PLASTIC HINGE LENGTH IN HIGH-RISE CONCRETE SHEAR WALLS by ALFREDO GUILLERMO ...

251 Pages·2009·23.18 MB·English

PLASTIC HINGE LENGTH IN HIGH-RISE CONCRETE SHEAR WALLS
by
ALFREDO GUILLERMO BOHL ARBULU
B.Sc, Universidad Peruana de Ciencias Aplicadas, Peru, 2003
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF APPLIED SCIENCE
in
THE FACULTY OF GRADUATE STUDIES
(Civil Engineering)
THE UNIVERSITY OF BRITISH COLUMBIA
November 2006
© Alfredo Guillermo Bohl Arbulu, 2006
11
ABSTRACT
The fJexural displacement capacity of a concrete shear wall depends on the length of the plastic
hinge. Typical building codes and several researchers recommend the use of an equivalent plastic hinge
length at the base equal to half the wall length. However, the plastic hinge length is also influenced by
parameters other than the wall length. There are currently no recommendations on what should be the
plastic hinge length for parallel walls of different lengths in a high-rise building.
A parametric study was conducted to investigate the parameters that affect the length of the
plastic hinge in concrete walls. The walls were analyzed using program VecTor2. The analytical model
was validated with tests results performed on wall specimens.
The results obtained show that the inelastic curvatures vary linearly over the plastic hinge length.
The shape of the strain profile in slender walls after cracking depends on the amount of reinforcement.
Longer walls have larger plastic hinge lengths than shorter walls. Compressive axial loads reduce the
plastic hinge length, tensile axial loads have the opposite effect. A simple shear model was proposed to
estimate the increase in plastic hinge length when the shear stresses are high.
Walls of different lengths interconnected by rigid slabs at various levels have different curvature
distributions and plastic hinge lengths. The curvatures in the longer wall do not change whether it is alone
or combined with a wall of shorter length. The shorter length wall is subjected to larger curvatures at the
base when it is combined. A simple model was proposed to predict the maximum curvature in the shorter
wall.
iii
TABLE OF CONTENTS
ABSTRACT ii
TABLE OF CONTENTS iii
LIST OF TABLES vii
LIST OF FIGURES xii
LIST OF SYMBOLS xv
ACKNOWLEDGEMENTS xx
DEDICATION xxi
CHAPTER 1: INTRODUCTION 1
1.1 Research significance 1
1.2 Objective of the thesis 3
1.3 Organization of the thesis 4
CHAPTER 2: LITERATURE REVIEW 5
2.1 Concept of plastic hinge length 5
2.2 Chan (1955) 10
2.3 Baker (1956) 12
2.4 Cohn and Petcu (1963) 12
2.5 Baker and Amarakone (1964) 13
2.6 Sawyer (1964) 16
2.7 Mattock (1964) 17
2.8 Corley (1966) 19
2.9 Mattock (1967) 20
2.10 ACI-ASCE Committee 428 (1968) 20
2.11 Priestly, Park and Potangaroa (1981) 21
2.12 Park, Priestly and Gill (1982) 22
2.13 Oesterle, Aristizabal-Ochoa, Shiu and Corley (1984) 23
2.14 Paulay(1986) 24
2.15 Zahn, Park and Priestly (1986) 24
2.16 Priestly and Park (1987) 25
2.17 Paulay and Priestly (1992) 26
2.18 Wallace and Moehle( 1992) 27
2.19 Moehle(1992) 27
2.20 Paulay and Priestly (1993) 27
2.21 Sasani and Der Kiureghian (2001) 27
2.22 Mendis(2001) 28
iv
2.23 Panagiotakos and Fardis (2001) 30
2.24 Thomsen and Wallace (2004) 32
2.25 Summary 34
CHAPTER 3: ANALYTICAL METHODS. 38
3.1 Introduction to program VecTor2 38
3.2 Theoretical bases of program VecTor2 38
3.3 Finite element formulation 38
3.4 Models for concrete in compression 39
3.4.1 Compression pre-peak response 39
3.4.2 Compression post-peak response 40
3.4.3 Compression softening 41
3.4.4 Confinement strength 42
3.5 Models for concrete in tension 42
3.5.1 Tension stiffening 43
3.5.2 Tension softening 44
3.5.3 Cracking criterion 45
3.6 Models for slip distortions in concrete 45
3.6.1 Stress-based model 46
3.6.2 Constant rotation lag model 47
3.7 Models for reinforcement 47
3.7.1 Stress-strain response 47
3.7.2 Dowel action 49
CHAPTER 4: COMPARISON OF ANALYTICAL PREDICTIONS WITH ISOLATED WALL TEST
RESULTS 50
