The Study of Flexural and Ultimate Behavior of Ferrocement Lightweight Beam b...
Weldon bd042010d vol1
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
3. BEHAVIOR, DESIGN, AND ANALYSIS OF UNBONDED POST-TENSIONED
PRECAST CONCRETE COUPLING BEAMS
Abstract
by
Brad D. Weldon
This dissertation describes an experimental, analytical, and design investigation
on the nonlinear behavior of precast concrete coupling beams, where coupling of
reinforced concrete shear walls is achieved by post-tensioning the beams and the walls
together at the floor and roof levels. The new coupling system offers important
advantages over conventional systems with monolithic cast-in-place beams, such as
simpler detailing, reduced damage to the structure, and reduced residual lateral
displacements. Steel top and seat angles are used at the beam-to-wall joints to yield and
provide energy dissipation.
The results from eight half-scale experiments of unbonded post-tensioned precast
coupling beams under reversed-cyclic lateral loading are presented. Each test specimen
includes a coupling beam and the adjacent wall pier regions at a floor level. The test
parameters include the post-tensioning tendon area and initial stress, initial beam concrete
axial stress, angle strength, and beam depth. The results demonstrate excellent stiffness,
strength, and ductility of the specimens under cyclic loading, with considerable energy
dissipation concentrated in the angles. Compliance of the beams to established
4. Brad D. Weldon
acceptance criteria is demonstrated, validating the use of these structures in seismic
regions. The critical components of the structure that can limit the desired performance
include the post-tensioning anchors as well as the top and seat angles and their
connections.
The experimental results are also used to validate the analysis and design of the
new coupling system. Two different analytical models, one using fiber elements and the
other using finite elements, are investigated. In addition, an idealized coupling beam end
moment versus chord rotation relationship is developed as a design tool following basic
principles of equilibrium, compatibility, and constitutive relationships. The comparisons
demonstrate that the analytical and design models are able to capture the nonlinear
behavior of the structure, including global parameters such as the beam lateral force
versus chord rotation behavior as well as local parameters such as the neutral axis depth
at the beam ends. Using these models, the effects of several structural properties (such as
beam length) on the behavior of unbonded post-tensioned precast coupling beams is
analytically investigated to expand the results from the experiments.
5. CONTENTS
FIGURES ........................................................................................................................ xvii
TABLES .......................................................................................................................... lxii
ACKNOWLEDGMENTS ............................................................................................... lxv
NOTATION ................................................................................................................... lxvii
VOLUME I
CHAPTER 1:
INTRODUCTION ...............................................................................................................1
1.1
Problem Statement ...................................................................................................1
1.2
Research Objectives .................................................................................................7
1.3
Research Scope ........................................................................................................8
1.4
Research Significance ..............................................................................................9
1.5
Overview of Dissertation .......................................................................................10
CHAPTER 2:
BACKGROUND ...............................................................................................................12
2.1
Coupled Wall Structural Systems ..........................................................................12
2.2
Monotonic Cast-in-Place Concrete Coupled Wall Systems ..................................15
2.2.1 Behavior and Design of Cast-in-Place Concrete Coupling Beams ............16
2.2.2
Current Code Requirements for Cast-in-Place Concrete
Coupling Beams .........................................................................................17
ii
6. 2.2.3
Analysis and Modeling of Cast-in-Place Concrete Coupled
Wall Systems .............................................................................................20
2.2.4
Coupling Beam Database ...........................................................................22
2.3
Unbonded Post-Tensioning ....................................................................................24
2.4
Unbonded Post-Tensioned Hybrid Coupled Wall Systems ...................................26
2.5
Unbonded Post-Tensioned Precast Moment Frames .............................................35
2.5.1
2.6
Frames with Supplemental Energy Dissipation .........................................39
Behavior of Top and Seat Angles ..........................................................................45
2.6.1
Kishi and Chen (1990) and Lorenz et al. (1993) .......................................49
2.6.1.1 Tension angle initial stiffness, Kaixt ......................................................50
2.6.1.2 Tension angle yield force capacity, Tayx...............................................53
2.7
Chapter Summary ..................................................................................................54
CHAPTER 3:
PRECAST COUPLING BEAM SUBASSEMBLY EXPERIMENTS .............................56
3.1
Experiment Setup ...................................................................................................57
3.2
Test Subassembly Components .............................................................................65
3.2.1
Coupling Beam Specimens ........................................................................66
