star seismic powercat test 1 (tr-2003_04, star seismic final report)

STRUCTURAL SYSTEMS

RESEARCH PROJECT

Report No. TR-2003/04

SUBASSEMBLAGE TESTING OF STAR SEISMIC BUCKLING-RESTRAINED BRACES

by

STEVE MERRITT

CHIA-MING UANG

GIANMARIO BENZONI

Final Report to Star Seismic, LLC.

May 2003

Department of Structural Engineering University of California, San Diego La Jolla, California 92093-0085

University of California, San Diego

Department of Structural Engineering

Structural Systems Research Project

Report No. TR-2003/04

SUBASSEMBLAGE TESTING OF STAR SEISMIC BUCKLING-RESTRAINED BRACES

by

Steve Merritt

Graduate Student Researcher

Chia-Ming Uang

Professor of Structural Engineering

Gianmario Benzoni

Associate Research Scientist

Final Report to Star Seismic, LLC.

Department of Structural Engineering

University of California, San Diego

La Jolla, California 92093-0085

May 2003

i

ABSTRACT

Subassemblage testing of eight full-scale buckling-restrained braces for Star Seismic,

LLC was conducted using a shake table facility at the University of California, San Diego.

The specimens featured an A36 steel yielding element with concrete infill in a hollow

structural section (HSS) casing. Each specimen was pin-connected to a gusset knife plate at

each end. The shake table imposed both longitudinal and transverse deformations to one end

of the brace. Both modified Standard Loading and Low-cycle Fatigue tests as derived from

the proposed SEAOC-AISC Recommended Provisions for Buckling-Restrained Braced

Frames were conducted; one specimen was also subjected to a simulated Sylmar, Northridge

earthquake response in real-time.

All specimens performed well under the Standard Loading Protocol. Only two

specimens eventually fractured during the Low-cycle Fatigue tests in the yielding element.

The pin-connections were able to accommodate an end rotation of at least 0.013 radians in the

transverse direction. The hysteresis behavior of the braces was very stable prior to fracture,

and a significant amount of energy was dissipated by each specimen.

The relationship between the tensile strength adjustment factor, w, and the brace axial

deformation can be approximated by two straight lines. Based on the expression derived in

this study, the average value of w at 1.5Dbm is 1.44. The relationship between the

compression strength adjustment factor, β, and the brace axial deformation can be

approximated by a straight line; the average value of β at 1.5Dbm is 1.15.

A procedure that can be used to evaluate the cumulative inelastic axial deformation

capacity, η, in a consistent manner was developed. Only Specimens 1 and 2 failed at η values

of 900 and 600, respectively. The other six specimens that did not experience any fracture

were tested to η values of between 900 and 1,650, with the average being 1,180. This value is

significantly higher than that (140) required by the proposed SEAOC-AISC Recommended

Provisions for uniaxial testing.

ii

ACKNOWLEDGEMENTS

Funding for this project was provided by Star Seismic, LLC in Salt Lake City, Utah.

The design of the specimens was provided by Star Seismic. Star Seismic would like to thank

Messrs. Rafael Sabelli, Bradri Prassad, Walterio Lopez, and other engineers that provided

input for the project.

iii

TABLE OF CONTENTS

ABSTRACT............................................................................................................................... i

ACKNOWLEDGEMENTS..................................................................................................... ii

TABLE OF CONTENTS........................................................................................................ iii

LIST OF TABLES ................................................................................................................... v

LIST OF FIGURES ................................................................................................................ vi

LIST OF SYMBOLS ............................................................................................................ xiii

1. INTRODUCTION............................................................................................................ 1 1.1 General ....................................................................................................................... 1

1.2 Scope and Objectives ................................................................................................. 1

2. TESTING PROGRAM.................................................................................................... 2 2.1 Test Specimens .......................................................................................................... 2

2.2 Material Properties ..................................................................................................... 2

2.3 Test Setup and Connection Details ............................................................................ 2

2.4 End Connections ........................................................................................................ 3

2.5 Loading Protocol........................................................................................................ 3

2.6 Instrumentation .......................................................................................................... 6

2.7 Data Reduction........................................................................................................... 6

3. TEST RESULTS ............................................................................................................ 26 3.1 Introduction.............................................................................................................. 26

3.2 Test Set No. 1—Specimens 1, 2, 3, and 4................................................................ 27

3.3 Test Set No. 2—Specimens 5 and 6......................................................................... 29

3.4 Test Set No. 3—Specimens 7 and 8......................................................................... 30

4. COMPARISON OF TEST RESULTS....................................................................... 147 4.1 Fracture Mode ........................................................................................................ 147

4.2 Correction for Pinhole Elongation ......................................................................... 147

4.3 Hysteretic Energy, Eh, and Cumulative Inelastic Deformation, η ......................... 148

4.4 Tension Strength Adjustment Factor, w................................................................. 148

4.5 Compression Strength Adjustment Factor, β ......................................................... 149

iv

4.6 Comparison at the SEAOC-AISC Limit State ....................................................... 149

4.7 Equivalent Viscous Damping................................................................................. 150

5. SUMMARY AND CONCLUSIONS .......................................................................... 164 5.1 Summary ................................................................................................................ 164

5.2 Conclusions............................................................................................................ 164

REFERENCES..................................................................................................................... 166

v

LIST OF TABLES

Table 2.1 Specimen Dimensions.............................................................................................. 10

Table 2.2 Mechanical Properties of Steel Core Plates ............................................................. 11

Table 2.3 Member Properties................................................................................................... 11

Table 2.4 Shake Table Peak Input Displacements ................................................................... 12

Table 2.5 Testing Sequence ..................................................................................................... 12

Table 3.1 Specimen 1 Peak Response Quantities .................................................................... 32








Table 4.1 Specimen Fractures in the Low-cycle Fatigue Test ............................................... 151

Table 4.2 Corrected Peak Longitudinal Brace Deformations (in.) ........................................ 151

Table 4.3 Tension Strength Adjustment Factor Idealization ................................................. 152

Table 4.4 Compression Strength Adjustment Factor Idealization ......................................... 153

Table 4.5 Select Quantities at 1.5Dbm (=7.5Dby) .................................................................... 153

vi

LIST OF FIGURES

Figure 2.1 All Specimens prior to Testing............................................................................... 13

Figure 2.2 Overall Geometry ................................................................................................... 14

Figure 2.3 Sections at Midspan (Specimens 1 to 4)................................................................. 15

Figure 2.4 Sections at Midspan (Specimens 5 to 8)................................................................. 16

Figure 2.5 SRMD Facility........................................................................................................ 17

Figure 2.6 Overall View of Specimens and SRMD (Strain Gage Locations also

Shown) ............................................................................................................................. 18

Figure 2.7 Typical Wall End Support (West End)................................................................... 19

Figure 2.8 Gusset Plate at West End (Strain Gages of Specimen 7 also shown)..................... 19

Figure 2.9 Standard Loading Sequence ................................................................................... 20

Figure 2.10 Sample Low-cycle Fatigue Loading Sequence (for Specimen 1) ........................ 21

Figure 2.11 Simulated Sylmar Response Loading Sequence................................................... 22

Figure 2.12 Displacement Transducer Instrumentation ........................................................... 23

Figure 2.13 Hysteresis Loop in the i-th Cycle ......................................................................... 24

Figure 2.14 Procedure for Calculating w* ................................................................................ 24

Figure 2.15 Comparison of Yield Force Definitions ............................................................... 25

Figure 3.1 Specimen 1: Testing Photos ................................................................................... 46

Figure 3.2 Specimen 1: Table Displacement Time Histories (Standard Test)......................... 47

Figure 3.3 Specimen 1: Brace Force versus Deformation (Standard Test).............................. 48

Figure 3.4 Specimen 1: Hysteretic Energy Time History (Standard Test) .............................. 48

Figure 3.5 Specimen 1: Table Displacement Time Histories (Low-cycle Fatigue Test)......... 49

Figure 3.6 Specimen 1: Brace Force versus Deformation (Low-cycle Fatigue Test).............. 50

Figure 3.7 Specimen 1: Hysteretic Energy Time History (Low-cycle Fatigue Test) .............. 50

Figure 3.8 Specimen 1: Table Displacement Time Histories (Both Tests Combined)............ 51

Figure 3.9 Specimen 1: Brace Force versus Deformation (Both Tests Combined)................. 52

Figure 3.10 Specimen 1: Hysteretic Energy Time History (Both Tests Combined) ............... 52

Figure 3.11 Specimen 1: Brace Response Envelope................................................................ 53

Figure 3.12 Specimen 1: β versus Deformation Level............................................................. 53

vii

Figure 3.13 Specimen 1: w and βw versus Deformation Level ............................................... 54

Figure 3.14 Specimen 2: Testing Photos.................................................................................. 55

Figure 3.15 Specimen 2: Table Displacement Time Histories (Standard Test)....................... 56

Figure 3.16 Specimen 2: Brace Force versus Deformation (Standard Test)............................ 57

Figure 3.17 Specimen 2: Hysteretic Energy Time History (Standard Test) ............................ 57

Figure 3.18 Specimen 2: Brace Force versus Brace Deformation (Low-cycle Fatigue

Test).................................................................................................................................. 58




Figure 3.22 Specimen 2: End Rotation Comparison................................................................ 61

Figure 3.23 Specimen 3: Testing Photo ................................................................................... 61




Figure 3.27 Specimen 3: Collar Strain Gage Time Histories (Standard Test)......................... 64

Figure 3.28 Specimen 3: HSS Strain Gage Time Histories (Standard Test) ........................... 65

Figure 3.29 Specimen 3: Table Displacement Time Histories (Sylmar Earthquake

Test).................................................................................................................................. 66

Figure 3.30 Specimen 3: Brace Force versus Deformation (Sylmar Earthquake Test) ........... 67

Figure 3.31 Specimen 3: Hysteretic Energy Time History (Sylmar Earthquake Test)............ 67

Figure 3.32 Specimen 3: Table Displacement Time Histories (Low-cycle Fatigue Test

No. 1)................................................................................................................................ 68

Figure 3.33 Specimen 3: Brace Force versus Deformation (Low-cycle Fatigue Test

No. 1)................................................................................................................................ 69

Figure 3.34 Specimen 3: Hysteretic Energy Time History (Low-cycle Fatigue Test No.

1) ...................................................................................................................................... 69

Figure 3.35 Specimen 3: Collar Strain Gage Time Histories (Low-cycle Fatigue Test

No. 1)................................................................................................................................ 70

Figure 3.36 Specimen 3: HSS Strain Gage Time Histories (Low-cycle Fatigue Test

No. 1)................................................................................................................................ 71

viii


No. 2)................................................................................................................................ 72


No. 2)................................................................................................................................ 73


2) ...................................................................................................................................... 73

Figure 3.40 Specimen 3: Collar Strain Gage Time Histories (Low-cycle Fatigue Test

No. 2)................................................................................................................................ 74

Figure 3.41 Specimen 3: HSS Strain Gage Time Histories (Low-cycle Fatigue Test

No. 2)................................................................................................................................ 75

Figure 3.42 Specimen 3: Table Displacement Time Histories (All Tests Combined)............. 76

Figure 3.43 Specimen 3: Brace Force versus Deformation (All Tests Combined) ................. 77

Figure 3.44 Specimen 3: Hysteretic Energy Time History (All Tests Combined) .................. 77









Figure 3.53 Specimen 4: Collar Strain Gage Time Histories (Standard Test)......................... 84

Figure 3.54 Specimen 4: HSS Strain Gage Time Histories (Standard Test) ........................... 85

Figure 3.55 Specimen 4: Table Displacement Time Histories (Low-cycle Fatigue Test)....... 86

Figure 3.56 Specimen 4: Brace Force versus Deformation (Low-cycle Fatigue Test)............ 87

Figure 3.57 Specimen 4: Hysteretic Energy Time History (Low-cycle Fatigue Test) ............ 87

Figure 3.58 Specimen 4: Collar Strain Gage Time Histories (Low-cycle Fatigue Test)......... 88

Figure 3.59 Specimen 4: HSS Strain Gage Time Histories (Low-cycle Fatigue Test)............ 89

Figure 3.60 Specimen 4: Table Displacement Time Histories (Both Tests Combined).......... 90

Figure 3.61 Specimen 4: Brace Force versus Deformation (Both Tests Combined)............... 91

Figure 3.62 Specimen 4: Hysteretic Energy Time History (Both Tests Combined) ............... 91

ix










No. 1)................................................................................................................................ 98


No. 1)................................................................................................................................ 99


1) ...................................................................................................................................... 99


No. 2).............................................................................................................................. 100


No. 2).............................................................................................................................. 101


2) .................................................................................................................................... 101

Figure 3.77 Specimen 5: Table Displacement Time Histories (All Tests Combined)........... 102

Figure 3.78 Specimen 5: Brace Force versus Deformation (All Tests Combined) ............... 103

Figure 3.79 Specimen 5: Hysteretic Energy Time History (All Tests Combined) ................ 103

Figure 3.80 Specimen 5: Brace Response Envelope.............................................................. 104

Figure 3.81 Specimen 5: β versus Deformation Level........................................................... 104

Figure 3.82 Specimen 5: w and βw versus Deformation Level ............................................. 105

Figure 3.83 Specimen 5: End Rotation Comparison.............................................................. 106

Figure 3.84 Specimen 6: Testing Photos................................................................................ 107

Figure 3.85 Specimen 6: Table Displacement Time Histories (Standard Test)..................... 108

Figure 3.86 Specimen 6: Brace Force versus Deformation (Standard Test).......................... 109

Figure 3.87 Specimen 6: Hysteretic Energy Time History (Standard Test) .......................... 109

x

Figure 3.88 Specimen 6: Table Displacement Time Histories (Low-cycle Fatigue Test)..... 110

Figure 3.89 Specimen 6: Brace Force versus Deformation (Low-cycle Fatigue Test).......... 111

Figure 3.90 Specimen 6: Hysteretic Energy Time History (Low-cycle Fatigue Test) .......... 111

Figure 3.91 Specimen 6: Table Displacement Time Histories (All Tests Combined)........... 112

Figure 3.92 Specimen 6: Brace Force versus Deformation (All Tests Combined) ............... 113

Figure 3.93 Specimen 6: Hysteretic Energy Time History (All Tests Combined) ................ 113

Figure 3.94 Specimen 6: Brace Response Envelope.............................................................. 114

Figure 3.95 Specimen 6: β versus Deformation Level........................................................... 114

Figure 3.96 Specimen 6: w and βw versus Deformation Level ............................................. 115

Figure 3.97 Specimen 6: End Rotation Comparison.............................................................. 116

Figure 3.98 Specimen 7: Testing Photos................................................................................ 117

Figure 3.99 Specimen 7: Table Displacement Time Histories (Standard Test)..................... 118

Figure 3.100 Specimen 7: Brace Force versus Deformation (Standard Test)........................ 119

Figure 3.101 Specimen 7: Hysteretic Energy Time History (Standard Test) ........................ 119

Figure 3.102 Specimen 7: Gusset Longitudinal Strain Gage Time Histories (Standard

Test)................................................................................................................................ 120

Figure 3.103 Specimen 7: Gusset Rosette Strain Gage Time Histories (Standard Test)....... 121

Figure 3.104 Specimen 7: Table Displacement Time Histories (Low-cycle Fatigue

Test No. 1)...................................................................................................................... 122


No. 1).............................................................................................................................. 123

Figure 3.106 Specimen 7: Hysteretic Energy Time History (Low-cycle Fatigue Test

No. 1).............................................................................................................................. 123

Figure 3.107 Specimen 7: Gusset Longitudinal Strain Gage Time Histories (Low-cycle

Fatigue Test No. 1)......................................................................................................... 124

Figure 3.108 Specimen 7: Gusset Rosette Strain Gage Time Histories (Low-cycle

Fatigue Test No. 1)......................................................................................................... 125


Test No. 2)...................................................................................................................... 126


No. 2).............................................................................................................................. 127

xi


No. 2).............................................................................................................................. 127

Figure 3.112 Specimen 7: Gusset Longitudinal Strain Gage Time Histories (Low-cycle

Fatigue Test No. 2)......................................................................................................... 128

Figure 3.113 Specimen 7: Gusset Rosette Strain Gage Time Histories (Low-cycle

Fatigue Test No. 2)......................................................................................................... 129

Figure 3.114 Specimen 7: Table Displacement Time Histories (All Tests Combined)......... 130

Figure 3.115 Specimen 7: Brace Force versus Deformation (All Tests Combined) ............. 131

Figure 3.116 Specimen 7: Hysteretic Energy Time History (All Tests Combined) .............. 131

Figure 3.117 Specimen 7: Brace Response Envelope............................................................ 132

Figure 3.118 Specimen 7: β versus Deformation Level......................................................... 132

Figure 3.119 Specimen 7: w and βw versus Deformation Level ........................................... 133

Figure 3.120 Specimen 7: End Rotation Comparison............................................................ 134

Figure 3.121 Specimen 8: Testing Photos ............................................................................. 135

Figure 3.122 Specimen 8: Table Displacement Time Histories (Standard Test)................... 136

Figure 3.123 Specimen 8: Brace Force versus Deformation (Standard Test)........................ 137

Figure 3.124 Specimen 8: Hysteretic Energy Time History (Standard Test) ........................ 137


Test No. 1)...................................................................................................................... 138


No. 1).............................................................................................................................. 139


No. 1).............................................................................................................................. 139


Test No. 2)...................................................................................................................... 140


No. 2).............................................................................................................................. 141


No. 2).............................................................................................................................. 141

Figure 3.131 Specimen 8: Table Displacement Time Histories (All Tests Combined)......... 142

Figure 3.132 Specimen 8: Brace Force versus Deformation (All Tests Combined) ............. 143

xii

Figure 3.133 Specimen 8: Hysteretic Energy Time History (All Tests Combined) .............. 143

Figure 3.134 Specimen 8: Brace Response Envelope............................................................ 144

Figure 3.135 Specimen 8: β versus Deformation Level......................................................... 144

Figure 3.136 Specimen 8: w and βw versus Deformation Level ........................................... 145

Figure 3.137 Specimen 8: End Rotation Comparison............................................................ 146

Figure 4.1 Hole Elongation Sources ...................................................................................... 154

Figure 4.2 Specimen 7: Brace Force versus Deformation Comparison................................. 155

Figure 4.3 All Specimens: Eh and η Time Histories .............................................................. 156

Figure 4.4 All Specimens: Eh and η Time Histories (Corrected)........................................... 157

Figure 4.5 All Specimens: w versus Brace Deformation ....................................................... 158

Figure 4.6 All Specimens: w versus Brace Deformation (Corrected).................................... 159

Figure 4.7 All Specimens: β versus Brace Deformation........................................................ 160

Figure 4.8 All Specimens: β versus Brace Deformation (Corrected) .................................... 161

Figure 4.9 Model for the Calculation of the Effective Viscous Damping ............................. 162

Figure 4.10 All Specimens combined: Equivalent Viscous Damping (Corrected) ............... 162

Figure 4.11 All Specimens individually: Equivalent Viscous Damping (Corrected)............ 163

xiii

LIST OF SYMBOLS

Ayz Area of yielding element

Dbm Deformation of brace in region L1 at Design Story Drift

Dby Deformation of brace in region L1 when steel core first yields

Eh Total hysteretic energy dissipated by brace

Es Young’s modulus of elasticity of steel

Fya Measured yield strength of steel core (average of coupon tests)

Fyn Nominal yield strength of steel core

Fua Measured tensile strength of steel core (average of coupon tests)

L1 Brace length defined in Figure 2.12(a) for calculating end rotation

Lb Total length of brace

Lyz Length of yielding element

P*y Effective yield force

P Actual resultant brace force

Pmax Maximum compression force

Pya Actual yield force, FyaAyz

Pyn Nominal yield force, FynAyz

Ry Material overstrength factor, Fya/Fyn

Tmax Maximum tensile force

w Tension strength adjustment factor, Tmax/Pyn

w* Tension strength adjustment factor at 5Dby

β Compression strength adjustment factor, Pmax/Tmax

xiv

∆ Actual brace deformation recorded by linear transducer L1

∆max Maximum axial deformation of brace in tension (end to end of brace)

∆min Minimum axial deformation of brace in compression

η Cumulative inelastic axial force deformation capacity, Eh/(DbyP*y)

1

1. INTRODUCTION

1.1 General

Using buckling-restrained braces (BRBs) for seismic resistance design of building

structures has been popular in Japan since the 1995 Kobe earthquake (Reina and Normike

1997). With the idea of preventing brace buckling under compression, one form of BRB

comprises a yielding steel core, which is encased in a concrete-filled steel hollow structural

section (HSS). The BRB system is also gaining acceptance by the design engineers in the

United States a few years after the 1994 Northridge, California earthquake (Clark et al. 1999,

Lopez 2001, Shuhaibar et al. 2002), and a number of buildings have been constructed with

BRBs in the past few years.

