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Behavior of ductile reinforced concrete frames subjected to multiple earthquakes
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Behavior of ductile reinforced concrete frames subjected to multiple earthquakes
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i
BEHAVIOR OF DUCTILE REINFORCED CONCRETE
FRAMES SUBJECTED TO MULTIPLE EARTHQUAKES
by
Ahmed Mantawy
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(CIVIL ENGINEERING)
May 2014
Copyright 2014 Ahmed Mantawy
i
TABLE OF CONTENTS
LIST OF FIGURES ......................................................................................................... V
LIST OF TABLES .......................................................................................................... XI
ABSTRACT .................................................................................................................. XIII
ACKNOWLEDGEMENTS ........................................................................................ XIV
CHAPTER (1): INTRODUCTION ................................................................................. 1
1.1 Problem .................................................................................................................................................... 2
1.1.1 Damage Accumulation ...................................................................................................................... 3
1.1.1.a Collapse of the Canterbury Television (CTV) building in Christchurch, NZ ............................ 4
1.1.1.b Collapse of Pyne Gould Corp. (PGC) building in Christchurch, NZ ......................................... 6
1.1.2 Low-Cycle Fatigue ............................................................................................................................ 8
1.2 Objectives ............................................................................................................................................... 10
1.3 Dissertation Layout ............................................................................................................................... 12
CHAPTER (2): BACKGROUND AND LITERATURE REVIEW ........................... 14
2.1 Design Concepts ..................................................................................................................................... 15
2.1.1 Avoiding Shear Failure .................................................................................................................... 15
2.1.2 Avoid Anchorage Failure ................................................................................................................ 16
2.1.2.a Confinement for heavily loaded sections: ................................................................................ 17
2.1.2.b Avoidance of anchorage or splice failure ................................................................................. 18
2.1.3 Strong Column-Weak Beam ............................................................................................................ 19
2.2 Other Failure Modes ............................................................................................................................. 20
2.3 Prior Research on Structural Performance during Multiple Earthquakes ..................................... 22
CHAPTER (3): DESCRIPTION OF CASE STUDY BUILDINGS ........................... 27
3.1 North Hollywood Building (20-Story).................................................................................................. 27
3.1.1 Building Description ........................................................................................................................ 27
3.1.2 Building Instrumentation ................................................................................................................. 32
3.1.3 Recorded Motions............................................................................................................................ 34
3.1.4 Earthquake Damage ......................................................................................................................... 36
ii
3.2 San Bruno Building (6-Story) ............................................................................................................... 37
3.2.1 Building Description ........................................................................................................................ 37
3.2.2 Instrumentation ................................................................................................................................ 41
3.2.3 Recorded Motions............................................................................................................................ 42
3.2.4 Earthquake Damage ......................................................................................................................... 43
3.3 Avalon Building (4-Story) ..................................................................................................................... 43
3.3.1 Building Description ........................................................................................................................ 43
3.3.2 Instrumentation ................................................................................................................................ 47
3.3.3 Recorded Motions............................................................................................................................ 47
3.3.4 Earthquake Damage ......................................................................................................................... 48
3.4 Adequacy of RC Members for Ductile Behavior ................................................................................ 49
3.4.1 RESPONSE-2000 ............................................................................................................................ 49
3.4.2 North Hollywood Building .............................................................................................................. 53
3.4.2.a Beam Design and Detailing ..................................................................................................... 53
3.4.2.b Column Design and Detailing .................................................................................................. 55
3.4.2.c Joint Design and Detailing ....................................................................................................... 56
3.4.2.d Adequacy ................................................................................................................................. 58
3.4.3 San Bruno Building ......................................................................................................................... 59
3.4.4 Avalon Building .............................................................................................................................. 60
CHAPTER (4): MODELING OF THE CASE STUDY BUILDINGS ....................... 62
4.1 Analysis Software (PERFORM-3D) .................................................................................................... 62
4.2 Building Models ..................................................................................................................................... 64
4.2.1 Geometry ......................................................................................................................................... 65
4.2.1.a North Hollywood Building ...................................................................................................... 66
4.2.1.b San Bruno Building ................................................................................................................. 66
4.2.1.c Avalon Building ....................................................................................................................... 69
4.2.2 Stiffness ........................................................................................................................................... 69
4.2.3 Mass ................................................................................................................................................. 69
4.2.4 Damping .......................................................................................................................................... 70
4.3 Modeling Parameters for Inelastic Behavior ...................................................................................... 71
4.3.1 Monotonic Backbone Curve ............................................................................................................ 71
4.3.2 Bar-Slip effect.................................................................................................................................. 72
4.3.3 Cyclic Backbone Curve ................................................................................................................... 75
4.3.4 Cyclic Degradation: ......................................................................................................................... 77
4.3.5 Joint Model ...................................................................................................................................... 78
4.4 Building Model Calibration .................................................................................................................. 80
4.4.1 North Hollywood Building .............................................................................................................. 80
4.4.1.a Building Period and Mode shapes ............................................................................................ 80
4.4.1.b Displacement Histories ............................................................................................................ 82
4.4.2 San Bruno Building ......................................................................................................................... 86
4.4.2.a Building Period and Mode shapes ............................................................................................ 86
4.4.2.b Displacement Histories ............................................................................................................ 88
4.4.3 Avalon Building .............................................................................................................................. 89
4.4.3.a Building Period and Mode shapes ............................................................................................ 89
4.4.3.b Displacement Histories ............................................................................................................ 90
iii
4.4.4 Conclusion ....................................................................................................................................... 91
CHAPTER (5): SELECTED EARTHQUAKE SCENARIOS ................................... 92
5.1 Selection Criteria ................................................................................................................................... 92
5.2 Short to Medium Duration Earthquakes with a Series of Fore- and After-shocks ......................... 94
5.3 Long Duration Earthquakes with their After-shocks ...................................................................... 103
5.4 Multiple Earthquakes with their Fore- and After-shocks ............................................................... 109
5.5 Nonlinear Time History Analysis ....................................................................................................... 113
CHAPTER (6): ANALYSIS RESULTS...................................................................... 114
6.1 Displacement Time Histories .............................................................................................................. 115
6.2 Story Displacements ............................................................................................................................ 135
6.3 Development of Plastic Hinges ........................................................................................................... 154
6.4 Hysteretic Behavior ............................................................................................................................. 173
6.5 Ductility Demand ................................................................................................................................. 183
CHAPTER (7): LOW-CYCLE FATIGUE OF REINFORCING BARS ................ 194
7.1 Fatigue Life Relationships .................................................................................................................. 194
7.1.1 Mander et al. (1994) ...................................................................................................................... 195
7.1.2 Brown and Kunnath (2004) ........................................................................................................... 196
7.1.3 Kunnath and Xiao (2009) .............................................................................................................. 196
7.1.4 Hawileh et al. (2010) ..................................................................................................................... 197
7.2 Strain Histories .................................................................................................................................... 197
7.3 Rain-flow Counting Method ............................................................................................................... 198
7.4 Palmgen-Miner Damage Rule ............................................................................................................ 200
7.5 Cumulative Fatigue Damage .............................................................................................................. 200
CHAPTER (8): SUMMARY AND CONCLUSIONS ................................................ 212
8.1 Summary .............................................................................................................................................. 212
8.2 Conclusion ............................................................................................................................................ 213
iv
REFERENCES .............................................................................................................. 216
APPENDIX (A): CODE PROVISIONS (ACI 318-11) .............................................. 223
A.1 Beam Design and Detailing ............................................................................................................. 223
A.2 Column Design and Detailing.......................................................................................................... 225
A.3 Joint Design and Detailing ............................................................................................................... 227
APPENDIX (B): STRUCTURAL DRAWINGS ........................................................ 229
B.1 North Hollywood Building .............................................................................................................. 229
B.2 San Bruno Building.......................................................................................................................... 233
B.3 Avalon Building ............................................................................................................................... 236
APPENDIX (C): RECODED MOTIONS ................................................................... 243
APPENDIX (D): CHECK OF DUCTILE BEHAVIOR ............................................ 246
D.1 San Bruno Building ......................................................................................................................... 246
D.2 Avalon Building............................................................................................................................... 248
v
LIST OF FIGURES
Figure 1.1: The CTV building before and after collapse during 22 February earthquake (Canterbury
Earthquakes Royal Commission, 2012). ......................................................................................................... 5
Figure 1.2: The PGC building before and after collapse on the 22 February earthquake (Canterbury
Earthquakes Royal Commission, 2012). ......................................................................................................... 8
Figure 1.3: Low-cycle fatigue failure, (a) rupture of vertical bars of RC wall, New Zealand (Buchanan et
al., 2011); (b) rupture of the main bars at the extreme end of RC wall, Chile (Naeim et al., 2011). ............... 9
Figure 2.1: Shear failure of a column in the Holiday Inn building during Northridge earthquake, 1994
(Faison et al, 2004). ....................................................................................................................................... 16
Figure 2.2: Failure of a column due to the lack of confinement steel in Olive View Hospital during San
Fernando earthquake, 1971 (Faison et al, 2004)............................................................................................ 17
Figure 2.3: Crushing of concrete core due to failure of the hoops in Imperial County Services building
during Imperial Valley earthquake, 1979 (Faison et al, 2004). ..................................................................... 18
Figure 2.4: Failure mechanisms for RC moment resisting frames (NIST 8-917-1). ..................................... 19
Figure 2.5: Schematic graph of the possible modes of failure for ductile RC frame components during
loading cycles (Dutta, 1998). ........................................................................................................................ 21
Figure 3.1: Location of the 20-story building in North Hollywood (Google Maps, 2013). .......................... 28
Figure 3.2: General view of North Hollywood building (Goel and Chadwell, 2007). .................................. 29
Figure 3.3: Typical transverse section of North Hollywood building (John A. Blume & Associates,
Engineers, 1971). ........................................................................................................................................... 30
Figure 3.4: Typical floor plan of North Hollywood building (John A. Blume & Associates, Engineers,
1971). ............................................................................................................................................................ 31
Figure 3.5: Sensor locations and orientations in North Hollywood building (CSMIP, 2005). ...................... 33
Figure 3.6: Recorded acceleration histories at the basement of North Hollywood building in the transverse
(N-S) direction............................................................................................................................................... 35
Figure 3.7: Displacement histories at the roof of North Hollywood building in the transverse (N-S)
direction. ........................................................................................................................................................ 36
Figure 3.8: Location of the 6-story building in San Bruno (Google Maps, 2013). ........................................ 38
Figure 3.9: General view of San Bruno building (Anderson and Bertero, 1997) .......................................... 39
Figure 3.10: Typical floor plan of San Bruno building (Anderson and Bertero, 1997). ................................ 40
Figure 3.11: Sensor locations and orientations in San Bruno building (CSMIP, 2005). ............................... 41
Figure 3.12: Recorded acceleration history at the ground level of San Bruno building in the longitudinal (N-
S) direction. ................................................................................................................................................... 42
vi
Figure 3.13: Displacement at the roof level of San Bruno building in the longitudinal (N-S) direction. ...... 42
Figure 3.14: Location of the 4-story building in Avalon (Google Maps, 2013). ........................................... 44
Figure 3.15: General view of Avalon building (Uma and Baguley, 2010). ................................................... 44
Figure 3.16: Typical transverse section of Avalon Building (Uma and Baguley, 2010). .............................. 45
Figure 3.17: Typical floor plan of Avalon building (Uma and Baguley, 2010). ........................................... 46
Figure 3.18: Sensor locations for Avalon building (Uma and Baguley, 2010). ............................................ 47
Figure 3.19: Recorded acceleration history at the ground level of Avalon building in the transverse (N-S)
direction. ........................................................................................................................................................ 48
Figure 3.20: Displacement at the roof level of Avalon building in the transverse (N-S) direction. .............. 48
Figure 3.21: Input data in RESPONSE-2000. ............................................................................................... 51
Figure 3.22: Member response output in RESPONSE-2000. ........................................................................ 51
Figure 3.23: Sectional analysis output in RESPONSE-2000. ....................................................................... 52
Figure 4.1: A frame model for nonlinear analysis as recommended by ATC 72-1. ...................................... 65
Figure 4.2: Rigid offsets within a beam-column joint (Pampanin et al., 2003). ............................................ 66
Figure 4.3: A view of the model for North Hollywood building. .................................................................. 67
Figure 4.4: A view of the model for San Bruno building. ............................................................................. 68
Figure 4.5: A view of the model for Avalon building. .................................................................................. 68
Figure 4.6: A typical frame component with lumped plasticity model (PERFORM-3D, User Manual, 2007).
