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BEHAVIOR, DESIGN, AND ANALYSIS OF UNBONDED POST-TENSIONED

PRECAST CONCRETE COUPLING BEAMS

VOLUME I

A Dissertation

Submitted to the Graduate School

of the University of Notre Dame

in Partial Fulfillment of the Requirements

for the Degree of

Doctor of Philosophy

by

Brad D. Weldon

Yahya C. Kurama, Director

Graduate Program in Civil Engineering and Geological Sciences

Notre Dame, Indiana

April 2010

© Copyright 2010

Brad D. Weldon

BEHAVIOR, DESIGN, AND ANALYSIS OF UNBONDED POST-TENSIONED

PRECAST CONCRETE COUPLING BEAMS

Abstract

by

Brad D. Weldon

This dissertation describes an experimental, analytical, and design investigation

on the nonlinear behavior of precast concrete coupling beams, where coupling of

reinforced concrete shear walls is achieved by post-tensioning the beams and the walls

together at the floor and roof levels. The new coupling system offers important

advantages over conventional systems with monolithic cast-in-place beams, such as

simpler detailing, reduced damage to the structure, and reduced residual lateral

displacements. Steel top and seat angles are used at the beam-to-wall joints to yield and

provide energy dissipation.

The results from eight half-scale experiments of unbonded post-tensioned precast

coupling beams under reversed-cyclic lateral loading are presented. Each test specimen

includes a coupling beam and the adjacent wall pier regions at a floor level. The test

parameters include the post-tensioning tendon area and initial stress, initial beam concrete

axial stress, angle strength, and beam depth. The results demonstrate excellent stiffness,

strength, and ductility of the specimens under cyclic loading, with considerable energy

dissipation concentrated in the angles. Compliance of the beams to established

Brad D. Weldon

acceptance criteria is demonstrated, validating the use of these structures in seismic

regions. The critical components of the structure that can limit the desired performance

include the post-tensioning anchors as well as the top and seat angles and their

connections.

The experimental results are also used to validate the analysis and design of the

new coupling system. Two different analytical models, one using fiber elements and the

other using finite elements, are investigated. In addition, an idealized coupling beam end

moment versus chord rotation relationship is developed as a design tool following basic

principles of equilibrium, compatibility, and constitutive relationships. The comparisons

demonstrate that the analytical and design models are able to capture the nonlinear

behavior of the structure, including global parameters such as the beam lateral force

versus chord rotation behavior as well as local parameters such as the neutral axis depth

at the beam ends. Using these models, the effects of several structural properties (such as

beam length) on the behavior of unbonded post-tensioned precast coupling beams is

analytically investigated to expand the results from the experiments.

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CONTENTS

FIGURES ........................................................................................................................ xvii

TABLES .......................................................................................................................... lxii

ACKNOWLEDGMENTS ............................................................................................... lxv

NOTATION ................................................................................................................... lxvii

VOLUME I

CHAPTER 1:

INTRODUCTION ...............................................................................................................1

1.1 Problem Statement ...................................................................................................1

1.2 Research Objectives .................................................................................................7

1.3 Research Scope ........................................................................................................8

1.4 Research Significance ..............................................................................................9

1.5 Overview of Dissertation .......................................................................................10

CHAPTER 2:

BACKGROUND ...............................................................................................................12

2.1 Coupled Wall Structural Systems ..........................................................................12

2.2 Monotonic Cast-in-Place Concrete Coupled Wall Systems ..................................15

2.2.1 Behavior and Design of Cast-in-Place Concrete Coupling Beams ............16

2.2.2 Current Code Requirements for Cast-in-Place Concrete Coupling Beams .........................................................................................17

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2.2.3 Analysis and Modeling of Cast-in-Place Concrete Coupled Wall Systems .............................................................................................20

2.2.4 Coupling Beam Database ...........................................................................22

2.3 Unbonded Post-Tensioning ....................................................................................24

2.4 Unbonded Post-Tensioned Hybrid Coupled Wall Systems ...................................26

2.5 Unbonded Post-Tensioned Precast Moment Frames .............................................35

2.5.1 Frames with Supplemental Energy Dissipation .........................................39

2.6 Behavior of Top and Seat Angles ..........................................................................45

2.6.1 Kishi and Chen (1990) and Lorenz et al. (1993) .......................................49

2.6.1.1 Tension angle initial stiffness, Kaixt ......................................................50

2.6.1.2 Tension angle yield force capacity, Tayx...............................................53

2.7 Chapter Summary ..................................................................................................54

CHAPTER 3:

PRECAST COUPLING BEAM SUBASSEMBLY EXPERIMENTS .............................56

3.1 Experiment Setup ...................................................................................................57

3.2 Test Subassembly Components .............................................................................65

3.2.1 Coupling Beam Specimens ........................................................................66

3.2.1.1 Maximum Moment Capacity at Beam-to-Wall Interfaces ...................75

3.2.1.2 Beam Transverse Reinforcement .........................................................78

3.2.1.3 Beam Longitudinal Mild Steel Reinforcement ....................................81

3.2.1.4 Confinement Reinforcement ................................................................86

3.2.1.5 Shear Slip at Beam-to-Wall Interfaces ................................................88

3.2.2 Reaction Block ...........................................................................................90

3.2.3 Load Block ...............................................................................................101

3.3 Testing Procedure ................................................................................................105

3.3.1 Wall Test Region Vertical Forces ............................................................106

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3.3.2 Beam Post-Tensioning Force ...................................................................109

3.3.3 Top and Seat Angle Connections .............................................................111

3.3.4 Test Day ...................................................................................................113

3.3.5 Summary of Test Procedure .....................................................................117

3.3.5.1 Virgin Beam Test Procedure ..............................................................117

3.3.5.2 Non-Virgin Beam Test Procedure .....................................................119

3.4 Chapter Summary ................................................................................................120

CHAPTER 4:

DESIGN AND MATERIAL PROPERTIES ...................................................................121

4.1 Design Material Properties ..................................................................................121

4.2 Measured Material Properties ..............................................................................122

4.2.1 Unconfined Concrete Strength .................................................................123

4.2.2 Fiber-Reinforced Grout Properties ..........................................................124

4.2.3 Post-tensioning Strand Properties ............................................................130

4.2.4 Mild Reinforcing Steel Properties ...........................................................136

4.2.5 Angle Steel Properties..............................................................................140

4.3 Chapter Summary ................................................................................................142

CHAPTER 5:

DATA INSTRUMENTATION AND SPECIMEN RESPONSE PARAMETERS ........144

5.1 Data Instrumentation ............................................................................................144

5.1.1 Instrumentation Overview .......................................................................145

5.1.2 Post-Tensioning Strand Load Cells .........................................................158

5.1.3 Wall Test Region Vertical Force Load Cells ...........................................166

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5.1.4 Load Block Global Displacement Transducers .......................................166

5.1.5 Reaction Block Global Displacement Transducers .................................169

5.1.6 Beam Global Displacement Transducers .................................................171

5.1.7 Gap Opening Displacement Transducers .................................................172

5.1.8 Wall Test Region Local Displacement Transducers ................................174

5.1.9 Beam Rotation Transducers .....................................................................176

5.1.10 Beam Looping Reinforcement Longitudinal Leg Strain Gauges ............177

5.1.11 Beam Transverse Reinforcement Strain Gauges .....................................179

5.1.12 Beam End Confinement Hoop Strain Gauges .........................................181

5.1.13 Beam Confined Concrete Strain Gauges .................................................184

5.1.14 Reaction Block Confinement Hoop Strain Gauges .................................186

5.1.15 Reaction Block Confined Concrete Strain Gauges ..................................189

5.2 Subassembly Response Parameters .....................................................................190

5.2.1 Coupling Beam Shear Force ....................................................................192

5.2.2 Coupling Beam End Moment ..................................................................194

5.2.3 Coupling Beam Post-Tensioning Force ...................................................194

5.2.4 Vertical Force on Wall Test Region ........................................................194

5.2.5 Angle Post-Tensioning Forces .................................................................195

5.2.6 Reaction Block Displacements ................................................................195

5.2.7 Load Block Displacements ......................................................................197

5.2.8 Beam Vertical Displacements ..................................................................201

5.2.9 Beam Chord Rotation ..............................................................................204

5.2.10 Gap Opening and Contact Depth at Beam-to-Wall Interface ..................205

5.3 Chapter Summary ................................................................................................210

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VOLUME II

CHAPTER 6:

VIRGIN BEAM SUBASSEMBLY EXPERIMENTAL RESULTS ...............................211

6.1 Overall Test Specimen Response .........................................................................211

6.2 Test 1 ....................................................................................................................214

6.2.1 Test Photographs ......................................................................................216

6.2.2 Beam Shear Force versus Chord Rotation Behavior ...............................222

6.2.3 Beam End Moment Force versus Chord Rotation Behavior ...................224

6.2.4 Beam Post-Tensioning Forces .................................................................225

6.2.5 Angle-to-Wall Connection Post-Tensioning Forces ................................229

6.2.6 Vertical Forces on Wall Test Region .......................................................232



6.2.9 Local Beam Rotations ..............................................................................240

6.2.10 Load Block Displacements and Rotations ...............................................242

6.2.11 Reaction Block Displacements and Rotations .........................................250

6.2.12 Contact Depth and Gap Opening at Beam-to-Wall Interfaces .................256

6.2.13 Wall Test Region Local Concrete Deformations .....................................267

6.2.14 Beam Looping Reinforcement Longitudinal Leg Strains ........................269

6.2.15 Beam Transverse Reinforcement Strains .................................................276

6.2.16 Beam Confined Concrete Strains .............................................................279

6.2.17 Beam End Confinement Hoop Strains .....................................................284

6.2.18 Wall Test Region Confined Concrete Strains ..........................................291

6.2.19 Wall Test Region Confinement Hoop Strains .........................................297

6.2.20 Crack Patterns ..........................................................................................299

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6.3 Test 2 ....................................................................................................................301




















6.3.20 Crack Patterns ..........................................................................................373

6.4 Test 3 ....................................................................................................................375




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6.4.19 Wall Test Region Confinement Hoops Strains ........................................444

6.4.20 Crack Patterns ..........................................................................................445

6.5 Test 4 ....................................................................................................................447








ix













6.5.20 Crack Patterns ..........................................................................................517

VOLUME III

CHAPTER 7:

POST-VIRGIN BEAM SUBASSEMBLY EXPERIMENTAL RESULTS ....................519

7.1 Test 3A .................................................................................................................519









x












7.1.20 Crack Patterns ..........................................................................................594

7.2 Test 3B .................................................................................................................595













xi








7.2.20 Crack Patterns ..........................................................................................667

7.3 Test 4A .................................................................................................................668












7.3.12 Gap Opening and Contact Depth at Beam-to-Wall Interfaces .................704





xii




7.3.20 Crack Patterns ..........................................................................................737

7.4 Test 4B .................................................................................................................738




















7.4.20 Crack Patterns ..........................................................................................812

xiii

VOLUME IV

CHAPTER 8:

SUMMARY AND OVERVIEW OF RESULTS FROM COUPLED WALL SUBASSEMBLY EXPERIMENTS ....................................................................813

8.1 Beam Shear Force versus Chord Rotation Behavior and Progression of Damage ........................................................................................814

8.2 Beam Post-Tensioning Tendon Force versus Chord Rotation Behavior .............824

8.3 Effect of Beam Post-Tensioning Tendon Area and Initial Concrete Stress .........827

8.4 Effect of Top and Seat Angles and Angle Strength .............................................829

8.5 Effect of Beam Depth ..........................................................................................831

8.6 Longitudinal Mild Steel Strains ...........................................................................832

8.7 Transverse Mild Steel Strains at Beam Ends .......................................................836

8.8 Transverse Mild Steel Strains at Beam Midspan .................................................839

8.9 Angle Connections ...............................................................................................841

8.10 Beam-to-Wall Connection and Grout Behavior ..................................................842

8.11 Compliance with ACI ITG-5.1 ............................................................................843

8.11.1 Probable Lateral Strength ........................................................................843

8.11.2 Relative Energy Dissipation Ratio ...........................................................844

8.11.3 Stiffness Requirements ............................................................................848

8.12 Comparisons with Monolithic Cast-in-Place Concrete Beams ............................850

8.13 Chapter Summary ................................................................................................853

CHAPTER 9:

ANALYTICAL MODELING OF PRECAST COUPLED WALL SUBASSEMBLIES .................................................................................854

9.1 Analytical Modeling Assumptions ......................................................................854

xiv

9.2 Fiber-Element Subassembly Model .....................................................................855

9.2.1 General Modeling of Concrete Members ................................................856

9.2.2 Modeling of Coupling Beam ...................................................................860

9.2.3 Modeling of Wall Regions .......................................................................865

9.2.4 Modeling of Gap Opening .......................................................................869

9.2.5 Modeling of Beam Post-Tensioning Tendons and Anchorages ..............872

9.2.6 Modeling of Top and Seat Angles ...........................................................876

9.2.6.1 Horizontal Angle Element Force-Deformation Model ......................879

9.2.6.2 Vertical Angle Element Force-Deformation Model ..........................881

9.3 Verification of Test Specimen Models ................................................................882


9.3.2 Beam Post-tensioning Force ....................................................................888

9.3.3 Contact Depth at Beam-to-Reaction-Block Interface ..............................895

9.3.4 Gap Opening at Beam-to-Reaction-Block Interface ................................903

9.3.5 Concrete Compressive Strains at Beam End ...........................................910

9.3.6 Longitudinal Mild Steel Strains at Beam End .........................................911

9.3.7 Longitudinal Mild Steel Strains at Beam Midspan ..................................920

9.3.8 Angle Behavior ........................................................................................924

9.4 ABAQUS Finite-Element Subassembly Model ..................................................926

9.5 Comparison of Fiber-Element and Finite-Element Models .................................929

9.5.1 Wall Pier and Coupling Beam Stresses ...................................................930

9.6 Chapter Summary ................................................................................................935

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CHAPTER 10:

PARAMETRIC INVESTIGATION AND CLOSED FORM ESTIMATION OF THE BEHAVIOR OF UNBONDED POST-TENSIONED PRECAST COUPLING BEAMS...........................................................................................936

10.1 Prototype Subassembly ........................................................................................936

10.2 Analytical Modeling ............................................................................................939

10.3 Subassembly Behavior Under Monotonic Loading .............................................941

10.4 Subassembly Behavior Under Cyclic Loading ....................................................944

10.5 Parametric Investigation ......................................................................................945

10.6 Tri-linear Estimation of Subassembly Behavior ..................................................954

10.6.1 Tension Angle Yielding State ..................................................................955

10.6.2 Tension Angle Strength State ..................................................................960

10.6.3 Confined Concrete Crushing State ...........................................................962

10.7 Analytical Verification of Tri-Linear Estimation ................................................965

10.8 Experimental Verification of Tri-linear Estimation .............................................965

10.9 Summary ..............................................................................................................969

CHAPTER 11:

SUMMARY, CONCLUSIONS, AND FUTURE WORK ..............................................971

11.1 Summary ..............................................................................................................971

11.2 Conclusions ..........................................................................................................972

11.2.1 Experimental Program .............................................................................972

11.2.2 Analytical Modeling and Parametric Investigation .................................974

11.2.3 Closed-form Estimations .........................................................................975

11.3 Future Work .........................................................................................................976

xvi

REFERENCES ...............................................................................................................978

Appendix A .....................................................................................................................989

Appendix B .....................................................................................................................992

Appendix C .....................................................................................................................996

Appendix D ...................................................................................................................1011

Appendix E ...................................................................................................................1039

Appendix F ...................................................................................................................1064

xvii

FIGURES

VOLUME I

CHAPTER 1:

Figure 1.1: Multi story coupled wall system. ..................................................................... 3

Figure 1.2: Coupled wall system floor-level subassembly. ................................................ 4

Figure 1.3: Coupled wall system floor-level subassembly idealized, exaggerated deformed configuration. .......................................................................................... 5

Figure 1.4: Coupling beam forces. ...................................................................................... 6

CHAPTER 2:

Figure 2.1: Coupled wall structures. ................................................................................. 13

Figure 2.2: Wall systems – (a) uncoupled wall; (b) coupled wall with strong beams; (c) coupled wall with weak beams. ....................................................................... 15

Figure 2.3: Reinforced concrete coupling beams [Paulay and Priestley (1992)] – (a) diagonal tension failure; (b) sliding shear failure; (c) diagonal reinforcement................................................................................................................................ 17

Figure 2.4: Diagonal reinforcement requirements for coupling beams [from ACI 318 (2008)] – (a) confinement of each group of diagonal bars; (b) confinement of entire beam cross-section. ..................................................................................... 19

Figure 2.5: Diagonally reinforced coupling beam (from Magnusson Klemencic Associates). ........................................................................................................... 20

Figure 2.6: Equivalent frame analytical models. .............................................................. 21

Figure 2.7: Measured ultimate sustained rotations for monolithic cast-in-place reinforced concrete coupling beams. ...................................................................................... 23

Figure 2.8: Hybrid coupled wall subassembly [from Shen and Kurama (2002b)]. .......... 27

xviii

Figure 2.9: Hybrid coupled wall subassembly experiments [adapted from Kurama et al. (2006)] – (a) measured coupling beam shear force versus chord rotation behavior; (b) photograph of displaced shape at beam end; (c) measured total beam post-tensioning force. .................................................................................................... 29

Figure 2.10: Low cycle fatigue fracture of top and seat angles. ....................................... 31

Figure 2.11: Hybrid coupled wall subassembly with no angles ....................................... 32

Figure 2.12: Hybrid coupled wall subassembly predicted behavior [from Shen et al. (2006)] – (a) coupling beam shear force versus chord rotation behavior; (b) total beam post-tensioning force. .................................................................................. 34

Figure 2.13: Unbonded post-tensioned precast moment frames – (a) structure; (b) interior beam-column subassembly; (c) idealized, exaggerated subassembly displaced shape. .................................................................................................... 37

Figure 2.14: Analytical investigation of unbonded post-tensioned precast beam-column subassemblies [from El-Sheikh et al. (1999, 2000)] – (a) moment-rotation relationship; (b) analytical model. ........................................................................ 39

Figure 2.15: Measured lateral force-displacement behavior [from Priestley and MacRae (1996)] – (a) interior joint; (b) exterior joint. ....................................................... 40

Figure 2.16: “Hybrid” precast concrete frame beam-column joint [adapted from Kurama (2002)]................................................................................................................... 41

Figure 2.17: Friction-damped post-tensioned precast moment frames [from Morgen and Kurama (2004)] – (a) test set-up schematic; (b) photograph of test set-up. ......... 43

Figure 2.18: Measured beam end moment versus chord rotation behavior [from Morgen and Kurama (2004)] – (a) without dampers; (b) with dampers. ........................... 44

Figure 2.19: Top and seat angle connection [adapted from Shen et al. (2006)] – (a) deformed configuration; (b) angle parameters. ............................................... 45

Figure 2.20: Angle model [adapted from Kishi and Chen (1990) and Lorenz et al. (1993)] – (a) cantilever model of tension angle; (b) assumed yield mechanism; (c) free body of angle horizontal leg. ................................................................................ 52

CHAPTER 3:

Figure 3.1: Simulation of floor level coupled wall subassembly displacements – (a) multi-story structure; (b) idealized displaced subassembly; (c) rotated subassembly. ......................................................................................................... 57

xix

Figure 3.2: Photograph of subassembly test setup. ........................................................... 60

Figure 3.3: Elevation view of test subassembly. ............................................................... 61

Figure 3.4: Plan view of test subassembly. ....................................................................... 62

Figure 3.5: East side view of loading frame. .................................................................... 63

Figure 3.6: North end view of loading and bracing frames. ............................................. 64

Figure 3.7: East side view of bracing frame and brace plate locations. ............................ 65

Figure 3.8: Photograph of beam formwork and details prior to casting (Beams 1 – 3). ... 67

Figure 3.9: Photograph of beam end prior to casting (Beams 1 – 3). ............................... 67

Figure 3.10: Photograph of beam end prior to casting (Beam 4 – increased depth). ........ 68

Figure 3.11: Duct locations for Beams 1 - 3. .................................................................... 70

Figure 3.12: Duct locations for Beam 4 (increased beam depth). .................................... 71

Figure 3.13: Mild steel reinforcement details for Beams 1 - 3. ........................................ 72

Figure 3.14: Mild steel reinforcement details for Beam 4. ............................................... 73

Figure 3.15: Photographs of mild steel reinforcement for Beams 1 – 3 – (a) No. 6 looping reinforcement; (b) No. 3 full-depth transverse and partial-depth confining hoops................................................................................................................................ 74

Figure 3.16: Maximum moment capacity at beam end. .................................................... 76

Figure 3.17: Beam maximum shear force demand. .......................................................... 78

Figure 3.18: High transverse tensile stresses in the vicinity of the gap tip. ...................... 80

Figure 3.19: Transverse (y-direction) stresses in element row 38 of full scale finite element beam model. ............................................................................................ 81

Figure 3.20: Design of beam longitudinal mild steel reinforcement – (a) critical section; (b) angle forces and beam moment at critical section; (c) beam moment diagram................................................................................................................................ 83

Figure 3.21: Equilibrium at critical section. ..................................................................... 84

Figure 3.22: Stress-strain model for confined concrete (Mander et al. 1988a). ............... 87

Figure 3.23: Reaction block duct details. .......................................................................... 92

xx

Figure 3.24: Dywidag Multiplane MA anchor components used with the beam post-tensioning strands.................................................................................................. 93

Figure 3.25: Modified Dywidag Multiplane MA anchor details. ..................................... 93

Figure 3.26: Reaction block reinforcement details. .......................................................... 96

Figure 3.27: Reaction and load block reinforcement hoops. ............................................ 97

Figure 3.28: Photograph of reaction and load block reinforcement cage. ........................ 98

Figure 3.29: Photograph of reaction block duct and reinforcement placement. ............... 99

Figure 3.30: Photograph of wall test region duct and reinforcement details. ................. 100

Figure 3.31: Load block duct details. .............................................................................. 103

Figure 3.32: Load block reinforcement details. .............................................................. 104

Figure 3.33: Photograph of load block duct and reinforcement details. ......................... 105

Figure 3.34: Post-tensioning operation – (a) single-strand jack; (b) jack operation; (c) anchor bearing plate. ..................................................................................... 110

Figure 3.35: Single use barrel/wedge type anchors with three-piece wedges and ring. . 111

Figure 3.36: Nominal lateral displacement loading history – (a) Test 1; (b) Tests 2 – 4B.............................................................................................................................. 115

CHAPTER 4:

Figure 4.1: Concrete cylinder specimens. ....................................................................... 123

Figure 4.2: Grout samples – (a) mortar mix; (b) epoxy grout. ....................................... 127

Figure 4.3: Photographs from a grout test. ..................................................................... 127

Figure 4.4: Stress-strain relationships for subassembly grout samples. ......................... 130

Figure 4.5: Post-tensioning strand test set-up. ................................................................ 133

Figure 4.6: Photograph of post-tensioning strand test. ................................................... 134

Figure 4.7: Photograph of post-tensioning strand wire fracture inside anchor. .............. 134

Figure 4.8: Stress-strain relationships for post-tensioning strand specimens. ................ 135

xxi

Figure 4.9: Limit of proportionality determination......................................................... 136

Figure 4.10: Photographs from a No. 3 reinforcing bar test. .......................................... 137

Figure 4.11: Stress-strain relationships for No. 3 bar specimens. .................................. 138

Figure 4.12: Stress-strain relationships for No. 6 bar specimens. .................................. 138

Figure 4.13: Photographs from an angle steel material test. ........................................... 140

Figure 4.14: Stress-strain relationships for angle steel material specimens. .................. 141

CHAPTER 5:

Figure 5.1: Photograph of beam-to-reaction-block interface and instrumentation

for Test 1. ............................................................................................................ 145

Figure 5.2: Load cell placement. ..................................................................................... 155

Figure 5.3: Displacement transducer placement. ............................................................ 156

Figure 5.4: Rotation transducer placement. .................................................................... 157

Figure 5.5: Strain gauge placement – reaction block. ..................................................... 157

Figure 5.6: Strain gauge placement – coupling beam. .................................................... 158

Figure 5.7: Photograph of load cells on beam post-tensioning strands. ......................... 159

Figure 5.8: Photograph of load cells on angle-to-reaction-block connection post-tensioning strands................................................................................................ 159

Figure 5.9: Photograph of post-tensioning strand load cells. .......................................... 160

Figure 5.10: Placement of post-tensioning strand load cells. ......................................... 161

Figure 5.11: Post-tensioning strand load cell calibration setup. ..................................... 163

Figure 5.12: Calibration data for the post-tensioning strand load cells. ......................... 164

Figure 5.13: Loading and unloading calibration data for Load Cells UND2 and UND3.............................................................................................................................. 165

Figure 5.14: Load block ferrule insert locations. ............................................................ 168

Figure 5.15: Reaction block ferrule insert locations. ...................................................... 170

Figure 5.16: Beam vertical displacement ferrule insert locations. .................................. 172

xxii

Figure 5.17: Beam gap opening ferrule insert locations. ................................................ 173

Figure 5.18: Reaction block wall test region ferrule insert locations – (a) inserts for Beams 1-3; (b) inserts for Beam 4. ..................................................................... 175

Figure 5.19: Beam rotation ferrule insert locations. ....................................................... 176

Figure 5.20: Photograph of beam strain gauges. ............................................................. 177

Figure 5.21: Beam looping reinforcement longitudinal leg strain gauge locations. ....... 178

Figure 5.22: Strain gauge designation system – longitudinal reinforcement. ................. 179

Figure 5.23: Beam transverse reinforcement strain gauge locations. ............................. 180

Figure 5.24: Strain gauge designation system – transverse reinforcement. .................... 181

Figure 5.25: Photograph of strain gauged confinement hoop. ........................................ 182

Figure 5.26: Beam end confinement hoop strain gauge locations. ................................. 183

Figure 5.27: Strain gauge designation system – beam end confinement hoops. ............ 184

Figure 5.28: Beam confined concrete strain gauge locations. ........................................ 185

Figure 5.29: Strain gauge designation system – beam confined concrete. ..................... 186

Figure 5.30: Reaction block confinement hoop strain gauge locations. ......................... 187

Figure 5.31: Strain gauge designation system – reaction block. ..................................... 188

Figure 5.32: Reaction block confined concrete strain gauge locations. ......................... 189

Figure 5.33: Subassembly displaced in positive direction. ............................................. 191

Figure 5.34: Subassembly displaced in negative direction. ............................................ 192

Figure 5.35: Reaction block displacements. ................................................................... 196

Figure 5.36: Load block displacements. ......................................................................... 198

Figure 5.37: Idealized exaggerated displaced shape of load block. ................................ 198

Figure 5.38: Idealized exaggerated displaced shape of test beam. ................................. 202

Figure 5.39: Gap opening and contact depth. ................................................................. 206

xxiii

VOLUME II

CHAPTER 6:

Figure 6.1: Displaced position of subassembly at θb = 3.33% – (a) Test 2; (b) Test 4. ........................................................................................... 212

Figure 6.2: Vb-θb behavior – (a) Test 2; (b) Test 4. ......................................................... 213

Figure 6.3: Test 1 beam and reaction block patched concrete regions. .......................... 216

Figure 6.4: Test 1 overall photographs – (a) pre-test undisplaced position; (b) θb = 3.0%; (c) θb = –3.0%; (d) θb = 8.0%; (e) θb = –8.0%; (f) final post-test undisplaced position. ............................................................................................................... 219

Figure 6.5: Test 1 beam south end photographs – (a) pre-test undisplaced position; (b) θb = 3.0%; (c) θb = –3.0%; (d) θb = 8.0%; (e) θb = –8.0%; (f) final post-test undisplaced position............................................................................................ 220

Figure 6.6: Test 1 beam south end damage propagation – positive and negative rotations.............................................................................................................................. 221

Figure 6.7: Test 1 gap opening and grout behavior at 8.0% rotation – (a) south end; (b) north end. ....................................................................................................... 221

Figure 6.8: Test 1 coupling beam shear force versus chord rotation behavior – (a) using beam displacements; (b) using load block displacements. ................................. 223

Figure 6.9: Test 1 photograph of north seat angle – (a) angle deformed shape; (b) low cycle fatigue fracture. ............................................................................. 224

Figure 6.10: Test 1 Mb-θb,lb behavior. ............................................................................. 225

Figure 6.11: Test 1 beam post-tensioning strand forces – (a) strand 1; (b) strand 2. ..... 227

Figure 6.12: Test 1 FLC-θb,lb behavior – (a) strand 1; (b) strand 2. .................................. 227

Figure 6.13: Test 1 beam post-tensioning force versus chord rotation behavior – (a) using beam displacements; (b) using load block displacements. ................................. 228

Figure 6.14: Test 1 south end top angle-to-wall connection strand forces – (a) east strand; (b) west strand. .................................................................................................... 230

Figure 6.15: Test 1 south end top angle-to-wall connection strand forces versus load block beam chord rotation – (a) FLC3-θb,lb; (b) FLC4-θb,lb. ................................... 230

Figure 6.16: Test 1 south end seat angle-to-wall connection strand forces – (a) east strand; (b) west strand. ........................................................................................ 231

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Figure 6.17: Test 1 south end seat angle-to-wall connection strand forces versus load block beam chord rotation – (a) FLC5-θb,lb; (b) FLC6-θb,lb. ................................... 231

Figure 6.18: Test 1 south end total angle-to-wall connection strand forces versus load block beam chord rotation – (a) top connection; (b) seat connection. ................ 232

Figure 6.19: Test 1 vertical force on wall test region, Fwt – (a) Fwt-test duration; (b) Fwt-θb,lb. .......................................................................................................... 233

Figure 6.20: Test 1 south end beam vertical displacements – (a) measured, ∆DT9; (b) adjusted, ∆DT9,y; (c) difference, ∆DT9,y-∆DT9. ........................................ 235

Figure 6.21: Test 1 north end beam vertical displacements – (a) measured, ∆DT10; (b) adjusted, ∆DT10,y; (c) difference, ∆DT10,y-∆DT10. .............................................. 236

Figure 6.22: Test 1 percent difference between measured and adjusted displacements – (a) south end, DT9; (b) north end, DT10. ........................................................... 236

Figure 6.23: Test 1 beam vertical displacements versus load block beam chord rotation –(a) ∆DT9-θb,lb; (b) ∆DT10-θb,lb. ................................................................................ 237

Figure 6.24: Test 1 beam chord rotation – (a) θb from ∆DT9 and ∆DT10; (b) θb,lb from ∆LB,y.............................................................................................................................. 238

Figure 6.25: Test 1 percent difference between θb and θb,lb. ........................................... 239

Figure 6.26: Test 1 difference between θb and θb,lb......................................................... 239

Figure 6.27: Test 1 beam inclinometer rotations – (a) near beam south end, θRT1; (b) near beam midspan, θRT2. ............................................................................................ 241

Figure 6.28: Test 1 percent difference between beam inclinometer rotations and beam chord rotations – (a) RT1; (b) RT2; (c) beam deflected shape. .......................... 242

Figure 6.29: Test 1 load block horizontal displacements – (a) measured, ∆DT3; (b) adjusted, ∆DT3,x; (c) percent difference. ......................................................... 245

Figure 6.30: Test 1 load block north end vertical displacements – (a) measured, ∆DT4; (b) adjusted, ∆DT4,y; (c) percent difference. ......................................................... 246

Figure 6.31: Test 1 load block south end vertical displacements – (a) measured, ∆DT5; (b) adjusted, ∆DT5,y; (c) percent difference. ......................................................... 247

Figure 6.32: Test 1 percent difference between measured and adjusted displacements versus load block beam chord rotation – (a) DT4; (b) DT5. .............................. 247

Figure 6.33: Test 1 load block displacements versus load block beam chord rotation – (a) ∆DT4-θb,lb; (b) ∆DT5-θb,lb; (c) ∆DT3,x-θb,lb. ......................................................... 248

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Figure 6.34: Test 1 load block centroid displacements – (a) x-y displacements; (b) rotation; (c) x-displacement; (d) y-displacement. .......................................... 249

Figure 6.35: Test 1 load block centroid displacements versus load block beam chord rotation – (a) x-displacement-θb,lb; (b) y-displacement-θb,lb; (c) rotation-θb,lb..... 250

Figure 6.36: Test 1 reaction block displacements – (a) ∆DT6; (b) ∆DT7; (c) ∆DT8. ........... 252

Figure 6.37: Test 1 reaction block displacements versus load block beam chord rotation – (a) ∆DT7-θb,lb; (b) ∆DT8-θb,lb; (c) ∆DT6-θb,lb. ........................................................... 253

Figure 6.38: Test 1 reaction block centroid displacements – (a) x-y displacements; (b) rotation; (c) x-displacement; (d) y-displacement. .......................................... 254

Figure 6.39: Test 1 reaction block centroid displacements versus load block beam chord rotation – (a) x-displacements; (b) y-displacements; (c) rotation. ...................... 255

Figure 6.40: Test 1 beam-to-reaction-block interface top LVDT displacements – (a) measured, ∆DT11; (b) adjusted, ∆DT11,x; (c) percent difference. ...................... 257

Figure 6.41: Test 1 beam-to-reaction-block interface middle LVDT displacements – (a) measured, ∆DT12; (b) adjusted, ∆DT12,x; (c) percent difference. ...................... 258

Figure 6.42: Test 1 beam-to-reaction-block interface bottom LVDT displacements – (a) measured, ∆DT13; (b) adjusted, ∆DT13,x; (c) percent difference. ...................... 259

Figure 6.43: Test 1 beam-to-reaction-block interface LVDT displacements versus load block beam chord rotation – (a) ∆DT11-θb,lb; (b) ∆DT13-θb,lb; (c) ∆DT12-θb,lb. ......... 260

Figure 6.44: Test 1 contact depth at beam-to-reaction-block interface – (a) method 1 using DT11, DT12, and DT13; (b) method 2 using RT2, DT11, and DT13; (c) method 3 using RT2 and DT12; (d) method 4 using θb,lb and DT12; (e) method 5 using θb,lb, DT11, and DT13. .............................................................................. 264

Figure 6.45: Test 1 gap opening at beam-to-reaction-block interface – (a) method 1 using DT11, DT12, and DT13; (b) method 2 using RT2, DT11, and DT13; (c) method 3 using RT2 and DT12; (d) method 4 using θb,lb and DT12; (e) method 5 using θb,lb, DT11, and DT13. ................................................................................................ 265

Figure 6.46: Test 1 gap opening at beam-to-reaction-block interface using method 4. . 266

Figure 6.47: Test 1 contact depth at beam-to-reaction-block interface using method 4 – (a) entire data; (b) 2.0% beam chord rotation cycle; (c) 5.0% beam chord rotation cycle. ................................................................................................................... 266

Figure 6.48: Test 1 wall test region concrete deformations – (a) ∆DT14; (b) ∆DT15.......... 268

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Figure 6.49: Test 1 wall test region concrete deformations versus load block beam chord rotation – (a) ∆DT14-θb,lb; (b) ∆DT15-θb,lb. .............................................................. 269

Figure 6.50: Test 1 beam looping reinforcement top longitudinal leg strains – (a) ε6(1)T-E; (b) ε6(1)T-W; (c) ε6(2)T-E; (d) ε6(2)T-W; (e) ε6(3)T-E; (f) ε6(3)T-W; (g) ε6MT-E; (h) ε6MT-W. ............................................................................................................ 270

Fig 6.51: Test 1 beam looping reinforcement bottom longitudinal leg strains – (a) ε6(1)B-E; (b) ε6(1)B-W; (c) ε6(2)B-E; (d) ε6(2)B-W; (e) ε6(3)B-E; (f) ε6(3)B-W; (g) ε6MB-E; (h) ε6MB-W. ............................................................................................................ 272

Figure 6.52: Test 1 beam looping reinforcement top longitudinal leg strains versus load block beam chord rotation – (a) ε6(1)T-E-θb,lb; (b) ε6(1)T-W-θb,lb; (c) ε6(2)T-E-θb,lb; (d) ε6(2)T-W-θb,lb; (e) ε6(3)T-E-θb,lb; (f) ε6(3)T-W-θb,lb; (g) ε6MT-E-θb,lb; (h) ε6MT-W-θb,lb. ..................................................................................................... 273

Figure 6.53: Test 1 beam looping reinforcement bottom longitudinal leg strains versus load block beam chord rotation – (a) ε6(1)B-E-θb,lb; (b) ε6(1)B-W-θb,lb; (c) ε6(2)B-E-θb,lb; (d) ε6(2)B-W-θb,lb; (e) ε6(3)B-E-θb,lb; (f) ε6(3)B-W-θb,lb; (g) ε6MB-E-θb,lb; (h) ε6MB-W-θb,lb. ..................................................................................................... 275

Figure 6.54: Test 1 beam looping reinforcement vertical leg strains – (a) ε6SE(E)-E; (b) ε6SE(E)-W; (c) ε6SE(I)-E; (d) ε6SE(I)-W. ................................................................... 277

Figure 6.55: Test 1 beam looping reinforcement vertical leg strains versus load block beam chord rotation – (a) ε6SE(E)-E-θb,lb; (b) ε6SE(E)-W-θb,lb; (c) ε6SE(I)-E-θb,lb; (d) ε6SE(I)-W-θb,lb. ................................................................................................... 278

Figure 6.56: Test 1 beam midspan transverse hoop reinforcement strains – (a) εMH-E; (b) εMH-W. ............................................................................................................. 278

Figure 6.57: Test 1 beam midspan transverse hoop reinforcement strains versus load block beam chord rotation – (a) εMH-E-θb,lb; (b) εMH-W-θb,lb. ................................ 279

Figure 6.58: Test 1 No. 3 top hoop support bar strains – (a) ε3THT-(1); (b) ε3THB-(1); (c) ε3THT-(2); (d) ε3THB-(2). ...................................................................................... 281

Figure 6.59: Test 1 No. 3 bottom hoop support bar strains – (a) ε3BHB-(1); (b) ε3BHT-(1); (c) ε3BHB-(2); (d) ε3BHT-(2). ...................................................................................... 282

Figure 6.60: Test 1 No. 3 top hoop support bar strains versus load block beam chord rotation – (a) ε3THT-(1)-θb,lb; (b) ε3THB-(1)-θb,lb; (c) ε3THT-(2)-θb,lb; (d) ε3THB-(2)-θb,lb. .................................................................................................. 283

Figure 6.61: Test 1 No. 3 bottom hoop support bar strains versus load block beam chord rotation – (a) ε3BHB-(1)-θb,lb; (b) ε3BHT-(1)-θb,lb; (c) ε3BHB-(2)-θb,lb; (d) ε3BHT-(2)-θb,lb. .................................................................................................. 284

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Figure 6.62: Test 1 beam end confinement hoop east leg strains – (a) ε1HB-E; (b) ε2HB-E; (c) ε3HB-E; (d) ε4HB-E. ............................................................................................ 286

Figure 6.63: Test 1 beam end confinement hoop west leg strains – (a) ε1HB-W; (b) ε2HB-W; (c) ε3HB-W; (d) ε4HB-W. ........................................................................................... 287

Figure 6.64: Test 1 beam end confinement hoop east leg strains versus load block beam chord rotation – (a) ε1HB-E-θb,lb; (b) ε2HB-E-θb,lb; (c) ε3HB-E-θb,lb; (d) ε4HB-E-θb,lb. ..................................................................................................... 288

Figure 6.65: Test 1 beam end confinement hoop west leg strains versus load block beam chord rotation – (a) ε1HB-W-θb,lb; (b) ε2HB-W-θb,lb; (c) ε3HB-W-θb,lb; (d) ε4HB-W-θb,lb. ..................................................................................................... 289

Figure 6.66: Photograph of damage on south end of beam – (a) east side; (b) west side.............................................................................................................................. 290

Figure 6.67: Confinement hoop strains – (a) photograph of strain gauged hoop; (b) outward bending of the vertical leg. .............................................................. 291

Figure 6.68: Test 1 reaction block corner bar strains – (a) εCBB1E; (b) εCBB1W; (c) εCBB2E; (d) εCBB2W; (e) εCBB3E; (f) εCBB3W. ......................................................................... 293

Figure 6.69: Test 1 reaction block corner bar strains – (a) εCBM1E; (b) εCBM1W; (c) εCBM3E; (d) εCBM3W. ........................................................................................................... 294

Figure 6.70: Test 1 reaction block corner bar strains versus load block beam chord rotation – (a) εCBB1E-θb,lb; (b) εCBB1W-θb,lb; (c) εCBB2E-θb,lb; (d) εCBB2W-θb,lb; (e) εCBB3E-θb,lb; (f) εCBB3W-θb,lb. .................................................................................. 295

Figure 6.71: Test 1 reaction block corner bar strains versus load block beam chord rotation – (a) εCBM1E-θb,lb; (b) εCBM1W-θb,lb; (c) εCBM3E-θb,lb; (d) εCBM3W-θb,lb. ....... 296

Figure 6.72: Test 1 reaction block corner bar average strains – (a) test duration; (b) versus load block beam chord rotation. .......................................................................... 296

Figure 6.73: Test 1 reaction block hoop strains – (a) ε1THM; (b) ε1MHM; (c) ε1BHE. .......... 298

Figure 6.74: Test 1 reaction block hoop strains versus load block beam chord rotation – (a) ε1THM-θb,lb; (b) ε1MHM-θb,lb; (c) ε1BHE-θb,lb. ....................................................... 299

Figure 6.75: Test 1 crack patterns – (a) θb = 0.35%; (b) θb = 0.5%; (c) θb = 0.75%; (d) θb = 1.0%; (e) θb = 1.5%; (f) θb = 2.0%; (g) θb = 3.0%. ................................ 300

Figure 6.76: Test 2 overall photographs – (a) pre-test undisplaced position; (b) θb = 3.33%; (c) θb = –3.33%; (d) θb = 6.4%; (e) θb = –6.4%; (f) final post-test undisplaced position............................................................................................ 304

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Figure 6.77: Test 2 beam south end photographs – (a) pre-test undisplaced position; (b) θb = 3.33%; (c) θb = –3.33%; (d) θb = 6.4%; (c) θb = –6.4%; (f) final post-test undisplaced position............................................................................................ 305

Figure 6.78: Test 2 beam south end damage propagation – positive and negative rotations............................................................................................................... 306

Figure 6.79: Test 2 grout and gap opening behavior at south end – (a) θb = -0.5%; (b) θb = -5.0%. ..................................................................................................... 306


Figure 6.81: Test 2 damage to beam ends (upon angle removal after completion of test) – (a) south end; (b) north end. ................................................................................ 310

Figure 6.82: Test 2 Mb-θb,lb behavior. ............................................................................. 311

Figure 6.83: Test 2 beam post-tensioning strand forces – (a) strand 1; (b) strand 2; (c) strand 3; (d) strand 4. ..................................................................................... 313

Figure 6.84: Test 2 FLC-θb,lb behavior – (a) strand 1; (b) strand 2; (c) strand 3; (d) strand 4. ......................................................................................................... 314

Figure 6.85: Test 2 beam post-tensioning force versus chord rotation behavior – (a) using beam displacements; (b) using load block displacements. ................................. 315

Figure 6.86: Use of additional anchor barrel to prevent strand wire fracture. ................ 316

Figure 6.87: Test 2 south end top angle-to-wall connection strand forces – (a) east strand; (b) west strand. .................................................................................................... 318

Figure 6.88: Test 2 south end top angle-to-wall connection strand forces versus load block beam chord rotation – (a) FLC3-θb,lb; (b) FLC4-θb,lb. ................................... 318


Figure 6.90: Test 2 south end seat angle-to-wall connection strand forces versus load block beam chord rotation – (a) FLC5-θb,lb; (b) FLC6-θb,lb. ................................... 319

Figure 6.91: Test 2 south end total angle-to-wall connection strand forces versus load block beam chord rotation – (a) top connection; (b) seat connection. ................ 320

Figure 6.92: Test 2 vertical force on wall test region, Fwt – (a) Fwt-test duration; (b) Fwt-θb,lb. .......................................................................................................... 321

Figure 6.93: Test 2 south end beam vertical displacement. ............................................ 322

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Figure 6.96: Test 2 beam vertical displacements versus load block beam chord rotation –(a) ∆DT9-θb,lb; (b) ∆DT10-θb,lb. ................................................................................ 324

Figure 6.97: Test 2 beam chord rotation – (a) θb from ∆DT10 with ∆DT9 taken as zero; (b) θb,lb from ∆LB,y. ............................................................................................... 325

Figure 6.98: Test 2 percent difference between θb and θb,lb. ........................................... 326

Figure 6.99: Test 2 difference between θb and θb,lb......................................................... 326


Figure 6.101: Test 2 difference between beam inclinometer rotations and beam chord rotations – (a) RT1; (b) RT2; (c) beam deflected shape. .................................... 328




