Eric Lumpkin Thesis

Concentrically Brace Frames using a Balanced Design
Procedure
requirements for the degree of
Master of Science in Civil Engineering
University of Washington
Department of Civil and Environmental Engineering
University of Washington
Graduate School
This is to certify that I have examined this copy of a masters thesis by
Eric J. Lumpkin
and have found that it is complete and satisfactory in all respects,
and that any and all revisions required by the final
examining committee have been made.
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Date:
In presenting this thesis in partial fulfillment of the requirements for a masters degree at the
University of Washington, I agree that the Library shall make its copies freely available for
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Signature
Date
Eric J. Lumpkin
Department of Civil and Environmental Engineering
Special concentrically braced frames (SCBF) are a commonly employed lateral load resisting
systems, specifically designed to resist large seismic excitations in steel structures. Although prior
research has focused on the behavior of the cyclic response of brace frame components, very few
studies have simulated the response of multi-story systems. A collaborative project, undertaken by
researchers at the University of Washington (UW) and the National Center for Research on
Earthquake Engineering (NCREE) in Taiwan, has developed, tested, and evaluated the
performance of both two and three story SCBFs; with the focus of this research program being the
three story specimens. For this test series, entitled “Tomorrows Concentrically Brace Frame 2”
(TCBF2), a total of three tests were conducted on a reusable, three story test frame complete with
composite concrete slabs on each story. The three tests were designed using a combination of
prior test results, improved design techniques and high-resolution finite element analyses. All three
specimens had an identical brace configuration of a multi-story X-brace on the lower two stories
and a chevron brace configuration on the third story.
Two of the test specimens, TCBF2-HSS and TCBF2-WF, were designed with out-of-plane (OOP)
buckling hollow structural sections (HSS) and wide flange brace shapes. The principal area of
investigation for these two specimens was to assess the inelastic performance of new compact
corner and middle gusset plates designed with an elliptical and vertical beam offset, respectively,
with the intent of increasing the connection compactness while permitting adequate ductility. The
third test specimen, TCBF2-IP, was designed with an innovative in-plane rotating connection that
permitted in-plane brace buckling through a hybrid gusset and knife plate connection. Moreover,
all the TCBF2 connections were designed with a proposed balanced design procedure that
encourages ductility by allowing for yielding in elements which would improve system performance
while discouraging failure mechanisms that would result in irrecoverable damage. The impact of
the brace shape and buckling direction was also thoroughly investigated.
To date, these three specimens have been the most accurate representation of the size, scale and
boundary conditions of SCBFs constructed in the field. This research has shown that the balanced
design procedure and novel connection clearances employed in the TCBF2 specimens permit
substantial ductility and connection strengths that are adequate to initiate fracture in the brace
instead of the connection. Additionally, the performance of in-plane buckling SCBFs was found to
be comparable to OOP buckling SCBFs with an increased post-earthquake serviceability.
Furthermore, the results show that proper design and detailing of SCBF connections can lead to
improved inelastic connection and system behavior with drift ranges exceeding 5%.
Acknowledgements
The author would like to take this opportunity to acknowledge a few people and institutions for
making this research and corresponding thesis possible. First and foremost, these tests could not
have been completed without the guidance, support and hospitality of K.C. Tsai () and his
NCREE staff, including: Chih-Yu Wei (), Ching-Yi Tsai ( ), An-Chien Wu ( )
and Chih-Han Lin ( ). The author would also like to thank fellow graduate students Po-
Chien Hsiao () for his support in the design, instrumentation and testing of the specimens
at NCREE, as well as Kelly Clark and Jake Powell for their ongoing advice.
The author would like to acknowledge the faculty and staff at the Department of Civil and
Environmental Engineering for their hard work in providing an excellent program. Particularly
professors Charles Roeder and Dawn Lehman for their guidance and allowing him to travel to
Taiwan to conduct such innovative research. Laura Lowes is also thanked for serving on the
defense committee and for reviewing this thesis.
This international test program would not have been possible without the financial support from
NEES, NSF and material donations from AISC. Further, the author would like to thank World
Cargo International for coordinating the shipping of the steel used in the TCBF2 specimens. Also,
the UW laboratory undergraduate students for their help in preparing the steel for fabrication and
shipping.
On a more personal note, the author would like to express thanks to his teachers and mentors for
imparting on him the knowledge that was necessary to be successful in life and graduate school.
Also, the author would like to thank his girlfriend, Liz Harmon and his parents, Steve and Diane
Lumpkin, for their ongoing love and support.
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1.1 Introduction ................................................................................................................................ 1
1.3 Overview of TCBF2 .................................................................................................................. 2
1.4 Overview of NCREE ................................................................................................................ 3
1.5 Overview of CBFs .................................................................................................................... 4
1.6 General Theory of SCBF Design ............................................................................................ 5
1.6.1 Lateral Force Distribution ............................................................................................... 6
1.6.2 Brace and Connection Design ........................................................................................ 6
1.6.3 Yield Mechanisms and Failure Modes in SCBFs ......................................................... 7
1.7 Balanced Design Procedure ..................................................................................................... 8
1.8 Research Objectives ................................................................................................................... 9
2.1 Introduction .............................................................................................................................. 11
2.2.1 Abolhassan Astaneh-Asl, Subhash Goel, Robert Hanson (1982) ........................... 11
2.2.1.1 Summary of Test Program ........................................................................................ 11
2.2.1.2 Objectives .................................................................................................................... 12
2.2.2.2 Objectives .................................................................................................................... 15
2.2.3.2 Objectives .................................................................................................................... 16
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2.2.4.2 Objectives .................................................................................................................... 18
2.3.1 Patxi Uriz, Stephen Mahin (2004) ................................................................................ 19
2.3.1.2 Objectives .................................................................................................................... 20
2.3.2.2 Objectives .................................................................................................................... 23
2.3.2.4 Discussion ................................................................................................................... 24
2.4 Full System Testing in University of Washington Test Program ..................................... 25
2.4.1 Shawn Johnson (2005), David Herman (2006), Brandon Kotulka (2007), Jake Powell (2009) ..................................................................................................................................... 25
2.4.1.2 Objectives .................................................................................................................... 31
2.4.2.2 Objectives .................................................................................................................... 36
3.1 Introduction .............................................................................................................................. 39
3.4.1 Design Philosophy .......................................................................................................... 46
3.4.4 Brace Net Section ........................................................................................................... 48
3.4.5 Whitmore Yielding and Fracture .................................................................................. 50
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3.4.10 Interface Welds ............................................................................................................... 55
3.5.1 Overview .......................................................................................................................... 55
3.5.3 Balanced Design Whitmore Yielding........................................................................... 57
3.5.5 Balanced Design Comparison ....................................................................................... 58
3.6 TCBF2 Connection Design .................................................................................................... 59