3.2.1.1 Maximum Moment Capacity at Beam-to-Wall Interfaces...................75
3.2.1.2 Beam Transverse Reinforcement .........................................................78
3.2.1.3 Beam Longitudinal Mild Steel Reinforcement ....................................81
3.2.1.4 Confinement Reinforcement ................................................................86
3.2.1.5 Shear Slip at Beam-to-Wall Interfaces ................................................88
3.2.2
3.2.3
3.3
Reaction Block ...........................................................................................90
Load Block ...............................................................................................101
Testing Procedure ................................................................................................105
3.3.1
Wall Test Region Vertical Forces ............................................................106
iii
7. 3.3.2
Beam Post-Tensioning Force ...................................................................109
3.3.3
Top and Seat Angle Connections .............................................................111
3.3.4
Test Day ...................................................................................................113
3.3.5
Summary of Test Procedure.....................................................................117
3.3.5.1 Virgin Beam Test Procedure ..............................................................117
3.3.5.2 Non-Virgin Beam Test Procedure .....................................................119
3.4
Chapter Summary ................................................................................................120
CHAPTER 4:
DESIGN AND MATERIAL PROPERTIES ...................................................................121
4.1
Design Material Properties ..................................................................................121
4.2
Measured Material Properties ..............................................................................122
4.2.1 Unconfined Concrete Strength .................................................................123
4.2.2
4.2.3
Post-tensioning Strand Properties ............................................................130
4.2.4
Mild Reinforcing Steel Properties ...........................................................136
4.2.5
4.3
Fiber-Reinforced Grout Properties ..........................................................124
Angle Steel Properties..............................................................................140
Chapter Summary ................................................................................................142
CHAPTER 5:
DATA INSTRUMENTATION AND SPECIMEN RESPONSE PARAMETERS ........144
5.1
Data Instrumentation ............................................................................................144
5.1.1
Instrumentation Overview .......................................................................145
5.1.2
Post-Tensioning Strand Load Cells .........................................................158
5.1.3
Wall Test Region Vertical Force Load Cells ...........................................166
iv
8. 5.1.4
Load Block Global Displacement Transducers .......................................166
5.1.5
Reaction Block Global Displacement Transducers .................................169
5.1.6 Beam Global Displacement Transducers .................................................171
5.1.7
Gap Opening Displacement Transducers.................................................172
5.1.8
Wall Test Region Local Displacement Transducers ................................174
5.1.9
Beam Rotation Transducers .....................................................................176
5.1.10 Beam Looping Reinforcement Longitudinal Leg Strain Gauges ............177
5.1.11 Beam Transverse Reinforcement Strain Gauges .....................................179
5.1.12 Beam End Confinement Hoop Strain Gauges .........................................181
5.1.13 Beam Confined Concrete Strain Gauges .................................................184
5.1.14 Reaction Block Confinement Hoop Strain Gauges .................................186
5.1.15 Reaction Block Confined Concrete Strain Gauges ..................................189
5.2
Subassembly Response Parameters .....................................................................190
5.2.1 Coupling Beam Shear Force ....................................................................192
5.2.2
Coupling Beam End Moment ..................................................................194
5.2.3 Coupling Beam Post-Tensioning Force ...................................................194
5.2.4
Vertical Force on Wall Test Region ........................................................194
5.2.5
Angle Post-Tensioning Forces .................................................................195
5.2.6
Reaction Block Displacements ................................................................195
5.2.7
Load Block Displacements ......................................................................197
5.2.8
Beam Vertical Displacements ..................................................................201
5.2.9
Beam Chord Rotation ..............................................................................204
5.2.10 Gap Opening and Contact Depth at Beam-to-Wall Interface ..................205
5.3
Chapter Summary ................................................................................................210
v
9. VOLUME II
CHAPTER 6:
VIRGIN BEAM SUBASSEMBLY EXPERIMENTAL RESULTS ...............................211
6.1
Overall Test Specimen Response.........................................................................211
6.2
Test 1....................................................................................................................214
6.2.1
Test Photographs ......................................................................................216
6.2.2
Beam Shear Force versus Chord Rotation Behavior ...............................222
6.2.3
Beam End Moment Force versus Chord Rotation Behavior ...................224
6.2.4
Beam Post-Tensioning Forces .................................................................225
6.2.5
