Weldon bd042010d vol1

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Weldon bd042010d vol1

  1. 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. 2. © Copyright 2010 Brad D. Weldon
  3. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 19. REFERENCES ...............................................................................................................978 Appendix A .....................................................................................................................989 Appendix B .....................................................................................................................992 Appendix C .....................................................................................................................996 Appendix D ...................................................................................................................1011 Appendix E ...................................................................................................................1039 Appendix F ...................................................................................................................1064 xvi
  20. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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 xxix
  33. 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. 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. 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. 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. 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. 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. 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. 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 xxxvii

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