Figure 6.105: Test 2 percent difference between measured and adjusted displacements – (a) DT4; (b) DT5. ................................................................................................ 334

Figure 6.106: Test 2 load block displacements versus load block beam chord rotation – (a) ∆DT4-θb,lb; (b) ∆DT5-θb,lb; (c) ∆DT3,x-θb,lb. ......................................................... 334

Figure 6.107: Test 2 load block centroid displacements – (a) x-y displacements; (b) rotation; (c) x-displacements; (d) y-displacements. ....................................... 335

Figure 6.108: Test 2 load block centroid displacements versus load block beam chord rotation – (a) x-displacement-θb,lb; (b) y-displacement-θb,lb; (c) rotation-θb,lb..... 336

Figure 6.109: Test 2 reaction block displacements – (a) ΔDT6; (b) ΔDT7; (c) ΔDT8. ......... 338

Figure 6.110: Test 2 reaction block displacements versus load block beam chord rotation – (a) ∆DT7-θb,lb; (b) ∆DT8-θb,lb; (c) ∆DT6-θb,lb. ........................................................ 339

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Figure 6.111: Test 2 reaction block centroid displacements – (a) x-y displacements; (b) rotation; (c) x-displacements; (d) y-displacements. ...................................... 340

Figure 6.112: Test 2 reaction block centroid displacements versus load block beam chord rotation – (a) x-displacements; (b) y-displacements; (c) rotation. ...................... 341




Figure 6.116: Test 2 beam-to-reaction-block interface LVDT displacements versus load block beam chord rotation – (a) ∆DT11-θb,lb; (b) ∆DT13-θb,lb; (c) ∆DT12-θb,lb. ......... 346

Figure 6.117: Test 2 contact depth at beam-to-reaction-block interface – (a) method 1 using DT11, DT12, and DT13; (b) method 2 using RT2, DT11, and DT13; (c) method 3 using RT2 and DT12; (d) method 4 using θb,lb and DT12; (e) method 5 using θb,lb, DT11, and DT13. .............................................................................. 349

Figure 6.118: Test 2 gap opening at beam-to-reaction-block interface – (a) method 1 using DT11, DT12, and DT13; (b) method 2 using RT2, DT11, and DT13; (c) method 3 using RT2 and DT12; (d) method 4 using θb,lb and DT12; (e) method 5 using θb,lb, DT11, and DT13. .............................................................................. 350

Figure 6.119: Test 2 gap opening at beam-to-reaction-block interface using method 4. ................................................................................................... 351

Figure 6.120: Test 2 contact depth at beam-to-reaction-block interface using method 4 –(a) entire data; (b) 2.25% beam chord rotation cycle; (c) 5.0% beam chord rotation cycle. ...................................................................................................... 351

Figure 6.121: Test 2 wall test region concrete deformations – (a) DT14; (b) DT15. ..... 353

Figure 6.122: Test 2 wall test region concrete deformations versus load block beam chord rotation – (a) ∆DT14-θb,lb; (b) ∆DT15-θb,lb. .............................................................. 354


Figure 6.124: Test 2 beam looping reinforcement bottom longitudinal leg strains – (a) ε6(1)B-E; (b) ε6(1)B-W; (c) ε6(2)B-E; (d) ε6(2)B-W; (e) ε6(3)B-E; (f) ε6(3)B-W; (g) ε6MB-E; (h) ε6MB-W. ............................................................................................................ 357

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Figure 6.125: Test 2 beam looping reinforcement top longitudinal leg strains versus load block beam chord rotation – (a) ε6(1)T-E-θb,lb; (b) ε6(1)T-W-θb,lb; (c) ε6(2)T-E-θb,lb; (d) ε6(2)T-W-θb,lb; (e) ε6(3)T-E-θb,lb; (f) ε6(3)T-W-θb,lb; (g) ε6MT-E-θb,lb; (h) ε6MT-W-θb,lb. ............................................................................................................................. 358

Figure 6.126: Test 2 beam looping reinforcement bottom longitudinal leg strains versus load block beam chord rotation – (a) ε6(1)B-E-θb,lb; (b) ε6(1)B-W-θb,lb; (c) ε6(2)B-E-θb,lb; (d) ε6(2)B-W-θb,lb; (e) ε6(3)B-E-θb,lb; (f) ε6(3)B-W-θb,lb; (g) ε6MB-E-θb,lb; (h) ε6MB-W-θb,lb. ............................................................................................................................. 360


Figure 6.128: Test 2 beam looping reinforcement vertical leg strains versus load block beam chord rotation – (a) ε6SE(E)-E-θb,lb; (b) ε6SE(E)-W-θb,lb; (c) ε6SE(I)-E-θb,lb; (d) ε6SE(I)-W-θb,lb. ................................................................................................... 363


Figure 6.130: Test 2 beam midspan transverse hoop reinforcement strains versus load block beam chord rotation – (a) εMH-E-θb,lb; (b) εMH-W-θb,lb. ................................ 364

Figure 6.131: Test 2 No. 3 top hoop support bar strains– (a) ε3THT-(1); (b) ε3THB-(1); (c) ε3THT-(2); (d) ε3THB-(2). ...................................................................................... 365


Figure 6.133: Test 2 No. 3 top hoop support bar strains versus load block beam chord rotation – (a) ε3THT-(1)-θb,lb; (b) ε3THB-(1)-θb,lb; (c) ε3THT-(2)-θb,lb; (d) ε3THB-(2)-θb,lb. . 367

Figure 6.134: Test 2 No. 3 bottom hoop support bar strains versus load block beam chord rotation – (a) ε3BHB-(1)-θb,lb; (b) ε3BHT-(1)-θb,lb; (c) ε3BHB-(2)-θb,lb; (d) ε3BHT-(2)-θb,lb. . 368



Figure 6.137: Test 2 beam end confinement hoop east leg strains versus load block beam chord rotation – (a) ε1HBE-θb,lb; (b) ε2HBE-θb,lb; (c) ε3HBE-θb,lb; (d) ε4HBE-θb,lb. ...... 371

Figure 6.138: Test 2 beam end hoop west leg confinement strains versus load block beam chord rotation – (a) ε1HBW-θb,lb; (b) ε2HBW-θb,lb; (c) ε3HBW-θb,lb; (d) ε4HBW-θb,lb. .... 372

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Figure 6.139: Test 2 crack patterns – (a) θb = 0.5%; (b) θb = 0.75%; (c) θb = 1.0%; (d) θb = 1.5%; (e) θb = 2.25%; (f) θb = 3.33%; (g) θb = 5.0%; (h) θb = 6.4%. .... 373

Figure 6.140: Test 3 overall photographs – (a) pre-test undisplaced position; (b) θb = 3.33%; (c) θb = 3.33%; (d) θb = 5.0%; (e) θb = –5.0%; (f) final post-test undisplaced position............................................................................................ 378

Figure 6.141: Test 3 beam south end photographs – (a) pre-test undisplaced position; (b) θb = 3.33%; (c) θb = –3.33%; (d) θb = 5.0%; (c) θb = –5.0%; (f) final post-test undisplaced position............................................................................................ 379


Figure 6.143: Test 3 angle strips at south top connection. .............................................. 380

Figure 6.144: Test 3 coupling beam shear force versus chord rotation behavior – (a) using beam displacements; (b) using load block displacements. .................. 382

Figure 6.145: Test 3 Mb-θb behavior. .............................................................................. 383

Figure 6.146: Test 3 beam post-tensioning strand forces – (a) strand 1; (b) strand 2; (c) strand 3. ......................................................................................................... 385

Figure 6.147: Test 3 FLC-θb behavior – (a) strand 1; (b) strand 2; strand 3. ................... 386

Figure 6.148: Test 3 beam post-tensioning force versus chord rotation behavior – (a) using beam displacements; (b) using load block displacements. .................. 387

Figure 6.149: Test 3 south end top angle-to-wall connection strand forces – (a) east strand; (b) west strand. ........................................................................................ 389

Figure 6.150: Test 3 south end top angle-to-wall connection strand forces versus beam chord rotation – (a) FLC3-θb; (b) FLC4-θb.............................................................. 390


Figure 6.152: Test 3 south end seat angle-to-wall connection strand forces versus beam chord rotation – (a) FLC5-θb; (b) FLC6-θb.............................................................. 391

Figure 6.153: Test 3 south end total angle-to-wall connection strand forces versus beam chord rotation– (a) top connection; (b) seat connection. .................................... 391

Figure 6.154: Test 3 vertical force on wall test region, Fwt – (a) Fwt-test duration; (b) Fwt-θb ............................................................................................................. 392

Figure 6.155: Test 3 south end beam vertical displacements – (a) measured, ∆DT9; (b) adjusted, ∆DT9,y; (c) difference, ∆DT9,y-∆DT9. .................................................. 394

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Figure 6.157: Test 3 percent difference between measured and adjusted displacements versus beam chord rotation – (a) south end, DT9; (b) north end, DT10. ............ 395

Figure 6.158: Test 3 beam vertical displacements versus beam chord rotation – (a) ∆DT9-θb; (b) ∆DT10-θb. ..................................................................................... 396

Figure 6.159: Test 3 beam chord rotation – (a) θb from ∆DT9 and ∆DT10; (b) θb,lb from ∆LB,y.............................................................................................................................. 397

Figure 6.160: Test 3 percent difference between θb and θb,lb. ......................................... 397

Figure 6.161: Test 3 difference between θb and θb,lb....................................................... 398

Figure 6.162: Test 3 beam inclinometer rotations – (a) near beam south end, θRT1; (b) near beam midspan, θRT2. .............................................................................. 399






Figure 6.168: Test 3 load block displacements versus beam chord rotation – (a) ∆DT4-θb; (b) ∆DT5-θb; (c) ∆DT3,x-θb. ..................................................................................... 406


Figure 6.170: Test 3 load block centroid displacements versus beam chord rotation – (a) x-displacement-θb; (b) y-displacement-θb; (c) rotation-θb. ............................ 408


Figure 6.172: Test 3 reaction block displacements versus beam chord rotation – (a) ∆DT7-θb; (b) ∆DT8-θb; (c) ∆DT6-θb. ................................................................... 411

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Figure 6.173: Test 3 reaction block centroid displacements – (a) x-y displacements; (b) rotation; (c) x-displacements; (d) y-displacements. ....................................... 412

Figure 6.174: Test 3 reaction block centroid displacements versus beam chord rotation – (a) x-displacements; (b) y-displacements; (c) rotation. ....................................... 413




Figure 6.178: Test 3 beam-to-reaction-block interface LVDT displacements versus beam chord rotation – (a) ∆DT11-θb; (b) ∆DT13-θb; (c) ∆DT12-θb. ..................................... 418

Figure 6.179: Test 3 contact depth at beam-to-reaction-block interface – (a) method 1 using DT11, DT12, and DT13; (b) method 2 using RT1, DT11, and DT13; (c) method 3 using RT1 and DT12; (d) method 4 using θb and DT12; (e) method 5 using θb, DT11, and DT13. ................................................................................. 421

Figure 6.180: Test 3 gap opening at beam-to-reaction-block interface – (a) method 1 using DT11, DT12, and DT13; (b) method 2 using RT1, DT11, and DT13; (c) method 3 using RT1 and DT12; (d) method 4 using θb and DT12; (e) method 5 using θb, DT11, and DT13. ................................................................................. 422




Figure 6.184: Test 3 wall test region concrete deformations versus beam chord rotation – (a) ∆DT14-θb; (b) ∆DT15-θb. .................................................................................... 425



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Figure 6.187: Test 3 beam looping reinforcement top longitudinal leg strains versus beam chord rotation – (a) ε6(1)T-E-θb; (b) ε6(1)T-W-θb; (c) ε6(2)T-E-θb; (d) ε6(2)T-W-θb; (e) ε6(3)T-E-θb; (f) ε6(3)T-W-θb; (g) ε6MT-E-θb; (h) ε6MT-W-θb. ..................................... 430

Figure 6.188: Test 3 beam looping reinforcement bottom longitudinal leg strains versus beam chord rotation – (a) ε6(1)B-E-θb; (b) ε6(1)B-W-θb; (c) ε6(2)B-E-θb; (d) ε6(2)B-W-θb; (e) ε6(3)B-E-θb; (f) ε6(3)B-W-θb; (g) ε6MB-E-θb; (h) ε6MB-W-θb. ..................................... 432


Figure 6.190: Test 3 beam looping reinforcement vertical leg strains versus beam chord rotation – (a) ε6SE(E)-E-θb; (b) ε6SE(E)-W-θb; (c) ε6SE(I)-E-θb; (d) ε6SE(I)-W-θb. ............. 435


Figure 6.192: Test 3 beam midspan transverse hoop reinforcement strains versus beam chord rotation – (a) εMH-E-θb; (b) εMH-W-θb. ......................................................... 436



Figure 6.195: Test 3 No. 3 top hoop support bar strains versus beam chord rotation – (a) ε3THT-(1)-θb; (b) ε3THB-(1)-θb; (c) ε3THT-(2)-θb; (d) ε3THB-(2)-θb. ............................. 439

Figure 6.196: Test 3 No. 3 bottom hoop support bar strains versus beam chord rotation – (a) ε3BHB-(1)-θb; (b) ε3BHT-(1)-θb; (c) ε3BHB-(2)-θb; (d) ε3BHT-(2)-θb. ............................ 440

Figure 6.197: Test 3 beam end confinement hoop east leg strains – (a) ε1HBE; (b) ε2HBE; (c) ε3HBE; (d) ε4HBE. .............................................................................................. 441

Figure 6.198: Test 3 beam end confinement hoop west leg strains – (a) ε1HBW; (b) ε2HBW; (c) ε3HBW; (d) ε4HBW. ............................................................................................. 442

Figure 6.199: Test 3 beam end confinement hoop east leg strains versus beam chord rotation – (a) ε1HBE-θb; (b) ε2HBE-θb; (c) ε3HBE-θb; (d) ε4HBE-θb. ........................... 443

Figure 6.200: Test 3 beam end confinement hoop west leg strains versus beam chord rotation – (a) ε1HBW-θb; (b) ε2HBW-θb; (c) ε3HBW-θb; (d) ε4HBW-θb. ......................... 444

Figure 6.201: Test 3 crack patterns – (a) θb = 0.125%; (b) θb = 0.175%; (c) θb = 0.25%; (d) θb = 0.35%; (e) θb = 0.5%; (f) θb = 0.75%; (g) θb = 1.0%; (h) θb = 1.5%; (i) θb = 2.25%; (j) θb = 3.33%; (k) θb = 5.0%. ..................................................... 445

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Figure 6.202: Test 4 overall photographs – (a) pre-test undisplaced position; (b) θb = 3.33%; (c) θb = –3.33%; (d) final post-test undisplaced position. ......... 450

Figure 6.203: Test 4 beam south end photographs – (a) pre-test undisplaced position; (b) θb = 3.33%; (c) θb = –3.33%; (d) final post-test undisplaced position. ......... 451


Figure 6.205: Test 4 angle-to-wall connection plates. .................................................... 452

Figure 6.206: Test 4 wall test region patch. .................................................................... 453


Figure 6.208: Test 4 Mb-θb behavior. .............................................................................. 456

Figure 6.209: Test 4 beam post-tensioning strand forces – (a) strand 1; (b) strand 2; (c) strand 3. ......................................................................................................... 458

Figure 6.210: Test 4 FLC-θb behavior – (a) strand 1; (b) strand 2; (c) strand 3. .............. 459

Figure 6.211: Test 4 beam post-tensioning force versus chord rotation behavior – (a) using beam displacements; (b) using load block displacements. .................. 460

Figure 6.212: Test 4 south end top angle-to-wall connection strand forces – (a) east strand; (b) west strand. ........................................................................................ 462

Figure 6.213: Test 4 south end top angle-to-wall connection strand forces versus beam chord rotation – (a) FLC3-θb; (b) FLC4-θb.............................................................. 462


Figure 6.215: Test 4 south end seat angle-to-wall connection strand forces versus beam chord rotation – (a) FLC5-θb; (b) FLC6-θb.............................................................. 463

Figure 6.216: Test 4 south end total angle-to-wall connection strand forces versus beam chord rotation – (a) top connection; (b) seat connection. ................................... 464

Figure 6.217: Test 4 vertical force on the wall test region, Fwt – (a) Fwt-test duration; (b) Fwt-θb ............................................................................................................. 465

Figure 6.218: Test 4 south end beam vertical displacements – (a) measured, ∆DT9; (b) adjusted, ∆DT9,y; (c) difference, ∆DT9,y-∆DT9. .................................................. 467


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Figure 6.221: Test 4 beam vertical displacements versus beam chord rotation – (a) ∆DT9-θb; (b) ∆DT10-θb. ..................................................................................... 469

Figure 6.222: Test 4 beam chord rotation – (a) θb from ∆DT9 and ∆DT10; (b) θb,lb from ∆LB,y. ............................................................................................... 470

Figure 6.223: Test 4 percent difference between θb and θb,lb. ......................................... 470

Figure 6.224: Test 4 difference between θb and θb,lb....................................................... 471







Figure 6.231: Test 4 load block displacements versus beam chord rotation – (a) ∆DT4-θb; (b) ∆DT5-θb; (c) ∆DT3,x-θb. ..................................................................................... 479


Figure 6.233: Test 4 load block centroid displacements versus beam chord rotation – (a) x-displacement-θb; (b) y-displacement-θb; (c) rotation-θb. ............................ 481


Figure 6.235: Test 4 reaction block displacements versus beam chord rotation – (a) ∆DT7-θb; (b) ∆DT8-θb; (c) ∆DT6-θb. ................................................................... 484

Figure 6.236: Test 4 reaction block centroid displacements – (a) x-y displacements; (b) rotation; (c) x-displacements; (d) y-displacements. ....................................... 485

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Figure 6.237: Test 4 reaction block centroid displacements versus beam chord rotation – (a) x-displacements; (b) y-displacements; (c) rotation. ....................................... 486




Figure 6.241: Test 4 beam-to-reaction-block interface LVDT displacements versus beam chord rotation – (a) ∆DT11-θb; (b) ∆DT13-θb; (c) ∆DT12-θb. ..................................... 491

Figure 6.242: Test 4 contact depth at beam-to-reaction-block interface – (a) method 1 using ∆DT11, ∆DT12, and ∆DT13; (b) method 2 using RT2, DT11, and DT13; (c) method 3 using RT2 and DT12; (d) method 4 using θb and DT12; (e) method 5 using θb, DT11, and DT13. ................................................................................. 494

Figure 6.243: Test 4 gap opening at beam-to-reaction-block interface – (a) method 1 using ∆DT11, ∆DT12, and ∆DT13; (b) method 2 using RT2, DT11, and DT13; (c) method 3 using RT2 and DT12; (d) method 4 using ∆DT12 and θb; (e) method 5 using θb, DT11, and DT13. ................................................................................. 495




Figure 6.247: Test 4 wall test region concrete deformations versus beam chord rotation –(a) ∆DT14-θb; (b) ∆DT15-θb. .................................................................................... 498



Figure 6.250: Test 4 beam looping reinforcement top longitudinal leg strains versus beam chord rotation – (a) ε6(1)T-E-θb; (b) ε6(1)T-W-θb; (c) ε6(2)T-E-θb; (d) ε6(2)T-W-θb; (e) ε6(3)T-E-θb; (f) ε6(3)T-W-θb; (g) ε6MT-E-θb; (h) ε6MT-W-θb. ..................................... 502

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Figure 6.251: Test 4 beam looping reinforcement bottom longitudinal leg strains versus beam chord rotation – (a) ε6(1)B-E-θb; (b) ε6(1)B-W-θb; (c) ε6(2)B-E-θb; (d) ε6(2)B-W-θb; (e) ε6(3)B-E-θb; (f) ε6(3)B-W-θb; (g) ε6MB-E-θb; (h) ε6MB-W-θb. ..................................... 504

Figure 6.252: Test 4 beam looping reinforcement vertical leg strains – (a) ε6SE(E)-E; (b) ε6SE(E)-W; (c) ε6SE(I)-E; (d) ε6SE(I)-W. .................................................................. 506

Figure 6.253: Test 4 beam looping reinforcement vertical leg strains versus beam chord rotation – (a) ε6SE(E)-E-θb; (b) ε6SE(E)-W-θb; (c) ε6SE(I)-E-θb; (d) ε6SE(I)-W-θb. ............. 507


Figure 6.255: Test 4 beam midspan transverse hoop reinforcement strains versus beam chord rotation – (a) εMH-E-θb; (b) εMH-W-θb. ......................................................... 508



Figure 6.258: Test 4 No. 3 top hoop support bar strains versus beam chord rotation – (a) ε3THT-(1)-θb; (b) ε3THB-(1)-θb; (c) ε3THT-(2)-θb; (d) ε3THB-(2)-θb. ............................. 511

Figure 6.259: Test 4 No. 3 bottom hoop support bar strains versus beam chord rotation –(a) ε3BHB-(1)-θb; (b) ε3BHT-(1)-θb; (c) ε3BHB-(2)-θb; (d) ε3BHT-(2)-θb. ............................ 512



Figure 6.262: Test 4 beam end confinement hoop east leg strains versus beam chord rotation – (a) ε1HB-E-θb; (b) ε2HB-E-θb; (c) ε3HB-E-θb; (d) ε4HB-E-θb. ........................ 515

Figure 6.263: Test 4 beam end confinement hoop west leg strains versus beam chord rotation – (a) ε1HB-W-θb; (b) ε2HB-W-θb; (c) ε3HB-W-θb; (d) ε4HB-W-θb....................... 516

Figure 6.264: Test 4 crack patterns – (a) θb = 0.125%; (b) θb = 0.175%; (c) θb = 0.25%; (d) θb = 0.35%; (e) θb = 0.5%; (f) θb = 0.75%; (g) θb = 1.0%; (h) θb = 1.5%; (i) θb = 2.25%; (j) θb = 3.33%. ............................................................................ 517

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VOLUME III

CHAPTER 7:

Figure 7.1: Test 3A angle – (a) hole pattern and locations; (b) photograph of angle. .... 521

Figure 7.2: Test 3A overall photographs – (a) pre-test undisplaced position; (b) θb = 3.33%; (c) θb = –3.33%; (d) θb = 5.0%; (e) θb = –5.0%; (f) final post-test undisplaced position............................................................................................ 524

Figure 7.3: Test 3A beam south end photographs – (a) pre-test undisplaced position; (b) θb = 3.33%; (c) θb = –3.33%; (d) θb = 5.0%; (e) θb = –5.0%; (f) final post-test undisplaced position............................................................................................ 525

Figure 7.4: Test 3A south beam end damage propagation – positive and negative rotations............................................................................................................... 526

Figure 7.5: Test 3A coupling beam shear force versus chord rotation behavior – (a) using beam displacements; (b) using load block displacements. ................................. 528

Figure 7.6: Test 3A angle fracture – (a) side view; (b) front view. ................................ 529

Figure 7.7: Test 3A Mb-θb behavior. ............................................................................... 530

Figure 7.8: Test 3A beam post-tensioning strand forces – (a) strand 1; (b) strand 2; (c) strand 3. ......................................................................................................... 532

Figure 7.9: Test 3A FLC-θb behavior – (a) strand 1; (b) strand 2; strand 3. ..................... 533

Figure 7.10: Test 3A beam post-tensioning force versus chord rotation behavior – (a) using beam displacements; (b) using load block displacements. .................. 534

Figure 7.11: Test 3A south end top angle-to-wall connection strand forces – (a) east strand; (b) west strand. ........................................................................................ 536

Figure 7.12: Test 3A south end top angle-to-wall connection strand forces versus beam chord rotation – (a) FLC3-θb; (b) FLC4-θb.............................................................. 537

Figure 7.13: Test 3A south end seat angle-to-wall connection strand forces – (a) east strand; (b) west strand. ........................................................................................ 537

Figure 7.14: Test 3A south end seat angle-to-wall connection strand forces versus beam chord rotation – (a) FLC5-θb; (b) FLC6-θb.............................................................. 538

Figure 7.15: Test 3A south end total angle-to-wall connection strand forces versus beam chord rotation – (a) top connection; (b) seat connection. ................................... 538

Figure 7.16: Test 3A vertical force on wall test region, Fwt – (a) Fwt-test duration; (b) Fwt-θb. ............................................................................................................ 540

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Figure 7.17: Test 3A south end beam vertical displacements – (a) measured, ∆DT9; (b) adjusted, ∆DT9,y; (c) difference, ∆DT9,y-∆DT9. .................................................. 542

Figure 7.18: Test 3A north end beam vertical displacements – (a) measured, ∆DT10; (b) adjusted, ∆DT10,y; (c) difference, ∆DT10,y-∆DT10. .............................................. 543

Figure 7.19: Test 3A percent difference between measured and adjusted displacements versus beam chord rotation – (a) south end, DT9; (b) north end, DT10. ............ 544

Figure 7.20: Test 3A beam vertical displacements versus beam chord rotation – (a) ∆DT9-θb; (b) ∆DT10-θb. ..................................................................................... 544

Figure 7.21: Test 3A beam chord rotation – (a) θb from ∆DT9 and ∆DT10; (b) θb,lb from ∆LB,y. ............................................................................................... 545

Figure 7.22: Test 3A percent difference between θb and θb,lb. ........................................ 546

Figure 7.23: Test 3A difference between θb and θb,lb. ..................................................... 546

Figure 7.24: Test 3A beam inclinometer rotations – (a) near beam south end, θRT1; (b) near beam midspan, θRT2. .............................................................................. 548

Figure 7.25: Test 3A difference between beam inclinometer rotations and beam chord rotations – (a) RT1; (b) RT2; (c) beam deflected shape. .................................... 549

Figure 7.26: Test 3A load block horizontal displacements – (a) measured, ∆DT3; (b) adjusted, ∆DT3,x; (c) percent difference. ......................................................... 552

Figure 7.27: Test 3A load block north end vertical displacements – (a) measured, ∆DT4; (b) adjusted, ∆DT4,y; (c) percent difference. ......................................................... 553

Figure 7.28: Test 3A load block south end vertical displacements – (a) measured, ∆DT5; (b) adjusted, ∆DT5,y; (c) percent difference. ......................................................... 554

Figure 7.29: Test 3A percent difference between measured and adjusted displacements versus beam chord rotation – (a) DT4; (b) DT5. ................................................ 554

Figure 7.30: Test 3A load block displacements versus beam chord rotation – (a) ∆DT4-θb; (b) ∆DT5-θb; (c) ∆DT3,x-θb. ..................................................................................... 555

Figure 7.31: Test 3A load block centroid displacements – (a) x-y displacements; (b) rotation; (c) x-displacements; (d) y-displacements. ....................................... 556

Figure 7.32: Test 3A load block centroid displacements versus beam chord rotation – (a) x-displacement-θb; (b) y-displacement-θb; (c) rotation-θb. ............................ 557

Figure 7.33: Test 3A reaction block displacements – (a) ΔDT6; (b) ΔDT7; (c) ΔDT8. ........ 559

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Figure 7.34: Test 3A reaction block displacements versus beam chord rotation – (a) ∆DT7-θb; (b) ∆DT8-θb; (c) ∆DT6-θb. ................................................................... 560

Figure 7.35: Test 3A reaction block centroid displacements – (a) x-y displacements; (b) rotation; (c) x-displacements; (d) y-displacements. ....................................... 561

Figure 7.36: Test 3A reaction block centroid displacements versus beam chord rotation – (a) x-displacements; (b y-displacements; (c) rotation. ........................................ 562

Figure 7.37: Test 3A beam-to-reaction-block interface top LVDT displacements – (a) measured, ∆DT11; (b) adjusted, ∆DT11,x; (c) percent difference. ...................... 564

Figure 7.38: Test 3A beam-to-reaction-block interface middle LVDT displacements – (a) measured, ∆DT12; (b) adjusted, ∆DT12,x; (c) percent difference. ...................... 565

Figure 7.39: Test 3A beam-to-reaction-block interface bottom LVDT displacements – (a) measured, ∆DT13; (b) adjusted, ∆DT13,x; (c) percent difference. ...................... 566

Figure 7.40: Test 3A beam-to-reaction-block interface LVDT displacements versus beam chord rotation – (a) ∆DT11-θb; (b) ∆DT13-θb; (c) ∆DT12-θb. ..................................... 567

Figure 7.41: Test 3A contact depth at beam-to-reaction-block interface – (a) method 1 using ∆DT11, ∆DT12, and ∆DT13; (b) method 2 using RT1, DT11, and DT13; (c) method 3 using RT1 and DT12; (d) method 4 using ∆DT12 and θb; (e) method 5 using θb, DT11, and DT13. ................................................................................. 570

Figure 7.42: Test 3A gap opening at beam-to-reaction-block interface – (a) method 1 using ∆DT11, ∆DT12, and ∆DT13; (b) method 2 using RT1, DT11, and DT13; (c) method 3 using RT1 and DT12; (d) method 4 using ∆DT12 and θb; (e) method 5 using θb, DT11, and DT13. ................................................................................. 571

Figure 7.43: Test 3A gap opening at beam-to-reaction-block interface using method 4.............................................................................................................................. 572

Figure 7.44: Test 3A contact depth at beam-to-reaction-block interface – (a) method 4 using ∆DT12 and θb; (b) 2.25% beam chord rotation cycle; (c) 5.0% beam chord rotation cycle. ...................................................................................................... 572

Figure 7.45: Test 3A wall test region concrete deformations – (a) DT14; (b) DT15. .... 574

Figure 7.46: Test 3A wall test region concrete deformations versus beam chord rotation –(a) ∆DT14-θb; (b) ∆DT15-θb. .................................................................................... 574

Figure 7.47: Test 3A beam looping reinforcement top longitudinal leg strains – (a) ε6(1)T-E; (b) ε6(1)T-W; (c) ε6(2)T-E; (d) ε6(2)T-W; (e) ε6(3)T-E; (f) ε6(3)T-W; (g) ε6MT-E; (h) ε6MT-W. ............................................................................................................ 576

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Figure 7.48: Test 3A beam looping reinforcement bottom longitudinal leg strains – (a) ε6(1)B-E; (b) ε6(1)B-W; (c) ε6(2)B-E; (d) ε6(2)B-W; (e) ε6(3)B-E; (f) ε6(3)B-W; (g) ε6MB-E; (h) ε6MB-W. ............................................................................................................ 577

Figure 7.49: Test 3A beam looping reinforcement top longitudinal leg strains versus beam chord rotation – (a) ε6(1)T-E-θb; (b) ε6(1)T-W-θb; (c) ε6(2)T-E-θb; (d) ε6(2)T-W-θb; (e) ε6(3)T-E-θb; (f) ε6(3)T-W-θb; (g) ε6MT-E-θb; (h) ε6MT-W-θb. ..................................... 579

Figure 7.50: Test 3A beam looping reinforcement bottom longitudinal leg strains versus beam chord rotation – (a) ε6(1)B-E-θb; (b) ε6(1)B-W-θb; (c) ε6(2)B-E-θb; (d) ε6(2)B-W-θb; (e) ε6(3)B-E-θb; (f) ε6(3)B-W-θb; (g) ε6MB-E-θb; (h) ε6MB-W-θb. ..................................... 580

Figure 7.51: Test 3A beam looping reinforcement vertical leg strains – (a) ε6SE(E)-E; (b) ε6SE(E)-W; (c) ε6SE(I)-E; (d) ε6SE(I)-W. .................................................................. 583

Figure 7.52: Test 3A beam looping reinforcement vertical leg strains versus beam chord rotation – (a) ε6SE(E)-E-θb; (b) ε6SE(E)-W-θb; (c) ε6SE(I)-E-θb; (d) ε6SE(I)-W-θb. ............. 584

Figure 7.53: Test 3A beam midspan transverse hoop reinforcement strains – (a) εMH-E; (b) εMH-W. ............................................................................................................. 584

Figure 7.54: Test 3A beam midspan transverse hoop reinforcement strains versus beam chord rotation – (a) εMH-E-θb; (b) εMH-W-θb. ......................................................... 585

Figure 7.55: Test 3A No. 3 top hoop support bar strains – (a) ε3THT-(1); (b) ε3THB-(1); (c) ε3THT-(2); (d) ε3THB-(2). ...................................................................................... 586

Figure 7.56: Test 3A No. 3 bottom hoop support bar strains – (a) ε3BHB-(1); (b) ε3BHT-(1); (c) ε3BHB-(2); (d) ε3BHT-(2). ...................................................................................... 587

Figure 7.57: Test 3A No. 3 top hoop support bar strains versus beam chord rotation – (a) ε3THT-(1)-θb; (b) ε3THB-(1)-θb; (c) ε3THT-(2)-θb; (d) ε3THB-(2)-θb. ............................. 588

Figure 7.58: Test 3A No. 3 bottom hoop support bar strains versus beam chord rotation –(a) ε3BHB-(1)-θb; (b) ε3BHT-(1)-θb; (c) ε3BHB-(2)-θb; (d) ε3BHT-(2)-θb. ............................ 589

Figure 7.59: Test 3A beam end confinement hoop east leg strains – (a) ε1HB-E; (b) ε2HB-E; (c) ε3HB-E; (d) ε4HB-E. ............................................................................................ 590

Figure 7.60: Test 3A beam end confinement hoop west leg strains – (a) ε1HB-W; (b) ε2HB-W; (c) ε3HB-W; (d) ε4HB-W. ........................................................................................... 591

Figure 7.61: Test 3A beam end confinement hoop east leg strains versus beam chord rotation – (a) ε1HBE-θb; (b) ε2HBE-θb; (c) ε3HBE-θb; (d) ε4HBE-θb. ........................... 592

Figure 7.62: Test 3A beam end confinement hoop west leg strains versus beam chord rotation – (a) ε1HBW-θb; (b) ε2HBW-θb; (c) ε3HBW-θb; (d) ε4HBW-θb. ......................... 593

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Figure 7.63: Test 3B overall photographs – (a) pre-test undisplaced position; (b) θb = 3.33%; (c) θb = –3.33%; (d) θb = 8.0%; (e) θb = –8.0%; (f) final post-test undisplaced position............................................................................................ 598

Figure 7.64: Test 3B beam south end photographs – (a) pre-test undisplaced position; (b) θb = 3.33%; (c) θb = –3.33%; (d) θb = 8.0%; (e) θb = –8.0%; (f) final post-test undisplaced position............................................................................................ 599

Figure 7.65: Test 3B beam south end damage propagation – positive and negative rotations............................................................................................................... 600

Figure 7.66: Test 3B angle fracture – (a) side view; (b) isometric view. ....................... 600

Figure 7.67: Test 3B angle-to-wall connection plates. ................................................... 601

Figure 7.68: Test 3B coupling beam shear force versus chord rotation behavior – (a) using beam displacements; (b) using load block displacements. ................................. 603

Figure 7.69: Test 3B Mb-θb behavior. ............................................................................. 604

Figure 7.70: Test 3B beam post-tensioning strand forces – (a) strand 1; (b) strand 2; (c) strand 3. ......................................................................................................... 606

Figure 7.71: Test 3B FLC-θb behavior – (a) strand 1; (b) strand 2; (c) strand 3. ............. 607

Figure 7.72: Test 3B beam post-tensioning force versus chord rotation behavior – (a) using beam displacements; (b) using load block displacements. .................. 608

Figure 7.73: Test 3B south end top angle-to-wall connection strand forces – (a) east strand; (b) west strand. ........................................................................................ 610

Figure 7.74: Test 3B south end top angle-to-wall connection strand forces versus beam chord rotation – (a) FLC3-θb; (b) FLC4-θb.............................................................. 610

Figure 7.75: Test 3B south end seat angle-to-wall connection strand forces – (a) east strand; (b) west strand. ........................................................................................ 611

Figure 7.76: Test 3B south end seat angle-to-wall connection strand forces versus beam chord rotation – (a) FLC5-θb; (b) FLC6-θb.............................................................. 611

Figure 7.77: Test 3B south end total angle-to-wall connection strand forces versus beam chord rotation – (a) top connection; (b) seat connection. ................................... 612

Figure 7.78: Test 3B vertical force on the wall test region, Fwt – (a) Fwt-test duration; (b) Fwt-θb. ............................................................................................................ 613

Figure 7.79: Test 3B south end beam vertical displacements – (a) measured, ∆DT9; (b) adjusted, ∆DT9,y; (c) difference, ∆DT9,y-∆DT9. .................................................. 615

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Figure 7.80: Test 3B north end beam vertical displacements – (a) measured, ∆DT10; (b) adjusted, ∆DT10,y; (c) difference, ∆DT10,y-∆DT10. .............................................. 616

Figure 7.81: Test 3B percent difference between measured and adjusted displacements versus beam chord rotation – (a) south end, DT9; (b) north end, DT10. ............ 617

Figure 7.82: Test 3B beam vertical displacements versus beam chord rotation – (a) ∆DT9-θb; (b) ∆DT10-θb. ..................................................................................... 617

Figure 7.83: Test 3B beam chord rotation – (a) θb from ∆DT9 and ∆DT10; (b) θb,lb from ∆LB,y. ............................................................................................... 618

Figure 7.84: Test 3B percent difference between θb and θb,lb. ........................................ 619

Figure 7.85: Test 3B difference between θb and θb,lb. ..................................................... 619

Figure 7.86: Test 3B beam inclinometer rotations – (a) near beam south end, θRT1; (b) near beam midspan, θRT2. .............................................................................. 621

Figure 7.87: Test 3B difference between beam inclinometer rotations and beam chord rotations – (a) RT1; (b) RT2; (c) beam deflected shape. .................................... 622

Figure 7.88: Test 3B load block horizontal displacements – (a) measured, ∆DT3; (b) adjusted, ∆DT3,x; (c) percent difference. ......................................................... 625

Figure 7.89: Test 3B load block north end vertical displacements – (a) measured, ∆DT4; (b) adjusted, ∆DT4,y; (c) percent difference. ......................................................... 626

Figure 7.90: Test 3B load block south end vertical displacements – (a) measured, ∆DT5; (b) adjusted, ∆DT5,y; (c) percent difference. ......................................................... 627

Figure 7.91: Test 3B percent difference between measured and adjusted displacements versus beam chord rotation – (a) DT4; (b) DT5. ................................................ 627

Figure 7.92: Test 3B load block displacements versus beam chord rotation – (a) ∆DT4-θb; (b) ∆DT5-θb; (c) ∆DT3,x-θb. ..................................................................................... 628

Figure 7.93: Test 3B load block centroid displacements – (a) x-y displacements; (b) rotation; (c) x-displacements; (d) y-displacements. ....................................... 629

Figure 7.94: Test 3B load block centroid displacements versus beam chord rotation – (a) x-displacement-θb; (b) y-displacement-θb; (c) rotation-θb. ............................ 630

Figure 7.95: Test 3B reaction block displacements – (a) ΔDT6; (b) ΔDT7; (c) ΔDT8. ........ 632

Figure 7.96: Test 3B reaction block displacements versus beam chord rotation – (a) ∆DT7-θb; (b) ∆DT8-θb; (c) ∆DT6-θb. ................................................................... 633

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Figure 7.97: Test 3B reaction block centroid displacements – (a) x-y displacements; (b) rotation; (c) x-displacements; (d) y-displacements. ....................................... 634

Figure 7.98: Test 3B reaction block centroid displacements versus beam chord rotation – (a) x-displacements; (b y-displacements; (c) rotation. ........................................ 635

Figure 7.99: Test 3B beam-to-reaction-block interface top LVDT displacements – (a) measured, ∆DT11; (b) adjusted, ∆DT11,x; (c) percent difference. ...................... 637

Figure 7.100: Test 3B beam-to-reaction-block interface middle LVDT displacements – (a) measured, ∆DT12; (b) adjusted, ∆DT12,x; (c) percent difference. ...................... 638

Figure 7.101: Test 3B beam-to-reaction-block interface bottom LVDT displacements – (a) measured, ∆DT13; (b) adjusted, ∆DT13,x; (c) percent difference. ...................... 639

Figure 7.102: Test 3B beam-to-reaction-block interface LVDT displacements versus beam chord rotation – (a) ∆DT11-θb; (b) ∆DT13-θb; (c) ∆DT12-θb. ........................... 640

Figure 7.103: Test 3B contact depth at beam-to-reaction-block interface – (a) method 1 using ∆DT11, ∆DT12, and ∆DT13; (b) method 2 using RT1, DT11, and DT13; (c) method 3 using RT1 and DT12; (d) method 4 using ∆DT12 and θb; (e) method 5 using θb, DT11, and DT13. ................................................................................. 643

Figure 7.104: Test 3B gap opening at beam-to-reaction-block interface – (a) method 1 using ∆DT11, ∆DT12, and ∆DT13; (b) method 2 using RT1, DT11, and DT13; (c) method 3 using RT1 and DT12; (d) method 4 using ∆DT12 and θb; (e) method 5 using θb, DT11, and DT13. ................................................................................. 644

Figure 7.105: Test 3B gap opening at beam-to-reaction-block interface method 4. ...... 645

Figure 7.106: Test 3B contact depth at beam-to-reaction-block interface – (a) method 4 using ∆DT12 and θb; (b) 2.25% beam chord rotation cycle; (c) 5.0% beam chord rotation cycle. ...................................................................................................... 645

Figure 7.107: Test 3B wall test region concrete deformations – (a) DT14; (b) DT15. .. 647

Figure 7.108: Test 3B wall test region concrete deformations versus beam chord rotation – (a) ∆DT14-θb; (b) ∆DT15-θb. ................................................................................. 647

Figure 7.109: Test 3B beam looping reinforcement top longitudinal leg strains – (a) ε6(1)T-E; (b) ε6(1)T-W; (c) ε6(2)T-E; (d) ε6(2)T-W; (e) ε6(3)T-E; (f) ε6(3)T-W; (g) ε6MT-E; (h) ε6MT-W. ............................................................................................................ 649

Figure 7.110: Test 3B beam looping reinforcement bottom longitudinal leg strains – (a) ε6(1)B-E; (b) ε6(1)B-W; (c) ε6(2)B-E; (d) ε6(2)B-W; (e) ε6(3)B-E; (f) ε6(3)B-W; (g) ε6MB-E; (h) ε6MB-W. ............................................................................................................ 650

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Figure 7.111: Test 3B beam looping reinforcement top longitudinal leg strains versus beam chord rotation – (a) ε6(1)T-E-θb; (b) ε6(1)T-W-θb; (c) ε6(2)T-E-θb; (d) ε6(2)T-W-θb; (e) ε6(3)T-E-θb; (f) ε6(3)T-W-θb; (g) ε6MT-E-θb; (h) ε6MT-W-θb. ..................................... 652

Figure 7.112: Test 3B beam looping reinforcement bottom longitudinal leg strains versus beam chord rotation – (a) ε6(1)B-E-θb; (b) ε6(1)B-W-θb; (c) ε6(2)B-E-θb; (d) ε6(2)B-W-θb; (e) ε6(3)B-E-θb; (f) ε6(3)B-W-θb; (g) ε6MB-E-θb; (h) ε6MB-W-θb. ..................................... 653

Figure 7.113: Test 3B beam looping reinforcement vertical leg strains – (a) ε6SE(E)-E; (b) ε6SE(E)-W; (c) ε6SE(I)-E; (d) ε6SE(I)-W. ................................................................... 656

Figure 7.114: Test 3B beam looping reinforcement vertical leg strains versus beam chord rotation – (a) ε6SE(E)-E-θb; (b) ε6SE(E)-W-θb; (c) ε6SE(I)-E-θb; (d) ε6SE(I)-W-θb. ............. 657

Figure 7.115: Test 3B beam midspan transverse hoop reinforcement strains – (a) εMH-E; (b) εMH-W. ............................................................................................................. 657

Figure 7.116: Test 3B beam midspan transverse hoop reinforcement strains versus beam chord rotation – (a) εMH-E-θb; (b) εMH-W-θb. ......................................................... 658

Figure 7.117: Test 3B No. 3 top hoop support bar strains – (a) ε3THT-(1); (b) ε3THB-(1); (c) ε3THT-(2); (d) ε3THB-(2). ...................................................................................... 659

Figure 7.118: Test 3B No. 3 bottom hoop support bar strains – (a) ε3BHB-(1); (b) ε3BHT-(1); (c) ε3BHB-(2); (d) ε3BHT-(2). ...................................................................................... 660

Figure 7.119: Test 3B No. 3 top hoop support bar strains versus beam chord rotation – (a) ε3THT-(1)-θb; (b) ε3THB-(1)-θb; (c) ε3THT-(2)-θb; (d) ε3THB-(2)-θb. ............................. 661

Figure 7.120: Test 3B No. 3 bottom hoop support bar strains versus beam chord rotation – (a) ε3BHB-(1)-θb; (b) ε3BHT-(1)-θb; (c) ε3BHB-(2)-θb; (d) ε3BHT-(2)-θb. ......................... 662