4.1 Scope of analysis 50
4.2 High-rise shear wall tested at the University of British Columbia 50
4.2.1 Description of the wall specimen 50
4.2.2 Instrumentation 51
4.2.3 Test procedure 52
4.2.4 Test results 52
4.2.5 Analytical model of the wall specimen 55
4.2.6 Analytical results 58
4.2.7 Comparison of experimental and analytical results 59
4.2.8 Equivalent plastic hinge length 62
4.2.9 Distribution of inelastic curvatures 66
4.2.10 Analysis of strain profiles 68
4.3 Rectangular shear wall tested at Clarkson University 79
4.3.1 Description of the wall specimen 79
4.3.2 Instrumentation 80
4.3.3 Test procedure 80
4.3.4 Test results 80
4.3.5 Analytical model of the wall specimen 80
4.3.6 Analytical results 83
4.3.7 Comparison of experimental and analytical results 83
CHAPTER 5: PARAMETRIC STUDY OF CONCRETE WALLS 89
5.1 Scope of analysis 89
5.2 Description of wall models 89
5.3 Analytical model of walls 90
5.4 Analytical results 94
5.5 Revision of analytical results 99
5.6 Influence of wall length 102
5.7 Influence of shear span 105
5.8 Influence of diagonal cracking 107
5.9 Influence of axial load U9
5.10 Summary 127
CHAPTER 6: SYSTEMS OF WALLS OF DIFFERENT LENGTHS CONNECTED TOGETHER BY
RIGID SLABS 128
6.1 Scope of analysis 128
6.2 Wall 1 combined with Wall 2 128
6.2.1 Description of wall system model 128
6.2.2 Analytical model of wall system 129
6.2.3 Analytical results 133
6.2.4 Discussion of analytical results 137
6.3 Wall 1 combined with Wall 3 144
6.3.1 Description of wall system model 144
6.3.2 Analytical model of wall system 145
6.3.3 Analytical results 150
6.3.4 Discussion of analytical results 151
6.4 Wall 1 combined with Column 1 153
6.4.1 Description of wall system model 153
6.4.2 Analytical model of wall system 154
6.4.3 Analytical results 158
vi
6.4.4 Discussion of analytical results 158
CHAPTER 7: CONCLUSIONS 160
REFERENCES 162
APPENDIX A: UBC WALL TEST 168
APPENDIX B: CLARKSON UNIVERSITY WALL TEST 184
APPENDIX C: CALCULATIONS FOR PARAMETRIC STUDY 186
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LIST OF T A B L ES
Table 2.1 Summary of previous research done on plastic hinge length 37
Table 4.1 Material properties of UBC wall model 58
Table 4.2 UBC wall parameters 63
Table 4.3 Parameters required in plastic hinge length models 63
Table 4.4 Comparison of equivalent plastic hinge length models 64
Table 4.5 Material properties of UBC wall model with added reinforcement 75
Table 4.6 Material properties of specimen RW2 model 83
Table 4.7 Material properties of specimen RW2 model accounting for cover spalling 87
Table 5.1 Material properties of Wall 1 and 2 94
Table 5.2 Predicted and measured plastic hinge lengths for Wall 1 105
Table 5.3 Predicted and measured plastic hinge lengths for Wall 2 105
Table 5.4 Predicted and measured plastic hinge lengths for Wall 1 for a shear span of 35659mm 106
Table 5.5 Predicted and measured plastic hinge lengths for Wall 2 for a shear span of 35659mm 106
Table 5.6 Predicted and measured plastic hinge lengths for Wall 1 for a shear span of 27430mm 106
Table 5.7 Predicted and measured plastic hinge lengths for Wall 2 for a shear span of 27430mm 106
Table 5.8 Predicted and measured plastic hinge lengths for Wall 1 for a shear span of 19201mm 106
Table 5.9 Predicted and measured plastic hinge lengths for Wall 2 for a shear span of 19201mm 107
Table 5.10 Material properties of Wall 1 and 2 with a web thickness of 254mm 108
Table 5.11 Predicted and measured plastic hinge lengths for Wall 1 for a web thickness of 254mm and a
shear span of 27430mm 110
Table 5.12 Predicted and measured plastic hinge lengths for Wall 2 for a web thickness of 254mm and a
shear span of 27430mm 110
Table 5.13 Predicted and measured plastic hinge lengths for Wall 1 for a web thickness of 254mm and a
shear span of 19201mm 110
Table 5.14 Predicted and measured plastic hinge lengths for Wall 2 for a web thickness of 254mm and a
shear span of 19201mm Ill
Table 5.15 Yield drifts and shear stresses of Wall 1 and 2 Ill
