Adam Christopulos Thesis (BRB Reference-BRB04)

Improved Seismic Performance of

Buckling Restrained Braced Frames

Adam S. Christopulos

A thesis submitted in partial fulfillment of the requirements for the degree of

Master of Science in Civil Engineering

University of Washington

2005

Program Authorized to Offer Degree:

Department of Civil and Environmental Engineering

University of Washington

Graduate School

This is to certify that I have examined this copy of a master’s thesis by

Adam S. Christopulos

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.

Committee Members:

_______________________________________________

Dawn E. Lehman

_______________________________________________

Charles W. Roeder

_______________________________________________

Peter Mackenzie-Helnwein

Date:______________________________

In presenting this thesis in partial fulfillment of the requirements for a master’s degree

at the University of Washington, I agree that the Library shall make its copies freely

available for inspection. I further agree that extensive copying of this thesis is

allowable only for scholarly purposes, consistent with “fair use” as prescribed in the

U.S. Copyright Law. Any other reproduction for any purposes or by any means shall

not be allowed without my written permission.

Signature________________________________

Date____________________________________

i

TABLE OF CONTENTS

Page

List of Figures..................................................................................................................vi

List of Tables...............................................................................................................xviii

CHAPTER 1 Background and Objectives ......................................................................1

1.1 Background ..................................................................................................1

1.2 Concentrically Braced Frames .....................................................................3

1.3 The Buckling Restrained Brace (BRB)........................................................4

1.4 Objective and Scope of Research.................................................................7

1.5 Overview of Report......................................................................................8

CHAPTER 2 Literature Review......................................................................................9

2.1 Overview......................................................................................................9

2.2 BRB Performance ........................................................................................9

2.3 BRBF System Performance .......................................................................13

CHAPTER 3 BRBF and Specimen Design...................................................................24

3.1 Overview and Design of the Prototype Frame...........................................24

3.2 Description of AISC/SEOC Draft Provisions............................................29

3.3 Current Design Procedure..........................................................................31

3.3.1 BRB and Bolt Design Procedure.............................................31

3.3.2 Splice Plate Design Procedure.................................................34

3.3.3 Gusset and Rib Plate Design Procedure ..................................35

3.3.4 Gusset-to-Beam/Column Weld Design Procedure..................42

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3.3.5 Rib-to-Gusset Weld Design Procedure ...................................45

3.3.6 Framing Member Design Procedure .......................................46

3.3.7 Beam-to-Column Connection Design Procedure ....................46

3.4 Specimen Design........................................................................................49

3.4.1 Specimen BRBs.......................................................................49

3.4.2 Reference Specimen Connection Design ................................51

3.4.3 Reference Specimen Frame Design.........................................52

3.5 Proposed Alternative Design Procedure and Possible Design Variations .54

3.6 BRB02 Specimen Design – Tapered Gusset Plate.....................................59

3.7 BRB03 Specimen Design – Bearing Bolt Connection...............................60

3.8 BRB04 Specimen Design – Rotated BRB Cross Section..........................61

CHAPTER 4 Testing Apparatus, Procedure, and Instrumentation ...............................63

4.1 Overview and General Discussion.............................................................63

4.1.1 Strong Wall (1) and Strong Floor (2) ......................................63

4.1.2 Channel Assembly (3) .............................................................65

4.1.3 Load Beam (4) .........................................................................67

4.1.4 Actuator (5) and Reaction Block (6) .......................................68

4.1.5 Out of Plane Restraints (7) ......................................................69

4.1.6 Column Axial Load System (8)...............................................70

4.2 Later Required Modifications ....................................................................71

4.3 Specimen Fabrication.................................................................................73

4.4 Instrumentation ..........................................................................................75

4.5 Data Acquisition and Test Documentation ................................................82

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4.6 Loading Protocol........................................................................................83

4.7 Chronology of Testing ...............................................................................85

CHAPTER 5 Experimental Results...............................................................................87

5.1 Overview....................................................................................................87

5.2 Damage States and Locations ....................................................................88

5.2.1 Anatomy of Force Displacement Responses...........................97

5.3 Drift Ranges ...............................................................................................99

5.3.1 Frame Drift Corrections ........................................................100

5.4 Response of Reference BRB....................................................................103

5.4.1 Description of Reference BRB Behavior ..............................106

5.4.2 Response and Failure Summary of Reference BRB..............124

5.5 Response of Specimen BRB02 ................................................................127




5.9 Comparison and Summary of Response ..................................................159

CHAPTER 6 Interpretation and Analysis of Results ..................................................170

6.1 Overview..................................................................................................170

6.2 Calculation Methods ................................................................................171

6.2.1 Beam/Column Moments and Shears .....................................171

6.2.2 Energy Dissipation and Equivalent Viscous Damping Ratio......

...........................................................................................................174

6.2.3 BRB Core Strains ..................................................................176

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6.2.4 Brace Forces ..........................................................................177

6.2.5 BRB Casing Shift ..................................................................178

6.2.6 BRB Casing, Gusset Plate, and Rib Plate Stresses................179

6.2.7 Beam/Column Relative Rotations .........................................182

6.3 Comparison of Response .........................................................................183

6.3.1 Drift and Force Comparisons ................................................183

6.3.2 Comparison of Moment and Shear Forces ............................187

6.3.3 Energy Dissipation and Equivalent Damping Ratio

Comparisons ..........................................................................196

6.3.4 Core Strain Comparisons.......................................................200

6.3.5 Brace Forces ..........................................................................205

6.3.6 BRB Casing Shift Comparisons ............................................207

6.3.7 Deformation Demands and Required Web Thickness

Estimates................................................................................208

6.3.8 Beam/Column Relative Rotation Comparisons.....................212

6.4 Summary of Specimen Performance........................................................217

CHAPTER 7 Conclusions and Recommendations......................................................219

7.1 Summary ..................................................................................................219

7.2 Failure Mode ............................................................................................222

7.3 Effects of Mildly Tapered Gusset Plates (BRB02, BRB03, BRB04)......223

7.4 Effects of Bearing Bolt Connections (BRB03, BRB04)..........................224

7.5 Effects of Orientation of BRB Core Plate (BRB04) ................................224

7.6 Displacement History of BRB01 .............................................................225

v

7.7 Recommendations for BRBF Connections ..............................................226

7.8 Recommendations for Future BRBF Testing...........................................226

List of References.........................................................................................................230

APPENDIX A Specimen Design and Detail Drawings ..............................................234

A.1 Reference Specimen and BRB Connection Design ................................234

A.1.1 Splice Plate Calculations ........................................................235

A.1.2 Gusset and Rib Plate Calculations..........................................236

A.1.3 Gusset-to-Beam/Column Weld Calculations..........................237

A.1.4 Rib-to-Gusset Weld Calculations ...........................................239

A.2 Beam-to-Column Connection Design .....................................................239

A.2.1 WFWW Calculations (Gusset Plate Corners) ........................240

A.2.2 Shear Tab Calculations (Opposite Gusset Plate Corners) ......241

A.3 BRB03 Connection Calculations ............................................................241

A.4 Specimen Detail Drawings......................................................................242

APPENDIX B Analysis Details ..................................................................................255

B.1 Material Tests ..........................................................................................255

B.2 Additional Analysis Details.....................................................................255

B.3 Force Displacement Discontinuities Due to Casing Shift .......................273

B.4 Beam-to-Column Relative Rotations ......................................................274

APPENDIX C Test Apparatus Detail Drawings .........................................................281

APPENDIX D Instrumentation Details.......................................................................292

D.1 Instrumentation Details ...........................................................................292

vi

LIST OF FIGURES

Figure Number Page

1.1.1 – Typical BRBF Gusset Plate Connections.............................................................2

1.2.1 – Hysteretic Behavior of Braced Frame Systems....................................................4

1.3.1 – Components of an Unbonded Brace BRB............................................................5

1.3.2 – Typical Flat Plate BRB Core and Splice Plates....................................................5

1.3.3 – Different BRB Cross Sections..............................................................................6

1.4.1 – Project Flow Chart................................................................................................7

2.2.1 – UC San Diego Testing of CoreBrace BRB ........................................................11

2.2.2 – Typical BRB Hysteresis .....................................................................................12

2.3.1 – UC Berkley Full-Scale Tests ..............................................................................14

2.3.2 – View of Connection............................................................................................15

2.3.3 – Test 1 North BRB Hysteresis Curves.................................................................16

2.3.4 – Test 2 Gusset Plate Damage ...............................................................................17

2.3.5 – Test 2 BRB Hysteresis Curves ...........................................................................17

2.3.6 – Results of Test 3 .................................................................................................18

2.3.7 – Test 3 BRB Hysteresis Curves ...........................................................................18

2.3.8 – Elevation of BRB/CFT Testing at NCREE........................................................20

2.3.9 – Detail of DCDT BRB .........................................................................................21

2.3.10 – First Floor Upper Gusset-to-DCDT BRB Connection .....................................21

2.3.11 – Gusset-to-BRB Connection ..............................................................................22

2.3.12 – Buckling of Second Floor Upper Gusset/BRB.................................................22

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3.1.1 – SAC Model Buildings and Selection of Prototype Frame..................................25

3.1.2 – Prototype BRBF .................................................................................................28

3.1.3 – Prototype Beam-to-Column Connections...........................................................28

3.1.4 – Prototype Gusset Plate Connection ....................................................................29

3.3.1 – BRB End Connection .........................................................................................32

3.3.2 – General Connection Layout................................................................................34

3.3.3 – Uniform Force Method.......................................................................................35

3.3.4 – Whitmore’s Method............................................................................................37

3.3.5 – Methods of Determining Gusset Plate Buckling Capacities ..............................38

3.3.6 – MTM with Relocated Equivalent Width ............................................................41

3.3.7 – Uniform Force Method.......................................................................................42

3.3.8 – Equilibrium Weld Forces ...................................................................................44

3.3.9 – Beam-to-Column Connection Forces .................................................................46

3.3.10 – Shear Tab Demands..........................................................................................48

3.4.1 – BRB Connection Details ....................................................................................50

3.4.2 – Reference Specimen Connection Design ...........................................................52

3.4.3 – Frame and Beam-to-Column Connection Details ..............................................53

3.5.1 – WFWW Connection Improvement.....................................................................55

3.6.1 – BRB02 Specimen Final Connection Detail ........................................................60

3.7.1 – BRB03 Specimen Final Connection Detail ........................................................61

3.8.1 – BRB04 Orientation.............................................................................................62

4.1.1 – Test Apparatus....................................................................................................64

4.1.2 – Test Apparatus....................................................................................................65

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4.1.3 – Channel Assembly Cross-Section ......................................................................66

4.1.4 – Shear Transfer Connection .................................................................................67

4.1.5 – Specimen-to-Channel Assembly Fit Up.............................................................67

4.1.6 – Load Beam..........................................................................................................68

4.1.7 – Actuator and Reaction Block Connection ..........................................................69

4.1.8 – Out-of-plane Restraints ......................................................................................70

4.1.9 – In-plane Sliding Surfaces ...................................................................................70

4.1.10 – Column Axial Load System .............................................................................71

4.2.1 – Restraint and Load Beam Modifications............................................................72

4.3.1 – Specimen Frame Dimensions and Allowable Tolerances ..................................74

4.4.1 – Actuator/Reaction Block Pot Layout..................................................................75

4.4.2 – Uniaxial Strain Gauge Locations........................................................................76

4.4.3 – Biaxial Strain Gauge Locations..........................................................................77

4.4.4 – Potentiometer Locations for Reference BRB Test .............................................79

4.4.5 – BRB01 Pot Locations (NE Corner) ....................................................................80

4.6.1 – BRBF Loading History.......................................................................................83

4.6.2 – Simple Analytical BRBF Model ........................................................................84

4.6.3 – Modified BRBF Loading History.......................................................................85

5.2.1 – Location Terminology ........................................................................................89

5.2.2 – Tension and Compression Excursions................................................................90

5.2.3 – Gusset Plate Yielding States...............................................................................92

5.2.4 – Frame Yielding States ........................................................................................93

5.2.5 – Frame Buckling Limit States..............................................................................94

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5.2.6 – Weld Damage States...........................................................................................94

5.2.7 – BRB Core Plate Hinging States..........................................................................95

5.2.8 – BRB Casing Performance States ........................................................................96

5.2.9 – Column Base Performance States ......................................................................96

5.2.10 – Reference BRB Force Displacement Response ...............................................97

5.3.1 – Locations of Potentiometers Used for Drift Correction ...................................101

5.3.2 – Rigid Body Frame Rotations ............................................................................101

5.4.1 – Reference BRB Displacement History.............................................................103

5.4.2 – Reference BRB Lateral Force History .............................................................104

5.4.3 – Reference BRB Force Displacement Response ...............................................104

5.4.4 – Reference BRB Core Plate Elongation.............................................................105

5.4.5 – Visual Determination of Core Yield.................................................................106

5.4.6 – Rib Plate Misalignment ....................................................................................107

5.4.7 – Selected Performance States During Yield Drift Range ..................................107

5.4.8 – Selected Performance States During Early Drift Range...................................108

5.4.9 – Selected Performance States During Mid Drift Range.....................................109

5.4.10 – Selected Performance States During Late Drift Range ..................................110

5.4.11 – Selected Performance States During Final Drift Range – Cycles 33&34 ......113

5.4.12 – Selected Performance States During Final Drift Range – Cycle 35...............113

5.4.13 – Selected Performance States During Final Drift Range – Cycle 36...............114

5.4.14 – Progression of Yielding in NE Column Inner Flange ....................................115

5.4.15 – Progression of Yielding in NE Column Outer Flange....................................115

5.4.16 – Progression of NE Inner Column Flange Local Buckling..............................116

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5.4.17 – Progression of Yielding in NE Column Web .................................................116

5.4.18 – Progression of Yielding in NE Beam Inner Flange........................................117

5.4.19 – Yielding and Buckling of North Beam at Load Beam ...................................117

5.4.20 – Progression of Yielding in SW Column.........................................................118

5.4.21 – Progression of Yielding in SW Beam Inner Flange .......................................119

5.4.22 – Progression of SW Beam Web Yielding/Buckling and Flange Buckling......120

5.4.23 – Beam-Column Relative Rotations..................................................................121

5.4.24 – Progression of Damage in SW Gusset Connection ........................................122

5.4.25 – BRB Hinging and Shifting of Casing.............................................................123

5.4.26 – Progression of Failure (SW Connection Cross Section) ................................125

5.4.27 – Hinged Core Plate with Surrounding Concrete and Casing Removed...........126

5.4.28 – SW Connection After Failure.........................................................................126

5.5.1 – BRB02 Displacement History ..........................................................................127

5.5.2 – BRB02 Lateral Force History...........................................................................128

5.5.3 – BRB02 Force Displacement History ................................................................128

5.5.4 – BRB02 Core Plate Elongation..........................................................................129

5.5.5 – NE Column at End of Test ...............................................................................130

5.5.6 – NE Beam Inside Face of Inner Flange at End of Test – Y2 .............................131

5.5.7 – North Beam at Load Beam at End of Test .......................................................131

5.5.8 – SW Column Outer Flange and Web at End of Test .........................................131

5.5.9 – Damage of SW Beam at End of Test................................................................132

5.5.10 – SW Gusset Plate Damage at End of Test .......................................................132

5.5.11 – SW Corner After Failure ................................................................................133

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5.6.5 – Bolt and Splice Plate Slip in NE Connection ...................................................137

5.6.6 – Slight Hole Bearing in BRB (NE Connection).................................................137

5.6.7 – NE Gusset Plate at End of Test ........................................................................138

5.6.8 – Yielding and Buckling in Top of West and East Columns at End of Test .......139


5.6.10 – NE Beam at End of Test .................................................................................140

5.6.11 – North Beam and Load Beam at End of Test...................................................141

5.6.12 – SW Column Outer Flange at End of Test.......................................................141

5.6.13 – SW Beam Web and Inner Flange at End of Test............................................141

5.6.14 – Weld Crack Openings in SW Gusset..............................................................142

5.6.15 – SW BRB End After Failure............................................................................142





5.7.5 – Torsional BRB Rotations During Cycle 37......................................................147

5.7.6 – Bolt and Splice Plate Slip in BRB04................................................................148

5.7.7 – SW Beam-to-Column Connection at End of Test ............................................149

5.7.8 – SW Gusset Plate Connection at End of Test ....................................................149

xii


5.7.10 – SW Beam at End of Test ................................................................................151

5.7.11 – Binding of BRB Cap Plate Against Core .......................................................151

5.7.12 – NE Beam at End of Test .................................................................................152

5.7.13 – SW Column at End of Test.............................................................................152





5.8.5 – SW Beam at End of Test ..................................................................................156

5.8.6 – Gusset Plates at End of Test .............................................................................157

5.8.7 – SW Connection After Failure...........................................................................157


5.8.9 – NE Beam and North Beam at Load Beam at End of Test ................................158

5.9.1 – Comparison of Yielding in SW Beam Webs....................................................161

6.2.1 – Model for Moment and Shear Calculations......................................................171

6.2.2 – Column Moment Diagrams ..............................................................................173

6.2.3 – Idealized Single Force Displacement Curve ....................................................175

6.2.4 – Equivalent Viscous Damping Model................................................................176

6.2.5 – Free Body Diagram of Frame...........................................................................177

6.2.6 – Comparison of Force Calculation Methods......................................................178

6.2.7 – Brace Cylinder Potentiometers.........................................................................178

6.2.8 – BRB01 Casing Stresses ....................................................................................180

xiii

6.2.9 – BRB01 NE Gusset Plate Stresses .....................................................................181

6.2.10 – BRB02 NE Rib Plate Stresses ........................................................................182

6.2.11 – Beam/Column Relative Rotations ..................................................................182

6.3.1 – Contribution of BRBF Components to System Stiffness .................................185

6.3.2 – Final Cycle Force Displacement Responses.....................................................186

6.3.3 – Peak Moments in North Beam Comparison.....................................................188

6.3.4 – Peak Moments in East Column at NE Gusset Edge .........................................189

6.3.5 – Peak Moments in NW Beam-to-Column Shear Tab Connections ...................190

6.3.6 – Peak Moments in SE Beam-to-Column Shear Tab Connections .....................190

6.3.7 – Column Moment Diagrams at +0.14% and -0.18% Drift Ratios .....................191



6.3.10 – Column Moment Diagrams at +0.91% and -0.93% Drift Ratios ...................194

6.3.11 – Peak Shears in West Column Comparisons ...................................................195

6.3.12 – Percent of Total Lateral Force Carried by Columns ......................................196

6.3.13 – Comparison of Total Energy Dissipation .......................................................197

6.3.14 – Comparison of Equivalent Viscous Damping Ratios .....................................198

6.3.15 – Distribution of Energy Dissipation.................................................................199

6.3.16 – Reference BRB Core Strain............................................................................201

6.3.17 – BRB02 Core Strain.........................................................................................202

6.3.18 – BRB03 Core Strain.........................................................................................202

6.3.19 – BRB04 Core Strain.........................................................................................203

6.3.20 – BRB01 Core Strain.........................................................................................203

xiv

6.3.21 – Percent of Lateral Force Carried in BRB .......................................................205

6.3.22 – Brace Forces ...................................................................................................206

6.3.23 – BRB02 Location of Casing at Zero Drifts......................................................207

6.3.24 – Gusset Plate and Frame Connection...............................................................208

6.3.25 – Yielding and Buckling in SW Beam ..............................................................209

6.3.26 – Yielding Length Ratios (a) ...........................................................................211

6.3.27 – Reference BRB NW Connection Moment Rotation Response ......................213

6.3.28 – Reference BRB SE Connection Moment Rotation Response ........................213

6.3.29 – NW Moment Rotation Envelopes ..................................................................214

6.3.30 – SE Moment Rotation Envelopes ....................................................................215

6.3.31 – Moment Rotation Best-Fit Lines ....................................................................216

A.2.1 – Splice Plates.....................................................................................................235

A.4.1 – Specimen Layout .............................................................................................243

A.4.2 – Reference BRB and BRB01 Connection Detail ..............................................244

A.4.3 – Reference BRB and BRB01 Gusset Plates......................................................245

A.4.4 – BRB02 Connection Detail ...............................................................................246

A.4.5 – BRB02, BRB03, and BRB04 Gusset Plates ....................................................247



A.4.8 – BRB Detail ......................................................................................................250

A.4.9 – BRB Connection Details .................................................................................251

A.4.10 – Splice Plates and Rib Plate Details................................................................252

A.4.11 – Specimen Frame Detail .................................................................................253

xv

A.4.12 – Shear Tab Detail ............................................................................................254

A.4.13 – Welded-Flange-Welded-Web and Erection Tab Detail.................................254

B.2.1 – Plot of Unreduced Drift Data...........................................................................256

B.2.2 – Plot of Reduced Drift Data ..............................................................................258

B.2.3 – Reference BRB Beam Moments......................................................................259

B.2.4 – BRB02 Beam Moments ...................................................................................259




B.2.8 – Reference BRB East Column Moments ..........................................................261

B.2.9 – BRB02 East Column Moments........................................................................262

B.2.10 – BRB03 East Column Moments......................................................................262



B.2.13 – Reference BRB West Column Moments .......................................................264

B.2.14 – BRB02 West Column Moments ....................................................................264




B.2.18 – Reference BRB Column Shears.....................................................................266

B.2.19 – BRB02 Column Shears..................................................................................267



xvi


B.3.1 – Force Displacement Response with Dips ........................................................273

B.3.2 – Brace Elongation at Selected Locations ..........................................................273

B.3.3 – Plot of Casing Shift..........................................................................................274

B.4.1 – Reference BRB NW Moment-Rotation Curves...............................................276

B.4.2 – Reference BRB SE Moment-Rotation Curves.................................................276

B.4.3 – BRB02 NW Moment-Rotation Curves............................................................277

B.4.4 – BRB02 SE Moment-Rotation Curves..............................................................277






B.4.10 – BRB01 SE Moment-Rotation Curves............................................................280

C.1.1 – Test Setup Plan ................................................................................................281

C.1.2 – Test Setup Elevation ........................................................................................282

C.1.3 – Channel Assembly Shear Connection Detail...................................................283

C.1.4 – Channel Assembly Shear Connection Section.................................................283

C.1.5 – Channel Assembly Rod and Bolt Layout ........................................................284

C.1.6 – Kicker Plate Details .........................................................................................285

C.1.7 – Load Beam Details...........................................................................................286

C.1.8 – Swivel Head and Swivel Washers Details .......................................................287

C.1.9 – Actuator Details ...............................................................................................288

xvii

C.1.10 – Reaction Block Details ..................................................................................289

C.1.11 – Column Cap Plate Details..............................................................................290

C.1.12 – Channel Assembly Rod Anchor Details ........................................................290

C.1.13 – Actuator Adapter Plate Detail........................................................................291

D.1.1 – Beam/Column Relative Rotation Devices .......................................................292

D.1.2 – Beam/Column Relative Rotation Devices .......................................................293

D.1.3 – Frame Corner Out-of-Plane Device.................................................................293

D.1.4 – Channel Assembly and Column Device Locations .........................................294

D.1.5 – Out of Plane Locations ....................................................................................294

D.1.6 – Column Uplift Measurement Device...............................................................295

D.1.7 – Frame Translation Device 36 ..........................................................................295

D.1.8 – Load Beam Slip Device...................................................................................296

D.1.9 – Brace Out-of-Plane Measurement Devices .....................................................297

D.1.10 – Brace and Frame Diagonal Elongation Measurement Devices .....................297

D.1.11 – Beam and Column Rotation Out of Plane Locations ....................................298

D.1.12 – Column Rotation Device Example ................................................................298

D.1.13 – Brace Rotation Devices .................................................................................299

D.1.14 – Example of Brace Rotation and Torsion Devices .........................................300

D.1.15 – Gusset Plate Out-of-Plane Devices................................................................300

xviii

LIST OF TABLES

Table Number Page

2.2.1 – CoreBrace Subassemblage Tests Summary ....................................................... 12

2.2.2 – Associated Bracing Uniaxial Tests Summary .................................................... 12

3.1.1 – Estimated Building Weights and Base Shears.................................................... 26

3.1.2 – Estimated Story Shears and Brace Forces .......................................................... 26

3.5.1 – Design Modifications ......................................................................................... 59

4.4.1 – Strain Gauges Used Per Test .............................................................................. 77

4.4.2 – Potentiometer Variances From Reference BRB Test ......................................... 80

5.1.1 – Experimental Testing Schedule .......................................................................... 87

5.1.2 – BRBF Specimen Components ............................................................................ 88

5.2.1 – Frame and Gusset Performance State Terminology........................................... 91

5.2.2 – BRB, Bolt, and Column Base Performance State Terminology ........................ 95

5.3.1 – Drift Ranges and Corresponding Cycle Numbers ............................................ 100

5.3.2 – Measured vs. Corrected Story Drifts for the Reference BRB .......................... 102

5.4.1 – Reference BRB Peak Values ............................................................................ 105

5.5.1 – BRB02 Peak Values ......................................................................................... 129

5.6.1 – BRB03 Peak Values ......................................................................................... 135

5.7.1 – BRB04 Peak Values ......................................................................................... 145

5.8.1 – BRB01 Peak Values ......................................................................................... 155

5.9.1 – Abbreviations Used in Tables 5.9.2 Through 5.9.6.......................................... 163

5.9.2 – Test Comparisons – Connections, Brace, and Column Bases.......................... 164

xix

5.9.3 – Test Comparisons – SW Beam......................................................................... 165

5.9.4 – Test Comparisons – NE Column...................................................................... 166

5.9.5 – Test Comparisons – SW Column ..................................................................... 167

5.9.6 – Test Comparisons – NE Beam and North Beam at Load Beam End ............... 168

5.9.7 – Peak Drift Ratio Comparisons.......................................................................... 169

5.9.8 – Peak Input Force Comparisons......................................................................... 169

6.1.1 – Material Properties of Specimens..................................................................... 170

6.3.1 – Comparison of Maximum Drift Range............................................................. 183

6.3.2 – Comparison of Maximum Lateral Force Range............................................... 184

6.3.3 – Theoretical Yield Moments .............................................................................. 187

6.3.4 – Total Energy Dissipated and Equivalent Viscous Damping Ratios ................. 198

6.3.5 – Energy Dissipation in Reference BRB Components........................................ 200

6.3.6 – Peak Core Strain Comparisons......................................................................... 201

6.3.7 – Maximum Strains and Cumulative Plastic Ductility ........................................ 204

6.3.8 – Maximum Brace Forces and Overstrength Factors .......................................... 207

6.3.9 – Web Yielding Estimates ................................................................................... 210

6.3.11 – Shear Tab Connection Stiffness Values ......................................................... 217

6.4.1 – Performance Summary ..................................................................................... 218

B.1.1 – Material Test Results ....................................................................................... 255

B.2.1 – North Beam Moments Peak Results ................................................................ 269

B.2.2 – South Beam Moments Peak Results ................................................................ 269

B.2.3 – NE Edge Column Moments Peak Results ....................................................... 270

B.2.4 – SW Edge Column Moments Peak Results....................................................... 270

xx

B.2.5 – NW Beam-to-Column Connection Moments Peak Results............................. 271

B.2.6 – SE Beam-to-Column Connection Moments Peak Results............................... 271

B.2.7 – East Column Shears Peak Results ................................................................... 272

B.2.8 – West Column Shears Peak Results .................................................................. 272

B.4.1 – SE Beam-to-Column Relative Rotation Comparisons..................................... 275

B.4.2 – NW Beam-to-Column Relative Rotation Comparisons................................... 275

D.1.1 – Reference BRB Instrumentation Locations..................................................... 301

D.1.2 – BRB02 Instrumentation Locations .................................................................. 302




xxi

ACKNOWLEDGEMENTS

I would like to thank my advisors Dr. Dawn E. Lehman and Dr. Charles W. Roeder for

their guidance and assistance over the past two years. Thanks to Dr. Peter Mackenzie-

Helnwein for reviewing and commenting on this paper. Also, thanks to the following

collaborators on this project: Shawn M. Johnson, Ingvar Gunnarson, Jung Han Yoo,

George Gimas, Nabil Kausal-Hayes, Pete Carney, Nathan Caney, Nick Kuffel, Vince

Chaijaroen, Ken Knowlan, and Yiming Liu. A big thanks to Mr. Mark Daniels.

Special thanks to the National Science Foundation for funding this project, Nucor

Yamoto Steel and AISC for donating steel used in this project. A big thanks to Nippon

Steel for the donation of the Unbonded Braces™. Thanks to John Hooper and Cheryl

Burwell of Magnusson Klemencic, Tim Fraser of Canron Western Constructors Ltd,

Walterio Lopes of Rutherford and Chekene, and Rafael Sabelli of Dasse Design Inc. for

technical advice. Thanks also to CoreBrace, Star Seismic, and Associated Bracing for

providing information on their buckling restrained braces.

I would like to thank my family, friends, and fellow graduate students. Moms, Big

Guy, T.H., Dani, Ems, Sara, Kelsey, Gma Marjorie, Gma Christopulos, Mariya, Dave,

Chris, Angela, John, Shawn, George, Julie, Brian, and all the rest.

“Just because some of us can read and write and do a little

math, that doesn’t mean we deserve to conquer the universe.”

“We are here for no purpose, unless we can invent one. Of that I am sure. The human

condition in an exploding universe would not have been altered one iota if, rather than

live as I have, I had done nothing but carry a rubber ice-cream cone from closet to

closet for sixty years.”

-Kurt Vonnegut, Jr.

xxii

DEDICATION

Dedicated To:

THE GNARLY HESSIAN CREW

Beans

Biggie

Bones Justice

Codfish

Motor

1CHAPTER 1

Background and Objectives

1.1 Background

Structural demands in high seismic zones require the use of strong lateral framing

systems. The structure must have adequate strength and stiffness to resist smaller,

frequent earthquakes with limited damage, but must also be able to sustain large

inelastic cyclic deformations to economically assure safety and stability during large,

infrequent earthquakes. This inelastic behavior provides significant energy dissipation

which dampens the structure’s dynamic response. Currently, there are several different

systems used to achieve this energy dissipation and inelastic performance. The most

frequently used steel systems, are the moment resisting frame (MRF) and the

concentrically braced frame (CBF). MRFs are relatively flexible structures that

primarily develop their inelastic deformations through beam flexure and panel zone

yielding [20]. CBFs are stiff, strong, and economical structural systems, and their

inelastic lateral response is dominated by inelastic deformation of the braces [20]. In

both systems the inelastic response of the structural members deliver very high force

and deformation demands to the connections and the remaining structural system.

Extensive research for MRFs by the SAC Joint Venture, has lead to significant

improvement in design and understanding of the demands placed on MRF connections

[e.g., 8, 18]. The improvements came from employment of a performance based design

approach to the MRF connections as described in more detail in Section 3.5 of this

document. By improving the beam-to-column connections in MRFs, the overall system

performance is enhanced through increased deformation and energy dissipation

capacities.

The current state of braced frame systems can be related to that of MRFs prior to the

described SAC design improvements. In braced frame structures, the inelastic demands

placed on the diagonal braces also result in high demands on the gusset plate

2connections. The gusset plates serve to transfer the lateral forces between the brace

and the framing members, and do so conveniently and economically. Currently, gusset

plate designs for BRBFs are varied, as shown in Figure 1.1.1.

Figure 1.1.1 – Typical BRBF Gusset Plate Connections

Although current design provisions yield very strong gusset plate connections, they do

not provide realistic estimates of the inelastic demands, and do not result in reliable

connection and system performance [20]. Since the brace connections are simply

required to be stronger than the brace, there is no assurance that the connection can

accommodate the deformations required. The connection must not only allow for

3adequate inelastic action of the brace, but it must also allow for the system

deformations that the structure has been designed for.

1.2 Concentrically Braced Frames

The strength and stiffness of concentrically braced frames results in an efficient and

economical lateral system. Two of the most widely used systems to date are special

concentrically braced frames (SCBFs) and buckling restrained braced frames (BRBFs).

SCBFs are designed using traditional buckling braces as the means of inelastic

deformation and energy dissipation. Individual braces often possess only limited

ductile capacity under cyclic loading [23]. Buckling braces suffer severe strength

deterioration due to inelastic, post-buckling deformation. The unbalanced response of

buckling braces yields an unsymmetrical hysteretic behavior, with severe pinching

during the compressive hysteretic excursions as shown in Figure 1.2.1a. Because of the

lopsided performance of a single buckling brace, SCBFs are designed using opposing

braces so that one brace will be in tension while the other is in compression. With the

use of opposing buckling braces, the resulting hysterisis curves are much more

symmetric, but are still quite pinched as shown in Figure 1.2.1b. Even with the

improved symmetric hysteresis, the energy dissipation capacity of SCBFs is limited.

Because of the limited ductility and energy dissipation capacity of SCBF systems,

significant effort has been made in development of braces which inhibit buckling.

Buckling restrained braces (BRBs) restrict buckling of the brace, and therefore allow

nearly equal tensile and compressive yielding to occur. The balanced yielding leads to

very full and balanced hysteretic behavior as shown in Figure 1.2.1c. This hysteretic

behavior shows the excellent energy dissipation and inelastic ductility of BRBFs.

