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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 3.2 Specimen 2 Peak Response Quantities .................................................................... 33
Table 3.3 Specimen 3 Peak Response Quantities .................................................................... 34
Table 3.4 Specimen 4 Peak Response Quantities .................................................................... 36
Table 3.5 Specimen 5 Peak Response Quantities .................................................................... 38
Table 3.6 Specimen 6 Peak Response Quantities .................................................................... 40
Table 3.7 Specimen 7 Peak Response Quantities .................................................................... 42
Table 3.8 Specimen 8 Peak Response Quantities .................................................................... 44
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 3.19 Specimen 2: Brace Response Envelope................................................................ 59
Figure 3.20 Specimen 2: β versus Deformation Level............................................................. 59
Figure 3.21 Specimen 2: w and βw versus Deformation Level ............................................... 60
Figure 3.22 Specimen 2: End Rotation Comparison................................................................ 61
Figure 3.23 Specimen 3: Testing Photo ................................................................................... 61
Figure 3.24 Specimen 3: Table Displacement Time Histories (Standard Test)....................... 62
Figure 3.25 Specimen 3: Brace Force versus Deformation (Standard Test)............................ 63
Figure 3.26 Specimen 3: Hysteretic Energy Time History (Standard Test) ............................ 63
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
Figure 3.37 Specimen 3: Table Displacement Time Histories (Low-cycle Fatigue Test
No. 2)................................................................................................................................ 72
Figure 3.38 Specimen 3: Brace Force versus Deformation (Low-cycle Fatigue Test
No. 2)................................................................................................................................ 73
Figure 3.39 Specimen 3: Hysteretic Energy Time History (Low-cycle Fatigue Test No.
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 3.45 Specimen 3: Brace Response Envelope................................................................ 78
Figure 3.46 Specimen 3: β versus Deformation Level............................................................. 78
Figure 3.47 Specimen 3: w and βw versus Deformation Level ............................................... 79
Figure 3.48 Specimen 3: End Rotation Comparison................................................................ 80
Figure 3.49 Specimen 4: Testing Photos.................................................................................. 81
Figure 3.50 Specimen 4: Table Displacement Time Histories (Standard Test)....................... 82
Figure 3.51 Specimen 4: Brace Force versus Deformation (Standard Test)............................ 83
Figure 3.52 Specimen 4: Hysteretic Energy Time History (Standard Test) ............................ 83
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
Figure 3.63 Specimen 4: Brace Response Envelope................................................................ 92
Figure 3.64 Specimen 4: β versus Deformation Level............................................................. 92
Figure 3.65 Specimen 4: w and βw versus Deformation Level ............................................... 93
Figure 3.66 Specimen 4: End Rotation Comparison................................................................ 94
Figure 3.67 Specimen 5: Testing Photos.................................................................................. 95
Figure 3.68 Specimen 5: Table Displacement Time Histories (Standard Test)....................... 96
Figure 3.69 Specimen 5: Brace Force versus Deformation (Standard Test)............................ 97
Figure 3.70 Specimen 5: Hysteretic Energy Time History (Standard Test) ............................ 97
Figure 3.71 Specimen 5: Table Displacement Time Histories (Low-cycle Fatigue Test
No. 1)................................................................................................................................ 98
Figure 3.72 Specimen 5: Brace Force versus Deformation (Low-cycle Fatigue Test
No. 1)................................................................................................................................ 99
Figure 3.73 Specimen 5: Hysteretic Energy Time History (Low-cycle Fatigue Test No.
1) ...................................................................................................................................... 99
Figure 3.74 Specimen 5: Table Displacement Time Histories (Low-cycle Fatigue Test
No. 2).............................................................................................................................. 100
Figure 3.75 Specimen 5: Brace Force versus Deformation (Low-cycle Fatigue Test
No. 2).............................................................................................................................. 101
Figure 3.76 Specimen 5: Hysteretic Energy Time History (Low-cycle Fatigue Test No.