3.6.1 Section and Material Properties .................................................................................... 60
3.6.2 TCBF2-HSS and TCBF2-WF Connection Design ................................................... 61
3.6.2.1 Corner Gusset Plate Geometry Elliptical Clearance Limit .................................. 61
3.6.2.2 Middle Gusset Plate Geometry Vertical Clearance Limit .................................... 62
3.6.2.3 Gusset Plate Buckling ................................................................................................ 65
3.6.2.4 Brace Slot ..................................................................................................................... 66
3.6.3.3 Knife Plate Hinge Region Dimensions and Clearance Limit .............................. 69
3.6.3.4 Knife Plate Geometry and Dimensions ................................................................. 71
3.6.3.5 Gusset Plate Geometry and Clearance Limit ......................................................... 72
3.6.3.6 Slot Details .................................................................................................................. 73
3.7.3 Beam Required Strength ................................................................................................ 74
3.7.4 Beam-to-Column Connections ..................................................................................... 75
3.8.6 Beam-to-Column Connections ..................................................................................... 81
3.8.7 Base Plate ......................................................................................................................... 83
3.10 Frame Location Designations ................................................................................................ 86
Chapter 4: Experimental Setup ..................................................................................................... 89
4.1 Introduction .............................................................................................................................. 89
4.3.3 Transfer Beam ................................................................................................................. 94
4.3.4 Edge Beams ..................................................................................................................... 94
4.3.5 Support Beams ................................................................................................................ 95
4.3.6 Concrete Slabs ................................................................................................................. 96
4.4 Out-of-Plane Frame ................................................................................................................ 98
4.4.2 Slab Rotational Restraints and Roller Guides ............................................................ 99
4.4.3 Modification of OOP Frame for TCBF2-IP ............................................................ 100
4.5 Loading Protocol.................................................................................................................... 101
4.6.1.2 2UNCCn, 2USCCn, 3LNCCn and 3LSCCn ....................................................... 107
4.6.1.3 1UMCn and 2LMCn ................................................................................................ 108
4.6.1.4 3UMCn ...................................................................................................................... 111
4.6.2.1 Knife Plate Rotation (TCBF2-IP).......................................................................... 113
4.6.3 Brace Center Displacement (TCBF2-HSS, TCBF2-IP) ......................................... 115
4.6.4 Brace Center Displacement (TCBF2-WF) ................................................................ 116
4.6.5 Brace Deformed Shape (All TCBF2)......................................................................... 117
4.6.7 Slab Rotation (TCBF2-HSS, TCBF2-WF) ............................................................... 118
4.6.8 Frame and Story Drift (All TCBF2) .......................................................................... 119
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4.6.9 Beam Vertical Deflection (All TCBF2) ..................................................................... 120
4.6.10 Shear Connection Rotation (All TCBF2) .................................................................. 121
4.6.11 Base Plate and Anchor Plate Slip and Uplift (All TCBF2) ..................................... 122
4.6.12 Strain Gauges ................................................................................................................. 123
4.9 Specimen Fabrication ............................................................................................................ 125
Chapter 5: Experimental Results ............................................................................................... 127
5.1 Introduction ............................................................................................................................ 127
5.2.1 Yielding (Y) .................................................................................................................... 129
5.2.2 Buckling (B) ................................................................................................................... 130
5.3 TCBF2-HSS ............................................................................................................................ 133
5.3.3 Pretest Observations .................................................................................................... 141
5.3.4 Initial Drift Range (0% ≤ Frame Drift Range ≤ 1.05%) ........................................ 141
5.3.5 Moderate Drift Range (1.05% < Frame Drift Range ≤ 2.78%) ............................ 144
5.3.6 Severe Drift Range (Frame Drift Range > 2.78%).................................................. 149
5.3.7 Post-Test ........................................................................................................................ 156
5.4 TCBF2-WF ............................................................................................................................. 170
5.4.3 Pretest Observations .................................................................................................... 178
5.4.7 Post-Test ........................................................................................................................ 195
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5.5.7 Post-Test ........................................................................................................................ 227
6.1 Introduction ............................................................................................................................ 235
6.2.4 Energy Dissipation ....................................................................................................... 243
6.3 Brace Behavior ....................................................................................................................... 245
6.3.1 Brace Displacements .................................................................................................... 245
6.3.3 Brace Elongation and Shortening .............................................................................. 250
6.4 Connection Behavior ............................................................................................................. 253
6.4.4 Connection Comparisons ............................................................................................ 262
6.5 Frame Behavior ...................................................................................................................... 265
6.5.1 Column Moments ......................................................................................................... 265
6.5.2 Column Shears .............................................................................................................. 268
6.5.5 Beam Moments ............................................................................................................. 276
6.5.6 Beam Shears ................................................................................................................... 279
6.5.9 Shear Plate Connection Rotations ............................................................................. 286
6.5.10 Third Story Beam Deflections .................................................................................... 287
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6.7 Performance State Pictorials ................................................................................................ 290
Chapter 7: Balance Design β Factor Determination ..................................................... 292
7.1 Introduction ............................................................................................................................ 292
7.3 Actual β Values ....................................................................................................................... 293
7.4 Design β Values ...................................................................................................................... 294
7.5 Whitmore Yielding ................................................................................................................. 294
7.6 Whitmore Fracture ................................................................................................................ 296
7.7 Block Shear ............................................................................................................................. 297
7.9 Net Section Fracture of the Brace ....................................................................................... 299
7.10 Interface Welds ....................................................................................................................... 301
7.12 Recent Block Shear and Whitmore Fracture Investigation ............................................. 304
Chapter 8: Conclusions and Recommendations .............................................................. 308