4

(a) Single Brace SCBF [12] (b) SCBF with Opposing Braces [21]

(c) Single Brace BRBF

Figure 1.2.1 – Hysteretic Behavior of Braced Frame Systems

1.3 The Buckling Restrained Brace (BRB)

The BRB concept was first explored in Japan during the early 1980’s, but the first BRB

use in the United States was not until early 2000 [7, 13]. Since 2000, interest and use of

BRBs has been growing rapidly. At this time, there are dozens of different types and

configurations of BRBs, but the most often used is the Unbonded Brace concept. This

concept is the original type of BRB, which was developed and produced in Japan during

the 1980’s. The brace consists of a steel core, which is prohibited from buckling by

encasing it in a steel tube filled with mortar/concrete, as shown in Figure 1.3.1. The

steel core takes the entire axial load applied to the brace, and contains a yield length,

along which all inelastic action takes place. Usually the core is either a cruciform shape

or a flat plate with stiffening ribs on the portion of the core that extends out of the outer

tube, as shown in Figure 1.3.2. The brace is designed so that the core does not buckle

5globally or locally, and the outer tube is sized against global buckling. The core

usually contains transition segments to ensure that buckling does not occur outside of

the restrained area, and to also ensure that yielding occurs entirely within the reduced

inner core segment. The braces are connected to gusset plates by use of multiple

numbers of splice plates as shown in Figure 1.3.2. These connections are usually made

through bolted slip-critical connections.

Figure 1.3.1 – Components of an Unbonded Brace BRB [5]

Figure 1.3.2 – Typical Flat Plate BRB Core and Splice Plates

6The steel core is allowed to deform independently from the surrounding concrete and

steel tube by use of a de-bonding substance placed between the core and the concrete.

The de-bonding substance differs depending on the BRB manufacturer, but they all

essentially serve the same purpose of separating the two BRB components. This de-

bonding material minimizes shear transfer between the core and the surrounding

concrete, and also allows for the lateral expansion of the core while in compression

(either by using a deformable de-bonding material, or including small air gaps) [5]. The

desired failure mechanism of these braces is for tensile rupture to occur in the core

plate. Essentially, the rupture of the core signifies that the maximum amount of energy

dissipation and inelastic deformation were obtained by the brace. Nippon Steel of Japan

manufactures and owns the patent on the Unbonded Brace. In the past few years, a

number of U.S. companies have begun to manufacture other BRBs [e.g., 15, 16, 17].

There are also dozens of different BRBs types that have been developed around the

world, although their use is not as common as the Unbonded Brace. Figure 1.3.3 shows

some of the various BRB types that have been manufactured, tested, or proposed, but

they all follow the same basic principals. That is they all consist of an inner core plate

or plates which are restrained from buckling by some means, and are separated so as to

avoid shear transfer to the restraining shell. Some types use unbonded concrete to

restrain buckling, while others use various steel section types and configurations

compliment with separating “air gaps”.

Figure 1.3.3 – Different BRB Cross Sections [14]

71.4 Objective and Scope of Research

A new design methodology similar to that done for MRFs following the 1994

Northridge earthquake [8, 18, 19] has been proposed, and is the basis of a research

project funded by the National Science Foundation (CMS-0301792, “Performance-

Based Design of Concentrically Braced Frames”). The research project addresses both

special concentrically braced frames (SCBFs), as well as buckling restrained braced

frames (BRBFs). The multi part project includes research, evaluation, and experimental

and analytical testing of both SCBFs and BRBFs. The main focus of the research is on

the brace gusset plate connections and how they affect overall system performance.

Figure 1.4.1 provides a flow chart of the different project components, and shows how

these components are used to obtain the final goal of balance equation development.

By following the process outlined in Figure 1.4.1, it is hoped to develop a performance

based design methodology that will improve the performance of SCBF and BRBF

systems.

Figure 1.4.1 – Project Flow Chart

The experimental program includes testing of full-scale BRBF and SCBF specimens.

The specimens were single story-single bay frames with a single diagonal brace,

designed to mimic structures currently being designed and built. The frame and BRB of

each specimen was left unmodified, whereas the gusset plate connections were modified

8to observe the effect on system performance. Five such BRBF specimens have been

tested to date, as described in the remainder of this document. Concurrent testing of

SCBFs was done by Shawn M. Johnson, and is reported in his Masters Thesis entitled

“Performance Based Design of Special Concentrically Braced Frames” [12]. Few

references to SCBFs will be made in this paper, however some incidental comments do

appear during Chapter 4 of this report. Additionally, analytical studies were conducted

by graduate students Ingvar Gunnarson [11] and Jung Han Yoo [34].

1.5 Overview of Report

This report is a discussion of the experimental testing of full-scale BRBFs under cyclic

deformations. Chapter 1 includes an introduction to lateral framing systems, buckling

restrained braces, BRBFs/SCBFs, and an overview of the research project. Chapter 2

discusses research that has previously been done on BRBs and BRBFs, and how the

previous research relates or affects this research project. Chapter 3 describes the current

design methods used to design the BRB, the gusset plate connection, and the framing

members in a BRBF. Chapter 3 also notes potential problems that may exist in current

design, and proposes an idea for an alternative design method. Chapter 4 describes in

detail how the BRBFs were tested and how data was recorded. Chapter 5 then discusses

the results of each test done and how the results compare to each other. Chapter 6

describes the methods used in data analysis and evaluation of the performance of each

test. Finally, Chapter 7 summarizes this report, provides conclusions on the

performance of the BRBFs, how the different connection modifications may or may not

have affected the system performance, and gives recommendations for BRBF

connections and for future experimental testing. Numerical design calculations are

preformed in Appendix A. Detail drawings of the BRBF specimens are also included in

Appendix A. Results of material testing for and additional analysis details are provided

in Appendix B. Detail drawings of the test setup are given in Appendix C. Detailed

information on instrumentation is given in Appendix D.

9CHAPTER 2

Literature Review

2.1 Overview

Before the experimental program was decided upon, it was important to get an idea of

the current level of understanding of BRBFs. Review of how previous BRB and

BRBFs have performed allowed the selection of important design considerations.

Previous tests have shown how connection configurations performed, and where system

deficiencies might exist. They also helped to develop specimens that properly test

realistic conditions in a lateral framing system. Previous tests also aided in

development of a test setup that would test BRBF systems under proper boundary

conditions. This section describes the research and other documents used to aid in the

aforementioned considerations. Isolated buckling restrained brace tests are discussed in

terms of governing qualification tests. The behavior of BRBF system tests are then

summarized and findings relevant to this project are discussed.

2.2 BRB Performance

Previous experimental research on buckling restrained braces, mainly includes isolated

brace tests. The design of a BRB must satisfy requirements for strength, inelastic

deformation, and energy dissipation. These measures are found through qualification

testing following guidelines prescribed in the AISC/SEOC provisions entitled,

“Recommended Provisions for Buckling-Restrained Braced Frames” [25]. Three

different measurements are used to determine the adequacy of a BRB. These

measurements are the compression strength adjustment factor (β ), the tension strength

adjustment factor (ω ), and the cumulative inelastic axial deformation capacity (η ).

Equations, 2-1, 2-2, and 2-3 define these measures.

max

max

TC

=β (2-1)

10

and scysc AF

Tmax=ω , (2-2)

where yscF is the nominal yield strength of the core material, scA is the cross sectional

area of the BRB core plate, maxC and maxT are the maximum compression and tension

forces measured in the specimen during testing, respectively. The cumulative inelastic

axial deformation (η ) is a normalized measure of the ratio of the total hysteretic energy

( hE ), to the average of the effective tensile ( +yP ) and compressive ( −

yP ) yield capacities

of the brace.

byy

h

DPE*=η , (2-3)

where 2

)(*−+ +

= yyy

PPP (2-4)

The total hysteretic energy ( hE ), is simply the sum of the areas enclosed by each

hysteretic loop of a test. byD is the yield axial elongation of the brace, and the

parameter used to normalize the cumulative inelastic axial deformation [15]. The

AISC/SEOC draft provisions [25] specify maximum β values of 1.3, and minimum η

values of 140 (for uniaxial testing). BRBs must be qualified under subassemblage

testing, not just uniaxial testing. Uniaxial tests are those subject only to concentric axial

forces following the loading pattern in Appendix T of the AISC/SEOC provisions [25].

Subassemblage tests impose the BRB connection to rotational demands combined with

axial loading. AISC/SEOC Appendix T prescribes the following loading sequence for

qualification tests [25].

• 6 cycles of loading corresponding to byb ∆=∆

• 4 cycles of loading at the deformation corresponding to bmb ∆=∆ 5.0



• Additional complete cycles of loading at the deformation corresponding to

bmb ∆=∆ 0.1 as required for the brace test specimen to achieve a cumulative

11inelastic axial deformation of at least 140 time the yield deformation (not

required for the subassemblage test)

Where by∆ is the deformation at the first significant yielding in the brace, bm∆ is the

design story drift of the bay in which the BRB will be located, and b∆ is the

deformation quantity used to control the loading of the test specimen. The provisions

do not explicitly prescribe a loading sequence for connection rotations, other than the

method must be representative of the actual demands that will be placed on the brace in

the design structure. Transverse deformations are commonly used to apply these

rotational demands [15, 16]. An example of a testing apparatus is shown in Figure

2.2.1.

Figure 2.2.1 – UC San Diego Testing of CoreBrace BRB [15]

Brace only tests have consistently shown that BRBs perform very well. These tests [15,

32, 5, 16, 17] typically show stable and full hysteretic curves which are nearly perfectly

symmetric like that shown in Figure 2.2.2.

12

Figure 2.2.2 – Typical BRB Hysteresis [15]

For purposes of demonstrating typical performance of buckling restrained braces, two

test series will be discussed. In the 2003 subassemblage tests of CoreBrace BRBs [15],

six BRB specimens were tested with properties and results as shown in Table 2.2.1. In

the 2003 uniaxial tests of Associated Bracing BRBs [17], two BRB specimens were

tested with properties and results as shown in Table 2.2.2. The yield strength values in

the tables are the actual yield strengths from coupon tests of the core plate materials.

The β and ω values correspond to drift levels of 1.5 bm∆ .

Table 2.2.1 – CoreBrace Subassemblage Tests Summary [15]

Table 2.2.2 – Associated Bracing Uniaxial Tests Summary [17]

13The average β values from these tests were both below the required value of 1.3.

Cumulative inelastic axial deformation capacities (η ) in these tests were far above the

minimum AISC/SEOC requirement of 140. The CoreBrace tests [15] had η values

ranging from 600 to 1400, with an average value of 1025. The Associated Bracing tests

[17] had η values of 700 and 1200. Maximum strains in BRB tests average between

0.025 and 0.035 [5, 15, 16, 17]. All of the different BRBs tested performed well under

the standard loading protocols from the qualification tests.

The implications of the isolated BRB testing is that the isolated braces perform

extremely well, and are well controlled for quality. Braces have also been able to

accommodate significant end rotations in the transverse direction, showing that they

have the ability to perform well under both axial and controlled rotational demands.

What this testing does not show however, is how realistic BRBF connections perform,

and how BRBFs perform as a total system. Although the subassemblage tests subject

BRBs to end rotations, the end rotations do not necessarily occur under realistic

boundary conditions. The elements the isolated BRBs are connected to are much more

substantial than would be seen in a real BRBF system, as shown in Figure 2.2.1. Also,

the rotations are very controlled, and no matter how the BRB responds to them, the end

supports are not affected by the response. In an actual BRBF, rotational demands

would not only be present in the BRB ends, but they would also be present in the gusset

plates and the framing elements. Realistically, the eccentricities that are placed between

the BRB end and the connection would have a significant effect on the overall

performance of the BRB and the overall system. Even without the rotational

considerations, compatibility between the brace, gusset plate, and beam/column are not

addressed by subassemblage brace testing.

2.3 BRBF System Performance

Performance of the buckling restrained brace itself, is only part of the overall

importance of system ductility and performance. In contrast with isolated brace testing,

BRBF system testing has been very limited since BRBs have been used. In the few

14tests that have been run on BRBFs, some possible problems in the connection and

framing elements have been identified. The following paragraphs are descriptions of

some of these tests and their results.

A series of three full-scale braced frame tests which used Unbonded Braces, were run at

the University of California-Berkley, beginning in January of 2002 [29, 30, 31]. Each

of the tests used the same testing apparatus and structural frame, but varied the layouts

of the BRB and gusset plate connections. The first test [29] used an inverted-V

concentric brace configuration as shown in Figure 2.3.1. Since the frame was reused in

all three tests, it had to be designed under more severe demands than a actual BRBF.

The general parameters of the tests are summarized as follows.

• W14x176 columns with a W21x93 beam spanning the bay.

• Bay size was 130.5 inches high by 240 inches wide

• The lateral force was transferred through W10x112 braces.

• Beam-to-Column connections had full penetration welds on the beam flanges,

and fillet welds on the beam web.

• Unbonded Braces were flat plate type

Figure 2.3.1 – UC Berkley Full-Scale Tests [29, 31]

The first test used a slip-critical bolted/splice plate BRB-to-gusset plate connection, and

fillet welded gusset-to-frame connections. The rib plates used in conjunction with the

gusset plates were extended just short of the beam flanges as shown in Figure 2.3.2.

15The two BRBs had 6.4 in2 core areas, with yield stresses of 40.9 ksi ( 260≈yscP kips).

Figure 2.3.2 – View of Connection [29]

The second and third tests used similar connection types, but employed a single

concentric BRB from the top left to the bottom right corners of the frame, as shown in

Figure 2.3.1. Test 2 had a BRB with the same cross section and yield strength as the

BRBs in the first test, but test 3 used a BRB with a 6.15 in2 core area ( 250≈yscP kips).

Additionally, the gusset plates were connected to the frame by full penetration welds in

tests 2 and 3. Test 3 was identical to Test 2, except that small stiffeners were added to

the free edges of the gusset plates at their connections to the frame. Additional

connection geometry for any of the tests was not readily available at the time this

material was reviewed. Also, it should be noted that the test reports reviewed had not

yet been verified, and served only as a general summary.

The first test was loaded according to the following loading sequence.

• 6 cycles at 39.0=∆b inches ( by∆ )

• 4 cycles at 86.0=∆b inches ( bm∆5.0 )



16No serious damage occurred in the BRB or the gusset plate connections. The gusset

plates yielded a fair amount, but no fracture or buckling occurred. No failure mode

occurred during these cycles in the brace or gusset plate connections. The estimated

hysteretic behavior of the “north” BRB was as shown in Figure 2.3.3.

Figure 2.3.3 - Test 1 North BRB Hysteresis Curves [29]

The second test was loaded according to the following loading sequence.





In the second test, damage did occur in the gusset plate. During the last cycles, fracture

occurred at both gusset plate connections due to frame action [30], as shown in

Figure 2.3.4a. Additionally, local buckling occurred at the free edge of the top gusset

plate as shown in Figure 2.3.4b. No problems were observed in the BRB or the gusset

plate connection. The estimated hysteretic behavior of the BRB is shown in Figure

2.3.5.

17

(a) Gusset Plate Fracture (b) Gusset Plate Buckling

Figure 2.3.4 – Test 2 Gusset Plate Damage [30]

Figure 2.3.5 – Test 2 BRB Hysteresis Curves [30]

The third test was loaded according to the following loading sequence.




• 1 cycle at 38.3=∆b inches ( bm∆5.1 )


During the first 1.5 bm∆ cycle, the entire bottom flange of the main beam fractured at the

gusset-to-beam connection. The beam fracture also caused out of plane deformation in

18the BRB as shown in Figure 2.3.6b. By the end of loading, the fracture had spread

into the web and the BRB severely hinged out of plane as shown in Figure 2.3.6. It

should be noted that this fracture occurred just inside of the beam web stiffener. The

estimated hysteretic behavior is shown in Figure 2.3.7.

(a) Beam Fracture (b) Hinging of BRB

Figure 2.3.6 – Results of Test 3 [31]

Figure 2.3.7 – Test 3 BRB Hysteresis Curves [31]

From the Berkley tests, a number of considerations were able to be made about the

design and testing of the BRBFs that are the topic of this report. It was seen from the

tests that limitations in the gusset plates and connected frame elements adversely

affected the overall system performance. The gusset plate buckling and fracture that

19occurred during test 2, showed that although the connections were designed for

strength according to current methods, they were not able to accommodate the large

inelastic deformations of the frame. The beam fracture that occurred in test 3, also

impacted the performance of the BRB by causing it to hinge out of plane. Because of

the reduced performance in the connection, the prescribed loading protocol could not be

completed. Since these three tests reused the same framing system, the frame had to be

stronger and stiffer than would usually be present in an actual building. Therefore, it

seems desirable to further investigate how the gusset plate connections would behave in

a more flexible framing system.

In October of 2003, full-scale testing of a 3-story 3-bay buckling restrained

brace/concrete filled tube (BRB/CFT) system was completed at Taiwan’s National

Center for Research on Earthquake Engineering (NCREE) [28]. The system was tested

first by pseudo-dynamic methods, and then by slow cyclic methods. The structure is

summarized below and shown in Figure 2.3.8.

• The bay sizes were 7 meters wide and 4 meters high

• The first story had H456x201x10x17 beams, the second story had

H450x200x9x14 beams, and the third story had H400x200x8x13 beams

• Exterior columns were 400x400x9 mm square CFTs, and interior columns were

400x9 round CFTs.

• The exterior beam-to-column connections were “moment” connections, whereas

the interior beam-to-column connections were “pinned” connections.

• 15 cm slabs were placed at each floor on top of corrugated metal decking.

• Details on the gusset plate connections were not readily available.

20

Figure 2.3.8 – Elevation of BRB/CFT Testing at NCREE [28]

Each story in the structure used a different type of BRBs oriented in an inverted-V

configuration as shown in Figure 2.3.8. All steel, double-core/double-tube (DCDT)

BRBs were used in the first story, Nippon Unbonded Braces were used in the second

story, and concrete-filled DCDT BRBs were used in the third story. The cross sections

off all the BRBs were flat plate type, with cross sectional areas as follows.

• The first story BRBs had core cross sectional areas of 30 cm2

• The second story BRBs had core cross sectional areas of 25 cm2

• The third story BRBs had core cross sectional areas of 15 cm2

The Taiwanese developed DCDT BRBs utilize two separate flat plate or built up T

sections, bolted together with a distance between each core that matches the gusset plate

thickness as shown in Figure 2.3.9. Details on the all steel DCDTs were not available.

Each separate core is bolted together through angles welded to the brace casing. The

connection detail of these braces allows for much fewer bolts than with Unbonded

Brace BRBs which use splice plate connections. DCDT BRBs have adequately met

qualifying BRB component and sub-assemblage tests using the AISC/SEAOC loading

protocol.

21

Figure 2.3.9 – Detail of DCDT BRB

Originally, the DCDT BRB connections did not use rib stiffeners on the gusset plate as

shown in Figure 2.3.10a. During testing, the first floor upper gusset plate for the north

brace buckled at a relatively low story drift of 0.005 radians as seen in Figure 2.3.10b.

The gusset plate buckling also caused hinging in the end of the BRB.

(a) Prior to Buckling (b) After Buckling

Figure 2.3.10 - First Floor Upper Gusset-to-DCDT BRB Connection [28]

In contrast to the DCDT BRB connections, the gusset-to-BRB connections on the

second story did not have any problems with buckling. These connections included rib

plates which were extended near the beam flange as shown in Figure 2.3.11.

22

Figure 2.3.11 – Gusset-to-BRB Connection [28]

After the buckling in the first floor gusset plates occurred, repairs were made to the

damaged gusset and brace, including addition of free edge stiffeners to the majority of

the gusset plates. The system was then taken through the remainder of the pseudo-

dynamic loading protocol without any further problems. After completion of the

pseudo-dynamic simulations, the system was tested in a cyclic manner. During the

cyclic tests, gusset plate buckling (and consequentially buckling of the BRBs), occurred

at all story levels during the drift range of 0.02 to 0.25 radians [28]. This buckling even

occurred at the second story gusset-to-BRB connection, which was with the Unbonded

Brace BRBs as shown in Figure 2.3.12.

Figure 2.3.12 – Buckling of Second Floor Upper Gusset/BRB [28]

23These tests again showed limitations in the gusset plate connections. Perhaps the

most obvious issue is of gusset plate buckling. This buckling proved to be very

detrimental to both the brace and overall connection performance, and occurred at

significantly low drifts. Although the addition of gusset plate free edge and rib

stiffeners extended the life of the system, the desired failure mechanism of BRB core

rupture was still not accomplished. Both the Berkley and Taiwan tests have shown that

it’s possible gusset plate connections designed under current procedures may not be

able to achieve the maximum levels of energy dissipation and inelastic deformation

possible in BRBF systems.

24 CHAPTER 3

BRBF and Specimen Design

3.1 Overview and Design of the Prototype Frame

Because BRBFs are a relatively new structural system, understanding of the

performance of BRB connections and their overall effect on system performance is

limited. The interaction of the surrounding frame, the gusset plates which connect the

brace to the frame, and the brace itself, is still relatively unknown. As was shown in

Chapter 2, potential deficiencies have been found in tested BRBF systems. Research is

needed to address the performance of BRB connections in realistic framing systems,

and to develop a design methodology which ensures the ductility of BRBF systems.

This chapter describes the most common procedures used for designing BRBFs. These

procedures were then used to design the five different BRBF specimens that were

tested.

To adequately investigate and improve the performance of BRBF connections, a

reference specimen based on the current design methods is required. The results of that

specimen will be used to develop the other test specimens. A prototype BRBF was

based on a one bay, one story frame from the SAC Model Buildings found in FEMA-

355C Appendix B [9]. The model buildings, which come from local area code designs

by three U.S. consulting firms, were 3, 9, and 20 stories tall as shown in Figure 3.1.1.

The corresponding one bay, one story prototype frame is also shown in Figure 3.1.1.

25

Figure 3.1.1 – SAC Model Buildings and Selection of Prototype Frame

FEMA-355C provides area loads for dead and live loads that are applicable to the

model building. The total structure weight (W) was estimated using these loads and the

structural dead loads. For the three different model buildings pictured in Figure 3.1.1,

the estimated structure weights were as shown in Table 3.1.1. Following the Equivalent

Lateral Force Procedure outlined in Section 5.4 of the 2000 NEHRP Seismic Provisions

[10], the base shear (V) for each structure was estimated as follows.

WCV s= , (3-1)

where R

ISC DSs = , (3-2)

and saDS SFS32

= , (3-3)

where sC is the seismic response coefficient, DSS is the design spectral response

acceleration at short periods, I is the occupancy importance factor, R is the response

modification coefficient, aF is the acceleration based site coefficient, and sS is the

mapped maximum considered earthquake spectral response acceleration for each model

building, as determined by the 2000 NEHRP Provisions. Assuming a site in the Seattle,

WA area, a seismic coefficient ( sC ) of approximately 0.1 was required. The resulting

base shears (V) were as shown in Table 3.1.1.

26Table 3.1.1 – Estimated Building Weights and Base Shears

The estimated base shears were then distributed to each story of the structure as

specified by Section 5.4.3 of the NEHRP Provisions. In the model buildings, it was

assumed there were two BRBF bays on each face of the structure, therefore a total of

four braces would resist the story shear demand in each direction. Therefore the

required brace forces can be found by dividing the story shear force by four. The final

story shear and brace forces are shown in Table 3.1.2.

Table 3.1.2 – Estimated Story Shears and Brace Forces

The resulting design forces were compared with the actuator capacity (350 to 400 kips)

in the structural laboratory. Therefore, the prototype BRBF was representative of the

lower stories in short buildings, and the upper stories in mid-rise and high-rise

buildings as highlighted in Figure 3.1.1 and Table 3.1.2. The bay size was determined

as 12 feet wide by 12 feet high, from review of the SAC model buildings and building

plans supplied by local design firms. Representative member sizes were determined to

27be W12 columns and W16 beams.

For the prototype BRBF, the beam-to-column connections were determined using

recommendations from both local design firms and BRB manufacturers. The beam-to-

column connections at the gusset plate corners were welded-flange-welded-web

(WFWW) connections, as shown in Figure 3.1.3. The beam-to-column connections at

the corners opposite of the gusset plates, were selected as simple shear tab connections

according to standard design practices, as shown in Figure 3.1.3.

For the prototype BRBF, the BRB type was the Unbonded Brace BRB with splice plate

connections, as depicted in Figures 3.1.2 and 3.1.4. This type of BRB is frequently

used, as mentioned in Section 1.3. A flat plate BRB met the estimated brace forces and

approximate length of the BRB.

Additional general connection details were based on designs by local area firms and

their recommendations, including:

• Gusset plate thickness ( pt ) equal to the BRB core plate thickness ( brt )

• Bolted slip-critical connection between brace and gusset plate

• Welded gusset-to-beam/column connections

• Bolt spacing between different planes is staggered

• ½” gap between end of BRB and furthermost edge of the gusset plate, to allow

small relative movements without impact

These details are highlighted in Figure 3.1.4. Also, based on observations of the BRBF

tests discussed in Chapter 2, the gusset plate rib plates were extended to within 1 inch of

the beam flange as shown in Figure 3.1.4. This was done to ensure that buckling of the

gusset plates would not occur.

28

Figure 3.1.2 – Prototype BRBF

Figure 3.1.3 – Prototype Beam-to-Column Connections

29

Figure 3.1.4 – Prototype Gusset Plate Connection

3.2 Description of AISC/SEOC Draft Provisions

BRBFs are a fairly new type of lateral structural system used in the United States, and

design provisions had not yet been included in any governing building codes at the time

the specimens were designed. A draft set of provisions has been developed by a joint

American Institute of Steel Construction (AISC) - Structural Engineers Association of

California (SEOC) committee. This draft provision, entitled “Recommended Provisions

for Buckling-Restrained Braced Frames” [25], has been incorporated into the 2005

edition of the “AISC Seismic Provisions for Structural Steel Buildings”. The initial

analysis and design process for this project occurred during 2003/2004, and was

primarily based off on the AISC/SEOC draft provisions. The provisions contain

general requirements for BRBs, the brace connections, and the framing members.

The required axial strength of the brace ( braceP ) should not exceed the design strength of

the steel core ( yscP ).

yscbrace PP φ< ( 9.0=φ ), (3-4)

where scyscysc AFP = (3-5)

30Where yscP is the yield strength of the core plate, and yscF and scA are the yield stress

and net area of the steel core, respectively.

The brace connections are designed to minimize connection yielding, and are therefore

designed for the maximum force that can be expected from the brace ( maxP ) at 1.5 times

the design story drift. The design story drift is determined by seismic analysis of the

entire structure, by any reasonable method determined by the design engineer.

maxPRconn ≥ , (3-6)

where yscPP βω=max (3-7)

connR is the capacity of the connection, and β and ω are the brace compression and

tension strength adjustment factors determined from BRB qualifying tests, as described

in Section 2.2. The product βω represents the overstrength of the brace past its

nominal yield capacity. The valueω , accounts for the strain hardening that occurs in

the steel. The valueβ is the ratio of the maximum compression force to the maximum

tension force. This value is usually greater than 1, since the compression force is

usually larger due to the Poisson expansion of the core and small amounts of friction

against the surrounding concrete [23]. Aside from specifying the required connection

strength, the only other connection requirements in the draft provisions, are that the

gusset plates should be designed under considerations of local and global buckling. The

provisions do not specify exactly how this should be done, but designers usually use

methods similar to those used in SCBF systems, as discussed later in this chapter.

The draft provisions also include requirements for the framing members. The beams

and columns must meet the limiting width-thickness ratios given in the AISC Seismic

Provisions, Table I-8-1 [2]. Additionally, the required strength of the members is

determined from applicable load combinations, where the seismic axial forces are

determined from the expected maximum brace forces in tension ( yscPω ) and

compression ( yscPβω ). Framing members must also follow the typical requirements in

31Section 8 of the AISC Seismic Provisions [2]. The provisions do not specify a type

of beam-to-column connection.

3.3 Current Design Procedure

With the prototype BRBF configuration and member sizes from Section 3.1, the

detailed design of the BRBF was done following current design procedures noted in

Section 3.2. The following outlines the design procedure, and provides the governing

design provisions.

• Design of BRB [25].

• Design of bolts ([25] and AISC LRFD [1]).

• Design of BRB connection end ([25] and [1]).

• Determination of BRB length from geometry and bolt spacing.

• Design of splice plates ([25] and [1]).

• Design of gusset and rib plates ([25] and [1]).

• Design of gusset-to-beam/column welds ([25], [1], and SEOC Design Manual

recommendations [26]).

• Design of rib-to-gusset welds ([25], [1], and [26]).

• Design of framing members ([25] and [1]).

• Design of beam-to-column connections ([25] and [1]).

The following subsections provide details of the design procedures used for this study.

3.3.1 BRB and Bolt Design Procedure

The design of the BRB is based on the provisions set forth by the AISC/SEOC draft

provisions as summarized in Section 3.2. The brace yield strength is determined using

equations 3-4 and 3-5. The required brace yield strength ( yscP ), core cross sectional

area ( scA ), and design story drift are given to the BRB manufacturer. For complete

design, the total brace length and bolt hole geometry are also supplied to the

manufacturer. The BRB manufacturer then designs the specific core yield length and

transition details (see Figure 1.3.2), and reports appropriate overstrength factors (βω )

32as described in Section 3.1. The number ( bn ) and size of bolts is determined using

the AISC/SEOC draft provisions [25] and the AISC LRFD specifications [1]. The

bolted connection is designed to resist the maximum force developed by the brace

(Equation 3-7). The use of slip critical bolts designed to this force is recommended by

the draft provisions, but not required. The initial number of bolts was found using

equation 3-8.

n

yscb r

Pn

φβω

= , (3-8)

where nrφ is the slip resistance per bolt from AISC LRFD Table 7-16 [1]. The diameter

of bolts should be determined to balance the number of bolts required with the resulting

connection geometry caused by the bolt diameter. That is, larger diameter bolts require

fewer bolts, but have larger spacing and clearance requirements. Smaller diameter bolts

require more bolts, but have smaller spacing and clearance requirements. The bolt

spacing is determined using AISC LRFD Section J.3 and the required tolerances for bolt

tensioning. Following this, the general BRB connection can be laid out as shown in

Figure 3.3.1.

Figure 3.3.1 – BRB End Connection

33The variables in Figure 3.3.1 are defined as follows.

ϕ is the bolt hole diameter and tbr is the thickness of the core plate and stiffening ribs.

cS , eS , and hS are the bolt spacing, bolt hole edge distance, and bolt row spacing,

respectively. The width of the brace end ( bracew ) is calculated by equation 3-9.

ehbrace SSw 2+= (3-9)

Yield on gross of core plate is checked using AISC LRFD Section D.1.

)2(29.0max brbracebryscn twtFRP −−=≤ ϕφ , (3-10)

where nRφ is the factored resistance of the limit state being checked. Fracture on net of

the core plate is checked using AISC LRFD Section D.1.

)2(275.0max brbracebruscn twtFRP −−=≤ ϕφ , (3-11)

where uscF is the ultimate strength of the core plate material. Additionally, the

following bolted connection limit states need to be checked, as are commonly done with

bolted type connections.

• Bolt Shear Strength (AISC LRFD Table 7-10 or 7-11).

• Bolt bearing, tearthrough, and tearout (AISC LRFD J.3.10).

• Block shear of core plate considering all possible failure paths (AISC LRFD

J.4.3).

Once the brace cross section dimensions and connection geometry are finalized, the

brace length is determined from the resulting connection geometry shown in

Figure 3.3.2. The distance between the brace connection and the beam/column flanges

is not specified, although minimum weld clearances between the rib/splice plates and

the beam/column flanges must be provided. The variables in Figure 3.3.2 are defined as

follows.

bw and cw are the lengths of connected gusset plate edges to the beam and column,

respectively. st and sw are the thickness and width of the splice plates, respectively.

wt is the thickness of rib plates, and bΘ is the angle of the brace with respect to the

column.

34

Figure 3.3.2 – General Connection Layout

3.3.2 Splice Plate Design Procedure

Using the geometry shown in Figure 3.3.2, the splice plates are sized and checked

against the following limit states. Yield on gross of the splice plates is checked using

AISC LRFD Section D.1.

plssysn ntwFRP )(9.0max ϕφ −=≤ , (3-12)

where ysF is the yield strength of the splice plate material, and pln is the number of

plates in the connection. Fracture on net of the splice plates is checked using AISC

LRFD Section D.1.

plssusn ntwFRP )(75.0max ϕφ −=≤ , (3-13)

Where usF is the ultimate strength of the splice plate material. Additionally, the

standard bolted connection limit states need to be checked for the splice plates.

• Bolt bearing, tearthrough, and tearout (AISC LRFD J.3.10).

• Block shear of core plate considering all possible failure paths (AISC LRFD

J.4.3).

353.3.3 Gusset and Rib Plate Design Procedure

Gusset plates are proportioned following the uniform force method as described in

Part 13 of the AISC LRFD specifications, with the work point at the

beam/column/brace centerlines intersection. Rib plates are usually sized to match the

BRB rib stiffeners. The Uniform Force Method (UFM) is used to size the gusset plate

such that no moments are introduced into the connection by the brace force. This is

done by solving equilibrium about a working point, which is the intersection point of

the beam, column, and brace centerlines as shown in Figure 3.3.3.

Figure 3.3.3 – Uniform Force Method

For equilibrium to be satisfied without the inclusion of moments, the gusset plate is

sized based on the beam and column sizes as follows.

2b

bde = , (3-14)

and 2

cc

de = , (3-15)

where ce and be are as defined in Figure 3.3.3. The resultant forces from maxP are

assumed to act at the mid length of the gusset plate edges (α and β ).

36

2bw

=α , (3-16)

and 2

cw=β (3-17)

In order to satisfy equilibrium, equation 3-18a must be true.