One type of BRBs that was developed by Star Seismic, LLC in the United States has

been experimentally investigated at the University of Utah; the study was limited to uniaxial

testing of the braces. According to the proposed Recommended Provisions for Buckling-

Restrained Braced Frames (SEAOC-AISC 2001), however, subassemblage testing of braces

that considers the effect of rotational restraint from the framing elements is also required to

evaluate the performance of the brace. This requires that both longitudinal and transverse

deformations be imposed to the brace subassemblage.

1.2 Scope and Objectives

A total of eight full-scale brace subassemblage were tested at the University of

California, San Diego. The objective of the testing was to evaluate the cyclic performance of

these subassemblage based on the acceptance criteria of the proposed Recommended

Provisions.

2

2. TESTING PROGRAM

2.1 Test Specimens

A total of eight full-scale specimens were tested with varying capacities and designs.

Figure 2.1 shows all eight specimens together prior to testing and Figure 2.2 shows the

geometry of a typical test specimen. Each specimen was composed of central steel core

plates, which were confined in concrete-filled rectangular HSS. (The reinforcing in all

sections was No. 4 rebar [See Figure 2.2(c)]). Table 2.1 shows the dimensions of each

specimen and the HSS size used.

The specimens were grouped into three sets for the purpose of presentation. The

specimens in the first set (1 through 4) varied in capacity but were similar in configuration.

Each comprised two flat steel core plates encased by a single HSS. On the contrary, the

second and third sets were each composed of two specimens that were identical in design

capacity but with differing configurations. See Table 2.1, Figure 2.2, Figure 2.3 and Figure

2.4 for detailed dimensions of the steel core plates and their geometric differences for each

section.

2.2 Material Properties

A36 steel, with a nominal yield strength, Fyn, of 36 ksi, was specified for the steel core

plates, and A500 Grade B steel was used for the HSS. Tensile coupon tests of the steel core

plates were conducted by Sherry Laboratories for the actual material properties; the results are

summarized in Table 2.2. Based on the average measured yield strength (Fya), the values of

material overstrength factor, Ry (=Fya/Fyn), and the brace yield forces are calculated and listed

in Table 2.3.

The specified 28-day concrete strength was 3,500 psi.

2.3 Test Setup and Connection Details

A shake table facility, called the Seismic Response Modification Device (SRMD)

facility, at the University of California, San Diego was employed to test the specimens. The

SRMD facility, which has six degrees of freedom, is shown in Figure 2.5(a). By attaching

one end of the specimen to the wall end, the longitudinal and vertical movements of the shake

3

table imposed both axial and transverse deformations to the specimen [specimen setup is

shown in Figure 2.5(b)]. Figure 2.6 shows the specimens and the test setup, and Figure 2.7

depicts the brace support at the wall end.

2.4 End Connections

The ends of each brace were pin-connected to a gusset plate (see Figure 2.8). The pin

used throughout testing was 4.5 in. diameter, grade A354BC steel in double shear with an

ultimate strength of 115 ksi. The figure also shows that the gusset plate was thickened around

the hole by welding a plate in order to increase the bearing capacity.

2.5 Loading Protocol

According to the proposed Recommended Provisions for Buckling-Restrained Braces

(SEAOC-AISC 2001), the design of braces shall be based upon results from qualifying cyclic

tests in accordance with the procedures and acceptance criteria of its Appendix. In addition to

the Standard Loading Protocol and Low-cycle Fatigue Loading Protocol that are stipulated in

the Recommended Provisions, a real-time dynamic test that simulates a seismic response was

also conducted for a specimen.

Standard Loading Protocol

According to the Appendix of the proposed Recommended Provisions, the following

loading sequence shall be applied to the test specimen, where the deformation is the axial

deformation of the steel core plates:

(1) 6 cycles of loading at the deformation corresponding to Dby,

(2) 4 cycles of loading at the deformation corresponding to 0.5Dbm,

(3) 4 cycles of loading at the deformation corresponding to 1.0Dbm,

(4) 2 cycles of loading at the deformation corresponding to 1.5Dbm, and

(5) Additional complete cycles of loading at the deformation corresponding to 1.0Dbm as

required for the Brace Test Specimen to achieve a cumulative inelastic axial deformation

of at least 140 times the yield deformation (not required for the Subassemblage Test

Specimen).

Note that the requirement of cumulative inelastic axial deformation is for uni-axial brace

testing, not subassemblage testing. The above loading sequence requires two quantities: Dby

4

and Dbm. Dby is defined as the axial deformation at first significant yield of the specimen, and

Dbm corresponds to the axial deformation of the specimen at the Design Story Drift.

Because item 5 in the loading sequence is not required for the subassemblage test

specimen, it was decided to establish a loading sequence as shown in Figure 2.9(a) for axial

deformation. This loading sequence, defined as the Standard Loading Protocol herein,

satisfies items 1 through 4. It further contains an addition cycle at 1.0Dbm, five cycles at

2.0Dbm and two cycles each at 2.5Dbm and 3.0Dbm. The additional cycles were added with the

intent to satisfy the OSHPD (Office of Statewide Health Planning and Development)

requirement for a cumulative inelastic axial deformation of at least 350 times the yield

deformation at this deformation level.

The calculation of Dby was based on the deformation expected over the gage length of

transducer L1 [see Figure 2.12(a)]. This initial pin-to-pin distance was 21’-0” (252 inches)

for all specimens. To establish the value of Dby, the following components were considered at

the actual yield force level, Pya:

(1) yield deformation of the steel core plates in the yielding length, Lyz [see Figure 2.2(a) and

Table 2.1 for Lyz], and

(2) elastic deformation of the steel core plates outside the yielding length, Lyz. This includes

Lkp and Ltz on each end of the steel core plates.

With a calculated Dby value for each specimen (see Table 2.3), the shake table

displacement protocol was created by adding additional displacement to account for the

following:

(1) elastic deformation of the gusset bracket, and

(2) elastic deformation due to flexibility of the end supports and reaction wall at the SRMD

facility (see Figure 2.7) based on a known total system stiffness of 4,090 kips/in.

This value was then increased conservatively for all specimens for testing purposes to ensure

yielding in the first 6 cycles. See the tabulated shake table input values in Table 2.4(a).

The value of Dbm needs not be taken as greater than 5Dby (SEAOC-AISC 2001). Once

these values were established, longitudinal amplitudes for the other cycles could be

determined (Table 2.4). Note that these amplitudes were adjusted upward slightly and, thus,

are more conservative than those shown in Figure 2.9(a).

5

The specimens were tested to simulate a 45-degree bracing configuration. With this

assumption, the corresponding amplitudes for the transverse movement of the shake table

were established in Table 2.4(a). Figure 2.9(b) shows that the transverse movement is in-

phase with the longitudinal movement in order to simulate a realistic frame action effect to

gusset connections. The transverse end deformations were imposed by vertical displacements

of the shake table.

Low-cycle Fatigue Loading Protocol

After the Standard Loading Protocol was imposed to the test specimen, low-cycle

fatigue testing followed. It will be defined as the Low-cycle Fatigue test sequence herein.

Each test corresponded to a different loading. See Figure 2.10 for a sample Low-cycle

Fatigue loading protocol. Table 2.4(b) shows the deformation amplitudes and number of

cycles for each specimen. The intention was that if the specimen did not fracture during the

test, the same test was repeated until the specimen fractured. Do to testing time constraints,

however, the specimen was removed before fracture after enduring a large amount of inelastic

low-cycle fatigue testing.

Note that the amplitudes used for Low-cycle Fatigue Testing were often more than

that (1.0Dbm) required by SEAOC-AISC for uni-axial low-cycle fatigue testing. High-

amplitude low-cycle fatigue testing is more demanding, which generally results in a reduced

energy dissipation capacity and cumulative inelastic axial deformation.

Simulated Sylmar Response

Specimen 3 was subject to a real-time dynamic test to simulate the effect of the

Sylmar ground motion that was recorded during the 1994 Northridge, California earthquake.

The test was performed after the Standard Test and before the Low-cycle Fatigue Test. For

this test, the specimen was only subject to uni-axial deformations.

Figure 2.11(a) shows the fault-normal component of the Sylmar ground acceleration

record that was used by the SAC Joint Venture (Somerville 1997). Since it was the simulated

axial deformation of the brace, not the ground motion, that was imposed to the specimen, a

nonlinear time-history analysis was conducted by R. Sabelli. The equivalent single-degree-

of-freedom system for a buckling-restrained braced frame is shown in Figure 2.11(b).

6

Assuming that the angle of inclination of the brace from the horizon is 45 degrees, the

resulting brace axial deformation time history is shown in Figure 2.11(b).

2.6 Instrumentation

Four displacement transducers [L1 through L4 in Figure 2.12(a)] measured the axial

deformation of the test specimen; Figure 2.12(b) shows the mounting device for these

transducers at one end of the specimen. As shown in Figure 2.12(a), the mounting points for

the transducers L1 through L3 were located at the centers of the pin for each specimen end for

consistency with the Dby calculation. The longitudinal and transverse movements of the shake

table were also recorded.

The force measured by the load cell in each of the four actuators that drove the shake

table was recorded. The resultant force components in both the longitudinal and transverse

directions were then computed from these measured forces.

Specimen 3 and 4 were instrumented with strain gages on the HSS and collar. The

gages on the collar were labeled “Top” and “Bottom” and were oriented transverse to the

axial load. The Top gage was one half inch from the edge of the three-foot collar. The

Bottom gage was 6 inches from the end plate. The gages on the HSS were labeled “North”

and “South” and were oriented longitudinal to the axial load at the one-third point along the

pin-to-pin brace length. The Bottom gage was omitted for Specimen 5. See Figure 2.6 for a

photo with the strain gage locations on these specimens.

The gusset plate of Specimen 7 was also instrumented was 4 strain gages as shown in

Figure 2.8. The gages were labeled as shown. Gages “A” and “B” were each 2.5 inches from

the centerline of the hole. Gages “R1” and “R2” were 3 inches below the centerline of the

hole.

An inclinometer was mounted on the gusset plate of every specimen except Specimen

1. It was mounted near the pin connection on the west end as shown in Figure 2.12(b).

2.7 Data Reduction

Brace Axial Deformation, ∆

In the following chapter, the brace axial deformation, ∆, corresponding to that

measured by the displacement transducer L1 in Figure 2.12(a) is reported.

7

Brace End Rotation

The brace end rotation is computed by dividing the measured table transverse (i.e.,

vertical) movement by the length L1 shown in Figure 2.12(a).

Resultant Brace Force, P

The resultant axial force in the brace was calculated as the square root of the sum of

the squares of the longitudinal and transverse forces that were recorded. By conducting a

simple empty-table displacement history and analyzing the longitudinal and transverse forces

recorded, it was determined the force of friction in the system was approximately 8 kips. This

value, roughly 2% or less of the peak axial forces, was subtracted from the resultant force

except near the displacement peaks where the shake table was essentially still.

Tension Strength Adjustment Factor, w

The proposed SEAOC-AISC Recommended Provision defines w as follows:

yzynyn AFT

PT

w maxmax == (2.1)

where Fyn = nominal yield strength, and Ayz = area of the yielding segment of steel core plates.

The variation of w with respect to the brace axial deformation (∆) for the Standard Loading

Protocol will be presented.

Compression Strength Adjustment Factor, β

The β value is computed as follows (SEAOC-AISC 2001):

max

maxβTP

= (2.2)

where Pmax is the maximum compressive force, and Tmax is the maximum tension force

corresponding to a brace deformation of 1.5Dbm. Note that, for capacity design, the product of

β and w represents the overstrength of the brace in compression beyond its nominal yield

strength.

8

Hysteretic Energy, Eh

The area enclosed by the P versus ∆ hysteresis loops represents the hysteretic energy

dissipated by the brace:

∫ ∆= dPEh (2.3)

Cumulative Inelastic Axial Deformation Capacity, η

Consider the i-th cycle of a hysteresis plot in Figure 2.13. Based on the idealized bi-

linear hysteresis loop, the cumulative inelastic axial deformation, ∆pi, is defined as:

−

−

+

+−+ +=∆+∆=∆

y

hi

y

hipipipi P

EPE

*y

hipi P

E≈∆ (2.4)

where +yP and −

yP are the effective yield forces of the brace in tension and compression, and

*yP is the average value. The effective yield force is defined herein as follows:

yny PwP ** = (2.5)

where *w is the tension strength adjustment factor defined in Eq. (2.1) at a deformation level

of 5Dby, which is the default value for Dbm per SEAOC-AISC (2001). Because there may not

be data points exactly at the value of 5Dby as shown in Figure 2.14, a procedure for

interpolating was developed. A linear least-squares fit was performed on all of the data points

to the right of 5Dby; this is referred to as Zone 2. Then a line was drawn from the point (Dby,

Ry) to the intersection of the least squares fit and 5Dby lines; this is referred to as Zone 1. The

slopes and intercepts of the two lines are presented in Chapter 4.

Therefore, the total cumulative inelastic axial deformation is:

∑ ∑ ==∆=∆ **y

h

y

hipip P

EPE

(2.6)

∆p can be normalized by the yield deformation of the brace, Dby, for the cumulative inelastic

axial deformation capacity, η:

byy

h

by

p

DPE

D *η =∆

= (2.7)

For uni-axial testing of buckling-restrained braces, the proposed SEAOC-AISC Provisions

(2001) requires that the value of η be at least 140. Although this requirement is not needed

9

for the subassemblage test specimen, for comparison purposes the η values will be presented

in Chapter 4.

A comparison between the different yield force definitions is shown in Figure 2.15 on

a typical specimen force-deformation response plot. The individual response plots for each

specimen will be presented in Chapter 3.

10

Table 2.1 Specimen Dimensions

(a) Member Core Geometry

Steel Core plates Transition Zone Yielding Zone Specimen

No. of plates tcp (in)btz (in) Ltz (in) byz (in) Lyz (in)

1 2 0.75 10 23.00 2.53 176.0 2 2 0.75 10 21.28 3.97 179.4 3 2 0.75 10 19.36 5.56 183.3 4 2 1.00 10 18.44 6.33 185.1 5 4 0.75 10 18.89 5.95 184.2 6 6 0.75 10 21.28 3.97 179.4 7 6 0.75 10 18.41 6.34 185.2 8 8 0.75 10 20.33 4.77 181.3

(b) HSS and Collar Configurations

Specimen HSS Configuration Collar Plate Size 1 one-12×10×3/8” 3/8×36” long 2 one -12×10×3/8” 3/8×36” long 3 one -12×10×3/8” 3/8×36” long 4 one -12×0×3/8” 1/2×48” long 5 two-12×8×1/2” 1/2×48” long 6 two-12×8×1/2”, 1-12×12×1/2” 5/8×60” long 7 two-12×8×1/2”, 1-12×12×1/2” 3/4×60” long 8 four-12×8×1/2” 3/4×60” long

(c) Member End Geometry

Knife Plate End Plate Specimen tkp (in) bkp (in) Lkp (in) tep (in)

1 1.5 14.5 14.0 1.0 2 1.5 14.5 14.0 1.0 3 1.5 14.5 13.0 2.0 4 1.5 14.5 13.0 2.0 5 1.5 18.5 12.0 3.0 6 1.5 22.0 12.0 3.0 7 1.5 22.0 12.0 3.0 8 1.5 22.0 12.0 3.0

11

Table 2.2 Mechanical Properties of Steel Core Plates

Specimens Heat No.a Coupon No.

Yield Strength (ksi)

Tensile Strength (ksi)

Yield Ratioc

Elong.d (%)

1 39.6 61.8 0.64 27 2 40.2 64.3 0.63 26 3 44.0 64.7 0.68 27

(4)b (42.4) (62.1) (0.68) (24) 1,2,3,5,6,7 325-4268

(5) (43.6) (63.0) (0.69) (27) 1 37.8 67.8 0.56 26 2 37.7 68.1 0.55 26 3 38.3 68.6 0.56 21

(4) (41.6) (63.1) (0.66) (24) 4 325-4272

(5) (42.2) (63.5) (0.66) (23) aNucor Bar Mill-Jewett bMaterial properties from Certified Mill Test Report are provided in parenthesis. cYield Ratio = Yield Strength / Tensile Strength dBased on 2-in. gage length; mill certificate value based on 8-in gage length.