....................................................................................................................................................................... 71
Figure 4.7: The effect of bar-slip on the monotonic moment-rotation relationship for the beam component
of the RC frame model for North Hollywood building. ................................................................................ 73
Figure 4.8: Linearization of the monotonic backbone curve for the beam component of the RC frame model
for North Hollywood building. ...................................................................................................................... 74
Figure 4.9: F-D relationship in PERFORM-3D (PERFORM-3D, User Manual, 2007)................................ 74
Figure 4.10: Difference between monotonic and cyclic backbone curves (ATC 72-1, 2010) ....................... 75
Figure 4.11: The difference between the monotonic and the cyclic backbone curves for the beam
component of the RC frame for North Hollywood building. ........................................................................ 76
Figure 4.12: Control of unloading stiffness in the hysteresis loops (PERFORM-3D, User Manual, 2007). . 77
Figure 4.13: Connection panel zone element (PERFORM-3D, User Manual, 2007). .................................. 78
Figure 4.14: Shear stress vs. Shear strain for the joint model (Unal, 2010). ................................................. 79
Figure 4.15: Mode shapes 1, 2, and 3 for the frame in the transverse direction (T
1
=2.589, T
2
=0.880, and
T
3
=0.524 seconds). ........................................................................................................................................ 81
Figure 4.16: Transfer functions of the recorded earthquakes for North Hollywood building. ...................... 83
Figure 4.17: Comparison between recorded and calculated displacement histories at the roof in the
transverse (N-S) direction of North Hollywood building. ............................................................................. 85
vii
Figure 4.18: Mode shapes 1, 2, and 3 for the frame in the longitudinal direction (T
1
=0.951, T
2
=0.309, and
T
3
=0.173 seconds). ........................................................................................................................................ 86
Figure 4.19: Transfer functions of the Loma-Prieta earthquake for San Bruno building. ............................. 87
Figure 4.20: Comparison between recorded and calculated displacement histories at the roof in the
longitudinal (N-S) direction of San Bruno building. ..................................................................................... 88
Figure 4.21: Mode shapes 1, 2, and 3 for the frame in the transverse direction (T
1
=0.407, T
2
=0.143, and
T
3
=0.079 seconds). ........................................................................................................................................ 89
Figure 4.22: Transfer functions of the Lake Grassmere earthquake for Avalon building. ............................ 89
Figure 4.23: Comparison between recorded and calculated displacement histories at the roof in the
transverse (N-S) direction of Avalon building. ............................................................................................. 91
Figure 5.1: Sequences for short to medium duration earthquakes. ................................................................ 97
Figure 5.2: Spectral Acceleration for short to medium duration earthquakes. ............................................ 100
Figure 5.3: Sequences for long-duration earthquakes. ................................................................................ 105
Figure 5.4: Sequences for long-duration earthquakes (cont’d). ................................................................... 106
Figure 5.5: Spectral Acceleration for long- duration earthquakes. .............................................................. 107
Figure 5.6: Spectral Acceleration for long- duration earthquakes (cont’d). ................................................ 108
Figure 5.7: Locations of the strong motion recording stations near the location of the CTV building
(Canterbury Earthquakes Royal Commission, 2012). ................................................................................. 110
Figure 5.8: Sequences for multiple earthquakes from Christchurch, New Zealand. ................................... 111
Figure 5.9: Spectral Acceleration for multiple earthquakes from Christchurch, New Zealand. .................. 112
Figure 6.1 Displacement histories at the roof level for Cape-Mendocino (1583) scenario. ........................ 117
Figure 6.2: Displacement histories at the roof level for Cape-Mendocino (89156) scenario. ..................... 118
Figure 6.3: Displacement histories at the roof level for Chalflant Valley scenario. .................................... 119
Figure 6.4: Displacement histories at the roof level for Mammoth Lakes scenario. ................................... 120
Figure 6.5: Displacement histories at the roof level for Chi-Chi (TCU079) scenario. ................................ 121
Figure 6.6: Displacement histories at the roof level for Chi-Chi (CHY036) scenario. ............................... 122
Figure 6.7: Displacement histories at the roof level for Kyushu scenario. .................................................. 123
Figure 6.8: Displacement histories at the roof level for Coalinga scenario. ................................................ 124
Figure 6.9: Displacement histories at the roof level for Mexico scenario. .................................................. 125
Figure 6.10: Displacement histories at the roof level for Tohoku (FKS012) scenario. ............................... 126
Figure 6.11: Displacement histories at the roof level for Tohoku (IBR013) scenario. ................................ 127
Figure 6.12: Displacement histories at the roof level for Valparaiso scenario. ........................................... 128
Figure 6.13: Displacement histories at the roof level for Honshu scenario. ................................................ 129
Figure 6.14: Displacement histories at the roof level for Tokachi scenario. ............................................... 130
Figure 6.15: Displacement histories at the roof level for Maule scenario. .................................................. 131
viii
Figure 6.16: Displacement histories at the roof level for Christchurch (CBGS) scenario. .......................... 132
Figure 6.17: Displacement histories at the roof level for Christchurch (RHSC) scenario. .......................... 133
Figure 6.18: Displacement histories at the roof level for Christchurch (TPLC) scenario. .......................... 134
Figure 6.19: Envelopes of lateral displacement for Cape-Mendocino (1583) scenario. .............................. 145
Figure 6.20: Envelopes of lateral displacement for Cape-Mendocino (89156) scenario. ............................ 145
Figure 6.21: Envelopes of lateral displacement for Chalflant Valley scenario. .......................................... 146
Figure 6.22: Envelopes of lateral displacement for Mammoth Lakes scenario. .......................................... 146
Figure 6.23: Envelopes of lateral displacement for Chi-Chi (TCU079) scenario. ...................................... 147
Figure 6.24: Envelopes of lateral displacement for Chi-Chi (CHY036) scenario. ...................................... 147
Figure 6.25: Envelopes of lateral displacement for Kyushu scenario. ........................................................ 148
Figure 6.26: Envelopes of lateral displacement for Coalinga scenario. ...................................................... 148
Figure 6.27: Envelopes of lateral displacement for Mexico scenario. ......................................................... 149
Figure 6.28: Envelopes of lateral displacement for Tohoku (FKS012) scenario. ........................................ 149
Figure 6.29: Envelopes of lateral displacement for Tohoku (IBR013) scenario. ........................................ 150
Figure 6.30: Envelopes of lateral displacement for Valparaiso scenario. .................................................... 150
Figure 6.31: Envelopes of lateral displacement for Honshu scenario. ........................................................ 151
Figure 6.32: Envelopes of lateral displacement for Tokachi scenario. ........................................................ 151
Figure 6.33: Envelopes of lateral displacement for Maule scenario. ........................................................... 152
Figure 6.34: Envelopes of lateral displacement for Christchurch (CBGS) scenario. .................................. 152
Figure 6.35: Envelopes of lateral displacement for Christchurch (RHSC) scenario. .................................. 153
Figure 6.36: Envelopes of lateral displacement for Christchurch (TPLC) scenario. ................................... 153
Figure 6.37: Development of plastic hinges in San Bruno building during Cape-Mendocino (89156)
scenario. ...................................................................................................................................................... 166
Figure 6.38: Development of plastic hinges in San Bruno building during Cape-Mendocino (89156)
scenario. ...................................................................................................................................................... 167
Figure 6.39: Development of plastic hinges in Avalon building during Cape-Mendocino (89156) scenario.
..................................................................................................................................................................... 168
Figure 6.40: Development of plastic hinges in San Bruno building during Christchurch (CBGS) scenario.