0tantan =+Θ−Θ− cbbb eeβα (3-18a)

If °=Θ 45b , equation 3-18a reduces to equation 3-18b.

cb ee −=− βα (3-18b)

Re-substituting equations 3-14 through 3-17 into equation 3-18b gives:

cbbc ddww +−= (3-19)

Therefore, the gusset plate is sized by choosing either bw or cw , and then using

equation 3-19 to solve for the other gusset plate length.

Whitmore’s method [33] is used to determine the tensile strength of the gusset plate,

including the effect of the rib plates. Whitmore’s method defines an equivalent width

( wb ) based on 30 degree extrapolations from the first row of bolts, as shown in

Figure 3.3.4a. To account for the rib plate, a second equivalent width ( wwb ) is

calculated perpendicular to the plane of the gusset plate. The brace width ( braceW ) is

usually less than the equivalent Whitmore width from 30 degree extrapolation. In this

case, the brace width should be used as the equivalent width. Additionally, the removed

material at the bolt hole locations should be accounted for to give effective yield widths

( wweffweff bb , ). Equations for the gusset/rib plate tensile strength can be developed using

the connection geometry in Figures 3.3.4a and 3.3.4b.

37

(a) Gusset Plate Plan View (b) Gusset Plate Cross Section

Figure 3.3.4 – Whitmore’s Method

The yield capacity of the gusset plate is calculated using equation 3-20.

[ ]ywwwweffyppweff FtbFtbRnP +=≤ 9.0max φ , (3-20)

where pwww tWb += 2 , (3-21)

)(2 ϕ−= wwwweff bb , (3-22)

)2)(30tan(2 chw SSb °+= , (3-23)

and )(2 ϕ−= wweff bb (3-24)

wW is the width of the rib plates, wt is the thickness of the rib plates, and ywF and ypF

are the yield strengths of the rib and gusset plate material, respectively.

Bolted connection limit states are also checked. These are usually adequate by

inspection because the geometry is identical to that of the brace, and the brace material

strengths are usually less than those of the gusset and rib plates.

• Bolt bearing, tearthrough, and tearout (AISC LRFD J.3.10)

• Block shear of gusset/rib plates considering all possible failure paths (AISC

LRFD J.4.3)

38Plate buckling capacity is determined using the Thornton (TM) or Modified Thornton

Methods (MTM) [27], as shown in Figures 3.3.5a and 3.3.5b.

(a) Thornton Method (b) Modified Thornton Method

Figure 3.3.5 – Methods of Determining Gusset Plate Buckling Capacities

Thornton’s Method uses a 30 degree extrapolation to determine an equivalent width

( wb ), as shown in Figure 3.3.5a. TM also uses a buckling length ( tl ) that is the smaller

of the average end and center lengths ( 1l , 2l , and 3l ) or the center length ( 2l ).

++

=3

,min 3212

lllllt (3-25)

The buckling length is then used to calculate a buckling coefficient ( tλ ).

EF

tkl yp

p

tt

12π

λ = , (3-26)

where E is the modulus of elasticity of steel, and the effective length factor (k) is taken

as 0.5 for square gusset plates, and 0.65 for tapered gusset plates (AISC LRFD

Section 13). The buckling coefficient is then used to calculate the critical buckling load

( crP ).

When 5.1≤tλ :

yptcr FAP t2

658.0 λ= , (elastic buckling) (3-27a)

39when 5.1≥tλ :

yptt

cr FAP 2877.0λ

= , (inelastic buckling) (3-27b)

where tA is the effective cross sectional area along the equivalent width ( wb ).

The Modified Thornton method uses a 45 degree extrapolation to determine an

equivalent width ( mtb ), as shown in Figure 3.3.5b. The MTM also uses a buckling

length (lmt) from the end of the splice plate connection, to the face of the beam or

column as shown in Figure 3.3.5b. Therefore, the buckling coefficient is found as:

EF

tkl yp

p

mtt

12π

λ = (3-28)

The critical buckling load is found using equations 3-27a or 3-27b, where tA is the

effective cross sectional area along the equivalent width ( mtb ).

When the buckling length extends into the beam/column as it does in Figure 3.3.5b, tA

is usually calculated from the areas in the gusset and beam webs, for both the TM and

MTM methods. For example, using Figure 3.3.5b leads to equations 3-29a and 2-39b.

When platemt bb ≤ :

pmtt tbA = , (3-29a)

when platemt bb ≥ :

( ) wbmtxpmtxmtt tbtbbA +−= , (3-29b)

where mtxb is the length of the equivalent width in the beam web, plateb is the width of

the plate along the equivalent width line, and wbt is the thickness of the beam web.

The Thornton and Modified Thornton methods were developed for flat gusset plates

without rib plates. The rib plates can be ignored as an easy capacity check, or to

determine a lower bound solution using the TM as follows.

40• Calculate a buckling length ( tl ) using equation 3-25 and the geometry shown

in Figure 3.3.5a.

• Calculate the buckling coefficient ( tλ ) using equation 3-28.

• Calculate the effective cross sectional area ( tA ) following equations 3-29a and

3-29b with wb in place of mtb .

• Calculate the critical buckling load ( crP ) using equation 3-27a or 3-27b.

If this check is not adequate, the rib plates can once again be ignored, but with use of

the MTM which will give slightly larger capacities. This is done as follows.

• Use a buckling length ( mtl ) from the geometry shown in Figure 3.3.5b.


• Calculate the effective cross sectional area ( tA ) using equations 3-29a and

3-29b.


If it is necessary or desired to include the effect of the rib plates, the Thornton Method

can be modified to include the rib plates in the effective cross sectional area as follows.

• Calculate a buckling length ( tl ) using equation 3-25 and the geometry shown in

Figure 3.3.5a.


• Calculate the cross sectional area ( tA ) using equations 3-30a and 3-30b.

When platew bb ≤ :

wpbracepwt ttWtbA )( −+= , (3-30a)

when platew bb ≥ :

( ) wpbracewbmtxpmtxwmt ttWtbtbbA )( −++−= (3-30b)


41These three methods do not address the location of the buckling width. In a gusset

plate that uses rib plates, buckling could more easily occur beyond the rib plates as

shown in Figure 3.3.6. This would give a different equivalent width (bmt4), as well as a

different buckling length (lmt4) as shown in Figure 3.3.6.

Figure 3.3.6 – MTM with Relocated Equivalent Width

In Figure 3.3.6, 4D is the distance of the equivalent width past the last row of bolt

holes. In this case, the capacity of the gusset/rib plates could be determined using the

MTM as follows.

• Use a buckling length ( mtl ) from the geometry shown in Figure 3.3.6.


• Calculate the equivalent buckling width (bmt4) using equation 3-31.

mtmt bDb += 44 2 (3-31)

• Calculate the effective cross sectional area ( tA ) using equations 3-29a and

3-29b with 4mtb in place of mtb .


423.3.4 Gusset-to-Beam/Column Weld Design Procedure

The gusset-to-beam/column welds are designed using the Uniform Force Method

(UFM) in AISC LRFD Section 13. The welds are oversized by 140 percent (SEAOC

Seismic Design Manual, Vol. III [26]), to improve the ductility of the welds by

accounting for the variation in the average stress in the weld. To determine the shear

and axial force demands on the welds, several methods are available. In the UFM, the

demands are based on the maximum brace force (Pmax), as shown in Figure 3.3.7.

Figure 3.3.7 – Uniform Force Method

The factored shear forces ( ucV and ubH ), and the factored axial forces ( ucH and ubV ),

on the gusset-to-beam welds are determined using equations 3-32 through 3-35.

maxPr

Vucβ

= , (3-32)

maxPreH c

uc = , (3-33)

maxPreV b

ub = , (3-34)

and maxPr

Hubα

= , (3-35)

where 22 )()( bc eer +++= βα (3-36)

α , β , be , and ce are found using equations 3-14 through 3-17. The design forces for

the welds ( ucP and ubP ) are found by transforming the factored shear and axial forces.

4322ucucuc HVP += , (3-37)

=Θ −

uc

ucc V

H1tan , (3-38)

22ububub HVP += , (3-39)

and

=Θ −

ub

ubbm H

V1tan , (3-40)

where cΘ and bmΘ are the angles between the design forces and the longitudinal axis of

the column and beam welds, respectively (Figure 3.3.7). The forces can be used to

determine the required weld group coefficient (C) from AISC LRFD Table 8-5. Since

values are only tabulated for forces at angles of 0,15,30,45,60, and 75 degrees, the

angles calculated from the above equations can be conservatively rounded up.

weldbuc DlCCP 1, ≤ , (3-41)

where 1C is the electrode strength coefficient from AISC LRFD Table 8-4, D is the

number of sixteenths-of-an-inch in the fillet weld size, and the weld length ( weldl ) is

found using equation 3-42.

chamferbcweld lwl −= , , (3-42)

where chamferl is the length of the chamfered back corner of the gusset plate that is

required for construction (Shown in Figure 3.3.2). D is solved for by rearranging

equation 3-41, and substituting in equation 3-42.

)( ,1

,

chamferbc

buc

lwCCP

D−

≥ (3-43)

Therefore, the column/beam weld size ( bcs , ) is found using equation 3-44.

164.1,

Ds bc = (3-44)

The UFM does not include effects of gusset plate bending, and may be unconservative

in some situations. A simple way to account for bending is to treat both forces as axial

forces, and directly sum them together. Since AISC provisions increase weld strengths

44by 1.5 for transverse loading, use of this method results in smaller weld capacities. In

this case the design forces ( bucP , ) can be found using equations 3-45 and 3-46.

bucbucbuc HVP ,,, += , (3-45)

and °=Θ 0,bc (3-46)

Therefore, the welds can be designed as longitudinal welds (AISC LRFD J2.4).

wbcchamferbcexxweeexxnbuc nslwFntLFRP ,,)( )(4242.06.0 −==≤ φφφ , (3-47)

where exxF is the nominal strength of the weld metal, and wn is the number of welds in

each gusset-to-beam/column connection. The required weld sizes ( bcs , ) are found by

rearranging equation 3-47, and multiplying by the 1.4 overstrength factor.

wchamferbcexx

bucbc nlwF

Ps

)(30.3

,

,, −≥

φ (3-48)

Alternatively, the applied weld forces can be determined directly from equilibrium.

This also gives more conservative weld sizes than the UFM. Figure 3.3.8 shows that

the resultant forces (Fb and Fc) are found at the mid-length of the edges of the gusset

plate (i.e., a, b from Figure 3.3.3).

Figure 3.3.8 – Equilibrium Weld Forces

Using the geometry shown above, expressions for Fb and Fc are developed as follows.

45

c

xbbc X

XXFF )( −= , (3-49)

and ucb PFF =+ , (3-50)

where )45cos()( °−= cbx eeX , (3-51)

)45cos( °= αbX , (3-52)

and xc XX +°= )45cos(β (3-53)

Fb and Fc are found by solving equations 3-49 and 3-50. Their shear and axial

components are as follows.

)45cos(,, °= bcbxcx FF , (3-54)

and )45sin(,, °= bcbycy FF (3-55)

The shear and axial forces are combined to give the resulting design forces ( bucP , ).

bycybxcxbuc FFP ,,, += , (3-56)

and °=Θ 0,bc (3-57)

The required weld sizes are then found using equation 3-48.

For each of the weld calculation methods, welds must also satisfy minimum size

requirements given in AISC LRFD Table J2.4. Finally, the base metal strengths must

satisfy the requirements of AISC LRFD Section J.5.

3.3.5 Rib-to-Gusset Weld Design Procedure

The rib-to-gusset plate welds are designed as longitudinal welds (4 total), with

concentric loads, according to AISC LRFD J2.4 and SEOC.

wrwexxweeexxnrib nslFntLFRP 707.06.06.0 φφφ ==≤ , (3-58)

where wl is the length of the wing plate, and ribP is the concentric force applied to the

rib plates. Therefore, the rib plate weld size ( rs ) is found using equation 3-59.

wwexx

ribr nlF

Psφ

30.3≥ (3-59)

46Welds must also satisfy minimum size requirements given in AISC LRFD Table J2.4.

Finally, the base metal strengths must satisfy the requirements of AISC LRFD Section

J.5.

3.3.6 Framing Member Design Procedure

Using the initial beam and column sizes from the prototype frame, the required

strengths of the members is determined from applicable load combinations. Framing

members are designed according to the requirements in Section 8 of the AISC Seismic

Provisions [2].

3.3.7 Beam-to-Column Connection Design Procedure

The following summarizes the design procedure for the welded flange/welded web

(WFWW) connections. Figure 3.3.9 shows the forces at the WWFW connection ( ubV

and wfwwM ), transferred from the BRB forces ( ubV and ubH ), as determined using the

Uniform Force Method (Figure 3.3.7). Complete penetration welds are used on both

flanges and the web. Vub is moved to the face of the column flange, and equilibrium is

applied to calculate the design forces ( ubV and wfwwM ).

Figure 3.3.9 – Beam-to-Column Connection Forces

Using the geometry in Figure 3.3.9, the design moment is as follows.

)5.0( bubwfww WVM = (3-60)

47The design forces, Hft and Hfb, can be found by solving equilibrium at the face of the

column flange. The shear capacity of the beam web is checked (AISC LRFD F.2) using

equation 3-61.

ybwebwbnub FltRV )6.0(75.0=≤ φ , (3-61)

where )(22 ahfbbweb tdl ϕ−−= , (3-62)

where wbt is the beam web thickness, ybF is the yield stress of the beam, fbt is the

thickness of the beam flanges, and ahϕ is the diameter of the weld access holes shown

in Figure 3.3.9. The beam flanges are checked for adequate tensile capacity (AISC

LRFD D.1) using equation 3-63.

ybfbfbnfbft FbtRHH 9.0),max( =≤ φ (3-63)

Web crippling and yielding of the beam and column needs to be checked in accordance

with the AISC LRFD specifications [1]. These web capacities are checked against the

shear forces calculated from the UFM, i.e. Vub, Huc. Web yielding is checked for

capacity (AISC LRFD K.3) using equation 3-64.

cwbcybcbnucub tFNkRHV ,,, )5.2(, +=≤ φφ (3-64)

Web Crippling is checked for capacity (AISC LRFD K.4) using equation 3-65.

cwb

cfbcyb

cfb

cwb

cbcwbnucub t

tEFtt

dNtRHV

,

,,

5.1

,

,

,

2, 2.04140.0,

−+=≤ φφ (3-65)

In the above equations, N is synonymous with the length of the gusset plate connected

to the beam/column (wb, wc).

The following summarizes the design procedure used for the shear tab connections.

Figure 3.3.9 shows the demand ( pbV and pbM ) used to design the shear tab connection.

The type of shear tab is based on the size of the framing members and the applied

forces. Typically, a simple single plate-single bolt row shear tab is adequate, and is the

most convenient to design. The connection is designed against the shear force ( pbV )

developed by the plastic moment capacity of the beam ( pbM ) as shown in

Figure 3.3.10.

48

Figure 3.3.10 – Shear Tab Demands

The demands on the shear tab connection are as follows.

bybpb ZFM = , (3-66)

and free

pbpb L

MV

5.1= , (3-67)

where freeL is the free length of beam, bZ is the plastic section modulus of the beam,

and the 1.5 factor is a common overstrength factor used by designers for shear tab

connections. With the design forces known, the connection is designed using Table

10-9 in the AISC LRFD Manual, and conservatively assuming a flexible connection.

Additionally, the plate bending capacity of the shear tab should be checked against the

moment demand. The capacity is calculated from the section modulus of the plate as

follows.

)(eVM pbplate = 6

2yststst Fltφ

≤ , (3-68)

where plateM is the moment demand on the shear tab from the shear force ( pbV ) acting

at an eccentric distance ( e ) away from the column face. stt is the thickness, stl is the

length, and ystF is the nominal yield strength of the shear tab. The resistance factor (φ )

is 0.9 for bending. The shear tab is also checked against typical bolted connection limit

states such as bolt bearing, tearthrough, and tearout (AISC LRFD J.3.10).

493.4 Specimen Design

Using the prototype BRBF and the design procedure outlined in Section 3.3, the test

specimens were designed. To ensure the design was suitable for testing, the test

configuration had to be considered. The test modeled a single bay BRBF subjected to a

lateral force (or story shear) at the top of the bay. The capacity of the hydraulic actuator

used to load the frame determined the maximum strength of the BRBF specimens. A

reference specimen had to be designed to provide a baseline and evaluation of current

design practice. The following paragraphs discuss the design of the reference BRB,

following the procedures outlined in Section 3.3.

3.4.1 Specimen BRBs

The same BRB was used for all of the tests, and was designed following the procedure

presented in Section 3.3.1. The yield strength ( yscP ), overall length ( brl ), connection

geometry, and the desired brace inelastic axial deformation capacity was designed and

provided to Nippon Steel, who then detailed and fabricated the BRBs. The prototype

BRB had initial brace forces between 350 and 400 kips. For testing, the maximum

lateral force was 312 kips, which was then reduced by 5% to estimate the actual force

capacity. An additional force loss due to inelastic action in the frame was

approximately 35 kips, or 10% of the nominal capacity. Finally to ensure that

specimens could be loaded until failure, and additional 5% reduction was made to the

nominal capacity. Therefore, the maximum brace force (Pmax) was:

352)45cos(

)05.001.005.01(*312max =

−−−=P kips

By following Section 3.3.1, the yield force was determined, however the βω value was

estimated. Review of BRB qualification tests [15, 16, 17], and discussion with BRB

manufacturers suggested an average βω value of 1.55. However, the qualification tests

indicated that the βω value could increase with increasing strain demand in the brace.

Therefore, a βω value of 1.6 was used, giving a yield force (Pysc) of 220 kips.

Additionally, the estimated inelastic deformation was calculated as +/- 5 inches based

on expected story drifts.

50The BRB connection was designed using the procedure outlined in Section 3.3.1.

Using the outlined design procedures, the final BRB design was as follows. The design

follows calculations provided in Appendix A.1.

• Bolts were 1 inch diameter A490. This selection was based on sampling of

previously designed BRB connections and the brace forces. A total of (10) 1

inch dia. A490 slip-critical bolts were used (Figure 3.4.1).

• Bolt holes were standard following recommendations from Nippon steel.

• Selection of bolt hole geometry was governed by clearance requirements for the

torque multiplier. The holes were spaced at 4 inches on center. Edge distances

of 2 inches were slightly over the minimum required. The resulting connection

geometry is shown in Figure 3.4.1.

The remaining components of the 220 kip brace were determined by Nippon Steel, and

are summarized below (Figure 3.4.1). BRB detail drawings are shown in Figure A.4.8.

• Brace total length of 3608 mm (11’-10”)

• 19x162 mm core plate (3/4”x6.4”)

• 2344.4 mm core length (92.3”)

• 250x250x6 mm steel tube casing (9.84”x9.84”x0.24”)

• Core material SN400B (Fybr = 46 ksi, Fubr = 58 ksi )

Figure 3.4.1 – BRB Connection Details

513.4.2 Reference Specimen Connection Design

The reference specimen connection details were designed using the BRB strength. The

bolt hole geometry matched the BRB connection. A square gusset plate shape was used

for the reference specimen. This was based on discussion with local structural

engineers and review of structural drawings. The splice plates and gusset/rib plates

were sized and checked according to the methods outlined in Sections 3.3.2 through

3.3.5.

The resulting connection for the reference specimen is summarized below and shown in

Figure 3.4.2. Calculations are provided in Appendix A.1.1 through A.1.4. Additional

detail drawings are shown in Figures A.4.1 through A.4.3.

• (10) 1 inch diameter A490 bolts designed for slip capacity

• Square ¾ inch gusset plates to match BRB core plate thickness width sizes as

shown in Figure 3.4.2

• Rib plates 5.125x17.125x3/4 inches (match BRB rib stiffener thickness)

• Splice Plates 4x24.5x1/2 inches

• Bolt spacing as shown in Figures 3.4.1 and 3.4.2

• Gusset-to-beam/column welds = ½ inch (from controlling weld method)

Additional considerations were made for the rib-to-gusset welds. Although the force

transfer can be idealized such that the gusset plate and rib plates each take half of the

maximum force, since the BRB is a flat plate type, it is possible that the force

distribution may not be even. If the welds were designed for the total maximum load,

the required weld size would be only 5/16 inch (compared to a minimum weld size of ¼

inch). Because of this small difference, the rib plate welds were designed for the total

maximum force (Pmax).

The size of the gusset plate connection was controlled by bolt hole geometry which was

based on clearance requirements for tensioning bolts. None of the limit states described

in Section 3.3 controlled the design of the gusset plate. In fact, the calculated capacities

of these limit states were all significantly higher than the required strengths needed in

52the connection as shown in the calculations of Appendix A.1.

Figure 3.4.2 – Reference Specimen Connection Design

3.4.3 Reference Specimen Frame Design

The W12 columns and W16 beams specified in the prototype BRBF, were designed to

sustain the maximum brace forces and the story shear forces, as discussed in

Section 3.4.1. Since the specimens did not include a slab, a heavier beam section was

chosen that would meet requirements for buckling, while still remaining realistically

flexible. The final frame design used W12x72 columns and W16x45 beams, as shown

in Figure 3.4.3.

The beam-to-column connections were designed according to the procedures outlined in

Section 3.3.7. The resulting connections are summarized below and shown in

Figure 3.4.3.

53• WFWW connection with CJP welds as detailed in Figure A.4.13. Also with

a ¼ inch erection tab as shown in Figure 3.4.3.

• Clearance between column flange and WFWW beam end to match requirements

for complete penetration weld specifications as detailed in Figure A.4.11.

• 13.5x4.5x1/2 inch shear tab connection with a single row of four ¾ inch

diameter A490 bolts, spaced as shown in Figure 3.4.3.

• Clearance between column flange and shear tab beam end to allow for

unrestrained rotations, as shown in Figure 3.4.3.

It should be mentioned that some of the final dimensions of the tab plates in

Figure 3.4.3 are slightly larger than the required dimensions found in the calculations

(A.2.2). These small differences came from the utilization of available steel. Complete

frame details are provided in Figures A.4.11 through A.4.13.

Figure 3.4.3 – Frame and Beam-to-Column Connection Details

543.5 Proposed Alternative Design Procedure and Possible Design Variations

Using the design procedures described in Section 3.3, it is expected that all inelastic

action will occur within the yielding segment of the steel core. To achieve this, the

connection and surrounding elements were all designed to remain elastic under the

maximum brace force. That is, the connection elements are designed to meet elastic

force demands based on capacity design principals. The proposed balance design

approach is similar to this method in that the framing elements are designed to meet the

elastic force demands, while specific elements are designed to yield to achieve the

desired plastic mechanism of the system [20]. The main difference in the balanced

design, is that instead of limiting inelastic action to one element, secondary yield

mechanisms are allowed to occur in other elements of the system. To ensure proper

overall performance of the system, a yielding hierarchy is developed. This hierarchy

ensures that desirable yield mechanisms occur first, less desirable mechanisms occur

thereafter, followed finally by critical failure modes. Furthermore, desirable and less

desirable mechanisms are separated to reduce the probability of less desirable yield

mechanisms and failure modes occurring [20]. Achieving this balance can improve

system strength, stiffness, energy dissipation, and inelastic deformation of the structure.

A description of how this type of balanced design has been applied, is given in the

following paragraphs.

The basis for the proposed performance based design procedure, was derived from

investigations into the behavior of SMRF connections by the SAC Steel Project. The

SAC Steel Project was a project undertaken by the SAC Joint Venture to address

performance problems found in SMRF connections after the 1994 Northridge

earthquake. The performance problems were addressed by the development of a

seismic design methodology based on balancing the yield mechanisms, and preventing

undesirable failure modes in moment resisting frames [20]. The current connection

performance was investigated to determine the effects of different yield and failure

mechanisms on overall ductility of the connection. Then, aspects of the connection

which contained very poor ductile behavior were improved where possible. Improved

55connection elements were then thoroughly tested in order to understand and quantify

their effect on ductility. Once the effect on the ductility of each mechanism was

understood, equations were developed which insured ductility increasing mechanisms

would occur before ductility hindering mechanisms. This was done by assigning

different β factors to each yield and failure mechanism. The beta factors not only

controlled the order of the mechanisms, but also controlled the proximity of the critical

failure mode and controlling yield mechanism resistances [19]. The use of these beta

factors developed a hierarchy that assured increased ductility and inelastic performance

of the MRF connection. One such example of connection performance can be found in

the welded-flange-welded-web (WFWW) connection. Figure 3.5.1a below shows a

WFWW connection which is not designed and detailed under the performance based

design procedures, whereas Figure 3.5.1b shows the moment rotation of the same

WFWW connection, which was designed and detailed under the performance based

design procedures. The two plots show that the connection performance is greatly

improved through use of the performance based methodology.

(a) Original WFWW (b) Improved WFWW

Figure 3.5.1 – WFWW Connection Improvement [19]

Prior to designing the remaining specimens, investigation of possible connection

variations was performed. Considerations included constructability and the effect of

each modification on the response of the frame. Possible variations are discussed in the

following paragraphs. As noted previously, due to the stiffness and strength of the thick

gusset and rib plates, the overall size of the connection was controlled by the bolt

56geometry, and the thickness of the plate was determined by the BRB core plate

thickness.

Bolt Spacing

Bolt spacing was one parameter which could have been modified. For the reference

specimen, a 4 inch bolt spacing was chosen to meet clearance requirements for the

torque multiplier that was used to tension the bolts. The bolt spacing could have been

reduced to about 3 inches, thus shortening the connection. With the connection

geometry, shortening the bolt spacing would only reduce the overall size of the gusset

plate less than an inch in each direction. It was expected that this shortening would

have very little effect on the overall strength and stiffness. Bolt spacing could not be

increased because of the fixed length of the BRB, but even if it could the spacing would

need to be unreasonably large before connection stiffness would be affected. Therefore,

the bolt spacing remained at 4 inches throughout all tests.

Gusset Plate Yielding

Theoretically, allowing yielding in the gusset plate is attractive because it should allow

for increased energy dissipation and ductility of the frame. It could also control the

demand in the framing elements, and prevent unwanted yielding. If the connection area

remains stable, detrimental effects to the BRB should be avoided. Physically this

modification posed problems, especially in the gusset plate. Because the overall size of

the gusset plate is determined by bolt geometry, the resulting tensile and buckling

strengths are many times larger than the required capacities. Discussion of using a

thinner gusset and rib plates were made, but it was suggested that use of spacers to

make up the differences between the BRB and the connection plates decreased the

constructability of the system. Even if the rib plates are ignored, the gusset capacities

are more than adequate. Because of these reasons, permitting yielding in the gusset

plates was not considered. More discussion on this topic is made in Chapter 7.

57Splice Plate Yielding

In addition, the research team considered splice plate yielding. Although the thickness

of the splice plates could not be reduced due to the high shear forces from the fully

tensioned bolts, their widths could be reduced slightly. The problems with this

modification is that it does not reduce the stiffness of the gusset/frame connection and

would likely have negligible effect on the overall ductility.

Taper Gusset Plates

To permit flexibility in the gusset/frame connection, use of tapered gusset plates was

investigated. This was intended to reduce the connection restraint. The gusset plate

strength remained quite large even with the taper. This modification was used for three

of the five specimens. The angle of taper ranged from a modest 15 degree taper, to a

greater 30 degree taper. The modest taper was chosen because it is commonly used in

current design. Further discussion of the more severe taper will be made in Chapter 7.

Use of Bearing Bolt Connections

Use of bearing bolt connections reduces the complexity of the connection. By basing

the connection design on the shear capacity of the bolts, the number of bolts in the

entire frame could be significantly reduced. Use of fewer holes reduces construction

time and labor costs. Labor time would also be reduced since the bolts would no longer

have to be fully tensioned. Traditional concerns with this type of connection, are that

the constant and dynamic slipping would reduce the overall performance of the

connection. Because BRB connections are somewhat known for their intensive labor

requirements, this modification was used for two specimens.

Removal of Rib/Wing Plate Extension

As discussed previously, the rib plates were extended to the back of the gusset plate.

This practice is used to restrict gusset plate buckling. However, extension of the rib

plates increases the stiffness of the connection. Initial discussions were made about

terminating the rib plates at the same location as the splice plates. In addition,

58shortening the rib plates such that they did not pass through the Whitmore section, to

achieve some yielding and increased flexibility, was also considered. Ultimately, it was

decided that use of only this modification could not increase the flexibility of the

connection enough to make a significant difference in the performance. Even without

the rib plates, the yielding and buckling capacities were still quite conservative

compared to the required capacities. Further discussion on this option will be made in

Chapter 7.

Stiffen Beam and Column at Gusset Plate

Preliminary research of previous BRBF experiments, showed that severe damage could

occur within the beam and column at the location of the gusset plate. This damage

leads to premature failure of the frame elements, the connection, or the BRB. To limit

this damage, stiffening the frame was discussed. A concern of the modification is the

increased labor costs that would occur due to the additional welding and fabrication of

web stiffeners or doubler plates. In addition, stiffening of the frame may delay or shift

damage. This modification was not adopted in the test series, but is discussed further in

Chapter 7.

Change Orientation of BRB

Changing the orientation of the BRB was considered after completing of the first test.

Originally the core plate of the BRB was oriented such that any out of plane movement

would cause the core to bend about its’ weak axis. This bending corresponded to beam

and column weak axis bending. Rotating the BRB 90 degrees might be a desirable

modification to increase the resistance in the out of plane direction. This modification

was adopted in one specimen.

The modifications chosen for each specimen are summarized in Table 3.5.1.

59Table 3.5.1 – Design Modifications

3.6 BRB02 Specimen Design – Tapered Gusset Plate

To investigate the effect of a tapered gusset plate, the gusset plate of specimen BRB02

was designed with a 15 degree taper. The remaining design of BRB02 was identical to

the reference specimen, and is summarized below and shown in Figure 3.6.1. The

differences in specimen BRB02 are circled in the figure. Additional details of specimen

BRB02 can be found in Figures A.4.4 and A.4.5.

• 15 degree tapered gusset plates – ¾ inch thick

• ½ inch gusset-to-column welds

• S.C. bolt spacing and number of bolts are identical to Reference BRB

• BRB, splice plates, and rib plates are identical to Reference BRB

• Frame members and frame connection details are identical to Reference BRB

60

Figure 3.6.1 – BRB02 Specimen Final Connection Detail

3.7 BRB03 Specimen Design – Bearing Bolt Connection

A shear and bearing bolt connection was designed for specimen BRB03. The objective

of this test was to determine if a bearing bolt connection is detrimental to the overall

system performance. The gusset plate for BRB03 matched the 15 degree taper and

weld sizes of specimen BRB02. To determine the number of bolts that would be used

in the connection, the procedures outlined in Section 3.3.1 were followed (calculated in

Appendix A.3). The controlling limit state, tearthrough, required seven bolts, however

eight were used for a symmetry. The remaining design details for BRB03 are identical

to BRB02. The resulting BRB03 specimen is summarized below and shown in Figure

3.7.1. The differences in specimen BRB03 are circled in the figure. Additional BRB03

details are shown in Figure A.4.6.

• (8) 1 inch diameter A490 bolts designed for bearing connection


61• ½ gusset-to-column welds

• BRB, splice plates, and rib plates used are identical to the Reference BRB


Figure 3.7.1 – BRB03 Specimen Final Connection Detail

3.8 BRB04 Design – Rotated BRB Cross Section

Specimen BRB04 was identical to specimen BRB03, except that the BRB was rotated

90 degrees about its longitudinal axis. The orientation of the flat plate BRBs in all the

earlier tests, was such that this out-of-plane bending had to be resisted by the cores’

bending capacity about its weak axis (Figure 3.8.1). By rotating the cross-section, the

out-of-plane bending was now about the strong axis of the BRB which was significantly

larger than the weak axis.

62

Figure 3.8.1 – BRB04 Orientation

Again, a bearing connection was used with (8) bolts and gusset plates had 15 degree

tapers. Refer to Figure 3.7.1 for details.

• BRB cross section rotated 90 degrees

• (8) 1 inch diameter A490 bolts designed for shear capacity


• ½ gusset-to-column welds

• BRB, splice plates, and rib plates used are identical to the Reference BRB


63 CHAPTER 4

Testing Apparatus, Procedure, and Instrumentation

4.1 Overview and General Discussion

Upon selection and design of the specimens as was discussed in Chapter 3, fabrication

methods and design of a test apparatus had to be finalized. The test setup was designed

to closely mimic actual boundary conditions in the prototype frame that was discussed

in Section 3.1. The design and fabrication of the test apparatus and test specimens are

described in the following sections of this chapter. The components of the test

apparatus are shown and numbered in Figure 4.1.1. Each specimen was tested in a

horizontal position, parallel to the floor of the structural laboratory as shown in Figures

4.1.1 and 4.1.2.

4.1.1 Strong Wall (1) and Strong Floor (2)

The test setup utilized the pre-existing concrete strong walls (1) and strong floor (2) in

the University of Washington’s structural research laboratory, as shown in Figures 4.1.1

and 4.1.2. These components supplied a solid means of anchoring the test specimens

and the actuator, which was used to load the BRBFs. The strong wall contained

openings through embedded conduit at 18 inches on center which were used to anchor

test setup components and to distribute in plane forces from the test specimens into the

strong floor. The strong floor contained open conduits with threaded anchors embedded

near the base, used to anchor elements to the floor, and were spaced at 3 feet on center.