Table 2.3 Member Properties

Specimen Fya (ksi) Ayz (in2) Pyn (kips) Pya (kips) Ry Dby (in) 1 42.0 3.80 137 160 1.17 0.275 2 42.0 5.96 215 250 1.17 0.290 3 42.0 8.34 300 350 1.17 0.304 4 39.5 12.66 456 500 1.10 0.294 5 42.0 17.85 643 750 1.17 0.311 6 42.0 17.87 643 750 1.17 0.294 7 42.0 28.53 1027 1198 1.17 0.311 8 42.0 28.62 1030 1202 1.17 0.300

12

Table 2.4 Shake Table Peak Input Displacements

(a) Standard Loading Protocol

Longitudinal Movement (in) Transverse Movement (in) Number of Cycles Number of Cycles Specimen

6 4 4 2 1 5 2 2 6 4 4 2 1 5 2 2 1 0.44 0.90 1.69 2.50 1.69 3.10 3.10 3.55 0.40 0.85 1.65 2.45 1.65 3.05 3.50 4.002 0.46 0.91 1.72 2.52 1.72 3.22 3.78 4.48 0.40 0.85 1.65 2.45 1.65 3.15 3.70 4.003 0.48 0.94 1.75 2.55 1.75 3.41 - - 0.40 0.85 1.65 2.45 1.65 3.30 - - 4 0.52 0.97 1.78 2.59 1.78 3.20 3.96 4.66 0.40 0.85 1.65 2.45 1.65 3.05 3.80 4.005 0.58 1.03 1.84 2.66 1.84 3.57 4.23 5.05 0.40 0.85 1.65 2.45 1.65 3.35 4.00 4.006 0.58 1.03 1.84 2.66 1.84 3.27 3.98 4.75 0.40 0.85 1.65 2.45 1.65 3.05 3.75 4.007 0.68 1.14 1.97 2.80 1.97 3.84 - - 0.40 0.85 1.65 2.45 1.65 3.45 - - 8 0.68 1.14 1.97 2.81 1.97 3.64 - - 0.40 0.85 1.65 2.45 1.65 3.25 - -

(b) Low-cycle Fatigue Loading Protocol

Specimen Cycles Longitudinal Movement (in) Transverse Movement (in) 1 30 1.69 1.65 2 30 1.72 1.65 3* 25 2.39 2.25 4 25 2.39 2.25 5 30 1.85 1.65 6 30 1.85 1.65 7 15 2.86 2.50 8 15 2.86 2.50

*Simulated Sylmar response test was conducted prior to the Low-cycle Fatigue Test

Table 2.5 Testing Sequence

Specimen Alias Date Tested Test Order 1 160 November 19, 2002 1st 2 250 November 20, 2002 2nd 3 350 November 21, 2002 6th 4 500 November 21, 2002 5th 5 750A November 20, 2002 3rd 6 750B November 20, 2002 4th 7 1200A November 25, 2002 8th 8 1200B November 22, 2002 7th

13

(a) End View

(b) Top view

Figure 2.1 All Specimens prior to Testing

14

(a) Typical Elevation (Rebar and Collar not shown for clarity)

(b) Typical Plan (Collar not shown for clarity)

(c) Typical Section A-A

Figure 2.2 Overall Geometry

15

(a) Specimen 1

(b) Specimen 2

(c) Specimen 3

(d) Specimen 4

Figure 2.3 Sections at Midspan (Specimens 1 to 4)

16

(a) Specimen 5

(b) Specimen 6

(c) Specimen 7

(d) Specimen 8

Figure 2.4 Sections at Midspan (Specimens 5 to 8)

17

(a) Three-Dimensional Rendering

(b) Setup Overview

Figure 2.5 SRMD Facility

Reaction Wall (Not shown)

Platen (Shake Table)

Adapting Brackets

Reaction Block

Pin Connections

Specimen (Brace)

Collars

18

(a) Specimen 3

(b) Specimen 4

Figure 2.6 Overall View of Specimens and SRMD (Strain Gage Locations also Shown)

NORTH North Gage

South Gauge

Top Gage

Bottom Gage

NORTH

North Gage

South Gage Top

Gage

19

Figure 2.7 Typical Wall End Support (West End)

Figure 2.8 Gusset Plate at West End (Strain Gages of Specimen 7 also shown)

Gage R2

Gage B Gage A

Gage R1

20

0 200 400 600 800-6

-4

-2

0

2

4

6

(a) Longitudinal Direction*

0 200 400 600 800-6

-4

-2

0

2

4

6

(b) Transverse Direction*

*See Table 2.4(a) for Peak Values and Cycle Variations

Figure 2.9 Standard Loading Sequence

SEAOC-AISC

Bra

ce D

efor

mat

ion

Bra

ce D

efor

mat

ion

1.5Dby 0.5Dbm

2.0Dbm

2.5D

bm

1.0Dbm

OSHPD

3.0D

bm

1.5D

bm

Time (sec)

Time (sec)

21

0 200 400 600 800 1000-6

-4

-2

0

2

4

6

(a) Longitudinal Direction*

0 200 400 600 800 1000-6

-4

-2

0

2

4

6

(b) Transverse Direction* *See Table 2.4(b) for Peak Values and Cycle Variations

Figure 2.10 Sample Low-cycle Fatigue Loading Sequence (for Specimen 1)

Bra

ce D

efor

mat

ion

Bra

ce D

efor

mat

ion

Time (sec)

Time (sec)

1.0Dbm

22

Gro

und

Acc

eler

atio

n (g

)

0 10 20 30 40-0.6

-0.4

-0.2

0.0

0.2

0.4

(a) Fault Normal Ground Acceleration Time History

(b) Equivalent Single-degree-of-freedom System

Bra

ce D

efor

mat

ion

(in)

0 10 20 30 40-2

-1

0

1

2

3

4

5

(c) Longitudinal Brace Displacement Time History

Figure 2.11 Simulated Sylmar Response Loading Sequence

Tabl

e D

ispl

acem

ent (

in.)

Time (sec)

W = 1,100 kips K = 200 kips/in T = 0.75 sec Cy = 0.225 (Yield Coeff.) ζ = 2% θ = 45 degrees

Time (sec)

θ

Gro

und

Acc

eler

atio

n (g

)

23

(a) Location of Displacement Transducers

(b) Displacement Transducers

Figure 2.12 Displacement Transducer Instrumentation

L2 L4 L3

Shake Table L1

Inclinometer

Displacement Transducers

24

Figure 2.13 Hysteresis Loop in the i-th Cycle

0 2 4 6 8 10 12 14 16

Normalized Brace Deformation

0 1 2 3 4

Brace Deformation (in)

0.0

0.5

1.0

1.5

2.0

Figure 2.14 Procedure for Calculating w*

P

∆

−∆ pi

+∆ pi

Idealized response

Actual response

Area = +hiE

Area = −hiE

−yP

+yP

yaP

w*

5Dby Dby

w (=

Tm

ax /

Pyn

)

Zone 2 Zone 1

Ry

Normalized Brace Deformation


25

Res

ulta

nt F

orce

(kip

s)

-6 -4 -2 0 2 4 6-400

-200

0

200

400


-20 -10 0 10 20Normalized Brace Deformation

Figure 2.15 Comparison of Yield Force Definitions

Pyn

Pya

*yP

26

3. TEST RESULTS

3.1 Introduction

For each of the test specimens, the following results are presented for both the

Standard Loading Protocol and Low-cycle Fatigue tests. In addition to showing results for

each test, for each specimen these results are also combined in another set of plots to

demonstrate the accumulative effects.

(1) Measured shake table movements in the longitudinal and transverse directions: These

movements represent the axial deformation and end rotation demand imposed to the

specimen-supporting frame assembly.

(2) Brace resultant force (P) versus brace axial deformation (∆) plot: The calculation of the

brace resultant force was presented in Section 2.7. The brace axial deformation refers to

the deformation measured by displacement transducer L1 in Figure 2.12(a). On the plots,

normalized brace deformation refers to ∆/Dby.

(3) Hysteretic energy (Eh) time history: The hysteretic energy is computed in accordance

with Eq. 2.3.

(4) Cumulative inelastic axial deformation (η) time history: the calculation of η is based on

Eq. 2.7. One ordinate is added to the plot of hysteretic energy time history to show the η

value achieved in the specimen.

(5) A table summarizing the peak brace forces and peak brace deformations: The peak brace

deformation was based on the measurement of displacement transducer L1.

(6) Compression strength adjustment factor (β) versus brace axial deformation plot: See Eq.

2.2 for the calculation of β. The variation of β with respect to the brace axial deformation

(∆) for the Standard Loading Protocol is presented.

(7) Tension strength adjustment factor (w) versus brace axial deformation plot: The

calculation of w is based on Eq. 2.1.

(8) Strain gage plots: Specimen 3 and 4 were instrumented with strain gages on the HSS and

collar. Specimen 7 was instrumented with strain gages on the gusset plate.

(9) Rotation comparison plots: All specimens except Specimen 1 were instrumented with an

inclinometer at the end of the brace near the pin. The inclinometer reading was compared

27

to that which was calculated based on transverse shake table displacement and brace

geometry. The relationship shows any relative rotation of the collar with respect to the

brace.

3.2 Test Set No. 1—Specimens 1, 2, 3, and 4

Specimens 1 through 4 were all fabricated with a single HSS (Figure 2.3). They all

used two sandwiched strands of steel core plate within as the yielding elements. However, the

dimensions of the core plates varied [Table 2.1(a)]. Thus, the capacities of the braces also

varied (Table 2.3).

3.2.1 Specimen 1

Figure 3.1(a) shows an overview of the specimen. The specimen performed well

during the Standard Loading Protocol test. The steel core plates ruptured in the 18th cycle

during the Low-cycle Fatigue test. See Figure 3.1(b) for the end of the brace after testing.

The following results are presented for Specimen 1:

(1) Standard Loading Protocol test: Figure 3.2 to Figure 3.4,

(2) Low-cycle fatigue test: Figure 3.5 to Figure 3.7,

(3) Combined test results: Figure 3.8 to Figure 3.10,

(4) Peak response values and response envelope: Table 3.1 and Figure 3.11, and

(5) β, w, and βw values: Table 3.1 and Figure 3.12 to Figure 3.13.

Note the horizontal shift near zero load in the hysteresis response plot in Figure 3.3. The

shift, which was caused by the gap between the pin and the gusset plate, grew bigger in later

tests because the same gusset plate and pin were used for the testing of all specimens.

3.2.2 Specimen 2

Figure 3.14(a) shows an overview of the specimen. The specimen performed well

during the Standard Loading Protocol test. The steel core plates ruptured in the first cycle

during the Low-cycle Fatigue test. See Figure 3.14(b) for the brace-collar interface after

testing. The following results are presented for Specimen 2:


(2) Low-cycle fatigue test: Specimen fractured in first cycle. Unfortunately, no data was

recorded, but a photo of the screen in the control room is shown in Figure 3.18. The raw

28

data plot shows the relationship between the longitudinal brace force and the pin-to-pin

brace deformation.

(3) Peak response values and response envelope: Table 3.2 and Figure 3.19,

(4) β, w, and βw values: Table 3.2 and Figure 3.20 to Figure 3.21, and

(5) End rotation comparison: Figure 3.22.

3.2.3 Specimen 3

The specimen performed well and the steel core plates did not rupture during all

testing (one Standard Loading Protocol test, one Simulated Sylmar Earthquake test, and two

Low-cycle Fatigue tests). See Figure 3.23 for a photo of the brace during testing. The

following results are presented for Specimen 3:

(1) Standard Loading Protocol test (including strain gage plots): Figure 3.24 to Figure 3.28,

(2) Sylmar Earthquake Record test: Figure 3.29 to Figure 3.31,

(3) Low-cycle Fatigue tests (including strain gage plots): Figure 3.32 to Figure 3.41,





Specimen 3 was instrumented with strain gages to explore the bulging stresses induced

in the collar as well as the stresses transferred to the HSS casing. See Figure 2.6(a) for the

locations of the gages. The plotted results can be seen in Figure 3.27 and Figure 3.28 for the

Standard Test and Figure 3.35, Figure 3.36, Figure 3.40, and Figure 3.41 for the Low-cycle

Fatigue Tests. In the plots, normalized strain is defined as ε/εy where εy is based on the

nominal yield strength (46 ksi for the HSS and 50 ksi for the collar).

The gages on the north and south sides of the HSS exhibited maximum longitudinal

strains of less than 0.2εy. The strains on the north and south faces are approximately equal in

magnitude but opposite in sign, characteristic of flexural stresses. This phenomenon is likely

either caused by a small loading eccentricity or by the steel core trying to buckle to one side

in a higher mode pattern.

On the top and bottom faces of the collar, the transverse strains were also small. The

maximum transverse strain on the top of the collar was 0.2εy and the maximum transverse

29

strain in the bottom was less than 0.05εy. The strain in the top of the collar shows that there

was some bulging, and thus, a small amount of relative displacement between the brace and

the collar.

3.2.4 Specimen 4

Figure 3.49(a) shows Specimen 4 during Low-cycle Fatigue testing. The specimen

performed well and the steel core plates did not rupture during all testing (one Standard

Loading Protocol test and one Low-cycle Fatigue test). See Figure 3.49(b) for the end of the

brace after all testing. The following results are presented for Specimen 4:

(1) Standard Loading Protocol test (including strain gage plots): Figure 3.50 to Figure 3.54,

(2) Low-cycle fatigue test (including strain gage plots): Figure 3.55 to Figure 3.59,





Specimen 4 was also instrumented with strain gages to explore the bulging stresses

induced in the collar as well as the stresses transferred to the HSS casing. See Figure 2.6(b)

for the locations of the gages. The plotted results can be seen in Figure 3.53 and Figure 3.54

for the Standard Test and Figure 3.58 & Figure 3.59 for the Low-cycle Fatigue Test. The

results were similar to Specimen 3.

3.3 Test Set No. 2—Specimens 5 and 6

Specimens 5 and 6 were nominally equivalent in capacity, however, they had differing

configurations of HSS and steel core plates [see Figure 2.4(a) and (b)].

3.3.1 Specimen 5

Figure 3.67(a) shows Specimen 5 during the Standard test. The specimen performed

well and the steel core plates did not rupture during all testing (one Standard Loading Protocol

test and two Low-cycle Fatigue tests). See Figure 3.67(b) for the brace-collar interface after

testing. The following results are presented for Specimen 5:


30

(2) Low-cycle fatigue tests: Figure 3.71 to Figure 3.76,





3.3.2 Specimen 6

Figure 3.84(a) shows Specimen 6 before testing. The specimen performed well and

did not rupture during all testing (one Standard Loading Protocol test and one Low-cycle

Fatigue test). See Figure 3.84(b) for the yielding of the knife plates after all testing. The



(2) Low-cycle fatigue test: Figure 3.88 to Figure 3.90,





3.4 Test Set No. 3—Specimens 7 and 8

Specimens 7 and 8 were also nominally equivalent in capacity; however, they too had

differing configurations of HSS and steel core plates [see Figure 2.4(c) and (d)].

3.4.1 Specimen 7

Figure 3.98(a) shows Specimen 7 during the Low-cycle fatigue testing. The specimen

performed well and the steel core plates did not rupture during all testing (one Standard

Loading Protocol test and two Low-cycle Fatigue tests). See Figure 3.98(b) for the yielding

of the knife plate after testing. The following results are presented for Specimen 7:




31




3.4.2 Specimen 8

Figure 3.121(a) shows Specimen 8 before testing. The specimen performed well and

the steel core plates did not rupture during all testing (one Standard Loading Protocol test and

two Low-cycle Fatigue tests). See Figure 3.121(b) for the end of the brace after testing. The








32

Table 3.1 Specimen 1 Peak Response Quantities

Brace Deformations (in) Test Cycle No. Tmax (kips) Pmax (kips) β w βw Longitudinal Transversea

1 173 -172 0.99 1.27 1.25 0.42 0.41 (0.002) 2 168 -170 1.01 1.23 1.24 0.41 0.41 (0.002) 3 163 -169 1.03 1.19 1.23 0.41 0.41 (0.002) 4 174 -168 0.97 1.27 1.24 0.41 0.41 (0.002) 5 167 -168 1.01 1.22 1.23 0.41 0.41 (0.002) 6 166 -169 1.02 1.22 1.24 0.41 0.41 (0.002) 7 170 -176 1.04 1.24 1.29 0.87 0.87 (0.003) 8 171 -176 1.03 1.25 1.29 0.87 0.87 (0.003) 9 173 -177 1.03 1.27 1.30 0.86 0.87 (0.003)

10 169 -179 1.06 1.24 1.31 0.87 0.87 (0.003) 11 181 -222 1.23 1.32 1.63 1.69 1.66 (0.007) 12 193 -213 1.10 1.41 1.55 1.69 1.68 (0.007) 13 199 -216 1.08 1.46 1.57 1.69 1.68 (0.007) 14 201 -218 1.08 1.47 1.59 1.69 1.68 (0.007) 15 203 -237 1.16 1.49 1.72 2.50 2.49 (0.010) 16 214 -240 1.12 1.57 1.75 2.50 2.49 (0.010) 17 211 -224 1.06 1.54 1.64 1.69 1.68 (0.007) 18 211 -256 1.22 1.54 1.88 3.13 3.10 (0.012) 19 221 -257 1.16 1.62 1.88 3.13 3.10 (0.012) 20 222 -258 1.16 1.62 1.88 3.13 3.10 (0.012) 21 221 -259 1.17 1.62 1.89 3.13 3.10 (0.012) 22 221 -262 1.18 1.62 1.91 3.13 3.10 (0.012) 23 227 -285 1.26 1.66 2.09 3.60 3.55 (0.014) 24 232 -294 1.27 1.70 2.16 3.60 3.55 (0.014) 25 234 -345 1.48 1.71 2.53 4.31 4.05 (0.016)

Stan

dard

Loa

ding

Pro

toco

l

26 239 -342 1.43 1.75 2.50 4.30 4.05 (0.016) 27 262 -262 1.00 1.92 1.92 1.69 1.67 (0.007) 28 239 -253 1.06 1.75 1.85 1.69 1.67 (0.007) 29 234 -249 1.06 1.71 1.82 1.69 1.67 (0.007) 30 225 -244 1.08 1.65 1.78 1.69 1.68 (0.007) 31 223 -242 1.09 1.63 1.78 1.68 1.68 (0.007) 32 218 -244 1.12 1.60 1.79 1.68 1.68 (0.007) 33 216 -245 1.13 1.58 1.79 1.68 1.68 (0.007) 34 214 -238 1.11 1.57 1.74 1.68 1.68 (0.007) 35 214 -241 1.13 1.57 1.77 1.69 1.68 (0.007) 36 214 -237 1.11 1.57 1.74 1.69 1.68 (0.007) 37 216 -244 1.13 1.58 1.79 1.69 1.67 (0.007) 38 212 -235 1.11 1.55 1.72 1.69 1.67 (0.007) 39 210 -243 1.15 1.54 1.77 1.69 1.67 (0.007) 40 210 -236 1.13 1.54 1.74 1.69 1.68 (0.007) 41 217 -234 1.08 1.59 1.72 1.69 1.67 (0.007) 42 208 -236 1.14 1.52 1.74 1.69 1.68 (0.007) 43 208 -236 1.13 1.52 1.72 1.69 1.67 (0.007)

Low

-cyc

le F

atig

ue

44 207 -243 1.18 1.52 1.79 1.69 1.68 (0.007) a values in parenthesis are for end rotation (rad.)