8.1 Introduction ............................................................................................................................ 308
8.2 Summary .................................................................................................................................. 308
8.2.1 TCBF2-HSS ................................................................................................................... 309
8.2.2 TCBF2-WF .................................................................................................................... 309
8.3.1 Correlation to UW Single Story, Single Bay Testing ............................................... 311
8.3.2 Reusable Test Frame .................................................................................................... 311
8.3.3 Brace Section Type ....................................................................................................... 312
8.3.4 Brace Buckling Direction............................................................................................. 313
8.3.6 Knife Plates .................................................................................................................... 314
8.3.8 Beam-to-Column Connection .................................................................................... 316
8.4 Design Recommendations .................................................................................................... 317
8.4.5 Knife Plates .................................................................................................................... 318
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8.5 Recommendations for Future Work ................................................................................... 319
Appendix A: Specimen Design ................................................................................................... 321
A.1 General .................................................................................................................................... 321
A.2.1.1 Brace-to-Gusset Connection .................................................................................. 323
A.2.1.3 Brace Compressive Buckling Capacity .................................................................. 325
A.2.1.4 Corner Gusset Plate Buckling Check .................................................................... 326
A.2.1.5 Middle Gusset Plate Buckling Check .................................................................... 327
A.2.1.6 Net Section Reinforcement Design ....................................................................... 328
A.2.1.7 Net Section Reinforcement Weld Design ............................................................ 329
A.2.1.8 Interface Weld Design ............................................................................................. 329
A.2.2 TCBF2-WF Connection Design ................................................................................ 330
A.2.2.1 Brace-to-Gusset Connection .................................................................................. 331
A.2.2.4 Corner Gusset Plate Buckling Check .................................................................... 333
A.2.2.5 Middle Gusset Plate Buckling Check .................................................................... 334
A.2.2.7 Net Section Reinforcement Weld Design ............................................................ 337
A.2.3 TCBF2-IP Connection Design ................................................................................... 339
A.2.3.1 Brace-to-Knife Plate Connection .......................................................................... 339
A.2.3.2 Knife Plate Dimension Checks .............................................................................. 340
A.2.3.5 Gusset Plate Thickness ............................................................................................ 343
A.2.4 Connection Design Summary ..................................................................................... 344
A.3 Frame Design.......................................................................................................................... 347
A.3.1.3 W24x94 3rd Story Beam ......................................................................................... 351
A.3.2 Brace Demands on Frame ........................................................................................... 353
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A.3.5 1st Story and 2nd Story Beam Capacity Check ........................................................ 358
A.3.6 3rd Story Beam Capacity Check ................................................................................. 359
A.3.7 1st Story Beam-to-Column Connection Design ...................................................... 359
Appendix B: Specimen Drawings ............................................................................................. 362
B.1 Introduction ............................................................................................................................ 362
B.1.2 TCBF2-WF Construction and Instrumentation Drawings .................................... 378
B.1.3 TCBF2-IP Construction and Instrumentation Drawings ...................................... 390
Appendix C: Data Hysteresis ....................................................................................................... 402
C.1 General .................................................................................................................................... 402
C.4 Corner Gusset Plate Rotation Hysteresis ........................................................................... 410
C.5 Middle Gusset Plate Rotation Hysteresis ........................................................................... 413
C.6 Knife Plate Rotation Hysteresis ........................................................................................... 416
C.7 Column Moments .................................................................................................................. 419
C.8 Column Shears ........................................................................................................................ 423
C.9 Beam Moments ...................................................................................................................... 427
C.10 Beam Shears ............................................................................................................................ 431
D.3 Brace Buckled Displacements .............................................................................................. 436
D.3.1 TCBF2-WF Midpoint .................................................................................................. 436
D.3.3 TCBF2-IP Buckled Shape ........................................................................................... 438
D.4 Gusset Plate Rotation ............................................................................................................ 439
D.5 Knife Plate Rotation .............................................................................................................. 440
D.6 Shear Plate Rotations ............................................................................................................. 440
D.7 Brace Axial Force ................................................................................................................... 441
D.8 Column Forces ....................................................................................................................... 441
D.8.2 Column Moment ........................................................................................................... 442
D.8.3 Column Shear ................................................................................................................ 443
D.9 Beam Forces ........................................................................................................................... 443
D.11 Energy Dissipation ................................................................................................................ 446
E.1 General .................................................................................................................................... 448
E.7 Interface Welds ....................................................................................................................... 454
E.7.2 Brace to Gusset Brace Base Material ......................................................................... 456
References .................................................................................................................................................. 457
Figure 1.4.1: NCREE Laboratory .................................................................................................................. 4
Figure 1.5.1: CBF Brace Configurations ....................................................................................................... 5
Figure 1.6.1: All Braces in Tension (or Compression) NG........................................................................ 6
Figure 1.6.2: Equal Distribution of Tension and Compression Braces -OK .......................................... 6
Figure 1.6.3: Yield Mechanisms and Fracture Modes of SCBFs ............................................................... 8
Figure 2.2.1: Subhash Goel Test Setup ....................................................................................................... 12
Figure 2.2.2: Subhash Goel (1985) in-Plane Buckling Picture ................................................................. 13
Figure 2.2.3: 2t Clearance............................................................................................................................... 14
Figure 2.2.4: Cross-Sections used in Subhash Goel 1989 Study ............................................................. 16
Figure 2.2.5: Minoru Wakabayshi Test Setup ............................................................................................. 18
Figure 2.3.1: Stephen Mahin Test Setup ..................................................................................................... 20
Figure 2.3.2: UC Berkeley Test Photo during Last Cycle ......................................................................... 21