..................................................................................................................................................................... 169
Figure 6.41: Comparison between the Sequence Analysis (Train) and the Individual Analysis (Single) for
North Hollywood building during the last after-shock of Tokachi scenario. .............................................. 170
Figure 6.42: Comparison between the Sequence Analysis (Train) and the Individual Analysis (Single) for
San Bruno building during the last after-shock of Valparaiso scenario. ..................................................... 171
Figure 6.43: Comparison between the Sequence Analysis (Train) and the Individual Analysis (Single) for
Avalon building during the last after-shock of Chi-Chi (TCU079) scenario. ............................................. 172
ix
Figure 6.44: Hysteretic behavior at sample beam elements during the first (to the left) and the last (to the
right) ground motions in the Coalinga scenario. ......................................................................................... 175
Figure 6.45: Hysteretic behavior at sample beam elements during the second (to the left) and the third (to
the right) ground motions in the Cape Mendocino (89156) scenario. ......................................................... 176
Figure 6.46: Hysteretic behavior at beam element #115 in North Hollywood building during the first and
the last ground motions of three different scenarios. ................................................................................... 177
Figure 6.47: Hysteretic behavior at beam element #86 in San Bruno building during the first and the last
ground motions of three different scenarios. ............................................................................................... 178
Figure 6.48: Hysteretic behavior at beam element #6 in Avalon building during the first and the last ground
motions of three different scenarios. ........................................................................................................... 179
Figure 6.49: Hysteretic behavior at beam element #109 in North Hollywood building during three ground
motions of the Christchurch (CBGS) scenario. ........................................................................................... 180
Figure 6.50: Hysteretic behavior at beam element #9 in San Bruno building during three ground motions of
the Christchurch (CBGS) scenario. ............................................................................................................. 181
Figure 6.51: Hysteretic behavior at beam element #7 in Avalon building during three ground motions of the
Christchurch (CBGS) scenario. ................................................................................................................... 182
Figure 6.52: Maximum ductility in floor beams for Cape-Mendocino (1583) scenario. ............................. 185
Figure 6.53: Maximum ductility in floor beams for Cape-Mendocino (89156) scenario. ........................... 185
Figure 6.54: Maximum ductility in floor beams for Chalflant Valley scenario. ......................................... 186
Figure 6.55: Maximum ductility in floor beams for Mammoth Lakes scenario. ......................................... 186
Figure 6.56: Maximum ductility in floor beams for Chi-Chi (TCU079) scenario. ..................................... 187
Figure 6.57: Maximum ductility in floor beams for Chi-Chi (CHY036) scenario. ..................................... 187
Figure 6.58: Maximum ductility in floor beams for Kyushu scenario. ....................................................... 188
Figure 6.59: Maximum ductility in floor beams for Coalinga scenario. ..................................................... 188
Figure 6.60: Maximum ductility in floor beams for Mexico scenario. ........................................................ 189
Figure 6.61: Maximum ductility in floor beams for Tohoku (FKS012) scenario. ....................................... 189
Figure 6.62: Maximum ductility in floor beams for Tohoku (IBR013) scenario. ....................................... 190
Figure 6.63: Maximum ductility in floor beams for Valparaiso scenario. ................................................... 190
Figure 6.64: Maximum ductility in floor beams for Honshu scenario. ....................................................... 191
Figure 6.65: Maximum ductility in floor beams for Tokachi scenario. ....................................................... 191
Figure 6.66: Maximum ductility in floor beams for Maule scenario. .......................................................... 192
Figure 6.67: Maximum ductility in floor beams for Christchurch (CBGS) scenario. ................................. 192
Figure 6.68: Maximum ductility in floor beams for Christchurch (RHSC) scenario. ................................. 193
Figure 6.69: Maximum ductility in floor beams for Christchurch (TPLC) scenario. .................................. 193
x
Figure 7.1: Sample strain histories for floor beams in the case study buildings during the Cape-Mendocino
(89156) scenario. ......................................................................................................................................... 199
Figure 7.2: Maximum cumulative fatigue damage for Cape-Mendocino (1583) scenario. ......................... 203
Figure 7.3: Maximum cumulative fatigue damage for Cape-Mendocino (89156) scenario. ....................... 203
Figure 7.4: Maximum cumulative fatigue damage for Chalflant Valley scenario. ...................................... 204
Figure 7.5: Maximum cumulative fatigue damage for Mammoth Lakes scenario. ..................................... 204
Figure 7.6: Maximum cumulative fatigue damage for Chi-Chi (TCU079) scenario. .................................. 205
Figure 7.7: Maximum cumulative fatigue damage for Chi-Chi (CHY036) scenario. ................................. 205
Figure 7.8: Maximum cumulative fatigue damage for Kyushu scenario. .................................................... 206
Figure 7.9: Maximum cumulative fatigue damage for Coalinga scenario. .................................................. 206
Figure 7.10: Maximum cumulative fatigue damage for Mexico scenario. .................................................. 207
Figure 7.11: Maximum cumulative fatigue damage for Tohoku (FKS012) scenario. ................................. 207
Figure 7.12: Maximum cumulative fatigue damage for Tohoku (IBR013) scenario. ................................. 208
Figure 7.13: Maximum cumulative fatigue damage for Valparaiso scenario. ............................................. 208
Figure 7.14: Maximum cumulative fatigue damage for Honshu scenario. .................................................. 209
Figure 7.15: Maximum cumulative fatigue damage for Tokachi scenario. ................................................. 209
Figure 7.16: Maximum cumulative fatigue damage for Maule scenario. .................................................... 210
Figure 7.17: Maximum cumulative fatigue damage for Christchurch (CBGS) scenario. ........................... 210
Figure 7.18: Maximum cumulative fatigue damage for Christchurch (RHSC) scenario. ........................... 211
Figure 7.19: Maximum cumulative fatigue damage for Christchurch (TPLC) scenario. ............................ 211
xi
LIST OF TABLES
Table 3.1: Properties of construction materials of North Hollywood building. ............................................ 32
Table 3.2: Characteristics of recorded ground motions at basement level of North Hollywood building. .... 34
Table 3.3: Section dimensions for the frame in the transverse direction of North Hollywood building. ...... 53
Table 3.4: Beam analysis values. .................................................................................................................. 54
Table 3.5: Beam detailing check. .................................................................................................................. 55
Table 3.6: Column analysis values. ............................................................................................................... 55
Table 3.7: Column detailing check. ............................................................................................................... 56
Table 3.8: Strong column-weak beam check. ................................................................................................ 57
Table 3.9: Joint shear check. ......................................................................................................................... 57
Table 3.10: Section dimensions for the frame in the longitudinal (N-S) direction of San Bruno building. .. 60
Table 4.1: Effective seismic weights and masses for North Hollywood building. ........................................ 70
Table 4.2: Effective seismic weights and masses for San Bruno building. ................................................... 70
Table 4.3: Effective seismic weights and masses for Avalon building. ........................................................ 70
Table 4.4: Joint model parameters for the frame in the transverse (N-S) direction of North Hollywood
building. ........................................................................................................................................................ 80
Table 4.5: Recorded and calculated maximum roof displacements for North Hollywood building. ............ 83
Table 5.1: List of short to medium duration earthquakes with their fore- and after-shocks. ........................ 95
Table 5.2: List of long-duration earthquakes with their after-shocks. ......................................................... 104
Table 5.3: List of multiple earthquake scenarios at selected locations in Christchurch, NZ. ...................... 110
Table 6.1: Roof displacements of North Hollywood building (Short to medium duration). ....................... 136
Table 6.2: Roof displacements of North Hollywood building (Long duration). ......................................... 137
Table 6.3: Roof displacements for North Hollywood building (Christchurch scenarios). .......................... 138
Table 6.4: Roof displacements of San Bruno building (Short to medium duration). .................................. 139
Table 6.5: Roof displacements of San Bruno building (Long duration). ..................................................... 140
Table 6.6: Roof displacements for San Bruno building (Christchurch scenarios). ...................................... 141
Table 6.7: Roof displacements of Avalon building (Short to medium duration). ....................................... 142
Table 6.8: Roof displacements of Avalon building (Long duration). .......................................................... 143
Table 6.9: Roof displacements for Avalon building (Christchurch scenarios). ........................................... 144
Table 6.10: Plastic hinges in North Hollywood building (Short to medium duration). ............................... 157
Table 6.11: Plastic hinges in North Hollywood building (Long duration). ................................................. 158
Table 6.12: Plastic hinges in North Hollywood building (Christchurch scenarios). ................................... 159
Table 6.13: Plastic hinges in San Bruno building (Short to medium duration). .......................................... 160
xii
Table 6.14: Plastic hinges in San Bruno building (Long duration). ............................................................ 161
Table 6.15: Plastic hinges in San Bruno building (Christchurch scenarios). ............................................... 162
Table 6.16: Plastic hinges in Avalon building (Short to medium duration). ............................................... 163
Table 6.17: Plastic hinges in Avalon building (Long duration). ................................................................. 164
Table 6.18: Plastic hinges in Avalon building (Christchurch scenarios). .................................................... 165
xiii
ABSTRACT
Since the ductile RC frame system is one of the most common systems for resisting
lateral loads, it is important to keep improving its design standards in the light of the most
recent earthquakes where incidents of structural failure or collapse were observed.
Therefore, the effect of multiple earthquake scenarios should be examined after the
earthquakes in New Zealand, Chile, and Japan where failure due to damage accumulation
is believed by experts to be one of the major reasons of failure.
Three case study buildings that have ductile RC moment resisting frames were selected in
order to investigate the effect of multiple earthquakes on the structural performance.
These buildings have recorded responses from several earthquakes during their service
lives which were used to calibrate the developed numerical model using PERFORM-3D.
After calibrating the numerical models for the case study buildings, the analysis was
extended by applying selected multiple earthquake scenarios that represent real cases
from all over the world. Eighteen scenarios in three categories were selected then applied
to the numerical models which resulted in different sets of output data.
The output results were in terms of displacement histories, distribution of plastic hinges,
and hysteresis loops at plastic hinges. These results, obtained for the three buildings, were
then used to analyze the structural response in terms of permanent (residual) lateral
displacement and ductility demands which showed the significant effect of the multiple
earthquake scenarios especially during after-shocks.
Finally, an investigation of the low-cycle fatigue behavior of the main reinforcing bars at
the critical locations was performed. The available fatigue life relationships were
presented then used to estimate the number of cycles to failure under specific amplitudes.
Then, the rain-flow counting method was used to calculate the equivalent constant
amplitude cycles of the strain histories obtained from the analysis in order to apply the
Palmgen-Miner rule to estimate the cumulative fatigue damage. It was found that a
significant reduction in the fatigue life is likely to occur due to the longer duration of
multiple earthquake scenarios especially for buildings of shorter fundamental periods.
xiv
ACKNOWLEDGEMENTS
First of all, I would like to thank the University of Southern California (USC) for offering
the Viterbi Doctoral Fellowship to me in 2008 and for the great life experience. Thanks to
all the faculty and staff of the Sonny-Astani Department of Civil and Environmental
Engineering for all the help during my journey at USC.
My appreciation and gratitude goes to my academic advisor Prof. James C. Anderson for
his help, support and guidance during my study for the Ph.D. degree. I would like also to
thank both Prof. L. Carter Wellford and Dr. Anders Carlson for being in my defense
committee and for the valuable comments on my work.
Special thanks to my colleagues and friends, Fabian Rojas and Asghar Amiri for our
discussions about research ideas and their helpful comments. I would like to thank my
brother Islam Mantawy for his help during the preparation of this dissertation and I wish
him the best of luck in his life and the highest success in his study at the University of
Nevada at Reno. I would like also to express my appreciation to my family, especially
my loving parents, for all the encouragement during my life.
Finally, no words can express my deep gratitude to my best friend Wael Elhaddad for all
his help and support during our 12 years of friendship and I wish him the best of luck in
his life.