Figure 7.121: Test 3B beam end confinement hoop east leg strains – (a) ε1HB-E; (b) ε2HB-E; (c) ε3HB-E; (d) ε4HB-E. ............................................................................................ 663

Figure 7.122: Test 3B beam end confinement hoop west leg strains – (a) ε1HB-W; (b) ε2HB-W; (c) ε3HB-W; (d) ε4HB-W........................................................................... 664

Figure 7.123: Test 3B beam end confinement hoop east leg strains versus beam chord rotation – (a) ε1HBE-θb; (b) ε2HBE-θb; (c) ε3HBE-θb; (d) ε4HBE-θb. ........................... 665

Figure 7.124: Test 3B beam end confinement hoop west leg strains versus beam chord rotation – (a) ε1HBW-θb; (b) ε2HBW-θb; (c) ε3HBW-θb; (d) ε4HBW-θb. ......................... 666

Figure 7.125: Test 4A angle with short tapered horizontal leg. ...................................... 669

Figure 7.126: Test 4A overall photographs – (a) pre-test undisplaced position; (b) θb = 3.33%; (c) θb = –3.33%; (d) final post-test undisplaced position. ......... 671

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Figure 7.127: Test 4A beam south end photographs – (a) pre-test undisplaced position; (b) θb = 3.33%; (c) θb = –3.33%; (d) final post-test un-displaced position. ........ 672

Figure 7.128: Test 4A beam south end damage propagation – positive and negative rotations............................................................................................................... 673

Figure 7.129: Test 4A coupling beam shear force versus chord rotation behavior – (a) using beam displacements; (b) using load block displacements. .................. 675

Figure 7.130: Test 4A Mb-θb behavior. ........................................................................... 676

Figure 7.131: Test 4A beam post-tensioning strand forces – (a) strand 1; (b) strand 2; (c) strand 3. ......................................................................................................... 678

Figure 7.132: Test 4A FLC-θb behavior – (a) strand 1; (b) strand 2; (c) strand 3. ........... 679

Figure 7.133: Test 4A beam post-tensioning force versus chord rotation behavior – (a) using beam displacements; (b) using load block displacements. .................. 680

Figure 7.134: Test 4A vertical force on the wall test region, Fwt – (a) Fwt-test duration; (b) Fwt-θb. ............................................................................................................ 682

Figure 7.135: Test 4A south end beam vertical displacements – (a) measured, ∆DT9; (b) adjusted, ∆DT9,y; (c) difference, ∆DT9,y-∆DT9. .................................................. 684

Figure 7.136: Test 4A north end beam vertical displacements – (a) measured, ∆DT10; (b) adjusted, ∆DT10,y; (c) difference, ∆DT10,y-∆DT10. .............................................. 685

Figure 7.137: Test 4A percent difference between measured and adjusted displacements – (a) south end, DT9; (b) north end, DT10. ........................................................... 686

Figure 7.138: Test 4A beam vertical displacement versus beam chord rotation – (a) ∆DT9-θb; (b) ∆DT10-θb. ..................................................................................... 686

Figure 7.139: Beam chord rotation – (a) θb from ∆DT9 and ∆DT10; (b) θb,lb from ∆LB,y. ... 688

Figure 7.140: Test 4A percent difference between θb and θb,lb. ...................................... 688

Figure 7.141: Test 4A difference between θb and θb,lb. ................................................... 689

Figure 7.142: Test 4A beam inclinometer rotations – (a) near beam south end, θRT1; (b) near beam midspan, θRT2. .............................................................................. 690

Figure 7.143: Test 4A difference between beam inclinometer rotations and beam chord rotations – (a) RT1; (b) RT2; (c) beam deflected shape. .................................... 691

Figure 7.144: Test 4A load block horizontal displacements – (a) measured, ∆DT3; (b) adjusted, ∆DT3,x; (c) percent difference. ......................................................... 694

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Figure 7.145: Test 4A load block north end vertical displacements – (a) measured, ∆DT4; (b) adjusted, ∆DT4,y; (c) percent difference. ......................................................... 695

Figure 7.146: Test 4A load block south end vertical displacements – (a) measured, ∆DT5; (b) adjusted, ∆DT5,y; (c) percent difference. ......................................................... 696

Figure 7.147: Test 4A percent difference between measured and adjusted displacements versus beam chord rotation – (a) DT4; (b) DT5. ................................................ 696

Figure 7.148: Test 4A load block displacements versus beam chord rotation – (a) ∆DT4-θb; (b) ∆DT5-θb; (c) ∆DT3,x-θb. ..................................................................................... 697

Figure 7.149: Test 4A load block centroid displacements – (a) x-y displacements; (b) rotation; (c) x-displacements; (d) y-displacements. ....................................... 698

Figure 7.150: Test 4A load block centroid displacements versus beam chord rotation – (a) x-displacement-θb; (b) y-displacement-θb; (c) rotation-θb. ............................ 699

Figure 7.151: Test 4A reaction block displacements – (a) ΔDT6; (b) ΔDT7; (c) ΔDT8. ...... 701

Figure 7.152: Test 4A reaction block displacements versus beam chord rotation – (a) ∆DT7-θb; (b) ∆DT8-θb; (c) ∆DT6-θb. ................................................................... 702

Figure 7.153: Test 4A reaction block centroid displacements – (a) x-y displacements; (b) rotation; (c) x-displacements; (d) y-displacements. ....................................... 703

Figure 7.154: Test 4A reaction block centroid displacements versus beam chord rotation – (a) x-displacements; (b y-displacements; (c) rotation. ..................................... 704

Figure 7.155: Test 4A beam-to-reaction-block interface top LVDT displacements – (a) measured, ∆DT11; (b) adjusted, ∆DT11,x; (c) percent difference. ...................... 706

Figure 7.156: Test 4A beam-to-reaction-block interface middle LVDT displacements – (a) measured, ∆DT12; (b) adjusted, ∆DT12,x; (c) percent difference. ...................... 707

Figure 7.157: Test 4A beam-to-reaction-block interface bottom LVDT displacements – (a) measured, ∆DT13; (b) adjusted, ∆DT13,x; (c) percent difference ....................... 708

Figure 7.158: Test 4A beam-to-reaction-block interface LVDT displacements versus beam chord rotation – (a) ∆DT11-θb; (b) ∆DT13-θb; (c) ∆DT12-θb. ........................... 709

Figure 7.159: Test 4A contact depth at beam-to-reaction-block interface – (a) method 1 using ∆DT11, ∆DT12, and ∆DT13; (b) method 2 using RT2, DT11, and DT13; (c) method 3 using RT2 and DT12; (d) method 4 using ∆DT12 and θb; (e) method 5 using θb, DT11, and DT13. ................................................................................. 712

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Figure 7.160: Test 4A gap opening at beam-to-reaction-block interface – (a) method 1 using ∆DT11, ∆DT12, and ∆DT13; (b) method 2 using RT2, DT11, and DT13; (c) method 3 using RT2 and DT12; (d) method 4 using ∆DT12 and θb; (e) method 5 using θb, DT11, and DT13. ................................................................................. 713

Figure 7.161: Test 4A gap opening at beam-to-reaction-block interface using method 4.............................................................................................................................. 714

Figure 7.162: Test 4A contact depth at beam-to-reaction-block interface – (a) method 4 using ∆DT12 and θb; (b) 0.75% beam chord rotation cycle; (c) 3.33% beam chord rotation cycle. ...................................................................................................... 714

Figure 7.163: Test 4A wall test region concrete deformations – (a) DT14; (b) DT15. .. 716

Figure 7.164: Test 4A wall test region concrete deformations – (a) ∆DT14-θb; (b) ∆DT15-θb.............................................................................................................................. 716

Figure 7.165: Test 4A beam looping reinforcement top longitudinal leg strains – (a) ε6(1)T-E; (b) ε6(1)T-W; (c) ε6(2)T-E; (d) ε6(2)T-W; (e) ε6(3)T-E; (f) ε6(3)T-W; (g) ε6MT-E; (h) ε6MT-W. ............................................................................................................ 719

Figure 7.166: Test 4A beam looping reinforcement bottom longitudinal leg strains – (a) ε6(1)B-E; (b) ε6(1)B-W; (c) ε6(2)B-E; (d) ε6(2)B-W; (e) ε6(3)B-E; (f) ε6(3)B-W; (g) ε6MB-E; (h) ε6MB-W. ............................................................................................................ 720

Figure 7.167: Test 4A beam looping reinforcement top longitudinal leg strains versus beam chord rotation – (a) ε6(1)T-E-θb; (b) ε6(1)T-W-θb; (c) ε6(2)T-E-θb; (d) ε6(2)T-W-θb; (e) ε6(3)T-E-θb; (f) ε6(3)T-W-θb; (g) ε6MT-E-θb; (h) ε6MT-W-θb. ..................................... 721

Figure 7.168: Test 4A beam looping reinforcement bottom longitudinal leg strains versus beam chord rotation – (a) ε6(1)B-E-θb; (b) ε6(1)B-W-θb; (c) ε6(2)B-E-θb; (d) ε6(2)B-W-θb; (e) ε6(3)B-E-θb; (f) ε6(3)B-W-θb; (g) ε6MB-E-θb; (h) ε6MB-W-θb. ..................................... 723

Figure 7.169: Test 4A beam looping reinforcement vertical leg strains – (a) ε6SE(E)-E; (b) ε6SE(E)-W; (c) ε6SE(I)-E; (d) ε6SE(I)-W. ................................................................... 726

Figure 7.170: Test 4A beam looping reinforcement vertical leg strains versus beam chord rotation – (a) ε6SE(E)-E-θb; (b) ε6SE(E)-W-θb; (c) ε6SE(I)-E-θb; (d) ε6SE(I)-W-θb. ............. 727

Figure 7.171: Test 4A beam midspan transverse hoop reinforcement strains – (a) εMH-E; (b) εMH-W. ............................................................................................................. 727

Figure 7.172: Test 4A beam midspan transverse hoop reinforcement strains versus beam chord rotation – (a) εMH-E-θb; (b) εMH-W-θb. ......................................................... 728

Figure 7.173: Test 4A No. 3 top hoop support bar strains – (a) ε3THT-(1); (b) ε3THB-(1); (c) ε3THT-(2); (d) ε3THB-(2). ...................................................................................... 729

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Figure 7.174: Test 4A No. 3 bottom hoop support bar strains – (a) ε3BHB-(1); (b) ε3BHT-(1); (c) ε3BHB-(2); (d) ε3BHT-(2). ...................................................................................... 730

Figure 7.175: Test 4A No. 3 top hoop support bar strains versus beam chord rotation – (a) ε3THT-(1)-θb; (b) ε3THB-(1)-θb; (c) ε3THT-(2)-θb; (d) ε3THB-(2)-θb. ............................. 731

Figure 7.176: Test 4A No. 3 bottom hoop support bar strains versus beam chord rotation – (a) ε3BHB-(1)-θb; (b) ε3BHT-(1)-θb; (c) ε3BHB-(2)-θb; (d) ε3BHT-(2)-θb. ......................... 732

Figure 7.177: Test 4A beam end confinement hoop east leg strains – (a) ε1HB-E; (b) ε2HB-E; (c) ε3HB-E; (d) ε4HB-E. ............................................................................................ 733


Figure 7.179: Test 4A beam end hoop confinement hoop east leg strains versus beam chord rotation – (a) ε1HB-E-θb; (b) ε2HB-E-θb; (c) ε3HB-E-θb; (d) ε4HB-E-θb. .............. 735

Figure 7.180: Test 4A beam end confinement hoop west leg strains versus beam chord rotation – (a) ε1HB-W-θb; (b) ε2HB-W-θb; (c) ε3HB-W-θb; (d) ε4HB-W-θb....................... 736

Figure 7.181: Test 4B overall photographs – (a) pre-test undisplaced position; (b) θb = 3.33%; (c) θb = –3.33%; (d) θb = 6.4%; (e) θb = –6.4%; (f) final post-test undisplaced position............................................................................................ 741

Figure 7.182: Test 4B beam south end photographs – (a) pre-test undisplaced position; (b) θb = 3.33%; (c) θb = –3.33%; (d) θb = 6.4%; (e) θb = –6.4%; (f) final post-test undisplaced position............................................................................................ 742

Figure 7.183: Test 4B beam south end damage propagation – positive and negative rotations............................................................................................................... 743

Figure 7.184: Test 4B coupling beam shear force versus chord rotation behavior – (a) using beam displacements; (b) using load block displacements. .................. 745

Figure 7.185: Test 4B failure. ......................................................................................... 746

Figure 7.186: Test 4B Mb-θb behavior. ........................................................................... 747

Figure 7.187: Test 4B beam post-tensioning strand forces – (a) strand 1; (b) strand 2; (c) strand 3; (d) strand 4. ..................................................................................... 749

Figure 7.188: Test 4B FLC-θb behavior – (a) strand 1; (b) strand 2; (c) strand 3; (d) strand 4. ......................................................................................................... 750

Figure 7.189: Test 4B beam post-tensioning force versus chord rotation behavior – (a) using beam displacements; (b) using load block displacements. .................. 751

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Figure 7.190: Test 4B south end top angle-to-wall connection strand forces – (a) east strand; (b) west strand. ........................................................................................ 753

Figure 7.191: Test 4B south end angle-to-wall connection strand forces versus beam chord rotation – (a) FLC3-θb; (b) FLC4-θb.............................................................. 753

Figure 7.192: Test 4B south end seat angle-to-wall connection strand forces – (a) east strand; (b) west strand. ........................................................................................ 754

Figure 7.193: Test 4B south end angle-to-wall connection strand forces versus beam chord rotation – (a) FLC5-θb; (b) FLC6-θb.............................................................. 754

Figure 6.194: Test 4B south end total angle-to-wall connection strand forces versus beam chord rotation – (a) top connection; (b) seat connection. ................................... 755

Figure 7.195: Test 4B vertical force on the wall test region, Fwt – (a) Fwt-test duration; (b) Fwt-θb. ............................................................................................................ 756

Figure 7.196: Test 4B south end beam vertical displacement – (a) measured, ∆DT9; (b) adjusted, ∆DT9,y; (c) difference, ∆DT9,y-∆DT9. .................................................. 758

Figure 7.197: Test 4B north end beam vertical displacement – (a) measured, ∆DT10; (b) adjusted, ∆DT10,y; (c) difference, ∆DT10,y-∆DT10. .............................................. 759

Figure 7.198: Test 4B percent difference between measured and adjusted displacements – (a) south end, DT9; (b) north end, DT10. ........................................................... 759

Figure 7.199: Test 4B beam vertical displacements versus beam chord rotation – (a) ∆DT9-θb; (b) ∆DT10-θb. ..................................................................................... 760

Figure 7.200: Test 4B beam chord rotation – (a) θb from ∆DT9 and ∆DT10; (b) θb,lb from ∆LB,y. ............................................................................................... 761

Figure 7.201: Test 4B percent difference between θb and θb,lb. ...................................... 762

Figure 7.202: Test 4B difference between θb and θb,lb. ................................................... 762

Figure 7.203: Test 4B beam inclinometer rotations – (a) near beam south end, θRT1; (b) near beam midspan, θRT2. .............................................................................. 764

Figure 7.204: Test 4B difference between beam inclinometer rotations and beam chord rotations – (a) RT1; (b) RT2; (c) beam deflected shape. .................................... 765

Figure 7.205: Test 4B load block horizontal displacements – (a) measured, ∆DT3; (b) adjusted, ∆DT3,x; (c) percent difference. ......................................................... 768

Figure 7.206: Test 4B load block north end vertical displacements – (a) measured, ∆DT4; (b) adjusted, ∆DT4,y; (c) percent difference. ......................................................... 769

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Figure 7.207: Test 4B load block south end vertical displacements – (a) measured, ∆DT5; (b) adjusted, ∆DT5,y; (c) percent difference. ......................................................... 770

Figure 7.208: Test 4B percent difference between measured and adjusted displacements versus beam chord rotation – (a) DT4; (b) DT5. ................................................ 770

Figure 7.209: Test 4B load block displacements versus beam chord rotation – (a) ∆DT4-θb; (b) ∆DT5-θb; (c) ∆DT3,x-θb. ..................................................................................... 771

Figure 7.210: Test 4B load block centroid displacements – (a) x-y displacements; (b) rotation; (c) x-displacements; (d) y-displacements. ....................................... 772

Figure 7.211: Test 4B load block centroid displacements versus beam chord rotation – (a) x-displacement-θb; (b) y-displacement-θb; (c) rotation-θb. ............................ 773

Figure 7.212: Test 4B reaction block displacements – (a) ΔDT6; (b) ΔDT7; (c) ΔDT8. ...... 775

Figure 7.213: Test 4B reaction block displacements versus beam chord rotation – (a) ∆DT7-θb; (b) ∆DT8-θb; (c) ∆DT6-θb. ................................................................... 776

Figure 7.214: Test 4B reaction block centroid displacements – (a) x-y displacements; (b) rotation; (c) x-displacements; (d) y-displacements. ....................................... 777

Figure 7.215: Test 4B reaction block centroid displacements versus beam chord rotation – (a) x-displacement-θb; (b) y-displacement-θb; (c) rotation-θb. ......................... 778

Figure 7.216: Test 4B beam-to-reaction-block interface top LVDT displacements – (a) measured, ∆DT11; (b) adjusted, ∆DT11,x; (c) percent difference. ...................... 780

Figure 7.217: Test 4B beam-to-reaction-block interface middle LVDT displacements – (a) measured, ∆DT12; (b) adjusted, ∆DT12,x; (c) percent difference. ...................... 781

Figure 7.218: Test 4B beam-to-reaction-block interface bottom LVDT displacements – (a) measured, ∆DT13; (b) adjusted, ∆DT13,x; (c) percent difference. ...................... 782

Figure 7.219: Test 4B beam-to-reaction-block interface LVDT displacements versus beam chord rotation – (a) ∆DT11-θb; (b) ∆DT13-θb; (c) ∆DT12-θb. ........................... 783

Figure 7.220: Test 4B contact depth at beam-to-reaction-block interface – (a) method 1 using DT11, DT12, and DT13; (b) method 2 using RT2, DT11, and DT13; (c) method 3 using RT2 and DT12; (d) method 4 using DT12 and θb; (e) method 5 using θb, DT11, and DT13. ................................................................................. 786

Figure 7.221: Test 4B gap opening at beam-to-reaction-block interface – (a) method 1 using ∆DT11, ∆DT12, and ∆DT13; (b) method 2 using RT2, DT11, and DT13; (c) method 3 using RT2 and DT12; (d) method 4 using ∆DT12 and θb; (e) method 5 using θb, DT11, and DT13. ................................................................................. 787

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Figure 7.222: Test 4B gap opening at beam-to-reaction-block interface using method 4.............................................................................................................................. 788

Figure 7.223: Test 4B contact depth at beam-to-reaction-block interface – (a) method 4 using ∆DT12 and θb,lb; (b) 2.25% beam chord rotation cycle; (c) 5.0% beam chord rotation cycle. ...................................................................................................... 788

Figure 7.224: Test 4B wall test region concrete deformations – (a) DT14; (b) DT15. .. 790

Figure 7.225: Test 4B wall test region concrete deformations versus beam chord rotation – (a) ∆DT14-θb; (b) ∆DT15-θb. ................................................................................. 790

Figure 7.226: Test 4B beam looping reinforcement top longitudinal leg strains – (a) ε6(1)T-E; (b) ε6(1)T-W; (c) ε6(2)T-E; (d) ε6(2)T-W; (e) ε6(3)T-E; (f) ε6(3)T-W; (g) ε6MT-E; (h) ε6MT-W. ............................................................................................................ 792

Figure 7.227: Test 4B beam looping reinforcement bottom longitudinal leg strains – (a) ε6(1)B-E; (b) ε6(1)B-W; (c) ε6(2)B-E; (d) ε6(2)B-W; (e) ε6(3)B-E; (f) ε6(3)B-W; (g) ε6MB-E; (h) ε6MB-W. ............................................................................................................ 794

Figure 7.228: Test 4B beam looping reinforcement top longitudinal leg strains versus beam chord rotation – (a) ε6(1)T-E-θb; (b) ε6(1)T-W-θb; (c) ε6(2)T-E-θb; (d) ε6(2)T-W-θb; (e) ε6(3)T-E-θb; (f) ε6(3)T-W-θb; (g) ε6MT-E-θb; (h) ε6MT-W-θb. ..................................... 795

Figure 7.229: Test 4B beam looping reinforcement bottom longitudinal leg strains versus beam chord rotation – (a) ε6(1)B-E-θb; (b) ε6(1)B-W-θb; (c) ε6(2)B-E-θb; (d) ε6(2)B-W-θb; (e) ε6(3)B-E-θb; (f) ε6(3)B-W-θb; (g) ε6MB-E-θb; (h) ε6MB-W-θb. ..................................... 796

Figure 7.230: Test 4B beam looping reinforcement vertical leg strains – (a) ε6SE(E)-E; (b) ε6SE(E)-W; (c) ε6SE(I)-E; (d) ε6SE(I)-W. .................................................................. 799

Figure 7.231: Test 4B beam looping reinforcement vertical leg strains versus beam chord rotation behavior – (a) ε6SE(E)-E-θb; (b) ε6SE(E)-W-θb; (c) ε6SE(I)-E-θb; (d) ε6SE(I)-W-θb.............................................................................................................................. 800

Figure 7.232: Test 4B beam midspan transverse hoop reinforcement strains – (a) εMH-E; (b) εMH-W. ............................................................................................................. 801

Figure 7.233: Test 4B beam midspan transverse hoop reinforcement strains versus beam chord rotation behavior – (a) εMH-E-θb; (b) εMH-W-θb. .......................................... 801

Figure 7.234: Test 4B No. 3 top hoop support bar strains – (a) ε3THT-(1); (b) ε3THB-(1); (c) ε3THT-(2); (d) ε3THB-(2). ...................................................................................... 803

Figure 7.235: Test 4B No. 3 bottom hoop support bar strains – (a) ε3BHB-(1); (b) ε3BHT-(1); (c) ε3BHB-(2); (d) ε3BHT-(2). ...................................................................................... 804

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Figure 7.236: Test 4B No. 3 top hoop support bar strains versus beam chord rotation – (a) ε3THT-(1)-θb; (b) ε3THB-(1)-θb; (c) ε3THT-(2)-θb; (d) ε3THB-(2)-θb. ............................. 805

Figure 7.237: Test 4B No. 3 bottom hoop support bar strains versus beam chord rotation – (a) ε3BHB-(1)-θb; (b) ε3BHT-(1)-θb; (c) ε3BHB-(2)-θb; (d) ε3BHT-(2)-θb. ......................... 806

Figure 7.238: Test 4B beam end hoop confinement strains (east legs) – (a) ε1HB-E; (b) ε2HB-E; (c) ε3HB-E; (d) ε4HB-E. ........................................................................... 808

Figure 7.239: Test 4B beam end hoop confinement strains (west legs) – (a) ε1HB-W; (b) ε2HB-W; (c) ε3HB-W; (d) ε4HB-W........................................................................... 809

Figure 7.240: Test 4B beam end hoop confinement strains (east legs) versus beam chord rotation – (a) ε1HB-E-θb; (b) ε2HB-E-θb; (c) ε3HB-E-θb; (d) ε4HB-E-θb. ........................ 810

Figure 7.241: Test 4B beam end hoop confinement strains (west legs) versus beam chord rotation – (a) ε1HB-W-θb; (b) ε2HB-W-θb; (c) ε3HB-W-θb; (d) ε4HB-W-θb....................... 811

VOLUME IV

CHAPTER 8:

Figure 8.1: Beam shear force versus chord rotation – (a) Test 1; (b) Test 2; (c) Test 3; (d) Test 3A; (e) Test 3B; (f) Test 4; (g) Test 4A; (h) Test 4B. ........................... 818

Figure 8.2: Beam south end damage propagation – (a) Test 1; (b) Test 2; (c) Test 3; (d) Test 3A; (e) Test 3B; (f) Test 4; (g) Test 4A; (h) Test 4B. ........................... 820

Figure 8.3: Beam north end damage propagation – (a) Test 1; (b) Test 2; (c) Test 3; (d) Test 3A; (e) Test 3B; (f) Test 4; (g) Test 4A; (h) Test 4B. ........................... 822

Figure 8.4: Beam post-tensioning tendon force versus chord rotation – (a) Test 1; (b) Test 2; (c) Test 3; (d) Test 3A; (e) Test 3B; (f) Test 4; (g) Test 4A; (h) Test 4B. ......................................................................................................... 824

Figure 8.5: Damage at north beam end at θb = 6.4% – (a) Test 1; (b) Test 2. ................ 829

Figure 8.6: Damage at south beam end at θb = -3.33% – (a) Test 4; (b) Test 4B; (c) Test 2; (d) Test 3. ........................................................................................... 831

Figure 8.7: Damage at south beam end at θb = -3.33% – (a) Test 3; (b) Test 4. ............. 832

Figure 8.8: Maximum longitudinal reinforcement strains – (a) versus θb; (b) at θb = 3.33%; (c) at ultimate sustained rotation. .......................................... 835

Figure 8.9: Maximum beam end transverse reinforcement strains – (a) versus θb; (b) at θb = 3.33%; (c) at ultimate sustained rotation. .......................................... 838

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Figure 8.10: Maximum beam midspan transverse reinforcement strains – (a) versus θb; (b) at θb = 3.33%; (c) at ultimate sustained rotation. .......................................... 840

Figure 8.11: Test 4 relative energy dissipation ratio calculations.. ................................ 846

Figure 8.12: Relative energy dissipation ratio versus beam chord rotation. ................... 847

Figure 8.13: Test 4 secant stiffness calculations. ............................................................ 849

Figure 8.14: Sustained coupling beam rotations. ............................................................ 851

CHAPTER 9:

Figure 9.1: DRAIN-2DX fiber-element subassembly model. ........................................ 856

Figure 9.2: Fiber element, segments, and fibers. ............................................................ 858

Figure 9.3: Compressive stress-strain relationships of unconfined and confined concrete (Mander et al. 1988a). ......................................................................................... 860

Figure 9.4: Modeling of beam cross-sections near the ends – (a) cross-section; (b) concrete types; (c) fiber discretization .......................................................... 861

Figure 9.5: Modeling of beam specimens. ...................................................................... 862

Figure 9.6: Length of first beam fiber segment, lcr – (a) model schematic; (b) influence on Vb-θb behavior. .................................................................................................... 864

Figure 9.7: Concrete compressive stress-strain relationships for virgin beam specimens –(a) unconfined concrete; (b) confined concrete. ................................................. 865

Figure 9.8: Modeling of wall contact regions – (a) wall cross-section in vertical plane; (b) slice 1; (c) slice 2; (d) slice 3. ........................................................................ 868

Figure 9.9: Compression-only concrete fiber (i.e., Types C1 and C2) stress-strain behavior – (a) unconfined concrete; (b) confined concrete. ............................... 870

Figure 9.10: Modeling of gap opening. .......................................................................... 872

Figure 9.11: Gap/contact “post-tensioning kink” elements – (a) idealized exaggerated displaced shape of tendon inside ducts; (b) gap/contact kink element. .............. 875

Figure 9.12: Post-tensioning tendon stress-strain behavior. ........................................... 876

Figure 9.13: Assumed force versus deformation behaviors of the angle elements (adapted from Shen et al. 2006) – (a) horizontal angle element; (b) vertical angle element.............................................................................................................................. 877

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Figure 9.14: Modeling of top and seat angles (from Shen et al. 2006). ......................... 878

Figure 9.15: Assumed concrete compressive stress-strain relationship for the patched region of the reaction block. ............................................................................... 884

Figure 9.16: Assumed concrete compressive stress-strain relationships for Test 3B – (a) unconfined concrete; (b) confined concrete. ................................................. 885

Figure 9.17: Assumed concrete compressive stress-strain relationships for Tests 4A and 4B – (a) unconfined concrete; (b) confined concrete. ......................................... 885

Figure 9.18: Experimental versus analytical Vb-θb behavior for Test 2. ......................... 886


Figure 9.20: Experimental versus analytical Vb-θb behavior for Test 3B. ...................... 887


Figure 9.22: Experimental versus analytical Vb-θb behavior for Test 4A. ...................... 888

Figure 9.23: Experimental versus analytical Vb-θb behavior for Test 4B. ...................... 888

Figure 9.24: Experimental versus analytical beam post-tensioning behavior for Test 2 – (a) Pbp-θb behavior; (b) load block horizontal displacement. .............................. 890


Figure 9.26: Experimental versus analytical beam post-tensioning behavior for Test 3B – (a) Pbp-θb behavior; (b) load block horizontal displacement. .............................. 892


Figure 9.28: Experimental versus analytical beam post-tensioning behavior for Test 4A – (a) Pbp-θb behavior; (b) load block horizontal displacement. .............................. 894

Figure 9.29: Experimental versus analytical beam post-tensioning behavior for Test 4B – (a) Pbp-θb behavior; (b) load block horizontal displacement. .............................. 895

Figure 9.30: Experimental versus analytical contact depth at beam-to-reaction-block interface for Test 2 – (a) method 1 using DT11, DT12, and DT13; (b) method 2 using RT2, DT11, and DT13; (c) method 3 using RT2 and DT12; (d) method 4 using θb and DT12; (e) method 5 using θb, DT11, and DT13. ............................ 897

Figure 9.31: Experimental versus analytical contact depth at beam-to-reaction-block interface for Test 3 – (a) method 1 using DT11, DT12, and DT13; (b) method 2

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using RT1, DT11, and DT13; (c) method 3 using RT1 and DT12; (d) method 4 using θb and DT12; (e) method 5 using θb, DT11, and DT13. ............................ 898

Figure 9.32: Experimental versus analytical contact depth at beam-to-reaction-block interface for Test 3B – (a) method 1 using DT11, DT12, and DT13; (b) method 2 using RT1, DT11, and DT13; (c) method 3 using RT1 and DT12; (d) method 4 using θb and DT12; (e) method 5 using θb, DT11, and DT13. ............................ 899

Figure 9.33: Experimental versus analytical contact depth at beam-to-reaction-block interface for Test 4 – (a) method 1 using DT11, DT12, and DT13; (b) method 2 using RT2, DT11, and DT13; (c) method 3 using RT2 and DT12; (d) method 4 using θb and DT12; (e) method 5 using θb, DT11, and DT13. ............................ 900

Figure 9.34: Experimental versus analytical contact depth at beam-to-reaction-block interface for Test 4A – (a) method 1 using DT11, DT12, and DT13; (b) method 2 using RT2, DT11, and DT13; (c) method 3 using RT2 and DT12; (d) method 4 using θb and DT12; (e) method 5 using θb, DT11, and DT13. ............................ 901

Figure 9.35: Experimental versus analytical contact depth at beam-to-reaction-block interface for Test 4B – (a) method 1 using DT11, DT12, and DT13; (b) method 2 using RT2, DT11, and DT13; (c) method 3 using RT2 and DT12; (d) method 4 using θb and DT12; (e) method 5 using θb, DT11, and DT13. ............................ 902

Figure 9.36: Experimental versus analytical gap opening at beam-to-reaction-block interface for Test 2 – (a) method 1 using DT11, DT12, and DT13; (b) method 2 using RT2, DT11, and DT13; (c) method 3 using RT2 and DT12; (d) method 4 using θb and DT12; (e) method 5 using θb, DT11, and DT13. ............................ 904


Figure 9.38: Experimental versus analytical gap opening at beam-to-reaction-block interface for Test 3B – (a) method 1 using DT11, DT12, and DT13; (b) method 2 using RT1, DT11, and DT13; (c) method 3 using RT1 and DT12; (d) method 4 using θb and DT12; (e) method 5 using θb, DT11, and DT13. ............................ 906


Figure 9.40: Experimental versus analytical gap opening at beam-to-reaction-block interface for Test 4A – (a) method 1 using DT11, DT12, and DT13; (b) method 2 using RT2, DT11, and DT13; (c) method 3 using RT2 and DT12; (d) method 4 using θb and DT12; (e) method 5 using θb, DT11, and DT13. ............................ 908

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Figure 9.41: Experimental versus analytical gap opening at beam-to-reaction-block interface for Test 4B – (a) method 1 using DT11, DT12, and DT13; (b) method 2 using RT2, DT11, and DT13; (c) method 3 using RT2 and DT12; (d) method 4 using θb and DT12; (e) method 5 using θb, DT11, and DT13. ............................ 909

Figure 9.42: Concrete compressive strains at beam end – (a) Test 2; (b) Test 3; (c) Test 4.............................................................................................................................. 911

Figure 9.43: Measured average strain calculations. ........................................................ 912

Figure 9.44: Fiber element slice locations used in strain predictions. ............................ 913

Figure 9.45: Experimental versus analytical beam end longitudinal reinforcement strains for Test 2 at 5.75 in. (146 mm) – (a) top leg; (b) bottom leg. ............................. 914

Figure 9.46: Experimental versus analytical beam end longitudinal reinforcement strains at 11.50 in. (292 mm) for Test 2 – bottom leg. ................................................... 914

Figure 9.47: Experimental versus analytical beam end longitudinal reinforcement strains at 5.75 in. (146 mm) for Test 3 – (a) top leg; (b) bottom leg. ............................. 915

Figure 9.48: Experimental versus analytical beam end longitudinal reinforcement strains at 11.50 in. (292 mm) for Test 3 – top leg. ......................................................... 915

Figure 9.49: Experimental versus analytical beam end longitudinal reinforcement strains at 5.75 in. (146 mm) for Test 3B – (a) top leg; (b) bottom leg. .......................... 916

Figure 9.50: Experimental versus analytical beam end longitudinal reinforcement strains at 5.75 in. (146 mm) for Test 4 – (a) top leg; (b) bottom leg. ............................. 917

Figure 9.51: Experimental versus analytical beam end longitudinal reinforcement strains at 11.50 in. (292 mm) for Test 4 – top leg. ......................................................... 917

Figure 9.52: Experimental versus analytical beam end longitudinal reinforcement strains at 5.75 in. (146 mm) for Test 4A – (a) top leg; (b) bottom leg. .......................... 918

Figure 9.53: Experimental versus analytical beam end longitudinal reinforcement strains at 11.50 in. (292 mm) for Test 4A – top leg. ...................................................... 918

Figure 9.54: Experimental versus analytical beam end longitudinal reinforcement strains at 5.75 in. (146 mm) for Test 4B – (a) top leg; (b) bottom leg. .......................... 919

Figure 9.55: Experimental versus analytical beam end longitudinal reinforcement strains at 11.50 in. (292 mm) for Test 4B – top leg. ...................................................... 919

Figure 9.56: Experimental versus analytical longitudinal reinforcement strains at beam midspan for Test 2 – bottom leg. ........................................................................ 921

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Figure 9.57: Experimental versus analytical longitudinal reinforcement strains at beam midspan for Test 3 – top leg. .............................................................................. 921

Figure 9.58: Experimental versus analytical longitudinal reinforcement strains at beam midspan for Test 3B – top leg. ............................................................................ 921

Figure 9.59: Experimental versus analytical longitudinal reinforcement strains at beam midspan for Test 4 – (a) top leg; (b) bottom leg. ................................................ 922

Figure 9.60: Experimental versus analytical longitudinal reinforcement strains at beam midspan for Test 4A – (a) top leg; (b) bottom leg. ............................................. 923

Figure 9.61: Experimental versus analytical longitudinal reinforcement strains at beam midspan for Test 4B – (a) top leg; (b) bottom leg. ............................................. 924

Figure 9.62: Comparison of last Vb-θb cycles from Tests 4 and 4A. .............................. 925

Figure 9.63: Difference between last Vb-θb cycles from Tests 4 and 4A. ....................... 926

Figure 9.64: ABAQUS finite-element model. ................................................................ 927

Figure 9.65: Confined concrete compressive stress-strain model. ................................. 929

Figure 9.66: Comparisons between fiber-element and finite-element model results – (a) coupling shear force versus chord rotation; (b) beam-to-wall contact depth. ............................................................................................................................. 930

Figure 9.67: Principal compression stresses – (a) wall pier and coupling beam; (b) close up view of coupling beam. .................................................................................. 931

Figure 9.68: Principal tension stresses – (a) wall pier and coupling beam; (b) close up view of coupling beam. ....................................................................................... 933

Figure 9.69: Regions where principal tension stresses are greater than assumed concrete cracking stress – (a) wall pier and coupling beam; (b) close up view of coupling beam. ................................................................................................................... 934

CHAPTER 10:

Figure 10.1: Full-scale prototype subassembly. ............................................................. 939

Figure 10.2: Subassembly analytical model used in the parametric investigation. ........ 940

Figure 10.3: Assumed force versus deformation behaviors of the angle elements in the parametric investigation (from Shen et al. 2006) – (a) horizontal angle element; (b) vertical angle element.................................................................................... 941

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Figure 10.4: Behavior of prototype subassembly under monotonic loading. ................. 942

Figure 10.5: Behavior under cyclic loading – (a) prototype subassembly; (b) normalized beam post-tensioning force; (c) thicker angles; (d) no angles. ........................... 945

Figure 10.6: Behavior of parametric subassemblies – (a) ta; (b) fbpi; (c) Abp; (d) fbpi and Abp; (e) lw; (f) bb; (g) hb; (h) lb; (i) lb and hb; (j) εccu. ........................................... 949

Figure 10.7: Behavior of parametric subassemblies – (a) ta; (b) fbpi; (c) Abp; (d) fbpi and Abp; (e) lw; (f) bb; (g) hb; (h) lb; (i) lb and hb; (j) εccu. ........................................... 951

Figure 10.8: Tri-linear estimation of subassembly behavior. ......................................... 955

Figure 10.9: Concrete stress distributions at beam end – (a) tension angle yielding state; (b) tension angle strength state; (c) confined concrete crushing state. ............... 956

Figure 10.10: Linear-elastic subassembly model – (a) model with wall-contact elements; (b) model without wall-contact elements. ........................................................... 959

Figure 10.11: Beam end displacements at the tension angle strength state. ................... 962

Figure 10.12: Estimation of plastic hinge length. ........................................................... 963

Figure 10.13: Tri-linear estimation of test subassembly behavior – (a) Test 1; (b) Test 2; (c) Test 3; (d) Test 3A; (e) Test 3B; (f) Test 4; (g) Test 4A; and (h) Test 4B. ... 968

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TABLES

VOLUME I

CHAPTER 3:

Table 3.1 Beam Mild Steel Reinforcement Details .........................................................75

Table 3.2 Subassembly Test Matrix ...............................................................................108

Table 3.3 Nominal Applied Displacement History ........................................................116

CHAPTER 4:

Table 4.1 Unconfined Concrete Strength .......................................................................124

Table 4.2 Preliminary Grout Mix Tests .........................................................................128

Table 4.3 Properties of Grout Used in Coupling Beam Test Subassemblies .................129

Table 4.4 Post-Tensioning Strand Material Properties ..................................................135

Table 4.5 No. 3 Reinforcing Bar Material Properties ....................................................139

Table 4.6 No. 6 Reinforcing Bar Material Properties ....................................................139

Table 4.7 Angle Steel Material Properties .....................................................................142

Table 4.8 Material Properties Summary ........................................................................143

CHAPTER 5:

Table 5.1 Summary of Load Cells .................................................................................148

Table 5.2 Summary of Displacement and Rotation Transducers ...................................149

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Table 5.3 Summary of Beam Looping Reinforcement Longitudinal Leg Strain Gauges .......................................................................................................150

Table 5.4 Summary of Beam Transverse Reinforcement Strain Gauges ......................151

Table 5.5 Summary of Beam End Confinement Hoop Strain Gauges...........................151

Table 5.6 Summary of Beam Confined Concrete Strain Gauges ..................................152

Table 5.7 Summary of Reactio nBlock Strain Gauges ..................................................153

Table 5.8 Transducer Details .........................................................................................154

Table 5.9 Load Cell Calibrations ...................................................................................165

VOLUME II

CHAPTER 6:

Table 6.1 Ruler Measurements of Gap Opening at North Beam End ............................267

Table 6.2 Ruler Measurements of Gap Opening at South Beam End ............................352



VOLUME III CHAPTER 7:





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VOLUME IV CHAPTER 8:

Table 8.1 Probable Lateral Strength ..............................................................................844

Table 8.2 Relative Energy Dissipation Ratio .................................................................847

Table 8.3 Secan Stiffness ...............................................................................................849

CHAPTER 9:

Table 9.1 Typical Fiber Discretization Along Beam Length .........................................863

Table 9.2 Typical Fiber Discretization of Wall Contact Regions ..................................869

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ACKNOWLEDGMENTS

My deepest appreciation goes out to all the people that have provided support,

both professional and personal, that made the writing of this dissertation possible. My

family and friends have helped me through it all, and with out them, this would not have

been possible. Mom and Dad – thanks for the support through everything, I would have

never made it without you. Becky, LeAnne, and Tinnie – thanks for keeping me sane

(somewhat). Melanie – thanks for the friendship and motivation (i.e., coffee and heaters).

Shawn, PJ, Sascha, Timo, Suzie, Cameron, HJ, Kelly, Andrea – thanks for a break from

all the madness.

The author would also like to acknowledge all those at the University of Notre

Dame who assisted with the investigations in this dissertation: the faculty and staff of the

Department of Civil Engineering and Geological Sciences; laboratory technician Brent

Bach; fellow graduate students Brian G. Morgen, Qiang Shen, Michael May;

undergraduate students Luke Nisley and Beth Ferris; and all other graduate students in

the Department of Civil Engineering and Geological Sciences who lent a helping hand

when asked.

A special thanks to my advisor and friend, Dr. Yahya C. Kurama, for your

guidance and patience through it all. I truly appreciate all that you have shared and taught

me and the support that you provided.

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Thanks to my committee members Drs. Ahsan Kareem, David Kirkner, and Kapil

Khandelwal for their time and help in my research endeavors.

In addition, the author also acknowledges the technical support provided by Cary

Kopczynski of Cary Kopczynski and Company, Inc.; contributions to the project through

material donation and assistance of the following companies: StresCore Inc., Precision

SURE-LOCK®, Dywidag-Systems International – this support is gratefully

acknowledged. Special thanks to John Reihl and Aaron Johnson of StresCore Inc. for

their assistance.

This research was funded by the National Science Foundation (NSF) under Grant

No. NSF/CMS 04-09114 and by a Precast/Prestressed Concrete Institute (PCI) Daniel P.

Jenny Fellowship. The support of the NSF Program Director Dr. P.N. Balaguru and

members of the PCI Research and Development Committee is gratefully acknowledged.

The findings and conclusions in the dissertation are those of the author and do not

necessarily reflect the views of the organizations and individuals acknowledged above.