Figure 2.3.3: UC Berkeley Test Photo of Fractured Column .................................................................. 22
Figure 2.3.4: Six Story Test Drawing ........................................................................................................... 23
Figure 2.3.5: Six Story Test Beam Splice Tear ............................................................................................ 25
Figure 2.4.1: UW Prototype Structure (Johnson, 2005)............................................................................ 26
Figure 2.4.2: UW Single Story Single Bay Test Setup (Johnson, 2005) .................................................. 26
Figure 2.4.3: Elliptical Clerance .................................................................................................................... 31
Figure 2.4.4: TCBF1 Test Setup ................................................................................................................... 34
Figure 2.4.5: TCBF1 Frame Dimensions and Member Sizes .................................................................. 34
Figure 2.4.6: TCBF1 Middle Gusset Plates................................................................................................. 35
Figure 2.4.7: Effect of Stiffeners of TCBF1 Middle Gusset Plates ........................................................ 37
Figure 3.2.1: TCBF2 Test Frame .................................................................................................................. 41
Figure 3.2.2: TCBF2-HSS Connections ...................................................................................................... 42
Figure 3.2.3: TCBF2-WF Connections ....................................................................................................... 43
Figure 3.2.4: TCBF2-IP Connections .......................................................................................................... 44
Figure 3.4.1: Brace Net Section Illustration ................................................................................................ 49
Figure 3.4.2: Whitmore Width Illustration.................................................................................................. 50
Figure 3.4.4: Gusset Plate Buckling Illustration ......................................................................................... 52
Figure 3.4.5: Uniform Force Method Diagram and AISC Gusset Plate Geometry ............................. 54
Figure 3.6.1: Corner Gusset Plate Elliptical Clearance Limit .................................................................. 62
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Figure 3.6.2: Middle Gusset Plate Vertical Clearance Limit..................................................................... 63
Figure 3.6.3: Middle Gusset Vertical Clearance Limit von Mises Stress, 2.67% Frame Drift, TCBF1
Model (Hsiao, 2009) ....................................................................................................................................... 64
Figure 3.6.4: EPS at Middle Gusset Plate Reentrant Corner ................................................................... 65
Figure 3.6.5: Middle Gusset Plate Buckling Lengths ................................................................................ 66
Figure 3.6.6: HSS Brace Slot Detail ............................................................................................................. 67
Figure 3.6.7: Wide Flange Brace Slot Detail ............................................................................................... 67
Figure 3.6.8: TCBF2-IP Typical Connection Detail .................................................................................. 68
Figure 3.6.9: Knife Plate von Mises Stress, 1.70% Frame Drift (ksi), (Hsiao, 2009) ........................... 70
Figure 3.6.10: Knife Plate with Taper von Mises Stress, 1.70% Frame Drift 260-mm x 20-mm, 2tkp
(ksi), (Hsiao, 2009) .......................................................................................................................................... 71
Figure 3.6.11: Final Knife Plate Dimensions .............................................................................................. 72
Figure 3.6.12: TCBF2-IP Gusset Plate Detail ............................................................................................ 72
Figure 3.6.13: TCBF2-IP Knife Plate and Gusset Plate Dual Slot Detail ............................................. 73
Figure 3.7.1: Unbalanced Braces Forces on SCBF Beams ....................................................................... 75
Figure 3.8.1: Column Base von Mises Stress, 2.00% Frame Drift (ksi), (Hsiao, 2009) ....................... 77
Figure 3.8.2: 1MB von Mises Stress, 2.00% Frame Drift (ksi), (Hsiao, 2009) ...................................... 78
Figure 3.8.3: 2SB von Mises Stress, 2.00% Frame Drift (ksi), (Hsiao, 2009) ........................................ 80
Figure 3.8.4: 3MB von Mises Stress Results, 2.00% Frame Drift (ksi), (Hsiao, 2009) ........................ 81
Figure 3.8.5: Plastic Rotation Method for Shear Plate Connections ...................................................... 82
Figure 3.10.1: TCBF2 Frame Location Designations ............................................................................... 87
Figure 4.2.1: Test Layout (West Elevation, Plan) ...................................................................................... 91
Figure 4.2.2: Test Layout (North Elevation) .............................................................................................. 92
Figure 4.3.1: Transfer Beam .......................................................................................................................... 94
Figure 4.3.2: Edge Beams .............................................................................................................................. 95
Figure 4.3.3: Support Beams ......................................................................................................................... 96
Figure 4.3.4: Typical Middle Gusset Plate Blockout ................................................................................. 97
Figure 4.3.5: Base Plate and Anchor Plate .................................................................................................. 97
Figure 4.4.1: Main Out-of-Plane Frame ...................................................................................................... 99
Figure 4.4.2: Slab Restraints ........................................................................................................................ 100
Figure 4.4.3: TCBF2-IP Restraint Kickers ................................................................................................ 101
Figure 4.4.4: Modification to OOP Frame for TCBF2-IP ..................................................................... 101
Figure 4.5.1: Loading Protocol ................................................................................................................... 103
Figure 4.6.1: 1LNCCn Instrumentation Layout ....................................................................................... 106
Figure 4.6.2: 1LNCCn TML LVDT Setup ............................................................................................... 106
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Figure 4.6.5: 2UNCCn TML LVDT Setup............................................................................................... 108
Figure 4.6.7: NDI Setup ............................................................................................................................... 110
Figure 4.6.8: 1UMCn NDI LED Setup ..................................................................................................... 110
Figure 4.6.9: 2LMCn TML LVDT Setup .................................................................................................. 111
Figure 4.6.10: 3UMCn Instrumentation Layout ...................................................................................... 112
Figure 4.6.11: 3UMCn String Pot. Setup ................................................................................................... 113
Figure 4.6.12: 2UNCKp Tiltmeter Dimensions ...................................................................................... 114
Figure 4.6.13: 2UNCKp Tiltmeter Setup .................................................................................................. 114
Figure 4.6.14: 3LNCG Movement Setup .................................................................................................. 115
Figure 4.6.15: 1NBr Parallel Brace Displacement Setup ........................................................................ 116
Figure 4.6.16: 1SBr Pivot Plate Setup ........................................................................................................ 116
Figure 4.6.17: 1SBr Perpendicular Displacement Setup ......................................................................... 117
Figure 4.6.18: 1SBr Perpendicular Brace Displacement Anchor .......................................................... 117
Figure 4.6.19: Framing Element Local Rotation Tiltmeters .................................................................. 118
Figure 4.6.20: Slab Rotation Tiltmeters and Tempo. LVDT Locations .............................................. 119
Figure 4.6.21: Slab Rotation Tiltmeters ..................................................................................................... 119
Figure 4.6.22: Frame Drift Tempo. LVDT's ............................................................................................ 120
Figure 4.6.23: Frame Drift Extension Angle ............................................................................................ 120
Figure 4.6.24: Beam Vertical Deflection Setup ........................................................................................ 121
Figure 4.6.25: 1NBShCn TML LVDT Setup ........................................................................................... 122
Figure 4.6.26: 1NBShCn Rotation Setup .................................................................................................. 122
