SUBASSEMBLAGE TESTING OF STAR SEISMIC BUCKLING-RESTRAINED BRACES

STRUCTURAL SYSTEMS RESEARCH PROJECT Report No. TR-23/4 SUBASSEMBLAGE TESTING OF STAR SEISMIC BUCKLING-RESTRAINED BRACES by STEVE MERRITT CHIA-MING UANG GIANMARIO BENZONI Final Report to Star Seismic, LLC. May 23 Department of Structural Engineering University of California, San Diego La Jolla, California 9293-85

University of California, San Diego Department of Structural Engineering Structural Systems Research Project Report No. TR-23/4 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 9293-85 May 23

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.13 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 1.5D bm 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 1.5D bm 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 9 and 6, respectively. The other six specimens that did not experience any fracture were tested to η values of between 9 and 1,65, with the average being 1,18. This value is significantly higher than that (14) required by the proposed SEAOC-AISC Recommended Provisions for uniaxial testing. i

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. ii

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... 3 4. COMPARISON OF TEST RESULTS... 147 4.1 Fracture Mode... 147 4.2 Correction for Pinhole Elongation... 147 4.3 Hysteretic Energy, E h, and Cumulative Inelastic Deformation, η... 148 4.4 Tension Strength Adjustment Factor, w... 148 4.5 Compression Strength Adjustment Factor, β... 149 iii

4.6 Comparison at the SEAOC-AISC Limit State... 149 4.7 Equivalent Viscous Damping... 15 5. SUMMARY AND CONCLUSIONS... 164 5.1 Summary... 164 5.2 Conclusions... 164 REFERENCES... 166 iv

LIST OF TABLES Table 2.1 Specimen Dimensions... 1 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... 4 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 1.5D bm (=7.5D by )... 153 v

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... 2 Figure 2.1 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)... 5 Figure 3.7 Specimen 1: Hysteretic Energy Time History (Low-cycle Fatigue Test)... 5 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 3.1 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 vi

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 3.2 Specimen 2: β versus Deformation Level... 59 Figure 3.21 Specimen 2: w and βw versus Deformation Level... 6 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 3.3 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)... 7 Figure 3.36 Specimen 3: HSS Strain Gage Time Histories (Low-cycle Fatigue Test No. 1)... 71 vii

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 3.4 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... 8 Figure 3.49 Specimen 4: Testing Photos... 81 Figure 3.5 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 3.6 Specimen 4: Table Displacement Time Histories (Both Tests Combined)... 9 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 viii

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 3.7 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)... 1 Figure 3.75 Specimen 5: Brace Force versus Deformation (Low-cycle Fatigue Test No. 2)... 11 Figure 3.76 Specimen 5: Hysteretic Energy Time History (Low-cycle Fatigue Test No. 2)... 11 Figure 3.77 Specimen 5: Table Displacement Time Histories (All Tests Combined)... 12 Figure 3.78 Specimen 5: Brace Force versus Deformation (All Tests Combined)... 13 Figure 3.79 Specimen 5: Hysteretic Energy Time History (All Tests Combined)... 13 Figure 3.8 Specimen 5: Brace Response Envelope... 14 Figure 3.81 Specimen 5: β versus Deformation Level... 14 Figure 3.82 Specimen 5: w and βw versus Deformation Level... 15 Figure 3.83 Specimen 5: End Rotation Comparison... 16 Figure 3.84 Specimen 6: Testing Photos... 17 Figure 3.85 Specimen 6: Table Displacement Time Histories (Standard Test)... 18 Figure 3.86 Specimen 6: Brace Force versus Deformation (Standard Test)... 19 Figure 3.87 Specimen 6: Hysteretic Energy Time History (Standard Test)... 19 ix

Figure 3.88 Specimen 6: Table Displacement Time Histories (Low-cycle Fatigue Test)... 11 Figure 3.89 Specimen 6: Brace Force versus Deformation (Low-cycle Fatigue Test)... 111 Figure 3.9 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 3.1 Specimen 7: Brace Force versus Deformation (Standard Test)... 119 Figure 3.11 Specimen 7: Hysteretic Energy Time History (Standard Test)... 119 Figure 3.12 Specimen 7: Gusset Longitudinal Strain Gage Time Histories (Standard Test)... 12 Figure 3.13 Specimen 7: Gusset Rosette Strain Gage Time Histories (Standard Test)... 121 Figure 3.14 Specimen 7: Table Displacement Time Histories (Low-cycle Fatigue Test No. 1)... 122 Figure 3.15 Specimen 7: Brace Force versus Deformation (Low-cycle Fatigue Test No. 1)... 123 Figure 3.16 Specimen 7: Hysteretic Energy Time History (Low-cycle Fatigue Test No. 1)... 123 Figure 3.17 Specimen 7: Gusset Longitudinal Strain Gage Time Histories (Low-cycle Fatigue Test No. 1)... 124 Figure 3.18 Specimen 7: Gusset Rosette Strain Gage Time Histories (Low-cycle Fatigue Test No. 1)... 125 Figure 3.19 Specimen 7: Table Displacement Time Histories (Low-cycle Fatigue Test No. 2)... 126 Figure 3.11 Specimen 7: Brace Force versus Deformation (Low-cycle Fatigue Test No. 2)... 127 x

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)... 13 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 3.12 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)... 14 Figure 3.129 Specimen 8: Brace Force versus Deformation (Low-cycle Fatigue Test No. 2)... 141 Figure 3.13 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 xi

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: E h and η Time Histories... 156 Figure 4.4 All Specimens: E h 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... 16 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 4.1 All Specimens combined: Equivalent Viscous Damping (Corrected)... 162 Figure 4.11 All Specimens individually: Equivalent Viscous Damping (Corrected)... 163 xii

LIST OF SYMBOLS A yz D bm D by E h E s F ya F yn F ua L1 L b L yz P * y P P max Area of yielding element Deformation of brace in region L1 at Design Story Drift Deformation of brace in region L1 when steel core first yields Total hysteretic energy dissipated by brace Young s modulus of elasticity of steel Measured yield strength of steel core (average of coupon tests) Nominal yield strength of steel core Measured tensile strength of steel core (average of coupon tests) Brace length defined in Figure 2.12(a) for calculating end rotation Total length of brace Length of yielding element Effective yield force Actual resultant brace force Maximum compression force P ya Actual yield force, F ya A yz P yn Nominal yield force, F yn A yz R y T max w Material overstrength factor, F ya /F yn Maximum tensile force Tension strength adjustment factor, T max /P yn w * β Tension strength adjustment factor at 5D by Compression strength adjustment factor, P max /T max xiii

max min Actual brace deformation recorded by linear transducer L1 Maximum axial deformation of brace in tension (end to end of brace) Minimum axial deformation of brace in compression η Cumulative inelastic axial force deformation capacity, E h /(D by P * y) xiv

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 21, Shuhaibar et al. 22), 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 21), 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. 1

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, F yn, of 36 ksi, was specified for the steel core plates, and A5 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 (F ya ), the values of material overstrength factor, R y (=F ya /F yn ), and the brace yield forces are calculated and listed in Table 2.3. The specified 28-day concrete strength was 3,5 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 2

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 21), 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 D by, (2) 4 cycles of loading at the deformation corresponding to.5d bm, (3) 4 cycles of loading at the deformation corresponding to 1.D bm, (4) 2 cycles of loading at the deformation corresponding to 1.5D bm, and (5) Additional complete cycles of loading at the deformation corresponding to 1.D bm as required for the Brace Test Specimen to achieve a cumulative inelastic axial deformation of at least 14 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: D by 3

and D bm. D by is defined as the axial deformation at first significant yield of the specimen, and D bm 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.D bm, five cycles at 2.D bm and two cycles each at 2.5D bm and 3.D bm. 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 35 times the yield deformation at this deformation level. The calculation of D by 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 - (252 inches) for all specimens. To establish the value of D by, the following components were considered at the actual yield force level, P ya : (1) yield deformation of the steel core plates in the yielding length, L yz [see Figure 2.2(a) and Table 2.1 for L yz ], and (2) elastic deformation of the steel core plates outside the yielding length, L yz. This includes L kp and L tz on each end of the steel core plates. With a calculated D by 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 4,9 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 D bm needs not be taken as greater than 5D by (SEAOC-AISC 21). 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). 4

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 inphase 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 2.1 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.D bm ) required by SEAOC-AISC for uni-axial low-cycle fatigue testing. Highamplitude 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-degreeof-freedom system for a buckling-restrained braced frame is shown in Figure 2.11(b). 5

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 D by 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. 6

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: Tmax Tmax w = = (2.1) P F A yn yn yz where F yn = nominal yield strength, and A yz = 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 21): Pmax β = (2.2) Tmax where P max is the maximum compressive force, and T max is the maximum tension force corresponding to a brace deformation of 1.5D bm. Note that, for capacity design, the product of β and w represents the overstrength of the brace in compression beyond its nominal yield strength. 7

Hysteretic Energy, E h The area enclosed by the P versus hysteresis loops represents the hysteretic energy dissipated by the brace: E h = P d (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 bilinear hysteresis loop, the cumulative inelastic axial deformation, pi, is defined as: where + P y and + + Ehi Ehi pi = pi + pi = + + Py Py E pi (2.4) P hi * y P y are the effective yield forces of the brace in tension and compression, and * P y is the average value. The effective yield force is defined herein as follows: where P * = w (2.5) * y P yn * w is the tension strength adjustment factor defined in Eq. (2.1) at a deformation level of 5D by, which is the default value for D bm per SEAOC-AISC (21). Because there may not be data points exactly at the value of 5D by 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 5D by ; this is referred to as Zone 2. Then a line was drawn from the point (D by, R y ) to the intersection of the least squares fit and 5D by 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: Ehi Eh p = pi = = (2.6) * * Py Py p can be normalized by the yield deformation of the brace, D by, for the cumulative inelastic axial deformation capacity, η: p Eh η = = (2.7) * Dby Py Dby For uni-axial testing of buckling-restrained braces, the proposed SEAOC-AISC Provisions (21) requires that the value of η be at least 14. Although this requirement is not needed 8

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. 9

Table 2.1 Specimen Dimensions (a) Member Core Geometry Steel Core plates Specimen Transition Zone Yielding Zone No. of plates t cp (in) b tz (in) L tz (in) b yz (in) L yz (in) 1 2.75 1 23. 2.53 176. 2 2.75 1 21.28 3.97 179.4 3 2.75 1 19.36 5.56 183.3 4 2 1. 1 18.44 6.33 185.1 5 4.75 1 18.89 5.95 184.2 6 6.75 1 21.28 3.97 179.4 7 6.75 1 18.41 6.34 185.2 8 8.75 1 2.33 4.77 181.3 (b) HSS and Collar Configurations Specimen HSS Configuration Collar Plate Size 1 one-12 1 3 / 8 3 / 8 36 long 2 one -12 1 3 / 8 3 / 8 36 long 3 one -12 1 3 / 8 3 / 8 36 long 4 one -12 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 6 long 7 two-12 8 1 / 2, 1-12 12 1 / 2 3 / 4 6 long 8 four-12 8 1 / 2 3 / 4 6 long (c) Member End Geometry Specimen Knife Plate End Plate t kp (in) b kp (in) L kp (in) t ep (in) 1 1.5 14.5 14. 1. 2 1.5 14.5 14. 1. 3 1.5 14.5 13. 2. 4 1.5 14.5 13. 2. 5 1.5 18.5 12. 3. 6 1.5 22. 12. 3. 7 1.5 22. 12. 3. 8 1.5 22. 12. 3. 1