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NOTATION

abp beam post-tensioning strand area

ab,max concrete compressive stress block depth at beam end when Mb,max is

reached

ap post-tensioning strand area

A reinforcing bar area

Aa cross-sectional area of angle leg

Abar cross-sectional area of tie down bar

Abp total beam post-tensioning tendon area

Ac cross-sectional area of beam concrete

Agross gross cross-sectional area of beam

Agt cross-sectional area of beam-to-wall interface grout

Ah area enclosed by hysteresis loop

Al longitudinal reinforcement area

ACI American Concrete Institute

ASTM American Society for Testing and Materials

bb beam width

bh center-to-center width/length of confinement hoop

c contact depth, neutral axis depth

c’ neutral axis depth perpendicular to beam axis

lxviii

cb neutral axis depth in vertical direction at bottom of beam

cb,ay neutral axis depth at tension angle yield state

cb,ccc neutral axis depth at confined concrete crushing state

cb’ neutral axis depth perpendicular to beam axis at bottom of beam

cb,max neutral axis depth when Mb,max is reached

ct neutral axis depth in vertical direction at top of beam

ct’ neutral axis depth perpendicular to beam axis at top of beam

Ca compression angle force

Casi initial slip critical force of angle-to-beam connection bolts

Cayx angle yield strength in compression

Cb compression force in beam

Cb,ay compression force in beam at tension angle strength state

Cb,ccc compression force in beam at confined concrete crushing state

Cb,max compression stress resultant in beam when Mb,max is reached

Cc compression force in concrete

C1 compression-only unconfined concrete type

C2 compression-only confined concrete type

C3 linear-elastic tension unconfined concrete type

C4 linear-elastic tension confined concrete type

CD coupling degree (or level)

CIP cast-in-place

dab angle connector bolt type and diameter

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db distance from extreme compression edge of beam to centerline of

longitudinal mild steel reinforcement on tension side

dh center-to-center depth of confinement hoop

DT displacement transducer

Ea Young’s modulus for angle steel

E1 peak lateral strength in positive direction of loading

E2 peak lateral strength in negative direction of loading

Ebar Young’s modulus of tie down bar steel

Ebp Young’s modulus of beam post-tensioning strand

Ec Young’s modulus of concrete

El Young’s modulus of longitudinal mild steel reinforcement

Emax peak measured lateral strength

Ent nominal lateral strength

Epr probable strength of specimen at peak load

fa angle steel stress

fam maximum strength of angle steel

fapu ultimate strength of angle-to-wall connection post-tensioning strand

fau ultimate strength of angle steel (0.85fam)

fay angle steel yield strength

fbci initial beam concrete nominal axial stress

fbp beam post-tensioning steel stress

fbpi initial beam post-tensioning steel stress

fbpl limit of proportionality stress of beam post-tensioning strand

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fbpu ultimate strength of beam post-tensioning strand

fbpy design yield strength of beam post-tensioning strand

fc stress of concrete at extreme compression face

f’c compressive strength of unconfined concrete

f’cc compressive strength of confined concrete

f’gt test day strength of beam-to-wall interface grout

fgti initial nominal stress in beam-to-wall interface grout

fhm maximum strength of beam hoop reinforcing steel

fhy yield strength of No. 3 mild steel reinforcement

fl stress in beam longitudinal mild steel reinforcement

flm maximum strength of beam longitudinal mild steel reinforcement

flu ultimate strength of beam longitudinal mild steel reinforcement

fly yield strength of beam longitudinal mild steel reinforcement

fpu maximum strength of post-tensioning strand

fpy design yield strength of post-tensioning strand

Faxis1 measured force in actuator axis 1

Faxis1,y vertical measured force in actuator axis 1

Faxis2 measured force in actuator axis 2

Faxis2,y vertical measured force in actuator axis 2

Fi,LC# initial measured force in load cell

FLCi force in Bar i

FLC# measured force in load cell

Fwt vertical force on wall test region

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Fwt,i initial vertical force on wall test region

FEMA Federal Emergency Management Agency

hb beam depth

hLB load block height

hRB reaction block height

hw wall pier height

HPFRCC high performance fiber reinforced cementious composite

Ia moment of inertia for angle leg cross-section

ka distance from heel to toe of fillet of angle

K initial stiffness in positive direction of loading

K’ initial stiffness in negative direction of loading

Kaixc initial stiffness of angle in compression

Kaixt initial stiffness of angle in tension

Kaiy initial stiffness of vertical angle element

Kbi initial stiffness

lA-DT# distance between point A and ferrule insert for displacement transducer

lDT10-DT9 horizontal distance between ferrule inserts for displacement transducers

DT9 and DT10

la angle length

laxis# length of actuator between top pin and bottom pin

lb beam length

lb,cr distance to critical section along beam length

lbp length of beam post-tensioning tendon

lxxii

lb,tg beam length including grout thickness at endes

lcr length of first beam fiber element segment

lgh gage length of angle-to-beam connectors

lgl length of vertical angle leg assumed to act as a cantilever

lgv gage length of angle-to-wall connectors

lg2 effective gage length

lLB load block length

lpl plastic deformation length

lRB reaction block length

lw wall pier length

Lc distance between centroids of tension and compression side walls

LC load cell

LVDT Linear Variable Displacement Transducer

Ma angle moment

Map plastic hinge moment

Mas moment at angle strength state

May beam end moment at tension angle yielding state

Ma0 plastic moment in vertical angle vertical leg without considering shear-

flexure interaction

Mb coupling beam end moment

Mb,a contribution of top and seat angles to beam end moment

Mb,b beam end moment without angles

Mb,cr beam moment demand at critical section

lxxiii

Mb,max maximum beam end moment strength

Mccc moment at confined concrete crushing state

Mcw base moment in compression side wall

Mdec decompression moment

Mtw base moment in tension side wall

Mw total base moment of coupled wall structure

Mw,unc base moment strength of uncoupled walls

nab number of bolts

Nap axial force in horizontal angle leg

Nb compressive axial force in beam

Ntwb tensile axial force in wall pier

Ncwb compressive axial force in wall pier

Pabu total design ultimate strength of angle-to-wall connection post-tensioning

strands

Papi,comp total initial force in compression angle-to-wall connection post-tensioning

strands

Pap,top total force in top angle-to-wall connection post-tensioning strands

Pap,seat total force in seat angle-to-wall connection post-tensioning strands

Pb post-tensioning force

Pb,as total force in beam post-tensioning tendon at angle strength state

Pb,ccc total force in beam post-tensioning tendon confined concrete crushing

state

Pbp beam post-tensioning tendon force

lxxiv

Pbi total initial force in beam post-tensioning tendon

Pbpy yield force of beam post-tensioning tendon

Pbpu total design ultimate strength of beam post-tensioning tendon

Pby yield force of beam post-tensioning tendon

P- second order effects

PT post-tensioning

RT rotation transducer

R2 coefficient of determination

sh hoop spacing

ta angle leg thickness

tg thickness of interface grout at beam ends

tw wall pier thickness

Ta tension angle force

Tasx maximum strength of horizontal angle element in tension

Tax force in tension angle parallel to coupling beam

Tayx horizontal force in horizontal leg of tension angle at angle yielding state

Tayy vertical force in horizontal leg of tension angle at angle yielding state

Tl tensile force in beam longitudinal mild steel reinforcement

ubp,as elongation of beam post-tensioning tendon at angle strength state

ubp,ccc elongation of beam post-tensioning tendon at confined concrete crushing

state

vmax Vmax/Agross

V vertical force

lxxv

Vap plastic shear force in vertical leg of tension angle including shear-flexure

interaction

Va0 plastic shear force without shear-flexure interaction considered

Vb beam shear force

Vb,max maximum measured beam shear strength

Vmax maximum shear force demand

Vbn nominal shear strength for beam

Vout sensor output voltage

Vns total shear slip capacity

Vsa shear slip capacity provided by angles

Vsbp shear friction capacity due to beam post-tensioning force

Vss shear slip capacity

Vmax maximum measured beam shear strength

wabw bolt head/nut width measured across flat-sides

xDT# horizontal distance to ferrule insert anchor

RBx horizontal distance to centroid of reaction block

yDT# vertical distance to ferrule insert anchor

RBy vertical distance to centroid of reaction block

za lever arm for top and seat angle force couple

zc lever arm for coupling beam compression force couple

α equivalent rectangular compressive stress block factor

α diagonal reinforcement inclination

lxxvi

αDT# angle change for displacement transducer string during displacement of

subassembly

αg gap opening rotation at beam end

β equivalent rectangular compressive stress block factor

βb relative energy dissipation ratio

asx tension deformation of horizontal angle element at angle strength state

ax tension deformation of horizontal angle element

ay deformation of vertical angle element

ayx tension deformation of horizontal angle element at angle yielding state

ayy yield deformation of vertical angle element

i,DT# initial extended length of displacement transducer

f,DT# final extended length of displacement transducer

Δaxis1 measured displacement of actuator axis 1

Δaxis2 measured displacement of actuator axis 2

Δaxis1,x measured horizontal displacement of actuator axis 1

Δaxis2,x measured horizontal displacement of actuator axis 2

Δaxis1,y measured vertical displacement of actuator axis 1

Δaxis2,y measured vertical displacement of actuator axis 2

ΔDT# measured displacement of displacement transducer

ΔDT#,x horizontal displacement of displacement transducer

ΔDT#,y vertical displacement of displacement transducer

Δg horizontal size of gap opening at beam end

Δgb gap opening at bottom of beam

lxxvii

Δgn gap opening at north beam end

Δgs gap opening at south beam end

Δgt gap opening top of beam

ΔLB,x horizontal displacement at load block centroid

ΔLB,y vertical displacement at load block centroid

ΔRB,x horizontal displacement at reaction block centroid

ΔRB,y vertical displacement at reaction block centroid

Δi,DT# initial extended length of displacement transducer string from transducer

body to ferrule insert location (including lead wire)

Δf,DT# final extended length of displacement transducer string from transducer

body to ferrule insert location (including lead wire)

a angle steel strain

am strain at fam

au strain at 0.85fam

ay angle steel yield strain

bp strain in beam post-tensioning steel

bpl strain at fbpl

bpu strain at fbpu

bpy fbpy divided by measured Young’s modulus

c concrete strain at extreme compression edge of beam

’c unconfined concrete crushing strain at f’c

cc strain at f’cc

cc,max maximum confined concrete strain

lxxviii

ccu ultimate crushing strain of confined concrete

’cu assumed unconfined concrete crushing strain

gtm strain at f’gt

gtu strain at 0.85f’gt

hu strain at 0.85fhm

hm strain at fhm

hy strain at fhy

l strain in beam longitudinal reinforcing steel in tension

LCi strain measurement in vertical tie down bar

lm strain at flm

lu strain at 0.85flm

ly strain at fly

py design yield strain of post-tensioning strand

# measured strain in strain gauge transducer

s strain in mild steel reinforcement

unl tension unloading stiffness factor for horizontal angle element

plastic hinge rotation

λ modification factor related to unit weight of concrete

μcc coefficient of friction for concrete-against-concrete surfaces

φ strength reduction factor

φh nominal diameter of hoop bars

φp nominal post-tensioning strand diameter

lxxix

φpi plastic curvature

as tension angle strength state beam chord rotation

ay tension angle yield state beam chord rotation

axis1 rotation of actuator axis 1

axis2 rotation of actuator axis 2

b beam chord rotation

b,lb beam chord rotation calculated from load block displacements

ccc confined concrete crushing state beam chord rotation

el elastic beam chord rotation

LB rotation at centroid of load block

pl plastic beam chord rotation

RB rotation at centroid of reaction block

RT# measured rotation in rotation transducer

1

CHAPTER 1

INTRODUCTION

This chapter provides an introduction for the dissertation as follows: (1) problem

statement; (2) research objectives; (3) research scope; (4) research significance; and (5)

overview of dissertation.

1.1 Problem Statement

Historically, concrete structural walls have performed extremely well as primary

lateral load resisting systems under earthquake loading. When coupled together,

structural walls demonstrate an increase in lateral strength and stiffness, allowing a

smaller length and/or number of walls to be used to achieve the required design lateral

strength and stiffness of a building. Coupling beams are used at the floor and roof levels

to transfer shear forces between the wall piers and to dissipate energy over the height of

the structure.

Previous research on coupled wall structural systems has focused on cast-in-place

reinforced concrete coupling beams monolithic with the wall piers and hybrid systems

using steel coupling beams embedded into the wall piers (e.g., Harries et al. 2000;

Harries 2001). More recent research at the University of Notre Dame (Shen and Kurama

2

2000, 2002a,b; Kurama and Shen 2004; Kurama et al. 2004, 2006; Shen et al. 2006) has

introduced a new type of hybrid coupled wall system using steel coupling beams that are

not embedded into the walls. In this system, coupling is achieved by post-tensioning the

beams and the wall piers together at the floor and roof levels using unbonded post-

tensioning strands. The application of similar methods has also been studied in precast

concrete moment frames (e.g., Cheok and Lew 1993; El-Sheikh et al. 1999; Priestley et

al. 1999; Ertas et al. 2006) and steel moment frames (e.g., Ricles et al. 2002;

Christopoulos et al. 2002; Rojas et al. 2005; Garlock et al. 2008; Kim and Christopoulos

2009).

Unbonded post-tensioned coupling beams offer important advantages over

conventional systems with monolithic cast-in-place reinforced concrete beams and

embedded steel beams, such as simpler detailing for the beams and the wall piers,

reduced damage to the structure, and an ability to self-center, thus reducing the residual

lateral displacements of the structure after a large earthquake. The research described in

this dissertation extends the use of post-tensioning to precast concrete coupling beams.

The use of precast beams provides the following advantages over unbonded post-

tensioned steel beams: (1) central location for the post-tensioning strands, resulting in

reduced post-tensioning hardware and operations; (2) better fire and environmental

protection for the post-tensioning strands, provided by the surrounding concrete; (3)

higher concrete-against-concrete friction resistance to resist sliding shear at the beam

ends; (4) simpler construction due to the use of high performance grout instead of steel

shim plates at the beam-to-wall interfaces for construction tolerances and beam

alignment; and (5) single trade construction.

3

As an example, Figure 1.1 shows an eight-story coupled wall system and Figure

1.2 shows a post-tensioned coupling beam subassembly consisting of a precast concrete

coupling beam and the adjacent concrete wall regions at a floor level (the highlighted

region in Figure 1.1). High-strength multi-strand tendons run through the wall piers and

the beams providing the post-tensioning force to the system. The post-tensioning tendons

are unbonded over their entire length (by placing the tendons inside ungrouted ducts) and

are anchored to the structure only at the outer ends of the wall piers. The beam-to-wall

connection regions include steel top and seat angles. High-performance fiber-reinforced

grout is used at the beam-to-wall interfaces for construction tolerances and for alignment

purposes.

lw lw lb

2nd floor

3rd floor

4th floor

5th floor

6th floor

7th floor

8th floor

roof

hw

wallpier

wallpier

Figure 1.1: Multi story coupled wall system.

4

A

coupling

post-tensioning tendon

wall

connection region

post-tensioningtendon anchorage

angle

lw

concrete confinement

beam

region

A

lw lb

fiber-reinforcedgrout

section at A-A

hbabp

bb confined concrete

Figure 1.2: Coupled wall system floor-level subassembly.

If the coupled wall structure is displaced with lateral forces acting from left to

right, the expected exaggerated idealized deformed configuration of the subassembly is

shown in Figure 1.3. The non-linear deformations of the beam occur primarily due to the

opening of gaps at the beam-to-wall interfaces. The application of the post-tensioning

force develops a friction force at the beam-to-wall interfaces, supporting the beam. Under

large displacements, a properly designed subassembly is expected to experience yielding

in the top and seat angles. The angles provide redundancy in support of the beam as well

as energy dissipation during an earthquake. The angles, which are designed to be

sacrificial and can be replaced after the earthquake, also provide a part of the moment

resistance at the beam ends and prevent sliding of the beam against the wall piers

(together with friction induced by post-tensioning). Bonded longitudinal mild steel

reinforcement is used in the beam to transfer the angle forces into the beam. The bonded

5

mild steel reinforcement is not continuous across the beam-to-wall interfaces, and thus,

does not contribute to the coupling forces.

contact

gap opening

region

reference line

beam-to-wall

Figure 1.3: Coupled wall system floor-level subassembly idealized exaggerated deformed configuration.

As gaps open at the beam-to-wall interfaces, large compressive stresses due to the

post-tensioning force are pushed toward the corners of the beam forming a diagonal

compression strut. As shown in Figure 1.4, it is through the formation of this large

compression strut that the coupling shear force Vb is developed. The amount of coupling

between the wall piers and the energy dissipation of the subassembly can be controlled by

varying the total post-tensioning force Pb (which controls the compression force in the

beam Cb), the tension and compression angle forces Ta and Ca, the beam depth hb, and the

beam length lb. To resist the compression stresses that develop in the coupling beam and

the wall piers due to the post-tensioning force, concrete confinement is provided in the

contact regions at the beam-to-wall interfaces.

6

coupling beamTa

=lb

Cb zc + (Ta + Ca) za

Ta

Ca

Ca

za

Cb

lb

Vb

Vb

Vb

zc hb

diagonal compressionstrut

Cb

Figure 1.4: Coupling beam forces.

As compared with monolithic cast-in-place reinforced concrete coupling beams,

unbonded post-tensioned precast concrete beams provide: (1) better quality control due to

factory casting; (2) simpler detailing due to lack of mild steel reinforcement crossing the

beam-to-wall joints and significantly reduced shear reinforcement in the beams; and (3)

self-centering capability due to the restoring effect of the post-tensioning force.

Before the initiation of gap opening, the post-tensioning force creates an initial

lateral stiffness in the precast concrete coupling beam similar to the initial uncracked

stiffness of a comparable monolithic cast-in-place reinforced concrete beam. Gap

opening at the ends of the precast beam results in a reduction in the lateral stiffness,

allowing the system to soften and undergo large nonlinear rotations. The post-tensioning

force controls the size of the gaps and the contact depth between the wall piers and the

coupling beam. As the wall is displaced laterally, the tensile forces in the post-tensioning

strands increase, thus, resisting gap opening. Upon removal of the lateral loads, the post-

tensioning strands provide a restoring force that tends to close the gaps, thus returning the

7

beam and the wall piers towards their undeformed configuration, leaving little or no

residual displacements (i.e., self-centering capability). Unbonding of the post-tensioning

strands has two important advantages: (1) it results in a uniform strain distribution in the

strands, thus, delaying the nonlinear straining (i.e., yielding) of the steel; and (2) it

significantly reduces the amount of tensile stresses transferred to the concrete as the

strands elongate under lateral loading, thus reducing cracking in the wall piers and the

coupling beam.

1.2 Research Objectives

No previous research exists on unbonded post-tensioned precast concrete

coupling beams. In accordance with the research need in this area, the broad objective of

this dissertation is to investigate the behavior, design, and analysis of these structures

under lateral loading. This can be further broken into five specific objectives:

(1) To conduct a large-scale experimental evaluation on the nonlinear lateral load

behavior of floor-level coupled wall subassemblies with unbonded post-tensioned

precast concrete coupling beams;

(2) To validate the use of unbonded post-tensioned precast concrete coupling beams

in seismic regions based on the test results;

(3) To develop and validate nonlinear analytical models for floor-level coupled wall

subassemblies with unbonded post-tensioned precast concrete coupling beams;

8

(4) To conduct a parametric analytical investigation on the behavior of these

structures under lateral loads, thus expanding the results from the experiments;

and

(5) To develop seismic design guidelines, design tools and procedures, and practical

application recommendations based on the experimental and analytical tasks

conducted.

1.3 Research Scope

To achieve the objectives above, the lateral load behavior and design of

reinforced concrete coupled wall subassemblies that use unbonded post-tensioned precast

concrete coupling beams are investigated in this dissertation. The research is limited to

the coupling of two identical walls with rectangular cross-section. The coupling of more

than two walls or of non-rectangular walls is not within the scope of the dissertation.

Furthermore, the study is limited to floor-level coupled wall subassemblies. The behavior

and design of multi-story coupled wall structures is not investigated.

Four half-scale coupled wall subassemblies are constructed to conduct eight tests

with varied design parameters, such as: (1) beam depth; (2) amount of post-tensioning

steel; and (3) angle thickness. The experimental results are used to evaluate the nonlinear

behavior of the coupling system as well as to investigate practical design and

construction applications.

A two-dimensional (in the plane of the walls) analytical model for the coupling

system is developed using the DRAIN-2DX program (Prakash et al. 1993). The model is

9

verified by comparing the analytical results with results obtained from the experimental

program as well as with results from a finite element model developed using the

ABAQUS program (Hibbitt et al. 2002). It is assumed that the structure undergoes in-

plane deformations only (i.e., torsional and out-of-plane deformations are not

considered). Interactions between the coupled wall system and the rest of the building

(e.g., the floor system/diaphragm) are not included.

To expand the results from the experiments, the analytical models are used to

conduct parametric nonlinear static monotonic and reversed cyclic lateral load analyses

of isolated coupled wall subassemblies. The effects of selected structural design

parameters on the lateral load behavior of the system are investigated, including: (1)

beam dimensions; (2) wall dimensions; (3) post-tensioning properties; (4) angle

properties; and (5) concrete properties. The findings from the parametric investigation are

used to develop simplified procedures and tools for the seismic design and nonlinear

response evaluation of coupled wall structures that use precast concrete coupling beams.

1.4 Research Significance

The research described in this dissertation provides fundamental information on

the lateral load analysis, behavior, design, and construction of a new type of precast

concrete coupling system. Ultimately, this information is needed as background for the

development of codified seismic analysis, design, and construction specifications for the

structure, comparable to those available for conventional coupling systems.

10

1.5 Overview of Dissertation

The remainder of the dissertation is organized into the following 10 chapters

(Chapters 2 – 11):

Chapter 2 presents a review of the previous analytical and experimental research

on the seismic behavior and design of coupled wall structures as well as structures with

unbonded post-tensioning.

Chapter 3 provides an overview of the half-scale experimental program that was

conducted on floor-level unbonded post-tensioned coupled wall subassemblies. The test

set-up, specimen design, and test procedure are presented.

Chapter 4 describes the material testing procedures and measured properties of

the materials used in the coupled wall subassembly experiments.

Chapter 5 describes the data instrumentation and response parameters for the

subassembly experiments.

Chapter 6 presents the results from the four “virgin” beam subassembly

experiments.

Chapter 7 presents the results from the four “non-virgin” beam (i.e., previously

tested beam) subassembly experiments.

Chapter 8 summarizes and compares the results from all eight subassembly

experiments conducted as part of this dissertation (i.e., both “virgin” and “non-virgin”

beam tests).

Chapter 9 describes the analytical modeling of floor-level unbonded post-

tensioned coupled wall subassemblies. The verification of the analytical models based on

comparisons with the results from the experimental program is presented.

11

Chapter 10 presents a parametric analytical investigation on the design and

behavior of unbonded post-tensioned coupled wall subassemblies under lateral loading. A

simplified closed-form procedure to estimate the monotonic lateral load behavior of the

subassemblies is developed based on fundamental principles of equilibrium, kinematics,

and constitutive relationships.

Finally, Chapter 11 summarizes the findings from the research program, presents

the conclusions, and describes the future work needed.

12

CHAPTER 2

BACKGROUND

This chapter provides an overview of background information on the following

topics related to the research described in this dissertation: (1) coupled wall structural

systems; (2) monolithic cast-in-place concrete coupled wall systems; (3) unbonded post-

tensioning; (4) unbonded post-tensioned hybrid coupled wall systems; (5) unbonded post-

tensioned precast concrete moment frames; and (6) behavior of top and seat angles.

2.1 Coupled Wall Structural Systems

Concrete structural walls can be designed as efficient primary lateral load

resisting systems particularly suited for ductile response with very good energy

dissipation characteristics when regular patterns of openings (e.g., windows, doors,

and/or mechanical penetrations) are arranged in a rational pattern (Park and Paulay 1975;

Paulay and Priestley 1992). Examples are shown in Figure 2.1 where wall piers are

interconnected or coupled to each other by beams at the floor and roof levels.

13

wallwall pier

couplingbeam

pier

Figure 2.1: Coupled wall structures.

The desired failure mechanism for a coupled wall structural system involves the

formation of plastic hinges in most or all of the coupling beams and also at the base of

each wall pier. In this manner, the dissipation of seismic input energy is distributed over

the height of the structure (rather than being concentrated in a few stories), similar to the

strong column-weak girder design philosophy for ductile moment resisting frames. The

behavior and mechanisms of lateral resistance of a single (i.e., uncoupled) wall and two

coupled wall systems are compared in Figure 2.2. The gravity loads acting on the walls

are ignored for this example and it is assumed that a lateral force in the plane of the walls

is applied at the top. The base moment resistance, Mw,unc of the uncoupled wall [Figure

2.2(a)] is developed in the traditional form by flexural stresses, while axial forces as well

as moments are resisted in the coupled wall systems [Figures 2.2(b) and 2.2(c)]. When a

coupled wall system is pushed from left to right under lateral loads, tensile axial forces

(Ntwb) develop in the left wall pier and compressive axial forces (Ncwb) develop in the

right wall pier due to the coupling effect. The magnitude of these wall axial forces is

14

equal to the sum of the shear forces of all the coupling beams at the upper floor and roof

levels; and thus, depends on the stiffness and strength of those beams.

As a result of the axial forces that develop in the walls, the lateral stiffness and

strength of a coupled wall system is significantly larger than the combined stiffness and

strength of the individual constituent walls (i.e., wall piers) with no coupling. The total

base moment, Mw of the coupled wall structures in Figures 2.2(b) and 2.2(c) can be

written as:

ccwbcwtww LNMMM (2.1)

where, Mtw and Mcw are the base moments in the tension and compression side walls,

respectively, Ncwb = Ntwb, and Lc is the distance between the centroids of the tension and

compression side walls. Then, the contribution of the wall axial forces from coupling to

the total lateral resistance of the system can be expressed by the coupling degree, CD as:

ccwbcwtw

ccwb

w

ccwb

LNMM

LN

M

LNCD

(2.2)

The coupling degree, which can be controlled by changing the strength and

stiffness of the beams relative to the wall piers as shown in Figures 2.2(b) and 2.2(c), is

an important parameter for the seismic behavior and design of coupled wall structures.

Too little coupling (i.e., too small a coupling degree) yields a system with behavior

similar to uncoupled walls and the benefits due to coupling are minimal. Too much

coupling (i.e., too large a coupling degree) will add excessive stiffness to the system,

causing the coupled walls to perform as a single pierced wall with little or no energy

dissipation provided by the beams, and will result in large axial forces in the foundation.

15

The desirable “range” for the amount of coupling lies in between these two extremes and

should be selected properly in seismic design as investigated by El-Tawil et al. (2002).

Mw,unc

(a) (b) (c)

Lc Lc

Mtw Mcw

strong beam

Mtw Mcw

weakbeam

Vb Vb

N =Ncwb twbNtwb N =Ncwb twbNtwb

Figure 2.2: Wall systems – (a) uncoupled wall; (b) coupled wall with strong beams; (c) coupled wall with weak beams.

2.2 Monotonic Cast-in-Place Concrete Coupled Wall Systems

During the last few decades, an extensive amount of experimental and analytical

research has been conducted on monolithic cast-in-place reinforced concrete coupled wall

systems for seismic regions (e.g., Paulay 1971, 1977; Paulay and Binney 1974;

Srichatrapimuk 1976; Paulay and Santhakumar 1976; Fintel and Ghosh 1980, 1982;

Aktan and Bertero 1981, 1984, 1987; Aktan et al. 1982; Aristizabal-Ochoa 1987;

Saatcioglu et al. 1987; Pekau and Cistra 1989; Subedi 1991a, 1991b; Chaallal 1992;

16

Chaallal and Gauthier 2000; Chaallal et al. 1996a, 1996b; Tassios et al. 1996; Harries et

al. 1998; Teshigawara 2000; Sugaya et al. 2000; Harries et al. 2000; Munshi and Ghosh

2000; Harries 2001; Cosenza and Pecce 2001; Paulay 2002; Lee and Watanabe 2003;

Canbolat et al. 2005; Wallace 2007; Baczkowski and Kuang 2008). The behavior and

design of the monolithic cast-in-place reinforced concrete coupling beams in these

systems are significantly different than the behavior and design of the unbonded post-

tensioned precast concrete coupling beams investigated in this research; and thus, a

complete review of the previous research listed above is beyond the scope of this

dissertation. However, some of the important findings and conclusions are summarized

below.

2.2.1 Behavior and Design of Cast-in-Place Concrete Coupling Beams

The primary role of coupling beams during an earthquake is the transfer of forces

from one wall pier to the other. In considering the seismic behavior and design of coupled

wall structures, it should be noted that significantly larger nonlinear deformations occur

in the coupling beams than in the wall piers that are coupled. The previous research has

shown that short monolithic cast-in-place reinforced concrete coupling beams with

conventional longitudinal and transverse steel reinforcement inevitably fail in diagonal

tension or sliding shear [Figures 2.3(a) and 2.3(b)], and have limited or no ductility

17

capacity (Paulay and Priestley 1992). The displacement capacity of these systems is

often exceeded by the demand (Harries 2001). The consideration of large ductility demands

under many load reversalshas led to the development of a bracing mechanism that

utilizes diagonal steel reinforcement in concrete coupling beams as shown in Figure 2.3(c).

This allows for the transfer of diagonal tension and compression forces to the

reinforcement during the lateral displacements of the beam, resulting in a considerably ductile

behavior with good energy dissipation characteristics.

(a) (b) (c)

Figure 2.3: Reinforced concrete coupling beams [Paulay and Priestley (1992)] – (a) diagonal tension failure; (b) sliding shear failure; (c) diagonal

reinforcement.

2.2.2 Current Code Requirements for Cast-in-Place Concrete Coupling Beams

For seismic design of cast-in-place concrete coupling beams, ACI 318-08 Section

21.9.7 specifies the required reinforcement to achieve adequate resistance and ductility.

Coupling beams with length to depth aspect ratios greater than 4 or less than 2 are outside

the typical range of coupling beams used in the U.S., and thus, are not discussed here.

Coupling beams with aspect ratios between 2 and 4 are provided with two design options.

In the first option, transverse and longitudinal reinforcement may be used according to

18

Sections 21.5.2 through 21.5.4. However, these sections are specific to flexural members

of special moment frames and it is stated in Section 21.5.1 of ACI 318-08 that:

Design rules derived from experience with relatively slender

members do not apply directly to members with length-to-depth ratios less than 4, especially with respect to shear strength.

The second option allows the coupling beam to be reinforced with two interesting

groups of diagonal bars placed symmetrically about the midspan. Test results have shown

that diagonal reinforcement is effective only if the bars are placed at a large inclination

(indicated by α in Figure 2.4); and thus, the use of diagonally reinforced coupling beams

is limited to beams with length-to-depth aspect ratios smaller than 4. Due to the presence

of high shear demands under large nonlinear reversed-cyclic rotations, the most common

practice for cast-in-place coupling beams with length-to-depth aspect ratios similar to the

beams investigated in this dissertation (i.e., aspect ratio < 4) is the diagonally-reinforced

system. Thus, the diagonal reinforcement requirements in ACI 318-08 are discussed

further below.

To provide the required lateral strength and ductility in seismic regions, diagonal

bars in coupling beams are typically placed symmetrically in two or more layers. Each

group of bars must have a minimum of four bars in two layers. The bars are then confined

with one of two different options. The first option provides transverse reinforcement on

each group of diagonal bars. The second option confines the entire beam cross-section

instead of confining each group of bars. These two different design options are shown in

Figure 2.4.

The use of diagonal reinforcement creates coupling beam designs that are very

difficult to construct due to the difficulty in placing the diagonal bars, especially at the

19

beam midspan regions where the two groups of bars intersect. The diagonal bars must

also extend into the wall piers, interfering with the construction of the walls and creating

a challenge for the placement of the reinforcement at the beam-to-wall interfaces. A

photograph of a typical diagonally reinforced coupling beam is shown in Figure 2.5.

(a)

(b)

Figure 2.4: Diagonal reinforcement requirements for coupling beams [from ACI 318 (2008)] – (a) confinement of each group of diagonal bars;

(b) confinement of entire beam cross-section.

20

Figure 2.5: Diagonally reinforced coupling beam (from Magnusson Klemencic Associates).

2.2.3 Analysis and Modeling of Cast-in-Place Concrete Coupled Wall Systems

As shown in Figure 2.6, previous research has often adopted an “equivalent

frame” analogy for the nonlinear inelastic hysteretic modeling and analysis of coupled

wall structural systems. The properties of the wall piers and the beams are concentrated at

the cetroid of each member. In the analytical model, rigid end zones (or kinematic

constraints) are typically necessary to model where the coupling beams frame into the

walls. Rigid end zones may also be needed in the wall piers depending on the stiffness of

the coupling beams. Nonlinear shear deformations in wall piers with aspect ratios, hw/lw

larger than 4 are often neglected (Paulay and Priestley 1992).

21

outline of structure

analyticalmodel

rigidend zones

hw

lw lw lw lwlb lb

Figure 2.6: Equivalent frame analytical models.

It is emphasized that the validity of the frame analogy used to model the behavior

of coupled wall structures can vary considerably depending on the stiffnesses assumed

for the members and the lengths of the rigid end zones. Furthermore, nonlinear shear

deformations in deep coupling beams and the axial “elongation” and “shortening” of the

tension and compression side wall piers due to axial-flexural interaction cannot be

represented using frame analogy. Nonlinear truss models have been used to predict the

nonlinear shear behavior of reinforced concrete members, including coupling beams

(Park and Eom 2007).

As described later in this dissertation, the nonlinear lateral load behavior of

unbonded post-tensioned coupling beams is governed by axial-flexural effects and gap

opening at the beam-to-wall interfaces rather than shear effects. Thus, the modeling of

22

the coupled wall structures in this research is done using fiber beam-column elements. A

significant advantage of using fiber elements instead of frame elements is that a

reasonably accurate model can be constructed accounting for axial-flexural interaction

(including axial elongation and shortening) in the beam and wall members, inelastic

behavior of concrete and steel, and gap opening at the beam-to-wall interfaces based only

on the dimensions of the model structure and uniaxial stress-strain properties for the

materials.

2.2.4 Coupling Beam Database

ACI ITG-5.1 (ACI 2008) defines minimum seismic acceptance criteria for

unbonded post-tensioned precast structural walls, including coupled walls, based on

experimental evidence and analysis. For use in comparisons with the unbonded post-

tensioned coupling beam specimens tested in this dissertation, Figure 2.7 shows the

measured ultimate sustained rotations of monolithic cast-in-place reinforced concrete

coupling beam test specimens that the author was able to find in the literature. The

database in Figure 2.7 [adapted from Dr. Kent Harries of the University of Pittsburgh

(personal communication)] includes research conducted by Barney et al. 1978; Bristowe

2000; Canbolat et al. 2005; Galano and Vignoli 2000; and Tassios et al. 1996. Based on

ACI ITG-5.1 (ACI 2008), the ultimate “sustained” rotation is defined as the largest

rotation that a beam is able to reach with no more than 20% drop in shear resistance

during three fully reversed cycles. The ultimate sustained rotation in Figure 2.7 is plotted

against the beam length-to-depth aspect ratio. The vertical highlighted region in the

figure denotes the most typical range of beam length-to-depth aspect ratios (between 2.5

23

and 4) used in the U.S., while the horizontal highlighted region depicts the FEMA 356

(2000) collapse prevention rotation level for monolithic cast-in-place coupling beams

with diagonal reinforcement. Note that, based on the ACI ITG-5.1 (ACI 2008) definition,

previous coupling beam tests under monotonic loading or under cyclic loading with fewer

than three repeated cycles at each displacement increment are not included in Figure 2.7.

00 1 2 3 4 5 6 7

2

4

8

10

beam length/depth (lb/hb) aspect ratio

ult

ima

te s

ust

ain

ed r

ota

tion

(%

)

typical US range

6

w/ diagonal reinforcement

diag. reinf. w/ HPFRCC

w/ rhombic reinforcement

w/o diagonal reinforcement

FEMA 356 level for CIPbeams with diagonal reinf.

Figure 2.7: Measured ultimate sustained rotations for monolithic cast-in-place reinforced concrete coupling beams.

24

2.3 Unbonded Post-Tensioning

An unbonded post-tensioned concrete structure is different than a bonded post-

tensioned structure in that the bond between the post-tensioning steel and the concrete is

intentionally prevented. This allows independent movement of the post-tensioning tendon

relative to the concrete member (except for anchorage locations at the ends); and thus, an

assumption of strain compatibility between the tendon and the adjacent concrete cannot

be made. Instead, the tendon’s change in strain is constant (ignoring friction forces) over

the unbonded length of the tendon. The change in strain at any point in an unbonded post-

tensioning tendon is the average change in strain due to member deformations in the

concrete adjacent to the tendon over the total unbonded length of the tendon. Therefore,

the tendon strain (and thus, stress) depends on the total change in the length of the

concrete adjacent to the tendon over the unbonded length rather than section

deformations. As a result of the uniform distribution of strains, unbonded tendons reach

the nonlinear strain range at larger overall member deformations than bonded tendons,

which is the main reason why they are preferred for seismic applications.

Unlike the axial-flexural behavior of structural members constructed using

unbonded post-tensioning, for a bonded post-tensioned member, it is reasonable and

customary to assume that the change in the tendon strain is the same as the change in the

concrete strain adjacent to the tendon. In other words, after grouting, an assumption of

strain compatibility between the tendon and the adjacent concrete can be made. Thus, the

strain at any point of the tendon can be calculated from the deformation of the

corresponding section (i.e., curvature and average axial strain) by assuming that plane

25

sections remain plane during axial-flexural deformations. Therefore, the change in strain

at any point in a bonded tendon depends only on the deformations at that section.

To achieve an unbonded post-tensioned system, tendons can be placed either

internal or external to the structural members (e.g., beams). Internal tendons are placed

inside ducts that, unlike the ducts in bonded construction, are not filled with grout.

Greased tendons and plastic sheathing may be used to reduce the friction forces that may

develop between the ducts and the tendons. Ducts may be oversized to ease the

placement of the tendons during construction and to prevent the tendons from coming

into contact with the ducts as the structure displaces. The elimination of the grouting

operation offers considerable advantages (i.e., reduced number of operations during

construction) in the application of post-tensioning. However, additional measures may be

needed for the corrosion protection of the tendons (e.g., the use of encapsulated anchors

and tendons).

Internal and external unbonded post-tensioned construction types differ in the

displaced shape of the tendon. The displaced shape of internal tendons follows the

displaced shape of the structural member, unless the ducts are sufficiently oversized. The

displaced shape of external tendons is generally different from that of the member except

at deviator or saddle point locations anchored to the concrete. The use of deviator points

in seismic applications is not common in order to achieve symmetric behavior under

reversed cyclic loading.

The application of unbonded post-tensioning in steel structural members is similar

to the application of external post-tensioning in concrete members. The post-tensioning

26

tendons can be placed outside or inside (as in the case of hollow cross-sections) the steel

member.

2.4 Unbonded Post-Tensioned Hybrid Coupled Wall Systems

Recent research at the University of Notre Dame (Shen and Kurama 2000,

2002a,b; Kurama and Shen 2004; Kurama et al. 2004, 2006; Shen et al. 2006)

investigated the use of unbonded post-tensioning to couple reinforced concrete walls with

steel coupling beams that are not embedded into the walls. As shown in Figure 2.8 for a

floor-level subassembly, coupling is achieved by post-tensioning the beams and the wall

piers together at the floor and roof levels, similar to the development of coupling in the

precast concrete system investigated in this dissertation. The beam-to-wall joint regions

include concrete confinement reinforcement, embedded steel plates, shim plates, and top

and seat angles. The embedded steel plates are used to transfer the large compression

stresses in the beam flanges into the wall concrete. The shim plates at the beam-to-wall

interfaces serve two purposes: (1) to ensure contact between the beam flanges and the

wall piers during the nonlinear cyclic lateral displacements of the structure; and (2) to

accommodate construction tolerances and facilitate alignment of the beam. If necessary,

reinforcing cover plates may be used to strengthen and stiffen the flanges in the large

compression stress regions at the beam ends.

27

section at A-A

A

coupling

PT tendon

joint

anchorage

embedded

angle

cover

plate

spiralbeam

plate

wall region

region

A

shimplate post-tensioning

tendons

Figure 2.8: Hybrid coupled wall subassembly [from Shen and Kurama (2002b)].

Figure 2.9(a) shows the measured coupling beam shear force versus beam chord

rotation behavior of a half-scale steel coupling beam subassembly similar to the one in

Figure 2.8 (Shen et al. 2006). The hysteresis loops indicate desirable seismic

characteristics with stable behavior up to 8.0% rotation and significant energy

dissipation. Figure 2.9(b) shows a close-up view of the beam end at 7.0% rotation,

demonstrating that most of the nonlinear rotations of the beam occur through the opening

of gaps at the ends. The rotations of the beam with respect to the wall piers result in the

yielding of the top and seat angles in tension and compression.

As a result of post-tensioning, the initial stiffness of an unbonded post-tensioned

steel coupling beam before the initiation of gap opening is similar to the initial stiffness

of an embedded steel coupling beam with the same dimensions. The hysteresis loops in

Figure 2.9(a) indicate that the post-tensioning strands provide a restoring force such that

the gaps are closed upon unloading, thus pulling the beam towards its undeformed

28

position with little residual displacements (i.e., upon unloading, the hysteresis loops go

towards the origin indicating a large self-centering capability). The initial stiffness of the

subassembly is preserved even after unloading from very large nonlinear rotations.

The sum of the coupling beam post-tensioning strand forces, Pb measured during

the test is plotted in Figure 2.9(c). The post-tensioning force is normalized with respect to

the total design strength of the post-tensioning strands, Σabpfbpu, where abp is the beam

post-tensioning strand area and fbpu is the ultimate design strength of the post-tensioning

strand. Before the initiation of gap opening, the forces in the post-tensioning strands are

similar to the initial post-tensioning forces. As the specimen is displaced further, the

strand forces increase, thus resisting gap opening. Due to the use of unbonded post-

tensioning strands, the strains in the strands remain small and the nonlinear straining (i.e.,

yielding) of the tendons is significantly delayed. Thus, most of the initial post-tensioning

force is maintained throughout the cyclic displacement history of the structure as long as

the anchorage regions for the tendons do not deteriorate.

29

0

beam chord rotation, θb (%)

bea

m s

hea

r fo

rce,

Vb [

kip

s (k

N)]

0-10 10

60(267)

-60(-267)

anglefracture

(a)

(b)

Figure 2.9: Hybrid coupled wall subassembly experiments [adapted from Kurama et al. (2006)] – (a) measured coupling beam shear force versus chord

rotation behavior; (b) photograph of displaced shape at beam end; (c) measured total beam post-tensioning force.

30

0


0-10 10

1

Pb

/ Σ

ab

p f

bp

u

prestress loss

initial force

final force

(c)

Figure 2.9 continued.

The most typical failure mode for the unbonded post-tensioned coupling system

in Figure 2.8 is the low-cycle fatigue fracture of the top and seat angles. For the test

specimen in Figure 2.9, the initiation of low cycle fatigue cracks was observed in the

vertical legs of the tension angles at a coupling beam chord rotation of about 7.0%. The

cracks occurred at the critical section adjacent to the fillet. The specimen was able to

sustain three cycles at 8.0% rotation with a steady, but not excessively large, reduction in

strength [see Figure 2.9(a)]. This reduction in strength occurred due to increased cracking

and necking of the vertical legs of the tension angles. Failure of the specimen eventually

occurred as a result of the complete fracture of the vertical leg of the seat angle at the

right end of the beam when 9.0% rotation was reached for the first time. The resistance of

31

the specimen at angle fracture was, approximately, 90% of the peak resistance. Figure

2.10 shows the fractured angle at 9.0% rotation. All four angles had sustained significant

damage at this stage resulting in a considerable amount of energy dissipation as shown in

Figure 2.9(a). The subassembly was unloaded and the test was terminated upon the

fracture of the first angle.

Figure 2.10: Low cycle fatigue fracture of top and seat angles.

To demonstrate the contribution of the top and seat angles to the coupling beam

behavior, Figure 2.11 shows the measured coupling beam shear force versus chord

rotation behavior of a subassembly similar to the one in Figure 2.9, but with no top and

seat angles. The behavior of the subassembly without angles is essentially bilinear-

elastic, caused mainly by gap opening at the beam ends. Comparing Figures 2.9(a) and

2.11, the significant increase in strength and energy dissipation occurs as a result of the

angles.

32

0


bea

m s

hea

r fo

rce,

Vb [

kip

s (k

N)]

0-10 10

60(267)

-60(-267)

Figure 2.11: Hybrid coupled wall subassembly with no angles [from Kurama et al. (2006)].

The experimental research summarized above has shown that unbonded post-

tensioned hybrid coupled wall subassemblies can be designed to go through large

nonlinear reversed cyclic displacements without receiving significant damage in the wall

piers or the beams, and with most of the damage occurring in the top and seat angles at

the beam-to-wall connections. The beams do not need to be replaced after a large

earthquake as long as the damaged, yielded, or fractured angles and post-tensioning

strands are replaced. Damage in the coupling regions of the wall piers can also be

prevented, including cracking and/or spalling of the cover concrete [see Figure 2.9(b)].

The post-tensioning anchors and the angle-to-wall and angle-to-beam connections are

critical components that can affect the performance of the structure (Kurama et al. 2006).

33

Analytical investigations of floor level unbonded post-tensioned hybrid coupling

beam subassemblies as well as of multi-story coupled wall systems were also conducted

by this previous research project. As an example, Figure 2.12(a) shows the predicted

coupling beam shear force versus chord rotation behavior and Figure 2.12(b) shows the

predicted coupling beam total post-tensioning force of the subassembly in Figures 2.9(a)

and 2.9(c), respectively, demonstrating the effectiveness of the analytical model in

capturing the measured response. A performance-based seismic design approach and

simplified design/analysis tools for the structure were also developed through the

investigation.

34

0


bea

m s

hea

r fo

rce,

Vb [

kip

s (k

N)]

0-10 10

60(267)

-60(-267)

(a)

0


0-10 10

1

Pb/Σ

ab

pf b

pu

(b)

Figure 2.12: Hybrid coupled wall subassembly predicted behavior [from Shen et al. (2006)] – (a) coupling beam shear force versus chord rotation behavior; (b) total beam post-

tensioning force.