1
1 CHAPTER (1): INTRODUCTION
Reinforced concrete (RC) frame system is one of the most commonly used structural
systems for buildings in many countries around the world. Moment resisting RC frame
systems are designed to resist both gravity and lateral loads such as wind and earthquake
loads. A significant change in the design provision was made following the San Fernando
earthquake (1971), when many design provisions were introduced to the building codes
for both design and detailing of RC moment frames components. The concepts of
“ductile” and “non-ductile” behavior were introduced based on the lessons learned from
this earthquake where numerous RC frame buildings suffered serious damage, mainly at
the beam-column connections. Intensive research was then conducted to investigate the
behavior of beam-column connections and to identify the main reasons for the damage
that occurred during the earthquake. The RC moment frame systems were classified
based on the structural behavior within the inelastic range due to seismic actions as
“ductile” and “non-ductile”. Ductile moment resisting RC frames are those that develop
plastic hinges at critical locations, without any premature brittle failure when subjected to
earthquake loading.
Considerable changes were made in the design guidelines in order to design safer and
more reliable frames. This was achieved through special requirements for the detailing of
reinforcement in the connection zone to assure ductile behavior. Many aspects were also
considered such as anchorage of longitudinal reinforcement, shear capacity of the
connected elements, and confinement of concrete at critical locations.
Major revisions have been made to the building codes through the years to improve the
guidelines based on the development of engineering research. Parameters like ductility
capacity and dissipated energy associated with seismic loading were studied and
presented in many publications. Therefore, the guidelines to date are based on a long
history of well-established research programs and extensive experimental work.
2
Therefore, it is important to continue developing new guidelines to assure more reliable
behavior.
The basic philosophy of the current design criteria depends on the idea of preventing total
collapse in the case of a severe earthquake, allowing repairable structural damage in the
case of a moderate earthquake, and allowing minimal damage of non-structural elements
in the case of a weak earthquake. This is achieved by designing for the “Maximum
Credible Earthquake” (MCE) which the most expected significant earthquake within a
specific return period based on the seismic zone and the site conditions of the building
area. This criterion ignores the fact that the occurrence of multiple earthquakes during the
service lives of the buildings can lead to the accumulation of structural damage within the
RC members during moderate earthquakes which can lead to catastrophic failure during a
later earthquake that might happen before any upgrade efforts are made.
This research is another step on the road of improving the seismic design of ductile RC
frame buildings and understanding the structural performance in order to make sure that
they can withstand multiple earthquakes in a sustainable manner to reduce both life loss
and economic loss.
1.1 Problem
The community of structural engineers and professionals around the world started to
realize the danger of the phenomenon of multiple earthquakes striking a certain area after
the severe damage and casualties during the most recent earthquakes in Chile, Japan and
New Zealand. The occurrence of multiple earthquakes can happen in the form of one
major earthquake accompanied with a number of fore- and after-shocks as in the case of
the 2010 Maule earthquake in Chile and the 2011 Tohoku earthquake in Japan or in the
form of several earthquakes within a relatively short period of time (from a few weeks to
a few months) as in the case of the 2010-2011 Christchurch earthquake sequence in New
Zealand. There were also prior cases of the occurrence of multiple earthquakes such as
the 1999 Kocaeli and Duzce earthquakes in Turkey (Erdik, 1999) and the 1997 Umberia-
Marche earthquake in Italy (Prete et al., 2005).
3
The occurrence of multiple earthquakes was also observed in the regions of high
seismicity in the United States especially in the State of California but without significant
attention being paid to the phenomenon. For example, the 1994 Northridge earthquake
was followed by several aftershocks but no information is available about any significant
structural damage during the after-shocks. Also, different earthquakes in both Northern
and Southern California had several aftershocks such as the 1992 Cape Mendocino
earthquake and the 1987 Whittier Narrows Earthquake among others.
In this section, two significant effects of the occurrence of multiple earthquakes are
discussed in the light of the observations from the most recent earthquakes in Chile and
New Zealnad. The goal of this discussion is to highlight the main factors that can affect
the structural performance of RC buildings during multiple earthquakes which may lead
to significant damage or collapse.
1.1.1 Damage Accumulation
According to current seismic design philosophies, the designed buildings are supposed to
resist minor earthquakes without damage, moderate earthquakes without significant
structural damage, and in the case of a major earthquake, some structural and non-
structural damage is allowed but without collapse. Numerous earthquakes happen every
year that may not be suddenly destructive but could lead to collapse or severe damage
because of the repetition of several moderate intensity earthquakes. Also, damage from
prior earthquakes shaking may be hidden by partitions and other non-structural features
which may delay the decision of repair or rehabilitation of the building before the next
earthquake.
The most recent evidence on the danger of damage accumulation in existing vulnerable
buildings due to multiple earthquakes is the severe damage that happened in numerous
buildings during New Zealand Earthquakes in late 2010 and early 2011. The city of
Christchurch in New Zealand was subjected to a 7.1 magnitude earthquake in September
2010, then another earthquake of 6.3 magnitude in February, 2011. Despite the fact that
the 2010 earthquake was stronger than the 2011 earthquake and its aftershocks, the
structural and non-structural damage in buildings during the 2011 earthquake was very
4
severe compared to the damage that occurred during the prior 2010 earthquake. The 2011
earthquake affected the society in New Zealand in a very harmful way through
causalities, a huge economic loss, and socio-economic impact in regional communities
and the nation. The main reason of such severe damage is believed to be the damage
accumulation within the elements of the existing structures during the 2010 and the 2011
earthquakes and their aftershocks. Two cases of catastrophic collapse are discussed in the
following sections which are related to the damage accumulation phenomenon.
1.1.1.a Collapse of the Canterbury Television (CTV) building in Christchurch, NZ
A clear example of the danger of damage accumulation within the member of an RC
building is the collapse of the Canterbury Television (CTV) building in Christchurch,
New Zealand during the 22 February, 2011 earthquake which caused the death of 115
persons and serious injuries for many of those who survived. According to a report
prepared by the “Canterbury Earthquakes Royal Commission”, the building is a six story
office building that was constructed in 1986 and had a structural system consisting of
precast concrete beams and columns supporting composite metal deck at each floor level
with RC shear walls to resist lateral loads. The original design of the building was made
by professional engineers who had experience designing similar buildings prior to the
design of this building. The structural design implemented the requirements of the NZS-
4023:1984 “Code of practice for general structural design and design loadings for
buildings” which followed the 1976 code in adopting the ductile behavior for resisting
seismic loads in the design requirements. The design was then checked and approved by
the “City Works and Planning Department” of the Christchurch City Council according
to the Local Government Act at that time and the building permit was issued.
The building withstood the first earthquake on 4 September, 2010 which of a magnitude
of 7.1 on the Richter scale. The building was inspected by a professional team after the
earthquake and they have reported visible cracks in the RC shear walls of almost two
meters length. After the inspection, an assessment was made by the Christchurch City
Council and they declared “No restriction on use or occupancy” of the building which
encouraged the owner to reopen the building before any repair or rehabilitation efforts
5
were made. The building also withstood several aftershocks of magnitude between 4.5
and 4.6 in the following few weeks then another inspection was made leading the City
Council to ask the owner for a repair plan but without any restrictions on the use or the
occupancy of the building.
On 22 February 2011 at 12:51 pm, the building was subjected to an earthquake of
magnitude 6.3 which caused the occupied building to collapse. This resulted in the death
of 115 persons out of 185 that lost their lives during the earthquake. The collapse of the
CTV building is considered a catastrophe. A post collapse investigation was made by
inspecting the debris of the buildings in order to draw conclusions about the cause of
failure of the building. Two photographs of the building that were taken before and after
collapse are shown in (Figure 1.1). The photograph on the left was taken on 5 September,
2010 after the first earthquake while the second photograph was taken after the collapse
of the building on 22 of February, 2011.
Figure 1.1: The CTV building before and after collapse during 22 February earthquake
(Canterbury Earthquakes Royal Commission, 2012).
6
The collapse of this building is believed by experts and professionals to be due to the
damage accumulation within the RC members due to the multiple earthquakes that
affected the building during a period of nearly 6 months between the first earthquake and
the collapse of the building (Mander, 2012) before any rehabilitation efforts were made
by the owner as required by the City Council prior to collapse.
As stated before, all the proper steps were made during all the phases of the building life
starting with a design by an experience professional engineer that complied with the
building code, a check of the design by the City Council which approved it and issued the
building permit, and an inspection after the first earthquake which was made by
professionals from the City Council. The delay in preparing and applying an appropriate
repair and rehabilitation plan was a huge mistake from the owner who wasted time
between the first and the second earthquakes without taking any significant action to
protect the building from a later earthquake. All the codes and regulations were followed
but it didn’t prevent the catastrophe from happening and killing 115 persons.
The case of the CTV building gives a strong indication about the significance of the
damage accumulation phenomenon due to multiple earthquakes with their after-shocks. It
highlights the need for research efforts to be conducted to investigate and study the
damage accumulation phenomenon in RC buildings.
1.1.1.b Collapse of Pyne Gould Corp. (PGC) building in Christchurch, NZ
The Pyne Gould Corp. (PGC) building collapsed during the 22 February earthquake
which resulted in the death of 18 persons and many injured. According to a report titled
“The Performance of Christchurch CBD Buildings: Volume 2” that was prepared by the
Canterbury Earthquakes Royal Commission, the PGC building had five RC floors
supported by gravity columns on the outer perimeter and RC core walls in the center of
the building. The building was designed in 1963 to comply with the structural design
practice at the time, and then the building permit was issued by the City Council and
approved for construction. The pre-1970 seismic design practice in New Zealand didn’t
require any special design or detailing for ductile response so the building was classified
as a “non-ductile” RC building.
7
A study of the structural condition of the building was performed in 1997 by a
professional consultant and it concluded that the building didn’t meet the structural
requirements for modern buildings and it is not expected to perform well during an
upcoming earthquake. The structural members were reported to meet only 30 to 40% of
the design level of the “NZS 4203:1992”. A recommendation was given to upgrade the
building structurally in order to meet the design standards at the time to be able to resist
future earthquakes but there is no available information about any upgrade. Then in 2007,
another study was made that recommended seismic strengthening to be applied to the
building but it didn’t classify it as a seismic hazard according to the policy of the City
Council of 2006.
The building was subjected to a 7.1 magnitude earthquake on 4 September. 2010 which
was almost the same design level specified in the “NZS 1170:2004”. On the following
day, an inspection team performed a rapid visual assessment of the damage where they
found cracks in the RC core walls but they declared “No restriction on use or occupancy”
and recommend a detailed structural assessment to be made. Ten days later, a
professional team investigated the building and identified the building as “Occupiable, no
immediate further investigation required”. By the end of the September 2010, another
inspection was made by the same team and concluded that the building is safe to occupy
and recommended to wait for the aftershocks to stop before starting the repair works. As
aftershocks continued, another team inspected the building after new cracks appeared in
the RC walls and they concluded that the building remained safe to occupy.