Table 5.16 Predicted and measured plastic hinge lengths for Wall 1 for a shear span of 19201mm using
shear model 117
Table 5.17 Predicted and measured plastic hinge lengths for Wall 1 for a web thickness of 254mm and a
shear span of 27430mm using shear model 118
Table 5.18 Predicted and measured plastic hinge lengths for Wall 1 for a web thickness of 254mm and a
shear span of 19201mm using shear model 118
Table 5.19 Yield curvature and yield moment of Wall 1 and 2 for different axial load ratios 122
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Table 5.20 Predicted and measured plastic hinge lengths for Wall 1 for a compressive axial load ratio of
0.3 122
Table 5.21 Predicted and measured plastic hinge lengths for Wall 2 for a compressive axial load ratio of
0.3 122
Table 5.22 Predicted and measured plastic hinge lengths for Wall 1 for a compressive axial load ratio of
0.2 122
Table 5.23 Predicted and measured plastic hinge lengths for Wall 2 for a compressive axial load ratio of
0.2 122
Table 5.24 Predicted and measured plastic hinge lengths for Wall 1 for no axial load 123
Table 5.25 Predicted and measured plastic hinge lengths for Wall 2 for no axial load 123
Table 5.26 Predicted and measured plastic hinge lengths for Wall 1 for a tensile axial load ratio of 0.02
123
Table 5.27 Predicted and measured plastic hinge lengths for Wall 2 for a tensile axial load ratio of 0.02
123
Table 5.28 Predicted and measured plastic hinge lengths for Wall 1 for a tensile axial load ratio of 0.05
123
Table 5.29 Predicted and measured plastic hinge lengths for Wall 2 for a tensile axial load ratio of 0.05
124
Table 5.30 Measured plastic hinge lengths at maximum drift 127
Table 6.1 Material properties in rectangular and triangular elements of Wall 1 and 2 132
Table 6.2 Material properties in truss elements of Wall 1 and 2 132
Table 6.3 Displacement components up to the fourth storey of Wall 1 and 2 combined for a drift of 2%
140
Table 6.4 Predicted and measured maximum curvature for Wall 2 combined 144
Table 6.5 Predicted and measured maximum curvature for Wall 3 combined 153
Table A. 1 List of zero readings 169
Table A.2 Mean values of zero readings 170
Table A.3 Experimental (pushing east) curvatures for a wall displacement of 105mm 171
Table A.4 Experimental (pushing west) curvatures for a wall displacement of 104mm 172
Table A.5 Experimental (pushing east) curvatures for a wall displacement of 132mm 173
Table A. 6 Experimental (pushing west) curvatures for a wall displacement of 138mm 174
Table A.7 Experimental (pushing east) curvatures for a wall displacement of 182mm 175
Table A.8 Experimental (pushing west) curvatures for a wall displacement of 187mm 176
Table A.9 Analytical curvatures for a wall displacement of 105mm 177
Table A. 10 Analytical curvatures for a wall displacement of 104mm 178
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Table A. 11 Analytical curvatures for a wall displacement of 132mm 179
Table A. 12 Analytical curvatures for a wall displacement of 138mm 180
Table A. 13 Analytical curvatures for a wall displacement of 182mm 181
Table A. 14 Analytical curvatures for a wall displacement of 187mm 182
Table A. 15 Plane sections analysis to determine ultimate curvature 183
Table B.l Analytical strain profile at base for a drift of 1.5% 185
Table B.2 Analytical strain profile at base for a drift of 2% 185
Table B.3 Analytical strain profile accounting for cover spalling at base for a drift of 1.5% 185
Table B.4 Analytical strain profile accounting for cover spallingat base for a drift of 2% 185
Table C. 1 Curvatures up to the mid-height of Wall 1 for a drift of 2% 187
Table C.2 Interpolation of curvatures at storey heights of Wall 1 for a drift of 2% 189
Table C.3 Bending moments along the height of Wall 1 for a drift of 2% 190
Table C.4 Curvatures up to the mid-height of Wall 2 for a drift of 2% 191
Table C.5 Interpolation of curvatures at storey heights of Wall 2 for a drift of 2% 193