Specimens Heat No. a Coupon No. 1,2,3,5,6,7 325-4268 4 325-4272 a Nucor Bar Mill-Jewett Table 2.2 Mechanical Properties of Steel Core Plates Yield Strength (ksi) Tensile Strength (ksi) Yield Ratio c Elong. d (%) 1 39.6 61.8.64 27 2 4.2 64.3.63 26 3 44. 64.7.68 27 (4) b (42.4) (62.1) (.68) (24) (5) (43.6) (63.) (.69) (27) 1 37.8 67.8.56 26 2 37.7 68.1.55 26 3 38.3 68.6.56 21 (4) (41.6) (63.1) (.66) (24) (5) (42.2) (63.5) (.66) (23) b Material properties from Certified Mill Test Report are provided in parenthesis. c Yield Ratio = Yield Strength / Tensile Strength d Based on 2-in. gage length; mill certificate value based on 8-in gage length. Table 2.3 Member Properties Specimen F ya (ksi) A yz (in 2 ) P yn (kips) P ya (kips) R y D by (in) 1 42. 3.8 137 16 1.17.275 2 42. 5.96 215 25 1.17.29 3 42. 8.34 3 35 1.17.34 4 39.5 12.66 456 5 1.1.294 5 42. 17.85 643 75 1.17.311 6 42. 17.87 643 75 1.17.294 7 42. 28.53 127 1198 1.17.311 8 42. 28.62 13 122 1.17.3 11

Table 2.4 Shake Table Peak Input Displacements (a) Standard Loading Protocol Specimen Longitudinal Movement (in) Transverse Movement (in) Number of Cycles Number of Cycles 6 4 4 2 1 5 2 2 6 4 4 2 1 5 2 2 1.44.9 1.69 2.5 1.69 3.1 3.1 3.55.4.85 1.65 2.45 1.65 3.5 3.5 4. 2.46.91 1.72 2.52 1.72 3.22 3.78 4.48.4.85 1.65 2.45 1.65 3.15 3.7 4. 3.48.94 1.75 2.55 1.75 3.41 - -.4.85 1.65 2.45 1.65 3.3 - - 4.52.97 1.78 2.59 1.78 3.2 3.96 4.66.4.85 1.65 2.45 1.65 3.5 3.8 4. 5.58 1.3 1.84 2.66 1.84 3.57 4.23 5.5.4.85 1.65 2.45 1.65 3.35 4. 4. 6.58 1.3 1.84 2.66 1.84 3.27 3.98 4.75.4.85 1.65 2.45 1.65 3.5 3.75 4. 7.68 1.14 1.97 2.8 1.97 3.84 - -.4.85 1.65 2.45 1.65 3.45 - - 8.68 1.14 1.97 2.81 1.97 3.64 - -.4.85 1.65 2.45 1.65 3.25 - - (b) Low-cycle Fatigue Loading Protocol Specimen Cycles Longitudinal Movement (in) Transverse Movement (in) 1 3 1.69 1.65 2 3 1.72 1.65 3 * 25 2.39 2.25 4 25 2.39 2.25 5 3 1.85 1.65 6 3 1.85 1.65 7 15 2.86 2.5 8 15 2.86 2.5 * 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 16 November 19, 22 1 st 2 25 November 2, 22 2 nd 3 35 November 21, 22 6 th 4 5 November 21, 22 5 th 5 75A November 2, 22 3 rd 6 75B November 2, 22 4 th 7 12A November 25, 22 8 th 8 12B November 22, 22 7 th 12

(a) End View (b) Top view Figure 2.1 All Specimens prior to Testing 13

(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 14

(a) Specimen 1 (b) Specimen 2 (c) Specimen 3 (d) Specimen 4 Figure 2.3 Sections at Midspan (Specimens 1 to 4) 15

(a) Specimen 5 (b) Specimen 6 (c) Specimen 7 (d) Specimen 8 Figure 2.4 Sections at Midspan (Specimens 5 to 8) 16

(a) Three-Dimensional Rendering Reaction Block Adapting Brackets Specimen (Brace) Reaction Wall (Not shown) Platen (Shake Table) Collars Pin Connections (b) Setup Overview Figure 2.5 SRMD Facility 17

NORTH North Gage South Gauge Top Gage Bottom Gage (a) Specimen 3 Top Gage South Gage North Gage NORTH (b) Specimen 4 Figure 2.6 Overall View of Specimens and SRMD (Strain Gage Locations also Shown) 18

Figure 2.7 Typical Wall End Support (West End) Gage A Gage B Gage R1 Gage R2 Figure 2.8 Gusset Plate at West End (Strain Gages of Specimen 7 also shown) 19

6 4 SEAOC-AISC OSHPD Brace Deformation Brace Deformation 2 1.5D by.5d bm -2 1.D bm -4-6 2 4 6 8 (a) Longitudinal Direction * 6 4 2-2 1.5Dbm 2.D bm 2.5Dbm 3.Dbm -4-6 2 4 6 8 (b) Transverse Direction * *See Table 2.4(a) for Peak Values and Cycle Variations Figure 2.9 Standard Loading Sequence 2

6 4 Brace Deformation 2-2 1.D bm -4-6 2 4 6 8 1 (a) Longitudinal Direction * 6 4 Brace Deformation 2-2 -4-6 2 4 6 8 1 (b) Transverse Direction * * See Table 2.4(b) for Peak Values and Cycle Variations Figure 2.1 Sample Low-cycle Fatigue Loading Sequence (for Specimen 1) 21

.4 Ground Acceleration (g).2. -.2 -.4 -.6 1 2 3 4 (a) Fault Normal Ground Acceleration Time History θ W = 1,1 kips K = 2 kips/in T =.75 sec C y =.225 (Yield Coeff.) ζ = 2% θ = 45 degrees (b) Equivalent Single-degree-of-freedom System 5 Table Displacement (in.) 4 3 2 1-1 -2 1 2 3 4 (c) Longitudinal Brace Displacement Time History Figure 2.11 Simulated Sylmar Response Loading Sequence 22

L2 L4 L3 L1 Shake Table (a) Location of Displacement Transducers Inclinometer Displacement Transducers (b) Displacement Transducers Figure 2.12 Displacement Transducer Instrumentation 23

P + pi + P y Area = + E hi P ya Area = E hi pi P y Actual response Idealized response Figure 2.13 Hysteresis Loop in the i-th Cycle 2. 2 4 6 8 1 12 14 16 Zone 1 Zone 2 w (= Tmax / Pyn) 1.5 1. R y w *.5. D by 5D by 1 2 3 4 Figure 2.14 Procedure for Calculating w * 24

4-2 -1 1 2 * P y Resultant Force (kips) 2-2 P ya P yn -4-6 -4-2 2 4 6 Figure 2.15 Comparison of Yield Force Definitions 25

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 /D by. (3) Hysteretic energy (E h ) 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 26

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 18 th 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 3.1, (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 27

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 3.2 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 3.4, and Figure 3.41 for the Low-cycle Fatigue Tests. In the plots, normalized strain is defined as ε/ε y where ε y is based on the nominal yield strength (46 ksi for the HSS and 5 ksi for the collar). The gages on the north and south sides of the HSS exhibited maximum longitudinal strains of less than.2ε y. 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.2ε y and the maximum transverse 28

strain in the bottom was less than.5ε y. 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 3.5 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 3.6 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 3.7, 29

(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 3.8, (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 3.9, (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 3.13, (2) Low-cycle fatigue tests: Figure 3.14 to Figure 3.113, (3) Combined test results: Figure 3.114 to Figure 3.116, 3

(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 3.12. 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 3.13, (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. 31

Table 3.1 Specimen 1 Peak Response Quantities Test Cycle No. T max (kips) P max (kips) β w βw Brace Deformations (in) Longitudinal Transverse a 1 173-172.99 1.27 1.25.42.41 (.2) 2 168-17 1.1 1.23 1.24.41.41 (.2) 3 163-169 1.3 1.19 1.23.41.41 (.2) 4 174-168.97 1.27 1.24.41.41 (.2) 5 167-168 1.1 1.22 1.23.41.41 (.2) 6 166-169 1.2 1.22 1.24.41.41 (.2) 7 17-176 1.4 1.24 1.29.87.87 (.3) 8 171-176 1.3 1.25 1.29.87.87 (.3) 9 173-177 1.3 1.27 1.3.86.87 (.3) 1 169-179 1.6 1.24 1.31.87.87 (.3) 11 181-222 1.23 1.32 1.63 1.69 1.66 (.7) 12 193-213 1.1 1.41 1.55 1.69 1.68 (.7) 13 199-216 1.8 1.46 1.57 1.69 1.68 (.7) 14 21-218 1.8 1.47 1.59 1.69 1.68 (.7) 15 23-237 1.16 1.49 1.72 2.5 2.49 (.1) 16 214-24 1.12 1.57 1.75 2.5 2.49 (.1) 17 211-224 1.6 1.54 1.64 1.69 1.68 (.7) 18 211-256 1.22 1.54 1.88 3.13 3.1 (.12) 19 221-257 1.16 1.62 1.88 3.13 3.1 (.12) 2 222-258 1.16 1.62 1.88 3.13 3.1 (.12) 21 221-259 1.17 1.62 1.89 3.13 3.1 (.12) 22 221-262 1.18 1.62 1.91 3.13 3.1 (.12) 23 227-285 1.26 1.66 2.9 3.6 3.55 (.14) 24 232-294 1.27 1.7 2.16 3.6 3.55 (.14) 25 234-345 1.48 1.71 2.53 4.31 4.5 (.16) 26 239-342 1.43 1.75 2.5 4.3 4.5 (.16) 27 262-262 1. 1.92 1.92 1.69 1.67 (.7) 28 239-253 1.6 1.75 1.85 1.69 1.67 (.7) 29 234-249 1.6 1.71 1.82 1.69 1.67 (.7) 3 225-244 1.8 1.65 1.78 1.69 1.68 (.7) 31 223-242 1.9 1.63 1.78 1.68 1.68 (.7) 32 218-244 1.12 1.6 1.79 1.68 1.68 (.7) 33 216-245 1.13 1.58 1.79 1.68 1.68 (.7) 34 214-238 1.11 1.57 1.74 1.68 1.68 (.7) 35 214-241 1.13 1.57 1.77 1.69 1.68 (.7) 36 214-237 1.11 1.57 1.74 1.69 1.68 (.7) 37 216-244 1.13 1.58 1.79 1.69 1.67 (.7) 38 212-235 1.11 1.55 1.72 1.69 1.67 (.7) 39 21-243 1.15 1.54 1.77 1.69 1.67 (.7) 4 21-236 1.13 1.54 1.74 1.69 1.68 (.7) 41 217-234 1.8 1.59 1.72 1.69 1.67 (.7) 42 28-236 1.14 1.52 1.74 1.69 1.68 (.7) 43 28-236 1.13 1.52 1.72 1.69 1.67 (.7) 44 27-243 1.18 1.52 1.79 1.69 1.68 (.7) Standard Loading Protocol Low-cycle Fatigue a values in parenthesis are for end rotation (rad.) 32

Table 3.2 Specimen 2 Peak Response Quantities Test Cycle No. T max (kips) P max (kips) β w βw Brace Deformations (in) Longitudinal Transverse a 1 266-265 1. 1.24 1.24.43.41 (.2) 2 257-258 1. 1.2 1.2.42.41 (.2) 3 259-258 1. 1.21 1.21.42.41 (.2) 4 265-256.96 1.24 1.19.42.41 (.2) 5 264-26.98 1.23 1.21.42.41 (.2) 6 255-264 1.4 1.19 1.24.42.41 (.2) 7 271-272 1. 1.26 1.26.88.87 (.3) 8 258-271 1.5 1.2 1.26.87.87 (.3) 9 257-273 1.6 1.2 1.27.87.87 (.3) 1 258-275 1.6 1.2 1.28.87.87 (.3) 11 275-316 1.15 1.28 1.48 1.7 1.68 (.7) 12 294-324 1.1 1.37 1.51 1.69 1.68 (.7) 13 33-329 1.9 1.41 1.54 1.69 1.68 (.7) 14 34-33 1.9 1.42 1.55 1.69 1.68 (.7) 15 311-358 1.15 1.45 1.67 2.51 2.5 (.1) 16 324-369 1.14 1.51 1.72 2.51 2.49 (.1) 17 319-339 1.6 1.49 1.58 1.69 1.68 (.7) 18 324-387 1.19 1.51 1.8 3.23 3.2 (.13) 19 337-397 1.18 1.57 1.85 3.22 3.21 (.13) 2 349-47 1.17 1.63 1.9 3.22 3.2 (.13) 21 345-49 1.18 1.61 1.9 3.22 3.2 (.13) 22 346-418 1.21 1.61 1.95 3.22 3.19 (.13) 23 35-445 1.27 1.63 2.7 3.8 3.74 (.15) 24 358-462 1.29 1.67 2.15 3.8 3.75 (.15) 25 364-55 1.39 1.7 2.36 4.5 4.4 (.16) 26 374-523 1.4 1.74 2.44 4.5 4.5 (.16) Standard Loading Protocol Low-cycle Fatigue No data recorded Fractured in first cycle a values in parenthesis are for end rotation (rad.) 33

