. The difference can be primarily attributed to the lower

14

slenderness ratio [8]. Both fixed-end specimens show larger enclosed areas and better energy

dissipation characteristics for the hysteretic curves as compared to those of the pinned-end

specimens. Post-buckling strength of the fixed-end specimens deteriorated less and the initial

stiffness for loading in tension were significantly higher.

The axial load vs. midspan lateral deflection curves for Struts 5 and 6 are given in Figs.

3.19 and 3.20. These midspan lateral deflections were about one-fifth of the values correspond­

ing to pinned-end specimens (Figs. 3.15 and 3.16) with the same axial displacement. These

smaller lateral deflections, and, hence, smaller plastic hinge rotations, helped delay local buck­

ling and maintain the strength of the fixed-end specimens during inelastic cycling. The

reported midspan lateral deflection for the fixed-end struts are displacement in the horizontal

plane. A vertical component of midspan lateral deflection also existed which measured approxi­

mately 25% and 15% of the horizontal components for Struts 5 and 6, respectively. The magni­

tude of vectorial sum of both components is approximated 3% and 1% higher than the magni­

tude of the horizontal component alone for Struts 5 and 6, respectively.

Normalized Load vs. Axial Displacement

To clarify the differences in behavior of the six specimens the load vs. axial displacement

plots for cycles 1 through 5 have been normalized by dividing the load and displacement, by Py

and By, respectively. These plots, shown in Figs. 3.26-3.28 emphasize the lower displacement

ductility levels of the loading histories for the unannealed struts. The unannealed struts exhi­

bited brittle behavior and could not sustain cycling at large tensile ductility levels. The reduced

compressive ductility levels for the unannealed struts are a consequence of the higher yield dis­

placements (By) The applied compressive displacements were approximately equal for all struts.

15

Deterioration of Buckling Loads

The difference in cyclic performance between struts is in part exemplified by the

deterioration of buckling loads. The cyclic buckling loads have been listed in Table 3.1 and are

graphically presented in normalized form in Fig. 3.29. This figure illustrates the superior per­

formance of the fixed-end struts over the pinned-end struts. Moreover, for each of three strut

pairs with D/t of 48 and 33, (pinned annealed, pinned unannealed, fixed annealed), the figure

shows that the struts with D/t=33 clearly outperformed the struts with D/t=48 in percentage

retainment of their original buckling load.

Deflected Shapes

The deflected shapes obtained from the photogrammetric data for the six struts are plotted

in Figs. 3.30 through 3.37. The deflections are deviations from the initial position at the begin­

ning of a test. The lateral deflections have been exaggerated to emphasize the shape.

The buckled shape of Strut I during cycles I and 2 (Fig. 3.30a and b) was sinusoidal.

During the compression stage of cycle 3, curvature concentrated within the center plastic region

(Fig. 3.30c). The deflected shape that remained after unloading in compression is shown in

Fig. 3.30d. The residual curvature that remained in the center region and the reverse curvature

adjacent thereto that developed while the specimen was loaded in tension is illustrated by Fig.

3.30e. During cycles 4, 5, and 6, the buckled shape of Strut I deteriorated due to local buck­

ling and residual curvature (Figs. 3.30f, g, h).

It was stated earlier that initial cambers were essentially removed by yielding in tension.

The small negative deflections seen in Fig. 3.3la for Strut 2, cycle 2, at load point A are due to

the removal of initial camber eccentricities by yielding in tension during the first loading cycle.

Although the deflected shape of Strut 2 during cycle 2 at load point C (Fig. 3.31 b) is

asymmetric, it gradually became symmetrical during cycles 3 and 4 (Figs. 3.31d and e). Resi­

dual curvature and deflection were evident by cycle 5 at point A (Fig. 3.310. The deflected

shape of the specimen gradually became irregular during cycles 5 through 8 (Figs.3.3lg and h).

16

The deflected shapes of the unannealed struts (Figs. 3.32 and 3.33) did not show a discer­

nible central plastic region in the early cycles. The deflected shape of Strut 3 was sinusoidal

until local buckling began (cycle 4), subsequently the curvature concentrated in the central

region (Fig. 3.33). The sinusoidal deflected shape of Strut 4 (Fig. 3.32) was remarkably regu­

lar throughout the test since no local buckling occurred.

The deflected shapes for the fixed-end Struts 5 and 6 are presented in Fig. 3.34 and 3.35.

Strut 5 had a asymmetric buckled shape (Fig. 3.34) with maximum deflections occurring off

center, closer to the foot end. Consequently, less inelastic rotations resulted at the head plastic

hinge and thus, this hinge did not develop local buckling. Strut 6 illustrates a classic fixed-fixed

buckled shape (Fig. 3.35). There was little deterioration in the shape through the first nine

cycles, since local buckling did not occur until cycle 10. For both fixed-end struts plastic rota­

tions can be noted at the ends of the members. These are plastic rotations occurring within the

member tubing. As mentioned previously, full fixity of the end plates was verified through

photogrammetric techniques.

The deflected shapes of individual specimens are compared in Fig. 3.36. The comparison

illustrates the following points:

a) For the same cycle and axial displacement, the deflected shape of the pinned-end,

thinner strut (D/t=48) shows a more irregular shape and greater concentrations of

plastic rotations than that of the thicker strut (D/t=33) (Fig. 3.36a).

b) The lateral deflection of the pinned-end specimen, Strut 2, was considerably greater

than that of the corresponding fixed-end specimen, Strut 6, at the same axial dis­

placement (Fig. 3.36b).

c) For the same cycle and compressive axial displacement, the lateral displacements of

the unannealed specimen, Strut 4, was 30% of that for the similar annealed speci­

men, Strut 2 {Fig. 3.36c).This is due to the lesser tensile stretching in the unan­

nealed specimens.

17

d) The difference between the tensile stretching of the annealed and unannealed struts

can be accounted for by considering the total travel of compressive axial displace­

ment from load point A to load point C. When plotted for equal amounts of total

compressive travel, the lateral deflections are approximately the same for both speci­

mens (Fig. 3.36d).

Further comparisons for deterioration in deflected shape are illustrated in Fig. 3.37. To

facilitate comparisons of changes in shape, the lateral displacements have been normalized by

the maximum lateral displacement in each cycle. The normalized deflected shapes for four of

the struts, plotted for cycles 3 and 6, emphasize the change in shape that occurred during those

three cycles of loading.

Energy Dissipation

Energy dissipation is an important response parameter for inelastic cyclic loading. The

energy dissipated during all loading cycles was measured for each of the six test struts from

their axial load vs. axial displacement plots; these values are listed in Table 3.3. The energy

dissipated during each loading cycle Ei was normalized by dividing it by the energy dissipation

of a nonbuckling, rigid-perfectly plastic element, RPi, with the same yield load (Py) and cycled

through the same displacements (See Fig. 3.38 insert). For purposes of this discussion, Ej/RPi'

is defined to be the energy dissipation efficiency of a test strut. Displacements and yield loads

as parameters are thus de-emphasized, which facilitates comparisons of energy dissipation

between struts with different displacement histories or yield loads. Moreover, the energy dissi­

pation of the rigid-perfectly plastic element represents the hypothetical maximum value for a

strut subjected to the same axial displacements. Thus, energy dissipation efficiencies are a

means of quantifying the deterioration of the capacity of a strut to dissipate energy with cycles.

The energy dissipation efficiency in each cycle (E/RPi) for the six test struts are listed in Table

3.3 as well as plotted in Fig. 3.38.

18

To facilitate comparisons of the energy dissipations, the cumulative sum of cycle dissipa­

tion efficiencies vs. cycle number are plotted in Fig. 3.39. Since the energy dissipation

efficiency of a rigid-perfectly plastic strut is equal to unity in each cycle, the cumulative dissipa­

tion efficiency is equal to the cycle number. In this way, the ordinate divided by the abscissa of

Fig. 3.39 represents the energy dissipation efficiency of the test struts cumulative over all

preceding cycles. The energy dissipation of the rigid-perfectly plastic element represents 100%

efficiency. The cumulative cycle dissipation efficiencies of an ideal elastic-perfectly plastic non­

buckling element were also calculated and plotted in Fig. 3.39.

The elastic-perfectly plastic element is useful for comparison. However, observe that dur­

ing early cycles of loading the test struts can dissipate more energy than the ideal elastic­

perfectly plastic element. For instance, prior to reaching the axial yield load the ideal elastic­

perfectly plastic nonbuckling element dissipates no energy. On the other hand, the test struts

may dissipate energy because of some inelastic material response or buckling.

The responses of the test struts with respect to efficiency of energy dissipation can be

grouped into three strut pairs with O/t of 48 and 33: pinned-unannealed, pinned-annealed,

and fixed-annealed (Fig.3.39). The response of each pair of specimens is similar until the later

loading cycles, at which time the specimens with a 0/t=48 prove less efficient. The cumula­

tive efficiency (ordinate divided by abscissa) of Struts 3 and 4 (pinned-unannealed specimens)

were the poorest, less than 22%. The cumulative efficiency of Struts 1 and 2 (pinned annealed

specimens) in cycle 3 was approximately 47% and 49%, respectively, and decreased to 31 % and

36% by cycle 7. The cumulative efficiency of Struts 5 and 6 (fixed-end specimens) was 37%

and 41% during cycle 3 and increased to 47% by cycle 7. The cumulative efficiency of the ideal

elastic-plastic element was 53% in cycle 3 and 70% in cycle 7.

The best energy dissipation of all test specimens was shown by Strut 6. The superior per­

formance of this strut is attributable to its fixed-ends and its lower O/t ratio. After nine cycles

of loading, the dissipation efficiency of Strut 6 was 65% of the efficiency of the ideal eJastic­

plastic element.

19

The quantification of the efficiency of a brace element in dissipating energy allows com­

parisons on the effectiveness of a braced frame to dissipate energy. As illustrated in Fig.3.38, a

properly detailed brace can absorb a significant amount of energy, although generally not as

efficiently as an ideal elastic-perfectly plastic element. A properly detailed beam in a moment­

resisting frame can at best be expected to behave as an elastic-perfectly plastic element. How­

ever, considering a braced frame and a moment resisting frame of similar geometry, and

designed for similar lateral loads, the braced frame will have the advantage of dissipating energy

at considerably lower values of frame lateral displacements.

20

CHAPTER 4

INELASTIC BEHAVIOR AT PLASTIC HINGES - ANNEALED STRUTS

For general structural design and analysis purposes, the overall behavior of the struts

described in Chapter 3 is of primary importance. Many of the aspects of this overall behavior

can be explained through study of the plastic hinge regions. In this chapter, data reduced from

the SR-4 strain gage readings will be examined and interpreted in an effort to gain insight into

variations in strain histories and local buckling phenomena.

Plots of several example strain gage readings are included in Appendix A (Figs. A.l

through A.22). Strain gage data have been reduced in a variety of ways in order to emphasize

certain aspects of response. The strains at a cross-section, for example, are reduced to cen­

troidal axial strains, cross sectional curvatures and subsequently to rotations over a length. All

data reduced from strain gage readings are reported only up to the point where local buckling is

detected. After local buckling has occurred, the strain gage readings near the section of local

buckling can neither be related to the centroidal axial strains nor to the cross-sectional curva­

tures. A knowledge of the inelastic strain history is important, because the material properties

of a strut and the development of local buckles are affected by the history of inelastic straining.

Local buckling is an extremely complex phenomenon. Data from tests on six strut speci­

mens hardly suffices as the basis from which the local buckling problem can be conclusively

resolved. In this report, parameters thought to be of importance in the evolution of local buck­

ling are analyzed. The underlying purpose is to present empirical data by which local buckling

can be estimated and, if possible, can later be incorporated into an analytical model of brace

behavior.

21

Basic Considerations of Brace Inelastic Buckling

The inelastic buckling of a strut results in the development of plastic hinges; that is,

regions where inelastic curvatures occur. The number of plastic hinges that will form in a given

strut is determined by the number of hinges required to form the collapse mechanism for that

strut. Thus, one plastic hinge forms in a pinned-end strut and three such hinges in a fixed-end

strut (Fig. 4.1). For purposes of these discussions, the center plastic hinge will be assumed to

consist of two equivalent plastic regions which extend from the section at which the inelastic

curvature is greatest to the sections where inelastic curvatures vanish. Using this definition, a

pinned-end strut may be said to have two equivalent plastic regions at the center (Fig. 4.1 a). At

the ends of a fixed-end strut, plastic regions are defined to extend from the specimen end plates

to those sections where inelastic curvatures have reduced to zero, and as for a pinned-end strut,

two more plastic regions can be identified at the center. On this basis a fixed-end strut may be

said to have four equivalent plastic regions (Fig. 4.1 b).

The static relationships between the axial force P, the fully plastic moment capacity Mp ,

and the midspan lateral deflection a for the ideal pinned-end and fixed-end struts are given in

Fig. 4.1. The plastic moment capacity Mp varies with the axial force P as given by the interac­

tion curves shown in Fig. 4.2.

The superior axial load vs. axial displacement performance of the fixed-end struts com­

pared to the pinned-end struts, noted in Chapter 3, can be explained with the aid of Figs. 4.1

and 4.2. According to the static equilibrium relationships, the PIMp ratio of a fixed-end strut is

double the PIMp ratio of a pinned-end strut, at equal midspan lateral deflections. For the same

size members with equal lateral displacement, the axial load capacity for a fixed-end strut is

larger than the axial load which can be carried by the pinned-end strut, but it is less than twice

as large because of the axial load-moment interaction (Fig. 4.2). The larger axial loads in the

fixed-end strut will cause an increase in the amount of compressive centroidal axial straining.

Increased compressive axial straining will result in a shorter centroidal axis length. If equal

compressive axial displacements are applied to both types of struts, the shorter centroidal axis

22

length of the fixed-end strut will result in lesser magnitudes of midspan lateral deflection for

this strut. Also, the reverse direction of curvature from the points of inflection to the ends of

the fixed-end strut, compared to the center portion of the strut (Fig. 4.1), will contribute to

lesser magnitudes of midspan lateral deflection. Consequently, the lesser midspan lateral

deflections that result when equal axial displacements are applied will further increase the axial

load capacity of the fixed-end strut relative to the pinned-end struct according to the static rela­

tionship. In agreement with these considerations, the experimentally observed midspan lateral

deflections of the fixed-end struts (reported in Chapter 3) were approximately one-fifth of the

magnitudes corresponding to pinned-end struts with the same axial displacements. Moreover,

the load carried by the fixed-end struts was larger as evidenced by the shape of the hysteretic

loops.

Curvature in Plastic Hinge Regions

Curvatures at a cross-section were calculated from the strain gage readings, by dividing

the difference of two strain gage readings by the distance between the gages. Plots of curva­

tures at a section are included in Appendix A, Figs. A.23 through A.59.

Strain readings were observed to differ up to 0.002 inlin. from an assumption of linear

strains within a cross-section. The variations from linear straining were investigated and attri­

buted to local bending within the wall of the tube. The variations due to local bending should

not exist at the mid-thickness of the tube wall. For the gross behavior of a cross-section the

assumption of plane sections remaining plane appears to be valid.

The strain gages were externally mounted on the tubes (Fig. 2.2). It was found that for

curvatures computed from two diametrically opposed strain gages the variations due to local

bending would cancel. Centroidal axial strains computed from two strain gages could include

variations up to 0.002 in.lin. due to local bending effects. For centroidal axial strains computed

from four strain gages the variations due to local bending would cancel.

23

Once a strut buckled, lateral buckling in subsequent cycles always occurred in the same

direction. Curvatures as reported in this discussion are established as positive for the directions

that result when a strut is in the primary buckled deflected shape. The lengtbs of plastic

regions for each cycle are measured as the regions where positive inelastic curvatures develop at

maximum compressive displacement. Curvatures for Strut 1 within the center plastic regions

are plotted in Figs. 4.3 and 4.4 at the load points that correspond to maximum compressive and

maximum tensile displacements, respectively. (For definition of load points see Fig. 2.l5a).

Similar plots for Strut 2 are shown in Figs. 4.5 and 4.6. Note, that these two struts differed

only in their wall thickness. The plastic hinge in Strut 1 extended beyond the strain-gaged

region and permitted data reduction for only one of the center plastic regions. The center of

the plastic hinge was chosen as the section with maximum curvature during cycle 1. The

reported data for Strut 2 are based on an average of both center plastic regions.

The following points can be summarized from the curvature plots for Struts 1 and 2:

1) Local buckling occurred at or adjacent to sections of maximum curvature.

2) Plastic hinges in Strut 2 (D/t=33) were approximately 36% shorter than those for

Strut 1 (D/t=48).

3) The magnitude of curvature within individual cycles was larger for Strut 2 than for

Strut 1.

4) Maximum curvatures at the onset of local buckling were 61% smaller for Strut 1

than for Strut 2.

5) The residual curvatures at maximum tensile displacement were larger for Strut 2

than for Strut 1.

Curvatures for Strut 5 are plotted in Figs. 4.7 and 4.8 for the foot plastic hinge region.

Similar plots for Strut 6 are shown in Figs. 4.9 and 4.10. Curvatures at load points for max­

imum compressive and tensile displacements are plotted for each cycle up to the load point of

local buckling. Foot hinge curvature results for Struts 5 and 6 can be summarized as follows:

24

1) Increased inelastic rotations are realized through a growth of plastic hinge length

rather than from greater curvature magnitudes.

2) Strut 6 (0/t=33) sustained maximum curvature excursions three times greater than

did Strut 5 (0/t=48) prior to local buckling.

3) For the first three loading cycles, Strut 5 did not buckle laterally, but did yield axi­

ally. Curvatures recorded for these cycles were apparently caused by adjusting to a

difference in angle between the strut and the end plate. No such curvatures were

observed in Strut 6.

For ideal symmetrically buckled struts with constant plastic moment capacity M p , the

moment gradient of a fixed-end strut is double that of a pinned-end strut of the same length.

The higher moment gradient should result in shorter plastic hinges for the idealized fixed-end

strut. However, the length of the plastic hinges of the test fixed-end struts were as long as the

plastic hinges of the pinned-end struts. (Tables 4.1 through 4.4). This can be attributed to

axial load-moment interaction. The higher axial loads in the fixed-end struts cause a reduction

in the plastic moment Mp capacity. A reduction in plastic moment will cause a reduction in the

moment gradient. Thus, a fixed-end strut could have equal or even smaller moment gradients

than a similar pinned-end strut. The length of the plastic hinge that will develop in either strut

will depend both on the moment gradient and the moment difference between the fully plastic

and first yield interaction curves (Fig. 4.2).

Detailed strain data were obtained only at the foot hinges for Struts 5 and 6. For ideal

symmetrically buckled fixed-end struts, the head and both center plastic regions should have

the same distribution of curvature as the foot plastic region. The test specimen were, of

course, not perfectly uniform and symmetric; initial imperfections, asymmetric buckling, slight

differences in end restraints, and welding effects contribute to differences in the distribution of

curvature. Although the distribution of curvature at the head, foot, and both center regions are

not precisely the same, the general characteristics of the different plastic regions should be simi­

lar.

25

Inelastic Rotations

Plastic hinge rotations were estimated from cross-section curvatures. The inelastic rota­

tions were obtained by integrating the cross-section curvatures (Fig. 4.3 through 4.10) over the

lengths of the plastic regions. Rotations for maximum displacement load points C and E are

listed in Tables 4.1 through 4.4. Rotations calculated at load points C and E include small elas­

tic rotations on the order of 0.003 rad./in. (0.118 rad/m.) as well as the inelastic rotations. The

magnitude of the elastic rotations is less than the accuracy of calculations (±0.005 rad.), thus

the inelastic rotations were taken equal to the total rotation.

The relation between inelastic rotation and maximum curvature is important in estimating

curvature when only rotation is known. The magnitude of rotation for maximum displacement

load points have been plotted against the maximum curvature within the plastic hinge (Fig.

4.1 1). Data from maximum tension and maximum compression load points have been

included in the same figure. While an accurate empirical relation cannot be developed from

these data, the plots serve to represent the rotation-curvature relation qualitatively.

The inelastic rotation excursion during a loading cycle is the difference between inelastic

rotations at load points C and E. Cumulative inelastic rotation is the sum of the absolute value

of the inelastic rotation excursions for both compressive and tensile loadings. The cumulative

rotation is a measure of the total flexural deformations at the plastic hinge. Cumulative inelas­

tic rotations are also listed in Tables 4.1 and 4.4. Significance of these calculations may be sum­

marized as follows:

1) Larger cumulative inelastic rotations occurred prior to local buckling for the plastic

regions of struts with a D/t=33 than for those of struts with a D/t=48.

2) Almost twice as much (190%) inelastic rotation was accumulated at the foot region

of fixed-end Strut 6 (D/t=33) than at the center region of pinned-end Strut 2

(D/t=33) before local buckling occurred.

26

3) At the foot region of fixed-end Strut 5 (D/t=48) the accumulated inelastic rotation

was 0.55 times that which occurred at the center hinge of pinned-end Strut 1

(D/t=48). This is an opposite trend to that in Struts 6 and 2, although in both

fixed-end struts local buckling occurs at a later cycle.

In summary, the cumulative inelastic rotations alone do not show a direct relation to the

occurrence of local buckling. One must conclude that other factors, such as curvatures and

strains, could be important parameters affecting the development of local buckling. These

parameters will be quantitatively examined in the following section.

Cumulative Curvature arud Centroidal Axial Strain

Cumulative inelastic curvature is defined as the sum of the absolute value of inelastic cur­

vature excursions for both compressive and tensile loading. Cumulative inelastic centroidal

axial strain is defined in an analogous manner.

Centroidal axial strain and cross sectional curvature completely define the strain distribu­

tion at a cross-section if it is assumed that plane sections remain plane. Accordingly, cumula­

tive inelastic centroidal axial strain and cumulative inelastic curvature are a measure of the ine­

lastic history for the entire cross-section. The material properties of the strut are affected by

inelastic straining and the inelastic strain history is important in the development of local buck­

les.

Inelastic curvature excursions and inelastic centroidal axial strain excursions have been

summed from the initial load points up to the first occurrence of local buckling. Cumulative

inelastic curvatures within plastic hinges are plotted in Figs. 4.12 to 4.15. The cumulative ine­

lastic centroidal axial strains along the lengths of the struts are plotted in Figs. 4.16 to 4.19.

The following observations can be made from these figures:

27

1) The axial strain along the struts was highly nonuniform; almost all inelastic axial

strain occurred in the plastic hinge regions.

2) In Struts 1 and 2 the section of maximum cumulative curvature at the center hinges

occurred near the centerline of the strut for all cycles, but varied Slightly in its loca­

tion for different cycles. In Struts 5 and 6 for all cycles the cumulative curvature at

the foot hinges occurred at a section nearest to the end plate.

3) The section of maximum cumulative axial strain occurred at the same section as the

maximum cumulative curvature for 96% of the load points plotted.

4) Local buckling occurred at the section where cumulative curvature was the max­

imum at some time during the loading history.

5) Inelastic curvatures can occur in early cycles near the end plates to accommodate

any slight initial difference in angle between the strut and the end plate. Such ine­

lastic curvature may also induce axial straining of the strut centroidal axis near the

end plates. During early loading cycles, such curvatures and axial strains were noted

in Strut 5.

The similar pattern in the cumulative axial strain and curvature graphs can be explained

from considerations of static equilibrium. The greater the inelastic curvature, the smaller is the

available effective area for resisting applied axial load. Since the axial load is equal along the

strut length, at the sections where the curvature is highest a greater axial strain must take place.

Hence, the cumulative axial strain gives an indication of the extent of inelastic curvature that

has occurred at a section. The relationship between axial load capacity and moment capacity at

a cross-section was noted previously in the section on basic considerations.

Occurrence of Local Buckling

API Recommendations state that braces with a diameter-to-wall thickness ratio of less

than 1300/F, are fully compact sections capable of developing their full plastic capacity through

large inelastic deformations [11]. Struts 2 and 6, with a D/t ratio of 33, are compact section

28

under this definition, but during severe cyclic loading developed local buckling and lost capa­

city. Criteria based on monotonic loading are not sufficient to preclude such local buckling of

braces under severe cyclic loading. According to API Recommendations, Struts 1 and 5, with a

O/t ratio of 48 should be capable of developing their full plastic load capacity, but only through

limited plastic rotations. These struts with a O/t of 48 did buckle locally before the similar

struts with O/t of 33. All of the annealed struts were able to develop their full plastic load

capacity prior to local buckling.

A summary of several parameters measured at the first occurrence of local buckling is

presented in Table 4.5. Cumulative inelastic curvature, axial strain, and compressive fiber

strain are reported for the four annealed struts at the section of local buckling. The location of

the compressive fiber is taken as the point where local buckling developed; the strain history for

this fiber is more severe than for any other fiber in the cross-section. Cumulative inelastic

strain and curvature are important parameters of strain history, but do not completely define it.

The magnitude of inelastic curvature excursions is also important. The maximum curvature

excursion is included in the table. The physical ramifications of this parameter imply that a

strut will respond differently to a few large cycles than it will to many small cycles, even if the

total cumulative inelastic deformation is the same. Also included in Table 4.5 are the strut

loads at the onset of local buckling and the cumulative energy dissipation. Conclusions which

can be reached from this table of strut parameters measured at the onset of local buckling are

as follows:

1) The struts with O/t of 48 buckled locally at approximately half the cumulative ine­

lastic axial strain and compressive fiber strain compared to the struts with a O/t of

33.

2) Larger maximum curvature excursions result in lesser cumulative inelastic strains at

local buckling.

29

3) The fixed-end Struts 5 and 6 accumulated 112% and 170% more axial strain, respec­

tively, than the corresponding pinned-end Struts 1 and 2.

4) The fixed-end Struts 5 and 6 dissipated 206% and 293% more energy, respectively,

than the corresponding pinned-end Struts 1 and 2. That the fixed-end struts dissi­

pate more energy than the pinned-end struts could be expected from the fact that

they have 4 equivalent plastic regions versus 2 such plastic regions for the pinned­

end struts. When only one-half of the total energy dissipation for the fixed-end

struts is considered, Struts 5 and 6 still dissipated 53% and 96% more energy than

the corresponding pinned-end Struts 1 and 2.

5) Struts 2 and 6 with O/t ratios of 33 dissipated 215% and 304% more energy, respec­

tively, than the corresponding Struts 1 and 5 with O/t ratios of 48. Higher energy

dissipations are to be expected because of the higher yield loads. If the energy dissi­

pations are divided by the yield load, thus removing yield load as a parameter, Struts

2 and 6 (0/t=33) still dissipated 119% and 183% more energy than Struts 1 and 5

(0/t=48).