64

Figu

re 4

.1.1

– T

est A

ppar

atus

65

Figure 4.1.2 – Test Apparatus

4.1.2 Channel Assembly (3)

A channel assembly made up of two C15x50 sections and various plate elements

(Figure 4.1.3), was used to transfer forces from the specimens into the strong wall. The

channel assembly was also used to place axial loads in the specimen columns and to

restrict overturning, by use of threaded rods (Section 4.1.6). The channel assembly was

anchored to the strong wall with several high strength threaded rods, which varied in

Channel AssemblyStrong Wall

Strong FloorLoad Beam

Out of Plane Restraints

Axial Force System

Swivel Head

Actuator

Load Cell

Reaction Block

Prestressing Rods

66 diameter and material strength. Exact rod size, location, and tensioning values are

given in Figures C.1.1 and C.1.5 of Appendix C. The frame was connected to the

channel assembly in only one location at the south beam, as seen in Figure 4.1.1 and

detailed in Figure 4.1.4. This short connection transferred shear forces from the frame

to the channel assembly, while allowing beam and beam-to-column connection

rotations with minimal amounts of restraint. To facilitate this connection, the specimen

columns were extended 1 inch past the bottom flange of the south beam as shown in

Figure 4.1.5. The connection used (10) 1 inch diameter A490 bolts to connect the south

beam of the frame, as shown in Figure 4.1.4. At the East end of the channel assembly, a

“kicker” plate and stiffeners (Detailed in Figure C.1.6 of Appendix C) were include to

ensure transfer of forces into the short end of the “L” shaped strong wall. Additional

channel assembly details are provided in Figures C.1.1 through C.1.6, and Figure

C.1.12 of Appendix C.

Figure 4.1.3 – Channel Assembly Cross-Section

Strong Wall

67

Figure 4.1.4 – Shear Transfer Connection

Figure 4.1.5 – Specimen-to-Channel Assembly Fit up

4.1.3 Load Beam (4)

The preceding components (1-3) distributed forces after they were applied to the

specimen. The forces were applied to the specimen by a load beam, composed of a

W21x62 section and various welded plates. The load beam transferred the force from

the actuator into the north beam of the specimen as shown in Figure 4.1.6. The load

beam was connected to the north beam of the frame by ten 1 inch diameter A490 bolts

as shown in Figure 4.1.1 and Figure 4.1.6. The length of the connection was spread out

along the beam to distribute the force into the north beam and reduce the potential for

local damage and stress concentrations. The load beam was connected to the actuator

Channel Assembly

South Beam

Strong Wall

68 swivel head by four 1 inch diameter A490 socket head bolts, which were fully tensioned

to avoid differential slip between the load beam and the actuator head. The primary

purpose of the continuity plates was to help transfer the applied column axial loads

described in Section 4.1.6. Detailed drawings of the load beam are given in Figure

C.1.7 of Appendix C.

Figure 4.1.6 – Load Beam

4.1.4 Actuator (5) and Reaction Block (6)

In order to deliver the required forces and displacements to the specimens, a hydraulic

actuator was used as shown in Figure 4.1.1. The actuator was stressed to a reaction

block (6) by six 1.125 inch diameter, 8 thread, B-7 threaded rods as shown in

Figure 4.1.7. The rods were tensioned to a combined force of 360 kips, which was not

expected to be exceeded by the actuator during testing. The reinforced concrete

reaction block provided a rigid support for the actuator, and resisted the reaction forces

from specimen loading. The reaction block was stressed to the strong floor (2) through

six 2 inch diameter threaded rods, which were threaded into the floor anchors and

stressed to 220 kips each (Figure 4.1.7). Hydro-stone was used underneath the reaction

block, and on top of the reaction block below the rod bearing plates to ensure a proper

bearing surface area (Figure 4.1.2). The square 12 inch by 2 inch thick elastomeric

bearing pad shown in Figure 4.1.7 was placed between the interface of the actuator base

W21x62 Load Beam

69 and the concrete block to allow small rotations between the reaction block and the

actuator.

Figure 4.1.7 – Actuator and Reaction Block Connection

The actuator swivel head shown in Figure 4.1.7, was attached to the actuator by a large

threaded steel pin. The steel pin was stressed to the maximum tensile force of the

actuator to ensure minimal deformation during testing. This was accomplished by use

of the spiral washers as shown in Figure 4.1.7. Detail drawings of the actuator, swivel

head, and reaction block are given in Figures C.1.8 through C.1.10 of Appendix C.

Figure 4.1.2 shows a photograph of the actuator and reaction block components.

4.1.5 Out of Plane Restraints (7)

To simulate the out of plane restraints that would be provided in a structure by

additional framing, an out of plane restraint system had to be developed that would both

restrict out of plane movement, and minimize the resistance to the in plane movements.

The system consisted of a series of W-Sections and/or channels that “sandwiched” the

frame members, as shown in Figure 4.1.8. The upper and lower restraints were held in

place by the threaded rod seen in Figure 4.1.8. Since the out of plane forces were small,

two 1” diameter threaded rods were adequate . The location of the out of plane

restraints are shown in Figures 4.1.1 and 4.1.2.

Reaction Block

Load Beam

70

Figure 4.1.8 – Out-of-plane Restraints

To minimize the friction between the specimen and the restraints, steel “skis”, notched

nylon tubes, and nylon plates were placed between all interfaces as shown in Figure

4.1.9. The steel “skis” were made of thin, smoothly polished steel, and were greased

with a silicon insulation gel. The upper out of plane restraints were only loosely

tightened to allow free movement of the frame and to minimize binding.

Figure 4.1.9 – In-plane Sliding Surfaces

4.1.6 Column Axial Load System (8)

In order to simulate realistic column conditions, each column was axially loaded using

two 1.375 inch diameter, high strength (150 ksi) Williams rods symmetrically placed

above and below each column web. Each rod was stressed to 175 kips, placing a 350

kip axial force on each column. The axial loads were applied to the top of each column

through 4 inch thick cap plates as shown in Figure 4.1.10a. The axial loads were

Steel “Skis”

Nylon Plate

Nylon Tubes

Threaded Rods

Out of PlaneRestraints

71 intended to simulate gravity loads that would be present in the prototype BRBF, as well

as to resist overturning of the frame.

(a) NE Cap Plate (b) SW Base Anchor

Figure 4.1.10 – Column Axial Load System

Spherical nuts and cupped bearing plates were used to allow rotation of the column

axial rods during loading (Figure 4.1.10). In addition to this, the holes in the cap plates

were significantly oversized to allow free movement of the rods, and the spherical nuts

were greased to minimize friction. The threaded rods were anchored to the channel

assembly described in Section 4.1.2. The rods passed through holes cut in the channel

flanges and through HSS4x4x1/2 sections as shown in Figure 4.1.10b. The HSS

sections were welded to the channel webs and flanges. Again, the same spherical nuts,

cupped bearing plates, and oversized holes were used. Detailed drawings of cap plates

and base anchors are provided in Figures C.1.11 and C.1.12 of Appendix C.

4.2 Later Required Modifications

The initial design of the test setup as described in Section 4.1 preformed quite well, but

ultimately a few minor modifications had to be made. After completing testing of the

first BRB specimen, it was learned that the original actuator did not have adequate

tensile capacity for the entire loading protocol. After this test, a new actuator with

larger tensile and compressive capacities were used. However, the new actuator had a

different base hole pattern (Figure C.1.9 – Appendix C) which was not compatible with

72 the hole pattern cast into the concrete reaction block. A 4 inch thick steel adapter plate

was designed and fabricated as shown in Figures 4.1.1 and 4.1.7. The adapter plate

included a countersunk hole pattern that matched the actuator on one side, and a

countersunk hole pattern that matched the reaction block on the other side. Two sets of

six 1.125 inch diameter, B-7 threaded rods were used to stress the adapter plate to the

actuator, and the adapter plate to the reaction block. Detailed drawings of the adapter

plate are given in Figure C.1.13 of Appendix C.

During testing of a buckling brace specimen [12], severe out of plane displacements

were noticed in the load beam and the adjacent portion of the frame. Not only was the

deformation unacceptable to the quality of the testing, but significant bending

deformation also occurred in the web of the load beam. An additional out of plane

restraint, made up of channel sections and rectangular tubing, was constructed around

both the north beam and load beam to control out of plane deformations for future

specimens (Figure 4.2.1).

Figure 4.2.1 – Restraint and Load Beam Modifications

In addition, web stiffeners were added to both sides of the load beam web as seen in

Figure 4.2.1. Eight total stiffeners (4 each side) were welded to both the web and

flanges of the load beam to stiffen the load beam (Figure C.1.7 of Appendix C).

Added WebStiffeners

Added Out of Plane Restraint

73 4.3 Specimen Fabrication

Fabrication techniques of the test specimens designed in Chapter 3, corresponded to

actual construction processes as closely as possible. Similar fabrication techniques

were used for all fabrication details including welds and bolting. The quality of the

welds was very important, since ductile behavior was required. A certified welder was

hired to ensure weld quality, and weld processes which assure matching metal and

adequate dynamic toughness were employed. The welder was certified by the

Washington Association of Building Officials for the FCAW – Semi-Automatic process

using E71T-X filler metal (E71T-8 was used). This certification included both grove

and fillet type welds in all positions.

The welded joint preparations for the WFWW beam-to-column connections were made

according to the details in Figure A.4.13 of Appendix A, and were done or checked by

the welder. Bolt hole details were 1/16” larger than nominal bolt dimensions. For slip

critical connections, surfaces were prepared and cleaned to meet Class A faying surface

requirements, and bolts were tensioned using direct tension indicators.

The beam-to-column connection details and member sizes were designed as discussed

in Section 3.4.3. The overall bay size of the specimens are dictated by the prototype

specimen as discussed in Section 3.1, at 12’-0” wide by 12’-0” high. However, in order

to ensure proper setup and testing of each specimen, specimen dimensions with

allowable tolerances had to be established to ensure proper fabrication and fit up with

the test apparatus. Figure 4.3.1 shows the complete frame dimensions including

allowable tolerances for each frame member. The columns were required to extend past

the beams at the WFWW locations a minimum of 0.5 inches for proper penetration

welds to be made, as shown in Figure 4.3.1. The south end of both columns had to

extend beyond the beam flanges as shown in Figure 4.3.1, for fit up with the channel

assembly. In order to facilitate the load beam connection, the north end of the west

column had to be flush with the north beam flange as shown in Figure 4.3.1. Shear tabs

and erection tabs are detailed again in Figure 4.3.1.

74

Figure 4.3.1 – Specimen Frame Dimensions and Allowable Tolerances

To ensure proper fit up, shim plates of several differing thicknesses were made for the

shear transfer connection and the connection between the load beam and the frame

north beam, with matching hole patterns as detailed in Figures C.1.5 and C.1.7 of

Appendix C. To distribute forces as evenly as possible and to ensure proper alignment

of the specimen, shim stock was used between the base of the columns and the channel

assembly, between the column cap plates and the top of the columns, and between the

out of plane systems and the strong floor.

75 4.4 Instrumentation*

Data for each specimen was acquired using potentiometers, strain gauges and visual

observations. Potentiometers were used to measure in-plane and out-of-plane motion

including values of translation and rotations. Strain gauges were attached to beams

columns and brace to monitor axial stress, shear forces, and moments. The force

applied to the specimen was measured by the load cell of the actuator. This section

provides a summary of the instrumentation configuration. Instrumentation of the

actuator and reaction block was identical for all tests, and was located as shown in

Figure 4.4.1. The arrows in the figures indicate the outward direction (extension) of the

potentiometers.

Figure 4.4.1 – Actuator/Reaction Block Pot Layout

Figures 4.4.2 and 4.4.3 show all possible locations of strain gauges used for the tests.

All beam and column strain gauges were centered vertically on their respective flanges.

Brace casing strain gauges are also centered on their respective faces of the casing tube,

as shown in Figure 4.4.2. Gusset and rib plate strain gauges shown in Figure 4.4.3 were

all bi-directional. All other strain gauges were unidirectional. The dimensions shown

in Figure 4.4.2 are applicable for tapered gusset plates also. The strain gauges used in

each test are summarized in Table 4.4.1.

* This section was written in collaboration with Shawn M. Johnson

76

Figure 4.4.2 – Uniaxial Strain Gauge Locations

77

Figure 4.4.3 – Biaxial Strain Gauge Locations

Table 4.4.1 – Strain Gauges Used Per Test

Uniaxial strain gauges were of part number FLA-6-11-5L. Biaxial strain gauges were

of part number FCA-6-11-5L. All gauges were manufactured by Tokyo Sokki

Kenkyujo Co. Ltd. All types of gauges had a nominal gauge factor of 2.12 with a 6 mm

gauge length. The gauges were intended for use in measuring elastic strains.

Therefore, any yielding that occurred in the location of a gauge made the gauge

ineffective. Due to this limitation, gauges were placed in areas where yielding was not

expected.

78 Potentiometers were used to measure linear motion. BEI DUNCAN model 600 and

model 9600 were used for most measurements taken. Measurements included:

• Frame translation

• Rotation of beams and columns

• Out-of-plane motion of the frame

• Out-of-plane bending of the gusset plates

• Rotation of the brace relative to the gusset plates

• Slip of the frame relative to the test setup

• Slip of the test setup relative to the strong floor and strong wall.

The potentiometer locations and numbering from testing of the Reference BRB

specimen are shown in Figure 4.4.4. Deviations in potentiometer instrumentation for

the remaining test specimens are summarized in Table 4.4.2.

79

Figure 4.4.4 – Potentiometer Locations for Reference BRB Test

80 Table 4.4.2 – Potentiometer Variances From Reference BRB Test

Additionally, for the BRB01 test, potentiometers 19 and 20 were used to measure NE

beam rotations as shown in Figure 4.4.5. The remaining tests did not include

measurements at this location.

Figure 4.4.5 – BRB01 Pot Locations (NE Corner)

81

Appendix D provides more detailed descriptions of potentiometer instrumentation. The

information provided includes:

• Exact Location of each device

• How the device was attached

• What the device measured

• Example photographs of each configuration type

Potentiometers that were used to measure rotation of the beam and column used

extensions to measure over a larger distance than the device alone could reach, as

shown in Figure D.1.12. The length of measurement was approximately 4/3 the depth of

the member for beam and columns as shown in Figures 4.4.4 and 4.4.5. This was done

to capture bending in the area of potential plastic hinging of the frame elements.

Springs were used on device model 9600 to ensure constant contact of the device to the

specimen/test setup. Potentiometers measuring out of plane rotation of the gusset plates

were attached to the floor for measuring out-of-plane motion of the southwest gusset

plate and a shelf for the northeast gusset plate. The shelf was attached to the column, in

the area by the gusset plate, which allowed the devices to move with the frame. By

doing this, relative movement between the potentiometers and the plate was kept to a

minimum.

UniMeasure model P510 string potentiometers were used to measure axial deformation

of the brace and the change in length along frame diagonal parallel to the brace

(Potentiometers 40 and 41 in Figure 4.4.4). Two potentiometers were used in

conjunction to measure out of plane motion of the brace. The two potentiometers were

attached perpendicularly to each other at the mid span of the brace (Potentiometers 53

and 54 in Figure 4.4.4). This made it possible to correct the measurements for in-plane

translation of the frame. All string potentiometers were attached to the specimen using

"music" wire. "Music" wire is light weight with a high tensile strength which made it

82 possible to span larger distances with little sag and little effect on the measurements

recorded during testing.

The lateral input force applied to the specimen was taken directly from the load cell in

the actuator. Therefore, force losses from small changes in the geometry of the

specimen and friction between the specimen and the lateral support were neglected in

the interpretation of data.

Whitewash was used to aid visual observations of yielding and relative movements

between attached elements. Whitewashing consisted of applying a mixture of

approximately 2.5 parts water to 2 parts Beadex Silverset 40 to the specimen in

expected areas of yielding as shown in Figure 4.1.2.

4.5 Data Acquisition and Test Documentation*

LabVIEW version 6.0 was used to control the data acquisition system. Equipment used

included a windows based personal computer system with National Instrument

hardware. A SCXI 1001 chassis was used in conjunction with SCXI 1100 and

SCXI 1300 modules for potentiometers, and SCXI 1121 and SCXI 1321 modules for

strain gauges. A Hewlett Packard E3611A DC power supply was used to supply the 10

volts needed for the potentiometers. LabVIEW was used to scan data channels and

convert readings to appropriate physical quantities before being recorded to the data

file. Measurements of voltage from the potentiometers were converted to units of

inches by using an appropriate calibration factor corresponding to each potentiometer.

Measurements of resistance from the strain gauges were converted to units of micro

strain using a built in function of LabVIEW. Voltage supply was recorded during

testing to monitor any change in voltage that would affect the readings being taken.

Readings from the instruments were recorded every second during testing to a tab

delimited file. Two camcorders recorded the testing, a digital camera that captured the

entire frame, and a VHS camcorder that captured a closer view of the entire BRB length

* This section was written in collaboration with Shawn M. Johnson

83 and gusset plate connections. Digital photographs were taken during the test with

record of the cycle in progress, to ensure properly analyzed results. Upon completion of

each test, test result documentation was preformed. This included written descriptions

and corresponding photographs of damage at every location in the frame and testing

apparatus, and also a record of the remaining stresses in the column axial force rods.

Since data was recorded continuously throughout the test, including pauses, the data

files were reduced to remove all pauses during the test. This was done according to the

description given in Appendix B.

4.6 Loading Protocol

The loading protocol for the experiments was established with guidance from ATC-24

“Guidelines for Cyclic Seismic Testing of Components of Steel Structures” [4], and the

SAC Steel Project (Report No. SAC/BD-97/02) [24] testing protocols. The protocol

follows a symmetrical, slow-cyclic, stepwise increasing loading pattern based on the

interstory drift angle of the frame at the onset of brace yielding (or yield drift angle),

Qy. Figure 4.6.1 shows the target loading protocol in terms of Qy.

Figure 4.6.1 – BRBF Loading History

The yield drift angle Qy, was estimated analytically by modeling the BRBF as a simple

frame in the structural analysis program, “Visual Analysis”. Two separate analytical

84 models were used in this determination. The first modeled the gusset plate corners of

the frame as pinned connections, while the second modeled the same corners as fixed

connections. The BRB was modeled in both cases as a member consisting of the core

plate only. Both models also included the applied axial forces in the columns as shown

in Figure 4.6.2.

Figure 4.6.2 – Simple Analytical BRBF Model

The model in Figure 4.6.2 was subjected to an increasing lateral force until the yield

force of the BRB core was reached. The respective Qy values of the frames were

recorded for each model as 0.00345 and 0.00352, for the pinned and fixed models

respectively. A Qy of 0.00347 (1/2 inch frame drift) was used since the actuator used

was controlled by peak displacements. The model is noticeably simple, and thus

contains small errors in the analysis. Rather than expend large amounts of time and

energy on a more sophisticated model, the simplified version was used with the flexible

loading protocol. During the tests the BRB’s were monitored for initial yielding, and

the corresponding drift angles were taken as Qy. Most of the specimens had initial

yielding at a target drift of 1.25Qy. In this case the loading protocol was modified so

that 2 cycles were run at 1.0Qy , 6 cycles were run at 1.25Qy , and the remainder of the

85 protocol remained the same as shown in Figure 4.6.3. The final consideration in the

loading protocol was the rate at which each cycle was run. Four different cycle lengths

were run as described below, in order to minimize changes in the loading rates. That is,

shorter drifts were run at shorter cycle lengths, and longer drifts were run at longer

cycle lengths.

For: yΘ<Θ≤ 0.10 60 second cycles

For: yy Θ<Θ≤Θ 0.20.1 80 second cycles

For: yy Θ<Θ≤Θ 0.40.2 120 second cycles

For: yΘ≤Θ 0.4 160 second cycles

Figure 4.6.3 – Modified BRBF Loading History

4.7 Chronology of Testing

Some details of the testing needs to be discussed in order to properly understand the

results and analysis. For clarification, preparation for testing was carried out as follows.

After the finished frame was placed and properly aligned in the testing apparatus, the

holes for the shear transfer connection in the south beam, and the load beam connection

in the north beam were drilled with templates to ensure proper fit up. Strain gauges

were then placed at all applicable locations on the frame, gusset/rib plates, and on the

86 BRB. The specimen was then bolted to the channel assembly, the BRB was placed in

the frame, bolts and splice plates were prepared, and then the bolts were tensioned to

the adequate force. Once the bolts were tensioned, the six brace pots were installed

(using tap screws), and the frame and connections were whitewashed. The remaining

instrumentation was then attached, placement of the upper members and sliding

surfaces of the out-of-plane restraints was completed, and shimming was done where

necessary. The load beam was then also bolted to the frame. Finally, the high strength

rods used for the column axial forces were placed and aligned, and then stressed to the

required 175 kips (stressing of the rods was staged to avoid extreme unbalanced loading

in the columns).

Once the test preparations had been made, cameras were readied and the loading

protocol was begun by first loading the brace in tension. In accordance with ATC-24

recommendations, pauses in the testing was limited to peaks and valleys whenever

possible. Data recording at 1 second intervals was continued throughout the entire test

including during pauses. The testing was monitored continuously and closely for any

problems in the loading, boundary conditions, instrumentation, or out of plane supports.

Photographs and testing notes were taken continuously as described in Section 4.5.

87CHAPTER 5

Experimental Results

5.1 Overview

Chapter 4 concluded by outlining how the specimens were prepared for testing, and

how the testing was carried out. This chapter summarizes observed during testing, and

concludes with a comparison of the specimen behaviors. Table 5.1.1 shows the

schedule of testing for both the SCBFs [12] and BRBFs.

Table 5.1.1 – Experimental Testing Schedule

A brief explanation of specimen BRB01 and the Reference BRB should be made.

Originally, BRB01 was intended to be the reference specimen. However, problems

encountered in the loading during testing made the results less appropriate to use as a

reference to future tests. Therefore, a fifth experiment was conducted with a specimen

nominally identical to specimen BRB01. This fifth specimen was loaded similarly to

the other BRB specimens, and was deemed the reference. Details on the loading used

for BRB01 are provided in Section 5.8. As a review, the general components of the five

BRBF specimens and what they evaluated are shown in Table 5.1.2. Details of each

specimen connection are described in Chapter 3.

88Table 5.1.2 – BRBF Specimen Components

5.2 Damage States and Locations

The majority yielding and failure modes that occur during testing are in similar

locations for each test. To effectively describe these mechanisms, these yielding

regions are highlighted and defined in Figure 5.2.1. The terminology shown for the

W-sections in Figure 5.2.1 is applicable for both the beams and columns of each

specimen.

89

Figure 5.2.1 – Location Terminology

To properly understand the demands placed on the system, and whether they are caused

by tensile or compressive brace forces, the following describes which yielding

mechanisms and failure modes occur and when they occur. The loading history is

divided into tension and compression excursions. Tension excursions begin after the

compressive peak and end at the tensile peak. Compressive excursions begin after the

tension peak and end at the compressive peak. Each are illustrated on the drift history

and force-displacement curves in Figure 5.2.2.

Strong Wall

Channel Assembly

90

Figure 5.2.2 – Tension and Compression Excursions

Mechanisms that occur during tension excursions:

• Yielding on the outside face of the inner flange – NE column, NE beam, SW

column, and SW Beam

• Local buckling of the inner flange – NE column, NE Beam, SW column, and

SW beam

• Yielding and out of plane deformation of the web – NE column and SW beam

• Yielding and buckling of the North beam at the load beam

• Slip of bolts

• Gusset plate yielding at the gusset corners

Mechanisms that occur during compression excursions:

• Yielding on the inside face of the inner flange – NE beam and SW column

• Yielding and buckling of the outer flange – NE column and SW column

• Out of plane rotation of the SW beam and gusset plate

• Hinging in the BRB core plate

• Shifting of the BRB casing and concrete surrounding the BRB core towards the

NE end of the brace

• Weld cracking at gusset-to-beam/column locations

91To understand the behavior of each specimen and facilitate comparison, the yield

mechanisms and failure modes are defined using the terminology presented in

Tables 5.2.1 and 5.2.2. These states define the different mechanisms such as yielding,

buckling, hinging, case shifting, bolt slip, and weld fracture of the specimen

components. Figures 5.2.3 through 5.2.9 provide photographs of what the predefined

states look like. The yielding states in Table 5.2.1 are defined for the gusset plates in

Figure 5.2.3, and the framing members in Figure 5.2.4. The pictures shown apply to all

beam and column flanges and webs. The buckling states are defined for the framing

members in Figure 5.2.5. The weld performance states are shown in Figure 5.2.6. The

performance states in Table 5.2.2 are defined in Figures 5.2.7 to 5.2.9.

Table 5.2.1 – Frame and Gusset Performance State Terminology

92

(a) Y1 – Initial Gusset Yielding

(b) Y2 – Mild Gusset Yielding

(c) Y3 – Moderate Gusset Yielding

Figure 5.2.3 – Gusset Plate Yielding States

93

(a) Y1 – Initial Yielding (b) Y2 – Mild Yielding

(c) Y3 – Moderate Yielding (d) Y4 – Initial Concentrated Yielding

(e) Y5 – Severe Yielding

Figure 5.2.4 – Frame Yielding States

94

(a) B1 – Initial Buckling

(b) B2 – Moderate Buckling

(c) B3 – Severe Buckling

Figure 5.2.5 – Frame Buckling Limit States

(a) WD – Weld Damage (b) WF – Weld Failure

Figure 5.2.6 – Weld Damage States

95Table 5.2.2 – BRB, Bolt, and Column Base Performance State Terminology

(a) H1 - Initial BRB Core Hinging

(b) H2 - BRB Core Plastic Hinging

Figure 5.2.7 – BRB Core Plate Hinging States

Hinge Angle

96

(a) Initial Casing Position (b) S1 – Initial Casing Shift

(SW End – No Applied Load)

(c) S2 – Severe Casing Shift (NE End – No Applied Load)

Figure 5.2.8 – BRB Casing Performance States

(a) B1 – Initial Buckling (b) – Initial Uplift

Figure 5.2.9 – Column Base Performance States

975.2.1 Anatomy of Force Displacement Responses

This section provides descriptions of how some performance states manifest themselves

in the force-displacement plots of each specimen. Figure 5.2.10 shows the force

displacement response for the reference BRB, which is representative of all specimens.

The circled locations in the figure highlight where sudden dips in the force deflection

behavior occurred.

Figure 5.2.10 – Reference BRB Force Displacement Response

Bolt slip and casing shifting were the two possible causes of the dips highlighted in

Figure 5.2.10. As the bolts slip, the hysteretic behavior shows a small reduction in

force, but quickly rebounds. When the slip occurs the brace is elongates equal to the

amount of slop in the bolt holes, but requires less force to do so. Dips caused from bolt

slip are noted in each specimens’ force displacement plot.

During testing the BRB casing shifted towards the NE end of the brace. Shifting of the

casing was when longer and longer sections of the SW end of the core plate would

extend out of the casing than compared to the NE end as shown in Figure 5.2.8. Slight

bending or hinging at the SW end of the BRB caused the core plate to drag against the

surrounding concrete. When the core plate shortened during compression cycles, it

98tried to shorten into the casing, but was resisted by friction between the core plate

surface and the surrounding concrete, and therefore the casing was restrained to move

towards the SW end. The casing continued to shift towards the NE end until it reached

the furthermost NE end as shown in Figure 5.2.8c. The shifting of the casing created

dips in the force displacement response of each specimen. This likely occurred when

the BRB core overcame the force restraining movement of the casing. This created a

short drop then return of the force input into the system as highlighted in Figure 5.2.10.

Any such dips in the force displacement responses not specifically labeled as bolt slip,

are due to this phenomenon. Additional details of this phenomenon are provided in

Appendix B.3.

BRB plastic hinging, or a substantial reduction in stiffness, is a significant change and

leveling of the input force during increasing drifts (change in slope). This mechanism is

noted in Figure 5.2.10 as point 1. In all of the specimens, plastic hinging continued

without an appreciable increase in force, until the BRB casing touched the floor

(Figure 5.2.7b). This is noted as point 2 in Figure 5.2.10, and signaled the completion

of the test.

The conditions of the test setup caused local buckling of the outer flanges at the bases of

both columns, as shown in Figure 5.2.9a. The lateral force that was applied to the frame

resulted in pivoting about the outer flanges. Large forces were thus concentrated in the

outer flanges and eventually made them buckle. Stiffeners welded into the column

bases minimized the local buckling, but did not prevent it. The buckling resulted in

shortening of the column, which in turn led to a loss of axial force in the pre-stressed

rods. As the axial forces were reduced, the hold down force on the columns was soon

exceeded by the uplift force, and a gap formed between the column base and the

channel assembly (Figure 5.2.9b), which resulted in a rigid body rotation of the frame.

Correction for the rigid body rotation of the frame is described in Section 5.3.1.

995.3 Drift Ranges

As discussed in Section 4.6, the specimens were tested using a displacement controlled

protocol. The actual drifts were different from the target values due to deformations in

the test apparatus, variances in the calibration of the actuator LVDT, and slip of the

specimen relative to the channel assembly. To improve the tests the target drifts were

sometimes modified, as discussed in Section 4.6. Reference Because of these facts,

descriptions of specimen behavior are discussed in terms of actual drifts.

The behavior of the specimens was similar, and the progression of yielding mechanisms

and failure modes in each specimen occurred during similar drift ranges. These drift

ranges are defined and used throughout the remainder of the document (Table 5.3.1).

Six different ranges which correspond to different cycle numbers are noted in

Table 5.3.1. The ranges generally correspond to performance states. The early range

corresponds to elastic deformation of all components, the yield range corresponds to

initial BRB core yielding, the early range corresponds to initial yielding in most of the

framing members, and the mid range corresponds to spreading of yielding and initial

buckling in the frames. The late range corresponds to the rapid spread of frame

damage, and the initial out of plane rotation in the SW beam and BRB. Finally, the

final range corresponds to drastic out of plane rotation, high levels of frame damage,

and ultimate failure.

100

Table 5.3.1 – Drift Ranges and Corresponding Cycle Numbers

5.3.1 Frame Drift Corrections

A potentiometer (No. 36) was placed at the face of the east column, in line with the

centerline of the north beam, as shown in Figure 5.3.1, to measure the overall drift of

the frame ( OD∆ ). To determine the actual drift of the frame, a corrected drift which

removed small rigid body rotations from column uplift, and lateral slip of the frame was

calculated. Lateral slip in the south beam-to-channel assembly shear connection was

measured by potentiometer 46 ( slip∆ ), as shown in Figure 5.3.1. Figure 5.3.2 shows the

idealized rigid body rotations resulting from column base uplift. Potentiometers 29 and

48 are as shown in Figure 5.3.1 were oriented such that uplifts of either column based

resulted in positive readings.

101

Figure 5.3.1 – Locations of Potentiometers Used for Drift Correction

Figure 5.3.2 – Rigid Body Frame Rotations

The pivot point (PP) of the frame is at the outside face of the column base outer flange.

Using the fact that the angles of rigid body rotation ( RBΘ ) are equal, the following

equations are developed.

OD

UW

W

WRB LL

U ∆==Θ , (5-1)

PP PP

102

and OD

UE

E

ERB LL

U ∆==Θ (5-2)

Therefore: W

WODUW L

UL=∆ , (5-3)

and E

EODUE L

UL=∆ , (5-4)

where UEUW ∆∆ , are the amount of frame drift caused by the rigid body rotation from

the uplift of the west and east columns, respectively. EW UU , are the measured uplifts in

the west (pot 48) and east (pot 29) columns, respectively. EW LL , are the distances from

the pivot point to potentiometers 29 and 48, and ODL is the distance from the pivot point

to potentiometer 36. Although the rotations have different signs, the direction of the

rotation is accounted for in the final corrected drift ( )corr∆ . To determine the corrected

drift ( )corr∆ , we simply account for the rigid body rotation and any lateral slip that

occurred in the shear connection ( 46∆ ).

slipUWUEODcorr ∆−∆−∆+∆=∆ (5-5)

Using the above equations, corrections to the measured frame drift ( OD∆ ) range from 0

to nearly 13% difference in the drift. Table 5.3.2 compares the measured drifts versus

the corrected drifts for the reference BRB.

Table 5.3.2 – Measured vs. Corrected Story Drifts for the Reference BRB

103The remainder of this chapter discusses the response of each test specimen during

testing, and then compare the performances of all the specimens. Instrumentation for

the specimens is provided in Section 4.4, and design details are given in Section 3.4 and

Sections 3.6 through 3.8. Values given to drifts and forces indicate loading of the brace

in tension when positive, and loading of the brace in compression when negative.

5.4 Response of Reference BRB

The specimen was tested to serve as a baseline or reference point for future specimens

with connection modifications. The reference specimen had full force displacement

curves as would be expected from a buckling restrained brace as shown in Figure 5.4.3.

The frame reached only moderate story drift angles of 2.2% and -2.1% before failure

occurred, with maximum loads of +315 and -356 kips. The deformation history for the

reference specimen is shown in Figure 5.4.1 below. Failure occurred during the

compression excursion of cycle 36. Figure 5.4.2 shows the lateral force history.

Table 5.4.1 summarizes the drifts and input forces with respect to the cycles. Figure

5.4.4 shows the elongation of the brace during testing, and gives peak elongation values

with corresponding drifts.

Figure 5.4.1 – Reference BRB Displacement History

104

Figure 5.4.2 – Reference BRB Lateral Force History

Figure 5.4.3 – Reference BRB Force Displacement Response

105Table 5.4.1 – Reference BRB Peak Values

Figure 5.4.4 – Reference BRB Core Plate Elongation

Initial yielding of the core plate occurred during 0.23% and -0.32% drift ratios.

Yielding of the brace increased throughout the test and brace elongation reached peak

values as high as 1.92 and -2.886 inches. Initial yielding of the BRB core was

determined visually during the test, and verified with core strain measurements.