Table 3.3 Specimen 3 Peak Response Quantities Test Cycle No. T max (kips) P max (kips) β w βw Brace Deformations (in) Longitudinal Transverse a 1 282-357 1.27.94 1.19.44.42 (.2) 2 38-348 1.13 1.3 1.16.45.42 (.2) 3 311-339 1.9 1.4 1.13.44.42 (.2) 4 313-348 1.11 1.4 1.16.45.42 (.2) 5 312-338 1.8 1.4 1.12.45.42 (.2) 6 299-346 1.16 1. 1.16.45.42 (.2) 7 353-358 1.1 1.18 1.19.9.87 (.3) 8 339-361 1.6 1.13 1.2.9.87 (.3) 9 342-362 1.6 1.14 1.21.9.86 (.3) 1 344-368 1.7 1.15 1.23.9.87 (.3) 11 364-418 1.15 1.21 1.39 1.73 1.68 (.7) 12 391-434 1.11 1.3 1.45 1.72 1.68 (.7) 13 42-441 1.1 1.34 1.47 1.72 1.68 (.7) 14 45-443 1.9 1.35 1.47 1.72 1.68 (.7) 15 418-48 1.15 1.39 1.6 2.55 2.49 (.1) 16 43-488 1.14 1.43 1.63 2.55 2.49 (.1) 17 427-456 1.7 1.42 1.52 1.72 1.68 (.7) 18 437-532 1.22 1.46 1.78 3.44 3.35 (.13) 19 457-545 1.19 1.52 1.81 3.43 3.35 (.13) 2 462-558 1.21 1.54 1.86 3.43 3.34 (.13) 21 466-568 1.22 1.55 1.89 3.43 3.34 (.13) 22 471-585 1.24 1.57 1.95 3.43 3.35 (.13) 23 436-564 1.29 1.45 1.87 2.42 2.28 (.9) 24 46-553 1.2 1.53 1.84 2.41 2.28 (.9) 25 458-547 1.19 1.53 1.82 2.4 2.28 (.9) 26 455-544 1.2 1.52 1.82 2.4 2.29 (.9) 27 451-541 1.2 1.5 1.8 2.4 2.26 (.9) 28 449-538 1.2 1.5 1.79 2.4 2.26 (.9) 29 447-541 1.21 1.49 1.8 2.4 2.29 (.9) 3 446-542 1.22 1.49 1.81 2.4 2.29 (.9) 31 444-537 1.21 1.48 1.79 2.4 2.27 (.9) 32 443-535 1.21 1.48 1.79 2.4 2.27 (.9) 33 441-535 1.21 1.47 1.78 2.4 2.28 (.9) 34 441-533 1.21 1.47 1.78 2.4 2.28 (.9) 35 44-534 1.21 1.47 1.77 2.4 2.26 (.9) 36 44-537 1.22 1.47 1.79 2.4 2.28 (.9) 37 441-537 1.22 1.47 1.79 2.4 2.27 (.9) 38 442-537 1.22 1.47 1.8 2.4 2.27 (.9) 39 439-539 1.23 1.46 1.8 2.4 2.27 (.9) 4 44-547 1.24 1.47 1.82 2.4 2.29 (.9) 41 445-547 1.23 1.48 1.82 2.4 2.29 (.9) 42 442-544 1.23 1.47 1.81 2.4 2.27 (.9) 43 445-545 1.22 1.48 1.81 2.39 2.28 (.9) 44 447-554 1.24 1.49 1.85 2.39 2.29 (.9) 45 443-547 1.24 1.48 1.83 2.39 2.27 (.9) 46 444-549 1.24 1.48 1.83 2.39 2.28 (.9) 47 445-56 1.26 1.48 1.87 2.39 2.28 (.9) Standard Loading Protocol Low-cycle Fatigue No. 1 34

48 493-588 1.19 1.64 1.95 2.34 2.3 (.9) 49 482-578 1.2 1.61 1.93 2.35 2.29 (.9) 5 472-572 1.21 1.57 1.9 2.37 2.28 (.9) 51 466-568 1.22 1.55 1.89 2.38 2.27 (.9) 52 461-567 1.23 1.54 1.89 2.4 2.28 (.9) 53 458-563 1.23 1.53 1.88 2.4 2.27 (.9) 54 457-564 1.23 1.52 1.87 2.4 2.29 (.9) 55 454-561 1.24 1.51 1.88 2.4 2.26 (.9) 56 454-559 1.23 1.51 1.86 2.4 2.28 (.9) 57 453-567 1.25 1.51 1.89 2.4 2.29 (.9) 58 452-562 1.24 1.51 1.87 2.39 2.29 (.9) 59 455-559 1.23 1.52 1.86 2.4 2.27 (.9) 6 452-561 1.24 1.51 1.87 2.4 2.28 (.9) 61 453-563 1.24 1.51 1.87 2.4 2.28 (.9) 62 454-564 1.24 1.51 1.88 2.39 2.28 (.9) 63 458-565 1.23 1.53 1.88 2.39 2.28 (.9) 64 455-577 1.27 1.52 1.92 2.39 2.29 (.9) 65 458-571 1.25 1.53 1.91 2.39 2.28 (.9) 66 467-573 1.23 1.56 1.91 2.39 2.28 (.9) 67 462-578 1.25 1.54 1.92 2.39 2.29 (.9) 68 463-577 1.25 1.54 1.93 2.39 2.28 (.9) 69 466-584 1.25 1.55 1.94 2.38 2.29 (.9) 7 468-584 1.25 1.56 1.95 2.39 2.28 (.9) 71 471-595 1.26 1.57 1.98 2.38 2.29 (.9) 72 474-599 1.26 1.58 1.99 2.38 2.28 (.9) a values in parenthesis are for end rotation (rad.) Low-cycle Fatigue No. 2 35

Table 3.4 Specimen 4 Peak Response Quantities Test Cycle No. T max (kips) P max (kips) β w βw Brace Deformations (in) Longitudinal Transverse a 1 436-537 1.23.96 1.18.44.43 (.2) 2 436-522 1.2.96 1.15.44.43 (.2) 3 449-513 1.14.99 1.12.45.43 (.2) 4 437-519 1.19.96 1.14.45.43 (.2) 5 448-515 1.15.98 1.13.45.43 (.2) 6 437-55 1.16.96 1.11.45.43 (.2) 7 551-553 1. 1.21 1.21.9.89 (.4) 8 52-543 1.5 1.14 1.2.89.89 (.4) 9 522-544 1.4 1.15 1.19.89.88 (.4) 1 52-542 1.4 1.14 1.19.89.89 (.4) 11 573-648 1.13 1.26 1.42 1.72 1.7 (.7) 12 614-666 1.8 1.35 1.45 1.71 1.7 (.7) 13 629-675 1.7 1.38 1.48 1.71 1.7 (.7) 14 636-678 1.6 1.4 1.48 1.71 1.7 (.7) 15 662-744 1.12 1.45 1.63 2.53 2.51 (.1) 16 681-752 1.1 1.49 1.64 2.52 2.51 (.1) 17 671-694 1.3 1.47 1.52 1.7 1.7 (.7) 18 691-797 1.15 1.52 1.74 3.15 3.1 (.12) 19 712-82 1.13 1.56 1.77 3.14 3.1 (.12) 2 716-84 1.12 1.57 1.76 3.14 3.1 (.12) 21 719-813 1.13 1.58 1.78 3.13 3.1 (.12) 22 719-89 1.13 1.58 1.78 3.14 3.1 (.12) 23 729-88 1.21 1.6 1.94 3.93 3.85 (.15) 24 742-885 1.19 1.63 1.94 3.92 3.84 (.15) 25 757-949 1.25 1.66 2.8 4.64 4.5 (.16) 26 774-98 1.27 1.7 2.16 4.64 4.5 (.16) 27 848-863 1.2 1.86 1.9 2.3 2.32 (.9) 28 774-84 1.8 1.7 1.83 2.32 2.29 (.9) 29 748-824 1.1 1.64 1.81 2.3 2.29 (.9) 3 731-812 1.11 1.6 1.78 2.3 2.28 (.9) 31 72-85 1.12 1.58 1.77 2.29 2.29 (.9) 32 714-798 1.12 1.57 1.75 2.3 2.28 (.9) 33 76-793 1.12 1.55 1.73 2.3 2.28 (.9) 34 72-79 1.13 1.54 1.74 2.3 2.28 (.9) 35 699-786 1.12 1.53 1.72 2.3 2.28 (.9) 36 693-783 1.13 1.52 1.72 2.3 2.28 (.9) 37 69-781 1.13 1.51 1.71 2.3 2.28 (.9) 38 688-78 1.13 1.51 1.71 2.3 2.29 (.9) 39 685-78 1.14 1.5 1.71 2.3 2.29 (.9) 4 685-779 1.14 1.5 1.71 2.3 2.28 (.9) 41 684-778 1.14 1.5 1.71 2.29 2.27 (.9) 42 684-782 1.14 1.5 1.71 2.29 2.29 (.9) 43 683-786 1.15 1.5 1.72 2.29 2.29 (.9) 44 682-784 1.15 1.5 1.72 2.29 2.28 (.9) 45 683-786 1.15 1.5 1.72 2.29 2.28 (.9) 46 683-787 1.15 1.5 1.72 2.29 2.28 (.9) 47 684-789 1.15 1.5 1.73 2.29 2.28 (.9) 48 685-793 1.16 1.5 1.74 2.29 2.28 (.9) Standard Loading Protocol Low-cycle Fatigue 36

49 686-8 1.17 1.51 1.76 2.3 2.29 (.9) 5 688-797 1.16 1.51 1.75 2.3 2.27 (.9) 51 691-89 1.17 1.52 1.77 2.29 2.28 (.9) a values in parenthesis are for end rotation (rad.) 37

