1. 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

2. © Copyright 2010
Brad D. Weldon

3. 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

4. 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.

5. 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
ii

6. 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
2.6
Frames with Supplemental Energy Dissipation .........................................39
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
3.2.3
3.3
Reaction Block ...........................................................................................90
Load Block ...............................................................................................101
Testing Procedure ................................................................................................105
3.3.1
Wall Test Region Vertical Forces ............................................................106
iii

7. 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
4.2.3
Post-tensioning Strand Properties ............................................................130
4.2.4
Mild Reinforcing Steel Properties ...........................................................136
4.2.5
4.3
Fiber-Reinforced Grout Properties ..........................................................124
Angle Steel Properties..............................................................................140
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
iv

8. 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
v

9. 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
6.2.7
Beam Vertical Displacements ..................................................................233
6.2.8
Beam Chord Rotation ..............................................................................237
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
vi

10. 6.3
Test 2....................................................................................................................301
6.3.1
Test Photographs ......................................................................................302
6.3.2
Beam Shear Force versus Chord Rotation Behavior ...............................307
6.3.3
Beam End Moment Force versus Chord Rotation Behavior ...................310
6.3.4
Beam Post-Tensioning Forces .................................................................311
6.3.5
Angle-to-Wall Connection Post-Tensioning Forces ................................316
6.3.6
Vertical Forces on Wall Test Region .......................................................320
6.3.7
Beam Vertical Displacements ..................................................................321
6.3.8
Beam Chord Rotation ..............................................................................324
6.3.9
Local Beam Rotations ..............................................................................327
6.3.10 Load Block Displacements and Rotations ...............................................328
6.3.11 Reaction Block Displacements and Rotations .........................................336
6.3.12 Contact Depth and Gap Opening at Beam-to-Wall Interfaces.................341
6.3.13 Wall Test Region Local Concrete Deformations .....................................352
6.3.14 Beam Looping Reinforcement Longitudinal Leg Strains ........................354
6.3.15 Beam Transverse Reinforcement Strains .................................................361
6.3.16 Beam Confined Concrete Strains .............................................................364
6.3.17 Beam End Confinement Hoop Strains .....................................................368
6.3.18 Wall Test Region Confined Concrete Strains ..........................................372
6.3.19 Wall Test Region Confinement Hoop Strains .........................................373
6.3.20 Crack Patterns ..........................................................................................373
6.4
Test 3....................................................................................................................375
6.4.1
Test Photographs ......................................................................................376
6.4.2
Beam Shear Force versus Chord Rotation Behavior ...............................381
6.4.3
Beam End Moment Force versus Chord Rotation Behavior ...................383
vii

11. 6.4.4
Beam Post-Tensioning Forces .................................................................383
6.4.5
Angle-to-Wall Connection Post-Tensioning Forces ................................388
6.4.6
Vertical Forces on Wall Test Region .......................................................392
6.4.7
Beam Vertical Displacements ..................................................................393
6.4.8
Beam Chord Rotation ..............................................................................396
6.4.9
Local Beam Rotations ..............................................................................398
6.4.10 Load Block Displacements and Rotations ...............................................400
6.4.11 Reaction Block Displacements and Rotations .........................................408
6.4.12 Contact Depth and Gap Opening at Beam-to-Wall Interfaces.................413
6.4.13 Wall Test Region Local Concrete Deformations .....................................424
6.4.14 Beam Looping Reinforcement Longitudinal Leg Strains ........................426
6.4.15 Beam Transverse Reinforcement Strains .................................................433
6.4.16 Beam Confined Concrete Strains .............................................................436
6.4.17 Beam End Confinement Hoop Strains .....................................................440
6.4.18 Wall Test Region Confined Concrete Strains ..........................................444
6.4.19 Wall Test Region Confinement Hoops Strains ........................................444
6.4.20 Crack Patterns ..........................................................................................445
6.5
Test 4....................................................................................................................447
6.5.1
Test Photographs ......................................................................................448
6.5.2
Beam Shear Force versus Chord Rotation Behavior ...............................453
6.5.3
Beam End Moment Force versus Chord Rotation Behavior ...................456
6.5.4
Beam Post-Tensioning Forces .................................................................457
6.5.5
Angle-to-Wall Connection Post-Tensioning Forces ................................461
6.5.6
Vertical Forces on Wall Test Region .......................................................464
6.5.7
Beam Vertical Displacements ..................................................................465
viii