From the information in the table it can be concluded that cumulative strain, cumulative

curvature, maximum curvature excursions, and energy dissipation are important in local buck­

ling. These parameters could be used to estimate the onset of local buckling in braces of simi­

lar cross-sections. However, not enough cases have been tested to adequately develop an

empirical relationship between local buckling and the parameters examined.

Once local buckling does occur, the deterioration of the brace capacity is controlled by the

local buckled region. Inelastic rotations after local buckling cause further deterioration in the

strength of the locally buckled section thereby reducing the strut capacity. Cumulative inelastic

rotations after local buckling were calculated from photogrammetric data. An empirical rela­

tionship between compressive capacity and cumulative inelastic rotation for pinned-end struts is

indicated in Fig. 4.20. Such empirical relations can be used to model the strut capacities after

local buckling. The cumulative brace energy dissipations (Table 3.3) could also serve as a

30

similar empirical parameter for local buckling. An analytical method of predicting compressive

cyclic capacity of struts before the onset of local buckling is presented in the next chapter.

31

CHAPTER 5

PREDICTION OF BUCKLING LOADS - ANNEALED STRUTS

It was observed in the experiments that the buckling load capacity of a column

deteriorates with each successive inelastic load cycle. While design code formulas prediet the

first buckling loads of columns, an alternative formulation is required to predict the reduced

buckling loads of columns or braces which have experienced previous inelastic straining.

The basic theory for predicting the first inelastic buckling loads of a column may be

credited to Engesser who first proposed a solution to this problem in 1889 [17]. Current design

code formulas employing similar methods have been verified by numerous experiments and can

be used with confidence to compute the initial buckling load of a column or brace. It must be

recognized, however, that the code formulas are for columns which have not been previously

yielded and with initial camber within the code allowances. A structure subjected to severe

earthquake, wind, or wave loadings, may develop yielding or buckling in the braces and

columns. The capacities of such structures could significantly reduce during and following such

loadings.

A large residual camber, resulting from a previous buckling excursion, is one reason to

expect a reduced buckling capacity in a subsequent buckling cycle. Not as apparent, but equally

important, is the fact that previous inelastic straining of a member will alter the mechanical pro­

perties of the material thereby causing a reduction in the compressive load carrying capacity. A

column that has experienced only tensile yielding or a buckled column that has been re­

straightened by tensile yielding will exhibit a reduced buckling load capacity as a result of these

changes. The extent of the changes depends on the inelastic strain history to which the column

has been subjected. The changes in the material stress-strain relationship due to previous ine­

lastic strains and strain reversals, commonly referred to as the Bauschinger effect, must be

accounted for in calculating the cyclic buckling capacity of columns. Development of cyclic

constitutive material property models for predicting changes in the material properties is a sub­

ject of current active research I161.

32

The prediction of buckling loads specified by the AISC has its theoretical basis in the

tangent modulus concept. According to this approach [l7] a column of homogeneous material

exhibiting nonlinear stress-strain properties will experience bifurcation of the equilibrium state

when the average axial stress, P/ A, is equal to:

p rr 2 E,er('l = A = (kL/r)2 (S.l)

Where E" the tangent modulus, is the slope der/ de of the stress-strain curve at the stress er ('I'

In the elastic range of material behavior this equation results in the Euler column load.

The AISC provisions for columns are given by two formulas [lO].

F = 12 rr2E . f /or kL r ~ C"

a 23 (kL/r)2'(S.2a)

where

[1 _ (kL/ r )2]F'

2C} J

Fa = -------''-------=-------:-1 + ~ (kL/r) _1 (kL/r)3 '3 8 C" 8 C}

for kL/r < Cc (S,2b)

d[l + ~ (kL/r)

an 3 8 Cc

1 (kL / r ) 3]. . bl f f8 3' IS a vana e sa ety actor.C"

The first formula (Eq. S.2a) for columns with large slenderness ratios, is applicable in the

elastic range of material behavior; the other (Eq. S.2b), is a parabolic approximation for a solu-

tion based on a variable tangent modulus. This second formula is applicable to stockier

columns and is suitable for residual stress distributions and material stress-strain relationships

typical of steel column sections used in the building industry. When the residual stress distri-

bution or the material stress-strain properties differ from those assumed in AISC formulas, it is

more accurate to determine the true stress-strain properties and to use the tangent modulus

33

formula for predicting buckling loads. The stress-strain properties should realistically account

for the residual stresses. For a previously buckled or yielded column both the material proper­

ties and the residual stress distribution differ from those assumed in the AISC formula. It will

be shown in the following section that a generalized tangent modulus approach can be

developed which will account for the degradation of compressive load capacity due to changes

in material properties of inelastically cycled columns, if a proper representation of the material

stress-strain relation is made.

A Generalized Tangent Modulus Procedure

The tangent modulus method assumes that the material of a column under consideration

is homogeneous. This assumption is not strictly true for an inelastically cycled column because

the inelastic strain history varies both within a cross-section and along the length of the

member and thus the material properties also vary. However, a critical section within the plas­

tic hinge of the column can be chosen that has material properties which may be assumed to

control the buckling load. The deteriorating load capacity of a column can be reasonably well

estimated if the changing material properties that correspond to the critical section are taken

into account.

These changes in material properties are related to the Bauschinger effect. The Bausch­

inger effect is an indication of the fact that the stress-strain curve becomes more rounded after

inelastic strain reversals (Fig. 2.2l). Within the rounded region, the tangent modulus of the

material at a given stress level is smaller when compared to that of the virgin material stress­

strain curve. Since the critical buckling stress is, according to Eq. 5.1, directly proportional to

the tangent modulus (holding all other parameters constant), it too will decrease. Typically, the

more severe the inelastic straining to which a material has been subjected, the more rounded

the stress-strain curve will become, and a column of this material will buckle at lower axial

loads.

34

Once buckling occurs, the material properties of the plastic hinge would be expected to

control the buckling load since these sections experience the most severe strain histories.

Thus, the critical section would lie within the plastic hinge region. The critical section is

chosen as the one with the most severe centroidal axial strain history. A close relationship

between centroidal axial strain and cross-section curvature has been noted previously in Chapter

4.

Once the critical cross-section has been identified the most representative strain history

within the cross-section must be chosen. To do this it will be assumed that the amount of

Bauschinger effect that results in the material is related to the cumulative sum of the inelastic

strains. Consider, for example, the critical cross-section of Strut 2 (strain gages 9, 10, 11, and

12 - Figs. A.6 and A. 7). During the first four cycles gage 10 located at the extreme tensile fiber

accumulates 0.026 in./in. inelastic strain, and the extreme compressive fiber at gage 12 accumu­

lates 0.112 in./in. inelastic strain. This strain pattern is similar to that for the plastic hinge

regions of the other struts tested -- that is, the compressive fibers experienced a more severe

strain history than the tensile fibers. Therefore, within the same member cross-section the

stress-strain curve for the compressive fiber would be more rounded than that for the tensile

fiber, and the compressive fiber would exhibit smal1er tangent moduli at equal stresses. The

centroidal fibers underwent an intermediate level of inelastic straining, 0.041 in./in. (average of

strain for gages 9 and 11).

Since the tangent modulus method considers only a single material relationship, the strain

history of the centroidal fiber (centroidal axial strain) is chosen to represent the material

behavior for the strut. The centroidal axial strain history represents an average of the material

properties for the critical cross-section. Moreover, for the purpose of applying the tangent

modulus theory of buckling, it is assumed in this treatment that the material properties at the

centroid of the critical section apply for the entire column.

The material properties used to determine the tangent modulus E, have been determined

from experimentally obtained stress-strain curves. The stress-strain curves from compression

35

tests on pipe stubs were used to predict the first buckling load of virgin struts. Stress-strain

curves from cyclic tests on short lengths of pipes were used to predict material properties and

buckling loads once the struts have undergone inelastic straining. Alternatively, the material

properties could be obtained by analytical means, if a comprehensive cyclic material constitutive

law with sufficient accuracy in predicting the first derivative is available.

Prediction of First Buckling Load

In Table 5.1, the first buckling loads as calculated by the tangent modulus method and by

AISC formulae are listed, along with the buckling loads observed during testing. The AISC­

predicted loads do not include the customary safety factor, and Fr = 31 ksi was used as

obtained from the material tests on pipe stubs.

The tangent modulus predictions of the first buckling loads for the struts with no previous

inelastic straining are based on stress-strain curves from the compression tests of pipe stubs

(Fig. 2.19). These curves exhibit classic elastic-perfectly plastic behavior. This was also true

for the coupon tests (Fig. 2.16), and the first loading of the cyclic test (Fig. 2.2l)

As noted in Chapter 3, strut 1 experienced inelastic straining prior to cycle 1. The buck­

ling load predicted for Strut 1 using the tangent modulus method (Table S.l) is based on the

stress-strain relationships for material with previous inelastic straining. The AISC formula,

which does not account for the effects of previous inelastic straining, predicted a higher load.

The method employed to estimate the reduction in buckling capacity because of changes in

material properties due to inelastic straining is discussed below.

Deterioration of Buckling Loads

As noted earlier, when inelastic strain reversals occur, a change in the stress-strain rela­

tionship of the material results. Therefore, the first step in predicting the deterioration of buck·

ling loads under cyclic loading is to devise a means of determining the material properties as a

function of inelastic strain history.

36

A cyclic test on a short pipe specimen of annealed material provides the characteristic

stress-strain curves for inelasticity cycled material. However, since the strain history of each

individual strut was different from that of the cyclic material test, strut strain histories must

somehow be related to the cyclic material test. This was done by matching the amount of

cumulative inelastic straining.

The basic cyclic material test (Figs. 2.21 and 5. I) can be best utilized when considered as

three separate curves. The portion of the cyclic test identified in these figures as curve 1 is a

stress-strain curve for previously unyielded (virgin) material. Note, that the compression test

curve (Fig. 2.19) and the cyclic test curve 1 are essentially the same. Cyclic test curve 2 is a

stress-strain curve for a material which had a previous inelastic tensile strain excursion of

0.0056 in.lin.. Cyclic test curve 3 is a stress-strain curve for a material which had an inelastic

tensile strain excursion of 0.0056 in./in. and an inelastic compressive strain excursion of

0.0104in.lin. resulting in a previous cumulative inelastic strain of 0.0160 in.lin .. Each succes­

sive curve corresponds to an increased cumulative inelastic strain (CIS) as well as to an increase

in the magnitude of strain excursion. In the experiments the struts were loaded such that the

maximum inelastic strain excursion in each successive cycle also increased. The increasing

magnitudes of strain excursions tend to accentuate the Bauschinger effect in each successive

cycle of either the strut loading, or material test.

The compression and cyclic test stress-strain relations for three different values of previ­

ous cumulative inelastic strain are used to develop data for predicting cyclic buckling loads of

the struts. For this purpose, tangent moduli for the three available stress-strain curves are

determined and plotted versus the corresponding stresses (Fig. 5.2), and Eq. 5.1 is rearranged

to yield the critical slenderness ratio in terms of the corresponding stress and tangent modulus:

(5.3)

Using Eq. 5.3 and Fig.5.2 the column curves shown in Fig. 5.3 have been constructed. From

these curves three different values of critical stress, each corresponding to a different value of

37

cumulative inelastic strain, can be obtained for a given slenderness ratio kLir. In Figs. 5.4a and

5.4b the variation of the critical stress as predicted by the tangent modulus method is plotted

versus the cumulative inelastic strain for column slenderness ratios of 25 and 54, respectively.

The experimentally observed critical stresses for the struts with the same slenderness ratios are

also plotted in these figures.

Critical stresses for the struts for any given cycle of loading prior to local buckling are

estimated by entering Fig. 5.4 with the total inelastic strain accumulated during preceding

cycles. The predicted buckling loads are given in Table 5.2. The curves in Fig. 5.4 clearly show

that the critical stresses decrease with increasing cumulative inelastic strain. For the annealed

struts (Struts 1,2,5, and 6), the experimentally observed critical stresses are in reasonably good

agreement with the predicted values.

The experimental results clearly demonstrate that the compressive load capacity of struts

deteriorates with inelastic cycling. The conventional AISC formulas by which column buckling

loads are predicted do not account for this deterioration under inelastic cycling and therefore

should not be used to predict column response for such conditions. The cyclic buckling load of

struts determined using the generalized tangent modulus method were in good agreement with

experimental values. (Table 5.2).

Observations on predicting the buckling loads of struts subjected to inelastic cycling as

described in this report can be summarized as follows:

1) Accurate information on the material properties under inelastic cyclic loading is

essential.

2) The procedure described does not apply after local buckling occurs.

3) The tangent modulus concept assumes the material properties of the column are

homogeneous. The strain history used for determining the material properties is

taken from the section within the plastic hinge region that has undergone the most

severe straining.

38

4) The inelastic strain history that best represents the average material properties of the

critical cross-section is that of the centroidal fiber.

5) Inelastic axial strain is related to inelastic curvature at a section.

6) Inelastic axial strain varies considerably along the length of a column. The average

axial strain (total deformation divided by a total column length) is not sufficient to

define the material properties of the critical section.

The generalized tangent modulus procedure described above provides an estimate in the

reduction of the buckling capacity of a column due to changes in the material properties. The

buckling capacity of a column will also reduce due to a large residual camber. If there is a

significant residual camber after load applications a reduction in the buckling capacity for

camber must also be applied. The loading sequence of the experimental struts was such that

the residual cambers were relatively small in the early cycles. In each cycle, compressive loads

were followed by tension yielding excursions of sufficient magnitude to re-straighten the

member. The axial load vs. midspan lateral deflection plots are given in Figs. 3.15, 3.16, 3.19

and 3.20 for the annealed struts.

For cycles in which buckling load predictions were made, Struts 1 and 6 actually had less

residual camber in later cycles than they did prior to cycle 1. Struts 2 and 5 had maximum resi­

dual cambers of 0.20 in. (5 mm) and 0.05 in. (l mm), respectively, for cycles in which buck­

ling predictions were made. These residual cambers were considered small and a camber reduc­

tion factor to the estimated buckling load was not applied. A method for estimating the reduc­

tion factor for residual camber is given in Ref. 9.

The generalized tangent modulus procedure for estimating reductions in the buckling

capacity of columns due to changes in material properties is applicable up to the point of local

buckling. Since local buckling is a major concern in thin-walled pipes, the predictions of cyclic

buckling loads for the test struts had this limitation.

39

CHAPTER 6

INELASTIC BEHAVIOR OF THE UNANNEALED STRUTS

The inelastic behavior of the unannealed struts is sufficiently different from that of the

annealed ones to be treated separately. The mechanical properties of the unannealed material

significantly differed from those for the annealed material as is evident from the coupon tests

(Fig. 2.18). These material properties also differ significantly from those found in members

used in the building and offshore industries. Therefore, the behavior of these unannealed

struts is of limited interest and a detailed study of their inelastic behavior was not pursued.

Characteristics of the Material Properties

The Drawn-aver-Mandril process utilized in manufacturing the pipes used in the experi­

ments imparts a high degree of work hardening into the steel. Some of the struts 0, 2, 5, and

6) were annealed to relieve this work hardening so that their material properties more closely

represent those of full scale structural members used in construction. The as received struts (3

and 4) were tested to evaluate the necessity of annealing the test specimens to be representa­

tive of the behavior of large pipes. The structural inelastic responses of the unannealed struts

were found to be significantly different from those of the annealed struts (Figs. 3.26 and 3.27).

Using a 0.2% offset strain, the coupon tests of the unannealed material indicate (J'y was 92

ksi (635 MPa) for the 0.083 in. (2.1 mm) wall thickness, and 74 ksi (511 MPa) for the 0.0120

in. (3.0 mm) wall thickness. These are 197% and 139% higher than the yield strengths of the

annealed material.

Stress-strain curves for unannealed material coupons, cyclic stub specimens, and compres­

sion stub tests are shown in Figs. 6.1 and 6.2. Because of the high degree of work hardening

already existing in the steel, the stress-strain curves differ with each pipe sample, type of test

employed and the direction of loading. For example, at a strain of 0.006 in.lin. on the thinner

walled pipe (Fig. 6.1) stresses from different tests range from 71 ksi (490 MPa) to 94 ksi (649

MPa). Therefore, a large scatter exists in the material stress-strain curves, both in stress and in

40

tangent modulus Et at any given strain level.

Prediction of Buckling Loads

As discussed in the previous chapter, estimations of the deterioration oT buckling loads

under cyclic loading depends on the ability to determine changes in material properties. For the

unannealed struts the increase in inelastic strain due to the applied cyclic strains is a small per­

centage of the inelastic strain already induced by the manufacturing process. Nevertheless, the

generalized tangent modulus procedure was applied to the unannealed struts, and the results are

presented in Table 6.1.

Tangent modulus predictions of the first buckling loads are given in Table 6.1a along with

the actual buckling loads and the buckling loads given by the AISC formulae. (Note, first buck­

ling of Struts 3 and 4 occurs in cycle 2.) The AISC load predictions are based on the yield

stresses determined by the 0.2% offset strain method for the coupon test results. The first

buckling loads for Struts 3 and 4 were 15% and 35%, respectively, below those given by the

AISC formulae.

As can be seen from Figs. 6.1 and 6.2, compression tests on the unannealed pipe show a

more rounded stress-strain curve and lower stress levels for a greater strain compared to the

coupon tensile tests. The tangent modulus method using the compression stub test stress-strain

curves predicts the first cycle buckling loads for Struts 3 and 4 to within 4% and 3% respec­

tively, of the actual values. The full cross-section compression tests include residual stress

effects present in the unannealed material.

Estimates of buckling loads in later cycles are based on the material stress-strain curves

obtained from the unannealed cyclic stub tests. Column curves for predicting the critical

stresses, Figs. 6.3 and 6.4, were prepared in the same way as for the annealed struts. These

curves were used to predict cyclic buckling loads for Struts 3 and 4. For example, the amount

of cumulative inelastic strain for the cyclic stub test curve 3 was matched with a similar amount

of cumulative inelastic strain for a cycle of the strut tests (Table 6.1 b). The loads predicted

41

using the corresponding tangent modulus were not in agreement with the actual loads. For

Strut 4 the buckling load for cycle 5 predicted using the cyclic material test results was higher

than the predicted load for cycle 2 using the compression test. The reason is the higher yield

stresses of the cyclic test. Note that all three curves of the cyclic stub test for the thick walled

material show yielding at significantly higher stress levels than the compression stub test (Fig.

6.2). Also, cyclic curve 3 for tension loading shows yielding at higher stress levels than cyclic

curve 2 for compression loading. Thus, the scatter in the material stress-strain curves due to

different sample of pipe and directions of loading are greater than the changes in the material

properties resulting from the cyclic loading.

To properly apply the generalized tangent modulus procedure as presented in Chapter 5,

to the unannealed struts, a considerably more comprehensive cyclic material test program would

be required. Since it appears that the unannealed struts do not realistically represent actual

tubular members used in practice, such a further evaluation is not warranted.

42

CHAPTER 7

CONCLUSIONS

The struts discussed in this report are grouped into three different pairs: pinned-end

annealed, pinned-end unannealed, and fixed-end annealed. Each pair consists of one strut with

a D/t of 48 and one with a D/t of 33. Based on the reported experimental results and their

evaluation, several important conclusions can be reached. These can be summarized as follows:

1) For all three pairs, the struts with D/t of 33 clearly out performed the ones with D/t

of 48 in percentage retainment of their original buckling load.

2) Local buckling of thin walled pipes greatly contributes to their deterioration. The

onset of local buckling is followed by a rapid deterioration in the overall structural

response of a strut with continued cyclic loadings. For all three pairs, local buckling

occurred later in the struts with D/t of 33 than in the struts with D/t of 48. Hence,

in the design of tubular structures for seismically active regions, bracing members

with the lower D/t ratio are preferable for avoiding local failures under repeated

cyclic loadings.

3) Cyclic inelastic load applications can cause local buckling and loss of capacity of

tubular members that, under API recommendations, are considered to be adequate

for maintaining their capacity through substantial concentrated inelastic deformation

(D/t::::;; 1300/Fy)' Hence, API criteria, based on monotonic loading, do not neces­

sarily preclude local buckling of tubular braces under severe cyclic loading.

4) Brace end conditions have a significant effect on the overall structural response of

strut members subjected to cyclic loadings. The responses of fixed-end pair of

braces showed less pinched hysteretic loops, slower deterioration of buckling capa­

city, delayed onset of local buckling and improved efficiency in energy dissipation

compared to those of the pinned-end braces. The superior performance of the

fixed-end struts is attributed to their lower kUr ratio.

43

5) In simulating the behavior of real braces using reduced-scale models, the steel tubes

must be annealed before testing. In small tubes the steel in the as-received condi­

tion may be highly work-hardened, and the stress-strain curves for such a material

bear little resemblance to the A36 steel used in the field. By annealing the speci­

mens, the typical mechanical behavior for mild steel is restored. Although residual

stresses associated with manufacture of large diameter welded tubing are not

present, the annealed tubing are more realistic than the as received material. The

pair of braces tested in the as-received condition proved to be too brittle to sustain

cyclic loading at large inelastic ductility levels, and failed in the welded regions. The

difference in the mechanical material properties of the unannealed pair caused a

significant difference in their overall structural response. Normalized axial loads and

axial displacements obtained by dividing the loads and displacements by the yield

loads and the yield displacements, respectively, are not sufficient to account for the

observed difference in cyclic response caused by the difference in material proper­

ties.

6) Cyclic inelastic loading causes changes in the mechanical properties of the material

in a strut which tend to reduce the strut's buckling load. If the changes in the

material properties can be adequately assessed, the reduction in the buckling load

can be estimated using the generalized tangent modulus procedure described in

Chapter 5. If the cyclic load applications result in increased residual brace cambers,

a camber reduction factor must also be applied [9].

Recommendations for Future Research

As previously stated, local buckling is a major concern for the thin-walled tubular braces

typical of those employed in braced steel structures. Local buckling can be expected in

members subjected to the large axial deformations which may be encountered during an excep­

tionally severe earthquake. The phenomenon of local buckling has not been isolated in this

44

investigation, nor studied in sufficient detail to accurately estimate its onset and effect on subse­

quent deterioration in brace capacity. Full size local buckling tests of tubular sections under

cyclic load application accompanied by analytical studies are suggested for investigating this

problem.

Realistic analytical models of brace elements are essential for accurate prediction of the

response of braced steel structures subjected to severe earthquake ground motions. Several

analytical models have previously been employed to represent the inelastic cyclic behavior of

bracing members [3, 5, 13, 151. In the light of new experimental data, these analytical models

should be re-examined and, if necessary, improved to better represent cyclic brace behavior.

Since the hysteretic response of a brace element is strongly dependent on the kL/r ratio, an

analytical model should account for this fact in a realistic manner. The reduction in buckling

load with cyclic load applications should be included in such a model.

45

REFERENCES

1. Sozen, M. A. and Roesset, J., "Structural Damage Caused by the 1976 Guatemala Earth­quake," Structural Research Series No. 426, University of Illinois, Urbana, Champaign,March 1976.

2. Popov, E. P., Takanashi, K., and Roeder, C. W., "Structural Steel Bracing Systems:Behavior Under Cyclic Loading," EERC Report No. 76-17, Earthquake EngineeringResearch Center, University of California, Berkeley, June 1976.

3. Roeder, C. W., and Popov, E. P., "Inelastic Behavior of Eccentrically Braced FramesUnder Cyclic Loading," EERC Report No. 77-18, Earthquake Engineering ResearchCenter, University of California, Berkeley, CA, August 1977.

4. Popov, E. P., and Roeder, C. W., "A Structural Support System for Long Span Roofs inSeismic Regions," Proceedings, AISS Conference, Alma-Ata, USSR. Vol. 2, Mir Publish­ers, 1977, pp. 274-281.

5. Nilforoushan, R., "Seismic Behavior of Multi-Story K-Braced Frame Structures," Universityof Michigan Research Report UMEE 73R9, November, 1973.

6. Hanson, R. D., Goel, S. C., And Berg, G. V., "Seismic Behavior of Staggered TrussFraming Systems - Design Procedure for Earthquake Loading," University of MichiganResearch Report UMEEE No. 175, January 1973.

7. Shign, P., "Seismic Behavior of Braces and Braced Steel Frames," University of MichiganResearch Report UMEE 77R1, July 1977.

8. Jain, A. L., Goel, S. C., and Hanson, R. D., "Hysteresis Behavior of Bracing Membersand Seismic Response of Braced Frames with Different Proportions," University of Michi­gan Research Report UMEE 78R3, July 1978.

9. Popov, E. P., "Inelastic Behavior of Steel Braces Under Cyclic Loading," Proceedings, 2ndU.S. National Conference on Earthquake Engineering, Stanford University, CA, Aug. 1979.

10. American Institute of Steel Construction, Manual of Steel Construction, Seventh Edition,New York, 1970.

11. American Petroleum Institute, "Recommended Practice for Planning, Designing, andConstructing Fixed Offshore Platforms," Dallas, Texas, Ninth Edition, November, 1977;Tenth Edition, March 1979.

12. Gates, W. E., Marshall, P. W., and Mahin, S. A., "Analytical Methods for Determiningthe Ultimate Earthquake Resistance of Fixed Offshore Structures," Proceedings, OffshoreTechnology Conference, Houston, Texas, 1977.

46

13. Jain, A. K. and Goel, S. C., "Hysteresis Models for Steel Members Subjected to CyclicBuckling or Cyclic End Moments and Buckling," University of Michigan Research ReportUMEE 78R6, December 1978.

14. Sherman, D. R., "Cyclic Inelastic Behavior of Beam Columns and Struts," Preprint 3302,ASCE Convention and Exposition, Chicago, October 1978.

15. Marshall, P. W., Gates, William E., and Anagnostopoulos, Stavros, "Inelastic DynamicAnalysis of Tubular Offshore Structures," Proceedings, Offshore Technology Conference,Houston, Texas, 1977.

16 Popov, Egor P. and Ortiz, Miguel, "Macroscopic and Microscopic Cyclic Metal Plasticity,"Proceedings, Third Engineering Mechanics Specialty Conference, ASCE, Austin, Texas,September 1979.