Table 3.5 Specimen 5 Peak Response Quantities Test Cycle No. T max (kips) P max (kips) β w βw Brace Deformations (in) Longitudinal Transverse a 1 697-756 1.8 1.8 1.17.47.42 (.2) 2 75-744 1.6 1.1 1.16.46.41 (.2) 3 725-722 1. 1.13 1.13.46.42 (.2) 4 724-713.99 1.13 1.12.46.42 (.2) 5 728-716.98 1.13 1.11.46.42 (.2) 6 715-721 1.1 1.11 1.12.46.42 (.2) 7 88-781.97 1.26 1.22.91.88 (.3) 8 741-774 1.5 1.15 1.21.9.88 (.3) 9 745-775 1.4 1.16 1.21.9.88 (.3) 1 746-778 1.4 1.16 1.21.9.87 (.3) 11 775-892 1.15 1.21 1.39 1.73 1.69 (.7) 12 843-925 1.1 1.31 1.44 1.7 1.69 (.7) 13 863-942 1.9 1.34 1.46 1.7 1.69 (.7) 14 873-95 1.9 1.36 1.48 1.7 1.69 (.7) 15 899-13 1.14 1.4 1.59 2.52 2.49 (.1) 16 929-149 1.13 1.45 1.63 2.53 2.5 (.1) 17 917-972 1.6 1.43 1.51 1.7 1.69 (.7) 18 945-1148 1.22 1.47 1.79 3.46 3.39 (.13) 19 985-119 1.21 1.53 1.85 3.44 3.39 (.13) 2 998-1215 1.22 1.55 1.89 3.45 3.39 (.13) 21 15-1234 1.23 1.56 1.92 3.45 3.39 (.13) 22 111-1245 1.23 1.57 1.94 3.45 3.39 (.13) 23 124-1323 1.29 1.59 2.6 4.14 4.4 (.16) 24 15-1344 1.28 1.63 2.9 4.14 4.4 (.16) 25 166-146 1.37 1.66 2.27 4.95 4.4 (.16) 26 199-158 1.37 1.71 2.34 4.94 4.4 (.16) 27 122-1225 1. 1.9 1.9 2.36 1.69 (.7) 28 1116-1188 1.6 1.74 1.84 2.35 1.69 (.7) 29 18-1166 1.8 1.68 1.82 2.34 1.7 (.7) 3 156-1152 1.9 1.64 1.79 2.35 1.69 (.7) 31 137-114 1.1 1.61 1.78 2.35 1.69 (.7) 32 123-1131 1.1 1.59 1.75 2.35 1.68 (.7) 33 111-112 1.11 1.57 1.75 2.35 1.69 (.7) 34 999-1113 1.11 1.55 1.73 2.35 1.69 (.7) 35 99-1116 1.13 1.54 1.74 2.35 1.69 (.7) 36 982-115 1.13 1.53 1.73 2.36 1.68 (.7) 37 975-111 1.13 1.52 1.71 2.35 1.69 (.7) 38 97-111 1.14 1.51 1.72 2.35 1.69 (.7) 39 964-195 1.14 1.5 1.71 2.36 1.69 (.7) 4 96-199 1.15 1.49 1.72 2.36 1.68 (.7) 41 954-19 1.14 1.48 1.69 2.36 1.69 (.7) 42 953-188 1.14 1.48 1.69 2.36 1.69 (.7) 43 949-187 1.15 1.48 1.7 2.36 1.69 (.7) 44 945-187 1.15 1.47 1.69 2.36 1.68 (.7) 45 944-194 1.16 1.47 1.7 2.36 1.68 (.7) 46 937-188 1.16 1.46 1.69 2.36 1.69 (.7) 47 939-184 1.16 1.46 1.7 2.36 1.68 (.7) 48 936-184 1.16 1.46 1.69 2.36 1.69 (.7) Standard Loading Protocol Low-cycle Fatigue No. 1 38

49 932-188 1.17 1.45 1.7 2.36 1.68 (.7) 5 93-185 1.17 1.45 1.69 2.36 1.68 (.7) 51 931-184 1.16 1.45 1.68 2.36 1.69 (.7) 52 93-188 1.17 1.45 1.69 2.36 1.69 (.7) 53 928-187 1.17 1.44 1.69 2.37 1.69 (.7) 54 924-186 1.18 1.44 1.7 2.37 1.68 (.7) 55 923-185 1.18 1.44 1.69 2.37 1.68 (.7) 56 924-195 1.19 1.44 1.71 2.37 1.69 (.7) 57 985-115 1.12 1.53 1.72 2.26 1.69 (.7) 58 965-1123 1.16 1.5 1.74 2.32 1.69 (.7) 59 955-1114 1.17 1.49 1.74 2.35 1.7 (.7) 6 948-1115 1.18 1.48 1.74 2.36 1.69 (.7) 61 943-119 1.18 1.47 1.73 2.36 1.69 (.7) 62 937-199 1.17 1.46 1.71 2.36 1.69 (.7) 63 937-112 1.18 1.46 1.72 2.36 1.69 (.7) 64 93-198 1.18 1.45 1.71 2.36 1.68 (.7) 65 93-194 1.18 1.45 1.71 2.36 1.69 (.7) 66 926-192 1.18 1.44 1.7 2.36 1.69 (.7) 67 925-19 1.18 1.44 1.7 2.36 1.69 (.7) 68 922-195 1.19 1.43 1.71 2.36 1.68 (.7) 69 918-188 1.19 1.43 1.7 2.36 1.69 (.7) 7 918-19 1.19 1.43 1.7 2.36 1.69 (.7) 71 917-187 1.19 1.43 1.7 2.36 1.69 (.7) 72 916-186 1.19 1.43 1.7 2.36 1.69 (.7) 73 912-193 1.2 1.42 1.7 2.37 1.68 (.7) 74 91-192 1.2 1.42 1.7 2.36 1.69 (.7) 75 91-191 1.2 1.42 1.7 2.36 1.69 (.7) 76 881-195 1.24 1.37 1.7 2.37 1.68 (.7) 77 754-181 1.43 1.17 1.68 2.37 1.68 (.7) 78 749-17 1.43 1.17 1.67 2.37 1.68 (.7) 79 749-174 1.43 1.17 1.67 2.37 1.69 (.7) 8 747-169 1.43 1.16 1.66 2.38 1.69 (.7) 81 74-164 1.44 1.15 1.66 2.37 1.69 (.7) 82 738-164 1.44 1.15 1.65 2.38 1.68 (.7) 83 738-169 1.45 1.15 1.67 2.38 1.68 (.7) 84 738-155 1.43 1.15 1.64 2.38 1.69 (.7) 85 737-159 1.44 1.15 1.65 2.38 1.69 (.7) 86 74-162 1.44 1.15 1.66 2.38 1.67 (.7) a values in parenthesis are for end rotation (rad.) Low-cycle Fatigue No. 2 39

Table 3.6 Specimen 6 Peak Response Quantities Test Cycle No. T max (kips) P max (kips) β w βw Brace Deformations (in) Longitudinal Transverse a 1 692-726 1.5 1.8 1.13.47.41 (.2) 2 691-79 1.3 1.7 1.11.46.42 (.2) 3 697-696 1. 1.8 1.8.45.41 (.2) 4 694-698 1.1 1.8 1.9.46.41 (.2) 5 71-696.99 1.9 1.8.46.41 (.2) 6 692-695 1. 1.8 1.8.45.41 (.2) 7 796-781.98 1.24 1.21.9.87 (.3) 8 751-775 1.3 1.17 1.2.89.86 (.3) 9 753-776 1.3 1.17 1.21.89.87 (.3) 1 754-781 1.3 1.17 1.21.89.87 (.3) 11 783-91 1.15 1.22 1.4 1.71 1.66 (.7) 12 854-932 1.9 1.33 1.45 1.69 1.67 (.7) 13 873-949 1.9 1.36 1.48 1.69 1.68 (.7) 14 881-955 1.8 1.37 1.48 1.69 1.68 (.7) 15 98-143 1.15 1.41 1.62 2.51 2.48 (.1) 16 935-155 1.13 1.45 1.64 2.5 2.48 (.1) 17 922-97 1.5 1.43 1.51 1.68 1.67 (.7) 18 943-1122 1.19 1.47 1.74 3.13 3.9 (.12) 19 975-1143 1.17 1.52 1.77 3.11 3.9 (.12) 2 986-1159 1.18 1.53 1.81 3.11 3.8 (.12) 21 991-117 1.18 1.54 1.82 3.11 3.8 (.12) 22 994-1177 1.18 1.55 1.82 3.11 3.9 (.12) 23 18-1278 1.27 1.57 1.99 3.84 3.79 (.15) 24 129-134 1.27 1.6 2.3 3.84 3.76 (.15) 25 145-1452 1.39 1.62 2.26 4.61 4.3 (.16) 26 182-1516 1.4 1.68 2.36 4.61 4.3 (.16) 27 1238-1164.94 1.92 1.81 1.68 1.71 (.7) 28 196-1146 1.5 1.7 1.79 1.68 1.68 (.7) 29 158-1131 1.7 1.65 1.76 1.66 1.68 (.7) 3 135-1114 1.8 1.61 1.74 1.66 1.66 (.7) 31 118-114 1.8 1.58 1.71 1.66 1.68 (.7) 32 13-194 1.9 1.56 1.7 1.67 1.68 (.7) 33 992-183 1.9 1.54 1.68 1.67 1.66 (.7) 34 984-176 1.9 1.53 1.67 1.67 1.66 (.7) 35 974-171 1.1 1.51 1.67 1.67 1.68 (.7) 36 966-165 1.1 1.5 1.65 1.67 1.67 (.7) 37 959-16 1.11 1.49 1.66 1.67 1.67 (.7) 38 954-158 1.11 1.48 1.65 1.67 1.68 (.7) 39 949-154 1.11 1.48 1.64 1.67 1.67 (.7) 4 946-152 1.11 1.47 1.63 1.67 1.67 (.7) 41 943-149 1.11 1.47 1.63 1.68 1.68 (.7) 42 938-148 1.12 1.46 1.63 1.68 1.67 (.7) 43 934-147 1.12 1.45 1.63 1.68 1.67 (.7) 44 93-146 1.12 1.45 1.62 1.68 1.66 (.7) 45 927-147 1.13 1.44 1.63 1.68 1.68 (.7) 46 924-142 1.13 1.44 1.62 1.68 1.66 (.7) 47 923-141 1.13 1.44 1.62 1.69 1.67 (.7) 48 92-142 1.13 1.43 1.62 1.68 1.67 (.7) Standard Loading Protocol Low-cycle Fatigue 4

49 921-144 1.13 1.43 1.62 1.68 1.68 (.7) 5 916-139 1.13 1.42 1.61 1.69 1.67 (.7) 51 915-138 1.14 1.42 1.62 1.69 1.67 (.7) 52 913-138 1.14 1.42 1.62 1.69 1.65 (.7) 53 912-138 1.14 1.42 1.62 1.69 1.66 (.7) 54 91-141 1.14 1.41 1.61 1.69 1.68 (.7) 55 911-137 1.14 1.42 1.61 1.69 1.66 (.7) 56 98-145 1.15 1.41 1.62 1.69 1.67 (.7) a values in parenthesis are for end rotation (rad.) 41

Table 3.7 Specimen 7 Peak Response Quantities Test Cycle No. T max (kips) P max (kips) β w βw Brace Deformations (in) Longitudinal Transverse a 1 9-1129 1.25.88 1.1.53.41 (.2) 2 878-192 1.24.85 1.6.52.41 (.2) 3 884-175 1.22.86 1.5.51.41 (.2) 4 885-173 1.21.86 1.4.51.41 (.2) 5 892-163 1.19.87 1.3.51.41 (.2) 6 891-164 1.19.87 1.3.51.41 (.2) 7 1267-1265 1. 1.23 1.23.95.87 (.3) 8 118-1219 1.3 1.15 1.18.93.87 (.3) 9 1183-1219 1.3 1.15 1.19.93.87 (.3) 1 1185-122 1.3 1.15 1.19.93.87 (.3) 11 1216-1366 1.12 1.18 1.33 1.76 1.68 (.7) 12 1316-1433 1.9 1.28 1.4 1.72 1.68 (.7) 13 1352-1457 1.8 1.32 1.42 1.72 1.67 (.7) 14 1367-1469 1.7 1.33 1.42 1.7 1.67 (.7) 15 1419-163 1.13 1.38 1.56 2.54 2.49 (.1) 16 1462-164 1.12 1.42 1.59 2.53 2.49 (.1) 17 1444-157 1.4 1.41 1.46 1.7 1.67 (.7) 18 1497-1816 1.21 1.46 1.76 3.59 3.49 (.14) 19 1564-1877 1.2 1.52 1.83 3.55 3.47 (.14) 2 159-19 1.19 1.55 1.84 3.52 3.48 (.14) 21 1597-195 1.19 1.55 1.85 3.41 3.45 (.14) 22 1596-191 1.19 1.55 1.85 3.28 3.46 (.14) 23 1637-1855 1.13 1.59 1.8 2.59 2.51 (.1) 24 1599-1854 1.16 1.56 1.81 2.53 2.57 (.1) 25 1578-1847 1.17 1.54 1.8 2.55 2.56 (.1) 26 1565-1838 1.17 1.52 1.78 2.56 2.53 (.1) 27 1555-1832 1.18 1.51 1.79 2.56 2.52 (.1) 28 1548-1834 1.19 1.51 1.79 2.56 2.54 (.1) 29 1541-1832 1.19 1.5 1.79 2.55 2.55 (.1) 3 1537-1828 1.19 1.5 1.78 2.56 2.54 (.1) 31 1529-1823 1.19 1.49 1.77 2.56 2.51 (.1) 32 1521-182 1.2 1.48 1.78 2.56 2.54 (.1) 33 1514-1816 1.2 1.47 1.77 2.56 2.51 (.1) 34 1511-189 1.2 1.47 1.77 2.54 2.53 (.1) 35 155-183 1.2 1.47 1.76 2.52 2.51 (.1) 36 151-1792 1.19 1.46 1.74 2.5 2.5 (.1) 37 1493-1786 1.2 1.45 1.74 2.46 2.53 (.1) 38 1584-1912 1.21 1.54 1.87 2.59 2.5 (.1) 39 157-1923 1.22 1.53 1.86 2.52 2.57 (.1) 4 1558-1918 1.23 1.52 1.87 2.53 2.56 (.1) 41 155-197 1.23 1.51 1.86 2.54 2.48 (.1) 42 1546-192 1.23 1.51 1.85 2.54 2.55 (.1) 43 1542-1894 1.23 1.5 1.85 2.53 2.55 (.1) 44 1534-1889 1.23 1.49 1.84 2.54 2.52 (.1) 45 1528-1884 1.23 1.49 1.83 2.54 2.54 (.1) 46 1524-1878 1.23 1.48 1.83 2.53 2.54 (.1) 47 1519-1878 1.24 1.48 1.83 2.53 2.54 (.1) 48 1516-1873 1.24 1.48 1.83 2.52 2.51 (.1) Standard Loading Protocol Low-cycle Fatigue No. 1 Low-cycle Fatigue No. 2 42