Figure 4.6.27: Base Plate and Anchor Plate Pots ..................................................................................... 123
Figure 4.7.1: Whitewash Plan ...................................................................................................................... 124
Figure 4.8.1: Data Acquisition and Servo Setup ...................................................................................... 125
Figure 5.2.1: Example of Y1 in a Gusset Plate ........................................................................................ 129
Figure 5.2.2: Example of Y2 on a Gusset Plate ....................................................................................... 130
Figure 5.2.3: Example of Y3 on a Gusset Plate ....................................................................................... 130
Figure 5.2.4: Example of Brace Buckling Performance States .............................................................. 130
Figure 5.2.5: Example of BC in a HSS Brace ........................................................................................... 131
Figure 5.2.6: Example of BC in a WF Brace ............................................................................................ 131
Figure 5.2.7: Example of Weld Damage Performance States ................................................................ 132
Figure 5.2.8: Example of Plate Cracking Performance State ................................................................. 132
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Figure 5.3.4: TCBF2-HSS 1st Story Force-Drift Hysteresis ................................................................... 136
Figure 5.3.5: TCBF2-HSS 2nd Story Force-Drift Hysteresis ................................................................ 137
Figure 5.3.6: TCBF2-HSS 3rd Story Force-Drift Hysteresis ................................................................. 137
Figure 5.3.7: 2NB Flange Y1 (+0.26% IFD) ............................................................................................ 141
Figure 5.3.8: 1UNMG Y1 (-0.26% IFD) .................................................................................................. 141
Figure 5.3.9: 1MB Y1 (+0.35% IFD) ........................................................................................................ 142
Figure 5.3.10: 2NB Flange Y2 (+0.52% IFD) .......................................................................................... 142
Figure 5.3.11: 1LSCo Flange Y1 (-0.52% IFD) ....................................................................................... 142
Figure 5.3.12: 3USMG Y2 (-0.52% IFD) .................................................................................................. 143
Figure 5.3.13: 3NBr B1 (+0.52% IFD) ..................................................................................................... 144
Figure 5.3.14: 1SBR B1 (-0.52% IFD) ....................................................................................................... 144
Figure 5.3.15: 3UNCo Y1 (+0.70% IFD) ................................................................................................. 144
Figure 5.3.16: 1UNMG Y2 (+0.70% IFD) ............................................................................................... 145
Figure 5.3.17: 1SBr B2 (-0.70% IFD) ........................................................................................................ 146
Figure 5.3.18: 2UNCo Y1 (-0.70% IFD) .................................................................................................. 146
Figure 5.3.19: 2LSMG Y2 (+1.05% IFD) ................................................................................................. 146
Figure 5.3.21: 2UNCG Y2 (-1.05% IFD) ................................................................................................. 147
Figure 5.3.22: 1UNMG PC (-1.05% IFD) ................................................................................................ 147
Figure 5.3.23: 2UNCG Wb-1 cm (+1.39% IFD) .................................................................................... 148
Figure 5.3.24: 1LNCG Y2 (+1.39% IFD) ................................................................................................ 148
Figure 5.3.25: 1SBr BC (-1.39% IFD) ....................................................................................................... 149
Figure 5.3.26: 2NBr B3 (-1.74% IFD) ....................................................................................................... 150
Figure 5.3.27: 1SBr B3 (-1.74 % IFD) ....................................................................................................... 150
Figure 5.3.28: 2SB Flange Y3 (+1.74% IFD) ........................................................................................... 150
Figure 5.3.29: 2SB Web Y1 (+1.74% IFD) .............................................................................................. 150
Figure 5.3.30: 3MB Y1 (-1.74% IFD) ........................................................................................................ 151
Figure 5.3.31: 2UNCo Y2 (-1.74% IFD) .................................................................................................. 151
Figure 5.3.32: 1LSCo Web Y2 (-1.74% IFD) ........................................................................................... 151
Figure 5.3.34: 2USCG Wb-3.5 cm (+1.74% IFD) .................................................................................. 152
Figure 5.3.35: 2UNCG Distortion (+1.74% IFD) .................................................................................. 153
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Figure 5.3.37: 1NBr BC (+1.74% IFD, Cycle 15) ................................................................................... 153
Figure 5.3.38: 1NBr Initial Tear Lines (-1.74% IFD, Cycle 15) ............................................................ 153
Figure 5.3.39: 1NBr Partial Fracture (-1.74% IFD, Cycle 16) ............................................................... 154
Figure 5.3.40: 1SBr BF (+2.08% IFD) ...................................................................................................... 154
Figure 5.3.41: 1NBr Reversal of Buckling Direction (+2.08% IFD) ................................................... 155
Figure 5.3.42: 1NBr Partial Fracture Opening (+2.08% IFD) .............................................................. 155
Figure 5.3.43: Y3 1LSCo (+2.08% IFD) ................................................................................................... 155
Figure 5.3.44: Y3 2LSMG Y3 (+2.08% IFD) .......................................................................................... 155
Figure 5.3.45: 1NBr Complete Fracture (-1.62% IFD) .......................................................................... 156
Figure 5.3.46: 2SBr Fracture after Actuator Surge .................................................................................. 157
Figure 5.3.47: 1LNCo Post-Test ................................................................................................................ 158
Figure 5.3.48: 1LNCo Post-Test ................................................................................................................ 158
Figure 5.3.49: 2USCo Flange (Post-Test) .................................................................................................. 159
Figure 5.3.50: 2UNCo Flange (Post-Test) ................................................................................................ 159
Figure 5.3.51: 2USCo Web (Post-Test) ..................................................................................................... 159
Figure 5.3.52: 3UNCo (Post-Test) ............................................................................................................. 160
Figure 5.3.53: 3USCo (Post-Test)............................................................................................................... 160
Figure 5.3.54: 2SB (Post-Test) .................................................................................................................... 161
Figure 5.3.55: 2NB (Post-Test) ................................................................................................................... 161
Figure 5.3.56: 1LSCG (Post-Test) .............................................................................................................. 162
Figure 5.3.57: 1LNCG (Post-Test) ............................................................................................................. 162
Figure 5.3.58: 1USMG (Post-Test) ............................................................................................................ 162
Figure 5.3.59: 1UNMG (Post-Test) ........................................................................................................... 162
Figure 5.3.60: 2LSMG (Post-Test) ............................................................................................................. 163
Figure 5.3.61: 2LNMG (Post-Test) ............................................................................................................ 163
Figure 5.3.62: 2USCG (Post-Test) ............................................................................................................. 163
Figure 5.3.63: 2UNCG (Post-Test) ............................................................................................................ 163
Figure 5.3.64: 3LSCG (Post-Test) .............................................................................................................. 164
Figure 5.3.65: 3LNCG (Post-Test) ............................................................................................................. 164
Figure 5.3.66: 3USMG (Post-Test) ............................................................................................................ 164
Figure 5.3.67: 3UNMG (Post-Test) ........................................................................................................... 164
Figure 5.3.68: Typical 1st and 2nd Story Slab Crack Map (+/- 1.05% IFD) ...................................... 166
Figure 5.3.69: Typical Corner Blockout Crack Progression (+/- 1.05% IFD) ................................... 167