17. Galambos, Theodore, Y., Structural Members and Frames, Prentice-Hall, 1968.

47

II::>OJ

Wall Initial Camber

Strut End Heat ThicknessDlt kL in. (rom)

Conditions Treatment in. (rrnn) rHorizontal Vertical

(1) (2) (3) (4) (5) (6) (7) (8)

1 Pinned Annealed 0.083 (2.1) 48 54 0.25 (6.4) 0.00 (0.0)

2 Pinned Annealed 0.120 (3.1) 33 54 0.06 (1.5) 0.03 (0.8)

3 Pinned As Received 0.083 (2.1) 48 54 o. 00 (0. 0) 0.00 (0.0)

4 Pinned As Received 0.120 (3.1) 33 54 0.03 (0.8) 0.00 (0.0)

5 Fixed Annealed 0.083 (2.1) 48 25 0.13 (3.3) 0.00 (0.0)

6 Fixed Annealed 0.120 (3.1) 33 25 0.18 (4.6) 0.03 (0.8)-

Table 2.1 Characteristics of 4~in. (102-rrnn) Diameter Strut Specimens

ay

Average Nominal LengthStrut Cross-Section P <5From of Tubing y yMaterial Area

Test(ksi) (in2) (in) (kips) (in)

1 31 1.02 55.38 31.6 0.058

2 31 1.46 55.38 45.3 0.058

3 92 1.02 55.38 93.8 0.173

4 74 1.46 55.38 108.0 0.139

5 31 1.02 70.25 31.6 0.074

6 31 1.46 70.25 45.3 0.074

Table 2.2 Strut Yield Loads PredictedFrom Material Test

(1 kip = 4.45 kN; 1 in. = 25.4 mm;1 ksi = 6.9 MFa)

49

lJ1o

CYCLE

Tal.1 2 3 4 5 6 7 8 9 10 11 12 13 14 (kips)

r-l * 19.5tp 23.0 21.5 16.2 13.8 10.8 4.1+-J Camp. Max.;::l ±0.5H+-J P 28.0 30.3 30.0 30.1 29.8 17.0 2.8tf.l Ten. Max.N * 23.5tp 43.7· 40.0 31. 3 27.5 22.0 16.8 14.0 6.0+-J Como. Max;::l ±0.5H+-J P 44.7 44.0 44.0 43.1 '43.0 38.6 33.0 19.0 6.0tf.l Ten. Max.C"'l * 44.8tp 51.0 60.4 46.9 24.0 19.2 13.7 6.6+-J Camp. Max.;::l ±0.5H+-J P 49.5 82.9 86.5 59.7 60.1 24.5 4.5 0.0tf.l Ten. Max.~ *P 40.7 57.5 54.5 55.7 41.9 38.9 37.6 . 38.4 38.4 39.0+-J Camp. Max.;::l ±0.5H+-J P 56.1 97.2 99.7 84.6 89.4 89.0 98.5 101.6 102.5 102.8tf.l Ten. Max.Lf') * 28.0t 12.0 i .9.8+-J

P 28.0 31.5 32.5 32.0 23.0 20.0 17.5 16.0 14.0 7.0Camp. Max.;::l ±1.0H 1+-J P 31.2 32.5 33.0 32.5 132.0 32.0 30.0 29.5 26.5 23.0 17.0 13.0 10.2tf.l Ten. Max.

'" 1(35.0t

+-Jp 28.0 42.0 44.5 40.0 38.5 37.5 37.0 36.5 35.5 34.5 i 30.5 28.0 27.0

;::l Camp. Max. ±1.0H+-J P 35.0 44.0 44.5 44.0 44.0 44.0 42.5 42.5 43.5 43.0 43.0 42.0 41.0 41.8tf.l Ten. Max.

*Cycle in which noticeable lateral buckling first occurred

tCycle in which local buckling first occurred

Table 3.1 Maximum Compressive and TensileLoads in Each Cycle

(1 kip = 4.45 kN)

U1i-'

CYCLE

1 2 3 4 5 6 7 8 9 10 11 12 13 14 TOL.(in. )

.-I0 -.212 -.367 -.369

.f-l Camp. Max -.072 -.142 -.282 -.356 -.367;::lH

0.f-l .076 .141 .210 .279 .346 .358 .359 .348til Ten. MaxN

cS -.073 -.140 -.216 -.282 -.357 -.358 -.363 -.360 -.350.f-l Camp. Max;::lH

cS .3451.f-l .074 .141 .209 .278 .350 .344 .341 .343til Ten. MaxC""l

0.f-l Camp. Max -.075 -.138 -.194 -.225 -.303 -.307 -.310 -.309;::lH

0 .082 1 I.f-l .072 .142 .170 .080 .067 .061 - itil Ten. Max-j

0 -.0701-.145 -.200 -.285 -.354 -.351 -.351 -.351 -.351 i-.351 i.f-l Camp. Max;::lH

0 .14- .164 .052 .112 .138 i.f-l .070 .065 .061 .100 .125til Ten. Max I I

Lr'l , ! ,0 -.068 -.144 -.218 -.284 -.358 -.354 -.356 -.403 -.454 -.500/-.553 -.668 -.703

.f-l Camp. Max;::lH

0 .062 .140 .210 .277 .347 .343 .346 .344 .343 .345 .346 .346.f-l .347til Ten. Max\0

0 -.065 -.143 -.213 -.286 -.358 -.367 -.416 -.473 -.527 -.578 -.627 -.674 -.680.f-l Camp. Max -.362;::lH

.394 .472 .576.f-l 0 .069 .142 .214 .282 .342 .338 .330 .330 .338 .372 .426til Ten. Max

Table 3.2 Maximum Compressive and TensileDisplacements in Each Cycle

(1 in. = 2.54 cm)

lJlN

CYCLES 1 2 3 4 5 6 7 8 9 10 11 12 13 14

E. 2.97 7.47 10.66 9.82 10.46 7.09 2.87~

Strut 1 RP. 6.95 14.50 23.19 31.92 40.67 44.05 44.94 E. =. energy absorbed i.n~

~ cycle i (kip-inch)Ei/RPi 0.43 0.52 0.46 0.31 0.26 0.16 0.06

E. 4.00 11.95 15.36 17.89 17.32 14.00 11.67 9.06 4.84 RPi =. energy absorbed in~

20.74 33.66ideal rigid-plastic

Strut 2 RP. 9.97 45.75 58.52 62.02 62.38 61.97 61. 38 element (kip-inch)~

E/RPi 0.40 0.58 0.46 0.39 0.30 0.23 0.19 0.15 0.08

Ei 0.56 9.18 15.00 12.59 8.45 7.29 3.21

Strut 3 RPi20.82 39.21 54.31 54.59 64.53 63.88 66.13

Ei/RPi0.03 0.23 0.28 0.23 0.13 0.11 0.05

E. 0.98 7.15 13.19 18.15 19.10 18.41 21.28 23.98 25.16~

Strut 4 RP i 22.68 46.44 60.05 67.72 79.27 77 .87 82.30 83.59 88.02,

Ei/RP i 0.04 0.15 0.22 0.27 0.24 0.24 0.26 0.29 0.29

E. 1.00 6.37 13.53 20.66 23.05 17.67 16.00 16.81 17.57 15.56 13.59 12.07 9.40~

Strut 5 RP. 6.26 13.52 22.69 30.87 39.72 41.87 41.87 44.94 48.13 51.00 54.42 i61. 68 63.611

Ei/RP i ' 0.16 0.47 0.60 0.67 0.58 0.42 0.38 0.37 0.37 0.31 i 0.150.25 ! 0.20I

Ei 0.82 9.30 15.24 24.22 32.33 33.59 32.87 34.92 38.59 39.36 44.18 43.07 43.51 46.47

Strut 6 RPi

9.01 19.39 31.26 43.94 56.31 59.34 59.16 63.28 68.81 75.56 82.94 90.01 97.85 105.14

E./RP . 0.09 0.48 0.49 0.55 0.57 0.57 0.56 0.55 0.56 0.52 0.53 0.48 0.44 0.44~ 1-

Table 3.3 Energy Absorption Per Cycle (1 kip-in =. 0.113 kN-m)

lJ1W

LoadLength of Inelastic Rotation Cum. Inelastic Max. Compo

PointsPlastic Region in Plastic Region Rotation in Plastic Region Load

±0.5 in (±12.7 mm) ±0.005 radian radians kips (kN)

lC 10.25 (260.3) 0.017 0.017 23.0 (102.3)

lE -0.006 0.040

2C 12.50 (317.5) 0.045 0.091 21.5 (95.7)

2E -0.005 0.141

3LB 13.00 (330.2) 0.057 0.203 19.5 (86.8)

Table 4.1 Plastic Region Inelastic Rotations - Strut 1

U1>!'>

Load Length of*

Inelastic Rotation Cum. Inelastic Max. Compo

PointsPlastic Region in Plastic Region Rotation in Plastic Region Load

iO.5 in (i12.7 mm) iO.005 radian radians kips (kN)

3C 8.25 (209.5) 0.060 0.060 31.5 (140.2)

3E 0.007 0.113

4C 8.75 (222.2) 0.093 0.199 27.5 (122.4)

4E 0.016 0.276

5LB 8.12 (206.2) 0.061 0.321 23.5 (104.6)

* t length of center plastic hinge.

Table ~.2 Plastic Region Inelastic Rotations ~ Strut 2

\Jl\Jl

LoadLength of Inelastic Rotation Cum. Inelastic Max. Compo

PointsPlastic Region in Plastic Region Rotation in Plastic Region Load

±0.5 in. (±12.7 rom) radians radians kips (kN)

1C 4 (101. 6) -0.0029 0.0029 28.0 (124.6)

IE -0.0087 0.0087

2C 6 (152.4) -0.0055 0.0119 31.5 (140.2)

2E -0.0165 0.0229

3C 10 (254.0) -0.0046 0.0348 32.5 (144.6)

3E -0.0145 0.0447

4C 10 (254.0) 0.0131 0.0723 32.0 (142.4)

4E -0.0135 0.0989

5LB 10 (254.0) -0.0014 0.1110 28.0 (124.6)

Table 4.3 Foot Plastic Region Inelastic Rotations - Strut 5

lJ1(J'I

Load Length of Inelastic Rotation Cum. Inelastic Max. Compo

PointsPlastic Region in Plastic Region Rotation in Plastic Region Load

±0.5 in. (±12.7 rom) radians radians kips (kN)

2E 0 0

3C 4 (101.6) 0.0135 0.0135 49.5 (220.3)

3E -0.0077 0.0347

4C 6 (152.4) 0.0217 0.0642 40.0 (178.0)

4E -0.0075 0.0935

5C 10 (254.0) 0.0372 0.1382 38.5 (171. 3)

5E 0.0005 0.1750

6C 10 (254.0) 0.0427 0.2172 37.5 (166.9)

6E -0.0042 0.2642

7C 10 (254.0) 0.0432 0.3117 37.0 (164.6)

7E -0.0037 0.3587

8C 10 (254.0) 0.0467 0.4092 36.5 (162.4)

8E 0.0005 0.4555

9C 10 (254.0) 0.0527 0.5077 35.5 (158.0)

9E I 0.0012 0.5592 II

10LB 10 (254.0) I 0.0580 0.6160 35.0 (155.7)

Table 4.4 Foot Plastic Region Inelastic Rotations - Strut 6

STRUT 1 STRUT 2 STRUT 5 STRUT 6

(D/t = 48) (D/t = 33) (D!t = 48) (D/t = 33)

Cycle at3 5 5 10Local Buckling

Load atLocal Buckling 12.2 17.8 28.0 30.6

(kips)

Cumulative InelasticCurvature 0.021 0.048 0.019 0.091

(radians/in. )

Cumulative InelasticAxial Strain 0.034 0.057 0.072 0.154

(in. /in.)

Cumulative Inelastic !Compressive Fiber 0.069 0.148 0.116 0.347Strain (in. /in.)

Maximum CurvatureExcursion 0.007 0.014 0.004 0.009

(radians/in.)

Cumulative InelaasticRotation 0.203 0.321 0.111 0.616(radians)

Cumulative EnergyDissipated 21.1 66.5 64.6* 261. 2 *

(kip-in. ) (32.3) (130.6)

Magnitude ofCurvature at L.B. 0.007 0.015 0.000 0.010

(radians/in.)

Magnitude ofCompressive Fiber -0.021 -0.039 -0.003 -0.038Strain at L.B.

(in. /in.)

* 12 total strut energy.

Table 4.5 Summary of Rotations, CurvaturesStrains, and Energy Dissipation atFirst Occurrence of Local Buckling

(1 kip = 4.45 kN, 1 in. = 25.4 mm)

57

Buckling LoadBuckling Load by

AISC FormulasStrut by Tangent (Without Factor of First Buckling

No. Hodulus Safety) Load from TestMethod(kips) (kips) (kips)

1 24.3 29.2 23

2 45.3 41. 7 43.7

5 31.6 31.1 31.5

6 45.3 44.5 44.5

Note: Tolerances of predicted loads are ±O.5 k due to curve plottingaccuracy limits.

Table 5.1 Predictions of FirstBuckling Loads-Annealed Struts

(1 kip = 4.45 kN)

58

Cumulative Predicted ActualInelastic Buckling BucklingCentroidalStrain* Load Load

(in/in) (kips) (kips)

CYI .00407 24.3 23.0

CY 2 .01017 20.0 21.5

Strut CY 3 .01815 19.4 19.51

CY 4 .03115 Beyond Local16.2Buckling

CY 5 .03979 Beyond Local 13.8Buckling

CY 1 0 45.3 43.7

CY 2 .0002 43.8 40.0

Strut CY 3 .01470 28.2 31.32

CY 4 .03070 26.0 27.5

CY 5 .04885 Beyond Local 23.5Buckling

CYI 0 31.6 Elastic Cycle;No Buckling

CY 2 - 0 31.6 31.5

Strut GY 3 - 0 31.6 32.55

CY 4 .00010 31.6 32.0

CY 5 .01591 27.9 28.0

CY 1 0 45.3 Elastic Cycle;No Buckling

CY 2 0 45.3 42.0

Strut CY 3 .00020 45.3 44.56

CY 4 .00119 43.1 40.0I !

CY 5 .01062 40.0 38.5

*Based on center hinge

Table 5.2 Predicted Buckling Loads for Annealed Struts (lkip = 4.45 kN)

59

Strut Tangent AISC Formulae Actual First

No. Modulus (Without Factor Buckling LoadMethod of Safety) in Test

(kips) (kips) (kips)

3 57.8 70.8 60.4

I4 59.5 88.0 57.5

(A) First Buckling Load

CumulativeCycle of Cumulative Predicted

Inelastic Strut Test Inelastic Buckling Actual

Strain in With Centroida1 Load Buckling

CyclicSimilar Strain From Load in

Cumulative Preceding Cyclic NotedMaterial Strain Strut Test Material Cycle

Test History Cycle Noted Test

(in/in) (in/in) (kips) (kips)

Strut 3 .017 4th .013 52.3 44.8

Strut 4 .020 5th .017 65.1 55.7

(B) Buckling Load in Later Cycle

Table 6.1 Predicted Buckling Loads for Unannealed Struts

(1 kip = 4.45 kN)

60

FIGURES

61

B

p

t , , t t t

("\ ( \ "\ 1t t t , , ,

O-A A-B B-C C-D D-E E-F

A) Hysteretic Behavior B) Zones of Behavior

Fig. 1.1 Typical load deformation Relationship of a Brace Member [2]

p

2

5

3

Fig. 1.2 Linearized Model of Post-Buckling Brace Behavior [3]

62

120"

4"¢I STRUTS I

I..., 120" ... 1

MSL

MUDLINE

It)

N

oo

+1

o10

olD

J~lD,

§~.

Nr-.

...Q

QUi"'Z,..-5~Q:­", ...

..,0:)0oJ";:)

zeZN.. r-.

,- - - - roO'XIOO'- - ~ --II DECK MODULE II DL+ LL = 5000k II IL - -" - -,rr- - - -.::,- - T r - _...J I

1 I 'i<-36¢ .750........' I 1I 1/,/ FLD.INST. ""' 1::-1

/ ,j, " -,-=18'f .375-----.. '

"'Ii'

7 i4> 1.125-----.J

244> .500

24«> 1.00 I +---'

<YlW

a) Frame Elevation b) 1:6 Scale Model of a Braced Panel

Fig. 2.1 Southern California Example Structure (1 in. 25.4 nun)

4" 0Tubing

~DT 17

11

55.3a"

I

L-.A

o 0000o 0

SECTIONA-A

STRUTS 1,2

4" ellTubing

~DT

74.3."

End Plate

o 0)-1.3

0\)0o 0

SECTIONB-B

STRUTS 3,4

SECTIONC-C

nd Plete

4" 0T I

1144 '-- 70_._25_H -.,~

ub "g

L.P.

2.13u

15.38# 17.50" i7.S0H

7.38N ." .u

'~/,..... c..-- 2" .

1 5 II 13 17 ~~,~ .

}4~DT' " (!) 1IJ12 l' 20!M.-;!I

L.P.- 3 7 r 15 III 23 27 31-

'- C4- '-

STRUTS 5, 6

o . Itraln gag.

~ - linear potentiometer (L.P.)or LVDT (linear variabledifferential transformer)

Fig. 2.2 Test Specimens (1 in. 25.4 mm)

64

REACTIONFRAME

7'-0"

REACTIONBLOCK

7'-101/4"

7'-6"

SIDE ARM

LOAD TESTCELL SPECIMEN

6'- 2 3/8"

91/4"

22'- 3"

FOOT PIN

SPACER PLATES

5'-103/4"

4"

10" BEAM

REACTIONBLOCK

(a) PINNED- PINNED TEST LAYOUT

REACTIONFRAME

REACTIONBLOCK

PINCONNECTION

(TYP)

SIDE ARM

6" INITIALEXTENSION

7'-4"

1'-41/4"

HEADUNIT

2'-51/4"

16'-13/4"

~:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

TESTSPECIMEN

6'-15/8"

10" BEAM

FOOT FRAME

4'-2"REACTION

BLOCK

(b) FIXED-FIXED TEST LAYOUT

Fig. 2.3 Experimental Test Set-Up (1 in. = 25.4 rom)

65

Fig. 2.4 Fixed-Fixed Experimental Setup

66

a) Head Unit

b) Specimen Connection to Foot Frame

Fig. 2.5 Fixed-Fixed Experimental Setup

67

a) Load Control Equipment

b) Clevis Used for Pin Connection

Fig. 2.6 Experimental Equipment

68

a) LVDT Used for Measuring Axial Displacement

b) Specimen with Strain Gages and LVDT

Fig. 2.7 Instrumentation

69

a) Data Feedback -- Continuous Recording on X-Y Plotters

b) Recording Visual Observations

Fig. 2.8 Data Recording

70

INITIAL YIELDDISP. (0= 0.06 IN.)

....zw~woec..Ia.~Q

..Iec)(ec

zoCDzw~

zoCDCDW0::a..~oo

0.4

0.2

Ol-----.--f--lr-+-+-+-+-I-+-+-+-+-+--I--+-+....L.....-----

0.2

0.4

CY I OY2 OY3 OY4 eY5 eY6 OV7 eve eyg cy 10I I I I I I I I I I I

CYCLE NUMBER

Fig. 2.9 Loading Sequence - Strut 1 (1 in.

71

25.4 mm)

0.4

Z0(J) 0.2Zwf-

a

.5

~Zw::Iw()c:r:....IQ.

~C

....Ic:r:><c:r:

zoen(J)w0:::a..~o()

0.2

0.4

INITIAL YIELDDISP. (6 = 0.06 IN.>

CYJ CY2 CY3 CY4 CY5 CY6 CY7 cye CY9 CYIO CY III I I I I I I I I I I I

CYCLE NUMBER

Fig. 2.10 Loading Sequence - Strut 2 (1 in.

72

25.4 mrn)

0.4

INITIAL YIELD/ DISP. <6= 0.17 IN.>

~ ~--FRACTURE

01----......-~\--I_4__++__I_\___I__+_++__+_!tr_r_-------

0.2

0.4

0.2

zo(J)zwI-

zo(J)(J)wa::Q.~oo

..J:!><ce

...zw~w()ce..J0.tnQ

CYI CY2 CY3 CY4 pY5 OY6 OY7 OYS Cyg OYIOI I I I I I I I I I I

CYCLE NUMBER

Fig. 2.11 Loading Sequence - Strut 3 (1 in. 25.4 rom)

73

0.4

Z0(Jj 0.2ZWI-

0

.S

...Zw:Ewoce..Ia..eno

..Ice><ce

zoU5(/)wa::a..Loo

0.2

0.4

,CY t ,CY2, CY3, CY4, CY5, Cye, CY7 ,eYe, CY9,CYIO,CYJI ,

CYCLE NUMBER

Fig. 2.12 Loading Sequence - Strut 4 (1 in.

74

25.4 mm)

0.6 I-

INITIAL YIELD~ DISP. ( <5 = 0.07 IN.>

0.4 ~

.E z ""0en 0.2 ~

~I- ZZ W ,

~w l- f-:::Iw ~~I\

0 0c(

V ~\....I

a. Z -en 02i en ,....I en 0.2 -c( W>< a::c( Q.

~0 0.4 -0

~

0.6 ~

~

eYI CY2 OY3 OY4 OY5 OY6 OY? oye Oyg CYIO OYII OVI2 OVI3I I I I tit I I I I I I I

CYCLE NUMBER

Fig. 2.13 Loading Sequence - Strut 5 (1 in.

75

25.4 rom)

0.6 INITIAL YIELDDISP. (<5 = 0.07 IN.>

0.4

.E Z0

~ en 0.2Z Zw w::E /-w0

0<..JQ.

~ Z0 0

U5 0.2..J en< w>< 0:::< a..

:::E0 0.40

0.6

CYI CY2 CY3 CY4 CYS CY6 CY7 CY8 CY9 CYID CYII CYI2 CYI3 CYI4 CYIS CYI6I I I I I I I I I I I I I I I I I

CYCLE NUMBER

Fig. 2.14 Loading Sequence - Strut 6 (1 in.

76

25.4 rom)

C-MAXIMUMCOMPRESSIVEDISPLACEMENT

a)

P (KIPS)

...,.-E- MAXIMUM. TENSILE

DISPLACEMENT

F-ZERO LOAD/I AFTER TENSION

\ 811NCHESI

A-ZERO LOADBEFORE COMPRESSION

(MAX'MUMCOMPRESSIVELOAD

Typical Hysteretic Response

STRUT

A+B

t

+C

t0(01

) E F (A OF NEXTCYCLE)

b) Loading Schematic

Fig. 2.15 Load Points on a Typical Cycle

77

OV'ELD =36 KS I40...-

en~

enen 20wa:I-en

0

AREA=0.083IN.2

0.002 0.004 0.006 0.008 0.010STRAIN (IN/IN)

(0) 0.083" WALL TH ICKNESS

40

enenw 20a:I­en

o0.002

"YIELD =35 KSI

~p

AREA =0.120IN.2

0.010

Fig. 2.16 Coupon Test Results - Annealed Material at Small Strains(1 ksi = 6.9 MPa)

78

120

cry (0.2 % OFFSET)= 92 KSI crULT = 97 KSI100

C/) 80 /~

C/)60 /

C/)

/wa::l- IC/) 40

20/

/0

0 .002 .004 .006 .008 .010 .012 .014 .016 .018 .020

STRAIN (IN/IN)

(0) 0.083" WALL THICKNESS

120

100 cry (0.2 % OFFSET) =74 KSI crULT =88 KSI

80C/)~

Cf) 60 /Cf)wa:: /I-

40C/)

/20 /

/0

0 .002 .004 .006 .008 .010 .012 .014 .016 .018 .020

STRAIN (IN/IN)

(b) 0.120" WALL THICKNESS

Fig. 2.17 Coupon Test Results - Unannealed Material at Small Strains(1 ksi = 6.9 MPa)

79

tP

100OULT =97 KSI AREA =

0.120 IN.2

80

UNANNEALED tp-CJ) MATERIAL CTULT = 58 KSI~~ 60-CJ)

CTYIELD =36 KSICJ)w

~0:: 40~CJ)

ANNEALED

20MATERIAL

o0.02 0.04 0.06 0.08 0.10 0.12

100

80

-CJ) 60~-CJ)CJ)W0:: 40~CJ)

20

STRAIN (INI IN)

(0) 0.083" WALL THICKNESS

~CTULT=88 KSI

&---- UNANNEALEDMATERIAL

ANNEALEDMATERIAL

AREA =20.082 IN.

OL.-__........__L-_---J__--L__---L__.........__~

0.02 0.04 0.06 0.08 0.10

STRAIN (IN liN)

( b) 0.120" WALL TH ICKNESS

0.12

Fig. 2.18 Coupon Test Results - Annealed & Unannea1ed at Large Strains(1 ksi = 6.9 MPa)

80

fPI 4 IN. 0.0.l/TUBEII

T,12" I-i l

c:::;:~

60

OVIELD =31 KSI

O------.L----...L-----.a.----.......---_....

- 40en~

enenw0:~ 20

0.002 0.004 0.006 0.008 0.010

STRAIN (IN/IN)

Fig. 2.19 Compression Test of Full Section - Annealed Material(1 ksi = 6.9 MPa)

81

80

60

~ 40wa:l­en

20

OL-----"-----L----L.---...L-----.J0.0200.0160.004 0.008 0.012

STRAIN (IN/IN)

(0) 0.083" WALL THICKNESS

80

60-en 40enwa:::l-en

20

0L-__--1i...-__......L -L. .L-__---J

0.0200.0160.004 0.008 0.012

STRAIN (IN/IN)

(b) 0.120" WALL THICKNESS

Fig. 2.20 Compression Test of Full Section - Unannealed Material(1 ksi = 6.9 :MFa)

82

OVIELD =31 KSI

ANNEALED PIPE(t=0.08311

)

20

30

40r-------------r---'-------------.

-30

-20

~ 0 1----....L--+---'----'---f-----''---.....1---f-'------i

W0:::~(f) -10

(f) 10~.......

-

-40'------'-----L.---'----'-----''---.....1-----'-----'

- 0.006 - 0.002 0 0.002 0.006

STRAIN (IN/IN)

. Fig. 2.21 Cyclic Test - Annealed Material(1 ksi = 6.9 MFa)

83

UNANNEALED PIPE

-80

-60

-40

-100' , I I I , I , ,

-0.004 00.004 0.008 0.012 0.016 0.020STRAIN (IN/IN)

100

80

60

40

--CJ) 20~-CJ)

0CJ)

IJJQ::I-CJ) -20

UNANNEALED PIPE

60

80

40

-40

-80

-60

100, ,I

-100" , I , I I I I

-0.016 -0.012 -0.008 -0.004 0 0.004 0.008STRAI N (IN/IN)

CJ) 20~-CJ) 0

(» CJ)

"'" WQ::I-CJ) -20

(a) 0.120" WALL THICKNESS (b) 0.083" WALL THICKNESS

Fig. 2.22 Cyclic Test - Unannealed Material(1 ksi = 6.9 MPa)

601, ------------r'----------i

40

STRUT I 411ep X 0.083

11

PINNED - PINNED END CONDITIONS

20

..-Cf)a..- 0::s:::-a..