Angle-to-Wall Connection Post-Tensioning Forces ................................229
6.2.6
Vertical Forces on Wall Test Region .......................................................232
6.2.7
Beam Vertical Displacements ..................................................................233
6.2.8
Beam Chord Rotation ..............................................................................237
6.2.9
Local Beam Rotations ..............................................................................240
6.2.10 Load Block Displacements and Rotations ...............................................242
6.2.11 Reaction Block Displacements and Rotations .........................................250
6.2.12 Contact Depth and Gap Opening at Beam-to-Wall Interfaces.................256
6.2.13 Wall Test Region Local Concrete Deformations .....................................267
6.2.14 Beam Looping Reinforcement Longitudinal Leg Strains ........................269
6.2.15 Beam Transverse Reinforcement Strains .................................................276
6.2.16 Beam Confined Concrete Strains .............................................................279
6.2.17 Beam End Confinement Hoop Strains .....................................................284
6.2.18 Wall Test Region Confined Concrete Strains ..........................................291
6.2.19 Wall Test Region Confinement Hoop Strains .........................................297
6.2.20 Crack Patterns ..........................................................................................299
vi
10. 6.3
Test 2....................................................................................................................301
6.3.1
Test Photographs ......................................................................................302
6.3.2
Beam Shear Force versus Chord Rotation Behavior ...............................307
6.3.3
Beam End Moment Force versus Chord Rotation Behavior ...................310
6.3.4
Beam Post-Tensioning Forces .................................................................311
6.3.5
Angle-to-Wall Connection Post-Tensioning Forces ................................316
6.3.6
Vertical Forces on Wall Test Region .......................................................320
6.3.7
Beam Vertical Displacements ..................................................................321
6.3.8
Beam Chord Rotation ..............................................................................324
6.3.9
Local Beam Rotations ..............................................................................327
6.3.10 Load Block Displacements and Rotations ...............................................328
6.3.11 Reaction Block Displacements and Rotations .........................................336
6.3.12 Contact Depth and Gap Opening at Beam-to-Wall Interfaces.................341
6.3.13 Wall Test Region Local Concrete Deformations .....................................352
6.3.14 Beam Looping Reinforcement Longitudinal Leg Strains ........................354
6.3.15 Beam Transverse Reinforcement Strains .................................................361
6.3.16 Beam Confined Concrete Strains .............................................................364
6.3.17 Beam End Confinement Hoop Strains .....................................................368
6.3.18 Wall Test Region Confined Concrete Strains ..........................................372
6.3.19 Wall Test Region Confinement Hoop Strains .........................................373
6.3.20 Crack Patterns ..........................................................................................373
6.4
Test 3....................................................................................................................375
6.4.1
Test Photographs ......................................................................................376
6.4.2
Beam Shear Force versus Chord Rotation Behavior ...............................381
6.4.3
Beam End Moment Force versus Chord Rotation Behavior ...................383
vii
11. 6.4.4
Beam Post-Tensioning Forces .................................................................383
6.4.5
Angle-to-Wall Connection Post-Tensioning Forces ................................388
6.4.6
Vertical Forces on Wall Test Region .......................................................392
6.4.7
Beam Vertical Displacements ..................................................................393
6.4.8
Beam Chord Rotation ..............................................................................396
6.4.9
Local Beam Rotations ..............................................................................398
6.4.10 Load Block Displacements and Rotations ...............................................400
6.4.11 Reaction Block Displacements and Rotations .........................................408
6.4.12 Contact Depth and Gap Opening at Beam-to-Wall Interfaces.................413
6.4.13 Wall Test Region Local Concrete Deformations .....................................424
6.4.14 Beam Looping Reinforcement Longitudinal Leg Strains ........................426
6.4.15 Beam Transverse Reinforcement Strains .................................................433
6.4.16 Beam Confined Concrete Strains .............................................................436
6.4.17 Beam End Confinement Hoop Strains .....................................................440
6.4.18 Wall Test Region Confined Concrete Strains ..........................................444
6.4.19 Wall Test Region Confinement Hoops Strains ........................................444
6.4.20 Crack Patterns ..........................................................................................445
6.5
Test 4....................................................................................................................447
6.5.1
Test Photographs ......................................................................................448
6.5.2
Beam Shear Force versus Chord Rotation Behavior ...............................453
6.5.3
Beam End Moment Force versus Chord Rotation Behavior ...................456
6.5.4
Beam Post-Tensioning Forces .................................................................457