35

2.5 Unbonded Post-Tensioned Precast Moment Frames

Precast concrete construction results in cost-effective structures that provide high

quality production and rapid erection. However, the use of precast concrete buildings in

seismic regions of the United States has been limited due to uncertainty about their

performance during earthquakes. Since the 1990s, a significant amount of research has

been conducted on the seismic behavior and design of these structures. One of the precast

concrete frame systems that has successfully emerged from these research efforts uses

unbonded post-tensioning between the precast beam and column members to achieve the

lateral load resistance needed in seismic regions (e.g., Cheok and Lew 1991, 1993; Cheok

et al. 1993; Priestley and Tao 1993; MacRae and Priestley 1994; Priestley and MacRae

1996; El-Sheikh et al. 1997, 1999, 2000).

As an example, Figure 2.13(a) shows a multi-story precast concrete frame

structure and Figure 2.13(b) shows an interior unbonded post-tensioned precast beam-

column subassembly. The lateral load behavior of these structures is governed by the

opening of gaps at the beam-to-column joints [Figure 2.13(c)], similar to the opening of

gaps at the beam-to-wall joints of unbonded post-tensioned coupling beams. Thus, the

previous research on unbonded post-tensioned precast concrete moment frames is

important for this dissertation. The major findings and conclusions from this previous

research, some of which are similar to the findings from the previous research on

unbonded post-tensioned steel coupling beams described above, are:

(1) As a result of post-tensioning, the initial linear-elastic lateral stiffness of an

unbonded post-tensioned precast concrete frame structure is similar to the initial stiffness

of a monolithic cast-in-place reinforced concrete frame structure.

36

(2) Unbonded post-tensioned precast concrete frames can soften (indicating a

significant reduction in the lateral stiffness) and go through large nonlinear cyclic lateral

displacements without significant damage, and thus, without significant strength

degradation (as compared to precast concrete frames with bonded tendons or monolithic

cast-in-place reinforced concrete frames).

(3) Unbonding of the post-tensioning tendons significantly reduces the amount of

tensile stresses transferred to the concrete, thus reducing damage due to concrete

cracking.

(4) Large compression strains develop at the corners of the beams at the beam-to-

column interfaces due to the post-tensioning force. Therefore, transverse reinforcement

(e.g., spiral or closed hoop reinforcement) is necessary to confine the concrete at the

beam ends.

(5) Upon unloading from a large nonlinear lateral displacement, the post-

tensioning force provides a restoring effect (i.e., self-centering capability) that tends to

close the gaps and pull the frame back towards its original undeformed (i.e., plumb)

position without significant residual lateral displacements.

(6) The friction resistance that develops due to post-tensioning is sufficient to

transfer the shear forces from gravity and lateral loads without the need for corbels or

shear keys at the beam-to-column interfaces. As long as the post-tensioning force is

maintained, the shear slip resistance at the beam-to-column interfaces is maintained

during large cyclic lateral displacements of the structure.

(7) Unbonded post-tensioning alters the shear resistance mechanism in the beams

and in the beam-to-column joint panel regions (as compared with bonded post-tensioned

37

and monolithic cast-in-place reinforced concrete structures), in which the shear force is

transferred by a large diagonal compression strut, greatly simplifying the design of the

beam and joint shear reinforcement, and reducing damage.

precast column

precast beam

column

beam

unbonded post-tensioning

(a)

(b)

gap opening atbeam-to-columninterface

(c)

Figure 2.13: Unbonded post-tensioned precast moment frames – (a) structure; (b) interior beam-column subassembly; (c) idealized,

exaggerated subassembly displaced shape.

The previous research summarized above has shown that provided that the

unbonded length of the post-tensioning steel is sufficient to prevent the yielding of the

tendons, and the compression zones in the contact regions and anchor details for the

tendons are satisfactory, then unbonded post-tensioned structures can reach design level

38

lateral displacements and beyond with little damage under cyclic loads. According to El-

Sheikh et al. (1999), the nonlinear moment versus rotation behavior of a typical

unbonded post-tensioned precast concrete beam-column joint subassembly can be

idealized using a trilinear relationship as shown in Figure 2.14(a). The five limit states

marked on the smooth moment-rotation relationship, which form the basis for the

idealized relationship, are as follows: Point (1) represents the initiation of gap opening

(i.e., decompression) at the beam-to-column interfaces; Point (2) represents a significant

reduction in the stiffness of the subassembly (i.e., softening), which occurs primarily due

to increased gap opening at the beam-to-column interfaces; Point (3) represents the

initiation of cover concrete spalling at the beam ends; Point (4) represents the initiation of

yielding (i.e., nonlinear straining) of the unbonded post-tensioning steel; and Point (5)

represents the axial-flexural failure of the subassembly due to the crushing of the

confined concrete at the beam ends.

Figure 2.14(b) shows the analytical model of an interior unbonded post-tensioned

precast concrete beam-column joint subassembly developed by El-Sheikh et al. (1999,

2000). This model was used to generate the smooth subassembly moment-rotation

relationship in Figure 2.14(a) and includes the following elements in the DRAIN-2DX

structural analysis program (Prakash et al. 1993): (1) fiber beam-column elements to

model the lengths of the beams with unbonded post-tensioning steel; (2) linear-elastic

frame beam-column elements to model the column as well as the lengths of the beams

with bonded post-tensioning steel (if any), where only linear-elastic deformations are

expected to occur; (3) truss elements to model the unbonded length of the post-tensioning

tendons; (4) a zero-length rotational spring element to model the joint panel zone shear

39

deformations of the column member; (5) kinematic constraints (rigid links) for the beam

elements and rigid end zones for the column elements to model the axial and flexural

stiffnesses (assumed to be infinitely large) within the panel zone; and (6) kinematic

constraints to model the ends of the unbonded length of the post-tensioning tendons. The

gap opening behavior at the beam-to-column interfaces is modeled using compression-

only concrete stress-strain relationships for the fiber elements at the beam ends. The

results obtained from the analytical model were found to compare well with experimental

results reported by Cheok and Lew (1993).

2.5.1 Frames with Supplemental Energy Dissipation

Figures 2.15(a) and 2.15(b) show the typical measured lateral force versus

displacement behavior of interior and exterior unbonded post-tensioned precast beam-

column subassemblies under reversed cyclic lateral loading. Since the structure

(a) (b)

Figure 2.14: Analytical investigation of unbonded post-tensioned precast beam-column subassemblies [from El-Sheikh et al. (1999, 2000)] – (a) moment-rotation relationship;

(b) analytical model.

40

experiences little damage, the behavior is essentially elastic through nonlinear

displacements (i.e., nonlinear-elastic) dominated by gap opening, with very little energy

dissipation. As a result of the small amount of energy dissipation, the peak lateral

displacements of unbonded post-tensioned precast frame structures under earthquakes

can be, on average, 1.40 times the peak displacements of comparable monolithic cast-in-

place reinforced concrete frames (Priestley and Tao 1993; Seo and Sause 2005). Thus,

the greatest setback to the use of these structures in seismic regions has been that their

lateral displacement demands during a severe earthquake may be larger than acceptable.

(a) (b)

Figure 2.15: Measured lateral force-displacement behavior [from Priestley and MacRae (1996)] – (a) interior joint; (b) exterior joint.

In order to reduce the lateral displacement demands during a seismic event, the

use of bonded mild steel reinforcement (e.g., Grade 60 reinforcement) through the precast

beam-column joints, in addition to the unbonded post-tensioning steel, has been

investigated (Cheok and Stone 1994; Stone et al. 1995; Cheok et al. 1996, 1998; Stanton

et al. 1997; Nakaki et al. 1999; Priestley et al. 1999; Stanton and Nakaki 2002; Hawileh

et al. 2006; Rahman and Sritharan 2007). These partially prestressed systems are often

41

referred to as “hybrid” precast concrete frame structures in the literature due to the mixed

use of mild steel and post-tensioning steel reinforcement across the beam-column joints

as shown in Figure 2.16. Properly designed and detailed mild steel reinforcement yields

in tension and compression during the cyclic gap opening rotations that occur at the

beam-to-column interfaces, thus dissipating energy. The bond between the mild steel bars

and the concrete is typically prevented over a short predetermined length at the ends of

the beams (by wrapping the bars) to ensure that the design lateral displacement can be

achieved without low-cycle fatigue fracture of the mild steel reinforcement and to reduce

the cracking of the concrete during the deformations of the bars in tension.

beam

wrapped length

PT tendon

mild steel bar

unbonded length

fiber reinforced grout

trough

beam

beam-to-column interface

A

A

B

B

column

section A-A

central ductfor post-tensioningtendon

section B-B

mild steel bars (tranreinforcement not sh

Figure 2.16: “Hybrid” precast concrete frame beam-column joint [adapted from Kurama (2002)].

42

More recently, Morgen and Kurama (2005, 2007, 2008, 2009) developed a new

type of friction damper that can be used at the beam ends of unbonded post-tensioned

precast concrete frames. Figure 2.17(a) shows the test set-up schematic and Figure

2.17(b) shows a photograph of the test set-up, where the beam is oriented in the vertical

configuration due to space limitations in the laboratory. Figure 2.18 compares the beam

end moment versus chord rotation behavior of a test subassembly without friction

dampers and a test subassembly with friction dampers. The results from this 80% scale

experimental investigation and accompanying analytical investigations have shown that

the unique gap opening behavior between the beam and column members of these

structures allows for the development of innovative energy dissipation systems that can

be used to reduce the lateral displacements while maintaining the desirable self-centering

capability and the ability to undergo large nonlinear displacements with little damage.

43

hb = 24" or 32"

126 3/4"

80"

58" 58"100"

198"

support

fixture

106 3/4"

H

test beam

friction damper

column fixture

80% scale

strong

floor

loading and

bracing frame

not shown

support

fixture

beam-to-column

interface with fiber

reinforced grout

(3/4" thick)

Two Dywidag Spiro

ducts and unbonded

post-tensioning tendons

TM

Two Dywidag

Multiplane AnchorsTM

8 3/4"

(a)

(b)

Figure 2.17: Friction-damped post-tensioned precast moment frames [from Morgen and Kurama (2004)] – (a) test set-up schematic; (b) photograph of test set-up.

44

Test 43


-5.0 5.02.50-2.5

0

bea

m e

nd

mo

men

t, M

b

[kip

-ft

(kN

-m)]

(-1016)-750

-500

-250

250

500

750(1016) without dampers

(a)

Test 44

with dampers


-5.0 5.02.50-2.5

0

bea

m e

nd

mo

men

t, M

b

[kip

-ft

(kN

-m)]

(-1016)-750

-500

-250

250

500

750(1016)

(b)

Figure 2.18: Measured beam end moment versus chord rotation behavior [from Morgen and Kurama (2004)] –

(a) without dampers; (b) with dampers.

45

2.6 Behavior of Top and Seat Angles

Unbonded post-tensioned frame and wall structures can use supplemental passive

energy dissipation where gap opening occurs to reduce the lateral displacement demands

while maintaining their unique and desirable characteristics under seismic loads. Steel

top and seat angles offer an economical and readily available method for providing

energy dissipation and increasing structural redundancy at the beam-to-column or beam-

to-wall joints as shown in Figure 2.19.

(a) (b)

ax

vertical leg

horizontal legtension angle

column

loading

beam

bolts

vertical leg

bolt head

innermost bolt

fillethorizontal leg

heel

compression angle

wabw

lgv

ka

ta

lgh

hb

lg2

Figure 2.19: Top and seat angle connection [adapted from Shen et al. (2006)] – (a) deformed configuration; (b) angle parameters.

The behavior of steel beam-to-column connections with top and seat angles has

been extensively studied (e.g., Azizinamini 1985; Aktan et al. 1989; Youssef-Agha et al.

46

1989; Kishi and Chen 1990; Lorenz et al. 1993; Bernuzzi et al. 1994, 1997; Leon and

Shin 1994; Mander et al. 1994; Sarraf and Bruneau 1996; Bernuzzi 1998; Kasai et al.

1998; Kukreti and Abolmaali 1999; Swanson and Leon 1999; Shen and Astaneh-Asl

1999a, 1999b, 2000; Sims 2000; Ricles et al. 2001, 2002; Garlock 2002; Garlock et al.

2003, 2005). Figure 2.19(a) shows the idealized exaggerated deformed configuration of a

top-and-seat-angle steel frame connection, which is a semi-rigid connection comprised of

a pair of steel angles bolted to the flanges of the beam and the column. Figure 2.19(b)

shows some of the design parameters for an angle.

The flexural stiffness, strength, and ductility of a top-and-seat-angle beam-to-

column connection are influenced by many design parameters, including: (1) beam depth,

hb; (2) angle length, la; (3) angle leg thickness, ta; (4) angle steel yield strength, fay; (5)

angle-to-column connection gage length, lgv, measured from the heel of the angle to the

center of the innermost angle-to-column connectors; (6) angle-to-beam connection gage

length, lgh, measured from the heel of the angle to the centroid of the angle-to-beam

connector bolt group; (7) angle fillet length, ka, measured from the angle heel to the toe of

the angle fillet; (8) angle connector bolt type and diameter, dab; (9) bolt head/nut width

measured across flat sides, wabw; and (10) number of bolts, nab.

The behavior of the top and seat angles in the precast concrete coupled wall

system investigated in this dissertation is similar to the behavior of the angles in the

hybrid coupled wall system investigated by Shen et al. (2006) and the angles in the post-

tensioned steel frame connections investigated by Kishi and Chen (1990), Lorenz et al.

(1993), Sims (2000), Garlock et al. (2003), and Ricles et al. (2001). Important findings

from Sims (2000), Ricles et al. (2001), Garlock et al. (2003), and Shen et al. (2006) are

47

described below. The research conducted by Kishi and Chen (1990) and Lorenz et al.

(1993) is used in the modeling of the angles in this dissertation, and thus, is discussed in

more detail in Section 2.6.1.

(1) Sims (2000) identified five potential failure modes for the angles as follows:

(i) bolt thread failure; (ii) bolt/angle flexural mechanism; (iii) shear mechanism; (iv)

vertical-leg/horizontal-leg combination mechanism; and (v) vertical-leg mechanism.

According to Sims, the vertical leg mechanism represents an ideal mode with the lowest

maximum strain in the angle.

(2) After the formation of a plastic hinge mechanism, the angle stiffness in tension

greatly decreases but does not become zero. This post-yield stiffness is nearly linear and

is comprised of both geometric hardening and material hardening. The geometric

hardening accounts for slightly less than half of the total post-yield strength (Garlock et

al. 2003).

(3) The boundary conditions assumed for the horizontal leg (i.e., leg parallel to

the beam) are important in understanding the behavior of top and seat angles. Sims

(2000) found that for angle configurations with vertical leg mechanism failure modes, the

model developed by Kishi and Chen (1990) and Lorenz et al. (1993) can be used to

estimate the angle yield force, Tayx. However, the plastic deformations in the horizontal

leg and the effects of bolt response are neglected in this model, resulting in an

overestimation of the angle yield force for other failure modes, especially for angle

configurations with non-negligible bolt response (e.g., bolt elongation, slip, yielding,

fracture).

48

(4) Sims (2000) also concluded that bolt response reduces the strength, stiffness,

and ductility of the angle system. Due to the smaller ductility of high strength bolts as

compared to angle sections, configurations with bolt fracture are less ductile than those

with angle fracture. Thus, bolt failure in top-and-seat angle connections should be

avoided. Furthermore, bolt slip in the angle horizontal leg is a cause of significant

stiffness reduction for the connection.

(5) Catenary effects at large angle deformations in tension play a very significant

role on the angle behavior. Inclusion of large deflections (i.e., second order geometric

effects) in the analytical modeling of top-and-seat angle connections is needed to

accurately capture these effects (Sims 2000).

(6) Both Sims (2000) and Garlock et al. (2003) found that an important

consideration in the behavior of top and seat angles is the angle vertical leg connection

gage length, lgv, measured from the heel of the angle to the center of the innermost

connectors for the vertical leg. Sims (2000) found that for short “effective” gage length

lg2 values, the maximum strain in the angle occurs along the innermost edge of the

vertical leg connection bolt heads/nuts. For long lg2 values, the maximum strain occurs

along the toe of the fillet in the vertical leg. For intermediate lg2 values, the maximum

strain in the angle occurs along the toe of the fillet in the horizontal leg. Garlock et al.

(2003) noted that angles with smaller gage length to angle thickness ratio (lg2/ta) dissipate

more energy for a given value of angle displacement and are stronger and stiffer than

angles with larger lg2/ta ratios. However, angles with smaller lg2/ta ratios have less

resistance to low-cycle fatigue. Thus, the angle gage length and thickness must be

49

selected carefully considering the stiffness, strength, energy dissipation, and ductility

requirements of the connection.

(7) Ricles et al. (2001) successfully modeled the top and seat angles in a post-

tensioned steel beam-to-column connection using two parallel bilinear truss element

springs in the DRAIN-2DX program (Prakash et al. 1993). The truss element springs

represent the behavior of the angle when gap opening occurs at the beam-to-column

interface.

(8) The top and seat angles used in Shen et al. (2006) were shown to provide

adequate energy dissipation to unbonded post-tensioned hybrid coupled wall structures.

These angles typically failed due to low cycle fatigue fracture of the vertical legs.

2.6.1 Kishi and Chen (1990) and Lorenz et al. (1993)

A model developed by Kishi and Chen (1990) and Lorenz et al. (1993) is used to

describe the behavior of the top and seat angles at the beam-to-wall connections of the

coupled wall system investigated in this dissertation. The model, developed for the

analysis and design of steel top-and-seat-angle beam-to-column connections, is based on

equilibrium considerations with assumed internal force distributions and boundary

conditions for the angles. Other researchers (e.g., Goto et al. 1991; Matsuoka et al. 1993)

have also used this model to investigate the behavior of semi-rigid steel frame

connections. Several other similar top-and-seat-angle connection models exist (e.g.,

Sarraf and Bruneau 1996; Aktan et al. 1989); however, these are not used in this

dissertation.

50

Note that the model developed by Kishi and Chen (1990) and Lorenz et al. (1993)

can only be used to estimate the initial stiffness and yield force capacity of the tension

angle in a top-and-seat-angle connection under monotonic loading. The post-yield

behavior of the tension angle, the behavior of the compression angle, or the behavior of

the connection under cyclic loading is not addressed in their investigation.

2.6.1.1 Tension Angle Initial Stiffness, Kaixt

The initial linear-elastic stiffness of the tension angle is determined by making the

following assumptions (see Figure 2.20):

(1) The vertical leg of the angle is fixed along the innermost (i.e., closest to the beam)

edge of the angle-to-column connection bolt head; and

(2) The horizontal leg of the angle moves horizontally when pulled by the beam

flange (i.e., the rotation of the horizontal leg with respect to the vertical leg, which

occurs due to the rotation of the beam with respect to the column, is ignored).

Based on these assumptions and considering the shear deformations of the vertical

leg, it can be shown that the initial linear-elastic stiffness of the angle, Kaixt is given as:

)0.78t(ll

I3E

δ

TK

2a

2g1g1

aa

ax

axaixt

(2.3)

where, Tax is the force in the tension angle parallel to the beam, δax is the horizontal

displacement of the heel of the angle, EaIa is the flexural stiffness of the angle vertical leg

cross section, ta is the thickness of the angle leg, and lg1 is the length of the vertical leg

that is assumed to act as a cantilever. Using centerline dimensions for the angle legs and

referring to Figure 2.20(a),

51

2

t

2

wll aabwgvg1 (2.4)

where, wabw is the width (across flats) of the angle-to-column connector bolt head/nut and

lgv is the angle vertical leg connection gage length measured from the heel of the angle to

the center of the innermost angle-to-column connectors.

52

(a)

(b)

(c)

vertical leg

bolt head

innermost bolt

fixed support

wabw

lgv lg1

ka

ta

ka

ka

lgv l g2

δayx δayx

plastichinges

Nap

MapVap

Ma

Tayy

Tayx

Figure 2.20: Angle model [adapted from Kishi and Chen (1990) and Lorenz et al. (1993)] – (a) cantilever model of tension angle; (b) assumed yield mechanism; (c) free body of

angle horizontal leg.

53

2.6.1.2 Tension Angle Yield Force Capacity, Tayx

Based on the assumption of the formation of two plastic hinges in the vertical leg

of the angle as shown in Figure 2.20(b), the yield force capacity, Tayx of the tension angle

can be determined. One of the plastic hinges is located along the innermost edge of the

angle-to-column connection bolt heads/nuts and the second plastic hinge is located along

the toe of the fillet. The work equation for the tension angle at this plastic mechanism

state is:

κκ2 2gapap lVM (2.5)

where, Map is the plastic moment, Vap is the plastic shear force in the vertical leg, and κ is

the plastic hinge rotation. By using the free body diagram of the angle horizontal leg in

Figure 2.20(c), the tension angle yield force, Tayx is equal to the plastic shear force Vap in

the vertical leg.

The distance lg2 in Equation (2.5) is the “effective” gage length for the assumed

plastic hinge mechanism, and is equal to the distance between the two plastic hinges as:

aabw

gvg kw

ll 22 (2.6)

where, ka is the distance from the angle heel to the toe of the fillet. This effective gage

length is usually a short distance; and thus, the effect of the shear force on the plastic

moment capacity is considered through a shear-flexure interaction equation as follows:

1

4

00

a

ap

a

ap

V

V

M

M (2.7)

where, Ma0 and Va0 are the plastic moment and plastic shear force, respectively, in the

vertical leg without considering shear-flexure interaction as:

54

4

2

0aaay

a

tlfM (2.8)

20

aaaya

tlfV (2.9)

in which fay is the yield strength of the angle steel and la is the length of the angle.

Substituting Equations (2.5), (2.8), and (2.9) into Equation (2.7), the angle yield force

Tayx = Vap can be determined from:

14

00

2

a

ap

a

ap

a

g

V

V

V

V

t

l (2.10)

Note that in Figure 2.20(c), the horizontal leg of the angle is cut along the

innermost edge of the angle-to-beam connectors. The shear force, Tayy in the horizontal

leg and the corresponding axial force, Nap in the vertical leg are ignored in the above

formulation. The moment Ma is also small, and thus, is ignored.

2.7 Chapter Summary

This chapter presents a summary of the previous research on coupled wall

structures and on unbonded post-tensioned systems for use in seismic regions. Important

findings from the literature are summarized below.

(1) Coupled wall structural systems are effective primary lateral load resisting

systems for seismic regions.

(2) Monolithic cast-in-place reinforced concrete coupling beams often require the

use of diagonal reinforcement to prevent premature failure modes due to diagonal tension

and sliding shear. However, this diagonal reinforcement is very difficult to construct and

place.

55

(3) Unbonded post-tensioning has been successfully applied to different types of

building systems in seismic regions. In an unbonded post-tensioned structure, the

nonlinear behavior occurs primarily as a result of the opening of gaps along the joints

between the structural members, and not as a result of material nonlinearity. The gap

opening behavior enables these structures to undergo large lateral displacements with

little damage. The post-tensioning steel provides a significant restoring force resulting in

a large self-centering effect. Limited energy dissipation in unbonded post-tensioned

structures may result in larger than acceptable lateral displacement demands during a

severe earthquake.

(4) Post-tensioned steel coupling beams can provide stable levels of coupling

between concrete walls over large nonlinear reversed-cyclic deformations.

(5) Fiber beam-column elements have been successfully used to model the

nonlinear hysteretic behavior of different types of unbonded post-tensioned structures,

including the opening of gaps at the joints between the structural members.

(6) Steel top and seat angles are effective structural components that can be used

at the gap opening connections to provide energy dissipation and structural redundancy

during an earthquake. In a properly-designed post-tensioned top-and-seat-angle

connection, the only components to receive significant damage are the angles, which can

be replaced after the earthquake.

56

CHAPTER 3

PRECAST COUPLING BEAM SUBASSEMBLY EXPERIMENTS

This chapter provides a description of the half-scale experimental program that

was conducted in the Structural Systems Laboratory at the University of Notre Dame to

investigate the nonlinear lateral load versus deformation behavior of unbonded post-

tensioned coupled wall subassemblies using precast concrete coupling beams. Please

refer to Chapter 10 for the description and details for the full-scale prototype.

Eight coupled wall subassemblies (Tests 1 – 4B) are tested using four coupling

beam specimens. Each subassembly includes a coupling beam and the adjacent concrete

wall regions at a floor level. The effects of the following parameters are investigated: (1)

beam post-tensioning tendon area and initial stress; (2) initial beam concrete stress; (3)

angle strength; and (4) beam depth. Tests 1, 2, 3B, and 4B are conducted using a

predetermined displacement loading history until failure of the specimen is achieved.

Tests 3, 3A, 4, and 4A are conducted under a similar displacement history but are stopped

prior to failure so that the beam specimen may be reused.

The experimental program has the following objectives: (1) to investigate the

nonlinear lateral load-deformation behavior of unbonded post-tensioned precast concrete

coupling beam subassemblies; (2) to verify the analytical models; (3) to verify the design

of the subassemblies; and (4) to develop practical application recommendations. The

57

remainder of this chapter is divided into the following sections: (1) experiment setup; (2)

test subassembly components; and (3) testing procedure.

3.1 Experiment Setup

Figure 3.1(a) shows an eight-story coupled wall system under lateral loads and

Figure 3.1(b) shows the idealized exaggerated displaced shape of a floor level

subassembly. With respect to the “reference line” in Figure 3.1(b), it can be seen that the

same subassembly displaced shape can be achieved through the vertical displacements of

the right wall pier region as shown in Figure 3.1(c). This concept is used for the design of

the test setup for the experimental program. It is assumed that the left and right wall pier

regions in Figure 3.1(b) rotate by the same amount.

lw lw lb

2nd floor

3rd floor

4th floor

5th floor

6th floor

7th floor

8th floor

roof

hw

wallpier

wallpier

reference line

reference line

(b)

(c)

left wall regionright wall region

left wall region

right wall region

(a)

Figure 3.1: Simulation of floor level coupled wall subassembly displacements – (a) multi-story structure; (b) idealized displaced subassembly; (c) rotated subassembly.

58

Note that the subassembly test setup does not model the wall pier shear forces that

develop in a multi-story structure; and thus, does not capture the effect of the wall piers

on the coupling beam axial forces during the application of lateral loads on the system.

The effect of the wall piers on the coupling beam axial forces may be significant in the

lower floor level beams; however, they are negligible for the coupling beams in the upper

floor and roof levels (Kurama and Shen 2004). Therefore, the subassembly configuration

used in the experimental program is more representative of mid to upper floor and roof

levels in a multi-story coupled wall structure.

As shown in Figures 3.2 – 3.4, each test subassembly consists of two concrete

wall pier regions, referred to as the reaction block and load block, that are connected, or

coupled using a precast concrete coupling beam in between. More details on the coupling

beam, reaction block, and load block components of the test subassembly can be found in

the next section. The subassembly components are connected together using an unbonded

post-tensioning tendon comprised of two, three, or four ASTM A416 low-relaxation

strands with a nominal strand diameter of φp = 0.6 in. (15.2 mm), cross-sectional area of

ab = 0.217 in2 (140 mm2), and design maximum strength of fpu = 270 ksi (1862 MPa). The

post-tensioning strands are placed inside a 1 in. by 3 in. (25 mm by 76 mm) nominal size

Dywidag® Spiro duct located at the beam centerline, and run the length of the test

subassembly through matching ducts inside the reaction block and load block. Bond is

prevented between the strands and the concrete by not placing grout in the post-

tensioning ducts over the entire length of the strands between the anchors. This is done to

delay or prevent the “yielding” of the post-tensioning steel [at an assumed design yield

59

strain of εpy = 0.0086 and yield strength of fpy = 245 ksi (1689MPa), (PCI 2004)] during

the experiments.

High-strength [with 28-day compressive strength ranging from 8.0 to 12 ksi (55 –

83 MPa)] fiber-reinforced grout is used at the beam-to-wall interfaces to provide

alignment and good matching surfaces between the coupling beam and the wall fixtures.

A non-flowing grout mixture with a low water-to-cement ratio is designed for this

purpose as described in more detail in Chapter 4. Cresset® Crete-Lease 880-VOC or 20-

VOC release agent (bond breaker) is used between the fiber-reinforced grout and the wall

surfaces to help force the gap opening to occur between the grout and the wall face. Note

that despite the use of a bond breaker agent on the wall surfaces, during large rotations of

the beam in many of the tests, gaps occurred at both sides of the grout as described in

more detail in Chapter 6.

60

Figure 3.2: Photograph of subassembly test setup.

llooaadd bblloocckk

llooaaddiinngg ffrraammee

ssttrroonngg fflloooorr

rreeaaccttiioonn bblloocckk

bbrraacciinngg ffrraammee

tteesstt bbeeaamm

wwaallll tteesstt rreeggiioonn

NN

61

60" (1.52m) 46" (1.17m) 60" (1.52m)

COUPLING BEAM

strong floor

anchor plate

actuatoraxis 2

actuatoraxis 1

steel loading frame

40 " (1.0m)

steel connection beam

tie-down bar

wall testregion

spreader beam

beam PT tendon/duct

REACTION BLOCK

N

LOAD BLOCK

angle-to-wall connection post-tensioning duct/strand

fiber-reinforced grout[0.5 in. (13mm) thick]

loading and bracingframes not shown(see Figures 3.4 and 3.5)

angle

Figure 3.3: Elevation view of test subassembly.

62

60" (1.52m)

58"(1.47m)

35"(0.89m)

60" (1.52m)

46" (1.17m)

Nreaction block

coupling beam

load block

wall testregion

Figure 3.4: Plan view of test subassembly.

More details on the subassembly test setup, including the loading and bracing

frames, are shown in Figures 3.5 – 3.7. The reaction block is fixed to a 60 in. (1524 mm)

thick strong floor while the load block is connected to two hydraulic actuators [220 kip

(979 kN) Shore Western Model No. 924D-73.4/95.0-20-4-1348 (Serial Nos. 90711 and

90712) actuators] hanging from a stiff steel loading frame. The desired displaced shape in

Figure 3.1 is achieved by moving the load block vertically using the hydraulic actuators.

The load block is free to move in the horizontal (north-south) direction. In the vertical

direction, the actuators are moved to the same displacements (resulting in actuator forces

in opposite directions), thus restraining the load block from rotating in the vertical plane.

During each test, the subassembly is subjected to a quasi-static reversed cyclic

loading history based on the beam chord rotation. The actuators are operated in

displacement control at a rate of approximately 0.05 – 0.6 inches (1.2 - 15.2 mm) per

minute (more details on the applied displacement history can be found in Section 3.3). A

two-channel (axis) Instron 8800 controller (Serial No. 8800RK1566) is used to send the

63

displacement command signal to the actuators near-simultaneously to prevent significant

lag between them.

An inner bracing frame is used to prevent out-of-plane displacements of the load

block at three brace points and of the coupling beam near midspan as shown in Figures

3.6 and 3.7. Grease is applied between matching bracing plates on the bracing frame, load

block, and beam to allow in-plane movements of the subassembly, while the out-of-plane

movements are prevented.

reaction block

coupling beam

strong floor

actuator beamW30x326

side beamW33x118

columnW12x87

actuatoraxis 1

actuatoraxis 2

end beamW33x118

angleL5x5x3/4

angleL7x4x3/4

braceC12x25

N

157" (3.99 m)

66" (1.68m)

104" (2.64m)

70" (1.78m)

inner bracing frame not shown

connection beamW14x283

load block

Figure 3.5: East side view of loading frame.

64

strong floor

actuator beamW30x326

columnW12x87

end beamW33x118

braceC12x25

W10X100 W12X87

load block

columnW12x87

actuator

stiffener

118" (3.00m)

39" (998mm)

79" (2.00m)

connectionbeam

couplingbeam

W

42" (1.1m)

24

" (

61

0m

m)

48

" (

12

19

mm

)

Figure 3.6: North end view of loading and bracing frames.

65

columnW12x87

loadblock

load block out-of-plane support plate

reaction block

coupling beam

66" (1.68m)

connection beamW14x283

W12x87

W12x87

columnW12x87

load block out-of-plane support plates

coupling beamout-of-plane support plate

N

24"(610mm)

48"(1219mm)

118" (3.00m)strong floor

Figure 3.7: East side view of bracing frame and brace plate locations.

3.2 Test Subassembly Components

This section provides the design and construction details of the beam test

specimens and the wall pier regions (i.e., the load block and the reaction block) from the

subassembly experimental program. A 1/16 in. (1.5875 mm) tolerance was specified for

precast concrete production; however, this tolerance limit was not possible to hold for the

placement of the mild steel reinforcement due to dimensional variations in the bending of

the steel.

The test components were cast using concrete with a design strength of 6.0 ksi (41

MPa, see Appendix A for the mix design). Several different concrete mixes were tested

prior to the casting of the subassembly components to ensure that the 28-day strength was

as close to the design strength of 6.0 ksi (41 MPa) as possible.

Note that both the load block and the reaction block were designed to be re-used

in all of the experiments conducted as part of this dissertation. However, due to

unforeseen circumstances as described in Chapter 5, the reaction block was replaced after

66

Test 1 and the replacement reaction block, which had identical design details as the

original block, was repaired a number of times throughout the remainder of the test

program. The load block did not receive any damage and was re-used in all eight tests.

3.2.1 Coupling Beam Specimens

Four precast concrete coupling beam specimens (Beams 1 – 4) were cast. Beams

1 through 3 have a depth of hb = 14 in. (356 mm). These beams, with typical details

shown in Figures 3.8 through 3.10, are half-scale models. The last specimen (Beam 4)

has an increased depth of hb = 18 in. (457 mm) for parameter variation. The beam length-

to-depth aspect ratio for Beams 1 – 3 is 3.21 and 2.5 for Beam 4. These aspect ratios are

within the range of typical beam aspect ratios for coupling beams used in U.S. practice

(ranging between 2.5 and 4.0).

67

Figure 3.8: Photograph of beam formwork and details prior to casting (Beams 1 – 3).

Figure 3.9: Photograph of beam end prior to casting (Beams 1 – 3).

68

Figure 3.10: Photograph of beam end prior to casting (Beam 4 – increased depth).

Figures 3.11 and 3.12 show the duct details for Test Beams 1 through 4. Note that

Beam 4 with the greater depth has the same duct placement as the shallower Beams 1 – 3.

In addition to the central 1 in. by 3 in. (25 mm by 76 mm) duct for the main post-

tensioning strands used for coupling, there are four 1.0 in. (25 mm) diameter vertical

ducts for the angle-to-beam connections at each beam end. Due to space constraints with

the half-scale modeling and the amount of reinforcement at the beam ends, the PVC pipes

used for the ducts were removed after casting to allow for 7/8 in. (22 mm) diameter

threaded angle-to-beam connection bolts to be placed through the openings.

Each test beam includes bonded ASTM A615 Gr. 60 mild steel reinforcement as

follows: (1) two rectangular No. 6 reinforcement looping around the beam perimeter

along its length; (2) “full-depth” No. 3 rectangular hoop transverse reinforcement at

69

nominal spacing in the beam midspan region; and (3) “partial-depth” No. 3 rectangular

hoop concrete confining reinforcement closely spaced at the beam ends. The beam

reinforcement details are shown in Figures 3.13 through 3.15 and are tabulated in Table

3.1.

Further beam design details are presented in the subsequent sections as follows:

(1) maximum moment capacity at beam-to-wall interfaces; (2) transverse reinforcement;

(3) longitudinal mild steel reinforcement; (4) confinement reinforcement; and (5) shear

slip at beam-to-wall interfaces. CAD drawings for the beam specimens can be found in

Appendix C.

70

3.551"(90mm)

1.554"(40mm)

14"(356mm)

3.75"(95mm)

7.5"(191mm)

7.0"(178mm)

7.5"(191mm)

7.0"(178mm)

3.75"(95mm)

14"(356mm)

7.0"(178mm)

7.0"(178mm)

2.25"(57mm)

2.47" (63mm)

2.55" (65mm)

3.5"(89mm)33.5" (851mm)

45" (1143mm)

45" (1143mm)

2.47" (63mm)

2.25"(57mm)

3.5"(89mm)

1" [(25mm) nominal] angle-to-beam connection duct

1" x 3" [(90mm x 40mm)nominal] central post-tensioning duct

beam end view

central post-tensioning duct

side view

top view

Figure 3.11: Duct locations for Beams 1 - 3.

71

7.5"(191 mm)

9.0"(229mm)

9.0"(229mm)

18"(457mm)

9.0"(229mm)

18"(457mm)

9.0"(229mm)

3.75"(95mm)

7.5"(191mm)

3.75"(95mm)

2.25"(57mm)

2.47" (63mm)

2.55" (65mm)

3.5"(89mm)33.5" (851mm)

45" (1143mm)

45" (1143mm)

2.47" (63mm)

2.25"(57mm)

3.5"(89mm)

1" [(25mm) nominal] angle-to-beam connection duct

1" x 3" [(90mm x 40mm)nominal] central post-tensioning duct

beam end view


side view

top view

3.551"(90mm)

1.554"(40mm)

Figure 3.12: Duct locations for Beam 4 (increased beam depth).

72

12.675"(322mm)

0.66" (17mm)

0.66" (17mm)

0.6875"(17mm)

6.125"(156mm)

4.375"(111mm)

0.19

" (5m

m)

6.81"(173mm)

7.00"(178mm)2.

25" (5

7mm

)

2.50

" (64m

m)

1.5"

(38m

m)

4.43"(113mm)

0.69" (18mm)

0.69" (18mm)0.85" (22mm)

0.85" (22mm)

45" (1143mm)

4.375"(111mm)

0.6875"(17mm)

7.00"(178mm)

6.81"(173mm)2.

25" (5

7mm

)

2.25

" (57m

m)

2.25

" (57m

m)

0.19

" (5m

m)

2.50

" (64m

m)

1.5"

(38m

m)

0.66" (17mm)

0.66" (17mm)

3.625"(92mm)

beam end view

side view

top view

45" (1143mm)

14"(356mm)

7.5"(191mm)

7.5"(191mm)

14"(356mm)

Figure 3.13: Mild steel reinforcement details for Beams 1 - 3.

73

16.675"(424mm)

0.6875"(17mm)

6.125"(156mm)

0.19

" (5m

m)

6.81"(173mm)

7.00"(178mm)2.

25" (5

7mm

)

2.50

" (64m

m)

1.5"

(38m

m)

4.43"(113mm)

0.69" (18mm)

0.69" (18mm)0.85" (22mm)

0.85" (22mm)

45" (1143mm)

0.6875"(17mm)

7.00"(178mm)

6.81"(173mm)2.

25" (5

7mm

)

2.25

" (57m

m)

2.25

" (57m

m)

0.19

" (5m

m)

2.50

" (64m

m)

1.5"

(38m

m)

beam end view

side view

top view

7.5"(191mm)

7.5"(191mm)

45" (1143mm)

18"(457mm)

18"(457mm)

0.66" (17mm)

0.66" (17mm)

4.375"(111mm)

4.375"(111mm)

0.66" (17mm)

0.66" (17mm)

7.925"(202mm)

Figure 3.14: Mild steel reinforcement details for Beam 4.

74

(a)

(b)

Figure 3.15: Photographs of mild steel reinforcement for Beams 1 – 3 – (a) No. 6 looping reinforcement; (b) No. 3 full-depth transverse and partial-depth confining hoops.

75

TABLE 3.1

BEAM MILD STEEL REINFORCEMENT DETAILS

Looping

ReinforcementHoop Reinforcement

Full-depth Partial-depth U.S. Grade 60 60 60

U.S. bar size No. 6 No. 3 No. 3 1A

[in.2 (mm2)] 0.44 (284) 0.11 (71) 0.11 (71)

2dh (shallow and deep beams)

[in. (mm)]

12.275 (312) 12.675 (322)4.375 (111)

16.275 (413) 16.675 (424)

3bh

[in. (mm)] 43.5 (1105) 6.125 (156) 6.125 (156)

1A = reinforcing bar area. 2dh = center-to-center depth. 3bh = center-to-center width/length

3.2.1.1 Maximum Moment Capacity at Beam-to-Wall Interfaces

For the subassembly test setup, the maximum expected moment capacity, Mb,max

at the beam-to-wall interfaces can be estimated from equilibrium of the beam end as

shown in Figure 3.16. It is assumed that the maximum moment capacity occurs when the

confined concrete crushes at the beam ends. To obtain an upper-bound estimate of Mb,max

for capacity design purposes, it is assumed that the entire beam is confined (i.e., there is

no cover concrete). In addition, the following assumptions are made for the state when

the confined concrete crushes: (1) the bending moment and shear force in the horizontal

legs of the angles are ignored, with only the axial force in the horizontal legs considered

(more details on angle modeling can be found in Chapter 9); (2) the force in the tension

76

angles is equal to Tasx (see Figure 9.13), (3) the force in the compression angles is equal

to the angle-to-beam connection slip force, Cayx (see Figure 9.13); (4) the compressive

stresses in the beam at the beam-to-wall interfaces have a uniform (i.e., rectangular)

distribution; and (5) the post-tensioning tendon is at the yield stress.

PT-tendon

wall region

cb,max

tensionangle

couplingbeam

0.5hb

ta

compressionangle

lw

X

Yab,max = βcb,max

hb

αfcc

Cayx

Tasx

Mb,max

Nb

Cb,max

CL

hb

grout

Figure 3.16: Maximum moment capacity at beam end.

The parameters used in the design formulation are defined as: Nb = axial force in

the beam from the post-tensioning force; Pbpy = post-tensioning tendon yield force; Abp =

post-tensioning tendon area; fbpy = post-tensioning tendon yield stress; hb = beam height;

bb = beam width; ta = angle thickness; Cb,max = compression stress resultant when Mb,max

is reached; cb,max = neutral axis depth when Mb,max is reached; ab,max = concrete

compressive stress block depth; α and β = equivalent rectangular compressive stress

block factors for confined concrete (from Paulay and Priestley 1992); and f’cc =

maximum compressive strength of the confined concrete.

77

By definition, the confined concrete crushing state is reached when the extreme

confined concrete strain reaches the crushing strain, εccu. The assumed uniform stress

distribution is expected to provide a reasonable representation of the confined concrete

stress resultant at this state.

The compressive axial force at the beam-to-wall interface is assumed to be equal to:

Nb =Pbpy = Abp fbpy (3.1)

Using the above assumptions, the maximum compression stress resultant, Cb,max at the

beam end can be determined as:

asyasxbpymaxb CTPC , (3.2)

where:

bmaxbccmaxb bafC ,, α (3.3)

The depth of the compression (i.e., contact) region at the beam end is given as:

β,

,maxb

maxb

ac (3.4)

where, the equivalent rectangular stress block depth, ab,max, can be solved by substituting

Equation 3.2 into Equation 3.3 to get:

bcc

asyasxbpymaxb bf

CTPa

α, (3.5)

Then, the maximum moment capacity, Mb,max can be estimated by taking moments

about the beam centerline:

abasxasymaxbb

maxbmaxb thTCah

CM

2

1

2,

,, (3.6)

78

The equivalent rectangular stress block parameters for the confined concrete used in the

experimental program are close to 1.0 (ranging between approximately 0.95 – 1.0); and

thus, the above equations can be simplified by assuming α = β = 1.0.

3.2.1.2 Beam Transverse Reinforcement

To ensure that the beam test specimens do not fail in shear, it is required that:

maxbbn VV , (3.7)

where, Vb,max is the maximum shear force demand and Vbn is the nominal shear strength

for the beam. The beam maximum shear force demand, Vb,max is determined based on

capacity design principles (see Figure 3.17) using the maximum expected moment

capacity, Mb,max at the beam-to-wall interface as:

b

bmaxb l

MV max,

,

2 (3.8)

Mb,maxVb,max

Mb,maxVb,max

lb

Figure 3.17: Beam maximum shear force demand.

Due to gap opening at the beam ends and the formation of a large diagonal

compression strut as discussed in Chapter 2, the diagonal tension reinforcement

79

requirements for unbonded post-tensioned precast coupling beams are significantly

reduced as compared with conventional reinforced concrete coupling beams where the

beam is cast monolithically with the wall piers. This assertion is validated later in the

dissertation based on the experimental results provided in Chapters 6 and 7, and the

analytical results using an ABAQUS finite element model in Chapter 9. The experimental

and analytical results show that concrete cracking does not occur in the midspan regions

of unbonded post-tensioned precast coupling beams even though the shear force is

constant over the beam length. As a result, ACI 318 (ACI 2005) minimum shear

reinforcement requirements are used to design the transverse reinforcement along the

length of the test beams, which is provided by a total of five full-depth No. 3 hoops

nominally-spaced at approximately 7.0 in. (178 mm) in between the partial-depth

confinement hoops at the beam ends.

The most critical locations for the design of the transverse reinforcement in

unbonded post-tensioned precast concrete coupling beams occur adjacent to the beam end

surfaces. In the vicinity of the gap tip at each beam end as shown in Figure 3.18, high

transverse tensile stresses significantly greater than the concrete cracking strength are

expected to develop as a result of the opening of a gap immediately adjacent to a contact

region. The design of the transverse reinforcement in these end regions of the test

specimens utilizes the ABAQUS finite element analysis results in Chapter 9. For this

purpose, the transverse tensile stresses in each row of finite elements at the beam ends are

integrated to determine the resultant tensile forces. These forces are then used to

determine the amount of transverse steel reinforcement needed at the beam ends, which is

provided by the vertical legs of the two No. 6 looping reinforcement in each beam.