-20

<XllJ1

-40

-60' I I I I I I , , , ,

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.58 (IN)

Fig. 3.1 Axial Load vs. Axial Displacement - Strut 1, Cycles 1-5(1 kip = 4.45 kN; 1 in. = 25.4 rom)

,60. I

40

20

.--.(f)

0-~ 0........0-

OJ

-20

'"-40

7

STRUT 1 4"epxO.083"PINNED - PINNED END CONDITIONS

-60 1 I I I I I I I , I I , I

-0.5 -0.4 -0.3 -0.2 -0.1 o8 (IN)

0.1 0.2 0.3 0.4 0.5

Fig. 3.2 Axial Load vs. Axial Displacement - Strut 1, Cycles 6-8(1 kip = 4.45 kN; 1 in. = 25.4 rom)

STRUT 2 4'~ X 0.120"PINNED - PINNED END CONDITIONS

60, i i

40

20

-(J)a..~ 0-a..

(Xl

-201 C5

-....l

-40

0.50.40.30.20.1-0.2 -0.1-0.3-60' I I I I I I I I I I

-0.5 -0.4

Fig. 3.3 Axial Load vs. Axial Displacement - Strut 2. Cycles 1-5(1 kip = 4.45 kN; 1 in. = 25.4 rom)

60, I I

40

20

.-..if)(L

0~-(L

00 -2000

-40 STRUT 2 4"ep X 0.120"PINNED - PINNED END CONDITIONS

-60' I , I I , I , I I , I ,

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.58 (IN)

Fig. 3.4 Axial Load vs. Axial Displacement - Strut 2. Cycles 6-9

STRUT 3 4''¢ X 0.083"PINNED- PINNED ENDCONDITIONS

3

60

40

-20

80

20

-60

-40

(J)a..~ 0 I ,::::>4 /' f I I.',',' I I I I-a..

CXJ\.D

0.40.30.2-0.1-0.2-0.3-80 1 I I I I I I I I

-0.4

Fig. 3.5 Axial Load vs. Axial Displacement - Strut 3. Cycles 1-5(1 kip = 4.45 kN; 1 in. = 25.4 mm)

100

80

60

40

L/20

-(/)~ a.. 00

~-a..

-20

-40

-60 STRUT 3 4"4> x 0.083"PINNED - PINNED END

-0.5

Fig. 3.6 Axial Load vs. Axial Displacement - Strut 3, Cycles 6-8(1 kip = 4.45 kN; 1 in. = 25.4 mm)

STRUT 4 41\p x0.120

PINNED - PINNED ENDCONDITIONS

100

60

-20

40

80

20

-60

-40

a..

(J)a..~ 01 I l '/ IIr (V /11 I

I I I\0I-'

-80' I I I I I I I ,

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.48 (IN)

Fig. 3.7 Axial Load vs. Axial Displacement - Strut 4, Cycles 1-5(1 kip = 4.45 kN; 1 in. = 25.4 mm)

100

80

60

40

--- 20if)Q..

~\.0~

tvQ.. 0

-20

-40

-60 STRUT 4 4"ep xO.12011

PINNED - PINNED END CONDITIONS

-0.5 -0.4 -0.3 0.4

Fig. 3.8 Axial Load vs. Axial Displacement - Strut 4, Cycles 6-10(1 kip = 4.45 kN; 1 in. = 25.4 mm)

GOr'--------,'---------.,

40

20

-0

enw

a..~ 0-a..

-20

-40STRUT 5 4"¢ x0.083"FIXED- FIXED END CONDITIONS

-GO' I I , , , , I I

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.48 (IN)

Fig. 3.9 Axial Load vs. Axial Displacement - Strut 5, Cycles 1-5(1 kip = 4.45 kN; 1 in. = 25.4 rom)

60

40

20

-Cf)a..~ 0-a..

1.0 -20o!'>

-40

-60 STRUT 5 41C/J X 0.083"

FIXED-FIXED END CONDITIONS

-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 o 0.18 (IN)

0.2 0.3 0.4 0.5 0.6

Fig. 3.10 Axial Load vs. Axial Displacement - Strut 5, Cycles 6-10(1 kip = 4.45 kN; 1 in. = 25.4 rom)

'!lU1

20

~~O-a..

-20

- - ~J:i2~

I I I I I I I /1 I I-:;.-" .--

~

~ 14~ ~ dD I-

STRUT 5 4"<p x 0.08311

FIXED-FIXED END CONDITIONS

I I I I I I I I I I I I I-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 o 0.1

8 (IN)

0.2 0.3 0.4 0.5 0.6 0.7

Fig. 3.11 Axial Load vs. Axial Displacement - Strut 5, Cycles 11-13(1 kip = 4.45 kN; 1 in. = 25:4 mm)

80 I I I

60

40

20

-if)(L

~ 0---(L

'"' -20(J'I

-40

-60STRUT 6 4"ep X0.120FIXED-FIXED END CONDITIONS

-80 I I I I I I I I

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.48 (IN)

Fig 3.12 Axial Load vs. Axial Displacement - Strut 6, Cycles 1-5(1 kip = 4.45 kN; 1 in. = 25.4 rom)

60

40

20

-(f)a.. 0:lI:::-a..\.0

-...J

-20

-40

-60 STRUT 6 4" c/> X 0.12011

FIXED-FIXED END CONDITIONS

-0.6 -0.5 -0.4 -0.3 -0.2 o 0.18 (IN)

0.2 0.3 0.4 0.5 0.6 .

Fig. 3.13 Axial Load vs. Axial Displacement - Strut 6, Cycles 6-10(1 kip = 4.45 kN; 1 in. = 25.4 rom)

STRUT 6 4" ep X 0.120"FIXED-FIXED END CONDITIONS

60.---,-------------,'-----~~~~~-l'

40

20

-(f)(L- 0~~

(L

-20

'.0CD

-40

-0.7 -0.6 -0.5 0.5 0.6

Fig. 3.14 Axial Load vs. Axial Displacement - Strut 6~ Cycles 11-16(1 kip = 4.45 kN; 1 in. = 25.4 rom)

80r---------r-------------------,

60

-40STRUT I 41lp X 0.083"PINNED - PINNED END CONDITIONS

- 60 '--__.l--__.l..-.__.l..-.__...I--__-L-__-L-__....L-__....L.-_---'

-3 -2 -I 0 2 3 4 5 66, (IN)

Fig. 3.15 Axial Load vs. Lateral Displacement - Strut 1, Cycles 1-5(1 kip = 4.45 kN; 1 in. = 25.4 rom)

99

80r-----------------...-------------~

STRUT 2 4"ep)( 0.120"PINNED - PINNED ENDCONDITIONS

20

60

-20

40

-40

-ena..~Of----.l.-...:""e..-~--....L--+--.....L----+---lI-IHI-----L--...-.....l--.---JL-----J

a..

432o.6. (IN)

-I-2-3-4-5- 60~__-'---__-l..-__....L___.....L______'_______L.___...l..______.l_____lL..__ ____I

-6

Fig. 3.16 Axial Load vs. Lateral Displacement - Strut 2, Cycles 1-5(1 kip = 4.45 kN; 1 in. = 25.4 rom)

100

120r----------.-------------....,

100

2

STRUT 3 4''cp X 0.083"PINNED- PINNED ENDCONDITIONS

60

40

-20

80

20

-6J

-40

ena..0r---"-----"-----+r--+-L-.l-\---~:__-..L......--____l~

a..

432-I 0!::J. (IN)

-2- 80 '---__"---__"---_---'- "---__"---__.1--_---1

-3

Fig. 3.17 Axial Load vs. Lateral Displacement - Strut 3, Cycles 1-5(1 kip = 4.45 kN; 1 in. = 25.4 rom)

101

120 r------------,.--------------,

100 2

STRUT 4 411ep x 0.120

11

PINNED - PINNED ENDCONDITIONS

20

80

40

60

-20

-60

-40

a...

-ena...~Ot----...L...--~f'--f----"--t-+-'t--tt-----l------'-----''------j

432-I-2-3- 80 L...-__..L-.__--'---____"____---L-____l___---''---__'--_---'

-4

Fig. 3.18 Axial Load vs. Lateral Displacement - Strut 4, Cycles 1-5(1 kip = 4.45 kN; 1 in. = 25.4 rom)

102

80r-------------y------------.

60

40

20

(f)a..~ 0

a.. I,@-20

5

-40

-60STRUT 5 4

1:P X 0.083FIXED- FIXED END CONDITIONS

432olJ. (IN)

-I-2- 80 L--__.L..--__.L..--__"'-__.L-__.L.-__.L.-_---l

-3

Fig. 3.19 Axial Load vs. Lateral Displacement - Strut 5, Cycles 1-5(1 kip = 4.45 kN; 1 in. = 25.4 rom)

103

80...-----------,...------------.,

60

40

20

CJ)a..-0~-a..

-20

3-40

-60STRUT 6 4'<p )( O. 120"FIXED- FIXED END CONDITIONS

- 80 '--__"--__"--__L..--__~__~__~_---'

-3 -2 -I 0 2 3 46. (IN)

Fig. 3.20 Axial Load vs. Lateral Displacement ~ Strut 6, Cycles 1-5(1 kip = 4.45 kN; 1 in. = 25.4 rom)

104

Fig. 3.21 View of Overall Buckled Strut

105

.- fo'r

a) Orip,inal Local Buckle

b) Strai"htening After Tension

Fig. 3.22 Local Buckling at Selected Load Points forStrut 5 - Center Hinge

106

a) Severe Local Buckle

SPEC

E

cy 10b) Tearing in Tension

Fig. 3.23 Local Buckling at Selected Load Points forStrut 5 - Center Hinge

107

/

a) Severe Tearing in Tension

b) Post-Tearing Buckle

Fig. 3.24 Local Buckling at Selected Load Points forStrut 5 - Center Hinge

108

a) Severe Local Buckle

b) Tensile Tearing

Fig. 3.25 Local Buckling at Foot Hinge - Strut 5

109

",------------------,------------------,

10

" " " "~.. 05

"'..0<l 00 .0 3D-' 'C <C0 3C..,N

-' -05<l

'"a:0z -10

-,.-10 -8 -. -4 -, 0 , 4 • 8 10

NORMALIZED DISPLACEMENT, 8/8,(0) STRUT I

15,------------------,-----------------,

/,'j""""~E~~--i3e 4E "~

~ 05.. I

Ior---------:7<lnili-;,f.,--Iro--1\DJfr-~"'-r_~'--'--------___\'"<l

'"-'

'"..,N...J -05<l

'"a:oz

-I ~1"0-----'8,------.':.----'-4'-----J,,----C0'----J,'----4L-----'.----8L-----',0

NORMALIZED DISPLACEMENT, 8/8,(b) STRUT 2

Fig. 3.26 Axial Load vs. Axial Displacement - Normalized

110

1.5.---------------------,r;--------------------,

-0.5

01---------------rT--HHf------------------l

1.03E2E

>-a. 0.5~

Qc(ooJ

oLLINoJc(::E

~Z -1.0

10

-1.5 '-__--':-__----': -':-__-..L__-----''-__...L______L L-__---L__---!

~ 0

NORMALIZED DISPLACEMENT, 8/8y(0) STRUT 3

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

1.0

-0.5

>-~ 0.5a.

01---------------f--fL-+-i'(--ffL-------------------IQc(

9oLLINoJc(

::E0::oZ -1.0

-I.:I'::-O--~:-----'::----L---~---!O:-----'::-------L---~--~----.JIO

NORMALIZED DISPLACEMENT, 8/8y(b) STRUT 4

Fig. 3.27 Axial Load vs. Axial Displacement - Normalized

111

5C

01----------+-+..L---1--..f--b-I.,..L---f---I--I--.L---------~

-0.5

1.5

••

1.0

,..0- 0.5Ci:'

oct9oI&JN-Ict:ia::oz -1.0

'C

-1·:ILO----'_S:----_...LS---_.L4---_2L-----lO---.l.----4.L---....JS-----lS-----l,o

NORMALIZED 01 SPLACEMENT, 8/8y(0) STRUT 5

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

1.0

,..0- 0.5

~

o~ OI------------+-....I-~..J__I__IIIc--+__J.-+__-----------_l

-I

oI&JN:::i -0.5ct:ia::oz -1.0

-1.5 L-__--.L__----l .l.-__---L__--',--__-'--__---.L__--'c--__-"-__---:"~o 0 2 4 S S ~

NORMALIZED DIS PLACEMENT, 8/8y

(b) STRUT 6

Fig. 3.28 Axial Load vs. Axial Displacement - Normalized

112

pinned, annealed, Dlt = 48pinned, annealed, Dlt = 33pinned, unannealed, D/t = 48pinned, unannlealed, Dlt = 33fixed. annealed, Dlt = 48fixed, annealed, Dlt = 33

Strut 1:Strut 2:Strut 3:Strut 4:Strut 5:Strut 6:

7 8 9 10 II 12 13 14 15 16CYCLE

653 42

., ~"''''''. \~\

\

'\ \ A _..A "'6......\ \ ~--~ A.......".\ ~ ~...... ........I::r--.u .. "-.... .. ......

X \ \ \::"" STRUT'\. '\. \ ••t>..••--l1--_-6-.-t>@*, '\. 0,. ' ....

'X ',- 0,....\'" --a '0............_..t~~~ \ ....0-.,'. " " '0..

X • ..lit. __ ,

• "'---"'lIl'r"-,~.-_••~. ~ 'b\ X \ "

+-•....,\ \ '''---o...--o®'\ ~~ -..e;~'• .ifi\\.!r '~

1.0

~ 0.99

0.80-J

0.7w->-....... 0.6

t-' 0t-' <l 0.5(.V

0-J

W> 0.4enen

0.3w0::a..::t 0.20u. 0.1x<l:E 0

Fig. 3.29 Deterioration of Buckling Loads

8. 0 8. 0

7.0 CYCLE 1 POINT C7 . 0t CYCLE 2 POINT C

AXIAL DISP.= -0.07~

AXIAL DISP.= -0.1'16. 0 z 6. 0-S. 0

~

S. 0c.. 4,0 c.. 4,0'" '"

3 . 0 - 3.0CJ

>- 2. 0>- 2. 0

<: 1.0 <: 1.0....J ....J

>- >- 0

-1.0 -1.00 .1 .2 .3 . i . 5 .6 . 7 . 8 .9 1.0 0 .1 .2 .3 . i .5 .6 . 7 .6 .9 1.0

XlL DIST. ALONG MEM8ER AXIS (NORM) X/L DIST. ALONG MEM8ER AXIS (N aRM)

(0) (b)t-'t-'

"""8. a 8 . 0

7 . 0 CYCLE 3 POINT C7.0t

CYCLE 3 POINT 0

AXIAL DIS P. = - 0.21~

AXIAL OISP.= -0.166.0 z- 6. 0

s. 0~ s. 0

c.. 4,0 Q. 4,0'" '"- 3.0 - 3.0CJ CJ

>- 2. 0 >-2.0

«: 1.0<: 1.0....J ....J

>- >-

-1.0 -1.00 .1 .2 .3 • 4 .5 .6 . 7 .8 .9 1.0 0 .1 .2 .3 • i .5 .6 .7 .6 .9 1.0

X/L 01 ST. ALONG MEMBER AXIS ( NORM) X/L 01 ST. ALONG MEMBER AXIS (NORM)

(C) (d)

8.0 8.0

7. 0 CYCLE 3 POINT E7. 0 ~ CYCLE 4 POINT C

A XI A L OISP.= +0.21 - AXIAL OISP.= -0.266. 0 z 6.0-5. 0

~

5.0

0- 1.0 0- 1.0V) V)- 3.0 - 3.0CJ Cl

I-2. 0 2.0

I-< 1.0 < 1.0--' --'

>- >-

-1.0 -1.00 .1 .2 • 3 • 4 .5 .6 • 7 .8 .9 1.0 0 .1 • 2 .3 • 4 • 5 .6 • 7 .6 .9 1.0

X/L 01 ST • ALONG MEM6ER AXIS (NORM) X/L 01 ST. ALONG MEM6ER AXIS (N 0 RM)

(e) (f)

I-' 8.0 8.0I-' CYCLE 5 POINT C

7 • 0 r CYCLE 6 POI NT CU1 7. 0- A X I A L OISP.= -0.35 - AXIAL OISP.= -0.35z 6. 0 z 6. 0-

5. 0~

5. 0

0- LD 0- 4.0V) V)- 3.0 - 3.0Cl <=>

I-2.0

I-2.0

< 1.0 "" 1 • 0--' --'

>- >- --1.0 -1.0

0 .1 .2 .3 • 4 .5 .6 • 7 • 8 .9 1.0 0 .1 • 2 .3 • 4 .5 .6 . 7 .6 .9 1.0

X/L 01 ST • ALONG MEM6ER AXIS (NORM) X/L OIST. ALONG MEM6ER AXIS (NORM)

(g) (h)

Fig. 3.30 Deflected Shapes - Strut 1 (1 in. 25.4 nun)

8.0 8. 0

7. 0 CYCLE 2 POINT A7. 0t

CYCLE 2 POINT C

AXIAL OISP.= +0.02~

AXIAL OISP,= -0.146. 0 z- 6. 0~

S. 05.0a- LO a- LO'" '"

3.0 - 3. 0c

2. 0 I-2. 0

I-< 1.0 <

I.°t~-I ...J

~>- >- o . .

- 1.0 -1.00 . I . 2 . 3 • 4 . 5 .6 . 7 . 8 .9 1.0 0 . I .2 .3 • 4 .5 .6 . 7 . 8 . 9 1.0

XIl 01 ST. ALONG MEMBER AXIS (NORM) XIl 01 ST. ALONG MEMBER AXIS (NORM)

f-'(a) (b)

f-'0'

8.0 8.0

7.0 CYCLE 2 POINT F7. 0 ~ CYCLE 3 POINT ~

AXIAL OISP.= +0.10~

AXIAL OISP.= -0.216.0 z 6.0-~ s. 05.0

Co. LO a- LO'" '"- 3.0 - 3.0c c

2.0 I-2.0

I-< 1.0 < 1.0...J -I

>- >-

-1.0 -1.00 • I .2 .3 • 4 .5 .6 . 7 .8 .9 1.0 0 .1 .2 .3 • 4 . 5 .6 . 7 .8 .9 1.0

XIl OIST. ALONG MEMBER AXIS (NORM) X/L DIST. ALONG MEMBER AXIS (NORM)

(c) (d)

8. 0 8. 0

7.0 CYCLE 4 POINT C 7,Or

CYCLE 5 POINT A

AXIAL DIS P . = - 0 . 28~

AXIAL DISP.= +0.23% 6. 0 " 6. 0-5. 0

~

5. 0a- 4 . 0 a- 4.0V> ''>- 3. 0 - 3. 0Cl Cl

>- 2. 0 >-2. 0

< I .0 <1. 0I...J ....J

. -~ ~

>- >- 0

-1. 0 -1.00 . I . 2 . 3 . 4 . 5 . 6 . 7 .8 .9 1.0 0 . I .2 .3 . 4 . 5 .6 . 7 .8 .9 1.0

X/L OIST. ALONG MEMBER AXI S (NORM) Xil OIST. ALONG MEMBER AXIS (N 0 RM)

(e) (f)

I--' 8. 0 8.0I--'

CYCLE 5 POINT C7. 0t

CYCLE POINT C-J 7. 0 8

AXI AL 01 S P . = - O. 35 ~

AXIAL DISP.= -0.356.0 z- 6.0

5. 0~

5. 0a- 4 . 0 a- 4.0V> V>

3.0 - 3.0Cl

>- 2.0 >-2.0

< 1 . 0 < 1.0...J ...J

>- >-

- I . 0 - I. 00 . I .2 . 3 .4 .5 .6 . 7 .8 .9 1.0 0 .1 .2 .3 . 1 .5 .6 .7 .8 .9 1.0

X/L OIST. ALONG MEMBER AXIS (NORM) X/L 01 ST. ALONG MEMBER AXIS (N 0 RM)

(g) (h)

Fig. 3.31 Deflected Shapes - Strut 2 (1 in. = 25.4 mm)

8. 0 8.0

7.0 CYCLE 3 POINT C7. 0t CYCLE 5 POINT C

AXIAL OISP.= - 0 . 20~

AXIAl OISP.= -0.35z 6.0 z 6.0-5. 0

~

5.00- 400 0- 400V) '"- 3 . 0 - 3.00 Cl

...... 2. 0 ...... 2.0< 1.0 <-' -' 1.0>- >-

-1.0 -1.00 . 1 .2 .3 • 1 .5 .6 .7 .8 .9 1.0 0 . 1 .2 .3 • 1 .5 .6 .7 .8 .9 1.0

X/L OIST. ALONG MEMBER AXIS (NORM) X/L OIST. ALONG MEM8ER AXIS (NORM)

(a) (b)

/-' 8. 0 8.0/-'00 7. 0 CYCLE 6 POINT A

7 . 0t CYCLE 6 POINT C~

AXIAL OISP.= - 0 . 05~

AXIAL OISP.= -0.35z 6. 0 z 6.0-5 . 0

~

5.00- 400 Q. 400V) V)

3.0 - 3. 0Cl

...... 2.0 ...... 2.0< 1.0 < 1.0-' -'

>- >-

- 1.0 -1.00 .1 .2 .3 • 1 .5 .6 . 7 .8 .9 1.0 0 . 1 .2 .3 . 1 .5 .6 .7 .8 .9 1 . 0

X/L 01 ST. ALONG MEMBER AXIS (NORM) X/L OIST. ALONG MEMBER AXIS (NORM)

(c) (d)

B. 0 8.0

7 . 0 CYC LE 6 POINT E7. 0 ~ CYCLE 6 POINT f

AXIAL OISP.= +0.05~

AXIAL 01 S P • = - O. 056. 0 . z 6.0-5. 0

~

5.00- 1.0 0- 4.0'" V)- :3. 0 - :3. 0Cl Cl

I-2 . 0 2.0

I-< 1.0 < 1.0--' --'

>- >-

-1.0 - 1.00 . I .2 .3 • 1 .5 .6 . 7 • B .9 1.0 0 . 1 .2 .3 • 1 .5 .6 .7 .8 .9 1.0

X/L 01 ST. ALONG MEMBER AXIS (N 0 RM) X/L OIST. ALONG MEMBER AXIS (N 0 RM)

(e) ( f )

8.0 8.0

I-' 7.0 CYCLE 7 POINT C7. 0 ~ CYCLE 9 POINT C

I-'~ ~

\.0 ~ 6. 0 AXIAL DISP.= -0.35 z 6.0AXIAL OISP.= -0.35-

5. 0~

5.0

0- 1.0 a. 4.0V) V)

:3. 0 - :3.0Cl

I-2.0

I-2. 0

< 1.0 < 1.0--' --'

>- >- v

- 1.0 -I. 00 .1 .2 .3 • 1 .5 .6 • 7 .8 .9 1.0 0 • 1 .2 .3 . 1 .5 .6 • 7 .8 .9 1.0

X/L OIST. ALONG MEMBER AXIS (NORM) X/L OIST. ALONG MEMBER AXIS (NORM)

(g) (h)

Fig. 3.32 Deflected Shapes - Strut 4 (1 in. = 25.4 rom)

8.0 8.0

7 . 0 CYCLE 3 POINT C7. 0t

CYCLE 5 POINT C

AXIAL OISP.~ -0.20~

AXIAL OISP.~ -0.30z 6.0 z 6. 0-~

5.05. 0Cl. i.0 C1. i.0V"l V"l

3. 0 - 3.0c

..... 2.0 ..... 2.0< I . 0 < 1.0...J ...J

>- >-

-1.0 -1.00 .1 . 2 .3 • 1 • 5 . 6 . 7 .8 .9 1.0 0 . I .2 .3 • 1 . 5 .6 . 7 .8 .9 1.0

XIL OIST. ALONG MEMBER AXIS (NORM) X/L 01 ST. ALONG MEMBER AXIS (NORM)

(a) (b)

I-' 8.0 8. 0N CYCLE 6 POINT A

7. 0tCYCLE 6 POINT C0 7 . 0

AXIAL OlSP.= +0.01~

AXIAL OISP.~ -0.306. 0 z- 6.0~

5.0S. 0C1. i.0 C1. i.0V"l V"l- 3. 0 - 3. 0"" ""

2.0 ..... 2.0.....< 1.0 < 1.0...J ...J

>- >-

-1.0 -1.00 .1 .2 . 3 • 1 . 5 .6 . 7 . 8 .9 1.0 0 • I .2 .3 • 1 .5 .6 .7 .8 .9 1.0

XIL OIST. ALONG MEMBER AXIS (NORM) X/L OIST. ALONG MEMBER AXIS (NORM)

(c) (d)

Fig. 3.33 Deflected Shapes - Strut 3 (1 in. = 25.4 rom)

B. a 8.0

7.0 CYCLE 1 POINT C7 . U~ CYCLE 5 POINT C

AXIAL DISP.= - 0 . 22~

AX I AL DIS P. = - O. 35z 6.0 z 6. 0-s. a - 5 . 0

c.. 1.0 c.. 1.0'" '"

3.0 - 3 . a'"f-

2. a ..... 2 • a<:

1. a <:1 . 0...J ...J

>- ~ >-

-1.0 - 1 • 00 .1 . 2 . 3 . 1 .5 . 6 . 7 . B • 9 1.0 0 .1 • 2 . 3 .1 . 5 .6 . 7 .8 .9 1.0

X/L DIS T. ALONG MEMBER AXIS (N DRM) X/L o[S T. ALONG MEMBER AXIS ( NORM)

(0 ) (b)

8 . 'J B. 0f-'

7 . 0 CYCLE 8 Pa I NT C 7.0~ CYCL E 10 POINT CNf-' ~

AXiAL 0; .') P . ~ ,0. 10~

AXIAL OJ SP. = - O. SO6.0 z 6. a-5. 0 - s. 0

a.. 1 . 0 ~ 1.0'" ""

1.0 - 3 . a-=>

f-l. 0 ,- 2. 0

< 1 . a < 1 . 0...J ~

>- >-

- 1 . 0 -,1 . 0a .1 • 2 .3 .1 • S • 6 . 7 . 8 . 3 I . 0 0 .1 . 2 • 3 . 1 • 5 . 6 . 7 . 9 . 9 1.0

XI L DIS T. ALONG MEMBER AXI" (N 0 RM) X/L oI ST. ALONG MEMBtR AXIS (N 0 RM)

(C) (d)

Fig. 3.34 Deflected Shapes - Strut 5 (1 in. 25.4 mm)

8.0 8.0

7.0 CYCLE 3 POINT C7.0t

CYCLE 5 POINT C

AXIAL OISP.= - 0.21~

AXIAL OISP.= -0.35z 6.0 z- 6.0

5.0~

5.00.. 1.0 0.. 1.0V) V)- 3.0 - 3.0'" '"I-

2.0I-

2.0< 1,0 <

I. Or-' -'

>- >- 0

-1.0 -1.00 .1 .2 .3 • 1 .5 .6 .7 .8 .9 1.0 0 .1 .2 .3 • 1 .5 .6 . 7 .8 .9 1.0

X/L 01 ST • ALONG MEMBER AXIS (NORM) X/L OIST. ALONG MEMBER AXIS (NORM)

(0 ) (b)~NN

8.0 8.0

7. 0 CYCLE 6 POINT C7 . 0t

CYCLE 6 POINT 0

AXIAL 01 SP. = - 0 . 35~

AXIAL OISP.= -0.26z 6. 0 z- 6.0

5. 0~

5.00.. 1.0 0.. 1.0V) V)- 3.0 - 3. 0'" '"I-

2.0I-

2 . 0< 1.0 < 1.0..J -'

>- >-

-1.0 -I. 00 .1 .2 .3 • 1 . 5 .6 .7 • 8 .9 1.0 0 .1 . 2 .3 . 1 . 5 .6 . 7 .8 • 9 1.0

X/L OIST. ALONG MEMBER AXIS (NORM) X/L OIST; ALONG MEM8ER AXIS (NORM)

(c) (d)

8.0 8.0

7.0 CYCLE 7 POINT A7.0t

CYCLE 7 POINT C

AXIAL DISP.= +0.26 ~ AXIAL OISP.= -0.35z 6.0 z 6.0-5.0 ~

5. 0"- LO "- LO"" ""- 3.0 -Q Q 3.0

to-2.0

to-2.0

< 1.0 <-J -J 1.0>- >-

-1.0 -1.00 .1 .2 .3 . 1 .5 .6 .7 .8 .9 1.0 0 .1 .2 .3 . 1 .5 .6 . 7 .8 .9 1.0

X/L OIST. ALONG MEMBER AXIS (/IORM) X/L OJ _ -;- . ALONG MEMBER AXIS (/IORM)

(e) ( f )

8.0 8.0

7.0 CYCLE 9 POINT C7. 0~ CYCLE 11 POINT C

AXIAL OISP.= -0.15~ AXIAL DISP.= -0.55I-' z 6.0 z 6.0tv - -w ~

5.0~

5.0"- 1 . 0 c.. LOV) V)- 3.0 - 3.0Q Q

to-2,0

to-2.0

< 1.0 < 1.0...... ......>- >-

-1.0 - 1.00 • I .2 .3 • 1 .5 .6 .7 .8 .9 1.0 0 .1 .2 .3 . 1 .5 .6 .7 .8 .9 1.0

XIl oI ST. ALONG MEM8ER AXIS (/IORM) X/L oI ST. ALONG MEM8ER AXIS (NORM)

(g) (h)

Fig. 3.35 Deflected Shapes - Strut 6 (1 in. = 2.54 rom)

8.0 8. 0

7.0 7.0~ -:z: 6.0 z

6. 0 [~ ~ \ STRUT 2, LP-4C

5.0STRUT 2, LP-4C - ( PINNED)(THICK WALL) 5. 0

a.. LO Q. LOV)

/----~V')

~

3.0~

3.0t::I 0

2.0y'" "if<....