6.5.5
Angle-to-Wall Connection Post-Tensioning Forces ................................461
6.5.6
Vertical Forces on Wall Test Region .......................................................464
6.5.7
Beam Vertical Displacements ..................................................................465
viii
12. 6.5.8
Beam Chord Rotation ..............................................................................469
6.5.9
Local Beam Rotations ..............................................................................471
6.5.10 Load Block Displacements and Rotations ...............................................473
6.5.11 Reaction Block Displacements and Rotations .........................................481
6.5.12 Contact Depth and Gap Opening at Beam-to-Wall Interfaces.................486
6.5.13 Wall Test Region Local Concrete Deformations .....................................497
6.5.14 Beam Looping Reinforcement Longitudinal Leg Strains ........................499
6.5.15 Beam Transverse Reinforcement Strains .................................................505
6.5.16 Beam Confined Concrete Strains .............................................................508
6.5.17 Beam End Confinement Hoop Strains .....................................................512
6.5.18 Wall Test Region Confined Concrete Strains ..........................................516
6.5.19 Wall Test Region Confinement Hoop Strains .........................................517
6.5.20 Crack Patterns ..........................................................................................517
VOLUME III
CHAPTER 7:
POST-VIRGIN BEAM SUBASSEMBLY EXPERIMENTAL RESULTS ....................519
7.1
Test 3A .................................................................................................................519
7.1.1
Test Photographs ......................................................................................522
7.1.2
Beam Shear Force versus Chord Rotation Behavior ...............................526
7.1.3
Beam End Moment Force versus Chord Rotation Behavior ...................529
7.1.4
Beam Post-Tensioning Forces .................................................................530
7.1.5
Angle-to-Wall Connection Post-Tensioning Forces ................................535
7.1.6
Vertical Forces on Wall Test Region .......................................................539
7.1.7
Beam Vertical Displacements ..................................................................540
7.1.8
Beam Chord Rotation ..............................................................................545
ix
13. 7.1.9
Local Beam Rotations ..............................................................................547
7.1.10 Load Block Displacements and Rotations ...............................................549
7.1.11 Reaction Block Displacements and Rotations .........................................557
7.1.12 Contact Depth and Gap Opening at Beam-to-Wall Interfaces.................562
7.1.13 Wall Test Region Local Concrete Deformations .....................................573
7.1.14 Beam Looping Reinforcement Longitudinal Leg Strains ........................575
7.1.15 Beam Transverse Reinforcement Strains .................................................581
7.1.16 Beam Confined Concrete Strains .............................................................585
7.1.17 Beam End Confinement Hoop Strains .....................................................589
7.1.18 Wall Test Region Confined Concrete Strains ..........................................593
7.1.19 Wall Test Region Confinement Hoop Strains .........................................594
7.1.20 Crack Patterns ..........................................................................................594
7.2
Test 3B .................................................................................................................595
7.2.1
Test Photographs ......................................................................................596
7.2.2
Beam Shear Force versus Chord Rotation Behavior ...............................601
7.2.3
Beam End Moment Force versus Chord Rotation Behavior ...................604
7.2.4
Beam Post-Tensioning Forces .................................................................605
7.2.5
Angle-to-Wall Connection Post-Tensioning Forces ................................609
7.2.6
Vertical Forces on Wall Test Region .......................................................612
7.2.7
Beam Vertical Displacements ..................................................................613
7.2.8
Beam Chord Rotation ..............................................................................618
7.2.9
Local Beam Rotations ..............................................................................620
7.2.10 Load Block Displacements and Rotations ...............................................622
7.2.11 Reaction Block Displacements and Rotations .........................................630
7.2.12 Contact Depth and Gap Opening at Beam-to-Wall Interfaces.................635
x
14. 7.2.13 Wall Test Region Local Concrete Deformations .....................................646
7.2.14 Beam Looping Reinforcement Longitudinal Leg Strains ........................648
7.2.15 Beam Transverse Reinforcement Strains .................................................655
7.2.16 Beam Confined Concrete Strains .............................................................658
7.2.17 Beam End Confinement Hoop Strains .....................................................662
7.2.18 Wall Test Region Confined Concrete Strains ..........................................666
7.2.19 Wall Test Region Confinement Hoop Strains .........................................667
7.2.20 Crack Patterns ..........................................................................................667
7.3
Test 4A .................................................................................................................668
7.3.1
Test Photographs ......................................................................................669
7.3.2
Beam Shear Force versus Chord Rotation Behavior ...............................673
7.3.3