33



1 266 -265 1.00 1.24 1.24 0.43 0.41 (0.002) 2 257 -258 1.00 1.20 1.20 0.42 0.41 (0.002) 3 259 -258 1.00 1.21 1.21 0.42 0.41 (0.002) 4 265 -256 0.96 1.24 1.19 0.42 0.41 (0.002) 5 264 -260 0.98 1.23 1.21 0.42 0.41 (0.002) 6 255 -264 1.04 1.19 1.24 0.42 0.41 (0.002) 7 271 -272 1.00 1.26 1.26 0.88 0.87 (0.003) 8 258 -271 1.05 1.20 1.26 0.87 0.87 (0.003) 9 257 -273 1.06 1.20 1.27 0.87 0.87 (0.003)

10 258 -275 1.06 1.20 1.28 0.87 0.87 (0.003) 11 275 -316 1.15 1.28 1.48 1.70 1.68 (0.007) 12 294 -324 1.10 1.37 1.51 1.69 1.68 (0.007) 13 303 -329 1.09 1.41 1.54 1.69 1.68 (0.007) 14 304 -330 1.09 1.42 1.55 1.69 1.68 (0.007) 15 311 -358 1.15 1.45 1.67 2.51 2.50 (0.010) 16 324 -369 1.14 1.51 1.72 2.51 2.49 (0.010) 17 319 -339 1.06 1.49 1.58 1.69 1.68 (0.007) 18 324 -387 1.19 1.51 1.80 3.23 3.20 (0.013) 19 337 -397 1.18 1.57 1.85 3.22 3.21 (0.013) 20 349 -407 1.17 1.63 1.90 3.22 3.20 (0.013) 21 345 -409 1.18 1.61 1.90 3.22 3.20 (0.013) 22 346 -418 1.21 1.61 1.95 3.22 3.19 (0.013) 23 350 -445 1.27 1.63 2.07 3.80 3.74 (0.015) 24 358 -462 1.29 1.67 2.15 3.80 3.75 (0.015) 25 364 -505 1.39 1.70 2.36 4.50 4.04 (0.016)

Stan

dard

Loa

ding

Pro

toco

l

26 374 -523 1.40 1.74 2.44 4.50 4.05 (0.016)

Low

-cyc

le F

atig

ue

a values in parenthesis are for end rotation (rad.)

No data recorded—Fractured in first cycle

34



1 282 -357 1.27 0.94 1.19 0.44 0.42 (0.002) 2 308 -348 1.13 1.03 1.16 0.45 0.42 (0.002) 3 311 -339 1.09 1.04 1.13 0.44 0.42 (0.002) 4 313 -348 1.11 1.04 1.16 0.45 0.42 (0.002) 5 312 -338 1.08 1.04 1.12 0.45 0.42 (0.002) 6 299 -346 1.16 1.00 1.16 0.45 0.42 (0.002) 7 353 -358 1.01 1.18 1.19 0.90 0.87 (0.003) 8 339 -361 1.06 1.13 1.20 0.90 0.87 (0.003) 9 342 -362 1.06 1.14 1.21 0.90 0.86 (0.003)

10 344 -368 1.07 1.15 1.23 0.90 0.87 (0.003) 11 364 -418 1.15 1.21 1.39 1.73 1.68 (0.007) 12 391 -434 1.11 1.30 1.45 1.72 1.68 (0.007) 13 402 -441 1.10 1.34 1.47 1.72 1.68 (0.007) 14 405 -443 1.09 1.35 1.47 1.72 1.68 (0.007) 15 418 -480 1.15 1.39 1.60 2.55 2.49 (0.010) 16 430 -488 1.14 1.43 1.63 2.55 2.49 (0.010) 17 427 -456 1.07 1.42 1.52 1.72 1.68 (0.007) 18 437 -532 1.22 1.46 1.78 3.44 3.35 (0.013) 19 457 -545 1.19 1.52 1.81 3.43 3.35 (0.013) 20 462 -558 1.21 1.54 1.86 3.43 3.34 (0.013) 21 466 -568 1.22 1.55 1.89 3.43 3.34 (0.013)

Stan

dard

Loa

ding

Pro

toco

l

22 471 -585 1.24 1.57 1.95 3.43 3.35 (0.013) 23 436 -564 1.29 1.45 1.87 2.42 2.28 (0.009) 24 460 -553 1.20 1.53 1.84 2.41 2.28 (0.009) 25 458 -547 1.19 1.53 1.82 2.40 2.28 (0.009) 26 455 -544 1.20 1.52 1.82 2.40 2.29 (0.009) 27 451 -541 1.20 1.50 1.80 2.40 2.26 (0.009) 28 449 -538 1.20 1.50 1.79 2.40 2.26 (0.009) 29 447 -541 1.21 1.49 1.80 2.40 2.29 (0.009) 30 446 -542 1.22 1.49 1.81 2.40 2.29 (0.009) 31 444 -537 1.21 1.48 1.79 2.40 2.27 (0.009) 32 443 -535 1.21 1.48 1.79 2.40 2.27 (0.009) 33 441 -535 1.21 1.47 1.78 2.40 2.28 (0.009) 34 441 -533 1.21 1.47 1.78 2.40 2.28 (0.009) 35 440 -534 1.21 1.47 1.77 2.40 2.26 (0.009) 36 440 -537 1.22 1.47 1.79 2.40 2.28 (0.009) 37 441 -537 1.22 1.47 1.79 2.40 2.27 (0.009) 38 442 -537 1.22 1.47 1.80 2.40 2.27 (0.009) 39 439 -539 1.23 1.46 1.80 2.40 2.27 (0.009) 40 440 -547 1.24 1.47 1.82 2.40 2.29 (0.009) 41 445 -547 1.23 1.48 1.82 2.40 2.29 (0.009) 42 442 -544 1.23 1.47 1.81 2.40 2.27 (0.009) 43 445 -545 1.22 1.48 1.81 2.39 2.28 (0.009) 44 447 -554 1.24 1.49 1.85 2.39 2.29 (0.009) 45 443 -547 1.24 1.48 1.83 2.39 2.27 (0.009) 46 444 -549 1.24 1.48 1.83 2.39 2.28 (0.009)

Low

-cyc

le F

atig

ue N

o. 1

47 445 -560 1.26 1.48 1.87 2.39 2.28 (0.009)

35

48 493 -588 1.19 1.64 1.95 2.34 2.30 (0.009) 49 482 -578 1.20 1.61 1.93 2.35 2.29 (0.009) 50 472 -572 1.21 1.57 1.90 2.37 2.28 (0.009) 51 466 -568 1.22 1.55 1.89 2.38 2.27 (0.009) 52 461 -567 1.23 1.54 1.89 2.40 2.28 (0.009) 53 458 -563 1.23 1.53 1.88 2.40 2.27 (0.009) 54 457 -564 1.23 1.52 1.87 2.40 2.29 (0.009) 55 454 -561 1.24 1.51 1.88 2.40 2.26 (0.009) 56 454 -559 1.23 1.51 1.86 2.40 2.28 (0.009) 57 453 -567 1.25 1.51 1.89 2.40 2.29 (0.009) 58 452 -562 1.24 1.51 1.87 2.39 2.29 (0.009) 59 455 -559 1.23 1.52 1.86 2.40 2.27 (0.009) 60 452 -561 1.24 1.51 1.87 2.40 2.28 (0.009) 61 453 -563 1.24 1.51 1.87 2.40 2.28 (0.009) 62 454 -564 1.24 1.51 1.88 2.39 2.28 (0.009) 63 458 -565 1.23 1.53 1.88 2.39 2.28 (0.009) 64 455 -577 1.27 1.52 1.92 2.39 2.29 (0.009) 65 458 -571 1.25 1.53 1.91 2.39 2.28 (0.009) 66 467 -573 1.23 1.56 1.91 2.39 2.28 (0.009) 67 462 -578 1.25 1.54 1.92 2.39 2.29 (0.009) 68 463 -577 1.25 1.54 1.93 2.39 2.28 (0.009) 69 466 -584 1.25 1.55 1.94 2.38 2.29 (0.009) 70 468 -584 1.25 1.56 1.95 2.39 2.28 (0.009) 71 471 -595 1.26 1.57 1.98 2.38 2.29 (0.009)

Low

-cyc

le F

atig

ue N

o. 2


36



1 436 -537 1.23 0.96 1.18 0.44 0.43 (0.002) 2 436 -522 1.20 0.96 1.15 0.44 0.43 (0.002) 3 449 -513 1.14 0.99 1.12 0.45 0.43 (0.002) 4 437 -519 1.19 0.96 1.14 0.45 0.43 (0.002) 5 448 -515 1.15 0.98 1.13 0.45 0.43 (0.002) 6 437 -505 1.16 0.96 1.11 0.45 0.43 (0.002) 7 551 -553 1.00 1.21 1.21 0.90 0.89 (0.004) 8 520 -543 1.05 1.14 1.20 0.89 0.89 (0.004) 9 522 -544 1.04 1.15 1.19 0.89 0.88 (0.004)

10 520 -542 1.04 1.14 1.19 0.89 0.89 (0.004) 11 573 -648 1.13 1.26 1.42 1.72 1.70 (0.007) 12 614 -666 1.08 1.35 1.45 1.71 1.70 (0.007) 13 629 -675 1.07 1.38 1.48 1.71 1.70 (0.007) 14 636 -678 1.06 1.40 1.48 1.71 1.70 (0.007) 15 662 -744 1.12 1.45 1.63 2.53 2.51 (0.010) 16 681 -752 1.10 1.49 1.64 2.52 2.51 (0.010) 17 671 -694 1.03 1.47 1.52 1.70 1.70 (0.007) 18 691 -797 1.15 1.52 1.74 3.15 3.10 (0.012) 19 712 -802 1.13 1.56 1.77 3.14 3.10 (0.012) 20 716 -804 1.12 1.57 1.76 3.14 3.10 (0.012) 21 719 -813 1.13 1.58 1.78 3.13 3.10 (0.012) 22 719 -809 1.13 1.58 1.78 3.14 3.10 (0.012) 23 729 -880 1.21 1.60 1.94 3.93 3.85 (0.015) 24 742 -885 1.19 1.63 1.94 3.92 3.84 (0.015) 25 757 -949 1.25 1.66 2.08 4.64 4.05 (0.016)

Stan

dard

Loa

ding

Pro

toco

l

26 774 -980 1.27 1.70 2.16 4.64 4.05 (0.016) 27 848 -863 1.02 1.86 1.90 2.30 2.32 (0.009) 28 774 -840 1.08 1.70 1.83 2.32 2.29 (0.009) 29 748 -824 1.10 1.64 1.81 2.30 2.29 (0.009) 30 731 -812 1.11 1.60 1.78 2.30 2.28 (0.009) 31 720 -805 1.12 1.58 1.77 2.29 2.29 (0.009) 32 714 -798 1.12 1.57 1.75 2.30 2.28 (0.009) 33 706 -793 1.12 1.55 1.73 2.30 2.28 (0.009) 34 702 -790 1.13 1.54 1.74 2.30 2.28 (0.009) 35 699 -786 1.12 1.53 1.72 2.30 2.28 (0.009) 36 693 -783 1.13 1.52 1.72 2.30 2.28 (0.009) 37 690 -781 1.13 1.51 1.71 2.30 2.28 (0.009) 38 688 -780 1.13 1.51 1.71 2.30 2.29 (0.009) 39 685 -780 1.14 1.50 1.71 2.30 2.29 (0.009) 40 685 -779 1.14 1.50 1.71 2.30 2.28 (0.009) 41 684 -778 1.14 1.50 1.71 2.29 2.27 (0.009) 42 684 -782 1.14 1.50 1.71 2.29 2.29 (0.009) 43 683 -786 1.15 1.50 1.72 2.29 2.29 (0.009) 44 682 -784 1.15 1.50 1.72 2.29 2.28 (0.009) 45 683 -786 1.15 1.50 1.72 2.29 2.28 (0.009) 46 683 -787 1.15 1.50 1.72 2.29 2.28 (0.009) 47 684 -789 1.15 1.50 1.73 2.29 2.28 (0.009)

Low

-cyc

le F

atig

ue

48 685 -793 1.16 1.50 1.74 2.29 2.28 (0.009)

37

49 686 -800 1.17 1.51 1.76 2.30 2.29 (0.009) 50 688 -797 1.16 1.51 1.75 2.30 2.27 (0.009)


38



1 697 -756 1.08 1.08 1.17 0.47 0.42 (0.002) 2 705 -744 1.06 1.10 1.16 0.46 0.41 (0.002) 3 725 -722 1.00 1.13 1.13 0.46 0.42 (0.002) 4 724 -713 0.99 1.13 1.12 0.46 0.42 (0.002) 5 728 -716 0.98 1.13 1.11 0.46 0.42 (0.002) 6 715 -721 1.01 1.11 1.12 0.46 0.42 (0.002) 7 808 -781 0.97 1.26 1.22 0.91 0.88 (0.003) 8 741 -774 1.05 1.15 1.21 0.90 0.88 (0.003) 9 745 -775 1.04 1.16 1.21 0.90 0.88 (0.003)

10 746 -778 1.04 1.16 1.21 0.90 0.87 (0.003) 11 775 -892 1.15 1.21 1.39 1.73 1.69 (0.007) 12 843 -925 1.10 1.31 1.44 1.70 1.69 (0.007) 13 863 -942 1.09 1.34 1.46 1.70 1.69 (0.007) 14 873 -950 1.09 1.36 1.48 1.70 1.69 (0.007) 15 899 -1030 1.14 1.40 1.59 2.52 2.49 (0.010) 16 929 -1049 1.13 1.45 1.63 2.53 2.50 (0.010) 17 917 -972 1.06 1.43 1.51 1.70 1.69 (0.007) 18 945 -1148 1.22 1.47 1.79 3.46 3.39 (0.013) 19 985 -1190 1.21 1.53 1.85 3.44 3.39 (0.013) 20 998 -1215 1.22 1.55 1.89 3.45 3.39 (0.013) 21 1005 -1234 1.23 1.56 1.92 3.45 3.39 (0.013) 22 1011 -1245 1.23 1.57 1.94 3.45 3.39 (0.013) 23 1024 -1323 1.29 1.59 2.06 4.14 4.04 (0.016) 24 1050 -1344 1.28 1.63 2.09 4.14 4.04 (0.016) 25 1066 -1460 1.37 1.66 2.27 4.95 4.04 (0.016)

Stan

dard

Loa

ding

Pro

toco

l

26 1099 -1508 1.37 1.71 2.34 4.94 4.04 (0.016) 27 1220 -1225 1.00 1.90 1.90 2.36 1.69 (0.007) 28 1116 -1188 1.06 1.74 1.84 2.35 1.69 (0.007) 29 1080 -1166 1.08 1.68 1.82 2.34 1.70 (0.007) 30 1056 -1152 1.09 1.64 1.79 2.35 1.69 (0.007) 31 1037 -1140 1.10 1.61 1.78 2.35 1.69 (0.007) 32 1023 -1131 1.10 1.59 1.75 2.35 1.68 (0.007) 33 1011 -1120 1.11 1.57 1.75 2.35 1.69 (0.007) 34 999 -1113 1.11 1.55 1.73 2.35 1.69 (0.007) 35 990 -1116 1.13 1.54 1.74 2.35 1.69 (0.007) 36 982 -1105 1.13 1.53 1.73 2.36 1.68 (0.007) 37 975 -1101 1.13 1.52 1.71 2.35 1.69 (0.007) 38 970 -1101 1.14 1.51 1.72 2.35 1.69 (0.007) 39 964 -1095 1.14 1.50 1.71 2.36 1.69 (0.007) 40 960 -1099 1.15 1.49 1.72 2.36 1.68 (0.007) 41 954 -1090 1.14 1.48 1.69 2.36 1.69 (0.007) 42 953 -1088 1.14 1.48 1.69 2.36 1.69 (0.007) 43 949 -1087 1.15 1.48 1.70 2.36 1.69 (0.007) 44 945 -1087 1.15 1.47 1.69 2.36 1.68 (0.007) 45 944 -1094 1.16 1.47 1.70 2.36 1.68 (0.007) 46 937 -1088 1.16 1.46 1.69 2.36 1.69 (0.007) 47 939 -1084 1.16 1.46 1.70 2.36 1.68 (0.007)

Low

-cyc

le F

atig

ue N

o. 1

48 936 -1084 1.16 1.46 1.69 2.36 1.69 (0.007)

39

49 932 -1088 1.17 1.45 1.70 2.36 1.68 (0.007) 50 930 -1085 1.17 1.45 1.69 2.36 1.68 (0.007) 51 931 -1084 1.16 1.45 1.68 2.36 1.69 (0.007) 52 930 -1088 1.17 1.45 1.69 2.36 1.69 (0.007) 53 928 -1087 1.17 1.44 1.69 2.37 1.69 (0.007) 54 924 -1086 1.18 1.44 1.70 2.37 1.68 (0.007) 55 923 -1085 1.18 1.44 1.69 2.37 1.68 (0.007)