2 0~ ~STRUT 6, LP-4C..... /Y~STRUT 1, LP-4C '-- ..... • (FIXED)< 1.0 // (THIN WALL) -.....;: «:

1.0 *--*-....J "" ....J

V "'" " ---~-~. . ~~~->- >-

-1.0 - 1 . 00 .1 • 2 .3 . 1 • 5 .6 . 7 .8 .9 1.0 0 . 1 . 2 .3 • 4 . 5 .6 • 7 • B • 9 1.0

XIL OIST. ALONG MEMBER AXIS (NORM) XIL 01 ST. ALONG MEMBER AXIS (N 0 RM)

(a) THICK WALL (ST. 2) YS. THIN WALL (ST. I) (b) PINNED (ST.2) VS. FIXED (ST.6)

8. 0 8. 0

I-' 7 • 0 7. 0t\.) - ->I:> :z: 6.0 z 6. 0

~ ~- 5. 05. 0

a.. 4 • 0STRUT 2, LP-3C Q. 4.0 STRUT 2, LP-4C

V) (ANNEALED) V') (ANNEALED)~

3. 0~

3.00

""-2 . 0 ..... 2. 0 ~.....

«:1 . 0 *-*--*-~ «:

1.0 ~....J _--¥- ....J

>- ---- >- 0,

- 1 • 0- 1 . 00 . I . 2 .3 • 4 .5 .6 . 7 . B .9 I . 0 0 • I . 2 .3 • 4 • 5 • 6 . 7 . B . 9 1 . 0

XIL [': CT. ALONG MEMBER AXI S ( NORM) X/L DIST. ALONG MEMBER AXIS ( NORM)

(c) ANNEALED (ST. 2) VS. UNANNEALED (ST.4) (d) ANNEALED (ST. 2) VS. UNANNEALED (ST. 4)

Fig. 3.36 Deflected Shapes - Comparisons between Struts(1 in. = 25.4 rom)

1.6 1.6~ ~

I: 1 • 4 I: 1 . 4a: a:0 0

1.2z 1 . 2 z~

1.0 1 • 0 LP-3Cc.. c.. LP-6CV)

· BV)

· B~ ~

0 0

~,· 6 .6 /'f-- f-- ')If

'-.:~< • 4 < · 4 /'-' ~ ...J /" ~)-. · 2

~ )-. • 2 ~ ~

~~

.1 . 2 . 3 • 4 . 5 .6 . 7 .8 . 9 1.0 0 .1 . 2 . 3 • 4 . 5 . 6 • 7 .8 .9 1.0

X/L DIST. ALONG MEMBER AXIS [N 0RM) X/l DIST. ALONG MEMBER AXIS [NORM)

(0) STRUT I (b) STRUT 2

1.6 1.6~ ~

I-' :E: 1 • 4 :E: 1 . 4N a: c:U1 0

1 • 20

1 .2z z~

1.0 1.0c.. LP-3C /" c..V)

· B r V) .8 LP-3C~ ~

0

V~LP-6C ~ 0

/~LP&.6 .6f--

~ "" f-- ~< · 4 < · 4...J 7' ...J.~

)-. .2 f" )-. · 2 "y~~, I . I I I

0 .1 • 2 . 3 • 4 .5 . 6 • 7 .8 .9 J • 0 0 .1 • 2 • 3 • 4 . 5 • 6 • 7 .8 • 9 1.0

X/L DIST. ALONG MEMBER AXIS [NORM) X/L DIST. ALONG MEMBER AXIS [NORM)

(C) STRUT 4 (d) STRUT 6

Fig. 3.37 Deflected Shapes - Comparisons between Cycles

8

1514

®

1312II10

RIDGID PLASTIC P~

ELEMENT~__ !lEi:

I: IPy :

t "Py I __I-*-- L + I 8

\-8Ci -I I-- Ai

Ej =STRUT ENERGY DISSIPATED IN CYCLE i

RPj= Py <8Ei + 28Ci +8Ai )

97 8CYCLE

+--+-+-+~+--+~ STRUT

+~+-+®

543

pinned, annealed, D/t = 48pinned, annealed. D/t = 33pinned, unannea1ed. D/t = 48pinned, unannealed. D/t = 33fixed. annealed. D/t = 48fixed, annealed. D/t = 33

2

Strut 1:Strut 2:Strut 3:Strut 4:Strut 5:Strut 6:

0' , I , I , , , I , , , , , , ,

o

1.0

>­uzwU

LLLL 05w·za.....(feneno

wl~II

f-Jtv(j\

Fig. 3.38 Energy Dissipation Efficiencies per Cycle

161412108CYCLE

642O· • ' , , , , , , , , , , , , , ,o

7 IUt:AL IDEAL STRUTr- _. _.- _.. -_. I 1 ELASTIC-PLASTIC /:t-@6

, ELEMENT

.-1 a:- {IUU-lot:t"t"Il.. It.NI.T} I /"---" /WIll:: /'6 ,*(/) , /~ I

JH~ /,/ /: 5 1,1 /:t= .-c@u /' ~~ / ~u IlL. 4 /,.J..: ;LL /' ~~ W ,

N ,~ W ,

d /,' Strut 1: pinned, annealed, D/t = 48G :3 , Strut 2: pinned, annealed, D!t = 33/ " Z·+ x--X

@Strut3:Pinned,unannealed,DIt=48~ /': x""""'"x Strut 4: pinned, unannea1ed, D!t = 33t- ,/ ~-..ACD Strut 5: fixed, annealed, D/t = 48« 2 I A"" Jt.@ Strut 6: fixed, annealed, D!t = 33~ /' /::::> , ....

~ / _~_.... E'I =STRUT ENERGY DISSIPATED IN CYCLE i" ......, JiI'.

-- -4fi'1 8 8 8-~ RPj = Py ( Ei + 2 Ci + Ai)

Fig. 3.39 Cumulative Cycle Efficiencies

CENTERPLASTICREGION #1

P = Mp~

P IMp =7: I~...---- L/2---.j

~--P

a) PINNED - END STRUT

HEADPLASTICREGION

y~

CENTERPLASTICREGION#I

PLASTIC

I...HINGE .1

POINTS OFINFLECTION

FOOTPLASTICREGION

~

2MpP=TP 2

Mp= /:1

-p~-M p I

b) FIXED - END STRUT

Fig. 4.1 Formation of Plastic Hinges

128

fL =~ cos (77 ~ )",,"""'\.

","'\.

I I "I I I I I '\.I I I I I •

//1.0

//

//

//

//

////

77=l/Py

1.0

~/

//

//

///

//

//

FULLY PLASTICINTERACTION CURVE

FIRST YEILDINTERACTION CURVE

t-'tv\D

Fig. 4.2 Axial Load-Bending Moment Interaction Curves forElastic-Perfectly Plastic Thin Tubular Pipe Section

3LB2C

3

SECTION OFLOCAL BUCKLING

CENTER OFPLASTIC HINGE

LENGTH OFPLASTIC REGION (d'JLOCAL BUCKLING

5 __ .-- __ ,,-.--- .:::.:::- /'" .A- -,-__ - """" __-/ .,..t-. __

.,.'.,.- ..".,.--- • - •__ """W'",;'. • .........., '.,. .,. ..".,.- . .--........... I .~"".,. .,. ......- . .----ok"":"'''' .,............ .--.• IC

i

£ f f f t f f f]17 15 13 10 7 5

GAGE LOCATIONS

15

10L. 13 IN.

~

'0)(-z-........

enz«-0«0::-f-'

W

W0

0:::::>

~>0:::::>u

Fig. 4.3 Curvatures within Plastic Hinge - Strut 1 (Load Points C)(1 in. = 25.4 rom)

rt)

'0)(

CENTER OF-ZPLASTIC REGION- 5.........

Ienz«

2E-0

"« 0 -

""e----_-e IEa:: --- -- -- --W

-;........

lSECTION OF

a::I-' ::>w J- -5I-' «

I LOCAL BUCKLING>a::::>

iU

b I I Itt t t d17 15 13 10 7

GAGE LOCATIONS5 3

Fig. 4.4 Curvatures within Plastic Hinge - Strut 1 (Load Point E)(1 in. = 25.4 mm)

20

/rt~,. "/ I~.""""'. '"/ .1'" ...........~

/ .T 'I ~.,/ ,-/ /' ,~._.,

//' ~3g~tE '--.. '-- "~. SECTION ~, '''.

,/ ) '" ~'/If "

/ /~ " ~ 3C, I '~~4C

I LENGTH OF PLASTIC HINGE (fY 4C = ISIN ~'.. 5LB... ~ ·1

~ f f f t f f f----~17 15 13 10 7 5 3

GAGE LOCATIONS

o

5

10

15

fC')

'0)(-z-'"(/)Z<t:-0<t:0::-

f-' Ww 0::N

:::>t-

~0:::::>U

Fig. 4.5 Curvatures within Plastic Hinge - Strut 2 (Load Points C)(1 in. = 25.4 mm)

35

t.

13 10 7

GAGE LOCATIONS

LOCALBUCKLESECTION

. ~,/r ', -/ .

~~I~I

II

5

0 1 '" I ~r ~ <

b f f f t f f f ~17 15

10

-5

rt>10)(-z-"'-enz<{-0<{a::-

I-' WLV a::LV

:::::>.....<{>0::::::>u

Fig. 4.6 Curvatures within Plastic Hinge - Strut 2 (Load Points E)(1 in. = 25.4 rom)

5

)(z 0

"­(J)

z«o -520«Q: 5-

24 28

FOOTPLATE

IC

-- IE

32

-- 2C-- 2E

WQ::::>

~ 0.-.------.-~~~------1Q::::>U

-5 '--- ---I ....L.-__--L _

20 24 28 32GAGE LOCATION

Fig. 4.7 Curvatures within Foot Plastic Region - Strut 5(1 in. = 25.4 mm)

134

5FOOTPLATE

3228

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

24

,-,----41,..---.... - -

-5 I20 24 28 32

GAGE LOCATION

)(

- 0 I-----~~:::::::~~-...",..----j:

wa:::::>

~ a t---:;;;;~7~?~~=~~-­a:::>u

z

"enz<X:o -520<X:a: 5-

rt)

'0

Fig. 4.8 Curvatures within Foot Plastic Region - Strut 5(1 in. = 25.4 ~)