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
Figure 3.105 Specimen 7: Brace Force versus Deformation (Low-cycle Fatigue Test
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
Figure 3.109 Specimen 7: Table Displacement Time Histories (Low-cycle Fatigue
Test No. 2)...................................................................................................................... 126
Figure 3.110 Specimen 7: Brace Force versus Deformation (Low-cycle Fatigue Test
No. 2).............................................................................................................................. 127
xi
Figure 3.111 Specimen 7: Hysteretic Energy Time History (Low-cycle Fatigue Test
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
Figure 3.125 Specimen 8: Table Displacement Time Histories (Low-cycle Fatigue
Test No. 1)...................................................................................................................... 138
Figure 3.126 Specimen 8: Brace Force versus Deformation (Low-cycle Fatigue Test
No. 1).............................................................................................................................. 139
Figure 3.127 Specimen 8: Hysteretic Energy Time History (Low-cycle Fatigue Test
No. 1).............................................................................................................................. 139
Figure 3.128 Specimen 8: Table Displacement Time Histories (Low-cycle Fatigue
Test No. 2)...................................................................................................................... 140
Figure 3.129 Specimen 8: Brace Force versus Deformation (Low-cycle Fatigue Test
No. 2).............................................................................................................................. 141
Figure 3.130 Specimen 8: Hysteretic Energy Time History (Low-cycle Fatigue Test
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
Brace Deformation (in)
25
Res
ulta
nt F
orce
(kip
s)
-6 -4 -2 0 2 4 6-400
-200
0
200
400
Brace Deformation (in)
-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:
(1) Standard Loading Protocol test: Figure 3.15 to Figure 3.17,
(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,
(4) Combined test results: Figure 3.42 to Figure 3.44,
(5) Peak response values and response envelope: Table 3.3 and Figure 3.45,
(6) β, w, and βw values: Table 3.3 and Figure 3.46 to Figure 3.47, and
(7) End rotation comparison: Figure 3.48.
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,
(3) Combined test results: Figure 3.60 to Figure 3.62,
(4) Peak response values and response envelope: Table 3.4 and Figure 3.63,
(5) β, w, and βw values: Table 3.4 and Figure 3.64 to Figure 3.65, and
(6) End rotation comparison: Figure 3.66.
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:
(1) Standard Loading Protocol test: Figure 3.68 to Figure 3.70,
30
(2) Low-cycle fatigue tests: Figure 3.71 to Figure 3.76,
(3) Combined test results: Figure 3.77 to Figure 3.79,
(4) Peak response values and response envelope: Table 3.5 and Figure 3.80,
(5) β, w, and βw values: Table 3.5 and Figure 3.81 to Figure 3.82, and
(6) End rotation comparison: Figure 3.83.
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
following results are presented for Specimen 6:
(1) Standard Loading Protocol test: Figure 3.85 to Figure 3.87,
(2) Low-cycle fatigue test: Figure 3.88 to Figure 3.90,
(3) Combined test results: Figure 3.91 to Figure 3.93,
(4) Peak response values and response envelope: Table 3.6 and Figure 3.94,
(5) β, w, and βw values: Table 3.6 and Figure 3.95 to Figure 3.96, and
(6) End rotation comparison: Figure 3.97.
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:
(1) Standard Loading Protocol test: Figure 3.99 to Figure 3.103,
(2) Low-cycle fatigue tests: Figure 3.104 to Figure 3.113,
(3) Combined test results: Figure 3.114 to Figure 3.116,
31
(4) Peak response values and response envelope: Table 3.7 and Figure 3.117,
(5) β, w, and βw values: Table 3.7 and Figure 3.118 to Figure 3.119, and
(6) End rotation comparison: Figure 3.120.
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
following results are presented for Specimen 8:
(1) Standard Loading Protocol test: Figure 3.122 to Figure 3.124,
(2) Low-cycle fatigue tests: Figure 3.125 to Figure 3.130,
(3) Combined test results: Figure 3.131 to Figure 3.133,
(4) Peak response values and response envelope: Table 3.8 and Figure 3.134,
(5) β, w, and βw values: Table 3.8 and Figure 3.135 to Figure 3.136, and
(6) End rotation comparison: Figure 3.137.
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
Table 3.2 Specimen 2 Peak Response Quantities
Brace Deformations (in) Test Cycle No. Tmax (kips) Pmax (kips) β w βw Longitudinal Transversea
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
Table 3.3 Specimen 3 Peak Response Quantities
Brace Deformations (in) Test Cycle No. Tmax (kips) Pmax (kips) β w βw Longitudinal Transversea
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
72 474 -599 1.26 1.58 1.99 2.38 2.28 (0.009) a values in parenthesis are for end rotation (rad.)
36
Table 3.4 Specimen 4 Peak Response Quantities
Brace Deformations (in) Test Cycle No. Tmax (kips) Pmax (kips) β w βw Longitudinal Transversea
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)
51 691 -809 1.17 1.52 1.77 2.29 2.28 (0.009) a values in parenthesis are for end rotation (rad.)