Beam End Moment Force versus Chord Rotation Behavior ...................676
7.3.4
Beam Post-Tensioning Forces .................................................................677
7.3.5
Angle-to-Wall Connection Post-Tensioning Forces ................................681
7.3.6
Vertical Forces on Wall Test Region .......................................................681
7.3.7
Beam Vertical Displacements ..................................................................682
7.3.8
Beam Chord Rotation ..............................................................................687
7.3.9
Local Beam Rotations ..............................................................................689
7.3.10 Load Block Displacements and Rotations ...............................................691
7.3.11 Reaction Block Displacements and Rotations .........................................699
7.3.12 Gap Opening and Contact Depth at Beam-to-Wall Interfaces.................704
7.3.13 Wall Test Region Local Concrete Deformations .....................................715
7.3.14 Beam Looping Reinforcement Longitudinal Leg Strains ........................717
7.3.15 Beam Transverse Reinforcement Strains .................................................724
7.3.16 Beam Confined Concrete Strains .............................................................728
xi
15. 7.3.17 Beam End Confinement Hoop Strains .....................................................732
7.3.18 Wall Test Region Confined Concrete Strains ..........................................736
7.3.19 Wall Test Region Confinement Hoops Strains ........................................737
7.3.20 Crack Patterns ..........................................................................................737
7.4
Test 4B .................................................................................................................738
7.4.1
Test Photographs ......................................................................................739
7.4.2
Beam Shear Force versus Chord Rotation Behavior ...............................743
7.4.3
Beam End Moment Force versus Chord Rotation Behavior ...................746
7.4.4
Beam Post-Tensioning Forces .................................................................747
7.4.5
Angle-to-Wall Connection Post-Tensioning Forces ................................752
7.4.6
Vertical Forces on Wall Test Region .......................................................755
7.4.7
Beam Vertical Displacements ..................................................................756
7.4.8
Beam Chord Rotation ..............................................................................760
7.4.9
Local Beam Rotations ..............................................................................762
7.4.10 Load Block Displacements and Rotations ...............................................765
7.4.11 Reaction Block Displacements and Rotations .........................................773
7.4.12 Contact Depth and Gap Opening at Beam-to-Wall Interfaces.................778
7.4.13 Wall Test Region Local Concrete Deformations .....................................789
7.4.14 Beam Looping Reinforcement Longitudinal Leg Strains ........................791
7.4.15 Beam Transverse Reinforcement Strains .................................................798
7.4.16 Beam Confined Concrete Strains .............................................................801
7.4.17 Beam End Confinement Hoop Strains .....................................................806
7.4.18 Wall Test Region Confined Concrete Strains ..........................................811
7.4.19 Wall Test Region Confinement Hoops Strains ........................................812
7.4.20 Crack Patterns ..........................................................................................812
xii
16. VOLUME IV
CHAPTER 8:
SUMMARY AND OVERVIEW OF RESULTS FROM COUPLED WALL
SUBASSEMBLY EXPERIMENTS ....................................................................813
8.1
Beam Shear Force versus Chord Rotation Behavior and
Progression of Damage ........................................................................................814
8.2
Beam Post-Tensioning Tendon Force versus Chord Rotation Behavior .............824
8.3
Effect of Beam Post-Tensioning Tendon Area and Initial Concrete Stress.........827
8.4
Effect of Top and Seat Angles and Angle Strength .............................................829
8.5
Effect of Beam Depth ..........................................................................................831
8.6
Longitudinal Mild Steel Strains ...........................................................................832
8.7
Transverse Mild Steel Strains at Beam Ends .......................................................836
8.8
Transverse Mild Steel Strains at Beam Midspan .................................................839
8.9
Angle Connections ...............................................................................................841
8.10
Beam-to-Wall Connection and Grout Behavior ..................................................842
8.11
Compliance with ACI ITG-5.1 ............................................................................843
8.11.1 Probable Lateral Strength ........................................................................843
8.11.2 Relative Energy Dissipation Ratio ...........................................................844
8.11.3 Stiffness Requirements ............................................................................848
8.12
Comparisons with Monolithic Cast-in-Place Concrete Beams ............................850
8.13
Chapter Summary ................................................................................................853
CHAPTER 9:
ANALYTICAL MODELING OF PRECAST COUPLED
WALL SUBASSEMBLIES .................................................................................854
9.1
Analytical Modeling Assumptions ......................................................................854
xiii
17. 9.2
Fiber-Element Subassembly Model .....................................................................855
9.2.1
General Modeling of Concrete Members ................................................856
9.2.2