80

As described in Chapter 9, the beam is modeled at full-scale using 72 rows of

plane stress elements. In Figure 3.19, the transverse (i.e., y-direction) stresses (at a beam

chord rotation of 9.0%) are plotted over the beam length for element row 38, which has

the highest transverse stresses in the beam. Integrating the tensile stresses at each beam

end gives 114 kips as the maximum tension force and a required steel area [assuming 75

ksi (517 MPa) yield strength for the steel] of 1.5 in.2 (968 mm2) for a full-scale beam.

Scaling this to half-scale for the design of the precast beam specimen gives a required

steel area of 0.38 in.2 (323 mm2), much less than the area of the vertical legs of the two

No. 6 looping reinforcing bars [0.88 in.2 (568 mm2)]. Note that the design of the two No.

6 bars was governed by the beam longitudinal bonded mild steel reinforcement

requirements described in the next section. Note also that the 9.0% beam chord rotation

used in Figure 3.19 is larger than what would be used in typical design practice.

couplingbeam

high transversetensile stresses

Figure 3.18: High transverse tensile stresses in the vicinity of the gap tip.

81

beam length, lb [in. (mm)]

0 90(2286)

1.0(6.9)

tra

nsv

erse

str

ess

[ksi

(k

N)]

Figure 3.19: Transverse (y-direction) stresses in element row 38 of full scale finite element beam model.

3.2.1.3 Beam Longitudinal Mild Steel Reinforcement

Longitudinal bonded mild steel reinforcement is needed to transfer the tension

angle forces into the beam test specimens along the top and bottom surfaces. This

reinforcement is designed to remain linear elastic under the maximum angle forces

developed during the loading history. Due to the half-scale modeling of the test

specimens, there is not enough space to fully develop the longitudinal reinforcement

within the length and depth of the beam, including the use of hooks. Therefore, full hoops

that loop around the beam perimeter in the vertical direction are designed for the

longitudinal reinforcement. In full-scale design, each looping reinforcing bar could be

replaced with two U-shaped bars, making the placement of the reinforcement simpler.

The vertical legs of the looping reinforcement are used as transverse reinforcement at the

beam ends as described in the previous section.

82

The critical section for the design of the longitudinal mild steel reinforcement is

assumed to be at the centroid of the angle-to-beam connection bolts. It must be ensured

that the mild steel reinforcement does not yield at the critical section, since this would

result in a large crack at the critical section and prevent the opening of a gap at the beam-

to-wall interface. The critical section is shown in Figure 3.20(a), and the effect of the

angle forces on the beam moment diagram can be seen in Figures 3.20(b) and 3.20(c).

There is a drop in the beam moment diagram at the location of the angles, where Mb,a is

the moment contribution from the angle forces. The slopes of the beam moment diagram

to the left and right of the critical section are assumed to be the same since the vertical

(shear) force from the angles is ignored. Note that the end moment for a beam without

angles and Mb,b in Figure 3.18(c) are not the same because of the effect of the angle

forces on the axial force at the beam end.

It can be seen from Figure 3.18 that the beam moment demand at the critical

section is given as:

2,

max,,crb

bcrb

lVM (3.9)

83

(a)

Mb,cr

Mb,a

Mb,cr

Cayx

Tasx

Mb,max

Mb,b

lb,cr /2

CL

Vb,max

Nb

criticalsection

grout

beam-to-wallinterface

looping reinforcement

coupling beam

(b)

(c)

coupling beam

Figure 3.20: Design of beam longitudinal mild steel reinforcement – (a) critical section; (b) angle forces and beam moment at critical section; (c) beam moment diagram.

84

For the design of the longitudinal reinforcement at the critical section, the following

assumptions are made: (1) the concrete in tension is cracked (i.e., concrete has no tensile

strength); and (2) the concrete at the critical section is linear elastic in compression.

hb

Mb,cr

Nb

Cc

CLdb

c

db-c

n.a.

c/3

Tl

criticalsection

straindistribution

stressresultants

fcεc

εlAl

Al = Al

Figure 3.21: Equilibrium at critical section.

Looking immediately to the right side of the critical section in Figure 3.21 and summing

the forces in the longitudinal direction while the compression reinforcement is ignored:

lbc TNC (3.10)

with:

bcc cbfC2

1 (3.11)

lll fAT (3.12)

and,

bpbpbpb fAPN (3.13)

where, Tl = tensile force in the beam longitudinal mild steel reinforcement; fc = stress of

the concrete at the extreme compression face; Al = area of the longitudinal mild steel

reinforcement in tension; db = distance from the extreme concrete compression fiber to

85

the centroid of the longitudinal mild steel reinforcement in tension; Al = longitudinal

reinforcement area; and fl = stress in the longitudinal mild steel reinforcement in tension.

Using strain compatibility, the strain, εc and stress, fc at the extreme compression

face of the concrete can be calculated as:

cd

c

blc εε (3.14)

and

l

c

blc E

E

cd

cff

(3.15)

where, εl = strain in the longitudinal mild steel reinforcement in tension; and Ec and El =

Young’s moduli for concrete and longitudinal mild steel reinforcement, respectively.

Substituting Equations 3.11 – 3.15 into Equation 3.10 yields:

llbpbpl

cb

bl fAfA

E

Eb

cd

cf

2

2

1 (3.16)

The moments can also be summed about the location of Cc to give:

332,

cdfA

chfAM bll

bbpbpcrb (3.17)

where, Mb,cr is the beam moment at the critical section as determined from Equation 3.9.

The required area of the longitudinal mild steel reinforcement, Al at the critical

section is determined by setting the stress in the reinforcement, fl equal to the design yield

strength, fly. Rearranging Equation 3.17 for Al and substituting into Equation 3.16 gives:

86

3

32

2

1 ,2

cd

chfAM

fAE

Eb

cd

cf

b

bbpbpcrb

bpbpl

cb

bly (3.18)

Then, Equation 3.18 is solved for c based on the following two limiting conditions for the

stress in the post-tensioning steel: (1) fbp = fbpi (i.e., the post-tensioning steel stress is

equal to the initial stress); and (2) fbp = fbpy (i.e., the post-tensioning steel stress is equal to

the design yield strength). Finally, the calculated c values are used in Equation 3.17 (with

fl = fly) to determine the required longitudinal steel area, Al, selecting the conservative

(i.e., larger) design.

3.2.1.4 Confinement Reinforcement

In addition to the transverse and longitudinal mild steel reinforcement,

confinement hoops are provided at the ends of the beam specimens in areas where large

concrete compressive stresses are expected to develop.

The compressive stress-strain relationship of the confined concrete was

determined using a model developed by Mander et al. (1988a) as shown in Figure 3.20.

The confined concrete compressive stress-strain parameters, which include the maximum

strength, f’cc, strain at maximum strength, εcc, and ultimate strain, εccu, depend on the

properties of the confining reinforcement hoops, the longitudinal mild steel reinforcement

placed within the hoops (which was ignored for the confined concrete properties of the

test specimens), and the unconfined concrete. The diameter of the hoop bars, φh, the

geometry of the hoops (i.e., width, bh, and depth, dh), the hoop spacing, sh, the yield

strength of the hoop steel, fhy, the strain, εhm, at the maximum strength of the hoop steel,

87

and the maximum compressive strength of the unconfined concrete, f’c (assumed to be

reached at a strain of 0.002) are specified to determine the confined concrete model. The

ultimate confined concrete strain, εccu, is assumed to be reached when the fracture of the

reinforcing hoops occurs, resulting in a loss of confinement and crushing of the confined

concrete.

confined concrete

confinement fracture

0.002 εcc εccu

compressive strain, εc

fcc

fc

com

pre

ssiv

e st

ress

, f

c

unconf ined concrete

Figure 3.22: Stress-strain model for confined concrete (Mander et al. 1988a).

The hoop reinforcement in the test specimens is designed to confine the maximum

amount of concrete at the beam corners by minimizing the amount of cover concrete

outside the hoop bar bend locations. Due to the half-scale modeling of the test specimens,

the hoop bends require a smaller radius of curvature to fit in the small area and maximize

the amount of concrete that is confined (minimizing the cover concrete). To achieve this,

the confining hoops were manufactured in the Structural Systems Laboratory at the

University of Notre Dame and had bends that did not abide by the ACI 318 Section 7.2

88

(ACI 2005) minimum bend criteria, which state that the diameter of bend measured on

the inside of the bar shall not be less than 6db for No. 3 through No. 8 bars; where, db is

the bar diameter. For No. 3 bars, this requires a bend diameter of 2.25 in. (57 mm);

whereas, the bend diameter for the No. 3 hoops manufactured at the University of Notre

Dame range between 1.0 – 1.25 in. (25 – 32 mm).

The amount of hoop reinforcement in the beam specimens is designed based on

the maximum confined concrete strain, εcc,max, reached at a beam chord rotation of 9.0%

using an analytical model in DRAIN-2DX (Prakash et al. 1993). This analytical model is

described in detail in Chapter 9. Using the analytical results, the maximum confined

concrete strain demand is estimated as εcc,max = 0.030. Then, an adequate amount of hoop

reinforcement is provided to result in a confined concrete ultimate strain, εccu greater than

εcc,max in the beam-to-wall contact regions. The confinement reinforcement is terminated

after the compressive strain in the contact regions decreases to the design unconfined

concrete crushing strain of εcu = 0.003.

Using the model by Mander et al. (1988a) as discussed above, the No. 3 steel

closed rectangular hoops confining the concrete above and below the post-tensioning

duct at each end of the test beam result in an estimated confined concrete compressive

strength of 12.5 ksi (86 MPa) with an ultimate strain at crushing of 0.035 (assumed to be

reached when the hoop steel fractures causing ultimate failure of the confined concrete).

3.2.1.5 Shear Slip at Beam-to-Wall Interfaces

An undesirable mode of failure for the test subassembly is shear slip of the beam

at the beam-to-wall interfaces. To prevent this failure mode, the nominal shear slip

89

capacity provided by shear friction at each beam-to-wall interface must be greater than

the maximum shear force demand at the interface:

maxbss VV , (3.19)

The maximum shear force demand, Vb,max is determined from Equation 3.8. To determine

the shear slip capacity, Vss, the shear friction capacity due to the beam post-tensioning

force, Vsbp and the shear slip capacity provided by the angles, Vsa must be determined as:

sasbpss VVV (3.20)

The shear slip capacity due to the beam post-tensioning force can be calculated

as:

biccsbp PV μ (3.21)

where, Pbi = initial post-tensioning force in the beam post-tensioning tendon; and μcc =

coefficient of friction for concrete-against-concrete surfaces. The increase in the beam

post-tensioning force due to the elongation of the strands under lateral loading is

conservatively ignored.

As a conservative estimate of the nominal shear slip capacity at the beam-to-wall

interfaces, only the contribution of the compression angle, Vsa is considered. As described

in Section 3.3.3, each angle-to-wall connection in the test specimens consists of two

unbonded post-tensioned strands [ASTM 416 low-relaxation strands with 0.6 in. (15.2

mm) diameter]. The shear slip capacity provided by the compression angle-to-wall

connection can be determined as:

compapiccsa PV ,μ (3.22)

where, Papi,comp is the total initial force in the compression angle connection post-

tensioning strands. Note that the tension angles also help to prevent the beam from

90

slipping vertically at the beam-to-wall interfaces; however, they were conservatively

ignored in the shear slip design of the test specimens.

The total shear slip capacity then becomes:

bicompapiccns PPV ,μ (3.23)

Section 11.7.4.3 of ACI 318 (ACI 2005) permits a coefficient of friction, μcc,

equal to 1.4λ for concrete placed monolithically, 1.0λ for concrete placed against

hardened concrete with surfaces intentionally roughened, and 0.6λ for concrete placed

against hardened concrete not intentionally roughened, where λ = 1.0 for normal weight

concrete. For the design of the test specimens, a value of μcc = 0.6 was used.

3.2.2 Reaction Block

As shown in Figure 3.21, the length of the reaction block in the N-S direction is

60 in. (1.52 m); however, the reaction block does not have a uniform thickness. Adjacent

to the coupling beam, the reaction block is 7.5 in. (191 mm) thick, modeling the thickness

of the prototype wall pier at half-scale. This region of the reaction block is referred to as

the “wall test region.” The wall test region is 30 in. (762 mm) long and 48 in. (1219 mm)

high. The other regions of the reaction block are 58 in. (1.47 m) wide to provide lateral

stability to the block and to accommodate anchorage to the strong floor. A total of sixteen

1.0 in. (25 mm) diameter rods tie the reaction block to the strong floor. Eight of these

rods are used to apply vertical forces to the wall test region through a spreader beam (see

Figures 3.2 and 3.3), representing the wall pier axial forces. The total vertical force

applied on the wall test region ranges between 150 – 160 kips (667 – 712 kN).

91

Figure 3.21 shows the duct details for the reaction block. There are sixteen

vertical Dywidag Spiro 4.0 in. (102 mm) nominal diameter ducts used for the 1.0 in. (25

mm) diameter tie down rods connecting the reaction block to the strong floor. The ducts

are oversized so that the placement of the reaction block can be adjusted as needed. There

are a total of twelve 1.0 in. (25 mm) nominal diameter ducts running in the horizontal

(north-south) direction to attach the top and seat angles to the reaction block (Dywidag

grout tubes were used for these ducts). Note that only two post-tensioning strands are

used to attach each angle to the reaction block; the additional ducts allow for the reaction

block to accommodate test beams with different depths as described in Section 3.2.1.

The central post-tensioning duct in the reaction block uses a Dywidag 1 in. by 3

in. (25 mm by 76 mm) nominal duct that matches the central post-tensioning duct in the

beam, which then transitions to a 2.375 in. (60 mm) nominal diameter duct that connects

to an embedded Dywidag Multiplane Anchorage MA 7 - 0.6 in. anchor. As shown in

Figure 3.22, the anchorage system used for the beam post-tensioning strands consists of

an MA anchor, a trumpet for the transition from the anchor to the duct, and a reinforcing

spiral to accommodate the high stresses at the anchor location. The 7-strand MA anchor

allows the use of two, three, or four post-tensioning strands in each test beam.

Furthermore, these strands can be separated at the anchor location, permitting a load cell

to be placed at the end of each strand as described in Chapter 5 and shown in Figure 3.23.

To accommodate these load cells, individual barrel/wedge type anchors and an anchor

plate are used for the strands instead of the forged wedge plate and wedges that are part

of the standard MA anchor.

92

7.5"(114mm)

60"(1.52m)

58" (1.47m)

6.375"(162mm)

8.0"(203mm)

11.875"(302mm)

11.875"(302mm)

8.0"(203mm) 5.375"

(137mm)

8.0"(203mm)5.375"

(137mm)

15.625"(397mm)

15.625"(397mm)

8.0"(203mm)

6.375"(162mm)

66"

(1.67m)

25.25"

(641mm)

30" (762mm)60" (1.52m)

58" (1.47m)

7.5"

(114mm)

10.0"(25mm)

2.0" (51mm)

18"(457mm)

48"(1219mm)

3.5"(89mm)

58" (1.47m)

7.5"(114mm)

25.25" (641mm) 25.25" (641mm)

18"(457mm)

48"(1219mm)

60" (1.52m)

66"(1.67m)

24"

(610m

m)

42"

(1067m

m)

30" (762mm) 30" (762mm)

N

wall testregion

tie down duct


angle-to-wallconnection duct

N

top view

side viewnorth end view

N

wall testregion

embeddedMA anchorWE

66"(1.67m)

10.0"(25mm)

10.0"(25mm)

2.0" (51mm)

2.0" (51mm)

2.0" (51mm)

tie down duct


duct transitionregion


duct transitionregion

tie down ducttie down duct





Figure 3.23: Reaction block duct details.

93

Figure 3.24: Dywidag Multiplane MA anchor components used with the beam post-tensioning strands.

anchorplate

barrel/wedgeanchor

post-tensioningstrand

wall face

MA anchor

reinforcingspiral

trumpet

load cell

Figure 3.25: Modified Dywidag Multiplane MA anchor details.

94

Figure 3.24 shows the reinforcement details of the reaction block. The reaction

block is designed to be reused for the entire experimental program and therefore must be

able to accommodate both the shallow test beams (Beams 1 – 3) and the deep test beam

(Beam 4). To resist similar levels of compressive stresses as those that develop at the

beam ends during gap opening, confining hoops are required in the beam-to-wall contact

regions of the reaction block. The location of the contact region changes with the

increased beam depth in Test 4. Furthermore, the size and placement of the confinement

hoops must accommodate the angle-to-wall connection ducts and the central post-

tensioning duct. The confinement details also must limit the amount of nonlinear concrete

strains in the test wall region since the reaction block is to be used for the entire

experimental program. To achieve this, a higher confined concrete strength (i.e., more

confinement) is used in the wall test region than in the coupling beam. Due to the high

confinement demands, three layers of hoops [2 layers of 6.125 in. by 2.625 in. (156 mm

by 67 mm) hoops and one layer of 6.125 in. by 3.125 in. (156 mm by 79 mm) hoops] are

used above and below the central post-tensioning duct. In each layer, five hoops are

placed at a spacing of 1.5 in. (38 mm). Behind these five hoops, five additional deeper

6.125 in. by 9.375 in. (156 mm by 238 mm) hoops are used at the same spacing of 1.5 in.

(38 mm).

Figure 3.25 shows the confining hoops used in the reaction block and Figure 3.26

shows the hoop cages placed above and below the central post-tensioning duct in the wall

test region. Similar to the hoops for the test beams, the hoops used in the reaction block

were manufactured in the Structural Systems Laboratory at the University of Notre Dame

and do not meet ACI 318 Section 7.2 (ACI 2005) minimum bend requirements in order to

95

minimize the amount of cover concrete in the half-scale specimens. Additional

reinforcement in the reaction block includes W4.0xW4.0 – 4x4 welded wire mesh (which

is not continuous over the confining hoop cages), vertical No. 6 bars, No. 4 corner bars,

and lifting anchors. This reinforcement does not affect the behavior or design of the wall

test region; and thus, is not discussed here. Photographs of the reaction block details prior

to the casting of the concrete are provided in Figures 3.27 and 3.28. More detailed

drawings, including all reinforcement in the reaction block, can be found in Appendix D.

96

60"(1.52m)

58" (1.47m)

6.125"(156mm)

3.4375"

3.125"

2.8125"

1.9375"1.9375"

2.8125"

3.125"

3.4375"

66

" (

1.6

7m

)

58" (1.47m)

7.5"(114mm)

25.25" (641mm) 25.25" (641mm)60" (1.52m)

24"

(610m

m)

42"

(1067m

m)

30" (762mm) 30" (762mm)

angle ducts not shown


top view

north end view side view

66

" (

1.6

7m

)wall test region

6.125"(156mm)

10 @ 1.5"(38mm) spacing

N

N

WE

10 @ 1.5" (38mm) spacing

87mm

79mm

71mm

49mm49mm

71mm

79mm

87mm

48"

(1219m

m)

18"

(457m

m)

48"

(1219m

m)

18"

(457m

m)

Figure 3.26: Reaction block reinforcement details.

97

Figure 3.27: Reaction and load block reinforcement hoops.

98

Figure 3.28: Photograph of reaction and load block reinforcement cage.

99

Figure 3.29: Photograph of reaction block duct and reinforcement placement.

100

Figure 3.30: Photograph of wall test region duct and reinforcement details.

101

3.2.3 Load Block

Similar to the reaction block, the load block has a horizontal length of 60 in. (1.52

m) and a height of 36 in. (914 mm). The load block has a uniform thickness (width) of 35

in. (889 mm) along its length to allow for connections to the actuators and to prevent

damage to the block during testing (the load block was re-used in all of the tests in the

experimental program).

Figure 3.29 shows the duct details inside the load block. In the vertical direction,

there are eight Dywidag Spiro1.58 in. (41 mm) nominal diameter ducts and twenty-four

Dywidag Spiro 1.0 in. (25mm) nominal diameter ducts. Ten 1.0 in. (25 mm) diameter and

eight 0.5 in. (12 mm) diameter threaded rods run through these vertical ducts to secure

the load block to the two steel connection beams above. The threaded rods are bolted to

the load block at the bottom and to the bottom flanges of the connection beams at the top.

Two servo-controlled hydraulic actuators are bolted to the connection beams and are used

to displace the load block vertically through a quasi-static reversed cyclic displacement

history while preventing its rotations. Note that some of the vertical ducts in the load

block remain unused in this process.

The horizontal ducts in the load block are the same as the ducts in the reaction

block. There are a total of twelve 1.0 in. (25 mm) nominal diameter ducts to attach the

top and seat angles to the load block (Dywidag grout tubes are used for these ducts).

Similar to the reaction block, two post-tensioning strands are used to attach each angle to

the load block; the additional ducts allow for the load block to accommodate test beams

with different depths as described in Section 3.2.1. The central MA post-tensioning

anchor is embedded in the north end of the load block with the post-tensioning duct

102

transitioning from a 1 in. by 3 in. (25 mm by 76 mm) nominal duct at the south end to the

MA anchor at the north end (similar to the reaction block).

Figure 3.30 shows the reinforcement used in the load block, which is the same as

that described for the reaction block (see Figures 3.25 and 3.26 for photographs of the

No. 3 hoops and cages used in the load block). Figure 3.31 shows a photograph of the

duct and reinforcement details for the load block, with more complete details and

drawings provided in Appendix E. The load block was cast with the top side at the

bottom so that a smooth formed surface was achieved for attachment to the steel

connection beams in the final configuration.

103

6.125"(156mm)

35"(889mm)

35" (889mm)

9.375"(238mm)

13.5" (343mm)

6.125"(156mm)

60" (1524mm)

60" (1524mm)

36"(914mm)

36"(914mm)

EW

top view

N

N

side view


10 @ 1.5" (38mm) spacing

angle and connection beam ducts not shown

10 @ 1.5" (38mm) spacing

3.4375"

3.125"

2.8125"

1.9375"1.9375"

2.8125"

3.125"

3.4375"

south end view

87mm

79mm

71mm

49mm49mm

71mm

79mm

87mm

Figure 3.31: Load block duct details.

104

6.125"(156mm)

35"(889mm)

35" (889mm)

9.375"(238mm)

13.5" (343mm)

6.125"(156mm)

60" (1524mm)

60" (1524mm)

36"(914mm)

36"(914mm)

EW

top view

N

N

side view


10 @ 1.5" (38mm) spacing

angle and connection beam ducts not shown

10 @ 1.5" (38mm) spacing

3.4375"

3.125"

2.8125"

1.9375"1.9375"

2.8125"

3.125"

3.4375"

south end view

87mm

79mm

71mm

49mm49mm

71mm

79mm

87mm

Figure 3.32: Load block reinforcement details.

105

Figure 3.33: Photograph of load block duct and reinforcement details.

3.3 Testing Procedure

The procedure for each subassembly test requires a multi-day process. The first

day involves the initial and final alignment of the coupling beam, the load block, and the

reaction block; application of the vertical forces (representing the wall pier axial forces)

on the wall test region of the reaction block; tamping (packing) of the grout into the

beam-to-wall interfaces; and application of a small amount of central post-tensioning

force to close the gaps at the beam-wall-joints. The grout is then allowed to cure for 8

days. On the ninth day, full post-tensioning is applied to the system and the top and seat

angles are connected to the beam and to the load and reaction blocks. The load block and

the coupling beam are supported on screw jacks during this entire process to prevent

106

settling. On the tenth day (test day), the temporary jacks are removed, the self-weight of

the subassembly is counteracted using the hydraulic actuators, and finally, the structure is

tested by moving the load block vertically through a predetermined displacement history.

As described previously, the experimental program consists of eight floor level

subassembly tests using four precast coupling beam specimens, investigating the

following primary design parameters: (1) beam post-tensioning tendon area and initial

stress; (2) beam initial concrete stress; (3) angle strength; and (4) beam depth (beam

length-to-depth aspect ratio). Details on the variation of these design parameters, as well

as more information on the experimental program, are depicted in Table 3.2. A new beam

is used in the first test of each series of tests.

3.3.1 Wall Test Region Vertical Forces

Before the final alignment of the coupling beam with respect to the reaction and

load blocks, vertical forces are applied to the wall test region of the reaction block to

represent the effect of the wall pier axial forces on the coupling region. The forces are

applied using eight 1.0 in. (25 mm) rods that run through a spreader beam (see Figures

3.2 and 3.3) and connect the reaction block to the strong floor. The total target initial

vertical force applied on the wall test region ranges between 150 – 160 kips (667 – 712

kN). Following the application of the vertical force, any final adjustment/alignment of the

beam with respect to the reaction and load blocks is done.

A hydraulic torque wrench is used to tighten the eight vertical tie-down rods

incrementally. The outermost east and west rods are tightened first, followed by the inner

rods. To keep a uniform application of force on the wall test region, after the tightening

107

of each rod, the rod on the opposite side is tightened (e.g., north-east rod followed by

south-west rod). This procedure is continued until the desired initial forces are achieved

as monitored using strain gauges attached to the rods as described in Chapter 5. Note that

the forces in the tie-down rods vary as the subassembly is subjected to lateral

displacements during testing. As discussed in Chapters 6 and 7, the variations in the

vertical forces are generally small, with the total vertical force in the wall test region

remaining compressive throughout a test. The wall pier axial forces in a multi-story

coupled wall structure can undergo significant variations, including tension-compression

load cycles, during an earthquake. These large variations cannot be captured by the tie-

down rods applying vertical forces to the wall test region of the reaction block.

108

TABLE 3.2

SUBASSEMBLY TEST MATRIX

Test No.

Test Date

Coupling Beam Dimensions [in. (mm)]

1Angles

2lgv [in.

(mm)]

3la [in.

(mm)]

Beam PT Tendon

4Σabp [in2

(mm2)] bpu

bpi

f

f5

6fbci [ksi

(MPa)] c

bci

f

f

7

gt

gti

f

f

8

cf

v

max

9

Primary Test Parameter(s)

hb bb lb

1 10/17/06 14

(356) 7.5

(191) 45

(1143) L8x8x1/2 5 (127)

7.5 (191)

2 – 0.6” (15.2mm)

0.434 (280)

0.50 0.58 (4.0)

0.076 0.069 5.0 (0.42) 10patched beam

2 01/26/07 14

(356) 7.5

(191) 45

(1143) L8x8x1/2 5 (127)

7.5 (191)

4 – 0.6” (15.2mm)

0.868 (560)

0.36 0.82 (5.7)

0.114 0.089 6.5 (0.54)

beam PT tendon area and

initial stress; beam initial

concrete stress

3 02/19/07 14

(356) 7.5

(191) 45

(1143) L8x8x1/2 5 (127)

2 x 2.5 (64)

3 – 0.6” (15.2mm)

0.651 (420)

0.39 0.68 (4.7)

0.089 0.073 5.4 (0.45) 11angle strength

3A 03/15/07 14

(356) 7.5

(191) 45

(1143) L8x8x1/2 5 (127)

7.5 (191)

3 – 0.6” (15.2mm)

0.651 (420)

0.34 0.59 (4.1)

0.077 0.063 4.3 (0.45) 12angle strength

3B 04/04/07 14

(356) 7.5

(191) 45

(1143) L8x8x1/2 5 (127)

2 x 2.5 (64)

3 – 0.6” (15.2mm)

0.651 (420)

0.34 0.58 (4.0)

0.076 0.062 5.1 (0.36) 13angle strength

4 05/23/07 18

(457) 7.5

(191) 45

(1143) L8x8x1/2 5 (127)

2 x 2.5 (64)

3 – 0.6” (15.2mm)

0.651 (420)

0.43 0.58 (4.0)

0.087 0.075 5.4 (0.42) beam depth

4A 06/08/07 18

(457) 7.5

(191) 45

(1143) - - -

3 – 0.6” (15.2mm)

0.651 (420)

0.39 0.52 (3.6)

0.083 0.068 3.4 (0.45) no angles

4B 06/12/07 18

(457) 7.5

(191) 45

(1143) L8x8x1/2 5 (127)

7.5 (191)

4 – 0.6” (15.2mm)

0.868 (560)

0.41 0.73 (5.0)

0.116 0.094 7.6 (0.63) 14angle strength 1 U.S. shape. 2Angle vertical leg gage length measured from centroid of angle-to-wall connection strands to heel of angle. 3Angle length (in Tests 3, 3B, and 4, two short angles were used at each top and seat beam-to-wall connection location as described in Chapters 6 and 7). 4 Σabp=total area of coupling beam post-tensioning tendon. 5fbpi/ fbpu = average initial coupling beam post-tensioning strand stress; where, fbpu = 270 ksi (1862 MPa) is the design maximum strength of the post-tensioning steel. 6fbci = Pbi /Ac = initial coupling beam concrete nominal stress; where, Pbi = total initial force measured in coupling beam post-tensioning tendon; Ac = actual cross-sectional area of beam (with

central PT duct area taken out); 7f’c = test day strength of unconfined beam concrete. 8 fgti = Pbpi /Agt = initial grout nominal stress; where, Agt = actual cross-sectional area of beam-to-wall interface grout (with central PT duct area taken out); f’gt = test day strength of grout. 9vmax = Vmax/Agross (note: vmax/√f’c values in units of psi (MPa); where, Vmax = maximum measured beam shear strength; Agross = gross cross-sectional area of beam (central PT duct area not

taken out). 10First beam specimen was patched at south end as described in Chapter 6. 11Angle strength was reduced by using two 2.5 in. (64 mm) short angles. 12Angle strength was reduced by drilling holes in angle vertical leg as described in Chapter 7. 13Angle strength was reduced by using two 2.5 in. (64 mm) short angles along with angle-to-wall connection plates as described in Chapter 7. 14Angle strength was increased by using 7.5 in. (191 mm) long angles as described in Chapter 7.

108

109

3.3.2 Beam Post-Tensioning Force

The application of the beam post-tensioning force is done using a single-strand

(Figure 3.32) hydraulic post-tensioning jack (manufactured by Jacks & Accessories,

Inc®) at the north end of the load block. Single use barrel/wedge type anchors with three-

piece wedges and ring are used to anchor the post-tensioning strands at both the live end

(i.e., jacking end) and the dead end (Figure 3.33).

Following the curing of the grout at the beam-to-wall interfaces, a series of pulls

are applied to achieve the desired initial forces in the post-tensioning strands. First, each

strand is incrementally pulled [approximately to 2.0 – 4.0 kips (9.0 – 18 kN) of force] to

remove any slack in the strand. Then, the strands are incrementally pulled [frist,

approximately to 15 – 18 kips (67 – 80 kN) of force, and then, to 26 – 33 kips (116 – 147

kN) of force] until the desired initial force is reached. The incremental jacking procedure

helps apply uniform stresses to the beam and allow for better control of the strand force.

Each prestress increment is selected to ensure that the wedges seat in new location on the

strand allowing for an increase in the post-tensioning force. The force in each strand is

monitored using a load cell mounted between the barrel/wedge anchor and the bearing

plate [Figure 3.32(c)] at the reaction block end (i.e., dead end) as described in Chapter 5.

The post-tensioning jack has a hydraulic ram that attempts to evenly seat the anchor

wedges as part of the jacking process. To achieve the desired force, the strand is pulled to

a jacking force slightly higher than the desired initial force since considerable losses

occur during the seating of the anchor wedges (due to the relatively short length of the

post-tensioning strands).

110

(a) (b)

6.0" (152mm)

0.75"(19mm)

15" (381mm)

7.5" (191mm)

3.0" (76mm)

3.0"(76mm)

2.25"(57mm)

1.5"(38mm)

3.0"(76mm)

3.0"(76mm)

1.5"(38mm)

1.5"(38mm)

front view side view

(c)

Figure 3.34: Post-tensioning operation – (a) single-strand jack; (b) jack operation; (c) anchor bearing plate.

111

Figure 3.35: Single use barrel/wedge type anchors with three-piece wedges and ring.

3.3.3 Top and Seat Angle Connections

Following the stressing of the beam post-tensioning strands, each set of top and

seat angles are connected to the test beam using four 7/8 in. (22 mm) diameter threaded

rods passing through the vertical ducts cast inside each end of the beam (see Figures 3.11

and 3.12). First, the nuts on the threaded rods are hand-tightened to snug-tight condition.

Then, the bolts are tightened to slip critical condition following the “turn-of-nut

pretensioning method” as described in the LRFD Manual of Steel Construction (AISC

2001) using a hydraulic torque wrench. The number and size of the angle-to-beam

connection bolts is determined such that the slip-critical strength of the connection is

larger than the anticipated maximum strength of the angles in tension.

Once the angle-to-beam connections are secured, the angle vertical legs are

attached to the load and reaction blocks using two unbonded post-tensioning strands per

112

angle [ASTM A416 low-relaxation strands with 0.6 in. (15.2 mm) diameter]. Two-piece

wedges and barrels are used for the anchorage system for the angle-to-wall connections.

The stressing of the angle post-tensioning strands is done similar to the beam post-

tensioning strands using an incremental procedure (usually in a three-step jacking

procedure). A small amount of stress is first applied to remove any slack in each strand

[approximately to 2.0 – 4.0 kips (9.0 – 18 kN) of force]. Then, a series of pulls are made

[first, approximately to 15 – 18 kips (67 – 80 kN) of force, and then, to 26 – 33 kips (116

– 147 kN) of force] until the desired force of approximately 20 kips (89 kN) is reached in

each strand. The incremental prestressing procedure helps apply uniform stresses to the

wall test region of the reaction block and allow for better control of the strand force. Each

prestress increment is selected to ensure that the wedges seat in a new location on the

strand, allowing for an increase in the post-tensioning force.

The desired angle-to-wall connection force of 40 kips (178 kN) for the two

strands is determined based on the anticipated maximum strength of the angles in tension,

including prying effects. Four load cells (as described in Chapter 5) are used at the north

end of the angle-to-reaction-block connection strands to monitor the forces in the

connection strands. Note that even though the angle-to-wall connection strands are taken

to similar jacking forces as the beam post-tensioning strands, due to their short length,

they experience much higher anchor seating losses resulting in lower initial forces.

113

3.3.4 Test Day

Prior to each test, the forces in the actuators due to the self-weight of the

subassembly (i.e., the load block, steel connection beam and bolts, coupling beam

specimen, strands, angles, etc.) are measured. On the test day, these forces are applied to

the subassembly (by operating the actuators in load control) in the opposite direction to

counteract the effect of the structure self-weight on the coupling beam. These initial

forces applied to the structure are subtracted from the coupling beam shear force (since

the initial actuator forces are equal and opposite to the forces due to the structure self-

weight) to initialize the shear force measurement to zero.

Following this pre-test procedure and the application of the self-weight forces, a

pre-determined cyclic lateral displacement loading history is applied to the test beam.

The beam chord rotation, θb, which is used to specify the applied displacement history,

represents the relative transverse displacement between the beam ends. The nominal

displacement history for Test 1 is shown in Figure 3.33(a) and Table 3.3. The amplitude

of each set of three cycles is taken as 1.25 – 1.5 times the amplitude of the preceding set

of three cycles. After 0.25% beam chord rotation, each set of three fully reversed

displacement cycles is followed by one single smaller cycle to a displacement amplitude

equal to 30% of the preceding set of three cycles (with the exception of the last set). This

displacement history was determined based on the recommendations of ACI ITG 5.1

(ACI 2008).

A slightly different displacement loading history, still satisfying ACI ITG 5.1

recommendations, is used in the remaining tests (Tests 2 – 4B) [see Figure 3.33(b) and

Table 3.3]. Changes to the loading history include the following: (1) all small cycles with

114

amplitudes equal to 30% of the preceding set of three cycles are removed; and (2) the

increase in amplitude between each set of three cycles is modified from that used for the

displacement history in Test 1.

Note that the actual beam chord rotations, θb (i.e., relative vertical displacement

between the beam ends divided by the beam length) reached during testing are slightly

different than the nominal loading histories in Figure 3.34. The actual actuator

displacements and beam displacements measured during each test, as well as the

maximum beam rotations reached, are provided in Chapters 6 and 7.

The rate of displacement of the load block varied throughout the duration of each

test, ranging between 0.05 in. – 0.6 in. (1.2 mm – 15.2 mm) per minute as shown in Table

3.3. The small cycles used a slower displacement rate to help better control the two

actuators and observe the response of the structure. As the target displacement of the load

block increased, the displacement rate was also increased.

The data instrumentation used in the experimental program is described in

Chapter 5. During each test, a collection of linear displacement transducers, rotation

transducers, strain gauges, and loads cells are used to monitor the behavior of the

structure. To obtain a visual record of the progression of damage, digital photographs are

taken at the peaks and zeros of the first and third displacement cycles at each different

amplitude of the displacement loading history. In addition, concrete crack propagation is

marked on the test beam and recorded on paper at the peak positive and negative

displacements.

115

-10

0

10

bea

m c

hord

rot.

, θ

b (

%)

0 70cycle number

Note: After 0.25% rotation, eachset of three fully reversed cycles isfollowed by a single cycle to an amplitude equal to 30% of the preceding set of three cycles.

(a)

0

-10

10

bea

m c

hord

rot.

, θ

b (

%)

0 60cycle number

(b)

Figure 3.36: Nominal lateral displacement loading history – (a) Test 1; (b) Tests 2 – 4B.

116

TABLE 3.3

NOMINAL APPLIED DISPLACEMENT HISTORY

Test 1 Tests 2 – 4B

Beam Chord Rotation, θb

(%)

Number

of Cycles

Loading Rate [in./min

(mm/min)]

Beam Chord Rotation, θb

(%)

Number of Cycles

Loading Rate [in./min

(mm/min)]

0.044 3

0.05 (1.2)

0.044 3

0.05 (1.2)

0.067 3 0.067 3

0.10 3 0.10 3

0.125 3 0.125 3

0.175 3 0.175 3

0.25 3 0.25 3

0.10 (2.5) 0.075 1

0.35 3

0.10 (2.5)

0.35 3 0.105 1

0.50 3 0.50 3

0.20 (5.1) 0.15 1

0.75 3 0.75 3

0.225 1

1.0 3 1.0 3

0.30 (7.6) 0.30 1

1.5 3

0.30 (7.6)

1.5 3 0.45 1

2.0 3 2.25 3

0.40 (10.2) 0.60 1

3.0 3 3.33 3

0.90 1

4.0 3

0.60 (15.2)

5.0 3

0.50 (12.7) 1.20 1

5.0 3 6.4 3

1.50 1

6.4 3 8.0 3 0.60 (15.2)

1.92 1

8.0 3 Note: The actual maximum cycle rotations reached in each test are given in Chapters 6 and 7.

117

3.3.5 Summary of Test Procedure

This section provides a summary of the subassembly testing procedures used in

the experimental program for both the virgin and non-virgin subassembly tests.

3.3.5.1 Virgin Beam Test Procedure

Day 1

1. Spray the beam-to-wall connection interfaces of the reaction block and load block

with a bond breaker.

2. Epoxy wooden shims to each end of the beam to ensure uniform grout thickness

of 0.5 in. (13 mm) at the beam-to-wall interfaces.

3. Position the test beam in between the load and reaction blocks, ensuring that the

entire subassembly is lined up and the post-tensioning ducts are properly aligned.

4. Install (but do not stress) the beam and angle post-tensioning strands and anchors.

5. Zero the strain gauges in the reaction block.

6. Zero the load cells on the eight tie-down bars that apply vertical forces to the wall

test region of the reaction block.

7. Apply a total initial vertical force of approximately 150 – 160 kips (667 – 712

kN) to the wall test region.

8. Record the forces in the actuators due to the self-weight of the test subassembly.

9. Complete final adjustment/alignment of the beam with respect to the reaction and

load blocks and record the actuator positions.

118

10. Support the test beam and load block on temporary screw jacks (note that screw

jacks are used to minimize the settlement of the load block and beam until

testing).

11. Pack 0.5 in. (12.7 mm) thick grout between the beam ends and the reaction and

load block faces.

12. Zero the beam post-tensioning anchor load cells.

13. Zero the beam strain gauges.

14. Zero all horizontal (i.e., along the beam length) displacement transducers.

15. Apply a small amount of initial force [approximately 2.0 to 4.0 kips (9.0 – 18

kN)] to the beam post-tensioning strands to close the gaps between the beam and

the reaction and load blocks. Remove any excess grout “squeezed” out of the

beam-to-wall interfaces due to the application of this force.

16. Let the grout cure for 8 days, applying moisture to it during this time.

Day 9

17. Stress the beam post-tensioning strands to the desired initial force.

18. Tighten the angle-to-beam connection bolts to snug tight by hand, and then, using

a hydraulic torque wrench, to slip critical.

19. Zero the angle post-tensioning anchor load cells.

20. Stress the angle-to-wall connection stands to the desired initial force

[approximately 20 kips (89 kN)].

119

Test Day

21. Move the actuators to the “zero” (i.e., level) position of the subassembly recorded

in Step 9 of Day 1.

22. Remove the temporary screw jacks supporting the test beam and the load block.

23. Switch actuators to load control and apply the self weight forces from Step 8 of

Day 1. Record the new “zero” position of each actuator.

24. Zero the displacement transducers on the load block and reaction block, as well as

the vertical displacement transducers on the beam, rotation transducers on the

beam, and load cells in the actuators (instrumentation described in Chapter 5).

25. Switch the actuators to displacement control and apply the cyclic lateral

displacement history in Figure 3.33, while continuously recording all sensor data.

3.3.5.2 Non-Virgin Beam Test Procedure

After angles have been removed from previous test.

Day 1

1. Stress the beam post-tensioning strands to the desired initial force (i.e., add or

take away post-tensioning strands).

2. Tighten the angle-to-beam connection bolts to snug tight by hand, and then, using

a hydraulic torque wrench, to slip critical.

3. Zero the angle post-tensioning anchor load cells.

4. Stress the angle-to-wall connection stands to the desired initial force

[approximately 20 kips (89 kN)].

120

Test Day

5. Move the actuators to the “zero” (i.e., level) position of the subassembly recorded

at end of virgin beam test.

6. Remove the temporary screw jacks supporting the test beam and the load block.

7. Switch actuators to load control and apply the self weight forces from Step 8 of

Day 1 from virgin beam test procedure. Record the new “zero” position of each

actuator.

8. Zero the displacement transducers on the load block and reaction block, as well as

the vertical displacement transducers on the beam, rotation transducers on the

beam, and load cells in the actuators (instrumentation described in Chapter 5).

9. Switch the actuators to displacement control and apply the cyclic lateral

displacement history in Figure 3.33, while continuously recording all sensor data.

3.4 Chapter Summary

This chapter provides an overview of the half-scale experimental program on the

lateral load behavior of floor-level unbonded post-tensioned precast concrete coupling

beam subassemblies. The experiment setup, subassembly test components, and testing

procedure are described in the chapter.

121

CHAPTER 4

DESIGN AND MATERIAL PROPERTIES

This chapter describes the design and measured properties of the materials used in

the subassembly experiments.

4.1 Design Material Properties

The design compressive strength for the unconfined concrete used in the beam

specimens and the reaction and load block fixtures is f’c = 6.0 ksi (41 MPa). Several

different concrete mixes were tested prior to the casting of the subassembly specimens to

ensure that the 28-day strength is as close to 6.0 ksi (41 MPa) as possible and minimize

overstrength.

The design compressive strength for the fiber-reinforced grout used at the beam-

to-wall joints is f’gt = 10 ksi (69 MPa). The grout is designed to have a strength and

stiffness slightly under the confined concrete used in the beam specimens and the

reaction and load block fixtures without compromising workability and ductility (see

Section 3.2.1.4). The slightly lower grout strength and stiffness are expected to force the

compression strains (deformations) to occur within the fiber-reinforced grout rather than

the beam or wall concrete.

122

The design yield strength and maximum strength of the post-tensioning strands is

fpy = 245 ksi (1689 MPa) and fpu = 270 ksi (1862 MPa), respectively. The post-tensioning

steel meets ASTM A416 low-relaxation strand requirements.

The design yield strength of the No. 3 hoop reinforcement used in the beam

specimens and the reaction and load block fixtures is fhy = 60 ksi (414 MPa). These bars

meet ASTM A615 Gr. 60 reinforcement requirements.

The design yield strength of the No. 6 looping reinforcement used in the beams is

fly = 75 ksi (517 MPa). These bars also meet ASTM A615 Gr. 60 reinforcement

requirements; however, they are selected to have a high yield strength based on the mill

certifications.

All other mild steel reinforcement used in the subassembly components has a

design yield strength of 60 ksi (414 MPa, ASTM A615 Gr. 60 reinforcement).