56 924 -1095 1.19 1.44 1.71 2.37 1.69 (0.007) 57 985 -1105 1.12 1.53 1.72 2.26 1.69 (0.007) 58 965 -1123 1.16 1.50 1.74 2.32 1.69 (0.007) 59 955 -1114 1.17 1.49 1.74 2.35 1.70 (0.007) 60 948 -1115 1.18 1.48 1.74 2.36 1.69 (0.007) 61 943 -1109 1.18 1.47 1.73 2.36 1.69 (0.007) 62 937 -1099 1.17 1.46 1.71 2.36 1.69 (0.007) 63 937 -1102 1.18 1.46 1.72 2.36 1.69 (0.007) 64 930 -1098 1.18 1.45 1.71 2.36 1.68 (0.007) 65 930 -1094 1.18 1.45 1.71 2.36 1.69 (0.007) 66 926 -1092 1.18 1.44 1.70 2.36 1.69 (0.007) 67 925 -1090 1.18 1.44 1.70 2.36 1.69 (0.007) 68 922 -1095 1.19 1.43 1.71 2.36 1.68 (0.007) 69 918 -1088 1.19 1.43 1.70 2.36 1.69 (0.007) 70 918 -1090 1.19 1.43 1.70 2.36 1.69 (0.007) 71 917 -1087 1.19 1.43 1.70 2.36 1.69 (0.007) 72 916 -1086 1.19 1.43 1.70 2.36 1.69 (0.007) 73 912 -1093 1.20 1.42 1.70 2.37 1.68 (0.007) 74 910 -1092 1.20 1.42 1.70 2.36 1.69 (0.007) 75 910 -1091 1.20 1.42 1.70 2.36 1.69 (0.007) 76 881 -1095 1.24 1.37 1.70 2.37 1.68 (0.007) 77 754 -1081 1.43 1.17 1.68 2.37 1.68 (0.007) 78 749 -1070 1.43 1.17 1.67 2.37 1.68 (0.007) 79 749 -1074 1.43 1.17 1.67 2.37 1.69 (0.007) 80 747 -1069 1.43 1.16 1.66 2.38 1.69 (0.007) 81 740 -1064 1.44 1.15 1.66 2.37 1.69 (0.007) 82 738 -1064 1.44 1.15 1.65 2.38 1.68 (0.007) 83 738 -1069 1.45 1.15 1.67 2.38 1.68 (0.007) 84 738 -1055 1.43 1.15 1.64 2.38 1.69 (0.007) 85 737 -1059 1.44 1.15 1.65 2.38 1.69 (0.007)

Low

-cyc

le F

atig

ue N

o. 2


40



1 692 -726 1.05 1.08 1.13 0.47 0.41 (0.002) 2 691 -709 1.03 1.07 1.11 0.46 0.42 (0.002) 3 697 -696 1.00 1.08 1.08 0.45 0.41 (0.002) 4 694 -698 1.01 1.08 1.09 0.46 0.41 (0.002) 5 701 -696 0.99 1.09 1.08 0.46 0.41 (0.002) 6 692 -695 1.00 1.08 1.08 0.45 0.41 (0.002) 7 796 -781 0.98 1.24 1.21 0.90 0.87 (0.003) 8 751 -775 1.03 1.17 1.20 0.89 0.86 (0.003) 9 753 -776 1.03 1.17 1.21 0.89 0.87 (0.003)

10 754 -781 1.03 1.17 1.21 0.89 0.87 (0.003) 11 783 -901 1.15 1.22 1.40 1.71 1.66 (0.007) 12 854 -932 1.09 1.33 1.45 1.69 1.67 (0.007) 13 873 -949 1.09 1.36 1.48 1.69 1.68 (0.007) 14 881 -955 1.08 1.37 1.48 1.69 1.68 (0.007) 15 908 -1043 1.15 1.41 1.62 2.51 2.48 (0.010) 16 935 -1055 1.13 1.45 1.64 2.50 2.48 (0.010) 17 922 -970 1.05 1.43 1.51 1.68 1.67 (0.007) 18 943 -1122 1.19 1.47 1.74 3.13 3.09 (0.012) 19 975 -1143 1.17 1.52 1.77 3.11 3.09 (0.012) 20 986 -1159 1.18 1.53 1.81 3.11 3.08 (0.012) 21 991 -1170 1.18 1.54 1.82 3.11 3.08 (0.012) 22 994 -1177 1.18 1.55 1.82 3.11 3.09 (0.012) 23 1008 -1278 1.27 1.57 1.99 3.84 3.79 (0.015) 24 1029 -1304 1.27 1.60 2.03 3.84 3.76 (0.015) 25 1045 -1452 1.39 1.62 2.26 4.61 4.03 (0.016)

Stan

dard

Loa

ding

Pro

toco

l

26 1082 -1516 1.40 1.68 2.36 4.61 4.03 (0.016) 27 1238 -1164 0.94 1.92 1.81 1.68 1.71 (0.007) 28 1096 -1146 1.05 1.70 1.79 1.68 1.68 (0.007) 29 1058 -1131 1.07 1.65 1.76 1.66 1.68 (0.007) 30 1035 -1114 1.08 1.61 1.74 1.66 1.66 (0.007) 31 1018 -1104 1.08 1.58 1.71 1.66 1.68 (0.007) 32 1003 -1094 1.09 1.56 1.70 1.67 1.68 (0.007) 33 992 -1083 1.09 1.54 1.68 1.67 1.66 (0.007) 34 984 -1076 1.09 1.53 1.67 1.67 1.66 (0.007) 35 974 -1071 1.10 1.51 1.67 1.67 1.68 (0.007) 36 966 -1065 1.10 1.50 1.65 1.67 1.67 (0.007) 37 959 -1060 1.11 1.49 1.66 1.67 1.67 (0.007) 38 954 -1058 1.11 1.48 1.65 1.67 1.68 (0.007) 39 949 -1054 1.11 1.48 1.64 1.67 1.67 (0.007) 40 946 -1052 1.11 1.47 1.63 1.67 1.67 (0.007) 41 943 -1049 1.11 1.47 1.63 1.68 1.68 (0.007) 42 938 -1048 1.12 1.46 1.63 1.68 1.67 (0.007) 43 934 -1047 1.12 1.45 1.63 1.68 1.67 (0.007) 44 930 -1046 1.12 1.45 1.62 1.68 1.66 (0.007) 45 927 -1047 1.13 1.44 1.63 1.68 1.68 (0.007) 46 924 -1042 1.13 1.44 1.62 1.68 1.66 (0.007) 47 923 -1041 1.13 1.44 1.62 1.69 1.67 (0.007)

Low

-cyc

le F

atig

ue

48 920 -1042 1.13 1.43 1.62 1.68 1.67 (0.007)

41

49 921 -1044 1.13 1.43 1.62 1.68 1.68 (0.007) 50 916 -1039 1.13 1.42 1.61 1.69 1.67 (0.007) 51 915 -1038 1.14 1.42 1.62 1.69 1.67 (0.007) 52 913 -1038 1.14 1.42 1.62 1.69 1.65 (0.007) 53 912 -1038 1.14 1.42 1.62 1.69 1.66 (0.007) 54 910 -1041 1.14 1.41 1.61 1.69 1.68 (0.007) 55 911 -1037 1.14 1.42 1.61 1.69 1.66 (0.007)


42



1 900 -1129 1.25 0.88 1.10 0.53 0.41 (0.002) 2 878 -1092 1.24 0.85 1.06 0.52 0.41 (0.002) 3 884 -1075 1.22 0.86 1.05 0.51 0.41 (0.002) 4 885 -1073 1.21 0.86 1.04 0.51 0.41 (0.002) 5 892 -1063 1.19 0.87 1.03 0.51 0.41 (0.002) 6 891 -1064 1.19 0.87 1.03 0.51 0.41 (0.002) 7 1267 -1265 1.00 1.23 1.23 0.95 0.87 (0.003) 8 1180 -1219 1.03 1.15 1.18 0.93 0.87 (0.003) 9 1183 -1219 1.03 1.15 1.19 0.93 0.87 (0.003)

10 1185 -1220 1.03 1.15 1.19 0.93 0.87 (0.003) 11 1216 -1366 1.12 1.18 1.33 1.76 1.68 (0.007) 12 1316 -1433 1.09 1.28 1.40 1.72 1.68 (0.007) 13 1352 -1457 1.08 1.32 1.42 1.72 1.67 (0.007) 14 1367 -1469 1.07 1.33 1.42 1.70 1.67 (0.007) 15 1419 -1603 1.13 1.38 1.56 2.54 2.49 (0.010) 16 1462 -1640 1.12 1.42 1.59 2.53 2.49 (0.010) 17 1444 -1507 1.04 1.41 1.46 1.70 1.67 (0.007) 18 1497 -1816 1.21 1.46 1.76 3.59 3.49 (0.014) 19 1564 -1877 1.20 1.52 1.83 3.55 3.47 (0.014) 20 1590 -1900 1.19 1.55 1.84 3.52 3.48 (0.014) 21 1597 -1905 1.19 1.55 1.85 3.41 3.45 (0.014)

Stan

dard

Loa

ding

Pro

toco

l

22 1596 -1901 1.19 1.55 1.85 3.28 3.46 (0.014) 23 1637 -1855 1.13 1.59 1.80 2.59 2.51 (0.010) 24 1599 -1854 1.16 1.56 1.81 2.53 2.57 (0.010) 25 1578 -1847 1.17 1.54 1.80 2.55 2.56 (0.010) 26 1565 -1838 1.17 1.52 1.78 2.56 2.53 (0.010) 27 1555 -1832 1.18 1.51 1.79 2.56 2.52 (0.010) 28 1548 -1834 1.19 1.51 1.79 2.56 2.54 (0.010) 29 1541 -1832 1.19 1.50 1.79 2.55 2.55 (0.010) 30 1537 -1828 1.19 1.50 1.78 2.56 2.54 (0.010) 31 1529 -1823 1.19 1.49 1.77 2.56 2.51 (0.010) 32 1521 -1820 1.20 1.48 1.78 2.56 2.54 (0.010) 33 1514 -1816 1.20 1.47 1.77 2.56 2.51 (0.010) 34 1511 -1809 1.20 1.47 1.77 2.54 2.53 (0.010) 35 1505 -1803 1.20 1.47 1.76 2.52 2.51 (0.010) 36 1501 -1792 1.19 1.46 1.74 2.50 2.50 (0.010)

Low

-cyc

le F

atig

ue N

o. 1

37 1493 -1786 1.20 1.45 1.74 2.46 2.53 (0.010) 38 1584 -1912 1.21 1.54 1.87 2.59 2.50 (0.010) 39 1570 -1923 1.22 1.53 1.86 2.52 2.57 (0.010) 40 1558 -1918 1.23 1.52 1.87 2.53 2.56 (0.010) 41 1550 -1907 1.23 1.51 1.86 2.54 2.48 (0.010) 42 1546 -1902 1.23 1.51 1.85 2.54 2.55 (0.010) 43 1542 -1894 1.23 1.50 1.85 2.53 2.55 (0.010) 44 1534 -1889 1.23 1.49 1.84 2.54 2.52 (0.010) 45 1528 -1884 1.23 1.49 1.83 2.54 2.54 (0.010) 46 1524 -1878 1.23 1.48 1.83 2.53 2.54 (0.010) 47 1519 -1878 1.24 1.48 1.83 2.53 2.54 (0.010) L

ow-c

ycle

Fat

igue

No.

2

48 1516 -1873 1.24 1.48 1.83 2.52 2.51 (0.010)

43

49 1511 -1864 1.23 1.47 1.81 2.50 2.52 (0.010) 50 1508 -1852 1.23 1.47 1.81 2.49 2.51 (0.010) 51 1507 -1844 1.22 1.47 1.79 2.46 2.51 (0.010)


44



1 1067 -1158 1.09 1.04 1.13 0.50 0.43 (0.002) 2 1078 -1139 1.06 1.05 1.11 0.49 0.43 (0.002) 3 1080 -1105 1.02 1.05 1.07 0.49 0.43 (0.002) 4 1085 -1107 1.02 1.05 1.07 0.49 0.43 (0.002) 5 1097 -1097 1.00 1.06 1.06 0.49 0.41 (0.002) 6 1088 -1094 1.01 1.06 1.07 0.48 0.42 (0.002) 7 1283 -1251 0.98 1.25 1.22 0.94 0.88 (0.003) 8 1199 -1235 1.03 1.16 1.20 0.93 0.88 (0.004) 9 1201 -1239 1.03 1.17 1.20 0.93 0.88 (0.004)

10 1201 -1240 1.03 1.17 1.20 0.93 0.88 (0.004) 11 1235 -1407 1.14 1.20 1.37 1.77 1.69 (0.007) 12 1344 -1455 1.08 1.30 1.41 1.74 1.69 (0.007) 13 1376 -1475 1.07 1.34 1.43 1.74 1.69 (0.007) 14 1388 -1483 1.07 1.35 1.44 1.73 1.70 (0.007) 15 1436 -1611 1.12 1.39 1.56 2.58 2.48 (0.010) 16 1478 -1636 1.11 1.43 1.59 2.57 2.48 (0.010) 17 1464 -1521 1.04 1.42 1.48 1.73 1.67 (0.007) 18 1506 -1775 1.18 1.46 1.72 3.43 3.28 (0.013) 19 1565 -1816 1.16 1.52 1.76 3.39 3.28 (0.013) 20 1576 -1819 1.15 1.53 1.76 3.29 3.29 (0.013) 21 1577 -1811 1.15 1.53 1.76 3.16 3.30 (0.013)

Stan

dard

Loa

ding

Pro

toco

l

22 1569 -1804 1.15 1.52 1.75 3.07 3.31 (0.013) 23 1638 -1821 1.11 1.59 1.76 2.63 2.54 (0.010) 24 1604 -1809 1.13 1.56 1.76 2.58 2.56 (0.010) 25 1583 -1798 1.14 1.54 1.75 2.57 2.56 (0.010) 26 1571 -1786 1.14 1.52 1.74 2.58 2.55 (0.010) 27 1561 -1779 1.14 1.52 1.73 2.58 2.55 (0.010) 28 1551 -1773 1.14 1.51 1.72 2.58 2.55 (0.010) 29 1543 -1766 1.14 1.50 1.71 2.58 2.54 (0.010) 30 1536 -1762 1.15 1.49 1.71 2.58 2.55 (0.010) 31 1531 -1758 1.15 1.49 1.71 2.59 2.55 (0.010) 32 1527 -1753 1.15 1.48 1.70 2.59 2.54 (0.010) 33 1521 -1753 1.15 1.48 1.70 2.59 2.52 (0.010) 34 1516 -1749 1.15 1.47 1.69 2.59 2.53 (0.010) 35 1511 -1744 1.15 1.47 1.69 2.58 2.54 (0.010) 36 1506 -1740 1.16 1.46 1.70 2.57 2.54 (0.010)

Low

-cyc

le F

atig

ue N

o. 1

37 1501 -1739 1.16 1.46 1.69 2.54 2.50 (0.010) 38 1623 -1867 1.15 1.58 1.81 2.64 2.52 (0.010) 39 1599 -1859 1.16 1.55 1.80 2.57 2.57 (0.010) 40 1580 -1846 1.17 1.53 1.79 2.56 2.57 (0.010) 41 1566 -1833 1.17 1.52 1.78 2.57 2.53 (0.010) 42 1557 -1823 1.17 1.51 1.77 2.57 2.51 (0.010) 43 1549 -1817 1.17 1.50 1.76 2.57 2.55 (0.010) 44 1542 -1814 1.18 1.50 1.77 2.57 2.55 (0.010) 45 1535 -1811 1.18 1.49 1.76 2.57 2.54 (0.010) 46 1533 -1807 1.18 1.49 1.76 2.57 2.53 (0.010) 47 1527 -1802 1.18 1.48 1.75 2.57 2.49 (0.010) L

ow-c

ycle

Fat

igue

No.

2

48 1524 -1801 1.18 1.48 1.75 2.57 2.52 (0.010)

45

49 1520 -1799 1.18 1.48 1.74 2.57 2.54 (0.010) 50 1518 -1791 1.18 1.47 1.74 2.57 2.51 (0.010) 51 1513 -1782 1.18 1.47 1.73 2.55 2.49 (0.010)


46

(a) during Standard Test (Overview)

(b) after Standard Test (West End)

Figure 3.1 Specimen 1: Testing Photos

47

Long

itudi

nal D

ispl

acem

ent (

in)

0 200 400 600 800-6

-4

-2

0

2

4

6

Time (sec) (a) Longitudinal Direction

Tran

sver

se D

ispl

acem

ent (

in)

0 200 400 600 800-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (r

ad.)

(b) Transverse Direction

Figure 3.2 Specimen 1: Table Displacement Time Histories (Standard Test)

48

Res

ulta

nt F

orce

(kip

s)

-6 -4 -2 0 2 4 6-400

-200

0

200

400



Figure 3.3 Specimen 1: Brace Force versus Deformation (Standard Test)

Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 200 400 600 8000

5

10

15

20

25

30

35

Time (sec)

0

100

200

300

400

500

600

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)

Figure 3.4 Specimen 1: Hysteretic Energy Time History (Standard Test)

Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

49

Long

itudi

nal D

ispl

acem

ent (

in)

0 100 200 300 400 500 600-6

-4

-2

0

2

4

6


Tran

sver

se D

ispl

acem

ent (

in)

0 100 200 300 400 500 600-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (ra

d.)


Figure 3.5 Specimen 1: Table Displacement Time Histories (Low-cycle Fatigue Test)

50

Res

ulta

nt F

orce

(kip

s)

-6 -4 -2 0 2 4 6-400

-200

0

200

400



Figure 3.6 Specimen 1: Brace Force versus Deformation (Low-cycle Fatigue Test)

Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 100 200 300 400 500 6000

5

10

15

20

Time (sec)

0

50

100

150

200

250

300

350

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)

Figure 3.7 Specimen 1: Hysteretic Energy Time History (Low-cycle Fatigue Test)

Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

18-th cycle

51

Long

itudi

nal D

ispl

acem

ent (

in)

0 200 400 600 800 1000 1200 1400-6

-4

-2

0

2

4

6

Time (sec)

(a) Longitudinal Direction

Tran

sver

se D

ispl

acem

ent (

in)

0 200 400 600 800 1000 1200 1400-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (r

ad.)


Figure 3.8 Specimen 1: Table Displacement Time Histories (Both Tests Combined)

52

Res

ulta

nt F

orce

(kip

s)

-6 -4 -2 0 2 4 6-400

-200

0

200

400



Figure 3.9 Specimen 1: Brace Force versus Deformation (Both Tests Combined)

Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 200 400 600 800 1000 1200 14000

10

20

30

40

50

Time (sec)

0

200

400

600

800N

orm

aliz

ed C

umul

ativ

e In

elas

tic D

isp.