Figure 5.3.70: Typical Inner Corner Blockout Crack (1st and 2nd Story, +/- 1.74% IFD) ............. 167
xvi
Figure 5.3.71: Typical Outer Corner Blockout Crack (1st Story, +/- 1.74% IFD) ........................... 167
Figure 5.3.72: 3SB Slab Cracking (Post-Test) ........................................................................................... 168
Figure 5.3.73: Typical Outer Corner Blockout Crack (1st Story, +2.08% IFD) ................................ 168
Figure 5.3.74: 1st Story Slab Crack Map (Post-Test) .............................................................................. 169
Figure 5.3.75: 2nd Story Slab Crack Map (Post-Test) ............................................................................. 169
Figure 5.3.76: 3rd Story Slab Crack Map (Post-Test) .............................................................................. 169
Figure 5.4.1: TCBF2-WF Induced Frame Drift ....................................................................................... 170
Figure 5.4.2: TCBF2-WF Applied Lateral Load ...................................................................................... 171
Figure 5.4.3: TCBF2-WF Frame Force-Drift Hysteresis ....................................................................... 173
Figure 5.4.4: TCBF2-WF 1st Story Force-Drift Hysteresis ................................................................... 173
Figure 5.4.5: TCBF2-WF 2nd Story Force-Drift Hysteresis .................................................................. 174
Figure 5.4.6: TCBF2-WF 3rd Story Force-Drift Hysteresis .................................................................. 174
Figure 5.4.7: Pre-Yielding of the 1LNCo Web ........................................................................................ 178
Figure 5.4.8: Pre-Yielding of the 1LNCG ................................................................................................. 178
Figure 5.4.9: Yielding of the 1NBr (Test Cycle) ...................................................................................... 179
Figure 5.4.10: 2UNCG Y1 (+0.26% IFD) ................................................................................................ 180
Figure 5.4.11: 2SBr B2 (+0.52% IFD) ...................................................................................................... 181
Figure 5.4.12: 1SBr B2 (-0.52% IFD) ........................................................................................................ 181
Figure 5.4.13: 1USMG Y2 (-0.52% IFD) .................................................................................................. 182
Figure 5.4.14: 1LSCG Y2 (-0.52% IFD) ................................................................................................... 182
Figure 5.4.15: Brace and Net Section Yielding (-0.52% IFD) ............................................................... 182
Figure 5.4.16: 1MB Web Y1 (-0.52% IFD) .............................................................................................. 183
Figure 5.4.17: 2UNCG Y2 (+1.04% IFD) ................................................................................................ 184
Figure 5.4.18: 1MB Y1 (+1.04% IFD) ...................................................................................................... 184
Figure 5.4.19: 1LNCo Flange Y2 (+1.39% IFD) .................................................................................... 184
Figure 5.4.20: 2UNCo Flange Y1 (+1.39% IFD) .................................................................................... 184
Figure 5.4.21: 2UNCG Y3 (+1.39% IFD) ................................................................................................ 185
Figure 5.4.22: 1LSCG Y3 (+1.39% IFD) .................................................................................................. 185
Figure 5.4.23: 1LNCG Distortion (-1.39% IFD) .................................................................................... 186
Figure 5.4.25: 2NB Y1 (+1.73% IFD) ...................................................................................................... 186
Figure 5.4.26: 3NBr B2 (+1.73% IFD) ..................................................................................................... 187
Figure 5.4.27: 2SBr BC (+1.73% IFD) ...................................................................................................... 187
Figure 5.4.28: 3LNCG Y2 (+1.73% IFD) ................................................................................................ 188
Figure 5.4.29: 1USMG Y3 (-1.73% IFD) .................................................................................................. 188
xvii
Figure 5.4.31: 2UNCG WBb-2.5 cm (-1.73% IFD) ................................................................................ 189
Figure 5.4.32: 1USMG PC (+1.73% IFD) ................................................................................................ 189
Figure 5.4.33: 2NB Flange Y3 (+2.08% IFD) .......................................................................................... 189
Figure 5.4.34: 1LNCo Web Y2 (+2.08% IFD) ........................................................................................ 189
Figure 5.4.35: 1SBr B3 (-2.08% IFD) ........................................................................................................ 190
Figure 5.4.36: 2SBr B3 (+2.08% IFD) ...................................................................................................... 190
Figure 5.4.37: 1SB Flange Binding on Column (-2.08% IFD) .............................................................. 191
Figure 5.4.38: 1LNCo Y3 (-2.43% IFD) ................................................................................................... 192
Figure 5.4.39: Brace and Net-Section Yielding (-2.43% IFD) ............................................................... 192
Figure 5.4.40: 2UNCG WBb-16cm (-2.43% IFD) .................................................................................. 192
Figure 5.4.41: 3UNMG WBb-1 cm (+2.43% IFD) ................................................................................ 192
Figure 5.4.42: 1LNCG Distortion (-2.43% IFD) .................................................................................... 193
Figure 5.4.44: 1SBr Initial Tearing (+2.43% IFD) .................................................................................. 194
Figure 5.4.45: 2SBr BC (+2.43% IFD) ...................................................................................................... 194
Figure 5.4.46: 2SBr BF (-2.43% IFD) ........................................................................................................ 194
Figure 5.4.47: 1LNCo Flange (Post-Test) ................................................................................................. 195
Figure 5.4.48: 1LNCo Web (Post-Test) .................................................................................................... 195
Figure 5.4.49: 1LSCo Flange (Post-Test) .................................................................................................. 196
Figure 5.4.50: 1LSCo Web (Post-Test) ...................................................................................................... 196
Figure 5.4.52: 3USCo (Post-Test)............................................................................................................... 197
xviii
Figure 5.4.67: 3MB Slab Cracking (Post-Test) ......................................................................................... 202
Figure 5.5.1: TCBF2-IP Induced Frame Drift ......................................................................................... 203
Figure 5.5.2: TCBF2-IP Applied Lateral Load ......................................................................................... 204
Figure 5.5.3: TCBF2-IP Frame Force-Drift Hysteresis .......................................................................... 206
Figure 5.5.4: TCBF2-IP 1st Story Force-Drift Hysteresis ...................................................................... 206
Figure 5.5.5: TCBF2-IP 2nd Story Force-Drift Hysteresis .................................................................... 207
Figure 5.5.6: TCBF2-IP 3rd Story Force-Drift Hysteresis ..................................................................... 207
Figure 5.5.7: Gouging of 2SB ...................................................................................................................... 212
Figure 5.5.8: 2USCKp Y1 (-0.26% IFD)................................................................................................... 213
Figure 5.5.11: 1LNCC Net-Section Plate Yielding (-0.52% IFD) ......................................................... 215
Figure 5.5.12: 1SBr B2 (-0.70% IFD) ........................................................................................................ 216
Figure 5.5.13: 2SBr B2 (+0.70% IFD) ...................................................................................................... 216
Figure 5.5.14: 3UNMC OOP Rotation (+1.04% IFD) .......................................................................... 217
Figure 5.5.15: 3NBr OOP Buckling (+1.04% IFD) ................................................................................ 217
Figure 5.5.16: 3USMKp Y3 (-1.05% IFD) ............................................................................................... 218
Figure 5.5.17: 2NB Y1 (+1.39% IFD) ...................................................................................................... 218
Figure 5.5.18: 2USCKp Y3 (+1.39% IFD) ............................................................................................... 220
Figure 5.5.19: 1USMKp Y3 (+1.39% IFD) .............................................................................................. 220
Figure 5.5.20: 1USMKp PC (+1.39% IFD) ............................................................................................. 221
Figure 5.5.21: 2USCG Y2 (-1.39% IFD) ................................................................................................... 221
Figure 5.5.22: 3LNCG Y2 (+1.39% IFD) ................................................................................................ 221