12. 6.5.8
Beam Chord Rotation ..............................................................................469
6.5.9
Local Beam Rotations ..............................................................................471
6.5.10 Load Block Displacements and Rotations ...............................................473
6.5.11 Reaction Block Displacements and Rotations .........................................481
6.5.12 Contact Depth and Gap Opening at Beam-to-Wall Interfaces.................486
6.5.13 Wall Test Region Local Concrete Deformations .....................................497
6.5.14 Beam Looping Reinforcement Longitudinal Leg Strains ........................499
6.5.15 Beam Transverse Reinforcement Strains .................................................505
6.5.16 Beam Confined Concrete Strains .............................................................508
6.5.17 Beam End Confinement Hoop Strains .....................................................512
6.5.18 Wall Test Region Confined Concrete Strains ..........................................516
6.5.19 Wall Test Region Confinement Hoop Strains .........................................517
6.5.20 Crack Patterns ..........................................................................................517
VOLUME III
CHAPTER 7:
POST-VIRGIN BEAM SUBASSEMBLY EXPERIMENTAL RESULTS ....................519
7.1
Test 3A .................................................................................................................519
7.1.1
Test Photographs ......................................................................................522
7.1.2
Beam Shear Force versus Chord Rotation Behavior ...............................526
7.1.3
Beam End Moment Force versus Chord Rotation Behavior ...................529
7.1.4
Beam Post-Tensioning Forces .................................................................530
7.1.5
Angle-to-Wall Connection Post-Tensioning Forces ................................535
7.1.6
Vertical Forces on Wall Test Region .......................................................539
7.1.7
Beam Vertical Displacements ..................................................................540
7.1.8
Beam Chord Rotation ..............................................................................545
ix

13. 7.1.9
Local Beam Rotations ..............................................................................547
7.1.10 Load Block Displacements and Rotations ...............................................549
7.1.11 Reaction Block Displacements and Rotations .........................................557
7.1.12 Contact Depth and Gap Opening at Beam-to-Wall Interfaces.................562
7.1.13 Wall Test Region Local Concrete Deformations .....................................573
7.1.14 Beam Looping Reinforcement Longitudinal Leg Strains ........................575
7.1.15 Beam Transverse Reinforcement Strains .................................................581
7.1.16 Beam Confined Concrete Strains .............................................................585
7.1.17 Beam End Confinement Hoop Strains .....................................................589
7.1.18 Wall Test Region Confined Concrete Strains ..........................................593
7.1.19 Wall Test Region Confinement Hoop Strains .........................................594
7.1.20 Crack Patterns ..........................................................................................594
7.2
Test 3B .................................................................................................................595
7.2.1
Test Photographs ......................................................................................596
7.2.2
Beam Shear Force versus Chord Rotation Behavior ...............................601
7.2.3
Beam End Moment Force versus Chord Rotation Behavior ...................604
7.2.4
Beam Post-Tensioning Forces .................................................................605
7.2.5
Angle-to-Wall Connection Post-Tensioning Forces ................................609
7.2.6
Vertical Forces on Wall Test Region .......................................................612
7.2.7
Beam Vertical Displacements ..................................................................613
7.2.8
Beam Chord Rotation ..............................................................................618
7.2.9
Local Beam Rotations ..............................................................................620
7.2.10 Load Block Displacements and Rotations ...............................................622
7.2.11 Reaction Block Displacements and Rotations .........................................630
7.2.12 Contact Depth and Gap Opening at Beam-to-Wall Interfaces.................635
x

14. 7.2.13 Wall Test Region Local Concrete Deformations .....................................646
7.2.14 Beam Looping Reinforcement Longitudinal Leg Strains ........................648
7.2.15 Beam Transverse Reinforcement Strains .................................................655
7.2.16 Beam Confined Concrete Strains .............................................................658
7.2.17 Beam End Confinement Hoop Strains .....................................................662
7.2.18 Wall Test Region Confined Concrete Strains ..........................................666
7.2.19 Wall Test Region Confinement Hoop Strains .........................................667
7.2.20 Crack Patterns ..........................................................................................667
7.3
Test 4A .................................................................................................................668
7.3.1
Test Photographs ......................................................................................669
7.3.2
Beam Shear Force versus Chord Rotation Behavior ...............................673
7.3.3
Beam End Moment Force versus Chord Rotation Behavior ...................676
7.3.4
Beam Post-Tensioning Forces .................................................................677
7.3.5
Angle-to-Wall Connection Post-Tensioning Forces ................................681
7.3.6
Vertical Forces on Wall Test Region .......................................................681
7.3.7
Beam Vertical Displacements ..................................................................682
7.3.8
Beam Chord Rotation ..............................................................................687
7.3.9
Local Beam Rotations ..............................................................................689
7.3.10 Load Block Displacements and Rotations ...............................................691
7.3.11 Reaction Block Displacements and Rotations .........................................699
7.3.12 Gap Opening and Contact Depth at Beam-to-Wall Interfaces.................704
7.3.13 Wall Test Region Local Concrete Deformations .....................................715
7.3.14 Beam Looping Reinforcement Longitudinal Leg Strains ........................717
7.3.15 Beam Transverse Reinforcement Strains .................................................724
7.3.16 Beam Confined Concrete Strains .............................................................728
xi