135

- 6C

FOOTPLATE

•••~--.._------'Itc--___I!!~ 6 E

!!~

5

5

~~~ 4C

111...o---.......-+-~-~::.:r4E

•••- 5 '-----'------''---'---

10

3E

:~: 5C

FOOTPLATE

- 3C5

It)

'0)(

0-z........enz« -5-0« 10a::-wa::::::>.- 5«>a::::::>u

0

-5 24 28 32 -5 24 28 32

GAGE LOCATION

Fig. 4.9 Curvatures within Foot Plastic Region - Strut 6(1 in. = 25.4 mm)

136

- LB

FOOTPLATE

,--...-- BC

5

5

o

-5 '----...1-_1...---1..__

- 9C

- 7C

FOOTPLATE

,',

.',

';:...... ..-of

5

5

o1-----7-----1

wa::::::>l­e::{

>a::::::>u

-

z"­(f)

z 5« _ ~ ..L.-_I...---1..__

~ 10a:::

.'..'.::::::

'?o 111'.'

:. 0 I----~--~-_t!~! 7E

i

-5 2~ 28 3'2 -5 24 28 32

GAGE LOCATION

Fig. 4.10 Curvatures within Foot Plastic Region - Strut 6(1 in. = 25.4 mm)

137

I-'W00

20wa::::Jrt>~ 1015> )(a:: -::J Zu ::::

(/) 10~ Z::J «~ 0X « 5« a::~ -

Strut 1:Strut 2:Strut 5:Strut 6:

pinned, annealed, D/t = 48pinned, annealed, D/t = 33fixed, annealed, D/t = 48fixed, annealed, D/t = 33

10 20 30 40 50 60 70

INELASTIC ROTATION (RADIANS X 10-3)

80 90

Fig. 4.11 Maximum Curvature vs. Inelastic Rotation(1 in. = 25.4 mm)

wc::::::>

~40> SECTION OFc::

::::>", LOCALU'O BUCKLINGU-;~ _30enz«-..J'Wen ~ LOAD

I-' Z ~ 20 -. POINTw - -\.D

W 0 I ------- I

~ ~3LB>«_0: ~ ..-------- ~:3A~ - 10

2D..J::::>~

0 1 r:=:== ! t ~r r ----.... 2A::::> ,.. I DU

17 15 13 10 7 5 :3

GAGE LOCATIONS

Fig. 4.12 Cumulative Inelastic Curvatures with the Center Plastic Hinge - Strut 1(1 in. = 25.4 rom)

SECTION OF

w . - - ._ LOCAL BUCKLING

0:: 50::>.-~0:: 40::>UoU-;try Z 30<3:::::: .

~ ~'"LOAD...J en I IWz I ~ POINT

I-' Z « 20of:>, - ~ ~5LB0 wO>«

~i5A-0::

---------r-- 4D<3: 10...J:::::> I I I ~ ~4A~::>

0 1.

"'3DU I I I 1 I I17 15 13 /0 7 5 3

GAGE LOCATIONS

Fig. 4.13 Cumulative Inelastic Curvatures within the Center Plastic Hinge - Strut 2(1 in. = 25.4 mm)

",

·0)(

U -40- zI- SECTION OFCf) .......

rLOCAL BUCKLING<t Cf)

-J ZW <t 30Z -

0

W<t LOAD0::

> - 'POINT- 20I- w 5LB<t 0:: 5A-J :::> 4D:::> I-~ ~:::> 10 4AU 0:: 3D:::>

u 3A 2D2A

020 24 28 32

GAGE LOCATIONS

Fig. 4.14 Cumulative Inelastic Curvatures within the Foot PlasticRegion - Strut 5 (1 in. = 25.4 mm)

141

LOAO", SECTIONOF~ POINT·0

LOCAL 10LB)( 90 BUCKLING-z-" lOAenz 80<{ 90-0<{a:: 70- 9Awa::::J 80r- 60~

8Aa::::JU

50U 70r-en 7A<t....J 40w 60Z

w 6A> 30-r-<t 50....J::J 5A~ 20::J 40U

4A10

30

020 24 28 32

GAGE LOCATIONS

Fig. 4.15 Cumulative Inelastic Curvatures within the Foot PlasticRegion - Strut 6 (1 in. = 25.4 nun)

142

0

M

ol-I;jl-Iol-Itf.l

I

l=:T'lClll-I

(J)ol-Itf.l

0 It) Z M

0 Cll'r-!

0 10

~~

I'- tJ0 U 'r-!-., ---+- 0 ol-I0 0 CIl

CllIt) --I M

Q)

10 Wl=:

0 H

C> Q)

« :>I'- 'r-!

0 (!) ol-ICll

I I M

§<{ 0 <{ t.)

r() N N\0M.-::t

btlT'l~

w ~ N 0o 0 0 r-----1_--L_....

o 0 d(NI/NI) NI'i1~.LS 31\1.L'i1lnV\ln::>

143

<t

z....... 0.06z ,

50-z I 5A-«cr

~ 0.04 40-I.LJ>~ 4A-

t-'II:> ...JII:> :=)

~ 0.021 30-

:=)

1 3A-u

20-

t- 1° ' tt1tttj ~ +17 15 13 10 7 5 3

GAGE LOCATIONS

Fig. 4.17 Cumulative Inelastic Axial Strain - Strut 2

(f.0.10

-3D

-10

-3A

-60-6A-50-5A

-40enI-

-4A ~oa..cg.....J

-20

-2A

+I CENTER OF

$LASTIC HINGE60

6AI

50/

5A/

40/

4AI

3D/

3AI

20

o

0.08

0.02

0.06

0.04

z.......z

Z<t0:

Inw>~.....J::::>::!:::::>u

i-'

*'"1Jl

c c c c c c c c

4 8 12

GAGE LOCATIONS16 20 24 28 32

Fig. 4.18 Cumulative Inelastic Axial Strain - Strut 5

oc c c ccccc

2Atj;t ~

10

~I

0.10I

6D-\\ II

+ 0.08 -:2-"

I

:21 --0.06 :2

«£r60 ....en60

6A lLJ>

en

0.04 ....

.... 4A-

50 «

:2

....J

0

5A =>

I-'

~

"'" a.. 3D-

=>

(J\

0

40"",,- (,)

<t0

4A.0.02

....J "'2/\ _

4 8 12

GAGE LOCATIONS16 20 2428 32

Fig. 4.19 Cumulative Inelastic Axial Strain - Strut 6

30

25-en~- o STRUT 1 : PINNED, ANNEALED, 0.083 IN. WALLen

20~ L.B.en [J STRUT 2: PINNED,ANNEALED, 0.120IN. WALLlIJ _/a::~enlIJ>- 15 L - "'- [Jen

f-' eno!'> lIJ-.J a:a..::?10u

10::?1:::>::?1-x<t::?1 5

oo 0.500 1.000

CUMULATIVE INELASTIC ROTATION

1.500

Fig. 4.20 Maximum Compressive Stress vs. Cumulative Inelastic Rotation(1 ksi = 6.9 }Wa)

40

COMPRESSION TEST (CYCLIC CURVE I)

30~ r -- -::::::-:=:::- . 12!±llJ $

.".,.. ..".,...- "",..,..- ".. .CYCLIC (j(f)

X~CYCLICCURVE 3~ TEST-(f) 20 I~/ CYCLIC CURVE 2(f) / ./

I-'w

..,. 0:: ~ ./ I , I ECD .- •(f) /

10 ./.

o r ! I I I I I COMPRESSION0.0 0.004 0.008 0.012 TEST

I I I I I I I

0.0056 0.0096 0.0136 0.0176 CYCLIC CURVE 2I I I I I I I

0.0160 0.0200 0.0240 0.0280 CYCLIC CURVE 3

CUMULATIVE INELASTIC STRAIN

Fig. 5.1 Stress-Strain Curves from Cyclic Test - Annealed Material(1 ksi = g.9 MPa)

40..-

/COMPRESSION TEST

enen 20 I-W0::l-en

101-

en~

_ 30F,

'\

~.~

".". /CYCLIC CURVE 2" . ......... ,,--L...._" ------. --'--'" ------

·'.,<,CYCLIC CURVE 3

."""-...............--

01 1 I 1 I ·-·=j=°-·-·IL.- _10 20 30

TANGENT MODULUS, Et (KSI x 10-3)

-I-'

"'"\rJ

Fig. 5.2 Stress-Et

Curves, Annealed Material (1 ksi = 6.9 MPa)

40

KL/r =25 54 COMPRESSION TEST

30

--(/)~-

I-'(/) 20

U10

(/)wa::l-(/)

10

jCYCLIC CURVE 2~,.'..........." ""."...........~.; ------. ----........................... ----.--.

CYCLIC CURVE 3 --.---_._

o I 20 I 40 I 6'0 80 100 120 140 160 180

KL/r

Fig. 5.3 Stress-KL!r Curves, Annealed Material (1 ksi = 6.9 MFa)

x30

en 0en 0w 20a::I-en...J THEORETICAL<{u Kt/r =54I- 15a:: o BRACE Iu

[] BRACE 2

0.005 0.010 0.015 0.020

CUMULATIVE INELASTIC STRAIN (IN/IN)

o

THEORETICAL

0.005 0.010 0.015 0.020

CUMULATIVE INELASTIC STRAIN (IN/IN)

K t/r = 25

o STRUT 5

[J STRUT 6

o

30

enenwa::I-en 20...J<{U

I-a::u

-

Fig. 5.4 a VS. CIScr

(1 ksi = 6.9 MPa)

151

100

90

80

70

-en 60~-en 50enw0:::

~ 40

30

20

10

-- CYCLIC I-- CYCLIC 2--- CYCLIC 3

-- SPECIMEN 3 TEST-.-- COMPRESSION TEST_.-.- COUPON TEST

CYCLICTEST I

---ff--+--~ E

OIL..------..L...--..L-_--L-__....L.-_---'-__.....a...-_----'

0.002 0.012 0.014

Fig. 6.1 Variation in Stress-Strain Curves (D/t=48)Unannealed Material (1 ksi = 6.9 MPa)

152

90

80

70

60-en~ 50enenw 400:::I­en

30

20

10

.-. ---_.-.. -........ .........--.:..--."'" ~. -::;..;.-­.." ~.~. "/;?""

P/,/

/ /' --- --- ---// ---

.'/ ...---# ,....---"'-'I //"",.... CYCLIC I

I~· / -- CYCLIC 2l' // _.- CYCLIC 3

.' / SPECIMEN 4 TEST~I/ --- COMPRESSION TESTV _._.- COUPON TEST

CYCLICTEST

3

-,..--+-+----:)1- E

2

O-----'---~----'---'---..&....-..:--~-----~----:"0.002

Fig. 6.2 Variation in Stress-Strain Curves (D/t=33)Unannealed Material (1 ksi = 6.9 MPa)

153

202020

COMPRESSION TEST--- CYCLIC 3

1001 100r 100

..--/~

80 I- ~ 80~\\ 80--en~

~ 60~ Ii 601- '\."'-. 60

enW

I-' 0:::U1~

~ 40~ I 401- ........ --, 40

0 0 I 0.004 I 0.008 I 0.012 I 00 10 20 30

TANGENT MODULUS, Et (KSIx 10-3 )

Fig. 6.3 Stress vs. Strain, Et

, L/r (0.083" w.t.), Unannealed Material(1 ksi = 6.9 MFa)

COMPRESSION TEST--- CYCLIC 3

IOO~100

IOO~---...-

"/' 80 '\80 / 80 \- / \ \- \en / \~ \~ 60 / 60 \ 60 \\en / \

I-' W \\U1 0:: \U1 t- \U) 40 40 , 40

~ :.\

20U 20L

~~. 20

, II I __ • __O· '-..2-. 1 _

o 00 10 20 30

TANGENT MODULUS, Et (KSIx 10-3 )

Fig. 6.4 Stress vs. Strain. E • L/r(1 ksi = 6.9 MFa) t

(0.120" w. to), Unannea1ed Material

50,------------,------------------..,------------,

IE 2E

Ie

2B

2E

IE

LB

OTUBING

7G 8G

20

30

40

-30

-20

~52 10

C 3A« 01-------/Y'----+ft"-'I:.:.A-----------------::::-':ltHl''------t-HL-L\--\-------j9.J~ -10

~

-40

0030.020.01o-0.01-0.020.020.01o-0.01-0.02-50 '------'-----'----"'--------'------'-----'------'-----'----"'--------'-----'

-003

STRAIN, INCHES I INCH

Fig. A.1 Strut 1 - Axial Load VB. Strain (Gages 7 and 8 - Cycles 1-5)

50,-------------.;------------------..,------------,

IB

2E

IB

0"""Gil20

40

30

-30

-20

ena.52 10

ci'« Of---------7Iy+tf'---,i/'t-t-'---------------'7I'c-"f--Jc--!f"''-+1I<c::-f---'--------j9.J~ -10

~

-40

0030020.01o-0.01-0.020.020.01o-0.01-0.02

-50 L-__--'- -'-- L-__--'- --'- -'--__--'- -'-- L-__-----'- -'

-0.03

STRAIN, INCHES liNCH

Fig. A.2 Strut 1 - Axial Load vs. Strain (Gages 9 and 11 - Cycles 1-5)

156

50

40 0'""'"lOG. 12G

2E 2E 3E 4E 5E30 IE IE

20

rnQ.

10~

0<l:

00

9 2...J~ -10X<l:

LB-20 2C4B

3BIB 2B

-30GAUGE 10 ~

-40

-50-0.03 -0.02 -0.01 0 0.01 0.02 -0.02 -0.01 0 0.01 0.02 0.03

STRAIN. INCHES / INC H

Fig. A.3 Strut 1 - Axial Load vs. Strain (Gages 10 and 12 - Cycles 1-5)

IEZE IE 2E 3E3E

'( I4E 4E'0IG 2G

- TUBING

-

-20

Ili~ l?iA ~~ /4A5A

It:3A 20/ /' '\ 5A

'" 403D 40

r- 3D 3A

I-

5B5B

13B

4BI- 48

36 GAUGE 2 GAUGE I

f-- 2826

I II

I I I IIB I I

50

40

30

20

rnQ.~ 10

oC3 0.::J

~ -10X<l:

-20

-30

-40

-50-0.03 -0.02 -0.01 o 0.01 0.02 -0.02 -0.01 o 0.01 0.02 003

STRAIN. INCHES / INCH

Fig. A.4 Strut 2 - Axial Load vs. Strain (Gages 1 and 2 - Cycles 1-5)

157

503E

3E4E 4E

40 0'"""7G 8G30

20

(J)a.~ 10

ci<t

09 3A 4A 3D SA....J<t -10 5CX<t

4C-20

4B 5B 4B-30

3B 3B

-40GAUGE B GAUGE 7

'"<:

-50-0,06 -0.05 -0,04 -0,03 -0.02 -001 0 0,01 -0.01 0 0.01 002 0.03

STRAIN,INCHES / INCH

Fig. A.5 Strut 2 - Axial Load vs. Strain (Gages 7 and 8 - Cycles 1-5)

50~----------.,.--------------------,-----------_,

4E

5A

3E

4B

38INITIAL

BUCKLING

5C

4A

5A

3E

4E

5B

Gil20

40

30

-30

-40

-20

~:;z 10

og ol-------------'ifC-----,H'k---------------+t'---7f-+------------j....J....Jg -10X<t

0,030,020.01o-0.01-0,020.020,01o-0,01-0.02

_50L.....__---l. --'- ..L...__----' --'- ...L...__----' --'- -'- -'--__--'

-0.03

STRAIN, INCHES / INCH

Fig. A.6 Strut 2 - Axial Load vs. Strain (Gages 9 and 11 - Cycles 1-5)

158

4E3E

3A 4A

4E3E

5B 4B

3B3B INITIAL

INITIAL BUCKLINGBUCKLING

GAUGE 12 GAUGE 10

-003 -002 -DOl 0 0.01 -0.01 0 0.01 0.02 0.03

50

40 0'""'"lOG 12G30

20

(/)a..:lo: 10

0octg 0

-oJoct -10Xoct

-20

-30

-40

-50-0.06 -0.05 -0.04

STRAIN ,INCHES I INCH

Fig. A.7 Strut 2 - Axial Load vs. Strain (Gages 10 and 12 - Cycles 1-5)

50

4E 3E 3E 4E

40 0'""'"13G 14G30

20

(/)a..:lo: 10

0 4D 4A

3 3A 4A0

3D-oJ 5Aoct -10Xoct

4C 3C-20

LB

3C 5B\B-30

3B3B

-40 GAUGE 14 GAUGE 13

-50-0.06 -005 -004 -003 -002 -DOl 0 0.01 -0.01 0 0.01 002 003

STRAIN, INCHES liNCH

Fig. A.8 Strut 2 _. Axial Load vs. Strain (Gages 13 and 14 - Cycles 1-5)

159

0.030.020.01o-0.01

4C

-0.020.020.01

3E

2E

o-0.01

4C

G5

G3

0"""

-0.02

120

100

80

60

(f)

~ 40lIl:0g 20

...J<l: 0X<l:

-20

-40

-60

-80-0.03

STRAIN t INCHES / INCH

Fig. A.9 Strut 3 - Axial Load vs. Strain (Gages 3 and 5 - Cycles 1-5)

120,-------------,------------------,------------,

4C

4E

3E

2E

IE

IC

IE

3E2E

4C

O TU81NG

4G 6G

60

80

-60

100

-40

-20

(f)

~ 40lIl:

o<l: 209...JS Of---------++--+--+-------~~-------___trr_r_-------_____jx<l:

0.030.02o-0.01-0.020.020.01o-0.01-0.02

-80 L-__-'-- L-__-'-- L-__-'-- L-__--'-__--' --'-__--' -'

-0.03

STRAIN t INCHES

Fig. A.10 Strut 3 - Axial Load vs. Strain (Gages 4 and 6 - Cycles 1-5)

160

4C GAUGE 52C

3CIC

120 G3

100

0,,",,"80

60

-60

-40

-20

C/)

~ 40~

og 20

..J<l OI---------I-+---+tIl------------------+-.jIL----------~

~

0.030.020.01o-0.01-0.020.02001o-001-0.02

_80'---__--'- --'- -'----__--'- -'--- -'---__----'- -'-- L-__----'- -l

-003

STRAIN. INCHES / INCH

Fig. A.ll Strut 4 - Axial Load vs. Strain (Gages 3 and 5 - Cycles 1-5)

0.030.02001o

IB

-0.01-002002

120

0"""" "100 3E4G 6G 6E

5E

804E

60 IE

C/)

~ 40~

0

~ 20..J..JS; 0X<l

-20

-40

-60 IGAUGE 6

2C

-80-003 -0.02 -001 0 001

STRAIN. INCHES / INC H

Fig. A.12 Strut 4 - Axial Load vs. Strain (Gages 4 and 6 - Cycles 1-5)

161

G9

-

O'""~ 4E 4Er---

(II-Gil

l-

I 'sA \A

I-

~Ul-

I--5C

GAUGE 9 GAUGE II

l-

I I I I I I I I

50

40

30

20

(J)0..~ 10

o<t 09...Jg -10

~-20

-30

-40

-50-003 -0.02 -0.01 o 0.01 0.02 -002 -0.01 o 0.01 0.02 003

STRAIN ,INCHES / INCH

Fig. A.13 Strut 5 - Axial Load vs. Strain (Gages 9 and 11 - Cycles 1-5)

0.030020.01o-0.01-0020.020.01o-0.01-0.02

I- 0'"""12G lOG 4E .......4Ey---.I--

r~I--

I-

'~ 5A

-

J--

5C- 58

GAUGE 10 GAUGE 12

-

I I I I I I I I

-40

-50-0.03

-20

(J)

~ 10

o<t 09...Jg -10X<t

20

30

-30

50

STRAIN. INCHES / INCH

Fig. A.14 Strut 5 - Axial Load vs. Strain (Gages 10 and 12 - Cycles 1-5)

162

50,------------,---------------------,-------------,

G29

O'""~3E 4E 3E 2E2E

IE IE

G31

IA3A 5A

4A 2A3A

-30

-40

-20

30

20

40

(f)

~ 10:l<::ci~ ol---------''iYf-++--+IJ+'-------------------''-'<t'':U+t'-I'-----;oif-+--------1...J...Jg -10XeX

0.030.020.01o-0.01-0.020.020.01o-0.01-0.02

_50'----__---'- ---'--- .L-__---' ---'-- --'-__--'- ---'--- -'-__-----' -'

-0.03

STRAIN, INCHES/ INCH

Fig. A.15 Strut 5 - Axial Load vs. Strain (Gages 29 and 31 - Cycles 1-5)

50

40

0'OO'~ 4E 3E 4E32G 30G 2E IE

30 IE

20

(f)Q. 10~

a ID

« 2D 2A

g 04A 3A

...Jg -10X«

-20 18

-30 Ie

-40

0.030.020.01o-0.01-0.020.020.01o-0.01-0.02

-50 L-__--'- -"- "--__--'- -L -'-__..-L ---'--- "--__---' -'

-0.03

STRAIN ,INCHES / INCH

Fig. A.16 Strut 5 - Axial Load vs. Strain (Gages 30 and 32 - Cycles 1-5)

163

G93E 5E 4EV;{--4E 5E

I- 0'"""I-

'" Ii (l-

I-

L/5A 1/6A

~1'-4A 5A3A

l-

I-

~ tJ'-., GAUGE 9 GAUGE III- 5C 2

4C

I I 3C 38I I I I I I

50

40

30

20

eng, 10~

oC3 0.=J....J~ -10

~-20

-30

-40

-50-0.03 -0.02 -0.01 o 0.01 0.02 -002 -0.01 o 0.01 0.02 0.03

STRAIN, INCHES II NCH

Fig. A.17 Strut 6 - Axial Load vs. Strain (Gages 9 and 11 - Cycles 1-5)

3[5 2E 3E 4E 5Ev 4 r----- ---< ~I- 0"-12G lOG

l-

I-

I-

3D 50 40, 4~ 50"

4A/ 6A5A f'SA;:;'6A

l-

I-

I- (5C- 4C" /58

I- 3(48

38~ 48 58GAUGE 12 GAUGE 10

I I I---I

I I I38

I--1-

50

40

30

20

~~ 10

~9 0

<J.- -10

~

-20

-30

-40

-50-0.06 -0.05 -0.04 -0.03 -0.02 -0.01 o 0.01 -0.01 o 0.01 0.02 0.03

STRAIN,INCHES liNCH

Fig. A.18 Strut 6 - Axial Load vs. Strain (Gages 10 and 12 - Cycles 1-5)

164

OW""3E~ 4E

~.2E

VE rP 3E

-

~-

- G30

-

6:\6A SA

\ I\A ~O '4A

- 4A

-

f---

5C iJ 1//f--- 5E"--- GAUGE 29

4C~~GAUGE 31

I I I I I36

II 1

50

40

30

20

~S2 10

ci<5 0...J...J~ -10

~-20

-30

-40

-50-0.03 -0.02 -001 o 0.01 002 -0.02 -0.01 o 0.01 0.02 003

STRAIN, INCHES / INCH

Fig. A.19 Strut 6 - Axial Load vs. Strain (Gages 29 and 31 - Cycles 1-5)

9EirE IOE

9E8E7EG29

7~6E -~ 6E

0""" I

(G31

1008010~

1/o9AI~g\

9A90 8A 70

60 70 \ 6A 80 6~0{ 6A

7A 7A

9~~ IOJ!)/ j8C ~

7C6c],1 68988676

50

40 f---

30 I-

20 I-

~ 10S20

~ 0...J...J~ -10X<l:

-20 -

-30 -

-40

-50-0.03

I-002

I-0.01 o

GAUGE 29

I0.01

I0.02

10C

9C

I

-0.02

I

-0.01 oI

0.01

I

002 003

STRAIN, INCHES/INCH

Fig. A.20 Strut 6 - Axial Load vs. Strain (Gages 29 and 31 - Cycles 6-10)

165

0/""&E 5~ 3E

1- 32G 30~ IF

l-

I-

I-

5A

/1 6A 1/4A

36 5614(

l-

I--

1/I--

5B

V GAUGE 30 GAUGE 32I--

3C 5C 4B4C

I I3B

I I I I I I

50

40

30

20

C/)Q.i: 10

o<t 09-lS -10

~-20

-30

-40

-50-003 -0.02 -0.01 o 0.01 0.02 -0.02 -0.01 o 0.01 0.02 003

STRAIN, INCHES / INCH

Fig. A.21 Strut 6 - Axial Load vs. Strain (Gages 30 and 32 - Cycles 1-5)

50,-----------------------,------------,---------------,

0.030.020.01o-0.010.01o-001-002-003-004-005

~TUBING

32G~30G

20

30

LB

40

-30

_50L-__-L .L...--__-L -'-__-L -'-__---' -'--__--'- -'--__-.l.__----'

-006

-20

-40

C/)Q.:s: 10

ci<t9 ol-------------71------:;"f------:;+--++---7I--7I-tr-k-k-:---------tttt------------j

<J.- -10

~

STRAIN ,INCHES / INCH

Fig. A.22 Strut 6 - Axial Load vs. Strain (Gages 30 and 32 - Cycles 6-10)

166

50

40 0"""3G 4G 2E30 IE

20

(/lQ.

10i;2c:i 2AoCt

9 0

...JoCt

-10 3CXoCt

-20

-30

-40

-50-0.010 -0.005 0 0.0050.005o-0.005

- 0"""IG 2G-

-

-

-

t-

t-

t-

I

-20

-10

50

20

10

o

40

30

-30

-40

-50-0.010

CURVATURE, RADIANS/INCH CURVATURE, RADIANS/INCH

Fig. A.23 Strut 1 - Axial Load vs.Section Curvature(Gages 1,2 - Cycles 1-5)

Fig. A.24 Strut 1 - Axial Load vs.Section Curvature(Gages 3,4 - Cycles 1-5)

50 50

40 0'""" 40 0'"""5G 6G 2E7G 8G

30 IE 30

20 20

(/l (/lQ.

10Q.

10i;2 i;2c:i c:ioCt

0oCt

09 9...J ...JoCt

-10oCt

-10X XoCt oCt

-20 -20

-30 -30

-40 -40

-50 -50-0.010 -0.005 0 0.005 -0.010 -0.005

2E

IE

o 0.005

CURVATURE, RADIANS/INCH CURVATURE, RADIANS /INCH

Fig. A.25 Strut 1 - Axial Load vs.Section Curvature(Gages 5,6 - Cycles 1-5)

Fig. A.26 Strut 1 - Axial Load vs.Section Curvature(Gages 7,8 - Cycles 1-5)

167

50 50

40 0""" 40

lOG 12G 2E 0 2E30 IE 30 IE

TUBING

20 20

C/) C/)Q.

10Q.

i2 i2 10

ci 3A ci 3A~

0 ~ 2A9 9 0

IA...J ...J~

-10 ~ 3CX -10~ ~

-20 -20

IB3B 2B

-30 -30

-40 -40

-50 -50-0.010 -0.005 0 0.005 -0.010 -0.005 0 0.005

CURVATURE, RADIANSIINCH CURVATURE, RADIANS liNCH

Fig. A.27 Strut 1 - Axial Load vs.Section Curvature(Gages 10,12 - Cycles 1-5)

Fig. A.28 Strut 1 - Axial Load vs.Section Curvature(Gages 7,8 - Cycles 1-5)

50 50

40 0'"'' 40 0"""15G 16G 2E 17G IBG 2E30 IE 30 IE

20 20

C/)~!l-

10 10i2 i2ci ci 3A

92A ~ 2A

0 9 0IA

...J ...J~ -10 3C ~

-10 3C

~ X~

-20 -20

IB 2BB

-30 -30

-40 -40

-50 -50-0.010 -0.005 0 0.005 -0.010 -0.005 0 0.005

CURVATURE, RADIANS liNCH CURVATURE, RADIANS/INCH

Fig. A.29 Strut 1 - Axial Load vs.Section Curvature(Gages 15,16 - Cycles 1-5)

Fig. A.30 Strut 1 - Axial Load vs.Section Curvature(Gages 17,18 - Cycles 1-5)

168

0.0150.010-0.005 0 0.005

CURVATURE, RADIANS/INCH-0.010

2E'' 3E,-4Eeo,"""IG 2G

f-

f-

f-

f-

f-

\1;8f--- 48

3B

f-28

18J I I I

-40

-50-0.015

-30

50

-20

20

30

40

~52 10

~ 0

..J~X -10~

Fig. A.3l Strut 2 - Axial Load vs. Section Curvature(Gages 1,2 - Cycles 1-5)

50,--------------------,--------------------,3E

40

30 O TU81NG

3G 4G

20

3C

303A

-20

Cf)ll..~ 10

~g ol------------:+--+-----\--'i\''--------------------i

..J

~ -K)

~

-3048 58

38

-40

0.0150.0100.005o-0.005-0.010

_50L- ---l --L -L J- --'- ----'

-0.015

CURVATURE, RADIANS/INCH

Fig. A.32 Strut 2 - Axial Load vs. Section Curvature(Gages 3,4 - Cycles 1-5)

169

4B

50

40 0'"""5 6G30

20

(/)a..~ 10

~9 0

...J«-10X«

-20

,30

-40

-50-0.015 -0.010

3B

-0.005 0 0.005

CURVATURE t RADIANS /1 NCH0.010

40

4C

0.015

Fig. A.33 Strut 2 - Axial Load vs. Section Curvature

(Gages 5.6 - Cycles 1-5)

50.-------------------,------------------,

3E 4E

40

30 OTUBING

7G 8G

20

3A

-20

-30

(/)a..~ 10

~9 of-----------------7Ic_--~c_-*---___\"''''--------l;H

...J«X -10«

3B

-40

0.0150.0100.005o-0.005-0.010_50'----------'-------'---------''-------'------..L-------'-0.015

CURVATURE, RADIANS/INCH

Fig. A.34 Strut 2 - Axial Load vs. Section Curvature(Gages 7,8 - Cycles 1-5)

170

-0.005 0 0.005

CURVATURE t RADIANS liNCH

50

40

30

20

UlQ.

~ 10

~9 0

..J<{

-10X<{

-20

-30

-40

-50-0.015

O. TUBING

lOG 12G

-0.010

3E

36

4E

4B

0.010 0.015

Fig. A.35 Strut 2- Axial Load vs. Section Curvature

(Gages 10,12 - Cycles 1-5)

50,-------,------------------------------,

,f'\~

TUBIY

4E

4B

4A

3E

3A

2E

20

40

30

-20

-30

UlQ.~ 10

ci~ 01---------+--+-------+:------71--"""'--------,1------------1..J..J

~ -10<{

36

-40

0.0250.0200.01500100.005o-50 '---------'-------'--------'--------'---------'---------'-0.005

CURVATURE, RADIANSIINCH

Fig. A.36 Strut 2-Axia1 Load vs. Section Curvature(Gages 13,14 - Cycles 1-5)

171

50r---------,----------~-----------------___,2E 3E 4E

5C

4C

TU81NGO

15G. 16G

L8

3C

58

4A

30

40

20

-20

enll.52 10

~ 01--------Ir---,,\-----~*____7~--------*-------_____i...J<lX -10 -<l

-30

38

-40

0.0250.0200.0150.0100.005o-50 L- --' ----'- -'-- ___'___ _L_ ___'

-0.005

CURVATURE, RADIANS/INCH

Fig. A.37 Strut 2 - Axial Load vs. Section Curvature(Gages 15,16- Cycles 1-5)

-20

-30

-4028

0.0150.010-0.005 0 0.005

CURVATURE, RADIANS/INCH-0.010

_50L...... ---.l -L ~ ___'___ _L_ ___'

-0.015

Fig. A.38 Strut 2-Axia1 Load vs. Section Curvature

(Gages 17,18 - Cycles 1-5)

172

120

100 0'"""804G G

60

ena-s;;: 40

0<t9 20

..J<t 0X<t

-20

-40

-60

-80-0.015 -0.010

3E

2E

IE

4C

IC2C

-0.005 0 0.005

CURVATURE, RADIANS/INCH0.010 0015

Fig. A.39 Strut 3 - Axial Load vs. Section Curvature(Gages 4 , 6 - Cycles 1-5)

12o...-------------------,-----------------,

3C2C

IC

OTUBING

4G 6G

80

-60

100

-20

-40

60ena-~ 40

o<t9 20

..J~o~---------------__+-H+-\_It\--...l\_-~'"""--------_fx<t

00150.010-0005 0 0.005

CURVATURE, RADIANS/INCH-0.010

_80L-------L-----...L-------'--------'---------''-------'-0.015

Fig. A.40 Strut 4 - Axial Load vs. Section Curvature(Gages 4,6 - Cycles 1-5)

173

0.0150.0100.005o-0.005-0.010

- om"," 4E12G lOG

-

-

-

["'sA-

-

)- /-

-

I I I I-50-0.015

-40

50

-30

-20

20

30

40

ffi;2 10

C«9 0

...J« -10

~

CURVATURE, RADIANS/INCH

Fig. A.41 Strut 5 - Axial Load vs. Section Curvature(Gages 10,12 - Cycles 1-5)

0.0150.010-0.005 0 0.005

CURVATURE, RADIANS/INCH-0.010

~ om,,",J~3E

16G 14Gf-

f-

-

./4A

5( \0-

- ..~,)\f-

4C 4Bf-

I I I I i-40

50

-30

-20

-50-0.015

20

40

~i;2 10

C«9 0

<J.- -10~

Fig. A.42 Strut 5- Axial Load vs. Section Curvature

(Gages 14,16 - Cycles 1-5)

174

0.0150.0100.005o-0.005-0.010

CO20G 18G 4E3J

I- TUBING

I-

-

~·'40 ~A3A 20SA 4A

-1\

- / I~ :::;.

3B- 3 58 4B 4C

(L.B.)

I I I I-50-0.015

-40

50

-30

-20

20

30

40

~~ 10

~9 0

...J<l: -10

~

CURVATURE, RADIANS/INCH

Fig. A.43 Strut 5-Axial Load vs. Section Curvature

(Gages 18,20-Cycles 1-5)

0.0150.0100.005o-0.005-0.010

Co""" 2\ ~~E24G 22GI-

'\l-

I-20

riA

3Aj:'--30 "'40

I- 5~/

I- iv

~~I-

3BI:z~ 4C4B

I- 3C

I I I I-50-0.015

-40

50

-30

-20

20

30

40

~~ 10

~9 0

...J<l:X -10<l:

CURVATURE, RADIANS/INCH

Fig. A.44 Strut 5 - Axial Load vs. Section Curvature(Gages 22,24-Cycles 1-5)

175

0.0150.0100.005o-0.005-0.010

:"'~"" 4E ~ E

~~TUBING

~e-

e-

~O /40

~ ~~~'-

- \ 2B

- b-.J(L.Bl5B

3B4~4C

3C,- 2C

I 1 I I

-40

-50-0.015

40

50

-20

-30

20

30

~52 10

~9 Q.

;;1X -10c(

CURVATURE, RADIANS/I NCH

Fig. A.45 Strut 5-Axial Load vs. Section Curvature(Gages 26,28- Cycles 1-5)

50r---------------~_.----------------_,

40-

O TUBING 2E 3E fE

32G 30G IE

~ :~ ~:~/'"9 o~------------/,H--\¥--_--Jk.~.hdf':...-3D-¥-----------------j

2"/ 5A 10;;1 ~ ~X -10-c(

-20 -

-30-

-40f-

0.015_50L-----l-I----il-------.l-----L-I----.L-1 ------'-0.015 -0.010 -0005 0 0.005 0.010

CURVATURE, RADIANS/INCH

Fig. A.46 Strut 5-Axia1 Load vs. Section Curvature(Gages 30,32 - Cycles 1-5)

176

50r--------------------,-------------------

28

5C

-30

-40

-20

IIIa..~ 10

o<l:9 ol-------------.:::.~~---':3./____,_,IIH_,/_If~~--------------~

...J<l:X -10<l:

0.0150.0100.005o-0.005-0.010

-50 "-- --' ----'- -'-- -"- --'--- -----.J

-0.015

CURVATURE, RADIANS /INCH

Fig. A.47 Strut 6 - Axial Load vs. Section Curvature(Gages 2,4 - Cycles 1-5)