Modeling of Coupling Beam ...................................................................860
9.2.3 Modeling of Wall Regions .......................................................................865
9.2.4
Modeling of Gap Opening .......................................................................869
9.2.5
Modeling of Beam Post-Tensioning Tendons and Anchorages ..............872
9.2.6
Modeling of Top and Seat Angles ...........................................................876
9.2.6.1 Horizontal Angle Element Force-Deformation Model ......................879
9.2.6.2 Vertical Angle Element Force-Deformation Model ..........................881
9.3
Verification of Test Specimen Models ................................................................882
9.3.1
Beam Shear Force versus Chord Rotation Behavior ...............................886
9.3.2
Beam Post-tensioning Force ....................................................................888
9.3.3
Contact Depth at Beam-to-Reaction-Block Interface ..............................895
9.3.4
Gap Opening at Beam-to-Reaction-Block Interface ................................903
9.3.5
Concrete Compressive Strains at Beam End ...........................................910
9.3.6
Longitudinal Mild Steel Strains at Beam End .........................................911
9.3.7
Longitudinal Mild Steel Strains at Beam Midspan ..................................920
9.3.8
Angle Behavior ........................................................................................924
9.4
ABAQUS Finite-Element Subassembly Model ..................................................926
9.5
Comparison of Fiber-Element and Finite-Element Models .................................929
9.5.1
9.6
Wall Pier and Coupling Beam Stresses ...................................................930
Chapter Summary ................................................................................................935
xiv
18. CHAPTER 10:
PARAMETRIC INVESTIGATION AND CLOSED FORM ESTIMATION OF
THE BEHAVIOR OF UNBONDED POST-TENSIONED PRECAST
COUPLING BEAMS...........................................................................................936
10.1
Prototype Subassembly ........................................................................................936
10.2
Analytical Modeling ............................................................................................939
10.3
Subassembly Behavior Under Monotonic Loading .............................................941
10.4
Subassembly Behavior Under Cyclic Loading ....................................................944
10.5
Parametric Investigation ......................................................................................945
10.6
Tri-linear Estimation of Subassembly Behavior ..................................................954
10.6.1 Tension Angle Yielding State ..................................................................955
10.6.2 Tension Angle Strength State ..................................................................960
10.6.3 Confined Concrete Crushing State...........................................................962
10.7
Analytical Verification of Tri-Linear Estimation ................................................965
10.8
Experimental Verification of Tri-linear Estimation .............................................965
10.9
Summary ..............................................................................................................969
CHAPTER 11:
SUMMARY, CONCLUSIONS, AND FUTURE WORK ..............................................971
11.1
Summary ..............................................................................................................971
11.2
Conclusions ..........................................................................................................972
11.2.1 Experimental Program .............................................................................972
11.2.2 Analytical Modeling and Parametric Investigation .................................974
11.2.3 Closed-form Estimations .........................................................................975
11.3
Future Work .........................................................................................................976
xv
19. REFERENCES ...............................................................................................................978
Appendix A .....................................................................................................................989
Appendix B .....................................................................................................................992
Appendix C .....................................................................................................................996
Appendix D ...................................................................................................................1011
Appendix E ...................................................................................................................1039
Appendix F ...................................................................................................................1064
xvi
20. FIGURES
VOLUME I
CHAPTER 1:
Figure 1.1: Multi story coupled wall system. ..................................................................... 3
Figure 1.2: Coupled wall system floor-level subassembly. ................................................ 4
Figure 1.3: Coupled wall system floor-level subassembly idealized, exaggerated
deformed configuration. .......................................................................................... 5
Figure 1.4: Coupling beam forces. ...................................................................................... 6
CHAPTER 2:
Figure 2.1: Coupled wall structures. ................................................................................. 13
Figure 2.2: Wall systems – (a) uncoupled wall; (b) coupled wall with strong beams;
(c) coupled wall with weak beams. ....................................................................... 15
Figure 2.3: Reinforced concrete coupling beams [Paulay and Priestley (1992)] –
(a) diagonal tension failure; (b) sliding shear failure; (c) diagonal reinforcement.