15. 7.3.17 Beam End Confinement Hoop Strains .....................................................732
7.3.18 Wall Test Region Confined Concrete Strains ..........................................736
7.3.19 Wall Test Region Confinement Hoops Strains ........................................737
7.3.20 Crack Patterns ..........................................................................................737
7.4
Test 4B .................................................................................................................738
7.4.1
Test Photographs ......................................................................................739
7.4.2
Beam Shear Force versus Chord Rotation Behavior ...............................743
7.4.3
Beam End Moment Force versus Chord Rotation Behavior ...................746
7.4.4
Beam Post-Tensioning Forces .................................................................747
7.4.5
Angle-to-Wall Connection Post-Tensioning Forces ................................752
7.4.6
Vertical Forces on Wall Test Region .......................................................755
7.4.7
Beam Vertical Displacements ..................................................................756
7.4.8
Beam Chord Rotation ..............................................................................760
7.4.9
Local Beam Rotations ..............................................................................762
7.4.10 Load Block Displacements and Rotations ...............................................765
7.4.11 Reaction Block Displacements and Rotations .........................................773
7.4.12 Contact Depth and Gap Opening at Beam-to-Wall Interfaces.................778
7.4.13 Wall Test Region Local Concrete Deformations .....................................789
7.4.14 Beam Looping Reinforcement Longitudinal Leg Strains ........................791
7.4.15 Beam Transverse Reinforcement Strains .................................................798
7.4.16 Beam Confined Concrete Strains .............................................................801
7.4.17 Beam End Confinement Hoop Strains .....................................................806
7.4.18 Wall Test Region Confined Concrete Strains ..........................................811
7.4.19 Wall Test Region Confinement Hoops Strains ........................................812
7.4.20 Crack Patterns ..........................................................................................812
xii

16. 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
xiii

17. 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
9.3.1
Beam Shear Force versus Chord Rotation Behavior ...............................886
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
9.6
Wall Pier and Coupling Beam Stresses ...................................................930
Chapter Summary ................................................................................................935
xiv

18. 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
xv

19. REFERENCES ...............................................................................................................978
Appendix A .....................................................................................................................989
Appendix B .....................................................................................................................992
Appendix C .....................................................................................................................996
Appendix D ...................................................................................................................1011
Appendix E ...................................................................................................................1039
Appendix F ...................................................................................................................1064
xvi

20. 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
xvii

21. 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 posttensioning 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
xviii

22. 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
xix

23. Figure 3.24: Dywidag Multiplane MA anchor components used with the beam posttensioning 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
xx

24. 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 posttensioning 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
xxi

25. 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
xxii

26. 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
xxiii

27. 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
xxiv

28. 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
xxv

29. 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
xxvi

30. 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
xxvii

31. 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 6.80: Test 2 coupling beam shear force versus chord rotation behavior – (a) using
beam displacements; (b) using load block displacements. ................................. 309
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 6.89: Test 2 south end seat angle-to-wall connection strand forces – (a) east
strand; (b) west strand. ........................................................................................ 319
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
xxviii