38
Table 3.5 Specimen 5 Peak Response Quantities
Brace Deformations (in) Test Cycle No. Tmax (kips) Pmax (kips) β w βw Longitudinal Transversea
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
86 740 -1062 1.44 1.15 1.66 2.38 1.67 (0.007) a values in parenthesis are for end rotation (rad.)
40
Table 3.6 Specimen 6 Peak Response Quantities
Brace Deformations (in) Test Cycle No. Tmax (kips) Pmax (kips) β w βw Longitudinal Transversea
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)
56 908 -1045 1.15 1.41 1.62 1.69 1.67 (0.007) a values in parenthesis are for end rotation (rad.)
42
Table 3.7 Specimen 7 Peak Response Quantities
Brace Deformations (in) Test Cycle No. Tmax (kips) Pmax (kips) β w βw Longitudinal Transversea
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)
52 1498 -1833 1.22 1.46 1.78 2.42 2.47 (0.010) a values in parenthesis are for end rotation (rad.)
44
Table 3.8 Specimen 8 Peak Response Quantities
Brace Deformations (in) Test Cycle No. Tmax (kips) Pmax (kips) β w βw Longitudinal Transversea
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)
52 1510 -1780 1.18 1.47 1.73 2.50 2.52 (0.010) a values in parenthesis are for end rotation (rad.)
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
Brace Deformation (in)
-20 -10 0 10 20Normalized Brace Deformation
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
Time (sec) (a) Longitudinal Direction
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.)
(b) Transverse Direction
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
Brace Deformation (in)
-20 -10 0 10 20Normalized Brace Deformation
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.)
(b) Transverse Direction
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
Brace Deformation (in)
-20 -10 0 10 20Normalized Brace Deformation
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
Brace Deformation (in)
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
Brace Deformation (in)
Figure 3.12 Specimen 1: β versus Deformation Level
β (=
P max
/Tm
ax )
Brace Deformation (in)
54
w (=
Tmax
/Pyn
)
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 40.0
0.5
1.0
1.5
2.0
(a) Tension
Cm
ax/P
yn
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
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)
Brace Deformation (in)
Brace Deformation (in)
55
(a) after Standard Test (Overview)
(b) Grinding between Collar and Brace (East End)
Figure 3.14 Specimen 2: Testing Photos
56
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 3.15 Specimen 2: Table Displacement Time Histories (Standard Test)
57
Res
ulta
nt F
orce
(kip
s)
-6 -4 -2 0 2 4 6-600
-400
-200
0
200
400
600
Brace Deformation (in)
-20 -15 -10 -5 0 5 10 15 20Normalized Brace Deformation
Figure 3.16 Specimen 2: Brace Force versus Deformation (Standard Test)
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
)
Figure 3.17 Specimen 2: 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
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
Brace Deformation (in)
Res
ulta
nt F
orce
(kip
s)
Figure 3.19 Specimen 2: 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
Brace Deformation (in)
Figure 3.20 Specimen 2: β versus Deformation Level
β (=
P max
/Tm
ax )
Brace Deformation (in)
60
w (=
Tmax
/Pyn
)
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
Brace Deformation (in)
(a) Tension
Cm
ax/P
yn
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
Brace Deformation (in)
(b) Compression
Figure 3.21 Specimen 2: w and βw versus Deformation Level
w (=
Tm
ax /
P yn)
βw
(= P
max
/ P y
n)
Brace Deformation (in)
Brace Deformation (in)
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
Time (sec) (a) 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.)
(b) Transverse Direction
Figure 3.24 Specimen 3: Table Displacement Time Histories (Standard Test)
63
Res
ulta
nt F
orce
(kip
s)
-6 -4 -2 0 2 4 6-600
-400
-200
0
200
400
600
Brace Deformation (in)
-15 -10 -5 0 5 10 15Normalized Brace Deformation
Figure 3.25 Specimen 3: Brace Force versus Deformation (Standard Test)
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
)
Figure 3.26 Specimen 3: 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
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
Time (sec) (a) Longitudinal Direction
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.)
(b) Transverse Direction
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
Brace Deformation (in)
-15 -10 -5 0 5 10 15Normalized Brace Deformation
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
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 (ra
d.)