Table C.6 Bending moments along the height of Wall 2 for a drift of 2% 194
Table C.7 Average shear stress in Wall 1 195
Table C.8 Average shear stress in Wall 2 195
Table C.9 Average shear stress in Wall 1 for a shear span of 35659mm 195
Table C. 10 Average shear stress in Wall 2 for a shear span of 35659mm 195
Table C. 11 Average shear stress in Wall 1 for a shear span of 27430mm 195
Table C. 12 Average shear stress in Wall 2 for a shear span of 27430mm 196
Table C. 13 Average shear stress in Wall 1 for a shear span of 19201mm 196
Table C. 14 Average shear stress in Wall 2 for a shear span of 19201mm 196
Table C. 15 Average shear stress in Wall 1 for a web thickness of 254mm and a shear span of 27430mm
196
Table C. 16 Average shear stress in Wall 2 for a web thickness of 254mm and a shear span of 27430mm
196
Table C.17 Average shear stress in Wall 1 for a web thickness of 254mm and a shear span of 19201mm
197
Table C.l8 Average shear stress in Wall 2 for a web thickness of 254mm and a shear span of 19201mm
197
Table C. 19 Average shear stress in Wall 1 for a compressive axial load ratio of 0.3 197
Table C.20 Average shear stress in Wall 2 for a compressive axial load ratio of 0.3 197
Table C.21 Average shear stress in Wall 1 for a compressive axial load ratio of 0.2 197
Table C.22 Average shear stress in Wall 2 for a compressive axial load ratio of 0.2 198
Table C.23 Average shear stress in Wall 1 for no axial load 198
Table C.24 Average shear stress in Wall 2 for no axial load 198
Table C.25 Average shear stress in Wall 1 for a tensile axial load ratio of 0.02 198
Table C.26 Average shear stress in Wall 2 for a tensile axial load ratio of 0.02 198
Table C.27 Average shear stress in Wall 1 for a tensile axial load ratio of 0.05 199
Table C.28 Average shear stress in Wall 2 for a tensile axial load ratio of 0.05 199
Table C.29 Curvatures up to the mid-height of Wall 1 combined with Wall 2 for a drift of 2% 200
Table C.30 Interpolation of curvatures at storey heights of Wall 1 combined with Wall 2 for a drift of 2%
202
Table C.31 Displacement components at the first storey of Wall 1 combined with Wall 2 for a drift of 2%
203
Table C.32 Displacement components at the second storey of Wall 1 combined with Wall 2 for a drift of
2% 203
Table C.33 Displacement components at the third storey of Wall 1 combined with Wall 2 for a drift of
2% 204
Table C.34 Displacement components at the fourth storey of Wall 1 combined with Wall 2 for a drift of
2% 204
Table C.35 Slopes up to the mid-height of Wall 1 combined with Wall 2 for a drift of 2% 205
Table C.36 Bending moments along the height of Wall 1 combined with Wall 2 for a drift of 2% 206
Table C.37 Curvatures up to the mid-height of Wall 2 combined with Wall 1 for a drift of 2% 207
Table C.38 Interpolation of curvatures at storey heights of Wall 2 combined with Wall 1 for a drift of 2%
209
Table C.39 Displacement components at the first storey of Wall 2 combined with Wall 1 for a drift of 2%
210
Table C.40 Displacement components at the second storey of Wall 2 combined with Wall 1 for a drift of
2% 210
Table C.41 Displacement components at the third storey of Wall 2 combined with Wall 1 for a drift of
2% 211
Table C.42 Displacement components at the fourth storey of Wall 2 combined with Wall 1 for a drift of
2% 211
Table C.43 Slopes up to the mid-height of Wall 2 combined with Wall 1 for a drift of 2% 212
Table C.44 Bending moments along the height of Wall 2 combined with Wall 1 for a drift of 2% 213
Table C.45 Curvatures up to the mid-height of Wall 3 for a drift of 2% 214
Table C.46 Interpolation of curvatures at storey heights of Wall 3 for a drift of 2% 216
Table C.47 Bending moments along the height of Wall 3 for a drift of 2% 217
Table C.48 Curvatures up to the mid-height of Wall 1 combined with Wall 3 for a drift of 2% 218
Table C.49 Curvatures up to the mid-height of Wall 3 combined with Wall 1 for a drift of 2% 220