49 1511-1864 1.23 1.47 1.81 2.5 2.52 (.1) 5 158-1852 1.23 1.47 1.81 2.49 2.51 (.1) 51 157-1844 1.22 1.47 1.79 2.46 2.51 (.1) 52 1498-1833 1.22 1.46 1.78 2.42 2.47 (.1) a values in parenthesis are for end rotation (rad.) 43

Table 3.8 Specimen 8 Peak Response Quantities Test Cycle No. T max (kips) P max (kips) β w βw Brace Deformations (in) Longitudinal Transverse a 1 167-1158 1.9 1.4 1.13.5.43 (.2) 2 178-1139 1.6 1.5 1.11.49.43 (.2) 3 18-115 1.2 1.5 1.7.49.43 (.2) 4 185-117 1.2 1.5 1.7.49.43 (.2) 5 197-197 1. 1.6 1.6.49.41 (.2) 6 188-194 1.1 1.6 1.7.48.42 (.2) 7 1283-1251.98 1.25 1.22.94.88 (.3) 8 1199-1235 1.3 1.16 1.2.93.88 (.4) 9 121-1239 1.3 1.17 1.2.93.88 (.4) 1 121-124 1.3 1.17 1.2.93.88 (.4) 11 1235-147 1.14 1.2 1.37 1.77 1.69 (.7) 12 1344-1455 1.8 1.3 1.41 1.74 1.69 (.7) 13 1376-1475 1.7 1.34 1.43 1.74 1.69 (.7) 14 1388-1483 1.7 1.35 1.44 1.73 1.7 (.7) 15 1436-1611 1.12 1.39 1.56 2.58 2.48 (.1) 16 1478-1636 1.11 1.43 1.59 2.57 2.48 (.1) 17 1464-1521 1.4 1.42 1.48 1.73 1.67 (.7) 18 156-1775 1.18 1.46 1.72 3.43 3.28 (.13) 19 1565-1816 1.16 1.52 1.76 3.39 3.28 (.13) 2 1576-1819 1.15 1.53 1.76 3.29 3.29 (.13) 21 1577-1811 1.15 1.53 1.76 3.16 3.3 (.13) 22 1569-184 1.15 1.52 1.75 3.7 3.31 (.13) 23 1638-1821 1.11 1.59 1.76 2.63 2.54 (.1) 24 164-189 1.13 1.56 1.76 2.58 2.56 (.1) 25 1583-1798 1.14 1.54 1.75 2.57 2.56 (.1) 26 1571-1786 1.14 1.52 1.74 2.58 2.55 (.1) 27 1561-1779 1.14 1.52 1.73 2.58 2.55 (.1) 28 1551-1773 1.14 1.51 1.72 2.58 2.55 (.1) 29 1543-1766 1.14 1.5 1.71 2.58 2.54 (.1) 3 1536-1762 1.15 1.49 1.71 2.58 2.55 (.1) 31 1531-1758 1.15 1.49 1.71 2.59 2.55 (.1) 32 1527-1753 1.15 1.48 1.7 2.59 2.54 (.1) 33 1521-1753 1.15 1.48 1.7 2.59 2.52 (.1) 34 1516-1749 1.15 1.47 1.69 2.59 2.53 (.1) 35 1511-1744 1.15 1.47 1.69 2.58 2.54 (.1) 36 156-174 1.16 1.46 1.7 2.57 2.54 (.1) 37 151-1739 1.16 1.46 1.69 2.54 2.5 (.1) 38 1623-1867 1.15 1.58 1.81 2.64 2.52 (.1) 39 1599-1859 1.16 1.55 1.8 2.57 2.57 (.1) 4 158-1846 1.17 1.53 1.79 2.56 2.57 (.1) 41 1566-1833 1.17 1.52 1.78 2.57 2.53 (.1) 42 1557-1823 1.17 1.51 1.77 2.57 2.51 (.1) 43 1549-1817 1.17 1.5 1.76 2.57 2.55 (.1) 44 1542-1814 1.18 1.5 1.77 2.57 2.55 (.1) 45 1535-1811 1.18 1.49 1.76 2.57 2.54 (.1) 46 1533-187 1.18 1.49 1.76 2.57 2.53 (.1) 47 1527-182 1.18 1.48 1.75 2.57 2.49 (.1) 48 1524-181 1.18 1.48 1.75 2.57 2.52 (.1) Standard Loading Protocol Low-cycle Fatigue No. 1 Low-cycle Fatigue No. 2 44

49 152-1799 1.18 1.48 1.74 2.57 2.54 (.1) 5 1518-1791 1.18 1.47 1.74 2.57 2.51 (.1) 51 1513-1782 1.18 1.47 1.73 2.55 2.49 (.1) 52 151-178 1.18 1.47 1.73 2.5 2.52 (.1) a values in parenthesis are for end rotation (rad.) 45

(a) during Standard Test (Overview) (b) after Standard Test (West End) Figure 3.1 Specimen 1: Testing Photos 46

6 Longitudinal Displacement (in) 4 2-2 -4-6 2 4 6 8 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 2 4 6 8 End Rotation (rad.) (b) Transverse Direction Figure 3.2 Specimen 1: Table Displacement Time Histories (Standard Test) 47

4-2 -1 1 2 Resultant Force (kips) 2-2 -4-6 -4-2 2 4 6 Figure 3.3 Specimen 1: Brace Force versus Deformation (Standard Test) Dissipated Hysteretic Energy Energy (x ( 1 1 kip-in), kip-in), Eh 35 3 6 25 5 2 4 15 3 1 2 5 1 2 4 6 8 Normalized Cumulative Cumulative Inelastic Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.4 Specimen 1: Hysteretic Energy Time History (Standard Test) 48

6 Longitudinal Displacement (in) 4 2-2 -4-6 1 2 3 4 5 6 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4.1 2. -2 -.1-4 -.2-6 1 2 3 4 5 6 End Rotation (rad.) (b) Transverse Direction Figure 3.5 Specimen 1: Table Displacement Time Histories (Low-cycle Fatigue Test) 49

4-2 -1 1 2 Resultant Force (kips) 2-2 18-th cycle -4-6 -4-2 2 4 6 Figure 3.6 Specimen 1: Brace Force versus Deformation (Low-cycle Fatigue Test) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 2 15 1 5 1 2 3 4 5 6 35 3 25 2 15 1 5 Cumulative Normalized Inelastic Cumulative Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.7 Specimen 1: Hysteretic Energy Time History (Low-cycle Fatigue Test) 5

6 Longitudinal Displacement (in) 4 2-2 -4-6 2 4 6 8 1 12 14 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 2 4 6 8 1 12 14 End Rotation (rad.) (b) Transverse Direction Figure 3.8 Specimen 1: Table Displacement Time Histories (Both Tests Combined) 51

4-2 -1 1 2 Resultant Force (kips) 2-2 -4-6 -4-2 2 4 6 Figure 3.9 Specimen 1: Brace Force versus Deformation (Both Tests Combined) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), 5 4 8 3 6 2 4 1 2 2 4 6 8 1 12 14 Normalized Cumulative Cumulative Inelastic Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.1 Specimen 1: Hysteretic Energy Time History (Both Tests Combined) 52

4 Resultant Force (kips) 2-2 -4-6 -4-2 2 4 6 Figure 3.11 Specimen 1: Brace Response Envelope 1.6 1.4 2 4 6 8 1 12 14 16 β (=Pmax β /Tmax ) 1.2 1..8.6.4.2. 1 2 3 4 (in) Figure 3.12 Specimen 1: β versus Deformation Level 53

2. 2 4 6 8 1 12 14 16 w (= Tmax / Pyn) (=Tmax/Pyn) 1.5 1..5. 1 2 3 4 (a) Tension 2 4 6 8 1 12 14 16 2. βw (= Pmax / Pyn) Cmax/Pyn 1.5 1..5. 1 2 3 4 (b) Compression Figure 3.13 Specimen 1: w and βw versus Deformation Level 54

(a) after Standard Test (Overview) (b) Grinding between Collar and Brace (East End) Figure 3.14 Specimen 2: Testing Photos 55

6 Longitudinal Displacement (in) 4 2-2 -4-6 2 4 6 8 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 2 4 6 8 (b) Transverse Direction End Rotation (rad.) Figure 3.15 Specimen 2: Table Displacement Time Histories (Standard Test) 56

6-2 -15-1 -5 5 1 15 2 4 Resultant Force (kips) 2-2 -4-6 -6-4 -2 2 4 6 Figure 3.16 Specimen 2: Brace Force versus Deformation (Standard Test) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 6 5 4 3 2 1 2 4 6 8 6 5 4 3 2 1 Normalized Cumulative Cumulative Inelastic Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.17 Specimen 2: Hysteretic Energy Time History (Standard Test) 57

tons 4 k -2. in. 2 k -1. in. 1. in. 2. in. -2 k -4 k tons Figure 3.18 Specimen 2: Brace Force versus Brace Deformation (Low-cycle Fatigue Test) 58

6 4 Resultant Force (kips) 2-2 -4-6 -6-4 -2 2 4 6 Figure 3.19 Specimen 2: Brace Response Envelope 1.6 1.4 2 4 6 8 1 12 14 16 β (=Pmax β /Tmax ) 1.2 1..8.6.4.2. 1 2 3 4 Figure 3.2 Specimen 2: β versus Deformation Level 59

2. 2 4 6 8 1 12 14 16 1.5 w (= / Pyn) (=Tmax/Pyn) 1..5. 1 2 3 4 (in) (a) Tension 2 4 6 8 1 12 14 16 2. βw (= Pmax / Pyn) Cmax/Pyn 1.5 1..5. 1 2 3 4 (in) (b) Compression Figure 3.21 Specimen 2: w and βw versus Deformation Level 6

Rotation from Displ. and Geometry (rad).2.1. -.1 -.2 -.2 -.1..1.2 Rotation from Inclinometer (rad) Figure 3.22 Specimen 2: End Rotation Comparison Figure 3.23 Specimen 3: Testing Photo (during Low-cycle Fatigue Test) 61