32. Figure 6.94: Test 2 north end beam vertical displacements – (a) measured, ∆DT10;
(b) adjusted, ∆DT10,y; (c) difference, ∆DT10,y-∆DT10. .............................................. 323
Figure 6.95: Test 2 percent difference between measured and adjusted displacements –
(a) south end, DT9; (b) north end, DT10. ........................................................... 323
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 6.100: Test 2 beam inclinometer rotations – (a) near beam south end, θRT1; (b) near
beam midspan, θRT2. ............................................................................................ 327
Figure 6.101: Test 2 difference between beam inclinometer rotations and beam chord
rotations – (a) RT1; (b) RT2; (c) beam deflected shape. .................................... 328
Figure 6.102: Test 2 load block horizontal displacements – (a) measured, ∆DT3;
(b) adjusted, ∆DT3,x; (c) percent difference. ......................................................... 331
Figure 6.103: Test 2 load block north end vertical displacements – (a) measured, ∆DT4;
(b) adjusted, ∆DT4,y; (c) percent difference. ......................................................... 332
Figure 6.104: Test 2 load block south end vertical displacements – (a) measured, ∆DT5;
(b) adjusted, ∆DT5,y; (c) percent difference. ......................................................... 333
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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33. 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 6.113: Test 2 beam-to-reaction-block interface top LVDT displacements –
(a) measured, ∆DT11; (b) adjusted, ∆DT11,x; (c) percent difference. ...................... 343
Figure 6.114: Test 2 beam-to-reaction-block interface middle LVDT displacements –
(a) measured, ∆DT12; (b) adjusted, ∆DT12,x; (c) percent difference. ...................... 344
Figure 6.115: Test 2 beam-to-reaction-block interface bottom LVDT displacements –
(a) measured, ∆DT13; (b) adjusted, ∆DT13,x; (c) percent difference. ...................... 345
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 6.123: Test 2 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. ............................................................................................................ 356
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
xxx

34. 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 6.127: Test 2 beam looping reinforcement vertical leg strains – (a) ε6SE(E)-E;
(b) ε6SE(E)-W; (c) ε6SE(I)-E; (d) ε6SE(I)-W. ................................................................... 362
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 6.129: Test 2 beam midspan transverse hoop reinforcement strains – (a) εMH-E;
(b) εMH-W. ............................................................................................................. 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 6.132: Test 2 No. 3 bottom hoop support bar strains – (a) ε3BHB-(1); (b) ε3BHT-(1);
(c) ε3BHB-(2); (d) ε3BHT-(2). ...................................................................................... 366
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 6.135: Test 2 beam end confinement hoop east leg strains – (a) ε1HB-E; (b) ε2HB-E;
(c) ε3HB-E; (d) ε4HB-E. ............................................................................................ 369
Figure 6.136: Test 2 beam end confinement hoop west leg strains – (a) ε1HB-W; (b) ε2HB-W;
(c) ε3HB-W; (d) ε4HB-W. ........................................................................................... 370
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
xxxi

35. 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 6.142: Test 3 beam south end damage propagation – positive and negative
rotations............................................................................................................... 380
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 6.151: Test 3 south end seat angle-to-wall connection strand forces – (a) east
strand; (b) west strand. ........................................................................................ 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
xxxii

36. Figure 6.156: Test 3 north end beam vertical displacements – (a) measured, ∆DT10;
(b) adjusted, ∆DT10,y; (c) difference, ∆DT10,y-∆DT10. .............................................. 395
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 6.163: Test 3 difference between beam inclinometer rotations and beam chord
rotations – (a) RT1; (b) RT2; (c) beam deflected shape. .................................... 400
Figure 6.164: Test 3 load block horizontal displacements – (a) measured, ∆DT3;
(b) adjusted, ∆DT3,x; (c) percent difference. ......................................................... 403
Figure 6.165: Test 3 load block north end vertical displacements – (a) measured, ∆DT4;
(b) adjusted, ∆DT4,y; (c) percent difference. ......................................................... 404
Figure 6.166: Test 3 load block south end vertical displacements – (a) measured, ∆DT5;
(b) adjusted, ∆DT5,y; (c) percent difference. ......................................................... 405
Figure 6.167: Test 3 percent difference between measured and adjusted displacements –
(a) DT4; (b) DT5. ................................................................................................ 405
Figure 6.168: Test 3 load block displacements versus beam chord rotation – (a) ∆DT4-θb;
(b) ∆DT5-θb; (c) ∆DT3,x-θb. ..................................................................................... 406
Figure 6.169: Test 3 load block centroid displacements – (a) x-y displacements;
(b) rotation; (c) x-displacements; (d) y-displacements........................................ 407
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 6.171: Test 3 reaction block displacements – (a) ΔDT6; (b) ΔDT7; (c) ΔDT8. ......... 410
Figure 6.172: Test 3 reaction block displacements versus beam chord rotation –
(a) ∆DT7-θb; (b) ∆DT8-θb; (c) ∆DT6-θb. ................................................................... 411
xxxiii