Compressive yielding occurred during cycles 9 and 10, but tensile yielding did not

occur until cycle 11, so cycles 11-16 were deemed the initial yield cycles. Brace

elongation was measured until plastic hinging (H2) occurred, after which the readings

Initial Yield Cycles

H2

106included out of plane deformation and were deemed inaccurate. The core was

marked before testing as shown in Figure 5.4.5, to manually measure elongation until it

was above values of expected elastic deformation.

Figure 5.4.5 – Visual Determination of Core Yield

5.4.1 Description of Reference BRB Behavior

Progression of the performance states are referenced to peak value drifts when each

state was observed. The mechanisms occurred at or during loading to the peak drift.

The descriptions have been separated in terms of the drift ranges described in

Section 5.3. Selected performance states are illustrated in figures (5.4.7 through 5.4.13)

at the end of each drift range paragraph to facilitate in the description. The performance

limit state and drift ratio at which it occurred are included in each figure. A summary of

the following detailed descriptions is given in Section 5.4.2.

The top rib plate on the SW gusset plate was welded slightly out of square, which

created a small misalignment between the gusset rib plate and the BRB rib stiffener,

which in turn caused bending in the splice plates when they bolted to the two ribs.

Figure 5.4.6 below shows the misalignment, splice plate curvature, and slight gaps that

were present in the connection. Since the connection was slip critical, it was felt that

this misalignment would have little or no effect on the performance of the connection.

The area was closely monitored during the tests, and no signs of problems or unusual

effects were observed.

107

Figure 5.4.6 – Rib Plate Misalignment

Yield Range Drifts (0.20% to 0.40%)

Initial yielding (Y1) in the BRB core plate occurred at a drift ratio of +/- 0.23%. No

other mechanisms were noted during this drift range.

Figure 5.4.7 – Selected Performance States During Yield Drift Range

Early Range Drifts (0.40% to 0.65%)

Y1 yielding occurred on the outside face of the NE column inner flange at drift ratios of

Slight Curvature

Slight Gap

1080.48% (Figure 5.4.14a). Y1 yielding also occurred on the outside face of the NE

beam inner flange at the same drift ratios (Figure 5.4.18a).

Figure 5.4.8 – Selected Performance States During Early Drift Range

Mid Range Drifts (0.65% to 1.25%)

Y1 yielding was observed on the inside face of the inner flange of the SW beam at -

0.93% drift ratios. The yielding in the outside face of the NE column inner flange

reached level Y2 at drift ratios of 1.17% (Figure 5.4.14b). Y1 yielding occurred on the

inside face of the NE column inner flange at drift ratios of -0.70%, and reached level Y2

at -1.18% drift ratios. Y1 yielding was seen on the outside face of the SW column inner

flange at drift ratios of 0.62% (Figure 5.4.20a). Y1 yielding also occurred on the

outside face of the SW column outer flange at drift ratios of -0.93%. Y1 yielding also

occurred on the inside face of the NE beam inner flange at -0.70% drift ratios. Y1

yielding started in the north beam at the load beam end, in the outer flange and web at

drift ratios of 1.17%. Initial column flange buckling at their bases (B1) was noticed

during drift ratios of 0.62% and -0.70%, and base uplift became visibly apparent (U1) at

drift ratios of 1.17% and -1.18%.

109

Figure 5.4.9 – Selected Performance States During Mid Drift Range

Late Range Drifts (1.25% to 1.75%)

The shifting of the BRB casing first was initially observed (S1) during the cycle

corresponding to drift ratios of 1.44% and -1.43%. Y1 yielding was seen on the outside

face of the SW beam inner flange at drift ratios of 1.44%, along with B1 buckling of the

inner flange. The yielding on the outside face of the inner flange increased to level Y2

at drift ratios of 1.69% (Figure 5.4.21a). Y1 yielding also occurred in the SW beam

web at 1.44% drift ratios (Figure 5.4.22a). B1 buckling occurred in the SW beam web

at drift ratios of 1.69%. B1 buckling was noticed in the bottom half of the NE column

inner flange, at drift ratios of 1.44% (Figure 5.4.16a). Yielding in the outside face of

the NE column inner flange reached level Y3 at drift ratios of 1.69% (Figure 5.4.14c).

Yielding on the inside face of the NE column inner flange also increased to level Y3

during -1.67% drift ratios. The NE column web also had Y1 yielding at drift ratios of

1.44%. Yielding increased in the outside face of the SW column outer flange to level

Y2 at drift ratios of -1.43% (Figure 5.4.20c), and further to level Y3 at -1.67%

110(Figure 5.4.20d). Y2 yielding was reached in the north beam at the load beam end

in the web and outer flange at drift ratios of 1.69%.

Figure 5.4.10 – Selected Performance States During Late Drift Range

Final Range Drifts (1.75% and Higher)

SW Corner during cycles 33 and 34 (1.93% and -1.94% drift ratios):

Yielding on the outside face of the SW beam inner flange increased to level Y3 during

1.93% drift ratios (Figure 5.4.21b). Buckling of the SW beam inner flange increased to

B2 levels at 1.93% drift ratios (Figure 5.4.22b). Yielding in the SW beam web jumped

to level Y3 during 1.93% drift ratios (Figure 5.4.22b). At the same drift ratios, the SW

beam web reached B2 buckling. This SW beam damage that occurred at 1.93% drift

ratios, caused slight out of plane rotation of the beam web and flange, and because of

the large stiffness of the SW gusset plate connection, was accompanied by a nearly rigid

body rotation of the SW gusset plate. The rotation of the SW gusset plate caused initial

BRB hinging to develop during the -1.94% drift ratios. During the -1.94% drift ratios

111of cycle 34, WD weld cracks began at the SW and NE gusset-to-column intersection

(Figure 5.4.24a).

SW Corner during cycles 35 and 36 (2.16% and -2.06% drift ratios):

Yielding on the outside face of the SW beam inner flange increased to level Y4 during

these drift ratios of cycle 35, and Y5 levels at the same drift ratios of cycle 36

(Figure 5.4.21c). Buckling of the SW beam inner flange increased to B3 levels by the

end of testing under 2.16% drift ratios (Figure 5.4.22c). Web buckling in the SW beam

increased to very severe level B3 during the tension excursions of these final drift ratios

(Figure 5.4.22d). SW beam web yielding also quickly increased during theses drift

ratios, to level Y5 (Figure 5.4.22c). During the final compression excursion (cycle 36),

the SW beam lost stability and began drastically rotating out of plane towards the strong

floor (Figure 5.4.24d). With these large beam rotations, the SW gusset plate rigid body

rotation and BRB hinging (H1) became quite evident during the compression

excursions of cycle 35 (Figures 5.4.24b and 5.4.25c). At this point, the BRB casing had

shifted completely (S2) to the NE end of the brace (Figure 5.4.25a). Y1 yielding

occurred in the corners of the SW gusset plate during compression excursions, but the

connection had very little bending or other yielding of any type. The SW and NE

gusset-to-column weld cracks propagated during the cycle 35 compression excursion,

but remained at level WD. Plastic hinging (H2) of the BRB occurred during the

compression excursion of cycle 36, when the gusset plate and BRB connection began to

quickly rotate out of plane with no increase in load (Figure 5.4.3). The hinging

continued until the brace finally touched the floor (Figure 5.4.25d). As these rotations

were increasing towards the strong floor, level WD weld cracks occurred in the SW

gusset-to-beam weld. The SW gusset-to-column weld crack opened along nearly its

entire length to level WF (Figure 5.4.24c). Y3 yielding also quickly appeared in the

SW gusset plate and splice plates at this time (Figure 5.4.24e).

Buckling in the bottom half of the NE column inner flange reached level B2, and was

accompanied by B1 buckling in the top half of the flange at drift ratios of 1.93%

112(Figure 5.4.16b). Buckling of the NE column inner flange reached level B3 by the

end of the test, under drift ratios as large as 2.16% (Figure 5.4.16c). Yielding in the

outside face of the NE column inner flange reached level Y4 at drift ratios of 1.93%.

This yielding increased during drift ratios of 2.16%, but did not quite reach level Y5

(Figure 5.4.14d). Yielding on the inside face of the NE column inner flange reached

level Y4 at drift ratios of -2.06% (Figure 5.4.15b). B1 buckling began in the NE

column web at 1.93% drift ratios, and reached level B2 by the final 2.16% drift ratios.

Yielding in the web increased to level Y2 around 1.93% drift ratios (Figure 5.4.17a),

and reached level Y3 under drift ratios of 2.16% (Figure 5.4.17b). Y1 yielding of the

NE column outer flange occurred at -1.94% drift ratios (Figure 5.4.15a). This yielding

increased to level Y3 by the -2.06% drift ratios (Figure 5.4.15b). The NE column outer

flange also had B1 buckling during the final -2.06% drift ratios, although the buckling

seemed more like global buckling of the flange rather than local buckling.

Yielding on the outside face of the SW column inner flange increased to level Y2 by the

end of testing, at drift ratios as high as 2.16% (Figure 5.4.20b). Yielding on the outside

face of the outer flange increased to level Y4 after the final -2.06% cycle

(Figure 5.4.20e). Yielding on the outside face of the NE beam inner flange increased to

level Y2 at drift ratios of 1.93%, and level Y3 at drift ratios of 2.16% (Figure 5.4.18b).

By the end of testing at -2.06% drift ratios, yielding on the inside face of the NE beam

inner face reached level Y2 (Figure 5.4.18c). Yielding in the north beam at the load

beam end reached level Y3 in the outer flange, and level Y2 in the web, at the final drift

ratios of 2.16% (Figure 5.4.19). Figure 5.4.19 also shows B1 buckling of the north

beam outer flange, which occurred at the same drift ratios.

Relative beam-to-column rotations at the shear tab connections were quite large by the

end of the test (Figure 5.4.23a). However, little or no yielding was seen in the beam

web or the shear tabs at these locations. The large rotations were accomplished by

slightly oversized (by 1/16 inch) bolt holes, but more so by elongation of the holes in

the beam web (Figure 5.4.23b).

113

Figure 5.4.11 – Selected Performance States During Final Drift Range – Cycles 33&34

Figure 5.4.12 – Selected Performance States During Final Drift Range – Cycle 35

114

Figure 5.4.13 – Selected Performance States During Final Drift Range – Cycle 36

115

(a) Cycle 21 – Y1 (b) Cycle 27 – Y2

(c) Cycle 31 – Y3 (d) End of Test – Y4

Figure 5.4.14 – Progression of Yielding in NE Column Inner Flange

(a) Cycle 33 – Y1 (b) End of Test

Figure 5.4.15 – Progression of Yielding in NE Column Outer Flange

Y3

Y4

116

(a) Cycle 29 – B1 (b) Cycle 33 – B2

(c) End of Test – B3

Figure 5.4.16 – Progression of NE Inner Column Flange Local Buckling

(a) Cycle 33 (b) End of Test

Figure 5.4.17 – Progression of Yielding in NE Column Web

Y2Y3

117

(a) Cycle 21 – Y1 (b) End of Test – Y3

(c) End of Test (Inside Face) – Y2

Figure 5.4.18 – Progression of Yielding in NE Beam Inner Flange

Figure 5.4.19 – Yielding and Buckling of North Beam at Load Beam – Cycle 33

Y2 Web

Y3 Flange

B1

118

(a) Cycle 27 Inner Flange – Y1 (b) End of Test Inner Flange

(c) Cycle 29 Outer Flange – Y2 (d) Cycle 31 Outer Flange – Y3

(e) End of Test Outer Flange – Y4

Figure 5.4.20 – Progression of Yielding in SW Column

Y2

119

(a) Cycle 31 – Y2

(b) Cycle 33 – Y3

(c) End of Test – Y5

Figure 5.4.21 – Progression of Yielding in SW Beam Inner Flange

120

(a) Cycle 29 (b) Cycle 33

(c) End of Test

(d) End of Test – B3 Web

Figure 5.4.22 – Progression of SW Beam Web Yielding/Buckling and Flange Buckling

Y1

Y3

B2

Y5

B3

121

(a) Shear Tab Rotation

(b) Bolt Hole Bearing in Beam Web

Figure 5.4.23 – Beam-Column Relative Rotations

122

(a) NE Gusset-to-Column Cycle 34 - WD (b) SW Gusset Cycle 35

(c) SW Gusset-to-Column Cycle 36 - WF (d) SW Gusset Cycle 36

(e) SW Gusset and Splice Plate Yielding (End of Test) – Y3

Figure 5.4.24 – Progression of Damage in SW Gusset Connection

123

(a) NE Casing at No Load Cycle 36 – Casing at Extreme NE End of Brace

(b) NE Casing at Tensile Peak of Cycle 36

(c) Slight Hinging of BRB Cycle 35 (d) Plastic Hinging of BRB

Figure 5.4.25 – BRB Hinging and Shifting of Casing

1245.4.2 Response and Failure Summary of Reference BRB

The response of the Reference BRB can be summarized as follows. All components of

the specimen remained elastic until the yield drift range, where the initial BRB core

plate yielding (Y1) occurred. Initial (Y1) and mild (Y2) yielding occurred throughout

the frame during early and mid drift ranges, and column uplift began to occur. During

the late drift range, the shifting of the BRB casing became evident (S1), after which

buckling initiated (B1) in the SW beam and NE column areas. During the final drift

range, damage throughout the frame increased drastically. The frame experienced large

deformations with extensive yielding (Y4 and Y5) and buckling (B2 and B3) of the

beams and columns adjacent to the gusset plates. Eventually the SW beam rotated out

of plane, and this instability allowed a nearly rigid body out of plane rotation of the SW

gusset plate. As the gusset plate rotated, an eccentricity was introduced into SW end of

the brace, which placed large out of plane deformation demands on the BRB. To

sustain this deformation, plastic rotations occurred in the BRB core plate and hinged at

the termination of the BRB stiffening ribs (Figure 5.4.27). Furthermore, the shifting of

the BRB casing to the NE end led to loss of confinement around this location, which

facilitated in the formation of the plastic hinge. Failure occurred shortly into the

compression excursion of cycle 36 (around a 1.1% drift ratio and -100 kips of lateral

force), and the rotation at the hinge increased without an increase in load. The SW

gusset plate and the BRB end continued to rotate until the brace casing eventually

touched the strong floor (approximately 12 inches below the bottom of the BRB casing

at the beginning of testing). These extremely large out of plane deformations caused

weld cracks (WD) in both of the gusset-to-beam column connections, weld failure (WF)

in the SW gusset-to-column connection, and moderate yielding (Y3) in the SW gusset

and splice plates. The progression to failure is illustrated in Figure 5.4.26. The

condition of the BRB core plate after failure is shown in Figure 5.4.27. Figure 5.4.28

gives an overall view of the brace and the SW connection at failure.

125

Figure 5.4.26 – Progression of Failure (SW Connection Cross Section)

126

Figure 5.4.27 – Hinged Core Plate with Surrounding Concrete and Casing Removed

Figure 5.4.28 – SW Connection After Failure

All of the test specimens performed in a similar manner to that described for the

reference BRB specimen. Following this section, the differences in each specimens’

results are summarized. For simplicity, the detailed response of the remaining four

specimens will be presented in Tables 5.9.2 through 5.9.6, after the summary of results

for each specimen.

Hinge Point

BRB Core Plate

Stiffening Ribs

Original Location of Casing

1275.5 Response of Specimen BRB02

Specimen BRB02 was tested to investigate the effect of a tapered gusset plate on

connection and overall system performance. Figure 5.5.1 gives the imposed

deformation history, where loading of the brace in compression is negative. It should

be noted that cycle 36 contains two tensile peak drifts as shown in the figure below.

This occurred when the pump which ran the actuator had to be switched with another

pump after the first tensile peak. For purposes of discussion, the two peaks will be

referred to as 36a and 36b as shown in Figure 5.5.1. Specimen BRB02 had full force

displacement curves as would be expected from a buckling restrained brace, as shown

in Figure 5.5.3. The frame reached only moderate story drift ratios of 2.4% and -2.3%

prior to failure, with maximum loads of +331 and -353 kips. Figure 5.5.2 shows the

lateral force history. Table 5.5.1 summarizes the drifts and input forces with respect to

the cycles. Figure 5.5.4 shows the elongation of the brace during testing, and gives

peak elongation values with corresponding lateral displacements.

Figure 5.5.1 – BRB02 Displacement History

128

Figure 5.5.2 – BRB02 Lateral Force History

Figure 5.5.3 – BRB02 Force Displacement Response

129Table 5.5.1 – BRB02 Peak Values

Figure 5.5.4 – BRB02 Core Plate Elongation


Yielding continued to increase throughout the test and brace elongation reached peak

values of 2.14 and -2.89 inches. Brace elongation was measured until plastic hinging

(H2) occurred, after which the readings included out of plane deformation and were

deemed inaccurate.

Initial Yield Cycles H2

130The behavior of specimen BRB02 was nearly identical to that of the reference BRB,

and failure resulted from the loss in stability of the SW beam and out of plane plastic

hinging of the BRB core plate. During cycle 35, the entire SW corner of the frame

slipped off the channel assembly. The column was jacked back into place, and testing

continued as scheduled. Data from all locations during this period of time was deleted

since it was no longer accurate. This problem was not experienced again during testing.

The condition of specimen components at the end of the test are shown in Figures 5.5.5

through 5.5.11. The response of specimen BRB02 is summarized in Tables 5.9.2

through 5.9.6.

(a) Inner Flange Yielding – Y4 (b) Inner Flange Buckling – B2

(c) Outer Flange and Inside Face of Inner Flange

Figure 5.5.5 – NE Column at End of Test

Y4

Y2

131

Figure 5.5.6 – NE Beam Inside Face of Inner Flange at End of Test – Y2

Figure 5.5.7 – North Beam at Load Beam at End of Test

Figure 5.5.8 – SW Column Outer Flange and Web at End of Test

B3

Y4 (View Obstructed)

Y2

B3

Y4

B1

Y4

132

(a) Outer Flange Yielding – Y5 (b) Outer Flange Buckling and Web Yielding

(c) Out of Plane Rotation

Figure 5.5.9 – Damage of SW Beam at End of Test

Figure 5.5.10 – SW Gusset Plate Damage at End of Test

Y4, B3

B3

WF

WFY3

133

Figure 5.5.11 - SW Corner After Failure


Specimen BRB03 was tested to investigate the effect of bearing connection on overall

system performance. However, the bolts were partially tensioned to avoid slip prior to

initial brace yielding (Y1). Figure 5.6.1 gives the imposed deformation history, where

loading of the brace in compression is negative. Specimen BRB03 had full force

displacement curves as would be expected from a buckling restrained brace, as shown

in Figure 5.6.3. The frame reached story drift ratios of 2.15% and -2.0% prior to failure

(cycle 39), with maximum loads of +306 and -346 kips. Figure 5.6.2 shows the lateral

force history. Table 5.6.1 summarizes the drifts and input forces with respect to the

cycles. Figure 5.6.4 shows the elongation of the brace during testing, and gives peak

elongation values with corresponding drifts.

134



135


Table 5.6.1 – BRB03 Peak Values

136




values of 1.78 and -2.70 inches.

The response of specimen BRB03 was nearly identical to that of the reference BRB

specimen and BRB02, and failure resulted from the loss of stability of the SW beam and

out of plane plastic hinging of the BRB core plate. The condition of specimen

components at the end of the test are shown in Figures 5.6.9 through 5.6.15. The

response of specimen BRB02 is summarized in Tables 5.9.2 through 5.9.6.

Specimen BRB03 was designed to investigate a bearing bolt connection. The initial slip

of the bolts occurred in the NE connection during the tension excursion of cycle. The

dynamic slip occurred at a brace force of 155 kips, which was a force less than the brace

had been subjected to previously, at a drift ratio of 0.13%. The bolt slip caused a small

jog in the hysteresis curve as noted in Figure 5.6.3. During the remaining cycles, the

splice plates seemed to slip more slowly as shown in Figure 5.6.5.


H2

137

Figure 5.6.5 – Bolt and Splice Plate Slip in NE Connection

The bearing connection sustained slight bolt hole elongation in the holes of the BRB

and the splice plates, but not in the gusset plates. The bearing deformation was nearly

undetectable to the naked eye, as shown in Figure 5.6.6. The performance of the gusset

plate connection was similar to the other specimens, but with additional local yielding

within the NE gusset plate. The yielding only reached Y2 levels towards the end of

testing as shown in Figure 5.6.7.

Figure 5.6.6 – Slight Hole Bearing in BRB (NE Connection)

138

Figure 5.6.7 – NE Gusset Plate at End of Test – Y2

The yielding and buckling in the north beam at the load beam that occurred during

testing of the specimens, happened during the testing of specimen BRB03.

Additionally, as B2 flange local buckling and B3 web buckling occurred in the north

beam, the actuator began to deflect out of plane (upwards), as the tip of the load beam

deflected out of plane (downwards) approximately 0.25 inches. At this point, the nylon

tube on the inner flange of the load beam fractured as shown in Figure 5.6.11b. The

resulting damage in the north beam is shown in Figure 5.6.11a.

One final behavioral difference of specimen BRB03 was the yielding at the north ends

of both the east and west columns. During the last few cycles, yield lines appeared at

the north end of the east column and spread to Y3 levels as shown in Figure 5.6.8a.

These yield lines ran parallel to the length of the column suggesting shear yielding, and

extended from the east column cap plate to almost the free edge of the gusset plate as

shown in Figure 5.6.8a. Yielding and buckling at the top of the west column also

occurred. At this location, the outer flange of the column began to buckle in plane

where it was in contact with the load beam as shown in Figure 5.6.8c. Y3 yielding and

B2 buckling in this area lead to formation of a gap between the top of the column and

the load beam as shown in Figure 5.6.8b and 5.6.8c.

139

(a) Longitudinal Yield Lines at Top of East Column – Y3

(b) Top of West Column (c) Buckling of West Column Outer Flange

Figure 5.6.8 – Yielding and Buckling in Top of West and East Columns at End of Test

GAP

B2

Y3

140

(a) Outside Face of Inner Flange – Y5 (b) Inside Face of Inner Flange and Web

(c) Inner Flange


Figure 5.6.10 – NE Beam at End of Test – Y3

B3

Y4

Y2

B3

141

(a) North Beam at Load Beam (b) Fracture of Nylon Tube

Figure 5.6.11 – North Beam and Load Beam at End of Test

Figure 5.6.12 – SW Column Outer Flange at End of Test – Y5

(a) Outer Flange Yielding – Y5 (b) Outer Flange Buckling and Web Yielding

Figure 5.6.13 – SW Beam Web and Inner Flange at End of Test

Fracture

B2

Y5

Y3

B2

Y5,B3

Y5

142

Figure 5.6.14 – Weld Crack Openings in SW Gusset

Figure 5.6.15 - SW BRB End After Failure

Y3

WF

WD


Specimen BRB04 was tested to investigate the effect rotating the BRB cross section (90

degrees) would have on the connection and overall system performance. Figure 5.7.1

gives the imposed deformation history, where the loading of the brace in compression is

negative. Specimen BRB04 had full force displacement curves as would be expected

from a buckling restrained brace, as shown in Figure 5.7.3. The frame reached

moderate story drift ratios of 2.3% and -2.2% prior to failure, with maximum loads of

+316 and -347 kips. Figure 5.7.2 shows the lateral force history. Table 5.7.1

summarizes the drifts and input forces with respect to the cycles. Figure 5.7.4 shows

the elongation of the brace during testing, and gives peak elongation values with

corresponding drifts.

The data recording system used during testing, shut off between the negative peak of

cycle 33 and slightly into the tension excursion of cycle 34. This coincided exactly with

the initial bolt slip of the BRB connection, and the impact from the slip most likely

caused the shut down. The data jumped from points (-2.94, -298.8) to (0.567,205.6),

and the resulting straight line between the two points is denoted as “Data Gap C33” in

Figure 5.7.3. This is obviously not how the specimen actually behaved, so for purposes

of energy dissipation calculations in Chapter 6, the missing data was assumed to match

that from cycle 34 along the same portion of the loading since they had the same target

drifts. Figure 5.7.3 shows that sets of cycles which have the same target drifts have

very similar hysteresis curves, and therefore this is a realistic estimate of the missing

data points. The portion of the corrected curve is shown by the dashed line labeled

“Estimated C33” in Figure 5.7.3.

144



145


Table 5.7.1 – BRB04 Peak Values

146





(H2) occurred. For this test, plastic hinging occurred first during cycle 37, which

corresponds to H2 in Figure 5.7.4.

The differences noted with specimen BRB04 relative to other specimens included

yielding and buckling at additional locations. The failure of specimen BRB04 occurred

in a similar manner to the reference specimen, with the following exceptions. Just as in

the other specimens, the out of plane rotation of the SW beam and gusset plate lead to

hinging in the BRB at the termination of the stiffening rib. The difference in specimen

BRB04 was that the brace hinged and deformed in strong axis bending of the core plate.

Large out of plane rotations and reduction in stiffness (H2) began during the

compression excursion of cycle 37 at approximately a -1.9% drift ratio. However, the

peak drift (-2.2%) was reached before failure of the system. Initial plastic hinging (H2)

began with in plane torsional rotation about the weak axis (Figure 5.7.5), which caused

initial hinging (H1) in the weak axis direction. Initial in plane hinging also occurred at

the NE end of the brace. However, with further compression drifts, out of plane hinging

occurred in the SW end of the brace. The rate of out of plane hinging was reduced

Initial Brace Yield

H3

147relative to the other specimens, and the brace remained 2 to 3 inches above the

floor. During the final compression excursion (cycle 38) the BRB hinged out of plane

until it touched the floor. The rate of stiffness reduction was much slower than in

previous specimens, as shown in Figure 5.7.3 (point 1 to point 2). The condition of

specimen components at the end of the test are shown in Figures 5.7.7 through 5.7.13.

Figure 5.7.5 – Torsional BRB Rotations During Cycle 37

The torsional rotation of the BRB caused in plane twisting of the SW gusset plate as

shown in Figure 5.7.8b. The inner flange of the SW column also rolled inward a small

amount, as shown in Figure 5.7.13d. The SW beam web buckled away from the strong

floor, and the pattern of web yielding was significantly different than in other specimens

(Figures 5.7.10c and 5.7.10d). Also, the SW beam initially began deforming away from

the strong floor, and web yielding spread to the beam-to-channel assembly connection.

This deformation remained in the beam even after failure of the specimen. The

torsional rotation of the BRB also caused problems between the casing and the core

plate. During cycles 33 and 34 at -1.66% drift ratios, the NE end BRB cap plate bound

on the edge of the BRB core plate, as shown in Figure 5.7.11. By 2.09% drift ratios

(cycles 35 and 36) the casing completely bound on the core plate. At the tension peaks

of these cycles, the brace extended out of its casing only at the SW end. The casing

completely shifted to the NE end of the brace (S2) by the end of the compression

excursion of cycle 37.

BRB04 used a bearing bolt connection (after brace yield), however no yielding was

TorsionalRotation

148observed in the gusset plates as it was with the BRB03 gussets. Dynamic slip (BS)

of the bolts also occurred four times instead of only once. The slips occurred as

summarized below.

• Initial slip (BS) occurred at the SW connection at a drift ratio of -1.66%

(cycle 33), and a lateral actuator force of -322 kips.

• The second slip (BS) occurred at the SW connection at a drift ratio of -0.29%


• The third slip (BS) occurred at the SW connection at a drift ratio of 1.56%

(cycle 37), and a lateral actuator force of 295 kips.

• The fourth slip (BS) occurred at the NE connection at a drift ratio of -1.55%


The bolt slips are plotted in Figure 5.7.6 and noted in the force displacement response

(Figure 5.7.3). Slight bolt hole elongation occurred in the BRB and the splice plates,

but not in the gusset plates.

Figure 5.7.6 – Bolt and Splice Plate Slip in BRB04

Unlike any of the other specimens, BRB04 had yielding that occurred in the around the

full penetration flange welds in the SW beam-to-column connection (Figure 5.7.7). The

149yielding was first noticed at level Y2 after cycle 37, and spread to level Y3 after

cycle 38 (Figure 5.7.7).

Figure 5.7.7 – SW Beam-to-Column Connection at End of Test

(a) Connection Damage (b) Twisting of Gusset Plate

Figure 5.7.8 – SW Gusset Plate Connection at End of Test

Y3

Y3

WF

150

(a) Outside Face of Inner Flange – Y4 (b) – Inner Flange B2

(c) Inside Face of Inner Flange and Web


Y4

Y2

B2

151

(a) Inner Flange – Y5 (b) Inner Flange – B3

(c) Web Yielding (d) Web Buckling and Beam Torsion

Figure 5.7.10 – SW Beam at End of Test

Figure 5.7.11 – Binding of BRB Cap Plate Against Core

Y4

Y4

152

(a) Web and Inside Face of Inner Flange (b) Outside Face of Inner Flange

Figure 5.7.12 – NE Beam at End of Test

(a) Outside Face of Outer Flange – Y5 (b) Inside Face of Flanges and Web

(c) Outside Face of Inner Flange – Y2 (d) Buckling and Rolling of Flanges

Figure 5.7.13 – SW Column at End of Test

Y4Y3

Y2

B2

Y4

Y2

Y3


Specimen BRB01 was nominally identical to the reference BRB, except that it was

loaded following a different deformation history. Specimen BRB01 was tested using a

different actuator than the other specimens. During the compression excursion of cycle

31, the actuators’ tensile capacity (brace compression) was met at a drift ratio of -0.9%,

and a force of -260 kip. For the remainder of the test the frame was loaded in the

positive direction according to the loading protocol, but could only be loaded in the

negative direction until the actuator’s capacity was reached. This created a very

unsymmetrical displacement history and force displacement response, as shown in

Figures 5.8.1 and 5.8.3. The force required to load the brace in compression exceeded

the capacity of the actuator in later cycles. Therefore, some of the later cycles were not

able to reach negative drifts. The frame to reached significantly higher positive drifts,

but the negative drifts only reached small magnitudes. The frame reached drift angles

of 3.3% and -0.9% prior to failure (cycles 44), and maximum loads of +306 and -260

kips. Figure 5.8.2 shows the lateral force history. Table 5.8.1 summarizes the drifts

and input forces with respect to the cycles. Figure 5.8.4 shows the elongation of the

brace during testing, and gives peak elongation values with corresponding drifts.


154



155Table 5.8.1 – BRB01 Peak Values






H2

156(H2) occurred, after which the readings included out of plane deformation and were

deemed inaccurate.

The behavior of specimen BRB01 was nearly identical to that of the reference BRB

other than the noted difference in loading. Failure resulted from the loss in stability of

the SW beam and out of plane plastic hinging of the BRB core plate. The out of plane

hinging caused fracture of the SW beam inner flange, at the gusset-to-beam location

(Figure 5.8.5b). The mechanisms due to brace compression were less severe compared

to the other specimens. The condition of specimen components at the end of the test are

shown in Figures 5.8.5 through 5.8.9. The response of specimen BRB01 is summarized

in Tables 5.9.2 through 5.9.6.

The gusset-to-beam/column welds in specimen BRB01 were 3/4 inch, compared to the

1/2 inch welds required by design and used in the other four specimens. Because of

these oversized welds there was no weld cracking during the testing, even in the SW

connection after failure. The BRB casing did not shift as much as in the other

specimens. This is not unexpected since the compressive loads were not as high.

(a) Web and Inner Flange (b) Outside Face of Inner Flange

Figure 5.8.5 – SW Beam at End of Test

Y5 B3

Y5

Fracture

157

(a) NE Gusset Plate (b) SW Gusset Plate

Figure 5.8.6 – Gusset Plates at End of Test

Figure 5.8.7 – SW Connection After Failure

Y2 Y2

Y3

158

(a) Outside Face of Inner Flange - Y5 (b) Flanges and Web


(a) NE Outside face of Inner Flange (b) Load Beam

Figure 5.8.9 – NE Beam and North Beam at Load Beam at End of Test

Y4,B1

B2

Y3 Y3,B2

B3

1595.9 Comparison and Summary of Response

This section compares the magnitudes of yielding and buckling among specimens, and

when they occurred. The comparisons are made at the areas of the specimen outlined in

Figure 5.2.1. Because the compressive loadings of specimen BRB01 were much

smaller than those in the other four tests, damages corresponding to brace compression

are not directly compared to the other specimens. Applicable comparisons are

highlighted (boxes drawn around drift ratios) in Tables 5.9.2 through 5.9.6. Peak drift

ratios and input forces are also directly compared in Tables 5.9.7 and 5.9.8.

Gusset-to-BRB Connection

There were low levels of damage in the gusset plate connections, and few differences

were observed. One difference was that Y2 level yielding occurred in the NE gusset

plate of specimen BRB03 before plastic hinging occurred. This yielding was most

likely caused by the bolt slip that occurred in specimen BRB03. It should be noted that

specimen BRB04 also saw bolt slip, but had no noticeable yielding in either of the

gusset plates before plastic hinging occurred. There also was in plane twisting of the

SW gusset plate in specimen BRB04 (Figure 5.7.8b), due to the torsional rotation of the

BRB discussed in Section 5.7.

BRB Hinging and Failure

The only difference in hinging of the BRBs occurred during the final cycles of the

testing of specimen BRB04. As noted in Section 5.7, the BRB initially hinged in plane

and rotated torsionally before hinging out of plane. The most noticeable difference in

the failure of specimen BRB04 was the rate at which the plastic hinge developed. In the

other specimens the stiffness degraded very quickly, the stiffness of specimen BRB04

degraded slowly and in a more controlled manner. There was no drastic force leveling

as there was in the other four specimens (Figure 5.7.3).