The building collapsed during the February earthquake which had a magnitude of 6.3
killing 18 persons who were trapped inside the building. The collapse was analyzed to be
due the failure of the RC core walls on both the east and west sides of the building which
yielded due to vertical tension followed by compression failure of the concrete. The
entire building collapsed in a catastrophic manner as shown in (Figure 1.2). The collapse
of the building was studied by different teams to reach the best conclusion about the main
reasons of the failure of the building and to identify the responsible party in this tragedy.
They concluded that the delay of the repair process after the first earthquake is a major
8
reason for the collapse but they didn’t see an effect of the damage from the first
earthquake on the collapse during the second earthquake.
Figure 1.2: The PGC building before and after collapse on the 22 February earthquake
(Canterbury Earthquakes Royal Commission, 2012).
This point of view of neglecting the effect of the damage prior to the second earthquake
seems to be unrealistic based on similar cases for non-ductile RC buildings that collapsed
or suffered from serious damage in Turkey after both the Koceili and Duzce earthquakes
in 1999 (Erdik, 1999). The cracks that appeared in the RC walls after the first earthquake
might have contributed to the failure of the RC core which was the main lateral resisting
system as per the original design.
1.1.2 Low-Cycle Fatigue
Another evidence on the danger of damage accumulation in RC structures (especially
those due to low-cycle fatigue effect) is the severe damage that happened in numerous
buildings during the Christchurch earthquake series. The 2010 Maule earthquake in Chile
with its aftershocks also had several observations of failure of RC members that is
9
believed to be due to low-cycle fatigue. When considering the large number of loading
cycles induced during the total duration of both earthquake series, there were reports of
damage accumulation such as low-cycle fatigue fracture of reinforcing bar in RC
members which occurred during another earthquake on 13 June, 2011 in Christchurch as
shown in (Figure 1.3a). Also, after the long duration Maule earthquake in Chile on 27
February, 2010 and its aftershocks, certain types of damage were observed repeatedly in
numerous existing buildings inspected by an investigation team of the Los Angeles Tall
Buildings Structural Design Council (Naeim et al., 2011). One of the most observed
failure modes was the rupture of main bars at the extreme ends of RC walls at the
location of failure, particularly when the main bars were bent as shown in (Figure 1.3b).
The investigation team reported that they believe that the tearing of these bars is related
to low-cycle fatigue caused by the numerous cycles of loading and unloading due to the
long duration of the strong ground motion during this earthquake.
a) b)
Figure 1.3: Low-cycle fatigue failure, (a) rupture of vertical bars of RC wall, New
Zealand (Buchanan et al., 2011); (b) rupture of the main bars at the extreme end of RC
wall, Chile (Naeim et al., 2011).
Based on the previous observations, it became obvious that the damage accumulation due
to a relatively small number of loading cycles (low-cycle fatigue) induced by the
occurrence of multiple earthquakes affecting the buildings during their lives could lead to
higher damage potential and a possibility of collapse.
10
Low-cycle fatigue in particular is a critical issue for buildings that may have been
through a number of inelastic cycles, and yet there is no accepted method for its
evaluation. This is a very significant research requirement, taking into account the
observations of performance during these earthquakes. Therefore, a study of the
accumulation of structural damage in RC structures due to low-cycle fatigue behavior of
the main reinforcing bars is required to help structural engineers estimate the extent of
damage suffered by buildings in active seismic regions.
1.2 Objectives
Based on the observations from several cases from previous earthquakes, the cumulative
damage due to small number of loading cycles induced by several earthquakes affecting a
building during its service life could lead to severe damage and the possibility of
collapse. Hence, in order to evaluate the current condition of an existing building or
design a new building against future ground shaking, a study of the structural behavior
under multiple earthquakes and the associated cumulative damage phenomenon is
required to help structural engineers making decisions for design or inspection purposes.
This research aims to study the behavior of ductile RC frame buildings which were
widely used in the US since the mid of the 20
th
century when subjected to multiple
earthquakes such as the case of an earthquake with its fore and after-shocks or a sequence
of separate earthquakes over a relatively long period. Code provisions for designing this
type of system have been updated through the years to overcome any inefficiency based
on the lessons learned from the previous earthquakes. So, this research is another step
toward improving the current seismic design codes to account for strength and stiffness
degradations due to the damage resulting from multiple earthquakes. Current state of
existing buildings should also be evaluated based on their history of earthquakes affecting
them as they could be vulnerable to severe damage during an upcoming earthquake. This
research could help evaluating the existing buildings in order to better estimate the
damage condition which may not be readily apparent to visual inspection. This overall
effect will assure better preparedness of the society for future events.
11
The objectives of this study can be summarized as follows:
1. Understanding the structural performance of ductile RC frames subjected to a
series of multiple earthquakes that could lead to damage accumulation within the
frame components.
2. Investigating the effect of applying different scenarios of multiple earthquakes on
the RC frame buildings with different ground motion characteristics such as peak
ground acceleration, frequency content and duration.
3. Investigating the effect of configuration and fundamental frequency of the RC
frame buildings on the structural performance during multiple earthquakes by
studying three different case study buildings of different heights and fundamental
periods.
4. Investigating the change in the ductility demand of the RC frame due the
accumulation of plastic deformations within the different components of the
frame during multiple earthquakes.
5. Investigating the change in the structural response in terms of displacement
histories and lateral distribution of floor displacements in order to examine the
effect of permanent deformations.
6. Investigating the effect of multiple earthquakes on the distribution of plastic
defamations as well as the development of plastic hinges during the ground
motions after the main shock.
7. Investigating the change in the hysteresis loops at plastic hinges due to the
loading cycles of during multiple earthquakes. The shape of the hysteresis loops
affects the dissipated energy by the building as well as the seismic damage.
8. Investigating the loss in the fatigue life of the main reinforcing steel bars of the
components of the RC frame due to the low-cycle fatigue behavior due to the
increased number of loading cycles during multiple earthquakes.
12
1.3 Dissertation Layout
In addition to this introductory chapter, this dissertation includes the following chapters
where each one is assigned to accomplish a certain task as shown below:
• Chapter (2): Background and Literature Review
This chapter introduces the main concepts for the design of ductile RC frame buildings
and the avoidance of the undesirable brittle failure modes. It discusses the possible modes
of failure for ductile RC frame in order to avoid their influences when the building is
subjected to multiple earthquakes.
Finally, the prior research regarding the effect of multiple earthquakes on the different
structural systems is also presented in this chapter to summarize the findings of the
previous studies which will help the development of the current research.
• Chapter (3): Description of Case Study Buildings
This chapter describes the information about the selected case study buildings based on
the available structural drawings and evaluation reports. The instrumentation layouts of
the buildings are presented as well as the recorded earthquakes during the life-time of
these buildings. Finally, a check of the adequacy of the case study buildings to be
considered as a ductile RC frame is performed using the ACI code formulae and the
section analysis program RESPONSE-2000 (Bentz, 2007).
• Chapter (4): Modeling of Case Study Buildings
This chapter describes the features of the structural analysis software PERFORM-3D
(CSI, 2007) which is used in analyzing the case study buildings under the effects of
multiple earthquakes. A description of the ductile RC frame model in terms of geometry,
stiffness, mass, and damping is also presented. The main parameters used in defining the
inelastic behavior of different components of the frame model are presented such as the
cyclic backbone curve, cyclic degradation, and joint model. Finally, the results of the
analysis of the frame model when subjected to the measured earthquakes are compared to
13
the recorded values in terms of fundamental period, maximum roof displacement, and
displacement history in order to calibrate the frame models.
• Chapter (5): Multiple Earthquake Scenarios
This chapter presents the selected multiple earthquake scenarios which will be applied to
the building model in PERFORM-3D in order to achieve the goals of this study. Three
major categories of earthquake scenario were selected to represent a wide spectrum of
ground motion characteristics.
• Chapter (6): Analysis Results
The results of the analysis are presented in terms of displacement histories, story
displacements, distribution of plastic hinges, hysteretic behavior at plastic hinges, and
ductility demands.
• Chapter (7): Low-cycle Fatigue of Reinforcing Bars
This chapter presents the available fatigue life relationships for reinforcing steel bars.
Then, the strain histories at plastic hinges are calculated using curvature histories
obtained from the analysis in chapter (6). The rain-flow counting method (Matsuishi and
Endo, 1968) and the Palmgen-Miner rule (Miner, 1945) which are used in counting the
cycles and calculating the low-cycle fatigue damage due to multiple earthquakes loading
are presented. Finally, the cumulative fatigue damage at each floor level shown using bar
charts provided at the end of this chapter.
• Chapter (8): Summary and Conclusions
This chapter includes a brief of the whole study followed by conclusions that have been
drawn from the analysis results of the case study buildings.
14
2 CHAPTER (2): BACKGROUND AND LITERATURE
REVIEW
The use of ductile (also known as special) moment resisting frames for concrete
construction in highly seismic zones is common for low and medium rise buildings as all
or part of their lateral force-resisting systems. The frame components (beams, columns,
and beam-column joints) are proportioned, designed, and detailed to resist the straining
actions that result from the loading reversals due to earthquake shaking in the form of
flexure, shear and axial forces. In order to achieve the required ductile response of the RC
frame under earthquake loading, special proportioning and detailing requirements are
required to avoid significant loss of stiffness and strength for the RC members. Ductile
RC moment-resisting frames are also named as “Special Moment Frames” as they need
special detailing requirements to enhance their resistance in comparison with the regular
RC frame construction which is known as “Ordinary Moment Frames”. A ductile
moment frame system enables the building to safely undergo the extensive inelastic
deformations which are expected in these high seismic regions.
The design concepts of RC ductile moment frames were first presented in the U.S. in
1961 by Blume, Newmark, and Cornin. The use of the ductile frame design in the early
1960’s was at the responsibility of the designer while it was first introduced in the
Uniform Building Code in 1970. It was not until 1973 that the Uniform Building Code
(ICBO, 1973) first mandated the use of the ductile frame details in high seismicity
regions. Also, detailing requirements were introduced for ductile RC frames which are
very close of those of current codes of practice. After the San Fernando earthquake in
1971, most of the RC frame buildings were designed and constructed as ductile (special)
moment frame systems.
The ductile RC frame systems have also been used for mixed construction with other
structural systems within the same building. One of these mixed designs was to use the
ductile RC frames with a gravity framing system which is a very common solution to
15
enhance the behavior. Some of the gravity-only frames behaved poorly during the
Northridge earthquake in 1994. This led to more strict changes in the detailing
requirements for the gravity-only frames in order to overcome the deficiency that caused
the damage during the Northridge earthquake. Ductile frames are also combined with RC
walls or braced frames in dual systems which enhance the response of the building
system during earthquake loading.
2.1 Design Concepts
The design and detailing of RC moment frames for buildings in high seismicity regions
should ensure that inelastic response under earthquake loading is ductile. The design
principles are formulated on an expected strength basis using the probable strength of the
construction materials. Members are designed to resist the design seismic forces and
gravity loads and, in addition, are required to resist forces generated by the probable
flexural strength of a member after strain hardening effects occur in the reinforcement.