0.0150.010-0.005 0 0.005

CURVATURE, RADIANS/INCH-0.010

-0'"""8G 6G-

-

~

l-

I--

I--

I--

I I I I-50-0.015

-40

-30

50

-20

20

30

40

IIIa..~ 10

o<l:9 0

...J<l:X -10<l:

Fig. A.48 Strut 6 - Axial Load vs. Section Curvature(Gages 6,8 - Cycles 1-5)

177

0.0150.0100.005o-0.005-0.010

~4Ei-

~5E

0'""" \1\\\12G lOGl-

i-

f-

/501\~~

,k1\3D4A

-

\ ----i-

i 5B 5C3B 4C

I I I-50-0015

-40

50

-30

·20

20

30

40

~iii: 10

o<l:9 0

..J<l: -10

~

CURVATURE, RADIANS/INCH

Fig. A.49 Strut 6-Axia1 Load vs. Section Curvature(Gages 10,12 - Cycles 1-5)

0.0150.0100.005o-0.005-0.010

:~Q'"TUBING

l-

I-

i-

l-

i-

i-

I I I I-50-0.015

-40

50

-30

-20

20

30

40

ena..i: 10

ci~ 0..J

..J<l: -10

~

CURVATURE, RADIANS/ INCH

Fig. A.50 Strut 6-Axia1 Load vs. Section Curvature(Gages 14,16 - Cycles 1-5)

178

0.0150.010-0.005 0 0.005

CURVATURE, RADIANS/INCH-0.010

:"Q'"TUBINGf--

f--

f--

i-

i-

f--

I I I I

-30

40

20

50

-20

30

-50-0.015

-40

CIlll..:;0: 10

o«9 0

..J« -10

~

Fig. A.51 Strut 6-Axia1 Load vs. Section Curvature(Gages 14,16- Cycles 6-10)

-20

-30

-40

507E BE

6E 9E

40 10E,00Q"'30

TUBING

20

CIlll..:;0: 10

0100

«9 0

70..J 6D

BO«X -10

9D«

0.0150010-0.005 0 0.005

CURVATURE, RADIANS/INCH-0.010

-50'-----------'--------'------'---------'-------'-------'-0.015

Fig. A.52 Strut 6 - Axial Load vs. Section Curvature

(Gages 16,18-Cyc1es 6-10)

179

0.0150.010-0.005 0 0.005

CURVATURE, RADIANS/INCH-0.010

-=o~0-TUBING

-

-

-

-

f0-

e-

I I I I

-40

50

-30

-20

-50-0.015

20

3

40

(J)a.i2 10

o<tg 0

...J<tX -10<t

Fig. A.53 Strut 6 - Axial Load vs. Section Curvature(Gages 18,20- Cycles 1-5)

0.0150.0100.005o-0.005-0.010

v5E4E,-

-

,.,~"-

TUBING-

-

~ 1"-5A

I-5D

e-

e-

e- 5C 58

1 I [ I-50-0.015

-40

50

-30

-20

20

30

40

lri2 10

o<tg 0

...J<tX -10<t

CURVATURE I RADIANS/INCH

Fig. A.54 Strut 6 - Axial Load vs. Section Curvature(Gages 22,24- Cycles 1-5)

180

-0.005 0 0.005

CURVATURE, RADIANS/INCH

6A

9A7A

0.0150.010

6E7EBE9EIOE

lOA

GO

L.B.

9C:-:::::::ry;~~~--+9BBC

7C 6C

50

40

"'~'"30

TUBING20

(J)a.52 10

ci<t9 0

..J<t -10X<t

-20

-30

-40

-50-0.015 -0.010

Fig. A.55 Strut 6-Axia1 Load vs. Section Curvature(Gages 22,24 - Cycles 6-10)

0.0150.0100.005o-0.005-0.010

4E ......5E

cO'"""2BG 26G

I-

-

5/ \,.-

-

l- )4C----'

y5CI-

4B/r----3B

I I I I

40

20

50

-30

-50-0.015

30

-20

-40

(J)a.52 10

Cl<;(

9 0

<J.X -10<t

CURVATURE, RADIANS/INCH

Fig. A.56 Strut 6 - Axial Load vs. Section Curvature

(Gages 26,28 - Cycles 1-5)

181

6E

10E

100

28G06G

TUBING

20

40

30

50r--------------=7E=----,--------------------,

f£j;2 10

8AC ~~ ~9 OI----------7hf4k----'-=':":""::O~fI+==='''''+-----------------_I

...J~X -10~

-20

-30

-40

L.B.

9C8C 7C 6C

7889

68

0.0150.0100.005o-0.005-0.010-50'---------"'--------'----------'--------'-------'-------'-0.015

CURVATURE, RADIANS/INCH

Fig. A.57 Strut 6-Axial Load vs. Section Curvature(Gages 26,28 - Cycles 6-10)

5C

4C

504E 5E 3E

40 0'"""32G 30G

30

20

10

4A

-30

-20

enCl.

lS:

~9 ol-------------+-+--+---II-++---I"---------------i<i 3DX -10~

-403C 28

38

0.0150.010-0.005 0 0.005

CURVATURE, RADIANS/ INCH-0.010

_50'---------"'---------'----------'--------'-------'-------'-0.015

Fig. A.58 Strut 6-Axia1 Load vs. Section Curvature(Gages 30,30 - Cycles 1-5)

182

50,-----------------------r-------------------,10E 9E BE IE 6E

0.0150.010

6B

-0.005 0 0.005

CURVATURE, RADIANS liNCH-0.010

L.B.

~TUBING

32G~30G

20

40

-30

-50L--------'--------'---------'-------'---------'--------'-0.015

-20

-40

(/)n.:ll:: 10

ci 7A«9 0

..J 6A

«-10X«

Fig. A.59 Strut 6-Axial Load vs. Section Curvature

(Gages 30,32 - Cycles 6-10)

183

185

EARTHQUAKE ENGINEERING RESEARCH CENTER REPORTS

NOTE: Numbers in parenthesis are Accession Numbers assigned by the National Technical Information Service; these arefollowed by a price code. Copies of the reports may be ordered from the National Technical Information Service, 5285Port Royal Road, Springfield, Virginia, 22161. Accession Numbers should be quoted on order.s for reports (PB --- ---)and remittance must accompany each order. Reports without this information were not available at time of printing.Upon request, EERC will mail inquirers this information when it becomes available.

EERC 67-1

EERC 68-1

EERC 68-2

EERC 68-3

EERC 68-4

EERC 68-5

EERC 69-1

EERC 69-2

EERC 69-3

EERC 69-4

EERC 69-5

EERC 69-6

EERC 69-7

EERC 69-8

"Feasibility Study Large-Scale Earthquake Simulator Facility," by J. Penzien, J.G. Bouwkamp, R.W. Cloughand D. Rea - 1967 (PB 187 905)A07

Unassigned

"Inelastic Behavior of Beam-to-Col umn Subassemblages Under Repeated Loading," by V. V. Bertero - 1968(PB 184 888)A05

"A Graphical Method for Solving the Wave Reflection-Refraction Problem," by H.D. McNiven and Y. Mengi - 1968(PB 187 943) A03

"Dynamic Properties of McKinley School Buildings,lI by D. Rea, J.G. Bouwkamp and R.W .. Clough -1968(PB 187 902)A07

"Characteristics of Rock Motions During Earthquakes," by H.B. Seed, LM. Idriss and F.W. Kiefer -1968(PB 188 338) A03

"Earthquake Engineering Research at Berkeley," - 1969 (PB 187 906) All

"Nonlinear Seismic Response of Earth Structures," by M. Dibaj and J. Penzien-1969 (PB 187 904)A08

"Probabilistic Study of the Behavior of Structures During Earthquakes," by R. Ruiz and J. Penzien - 1969(PB 187 886) A06

"Numerical Solution of Boundary Value Problems in Structural Mechanics by Reduction to an Initial ValueFormulation," by N. Distefano and J. Schujman - 1969 (PB 187 942)A02

"Dynamic Programming and the Solution of the Biharmonic Equation," by N. Distefano - 1969 (PB 187 941)A03

"Stochastic Analysis of Offshore Tower Structures," by A. K. Malhotra and J. Penzien - 1969 (PB 187 903) A09

"Rock Motion Accelerograms for High Magnitude Earthquakes," by H.B. Seed and I.M. Idriss -1969 (PB 187 940)A02

"Structural Dynamics Testing Facilities at the University of California, Berkeley~" by R.M. Stephen,J.G. Bouwkamp, R.t-I. Clough and J. Penzien -1969 (PB 189 111)A04

EERC 69-9 "Seismic Response of Soil Deposits Underlain by Sloping Rock Boundaries," by H. Dezfulian and H.B. Seed1969 (PB 189 114)A03

EERC 69-10 "Dynamic Stress Analysis of ' Axisymmetric Structures Under Arbitrary Loading," by S. Ghosh and E.L. Wilson1969 (PB 189 026)AIO

EERC 69-11 "Seismic Behavior of Multistory Frames Designed by Different Philosophies," by J.C. Anderson andV. V. Bertero - 1969 (PB 190 662)AIO

EERC 69-12 "Stiffness Degradation of Reinforcing Concrete Members Subjected to Cyclic Flexural Moments," byV.V. Bertero, B. Bresler and H. Ming Liao -1969 (PB 202 942)A07

EERC 69-13 "Response of Non-Uniform Soil Deposits to Travelling Seismic Waves," by H. Dezfulian and H.B. Seed -1969(PB 191 023)A03

EERC 69-14 "Damping Capacity of a Model Steel Structure," by D. Rea, R.W. Clough and J.G.Bouwkamp-1969 (PB190663)A06

EERC 69-15 "Influence of Local Soil Conditions on Building l'lamage Potential during Earthquakes," by H.B. Seed andI.M. Idriss - 1969 (PB 191 036)A03

EERC 69-16 "The Behavior of Sands Under Seismic Loading Conditions," by M.L. Silver and H.B. Seed-1969 (AD714982)A07

EERC 70-1 "Earthquake Response of Gravity Dams," by A.K. Chopra - 1970 (AD 709 640)A03

EERC 70-2 "Relationships between Soil Conditions and Building Damage in the Caracas Earthquake of July 29, 1967," byH.B. Seed, LM. Idriss and H. Dezfulian -1970 (PB 195 762)A05

EERC 70-3 "Cyclic Loading of Full Size Steel Connections," by E.P. Popov and R.M. Stephen -1970 (PB 213 545)A04

EERC 70-4 "Seismic Analysis of the Charaima Building, Caraballeda, Venezuela," by Subcommittee of the SEAONC ResearchCommittee: V.V. Bertero, P.F. Fratessa, S.A. Mahin, J.H. Sexton, A.C. Scordelis, E.L. Wilson, L.A. Wyllie,H.B. Seed and J. Penzien, Chairman-1970 (PB 201 455)A06

Preceding page blank

EERC 70-5

EERC 70-6

EERC 70-7

186

"A Computer Program for Earthquake Analysis of Dams," by A.K. Chopra and P. Chakrabarti -1970 (AD 723 994)A05

"The Propagation of Love Waves Across Non-Horizontally Layered Structures," by J. Lysrner and L.A. Drake1970 (PB 197 896)A03

"Influence of Base Rock Characteristics on Ground Response," by J. Lysmer, H.B. Seed and P.B. Schnabel1970 (PB 197 897)A03

EERC 70-8 "Applicability of Laboratory Test Procedures for Measuring Soil Liquefaction Characteristics under CyclicLoading," by H.B. Seed and W.H. Peacock - 1970 (PB 198 016)A03

EERC 70-9 "A Simplified Procedure for Evaluating Soil Liquefaction Potential," by II. B. Seed and 1. M. Idriss - 1970(PB 198 009)A03

EERC 70-10 "Soil Moduli and Damping Factors for Dynamic Response Analysis," by H.B. Seed and 1.M. Idriss -1970(PB 197 869)A03

EEEC 71-1 "Koyna Earthquake of December 11, 1967 and the Performance of Koyna Dam," by A.K. Chopra and P. Chakrabarti1971 (AD 731 496lAOG

EERC 71-2 "Preliminary In-Situ Measurements of Anelastic Absorption in Soils Using a Prototype Earthquake Simulator,"by R.D. Borcherdt and P.W. Rodgers - 1971 (PB 201 454)A03

EERC 71-3 "Static and Dvnamic Analysis of Inelastic Frame Structures," by F.L. Porter and G.H. Powell-1971(PB 210 135) A06

EERC 71-4 "Research Needs in Limit Design of Reinforced Concrete Structures," by V.V. Bertero -1971 (PB 202 943)A04

EERC 71-5 "Dynamic Behavior of a High-Rise Diagonally Braced Steel Building," by D. Rea, A.A. Shah and C".G. Bouw]cawp1971 (PB 203 584)A06

EERC 71-6 "Dynamic Stress Analysis of Porous Elastic Solids Saturated with Compressible Fluids," by J. Ghaboussi andE. L. Wilson" 1971 (PB 211 396)A06

EERC 71-7 IIInelastic Behavior of Steel Beam-to-Column Subassemblages," by H. Krawinkler, V.V. Bertero and E.P. Popov1971 (PB 211 335)A14

EERC 71-8

EERC 72-1

EERC 72-2

"Modification of Seismograph Records for Effects of Local Soil Conditions," by P. Schnabel, H.B. Seed andJ. Lysmer - 1971 (PB 214 450)A03

"Static and Earthquake Analysis of Three Dimensional Frame and Shear Wall Buildings," by E.L. Wilson andH.H. Dovey-1972 (PB 212 904)A05

"Accelerations in Rock for Earthquakes in the Western United States," by P.B. Schnabel and H.B. Seed-1972(PB 213 100)A03

EERC 72-3 "Elastic-Plastic Earthquake Response of Soil-Building Systems," by T. Minami -1972 (PB 214 8(8)A08

EERC 72-4 "Stochastic Inelastic Response of Offshore 'rowers to Strong /olotion Earthquakes," by M.K. Kaul-1972(PB 215 713) ADS

EERC 72-5 "Cyclic Behavior of Three Reinforced Concrete Flexural Members with High Shear," by E.P. Popcv, V.V. Berteroand H. Krawinkler - 1972 (PB 214 555)A05

EERC 72-6 "Earthquake Response of Gravity Dams Including Reservoir Interaction Effects," by P. Chakrabarti andA.K. Chopra - 1972 (AD 762 330)A08

EERC 72-7 "Dynamic Properties of Pine Flat Dam," by D. Rea, C.Y. Liaw and A.K. Chopra-1972 (AD 763 928)A05

EERC 72-8 "Three Dimensional Analysis of Building Systems," by E.L. Wilson and H.H. Dovey -1972 (PB 222 438)A06

EERC 72-9 "Rate of Loading Effects on Uncracked and Repaired Reinforced Concrete Members," by S. Mahin, V.V. Bertero,

D. Rea and M. Atalay - 1972 (PB 224 520) A08

EERC 72-10 "Computer Program for Static and Dynamic Analysis of Linear Structural Systems," by E.L. Wilson, K.-J. Bathe,J,E. Peterson and H,H.Dovey-1972 (PB 220 437)A04

EERC 72-11 "Literature Survey - Seismic Effects on Highway Bridges," by T. Iwasaki, J. Penzien and R. W. Clough - 1972

(PB 215 613) A19

EERC 72-12 "SHAKE-A Computer Program for Earthquake Response Analysis of Horizontally Layered Sites," by P.B. Schnabeland J. Lysmer - 1972 (PB 220 207) AD6

EERC 73-1 "Optimal Seismic Design of Multistory Frames," by V.V. Bertero and H. Kamil-1973

EERC 73-2 "Analysis of the Slides in the San Fernando Dams During the Earthquake of February 9, 1971," by H.B. Seed,K.L. Lee, 1.M. Idriss and F. Makdisi -1973 (PB 223 402)A14

187

EERC 73-3 "Computer Aided Ultimate Load Design of Unbraced Multistory Steel Frames," by M.B. EI-Hafez and G.H. Powell1973 (PB 248 315)A09

EERC 73-4 "Experimental Investigation into the Seismic Behavior of Critical Re~ions of Reinforced Concrete Componentsas Influenced by Moment and Shear," by M. Celebi and J. Penzien - 1973 (PB 215 884) A09

EERC 73-5 "Hysteretic Behavior of Epoxy-Repaired Reinforced Concrete Beams," by M. Celebi and J. Penzien - 1973{PB 239 568)A03

EERC 73-6 "General Purpose Computer Program for Inelastic Dynamic Response of Plane Structures, II .by A. Kanaan andG.H. Powell- 1973 (PB 221 260)A08

EERC 73-7 "A Computer Program for Earthquake Analysis of Gravity Dams Including Reservoir Interaction, II byP. Chakrabarti and A.K. Chopra - 1973 (AD 766 271)A04

EERC 73-8 "Behavior of Reinforced Concrete Deep Beam-'Column Subassemblages Under Cyclic Loads," by O. Kiistii andJ.G. Bouwkamp-1973 (PB 246 117)A12

EERC 73-9 "Earthquake Analysis of Structure-Foundation Systems," by A.K. Vaish and ".K. Chopra -1973 (AD 766 272)A07

EERC 73-10 "Deconvolution of Seismic Response for Linear Systems," by R.B. Reimer -1973 (PB 227 179)A08

EERC 73-11 "SAP IV: A Structural Analysis Program for Static and Dynamic Response of Linear Systems," by K.-J. Ba the,E.L. Wilson and F.E. Peterson -1973 (PB 221 967)A09

EERC 73-12 "Analytical Investigations of the Seismic Response of Long, Multiple Span Highway Bridges," by W.S. Tsengand J. Penzien -1973 (PB 227 8l6)AlO

EERC 73-13 "Earthquake Analysis of Multi-Story Buildings Including Foundation Interaction," by A. K. Chopra andJ.A. GutiRrrez-1973 (PB 222 970)A03

EERC 73-14 "ADAP: A Computer Program for Static and Dynamic Analysis of Arch Dams," by R.W. Clough, J.M. Raphael andS. Mojtahedi -1973 (PB 223 763)A09

EERC 73-15 "Cyclic Plastic Analysis of Structural Steel Joints," by R.B. Pinkney and R.W. Clough -1973 {PB 226 843)A08

EERC 73-16 "Ql.'AD-4: A Computer Program for Evaluating the Seismic Response of Soil Structures by Variable DampingFinite Element Procedures," by LM. Idriss, J. Lysmer, R. Hwang and H.B. Seed -1973 {PB 229 424)A05

EERC 73-17 "Dynamic ,,.'havior of a Multi-Story Pyramid Shaped Building," by R.M. Stephen, J.P. Hollings andJ.G. Bouwkamp -1973 (PB 240 718)A06

EERC 73-18 "Effect of Different Types of Reinforcing on Seismic Behavior of Short Concrete Columns," by V.V. Bertero,J. Hollings, O. Kiis tii , R. M. Stephen and J. G. Bouwkamp - 1973

EERC 73-19 "Olive View Medical Center Materials Studies, Phase I," by B. Bresler and V.V. Bertero -1973 (PB 235 986)A06

EERC 73-~O "Linear and Nonlinear Seismic Analysis Computer Programs for Long Multiple-Span Highway Bridges," byW. S. Tseng and J. Penzien - 1973

EERC 73-21 "Constitutive Models for Cyclic Plastic Deformation of Engineering Materials," by eLM. Kelly ilnd P.P. Gillis1973 (PB 226 024)A03

EERC 73-22 "DRAIN - 2D User's Guide," by G.H. Powell-1973 (PB 227 016)A05

EERC 73-23 "Earthquake Engineering at Berkeley - 1973," (1'8 226 033)All

EERC 73-24 Unassigned

EERC 73-25 "Earthquake Response of Axisymmetric Tower Structures Surrounded by Water," by C.Y. Liaw and A.K. Chopra1973 (fiD 773 052)A09

EERC 73-'26 "Investigation of the Failures of the Olive View Stairtowers During the San Fernando Earthquake and TheirImplications on Seismic Design," by V.V. Bertero and R.G. Collins -1973 (PB 235 106)A13

EERC 73-27 IIFurther Studies on Seismic Behavior of Steel Beam-Column Subassemblages," by V. V. Bertero, H. Krawir.k lerand E.P. Popov-1973 (PB 234 172)A06

EERC 74-1 "Seismic Risk Analysis," by C.S. Oliveira -1974 (PB 235 920)A06

EERC 74-2 "Settlement and Liquefaction of Sands Under Multi-Directional Shaking," by R. Pyke, C.K. Chan and H.B. Seed1974

EERC 74-3

EERC 74-4

"Optimum Design of Earthquake Resistant Shear Buildings," by D. Ray, K. S. Pister and A. K. Chopra - 1974(PB 231 172)A06

"LUSH - A Computer Program for Complex ResponSe Analysis of Soil-Structure Systems," by J. Lysmer, T. Udaka,H.B. Seed and R. Hwang -1974 (PB 236 796)A05

EERC 74-5

188

"Sensitivity Analysis for Hysteretic Dynamic Systems: Applications to Earthquake Engineering," by D. Ray1974 (PB 233 2l3)A06

EERC 74-6 "Soil Structure Interaction Analyses for Evaluating Seismic Response," by H.B. Seed, J. Lysmer and R. Hwang1974 (PB 236 519)A04

EERC 74-7 Unassigned

EERC 74-8 "Shaking Table Tests of a Steel Frame - A Progress Report," by R.W. Clough and D. Tang -1974 (PB 240 8,,9)A03

EERC 74-9 "Hysteretic Behavior of Reinforced Concrete Flexural Members with Special Web Reinforcement," byV.V. Bertero, E.P. Popov and T.Y. Wang - 1974 (PB 236 797)A07

EERC 74-10 "Applications of Reliability-Based, Global Cost Optimization to Design of Earthquake Resistant Structures,"by E. Vitiello and K.S. Pister -1974 (PB 237 23l)A06

EERC 74-11 "Liquefaction of Gravelly Soils Under Cyclic Loading Conditions," by R.T. Wong, H.B. Seed and C.K. Chan1974 (PB 242 042)A03

EERC 74-12 "Site-Dependent Spectra for Earthquake-Resistant Design," by H.B. Seed, C. Ugas and J. Lysmer -1974(PB 240 953)A03

EERC 74-13 "Earthquake Simulator Study of a Reinforced Concrete Frame," by P. Hidalgo and R.W. Clough -1974(PB 241 9f4)A13

EERC 74-14 "Nonlinear Earthquake Response of Concrete Gravity Dams," by N. Pal - 1974 {AD/A 006 583)A06

EERC 74-15 "Modeling and Identification in Nonlinear Structural Dynamics - I. One Degree of Freedom Models," byN. Distefano and A. Rath -1974 (PB 241 548)A06

EERC 75-1 "Determination of Seismic Design Criteria for the Dumbarton Bridge Replacement Structure, Vol. I: Description,Theory and Analytical Modeling of Bridge and Parameters," by F. Baron and S. -H. Pang - 1975 (PB 259 407) A15

EERC 75-2

EERC 75-3

EERC 75-4

EERC 75-5

EERC 75-6

FERC 75-7

lIDetermination of Seismic Design Criteria for the Dumbarton Bridge Replacement Structure, Vol. II: NumericalStudies and Establishment of Seismic Design Criteria," by F. Baron and S. -H. Pang - 1975 (PB 259 408) All(For set of EERC 75-1 and 75-2 (PB 259 406»)

"Seismic Risk Analysis for a Site and a Metropolitan Area," by C.S. Oliveira -1975 (PB 248 134)A09

"Analytical Investigations of Seismic Response of Short, Single or Multiple-Span Highway Bridges," byM.-C. Chen and J. Penzien - 1975 (PB 241 454)A09

"An Evaluation of Some Methods for Predicting Seismic Behavior of Reinforced Concrete Buildings," by S.A.Mahin and V. V. Bertero - 1975 (PB 246 306) Al6

"Earthquake Simulator Study of a Steel Frame Structure, Vol. I: Experimental Results," by R.W. Clough andD.T. Tang - 1975 (PB 243 98l)A13

lIDynamic Properties of San Bernardino Intake Tower," by D. Rea, C.-Y. Liaw and A.K. Chopra-1975 (AD/A008406)AOS

EERC 75-8 "Seismic Studies of the Articulation for the Dumbarton Bridge Replacement Structure, Vol. I: Description,Theory and Analytical Modeling of Bridge Components," by F. Baron and R.E. Hamati -1975 (PB 251 539)A07

EERC 75-9 "Seismic Studies of the Articulation for the Dumbarton Bridge Replacement Structure, Vol. 2: NumericalStudies of Steel and Concrete Girder Alternates," by F. Baron and R.E. Hamati -1975 (PB 251 540)AIO

EERC 75-10 "Static and Dynamic Analysis of Nonlinear Structures," by D.P. Mondkar and G.H. Powell-1975 (PB 242 434)A08

EERC 75-11 "Hysteretic Behavior of Steel Columns," by E.P. Popov, V.V. Bertero and S. Chandramouli -1975 {PB 252 3(;S)All

EERC 75-12 "Earthquake Engineering Research Center Library Printed Catalog," - 1975 (PB 243 711)A26

EERC 75-13 "Three Dimensional Analysis of Building Systems {Extended Version)," by E.L. Wilson, J.P. Hollings andIl.H. Dovey - 1975 {PB 243 989)A07

EERC 75-14 "Determination of Soil Liquefaction Characteristics by Large-Scale Laboratory Tests," by P. De Alba,C.K. Chan and H.B. Seed -1975 (NUREG 0027)A08

EFRC 75-15 "A Literature Survey - Compressive, Tensile, Bond and Shear Strength of Masonry," by R.L. Mayes and R.W.Clough - 1975 {PB 246 292)A10

EERC 75-16 "Hysteretic Behavior of Ductile Moment Resisting Reinforced Concrete Frame Components," by V.V. Bertero andE. P. Popov - 1975 (PB 246 388) A05

EERC 75-17 "Relationships Between Maximum Acceleration, Maximum Velocity, Distance from Source, Local Site Conditionsfor Moderately Strong Earthquakes," by H.B. Seed, R. Murarka, J. Lysmer and I.M. Idriss-1975 {PB 248 l72)A03

EERC 75-18 "The Effects of Method of Sample Preparation on the Cyclic Stress-Strain Behavior of Sands," by J. Mulilis,C.K. Chan and H.B. Seed - 1975 (Summarized in EERC 75-28)

189

EERC 75-19 "The Seismic Behavior of Critical Regions of Reinforced Concrete Components as Influenced by Moment, Shearand Axial Force," by M.B. Atalay and J. Penzien -1975 (PB 258 842)All

EERC 75-20 "Dynamic Properties of an Eleven Story Masonry Building," by R.M. Stephen, J.P. Hollings, J .G. Bouwkamp andD. Jurukovski - 1975 (PB 246 945)A04

EERC 75-21 "State-of-the-Art in Seismic Strength of Masonry - An Evaluation and Review," by R.L. Mayes and R.W. Clough

1975 (PB 249 040)A07

EERC 75-22 "Frequency Dependent Stiffness Matrices for Viscoelastic Half-Plane Foundations," by A.K. Chopra,P. Chakrabarti and G. Dasgupta -1975 (PB 248 121)A07

EERC 75-23 "Hysteretic Behavior of Reinforced Concrete Framed Walls," by T. Y. Wong, V. V. Bertero and E.P. Popov - 1975

EERC 75-24 "Testing Facility for Subassemblages of Frame-Wall Structural Systems," by V. V. Bertero, E.P. Popov andT. Endo - 1975

EERC 75-25 IlInfluence of Seismic History on the Liquefaction Characteristics of Sands," by H.B. Seed, K. Mari andC.K. Chan -1975 (Summarized in EERC 75-28)

EERC 75-26 "The Generation and Dissipation of Pore Water Pressures during Soil Liquefaction," by H.B. Seed, P.P. Martinand J. Lysmer - 1975 (PB 252 648) A03

EERC 75-27 "Identification of Research Needs for Improving Aseismic Design of Building Structures," by V.V. Bertero1975 (PB 248 136)A05

EERC 75-28 "Evaluation of Soil Liquefaction Potential during Earthquakes," by H.B. Seed, 1. Arango and C.K. Chan -1975(!\''UREG 0026)A13

EERC 75-29 "Representation of Irregular Stress Time Histories by Equivalent Uniform Stress Series in LiquefactionAnalyses," by H.B. Seed, 1.M. Idriss, F. Makdisi and N. Banerjee -1975 (PB 252 635)A03

EERC 75-30 "FLUSH - A Computer Program for Approximate 3-D Analysis of Soil-Structure Interaction Problems," byJ. Lysmer, T. Udaka, C.-F. Tsai and H.B. Seed -1975 (PB 259 332)A07

EERC 75-31 "ALUSH - A Computer Program for Seismic Response Analysis of Axisymmetric Soil-Structure Systems," byE. Berger, J. Lysmer and H. B. Seed - 1975