37. 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 6.175: Test 3 beam-to-reaction-block interface top LVDT displacements –
(a) measured, ∆DT11; (b) adjusted, ∆DT11,x; (c) percent difference. ...................... 415
Figure 6.176: Test 3 beam-to-reaction-block interface middle LVDT displacements –
(a) measured, ∆DT12; (b) adjusted, ∆DT12,x; (c) percent difference. ...................... 416
Figure 6.177: Test 3 beam-to-reaction-block interface bottom LVDT displacements –
(a) measured, ∆DT13; (b) adjusted, ∆DT13,x; (c) percent difference. ...................... 417
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 6.181: Test 3 gap opening at beam-to-reaction-block interface
using method 4. ................................................................................................... 423
Figure 6.182: Test 3 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. ...................................................................................................... 423
Figure 6.183: Test 3 wall test region concrete deformations – (a) DT14; (b) DT15. ..... 425
Figure 6.184: Test 3 wall test region concrete deformations versus beam chord rotation –
(a) ∆DT14-θb; (b) ∆DT15-θb. .................................................................................... 425
Figure 6.185: Test 3 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. ............................................................................................................ 427
Figure 6.186: Test 3 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. ............................................................................................................ 428
xxxiv

38. 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 6.189: Test 3 beam looping reinforcement vertical leg strains – (a) ε6SE(E)-E;
(b) ε6SE(E)-W; (c) ε6SE(I)-E; (d) ε6SE(I)-W. ................................................................... 434
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 6.191: Test 3 beam midspan transverse hoop reinforcement strains – (a) εMH-E;
(b) εMH-W. ............................................................................................................. 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 6.193: Test 3 No. 3 top hoop support bar strains – (a) ε3THT-(1); (b) ε3THB-(1);
(c) ε3THT-(2); (d) ε3THB-(2). ...................................................................................... 437
Figure 6.194: Test 3 No. 3 bottom hoop support bar strains – (a) ε3BHB-(1); (b) ε3BHT-(1);
(c) ε3BHB-(2); (d) ε3BHT-(2). ...................................................................................... 438
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
xxxv

39. 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 6.204: Test 4 beam south end damage propagation – positive and negative
rotations............................................................................................................... 452
Figure 6.205: Test 4 angle-to-wall connection plates. .................................................... 452
Figure 6.206: Test 4 wall test region patch. .................................................................... 453
Figure 6.207: Test 4 coupling beam shear force versus chord rotation behavior – (a) using
beam displacements; (b) using load block displacements. ................................. 455
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 6.214: Test 4 south end seat angle-to-wall connection strand forces – (a) east
strand; (b) west strand. ........................................................................................ 463
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
Figure 6.219: Test 4 north end beam vertical displacements – (a) measured, ∆DT10;
(b) adjusted, ∆DT10,y; (c) difference, ∆DT10,y-∆DT10. .............................................. 468
xxxvi

40. Figure 6.220: Test 4 percent difference between measured and adjusted displacements –
(a) south end, DT9; (b) north end, DT10. ........................................................... 468
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 6.225: Test 4 beam inclinometer rotations – (a) near beam south end, θRT1; (b) near
beam midspan, θRT2. ............................................................................................ 472
Figure 6.226: Test 4 difference between beam inclinometer rotations and beam chord
rotations – (a) RT1; (b) RT2; (c) beam deflected shape. .................................... 473
Figure 6.227: Test 4 load block horizontal displacements – (a) measured, ∆DT3;
(b) adjusted, ∆DT3,x; (c) percent difference. ......................................................... 476
Figure 6.228: Test 4 load block north end vertical displacements – (a) measured, ∆DT4;
(b) adjusted, ∆DT4,y; (c) percent difference. ......................................................... 477
Figure 6.229: Test 4 load block south end vertical displacements – (a) measured, ∆DT5;
(b) adjusted, ∆DT5,y; (c) percent difference. ......................................................... 478
Figure 6.230: Test 4 percent difference between measured and adjusted displacements –
(a) DT4; (b) DT5. ................................................................................................ 478
Figure 6.231: Test 4 load block displacements versus beam chord rotation – (a) ∆DT4-θb;
(b) ∆DT5-θb; (c) ∆DT3,x-θb. ..................................................................................... 479
Figure 6.232: Test 4 load block centroid displacements – (a) x-y displacements;
(b) rotation; (c) x-displacements; (d) y-displacements........................................ 480
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 6.234: Test 4 reaction block displacements – (a) ΔDT6; (b) ΔDT7; (c) ΔDT8. ......... 483
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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