Ductile RC moment frames are detailed to prevent anchorage failure prior to the
formation of plastic hinges within different frame members in order to ensure absorption
of seismic forces at large inelastic displacements without impairment of the structural
integrity. Also, a ductile moment frame should be expected to sustain multiple cycles of
inelastic response for the design-level earthquake motion. The design and detailing of
ductile RC frame should achieve the following goals:
2.1.1 Avoiding Shear Failure
The ductile response requires the prevention of brittle shear failure in order to have the
members yield in flexure. Brittle shear failure in columns can lead to rapid loss of lateral
strength and axial load-carrying capacity of the entire floor level. During past
earthquakes, column shear failure was one of the most frequent causes of concrete
building failures as shown in (Figure 2.1) for the Holiday Inn building during the
Northridge earthquake in 1994. Also for beams, shear failure should be avoided prior to
the formation of plastic hinges in order to ensure energy absorption during earthquakes.
16
Figure 2.1: Shear failure of a column in the Holiday Inn building during Northridge
earthquake, 1994 (Faison et al, 2004).
Using the capacity-design approach, potential flexural yielding regions are identified
(usually at ends of beams and columns), then designed for code-required moment
strengths. The design shears are calculated based on equilibrium assuming the flexural
yielding regions develop probable moment strengths. The calculation of the probable
moment strength should consider all the factors (such as strain hardening of the
reinforcing steel) that produce a higher estimate of the moment strength of the cross
section.
2.1.2 Avoid Anchorage Failure
Detailing of different RC frame member for ductile behavior is based on the following
concepts:
17
2.1.2.a Confinement for heavily loaded sections:
The maximum compressive strain for unconfined concrete is around 0.003 in/in which
limits the deformability of RC frame members especially in regions where plastic hinges
are expected and this can lead to limited ductility of the entire frame. Strain capacity can
be increased significantly by applying confining lateral pressure to the concrete using
reinforcing spirals or closed hoops. The hoops act to limit the volumetric change of the
core concrete when loaded in compression or flexure, and this confining pressure leads to
a significant increase in strength and enhanced strain capacity.
The hoops should be provided at the expected locations of plastic hinges which are
typically the ends of columns and beams. The lack of confinement steel was one of the
main reasons for damage to RC frame building during past earthquakes as shown in
(Figure 2.2) for the Olive View Hospital during San Fernando earthquake, 1971.
Figure 2.2: Failure of a column due to the lack of confinement steel in Olive View
Hospital during San Fernando earthquake, 1971 (Faison et al, 2004).
18
Effective hoops must enclose the concrete core of the concrete member except for the
concrete cover. The hoops must be closed by 135° hooks embedded in the core concrete
in order to prevent the hoops from opening if the concrete cover spalls off which will lead
to the loss of the confining pressure provided by the hoop and the concrete core will start
to dilate. The dilation of concrete will lead to the loss of the axial capacity which will be
followed by failure as shown in (Figure 2.3) for Imperial County Services building during
Imperial Valley earthquake, 1979. The spacing of the hoops along the length of the RC
member should be close enough in order to confine the concrete core and restrain
buckling of longitudinal reinforcement. Inadequate confinement steel can cause the
longitudinal steel to buckle under the axial loading and the resulting unconfined concrete
core to crush under the axial, flexural and shear forces.
Figure 2.3: Crushing of concrete core due to failure of the hoops in Imperial County
Services building during Imperial Valley earthquake, 1979 (Faison et al, 2004).
2.1.2.b Avoidance of anchorage or splice failure
Strong ground motions can cause spalling of the concrete cover, which will affect
development and lap-splice strength of longitudinal reinforcement. If lap splices are used
in an RC member, they must be located away from the ends of the members (beams and
columns) where maximum moments are expected. Also, closed hoops must be used
19
within the splice length to confine the splice in case of cover spalling. Code requirements
restrict beam bar sizes in order to reduce the bond stress within the beam-column joints.
Hooks should be used for longitudinal bars anchored in exterior joints in order to develop
yield strength at the far side of the joint.
2.1.3 Strong Column-Weak Beam
The lateral drift of a building during an earthquake affects the distribution of plastic
hinges over the height. If the columns of the buildings are weaker than the floor beams,
the drift could be localized in a few floor levels (Figure 2.4a) which can lead to failure of
all columns in these floors when the drift capacity is exceeded. On the other hand, strong
columns provide a uniform distribution of the drift over the building height (Figure 2.4c),
and reduce the possibility of localized damage. The failure of columns has more
dangerous effects on the buildings that can lead to complete collapse of the building as
these columns support the gravity load from all the floors above them while beams
support only the gravity loads from a certain floor.
Therefore, current code provisions adopt the concept of strong column-weak beam in
order to assure ductile behavior of the RC frame systems during strong ground motions.
This can be achieved by requiring that the sum of columns flexural capacities exceed the
sum of those for the beams at each frame connection of a special moment frame. An
intermediate mechanism (Figure 2.4b) is less desirable and it requires proper detailing to
avoid failure of the columns (NIST 8-917-1).
Figure 2.4: Failure mechanisms for RC moment resisting frames (NIST 8-917-1).
20
2.2 Other Failure Modes
The previously described failure modes were avoided by improving the seismic design
requirements through extensive research efforts. The ACI-318-11introduces the most
updated design requirements for ductile (Special) RC moment resisting frames as given
in “Chapter 21” of the code. This chapter provides the necessary design procedure and
detailing techniques to ensure ductile response of the frame components (beam, columns
and joints). The code formulae for the design of ductile (special) moment frames are
presented in Appendix (A).
The success of an RC frame design relies on providing ductile response at plastic hinge
locations by allowing some inelastic flexural deformations. These inelastic deformations
are the primary source of energy dissipation within the frame which requires a proper
care in detailing the locations where plastic hinges are expected to occur. This should
ensure the avoidance of failure modes such as shear failure within the plastic hinge
region, concrete failure due to lack of confinement, anchorage failure within the
connection, and join shear failure. The code provisions should ensure that these failure
modes that caused damage to many RC building during past earthquakes will not occur
during minor earthquakes of relatively frequent occurrence. For earthquakes of moderate
strength, the ductile response of the building will be utilized but with limited permanent
deformation that is generally considered acceptable while for strong earthquakes, large
inelastic defamations are permitted but without collapse.
Although, the fact that designing an RC frame for ductile response mostly prevents brittle
failure of happening doesn’t eliminate the other sources of failure that could occur to
different components of the frame. In order to avoid the reaming causes that could lead to
failure of the elements of a ductile RC frame, a proper understanding of the different
potential modes of failure is necessary for better design and detailing.
Based on experimental studies and observations from recent earthquakes, it was found
that the most critical locations of a ductile RC frame are the beam-column joints and their
vicinities. The possible modes of failure for frame joints are:
21
a) Low-cycle fatigue failure of longitudinal reinforcement.
b) Fracture of Transverse Reinforcement which could lead to confinement and
anchorage failures.
c) Failure of confined concrete due to compression bucking of reinforcing bars.
Modes (b) and (c) depend mainly on the amount and the spacing of the transverse
reinforcement while mode (a) is unavoidable and could suddenly happen after a certain
number of loading cycles as shown (Figure 2.5). The study of these three modes of
failure is crucial in order to prevent catastrophic structural failure through premature
failure of plastic hinge regions.
Figure 2.5: Schematic graph of the possible modes of failure for ductile RC frame
components during loading cycles (Dutta, 1998).
22
2.3 Prior Research on Structural Performance during Multiple
Earthquakes
The effect of cumulative damage on the seismic response of structures has been
investigated by many researchers following the Northridge earthquake in 1994 but
mainly for moment resisting steel frame buildings due to low-cycle fatigue damage(NIST
9-917-3). For reinforced concrete structures, only few analytical models were developed
for evaluating the extent of damage in RC elements due to seismic actions.
Few experimental programs were conducted to study the damage accumulation
phenomenon in different RC members. El Bahy et al. (1999) conducted an experimental
program to investigate the cumulative damage of RC structures under seismic actions
which studied the behavior of RC bridge columns under both constant and variable
amplitude lateral displacements. The constant amplitude tests were used to develop a
fatigue-based damage model which was used in comparison with variable amplitude test
to evaluate its reliability in estimating the damage extent. The variable amplitude cycles
were selected to represent different cases of multiple earthquakes with different
scenarios.
Erberik et al. (2004) followed the same process developed by El Bahy et al. by applying
both constant and variable amplitude loading on RC moment frame joints in order to
develop a damage model. Researchers developed a two-parameter energy-based model
which was used to estimate the damage of joints tested under variable amplitude loading.
The proposed model depends on the number and the amplitudes of the loading cycles
affecting the RC joint. They also recommended additional experiments to be conducted
in order to account for the axial force level, confinement level within the joint, and the
anchorage of the flexural reinforcement.
Other studies were performed by several research teams which investigated the behavior
of different structures using analytical models of SDOF systems under the effect of
multiple earthquakes such as Mahin (1980), Ascheim et al. (1999), Amadio et al. (2003),
Iancovici (2007), Oyazo-Vera et al. (2008), Hatzigeortgiou (2010), Moustafa et al.
(2010), and Goda (2012).
23
Another approach was followed by a set of research teams by developing representative
numerical models for different types of structures and studying their response under
multiple earthquakes using both artificial and real earthquakes sequences. Each research
team focused on a certain type of structures or a certain aspect of the structural response
by highlighting specific response parameters.
Anderson and Bertero (1997) studied the behavior of three steel frame buildings under
both the 1992 Landers and Big Bear earthquakes which affected Southern California
within three hours. They analyzed 2-story, 6-story, and 17-story steel frame buildings that
were subject to both earthquakes to both earthquakes. They concluded that multiple
strong ground motions can lead to excessive inelastic deformations especially if the first
ground motion is strong enough to drive the structure into the inelastic range. The second
earthquake could lead to accumulation in the plastic energy as well as increase in the
ductility demands.
Lee (2004) studied the damage potential of RC bridge piers due to multiple earthquakes
using numerical analysis of five span bridge models that was subjected to different
loading scenarios. The research concluded that the maximum displacement and the
ductility demands of the RC bridge piers are larger for the case of multiple earthquakes
than the case of a single earthquake. It also expected deterioration in the stiffness of the
bridge structure due the large number of cycles during multiple earthquakes. The damage
potential was addressed to be affected by the ground motion characteristics.