EERC 75-32 "TRIP and TRAVEL - Computer Programs for Soil-Structure Interaction Analysis with Horizontally TravellingWaves, II by T .. Udaka, ,..1. Lvsmer and H. B. Seed - 1975

EERC 75-33 "Predicting the Performance of Structures in Regions of High Seismicity," by J. Penzien -1975 (PB 248 l30)A".;

EERC 75-34 "Efficient Finite Element Analysis of Seismic Structure -Soil- Direction, II by J. Lysmer, H.B. Seed, T. Udaka,R.N. Hwang and C.-F. Tsai -1975 (PB 253 570)A03

EERC 75-35 "The Dynamic Behavior of a First Story Girder of a Three-Story Steel Frame Subjected to Earthquake Loading,'by R.W. Clough and L.-Y. Li-1975 (PB 248 841)A05

EERC 75-36 "Earthquake Simulator Study of a Steel Frame Structure, Volume II -Analytical Results," by D.T. Tang -1975(PB 252 926) AID

EERC 75-37 "ANSR-I General Purpose Computer Program for Analysis of Non-Linear Structural Response," by D.P. Mondkarand G.H. Powell-1975 (PB 252 386)A08

EERC 75-38 "Nonlinear Response Spectra for Probabilistic Seismic Design and Damage Assessment of Reinforced ConcreteStructures," by M. Mu~akami and J. Penzien -1975 (PB 259 530)A05

EERC 75-39 "Study of a Method of Feasible Directions for Optimal Elastic Design of Frame Structures Subjected to Eacj,quake Loading," by N.D. Walker and K.S. Pister -1975 (PB 257 781)A06

EERC 75-40 "An Alternative Represent.ation of the Elastic-Viscoelastic Analogy,I' by IJ. Dasgupta and J.L. Sackman -1975(PB 252 173)A03

EERC 75-41 "Effect of Multi-Directional Shaking on Liquefaction of Sands," by H. B. Seed, R. Pyke and G. R. Martin - 19"1'"(PB 258 781) A03

EERC 76-1 "Strength and Ductility Evaluation of Existing Low-Rise Reinforced Concrete Buildings - Screening Meth()il .. " c"T. Okada and B. Bresler-1976 (PB 257 906)All

EERC 76-2 "Experimental and Analytical Studies on the Hysteretic Behavior of Reinforced Concrete Rectangular andT-Beams," by S.-Y.M. Ma, E.P. Popov and V.V. Bertero -1976 (PB 260 843)1'.12

EERC 76- 3 "Dynamic Behavior of a Multistory Triangular-Shaped Building I" by J. Petrovski, R. M. Stephen, E. GartenbaUII)and J.G. Bouwkamp-1976 (PB 273 279)A07

EERC 76-4 "Earthquake Induced Deformations of Earth Darns," by N. Serff, H.B. Seed, F.I. Makdisi & C.-Y. Chang - 1976(PB 292 065)A08

190

EERC 76-5 "Analysis and Design of Tube-Type Tall Buildinq Structures," by H. de Clercq and G.H. Powell -1976 (PB 252220)AIO

EERC 76-6 "Time and Frequency Domain Analysis of Three-Dimensional Ground Motions, San Fernando Earthquake," by T. Kuboand J. Penzien {PB 260 556)All

EERC 76-7 "Expected Performance of Uniform Building Code Design Masonry Structures," by R. L. Mayes, Y. Ornote, S .1-1. Chenand R.W. Clough -1976 (PB 270 098)A05

EERC 76-8 "Cyclic Shear Tests of Masonry Piers, Volume 1 - Test Results, II by R. L. Mayes, Y. Ornote I R. W.Clough - 1976 (PB 264 424) A06

EERC 76-9 "A Substructure Method for Earthquake Analysis of Structure - Soil Interaction," by J .A. Gutierrez andA.K. Chopra - 1976 (PB 257 783)A08

EERC 76-10 "Stabilization of Potentially Liquefiable Sand Deposits using Gravel Drain Systems," by H.B. Seed andJ. R. Booker - 1976 (PB 258 820) A04

EERC 76-11 "Influence of Design and Analysis Assumptions on Computed Inelastic Response of Moderately Tall Frames," byG. H. Powell and D. G. Row - 1976 (PB 271 409) A06

EERC 76-12 "Sensitivity Analysis for Hysteretic Dynamic Systems: Theory and Applications," by D. Ray, K.S. Pister andE. Polak-1976 (PB 262 859)A04

EERC 76-13 "Coupled Lateral Torsional Response of Buildings to Ground Shaking," by C.L. Kan and A.K. Chopra ­1976 (PB 257 907)A09

EERC 76-14 "Seismic Analyses of the Banco de America," by V.V. Bertero, S.A. Mahin and J.A. Hollings - 1976

EERC 76-15 "Reinforced Concrete Frame 2: Seismic Testing and Analytical Correlation," by R.W. Clough andJ. Gidwani - 1976 (PB 261 323)A08

EERC 76-16 "Cyclic Shear Tests of Masonry Piers, Volume 2 - Analysis of Test Results," by R.L. Mayes, Y. Omoteand R.W. Clough - 1976

EERC 76-17 "Structural Steel Bracing Systems: Behavior Under Cyclic Loading," by E.P. Popov, K. Takanashi andC.W. Roeder - 1976 (PB 260 715)A05

EERC 76-18 "Experimental Model Studies on Seismic Response of High Curved Overcrossings," by D. Williams andW.G. Godden - 1976 (PB 269 548)A08

EERC 76-19 "Effects of Non-Uniform Seismic Disturbances on the Dumbarton Bridge Replacement Structure," byF. Baron and R.E. Hamati - 1976 (PB 282 98l)A16

EERC 76-20 "Investigation of the Inelastic Characteristics of a Single Story Steel Structure Using SystemIdentification and Shaking Table Experiments," by V.C. Matzen and H.D. McNiven - 1976 (PB 258 453)A07

EERC 76-21 "Capacity of Columns with Splice Imperfections," by E.P. Popov, R.M. Stephen and R. Philbrick - 1976(PB 260 378)A04

EERC 76-22 "Response of the Olive View Hospital Main Building during the San Fernando Earthquake," by S. A. Mahin,V.V. Bertero, A.K. Chopra and R. Collins - 1976 IPB 271 425)A14

EERC 76-23 "A Study on the Major Factors Influencing the Strength of Masonry Prisms," by N.M. Mostaghel,R.L. Mayes, R. W. Clough and S.W. Chen - 1976 (Not published)

EERC 76-24 "GADFLEA - A Computer Program for the Analysis of Pore Pressure Generation and Dissipation duringCyclic or Earthquake Loading," by J.R. Booker, M.S. Rahman and H.B. Seed - 1976 (PB 263 947)A04

EERC 76-25 "Seismic Safety Evaluation of a RiC School Building," by B. Bresler and J. Axley - 1976

EERC 76-26 "Correlative Investigations on Theoretical and Experimental Dynamic Behavior of a Model BridgeStructure," by K. Kawashima and J. Penzien - 1976 (PB 263 388)All

EERC 76-27 "EarthqUake Response of Coupled Shear Wall Buildings," by T. Srichatrapimuk - 1976 (PB 265 157) A07

EERC 76-28 "Tensile Capacity of Partial Penetration Welds," by E.P. Popov and R.M. Stephen - 1976 (PB 262 899)A03

EERC 76-29 "Analysis and Design of Numerical Integration Methods in Structural Dynamics," by H.M. Hilber - 1976{PB 264 410)A06

EERC 76-30 "Contribution of a Floor System to the Dynamic Characteristics of Reinforced Concrete Buildings," byL.E. Malik and V.V. Bertero - 1976 (PB 272 247)A13

EERC 76-31 "The Effects of Seismic Disturbances on the Golden Gate Bridge," by F. Baron, M. Arikan and R.E. Hamati _1976 (PB 272 279)A09

EERC 76-32 "Infilled Frames in Earthquake Resistant Construction," by R.E. Klingner and V. V. Bertero - 1976(PB 265 892)A13

191

UCB/EERC-77/0l "PLUSH - A Computer Program for Probabilistic Finite Element Analysis of Seismic soil-Structure Inter­action," by M.P. Forno Organista, J. Lysmer and H.B. Seed - 1977

UCB/EERC-77/02 "Soil-Structure Interaction Effects at the Humboldt Bay Power Plant in the Ferndale Earthquake of June7, 1975," by J.E. Valera, H.B. Seed, C.F. Tsai and J. Lysmer - 1977 (PB 265 795)A04

UCB/EERC-77/03 "Influence of Sample Disturbance on Sand Response to Cyclic Loading," by K. Mori, H.B. Seed and C.K.Chan - 1977 (PB 267 352)A04

UCB/EERC-77 /04 "Seismological Studies of Strong Motion Records," by J. Shoja-Taheri - 1977 {PB 269 655)A10

UCB/EERC-77/05 "Testing Facility for Coupled-Shear Walls," by L. Li-Hyung, V.V. Bertero and E.P. Popov - 1977

UCB/EERC-77/06 "Developing Methodologies for Evaluating the Earthquake Safety of Existing Buildings," by No. 1 ~

B. Bresler; No.2 - B. Bresler, T. Okada and D. Zisling; No.3 - T. Okada and B. Bresler, No.4 - V.V.Bertero and B. Bresler - 1977 (PB 267 354)A08

UCB/EERC-77/07 "A Literature Survey - Transverse Strength of Masonry Walls," by Y. Ornote, R.L. Mayes, S.W. Chen andR.W. Clough - 1977 (PB 277 933)A07

UCB/EERC-77/08 "DRAIN-TABS: A Computer Program for Inelastic Earthquake Response of Three· Dimensional Buildings," byR. Guendelman-Israel and G.H. Powell - 1977 (PB 270 693)A07

UCB/EERC-77/09 "SUBWALL: A Special Purpose Finite Element Computer Program for Practical Elastic Analysis and Designof Structural Walls with Substructure Option," by D.Q. Le, H. Peterson and E.P. Popov - 1977(PB 270 567)A05

UCB/EERC-77/l0 "Experimental Evaluation of Seismic Design Methods for Broad Cylindrical Tanks," by D. P. Clough(PB 272 280)A13

UCB/EERC-77 /11 "Earthquake Engineering Research at Berkeley - 1976," - 1977 (PB 273 507) A09

UCB/EERC-77/l2 "Automated Design of Earthquake Resistant Multistory Steel Building Frames," by N.D. Walker, Jr. - 1977(PB 276 526)A09

UCB/EERC-77 /13 "Concrete Confined by Rectangular Hoops Subjected to Axial Loads," by J. Vallenas, V. V. Bertero andE.P. Popov - 1977 (PB 275 l65)A06

UCB/EERC-77/l4 "Seismic Strain Induced in the Ground During Earthquakes," by Y. Sugimura - 1977 (PB 284 20l)AD4

UCB/EERC-77/l5 "Bond Deterioration under Generalized Loading," by V.V. Bertero, E.P. Popov and S. Viwathanatepa - 1977

UCB/EERC-77/l6 "Computer Aided Optimum Design of Ductile Reinforced Concrete Moment Resisting Frames," by S.W.Zagajeski and V.V. Bertero - 1977 (PB 280 l37)A07

UCB/EERC-77 /17 "Earthquake Simulation Testing of a Stepping Frame with Energy-Absorbing Devices," by J. M. Kelly andD.F. Tsztoo - 1977 (PB 273 506)A04

UCB/EERC-77/18 "Inelastic Behavior of Eccentrically Braced Steel Frames under Cyclic Loadings," by C.W. Roeder andE.P. Popov - 1977 (PB 275 526)A15

UCB/EERC-77/l9 "A Simpli lied Procedure for Estimating Earthquake-Induced Deformations in Darns and Embankments," by F. 1.Makdisi and H.B. Seed - 1977 (PB 276 820)A04

UCB/EERC-77/20 "The Performance of Earth Darns during Earthquakes," by H.B. Seed, F.1. Makdisi and P. de Alba - 1977(PB 276 821)A04

UCB/EERC-77/21 "Dynamic Plastic Analysis Using Stress Resul tant Finite Element Formulation, II by P. Lukkunapvasi t andJ.M. Kelly - 1977 {PB 275 453)A04

UCB/EERC-77/22 "Preliminary Experimental Study of Seismic Uplift of a Steel Frame," by R.W. Clough and A.A. Huckelbridgc1977 (PB 278 769)A08

UCB/EERC-77 /23 "Earthquake Simulator Tests of a Nine-Story Steel Frame with Columns Allowed to Uplift," by A. A.Huckelbridge - 1977 (PB 277 944)A09

UCB/EERC-77/24 "Nonlinear Soil-Structure Interaction of Skew Highway Bridges," by M.-C. Chen and J. Penzien - 1977(PB 276 176)A07

UCB/EERC-77/25 "Seismic Analysis of an Offshore Structure Supported on Pile Foundations," by D.D.-N. Liou and J. Penzien1977 (PB 283 180)A06

UCB/EERC-77/26 "Dynamic Stiffness Matrices for Homogeneous Viscoelastic Half-Planes," by G. Dasgupta and A.K. Chopra ­1977 (PB 279 654)A06

UCB/EERC-77/27 "A Practical Soft Story Earthquake Isolation System," by J. M. Kelly, J .~!. Eidinger and C. J. Derham ­1977 (PB 276 814)A07

UCB/EERC-77/28 "Seismic Safety of Existing Buildings and Incentives for Hazard Mitigation in San Francisco: AnExploratory Study," by A.J. Meltsner - 1977 (PB 281 970)A05

UCB/EERC-77/29 "Dynamic Analysis of Electrohydraulic Shaking Tables," by D. Rea, S. Abedi-Hayati and Y. Takahashi1977 (PB 282 569)A04

UCB/EERC-77/30 IIAn Approach for Improving Seismic - Resistant Behavior of Reinforced Concrete Interior Joints," byB. Galunic, V.V. Bertero and E.P. Popov - 1977 (PB 290 870)A06

UCB/EERC-78/01

UCB/EERC-78/02

UCB/EERC-78/03

UCB/EERC-78/04

UCB/EERC-78/05

UCB/EERC-78/06

UCB/EERC-78/07

UCB/EERC-78/08

UCB/EERC-78/09

UCB/EERC-78/10

UCB/EERC-78/11

UCB/EERC-78/12

UCB/EERC-78/13

UCB/EERC-78/14

UCB/EERC-78/15

UCB/EERC-78/16

192

"The Development of Energy-Absorbing Devices for Aseismic Base Isolation Systems," by J.M. Kelly andD.E. Tsztoo - 1978 (PB 284 978)A04

"Effect of Tensile Prestrain on the Cyclic Response of Structural Steel Connections, by J.G. Bouwkampand A. Mukhopadhyay - 1978

"Experimental Results of an Earthquake Isolation System using Natural Rubber Bearings," by J.M.Eidinger and J.M. Kelly - 1978 (PB 281 686)A04

"Seismic Behavior of Tall Liquid Storage Tanks," by A. Niwa - 1978 (PB 284 017)A14

"Hysteretic Behavior of Reinforced Concrete Columns Subjected to High Axial and Cyclic Shear Forces,1Iby S.W. Zagajeski, V.V. Bertero and J.G. Bouwkamp - 1978 (PB 283 858)A13

"Inelastic Beam-Column Elements for the ANSR-I Program," by A. Riahi, D.G. Rowand G.H. Powell - 1978

"Studies of Structural Response to Earthquake Ground Motion, II by O.A. Lopez and A.K. Chopra - 1978(PB 282 790)A05

"A Laboratory Study of the Fluid-Structure Interaction of Submerged Tanks and Caissons in Earthquakes,"by R.C. Byrd - 1978 (PB 284 957)A08

"Model for Evaluating Damageability of Structures," by r. Sakamoto and B. Bresler - 1978

"Seismic Performance of Nonstructural and Secondary Structural Elernents,1I by T. Sakamoto - 1978

"Mathematical Hodelling of Hysteresis Loops for Reinforced Concrete Colwnns," by S .. Nakata, T .. Sprouland J. Penzien - 1978

"Damageability in Existing Buildings," by T. Blejwas and B. Bresler - 1978

"Dynamic Behavior of a Pedestal Base Multistory Building," by R.M. Stephen, E.L. Wilson, J.G. Bouwkampand M. Button - 1978 (PB 286 650)A08

"Seismic Response of Bridges - Case Studies, II by R.A. Irnbsen, V .. Nutt and J. Penzien - 1978(PB 286 503)A10

"A Substructure Technique for Nonlinear Static and Dynamic Analysis," by D.G. Rowand G.H. Powell ­1978 (PB 288 077)A10

"Seismic Risk Studies for San Francisco and for the Greater San Francisco Bay Area," by C.S. Oliveira ­1978

UCB/EERC-78/17 "Strength of Timber Roof Connections Subjected to Cyclic Loads," by P. Gulkan, R.L. Mayes and R.W.Clough - 1978

CCB EERC-78/18 "Response of K-Braced Steel Frame Models to Lateral Loads," by J .G. Bouwkamp, R.M. Stephen andE.P. Popcv - 1978

CCB/EERC-78/19 II Rational Design Methods for Light Equipment in Structures Subj ected to Ground Motion, II byJ.L. Sackman and J.M. Kelly - 1978 (PB 292 357)A04

CCB./EERC-78/20 IITesting of a Wind Restraint for Aseismic Base Isolation,11 by J .M. Kelly and D.E. Chitty - 1978(PB 292 833) A03

UCB/EERC-78/2l "APOLLO - A Computer Program for the Analysis of Pore Pressure Generation and Dissipation in HorizontalSand Layers During Cyclic or Earthquake Loading," by P. P. Martin and H.B. Seed - 1978 (PB 292 835) A04

UCB/EERC-78/22 "Optimal Design of an Earthquake Isolation System," by M.A. Bhatti, K.S. Pister and E. Polak - 1978(PB 294 735)A06

UCB/EERC-78/23 "MASH - A Computer Program for the Non-Linear Analysis of Vertically Propagating Shear Waves inHorizontally Layered Deposits," by P.P. Martin and H.B. Seed - 1978 (PB 293 lOl)A05

UCB/EERC-78/24 "Investigation of the Elastic Characteristics of a Three Story Steel Frame Using System Identification,"by I. Kaya and H.D. McNiven - 1978

UCB/EERC-78/25 "Investigation of the Nonlinear Characteristics of a Three-Story Steel Frame Using SystemIdentification," by I. Kaya and H.D. McNiven - 1978

UCB/EERC-78/26 "Studies of Strong Ground Motion in Taiwan," by Y.M. Hsiung, B.A. Bolt and J. Penzien - 1978

UCB/EERC-78/27 "Cyclic Loading Tests of Masonry Single Piers: Volume 1 - Height to Width Ratio of 2," by P.A. Hidalgo,R.L. Mayes, H.D. McNiven and R.W. Clough - 1978

UCB/EERC-78/28 "Cyclic Loading Tests of Masonry Single Piers: Volume 2 - Height to Width Ratio of 1," by S. -W. J. Chen,P.A. Hidalgo, R.L. Mayes, R.W. Clough and H.D. McNiven - 1978

UCB/EERC-78/29 "Analytical Procedures in Soil Dynamics," by J. Lysmer - 1978

193

UCB/EERC-79/01 "Hysteretic Behavior of Lightweight Reinforced ConcreteBeam-Colunm Subassemblages," by B. Forzani, E.P. Popov,and V.V. Bertero - 1979

UCB/EERC-79/02 "The Development of a Mathematical Model to Predict theFlexural Response of Reinforced Concrete Beams to CyclicLoads, Using System Identification," by J.F. Stanton andH.D. McNiven - 1979

UCB/EERC-79/03 "Linear and Nonlinear Earthquake Response of SimpleTorsionally Coupled Systems," by C.L. Kan andA.K. Chopra - 1979

UCB/EERC-79/04 "A Mathematical Model of Masonry for Predicting ItsLinear Seismic Response Characteristics," by Y. Mengiand H.D. McNiven - 1979

UCB/EERC-79/05 "Mechanical Behavior of Lightweight Concrete Confinedby Different Types of Lateral Reinforcement," byM.A. Manrique, V.V. Bertero and E.P. Popov - 1979

UCB/EERC-79/06 "Static Tilt Tests of a Tall Cylindrical Liquid StorageTank," by R.W. Clough and A. Niwa - 1979

UCB/EERC-79/07 "The Design of Steel Energy Absorbing Restrainers andTheir Incorporation Into Nuclear Power Plants forEnhanced Safety: Volume 1 - Summary Report," byP.N. Spencer, V.F. Zackay, and E.R. Parker - 1979

UCB/EERC-79/08 "The Design of Steel Energy Absorbing" Restrainers andTheir Incorporation Into Nuclear Power Plants forEnhanced Safety: Volume 2 - The Development of Analysesfor Reactor System Piping," "Simple Systems" byM.C. Lee, J. Penzien, A.K. Chopra, and K. Suzuki"Complex Systems" by G.H. Powell, E.L. Wilson,R.W. Cloughand D.G. Row - 1979

UCB/EERC-79/09 "The Design of Steel Energy Absorbing Restrainers andTheir Incorporation Into Nuclear Power Plants forEnhanced Safety: Volume 3 - Evaluation of CommericalSteels," by W.S. Owen, R.t-1.N. Pel1oux, R.O. Ritchie,M. Faral, T. Ohhashi, J. Toplosky, S.J. Hartman, V.F.Zackay, and E.R. Parker - 1979

UCB/EERC-79/10 "The Design of Steel Epergy Absorbing Restrainers andTheir Incorporation Into Nuclear Power Plants forEnhanced Safety: Volume 4 - A Review of Energy-AbsorbingDevices," by J.M. Kelly and M.S. Skinner - 1979

UCB/EERC-79/ll "Conservatism In Summation Rules for Closely SpacedModes," by J.M. Kelly and J.L. Sackman - 1979

UCB/EERC-79/12

UCB/EERC-79/13

UCB/EERC-79/14

UCB/EERC-79/1S

UCB/EERC-79/16

UCB/EERC-79/l7

UCB/EERC-79/18

UCB/EERC-79/19

UCB/EERC-79/20

UCB/EERC-79/21

UCB/EERC-79/22

UCB/EERC-79/23

UCB/EERC";79/24

UCB/EERC-79/25

194

"Cyclic Loading Tests of Masonry Single Piers Volume3 - Height to Width Ratio of 0.5," by P.A. Hidalgo,R.L. Mayes, H.D. McNiven and R.W. Clough - 1979

"Cyclic Behavior of Dense Coarse-Grained Materials inRelation to the Seismic Stability of Dams," by N.G.Banerjee, H.B. Seed and C.K. Chan - 1979

"Seismic Behavior of Reinforced Concrete Interior Beam-ColumnSubassemblages," by S. Viwathanatepa, E.P. Popov andV.V. Bertero - 1979

"Optimal Design of Localized Nonlinear Systems withDual Performance Criteria Under Earthquake Excitations,"by M.A. Bhatti - 1979

"OPTDYN - A General Purpose Optimization Program forProblems with or without Dynamic Constraints," byM.A. Bhatti, E. Polak and K.S. Pister - 1979

"ANSR-II, Analysis of Nonlinear Structural Response,Users Manual," by D.P. Mondkar and G.H. Powell - 1979

"Soil Structure Interaction in Different SeismicEnvironments," A. Gomez-Masso, J. Lysmer, J.-C. Chenand H.B. Seed - 1979

"ARMA Models for Earthquake Ground Motions," by M.K.Chang, J.W. Kwiatkowski, R.F. Nau, R.M. Oliver andK.S. Pister - 1979

"Hysteretic Behavior of Reinforced Concrete StructuralWalls," by J.M. Val1enas, V.V. Bertero and E.P.Popov - 1979

"Studies on High-Frequency Vibrations of Buildings I:The Column Effects," by J. Lub1iner - 1979

"Effects of Generalized Loadings on Bond Reinforcing BarsEmbedded in Confined Concrete Blocks," by S. Viwathanatepa,E.P. Popov and V.V. Bertero - 1979

"Shaking Table Study of Single-Story Masonry Houses,Volume 1: Test Structures 1 and 2," by P. Gulkan,R.L. Mayes and R.W. Clough - 1979

"Shaking Table Study of Single-Story t·1asonry Houses,Volume 2: Test Structures 3 and 4," by P. Gulkan,R.L. Mayes and R.W.Clough - 1979

"Shaking Table Study of Single-Story Masonry Houses,Volume 3: Summary, Conclusions and Recommendations,"by R.W. Clough, R.L. Mayes and P. Gulkan - 1979

195

UCB/EERC-79/26 "Recommendations for a U.S.-Japan Cooperative ResearchProgram utilizing Large-Scale Testing Facilities," byU.S.-Japan Planning Group - 1979

UCB/EERC-79/27 "Earthquake-Induced Liquefaction Near Lake Amatitlan,Guatemala," by H.B. Seed, 1. Arango, C.K. Chan,A. Gomez-Masso and R. Grant de Asco1i - 1979

UCB/EERC-79/28 "Infi11 Panels: Their Influence on Seismic Response ofBuildings," by J.W. Axley and V.V. Bertero - 1979

UCB/EERC-79/29 "3D Truss Bar Element (Type 1) for the ANSR-II Program,"by D.P. Mondkar and G.H. Powell - 1979

UCB/EERC-79/30 "20 Beam-Column Element (Type 5 - Parallel ElementTheory) for the ANSR-II Program," by D.G. Row, G.H. Powelland D. P. Mondkar

UCB/EERC-79/31 "3D Beam-Column Element (Type 2 - Parallel ElementTheory) for the ANSR-II Program," by A. Riahi, G.H. Powelland D.P. Mondkar - 1979

UCB/EERC-79/32 "On Response of Structures to Stationary Excitation," byA. Der Kiureghian - 1979

UCB/EERC-79/33 "Undisturbed Sampling and Cyclic Load Testing of Sands,"by S. Singh, H.B. Seed and C.K. Chan - 1979

UCB/EERC-79/34 "Interaction Effects of Simultaneous Torsional andCompressional Cyclic Loading of Sand," by P.M. Griffinand W.N. Houston - 1979

UCB/EERC-80/01 "Earthquake Response of Concrete Gravity Dams IncludingHydrodynamic and Foundation Interaction Effects," byA.K. Chopra, P. Chakrabarti and S. Gupta - 1980

UCB/EERC-80/02 "Rocking Response of Rigid Blocks to Earthquakes,"by C.S. Yim, A.K. Chopra and J. Penzien - 1980

UCB/EERC-80/03 "Optimum Inelastic Design of Seismic-Resistant ReinforcedConcrete Frame Structures," by S.W. Zagajeski and V.V.Bertero - 1980

UCB/EERC-80/04 "Effects of Amount and Arrangement of Wall-PanelReinforcement on Hysteretic Behavior of ReinforcedConcrete Walls," by R. Iliya and V.V. Bertero - 1980

UCB/EERC-80/05 "Shaking Table Research on Concrete Dam Models," byR.W. Clough and A. Niwa - 1980

UCB/EERC-80/06 "piping with Energy Absorbing Restrainers: ParameterStudy on Small Systems," by G.H. powell, C. Oughourlianand J. Simons - 1980

196

UCB/EERC-80/07 "Inelastic Torsional Response of Structures Subjectedto Earthquake Ground Motions," by Y. Yamazaki - 1980

UCB/EERC-80/08 "Study of X-Braced Steel Frame Structures UnderEarthquake Simulation," by Y. Ghanaat - 19BO

UCB/EERC-BO/09 "Hybrid Modelling of soil-Structure Interaction," byS. Gupta, T.W. Lin, J. Penzien and C.S. Yeh - 1980

UCB/EERC-80/10 "General Applicability of a Nonlinear Model of a OneStory Steel Frame," by B. I. Sveinsson and :a. McNiven - 1980

UCB/EERC-BO/ll "A Green-Function Method for Wave Interaction with aSubmerged Body," by W. Kioka - 1.9BO

UCB/EERC-BO/12 "Hydrodynamic Pressure and Added Mass for AxisymmetricBodies," by F. Nilrat - 1980

UCB/EERC-BO/13 "Treatment of Non-Linear Drag Forces Acting on OffshorePlatforms," by B. V. Dao and J. Penzien - 1980

UCB/EERC-BO/14 "2D plane/Axisynunetric Solid Element (Type 3 - Elasticor Elastic-Perfectly Plastic) for the ANSR-II Program,"by D.P. Mondkar and G.H. Powell - 1980

UCB/EERC-BO/15 "A Response Spectrum Method for Random Vibrations," byA. Der Kiureghian - 1980

UCB/EERC-BO/16 "Cyclic Inelastic Buckling of Tubular Steel Braces," byV.A. Zayas, E.P. Popov and S.A. Mahin - June 1980