SW Beam

The SW beam in each specimen saw the largest levels of combined yielding and

160buckling in both the inner flange and web. This damage in each specimen

ultimately led to failure of the systems. In all specimens, low levels of yielding would

not start until at least the mid drift range. Initial buckling (B1) would not start until at

least the late drift range. However, both yielding and buckling would increase to high

levels (Y4/Y5 and B3) during the final drift range. In fact, only level Y3 yielding and

B2 buckling would occur before the second to last set of cycles of the test. At this

point, flange/web yielding and buckling would quickly increase to high levels (Y4/Y5

and B3). At this time initial out of plane rotation of the SW beam, gusset plate, and

BRB occurred. The next set of drifts would signal the impending doom of the

specimen, as the out of plane rotation quickly increased until plastic hinging occurred.

The drift at which yielding began, and the concentration of yielding in the SW beam

web varied in some specimens. The reference specimen initially buckled (B1) at drift

ratios of 1.69%. Level B1 buckling occurred at 8.9% larger drifts for specimen BRB02,

2.4% larger drifts for specimen BRB03, 8.9% larger drifts for specimen BRB04, and

54.4% larger drifts in specimen BRB01. These patterns are proportional to the

comparison of maximum drifts (with the exception of specimen BRB01). Figure 5.9.1

compares the yielding patterns in the SW beam web of the reference BRB specimen,

specimen BRB02, and specimen BRB04. The yielding in the reference BRB specimen

was more concentrated than the yielding of specimens BRB02 and BRB04, as seen in

Figure 5.9.1. The yielding pattern in specimen BRB04 was shaped differently than the

other two specimens, and the web was also the only one to buckle away from the strong

floor, due to the rotated orientation of the BRB core. The actual shape of the yielding is

not necessarily an important consideration, but the yielding was less concentrated in

specimen BRB04 like that of specimens BRB02 andBRB03. Each of these specimens

utilized 15 degree tapered gusset plates.

161

(a) Reference BRB SW Web (b) BRB02 SW Web

(c) BRB04 SW Web

Figure 5.9.1 – Comparison of Yielding in SW Beam Webs

NE Column

Yielding in the column web reached higher levels in the square gusset plate specimens

(BRB01 and Reference), than in the tapered gusset plate specimens. Web yielding

reached level Y3 and web buckling reached level B2 in the reference BRB specimen.

Web yielding reached level Y3 and web buckling reached level B1 in specimen BRB01.

Web yielding in specimens BRB02-04 reached level Y2, and web buckling did not

occur at all. There was also level Y3/B1 yielding/buckling in the outer flange of the

reference BRB specimen. Specimen BRB02 had level Y2 yielding and no buckling,

and specimen BRB03 had no yielding or buckling in the outer flange. BRB04 had level

Y1 yielding and no buckling in the outer flange.

162SW Column

There were very few notable differences in the yielding and buckling of the SW

column. The yielding in the SW column of specimen BRB04 occurred more on the

inside faces of the flanges, than on the outside face of the inner flange. Specimen

BRB04 also had higher levels of outer flange buckling (level B2 compared to level B1

in specimen BRB02, and no buckling in the other three specimens). Specimen BRB04

also had level Y3 web yielding, whereas the other specimens had level Y1 or no web

yielding. Specimen BRB01 performance states in the SW column was obviously

different due to the low compressive loads. In fact, no noticeable yielding occurred on

the outside face of the outer flange, or in the web.

NE Beam

Mechanisms in the NE beam were minor in all specimens, compared to the NE column

and SW beam areas. Yielding in the inner flange and beam web reached higher levels

in specimen BRB04 compared to all the other specimens (Table 5.9.6).

North Beam at Load Beam End

Damage in this location varied based on when the specimen was tested. The first three

specimens tested (specimens BRB01-03) saw large amounts of damage at this location.

The final two tests (specimen BRB04 and the reference BRB specimen) saw less

damage than in specimen BRB01-03 (Table 5.9.6). The differences in the mechanisms

were caused by the quality of the specimen fit up with the testing apparatus, specifically

with the out of plane support system. After the large amounts of yielding and buckling

that occurred in specimen BRB03, extra attention was paid to this fit up, and the

remaining two specimens (specimen BRB04 and the reference specimen) had smaller

amounts of yielding and buckling.

The differences in response for each specimen are provided in Tables 5.9.2 through

5.9.6. For each specimen, the tables correspond to the performance states described in

Section 5.2. Peak drift ratio (%), peak input force (kip), and cycle numbers are

163provided. However, the onset of the performance state did not necessarily occur at

the peak values. For later compressive drift cycles in specimen BRB01, the drifts were

small and may be listed as 0%. This is a result of the one sided loading history applied

to specimen BRB01, as described in Section 5.8. Although the drifts were small, the

compressive forces were still large enough to cause damages. Abbreviations used in

Tables 5.9.2 through 5.9.6 are defined in Table 5.9.1.

Table 5.9.1 – Abbreviations Used in Tables 5.9.2 Through 5.9.6

164

Tabl

e 5.

9.2

– Te

st C

ompa

rison

s – C

onne

ctio

ns, B

race

, and

Col

umn

Bas

es

165

Tabl

e 5.

9.3

– Te

st C

ompa

rison

s – S

W B

eam

166

Tabl

e 5.

9.4

– Te

st C

ompa

rison

s – N

E C

olum

n

167

Tabl

e 5.

9.5

– Te

st C

ompa

rison

s – S

W C

olum

n

168

Tabl

e 5.

9.6

– Te

st C

ompa

rison

s – N

E B

eam

and

Nor

th B

eam

at L

oad

Bea

m E

nd

169Table 5.9.7 – Peak Drift Ratio Comparisons

Table 5.9.8 – Peak Input Force Comparisons

170CHAPTER 6

Interpretation and Analysis of Results

6.1 Overview

The measured data was used to evaluate the performance of the components and

compare the specimens. Measurements included global response, brace response, and

connection response. First, the methods of calculating the individual responses are

described (Section 6.2). Then the results for each specimen are presented and compared

to each other to consider patterns or trends that occurred (Sections 6.3 and 6.4). Global

measures include frame drifts, peak input forces, moments and shear forces in the

framing members, total energy dissipated, and equivalent viscous damping ratios.

Measures of brace response include forces, core strains, shifting of the BRB casing, and

stresses in the casing. Connection measurements include stresses in the gusset/rib

plates, and moment rotation behavior of the shear tab connections. The material

properties of specimen components are used in the analysis and are given for review in

Table 6.1.1. The percent elongation is based on a 2 inch gauge length.

Table – 6.1.1 Material Properties of Specimens

1716.2 Calculation Methods

This section outlines the calculation methods used. The calculations in this section

commonly use i∆ variables which represent the measurement recorded by the ith

potentiometer or strain gauge. Potentiometer and strain gauge numbering, locations,

and other details are provided in Section 4.4 and Appendix D.

6.2.1 Beam/Column Moments and Shears

As described in Section 4.4, strain gauges were placed on columns and beams to

determine elastic moments and shears in the members. For purposes of moment and

shear calculations, Figure 4.4.2 was used to develop the model shown in Figure 6.2.1.

This model uses the centerlines of the framing members, and has a sign convention that

gives counter-clockwise moments a positive value.

All numerical values are given in kips and inches.

Figure 6.2.1 – Model for Moment and Shear Calculations

172Each variable si in Figure 6.3.1, represents the ith strain gauge as numbered in Figure

4.4.2 (one strain gauge on the outside face of each flange). The term cw is the length of

the gusset plate edge adjacent to the column. The terms cd and bd are the depths of the

columns and beams, respectively. Using the above model and basic relations for

determining moments, the following equations can be developed (applicable to elastic

strains only, i.e. yεε < ).

xcc

xc

xc

NE EIdssEI

dI

dM

−=

∆=

∆= 109εσ (6-1)

Similarly:

xcc

SE EIdssM

−= 87 (6-2)

xcc

NW EIdssM

−= 12 (6-3)

xcc

SW EIdssM

−= 34 (6-4)

xbb

Sb EIdssM

−= 65 (6-5)

xbb

Nb EIdssM

−= 1112 , (6-6)

where the IJM terms are the moments (counterclockwise is positive) at the locations

shown in Figure 6.2.1, the bxcI , terms are the moments of inertia of the columns or

beams, and E is the modulus of elasticity of steel. σ∆ and ε∆ are the difference in

stress and strain between the outer and inner flanges (across depth) at each location. If

the strain at any location rose above the yield strain, the corresponding equation could

not be used.

Once the moments were determined, moment and shear diagrams of each column

(Figure 6.2.2) were used to determine the column shears, moments at the beam-to-

173column shear tab connections, and moments at the gusset plate edges.

Figure 6.2.2 – Column Moment Diagrams

Using Figure 6.2.1 and 6.2.2:

( ) cbEASTWEST wdLL −−−== 5.0162144 , (6-7)

where WESTL and EASTL are the distances between column strain gauges, and the value

of 144 is the story height of the frame. The shear in each column is calculated as the

slope in the moment diagram.

EAST

NESEE L

MMV −= , (6-8)

and WEST

NWSWW L

MMV −= , (6-9)

where WV and EV are the shears in the west and east columns, respectively. The

moments shown in Figure 6.2.2 are calculated using equations 6-10 through 6-13.

+−=

216 b

WNWNWcornerdVMM (6-10)

( )WSWSWedge VMM 16+= (6-11)

174( )ENENEedge VMM 16−= (6-12)

++=

216 b

ESESEcornerdVMM (6-13)

6.2.2 Energy Dissipation and Equivalent Viscous Damping Ratio

Maximum drift and force values provide an initial comparison of specimen

performance, but can not ultimately be used to determine which specimens performed

better. Most of the specimens followed the same loading protocol, but actual drifts

differed from the target drifts from specimen to specimen. Because of this, the actual

total energy dissipated, may or may not be larger in specimens with larger drifts and/or

forces. To investigate the amount of energy dissipated, the area under the force

displacement curve of each cycle was estimated using trapezoidal step wise calculations

as shown in Figure 6.2.3. Using basic equations for trapezoidal areas, a single equation

can be developed that is applicable to each of the four zones and accounts for both

positive and negative areas as shown in Figure 6.2.3. The calculation is then made for

each time step throughout the test, and the individual values are summed to find the

total energy dissipated ( hE ).

( )iiii

hFFE δδ −

+∑= +

+1

1

2 (6-14)

Where iF and iδ are the force and displacement at a time step i, and 1+iF and 1+iδ are

the respective values at the subsequent time step.

175

Figure 6.2.3 – Idealized Single Force Displacement Curve

The energy dissipation calculation is made for the following three cases.

• Total System Energy Dissipation

Using the actuator Force and the story drift.

• BRB Energy Dissipation

Using the brace force from the equilibrium method described in Section

6.2.4, and the BRB elongation from potentiometer 40. (Measurement of the

brace axial elongation)

• BRB and Connection Energy Dissipation

Using the brace force from the equilibrium method described in Section

6.2.4, and the frame diagonal deflection from potentiometer 41.

The equivalent viscous damping ratio ( eqζ ) gives the component of total energy

dissipation ( hE ), that is due to equivalent viscous damping. eqζ is a measure of all

damping mechanisms present in the actual structure, and is essentially the ratio of the

hysteretic energy dissipation, and the energy dissipated by an equivalent single degree

of freedom, linear visco-elastic system ( soE ). soE is the triangular area under the secant

stiffness of a force displacement curve, as shown in Figure 6.2.4.

176

Figure 6.2.4 – Equivalent Viscous Damping Model

Since soE varies for the tensile ( +soE ) and compressive ( −

soE ) peaks, their average is used

in the equivalent viscous damping calculation. For the BRBF specimens, the equivalent

viscous damping ratio ( eqζ ) was calculated using equation 6-15 [16].

+=

−+

24 soso

heq EE

E

πζ (6-15)

6.2.3 BRB Core Strains

The maximum strain demand in the brace is an important measure of the performance.

The average strain demand was calculated using brace elongation measured by a string

potentiometer (No. 40), which extended between the brace ends.

obrace l

40∆=ε , (6-16)

where braceε is the calculated brace strain. The initial length ( ol ) is taken as the initial

core yield length (Figure 1.3.2) of the BRB. This calculation assumes that the

elongation occurs only within the core, which is a reasonable assumption since the

remaining portions of BRBs are designed to remain elastic. The string pot spans from

end to end of the brace, so it measures brace elongation only. However, this is not true

177after out of plane deformation occurs, and the respective data and figures presented

in Section 6.3.4 only include calculated values to the point of initial BRB hinging.

6.2.4 Brace Forces

Brace axial forces were calculated using two different methods. The first method used

the brace strain calculated from the brace diagonal string pot, as described in

Section 6.2.3. This method was used while the brace remained elastic. Using the strain

a simple equation for the brace force was developed.

sco

scbracescbrace Al

EAEAF

∆=== 40εσ , (6-17)

where scA is the cross sectional area of the steel core, braceε is the strain in the core

element, and ol is the initial yield length of the BRB core. The second method used

equilibrium of the actuator force and the column shears (Figure 6.2.5) to obtain the

brace force ( braceF ).

)45cos( °++

= EWactuatorbrace

VVFF , (6-18)

where actuatorF is the lateral force delivered from the actuator to the frame. This

calculation was valid while the beams and columns remained elastic at the strain gauge

locations. The two methods give similar results during elastic brace cycles, as shown in

Figure 6.2.6.

Figure 6.2.5 – Free Body Diagram of Frame

Faxial Faxial

178

Figure 6.2.6 – Comparison of Brace Force Calculation Methods

6.2.5 BRB Casing Shift

The BRB casing shifted relative to the core plate during testing (Section 5.2). To

quantify the amount of shifting, a series of three potentiometers that measured brace

elongation at each end were used. The potentiometers were mounted on the brace ribs

and measured off of the brace casing, as shown in Figure 6.2.7.

Figure 6.2.7 – Brace Cylinder Potentiometers

Theoretically, if the casing did not shift, the average measurement at each brace end

would be equal. Therefore, the amount of casing shift ( CS∆ ), is calculated as the

difference of the two averaged measurements.

Cylinder Potentiometers

3rd Cylinder Potentiometer (Hidden)

179

∆+∆+∆

−

∆+∆+∆

=∆−∆=∆33

241003891SWavgNEavgCS (6-19)

6.2.6 BRB Casing, Gusset Plate, and Rib Plate Stresses

Specimens BRB01 and BRB02 both used uniaxial and/or biaxial strain gauges to

measure stresses in the BRB casing, gusset plates, and rib plates. The calculations used

to determine stresses were from simple stress strain relationships as follows.

For uniaxial gauges (if stress perpendicular to surface is approximately zero):

εσ E= (6-20)

For biaxial gauges, Hooke’s Law is used with Poisson’s ratio, 3.0=ν :

( )yxxE νεεν

σ +−

= 21, (6-21)

and ( )xyyE νεεν

σ +−

= 21, (6-22)

with plane stress conditions and isotropic material. Specimen BRB01 had strain gauges

on each face of the BRB casing, to determine if any significant bending or pressure

stresses occurred during testing. These stresses could be caused by bending

deformations, local buckling inside the core, or even from friction between the core

plate and the surrounding concrete. Ideally, in buckling restrained braces the casing

stresses are minimal. Figure 6.2.8 shows that the stress levels in the casing of specimen

BRB01 were low.

Specimen BRB01 also used biaxial strain gauges located on the NE gusset plate. The

gusset plate strain gauges were used to estimate the forces in the connection.

Figure 6.2.9 shows the gusset plate stresses during testing of BRB01. Refer to

Figures 4.4.2 and 4.4.3 for strain gauge locations. As seen in Figure 6.2.9, the stresses

in the gusset plate remain below yield during the entire test. For most of the testing the

stresses were less than half of the nominal yield strength of the plate.

Specimen BRB02 used two biaxial strain gauges placed on both sides of the NE top rib

plate (Figure 4.4.3). These gauges were used to investigate the relative amount of

180stresses present in the rib plate compared to those that were found in the NE gusset

plate. As seen in Figure 6.2.10, the envelopes of the rib plate stresses in the in plane

direction (14 and 16) are on average only 3-5 ksi less than those found in the NE gusset

plate. Again, stresses remained less than half of the nominal yield stress of the plate.

Stresses in the out of plane direction (13 and 16) were quite small.

Figure 6.2.8 – BRB01 Casing Stresses

181

(a) East-West Direction

(b) North-South Direction

Figure 6.2.9 – BRB01 NE Gusset Plate Stresses

sy = 50 ksi

sy = 50 ksi

182

Figure 6.2.10 – BRB02 NE Rib Plate Stresses

6.2.7 Beam/Column Relative Rotations

Relative rotations between beams and column in the NW and SE corners were

measured using potentiometers along the inside face of each beam flange. These

instruments measured the rotation of the beam relative to the column at each shear tab

connection, as shown in Figure 6.2.11. The calculated rotations were used to quantify

the moment rotation response of the connection. Counterclockwise rotations are

considered positive following the sign convention discussed previously.

Figure 6.2.11 – Beam/Column Relative Rotations

sy = 50 ksi

183Using Figure 6.2.11, the SE and NW rotations ( SEθ and NWθ ) are calculated as

follows:

rSE L

2827 ∆−∆=θ , (6-23)

and r

NW L4544 ∆−∆

=θ (6-24)

Where fbbr tdL 2−= is the distance between the potentiometers, and bd and fbt are the

beam depth and flange thickness, respectively.

6.3 Comparison of Response

This section compares the specimen performance using the calculated measures

described in Section 6.2 and the test results of Chapter 5. Global response is discussed

first, including discussion of component contributions to stiffness and energy

dissipation. A detailed discussion of local responses measured in the brace and

connections follows.

6.3.1 Drift and Force Comparisons

The similarities and differences found in the drift ratios of each specimen (Chapter 5)

are discussed in terms of maximum range. Table 6.3.1 compares the range of drifts

experienced by each specimen.

Table 6.3.1 – Comparison of Maximum Drift Range

The two identical specimens, BRB01 and the reference BRB, had nearly identical

ranges even with the drastically different loading patterns. Specimen BRB02 had the

184largest range, which was 10.9% larger than that of the Reference BRB specimen.

Specimen BRB03 had the smallest range, which was 11.5% smaller than that of

Specimen BRB02. Specimen BRB04 had the second largest range, which was 10.1%

larger than that of specimen BRB03 and was 8.1% larger than the reference BRB range.

Lateral forces from the actuator for the specimens can be compared in the same manner

as the maximum drift ranges, as shown in Table 6.3.2.

Table 6.3.2 – Comparison of Maximum Lateral Force Range

In this comparison specimen BRB01 is quite different from the other four specimens,

but the forces in the other four specimens are all very similar to one another. The range

of lateral forces were very similar for each specimen with the exception of specimen

BRB01.

The contribution of the BRBF elements to the total system stiffness is also of interest.

The components which contribute to stiffness are the BRB itself, the gusset plate

connections, and the framing elements and connections. The component contributions

were similar in each specimen, so the reference BRB is used as a representative

specimen. The portion of stiffness due to the brace was the brace elongation transposed

into the lateral direction. The portion of the stiffness due to the gusset plate connections

and frame corners (Figure 6.3.1), was the difference between the frame diagonal

elongation and brace elongation (transposed into the lateral direction). The remaining

portion of stiffness was from the framing members, which was the difference between

the total stiffness and the sum of the brace and connection stiffness’. The contributions

of each component is shown in Figure 6.3.1. The plots in Figure 6.3.1 are given until

185the plastic hinging of the BRB occurred. The figure shows the percent of the total

stiffness, with a total of 1.0. The actual system stiffness gets smaller with larger drifts.

Figure 6.3.1 – Contribution of BRBF Components to System Stiffness

Simply considering the force and drift data of the specimens suggests that specimen

BRB02 performed better than the other four specimens. Specimen BRB01 showed that

higher drifts are achievable by the BRB, if stability of the connection and frame

elements can be maintained. These ranges essentially give the overall size of the force

displacement responses of each specimen. The trends in the maximum ranges can also

be seen in the final cycle force displacement responses shown in Figure 6.3.2. The

envelope for BRB01 was not included due to its highly non-symmetric behavior.

Initial Brace Yield

Connection & Corner

186

Figu

re 6

.3.2

– F

inal

Cyc

le F

orce

Dis

plac

emen

t Res

pons

es

187Inspection of the final cycle force displacement responses, show that the curve for

BRB02 surrounds the other three curves. The remaining three curves are very similar,

however the unloading portions of the BRB04 curve extend past those of BRB03 and

the reference BRB. The curves of BRB03 and the reference specimen are nearly

identical.

6.3.2 Comparison of Peak Moment and Shear Forces

The moments and shear forces in the framing members were compared following the

calculations described in Section 6.2.1. Column moments were calculated at the gusset

plate free edges, and at the shear tab connections. Beam moments were calculated at

locations 15 inches from the SW gusset plate for the south beam, and 22 inches from

the NE gusset plate for the north beam (Figure 4.4.2). As noted in Section 6.2.1, only

elastic moments and shear forces were calculated. Yielding at the gauge locations

usually occurred during the late range drifts for the north beam moments, the final range

drifts for the south beam moments, the mid range drifts for the east column moments

and shears, and the late range drifts for the west column moments and shears.

Therefore, the peak values presented in this section were not the maximum forces.

Table 6.3.3 shows the theoretical yield moment ( yM ) of the beams and columns for

each specimen, based on yield stresses in Table 6.1.1.

The following sign convention was used.

At tension peaks:

NE corner, NW corner, and south beam moments are positive. SE corner, SW

corner, and north beam moments are negative. Column shears are negative.

Table 6.3.3 – Theoretical Yield Moments

188Figure 6.3.3 compares the moments in the north beams of each specimen; all were

similar. As shown in Figure 6.3.3, the rate of moment increase in the north beam

changes after the brace yields in tension. The same phenomenon occurs when the brace

yields in compression, but is not as pronounced. These trends were also observed in the

south beams.

Both the north and south beams had larger moments during compressive drifts. This

results from larger forces needed to shorten the BRB, due to Poisson expansion of the

core and friction against the surrounding concrete. Plots and peak results of the

moments in the south and north beams for each specimen are provided in Appendix B.2.

Figure 6.3.3 - Peak Moments in North Beam Comparisons

Figure 6.3.4 shows that the column moments at the NE gusset plate edge were similar in

all specimens. The same pattern was seen in the west column at the gusset plate edge.

Plots and peak results of the moments in the NE and SW beam-to-column connections

for each specimen are provided in Appendix B.2.

189

Figure 6.3.4 – Peak Moments in East Column at NE Gusset Edge

Figures 6.3.5 and 6.3.6 show the moments in the shear tab connections of each

specimen. Differences in the NW shear tab positive moments occurred at larger tensile

drifts (Figure 6.3.5), and differences in the SE shear tab positive moments occurred at

larger compressive drifts (Figure 6.3.6). Post test inspection of the bolt holes in the

beam webs (Figure 5.4.23), showed that bolt hole elongation occurred mainly in one

direction. The NW corner elongation corresponded to the rotations during tension

drifts, and the SE corner elongation corresponded to the rotations during compression

drifts. Additionally, column uplift occurred at the base of the west column during

tension drifts and east column uplift occurred during compression drifts. It is likely that

the noted differences in NW and SE connection moments are due to variations in the

severity of uplift and bolt hole elongation. Plots and peak results of the moments in the

NE and SW shear tab connections for each specimen are provided in Appendix B.2.

190

Figure 6.3.5 – Peak Moments in NW Beam-to-Column Shear Tab Connections

Figure 6.3.6 - Peak Moments in SE Beam-to-Column Shear Tab Connections

Bolt Hole Elongation and Column Uplift

Bolt Hole Elongation and Column Uplift

191The preceding discussion showed that there were significant moments at both ends

of the columns. The current design procedures treat the shear tab connections as

“pinned” connections, which are assumed not to transfer moments. The experimental

results show that this is not the case. Figures 6.3.7 through 6.3.10 further illustrate the

relative magnitudes of the column moments at varying drift ratios. Each figure gives a

moment diagram at a specific drift level for the east and west columns of the reference

BRB specimen, at both the tensile and compressive peaks. The actual peak drifts are

also provided.

(a) East Column – Tensile Peak (b) West Column – Tensile Peak

(c) East Column – Compressive Peak (d) West Column – Compressive Peak

Figure 6.3.7 – Column Moment Diagrams at +0.14% and -0.18% Drift Ratios –

(Approximately Half of Yield Drift)

192



Figure 6.3.8 – Column Moment Diagrams at +0.23% and -0.32% Drift Ratios

The moment diagrams in Figure 6.3.8 are shown approximately at the yield drifts, or the

initial yield of the BRB core plate. No other performance states occurred.

193




The moment diagrams in Figure 6.3.9 are shown at approximately 2 times the yield

drift. During these drifts, level Y1 yielding occurred on the outside face of the NE

column inner flange, the outside face of the NE beam inner flange, and the outside face

of the SW column inner flange.

194




The moment diagrams in Figure 6.3.10 are shown at approximately 3 times the yield

drift. During these drifts, level Y1 yielding occurred on the outside face of the SW

beam inner flange, and the outside face of the SW column outer flange.

Figure 6.3.11 shows that the peak shears in the west column were similar for each

specimen. The same correlation was seen in the east columns. The column shear drift

response is nearly linear, with a small change in slope around the point of initial brace

yielding (approximately 0.2% drift ratio).

195

Figure 6.3.11 - Peak Shears in West Column Comparisons

The percentage of the total system lateral force (force from actuator) that is carried by

the columns is illustrated in Figure 6.3.12. Since the response of each specimen was

very similar, the averaged shear force values are shown in the figure. Plots and peak

results of the column shears for each specimen are provided in Appendix B.2. The

magnitudes of shear in the east and west columns were similar. That is, each column

carried nearly the same percentage of the total lateral force. As drifts increased, the

percentage of the total force carried by the columns increased compared to the lateral

force that was carried by the brace. The approximate initial yield drift is also noted in

Figure 6.3.12, and shows a change in shear distribution after brace yielding.

196

Figure 6.3.12 – Percent of Total Lateral Force Carried by Columns

The patterns of the moments and shears do not seem to indicate any significant

differences in the distribution of member forces from specimen to specimen. However,

it is possible that differences could develop during later test cycles, since the moments

and shears were only measured while yielding and buckling of the framing elements

remained relatively minor.

6.3.3 Energy Dissipation and Equivalent Viscous Damping Ratio Comparisons

The amount of energy dissipation in a system is an important measurement of system

performance. As noted in Section 6.2.2, dissipated energy can be calculated for the

total system, the BRB only, and the BRB including the gusset plate connections. Figure

6.3.13 shows the total energy dissipated by each specimen.

197

Figure 6.3.13 – Comparison of Total Energy Dissipation

The pattern of the total energy dissipation (Table 6.3.4) was similar to that seen with the

drift ranges, although the spread between BRB02 and the other BRBs was more

significant. In fact the second highest value from BRB04 was 15.2% smaller than that

of specimen BRB02. Specimen BRB02 dissipated 29.9% more energy than the

reference specimen, which had the smallest amount of energy dissipation. Specimen

BRB03 dissipated 19.4% less energy than specimen BRB02, and 4.8% more energy

than the reference BRB specimen. Specimen BRB04 dissipated the second highest

amount of energy, which was 5.2% greater than that of specimen BRB03 and 10.2%

greater than the reference BRB specimen. Even though the compression excursions of

specimen BRB01 were very small compared to the other specimens, it still dissipated

more energy than the reference BRB and BRB03 specimens, and was very close to the

amount of energy dissipated by specimen BRB04. This shows that even greater

amounts of energy could be dissipated by the systems if the framing elements can

remain stable.

198The portion of energy dissipated by equivalent viscous damping was calculated

according to equation 6-15 for every cycle. The values were then averaged at each

deformation level as shown in Figure 6.3.14. Both the total energy dissipation ( hE ) and

the maximum equivalent viscous damping ratio ( eqζ ) are given for each specimen in

Table 6.3.4.

Table 6.3.4 – Total Energy Dissipated and Equivalent Viscous Damping Ratios

6.3.14 – Comparison of Equivalent Viscous Damping Ratios

Equivalent viscous damping ratios for the specimens were very similar as shown in

Figure 6.3.14. The maximum damping ratio averaged 33%, compared to previous

isolated brace tests which averaged around 55% [16, 17]. The lower damping ratios are

199reasonable because of the premature failure of the BRBs and the additional

components in the BRBFs.

The contribution of the BRBF elements to the total energy dissipation is also of interest.

After the beams and columns yielded at the strain gauge locations, the brace forces were

estimated using the procedure outlined in Section 6.3.5. Equation 6-14 was used to

calculate the energy dissipation of the BRB and gusset plate connections. Figure 6.3.15

shows the energy dissipated by the brace, brace plus connection, and total system. The

component contributions were similar in each specimen, so the reference BRB is used

as a representative specimen. The amount of energy dissipated in the gusset plate

connections is the difference between the “BRB Only” and “BRB+Connections” curves

in the figure. The amount of energy dissipated in the framing elements is the difference

between the total “System” and the “BRB+Connections” curves. The resulting

distribution is shown in Table 6.3.5. The curves in Figure 6.3.15 and the values in

Table 6.3.5 are given until the plastic hinging of the BRB occurred.

Figure 6.3.15 – Distribution of Energy Dissipation

200Table 6.3.5 – Energy Dissipation in Reference BRB Components

At early drifts, nearly all of the energy was dissipated by the BRB. The curves in

Figure 6.3.15 began to separate when the framing members began to yield and buckle.

The vast majority of the total energy was dissipated in the BRB core element (82%), but

energy was also dissipated by the framing elements (16%). This is not an unreasonable

estimate based on the amount of damage that occurred in the frames. The gusset plate

connections contribute very little to energy dissipation in the system, which was

expected since they remained elastic.

6.3.4 Core Strain Comparisons

Core strains in each BRB specimen were computed as described in Section 6.2.3. Core

strain is a useful measurement for understanding the demands placed on each BRB

during the testing procedure. Previous testing of BRBs has shown strain capacities that

range from 0.025 to 0.03 in/in [5, 15, 16, 17]. Although the desired failure mechanism

of BRB core rupture was not achieved in any of the tests, strains typically reached

+0.02 and -0.03 in/in, which is similar to isolated brace tests. Figures 6.3.16 through

6.3.20 show the magnitudes of brace strain throughout the test. The peak core strain

values are summarized at peak drift ratios in Table 6.3.6. Theoretical yield strain for all

BRBs was 0.0015 in/in.

201Table 6.3.6 – Peak Core Strain Comparisons

Figure 6.3.16 – Reference BRB Core Strain

202

Figure 6.3.17 – BRB02 Core Strain


203



204The cumulative plastic ductility ( CPDε ) was also compared. CPDε is a normalized

measure of the amount of inelastic deformation that occurs in the brace, and is

calculated using equation 6-25.

yield

kkCPD ε

εεε

minmax −Σ= , (6-25)

where maxmin,kε are the peak strain values of the kth cycle with peaks above the yield

strain. EFysc

yield =ε is the yield strain of the core plate and yscF is the yield stress of the

steel core material (Table 6.1.1). The cumulative plastic ductility’s are provided in

Table 6.3.7.

Table 6.3.7 – Maximum Strains and Cumulative Plastic Ductility

In isolated Unbonded brace tests performed at the University of California – Berkley, a

similar size buckling restrained brace (Py=273 kips) had similar results of 324 [5]. The

cumulative plastic ductility for the reference BRB and BRB02-04 specimens follow the

same patterns as were seen in the drift ranges (Section 6.3.1). Specimen BRB02 had the

largest value of the four specimens, which was 12.3% larger than that of the Reference

BRB specimen. Specimen BRB03 had a value 12.0% smaller than that of specimen

BRB02, but was 5.7% larger than the reference BRB specimen. Specimen BRB04 had

a value that was 3.1% larger than that of specimen BRB03 and was 9.0% larger than the

reference BRB specimen. Specimen BRB01 had the largest value overall, which shows

that larger amounts of inelastic deformation are possible in the BRBs if plastic hinging

in the core plate can be avoided or delayed.

2056.3.5 Brace Forces

As has been previously mentioned, none of the buckling restrained braces sustained

tensile rupture in the core plate. The equilibrium method (Section 6.2.4) was used to

calculate the force in the brace and to estimate how far away tensile rupture was. Using

the actual yield stress of 44.7 ksi (Table 6.1.1) gives an actual yield strength ( yscP ) of

214 kips. The equilibrium method could only be used until cycles 25 and 26 for the

reference BRB specimen. The peak brace axial force ( braceP ) during these cycles was

254 kips. Using equation 3-7, that gives an approximate overstrength factor (ωβ ) of:

19.1214254

===ysc

brace

PPωβ (6-26)

This occurred at actuator lateral forces of 250 and -246 kips. Since this occurred at

small drifts and lateral forces, it is of interest to estimate the brace forces through the

remainder of the test. This was accomplished by comparing the percent of the lateral

actuator force that was carried by the brace and the column shears with increasing

drifts. Figure 6.3.21 shows the percent of lateral force that was carried in the brace

during cycles 1 through 26.

Figure 6.3.21 – Percent of Lateral Force Carried in BRB

206The percent lateral forces in the brace from initial brace yield to 0.93% drift ratios

(cycles 25 and 26), were used to develop a best-fit curve (Figure 6.3.21). For later

cycles, the percent lateral force ( pctF ) carried by the brace at a given drift, was

calculated from extrapolation of the best-fit curve. The brace axial force ( braceP ) was

then estimated at each drift, as shown in equation 6-27.