Eh/

(Pye

ff*D

by)

Figure 3.10 Specimen 1: Hysteretic Energy Time History (Both Tests Combined)

Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

53

-6 -4 -2 0 2 4 6-400

-200

0

200

400


Res

ulta

nt F

orce

(kip

s)

Figure 3.11 Specimen 1: Brace Response Envelope

β

0 2 4 6 8 10 12 14 16Normalized Brace Deformation

0 1 2 3 4Brace Deformation (in)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6


Figure 3.12 Specimen 1: β versus Deformation Level

β (=

P max

/Tm

ax )


54

w (=

Tmax

/Pyn

)


0 1 2 3 40.0

0.5

1.0

1.5

2.0

(a) Tension

Cm

ax/P

yn


0 1 2 3 40.0

0.5

1.0

1.5

2.0

(b) Compression

Figure 3.13 Specimen 1: w and βw versus Deformation Level

w (=

Tm

ax /

P yn)

βw

(= P

max

/ P y

n)



55

(a) after Standard Test (Overview)

(b) Grinding between Collar and Brace (East End)


56

Long

itudi

nal D

ispl

acem

ent (

in)

0 200 400 600 800-6

-4

-2

0

2

4

6


Tran

sver

se D

ispl

acem

ent (

in)

0 200 400 600 800-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (r

ad.)



57

Res

ulta

nt F

orce

(kip

s)

-6 -4 -2 0 2 4 6-600

-400

-200

0

200

400

600


-20 -15 -10 -5 0 5 10 15 20Normalized Brace Deformation


Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 200 400 600 8000

10

20

30

40

50

60

Time (sec)

0

100

200

300

400

500

600

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)


Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

58

Figure 3.18 Specimen 2: Brace Force versus Brace Deformation (Low-cycle Fatigue Test)

-1.0 in. 1.0 in. 2.0 in.

-400 k

-200 k

-2.0 in. 200 k

400 ktons

tons

59

-6 -4 -2 0 2 4 6-600

-400

-200

0

200

400

600


Res

ulta

nt F

orce

(kip

s)


β



0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6



β (=

P max

/Tm

ax )


60

w (=

Tmax

/Pyn

)



0.0

0.5

1.0

1.5

2.0


(a) Tension

Cm

ax/P

yn



0.0

0.5

1.0

1.5

2.0


(b) Compression


w (=

Tm

ax /

P yn)

βw

(= P

max

/ P y

n)



61

Rot

atio

n fro

m D

ispl

. and

Geo

met

ry (r

ad)

-0.02 -0.01 0.0 0.01 0.02-0.02

-0.01

0.0

0.01

0.02

Rotation from Inclinometer (rad)

Figure 3.22 Specimen 2: End Rotation Comparison

Figure 3.23 Specimen 3: Testing Photo

(during Low-cycle Fatigue Test)

62

Long

itudi

nal D

ispl

acem

ent (

in)

0 100 200 300 400 500 600 700-6

-4

-2

0

2

4

6


Tran

sver

se D

ispl

acem

ent (

in)

0 100 200 300 400 500 600 700-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (r

ad.)



63

Res

ulta

nt F

orce

(kip

s)

-6 -4 -2 0 2 4 6-600

-400

-200

0

200

400

600


-15 -10 -5 0 5 10 15Normalized Brace Deformation


Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 100 200 300 400 500 600 7000

10

20

30

40

50

Time (sec)

0

50

100

150

200

250

300

350

400

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)


Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

64

Stra

in (m

icro

stra

in)

0 100 200 300 400 500 600 700-400

-200

0

200

400

-0.2

-0.1

0.0

0.1

0.2

Nor

mal

ized

Stra

in

Time (sec) (a) Top Strain Gage (Transverse)

Stra

in (m

icro

stra

in)

0 100 200 300 400 500 600 700-400

-200

0

200

400

-0.2

-0.1

0.0

0.1

0.2

Nor

mal

ized

Stra

in

Time (sec)

(b) Bottom Strain Gage (Transverse)

Figure 3.27 Specimen 3: Collar Strain Gage Time Histories (Standard Test)

65

Stra

in (m

icro

stra

in)

0 100 200 300 400 500 600 700-400

-200

0

200

400

-0.2

-0.1

0.0

0.1

0.2

Nor

mal

ized

Stra

in

Time (sec)

(a) North Strain Gage (Longitudinal)

Stra

in (m

icro

stra

in)

0 100 200 300 400 500 600 700-400

-200

0

200

400

-0.2

-0.1

0.0

0.1

0.2

Nor

mal

ized

Stra

in

Time (sec)

(b) South Strain Gage (Longitudinal)

Figure 3.28 Specimen 3: HSS Strain Gage Time Histories (Standard Test)

66

Long

itudi

nal D

ispl

acem

ent (

in)

0 10 20 30 40-6

-4

-2

0

2

4

6


Tran

sver

se D

ispl

acem

ent (

in)

0 10 20 30 40-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (r

ad.)


Figure 3.29 Specimen 3: Table Displacement Time Histories (Sylmar Earthquake Test)

No Transverse Displacement Record

67

Res

ulta

nt F

orce

(kip

s)

-6 -4 -2 0 2 4 6-600

-400

-200

0

200

400

600



Figure 3.30 Specimen 3: Brace Force versus Deformation (Sylmar Earthquake Test)

Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 10 20 30 400

2

4

6

8

10

Time (sec)

0

20

40

60

80

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)

Figure 3.31 Specimen 3: Hysteretic Energy Time History (Sylmar Earthquake Test)

Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

68

Long

itudi

nal D

ispl

acem

ent (

in)

0 200 400 600 800-6

-4

-2

0

2

4

6


Tran

sver

se D

ispl

acem

ent (

in)

0 200 400 600 800-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (ra

d.)


Figure 3.32 Specimen 3: Table Displacement Time Histories (Low-cycle Fatigue Test No. 1)

69

Res

ulta

nt F

orce

(kip

s)

-6 -4 -2 0 2 4 6-600

-400

-200

0

200

400

600



Figure 3.33 Specimen 3: Brace Force versus Deformation (Low-cycle Fatigue Test No. 1)

Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 200 400 600 8000

20

40

60

80

Time (sec)

0

100

200

300

400

500

600

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)

Figure 3.34 Specimen 3: Hysteretic Energy Time History (Low-cycle Fatigue Test No. 1)

Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

70

Stra

in (m

icro

stra

in)

0 200 400 600 800-400

-200

0

200

400

-0.2

-0.1

0.0

0.1

0.2

Nor

mal

ized

Stra

in

Time (sec)

(a) Top Strain Gage (Transverse)

Stra

in (m

icro

stra

in)

0 200 400 600 800-400

-200

0

200

400

-0.2

-0.1

0.0

0.1

0.2

Nor

mal

ized

Stra

in

Time (sec)


Figure 3.35 Specimen 3: Collar Strain Gage Time Histories (Low-cycle Fatigue Test No. 1)

71

Stra

in (m

icro

stra

in)

0 200 400 600 800-400

-200

0

200

400

-0.2

-0.1

0.0

0.1

0.2

Nor

mal

ized

Stra

in

Time (sec)


Stra

in (m

icro

stra

in)

0 200 400 600 800-400

-200

0

200

400

-0.2

-0.1

0.0

0.1

0.2

Nor

mal

ized

Stra

in

Time (sec)


Figure 3.36 Specimen 3: HSS Strain Gage Time Histories (Low-cycle Fatigue Test No. 1)

72

Long

itudi

nal D

ispl

acem

ent (

in)

0 200 400 600 800-6

-4

-2

0

2

4

6


Tran

sver

se D

ispl

acem

ent (

in)

0 200 400 600 800-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (r

ad.)



73

Res

ulta

nt F

orce

(kip

s)

-6 -4 -2 0 2 4 6-600

-400

-200

0

200

400

600




Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 200 400 600 8000

20

40

60

80

Time (sec)

0

100

200

300

400

500

600

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)


Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

74

Stra

in (m

icro

stra

in)

0 200 400 600 800-200

0

200

400

600

-0.1

0.0

0.1

0.2

0.3

Nor

mal

ized

Stra

in

Time (sec)


Stra

in (m

icro

stra

in)

0 200 400 600 800-400

-200

0

200

400

-0.2

-0.1

0.0

0.1

0.2

Nor

mal

ized

Stra

in

Time (sec)


Figure 3.40 Specimen 3: Collar Strain Gage Time Histories (Low-cycle Fatigue Test No. 2)

75

Stra

in (m

icro

stra

in)

0 200 400 600 800-400

-200

0

200

400

-0.2

-0.1

0.0

0.1

0.2

Nor

mal

ized

Stra

in

Time (sec)


Stra

in (m

icro

stra

in)

0 200 400 600 800-400

-200

0

200

400

-0.2

-0.1

0.0

0.1

0.2

Nor

mal

ized

Stra

in

Time (sec)


Figure 3.41 Specimen 3: HSS Strain Gage Time Histories (Low-cycle Fatigue Test No. 2)

76

Long

itudi

nal D

ispl

acem

ent (

in)

0 500 1000 1500 2000 2500-6

-4

-2

0

2

4

6

Time (sec)


Tran

sver

se D

ispl

acem

ent (

in)

0 500 1000 1500 2000 2500-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (r

ad.)


Figure 3.42 Specimen 3: Table Displacement Time Histories (All Tests Combined)

77

Res

ulta

nt F

orce

(kip

s)

-6 -4 -2 0 2 4 6-600

-400

-200

0

200

400

600



Figure 3.43 Specimen 3: Brace Force versus Deformation (All Tests Combined)

Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 500 1000 1500 2000 25000

50

100

150

200

Time (sec)

0

500

1000

1500

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)

Figure 3.44 Specimen 3: Hysteretic Energy Time History (All Tests Combined)

Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

Standard Test

Sylmar E.Q.

Fatigue Test No. 1

Fatigue Test No. 2

78

-6 -4 -2 0 2 4 6-600

-400

-200

0

200

400

600


Res

ulta

nt F

orce

(kip

s)


β



0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6



β (=

P max

/Tm

ax )


79

w (=

Tmax

/Pyn

)


0 1 2 3 4B D f ti (i )

0.0

0.5

1.0

1.5

2.0

B D f ti (i )

(a) Tension

Cm

ax/P

yn



0.0

0.5

1.0

1.5

2.0


(b) Compression


w (=

Tm

ax /

P yn)

βw

(= P

max

/ P y

n)



80

Rot

atio

n fro

m D

ispl

. and

Geo

met

ry (r

ad)

-0.02 -0.01 0.0 0.01 0.02-0.02

-0.01

0.0

0.01

0.02

Rotation from Inclinometer (rad) Figure 3.48 Specimen 3: End Rotation Comparison

81

(a) during Low-cycle Fatigue Test (Overview)

(b) after all Tests (West End)


82

Long

itudi

nal D

ispl

acem

ent (

in)

0 200 400 600 800-6

-4

-2

0

2

4

6


Tran

sver

se D

ispl

acem

ent (

in)

0 200 400 600 800-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (r

ad.)



83

Res

ulta

nt F

orce

(kip

s)

-6 -4 -2 0 2 4 6-1000

-500

0

500

1000




Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 200 400 600 8000

20

40

60

80

100

Time (sec)

0

100

200

300

400

500

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)


Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

84

Stra

in (m

icro

stra

in)

0 200 400 600 800-400

-200

0

200

400

-0.2

-0.1

0.0

0.1

0.2

Nor

mal

ized

Stra

in

Time (sec)


Stra

in (m

icro

stra

in)

-0.010 -0.005 0.0 0.005 0.010-400

-200

0

200

400

-0.2

-0.1

0.0

0.1

0.2

Nor

mal

ized

Stra

inNo Bottom Gauge Installed

Time (sec)


Figure 3.53 Specimen 4: Collar Strain Gage Time Histories (Standard Test)

85

Stra

in (m

icro

stra

in)

0 200 400 600 800-400

-200

0

200

400

-0.2

-0.1

0.0

0.1

0.2

Nor

mal

ized

Stra

in

Time (sec)


Stra

in (m

icro

stra

in)

0 200 400 600 800-400

-200

0

200

400

-0.2

-0.1

0.0

0.1

0.2

Nor

mal

ized

Stra

in

Time (sec)


Figure 3.54 Specimen 4: HSS Strain Gage Time Histories (Standard Test)

86

Long

itudi

nal D

ispl

acem

ent (

in)

0 200 400 600 800-6

-4

-2

0

2

4

6


Tran

sver

se D

ispl

acem

ent (

in)

0 200 400 600 800-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (ra

d.)



87

Res

ulta

nt F

orce

(kip

s)

-6 -4 -2 0 2 4 6-1000

-500

0

500

1000




Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 200 400 600 8000

20

40

60

80

100

120

Time (sec)

0

100

200

300

400

500

600

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)


Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

88

Stra

in (m

icro

stra

in)

0 200 400 600 800-400

-200

0

200

400

-0.2

-0.1

0.0

0.1

0.2

Nor

mal

ized

Stra

in

Time (sec)


Stra

in (m

icro

stra

in)

-0.010 -0.005 0.0 0.005 0.010-400

-200

0

200

400

-0.2

-0.1

0.0

0.1

0.2

Nor

mal

ized

Stra

inNo Bottom Gauge Installed

Time (sec)


Figure 3.58 Specimen 4: Collar Strain Gage Time Histories (Low-cycle Fatigue Test)

89

Stra

in (m

icro

stra

in)

0 200 400 600 800-400

-200

0

200

400

-0.2

-0.1

0.0

0.1

0.2

Nor

mal

ized

Stra

in

Time (sec)


Stra

in (m

icro

stra

in)

0 200 400 600 800-400

-200

0

200

400

-0.2

-0.1

0.0

0.1

0.2

Nor

mal

ized

Stra

in

Time (sec)


Figure 3.59 Specimen 4: HSS Strain Gage Time Histories (Low-cycle Fatigue Test)

90

Long

itudi

nal D

ispl

acem

ent (

in)

0 500 1000 1500 2000-6

-4

-2

0

2

4

6

Time (sec)


Tran

sver

se D

ispl

acem

ent (

in)

0 500 1000 1500 2000-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (ra

d.)


Figure 3.60 Specimen 4: Table Displacement Time Histories (Both Tests Combined)

91

Res

ulta

nt F

orce

(kip

s)

-6 -4 -2 0 2 4 6-1000

-500

0

500

1000



Figure 3.61 Specimen 4: Brace Force versus Deformation (Both Tests Combined)

Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 500 1000 1500 20000

50

100

150

200

Time (sec)

0

200

400

600

800

1000

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)

Figure 3.62 Specimen 4: Hysteretic Energy Time History (Both Tests Combined)

Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

92

-6 -4 -2 0 2 4 6-1000

-500

0

500

1000


Res

ulta

nt F

orce

(kip

s)


β



0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6



β (=

P max

/Tm

ax )


93

w (=

Tmax

/Pyn

)



0.0

0.5

1.0

1.5

2.0


(a) Tension

Cm

ax/P

yn



0.0

0.5

1.0

1.5

2.0


(b) Compression


w (=

Tm

ax /

P ym)

βw (=

Pm

ax /

P yn)



94

Rot

atio

n fro

m D

ispl

. and

Geo

met

ry (r

ad)

-0.02 -0.01 0.0 0.01 0.02-0.02

-0.01

0.0

0.01

0.02

Rotation from Inclinometer (rad)

Figure 3.66 Specimen 4: End Rotation Comparison

95

(a) during Standard Test (Overview)



96

Long

itudi

nal D

ispl

acem

ent (

in)

0 200 400 600 800-6

-4

-2

0

2

4

6


Tran

sver

se D

ispl

acem

ent (

in)

0 200 400 600 800-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (ra

d.)



97

Res

ulta

nt F

orce

(kip

s)

-6 -4 -2 0 2 4 6-1500

-1000

-500

0

500

1000

1500




Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 200 400 600 8000

20

40

60

80

100

120

140

160

Time (sec)

0

100

200

300

400

500

600

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)


Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

98

Long

itudi

nal D

ispl

acem

ent (

in)

0 200 400 600 800 1000-6

-4

-2

0

2

4

6


Tran

sver

se D

ispl

acem

ent (

in)

0 200 400 600 800 1000-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (r

ad.)



99

Res

ulta

nt F

orce

(kip

s)

-6 -4 -2 0 2 4 6-1500

-1000

-500

0

500

1000

1500




Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 200 400 600 800 10000

20

40

60

80

100

Time (sec)

0

100

200

300

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)


Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

100

Long

itudi

nal D

ispl

acem

ent (

in)

0 200 400 600 800 1000-6

-4

-2

0

2

4

6

Time (sec)


Tran

sver

se D

ispl

acem

ent (

in)

0 200 400 600 800 1000-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (r

ad.)



101

Res

ulta

nt F

orce

(kip

s)

-6 -4 -2 0 2 4 6-1500

-1000

-500

0

500

1000

1500




Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 200 400 600 800 10000

20

40

60

80

100

Time (sec)

0

100

200

300N

orm

aliz

ed C

umul

ativ

e In

elas

tic D

isp.

Eh/

(Pye

ff*D

by)


Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

102

Long

itudi

nal D

ispl

acem

ent (

in)

0 500 1000 1500 2000 2500 3000-6

-4

-2

0

2

4

6

Time (sec)


Tran

sver

se D

ispl

acem

ent (

in)

0 500 1000 1500 2000 2500 3000-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (r

ad.)



103

Res

ulta

nt F

orce

(kip

s)

-6 -4 -2 0 2 4 6-1500

-1000

-500

0

500

1000

1500




Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 500 1000 1500 2000 2500 30000

50

100

150

200

250

300

350

Time (sec)

0

200

400

600

800

1000

1200

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)


Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

104

-6 -4 -2 0 2 4 6-1500

-1000

-500

0

500

1000

1500


Res

ulta

nt F

orce

(kip

s)


β



0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6



β (=

P max

/Tm

ax )


105

w (=

Tmax

/Pyn

)



0.0

0.5

1.0

1.5

2.0


(a) Tension

Cm

ax/P

yn



0.0

0.5

1.0

1.5

2.0


(b) Compression


w (=

Tm

ax /

P yn)

βw

(= P

max

/ P y

n)



106

Rot

atio

n fro

m D

ispl

. and

Geo

met

ry (r

ad)

-0.02 -0.01 0.0 0.01 0.02-0.02

-0.01

0.0

0.01

0.02


107

(a) before Standard Test (Overview)

(b) after all Tests (East End)


108

Long

itudi

nal D

ispl

acem

ent (

in)

0 200 400 600 800-6

-4

-2

0

2

4

6

Time (sec)


Tran

sver

se D

ispl

acem

ent (

in)

0 200 400 600 800-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (r

ad.)