............................................................................................................................... 17
Figure 2.4: Diagonal reinforcement requirements for coupling beams [from ACI 318
(2008)] – (a) confinement of each group of diagonal bars; (b) confinement of
entire beam cross-section. ..................................................................................... 19
Figure 2.5: Diagonally reinforced coupling beam (from Magnusson Klemencic
Associates). ........................................................................................................... 20
Figure 2.6: Equivalent frame analytical models. .............................................................. 21
Figure 2.7: Measured ultimate sustained rotations for monolithic cast-in-place reinforced
concrete coupling beams. ...................................................................................... 23
Figure 2.8: Hybrid coupled wall subassembly [from Shen and Kurama (2002b)]. .......... 27
xvii
21. Figure 2.9: Hybrid coupled wall subassembly experiments [adapted from Kurama et al.
(2006)] – (a) measured coupling beam shear force versus chord rotation behavior;
(b) photograph of displaced shape at beam end; (c) measured total beam posttensioning force. .................................................................................................... 29
Figure 2.10: Low cycle fatigue fracture of top and seat angles. ....................................... 31
Figure 2.11: Hybrid coupled wall subassembly with no angles ....................................... 32
Figure 2.12: Hybrid coupled wall subassembly predicted behavior [from Shen et al.
(2006)] – (a) coupling beam shear force versus chord rotation behavior; (b) total
beam post-tensioning force. .................................................................................. 34
Figure 2.13: Unbonded post-tensioned precast moment frames – (a) structure;
(b) interior beam-column subassembly; (c) idealized, exaggerated subassembly
displaced shape. .................................................................................................... 37
Figure 2.14: Analytical investigation of unbonded post-tensioned precast beam-column
subassemblies [from El-Sheikh et al. (1999, 2000)] – (a) moment-rotation
relationship; (b) analytical model. ........................................................................ 39
Figure 2.15: Measured lateral force-displacement behavior [from Priestley and MacRae
(1996)] – (a) interior joint; (b) exterior joint. ....................................................... 40
Figure 2.16: “Hybrid” precast concrete frame beam-column joint [adapted from Kurama
(2002)]................................................................................................................... 41
Figure 2.17: Friction-damped post-tensioned precast moment frames [from Morgen and
Kurama (2004)] – (a) test set-up schematic; (b) photograph of test set-up. ......... 43
Figure 2.18: Measured beam end moment versus chord rotation behavior [from Morgen
and Kurama (2004)] – (a) without dampers; (b) with dampers. ........................... 44
Figure 2.19: Top and seat angle connection [adapted from Shen et al. (2006)] –
(a) deformed configuration; (b) angle parameters. ............................................... 45
Figure 2.20: Angle model [adapted from Kishi and Chen (1990) and Lorenz et al. (1993)]
– (a) cantilever model of tension angle; (b) assumed yield mechanism; (c) free
body of angle horizontal leg. ................................................................................ 52
CHAPTER 3:
Figure 3.1: Simulation of floor level coupled wall subassembly displacements –
(a) multi-story structure; (b) idealized displaced subassembly; (c) rotated
subassembly. ......................................................................................................... 57
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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
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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
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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
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