6 Longitudinal Displacement (in) 4 2-2 -4-6 1 2 3 4 5 6 7 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 1 2 3 4 5 6 7 (b) Transverse Direction End Rotation (rad.) Figure 3.24 Specimen 3: Table Displacement Time Histories (Standard Test) 62

6-15 -1-5 5 1 15 4 Resultant Force (kips) 2-2 -4-6 -6-4 -2 2 4 6 Figure 3.25 Specimen 3: Brace Force versus Deformation (Standard Test) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 5 4 3 2 1 1 2 3 4 5 6 7 4 35 3 25 2 15 1 5 Cumulative Normalized Inelastic Cumulative Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.26 Specimen 3: Hysteretic Energy Time History (Standard Test) 63

4.2 Strain (microstrain) 2-2.1. -.1 Normalized Strain -4 1 2 3 4 5 6 7 -.2 (a) Top Strain Gage (Transverse) 4.2 Strain (microstrain) 2-2.1. -.1 Normalized Strain -4 1 2 3 4 5 6 7 -.2 (b) Bottom Strain Gage (Transverse) Figure 3.27 Specimen 3: Collar Strain Gage Time Histories (Standard Test) 64

4.2 Strain (microstrain) 2-2.1. -.1 Normalized Strain -.2-4 1 2 3 4 5 6 7 (a) North Strain Gage (Longitudinal) 4.2 Strain (microstrain) 2-2.1. -.1 Normalized Strain -.2-4 1 2 3 4 5 6 7 (b) South Strain Gage (Longitudinal) Figure 3.28 Specimen 3: HSS Strain Gage Time Histories (Standard Test) 65

6 Longitudinal Displacement (in) 4 2-2 -4-6 1 2 3 4 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 No Transverse Displacement Record 2.1. -2 -.1-4 -.2-6 1 2 3 4 End Rotation (rad.) (b) Transverse Direction Figure 3.29 Specimen 3: Table Displacement Time Histories (Sylmar Earthquake Test) 66

6-15 -1-5 5 1 15 4 Resultant Force (kips) 2-2 -4-6 -6-4 -2 2 4 6 Figure 3.3 Specimen 3: Brace Force versus Deformation (Sylmar Earthquake Test) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), 1 8 6 4 2 1 2 3 4 8 6 4 2 Cumulative Normalized Inelastic Cumulative Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.31 Specimen 3: Hysteretic Energy Time History (Sylmar Earthquake Test) 67

6 Longitudinal Displacement (in) 4 2-2 -4-6 2 4 6 8 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 2 4 6 8 End Rotation (rad.) (b) Transverse Direction Figure 3.32 Specimen 3: Table Displacement Time Histories (Low-cycle Fatigue Test No. 1) 68

6-15 -1-5 5 1 15 4 Resultant Force (kips) 2-2 -4-6 -6-4 -2 2 4 6 Figure 3.33 Specimen 3: Brace Force versus Deformation (Low-cycle Fatigue Test No. 1) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 8 6 4 2 2 4 6 8 6 5 4 3 2 1 Cumulative Normalized Inelastic Cumulative Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.34 Specimen 3: Hysteretic Energy Time History (Low-cycle Fatigue Test No. 1) 69

4.2 Strain (microstrain) 2-2.1. -.1 Normalized Strain -4 2 4 6 8 -.2 (a) Top Strain Gage (Transverse) 4.2 Strain (microstrain) 2-2.1. -.1 Normalized Strain -4 2 4 6 8 -.2 (b) Bottom Strain Gage (Transverse) Figure 3.35 Specimen 3: Collar Strain Gage Time Histories (Low-cycle Fatigue Test No. 1) 7

4.2 Strain (microstrain) 2-2.1. -.1 Normalized Strain -.2-4 2 4 6 8 (a) North Strain Gage (Longitudinal) 4.2 Strain (microstrain) 2-2.1. -.1 Normalized Strain -.2-4 2 4 6 8 (b) South Strain Gage (Longitudinal) Figure 3.36 Specimen 3: HSS Strain Gage Time Histories (Low-cycle Fatigue Test No. 1) 71

6 Longitudinal Displacement (in) 4 2-2 -4-6 2 4 6 8 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 2 4 6 8 (b) Transverse Direction End Rotation (rad.) Figure 3.37 Specimen 3: Table Displacement Time Histories (Low-cycle Fatigue Test No. 2) 72

6-15 -1-5 5 1 15 4 Resultant Force (kips) 2-2 -4-6 -6-4 -2 2 4 6 Figure 3.38 Specimen 3: Brace Force versus Deformation (Low-cycle Fatigue Test No. 2) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 8 6 4 2 2 4 6 8 6 5 4 3 2 1 Cumulative Normalized Cumulative Inelastic Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.39 Specimen 3: Hysteretic Energy Time History (Low-cycle Fatigue Test No. 2) 73

6.3 Strain (microstrain) 4 2.2.1. Normalized Strain -2 2 4 6 8 -.1 (a) Top Strain Gage (Transverse) 4.2 Strain (microstrain) 2-2.1. -.1 Normalized Strain -4 2 4 6 8 -.2 (b) Bottom Strain Gage (Transverse) Figure 3.4 Specimen 3: Collar Strain Gage Time Histories (Low-cycle Fatigue Test No. 2) 74

4.2 Strain (microstrain) 2-2.1. -.1 Normalized Strain -.2-4 2 4 6 8 (a) North Strain Gage (Longitudinal) 4.2 Strain (microstrain) 2-2.1. -.1 Normalized Strain -.2-4 2 4 6 8 (b) South Strain Gage (Longitudinal) Figure 3.41 Specimen 3: HSS Strain Gage Time Histories (Low-cycle Fatigue Test No. 2) 75

6 Longitudinal Displacement (in) 4 2-2 -4-6 5 1 15 2 25 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 5 1 15 2 25 End Rotation (rad.) (b) Transverse Direction Figure 3.42 Specimen 3: Table Displacement Time Histories (All Tests Combined) 76

6-15 -1-5 5 1 15 4 Resultant Force (kips) 2-2 -4-6 -6-4 -2 2 4 6 Figure 3.43 Specimen 3: Brace Force versus Deformation (All Tests Combined) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 2 15 1 5 Standard Test Sylmar E.Q. Fatigue Test No. 1 Fatigue Test No. 2 15 1 5 1 15 2 25 5 Normalized Cumulative Cumulative Inelastic Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.44 Specimen 3: Hysteretic Energy Time History (All Tests Combined) 77

6 4 Resultant Force (kips) 2-2 -4-6 -6-4 -2 2 4 6 Figure 3.45 Specimen 3: Brace Response Envelope 1.6 1.4 2 4 6 8 1 12 14 16 β (=Pmax β /Tmax ) 1.2 1..8.6.4.2. 1 2 3 4 Figure 3.46 Specimen 3: β versus Deformation Level 78

2. 2 4 6 8 1 12 14 16 1.5 w (= Tmax / Pyn) w (=Tmax/Pyn) 1..5. 1 2 3 4 BBrace DDeformation f (i (in) ) (a) Tension 2 4 6 8 1 12 14 16 2. βw (= Pmax / Pyn) Cmax/Pyn 1.5 1..5. 1 2 3 4 (in) (b) Compression Figure 3.47 Specimen 3: w and βw versus Deformation Level 79

Rotation from Displ. and Geometry (rad).2.1. -.1 -.2 -.2 -.1..1.2 Rotation from Inclinometer (rad) Figure 3.48 Specimen 3: End Rotation Comparison 8

(a) during Low-cycle Fatigue Test (Overview) (b) after all Tests (West End) Figure 3.49 Specimen 4: Testing Photos 81

6 Longitudinal Displacement (in) 4 2-2 -4-6 2 4 6 8 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 2 4 6 8 End Rotation (rad.) (b) Transverse Direction Figure 3.5 Specimen 4: Table Displacement Time Histories (Standard Test) 82

1-2 -15-1 -5 5 1 15 2 Resultant Force (kips) 5-5 -1-6 -4-2 2 4 6 Figure 3.51 Specimen 4: Brace Force versus Deformation (Standard Test) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 1 5 8 4 6 3 4 2 2 1 2 4 6 8 Figure 3.52 Specimen 4: Hysteretic Energy Time History (Standard Test) Normalized Cumulative Cumulative Inelastic Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) 83

4.2 Strain (microstrain) 2-2.1. -.1 Normalized Strain -4 2 4 6 8 -.2 (a) Top Strain Gage (Transverse) 4.2 Strain (microstrain) 2-2 No Bottom Gauge Installed.1. -.1 Normalized Strain -.2-4 -.1 -.5..5.1 (b) Bottom Strain Gage (Transverse) Figure 3.53 Specimen 4: Collar Strain Gage Time Histories (Standard Test) 84

4.2 Strain (microstrain) 2-2.1. -.1 Normalized Strain -.2-4 2 4 6 8 (a) North Strain Gage (Longitudinal) 4.2 Strain (microstrain) 2-2.1. -.1 Normalized Strain -.2-4 2 4 6 8 (b) South Strain Gage (Longitudinal) Figure 3.54 Specimen 4: HSS Strain Gage Time Histories (Standard Test) 85

6 Longitudinal Displacement (in) 4 2-2 -4-6 2 4 6 8 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 2 4 6 8 (b) Transverse Direction End Rotation (rad.) Figure 3.55 Specimen 4: Table Displacement Time Histories (Low-cycle Fatigue Test) 86

1-2 -15-1 -5 5 1 15 2 Resultant Force (kips) 5-5 -1-6 -4-2 2 4 6 Figure 3.56 Specimen 4: Brace Force versus Deformation (Low-cycle Fatigue Test) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 12 6 1 5 8 4 6 3 4 2 2 1 2 4 6 8 Normalized Cumulative Cumulative Inelastic Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.57 Specimen 4: Hysteretic Energy Time History (Low-cycle Fatigue Test) 87

4.2 Strain (microstrain) 2-2.1. -.1 Normalized Strain -4 2 4 6 8 -.2 (a) Top Strain Gage (Transverse) 4.2 Strain (microstrain) 2-2 No Bottom Gauge Installed.1. -.1 Normalized Strain -.2-4 -.1 -.5..5.1 (b) Bottom Strain Gage (Transverse) Figure 3.58 Specimen 4: Collar Strain Gage Time Histories (Low-cycle Fatigue Test) 88

4.2 Strain (microstrain) 2-2.1. -.1 Normalized Strain -.2-4 2 4 6 8 (a) North Strain Gage (Longitudinal) 4.2 Strain (microstrain) 2-2.1. -.1 Normalized Strain -.2-4 2 4 6 8 (b) South Strain Gage (Longitudinal) Figure 3.59 Specimen 4: HSS Strain Gage Time Histories (Low-cycle Fatigue Test) 89

6 Longitudinal Displacement (in) 4 2-2 -4-6 5 1 15 2 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 5 1 15 2 End Rotation (rad.) (b) Transverse Direction Figure 3.6 Specimen 4: Table Displacement Time Histories (Both Tests Combined) 9

1-2 -15-1 -5 5 1 15 2 Resultant Force (kips) 5-5 -1-6 -4-2 2 4 6 Figure 3.61 Specimen 4: Brace Force versus Deformation (Both Tests Combined) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 2 1 15 8 1 6 4 5 2 5 1 15 2 Normalized Cumulative Cumulative Inelastic Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.62 Specimen 4: Hysteretic Energy Time History (Both Tests Combined) 91

1 Resultant Force (kips) 5-5 -1-6 -4-2 2 4 6 Figure 3.63 Specimen 4: Brace Response Envelope 1.6 1.4 2 4 6 8 1 12 14 16 β (=Pmax β /Tmax ) 1.2 1..8.6.4.2. 1 2 3 4 Figure 3.64 Specimen 4: β versus Deformation Level 92

2. 2 4 6 8 1 12 14 16 1.5 w (= / Pym) (=Tmax/Pyn) 1..5. 1 2 3 4 Brace (in) (a) Tension 2 4 6 8 1 12 14 16 2. βw (= Pmax / Pyn) Cmax/Pyn 1.5 1..5. 1 2 3 4 (in) (b) Compression Figure 3.65 Specimen 4: w and βw versus Deformation Level 93