Figure 5.5.23: 2UNCo Y2 (-1.74% IFD) .................................................................................................. 222
Figure 5.5.24: 1SBr B3 (-1.39% IFD) ........................................................................................................ 223
Figure 5.5.25: 2NBr B3 (+1.39% IFD) ..................................................................................................... 223
Figure 5.5.26: 2NBr BC (-1.74% IFD) ...................................................................................................... 224
Figure 5.5.27: 2SBr BF (-1.74% IFD, Cycle 16) ...................................................................................... 224
Figure 5.5.28: 3USMG Y3 (-1.74% IFD) .................................................................................................. 224
Figure 5.5.29: 1USMKp PC (+1.74% IFD) ............................................................................................. 224
Figure 5.5.30: 1SBr B3 (1.67% IFD).......................................................................................................... 225
xix
Figure 5.5.35: 2USCo Flange (Post-Test) .................................................................................................. 228
Figure 5.5.36: 2SB Flange (Post-Test) ....................................................................................................... 228
Figure 5.5.37: 2NB Flange (Post-Test) ...................................................................................................... 228
Figure 5.5.38: 1LSCKp (Post-Test) ............................................................................................................ 229
Figure 5.5.39: 1LNCKp (Post-Test) .......................................................................................................... 229
Figure 5.5.40: 1USMKp (Post-Test) .......................................................................................................... 229
Figure 5.5.41: 1UNMKp (Post-Test) ......................................................................................................... 229
Figure 5.5.42: 2LSMKp (Post-Test) ........................................................................................................... 230
Figure 5.5.43: 2LNMKp (Post-Test).......................................................................................................... 230
Figure 6.2.1: Hysteresis Envelope Comparison ....................................................................................... 237
Figure 6.2.2: Story Drift Distribution Comparison ................................................................................. 242
Figure 6.2.3: Energy Dissipation Comparison ......................................................................................... 244
Figure 6.3.1: Brace Displacement Comparison ........................................................................................ 247
Figure 6.3.2: Brace Deformed Shape Comparison (1SBr) ..................................................................... 249
Figure 6.3.3: Brace Elongation Comparison ............................................................................................ 251
Figure 6.3.4: HSS and Wide Flange Local Buckling Pictures ................................................................ 252
Figure 6.4.1: TCBF2-HSS Gusset Plate Rotation Comparison ............................................................. 254
Figure 6.4.2: TCBF2-HSS Gusset Plate Rotations (+2.08% IFD, +2.17%SD) ................................. 255
Figure 6.4.3: TCBF2-WF Gusset Plate Rotation Comparison .............................................................. 257
Figure 6.4.4: TCBF2-WF Gusset Plate Yielding (-2.43% IFD, -2.57% SD) ....................................... 258
Figure 6.4.5: TCBF2-WF Gusset Plate Rotations (-2.43% IFD, -2.57% SD) .................................... 259
Figure 6.4.6: TCBF2-IP Knife Plate Rotation Comparison ................................................................... 260
Figure 6.4.7: TCBF2-IP 1USMKp Rotation (-1.74% IFD, -1.96% SD) .............................................. 261
Figure 6.4.8: Comparison of Gusset Plate Rotations .............................................................................. 262
Figure 6.4.9: Comparison of Knife Plate to Gusset Plate Rotations (HSS Braces) ........................... 263
xx
Figure 6.5.1: Column Moments at Edge of Gusset Plates ..................................................................... 266
Figure 6.5.2: 1SCo Web Yielding (Post-Test) ........................................................................................... 268
Figure 6.5.3: Column Shears ....................................................................................................................... 269
Figure 6.5.4: TCBF2-HSS Story Shear Distribution ............................................................................... 271
Figure 6.5.5: TCBF2-WF Story Shear Distribution ................................................................................. 272
Figure 6.5.6: TCBF2-IP Story Shear Distribution ................................................................................... 273
Figure 6.5.7: Column Axial Forces ............................................................................................................. 275
Figure 6.5.8: Beam Moments at Edge of Gusset Plate ........................................................................... 278
Figure 6.5.9: Beam Shears ............................................................................................................................ 280
Figure 6.5.10: Column Local Rotations at Edge of Gusset Plates ........................................................ 282
Figure 6.5.11: Beam Local Rotations at Edge of Gusset Plates ............................................................ 285
Figure 6.5.12: First Story Beam Shear Plate Rotations ........................................................................... 286
Figure 6.5.13: TCBF2-WF Shear Plate Rotation (-2.57% IFD) ............................................................ 287
Figure 6.5.14: 3rd Story Beam Deflection ................................................................................................. 288
Figure 6.7.1: TCBF2 Performance State Pictorials .................................................................................. 291
Figure 7.5.1: Whitmore Yielding Beta Values .......................................................................................... 295
Figure 7.6.1: Whitmore Fracture Beta Values .......................................................................................... 296
Figure 7.7.1: Block Shear Beta Values ....................................................................................................... 297
Figure 7.8.1: Gusset Plate Buckling Beta Values ..................................................................................... 299
Figure 7.9.1: Net Section Fracture Beta Values ....................................................................................... 300
Figure 7.10.1: Interface Weld Beta Values ................................................................................................ 301
Figure 7.11.1: Brace to Gusset Connection Weld Material Beta Values .............................................. 303
Figure 7.11.2: Brace to Gusset Connection Brace Base Material Beta Values .................................... 304
Figure 7.12.2: HSS-29 Force-Drift Response ........................................................................................... 305
Figure 7.12.1: HSS-29 Connection Drawings .......................................................................................... 305
Figure 7.12.3: HSS-29 Gusset Plate Yielding (3.71%) ............................................................................ 306
Figure 7.12.4: HSS-29 Bolt Hole Elongation and Necking (3.71%) .................................................... 307
Figure A.2.1: TCBF2-HSS 1L(N,S)CG Buckling Lines .......................................................................... 326
Figure A.2.2: TCBF2-HSS 1U(N,S)MG Buckling Lines ........................................................................ 327
Figure A.2.3: TCBF2-HSS Net-Section Dimensions .............................................................................. 328
Figure A.2.4: TCBF2-WF 1L(N,S)CG Buckling Lines ........................................................................... 334
Figure A.2.5: TCBF2-WF 1U(N,S)MG Buckling Lines ......................................................................... 335
Figure A.2.6: TCBF2-WF Net-Section Dimensions ............................................................................... 336
Figure A.2.7: TCBF2-IP Net-Section Dimensions.................................................................................. 342
xxi
Figure A.3.1 Plastic Neutral Axis in Slab of Composite Beam ............................................................. 350
Figure A.3.2: Frame Resultant Forces using Full Brace Forces ............................................................ 354
Figure A.3.3: Axial Load Diagram for Full Brace Forces ....................................................................... 354
Figure A.3.4: Moment Diagram for Full Brace Forces ........................................................................... 354
Figure A.3.5: Frame Resultant Forces using Residual Brace Forces .................................................... 355
Figure A.3.6: Axial Load Diagram for Residual Brace Forces ............................................................... 355
Figure A.3.7: Moment Diagram for Residual Brace Forces ................................................................... 355
Figure A.3.8: Shear Plate Connection Dimensions ................................................................................. 360
Figure C.2.1: TCBF2-HSS Brace Displacement Hysteresis ................................................................... 403
Figure C.2.2: TCBF2-WF Brace Displacement Hysteresis .................................................................... 404