Li et al. (2007) studied the performance of steel frame buildings when subjected to main
and after-shock earthquake sequences in order to estimate the level of structural damage
with the steel frame components. The researchers performed analyses on the 9-story and
the 20-story SAC buildings (FEMA-355/SAC) that were subject to scenarios of two
back-to-back identical earthquakes and other scenarios of main and aftershock of related
magnitudes according to Sunasaka and Kiremidjian (1993). No change in the damage
pattern was observed in the case of using two identical earthquakes while for the case of
using main and aftershock the damage pattern was different according to the
characteristics of the after-shock. It was concluded that the damage due to the after-shock
24
is expected to be small if the damage due to the main shock was small. It was also
concluded that the case of identical earthquakes leads to larger inter-story drift values.
The research proposed simple probabilistic tools to estimate the damage within the steel
elements of the building.
Hatzigeorgiou et al (2010) studied two sets of representative RC frames where the frames
in the first set were designed according to the seismic provisions of Eurocode-8 while the
frames in the second set were designed for gravity loads only. Each set includes four
frames of different heights and configurations. These two sets were subjected to five
earthquake scenarios using recorded accelerations at the same station in the same
direction which were normalized to have maximum peak ground acceleration (PGA) of
0.2g for the strongest earthquake in the scenario. The researchers concluded that the RC
frames experience larger later displacements and higher ductility demands at plastic
hinges. A simple empirical formula was developed to estimate the cumulative damage
under multiple earthquake sequence.
Adiyanto et al. (2011) studied the behavior of two representative models for 3-story and
18-story RC frame buildings using nonlinear time history analysis. The researchers
investigated three cases of multiple earthquake scenarios using a main shock only and a
main shock followed by an after-shock then a fore-shock with the main and after-shock.
The earthquakes records where scaled using the response spectrum of the Eurocode-8
resulting 20 loading scenarios. It was concluded that the structural behavior was not
affected by the loading scenarios neither single earthquake nor multiple earthquakes but it
was recommended to account for multiple earthquakes as they can lead to larger inter-
story drift values.
Wang et al (2011) analyzed the damage accumulation of an representative 12-story RC
frame building when subjected to a main and aftershock in terms of inter-story drifts and
development of damage. The same earthquake was used as the after-shock with a reduced
intensity based on the expected correlation between the characteristics of the main and
after-shocks. It was concluded that the second shock could cause damage and increase
inter-story drift which depends on the input ground motions.
25
Reghunandan et al. (2012) conducted research efforts for the assessment of main shock
damaged buildings using a numerical model of an artificial 4-story RC frame that was
designed to represent a typical pre-1970s non-ductile RC building in New Zealand. The
model was analyzed under 30 earthquake sequences from California earthquakes with un-
scaled PGA between 0.04 to 0.63g. The researcher developed fragility curves for the RC
frame model then concluded that buildings that suffer from moderate damage during a
main shock are expected to have the same collapse capacity as the undamaged buildings.
On the other hand, the buildings that suffered from severe damage should be “red tagged”
as the resistance to subsequent earthquakes is significantly decreased.
Huang et al. (2012) analyzed an representative 4-story RC frame which was designed
according to the “Code for Seismic Design of Buildings in China” (GB50011-2010)
under both a single main shock and a sequence of a main shock and different after-shocks
with scaled PGA varying between 0.1 and 0.5g. This research concluded that damage
state of a building depends on the damage history from prior earthquakes. It was also
concluded that there is a correlation between the damage state of the building and the
PGA of the after-shock.
Abdelnaby (2012) used numerical models to analyze a representative 3-story RC frame
which was designed three times with different design approaches. The building was
designed as a gravity frame, as a moment frame using the direct design approach to resist
the ASCE-07 equivalent static seismic forces, and as moment frame using capacity
design approach where the strong column-weak beam concept was included. These three
frames were analyzed under multiple earthquakes of three main categories, replicate
scenarios, a random earthquake scenarios, and real earthquake scenarios. The research
concluded that the damage from prior earthquakes have a significant effect on the
performance of the RC buildings under a subsequent earthquake. It was also concluded
that RC frames that were designed using the capacity design approach behave better than
those frames designed using gravity or direct design approaches.
Based on this review, further research efforts are needed in order to help establishing a
clear methodology to estimate the cumulative damage and characterize the structural
26
behavior of different structural system. Research is needed to address the effects of
multiple earthquakes on ductile RC frame buildings as for the case of an earthquake with
its fore and after-shocks. Initial damage due to first shock may be hard to identify in an
actual building as it may be covered by non-structural components which could increase
the damage when subjected to the following shocks So, this study is intended to help
understanding the behavior and the mechanism of cumulative damage in ductile RC
moment resisting frame systems.
27
3 CHAPTER (3): DESCRIPTION OF CASE STUDY
BUILDINGS
The ultimate objective of this research is to examine the inelastic response of ductile
reinforced concrete (RC) moment resisting frame buildings when they are subjected to
multiple earthquakes during their lives. Three existing ductile RC moment resisting frame
building were selected for investigation. Two of the case study buildings are located in
California and one is located in New Zealand and all of them have experienced several
earthquakes during since their construction. The RC buildings have 20-story, 6-story in
height and 4-story RC moment resisting frames in both directions with a regular and
nearly symmetric configuration. The original designs of these buildings were performed
to satisfy the seismic requirements of the code of practice at the time of construction.
Structural drawings, material properties, and loading conditions are available for use in
this study for these buildings.
This chapter presents the description, instrumentation, recorded motions, and the
observed damage after the major seismic events during the lives of the three buildings.
Also, a study of the moment resisting RC frames in the selected directions is performed
in order to check its adequacy for ductile behavior according to the seismic requirements
of the current ACI code. The Modified Compression Field Theory (MCFT) was used for
the section analysis using the software RESPONSE-2000 in order to evaluate the
capacities of each RC member in the frame. This goal of this study is to prove that these
buildings are capable of achieving the required ductile response during earthquakes.
3.1 North Hollywood Building (20-Story)
3.1.1 Building Description
This building is a hotel that is located in the North Hollywood area of Los Angeles,
California. This area lies at the southeast end of the San Fernando Valley near the eastern
terminus of the Santa Monica Mountains in Southern California as shown in (Figure 3.1).
28
Figure 3.1: Location of the 20-story building in North Hollywood (Google Maps, 2013).
Unlike most of the pre-1970 RC buildings which were designed as non-ductile frame
systems; this building was designed in 1966 as an RC ductile moment-resisting frame
structure meeting the requirements of Division 26 (Concrete) of the Los Angeles City
Building Code as amended November 7, 1966. Seismic provisions of this code
approximate the 1970 UBC which was the pioneer document introducing the ductile
frame design. It consists of 20 stories and one basement and its construction was
completed in 1968. Plan dimensions of the central tower portion, which runs from the
fourth floor to the roof, are typically 183 feet 6 inches long by 57 feet 10 inches wide. At
the third-floor level, the width becomes 96 feet 4 inches and the length extends to 198
feet 7 inches. A general view of the building is shown in (Figure 3.2).
29
Figure 3.2: General view of North Hollywood building (Goel and Chadwell, 2007).
The floor system carrying gravity loads consists of 4.5 to 6 inches thick two way RC
slabs supported by concrete beams, girders and columns. Typical framing consists of
columns spaced at about 19 feet on center in the transverse direction and at 13 feet on
center in the longitudinal direction, with interconnecting floor girders in each direction.
A reinforced concrete moment-resisting frame resists lateral forces in each direction
except at the basement level where 12-inch thick RC walls are employed. A typical
section showing the geometry of the RC frame in the transverse (N-S) direction is shown
in (Figure 3.3) and a plan of the typical floor is shown in (Figure 3.4). The foundation
system consists of spread footings below columns. Drawings of the building layout,
sections, and connection details are provided in Appendix (B).
The building was constructed mostly with lightweight aggregate concrete which was used
for all floors above the ground-floor level. Properties of the various materials used in the
construction are given in (Table 3.1).
30
Figure 3.3: Typical transverse section of North Hollywood building (John A. Blume &
Associates, Engineers, 1971).
31
Figure 3.4: Typical floor plan of North Hollywood building (John A. Blume &
Associates, Engineers, 1971).
32
Important design information for the structural system includes the following:
• The total building height is 193 feet and 8 inches with a ground story height of 14
feet, a second story height of 17 feet, and a typical story height of 8 feet and 9
inches.
• The plan dimensions of the central tower building are 57 feet and 10 inches (N-S
direction) by 183 feet and 6 inches (E-W direction).
• The typical non-prismatic exterior columns are 18” x 20” at the top and the
bottom of each story to 15” x 20” at mid-story height and oriented with the weak
axis parallel to the longitudinal direction of the building.
• The interior columns are 20” x 20” from the ground floor to the 10
th
floor level,
and 18” x 20” in the remaining floors.
• The typical dimensions of all beams in the transverse direction are 18 inches deep
by 12 inches wide.
• The typical slab thickness is 4.5 inches in the guest rooms and 6.0 inches thick in
corridors.
Table 3.1: Properties of construction materials of North Hollywood building.
Material Elements
Unit Weight
(pcf)
Strength
(ksi)
E (ksi)
Concrete
All elements, basement to ground floor 150 3.00 3,300
Columns, ground floor to 10th floor 110 4.00 2,400
Columns, 10th floor to roof 110 3.00 2,100
Beams and slabs, ground to roof 110 3.00 2,100
Steel
All elements, except columns A-305 40 29,000
Columns, foundations to 10th floor A-432 60 29,000
Columns, 10th floor to roof A-15 40 29,000
3.1.2 Building Instrumentation
The building was instrumented with three sets of accelerometers producing nine channels
of data prior to the 1971 San Fernando earthquake. The location of each set was at roof,
33
11
th
floor, and basement levels. This instrumentation was upgraded and expanded to
sixteen channels of data in 1983 as part of the California Strong Motion Instrumentation
Program (CSMIP). The accelerometers in the building measure both principal horizontal
accelerations at the basement level, 3
rd
floor, 9
th
floor, 16
th
floor, and roof levels; and
vertical acceleration at the basement as shown in (Figure 3.5).
The acceleration data from the 1971 San Fernando, 1987 Whittier Narrows and the 1994
Northridge earthquakes were recorded. The characteristics of the recorded acceleration
data at basement level for these earthquakes are given in (Table 3.2).
Figure 3.5: Sensor locations and orientations in North Hollywood building (CSMIP,
2005).
34
Table 3.2: Characteristics of recorded ground motions at basement level of North
Hollywood building.
Event Year Magnitude
PGA (g) PGA (g) PGA (g)
N-S E-W Vertical
San Fernando 1971 6.6 0.175 0.165 0.087
Whittier 1987 5.9 0.100 0.083 0.072
Northridge 1994 6.7 0.317 0.113 0.128
The recorded response for these three earthquakes will be used to calibrate the building
model through nonlinear time history analysis as it will be discussed in chapter (4).