Rotation from Displ. and Geometry (rad).2.1. -.1 -.2 -.2 -.1..1.2 Rotation from Inclinometer (rad) Figure 3.66 Specimen 4: End Rotation Comparison 94

(a) during Standard Test (Overview) (b) after all Tests (West End) Figure 3.67 Specimen 5: Testing Photos 95

6 Longitudinal Displacement (in) 4 2-2 -4-6 2 4 6 8 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 2 4 6 8 End Rotation (rad.) (b) Transverse Direction Figure 3.68 Specimen 5: Table Displacement Time Histories (Standard Test) 96

15-15 -1-5 5 1 15 1 Resultant Force (kips) 5-5 -1-15 -6-4 -2 2 4 6 Figure 3.69 Specimen 5: Brace Force versus Deformation (Standard Test) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 16 6 14 5 12 1 4 8 3 6 2 4 2 1 2 4 6 8 Normalized Cumulative Cumulative Inelastic Disp. Eh/(Pyeff*Dby) Inelastic Deformation, η Figure 3.7 Specimen 5: Hysteretic Energy Time History (Standard Test) 97

6 Longitudinal Displacement (in) 4 2-2 -4-6 2 4 6 8 1 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 2 4 6 8 1 (b) Transverse Direction End Rotation (rad.) Figure 3.71 Specimen 5: Table Displacement Time Histories (Low-cycle Fatigue Test No. 1) 98

15-15 -1-5 5 1 15 1 Resultant Force (kips) 5-5 -1-15 -6-4 -2 2 4 6 Figure 3.72 Specimen 5: Brace Force versus Deformation (Low-cycle Fatigue Test No. 1) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 1 8 6 4 2 2 4 6 8 1 3 2 1 Normalized Cumulative Cumulative Inelastic Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.73 Specimen 5: Hysteretic Energy Time History (Low-cycle Fatigue Test No. 1) 99

6 Longitudinal Displacement (in) 4 2-2 -4-6 2 4 6 8 1 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 2 4 6 8 1 End Rotation (rad.) (b) Transverse Direction Figure 3.74 Specimen 5: Table Displacement Time Histories (Low-cycle Fatigue Test No. 2) 1

15-15 -1-5 5 1 15 1 Resultant Force (kips) 5-5 -1-15 -6-4 -2 2 4 6 Figure 3.75 Specimen 5: Brace Force versus Deformation (Low-cycle Fatigue Test No. 2) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 1 8 3 6 2 4 1 2 2 4 6 8 1 Normalized Cumulative Cumulative Inelastic Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.76 Specimen 5: Hysteretic Energy Time History (Low-cycle Fatigue Test No. 2) 11

6 Longitudinal Displacement (in) 4 2-2 -4-6 5 1 15 2 25 3 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 5 1 15 2 25 3 End Rotation (rad.) (b) Transverse Direction Figure 3.77 Specimen 5: Table Displacement Time Histories (All Tests Combined) 12

15-15 -1-5 5 1 15 1 Resultant Force (kips) 5-5 -1-15 -6-4 -2 2 4 6 Figure 3.78 Specimen 5: Brace Force versus Deformation (All Tests Combined) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 35 3 25 2 15 1 5 12 1 5 1 15 2 25 3 Figure 3.79 Specimen 5: Hysteretic Energy Time History (All Tests Combined) 8 6 4 2 Cumulative Normalized Inelastic Cumulative Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) 13

15 1 Resultant Force (kips) 5-5 -1-15 -6-4 -2 2 4 6 Figure 3.8 Specimen 5: Brace Response Envelope 1.6 1.4 1.2 2 4 6 8 1 12 14 16 β (=Pmax β /Tmax ) 1..8.6.4.2. 1 2 3 4 Figure 3.81 Specimen 5: β versus Deformation Level 14

2. 2 4 6 8 1 12 14 16 w (= (=Tmax/Pyn) / Pyn) 1.5 1..5. 1 2 3 4 (in) (a) Tension 2 4 6 8 1 12 14 16 2. βw (= Cmax/Pyn Pmax / Pyn) 1.5 1..5. 1 2 3 4 (in) (b) Compression Figure 3.82 Specimen 5: w and βw versus Deformation Level 15

Rotation from Displ. and Geometry (rad).2.1. -.1 -.2 -.2 -.1..1.2 Rotation from Inclinometer (rad) Figure 3.83 Specimen 5: End Rotation Comparison 16

(a) before Standard Test (Overview) (b) after all Tests (East End) Figure 3.84 Specimen 6: Testing Photos 17

6 Longitudinal Displacement (in) 4 2-2 -4-6 2 4 6 8 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 2 4 6 8 (b) Transverse Direction End Rotation (rad.) Figure 3.85 Specimen 6: Table Displacement Time Histories (Standard Test) 18

15-2 -15-1 -5 5 1 15 2 Resultant Force (kips) 1 5-5 -1-15 -6-4 -2 2 4 6 Figure 3.86 Specimen 6: Brace Force versus Deformation (Standard Test) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 14 12 1 8 6 4 2 2 4 6 8 5 4 3 2 1 Normalized Cumulative Cumulative Inelastic Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.87 Specimen 6: Hysteretic Energy Time History (Standard Test) 19

6 Longitudinal Displacement (in) 4 2-2 -4-6 2 4 6 8 1 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 2 4 6 8 1 (b) Transverse Direction End Rotation (rad.) Figure 3.88 Specimen 6: Table Displacement Time Histories (Low-cycle Fatigue Test) 11

15-2 -15-1 -5 5 1 15 2 Resultant Force (kips) 1 5-5 -1-15 -6-4 -2 2 4 6 Figure 3.89 Specimen 6: Brace Force versus Deformation (Low-cycle Fatigue Test) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 1 8 6 4 2 2 4 6 8 1 35 3 25 2 15 1 5 Normalized Cumulative Cumulative Inelastic Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.9 Specimen 6: Hysteretic Energy Time History (Low-cycle Fatigue Test) 111

6 Longitudinal Displacement (in) 4 2-2 -4-6 5 1 15 2 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 5 1 15 2 End Rotation (rad.) (b) Transverse Direction Figure 3.91 Specimen 6: Table Displacement Time Histories (All Tests Combined) 112

15-2 -15-1 -5 5 1 15 2 1 Resultant Force (kips) 5-5 -1-15 -6-4 -2 2 4 6 Figure 3.92 Specimen 6: Brace Force versus Deformation (All Tests Combined) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 25 2 15 1 5 5 1 15 2 8 6 4 2 Cumulative Normalized Inelastic Cumulative Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.93 Specimen 6: Hysteretic Energy Time History (All Tests Combined) 113

15 Resultant Force (kips) 1 5-5 -1-15 -6-4 -2 2 4 6 Figure 3.94 Specimen 6: Brace Response Envelope 1.6 1.4 2 4 6 8 1 12 14 16 β (=Pmax /Tmax ) β 1.2 1..8.6.4.2. 1 2 3 4 Figure 3.95 Specimen 6: β versus Deformation Level 114

2. 2 4 6 8 1 12 14 16 1.5 w (= (=Tmax/Pyn) / Pyn) 1..5. 1 2 3 4 (in) (a) Tension 2 4 6 8 1 12 14 16 2. βw (= Pmax / Pyn) Cmax/Pyn 1.5 1..5. 1 2 3 4 (in) (b) Compression Figure 3.96 Specimen 6: w and βw versus Deformation Level 115

Rotation from Displ. and Geometry (rad).2.1. -.1 -.2 -.2 -.1..1.2 Rotation from Inclinometer (rad) Figure 3.97 Specimen 6: End Rotation Comparison 116

(a) during Low- Cycle Fatigue Test (Overview) (b) Knife Plate after all Tests (West End) Figure 3.98 Specimen 7: Testing Photos 117

6 Longitudinal Displacement (in) 4 2-2 -4-6 1 2 3 4 5 6 7 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 1 2 3 4 5 6 7 End Rotation (rad.) (b) Transverse Direction Figure 3.99 Specimen 7: Table Displacement Time Histories (Standard Test) 118

2-15 -1-5 5 1 15 Resultant Force (kips) 1-1 -2-6 -4-2 2 4 6 Figure 3.1 Specimen 7: Brace Force versus Deformation (Standard Test) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 14 12 3 1 25 8 2 6 15 4 1 2 5 1 2 3 4 5 6 7 Normalized Cumulative Cumulative Inelastic Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.11 Specimen 7: Hysteretic Energy Time History (Standard Test) 119

. -5 Strain (microstrain) -1-15 -2-25 -.5-1. -1.5 Normalized Strain -3-35 Gage Failed -2. 1 2 3 4 5 6 7 (a) Gage A (Longitudinal) -5. Strain (microstrain) -1-15 -2-25 -.5-1. -1.5 Normalized Strain -3-35 -2. 1 2 3 4 5 6 7 (b) Gage B (Longitudinal) Figure 3.12 Specimen 7: Gusset Longitudinal Strain Gage Time Histories (Standard Test) 12

Strain (microstrain) 6 4 2-2.3.2.1. -.1 Normalized Strain -4-6 -.2 -.3 1 2 3 4 5 6 7 (a) Gage R1 (Longitudinal) Strain (microstrain) 6 4 2-2.3.2.1. -.1 Normalized Strain -4-6 -.2 -.3 1 2 3 4 5 6 7 (b) Gage R2 (Transverse) Figure 3.13 Specimen 7: Gusset Rosette Strain Gage Time Histories (Standard Test) 121

6 Longitudinal Displacement (in) 4 2-2 -4-6 1 2 3 4 5 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 1 2 3 4 5 (b) Transverse Direction End Rotation (rad.) Figure 3.14 Specimen 7: Table Displacement Time Histories (Low-cycle Fatigue Test No. 1) 122

2-15 -1-5 5 1 15 Resultant Force (kips) 1-1 -2-6 -4-2 2 4 6 Figure 3.15 Specimen 7: Brace Force versus Deformation (Low-cycle Fatigue Test No. 1) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 16 14 35 12 3 1 25 8 2 6 15 4 1 2 5 1 2 3 4 5 Normalized Cumulative Cumulative Inelastic Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.16 Specimen 7: Hysteretic Energy Time History (Low-cycle Fatigue Test No. 1) 123

. -5 Strain (microstrain) -1-15 -2-25 Gauge Gage has Failed failed -.5-1. -1.5 Normalized Strain -3-35 -2. 1 2 3 4 5 (a) Gage A (Longitudinal). -5 Strain (microstrain) -1-15 -2-25 -.5-1. -1.5 Normalized Strain -3-35 -2. 1 2 3 4 5 (b) Gage B (Longitudinal) Figure 3.17 Specimen 7: Gusset Longitudinal Strain Gage Time Histories (Low-cycle Fatigue Test No. 1) 124

Strain (microstrain) 6 4 2-2.3.2.1. -.1 Normalized Strain -4-6 -.2 -.3 1 2 3 4 5 (a) Gage R1 (Longitudinal) Strain (microstrain) 6 4 2-2.3.2.1. -.1 Normalized Strain -4-6 -.2 -.3 1 2 3 4 5 (b) Gage R2 (Transverse) Figure 3.18 Specimen 7: Gusset Rosette Strain Gage Time Histories (Low-cycle Fatigue Test No. 1) 125

6 Longitudinal Displacement (in) 4 2-2 -4-6 1 2 3 4 5 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 1 2 3 4 5 End Rotation (rad.) (b) Transverse Direction Figure 3.19 Specimen 7: Table Displacement Time Histories (Low-cycle Fatigue Test No. 2) 126

2-15 -1-5 5 1 15 Resultant Force (kips) 1-1 -2-6 -4-2 2 4 6 Figure 3.11 Specimen 7: Brace Force versus Deformation (Low-cycle Fatigue Test No. 2) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 16 14 12 1 8 6 4 2 1 2 3 4 5 35 3 25 2 15 1 5 Cumulative Normalized Inelastic Cumulative Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.111 Specimen 7: Hysteretic Energy Time History (Low-cycle Fatigue Test No. 2) 127