109

Res

ulta

nt F

orce

(kip

s)

-6 -4 -2 0 2 4 6-1500

-1000

-500

0

500

1000

1500




Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 200 400 600 8000

20

40

60

80

100

120

140

Time (sec)

0

100

200

300

400

500

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)


Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

110

Long

itudi

nal D

ispl

acem

ent (

in)

0 200 400 600 800 1000-6

-4

-2

0

2

4

6

Time (sec)


Tran

sver

se D

ispl

acem

ent (

in)

0 200 400 600 800 1000-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (ra

d.)



111

Res

ulta

nt F

orce

(kip

s)

-6 -4 -2 0 2 4 6-1500

-1000

-500

0

500

1000

1500




Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 200 400 600 800 10000

20

40

60

80

100

Time (sec)

0

50

100

150

200

250

300

350

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)


Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

112

Long

itudi

nal D

ispl

acem

ent (

in)

0 500 1000 1500 2000-6

-4

-2

0

2

4

6

Time (sec)


Tran

sver

se D

ispl

acem

ent (

in)

0 500 1000 1500 2000-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (r

ad.)



113

Res

ulta

nt F

orce

(kip

s)

-6 -4 -2 0 2 4 6-1500

-1000

-500

0

500

1000

1500




Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 500 1000 1500 20000

50

100

150

200

250

Time (sec)

0

200

400

600

800N

orm

aliz

ed C

umul

ativ

e In

elas

tic D

isp.

Eh/

(Pye

ff*D

by)


Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

114

-6 -4 -2 0 2 4 6-1500

-1000

-500

0

500

1000

1500


Res

ulta

nt F

orce

(kip

s)


β



0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6



β (=

P max

/Tm

ax )


115

w (=

Tmax

/Pyn

)



0.0

0.5

1.0

1.5

2.0


(a) Tension

Cm

ax/P

yn



0.0

0.5

1.0

1.5

2.0


(b) Compression


w (=

Tm

ax /

P yn)

βw

(= P

max

/ P y

n)



116

Rot

atio

n fro

m D

ispl

. and

Geo

met

ry (r

ad)

-0.02 -0.01 0.0 0.01 0.02-0.02

-0.01

0.0

0.01

0.02


117

(a) during Low- Cycle Fatigue Test (Overview)

(b) Knife Plate after all Tests (West End)


118

Long

itudi

nal D

ispl

acem

ent (

in)

0 100 200 300 400 500 600 700-6

-4

-2

0

2

4

6


Tran

sver

se D

ispl

acem

ent (

in)

0 100 200 300 400 500 600 700-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (r

ad.)



119

-6 -4 -2 0 2 4 6-2000

-1000

0

1000

2000R

esul

tant

For

ce (k

ips)




Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 100 200 300 400 500 600 7000

20

40

60

80

100

120

140

Time (sec)

0

50

100

150

200

250

300

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)


Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

120

Stra

in (m

icro

stra

in)

0 100 200 300 400 500 600 700-3500

-3000

-2500

-2000

-1500

-1000

-500

0

-2.0

-1.5

-1.0

-0.5

0.0

Nor

mal

ized

Stra

in

Time (sec) (a) Gage A (Longitudinal)

Stra

in (m

icro

stra

in)

0 100 200 300 400 500 600 700-3500

-3000

-2500

-2000

-1500

-1000

-500

0

-2.0

-1.5

-1.0

-0.5

0.0

Nor

mal

ized

Stra

in

Time (sec)

(b) Gage B (Longitudinal)

Figure 3.102 Specimen 7: Gusset Longitudinal Strain Gage Time Histories (Standard Test)

Gage Failed

121

Stra

in (m

icro

stra

in)

0 100 200 300 400 500 600 700-600

-400

-200

0

200

400

600

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

Nor

mal

ized

Stra

in

Time (sec)

(a) Gage R1 (Longitudinal)

Stra

in (m

icro

stra

in)

0 100 200 300 400 500 600 700-600

-400

-200

0

200

400

600

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

Nor

mal

ized

Stra

in

Time (sec)

(b) Gage R2 (Transverse)

Figure 3.103 Specimen 7: Gusset Rosette Strain Gage Time Histories (Standard Test)

122

Long

itudi

nal D

ispl

acem

ent (

in)

0 100 200 300 400 500-6

-4

-2

0

2

4

6


Tran

sver

se D

ispl

acem

ent (

in)

0 100 200 300 400 500-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (r

ad.)



123

-6 -4 -2 0 2 4 6-2000

-1000

0

1000

2000R

esul

tant

For

ce (k

ips)




Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 100 200 300 400 5000

20

40

60

80

100

120

140

160

Time (sec)

0

50

100

150

200

250

300

350

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)


Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

124

Stra

in (m

icro

stra

in)

0 100 200 300 400 500-3500

-3000

-2500

-2000

-1500

-1000

-500

0

-2.0

-1.5

-1.0

-0.5

0.0

Nor

mal

ized

Stra

in

Gauge Failed


Stra

in (m

icro

stra

in)

0 100 200 300 400 500-3500

-3000

-2500

-2000

-1500

-1000

-500

0

-2.0

-1.5

-1.0

-0.5

0.0

Nor

mal

ized

Stra

in

Time (sec)


Figure 3.107 Specimen 7: Gusset Longitudinal Strain Gage Time Histories (Low-cycle Fatigue Test No. 1)

Gage has failed

125

Stra

in (m

icro

stra

in)

0 100 200 300 400 500-600

-400

-200

0

200

400

600

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

Nor

mal

ized

Stra

in

Time (sec)


Stra

in (m

icro

stra

in)

0 100 200 300 400 500-600

-400

-200

0

200

400

600

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

Nor

mal

ized

Stra

in

Time (sec)


Figure 3.108 Specimen 7: Gusset Rosette Strain Gage Time Histories (Low-cycle Fatigue Test No. 1)

126

Long

itudi

nal D

ispl

acem

ent (

in)

0 100 200 300 400 500-6

-4

-2

0

2

4

6

Time (sec)


Tran

sver

se D

ispl

acem

ent (

in)

0 100 200 300 400 500-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (ra

d.)



127

-6 -4 -2 0 2 4 6-2000

-1000

0

1000

2000R

esul

tant

For

ce (k

ips)




Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 100 200 300 400 5000

20

40

60

80

100

120

140

160

Time (sec)

0

50

100

150

200

250

300

350

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)


Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

128

Stra

in (m

icro

stra

in)

0 100 200 300 400 500-3500

-3000

-2500

-2000

-1500

-1000

-500

0

-2.0

-1.5

-1.0

-0.5

0.0

Nor

mal

ized

Stra

in

Gauge Failed


Stra

in (m

icro

stra

in)

0 100 200 300 400 500-3500

-3000

-2500

-2000

-1500

-1000

-500

0

-2.0

-1.5

-1.0

-0.5

0.0

Nor

mal

ized

Stra

in

Time (sec)


Figure 3.112 Specimen 7: Gusset Longitudinal Strain Gage Time Histories (Low-cycle Fatigue Test No. 2)

Gage has failed

129

Stra

in (m

icro

stra

in)

0 100 200 300 400 500-600

-400

-200

0

200

400

600

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

Nor

mal

ized

Stra

in

Time (sec)


Stra

in (m

icro

stra

in)

0 100 200 300 400 500-600

-400

-200

0

200

400

600

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

Nor

mal

ized

Stra

in

Time (sec)


Figure 3.113 Specimen 7: Gusset Rosette Strain Gage Time Histories (Low-cycle Fatigue Test No. 2)

130

Long

itudi

nal D

ispl

acem

ent (

in)

0 500 1000 1500 2000-6

-4

-2

0

2

4

6

Time (sec)


Tran

sver

se D

ispl

acem

ent (

in)

0 500 1000 1500 2000-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (r

ad.)



131

-6 -4 -2 0 2 4 6-2000

-1000

0

1000

2000R

esul

tant

For

ce (k

ips)




Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 500 1000 1500 20000

100

200

300

400

500

Time (sec)

0

200

400

600

800

1000

1200

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)


Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

132

-6 -4 -2 0 2 4 6-2000

-1000

0

1000

2000


Res

ulta

nt F

orce

(kip

s)


β



0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6



β (=

P max

/Tm

ax )


133

w (=

Tmax

/Pyn

)



0.0

0.5

1.0

1.5

2.0


(a) Tension

Cm

ax/P

yn



0.0

0.5

1.0

1.5

2.0


(b) Compression


w (=

Tm

ax /

P yn)

βw

(= P

max

/ P y

n)



134

Rot

atio

n fro

m D

ispl

. and

Geo

met

ry (r

ad)

-0.02 -0.01 0.0 0.01 0.02-0.02

-0.01

0.0

0.01

0.02


135

(a) before Standard Test (Overview)



136

Long

itudi

nal D

ispl

acem

ent (

in)

0 100 200 300 400 500 600 700-6

-4

-2

0

2

4

6

Time (sec)

(b) Longitudinal Direction

Tran

sver

se D

ispl

acem

ent (

in)

0 100 200 300 400 500 600 700-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (r

ad.)



137

-6 -4 -2 0 2 4 6-2000

-1000

0

1000

2000R

esul

tant

For

ce (k

ips)




Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 100 200 300 400 500 600 7000

20

40

60

80

100

120

140

Time (sec)

0

50

100

150

200

250

300

350

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)


Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

138

Long

itudi

nal D

ispl

acem

ent (

in)

0 100 200 300 400 500-6

-4

-2

0

2

4

6

Time (sec)


Tran

sver

se D

ispl

acem

ent (

in)

0 100 200 300 400 500-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (r

ad.)



139

-6 -4 -2 0 2 4 6-2000

-1000

0

1000

2000R

esul

tant

For

ce (k

ips)




Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 100 200 300 400 5000

20

40

60

80

100

120

140

160

Time (sec)

0

100

200

300

400

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)


Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

140

Long

itudi

nal D

ispl

acem

ent (

in)

0 100 200 300 400 500-6

-4

-2

0

2

4

6

Time (sec)


Tran

sver

se D

ispl

acem

ent (

in)

0 100 200 300 400 500-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (r

ad.)



141

-6 -4 -2 0 2 4 6-2000

-1000

0

1000

2000R

esul

tant

For

ce (k

ips)




Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 100 200 300 400 5000

20

40

60

80

100

120

140

160

Time (sec)

0

100

200

300

400

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)


Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

142

Long

itudi

nal D

ispl

acem

ent (

in)

0 500 1000 1500 2000-6

-4

-2

0

2

4

6

Time (sec)


Tran

sver

se D

ispl

acem

ent (

in)

0 500 1000 1500 2000-6

-4

-2

0

2

4

6

Time (sec)

-0.02

-0.01

0.0

0.01

0.02

End

Rot

atio

n (r

ad.)



143

-6 -4 -2 0 2 4 6-2000

-1000

0

1000

2000R

esul

tant

For

ce (k

ips)




Dis

sipa

ted

Ene

rgy

(x 1

000

kip-

in),

Eh

0 500 1000 1500 20000

100

200

300

400

500

Time (sec)

0

200

400

600

800

1000

1200

Nor

mal

ized

Cum

ulat

ive

Inel

astic

Dis

p. E

h/(P

yeff*

Dby

)


Cum

ulat

ive

Inel

astic

Def

orm

atio

n, η

Hys

tere

tic E

nerg

y (×

1000

kip

-in),

Eh

144

-6 -4 -2 0 2 4 6-2000

-1000

0

1000

2000


Res

ulta

nt F

orce

(kip

s)


β



0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6



β (=

P max

/Tm

ax )


145

w (=

Tmax

/Pyn

)



0.0

0.5

1.0

1.5

2.0


(a) Tension

Cm

ax/P

yn



0.0

0.5

1.0

1.5

2.0


(b) Compression


w (=

Tm

ax /

P yn)

βw

(= P

max

/ P y

n)



146

Rot

atio

n fro

m D

ispl

. and

Geo

met

ry (r

ad)

-0.02 -0.01 0.0 0.01 0.02-0.02

-0.01

0.0

0.01

0.02


147

4. COMPARISON OF TEST RESULTS

4.1 Fracture Mode

All of the specimens performed very well in the Standard Loading Protocol test. Only

Specimens 1 and 2 experienced a fracture during Low-cycle Fatigue testing (see Table 4.1).

No significant deformations in the outer HSS casing or collar were observed, which was

consistent with the low strain gage readings ( yε2.0≈ ) on Specimens 3 and 4 (see Sections

3.2.3 and 3.3.4).

4.2 Correction for Pinhole Elongation

The brace deformation reported in Chapter 3 was based on the measurement of

displacement transducer L1 [see Figure 2.12(a)], which was mounted on the gusset plates.

The hysteresis response near zero load generally shows a horizontal shift. The primary cause

of this phenomenon was the elongation of the pinholes, which was accentuated in the larger

braces and those that were tested toward the end of the program. There were plastic

deformations surrounding the holes, both in the re-used gusset plate [Figure 4.1(a)], as well as

in the knife plates at the end of each brace [Figure 4.1(b)]. The target displacements of the

shake table were calculated as described in Section 2.5; however, the calculation did not

include elongation of the pinhole. Therefore, the actual deformations in the steel core plates

were slightly less than expected and recorded.

Chapter 3 is based on the L1 transducer since it potentially represents the actual pin-

to-pin results. The displacement transducer L4 (as shown in Figure 2.12), on the other hand,

was installed at both ends of the brace specimen and, therefore, the measurement of brace

axial deformation would not be affected by the pinhole elongation. The L4 transducer is

based on a shorter gage length so the Dby values used to get the revised results were reduced

by the minuscule amount of elastic deformation in the knife plates. The actual brace

deformations, as measured by transducer L4, are presented in Table 4.2 and can be compared

to the original values in Table 3.1 through Table 3.8. Note that in the Chapter 3 tables, only

the longitudinal brace deformation values were affected by the pinhole elongation. In this

148

chapter, plots and response values are presented using both the L1 and the L4 transducers for

comparison. Results that are based on the L4 transducer are labeled “Corrected.”

Because Specimen 7 was the last and largest brace tested, it experienced the most

significant pinhole elongation. Example force-deformation plots for this specimen, are

presented in Figure 4.2 comparing the two different displacement transducers, L1 and L4.

The corrected values and plots are recommended for design because it is not likely that

practical applications of the brace would experience enough large amplitude cycles to result

in a significant pin elongation effect which was observed in testing over an accumulation of

specimens and loading protocols.

4.3 Hysteretic Energy, Eh, and Cumulative Inelastic Deformation, η

The hysteretic energy, Eh, and cumulative inelastic deformation, η, based on the

measurement of displacement transducer L1 are summarized in Figure 4.3 for all specimens.

Specimens 1 and 2 were the only specimens to experience fracture during Low-cycle Fatigue

testing, reaching η values of 900 and 600, respectively. The remainder of the specimens

could potentially undergo further inelastic deformation, thus, a comparison is applicable.

The hysteresis energy and cumulative inelastic deformation were re-computed based

on the measurement of displacement transducer L4 and are presented in Figure 4.4. A

comparison of Figure 4.3 and Figure 4.4 shows that these two quantities were not affected by

the pinhole elongation.

4.4 Tension Strength Adjustment Factor, w

The tension strength adjustment factor, w, versus brace deformation (based on L1) for

all specimens is presented in Figure 4.5. The slope (m) and y-intercept (b) of the idealized

plots, as defined in Section 2.7, are presented in Table 4.3(a). This table also includes the

quantity w*, which was defined as the w value at the point separating Zone 1 and Zone 2 at a

deformation of 5Dby. The corrected results based on L4 are presented in Figure 4.6 and Table

4.3(b).

149

To interpolate and solve for w at any point within the domain of the test data, use the

following equations along with Table 4.3:

11 bD

mwby

+

∆= (4.1a)

22 bD

mwby

+

∆= (4.1b)

Based on the average values of m and b for the corrected test results, the following

expressions can be used to evaluate w:

11.1102.48 3 +

∆×= −

byDw (4.2a)

18.1105.34 3 +

∆×= −

byDw (4.2b)

4.5 Compression Strength Adjustment Factor, β

The compression strength adjustment factor, β, versus brace deformation (based on

L1) for each specimen is presented in Figure 4.7. The slope and y-intercept of the least

squares fit idealization are presented in Table 4.4(a). The y-intercept was constrained to be

1.0 in the regression. The corrected results, based on L4 are presented in Figure 4.8 and Table

4.4(b). Based on the average values m and b found in Table 4.4, the following expression can

be used to evaluate β:

bD

mby

+

∆=β (4.3)

Based on the average values of m and b for the corrected test results, the following expression

can be used to evaluate w:

0.1104.19β 3 +

∆×= −

byD (4.4)

4.6 Comparison at the SEAOC-AISC Limit State

The proposed SEAOC-AISC Recommended Provisions (2001) uses the deformation

level of 1.5Dbm (= 7.5Dby) as a critical limit state for design. The values of w, β, and βw were

calculated at this limit state using the interpolation Eqs. 4.1(b) and 4.3 and are listed in Table

byD5<∆

byD5≥∆

byD5<∆

byD5≥∆

150

4.5. Note that the corrected average values of w and β in Table 4.5(b) can also be predicted

reliably by Eqs. 4.2(b) and 4.4, respectively. Using these equations, w is 1.44 and β is 1.15.

4.7 Equivalent Viscous Damping

The equivalent viscous damping, ζeq, can be computed for each brace based on the

energy dissipated in each hysteretic loop (Clough and Penzien 1993):

2)(4 CODAOB

deq AA

E+

=π

ζ (4.5)

where Ed = energy dissipated per cycle while AAOB and ACOD are the areas of the triangles

shown in Figure 4.9.

The results were plotted after averaging the ζeq values at each deformation level. A

non-linear regression was then fitted to the data as follows:

41

ζ

∆=

byeq D

c (4.6)

where c is a constant obtained from the regression.

In Figure 4.10, data for all of the specimens is shown in the same plot, and in Figure

4.11, each specimen is plotted individually. Based on the correlation of the regression fits for

the individual specimens, Eq. 4.6 was developed and used for the composite plot in Figure

4.10. The value of c from the composite regression in Figure 4.10 is 29.3 while the average

value of the c values from each individual regression is 29.5. Therefore, the following

equation can be used to approximate the effective damping of the brace:

41

3.29ζ

∆=

byeq D

(4.7)

151

Table 4.1 Specimen Fractures in the Low-cycle Fatigue Test

Specimen Fracture Cycle 1 18 2 1 3 No fracture (25 cycles × 2 tests) 4 No fracture (25 cycles × 1 test) 5 No fracture (30 cycles × 2 tests) 6 No fracture (30 cycles × 1 test) 7 No fracture (15 cycles × 2 tests) 8 No fracture (15 cycles × 2 tests)

Table 4.2 Corrected Peak Longitudinal Brace Deformations (in.)