Figure C.2.3: TCBF2-IP Brace Displacement Hysteresis ....................................................................... 405
Figure C.3.1: TCBF2-HSS Brace Elongation/Shortening Hysteresis .................................................. 407
Figure C.3.2: TCBF2-WF Brace Elongation/Shortening Hysteresis ................................................... 408
Figure C.3.3: TCBF2-IP Brace Elongation/Shortening Hysteresis ...................................................... 409
Figure C.4.1: TCBF2-HSS Corner Gusset Plate Rotation Hysteresis .................................................. 411
Figure C.4.2: TCBF2-WF Corner Gusset Plate Rotation Hysteresis ................................................... 412
Figure C.5.1: TCBF2-HSS Middle Gusset Plate Rotation Hysteresis .................................................. 414
Figure C.5.2: TCBF2-WF Middle Gusset Plate Rotation Hysteresis ................................................... 415
Figure C.6.1: TCBF2-IP Corner Knife Plate Rotation Hysteresis ........................................................ 417
Figure C.6.2: TCBF2-IP Middle Knife Plate Rotation Hysteresis ........................................................ 418
Figure C.7.1: TCBF2-HSS Column Moment Hysteresis ........................................................................ 420
Figure C.7.2: TCBF2-WF Column Moment Hysteresis ......................................................................... 421
Figure C.7.3: TCBF2-IP Column Moment Hysteresis ........................................................................... 422
Figure C.8.1: TCBF2-HSS Column Shear Hysteresis ............................................................................. 424
Figure C.8.2: TCBF2-WF Column Shear Hysteresis............................................................................... 425
Figure C.8.3: TCBF2-IP Column Shear Hysteresis ................................................................................. 426
Figure C.9.1: TCBF2-HSS Beam Moment Hysteresis at Edge of Gusset Plates ............................... 428
Figure C.9.2: TCBF2-WF Beam Moment Hysteresis at Edge of Gusset Plates................................. 429
Figure C.9.3: TCBF2-IP Beam Moment Hysteresis at Edge of Gusset Plates ................................... 430
Figure C.10.1: TCBF2-HSS Beam Shear Hysteresis at Edge of Gusset Plates ................................... 432
Figure C.10.2: TCBF2-WF Beam Shear Hysteresis at Edge of Gusset Plates .................................... 433
Figure C.10.3: TCBF2-IP Beam Shear Hysteresis at Edge of Gusset Plates ...................................... 434
Figure D.2.1: Frame and Story Drift Diagram ......................................................................................... 436
Figure D.3.1: Brace Displacement Method (TCBF2-HSS, TCBF2-IP) ............................................... 437
Figure D.3.2: TCBF2-IP Brace Buckled Shape Calculation................................................................... 438
Figure D.8.1: Column Forces Determination Diagram .......................................................................... 442
Figure D.9.1: Beam Forces Determination Diagram .............................................................................. 444
Figure D.9.2: Beam Strain Gauge Layout ................................................................................................. 444
Figure D.10.1: Beam and Column Local Rotation Determination Diagram ...................................... 446
Figure D.11.1: Energy Dissipation Determination Diagram ................................................................. 447
xxiii
Table 2.4.5: TCBF1 Test Summary .............................................................................................................. 36
Table 3.5.1: Limit State Resistances for AISC and Balanced Design Procedures ................................ 59
Table 3.6.1: TCBF2 Brace Capacities and Nominal Properties .............................................................. 60
Table 3.6.2: Plate Material Nominal Properties ......................................................................................... 61
Table 3.9.1: Framing Elements Steel Coupon Test Results ..................................................................... 84
Table 3.9.2: Connection Steel Coupon Test Results ................................................................................. 85
Table 3.10.1: TCBF2 Frame Location Designations Meanings .............................................................. 88
Table 4.2.1: Test Layout Designations and Names ................................................................................... 90
Table 4.5.1: Loading Protocol Values ........................................................................................................ 102
Table 4.6.1: Types of Instruments.............................................................................................................. 104
Table 4.6.3: 2UNCCn, 3LNCCn Instrumentation Dimensions (mm) ................................................. 108
Table 4.6.4: 1UMCn, 2LMCn Instrumentation Dimensions (mm) ...................................................... 110
Table 4.6.5: 3UMCn Instrumentation Dimensions (mm) ...................................................................... 112
Table 5.2.1: Performance State Notation .................................................................................................. 128
Table 5.3.1: Maximum Resistances and Drifts in Each Cycle in TCBF2-HSS ................................... 135
Table 5.3.2: TCBF2-HSS Brace and Gusset Plate Performance State Progression Table ................ 139
Table 5.3.3:TCBF2-HSS Beam and Column Plate Performance State Progression Table ............... 140
Table 5.3.4: Initial Brace Buckling Drift Values....................................................................................... 143
Table 5.3.5: B2 Exact Drift Values for Brace Buckling .......................................................................... 145
Table 5.3.7: Exact Drift Values for Complete Brace Fracture .............................................................. 156
Table 5.4.1: Maximum Resistances and Drifts in Each Cycle in TCBF2-WF .................................... 172
Table 5.4.2: TCBF2-WF Brace and Gusset Plate Performance State Progression Table ................. 176
Table 5.4.3: TCBF 2-WF Beam and Column Plate Performance State Progression Table .............. 177
Table 5.4.7: TCBF2-WF Residual Story Drifts ........................................................................................ 195
xxiv
Table 5.5.1: Maximum Resistances and Drifts in Each Cycle in TCBF2-IP ....................................... 205
Table 5.5.2: TCBF2-IP Brace and Corner Gusset Plate Performance State Progression Table ...... 209
Table 5.5.3: TCBF2-IP Middle Gusset Plate Performance State Progression Table ......................... 210
Table 5.5.4: TCBF 2-IP Beam and Column Plate Performance State Progression Table ................ 211
Table 5.5.8: Exact Drift Values for Complete Brace Fracture .............................................................. 226
Table 6.2.1: Summary of Maximum Sustained Drifts ............................................................................. 236
Table 6.2.2: Frame and Story Elastic Stiffness ......................................................................................... 238
Table 6.2.3: Specimen's Maximum Resistance ......................................................................................... 240
Table 6.3.1: Brace Displacements............................................................................................................... 246
Table 6.6.1: TCBF2-IP Elastic Stiffness, With and Without Braces .................................................... 289
Table 7.2.1: Overview of Yield Mechanisms and Failure Modes .......................................................... 293
Table 7.12.1: HSS-29 Limit State Design β Values ................................................................................. 305
Table A.2.1: Brace Section Properties ....................................................................................................... 322
Table A.2.2: TCBF2 Connection Limit State Resistance Summary ..................................................... 345
Table A.2.3: Connection Dimension Summary ....................................................................................... 346
Table A.3.1: Framing Element Properties ................................................................................................ 348
Table E.2.1: Whitmore Yielding Beta Values ........................................................................................... 449
Table E.3.1: Whitmore Fracture Beta Values ........................................................................................... 450
Table E.4.1: Block Shear Beta Values ........................................................................................................ 451
Table E.5.1: Gusset Plate Buckling Beta Values ...................................................................................... 452
Table E.6.1: Net Section Fracture Beta Values ........................................................................................ 453
Table E.7.1: Interface Weld Beta Values ................................................................................................. 454
Table 8.1.1: Brace to Gusset Welds Beta Values ..................................................................................... 455
Table 8.1.2: Brace to Gusset Brace Base Material Beta Values ............................................................. 456
1
1.1 Introduction
Special concentrically braced frames (SCBFs) are lateral load resisting systems, specifically designed
to resist large seismic excitations in structures. SCBFs are typically composed of diagonal bracing
connected to the beams and columns with a gusset plate or some other form of connection. To
minimize eccentricity, the centerline of the brace usually is lined up with the centerline of the beams
and columns. The braces are the main component in SCBFs that

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Eric Lumpkin Thesis