( ) °=

45cos100actuatorpct

brace

FFP , (6-27)

where actuatorF is the lateral input force from the actuator at a given drift. Equation 6-27

was used to estimate brace axial forces for the remainder of the test, as shown in

Figure 6.3.22. The plot of the calculated and estimated brace force resembles a typical

stress-strain plot with strain hardening. This method gives an estimated maximum

brace force of 327 kips, which using equation 6.26, gives an overstrength factor of 1.53.

Table 6.3.8 shows that estimation of brace forces in the other specimens were very

similar, with an average overstrength of 1.50. These values are near those found during

previous tests of isolated brace [e.g., 15, 16, 17], which averaged overstrength factors of

1.55. Therefore, it can be stated that the BRBs had significant inelastic ductility even

though tensile rupture of the core plate was not reached.

Figure 6.3.22 – Brace Forces

207Table 6.3.8 – Maximum Brace Forces and Overstrength Factors

6.3.6 BRB Casing Shift Comparisons

Shifting of the BRB casing occurred during all of the tests (Chapter 5). Typically

shifting was not noticeable until the late or final range drifts, when the casing quickly

shifted to the NE end of the brace (Figure 6.3.23). Figure 6.3.23 plots the casing

movement for specimen BRB02, and gives the location of the BRB casing after each

cycle was completed (i.e., zero drift). The increase in shifting of the casing in all

specimens coincided with the observations of out of plane rotation at the SW gusset

plate connection.

Figure 6.3.23 – BRB02 Location of Casing at Zero Drifts

2086.3.7 Deformation Demands and Required Web Thickness Estimates

The discussion in Section 6.3.6 shows that the failure of the specimen was much more

likely caused by deformation demands and/or force concentrations from deformation

demands. If the maximum estimated brace force was taken from the said discussion

(327 kips), and applied to the design procedures used in Chapter 3, the beam and

column sections would be deemed adequate under web crippling and yielding limit

states. In fact, the controlling limit state of beam web crippling would not be exceeded

until the brace force reached 550 kips (strength reduction factors included).

Furthermore, even if the entire maximum actuator load (356 kips) was transferred to the

brace, the resulting maximum brace axial force would only be:

kipsP 5.503)45cos(

356max == (6-28)

From this it seems that the cause of the severe buckling and yielding in the SW beam

web was not properly addressed by the current design methods. Based on the design

calculations of the gusset plates and the observations made during testing, it is

reasonable to assume that negligible deformation occurred in the gusset/rib plates.

During lower drifts, the beam and columns deformed to accommodate the deformation

of the frame. Since the gusset plate corners were very stiff as shown in Figure 6.3.24,

large local demands were placed on the beams and columns at the gusset-to-

beam/column intersections.

Figure 6.3.24– Gusset Plate and Frame Connection

209As drifts increased, the demand at the gusset-to-beam/column intersections also

increased. When the members could no longer accommodate the local rotational and

force demands, severe flange and web yielding and buckling occurred (Figure 6.3.25).

This occurred first in the SW beam, due to its smaller resistance, larger shear forces

from the brace, and the rotational restraint imposed by its’ connection to the channel

assembly. However, web buckling also occurred in the NE column during final range

drifts (Chapter 5).

Figure 6.3.25 – Yielding and Buckling in SW Beam

The failure mechanisms in the SW beam were always preceded by web yielding, as was

discussed in Chapter 5. Therefore it is postulated that if web yielding could be

prevented or delayed, the performance of the SW beam may be enhanced to allow

tensile rupture of the core plate.

The current design provisions [1] described in Chapter 3, determine the adequacy of the

web yielding using equation 3-64.

cwbcybcbcbnucub tFNkRHV ,,,, )5.2(, +=≤ φφ , (3-64)

where Vub and Huc are the shear forces on the beam and column webs, derived from the

Uniform Force Method (Section 3.3.4). The )5.2( ,, cbcb Nk + term represents the

effective yielding length over which the shear force is assumed to act ( cbN , is the length

of the gusset plate edge connected to the beam/column). The forces ubV and ucH can

be calculated at the observed points of initial web yielding (Y1), using the estimated

Line of Web Buckling

210brace forces (Section 6.3.5) and the Uniform Force Method (equations 3-33 and 3-

34). The “actual” yielding length ( yactualL ) can then be estimated by rearranging

equation 3-59 as follows.

cwbcyb

ucubyactual tF

HVL,,

,= (6-29)

The ratio of the “actual” length to the original design length ( cbN , ), is calculated using

equation 6-30.

cb

yactual

NL

,

=α (6-30)

Following this procedure, the estimated yielding lengths ( yactualL ) and ratios (α ) were

calculated for the five specimens as shown in Table 6.3.9. The actual yield stresses of

the columns and beams were used in the calculations (Table 6.1.1).

Table 6.3.9 – Web Yielding Estimates

According to this estimation, the yielding lengths were significantly smaller than those

considered by current design methods. The ratios for the tapered gusset plates were

consistently larger than those for the square gusset plates, as shown in Table 6.3.9. The

α values for both the SW beam and NE column webs were averaged for the tapered

and square gusset plates, as shown in Figure 6.3.26. The average α value was 0.27 for

211tapered gusset plates, and 0.21 for square gusset plates. These estimates suggest

that the tapered gusset plates give larger yielding lengths, which is consistent with the

post test observations (Section 5.9).

Figure 6.3.26 – Yielding Length Ratios (α )

The yielding capacity of the webs can be estimated by using the average α values (α )

and standard deviations ( ασ ), with the maximum expected brace ( maxP ) and shear

forces ( ucub HV , ) from design (Chapter 3).

( )( )cwbcybcbucub tFNHV ,,,, ασα −≤ (6-31)

This preceding discussion suggests that the actual yielding lengths in the webs are

nearly 75 percent smaller than those used by the AISC provisions. However, if

equation 6-31 is used to estimate required web thicknesses, the webs must only be 10 to

15 percent larger to meet the capacity check.

2126.3.8 Beam/Column Relative Rotation Comparisons

The moment rotation response of the shear tab connections were compared using the

moments (Section 6.2.1) and relative rotations (Section 6.2.7) The moment rotation

curves were used to calculate the stiffness of each shear tab connection. The rotation in

each specimen was similar for a given drift ratio. In general, the SE rotations at the

connection were larger than the NW connection. This was likely due to the rotational

restraint provided by the load beam to the NW connection.

Although shear tab connections are commonly treated as “pinned” connections in

design, Section 6.3.2 showed that there were significant moments transferred to the SE

and NW connections. The moment rotation response for the reference BRB specimen is

shown in Figures 6.3.27 and 6.3.28. The response of the NW connection was different

than the SE connection. The SE moment rotation response is influenced by the effects

of column base buckling and uplift. The moments in the SE connection were slightly

larger when the brace was in tension, but the rotations were similar in both brace

tension and compression, as shown in Figure 6.3.28. The moment rotation response of

the NW connections was fairly symmetric, as shown in Figure 6.3.27. Negative

rotations correspond to rotations that occurred during tensile loading and positive drifts,

for both the NW and SE connections. Moment rotation responses and peak rotation

values for all specimens are provided in Appendix B.4.

213

Figure 6.3.27 – Reference BRB NW Connection Moment Rotation Response

Figure 6.3.28 – Reference BRB SE Connection Moment Rotation Response

Brace Tension

Brace Compression

Brace Compression

Brace Tension

214The envelopes of the moment rotation curves for each specimen are plotted in

Figures 6.3.29 and 6.3.30. The initial portions of the envelopes are flat (near the

origin), which is likely due to slip of the bolts in the slightly oversized holes. The

figures also show that the stiffness deteriorated during brace tensile loading in the NW

connection, and brace compressive loading in the SE connection. This corresponds to

the one directional elongation of the bolt holes as previously discussed.

Figure 6.3.29 – NW Moment Rotation Envelopes

215

Figure 6.3.30 – SE Moment Rotation Envelopes

The stiffness of each connection was found by determining best-fit lines for each

envelope, as shown in Figure 6.3.31. The figure provides a bilinear best-fit line

construction for the positive moment envelope of the SE connection (Reference BRB).

Three points were used to fit a line to the initial elastic portion of the envelope, and a

second line to the inelastic portion of the envelope. Each secant stiffness (KST) was

then found by calculating the slope of each best-fit line. Table 6.3.11 lists the points

used, and the resulting secant stiffness for each connection. The sign convention is such

that NW connection stiffness values are negative.

216

Figure 6.3.31 – Moment Rotation Best-Fit Lines

The average elastic secant stiffness value (KSTe) for all connections was 5.7x105 kip-in.

The average inelastic secant stiffness value (KSTi) for all connections was 1.5x105.

These values are similar to previous research results on shear tab connections [22].

Table 6.3.11 shows that the inelastic portion of the stiffness is always greater during

brace tensile loading. The inelastic portion of the stiffness in the NW connection was

always greater during compressive loading.

217Table 6.3.11 – Shear Tab Connection Stiffness Values

6.4 Summary of Specimen Performance

The comparisons of the preceding sections can be summarized in terms of overall

specimen performance. The moments and shears within the beams and columns, and

the amount of beam/column relative rotations were very similar between each specimen

and were mainly dependant on the drift ratios. The lateral input force ranges also varied

very little from specimen to specimen, and the equivalent viscous damping ratios were

similar. This essentially leaves the drift ranges, cumulative plastic ductility of the core

plates, and the total energy dissipated as the best estimates of overall specimen

performance. The patterns discussed in the previous sections suggest that the overall

218performance of specimen BRB02 was better than that of the other specimens. Table

6.4.1 shows that BRB02 had the largest range of drifts and forces, the largest

cumulative plastic ductility (other than BRB01), and significantly greater total energy

dissipation. BRB04 consistently performed below BRB02, but better than the other

BRB specimens. The reference BRB and BRB03 had similar results in all

measurements. Although BRB01 underwent a very different loading history than the

other BRBs, its performance was quite comparable. BRB01 was able to sustain very

large positive drifts and had a very large amount of cumulative plastic ductility in the

BRB. BRB01 is a good indication of the potential BRBFs have if the desired failure

mechanism can be reached in the BRB before the surrounding frame deterioration

becomes to great.

Table 6.4.1 – Performance Summary

219CHAPTER 7

Conclusions and Recommendations

7.1 Summary

Buckling restrained braced frames provide excellent balanced inelastic ductility and

energy dissipation. Because BRBFs are a relatively new structural system, very few

experimental tests have been done that address the complete system performance.

Furthermore, understanding of the performance of BRB connections and how they

affect overall system performance is quite limited. In this study, five full-scale BRBFs

were tested using identical Nippon Steel Unbonded Brace™ type BRBs. All BRBs had

220 kip nominal yield capacities with flat core plate cross sections. Core material was

JIS SN400B steel (46 ksi nominal, 44.7 ksi actual), with a core area of 4.77 in2.

Variations in shape of the gusset plates, the type of bolted connection (slip-critical or

bearing), and orientation of the BRB cross section were made in four of the five

specimens. The fifth specimen was loaded under a different displacement history than

that of the other four specimens.

The BRBFs were tested under a step-wise increasing slow cyclic loading protocol,

based on ATC-24 [4] and SAC Steel Project [24] guidelines. Test results for the

various specimens varied, but in general the BRBFs exhibited a full, balanced hysteretic

behavior with an average of +2.3% and -2.2% story drift ratios, an average dissipated

energy of 18700 k-in, an average equivalent viscous damping ratio of 0.33, and an

average cumulative plastic ductility of 360. The desired failure mode of BRBF systems

is tensile rupture of the brace core plate; however none of the specimens reached this

failure mode. The frames experienced severe yielding and buckling of the beams and

columns adjacent to the gusset plates, which eventually led to an out of plane rotation of

the SW beam flange and web. At larger compressive drift ratios, the out of plane

rotation of the SW beam lead to a nearly rigid body, out of plane rotation of the SW

gusset plate. This introduced an eccentricity into SW end of the BRB which placed

220large out of plane deformation demands on the BRB, and resulted in out of plane

plastic rotations of the BRB core plate. The out of plane rotations made it difficult for

the core plate to shorten back into the BRB casing, and instead began to shift the casing

to the NE end of the brace. The shifting of the casing resulted in loss of confinement

around the SW end of the core plate, which further facilitated the out of plane rotations,

ultimately leading to plastic hinging in the core plate at the termination of the stiffening

ribs. Plastic hinging continued without any increase in load until the BRB casing

touched the strong floor and testing was halted.

The following paragraphs summarize each specimen and their response.

The reference BRB specimen used bolted slip-critical BRB-to-gusset connections with

square gusset plates and extended rib stiffeners. The connection was made by splice

plates and ten 1 inch diameter A490 bolts as was detailed in Figure 3.4.2. The gusset

plate was welded to the beam and column using fillet welds. The reference BRB

underwent drift ratios with a maximum range of 4.22%. Hysteretic behavior contained

symmetrical and full hysteresis curves with 16873 kip-inches of energy dissipation and

an equivalent viscous damping ratio of 0.34. Maximum core strains of +0.021 and

-0.031 were measured in the BRB, with a cumulative plastic ductility of 333. Test

details and results were provided in Section 5.4.

Specimen BRB02 was identical to the reference BRB specimen, except that it used 15

degree tapered gusset plates as was detailed in Figure 3.6.1. Specimen BRB02

underwent drift ratios with a maximum range of 4.68%. Hysteretic behavior contained

symmetrical and full hysteresis curves with 21875 k-in of energy dissipation and an

equivalent viscous damping ratio of 0.33. Maximum core strains of +0.023 and -0.031

were measured in the BRB, with a cumulative plastic ductility of 374. Test details and

results were provided in Section 5.6.

221Specimen BRB03 was identical to specimen BRB02 except that it used a bearing

bolt BRB-to-gusset connection rather than a slip-critical connection. The bearing bolt

connection was controlled by the shear and bearing capacities of the bolts against the

maximum expected brace force, and therefore required only eight bolts per connection.

The geometry of the connection was detailed in Figure 3.7.1. The bolts were partially

tensioned to resist slip until the BRB began to yield. Specimen BRB03 underwent drift

ratios with a maximum range of 4.14%. Hysteretic behavior contained symmetrical and

full hysteresis curves with 17641 k-in of energy dissipation and an equivalent viscous

damping ratio of 0.32. Maximum core strains of +0.019 and -0.029 were measured in

the BRB, with a cumulative plastic ductility of 352. Test details and results were

provided in Section 5.6.

Specimen BRB04 was identical to specimen BRB03 except that the orientation of the

buckling restrained brace was rotated 90 degrees about its local axis, so that out of plane

rotation coincided with the strong axis of the core plate (Figure 3.8.1). The geometry of

the connection is identical to that of BRB03 as was detailed in Figure 3.7.1. The bolts

were again partially tensioned so that slip would not occur until initial yielding of the

core plate. BRB04 underwent drift ratios with a maximum range of 4.56 radians.

Hysteretic behavior contained symmetrical and full hysteresis curves with 18555 k-in of

energy dissipation and an equivalent viscous damping ratio of 0.35. Maximum core

strains of +0.024 and -0.029 were measured in the BRB, with a cumulative plastic

ductility of 363. Failure occurred according to the description provided in the initial

paragraph of this section, except for the following differences. The BRB initially began

to hinge in plane and torsionally rotate during late cycles. This only occurred briefly

until the same out of plane hinging occurred that was present in the other specimens.

The rate at which the plastic hinge developed and the input force leveled off was much

more slow and controlled than it was in the other specimens. This is shown in the

hysterisis curves for specimen BRB04 (Figure 5.7.3). Test details and results were

provided in Section 5.7.

222The design of specimen BRB01 was identical to that of the reference BRB

specimen, and was shown in Figure 3.4.2. Specimen BRB01 had a very unsymmetrical

loading history due to reaching the negative capacity of the actuator. This occurred at a

drift ratio of -0.90% and a force of -260 kip. During the remainder of the test, the frame

was loaded in the positive direction according to the loading protocol, but could only be

loaded in the negative direction until the actuator’s capacity was reached. Due to frame

damage, the amount of force required to return the frame back to the zero point of

displacement became larger and larger as the test progressed. Eventually the magnitude

of this force exceeded the capacity of the actuator, and some later cycles never entered

the negative drift region. The unsymmetrical loading history allowed for the frame to

reach significantly higher positive drifts, but the negative drifts maxed out at very small

magnitudes and got smaller as the testing progressed However, specimen BRB01

underwent comparable drift ratios with a maximum range of 4.20%. Hysteretic

behavior contained full but unsymmetrical hysteresis curves with 18508 k-in of energy

dissipation and an equivalent viscous damping ratio of 0.32. Maximum core strains of

+0.034 and -0.011 were measured in the BRB, with a cumulative plastic ductility of

377. Failure of BRB01 was identical to the failures of the reference BRB, BRB02 and

BRB03 specimens except that it also included the fracture of the SW beam inner flange

as the brace was undergoing plastic hinging. Test details and results were provided in

Section 5.8.

7.2 Failure Mode

The undesirable failure mode of BRB core plate plastic hinging was found to be an

effect of deformation demands and/or force concentrations resulting from the

deformation demands placed on the frame (Section 6.3.7). Total forces in the gusset

plates were shown to be quite small compared to their capacities. According to the

current AISC web yielding and buckling equations, these forces should not have lead to

the damages in the beam web. Section 6.3.7 showed that the web shear forces were

distributed along a much shorter length than the connected length of the gusset plate.

The results of testing show that the localized demands on the beam web at the free edge

223of the gusset plate could not be met by the beam. However, it should also be noted

that these demands were compounded by the connection of the south beam to the

channel assembly. This connection further restrained the beam so that rotational

demands had to be met by the short length between the free edge of the gusset plate and

the channel assembly connection. However, the same problems in the SW beam would

still most likely occur at higher drifts. This is evident since the same problems began to

develop in the NE gusset-to-column connections. The column flanges had already

buckled severely, and the web buckling was increasing quickly at later drifts. This

occurred even though the column flanges and webs were much less slender than those

of the beams. Because these problems are related to deformation demands, increasing

flexibility and deformation capacity in the gusset plate corners of the frames seems like

the best solution.

7.3 Effects of Mildly Tapered Gusset Plates (BRB02, BRB03, BRB04)

Initial buckling of the SW beam webs occurred at larger drifts in the specimens which

used tapered gusset plates. This is of interest because the buckling of the beam web

would signal the impending failure of each BRB. Post test inspections of the SW beam

webs revealed more concentrated yielding patterns in the square gusset plate specimens

than in the tapered gusset plate specimens (Figure 5.9.1). The additional free beam

length between the channel assembly connection and the edge of the tapered gusset

plates supplied the beams with less deformation restriction, thereby spreading the

yielding along greater lengths and ultimately postponing failure for a short while. Low

levels of web yielding in the NE column occurred in the tapered gusset plate specimens,

and web buckling did not take place at all. In the square gusset plate specimens web

yielding reached higher levels, and web buckling was present in the NE column. The

direct comparison of specimen BRB02 to the reference BRB specimen shows that the

delayed and less localized frame damage lead to a higher maximum drift range,

cumulative plastic ductility, and total energy dissipation in specimen BRB02

(Table 6.4.1). Tapering of the gusset plates is by no means a complete solution,

especially since premature failure of the BRB still occurred. However, results tend to

224support the idea of increasing flexibility around the gusset plate connection to allow

for better rotational deformation capacity of the framing elements and overall system

ductility.

7.4 Effects of Bearing Bolt Connections (BRB03, BRB04)

The idea behind using bearing bolt connections was to reduce the required amount of

labor used in making the connection, while maintaining the same level of performance.

The bearing connections behaved differently than expected, in that they had few

instantaneous dynamic slips. As noted earlier, the bolts were partially tensioned to slip

around the yield force of the BRB. Theoretically, once the slip capacity of the bolts was

exceeded the bolts should have continued to dynamically slip near the same load each

time. Specimen BRB03 only slipped in this manner once at the initial threshold force of

the bolts. For the remainder of the test slow slippage was only noticeable from review

of the potentiometer data, which showed that the magnitude of slow slip grew smaller

and smaller as the test progressed. In specimen BRB04, the bolts dynamically slipped a

total of four times, but unlike specimen BRB03 the slip did not reduce in magnitude.

The bolt slip in specimen BRB03 caused low levels of yielding in the NE gusset plate,

but no gusset plate yielding occurred in specimen BRB04. In terms of system

performance, specimen BRB03 did not perform as well as specimen BRB02. Specimen

BRB03 sustained a smaller drift range, cumulative plastic ductility, and much less total

energy dissipated than BRB02 (Table 6.4.1). These results tend to suggest that the

bearing connection lead to reduced performance of the BRBF. However, there was no

indication of additional damage caused by the bolt slip. As the bolts slipped, the force

displacement response showed a small reduction in force, but quickly rebounded.

Therefore, it would be premature to state that bearing bolts reduce performance.

7.5 Effects of Orientation of BRB Core Plate (BRB04)

The out of plane hinging that occurred in all of the BRBs, did so against the weak axis

of the core plate. Rotation of the BRB cross section caused the out of plane

deformation to act against the strong axis of the core plate. The question was not

225whether the BRB would resist the out of plane hinging more, it was how much the

increased rotational resistance would improve the performance of the brace. The

rotated BRB did not drastically change the magnitude of damage that occurred in the

frame, but it did change the locations of some of the damages. The rotated cross section

in specimen BRB04 resisted out of plane rotation more than in the other specimens.

Because of the increased out of plane resistance, out of plane deformation in the SW

beam caused the core plate to hinge in plane against its weak axis. However, the in

plane stiffness of the gusset plate connection did not allow more than small amounts of

this deformation. The BRB eventually formed a plastic hinge about its strong axis,

although the rate of formation was much slower and more controlled; thus the failure

mode was less sudden. Because of this specimen BRB04 had larger a maximum drift

range, cumulative plastic ductility, and total energy dissipated than specimen BRB03.

As was shown in Figure 5.7.3, the strength reduction in specimen BRB04 occurred very

slowly and did not plateau until after two to three inches of additional frame drift. In

the other BRBFs, the strength plateau occurred almost instantly after very little

additional frame drift.

7.6 Displacement History of BRB01

The unsymmetrical loading of specimen BRB01 discussed in Section 5.8, provided a

useful measure of the effects of different deformation histories. The maximum drift

range of specimen BRB01 was comparable to the other specimens, and it showed that

the buckling restrained braces should be able to undergo even larger deformations than

were seen in the other tests. Specimen BRB01 had a higher cumulative plastic ductility

in the BRB core plate than the other four specimens. Because the compressive forces

remained small relative to the other tests, the eccentricity introduced into the SW

connection by the out of plane rotation of the SW beam was less detrimental. This

shows the importance of maintaining integrity of the frame, so that the full inelastic

deformation capability of the BRB can be utilized. It also shows that the overall system

performance was hindered more by the frame than by any other element of the

specimen.

2267.7 Recommendations for BRBF Connections

Although further research is needed to gain a complete understanding of the

performance of BRB connections, this research has demonstrated some important

things. The extreme stiffness that can occur in BRBF connections can lead to serious

restrictions of the deformation capacity of the frame. The typical practice of matching

the gusset plate thickness to the core plate thickness may ease constructability, but its

performance effects definitely need consideration. Furthermore, while isolated

buckling restrained brace tests have shown BRBs can tolerate significant but controlled

end rotations, full scale system testing has shown that BRBs do not survive unstable,

out of plane gusset plate and frame deformation. If weaknesses exist in the gusset plate

and framing elements, eccentric loading of the stiff BRBs can increase the demands on

the already strained connection elements, more so than a flexible brace would. The

importance of maintaining a flexible yet stable connection is apparent. This was shown

with even the small reduction of the restraint that occurred with the use of the tapered

gusset plates. However, as shown in other BRBF testing, excessive flexibility which

causes gusset plate buckling must also be avoided.

7.8 Recommendations for Future BRBF Testing

The testing done thus far has been valuable in determining the weaknesses possible in

BRBF systems, and has lead to some ideas for partial improvement of system

performance. Further research is needed to determine solutions to the deterioration that

can develop in the framing elements. Additional research is also needed to further

understand the effects of connection elements and how they affect overall system

performance. These investigations can then lead to development of balance equations

for use in the proposed performance based design methodology discussed in

Section 3.5. The following considerations are of interest for further study.

1) From the discussions in this report it was shown that the critical location during

testing was in the SW beam web. Damage at this location lead directly to failure in

each of the five specimens. Although the primary cause of this was from

227deformation and force incompatibility between the gusset plate and the beam,

the boundary conditions of the test apparatus compounded the problem. The shear

transfer connection in the south beam to the channel assembly placed the demands

along a short length of the beam (approximately 5 feet of free length between the

gusset edge and shear transfer connection). For future testing, the shear transfer

connection should be relocated further away from the SW gusset plate to increase

the free length of the beam. This will allow better evaluation of the beam web and

connection performance.

2) From the estimates made in Section 6.3.5 it seems that the BRBs in each specimen

were not far away from tensile rupture of the core plate. Therefore, a small

stiffening of the beam web may be enough to keep the beam web stable until the

core plate were able to rupture. Web doubler plates could strengthen the beam

enough to allow core plate rupture, without adversely affecting the deformation

capacity much. The web thickness estimates in Section 6.3.7 also support this idea.

According to the calculations done, a ¼ inch doubler plate could significantly

reduce the damage in the SW beam. At the very least, this modification would be

useful in further studying the effect of the beam web thickness to system

performance.

3) Increasing flexibility and allowing controlled yielding of the gusset plate is

desirable. Using a thinner gusset plate could help to increase the deformation

capability of the beams and columns, and help to reduce the localized demands at

the gusset-to-beam/column intersections. However, previous BRBF tests have

shown problems with gusset plate buckling. Providing a gusset plate with too little

out of plane stiffness (buckling capacity) would lead to gusset plate buckling and/or

hinging of the BRB. It is necessary to find a balance between an overly stiff BRB

connection and an overly flexible BRB connection. A proper balance of these two

considerations, in combination with proper design of the remaining BRBF elements,

should lead to optimized performance of BRBFs. Because of the rib plates, the

228gusset plate would need to be made quite thin according to the Whitmore

yielding criteria discussed in Chapter 3. In fact, the Whitmore method suggests that

a 3/8” gusset would have to be used with 1/4” rib plates. However, these

calculations may be conservative, and yielding may be able to occur if slightly

thinner gusset plates were used. For example, specimen saw mild gusset plate

yielding even with the 3/4” gusset and rib plates. From this is seems possible that

slightly thinner gusset plates may in fact yield, and may be a method of dealing with

the force and deformation incompatibilities between the gusset plates and the webs.

4) With the increased performance that was seen using the moderate 15 degree tapered

gusset plate, it would be desirable do evaluate the effect of a tapered gusset plate

with a greater taper degree. Use of the larger taper with a slightly reduced gusset

plate thickness could allow some yielding and increase flexibility in the gusset plate

and frame connections.

5) The use of bearing connections (with initial tensioning to the yield force of the

brace) should be investigated more in future testing. Although the results of

specimen BRB03 seemed to indicate reduced performance with bearing bolted

connections, the indications may in fact be misunderstood. The dynamic fluctuation

in loading that occurred when the bolted connections slipped, could have simply

compounded the problems in the SW beam and gusset plate. When the SW corner

became unstable, the added effect of the bolt slippage or even slow movement could

have added to the problem. In a BRBF which does not experience such extreme

frame degradation, the effects of bolt slippage may be minimal or non existent.

Additionally, there was negligible increase in damage to the specimens which used

bearing bolts. The force displacement responses showed only insignificant effects

from the bearing bolts as well. The reduced labor cost implications of using bearing

bolt connections are too great to throw the idea away without further investigation.

2296) The relative movement of the casing and the BRB core (shifting) was believed

to occur due to the out of plane deformations of the SW gusset plate and BRB end.

However, initial shifting occurred with small out of plane deformations which are

possible even if the SW beam damage was not so severe. The shifting of the casing

leaves a longer unrestrained length and therefore less resistance against hinging.

The use of a shear key or pin at the center of the brace may be advantageous, and

help guard against development of a plastic hinge in the BRB.

230List of References

1. AISC (2001) “Manual of Steel Construction, Load and Resistance Factor

Design”, 3rd Edition, American Institute of Steel Construction, Chicago, IL. 2. AISC (2002) “Seismic Provisions for Structural Steel Buildings”, American

Institute of Steel Construction, Chicago IL. 3. Astaneh-Asl, A. (1998) “Seismic Behavior and Design of Gusset Plates”, Steel

Tips, Structural Steel Educational Council. 4. ATC 24 (1992) “Guidelines for Cyclic Seismic Testing of Components of Steel

Structures”, Applied Technology Council. 5. Black, C., Makris, N., Aiken, I. (2002) “Component Testing, Stability Analysis

and Characterization of Buckling-Restrained Unbonded Braces™”, PEER Report 2002/08, Pacific Earthquake Engineering Research Center, University of California, Berkley, CA.

6. Clark, P., Kasai, K., Kimura, I., and Ko, E. “Design Procedures for Buildings

Incorporating Hysteretic Damping Devices”, Retrieved March 8, 2004, from http://www.siecorp.com/braces/

7. Fahnestock, L.A., Sause, R., and Ricles, J.M. (2003) “Analytical and

Experimental Studies on Buckling Restrained Braced Composite Frames”, Proceedings of International Workshop on Steel and Concrete Composite Construction, Taipei, Taiwan, pages 177-188.

8. FEMA 350 (2000) “Recommended Seismic Design Criteria for New Steel

Moment-Frame Buildings”, Federal Emergency Management Agency, Washington, D.C.

9. FEMA 355C (2000) “State of the Art Report on Systems Performance of Steel

Moment Frames Subject to Earthquake Ground Shaking”, Federal Emergency Management Agency, Washington, D.C.

10. FEMA (2000) “NEHRP Recommended Provisions for Seismic Regulations for

New Buildings and Other Structures – Part I: Provisions”, Federal Emergency Management Agency, Washington, D.C.

11. Gunnarson, I.R. (2004) “Numerical Performance Evaluation of Braced Frame

Systems”, MS Thesis, Dept. of Civil and Environmental Engineering, University of Washington, WA.

23112. Johnson, S.M. (2005) “Improved Seismic Performance of Special

Concentrically Braced Frames”, MS Thesis, Dept. of Civil and Environmental Engineering, University of Washington, WA.

13. Ko, E. and Field, C. “The Unbonded Brace™: From research to Californian

Practice”, ARUP. Retrieved April 24, 2005, from http://www.arup.com/ 14. Lai, J.W. and Tsai, K.C. (2004) “Research and Application of Buckling

Restrained Braces in Taiwan”, Proceedings of 2004 ANCER Meeting: Networking of Young Earthquake Engineering Researchers and Professionals, Honolulu, Hawaii. Retrieved March 15, 2005, from http://mceer.buffalo.edu/outreach/intActivity/ANCER/

15. Merritt, S., Uang, C.M. and Benzoni, G. (2003) “Subassemblage Testing of

CoreBrace Buckling-Restrained Braces”, Report No. TR-2003/01, University of California, San Diego, CA.

16. Merritt, S., Uang, C.M. and Benzoni, G. (2003) “Subassemblage Testing of Star

Seismic Buckling-Restrained Braces”, Report No. TR-2003/04, University of California, San Diego, CA.

17. Merritt, S., Uang, C.M. and Benzoni, G. (2003) “Uniaxial Testing of Associated

Bracing Buckling-Restrained Braces”, Report No. TR-2003/05, University of California, San Diego, CA.

18. Roeder, C.W. (2000) “State of the Art Report – Connection Performance”,

FEMA 355D, Federal Emergency Management Agency, Washington, D.C. 19. Roeder, C.W. (2002) “Connection Performance for Seismic Design of Steel

Moment Frames”, ASCE, Journal of Structural Engineering, Vol. 128, No. 4, pages 517-25.

20. Roeder, C.W., Lehman, D.E., and Yoo, J.H. “Improved Seismic Design of Steel

Frame Connections”, International Journal of Steel Structures, to appear. 21. Roeder, C.W. and Lehman, D.E. “Performance-Based Design of Concentrically

Braced Frames”, Research Project Proposal to National Science Foundation, CMS-0301792.

22. Roeder, C.W., MacRae, G., Leland, A., and Rospo, A. (2003) “Extending the

Fatigue Life of Riveted Coped Stringer Connections”, Journal of Bridge Engineering, Vol. 10, No. 1, pages 69-76.

23223. Sabelli, R., Mahin, S., and Chang, C. “Seismic Demands on Steel Braced

Frame Buildings with Buckling-Restrained Braces”, Retrieved March 9, 2004, from http://nisee.berkeley.edu/library/

24. SAC (1997) “Protocol for Fabrication, Inspection, Testing, and Documentation

of Beam-Column Connection Tests and Other Experimental Specimens”, Report No. SAC/BD-97/02, SAC Joint Venture.

25. SEAOC-AISC (2003) “Recommended Provisions for Buckling-Restrained

Braced Frames”, Structural Engineers Association of California and American Institute of Steel Construction.

26. SEOC (2000) “SEOC Seismic Design Manual”, Vol. III (1997 UBC), Structural

Engineers Association of California, Sacramento, CA. 27. Thornton, W.A. (1984) "Bracing Connections for Heavy Construction”,

Engineering Journal, AISC, Vol. 21, No. 3, pages 139-148. 28. Tsai, K.C., Lin, M.L., Chen C.H., and Hsiao, P.C. (2004) “Performance

Evaluation Tests of a Full-Scale Buckling Restrained Braced Frame”, Proceedings of The Third International Conference on Earthquake Engineering, Nanjing University of Technology, China, Ch.4, Paper #26.