Specimena Cycle 1 2 3 4 5 6 7 8

1 0.39 0.40 0.31 0.36 0.30 0.31 0.27 0.27 2 0.38 0.41 0.32 0.36 0.30 0.31 0.26 0.27 3 0.39 0.41 0.32 0.35 0.30 0.30 0.25 0.26 4 0.39 0.41 0.33 0.35 0.31 0.30 0.25 0.26 5 0.39 0.41 0.33 0.35 0.30 0.30 0.25 0.26 6 0.39 0.41 0.33 0.35 0.31 0.30 0.25 0.26 7 0.84 0.86 0.77 0.80 0.75 0.74 0.67 0.70 8 0.84 0.86 0.77 0.79 0.74 0.73 0.65 0.69 9 0.84 0.86 0.77 0.79 0.74 0.73 0.65 0.69 10 0.84 0.86 0.77 0.79 0.75 0.72 0.66 0.69 11 1.64 1.66 1.58 1.58 1.56 1.50 1.44 1.49 12 1.63 1.65 1.57 1.56 1.52 1.47 1.40 1.44 13 1.63 1.65 1.57 1.56 1.52 1.46 1.38 1.43 14 1.63 1.65 1.57 1.55 1.52 1.46 1.37 1.42 15 2.45 2.47 2.39 2.36 2.32 2.26 2.17 2.25 16 2.45 2.47 2.39 2.36 2.32 2.24 2.15 2.23 17 1.64 1.65 1.57 1.54 1.50 1.43 1.33 1.38 18 3.06 3.18 3.28 2.96 3.23 2.84 3.13 3.06 19 3.06 3.17 3.26 2.95 3.21 2.82 3.07 3.00 20 3.06 3.16 3.26 2.95 3.21 2.80 3.03 2.90 21 3.06 3.16 3.26 2.95 3.20 2.80 2.93 2.76 22 3.06 3.16 3.26 2.95 3.19 2.79 2.80 2.66 23 3.52 3.72 - 3.61 3.88 3.48 - - 24 3.52 3.71 - 3.68 3.85 3.46 - - 25 4.22 4.42 - 4.37 4.64 4.18 - - 26 4.21 4.41 - 4.36 4.61 4.13 - -

aStandard Test Only

152

Table 4.3 Tension Strength Adjustment Factor Idealization

(a) Uncorrected

Zone 1 Zone 2 Specimen w* m1 (×10-3) b1 m2 (×10-3) b2

1 1.404 59.2 1.11 31.4 1.25 2 1.365 49.7 1.12 34.7 1.19 3 1.299 33.1 1.13 36.0 1.12 4 1.356 64.7 1.03 31.9 1.20 5 1.316 37.4 1.13 35.1 1.14 6 1.323 39.2 1.13 32.4 1.16 7 1.289 30.5 1.14 38.1 1.10 8 1.294 32.0 1.14 36.1 1.11

Average 1.331 43.2 1.12 34.5 1.16

(b) Corrected

Zone 1 Zone 2 Specimen w* m1 (×10-3) b1 m2 (×10-3) b2

1 1.407 60.0 1.11 31.4 1.25 2 1.366 49.8 1.12 34.5 1.19 3 1.313 36.7 1.13 35.4 1.14 4 1.381 71.0 1.03 31.6 1.22 5 1.330 40.9 1.13 35.2 1.15 6 1.348 45.5 1.12 33.1 1.18 7 1.333 41.6 1.13 38.4 1.14 8 1.328 40.2 1.13 36.3 1.15

Average 1.351 48.2 1.11 34.5 1.18

153

Table 4.4 Compression Strength Adjustment Factor Idealization

(a) Uncorrected (b) Corrected

Specimen m (×10-3) b Specimen m (×10-3) b 1 20.0 1.0 1 20.3 1.0 2 19.8 1.0 2 19.7 1.0 3 19.7 1.0 3 20.3 1.0 4 14.9 1.0 4 15.6 1.0 5 20.5 1.0 5 21.4 1.0 6 19.6 1.0 6 21.6 1.0 7 18.4 1.0 7 20.4 1.0 8 14.0 1.0 8 15.8 1.0

Average 18.4 1.0 Average 19.4 1.0

Table 4.5 Select Quantities at 1.5Dbm (=7.5Dby)

(a) Uncorrected

Specimen w β βw 1 1.48 1.15 1.70 2 1.45 1.15 1.67 3 1.39 1.15 1.59 4 1.44 1.11 1.60 5 1.40 1.15 1.62 6 1.40 1.15 1.61 7 1.38 1.14 1.57 8 1.38 1.10 1.53

Average 1.42 1.14 1.61

(b) Corrected

Specimen w β βw 1 1.49 1.15 1.71 2 1.45 1.15 1.67 3 1.40 1.15 1.61 4 1.46 1.12 1.63 5 1.42 1.16 1.65 6 1.43 1.16 1.66 7 1.43 1.15 1.65 8 1.42 1.12 1.59

Average 1.44 1.15 1.65

154

(a) East Re-used Gusset Plate

(b) Typical Specimen Knife Plate

Figure 4.1 Hole Elongation Sources

155

-6 -4 -2 0 2 4 6-2000

-1000

0

1000

2000

Res

ulta

nt F

orce

(kip

s)



(a) Based on L1 Displacement Transducer

-6 -4 -2 0 2 4 6-2000

-1000

0

1000

2000

Res

ulta

nt F

orce

(kip

s)



(b) Based on L4 Displacement Transducer (Corrected)

Figure 4.2 Specimen 7: Brace Force versus Deformation Comparison

156

0 200 600 1000 14000

20

40

60

80

Time (sec)

0200400600800

100012001400

0 200 400 600 8000

20

40

60

80

100

120

Time (sec)

0200400600800100012001400

0 500 1000 1500 2000 25000

50

100

150

200

Time (sec)

0200400600800100012001400

0 500 1000 1500 2000

0

50

100

150

200

250

300

Time (sec)

0200400600800100012001400

0 500 1000 2000 30000

100

200

300

400

Time (sec)

0200400600800100012001400

0 500 1000 1500 2000

050

100150200250300350400

Time (sec)

0200400600800100012001400

0 500 1000 1500 20000

100

200

300

400

500

600

Time (sec)

0200400600800100012001400

0 500 1000 1500 2000

0

100

200

300

400

500

600

Time (sec)

0200400600800100012001400

Figure 4.3 All Specimens: Eh and η Time Histories

Eh (

×100

0 ki

p-in

)

η

Eh (

×100

0 ki

p-in

)

η

Eh (

×100

0 ki

p-in

)

η

Eh (

×100

0 ki

p-in

)

η

Eh (

×100

0 ki

p-in

)

η

Eh (

×100

0 ki

p-in

)

η

Eh (

×100

0 ki

p-in

)

η

Eh (

×100

0 ki

p-in

)

η

(a) Specimen 1 (b) Specimen 2

(c) Specimen 3 (d) Specimen 4

(e) Specimen 5 (f) Specimen 6

(g) Specimen 7 (h) Specimen 8

Did not fracture Did not

fracture

Did not fracture

Did not fracture

Did not fracture

Did not fracture

157

0 200 600 1000 14000

20

40

60

80

Time (sec)

0200400600800100012001400

0 200 400 600 800

0

20

40

60

80

100

120

Time (sec)

0200400600800

100012001400

0 500 1000 1500 2000 25000

50

100

150

200

Time (sec)

0200400600800100012001400

0 500 1000 1500 2000

0

50

100

150

200

250

300

Time (sec)

0200400600800100012001400

0 500 1000 2000 30000

100

200

300

400

Time (sec)

0200400600800100012001400

0 500 1000 1500 2000

050

100150200250300350

Time (sec)

0200400600800100012001400

0 500 1000 1500 20000

100

200

300

400

500

600

Time (sec)

0200400600800100012001400

0 500 1000 1500 2000

0

100

200

300

400

500

600

Time (sec)

0200400600800100012001400

Figure 4.4 All Specimens: Eh and η Time Histories (Corrected)

Eh (

×100

0 ki

p-in

)

η

Eh (

×100

0 ki

p-in

)

η

Eh (

×100

0 ki

p-in

)

η

Eh (

×100

0 ki

p-in

)

η

Eh (

×100

0 ki

p-in

)

η

Eh (

×100

0 ki

p-in

)

η

Eh (

×100

0 ki

p-in

)

η

Eh (

×100

0 ki

p-in

)

η





Did not fracture

Did not fracture

Did not fracture

Did not fracture

Did not fracture

Did not fracture

158



0.0

0.5

1.0

1.5

2.0

1.404

Dby 5Dby



0.0

0.5

1.0

1.5

2.0

1.365

Dby 5Dby



0.0

0.5

1.0

1.5

2.0

1.299

Dby 5Dby



0.0

0.5

1.0

1.5

2.0

1.356

Dby 5Dby



0.0

0.5

1.0

1.5

2.0

1.316

Dby 5Dby



0.0

0.5

1.0

1.5

2.0

1.323

Dby 5Dby



0.0

0.5

1.0

1.5

2.0

1.289

Dby 5Dby



0.0

0.5

1.0

1.5

2.0

1.294

Dby 5Dby

Figure 4.5 All Specimens: w versus Brace Deformation

w (=

Tm

ax /

Pyn

)

w (=

Tm

ax /

Pyn

)

w (=

Tm

ax /

Pyn

)

w (=

Tm

ax /

Pyn

)

w (=

Tm

ax /

Pyn

)

w (=

Tm

ax /

Pyn

)

w (=

Tm

ax /

Pyn

)

w (=

Tm

ax /

Pyn

)





159



0.0

0.5

1.0

1.5

2.0

1.407

Dby 5Dby



0.0

0.5

1.0

1.5

2.0

1.366

Dby 5Dby



0.0

0.5

1.0

1.5

2.0

1.313

Dby 5Dby



0.0

0.5

1.0

1.5

2.0

1.381

Dby 5Dby



0.0

0.5

1.0

1.5

2.0

1.33

Dby 5Dby



0.0

0.5

1.0

1.5

2.0

1.348

Dby 5Dby



0.0

0.5

1.0

1.5

2.0

1.333

Dby 5Dby



0.0

0.5

1.0

1.5

2.0

1.328

Dby 5Dby

Figure 4.6 All Specimens: w versus Brace Deformation (Corrected)

w (=

Tm

ax /

Pyn

)

w (=

Tm

ax /

Pyn

)

w (=

Tm

ax /

Pyn

)

w (=

Tm

ax /

Pyn

)

w (=

Tm

ax /

Pyn

)

w (=

Tm

ax /

Pyn

)

w (=

Tm

ax /

Pyn

)

w (=

Tm

ax /

Pyn

)





160



0.00.20.40.60.81.01.21.41.6



0.00.20.40.60.81.01.21.41.6



0.00.20.40.60.81.01.21.41.6



0.00.20.40.60.81.01.21.41.6



0.00.20.40.60.81.01.21.41.6



0.00.20.40.60.81.01.21.41.6



0.00.20.40.60.81.01.21.41.6



0.00.20.40.60.81.01.21.41.6

Figure 4.7 All Specimens: β versus Brace Deformation

β (=

Pm

ax /T

max

)

β (=

Pm

ax /T

max

)

β (=

Pm

ax /T

max

)

β (=

Pm

ax /T

max

)

β (=

Pm

ax /T

max

)

β (=

Pm

ax /T

max

)

β (=

Pm

ax /T

max

)

β (=

Pm

ax /T

max

)





161



0.00.20.40.60.81.01.21.41.6



0.00.20.40.60.81.01.21.41.6



0.00.20.40.60.81.01.21.41.6



0.00.20.40.60.81.01.21.41.6



0.00.20.40.60.81.01.21.41.6



0.00.20.40.60.81.01.21.41.6



0.00.20.40.60.81.01.21.41.6



0.00.20.40.60.81.01.21.41.6

Figure 4.8 All Specimens: β versus Brace Deformation (Corrected)

β (=

Pm

ax /T

max

)

β (=

Pm

ax /T

max

)

β (=

Pm

ax /T

max

)

β (=

Pm

ax /T

max

)

β (=

Pm

ax /T

max

)

β (=

Pm

ax /T

max

)

β (=

Pm

ax /T

max

)

β (=

Pm

ax /T

max

)





162

Figure 4.9 Model for the Calculation of the Effective Viscous Damping


0

10

20

30

40

50

60

70

c = 29.29

Figure 4.10 All Specimens combined: Equivalent Viscous Damping (Corrected)

P

∆

Total Area = Ed

O

A

B

Area = AAOB

D

C

Area = ACOD

∆max

∆min

ζ eq (

%)

163



010203040506070


(a) Specimen 1

c = 27.69



010203040506070


(b) Specimen 2

c = 28.12



010203040506070


(c) Specimen 3

c = 28.85



010203040506070


(d) Specimen 4

c = 29



010203040506070


(e) Specimen 5

c = 29.82



010203040506070


(f) Specimen 6

c = 30.65



010203040506070


(g) Specimen 7

c = 31.14



010203040506070


(h) Specimen 8

c = 30.35

Figure 4.11 All Specimens individually: Equivalent Viscous Damping (Corrected)

ζ eq (

%)

ζ eq (

%)

ζ eq (

%)

ζ eq (

%)

ζ eq (

%)

ζ eq (

%)

ζ eq (

%)

ζ eq (

%)

164

5. SUMMARY AND CONCLUSIONS

5.1 Summary

A total of eight buckling-restrained brace subassemblage tests were conducted for Star

Seismic. The nominal yield strength for these eight specimens varied from 160 to 1200 kips.

Flat steel yielding (or core) plates were used for all specimens; A36 steel was specified for all

of the steel core plates.

Each specimen was pin-connected to gusset plates at each end, and cyclically tested by

imposing both longitudinal and transverse movements at one end by a shake table. Each

specimen was subjected to a Standard Loading Protocol (Figure 2.9), followed by high

amplitude Low-cycle Fatigue testing (Figure 2.10). The loading protocols were developed in

accordance with the proposed SEAOC-AISC Recommended Provisions for Buckling-

Restrained Brace Frames (2001). These protocols included both longitudinal deformations as

well as transverse (i.e. vertical) deformations imposed by a shake table; see Table 2.4 for the

imposed shake table amplitudes. One specimen was also subject to a simulated dynamic

response from the Northridge, Sylmar earthquake record.

The proposed SEAOC-AISC Recommendation requires that the tensile strength

adjustment factor (w), the compression strength adjustment factor (β), and the cumulative

inelastic axial deformation (η) be reported. In this study, a procedure that can be used to

evaluate η in a consistent manner was also proposed (Section 2.7).

5.2 Conclusions

Based on the test results, the following conclusions can be made.

(1) All specimens performed well under the Standard Loading Protocol, and no fracture was

observed.

(2) Two specimens fractured during the Low-cycle Fatigue testing; see Table 4.1 for the

fracture cycles. Prior to fracture, the hysteresis behavior was very stable.

(3) Prior to fracture, all specimens were able to accommodate an end rotation of at least

0.013 radians in the transverse direction.

165

(4) The tension strength adjustment factor (w) as a function of the brace axial deformation in

Figure 4.6 can be approximated by two straight lines, and Eq. 4.2 can be used to evaluate

the w value. Taking Dbm as 5Dby (the maximum value per SEAOC-AISC Recommended

Provisions), the average w value from Eq. 4.2b is 1.44 at a deformation level of 1.5Dbm

(=7.5Dby) for the specimens tested.

(5) The compression strength adjustment factor (β) as a function of the brace axial

deformation in Figure 4.8 can be approximated by a straight line. Based on Eq. 4.4, the

average β value at a deformation of 1.5Dbm is 1.15. This value is smaller than the

limiting value of 1.3 in the SEAOC-AISC Recommended Provisions.

(6) Based on a normalized procedure outlined in Section 2.7, the value of cumulative

inelastic axial deformation reached in all test specimens ranged from 600 to 1,650. Only

Specimens 1 and 2 were tested to failure and reached η values of 900 and 600,

respectively. The remaining specimens, which did not experience fracture, reached an

average of 1,180. Note that this value is significantly higher than that (140) required by

the SEAOC-AISC Recommended Provisions for uniaxial testing.

166

REFERENCES

(1) AISC, Manual of Steel Construction: Load & Resistance Factor Design, American Institute of Steel Construction, Chicago, IL, 1998.

(2) Clark, P., Aiken, I., Kasai, K., Ko, E., and Kimura, I., “Design procedures for buildings

incorporating hysteretic damping devices.” Proceedings, 69th Annual Convention, SEAOC, Sacramento, CA, 1999.

(3) Clough, R.W. and Penzien J., Dynamics of structures, McGraw-Hill, 2nd ed., 1993.

(4) Lopez, W.A., “Design of unbonded braced frames.” Proceedings, 70th Annual

Convention, 23-31, SEAOC, Sacramento, CA, 2001. (5) Reina, P. and Normile, D., “Fully braced for seismic survival.” Engineering News

Record, July 21, 34-36, 1997.

(6) Sabelli, R., “Research on improving the design and analysis of earthquake-resistant steel-braced frames.” The 2000 NEHRP Professional Fellowship Report, EERI, Oakland, CA, 2001.

(7) SEAOC-AISC, Recommended provisions for buckling-restrained braced frames,

Proposed, SEAOC and AISC, 2001.

(8) Shuhaibar, C., Lopez, W.A., and Sabelli, R., “Buckling-restrained braced frames.” Proceedings, ATC-17-2, Seminar on Response Modification Technologies for Performance-Based Seismic Design, ATC and MCEER, 321-328, 2002.

(9) Somerville, P., et al. “Development of ground motion time histories for Phase 2.” Report

No. SAC/BD-97/04, SAC Joint Venture, Sacramento, CA, 1997.

UCSD Testing Program: PowerCat BracesBased on data for all braces

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0

Average Brace Strain (%)

Ave

rage

Bra

ce A

djus

tmen

t Fac

tors

15∆by

10∆by

10∆by

15∆by

12.5∆by

12.5∆byω

ωβ

y

y

εεε

εεεεω

>+

≤=

8953.02499.0145.09315.0)(

assumed backbone curve

y

y

εεε

εεεεωβ

<−

≥=

8549.04359.0145.09181.0)(

star seismic powercat test 1 (tr-2003_04, star seismic final report)

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