The design yield strength of the top and seat angle steel is fay = 36 ksi (248 MPa)

according to ASTM A709 Gr. 36.

4.2 Measured Material Properties

ASTM standards were followed to determine the actual properties of the

unconfined concrete, fiber-reinforced grout, post-tensioning steel, mild reinforcing steel,

and top and seat angle steel used in the subassembly test structure. The measured material

properties are described below.

123

4.2.1 Unconfined Concrete Strength

The compressive strengths of the unconfined concrete used in the two reaction

blocks, the load block, and the four beam specimens were obtained by conducting two or

three standard (ASTM C39/C 39M) 6.0 in. by 12 in. (152 mm by 305 mm) cylinder tests

using a 600 kip (2669 kN) SATEC® Model 600XWHVL universal testing machine.

Unbonded caps using rubber pads and retainer rings were used at both ends of the

cylinder specimens in accordance with ASTM C 1231/C 1231M (ASTM 2001). The

concrete cylinders were cast at the same time as the test specimens and fixtures, and were

kept under the same environmental conditions until testing.

The cylinder tests were conducted at 28-days for the reaction block, load block,

and beam concrete as well as on the day of subassembly testing (first test for beams

tested more than once) for the beam concrete. A loading rate of 20 pounds per second

(0.14 MPa per second) was used. Figure 4.1 shows three concrete cylinder specimens

after failure and Table 4.1 lists the results obtained from the cylinder tests. No strain

measurements were taken for the concrete cylinder specimens. The concrete mix design

can be found in Appendix A.

Figure 4.1: Concrete cylinder specimens.

124

TABLE 4.1

UNCONFINED CONCRETE STRENGTH

Sample No. Subassembly Component

Cast Date Subassembly

Test Date

f’c at Subassembly Test Day

[ksi (MPa)]

28-Day Test Date

f’c at 28-Days [ksi (MPa)]

1 Beam 1

Load Block Reaction Block 1

04/05/2006 10/18/2006

8.01 (55.2)

05/03/2006

6.08 (41.9) 2 7.99 (55.1) 6.11 (42.1) 3 6.71 (46.3) 6.61 (45.6)

Average 7.57 (52.2) 6.27 (43.2) 1

Beam 2 Reaction Block 2

12/15/2006 01/27/2007

7.98 (55.0)

01/12/2007

7.67 (52.9) 2 7.22 (49.8) 6.45 (44.5) 3 6.52 (44.9) 5.98 (41.2)

Average 7.24 (49.9) 6.70 (46.2) 1

Beam 3 12/15/2006 03/06/2007

8.21 (56.6)

01/12/2007 same batch as

Beam 2 2 7.84 (54.1) 3 6.83 (47.1)

Average 7.63 (52.6) 1

Beam 4 12/15/2006 05/24/2007

-

01/12/2007 same batch as

Beam 2 2 6.41 (44.2) 3 6.12 (42.2)

Average 6.27 (43.2) f’c = maximum (i.e., peak) strength of unconfined concrete.

4.2.2 Fiber-Reinforced Grout Properties

The fiber-reinforced grout used at the beam-to-wall interfaces is an integral part

of the test subassembly. A high-strength grout with adequate stiffness and ductility is

required, while maintaining its workability. To achieve this goal, several mixes were tried

prior to the selection of the final design mix. A number of mix parameters were

investigated including the water-to-cement ratio, amount of fibers, curing conditions, and

the use of epoxy grout.

A series of preliminary tests were done on trial mixes to determine the final grout

mix design properties for the coupling beam subassembly experiments. The compressive

strength of the grout was determined by testing 2.0 in. (50.8 mm) cube specimens using a

125

60 kip (267 kN) Instron Model 5590-67HVL hydraulic universal testing machine

(Figures 4.2 and 4.3). ASTM C 109/C 109M (ASTM 2001) requirements were followed

in preparing and testing the grout cubes. A relative machine displacement rate [0.04 in.

per minute (1.0 mm per minute)] corresponding to a loading rate of 0.20 to 0.40 kips per

second [900 to 1800 N per second] was used for testing. The cube specimens wear placed

directly against the bearing plates of the testing machine; and thus, the position

measurements from the testing machine were used to calculate the compressive strain of

the specimens. Specimen dimensions and weights were taken for each mix to ensure that

the densities of the different samples were approximately the same. Compressive strength

tests were then ran on each sample at 1, 3, 7, 10, 14, 21 and 28 days to determine the

curing time needed for the grout to reach the design strength of the mix. The grout was

then allowed to cure for this duration prior to testing in the experimental program. The

results from the preliminary tests are shown in Table 4.2. The ultimate strain of the grout

is assumed to be reached at a stress of 85% of the maximum stress (i.e., 0.85f’gt). The

initial stiffness (i.e., Young’s modulus) was calculated based on the slope from two

points within the linear-elastic portion of the measured stress-strain relationship. Note

that mixes 1 – 5 were not carried out to the full 28-day strength tests.

The workability of the grout was an important factor due to the need to pack the

grout into the 0.50 in. (13 mm) thick gap at the beam-to-wall interfaces of the

subassembly test setup. Each mix design was tested by forcing the grout through a 0.50

in. (13 mm) diameter funnel. Several different water-to-cement ratios were tested ranging

from 0.30 – 0.45, with different amounts of fibers. Based on the “funnel tests” and visual

126

inspection, it was determined that the minimum water-to-cement ratio to ensure adequate

workability was 0.375.

Several different amounts of fibers were tested for the grout mix. First, the largest

recommended amount of fibers (16.99 g/ft3) from Grace™ Microfibers was used. Then,

several different grout mixes were tried with factors of the recommended fiber amount

(e.g., 2 times, 4 times, 10 times, etc.). These mixes were investigated the workability,

strength, and ductility.

Other parameters, including the use of epoxy grout and curing conditions, were

also investigated. The epoxy grout was difficult to work with and therefore was not

practical for the subassembly test setup. It was also found that for best strength gain, the

grout should be kept moist during the curing process.

The preliminary testing on various trial grout mixes resulted in a fiber-reinforced

Type III cement grout (with Grace™ Microfibers) that achieved the desired strength,

stiffness, and ultimate strain requirements for the test structure (Mix 7 in Table 4.2). The

same mix was used in each subassembly test; however, during mixing, visual inspection

of the grout workability was ultimately used. The grout could neither be too wet or too

dry for proper placement at the beam-to-wall interfaces. The water-to-cement ratio

determined for the final mix design was never exceeded; however, the use of a smaller

water-to-cement ratio was possible for the grout in the subassembly experiments. The

final mix design for the fiber-reinforced grout can be found in Appendix A. Table 4.3

lists the measured properties for the actual grout samples from each of the four test

subassemblies and Figure 4.4 shows the stress-strain relationship for a grout sample from

each subassembly.

127

(a) (b)

Figure 4.2: Grout samples – (a) mortar mix; (b) epoxy grout.

Figure 4.3: Photographs from a grout test.

128

TABLE 4.2

PRELIMINARY GROUT MIX TESTS

Mix Parameter w/c

Ratio

Fibers (percent volume)

Workability

7-Day Properties 28-Day Properties

f’gt [ksi (MPa)]

εgtm

(%) εgtu

(%)

Initial Stiffness

[ksi (MPa)]

f’gt [ksi (MPa)]

εgtm

(%)

εgtu

(%)

Initial Stiffness

[ksi (MPa)]1 baseline 0.38 0.05 good 9.9 (68.1) 2.58 2.71 477 (3289) - - - - 2 w/c, fibers 0.35 0.07 difficult 8.9 ( 61.4) 2.63 3.24 406 (2799) - - - - 3 play sand 0.35 0.05 difficult 8.7 (60.0) 2.62 3.00 430 (2965) - - - -

4 non-shrink

grout 0.40 0.05 good 3.0 1.89 2.16 205 (1413) - - - -

5 cement paste

0.40 0.05 good 8.8 2.56 2.77 405 (2792) - - - -

6 Dayton Superior grout mix

- 0.07 okay 7.3 (50.4) 3.22 3.36 250 (1724) 8.0 (55.0) 2.62 2.89 344 (2372)

17 w/c, fibers 0.375 0.07 good 10.1 (69.3) 3.04 3.28 337 (2324) 9.1 (62.4) 2.62 2.74 396 (2730)8 fibers 0.375 0.13 okay 7.0 (48.3) 2.21 2.69 338 (2330) 7.7 (52.8) 2.34 2.74 362 (2496)

9 fibers/water cured

0.375 0.14 good 7.8 (53.8) 2.00 2.71 437 (3013) 7.1 (49.0) 2.50 2.78 323 (2227)

10 reduced

sand 0.375 0.13 good 9.1 (62.9) 1.67 1.96 581 (4006) 8.1 (55.6) 2.69 3.27 293 (2020)

11 epoxy grout

- - difficult 9.3 (64.1) 3.01 3.82 365 (2517) 8.9 (61) 3.22 4.95 329 (2268)

f’gt = maximum (i.e., peak) strength of grout. εgtm = strain at f’gt. εgtu = ultimate strain at 0.85f’gt. 1Grout mix used for subassembly experiments.

129

TABLE 4.3

PROPERTIES OF GROUT USED IN COUPLING

BEAM TEST SUBASSEMBLIES

Sample No.

Sub. Cast Date

Subassembly Test Day Properties 28-Day Properties

Subassembly Test Date

f’gt [ksi (MPa)]

εgtm (%)

εgtu (%)

Initial Stiffness

[ksi (MPa)]

28-Day Test Date

f’gt [ksi (MPa)]

εgtm (%)

εgtu (%)

Initial Stiffness

[ksi (MPa)]

1

1 10/05/2006 10/18/2006

8.72 (60.1) 2.54 2.80392

(2702)

11/02/2006

10.4 (71.7) 1.66 2.06634

(4371)

2 7.69 (53.0) 2.16 2.16370

(2551)9.97 (68.8) 1.91 2.19

569 (3923)

3 8.85 (61.0) 2.24 2.40426

(2937)9.66 (66.6) 2.14 2.34

444 (3061)

Average 8.42 (58.0) 2.31 2.45396

(2730)10.0 (69.0) 1.90 2.20

549 (3785)

1

2 01/17/2007 01/27/2007

9.81 (67.7) 1.90 2.10556

(3833)

02/14/2007

9.59 (66.1) 1.94 2.19633

(4364)

2 9.69 (66.8) 1.85 2.21530

(3654)10.1 (69.6) 1.84 2.19

726 (5006)

3 9.74 (66.8) 1.67 2.08626

(4316)9.25 (63.8) 1.93 2.39

576 (3971)

Average 9.75 (67.1) 1.81 2.13571

(3937)9.65 (66.5) 1.90 2.26

645 (4447)

1

3 02/07/2007 03/06/2007

9.84 (67.8) 1.76 2.13600

(4137)

03/07/2007

9.53 (65.7) 2.09 2.24428

(2951)

2 9.36 (64.5) 2.13 2.34427

(2944)10.0 (69.1) 2.16 2.40

498 (3434)

3 9.92 (68.4) 2.14 2.49487

(3358)9.55 (65.8) 2.00 2.14

509 (3509)

Average 9.71 (62.2) 2.01 2.32504

(3475)9.70 (66.9) 2.08 2.26

478 (3296)

1

4 05/08/2007 05/24/2007

9.39 (64.8) 1.52 2.03707

(4875)

06/05/2007

7.91 (54.5) 1.51 2.31620

(4275)

2 7.97 (55.0) 1.41 1.50577

(3978)9.18 (63.3) 1.75 2.24

533 (3675)

3 6.48 (44.7) 1.81 2.57454

(3130)9.28 (64.0) 1.64 2.23

654 (4509)

Average 7.95 (54.8) 1.58 2.02579

(3992)8.79 (60.6) 1.78 2.26

602 (4151)

f’gt = maximum (i.e., peak) strength of grout. εgtm = strain at f’gt. εgtu = ultimate strain at 0.85f’gt.

130

strain, εgt (%)

stre

ss, f g

t

[ksi

(M

Pa)]

0 0.04

10(69) Subassembly 1

Sample 1

maximum stress(εgtm , f gt )

Subassembly 2Sample 1



ultimate strain (εgtu , 0.85f gt )

Figure 4.4: Stress-strain relationships for subassembly grout samples.

4.2.3 Post-tensioning Strand Properties

The monotonic tensile stress-strain relationship of the post-tensioning strands was

measured by testing four specimens in a 600 kip (2669 kN) SATEC® Model 600XWHVL

hydraulic universal testing machine following ASTM 370 requirements. Figure 4.5 shows

the strand test set-up and Figure 4.6 shows a photograph from a strand test. The strains in

the strand specimens were measured using an MTS Model 634.25E-24 extensometer with

a 2.0 in. (50.8 mm) gauge length. Note that the International Code Council – Evaluation

Service (ICC-ES 2007) and the Post-Tensioning Institute (PTI 2003) require a minimum

extensometer gauge length of 36 in. (914.4 mm) for testing post-tensioning strand;

however, recent research (Walsh and Kurama 2009) has shown that the strain

131

measurements from 2.0 in. (50.8 mm) and 36 in. (914.4 mm) extensometers are nearly

identical. Thus, the strand strains presented in this dissertation are expected to be

accurate.

Precision SureLOCK® single strand steel wedge/barrel type post-tensioning

anchors (the same as the anchors that were used in the subassembly experiments) were

used to pull the strands until failure to provide anchor conditions similar to those in the

coupled wall subassembly experiments. Note that the seating of the anchor wedges in the

strand tests was not done using a post-tensioning jack, possibly resulting in slightly

different wedge seating conditions at the live end as compared with the subassembly

tests. The strand specimens were approximately 60 in. (1.5 m) long between the anchors

and were carefully positioned between the loading heads of the testing machine to

minimize end eccentricities. Thus, the end eccentricity that occurs in the subassembly

strands during the lateral displacements of the structure was not captured in the strand

material tests. Failure of all strand specimens occurred due to the fracturing of a post-

tensioning wire (one wire out of a total of seven wires) inside an anchor (see Figure 4.7).

The ultimate strain, εbpu of the post-tensioning strand is reached when the strand wire

fracture occurs at the maximum strength, fbpu. Note that since the wire fracture occurs in a

brittle manner, the maximum stress, fbpu corresponds to the fracture strain with no visible

necking in the fracture zone. Furthermore, the measured fracture strain, εbpu provides a

good representation of the overall strand strain even though the fracture occurs outside

the extensometer gauge length.

Three strand samples were tested using a loading rate of 0.375 in. per minute

(0.015 mm per minute) and one strand was tested at a slower rate of 0.05 in. per minute

132

(0.002 mm per minute), similar to the loading rate of the strands in the subassembly tests.

The results from the strand tests are shown in Figure 4.8 and tabulated in Table 4.4. The

limit of proportionality point (at fbpl, εbpl) was determined by monitoring the change in the

strand stiffness as shown in Figure 4.9. As can be seen in Figure 4.8, the limit of

proportionality is reached significantly before the “yielding” of the post-tensioning

strand.

133

Figure 4.5: Post-tensioning strand test set-up.

134

Figure 4.6: Photograph of post-tensioning strand test.

Figure 4.7: Photograph of post-tensioning strand wire fracture inside anchor.

135

specimens 1-3specimen 4

PT strand

strain, εbp

stre

ss,

f bp

[ksi

(M

Pa

)]

0.036

300(2100)

0

limit of proportionality (εbpl , fbpl )

strand wire fracture(εbpu , fbpu )

Figure 4.8: Stress-strain relationships for post-tensioning strand specimens.

TABLE 4.4

POST-TENSIONING STRAND MATERIAL PROPERTIES

Specimen No.

fbpl [ksi (MPa)]

εbpl (%)

fbpu [ksi (MPa)]

εbpu (%)

Rate of Loading [in/min (mm/min)]

1 167 (1150) 0.581 261 (1802) 3.21 0.375 (0.015) 2 173 (1191) 0.604 261 (1801) 3.20 0.375 (0.015) 3 167 (1148) 0.576 256 (1764) 2.47 0.375 (0.015) 4 159 (1094) 0.567 262 (1805) 3.27 0.05 (0.002)

Average 166 (1146) 0.582 260 (1793) 3.04 - fbpl = limit of proportionality of post-tensioning strand. εbpl = fbpl divided by measured Young’s modulus. fbpu = ultimate/maximum strength of post-tensioning strand. εbpu = ultimate strain of post-tensioning strand.

136

limit of proportionality, fbpl

increasing stress

dec

easi

ng

sti

ffn

ess

Figure 4.9: Limit of proportionality determination.

4.2.4 Mild Reinforcing Steel Properties

Three material samples each for the No. 6 and No. 3 reinforcing bars used in the

subassembly specimens were tested monotonically in tension using an Instron Model

5590-67HVL hydraulic universal testing machine with a 60 kip (267 kN) capacity. The

strains were measured using an Instron Model 2630-114 extensometer with a 2.0 in. (50.8

mm) gauge length. The failure of all specimens occurred within this gauge length. The

No. 6 specimens were approximately 12 in. (305 mm) long, while the No. 3 specimens

were approximately 8.0 in. (203 mm). Figure 4.10 shows photographs from a No. 3 bar

test. The measured monotonic tensile stress-strain relationships for the three No. 3 and

three No. 6 bar specimens are shown in Figures 4.11 and 4.12 respectively.

Tables 4.5 and 4.6 summarize the material properties from each of the rebar

specimens. The samples all show a distinct yield point. The yield strength was

determined as the lower yield point on the measured stress-strain relationship. The yield

137

strain was determined by dividing the yield strength with the measured Young’s

modulus, which was calculated based on the slope from two points on the linear-elastic

portion of the measured stress-strain relationship. The ○, , and markers in Figures

4.11 and 4.12 correspond to the yield stress, maximum (i.e., peak) stress, and ultimate

strain values, respectively, in Tables 4.5 and 4.6. The ultimate strain values are assumed

to occur at a stress of 85% of the maximum stress (i.e., 0.85fhm and 0.85flm for the No. 3

and No. 6 rebar, respectively).

Figure 4.10: Photographs from a No. 3 reinforcing bar test.

138

No. 3 bar

yield stress (εhy , fhy )

ultimate strain (εhu , fhu )

maximum stress(εhm , fhm

)

strain, εh

stre

ss,

f h[k

si

(MP

a)]

0.16

120(800)

0

Figure 4.11: Stress-strain relationships for No. 3 bar specimens.

strain, εl

stre

ss,

f l[k

si

(MP

a)]

0.18

120(800)

0

yield stress (εly , fly )

ultimate strain (εlu , flu )

maximum stress(εlm , f

lm )

No. 6 bar

Figure 4.12: Stress-strain relationships for No. 6 bar specimens.

139

TABLE 4.5

No. 3 REINFORCING BAR MATERIAL PROPERTIES

Specimen No.

fhy

[ksi (MPa)]hy (%)

fhm [ksi (MPa)]

hm (%)

fhu [ksi (MPa)]

hu

(%)

1 70.1 (483)

0.260 110

(759) 10.3

93.6 (646)

13.8

2 68.0 (469)

0.209 107

(737) 9.18

90.8 (626)

11.3

3 67.7 (466)

0.257 108 (738)

10.1 90.9 (627)

14.2

Average 68.6 (473)

0.242 108 (745)

9.86 91.8 (633)

13.1

fhy = lower yield strength. hy = fhy divided by measured Young’s modulus. fhm = maximum (i.e., peak) strength. hm = strain at fhm. fhu = 0.85fhm. hu = ultimate strain at 0.85fhm.

TABLE 4.6

No. 6 REINFORCING BAR MATERIAL PROPERTIES

Specimen

No. fly

[ksi (MPa)]ly

(%) flm

[ksi (MPa)]lm (%)

flu [ksi (MPa)]

lu

(%)

1 79.9 (551)

0.283 103

(707) 10.2

87.1 (601)

15.6

2 80.0 (551)

0.282 103

(707) 10.3

87.2 (601)

17.2

3 79.7 (550)

0.283 102

(706) 10.4

87.0 (600)

16.2

Average 79.9 (551)

0.283 103

(706) 10.3

87.1 (601)

16.3

fly = lower yield strength. ly = fly divided by measured Young’s modulus. flm = maximum (i.e., peak) strength. lm = strain at flm. flu = 0.85flm. lu = ultimate strain at 0.85flm.

140

4.2.5 Angle Steel Properties

Four material samples for the top and seat angle steel were saw-cut from the angle

legs in the direction perpendicular to the angle length. The samples were then machined

into 0.25 in. (6.40 mm) round specimens using the same proportions from standard

ASTM .505 specimens. The samples were smaller than standard ASTM .505 specimens

because of the limited thickness of the angle steel. A 2.0 in. (50.8 mm) gauge length was

used, the same as ASTM .505 requirements.

Photographs from an angle steel material test can be seen in Figure 4.13 and the

measured stress-strain relationships from the four specimens can be seen in Figure 4.14.

The specimens were tested in an Instron Model 5590-67HVL hydraulic universal testing

machine with a 60 kip (267 kN) capacity. The strains were measured using an Instron

Model 2630-114 extensometer with a 2.0 in. (50.8 mm) gauge length. The failure of all

specimens occurred within this gauge length.

Figure 4.13: Photographs from an angle steel material test.

141

The material properties of the angle steel specimens are listed in Table 4.7.

Similar to the mild steel reinforcing bars, the samples show a distinct yield point and the

yield strength was determined as the lower yield point on the measured stress-strain

relationship. The yield strain was determined by dividing the yield strength with the

measured Young’s modulus, which was calculated based on the slope from two points on

the linear-elastic portion of the measured stress-strain relationship. The ○, , and

markers in Figure 4.14 correspond to the yield strength, maximum (peak) strength, and

ultimate strain values, respectively, in Table 4.7. The ultimate strain values are assumed

to occur at a stress of 85% of the maximum stress (i.e., 0.85fam).

strain, εa

stre

ss,

f a[k

si

(MP

a)]

-0.05 0.30

80(550)

0

yield stress (εay , fay )

ultimate strain (εau , fau )

maximum stress(εam , fam

)

Figure 4.14: Stress-strain relationships for angle steel material specimens.

142

TABLE 4.7

ANGLE STEEL MATERIAL PROPERTIES

Specimen No.

fay

[ksi (MPa)]ay (%)

fam [ksi (MPa)]

am (%)

fau [ksi (MPa)]

au

(%)

1 51.7 (356)

0.175 75.7 (522)

13.7 56.0 (386)

19.7

2 50.7

(349) 0.171

74.9 (516)

16.9 56.2 (388)

23.6

3 51.1 (353)

0.173 75.7 (522)

17.5 56.6 (390)

25.7

4 50.1 (345)

0.169 74.6 (514)

15.2 55.6 (383)

20.4

Average 50.9 (351)

0.172 75.2 (518)

15.9 56.1 (387)

22.3

fay = lower yield strength. ay = fay divided by measured Young’s modulus. fam = maximum (i.e., peak) strength. am = strain at fam. fau = 0.85fam. au = ultimate strain at 0.85fam.

4.3 Chapter Summary

This chapter describes the design and actual properties of the materials used in the

subassembly test setup. Details of the material testing procedures, equipment, and

measured properties are presented. Table 4.8 summarizes the average material properties

from the experimental program.

143

TABLE 4.8

MATERIAL PROPERTIES SUMMARY

Material Test Series

1 2 3 4

Beam Concrete


6.27 (43.2)

6.70 (46.1)

f’c at Test Day [ksi (MPa)]

7.57 (52.2)

7.24 (49.9)

7.63 (52.6)

6.27 (43.2)

Reaction Block Concrete


6.27 (43.2)

6.70 (46.2)

Load Block Concrete


6.27 (43.2)

Grout

f’gt at 28-Days [ksi (MPa)]

10.0 (69.0)

9.65 (66.5)

9.70 (66.9)

8.79 (60.6)

εgtm (%) 1.90 1.90 2.08 1.78 εgtu (%) 2.20 2.26 2.26 2.26

Initial Stiffness [ksi (MPa)]

549 (3785)

645 (4447)

478 (3296)

602 (4151)

f’gt at Test Day [ksi (MPa)]

8.42 (58.0)

9.75 (67.1)

9.71 (62.2)

7.95 (54.8)

εgtm (%) 2.31 1.81 2.01 1.58 εgtu (%) 2.45 2.13 2.32 2.02

Initial Stiffness [ksi (MPa)]

396 (2730)

571 (3937)

504 (3475)

579 (3992)

Post-Tensioning Strand

fbpl [ksi (MPa)] 166 (1146) bpl (%) 0.582

fbpu [ksi (MPa)] 260 (1793) bpu (%) 3.04

No. 3 Reinforcing Bar

fhy [ksi (MPa)] 68.6 (473) hy (%) 0.242

fhm [ksi (MPa)] 108 (745) hm (%) 9.87

fhu [ksi (MPa)] 91.8 (633) hu (%) 13.1

No. 6 Reinforcing Bar

fly [ksi (MPa)] 79.9 (551) ly (%) 0.283

flm [ksi (MPa)] 103 (706) lm (%) 10.3

flu [ksi (MPa)] 87.1 (601) lu (%) 16.3

Angle Steel

fay [ksi (MPa)] 50.9 (351) ay (%) 0.172

fam [ksi (MPa)] 75.2 (518) am (%) 15.9

fau [ksi (MPa)] 56.1 (387) au (%) 22.3

All values are average values for samples ran for each material. f’c = maximum (i.e., peak) strength of unconfined concrete. f’gt = maximum (i.e., peak) strength of grout; εgtm = strain at f’gt; εgtu = ultimate strain at 0.85f’gt. fbpl = limit of proportionality of post-tensioning strand. εbpl = fbpl divided by measured Young’s modulus. fbpu = ultimate/maximum strength of post-tensioning strand. εbpu = ultimate strain of post-tensioning strand. fhy = lower yield strength; hy = fhy divided by measured Young’s modulus. fhm = maximum (i.e., peak) strength; hm = strain at fhm. fhu = 0.85fhm; hu = ultimate strain at 0.85fhm. fly = lower yield strength; ly = fly divided by measured Young’s modulus. flm = maximum (i.e., peak) strength; lm = strain at flm. flu = 0.85flm; lu = ultimate strain at 0.85flm. fay = lower yield strength; ay = fay divided by measured Young’s modulus. fam = maximum (i.e., peak) strength; am = strain at fam. fau = 0.85fam; au = ultimate strain at 0.85fam.

144

CHAPTER 5

DATA INSTRUMENTATION AND SPECIMEN RESPONSE PARAMETERS

This chapter describes the data instrumentation and response parameters for the

precast coupling beam floor level subassembly experiments.

5.1 Data Instrumentation

Up to 92 channels of data were collected during testing including: (1) load cells to

measure the forces in the hydraulic actuators, beam post-tensioning strands, angle-to-wall

connection post-tensioning strands, and the vertical forces (representing the wall pier

axial forces) applied to the wall test region of the reaction block; (2) displacement

transducers to measure the in-plane displacements of the actuators, load block, reaction

block, and coupling beam; the local horizontal deformations of the concrete in the beam-

to-wall contact region of the reaction block; and the gap opening displa cements at the

beam-to-reaction-block interface; (3) rotation transducers to measure the rotations of the

coupling beam near the midspan and near the reaction block (i.e., south) end; and (4)

strain gauges to measure the strains in the mild steel reinforcement and the confined

concrete in the beam and the reaction block. For each test, all sensors, instrumentation,

and data acquisition were initialized such that any data recorded was due to the

145

application of the post-tensioning forces and lateral loads. The data acquisition hardware

consisted of a National Instruments SCXI-1001 chassis daisy-chained to a SCXI-1000

chassis and the data was collected using LabView Version 7.0 at a sampling rate of once

every 3 seconds. During testing, important data and response parameters (e.g., beam

chord rotation, beam shear force, post-tensioning forces, etc.) were processed in real-time

and observed throughout the duration of the test.

5.1.1 Instrumentation Overview

The sensors used for testing, some of which are shown in Figure 5.1, include the

following:

Figure 5.1: Photograph of beam-to-reaction-block interface and instrumentation for Test 1.

146

Load cells:

(1) Two load cells (LC1 and LC2) to measure the forces in the servo-

controlled hydraulic actuators used to vertically displace the load block.

(2) Four load cells (LC3 – LC6) manufactured in the Structural Systems

Laboratory at the University of Notre Dame to measure the forces in the

angle-to-reaction-block connection post-tensioning strands.

(3) Eight load cells (LC7 – LC14) to measure the vertical forces (representing

the wall pier axial forces) in the 8 bars used to “tie-down” the wall test

region of the reaction block to the strong floor.

(4) Up to four load cells (LC15 – LC18) manufactured in the Structural

Systems Laboratory at the University of Notre Dame to measure the forces

in the beam post-tensioning strands.

Linear displacement transducers:

(1) Two linear displacement transducers (DT1 and DT2) to measure the axial

displacements of the servo-controlled hydraulic actuators used to

vertically displace the load block.

(2) Three linear displacement transducers (DT3 – DT5) to measure the

vertical and horizontal displacements of the load block in the plane of the

test subassembly.

(3) Three linear displacement transducers (DT6 – DT8) to measure the

vertical and horizontal displacements of the reaction block in the plane of

the test subassembly.

147

(4) Two linear displacement transducers (DT9 – DT10) to measure the

vertical displacements of the coupling beam in the plane of the test

subassembly.

(5) Three linear displacement transducers (DT11 – DT13) to measure the gap

opening displacements at the beam-to-reaction-block interface.

(6) Two linear displacement transducers (DT14 – DT15) to measure the local

horizontal deformations in the beam-to-wall contact region of the reaction

block.

Rotation transducers:

(1) Two rotation transducers (RT1 and RT2) to measure the rotations of

the coupling beam near the reaction block (i.e., south) end and near the

midspan.

Electrical resistance strain gauges:

(1) Up to 38 strain gauges to measure the strains in the mild steel

reinforcement and the hoop-reinforced concrete in the coupling beam.

(2) Thirteen strain gauges to measure the strains in the mild steel

reinforcement and the hoop-reinforced concrete in the beam-to-wall

contact region of the reaction block.

The data instrumentation used in the experimental program is summarized in

Tables 5.1 – 5.8. Figures 5.2 – 5.6 show the general placement of the load cells,

displacement transducers, rotation transducers, and reaction block and coupling beam

strain gauges, respectively. More detailed information on the instrumentation and on the

148

test subassembly response parameters calculated from the measured data is provided in

the remainder of this chapter.

Note that as mentioned in Chapters 3 and 4, two reaction blocks were cast for the

subassembly testing program. The same steel formwork was used for both reaction

blocks with the same reinforcement and concrete design parameters. The same number of

strain gauges were embedded in both reaction blocks; however, the strain gauge wires

coming out of the second reaction block were all severed during the removal of the

formwork. Thus, no strain gauge measurements could be made for the second reaction

block (Tests 2 – 4B) as discussed in more detail in Chapter 6.

TABLE 5.1

SUMMARY OF LOAD CELLS

Transducer No.

Measurement Description Sign

Convention Transducer Location

LC1 FLC1 actuator forces

compression positive

internal to actuator LC2 FLC2

LC3 FLC3 angle-to-reaction block connection

forces

between single strand anchor barrel and bearing plate

LC4 FLC4

LC5 FLC5

LC6 FLC6

LC7 FLC7

wall test region vertical forces

on individual vertical tie down bars at north end of reaction block

LC8 FLC8

LC9 FLC9

LC10 FLC10

LC11 FLC11

LC12 FLC12

LC13 FLC13

LC14 FLC14

LC15 FLC15

beam post-tensioning forces

between single strand anchor barrel and bearing plate

LC16 FLC16

LC17 FLC17

LC18 FLC18

149

TABLE 5.2

SUMMARY OF DISPLACEMENT AND ROTATION TRANSDUCERS

Transducer No.



DT1 ΔDT1 actuator displacements

extension positive

internal to actuator DT2 ΔDT2 externally attached to actuator

DT3 ΔDT3 load block horizontal

displacement

between insert in load block and fixed reference point

DT4 ΔDT4 load block vertical

displacement at north end

DT5 ΔDT5 load block vertical

displacement at south end

DT6 ΔDT6 reaction block

horizontal displacement

between insert in reaction block and fixed reference point

DT7 ΔDT7

reaction block vertical

displacement at north end

DT8 ΔDT8

reaction block vertical

displacement at south end

DT9 ΔDT9 beam vertical

displacement at south end between insert in beam and fixed

reference point DT10 ΔDT10

beam vertical displacement at

north end

DT11 ΔDT11 gap opening near

beam top between insert near beam end and reaction plate near beam-to-wall

interface of wall test region DT12 ΔDT12

gap opening at beam centerline

DT13 ΔDT13 gap opening near

beam bottom

DT14 ΔDT14 wall test region

contact deformation at top between insert in wall test region and

reaction plate near beam-to-wall interface of wall test region

DT15 ΔDT15 wall test region

contact deformation at bottom

RT1 θRT1 beam rotation at

south end clockwise positive

near south end of beam

RT2 θRT2 beam rotation near

midspan near midspan of beam

150

TABLE 5.3

SUMMARY OF BEAM LOOPING REINFORCEMENT

LONGITUDINAL LEG STRAIN GAUGES

Transducer No.



6(1)T-E ε6(1)T-E

beam No. 6 looping reinforcement longitudinal

(horizontal) leg strains

tension positive

on top leg, east reinforcement, 5.75” (146mm) from south end of beam

6(2)T-E ε6(2)T-E on top leg, east reinforcement, 11.5”

(292mm) from south end of beam

6(3)T-E ε6(3)T-E on top leg, east reinforcement, 17” (432mm) from south end of beam

6(1)T-W ε6(1)T-W on top leg, west reinforcement, 5.75”


6(2)T-W ε6(2)T-W on top leg, west reinforcement, 11.5”


6(3)T-W ε6(3)T-W on top leg, west reinforcement, 17” (432mm) from south end of beam

6(1)B-E ε6(1)B-E on bottom leg, east reinforcement, 5.75” (146mm) from south end of

beam

6(2)B-E ε6(2)B-E on bottom leg, east reinforcement, 11.5” (292mm) from south end of

beam

6(3)B-E ε6(3)B-E on bottom leg, east reinforcement, 17”


6(1)B-W ε6(1)B-W on bottom leg, west reinforcement, 5.75” (146mm) from south end of

beam

6(2)B-W ε6(2)B-W on bottom leg, west reinforcement, 11.5” (292mm) from south end of

beam

6(3)B-W ε6(3)B-W on bottom leg, west reinforcement, 17”


6MT-E ε6MT-E on top leg, east reinforcement,

midspan of beam

6MB-E ε6MB-E on bottom leg, east reinforcement,

midspan of beam

6MT-W ε6MT-W on top leg, west reinforcement,

midspan of beam

6MB-W ε6MB-W on bottom leg, west reinforcement,

midspan of beam

151

TABLE 5.4

SUMMARY OF BEAM TRANSVERSE REINFORCEMENT

STRAIN GAUGES

Transducer No.



6SE(I)-E ε6SE(I)-E

beam No. 6 looping reinforcement

transverse (vertical) leg strains

tension positive

on vertical leg, east reinforcement, midheight of leg (internal), south end

of beam

6SE(E)-E ε6SE(E)-E on vertical leg, east reinforcement,

midheight of leg (external), south end of beam

6SE(I)-W ε6SE(I)-W

on vertical leg, west reinforcement, midheight of leg (internal), south end

of beam

6SE(E)-W ε6SE(E)-W on vertical leg, west reinforcement,

midheight of leg (external), south end of beam

MH-E εMH-E beam midspan No. 3 transverse hoop

strains

on transverse hoop at beam midspan, midheight of east

vertical leg

MH-W εMH-W on transverse hoop at beam midspan,

midheight of west vertical leg

TABLE 5.5

SUMMARY OF BEAM END CONFINEMENT HOOP STRAIN GAUGES

Transducer No.



1HB-E ε1HB-E

beam end No. 3 confinement hoop

strains

tension positive

on 1st bottom hoop from south end, midheight of east vertical leg

2HB-E ε2HB-E on 2nd bottom hoop from south end,

midheight of east vertical leg

3HB-E ε3HB-E on 3rd bottom hoop from south end,


4HB-E ε4HB-E on 4th bottom hoop from south end,


1HB-W ε1HB-W on 1st bottom hoop from south end,


2HB-W ε2HB-W on 2nd bottom hoop from south end,


3HB-W ε3HB-W on 3rd bottom hoop from south end,


4HB-W ε4HB-W on 4th bottom hoop from south end,


152

TABLE 5.6

SUMMARY OF BEAM CONFINED CONCRETE STRAIN GAUGES

Transducer No.



3THT-(1) ε3THT-(1)

beam confined concrete strains

tension positive

on No. 3 support bar, top of top confining hoops, approximately 0.25”


3THT-(2) ε3THT-(2) on No. 3 support bar, top of top

confining hoops, approximately 3” (76mm) from south end of beam

3THB-(1) ε3THB-(1) on No. 3 support bar, bottom of top

confining hoops, approximately 0.25” (6mm) from south end of beam

3THB-(2) ε3THB-(2) on No. 3 support bar, bottom of top confining hoops, approximately 3”


3BHT-(1) ε3BHT-(1) on No. 3 support bar, top of bottom

confining hoops, approximately 0.25” (6mm) from south end of beam

3BHT-(2) ε3BHT-(2) on No. 3 support bar, top of bottom confining hoops, approximately 3”


3BHB-(1) ε3BHB-(1)

on No. 3 support bar, bottom of bottom confining hoops,

approximately 0.25” (6mm) from south end of beam

3BHB-(2) ε3BHB-(2)

on No. 3 support bar, bottom of bottom confining hoops,

approximately 3” (76mm) from south end of beam

153

TABLE 5.7

SUMMARY OF REACTION BLOCK STRAIN GAUGES

Transducer No.



1THM ε1THM

reaction block No. 3 confinement hoop

strains

tension positive

on 1st (from north face) top hoop below central PT duct, midlength of

bottom horizontal leg

1MHM ε1MHM on 1st (from north face) middle hoop below central PT duct, midlength of

bottom horizontal leg

1BHE ε1BHE on 1st (from north face) bottom hoop below central PT duct, midheight of

east vertical leg

CBM1E εCBM1E

reaction block confined concrete

strains

on No. 3 corner bar, middle hoops below central PT duct, east side, 1.5”

(38mm) from north face

CBM3E εCBM3E on No. 3 corner bar, middle hoops below central PT duct, east side, 6”


CBM1W εCBM1W on No. 3 corner bar, middle hoops

below central PT duct, west side, 1.5” (38mm) from north face

CBM3W εCBM3W on No. 3 corner bar, middle hoops

below central PT duct, west side, 6” (152mm) from north face

CBB1E εCBB1E on No. 3 corner bar, bottom hoops

below central PT duct, east side, 1.5” (38mm) from north face

CBB2E εCBB2E on No. 3 corner bar, bottom hoops

below central PT duct, east side, 3.75” (95mm) from north face

CBB3E εCBB3E on No. 3 corner bar, bottom hoops below central PT duct, east side, 6”


CBB1W εCBB1W on No. 3 corner bar, bottom hoops

below central PT duct, west side, 1.5” (38mm) from north face

CBB2W εCBB2W on No. 3 corner bar, bottom hoops below central PT duct, west side,

3.75” (95mm) from north face

CBB3W εCBB3W on No. 3 corner bar, bottom hoops

below central PT duct, west side, 6” (152mm) from north face

154

TABLE 5.8

TRANSDUCER DETAILS

Transducer Type

Transducer No.

Manufacturer Model No. Serial No. Capacity Sensitivity Nonlinearity

Load Cell

LC1

Interface 1240AF – 200K

107431

±200 kips (±979 kN)

4.1634 mV/V (tension)

-0.047%

-4.1679 mV/V (comp.)

-0.040%

LC2 107340

4.1379 mV/V (tension)

-0.018%

-4.1363 mV/V (comp.)

-0.037%

LC3 University of Notre Dame

---

- 50 kips (comp.)

see Table 5.9 --- LC4 - LC5 - LC6 - LC7

Micro-Measurements®

CEA-06-250UN-120

-

--- Gauge Factor =

2.085 ---

LC8 - LC9 - LC10 - LC11 - LC12 - LC13 - LC14 - LC15

University of Notre Dame

---

- 50 kips (comp.)

see Table 5.9 --- LC16 - LC17 - LC18 -

Displacement Transducer

DT1 Balluff BTL-5-B11-

M0508-K-S32 ±10 in.

DT2

Houston ScientificTM

1850 Series Position

Transducer

15090-001 +30 in. 32.15 mV/V/in. -0.031% DT3 613539 +10 in. 92.29 mV/V/in. 0.057% DT4 13601-008

+80 in.

12.13 mV/V/in. -0.054% DT5 13601-004 12.13 mV/V/in. -0.047% DT6 13601-006 12.16 mV/V/in. 0.034% DT7 13601-007 12.14 mV/V/in. -0.037% DT8 13601-001 12.05 mV/V/in. 0.031% DT9 613540 +10 in. 92.30 mV/V/in. 0.066% DT10 14103-001 +20 in. 48.90 mV/V/in. -0.030% DT11

Sensotec Model VL7A

LVDT

L3329300 ±2.00 in.

2.1204 VRMS/in. 0.110% DT12 L3112700 2.1384 VRMS/in. 0.120% DT13 L3112400 2.1324 VRMS/in. 0.080% DT14

Sensotec Model VL7A

LVDT L3740700

±1.00 in. 2.4528 VRMS/in. 0.040%

DT15 L3739700 2.4552 VRMS/in. 0.120%

Rotation Transducer

RT1 Schaevitz®

Accustar™ Electronic

Inclinometer ---

± π/3 radians (±60 degrees)

π/3 mV/radian (60 mV/degree)

± π/30 radian (±0.1

degree) RT2

Strain Gauge all strain gauges

Micro-Measurements®

CEA-06-250UN-120

--- --- Gauge Factor =

2.085 ---

155

LC1 LC2

actuators

reaction block

load block

beam PT strandsLC15-LC18

LC7-LC14

LC3-4

LC5-6

strong floor

N

wall test region

spreaderbeam

Figure 5.2: Load cell placement.

156

actuators

reaction block

load block

beam PT strands

DT1 DT2

DT5 DT4

DT3

DT7

DT6

DT8 DT9 DT10

65" (1651mm)

see detailbelow

DT3-5 placed in center plane of load block.

DT6-8 placed in center plane of reaction block.

DT9-10 placed 1.7" (43 mm) from beam ends at centerline of west side surface.

regionDT12

DT14

DT13DT15

5.0" (127mm)

DT11

beam

6.0" (152mm)

0.7

5"

(19m

m)

0.7

5"

(19m

m)

wall test

fiber-reinforced grout

CL

N

6.0" (152mm)

Figure 5.3: Displacement transducer placement.

157

actuators

reaction block

load block

beam PT strands

RT2RT1

N

beammidspan

Figure 5.4: Rotation transducer placement.

1MHM

1BHE

1THM

1MHM

1BHE

1THM

CBB1E, CBB1WCBB2E, CBB2WCBB3E, CBB3W

wall test region

#3 hoop

#3 bar

1.0" (25mm) nominalangle-to-wallconnection duct

NWE

beamcenterline

post-tensioningduct

CBM1ECBM3ECBM1WCBM3W

Figure 5.5: Strain gauge placement – reaction block.

158

MH-EMH-W

6MT-E6MT-W

6MB-E6MB-W

6(1)T-E6(1)T-W

6(2)T-E6(2)T-W

6(1)B-E6(1)B-W

6(2)B-E6(2)B-W

6(3)B-E6(3)B-W

6(3)T-E6(3)T-W

3BHT-(1)3BHT-(2)

3BHB-(1)3BHB-(2)

3THT-(1)3THT-(2)

3THB-(1)3THB-(2)

6SE(I)-E6SE(E)-E6SE(I)-W6SE(E)-W

1HB-W2HB-W3HB-W4HB-W

1HB-E2HB-E3HB-E4HB-E

CL

#6 bar

#3 bar

N#3 hoop

#6 loopingreinforcement

Figure 5.6: Strain gauge placement – coupling beam.

5.1.2 Post-Tensioning Strand Load Cells

As described in Chapter 3, the beam post-tensioning tendon in each test is

comprised of two, three, or four 7-wire 0.6 in. (15.2 mm) diameter strands. Up to four

load cells (LC15 – LC18, see Tables 5.1 and 5.8) are used to measure the forces in these

strands. A single-use Precision SURELOCK® steel barrel anchor with three-piece wedges

and ring is used at the dead (south) and live (north, jacking) end of each strand. As shown

in Figure 5.7, a 1.5 in. (38 mm) thick bearing plate is placed for the anchor barrels to

react against at both ends. The force in each post-tensioning strand is measured using a

load cell between the barrel anchor and the bearing plate at the dead (south) end.