29. Uriz, P., “Summary of Full-Scale Braced Frame Test Using Buckling-Restrained

Braces, UCB2002-Test 1”, Retrieved October 28, 2003, from http://www.ce.berkeley.edu/~patxi/





32. Watanabe, A. (1989) “Properties of Brace Encased in Buckling-Restrained

Concrete and Steel Tube”, Proceedings of Ninth World conference on Earthquake Engineering, Tokyo, Japan, Vol. IV, pages 719-724, Paper 6-7-4.

33. Whitmore, R.E. (1952) "Experimental Investigation of Stresses in Gusset

Plates”, Bulletin No. 16, Engineering Experiment Station, University of Tennessee, Knoxville, Tennessee.

23334. Yoo, J.H. "Analytical Investigation on the Behavior of Braced Frames"

Department of Civil Engineering,University of Washington, Seattle, Washington, Expected June, 2006.

234APPENDIX A

Specimen Design and Detail Drawings

A.1 Reference Specimen and BRB Connection Design

All plate steel is A572 grade 50(Fyp=46 ksi and Fup=58 ksi). BRB steel is Fysc=46 ksi

and Fusc=58 ksi.

Definitions (Also see Appendix A.2):

Pmax = 352.19kips Pysc = Pmax /1.6 = 220.12 k Pslip = 286.2

Se = 2.0” Sc = 4.0” Sh = 7.0”(from geometry of brace and splice plates)

ϕ = 1.0625” (standard holes) tbr = tg = tw =0.75” "11)2(27 =+=bracew °=Θ 45b

Determine diameter and number of bolts Try 1” diameter A490:

nrφ = 33 kips/bolt

∴== 7.833

2.286bn use (10)-1”dia. A490 bolts

force per bolt = kips2.3510

2.352=

Check Bearing:

adequatekkFdtr uscbrn ∴≥=== 2.353.78)58)(75.0)(1)(4.2)(75.0(4.2φφ

Check Tearthrough:

usccn tFLr 2.1φφ = and ϕ−= cc SL , so adequatekkrn ∴≥= 2.35115φ

Check Tearout:

usccn tFLr 2.1φφ = and ϕ5.0−= cc SL , so adequatekkrn ∴≥= 2.355.57φ

Check yield on gross:

adequatekkRn ∴≥=−−= 2.352505)75.0)0625.1)(2(11)(2)(75.0)(50(9.0φ

Check fracture on net:

adequatekkRn ∴≥=−−= 2.352530)75.0)0625.1)(2(11)(2)(75.0)(65(75.0φ

235A.1.1 Splice Plate Calculations

Since Se = 2” try ws = 4” and try ts = 0.5”, check yield on gross:

)8)(5.0)(0625.14)(50(9.0 −=nRφ adequatekk ∴≥= 2.352529


)8)(5.0)(0625.14)(65(75.0 −=nRφ adequatekk ∴≥= 2.352573

Check block shear:

3 HOLE 2 HOLE

cegv SSa 2+= sgt Wa 5.0= cgv Sa 2= sgt ea 5.0=

ϕ5.2−= gvnv aa ϕ5.0−= gtnt aa ϕ5.1−= gvnv aa ϕ5.0−= gtnt aa

Figure A.2.1 – Splice Plates

Total

[ ] 236)2(4)2(4 inSSStA ccesgv =++= 216)5.0(8 intWA ssgt ==

[ ] 25.27)5.1(4)5.2(4 intAA sgvnv =−−= ϕϕ 29.13)5.0(8 intAA sgtnt =−= ϕ

Therefore, nRφ is the lesser of:

[ ] kipsAFAF ntupgvyp 14876.0 =+φ (Shear Yield/Tensile Fracture)

[ ] kipsAFAF gtypnvup 14046.0 =+φ (Shear Fracture/Tensile Yield)

[ ] kipsAFAF ntupnvup 14806.0 =+φ (Shear Fracture/Tensile Fracture)

adequatekipskipsRn ∴≥=∴ 2.3521404φ

236A.1.2 Gusset and Rib Plate Calculations

Uniform Force Method:

Based on bolt hole geometry try "9.20=bw

"1.173.121.169.20 =+−=∴ cw

Yielding by Whitmore’s Method:

From the geometry of the connection:

"48.31 =l "91.82 =l "79.03 =l

"1175.0)125.5(2 =+=∴ wwb and "875.8)0625.1(211 =−=ewweffectivb

"24.16)4)(2)(30tan(27 =°+=∴ wb and "11.14)0625.1(224.16 =−=weffectiveb

[ ] adequatekkRn ∴≥=+=∴ 2.352776)50)(75.0)(875.8()50)(75.0)(11.14(9.0φ

Buckling Method 1:

29000

)50(12)75.0()9.6)(5.0(

πλ =t = 0.211 < 1.5

kipsPcr 2.751)50)(75.0)(41.20(658.02)211(. ==

adequatekkRn ∴≥== 2.3526.638)2.751(85.0φ

Buckling Method 2:

"4.43

8.09.85.3;9.8min =

++

=tl

287.19)11)(75.0()75.024.16)(75.0( inAt =+−=

5.113.029000

)50(12)75.0()4.4)(5.0(

≤==π

λt

kipsPcr 8.985)50)(87.19(658.02)13.0( ==

adequatekkRn ∴≥== 2.352838)8.985(85.0φ

Buckling Method 3: 218.12)24.16)(75.0( inAt == and again, "4.4=tl

237

5.113.029000

)50(12)75.0()4.4)(5.0(

≤==π

λt

kipsPcr 3.604)50)(18.12(658.02)13.0( ==

adequatekkRn ∴≥== 2.3527.513)3.604(85.0φ

Method 4 (Modified Thornton Method):

29000

)50(12)75.0()9.6)(5.0(

πλ =t = 0.211 < 1.5

"52.164 =mtb , so kipsPcr 9.607)50)(75.0)(52.16(658.02)211(. ==

adequatekkRn ∴≥== 2.3527.516)9.607(85.0φ

Bolt bearing, tearout, and tearthrough are adequate by inspection since the brace has an

equivalent thickness, and smaller yield and ultimate strengths compared to gusset/rib

and splice plates. Bolt shear is adequate by inspection.

A.1.3 Gusset-to-Beam/Column Weld Calculations

Weld Method 1:

"48.23)05.855.8()15.645.10( 22 =+++=r

kVuc 3.1282.35248.23

55.8== and kHuc 3.922.352

48.2315.6

==

kVub 8.1202.35248.23

05.8== and kHub 8.1562.352

48.2345.10

==

kPuc 158)3.92()3.128( 22 =+=∴ and °=

=Θ − 7.35

3.1283.92tan 1

c

kPub 9.197)8.156()8.120( 22 =+=∴ and °=

=Θ − 6.37

8.1568.120tan 1

bm

Gusset-to-Beam:

61.3=bC 11 =C

98.2)5.29.20)(1)(61.3(

9.197=

−≥∴ bD , so ""26.0

1698.24.1 16

5usesb ∴=

=

238Check Minimum Weld:

Max joined thickness = 0.75”, 41

min =∴ bs

Therefore use 5/16” welds.

Check Base Metal Strengths (Beam flange controls):

weldsbubfbn wFtR )#5.2(6.0 −= φφ

adequatekRn ∴=−= 2.608)2)(5.29.20)(65)(565.0)(6.0)(75.0(φ

Gusset-to-Column:

61.3=cC 11 =C

0.3)5.21.17)(1)(61.3(

158=

−≥∴ cD , so ""262.0

160.34.1 16

5usesc ∴=

=

Minimum welds and base metal adequate by inspection.

Weld Method 2:

ububucuc HVHV ,,, as computed above in method 1

kPub 5.2778.1208.156 =+= , kPuc 5.2203.1283.92 =+= and °=Θ 0,bc

"474.0)2(707.0)5.29.20)(70)(6.0)(75.0(

5.2774.1 21usesb ∴=

−≥

"475.0)2(707.0)5.21.17)(70)(6.0)(75.0(

5.2204.1 21usesc ∴=

−≥

Minimum welds and base metal strengths are identical to method 1, therefore adequate.


Weld Method 3:

"344.1)45cos()15.605.8( =°−=xX , "39.7)45cos()45.10( =°=bX , and

"39.7344.1)45cos()55.8( =+°=cX

39.7

)344.139.7( −= b

cFF and kFF cb 2.352=+

Solving the two above equations simultaneously:

kFb 7.193= and kFc 5.158=

239 kFcx 1.112)45cos()5.158( =°=∴ and kFcy 1.112)45sin()5.158( =°=

kFbx 0.137)45cos()7.193( =°=∴ and kFby 0.137)45sin()7.193( =°=

kPuc 2.2241.1121.112 =+=∴ and °=Θ 0c

kPub 274137137 =+=∴ and °=Θ 0c

"468.0)2(707.0)5.29.20)(70)(6.0)(75.0(

0.2744.1 21usesb ∴=

−≥

"483.0)2(707.0)5.21.17)(70)(6.0)(75.0(

2.2244.1 21usesc ∴=

−≥

Minimum welds and base metal strengths are identical to methods 1 and 2, and

therefore adequate.


A.1.4 Rib-to-Gusset Weld Calculations

E71T-8 electrode ksiFexx 70=

"252.0)4)(707.0)(112)(70)(6.0)(75.0(

2.3524.1 =−

≥ws

Check minimum weld:

Max joined thickness = 0.75”, 41

min =∴ ws


A.2 Beam-to-Column Connection Design

W12x72 Column W16x45 Beam

dc = 12.3” db = 16.1”

bfc = 12.0” bfb = 7.04”

tfc = 0.670” tfb = 0.565”

twc = 0.430” twb = 0.345”

kc = 1.270” kb = 0.967”

Zx = 82.3 in3

240A.2.1 WFWW Calculations (Gusset Plate Corners):

)9.20(5.0)77.120(=wfwwM =1262 k-in

and by summing moments and horizontal forces: Hft = 78.4 k and Hfb = 78.4 k

Beam web shear capacity:

"97.12)0.1(2)565.0(21.16 =−−=webl

inadequatekkRn ∴<== 77.12067.100)50)(97.12)(345.0)(6.0(75.0φ

However, if the erection tab (See Figure 3.4.3) is fillet welded to the beam, the

additional capacity will be sufficient.

Beam flange tensile capacity:

adequatekkRn ∴>== 4.78179)50)(04.7)(565.0(9.0φ

Beam and Column Web Checks:

From Methods 1,2, and 3 the maximum shear forces are:

kFby 0.137= , and kFcx 1.112=

Beam Web Yielding:

adequatekkRn ∴≥=+= 0.137402)345.0)(50](9.20)967.0(5.2[9.0φ

Beam Web Crippling:

345.0)565.0)(50)(29000(

565.0345.02.0

1.16)5.19.20(41)345.0)(40.0)(85.0(

5.12

−

−+=nRφ

adequatekkRn ∴≥=∴ 0.1371.235φ

Column Web Yielding:

adequatekkRn ∴≥=+= 1.1129.435)430.0)(50](1.17)27.1(5.2[9.0φ

Column Web Crippling:

430.0)670.0)(50)(29000(

670.0430.02.0

3.12)5.11.17(41)430.0)(40.0)(85.0(

5.12

−

−+=nRφ

adequatekkRn ∴≥=∴ 1.1123.321φ

241

A.2.2 Shear Tab Calculations (Opposite Gusset Plate Corners)

)3.82)(50(=pbM = 4115 k-in 7.92

)4155(5.1=pbV = 66.6 kips

From Table 10-9 with: (4) – ¾” dia. A490X bolts w/ std holes

13”x4.5”x0.375” shear tab

5/16” tab-to-column flange welds (both sides)

adequatekkRn ∴≥= 6.668.69φ

Check bearing on beam web:

kipsdtFR ubn 3.30)65)(345.0)(75.0)(4.2)(75.0(4.2 === φφ

from AISC Table 7-12, each bolt has a bearing capacity, OKkipsrn ∴= 9.24φ

Check bolt tearout on beam web:

OKkktFLR ubcn ∴≥=−== 9.245.84)65)(345.0)(*5.05.2)(4.2)(75.0(4.2 1613φφ

Check plate bending:

)5.2)(6.66(=plateM = 166.5 k-in

6

)50()5.13)(375.0)(9.0( 2

=nRφ = 475 k-in > 166.5 adequate∴

A.3 BRB03 Connection Calculations

Determine diameter and number of bolts Try 1” diameter A490 in shear:

nrφ = 88.4 kips/bolt

∴== 98.34.882.352

bn can use (4) bolts, but very close

force per bolt = kips05.884

2.352=

Brace controls bolt hole limit states

242Check Bearing:

inadequatekkFdtr uscbrn ∴<=== 05.883.78)58)(75.0)(1)(4.2)(75.0(4.2φφ

Try 5 bolts force per bolt = adequatekkips ∴<= 3.7844.705

2.352

Check Tearthrough:

usccn tFLr 2.1φφ = and ϕ−= cc SL , so adequatekkrn ∴≥= 44.70115φ

Check Tearout:

usccn tFLr 2.1φφ = and ϕ5.0−= cc SL , so inadequatekkrn ∴<= 44.705.57φ

Try 7 bolts force per bolt = adequatekkips ∴<= 5.573.507

2.352

Check yield on gross:

adequatekkRn ∴≥=−−= 2.352505)75.0)0625.1)(2(11)(2)(75.0)(50(9.0φ


adequatekkRn ∴≥=−−= 2.352530)75.0)0625.1)(2(11)(2)(75.0)(65(75.0φ

So we need at least (7) - 1” diameter A490 bolts for the bearing connection

A.4 Specimen Detail Drawings

The drawings on the following pages contain the detail drawings for each of the five

BRBF specimens. The specimens each used identical frames, BRBs, splice plates, and

rib plates.

243

Figure A.4.1 – Specimen Layout

244

Figure A.4.2 – Reference BRB and BRB01 Connection Detail

245

Figure A.4.3 – Reference BRB and BRB01 Gusset Plates

246

Figure A.4.4 – BRB02 Connection Detail

247

Figure A.4.5 – BRB02, BRB03, and BRB04 Gusset Plates

248


249


250

Figu

re A

.4.8

– B

RB

Det

ail (

Cou

rtesy

Nip

pon

Stee

l)

SEE

DET

AIL

H F

OR

CO

NN

ECTI

ON

DET

AIL

S

BR

B D

ETA

ILS

G

251

Figure A.4.9 – BRB Connection Details

252

Figure A.4.10 – Splice Plates and Rib Plate Details

253

Figure A.4.11 – Specimen Frame Detail

254

Figure A.4.12 – Shear Tab Detail

Figure A.4.13 – Welded-Flange-Welded-Web and Erection Tab Detail

255 APPENDIX B

Analysis Details

B.1 Material Tests

Material tests were done for all BRBF components as shown in Table B.1.1. Testing

was done by Northwest Laboratories of Seattle, Inc.

Table B.1.1 – Material Test Results

B.2 Additional Analysis Details

This section provides additional details, plots, and tables that were omitted from the

main document in the Chapter 6 analysis. The initial step of data analysis was to reduce

the data recorded during the tests. Data was recorded continuously during the tests,

including all pauses in between cycles and at certain peaks. An example of the frame

raw drift data from the reference BRB specimen is shown in Figure B.2.1.

256

Figure B.2.1 – Plot of Unreduced Drift Data

The plateaus that arose from the testing pauses were filtered out based on percent

difference calculations for both the actuator force and frame drift data. The peak

pauses, and the majority of the pauses between cycles, were filtered out based on the

following criteria. The percent difference was checked against both the preceding and

following data points, that is:

diffi

ii %1 <− −

δδδ (B-1) and diff

i

ii %1 <− +

δδδ (B-2)

If both of the above statements were true, then the drift reading was tentatively marked

for deletion with a 0. Identical checks were then made for the actuator force readings

from the actuator load cell.

diffFFFi

ii %1 <− − (B-3) and diff

FFFi

ii %1 <− + (B-4)

If both of the above statements were true, then the force reading was tentatively marked

for deletion with a 0. Finally, to determine if all data points for a certain time step were

to be deleted, the tentative deletions were reviewed. If iδ , 1+iδ , iF , and 1+iF were all

257marked as 0, then data for the entire time step i , was deleted. Both the current time

step and the following time step were used to determine deletion in order to avoid loss

of minimum and maximum peak values. The data had a tendency to slowly level off at

these peaks, so the percent difference method would have ended up eliminating the

peaks if this measure was not taken. The minimum allowable percent difference values

used in data reduction ended up being 1.5%. This value was chosen based on the trial

and error of several different percent difference values. Values from 0.5% to 5% were

used, and then resulting data was reviewed to determine adequacy. Smaller values did

not eliminate all of the plateaus in the data. Larger values eliminated data points that

were at the positive and negative peaks and near zero. The 1.5% value cased no

elimination of peak data while filtering out a large amount of the plateaus.

After this initial data elimination, some plateaus near the zero points still existed

because large percentage variation is possible even with small numerical changes at

these zero points. Therefore, the drifts were used simply to ensure that points where

forces leveled but drifts increased, would not be deleted. These drifts were filtered as

follows.

1.0<iδ (B-5) and diffi

ii %1 <− −

δδδ (B-6)

Again, if both of the above statements were true, then the drift reading was tentatively

marked for deletion with a 0. The drift was initially checked against the 0.1 inch value

to remain focused only on non-peak values. The percent difference was then checked

using a smaller allowable percent difference of 0.1%. For the filtering of the actuator

forces, a lager percent difference was used in the equation below.

diffFFFi

ii %1 <− − (B-7)

A 5% difference was determined appropriate for this step of data reduction because it

eliminated the stubborn low value plateau areas. Again, if iδ , 1+iδ , iF , and 1+iF were all

marked as 0, then data for the entire time step, i , was deleted.

258Once the pauses were eliminated from the data, any outliers that existed were

removed. Outliers were uncommon, but occurred occasionally as seen in Figure B.2.1.

These outliers were simply removed on a point by point basis, if there were extreme and

unreasonable jumps in the data collection devices. During testing of all BRB

specimens, the pumps used to control the actuator were exchanged later in the test.

When this was done, residual hydraulic pressure variations caused changes in the

applied load, while the displacement was nearly constant. The data during this time was

simply removed. Following these procedures the data files were reduced to 25 to 35

percent of the original size. For the reference BRB, the raw drift data of Figure B.2.1

was reduced as shown in Figure B.2.2 below.

Figure B.2.2 – Plot of Reduced Drift Data

Reduced data was then analyzed as discussed in Chapter 6 of this document. Beam and

column moments and shears were calculated as discussed in Section 6.2.1. These are

plotted for each specimen in the following figures. Figures B.2.3 through B.2.7 show

the north and south beam moments for each specimen. Figures B.2.8 through B.2.12

show the east column moments for each specimen. Figures B.2.13 through B.2.17 show

the west column moments for each specimen. Figures B.2.18 through B.2.22 show the

column shears for all specimens. Peak results are given in Tables B.2.1 through B.2.8.

These figures and tables are given here for comparison purposes, but observations and

patterns are summarized in Section 6.3.2.

259

Figure B.2.3 – Reference BRB Beam Moments

Figure B.2.4 – BRB02 Beam Moments

260



261

Figure B.2.7 - BRB01 Beam Moments

Figure B.2.8 – Reference BRB East Column Moments

262

Figure B.2.9 – BRB02 East Column Moments


263



264

Figure B.2.13 – Reference BRB West Column Moments

Figure B.2.14 – BRB02 West Column Moments

265



266


Figure B.2.18 – Reference BRB Column Shears

267

Figure B.2.19 – BRB02 Column Shears


268



269Table B.2.1 – North Beam Moments Peak Results

Table B.2.2 – South Beam Moments Peak Results

270Table B.2.3 – NE Edge Column Moments Peak Results

Table B.2.4 – SW Edge Column Moments Peak Results

271Table B.2.5 – NW Beam-to-Column Connection Moments Peak Results

Table B.2.6 – SE Beam-to-Column Connection Moments Peak Results

272Table B.2.7 –East Column Shears Peak Results

Table B.2.8 – West Column Shears Peak Results

273B.3 Force Displacement Discontinuities Due to Casing Shift

The following supports the statements made in Section 5.2.1, on the effect of casing

shift in the force displacement response. Figures B.3.1 through B.3.3 show that the

drops in force coincide with leveling of the rate of elongation of the brace, as well as

drops in the plot of casing shift. Positive shifts correspond to movement towards the

NE end of the brace. The drops in Figure B.3.1c signify that the casing suddenly moves

back towards the SW end. This phenomena was evident in the hysteretic behavior of all

five specimens.

Figure B.3.1 – Force Displacement Response with Dips

Figure B.3.2 - Brace Elongation at Selected Locations

274

Cas

ing

Shift

(in)

Figure B.3.3 - Plot of Casing Shift

B.4 Beam-to-Column Relative Rotations

The shear tab connection moment rotation responses were discussed is Section 6.3.8.

Additional details are provided in this section. Tables B.4.1 and B.4.2 show the peak

relative rotations for both the SE and NW shear tab connections at increasing drift

ratios. Figures B.4.1 through B.4.10 plot the moment rotation response of the shear tab

connections for each specimen.

275Table B.4.1 – SE Beam-to-Column Relative Rotation Comparisons

Table B.4.2 – NW Beam-to-Column Relative Rotation Comparisons

276

Figure B.4.1 – Reference BRB NW Moment-Rotation Curves

Figure B.4.2 – Reference BRB SE Moment-Rotation Curves

277

Figure B.4.3 – BRB02 NW Moment-Rotation Curves

Figure B.4.4 – BRB02 SE Moment-Rotation Curves

278



279



280



281

Figu

re C

.1.1

– T

est S

etup

Pla

n

APPENDIX C

Test Apparatus Detail Drawings

282

Figu

re C

.1.2

– T

est S

etup

Ele

vatio

n

283

Figure C.1.3 – Channel Assembly Shear Connection Detail

Figure C.1.4 – Channel Assembly Shear Connection Section

284

Figu

re C

.1.5

– C

hann

el A

ssem

bly

Rod

and

Bol

t Lay

out

285

Figu

re C

.1.6

– K

icke

r Pla

te D

etai

ls

286

Figure C.1.7 – Load Beam Details

287

Figure C.1.8 – Swivel Head and Swivel Washer Details

288

Figu

re C

.1.9

– A

ctua

tor D

etai

ls

289

Figure C.1.10 – Reaction Block Details

290

Figure C.1.11 – Column Cap Plate Detail

Figure C.1.12 – Channel Assembly Rod Anchor Details

291

Figure C.1.13 – Actuator Adapter Plate Detail

292

APPENDIX D

Instrumentation Details

D.1 Instrumentation Details1

Methods of instrumentation were described in Section 4.4 of this document. This

section provides additional details of instrumentation including descriptions of what the

instruments measured and how they measured it, detailed locations of the instruments,

and notes on inconsistencies or loss of instruments during testing. Any changes made

to instrumentation configurations are also provided. Figures 4.4.1 through 4.4.5 should

be used for potentiometer (hereby referred to as “pots” or “devices”) numbering and

relative dimensions. As needed, figures and tables are provided to indicate the location

of each instrument for each specimen. The pot numbers in the figures are for the

reference BRB specimen. Changes in pot numbering for other tests are as noted in

Table 4.4.2.

Pots used to measure the NW and SE shear connection rotations were spaced as shown

in Figure D.1.1 in all specimens. These devices were attached to the beam flange using

hot glue. An example of these devices is illustrated in Figure D.1.2.

Figure D.1.1 – Beam/Column Relative Rotation Devices

1 This section was written in collaboration with Shawn M. Johnson

293

Figure D.1.2 – Beam/Column Relative Rotation Devices

Devices connected to channels 14, 21, 35, and 49, were used to measure out-of-plane

movement of the frame corners. All devices, with the exception of device 49, were

located at the beam and column centerline intersection points. Device 49 was located

along the column centerline out from the base the dimension shown in Figure D.1.4.

The exact dimension is given in the instrumentation location tables for each specimen

test later in this section. The device was moved to allow placement of a W-section that

was used to prevent the SW corner from sliding down. In order to accommodate the

movement of the frame at the north end devices 14 and 35 rested against a shelf with a

sheet of stainless steel. The surface was lubricated with silicon grease to reduce friction

and allow frame movement without disturbing the device. An example of these types of

devices is shown in Figure D.1.3.

Figure D.1.3 - Frame Corner Out-of-Plane Device

Devices

294

Device 30 was used to measure any slip of the channel assembly relative to the wall.

Device 29 and 48 were used to measure any uplift of the columns relative to the channel

assembly. Devices 42 and 47 were used to measure any uplift of the channel assembly

relative to the strong wall. Devices 43 and 50 were used to measure slip of the column

relative to the channel assembly. Device 46 was used to measure the lateral slip of the

frame relative to the column assembly. The in plane locations of these devices are

shown in Figure D.1.4, and the out of plane locations of these devices are shown in

Figure D.1.5. For exact locations of the devices with variable distances are given in the

instrumentation location tables for each test later in this section. An example of the

column uplift devices is shown in Figure D.1.6.

Figure D.1.4 – Channel Assembly and Column Device Locations

Figure D.1.5 – Out of Plane Locations

295

Figure D.1.6 - Column Uplift Measurement Device

Device 36 was used to measure frame translation and was located at the east column

face of the east column at the beam center line for all specimens as shown in Figure

4.4.4. This device rested against a piece of polished lubricated steel to allow for

movement of the frame without disturbing the device. Figure D.1.7 shows how this

device was used.

Figure D.1.7 - Frame Translation Device 36

Device 22 was used to measure the slip of the load beam relative to the specimen. The

application of this device is shown in Figure D.1.8. The device was centered vertically

on the north beam flange for all tests.

296

Figure D.1.8 - Load Beam Slip Device

Devices 51 and 52 were used to measure movement of the reaction block relative to the

strong floor. Device 34 measure the movement of the actuator relative to the reaction

block. The locations of these devices are shown in Figure 4.4.1. Device 34 was located

at the top of the actuator parallel to the centerline of the actuator.

In order to measure out-of-plane displacement of the BRB, string pots 53 and 54 were

added for all specimens but BRB01. The two instruments were attached perpendicular

to each other at the midspan of the brace. String pot 54 was oriented parallel to the

frame translation and string pot 53 was oriented perpendicular to the strong floor. This

was done in order to triangulate the measured displacement of the two devices. This

was needed in order to calculate the true out-of-plane motion due to the fact that frame

translation would affect the out-of-plane measurement recorded by string pot 53. The

two devices were attached using "music" wire by tap screwing into the bottom of the

BRB casing at the midspan of the brace. Figure D.1.9 shows the string pots in a

buckling brace specimen. These string pots were located and attached identically for

BRB specimens.

297

Figure D.1.9 - Brace Out-of-Plane Measurement Devices

String Pot 40 was used to measure brace elongation, and string pot 41 was used to

measure the change in length along the frame diagonal. These devices were attached to

both ends of the brace using music wire as shown in Figure D.1.10.

(a) Brace Length – String Pot 40 (b) Frame Diagonal – String Pot 41

Figure D.1.10 – Brace and Frame Diagonal Elongation Measurement Devices

Start

End

End

298

Devices 2, 11, 14, 15, 19, 20 were used to measure beam and column rotations at the

gusset plate edge, as shown in Figures 4.4.4 and 4.4.5. These figures also show the

locations of the devices along the beam and columns. The out of plane locations are

dimensioned in Figure D.1.11, and the exact locations for each test are given in the

instrumentation location tables located later in this section. An example of how beam

and column rotations were measured is shown in Figure D.1.12.

Figure D.1.11 - Beam and Column Rotation Out of Plane Locations

Figure D.1.12 - Column Rotation Device Example

299

The rotation of the brace relative to the gusset plate was measure using the devices

shown in Figure D.1.13. Also shown in this figure are the devices used to measure

brace torsion. The application of the devices is shown in Figure D.1.14. Devices 10 and

24 on the top rib of the brace were used to measure out-of-plane rotations relative to the

gusset plate, and were oriented parallel to the centerline of the brace. Devices 0, 24, 1,

and 9 on the side ribs of the brace were used to measure in plane rotations relative to the

gusset plate, and were oriented parallel to the centerline of the brace. The out of plane

locations of these devices are also shown in Figure D.1.13, and exact dimensions are

given in the instrumentation tables located later in this section. Dimensions are taken to

the center of the potentiometers.

Figure D.1.13 - Brace Rotation Devices

300

Figure D.1.14 – Example of Brace Rotation and Torsion Devices

Out-of-plane rotations of the gusset plate were measured using the devices shown in

Figures 4.4.4 and 4.4.5. The numbering of these devices changed according to Table

4.4.2 for each test. These devices rested directly against the underside of each gusset

plate. The devices on the SW end were secured to the strong floor, whereas the devices

on the NE gusset were supported by a platform which moved with the frame. The

application of these devices is shown in Figure D.1.15. The exact locations of these

devices are given in the instrumentation location tables later in this section.

(a) NE Gusset Shelf Mounted (b) SW Gusset Floor Mounted

Figure D.1.15 - Gusset Plate Out-of-Plane Devices

12

1

38

9

301

The following paragraphs give the exact locations of the pre-described devices,

according to the dimensions in Figures D.1.1 through D.1.15. Additional notes on

instrumentation are also given for each specimen test.

Exact locations for the reference BRB devices were as shown in Table D.1.1. Pots not

dimensioned explicitly have the locations as previously described.

Table D.1.1 – Reference BRB Instrumentation Locations

For use with inspection of data, the following is a description of any jumps or

inconsistencies that occurred in the instrumentation.

• Pot 15 was not functioning at the start of the test and was removed prior to

testing.

• Pot 32 was removed after returning to zero from the peak of cycle 35, and may

have been fully depressed prior to removal.

• Pots 9, 38, and 1 were removed after the casing shifted completely to the NE

302

end during the compression excursion of cycle 35. These pots were fully

depressed at this point.

• Pots 0, 10, and 24 were fully extended with about a 1 inch gap at the tension

peak of cycle 36.

• Pots 4, 40, 41, 53, and 54 were removed during the compression excursion of

cycle 36 to avoid damaging them.

Exact locations for the BRB02 devices were as shown in Table D.1.2. Pots not

dimensioned explicitly have the locations as previously described. Refer to Table 4.4.2

for variances in pot locations. All dimensions from the gusset-to-beam/column

intersections are applicable to the tapered gusset plates as well.

Table D.1.2 – BRB02 Instrumentation Locations

For use with inspection of data, the following is a description of any jumps or other

inaccuracies that may have occurred in the instrumentation during testing.

303

• Pots 12 and 32 slipped off of their resting plates, and were removed during

cycles 29 and 30.

• Pot 7 was found rotated during cycles 29 and 30. The pot was fixed, but data

prior to these cycles is inaccurate.

• Pots 1, 9, and 38 were fully depressed by the shifted BRB casing during cycles

37 and 38, and were thus removed.

• Pots 0, 10, and 24 were removed after being fully extended at the peak tensile

drift of cycle 39.

• Pots 40, 41, 53, 54, 5, 14, and 15 were removed during the compression

excursion of cycle 39 to avoid damaging them.






304

For use with the inspection of data, the following is a description of any jumps or

inconsistencies that may have occurred in the instrumentation during testing.

• Pot 12 was removed after bolt slippage knocked off the plate that the pot rested

against. This occurred during cycle 28.

• The piano wire connected to Pot 40 was bumped during cycle 24. The resulting

jump in the data was removed.

• Pot 21 was fully depressed during cycles 27 and 28, and was removed.

• Pots 0, 10, 24, 40, 41, 53, 54, 5, 32, and 15 were removed during the

compression excursion of cycle 39 to avoid damaging them.






305


inconsistencies that may have occurred in the instrumentation during testing.

• The data recording system stopped between the valley of cycle 33, and shortly

into the tension excursion of cycle 34, as discussed in Section 5.6.7.

• Pot 2 was accidentally disconnected between cycle 22 and the start of cycle 23.

• Pots 13 and 3 became unattached after bolt slip occurred during the compression

excursion of cycle 34, and were left unattached thereafter.

• Pots 15 and 12 were removed during the compression excursion of cycle 35.

• Pot 0 was fully extended at the tensile peak of cycle 36, with approximately a

1/8 inch gap to its plate.

• Pot 31 began to fall off after bolt slip during the tension excursion of cycle 37.

It was reattached and was reading 0.6 before readjustment.

• Pots 0, 10, and 24 were fully extended at the tension peak of cycle 37, with

approximately a 0.5 inch gap to their plates.

• Pot 32 was removed during the compression excursion of cycle 37 because it

was nearly depressed the entire way.

• Pots 1, 9, 38, and 22 were removed during the compression excursion of cycle

37 to avoid damaging them.

• Pots 0, 10, 24, 40, 41, 53, 54, and 5 were also removed during the compression

excursion of cycle 37 to avoid damaging them.





306



inaccuracies that may have occurred in the instrumentation during testing.

• Pot 38 stuck during cycle 28, and was repaired afterwards. Corresponding data

during this period was ignored.

• Pot 2 was pushed outward by the buckling of the SW beam flange. This

occurred around cycles 40 and 41.

• Pots 0, 10, and 24 were fully extended during cycle 44. Data was corrected

accordingly.

• Pot 22 fell off of the north beam sometime during the test.

• Readings from pots 1, 9, 38, 0, 10, 24, 40, 41, 53, and 54 were inaccurate during

the compression excursion of cycle 44.

• Strain Gauge 29 was not reading during the entire test.

Adam Christopulos Thesis (BRB Reference-BRB04)

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