. -5 Strain (microstrain) -1-15 -2-25 Gauge Gage has Failed failed -.5-1. -1.5 Normalized Strain -3-35 -2. 1 2 3 4 5 (a) Gage A (Longitudinal). -5 Strain (microstrain) -1-15 -2-25 -.5-1. -1.5 Normalized Strain -3-35 -2. 1 2 3 4 5 (b) Gage B (Longitudinal) Figure 3.112 Specimen 7: Gusset Longitudinal Strain Gage Time Histories (Low-cycle Fatigue Test No. 2) 128

Strain (microstrain) 6 4 2-2.3.2.1. -.1 Normalized Strain -4-6 -.2 -.3 1 2 3 4 5 (a) Gage R1 (Longitudinal) Strain (microstrain) 6 4 2-2.3.2.1. -.1 Normalized Strain -4-6 -.2 -.3 1 2 3 4 5 (b) Gage R2 (Transverse) Figure 3.113 Specimen 7: Gusset Rosette Strain Gage Time Histories (Low-cycle Fatigue Test No. 2) 129

6 Longitudinal Displacement (in) 4 2-2 -4-6 5 1 15 2 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 5 1 15 2 End Rotation (rad.) (b) Transverse Direction Figure 3.114 Specimen 7: Table Displacement Time Histories (All Tests Combined) 13

2-15 -1-5 5 1 15 Resultant Force (kips) 1-1 -2-6 -4-2 2 4 6 Figure 3.115 Specimen 7: Brace Force versus Deformation (All Tests Combined) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 5 12 4 1 8 3 6 2 4 1 2 5 1 15 2 Normalized Cumulative Cumulative Inelastic Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.116 Specimen 7: Hysteretic Energy Time History (All Tests Combined) 131

2 Resultant Force (kips) 1-1 -2-6 -4-2 2 4 6 Figure 3.117 Specimen 7: Brace Response Envelope 1.6 1.4 2 4 6 8 1 12 14 16 β (=Pmax β /Tmax ) 1.2 1..8.6.4.2. 1 2 3 4 Figure 3.118 Specimen 7: β versus Deformation Level 132

2. 2 4 6 8 1 12 14 16 w (= Tmax / Pyn) (=Tmax/Pyn) 1.5 1..5. 1 2 3 4 (in) (a) Tension 2 4 6 8 1 12 14 16 2. βw (= Cmax/Pyn Pmax / Pyn) 1.5 1..5. 1 2 3 4 (in) (b) Compression Figure 3.119 Specimen 7: w and βw versus Deformation Level 133

Rotation from Displ. and Geometry (rad).2.1. -.1 -.2 -.2 -.1..1.2 Rotation from Inclinometer (rad) Figure 3.12 Specimen 7: End Rotation Comparison 134

(a) before Standard Test (Overview) (b) after all Tests (West End) Figure 3.121 Specimen 8: Testing Photos 135

6 Longitudinal Displacement (in) 4 2-2 -4-6 1 2 3 4 5 6 7 (b) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 1 2 3 4 5 6 7 (b) Transverse Direction End Rotation (rad.) Figure 3.122 Specimen 8: Table Displacement Time Histories (Standard Test) 136

-2-15 -1-5 5 1 15 2 2 Resultant Force (kips) 1-1 -2-6 -4-2 2 4 6 Figure 3.123 Specimen 8: Brace Force versus Deformation (Standard Test) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 14 12 1 8 6 4 2 1 2 3 4 5 6 7 35 3 25 2 15 1 5 Normalized Cumulative Cumulative Inelastic Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.124 Specimen 8: Hysteretic Energy Time History (Standard Test) 137

6 Longitudinal Displacement (in) 4 2-2 -4-6 1 2 3 4 5 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 1 2 3 4 5 (b) Transverse Direction End Rotation (rad.) Figure 3.125 Specimen 8: Table Displacement Time Histories (Low-cycle Fatigue Test No. 1) 138

-2-15 -1-5 5 1 15 2 2 Resultant Force (kips) 1-1 -2-6 -4-2 2 4 6 Figure 3.126 Specimen 8: Brace Force versus Deformation (Low-cycle Fatigue Test No. 1) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 16 14 12 1 8 6 4 2 1 2 3 4 5 4 3 2 1 Normalized Cumulative Cumulative Inelastic Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.127 Specimen 8: Hysteretic Energy Time History (Low-cycle Fatigue Test No. 1) 139

6 Longitudinal Displacement (in) 4 2-2 -4-6 1 2 3 4 5 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 1 2 3 4 5 End Rotation (rad.) (b) Transverse Direction Figure 3.128 Specimen 8: Table Displacement Time Histories (Low-cycle Fatigue Test No. 2) 14

-2-15 -1-5 5 1 15 2 2 Resultant Force (kips) 1-1 -2-6 -4-2 2 4 6 Figure 3.129 Specimen 8: Brace Force versus Deformation (Low-cycle Fatigue Test No. 2) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 16 14 12 1 8 6 4 2 1 2 3 4 5 4 3 2 1 Cumulative Normalized Inelastic Cumulative Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.13 Specimen 8: Hysteretic Energy Time History (Low-cycle Fatigue Test No. 2) 141

6 Longitudinal Displacement (in) 4 2-2 -4-6 5 1 15 2 (a) Longitudinal Direction Transverse Displacement (in) 6.2 4 2.1. -2 -.1-4 -.2-6 5 1 15 2 End Rotation (rad.) (b) Transverse Direction Figure 3.131 Specimen 8: Table Displacement Time Histories (All Tests Combined) 142

-2-15 -1-5 5 1 15 2 2 Resultant Force (kips) 1-1 -2-6 -4-2 2 4 6 Figure 3.132 Specimen 8: Brace Force versus Deformation (All Tests Combined) Hysteretic Energy ( 1 kip-in), Eh Dissipated Energy (x 1 kip-in), Eh 5 12 4 1 3 8 6 2 4 1 2 5 1 15 2 Normalized Cumulative Cumulative Inelastic Deformation, Inelastic Disp. η Eh/(Pyeff*Dby) Figure 3.133 Specimen 8: Hysteretic Energy Time History (All Tests Combined) 143

2 Resultant Force (kips) 1-1 -2-6 -4-2 2 4 6 Figure 3.134 Specimen 8: Brace Response Envelope 1.6 1.4 2 4 6 8 1 12 14 16 β (=Pmax β /Tmax ) 1.2 1..8.6.4.2. 1 2 3 4 Figure 3.135 Specimen 8: β versus Deformation Level 144

2. 2 4 6 8 1 12 14 16 1.5 w (= (=Tmax/Pyn) / Pyn) 1..5. 1 2 3 4 (in) (a) Tension 2 4 6 8 1 12 14 16 2. βw (= Pmax / Pyn) Cmax/Pyn 1.5 1..5. 1 2 3 4 (b) Compression Figure 3.136 Specimen 8: w and βw versus Deformation Level 145

Rotation from Displ. and Geometry (rad).2.1. -.1 -.2 -.2 -.1..1.2 Rotation from Inclinometer (rad) Figure 3.137 Specimen 8: End Rotation Comparison 146

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 (.2ε y 3.2.3 and 3.3.4). ) on Specimens 3 and 4 (see Sections 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 pinto-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 D by 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 147

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, E h, and Cumulative Inelastic Deformation, η The hysteretic energy, E h, 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 9 and 6, 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 5D by. The corrected results based on L4 are presented in Figure 4.6 and Table 4.3(b). 148

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: w m = 1 + b 1 D < 5D by (4.1a) by w m = 2 + b 2 5D (4.1b) D by by Based on the average values of m and b for the corrected test results, the following expressions can be used to evaluate w: 3 48.2 1 w = + 1.11 (4.2a) < 5D D by by 3 34.5 1 w = + 1.18 5D (4.2b) by D by 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. 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: m β = + b (4.3) D by Based on the average values of m and b for the corrected test results, the following expression can be used to evaluate w: β = 19.4 1 3 D by + 1. (4.4) 4.6 Comparison at the SEAOC-AISC Limit State The proposed SEAOC-AISC Recommended Provisions (21) uses the deformation level of 1.5D bm (= 7.5D by ) 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 149

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, ζ eq, can be computed for each brace based on the energy dissipated in each hysteretic loop (Clough and Penzien 1993): ζ Ed eq = π ( A + A ) 2 (4.5) 4 AOB COD where E d = energy dissipated per cycle while A AOB and A COD are the areas of the triangles shown in Figure 4.9. The results were plotted after averaging the ζ eq values at each deformation level. A non-linear regression was then fitted to the data as follows: 1 4 ζ eq = c (4.6) Dby where c is a constant obtained from the regression. In Figure 4.1, 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 4.1. The value of c from the composite regression in Figure 4.1 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: ζ eq 29.3 = D by 1 4 (4.7) 15

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 (3 cycles 2 tests) 6 No fracture (3 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.) Cycle Specimen a 1 2 3 4 5 6 7 8 1.39.4.31.36.3.31.27.27 2.38.41.32.36.3.31.26.27 3.39.41.32.35.3.3.25.26 4.39.41.33.35.31.3.25.26 5.39.41.33.35.3.3.25.26 6.39.41.33.35.31.3.25.26 7.84.86.77.8.75.74.67.7 8.84.86.77.79.74.73.65.69 9.84.86.77.79.74.73.65.69 1.84.86.77.79.75.72.66.69 11 1.64 1.66 1.58 1.58 1.56 1.5 1.44 1.49 12 1.63 1.65 1.57 1.56 1.52 1.47 1.4 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 1.5 1.43 1.33 1.38 18 3.6 3.18 3.28 2.96 3.23 2.84 3.13 3.6 19 3.6 3.17 3.26 2.95 3.21 2.82 3.7 3. 2 3.6 3.16 3.26 2.95 3.21 2.8 3.3 2.9 21 3.6 3.16 3.26 2.95 3.2 2.8 2.93 2.76 22 3.6 3.16 3.26 2.95 3.19 2.79 2.8 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 - - a Standard Test Only 151

Table 4.3 Tension Strength Adjustment Factor Idealization (a) Uncorrected Zone 1 Zone 2 Specimen w * m 1 ( 1-3 ) b 1 m 2 ( 1-3 ) b 2 1 1.44 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. 1.12 4 1.356 64.7 1.3 31.9 1.2 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 3.5 1.14 38.1 1.1 8 1.294 32. 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 * m 1 ( 1-3 ) b 1 m 2 ( 1-3 ) b 2 1 1.47 6. 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. 1.3 31.6 1.22 5 1.33 4.9 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 4.2 1.13 36.3 1.15 Average 1.351 48.2 1.11 34.5 1.18 152

Table 4.4 Compression Strength Adjustment Factor Idealization (a) Uncorrected (b) Corrected Specimen m ( 1-3 ) b Specimen m ( 1-3 ) b 1 2. 1. 1 2.3 1. 2 19.8 1. 2 19.7 1. 3 19.7 1. 3 2.3 1. 4 14.9 1. 4 15.6 1. 5 2.5 1. 5 21.4 1. 6 19.6 1. 6 21.6 1. 7 18.4 1. 7 2.4 1. 8 14. 1. 8 15.8 1. Average 18.4 1. Average 19.4 1. Table 4.5 Select Quantities at 1.5D bm (=7.5D by ) (a) Uncorrected Specimen w β βw 1 1.48 1.15 1.7 2 1.45 1.15 1.67 3 1.39 1.15 1.59 4 1.44 1.11 1.6 5 1.4 1.15 1.62 6 1.4 1.15 1.61 7 1.38 1.14 1.57 8 1.38 1.1 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 1.4 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 1.65 153

(a) East Re-used Gusset Plate (b) Typical Specimen Knife Plate Figure 4.1 Hole Elongation Sources 154