(b) Transverse Direction
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
Brace Deformation (in)
-15 -10 -5 0 5 10 15Normalized Brace Deformation
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)
(b) Bottom Strain Gage (Transverse)
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)
(a) North Strain Gage (Longitudinal)
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)
(b) South Strain Gage (Longitudinal)
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
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 3.37 Specimen 3: Table Displacement Time Histories (Low-cycle Fatigue Test No. 2)
73
Res
ulta
nt F
orce
(kip
s)
-6 -4 -2 0 2 4 6-600
-400
-200
0
200
400
600
Brace Deformation (in)
-15 -10 -5 0 5 10 15Normalized Brace Deformation
Figure 3.38 Specimen 3: Brace Force versus Deformation (Low-cycle Fatigue Test No. 2)
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 3.39 Specimen 3: Hysteretic Energy Time History (Low-cycle Fatigue Test No. 2)
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)
(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)
(b) Bottom Strain Gage (Transverse)
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)
(a) North Strain Gage (Longitudinal)
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)
(b) South Strain Gage (Longitudinal)
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)
(a) Longitudinal Direction
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.)
(b) Transverse Direction
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
Brace Deformation (in)
-15 -10 -5 0 5 10 15Normalized Brace Deformation
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
Brace Deformation (in)
Res
ulta
nt F
orce
(kip
s)
Figure 3.45 Specimen 3: 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
Brace Deformation (in)
Figure 3.46 Specimen 3: β versus Deformation Level
β (=
P max
/Tm
ax )
Brace Deformation (in)
79
w (=
Tmax
/Pyn
)
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
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 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
Brace Deformation (in)
(b) Compression
Figure 3.47 Specimen 3: w and βw versus Deformation Level
w (=
Tm
ax /
P yn)
βw
(= P
max
/ P y
n)
Brace Deformation (in)
Brace Deformation (in)
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)
Figure 3.49 Specimen 4: Testing Photos
82
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 3.50 Specimen 4: Table Displacement Time Histories (Standard Test)
83
Res
ulta
nt F
orce
(kip
s)
-6 -4 -2 0 2 4 6-1000
-500
0
500
1000
Brace Deformation (in)
-20 -15 -10 -5 0 5 10 15 20Normalized Brace Deformation
Figure 3.51 Specimen 4: Brace Force versus Deformation (Standard Test)
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
)
Figure 3.52 Specimen 4: 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
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)
(a) Top Strain Gage (Transverse)
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)
(b) Bottom Strain Gage (Transverse)
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)
(a) North Strain Gage (Longitudinal)
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)
(b) South Strain Gage (Longitudinal)
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
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 (ra
d.)
(b) Transverse Direction
Figure 3.55 Specimen 4: Table Displacement Time Histories (Low-cycle Fatigue Test)
87
Res
ulta
nt F
orce
(kip
s)
-6 -4 -2 0 2 4 6-1000
-500
0
500
1000
Brace Deformation (in)
-20 -15 -10 -5 0 5 10 15 20Normalized Brace Deformation
Figure 3.56 Specimen 4: Brace Force versus Deformation (Low-cycle Fatigue Test)
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
)
Figure 3.57 Specimen 4: 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
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)
(a) Top Strain Gage (Transverse)
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)
(b) Bottom Strain Gage (Transverse)
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)
(a) North Strain Gage (Longitudinal)
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)
(b) South Strain Gage (Longitudinal)
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)
(a) Longitudinal Direction
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.)
(b) Transverse Direction
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
Brace Deformation (in)
-20 -15 -10 -5 0 5 10 15 20Normalized Brace Deformation
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
Brace Deformation (in)
Res
ulta
nt F
orce
(kip
s)
Figure 3.63 Specimen 4: 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
Brace Deformation (in)
Figure 3.64 Specimen 4: β versus Deformation Level
β (=
P max
/Tm
ax )
Brace Deformation (in)
93
w (=
Tmax
/Pyn
)
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
Brace Deformation (in)
(a) Tension
Cm
ax/P
yn
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
Brace Deformation (in)
(b) Compression
Figure 3.65 Specimen 4: w and βw versus Deformation Level
w (=
Tm
ax /
P ym)
βw (=
Pm
ax /
P yn)
Brace Deformation (in)
Brace Deformation (in)
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)
(b) after all Tests (West End)
Figure 3.67 Specimen 5: Testing Photos
96
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 (ra
d.)