Similarly, four load cells (LC3 – LC6, see Tables 5.1 and 5.8) are used to measure

the forces in the angle-to-reaction-block connection post-tensioning strands. On each

strand, a single-use Precision SURELOCK® steel barrel anchor with two-piece wedges

159

and ring is used at the dead end and the live end. At the live (south) end, a 1 in. (25 mm)

thick plate is placed for the anchor barrel to react against. At the dead end, the anchor

barrel bears directly on the vertical leg of the connection angle. Each load cell is placed at

the dead end of the strand between the anchor and the vertical angle leg as shown in

Figure 5.8.

Figure 5.7: Photograph of load cells on beam post-tensioning strands.

Figure 5.8: Photograph of load cells on angle-to-reaction-block connection post-tensioning strands.

160

These eight load cells were manufactured and calibrated at the University of

Notre Dame. Each load cell was manufactured by placing four Micro-Measurements®

(type CEA-06-250UN-120) strain gauges on a single-use Precision SURELOCK® post-

tensioning anchor barrel in a full bridge configuration (Figure 5.9). As shown in Figure

5.10, the load cell barrel was placed in the opposite orientation as the post-tensioning

anchor barrel to ensure better contact between the two barrels. Prior to the placement of

the strain gauges, each load cell barrel was first loaded in compression several times to a

force significantly larger than the expected force during coupling beam subassembly

testing to allow for any permanent deformations (nonlinear effects) that might occur in

the barrel. The strain gauges were then installed in a circular arrangement at the mid-

height of the barrel at a 90 degree spacing on the outside. After the load cells were wired

in a full bridge configuration, they were covered with a protective pad and sealed to help

prevent damage to the strain gauges or wiring.

Figure 5.9: Photograph of post-tensioning strand load cells.

161

Four strain gauges, 2 vertical and 2 horizontal, placed radially(90 degrees) around outside surfaceof barrel. Full bridge configurationwiring used.

load cellbarrel

PT strand

1.83"(46mm)

1.76" (45mm)

anchor bearing plate

1.83" (46mm)1.83" (46mm)

barrel/wedge anchor

load cellbarrel

top view

side view

configuration

Figure 5.10: Placement of post-tensioning strand load cells.

Calibration of the load cells was performed in pairs as shown in Figure 5.11 using

a 600 kip (2669 kN) SATEC® Model 600XWHVL hydraulic universal testing machine.

Each load cell was placed on a post-tensioning strand between a steel barrel/wedge

anchor and an anchor bearing plate. The load cell barrel was placed in the opposite

orientation as the anchor barrel as shown in Figure 5.10, thus, simulating the conditions

the load cell would experience during a coupling beam subassembly test. The post-

tensioning strand was then loaded in tension putting the load cells in compression.

Voltage measurements from the load cells were taken at various increments up to

approximately 45 kips (200 kN). The load cells were then unloaded, rotated 90 degrees,

and the test was repeated. This was repeated at least 4 times for each load cell and the

data was averaged to get the calibration equation for the load cell. Note that unlike the

162

subassembly experiments, the seating of the anchor wedges during the load cell

calibrations was done using the displacements of the universal testing machine heads and

not using a post-tensioning jack. Furthermore, each calibration test was conducted under

concentric axial loading, whereas in the subassembly tests, the ends of the tendon

displace in the transverse direction as well as axially due to the lateral displacements of

the structure.

Figure 5.12 shows the force versus voltage calibration data for the eight post-

tensioning strand load cells, with the regression calibration equations given in Table 5.9.

The calibration equations use the output voltage, Vout, from the data acquisition system to

give the load cell force in kips. The coefficient of determination, R2 indicates how closely

the regression line conforms to the calibration data, and ranges between 0 and 1, with 1

representing a perfect fit between the data and the regression line. The load cells with the

highest R2 value were used on the strands comprising the beam post-tensioning tendon

(i.e., LC15 – LC18). The other load cells were used on the strands that connect the angles

to the reaction block (i.e., LC3 – LC6).

Figure 5.13 shows the force versus voltage calibration data for Load Cells UND2

and UND3 during loading and unloading. The unloading voltage measurements were

taken to ensure that the calibration regression equations (which were determined from the

loading data) are valid upon unloading as well. It can be seen from Figure 5.13 that the

loading and unloading data points for each load cell are similar.

163

Figure 5.11: Post-tensioning strand load cell calibration setup.

164

forc

e [k

ips

(kN

)]

40 voltage (mV)

50(222)

Load Cell UND1

forc

e [k

ips

(kN

)]

30 voltage (mV)

50(222)

Load Cell UND2

forc

e [k

ips

(kN

)]

3.50 voltage (mV)

50(222)

Load Cell UND3

forc

e [k

ips

(kN

)]

50 voltage (mV)

50(222)

Load Cell UND4

forc

e [k

ips

(kN

)]

5.50 voltage (mV)

50(222)

Load Cell UND5

forc

e [k

ips

(kN

)]

30 voltage (mV)

50(222)

Load Cell UND6

forc

e [k

ips

(kN

)]

30 voltage (mV)

50(222)

Load Cell UND7

forc

e [k

ips

(kN

)]

30 voltage (mV)

50(222)

Load Cell UND8

Figure 5.12: Calibration data for the post-tensioning strand load cells.

165

TABLE 5.9

LOAD CELL CALIBRATIONS

Load Cell Calibration Regression Equation (kips) R2

UND1 13105 Vout 0.97 UND2 -2736905 Vout

2 + 24080 Vout 0.98 UND3 15669 Vout 0.97 UND4 172039Vout

2 + 10025 Vout 0.99 UND5 236090 Vout

2 + 8004 Vout 0.99 UND6 -3859378 Vout

2 + 27980 Vout 0.98 UND7 -2389914 Vout

2 + 24469 Vout 0.99 UND8 2579758171 Vout

3 – 1345851 Vout2 + 37304 Vout 0.98

voltage (mV)

forc

e [k

ips

(kN

)]

0 3

50(222)

UND2 loadingUND2 unloadingUND3 loadingUND3 unloading

Figure 5.13: Loading and unloading calibration data for Load Cells UND2 and UND3.

166

5.1.3 Wall Test Region Vertical Force Load Cells

Eight load cells (LC7 – LC14, see Tables 5.1 and 5.8) are used to measure the

vertical force on the wall test region of the reaction block. Each load cell consists of a

single electrical resistance strain gauge attached to one of the eight vertical bars used to

anchor the wall test region of the reaction block to the strong floor. The force in each bar

is determined from the corresponding strain measurement as:

barbarLCiLCi AEF ε (5.1)

where, εLCi = strain measurement in Bar i; Ebar = Young’s modulus for the bar steel [taken

as 29,000 ksi (200 GPa)]; and Abar = cross-sectional area of the bar [equal to 0.60 in.2

(388 mm2)].

5.1.4 Load Block Global Displacement Transducers

Three string pot linear displacement transducers (DT3 – DT5, see Tables 5.2 and

5.8) are used to measure the in-plane vertical and horizontal displacements of the load

block. Figure 5.3 shows the general placement of these displacement transducers.

Vertical displacements ∆DT4 and ∆DT5 (measured by DT4 and DT5) correspond to the

vertical displacements of the hydraulic actuators (i.e., displacements ∆DT1 and ∆DT2 as

measured by displacement transducers DT1 and DT2). The horizontal displacement ∆DT3

(measured using DT3) represents the movement of the load block in the north-south

direction.

The body of each string pot is attached to a fixed reference location and the string

end is attached to a Dayton-Superior® F-42 3/8”-16 loop ferrule insert embedded into the

load block as shown in Figure 5.14. Each ferrule insert is placed within the center plane

167

of the load block in the north-south direction. A lead wire is used with each transducer to

maximize the gain in the data acquisition system, and thus, minimize the measurement

noise. The use of a lead wire also allows the body of the string pot to be placed

significantly away from the corresponding ferrule insert, and thus, reduce the angular

movement of the string as the structure is displaced.

168

Dayton Superior F-42 loop

Ferrule Insert (3/8"-16)

WE

17.5" (445mm) 17.5" (445mm)

36"

(914mm)

35" (889mm)

CL

34"

(864mm)

1" (25mm)

1" (25mm)

North End

ΔDT4

17.5" (445mm) 17.5" (445mm)

36"

(914mm)

35" (889mm)

CL

35"

(889mm)

1" (25mm)

South End

ΔDT5

ΔDT3

(displacement in

N-S direction)

Figure 5.14: Load block ferrule insert locations.

169

5.1.5 Reaction Block Global Displacement Transducers

Three string pot linear displacement transducers (DT6 – DT8, see Tables 5.2 and

5.8) are used to measure the in-plane vertical and horizontal displacements of the reaction

block. Figure 5.3 shows the general placement of the displacement transducers. The

objective of these measurements is to ensure that the displacements of the reaction block

remain small throughout the duration of each test.

Similar to the load block string pots, the body of each reaction block string pot is

attached to a fixed reference location, and the string end is attached to a Dayton-

Superior® F-42 3/8”-16 loop ferrule insert embedded into the reaction block as shown in

Figure 5.15. Each ferrule insert is placed within the center plane of the reaction block in

the north-south direction. A lead wire is used with each transducer to maximize the gain

in the data acquisition system, and thus, minimize the measurement noise.

170

66"

(1676mm)

58" (1473mm)

CL

17"

(432mm)

29"

(737mm)

1" (25mm)

CL

66"

(1676mm)

58" (1473mm)

CL29"

(737mm)

19"

(483mm)

ΔDT7

ΔDT8

South End

North End

ΔDT6

Dayton Superior F-42 loop


(displacement in

N-S direction)

WE

Figure 5.15: Reaction block ferrule insert locations.

171

5.1.6 Beam Global Displacement Transducers

Two string pot linear displacement transducers (DT9 and DT10, see Tables 5.2

and 5.8) are used to measure the vertical displacements of the beam specimens. Figure

5.3 shows the general placement of these string pots. The displacements ∆DT9 and ∆DT10

are used to determine the beam chord rotation during each subassembly test.

Similar to the reaction block and load block string pots, the body of each beam

string pot is attached to a fixed reference location, and the string end is attached to a

Dayton-Superior® F-43 3/8”-16 plain ferrule insert embedded into the beam as shown in

Figure 5.16. Each ferrule insert is placed at the midheight of the beam on the west face. A

lead wire is used with each transducer to maximize the gain in the data acquisition

system, and thus, minimize the measurement noise. The use of a lead wire also allows for

the body of the string pot to be placed significantly away from the corresponding ferrule

insert, and thus, reduce the angular movement of the string as the structure is displaced.

172

Dayton Superior F-43 plain Ferrule Insert (3/8"-16)

CL

45"

14"

7"

7"

1.69"1.69"

ΔDT9 ΔDT10

CL

45"

18"

9"

9"

1.69"1.69"

ΔDT9 ΔDT10

NTest Beams 1-3

Test Beam 4

Figure 5.16: Beam vertical displacement ferrule insert locations.

5.1.7 Gap Opening Displacement Transducers

Three Linear Variable Displacement Transducers [LVDTs] (DT11 - DT13, see

Tables 5.2 and 5.8) are used to measure the gap opening displacements at the beam-to-

reaction-block interface. Figures 5.3 and 5.17 show the placement of these LVDTs. The

bodies of the LVDTs are attached to Dayton-Superior® F-43 3/8”-16 plain ferrule inserts

embedded into the beam specimen on the west face and the rod ends react against plates

173

mounted to Dayton-Superior® F-43 3/8”-16 plain ferrule inserts embedded into the wall

test region of the reaction block on the west face (see Figure 5.18).

CL

45" (1143mm)

14"(356mm)

7"(178mm)

6.25"(159mm)

5" (127mm)

Dayton Superior F-43 plain Ferrule Insert (3/8"-16)

CL

45" (1143mm)

18"(457mm)

9"(229mm)

9"(229mm)

8.25"(210mm)

8.25"(210mm)

5" (127mm)

ΔDT11

ΔDT12

ΔDT13

ΔDT11

ΔDT12

ΔDT13

N

Test Beams 1-3

Test Beam 4

6.25"(159mm)

7"(178mm)

Figure 5.17: Beam gap opening ferrule insert locations.

174

5.1.8 Wall Test Region Local Displacement Transducers

Two LVDTs (DT14 and DT15, see Tables 5.2 and 5.8) are used in the wall test

region to measure the local axial compression deformations in the contact regions of the

reaction block. Figures 5.3 and 5.18 show the placement of these transducers, the bodies

of which are attached to Dayton-Superior® F-43 3/8”-16 plain ferrule inserts placed into

the wall test region on the west face. The rod ends of the LVDTs react against plates (the

same plates used for transducers DT11 – DT13 measuring the gap opening displacements

at the beam-to-reaction-block interface) mounted to another set of Dayton-Superior® F-43

3/8”-16 plain ferrule inserts embedded into the reaction block as shown in Figure 5.18.

The placement of DT14 and DT15 on the reaction block lines up with the placement of

DT11 and DT13 on the beam specimen, respectively.

175

66"

(1676mm)

1" (25mm)

N

ΔDT14

60" (1524mm)

CLbeam

6.25"

(159mm)

6.25"

(159mm)

6.3125"

(160mm)

17.75"

(451mm)

17.75"

(451mm)

18"

(457mm)

ΔDT15

(a)

66"

(1676mm)

60" (1524mm)

CLbeam

18"

(457mm)

1" (25mm)

8.25"

(210mm)

8.25"

(210mm)

6.3125"

(160mm)

15.75"

(400mm)

15.75"

(400mm)

18"

(457mm)

ΔDT15

ΔDT14

Dayton Superior F-43 plain


(b)

Figure 5.18: Reaction block wall test region ferrule insert locations – (a) inserts for Beams 1-3; (b) inserts for Beam 4.

176

5.1.9 Beam Rotation Transducers

Two rotation transducers (RT1 and RT2, see Tables 5.2 and 5.8) are used to

measure the rotations of the beam specimens. Figures 5.4 and 5.19 show the placement of

these transducers. The bodies of the transducers are attached to acrylic (plexi-glass)

plates, which are then attached to the west side of the beam using Dayton-Superior® F-43

3/8”-16 plain ferrule inserts or LOCTITE® Power Grab epoxy. Note that the rotation

transducer at the beam midspan is placed 0.25 in. (6 mm) off the midspan location to

accommodate the lateral brace plates on the beam.

CL

45" (1143mm)

14"(356mm)

7"

(178mm)

7"

(178mm)

1.69"(43mm)

CL

45" (1143mm)

18"(457mm)

9"

(229mm)

9"

(229mm)

N

CL

CL0.25"

(6mm)

θRT1 θRT2

0.25"(6mm)

θRT1 θRT2

1.69"(43mm)

Test Beams 1-3

Test Beam 4

Dayton Superior F-43 plain


Figure 5.19: Beam rotation ferrule insert locations.

177

5.1.10 Beam Looping Reinforcement Longitudinal Leg Strain Gauges

Up to sixteen strain gauges (see Tables 5.3 and 5.8) are used to measure the

strains in the longitudinal (i.e., horizontal) legs of the two No. 6 looping mild steel

reinforcing bars in each beam specimen as shown in Figure 5.20. Figure 5.21 shows the

design placement of these strain gauges (note that the actual gauge locations may have

shifted during construction and/or casting) and Figure 5.22 gives the gauge designation

system. The strain gauges are concentrated near the angle-to-beam connection at the

reaction block (i.e., south) end of the beam, which is a critical design location as

discussed in Chapter 3. The strain measurements are used to determine if the design of

the longitudinal mild steel reinforcement is adequate to transfer the tension angle forces

into the beam.

Figure 5.20: Photograph of beam strain gauges.

178

6MT-E6MT-W

6MB-E6MB-W

6(1)T-E6(1)T-W

6(2)T-E6(2)T-W

6(1)B-E6(1)B-W

6(2)B-E6(2)B-W

6(3)B-E6(3)B-W

6(3)T-E6(3)T-W

CL5.5"

(140mm)5.75"

(146mm)5.5"

(140mm)5.75"

(146mm)

CL

6MT-E6MT-W

6(2)T-E 6(3)T-E6(3)T-W

6MB-E6MB-W

6(1)B-E6(1)B-W

6(2)B-E6(2)B-W

6(3)B-E6(3)B-W

6(1)T-E6(1)T-W

5.5"(140mm)

5.75"(146mm)

5.5"(140mm)

5.75"(146mm)

Test Beam 4

Test Beams 1 - 3 N



Note: Strain gauge locations shown

are design locations. Materials may

have shifted during construction

and/or casting.

1.22"(31mm)

1.22"(31mm)

1.22"(31mm)

1.22"(31mm)

Figure 5.21: Beam looping reinforcement longitudinal leg strain gauge locations.

179

Strain Gauge Designation System:

Longitudinal Reinforcement

6 (1) T - E

No. 6 bar

5.75" (146 mm) from south end of beam

top leg

east reinforcement

1: 5.75" (146 mm) from south end of beam


3: 17" (432 mm) from south end of beam

M: midspan of beam

T: top leg

B: bottom leg

E: east reinforcement

W: west reinforcement

Figure 5.22: Strain gauge designation system – longitudinal reinforcement.

5.1.11 Beam Transverse Reinforcement Strain Gauges

Up to six strain gauges (see Tables 5.4 and 5.8) are placed on the transverse mild

steel bars to verify the design of the transverse reinforcement in each beam. Figure 5.23

shows the design placement of these strain gauges (note that the actual gauge locations

may have shifted during construction and/or casting) and Figure 5.24 gives the gauge

designation system. Strain gauges are placed on the vertical legs of the No. 6 looping bars

at the south end, where finite element analysis results indicate high transverse stresses

will develop. Additional strain gauges are placed on the vertical legs of the No. 3 hoops

at the midspan of the beam. As discussed in Chapter 3, only a nominal amount of

transverse reinforcement is used away from the beam ends, and the strain measurements

taken at the midspan are used to verify the analytical models as well as the amount of this

transverse reinforcement.

180

CL


CLTest Beam 4

Test Beams 1 - 2

N

MH-EMH-W

6SE(I)-E6SE(E)-E6SE(I)-W6SE(E)-W

MH-W6SE(I)-E6SE(I)-W

CLTest Beam 3

MH-EMH-W6SE(I)-E

6SE(I)-W

9.0"(229mm)

9.0"(229mm)

CL

7.0"(178mm)

7.0"(178mm)

CL

7.0"(178mm)

7.0"(178mm)

CL



#3 hoop

#3 hoop

#3 hoop




and/or casting.

1.125"(29mm)

1.125"(29mm)

1.125"(29mm)

Figure 5.23: Beam transverse reinforcement strain gauge locations.

181


Transverse Reinforcement

6 SE (I) - E

No. 6 bar

south endinternal

east reinforcement

I: internal

E: external

E: east reinforcement

W: west reinforcement

MH - E

midspan hoop

east vertical leg

E: east vertical leg

W: west vertical leg

Figure 5.24: Strain gauge designation system – transverse reinforcement.

5.1.12 Beam End Confinement Hoop Strain Gauges

Up to eight strain gauges (see Tables 5.5 and 5.8) are used to measure the strains

in the No. 3 confinement hoops at the reaction block (i.e., south) end of each beam

specimen. The strain gauges are attached to the east and west legs of the bottom hoops as

shown in Figures 5.20 and 5.25. Figure 5.26 shows the design placement of these strain

182

gauges (note that the actual gauge locations may have shifted during construction and/or

casting) and Figure 5.27 gives the gauge designation system.

Figure 5.25: Photograph of strain gauged confinement hoop.

183


1HB-E2HB-E3HB-E4HB-E

#3 hoop

#6 bar

#3 bar

N

2.85"(72mm)

CL

4.15"(105mm)

7.0"(178mm)

Test Beams 1 - 2


1HB-E3HB-E

#3 hoop

#6 bar

#3 bar

2.85"(72mm)

CL

4.15"(105mm)

7.0"(178mm)

Test Beam 3

2.85"(72mm)

CL

6.15"(156mm)

9.0"(229mm)


1HB-E3HB-E

Test Beam 4

#3 hoop

12 3 4

12 3 4

12 3 4

0.19" (5mm

)

2.50" (64mm

)

1.5" (38mm

)

2.25" (57mm

)

0.19" (5mm

)

2.50" (64mm

)

1.5" (38mm

)

2.25" (57mm

)

0.19" (5mm

)

2.50" (64mm

)

1.5" (38mm

)

2.25" (57mm

)




and/or casting.

Figure 5.26: Beam end confinement hoop strain gauge locations.

184


Beam End Confinement Hoops

1 HB - E

1st bottom hoop fromsouth end of beam

bottom hoop

east vertical leg

E: east vertical leg

W: west vertical leg

1: 1st bottom hoop from south end of beam

2: 2nd bottom hoop from south end of beam

3: 3rd bottom hoop from south end of beam

4: 4th bottom hoop from south end of beam

Figure 5.27: Strain gauge designation system – beam end confinement hoops.

5.1.13 Beam Confined Concrete Strain Gauges

Up to eight strain gauges (see Tables 5.6 and 5.8) are used to measure the axial

strains inside the confined concrete at the reaction block (i.e., south) end of each beam

specimen. As shown in Figures 5.20 and 5.28, these strain gauges are attached to 8.0 in.

(203 mm) long deformed No. 3 mild steel support bars tied to the No. 3 confinement

hoops in the beam. Figure 5.29 gives the designation system for the beam confined

concrete strain gauges.

185

3BHT-(1)3BHT-(2)

3BHB-(1)3BHB-(2)

3THT-(1)3THT-(2)

3THB-(1)3THB-(2)

#3 support bar


2.75"(70mm)

0.25"(6mm)




and/or casting.

3BHB-(1)3BHB-(2)

2.75"(70mm)

0.25"(6mm)

3BHB-(1)3BHB-(2)

#3 support bar


Test Beam 3

Test Beam 1

3BHB-(1)3BHB-(2)

3THT-(1)3THT-(2)

#3 support bar

2.75"(70mm)

0.25"(6mm)


Test Beam 2

Test Beam 4

#3 support bar


N

2.75"(70mm)

0.25"(6mm)

1 2 1 2

1 2

1 2

1.0"(25mm)

4.0" (102mm)

1.0"(25mm)

1.0"(25mm)

1.0"(25mm)

Figure 5.28: Beam confined concrete strain gauge locations.

186


Beam Confined Concrete

3 T HT - (1)

No. 3 bar

top of confining hoop top hoop

HT: top hoop

HB: bottom hoop



0.25" (6 mm) from south end of beam

T: top of confining hoop

B: bottom of confining hoop

Figure 5.29: Strain gauge designation system – beam confined concrete.

5.1.14 Reaction Block Confinement Hoop Strain Gauges

Three strain gauges (see Tables 5.7 and 5.8) are attached to the No. 3 confinement

hoops in the wall test region of the reaction block specimens. The strain gauges are

attached to the first No. 3 hoop (closest to the beam end surface of the reaction block) for

each row of hoops in the bottom reinforcing cage below the main post-tensioning duct.

Figure 5.30 shows the design placement of these strain gauges (note that the actual gauge

locations may have shifted during construction and/or casting) and Figure 5.31 gives the

gauge designation system. Due to the small size of the two top hoops of the bottom cage,

the strain gauges had to be placed on the horizontal legs of the hoops. The slightly larger

size of the bottom hoop allowed for the strain gauge to be placed on the west vertical leg.

187

2.81"(71mm) 1MHM

wall test region

1BHE

1THM

#3 hoop

#3 bar


1MHM

1BHE

1THM

NWE

Note: Strain gauge locations shown are design locations. Materials mayhave shifted during construction and/or casting.

4.56"(116mm)

beamcenterline

2.03"(52mm)

post-tensioningduct

Figure 5.30: Reaction block confinement hoop strain gauge locations.

188


Reaction Block

CB M 1 E

corner bar

middle hoops below central PT duct

1.5" (38 mm) from north face

1: 1.5" (38 mm) from north face



E: east side

W: west side

east side

M: middle hoops below central PT duct

B: bottom hoops below central PT duct

1 TH M

1st hoop from north face

top hoopmidlength ofhorizontal leg

M: midlength of horizontal leg

E: midheight of east vertical leg

T: top hoop below central PT duct

M: middle hoop below central PT duct

B: bottom hoop below central PT duct

Figure 5.31: Strain gauge designation system – reaction block.

189

5.1.15 Reaction Block Confined Concrete Strain Gauges

Ten strain gauges (see Tables 5.7 and 5.8) are embedded into the wall test region

of the reaction block specimens inside the middle and bottom confinement hoops of the

bottom reinforcing cage below the main post-tensioning duct. These strain gauges are

used to measure the axial strains in the wall test region confined concrete. As shown in

Figure 5.32, the strain gauges are attached to 15 in. (381 mm) long deformed No. 3 mild

steel corner bars tied to the No. 3 confinement hoops. Figure 5.31 gives the designation

system for the reaction block confined concrete strain gauges.

CBB1E, CBB1WCBB2E, CBB2WCBB3E, CBB3W

2.25"(57mm)

2.25"(57mm)

1.5"(38mm)

wall test region

#3 hoop

#3 bar


NWE

Note: Strain gauge locations shown are design locations. Materials mayhave shifted during construction and/or casting.

beamcenterline

post-tensioningduct

123

13

CBM1ECBM3ECBM1WCBM3W

3.25"(83mm)

5.34"(136mm)

Figure 5.32: Reaction block confined concrete strain gauge locations.

190

5.2 Subassembly Response Parameters

This section describes the determination of the test subassembly response

parameters from the data measurements described above. Figures 5.33 and 5.34 show the

test subassembly displaced in the positive (i.e., load block moved downward) and

negative (i.e., load block moved upward) directions. The following parameters shown in

Figures 5.28 and 5.29 are defined as: θb = beam chord rotation; ∆gn = gap opening at the

north end of the beam; ∆gs = gap opening at the south end of the beam; Faxis1 = force in

actuator axis 1; Faxis2 = force in actuator axis 2; ∆axis1 = displacement of actuator axis 1;

and ∆axis2 = displacement of actuator axis 2.

The subassembly response parameters described below are: (1) coupling beam

shear force; (2) coupling beam end moment; (3) coupling beam post-tensioning force; (4)

vertical force on wall test region; (5) angle-to-wall connection post-tensioning force; (6)

reaction block displacements; (7) load block displacements; (8) beam vertical

displacements; (9) beam chord rotation; and (10) gap opening and contact depth at beam-

to-wall interface. Note that in data manipulations, rotations (e.g., θb, θb,lb, θRT1, etc.) are in

radians.

191

lRB = 60" (1.52m) lb,tg ~ 46" (1.17m)

COUPLING BEAM

strong floor

anchor plate

axis 1 axis 2

steel loading frame

40 " (1.0m)

steel connection beam

wall testregion

spreader beam

REACTION BLOCK

N

LOAD BLOCK

lLB = 60" (1.52m)


actuators

+Faxis1

+Δaxis1

+ θb

Δgn

Δgs

X

Y-Faxis2

−Δaxis2

grout

angle

Figure 5.33: Subassembly displaced in positive direction.

192

lRB = 60" (1.52m) lb,tg ~ 46" (1.17m)

COUPLING BEAM

strong floor

anchor plate

axis 1 axis 2

steel loading frame

40 " (1.0m)

steel connection beamwall testregion

spreader beam

REACTION BLOCK

N

LOAD BLOCK

lLB = 60" (1.52m)


actuators

-Faxis1

−Δaxis1

- θb

Δgn

Δgs

X

Y

+Faxis2

+Δaxis2

grout

angle

Figure 5.34: Subassembly displaced in negative direction.

5.2.1 Coupling Beam Shear Force

The coupling beam shear force, Vb is equal to the sum of the vertical components

of the forces in the two hydraulic actuators, Faxis1 and Faxis2, where Faxis1 = FLC1 and Faxis2

= FLC2 as depicted Figures 5.33 and 5.34. Thus,

193

2211,2,1 θcosθcos axisLCaxisLCyaxisyaxisb FFFFV (5.2)

where,

yaxisaxis

xaxisaxis l ,11

,111 tanθ (5.3)

yaxisaxis

xaxisaxis l ,22

,212 tanθ (5.4)

where, laxis1 = laxis2 = length of the actuators between the top pin and the bottom pin at the

beginning of each test. It is assumed that cos(θaxis1) = cos(θaxis2) ≈ 1.0 for the small

horizontal displacements of the load block during testing. Thus, the beam shear force can

be determined directly from the measured actuator forces as:

21 LCLCb FFV (5.5)

Note that as discussed in Chapter 3, prior to each test, the forces in the actuators

due to the self-weight of the subassembly (i.e., the load block, steel connection beam and

bolts, coupling beam specimen, strands, angles, etc.) are measured. Before the application

of the lateral displacement history, these forces are applied to the subassembly (by

operating the actuators in load control) in the opposite direction to counteract the effect of

the structure self-weight on the coupling beam. These initial forces applied to the

structure are subtracted from the coupling beam shear force (since the initial actuator

forces are equal and opposite to the forces due to the structure self-weight) to initialize

the shear force measurement to zero.

194

5.2.2 Coupling Beam End Moment

The coupling beam end moment, Mb is calculated from the beam shear force, Vb

and the length of the beam including the thickness of the grout, lb,tg as:

22

,21, tgbLCLCtgbbb

lFFlVM

(5.6)

where, lb,tg = lb + 2tg; and tg = thickness of the grout at each end.

5.2.3 Coupling Beam Post-Tensioning Force

The total coupling beam post-tensioning force, Pb, is calculated by summing the

measured forces in the individual post-tensioning strands. Thus, for a specimen with four

beam post-tensioning strands,

18171615 LCLCLCLCb FFFFP (5.7)

5.2.4 Vertical Force on Wall Test Region

The total vertical force, Fwt (representing the wall pier axial forces) on the wall

test region of the reaction block is determined by summing the forces in the eight tie-

down bars as:

1413121110987 LCLCLCLCLCLCLCLCwt FFFFFFFFF (5.8)

195

5.2.5 Angle Post-Tensioning Forces

The post-tensioning forces Pap,top and Pap,seat used to connect the top angles and

seat angles, respectively, to the reaction block, are determined from load cells LC3 – LC6

as:

43, LCLCtopap FFP (5.9)

and

65, LCLCseatap FFP (5.10)

5.2.6 Reaction Block Displacements

Assuming that the reaction block behaves as a rigid body, the measurements from

displacement transducers DT6 – DT8 can be used to calculate the horizontal and vertical

displacements and the rotation at the centroid of the block (see Figure 5.35). Note that the

non-uniform shape of the reaction block needs to be considered in the calculation of the

block centroid.

196

N

lRB = 60" (1524mm)

xRB

yRB

ΔRB,y

ΔRB,xθRB

66"(1676mm)

hRB =

ΔDT8 ΔDT7

ΔDT6

reaction blockcentroid

1" (25mm)

yDT6

Figure 5.35: Reaction block displacements.

Using the measurements from displacement transducers DT7 and DT8, the

rotation, θRB at the centroid of the reaction block can be calculated as:

RB

DTDTRB l

87θ

(5.11)

The horizontal displacement at the centroid of the reaction block, ∆RB,x can be

calculated as:

RBDTRB

DTDTDTRBDTRBDTxRB yy

lyy

6

87666, θ (5.12)

197

Finally, the vertical displacement at the centroid of the reaction block, ∆RB,y can

be determined as:

RBRB

DTDTDTRBRBDTyRB x

lx

87

88, θ (5.13)

or

RBRBRB

DTDTDTRBRBRBDTyRB xl

lxl

87

77, θ (5.14)

As will be shown later in Chapter 6, the displacements of the reaction block were

negligible during the experiments.

5.2.7 Load Block Displacements

Assuming that the load block behaves as a rigid body, the displacement

measurements from DT3 – DT5 can be used to determine the horizontal and vertical

displacements and the rotation of the block centroid. Figure 5.37 shows an exaggerated

displaced shape of the load block. As the test subassembly is displaced and gaps open at

the beam ends, the load block is pushed in the horizontal (north) direction. Furthermore,

even though the two actuators are displaced vertically by the same amount, the load block

may undergo a small amount of rotation. The adjustments that need to be made on the

displacement measurements from DT3, DT4, and DT5 (due to the angular movement of

the string pot strings as the structure is displaced) and the resulting displacements at the

centroid of the load block are described below.

198

ΔLB,y

ΔLB,xθLB

lLB

hLB

N

ΔDT4ΔDT5

ΔDT3

1.0" (25mm)

load blockcentroid

yDT3

hLB /2

lLB /2

Figure 5.36: Load block displacements.

DT3

DT5

DT4

i,DT3

f,DT3

i,DT4

f,DT4

i,DT5

f,DT5

LB,y

LB,xLB

lLB

hLB

N

DT3,y

DT4,x

DT5,x

Figure 5.37: Idealized exaggerated displaced shape of load block.

199

The following parameters, some of which are shown in Figures 5.36 and 5.37, are

used in the formulation: lLB = length of the load block; hLB = height of the load block; yDT3

= vertical location of the ferrule insert to which displacement transducer DT3 is attached;

∆DT3, ∆DT4, and ∆DT5 = original, unadjusted measurements from displacement transducers

DT3, DT4, and DT5, respectively; δi,DT3, δi,DT4, and δi,DT5 = initial extended lengths of

DT3, DT4, and DT5, respectively, from the string pot body to the ferrule insert location

(i.e., including the lead wires); δf,DT3, δf,DT4, and δf,DT5 = final extended lengths of DT3,

DT4, and DT5, respectively (including the initial extended lengths so that δf,DT3 = δi,DT3 -

∆DT3, δf,DT4 = δi,DT4 - ∆DT4, and δf,DT5 = δi,DT5 + ∆DT5); and αDT3, αDT4, and αDT5 = angles that

the strings of DT3, DT4 and DT5, respectively, undergo during the displacement of the

block. The procedure to determine the horizontal displacement, vertical displacement,

and rotation (∆LB,x, ∆LB,y, and θLB, respectively) at the centroid of the load block is as

follows.

1. Use the measurements from DT4 and DT5 to calculate the rotation, θLB at the

centroid of the load block as:

LB

DTDTLB l

54θ

(5.15)

2. Determine the horizontal displacement, ∆LB,x at the centroid of the load block

as:

22θ 3

54333,

LBDT

LB

DTDTDT

LBDTLBDTxLB

hy

l

hy

(5.16)

3. Determine the vertical displacement, ∆LB,y at the centroid of the load block as:

200

22

2θ 5455, LB

DTDTDTLBLBDTyLB ll

(5.17)

or

22

2θ 5444, LB

DTDTDTLBLBDTyLB ll

(5.18)

4. Use the displacements at the load block centroid to determine the horizontal

measurements of DT4 and DT5 as:

2/θ,,4 LBLBxLBxDT h (5.19)

2/θ,,5 LBLBxLBxDT h (5.20)

5. Determine the angular movement that the strings of DT4 and DT5 undergo as:

4,

,414 δ

sinαDTf

xDTDT (5.21)

5,

,515 δ

sinαDTf

xDTDT (5.22)

6. Determine the adjusted vertical measurements for DT4 and DT5 as:

4,4,4,4 δ-δαcos DTiDTfDTyDT (5.23)

5,5,5,5 δ-δαcos DTiDTfDTyDT (5.24)

7. Use the displacements of the load block centroid to determine the vertical

displacement of DT3 as:

(5.25)

8. Determine the angular movement that the string of DT3 undergoes as:

3,

,313 sinα

DTf

yDTDT

(5.26)

2θ,,3 LBLByLByDT l

201

9. Determine the adjusted horizontal measurement for DT3 as:

3,3,3,3 δ-δαcos DTiDTfDTxDT (5.27)

10. Use the adjusted measurements for DT3, DT4, and DT5 in Steps 1 – 3 and

iterate the entire procedure until the additional adjustments needed are

sufficiently small (i.e., until the displacements converge).

5.2.8 Beam Vertical Displacements

The vertical displacements of the beam can be calculated using the displacement

measurements from DT9 and DT10. Figure 5.38 shows an idealized exaggerated

displaced configuration of the beam. Similar to the load block displacements, adjustments

may be needed on the measurements from DT9 and DT10 due to the angular movement

of the string pot strings as the structure is displaced.

202

θb

αDT9

CL

hb/2

undisplaced position of ferrule insert

displaced position of ferrule insert

αDT10

δi,DT10

δf,DT10

hb/2

δi,DT9

δf,DT9

A

C

B

A

C

B

lA-DT10 dDT10

D

FE

G

FE

θb

dDT9

lA-DT9

lDT10-DT9

N

Figure 5.38: Idealized exaggerated displaced shape of test beam.

The following parameters, some of which are shown in Figure 5.38, are defined

as: hb = height of the beam; θb = chord rotation of the beam; ∆DT9 and ∆DT10 = original,

unadjusted measurements from displacement transducers DT9 and DT10, respectively; lA-

DT9 and lA-DT10 = distances between point A and the ferrule insert to which DT9 and

DT10, respectively, are attached; lDT10-DT9 = horizontal distance between the ferrule

203

inserts for DT9 and DT10 in the undisplaced configuration; δi,DT9 and δi,DT10 = initial

extended lengths of DT9 and DT10, respectively, from the string pot body to the ferrule

insert location (i.e., including the lead wires); δf,DT9 and δf,DT10 = final extended lengths of

DT9 and DT10, respectively (including the initial extended lengths so that δf,DT9 = δi,DT9 +

∆DT9 and δf,DT10 = δi,DT10 + ∆DT10); and αDT9 and αDT10 = angles that the strings of DT9 and

DT10, respectively, undergo during the displacement of the beam. It is assumed that any

shifting in the positions of the ferrule inserts due to the nonlinear deformations of the

beam concrete are negligible in the formulations below.

The procedure to determine the vertical displacements at the south and north ends

of the beam, ∆bs,y and ∆bn,y, respectively, is as follows.

1. Use the measurements from DT9 and DT10 to determine the rotation, θb, of

the beam as:

910

109θDTDT

DTDTb l

(5.28)

Note that θb is positive in the clockwise direction (opposite the direction

shown in Figure 5.38).

2. Use triangles AEF and ABC to determine dDT9 and dDT10, respectively, as:

99 θ DTAbDT ld (5.29)

1010 θ DTAbDT ld (5.30)

3. Use triangles EFG and BCD and the law of cosines to determine αDT9 and

αDT10, respectively, as:

9,9,

29

29,

29,1

9 δδ2

δδcosα

DTiDTf

DTDTiDTfDT

d (5.31)

204

10,10,

210

210,

210,1

10 δδ2

δδcosα

DTiDTf

DTDTiDTfDT

d (5.32)

4. Determine the adjusted vertical measurements for DT9 and DT10 as:

9,9,9,9 δδαcos DTiDTfDTyDT (5.33)

10,10,10,10 δδαcos DTiDTfDTyDT (5.34)

5. Use the adjusted measurements for DT9 and DT10 in Step 1 and iterate the

entire procedure until the additional adjustments needed are sufficiently small

(i.e., until the displacements converge).

Note that in Figure 5.38, the beam is assumed to rotate as a rigid body about its

corner at point A, ignoring the deformations in the beam and/or reaction block concrete.

This results in a larger estimation of the adjustments needed in the measurements from

DT9 and DT10. In Chapter 6, it is shown that the angles αDT9 and αDT10 (based on the

above procedure) remain very small during testing. As a result, the vertical (i.e., y-

direction) displacements of the test beam are taken as the original (i.e., unadjusted)

measurements ΔDT9 and ΔDT10 from displacement transducers DT9 and DT10,

respectively.

5.2.9 Beam Chord Rotation

The beam chord rotation, θb, is defined as the relative vertical displacement

between the beam ends divided by the beam length. As demonstrated in Chapter 6 and

described in the previous section, the vertical displacements of the beam are taken as the

original (i.e., unadjusted) measurements from displacement transducers DT9 and DT10.

Thus,

205

910

109θDTDT

DTDTb l

(5.35)

Note that in some of the tests, measurements from DT9 and/or DT10 could not be

obtained (e.g., due to the spalling of the ferrule inserts). Under these conditions, the beam

chord rotation is approximated using the vertical displacement at the centroid of the load

block as (see Chapters 6 and 7):

b

yLBb,lbb l

,θθ

(5.36)

In Equation 5.36, it is assumed that the displacements of the reaction block are negligible.

5.2.10 Gap Opening and Contact Depth at Beam-to-Wall Interface

Three LVDTs (DT11 – DT13) are used to measure the gap opening displacements

at the beam-to-reaction-block interface at the south end of the beam. In addition, rotation

transducer RT1 is used to measure the rotation at the beam centerline approximately 1 in.

(25 mm) away from the beam south end. As depicted in Figures 5.34 and 5.39, as the test

beam is displaced in the negative direction (i.e., counterclockwise), a gap opens at the

bottom of the beam at the south end and at the top of the beam at the north end. The gap

opening and contact corners of the beam are reversed as the beam displacements are

reversed.

206

CL

xDT11

CL

yDT11

αg

ct' yDT12

yDT13yDT12-ct

ct

yDT13

yDT12

yDT11

DT11

DT13

DT12

N

xDT12

xDT13

grout

Δgb

Figure 5.39: Gap opening and contact depth.

The following parameters are defined in Figure 5.39 as: xDT11, xDT12, and xDT13 =

horizontal locations of the ferrule inserts to which displacement transducers DT11, DT12,

and DT13, respectively, are attached; yDT11, yDT12, and yDT13 = vertical locations of the

ferrule inserts to which DT11, DT12, and DT13 are attached (measured from the

compression fiber of the beam); c = neutral axis depth in the vertical direction; and c’ =

neutral axis depth perpendicular to the beam axis. It is assumed that any shifting in the

position of the ferrule inserts due to the nonlinear deformations of the beam concrete are

negligible in the formulations below.

As shown in Figure 5.39, the LVDTs rotate with the beam as a gap opens. The

rotation of the LVDTs is assumed to be equal to the gap opening rotation at the beam

end, which can be calculated as:

1213

1213αDTDT

DTDTg yy

(5.37)

207

Then, the adjusted horizontal measurements for DT11, DT12, and DT13 can be

calculated as:

11,11 αcos DTgxDT (5.38)



It will be shown in Chapter 6 that the angular adjustments for DT11, DT12, and

DT13 are small; and thus, the LVDT measurements in the x-direction are taken as the

original measurements from these transducers. Referring to Figure 5.39, there are several

different methods that can be implemented to determine the gap opening displacements

of the beam as follows: (1) linear interpolation from the centerline and outer LVDT data;

(2) from RT1 and outer LVDT data; (3) from RT1 and centerline LVDT data; (4) from θb

and centerline LVDT data; and (5) from θb and outer LVDT data. The corresponding

equations to determine the gap opening displacements Δgb and Δgt at the bottom and top,

respectively, of the beam are listed below.

Method (1):

121213

121312 DTb

DTDT

DTDTDTgb yh

yy

(5.41)

121211

121112 DTb

DTDT

DTDTDTgt yh

yy

(5.42)

Method (2):

13113 θ DTbRTDTgb yh (5.43)

11111 θ DTbRTDTgt yh (5.44)

208

Method (3):

12112 θ DTbRTDTgb yh (5.45)

12112 θ DTbRTDTgt yh (5.46)

Method (4):

1212 θ DTbbDTgb yh (5.47)

1212 θ DTbbDTgt yh (5.48)

Method (5):

1313 θ DTbbDTgb yh (5.49)

1111 θ DTbbDTgt yh (5.50)

Note that Equations 5.41, 5.42, 5.45, 5.46, 5.47, and 5.48 are valid only when

ΔDT12 is positive (i.e., gap extends beyond the level of DT12).

Similarly one of the following four methods can be used to calculate the contact

depth, c at the beam end. The small differences between c and c’ (see Figure 5.39) are

ignored in this formulation.

Method (1):

1213

12131212

DTDT

DTDTDTDTt

yyyc (5.51)

1211

12111212

DTDT

DTDTDTDTb

yyyc (5.52)

Method (2):

1

1313 θRT

DTDTt yc

(5.53)

209

1

1111 θRT

DTDTb yc

(5.54)

Method (3):

1

1212 θRT

DTDTt yc

(5.55)

1

1212 θRT

DTDTb yc

(5.56)

Method (4):

b

DTDTt yc

θ12

12

(5.57)

b

DTDTb yc

θ12

12

(5.58)

Method (5):

b

DTDTt yc

θ13

13

(5.59)

b

DTDTb yc

θ11

11

(5.60)

Note that Equations 5.51, 5.52, 5.55, 5.56, 5.57, and 5.58 are valid only when

ΔDT12 is positive (i.e., gap extends beyond the level of DT12).

210

5.3 Chapter Summary

This chapter describes the data instrumentation for the subassembly experiments,

including the description of the force, displacement, rotation, and strain transducers.

Additionally, the specimen response parameters determined from the subassembly

experiments are presented.

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