(b) Transverse Direction
Figure 3.68 Specimen 5: Table Displacement Time Histories (Standard Test)
97
Res
ulta
nt F
orce
(kip
s)
-6 -4 -2 0 2 4 6-1500
-1000
-500
0
500
1000
1500
Brace Deformation (in)
-15 -10 -5 0 5 10 15Normalized Brace Deformation
Figure 3.69 Specimen 5: Brace Force versus Deformation (Standard Test)
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
)
Figure 3.70 Specimen 5: 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
98
Long
itudi
nal D
ispl
acem
ent (
in)
0 200 400 600 800 1000-6
-4
-2
0
2
4
6
Time (sec) (a) Longitudinal Direction
Tran
sver
se D
ispl
acem
ent (
in)
0 200 400 600 800 1000-6
-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 3.71 Specimen 5: Table Displacement Time Histories (Low-cycle Fatigue Test No. 1)
99
Res
ulta
nt F
orce
(kip
s)
-6 -4 -2 0 2 4 6-1500
-1000
-500
0
500
1000
1500
Brace Deformation (in)
-15 -10 -5 0 5 10 15Normalized Brace Deformation
Figure 3.72 Specimen 5: Brace Force versus Deformation (Low-cycle Fatigue Test No. 1)
Dis
sipa
ted
Ene
rgy
(x 1
000
kip-
in),
Eh
0 200 400 600 800 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
)
Figure 3.73 Specimen 5: 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
100
Long
itudi
nal D
ispl
acem
ent (
in)
0 200 400 600 800 1000-6
-4
-2
0
2
4
6
Time (sec)
(a) Longitudinal Direction
Tran
sver
se D
ispl
acem
ent (
in)
0 200 400 600 800 1000-6
-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 3.74 Specimen 5: Table Displacement Time Histories (Low-cycle Fatigue Test No. 2)
101
Res
ulta
nt F
orce
(kip
s)
-6 -4 -2 0 2 4 6-1500
-1000
-500
0
500
1000
1500
Brace Deformation (in)
-15 -10 -5 0 5 10 15Normalized Brace Deformation
Figure 3.75 Specimen 5: Brace Force versus Deformation (Low-cycle Fatigue Test No. 2)
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)
Figure 3.76 Specimen 5: Hysteretic Energy Time History (Low-cycle Fatigue Test No. 2)
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)
(a) Longitudinal Direction
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.)
(b) Transverse Direction
Figure 3.77 Specimen 5: Table Displacement Time Histories (All Tests Combined)
103
Res
ulta
nt F
orce
(kip
s)
-6 -4 -2 0 2 4 6-1500
-1000
-500
0
500
1000
1500
Brace Deformation (in)
-15 -10 -5 0 5 10 15Normalized Brace Deformation
Figure 3.78 Specimen 5: Brace Force versus Deformation (All Tests Combined)
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
)
Figure 3.79 Specimen 5: 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
104
-6 -4 -2 0 2 4 6-1500
-1000
-500
0
500
1000
1500
Brace Deformation (in)
Res
ulta
nt F
orce
(kip
s)
Figure 3.80 Specimen 5: 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
Brace Deformation (in)
Figure 3.81 Specimen 5: β versus Deformation Level
β (=
P max
/Tm
ax )
Brace Deformation (in)
105
w (=
Tmax
/Pyn
)
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
Brace Deformation (in)
(a) Tension
Cm
ax/P
yn
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
Brace Deformation (in)
(b) Compression
Figure 3.82 Specimen 5: w and βw versus Deformation Level
w (=
Tm
ax /
P yn)
βw
(= P
max
/ P y
n)
Brace Deformation (in)
Brace Deformation (in)
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
Rotation from Inclinometer (rad) Figure 3.83 Specimen 5: End Rotation Comparison
107
(a) before Standard Test (Overview)
(b) after all Tests (East End)
Figure 3.84 Specimen 6: Testing Photos
108
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 3.85 Specimen 6: Table Displacement Time Histories (Standard Test)
109
Res
ulta
nt F
orce
(kip
s)
-6 -4 -2 0 2 4 6-1500
-1000
-500
0
500
1000
1500
Brace Deformation (in)
-20 -15 -10 -5 0 5 10 15 20Normalized Brace Deformation
Figure 3.86 Specimen 6: Brace Force versus Deformation (Standard Test)
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
)
Figure 3.87 Specimen 6: 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
110
Long
itudi
nal D
ispl
acem
ent (
in)
0 200 400 600 800 1000-6
-4
-2
0
2
4
6
Time (sec)
(a) Longitudinal Direction
Tran
sver
se D
ispl
acem
ent (
in)
0 200 400 600 800 1000-6
-4
-2
0
2
4
6
Time (sec)
-0.02
-0.01
0.0
0.01
0.02
End
Rot
atio
n (ra
d.)
(b) Transverse Direction
Figure 3.88 Specimen 6: Table Displacement Time Histories (Low-cycle Fatigue Test)
111
Res
ulta
nt F
orce
(kip
s)
-6 -4 -2 0 2 4 6-1500
-1000
-500
0
500
1000
1500
Brace Deformation (in)
-20 -15 -10 -5 0 5 10 15 20Normalized Brace Deformation
Figure 3.89 Specimen 6: Brace Force versus Deformation (Low-cycle Fatigue Test)
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
)
Figure 3.90 Specimen 6: 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
112
Long
itudi
nal D
ispl
acem
ent (
in)
0 500 1000 1500 2000-6
-4
-2
0
2
4
6
Time (sec)
(a) Longitudinal Direction
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.)
(b) Transverse Direction
Figure 3.91 Specimen 6: Table Displacement Time Histories (All Tests Combined)
113
Res
ulta
nt F
orce
(kip
s)
-6 -4 -2 0 2 4 6-1500
-1000
-500
0
500
1000
1500
Brace Deformation (in)
-20 -15 -10 -5 0 5 10 15 20Normalized Brace Deformation
Figure 3.92 Specimen 6: Brace Force versus Deformation (All Tests Combined)
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)
Figure 3.93 Specimen 6: 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
114
-6 -4 -2 0 2 4 6-1500
-1000
-500
0
500
1000
1500
Brace Deformation (in)
Res
ulta
nt F
orce
(kip
s)
Figure 3.94 Specimen 6: 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
Brace Deformation (in)
Figure 3.95 Specimen 6: β versus Deformation Level
β (=
P max
/Tm
ax )
Brace Deformation (in)
115
w (=
Tmax
/Pyn
)
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
Brace Deformation (in)
(a) Tension
Cm
ax/P
yn
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
Brace Deformation (in)
(b) Compression
Figure 3.96 Specimen 6: w and βw versus Deformation Level
w (=
Tm
ax /
P yn)
βw
(= P
max
/ P y
n)
Brace Deformation (in)
Brace Deformation (in)
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
Rotation from Inclinometer (rad) Figure 3.97 Specimen 6: End Rotation Comparison
117
(a) during Low- Cycle Fatigue Test (Overview)
(b) Knife Plate after all Tests (West End)
Figure 3.98 Specimen 7: Testing Photos
118
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) (a) 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.)
(b) Transverse Direction
Figure 3.99 Specimen 7: Table Displacement Time Histories (Standard Test)
119
-6 -4 -2 0 2 4 6-2000
-1000
0
1000
2000R
esul
tant
For
ce (k
ips)
Brace Deformation (in)
-15 -10 -5 0 5 10 15Normalized Brace Deformation
Figure 3.100 Specimen 7: Brace Force versus Deformation (Standard Test)
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
)
Figure 3.101 Specimen 7: 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
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
Time (sec) (a) Longitudinal Direction
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.)
(b) Transverse Direction
Figure 3.104 Specimen 7: Table Displacement Time Histories (Low-cycle Fatigue Test No. 1)
123
-6 -4 -2 0 2 4 6-2000
-1000
0
1000
2000R
esul
tant
For
ce (k
ips)
Brace Deformation (in)
-15 -10 -5 0 5 10 15Normalized Brace Deformation
Figure 3.105 Specimen 7: Brace Force versus Deformation (Low-cycle Fatigue Test No. 1)
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
)
Figure 3.106 Specimen 7: 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
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
Time (sec) (a) Gage A (Longitudinal)
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)
(b) Gage B (Longitudinal)
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)
(a) Gage R1 (Longitudinal)
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)
(b) Gage R2 (Transverse)
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)
(a) Longitudinal Direction
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.)
(b) Transverse Direction
Figure 3.109 Specimen 7: Table Displacement Time Histories (Low-cycle Fatigue Test No. 2)
127
-6 -4 -2 0 2 4 6-2000
-1000
0
1000
2000R
esul
tant
For
ce (k
ips)
Brace Deformation (in)
-15 -10 -5 0 5 10 15Normalized Brace Deformation
Figure 3.110 Specimen 7: Brace Force versus Deformation (Low-cycle Fatigue Test No. 2)
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
)
Figure 3.111 Specimen 7: Hysteretic Energy Time History (Low-cycle Fatigue Test No. 2)
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
Time (sec) (a) Gage A (Longitudinal)
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)
(b) Gage B (Longitudinal)
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)
(a) Gage R1 (Longitudinal)
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)
(b) Gage R2 (Transverse)
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)
(a) Longitudinal Direction
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.)
(b) Transverse Direction
Figure 3.114 Specimen 7: Table Displacement Time Histories (All Tests Combined)
131
-6 -4 -2 0 2 4 6-2000
-1000
0
1000
2000R
esul
tant
For
ce (k
ips)
Brace Deformation (in)
-15 -10 -5 0 5 10 15Normalized Brace Deformation
Figure 3.115 Specimen 7: Brace Force versus Deformation (All Tests Combined)
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
)
Figure 3.116 Specimen 7: 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
132
-6 -4 -2 0 2 4 6-2000
-1000
0
1000
2000
Brace Deformation (in)
Res
ulta
nt F
orce
(kip
s)
Figure 3.117 Specimen 7: 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
Brace Deformation (in)
Figure 3.118 Specimen 7: β versus Deformation Level
β (=
P max
/Tm
ax )
Brace Deformation (in)
133
w (=
Tmax
/Pyn
)
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
Brace Deformation (in)
(a) Tension
Cm
ax/P
yn
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
Brace Deformation (in)
(b) Compression
Figure 3.119 Specimen 7: w and βw versus Deformation Level
w (=
Tm
ax /
P yn)
βw
(= P
max
/ P y
n)
Brace Deformation (in)
Brace Deformation (in)
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
Rotation from Inclinometer (rad) Figure 3.120 Specimen 7: End Rotation Comparison
135
(a) before Standard Test (Overview)
(b) after all Tests (West End)
Figure 3.121 Specimen 8: Testing Photos
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.)
(b) Transverse Direction
Figure 3.122 Specimen 8: Table Displacement Time Histories (Standard Test)
137
-6 -4 -2 0 2 4 6-2000
-1000
0
1000
2000R
esul
tant
For
ce (k
ips)
Brace Deformation (in)
-20 -15 -10 -5 0 5 10 15 20Normalized Brace Deformation
Figure 3.123 Specimen 8: Brace Force versus Deformation (Standard Test)
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
)
Figure 3.124 Specimen 8: 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
138
Long
itudi
nal D
ispl
acem
ent (
in)
0 100 200 300 400 500-6
-4
-2
0
2
4
6
Time (sec)
(a) Longitudinal Direction
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.)
(b) Transverse Direction
Figure 3.125 Specimen 8: Table Displacement Time Histories (Low-cycle Fatigue Test No. 1)
139
-6 -4 -2 0 2 4 6-2000
-1000
0
1000
2000R
esul
tant
For
ce (k
ips)
Brace Deformation (in)
-20 -15 -10 -5 0 5 10 15 20Normalized Brace Deformation
Figure 3.126 Specimen 8: Brace Force versus Deformation (Low-cycle Fatigue Test No. 1)
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
)
Figure 3.127 Specimen 8: 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
140
Long
itudi
nal D
ispl
acem
ent (
in)
0 100 200 300 400 500-6
-4
-2
0
2
4
6
Time (sec)
(a) Longitudinal Direction
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.)
(b) Transverse Direction
Figure 3.128 Specimen 8: Table Displacement Time Histories (Low-cycle Fatigue Test No. 2)
141
-6 -4 -2 0 2 4 6-2000
-1000
0
1000
2000R
esul
tant
For
ce (k
ips)
Brace Deformation (in)
-20 -15 -10 -5 0 5 10 15 20Normalized Brace Deformation
Figure 3.129 Specimen 8: Brace Force versus Deformation (Low-cycle Fatigue Test No. 2)
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
)
Figure 3.130 Specimen 8: Hysteretic Energy Time History (Low-cycle Fatigue Test No. 2)
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)
(a) Longitudinal Direction
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.)
(b) Transverse Direction
Figure 3.131 Specimen 8: Table Displacement Time Histories (All Tests Combined)
143
-6 -4 -2 0 2 4 6-2000
-1000
0
1000
2000R
esul
tant
For
ce (k
ips)
Brace Deformation (in)
-20 -15 -10 -5 0 5 10 15 20Normalized Brace Deformation
Figure 3.132 Specimen 8: Brace Force versus Deformation (All Tests Combined)
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
)
Figure 3.133 Specimen 8: 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
144
-6 -4 -2 0 2 4 6-2000
-1000
0
1000
2000
Brace Deformation (in)
Res
ulta
nt F
orce
(kip
s)
Figure 3.134 Specimen 8: 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
Brace Deformation (in)
Figure 3.135 Specimen 8: β versus Deformation Level
β (=
P max
/Tm
ax )
Brace Deformation (in)
145
w (=
Tmax
/Pyn
)
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
Brace Deformation (in)
(a) Tension
Cm
ax/P
yn
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
Brace Deformation (in)
(b) Compression
Figure 3.136 Specimen 8: w and βw versus Deformation Level
w (=
Tm
ax /
P yn)
βw
(= P
max
/ P y
n)
Brace Deformation (in)
Brace Deformation (in)
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
Rotation from Inclinometer (rad) Figure 3.137 Specimen 8: End Rotation Comparison
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)
Brace Deformation (in)
-15 -10 -5 0 5 10 15Normalized Brace Deformation
(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)
Brace Deformation (in)
-15 -10 -5 0 5 10 15Normalized Brace Deformation
(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
(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
158
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
1.404
Dby 5Dby
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
1.365
Dby 5Dby
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
1.299
Dby 5Dby
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
1.356
Dby 5Dby
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
1.316
Dby 5Dby
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
1.323
Dby 5Dby
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
1.289
Dby 5Dby
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
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
)
(a) Specimen 1 (b) Specimen 2
(c) Specimen 3 (d) Specimen 4
(e) Specimen 5 (f) Specimen 6
(g) Specimen 7 (h) Specimen 8
159
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
1.407
Dby 5Dby
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
1.366
Dby 5Dby
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
1.313
Dby 5Dby
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
1.381
Dby 5Dby
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
1.33
Dby 5Dby
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
1.348
Dby 5Dby
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.0
0.5
1.0
1.5
2.0
1.333
Dby 5Dby
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
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
)
(a) Specimen 1 (b) Specimen 2
(c) Specimen 3 (d) Specimen 4
(e) Specimen 5 (f) Specimen 6
(g) Specimen 7 (h) Specimen 8
160
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.00.20.40.60.81.01.21.41.6
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.00.20.40.60.81.01.21.41.6
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.00.20.40.60.81.01.21.41.6
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.00.20.40.60.81.01.21.41.6
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.00.20.40.60.81.01.21.41.6
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.00.20.40.60.81.01.21.41.6
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.00.20.40.60.81.01.21.41.6
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
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
)
(a) Specimen 1 (b) Specimen 2
(c) Specimen 3 (d) Specimen 4
(e) Specimen 5 (f) Specimen 6
(g) Specimen 7 (h) Specimen 8
161
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.00.20.40.60.81.01.21.41.6
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.00.20.40.60.81.01.21.41.6
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.00.20.40.60.81.01.21.41.6
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.00.20.40.60.81.01.21.41.6
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.00.20.40.60.81.01.21.41.6
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.00.20.40.60.81.01.21.41.6
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
0.00.20.40.60.81.01.21.41.6
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
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
)
(a) Specimen 1 (b) Specimen 2
(c) Specimen 3 (d) Specimen 4
(e) Specimen 5 (f) Specimen 6
(g) Specimen 7 (h) Specimen 8
162
Figure 4.9 Model for the Calculation of the Effective Viscous Damping
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
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
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
010203040506070
Brace Deformation (in)
(a) Specimen 1
c = 27.69
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
010203040506070
Brace Deformation (in)
(b) Specimen 2
c = 28.12
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
010203040506070
Brace Deformation (in)
(c) Specimen 3
c = 28.85
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
010203040506070
Brace Deformation (in)
(d) Specimen 4
c = 29
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
010203040506070
Brace Deformation (in)
(e) Specimen 5
c = 29.82
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
010203040506070
Brace Deformation (in)
(f) Specimen 6
c = 30.65
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
010203040506070
Brace Deformation (in)
(g) Specimen 7
c = 31.14
0 2 4 6 8 10 12 14 16Normalized Brace Deformation
0 1 2 3 4Brace Deformation (in)
010203040506070
Brace Deformation (in)
(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)(