3.1.3 Recorded Motions
The available data for the recorded earthquakes are given in acceleration histories for
each sensor then velocity and displacement histories were obtain after processing the
recorded data. The moment resisting RC frame in the transverse (N-S) direction is
considered for the analysis therefore; the records from sensors 1 to 9 and sensor 16 are
the only ones to be considered.
The corrected acceleration histories for the three earthquakes in the transverse (N-S)
direction at the basement level are presented in (Figure 3.6). These records at the
basement will be used as the input for the numerical model of the RC frame in the
transverse direction later in this study. The results of the numerical model in the form of
displacement histories will be compared with the recorded histories at the corresponding
floor levels in order to calibrate the numerical model of the RC frame. The displacement
histories obtained from sensor number (2) which is located at the roof level recording the
motion in the (N-S) direction are shown in (Figure 3.7) for the three earthquakes.
All the available data in terms of displacements in the transverse (N-S) direction at each
floor for all earthquakes is presented in Appendix (C).
35
Figure 3.6: Recorded acceleration histories at the basement of North Hollywood building
in the transverse (N-S) direction.
36
Figure 3.7: Displacement histories at the roof of North Hollywood building in the
transverse (N-S) direction.
3.1.4 Earthquake Damage
As mentioned before, the building was subjected to three earthquakes during its 44 years
service life. Among these earthquakes, the San Fernando 1971 and Northridge 1994
earthquakes were the most significant events. Experts had examined the building after
both earthquakes and a number of reports were provided to describe the state of damage
that could have happened to both structural and non-structural elements.
According to the investigation performed by John A. Blume & Associates, Engineers
after the San Fernando earthquake in 1971, the building didn't suffer any significant
structural damage and it was believed that the beams and the columns of the lateral
37
resisting RC frame behaved elastically during the earthquake. The building suffered only
minor damage to non-structural elements such as cracking of the plaster walls, cracking
in partitions and diagonal cracks from the upper corners of the doors to the ceiling.
Another investigation was performed following the Northridge earthquake in 1994 by
John A. Martin, Assoc. which reported that the building suffered heavy non-structural
and content damage with no sign of significant structural damage (Naeim, 1997).
Nonstructural damage varied from damage to partitions, doors, bathroom fixtures and
tiles, and chandeliers.
Then, these observations show that the building would be keeping almost the same
properties of different structural elements (stiffness, strength … etc) during its lifetime
without experiencing significant plastic deformations or residual stresses.
3.2 San Bruno Building (6-Story)
3.2.1 Building Description
This is an office building located in the San Bruno Area of San Mateo, California. This
area lies between the San Francisco Bay and the foothills of the Santa Cruz Mountains in
Northern California as shown in (Figure 3.8).
The building consists of 6 stories and was built in 1978 with ductile RC moment resisting
frames in both directions according to the seismic code requirements after the San
Fernando earthquake in 1971. The building has a rectangular plan which is 89 feet by 201
feet. A general view of the building is shown in (Figure 3.9).
The floor system carrying gravity loads consists of 5.5 to 6.75 inches thick one way RC
slabs supported by precast concrete girders and columns. Typical framing consists of four
RC ductile RC frames located on the perimeter with columns spaced at 16 feet. Another
transverse frame is located near the center of the building with and offset from the
centerline by 16 feet (one bay) in the longitudinal direction. Two frames are resisting
lateral forces in the longitudinal (N-S) direction while three frames are resisting lateral
forces in the transverse (E-W) direction. A line of gravity columns is located at the center
of the building in the transverse direction to support the precast girders. A plan of a
38
typical floor is shown in (Figure 3.10). The foundation system consists of spread footings
for the columns of the moment frames connected by heavy grade beams. The available
drawings and details of the building are provided in Appendix (B).
Light weight concrete was used for the RC members with strength of 5000 psi and the
reinforcing steel is Grade 60.
Figure 3.8: Location of the 6-story building in San Bruno (Google Maps, 2013).
39
Figure 3.9: General view of San Bruno building (Anderson and Bertero, 1997)
Important design information for the structural system includes the following:
• The total building height is 76 feet and 6 inches with a ground story height of 14
feet and a typical story height of 12 feet and 6 inches.
• The plan dimensions of the building are 89 feet in the transverse direction (E-W
direction) and 201 feet in the longitudinal direction (N-S direction).
• The typical exterior columns are 23”x24.5” on the perimeter except the columns
at the intersections of axes (A) and (F) with axis (8) which are 22”x24”. Two
columns are located at each corner of the building which are 23”x26” and are
connected by nonstructural precast shells.
• The typical beam dimensions are 29 inches deep by 22 inches wide except for the
first floor where the typical beam depth is 30 inches.
• The typical slab thickness is 5.5 inches except the two end bays at each side of the
building where the slab is varying from 5.5 to 6.75 inches.
40
•
Figure 3.10: Typical floor plan of San Bruno building (Anderson and Bertero, 1997).
41
3.2.2 Instrumentation
This building was instrumented with 13 strong motion sensors as part of the California
Strong Motion Instrumentation Program (CSMIP). The accelerometers in the building
measure both principle horizontal accelerations at ground floor, second floor, fourth
floor, and roof levels and one accelerometer measures the vertical acceleration at the
ground floor level as shown in (Figure 3.11).
The acceleration data from the 1989 Loma-Prieta Earthquake which had a magnitude of
7.0 was recorded. The records indicated peak values of 0.14g for horizontal accelerations
and 0.12g for vertical accelerations.
Figure 3.11: Sensor locations and orientations in San Bruno building (CSMIP, 2005).
42
3.2.3 Recorded Motions
The available data from the CSMIP database for the building during the Loma-Prieta
earthquake is given in acceleration, velocity and displacement histories for each sensor.
The moment resisting RC frame in the longitudinal direction (N-S direction) is
considered for the analysis therefore; the records from sensors 10 to 13 are the only ones
to be considered.
The corrected acceleration history for the 1989 Loma-Prieta earthquake in the
longitudinal (N-S) direction at the ground level is presented in (Figure 3.12) which will
be used as the input for the numerical model of the RC frame later in this study. The
displacement history obtained from processing the measured acceleration by sensor (10)
which is located at the roof level is shown in (Figure 3.13).
All the available data in terms of displacements in the longitudinal (N-S) direction at each
floor for all earthquakes is presented in Appendix (C).
Figure 3.12: Recorded acceleration history at the ground level of San Bruno building in
the longitudinal (N-S) direction.
Figure 3.13: Displacement at the roof level of San Bruno building in the longitudinal (N-
S) direction.
43
3.2.4 Earthquake Damage
The building was subjected to the Loma-Prieta earthquake which was the most significant
recorded ground motion during the lifetime of the building. The building was initially
inspected after the earthquake where no visible damage was observed. A later detailed
inspection was performed which showed cracking in the precast shells of the exterior
columns at the ground floor level. The beams and the girders of the RC frames were
inspected at a few locations by removing parts of the hung ceiling where cracking were
observed which is believed to be due the inelastic response during the earthquake.
3.3 Avalon Building (4-Story)
3.3.1 Building Description
This building is a part of the GNS Science complex which is located in the Avalon area
of Lower Hutt in New Zealand. This area lies in the Wellington region of the Northern
Island of New Zealand near the Hutt Valley and the eastern shores of the Wellington
harbor as shown in (Figure 3.14).
The GNS Science complex was constructed prior to 1976 and consists of several units;
two of which are RC frame buildings. The building under consideration is (Unit-2)
consists of 3 floors and one basement and has a rectangular plan of 186 feet 8 inches
length by 40 feet width. A general view of the building is shown in (Figure 3.15).
The floor system carrying gravity loads consists of 5 inches thick two way RC slabs
supported by concrete beams, girders and columns except for the roof where the
perimeter columns were extended to carry a steel joist spanning over the whole width of
the building. Typical framing consists of columns spaced at 17 feet 6 inches and 22 feet 6
inches in the transverse direction and at 26 feet 8 inches in the longitudinal direction with
interconnecting floor beams and girders in each direction except for the roof. A typical
transverse section showing the geometry of the RC frame in the transverse (N-S)
direction is shown in (Figure 3.16) and a plan of the typical floor is shown in (Figure
3.17). The foundation system consists of isolated footings below columns. Drawings of
the building layout, sections, and connection details are provided in Appendix (B).
44
Figure 3.14: Location of the 4-story building in Avalon (Google Maps, 2013).
Figure 3.15: General view of Avalon building (Uma and Baguley, 2010).
45
The properties of the construction materials are not provided in the available structural
drawings. It was assumed that the building was constructed using normal weight concrete
of strength 5000 psi and reinforcing steel of Grade 60.
Important design information for the structural system includes the following:
• The total building height is 44 feet with a basement story height of 9 feet 6 inches
and a typical story height of 11 feet 6 inches.
• The plan dimensions of the building are 40 feet in the transverse direction (N-S
direction) and 186 feet 8 inches in the longitudinal direction (E-W direction).
• All exterior columns are 24”x24” from the basement to the roof floor. The interior
columns are 24”x24” from the basement to the second floor.
• The typical dimensions for all the interior beams are 24 inches deep by 24 inches.
The typical dimensions for all the interior beams are 30 inches deep by 14 inches.
• The typical slab thickness is 5 inches.
Figure 3.16: Typical transverse section of Avalon Building (Uma and Baguley, 2010).
46
Figure 3.17: Typical floor plan of Avalon building (Uma and Baguley, 2010).
47
3.3.2 Instrumentation
The building was instrumented with five sets of accelerometers producing 15 channels of
data in 2007 as a part of the GeoNet Building Instrumentation Programme (Uma and
Banguley, 2010). The accelerometers in the building measure both principle horizontal
accelerations and the vertical acceleration at the basement, second and roof levels as
shown in (Figure 3.18).
The acceleration data from several ground motions has been recorded since the
installation of the sensors in 2007. The most significant earthquake was the 2013 Lake
Grassmere Earthquake which had a magnitude of 6.6.
Figure 3.18: Sensor locations for Avalon building (Uma and Baguley, 2010).
3.3.3 Recorded Motions
The data for the recorded earthquakes that affected the building since the 2007 Gisborne
earthquake which was the first to affect the building is available via the online database
(www.geonet.org.nz). Most of these earthquakes had very weak effects on the building
which was reflected in very small roof accelerations and displacements.
The most significant earthquake was the 2013 Lake Grassmere Earthquake which
resulted in the largest acceleration and displacement responses in the building. The
acceleration history in the transverse (N-S) direction at the basement level is presented in
48
(Figure 3.19). The displacement history at the roof level is also presented in (Figure 3.20)
for the transverse (N-S) direction.
Figure 3.19: Recorded acceleration history at the ground level of Avalon building in the
transverse (N-S) direction.
Figure 3.20: Displacement at the roof level of Avalon building in the transverse (N-S)
direction.
3.3.4 Earthquake Damage
Since the Lake Grassmere Earthquake is the most significant earthquake within the
recorded history of the building, no inspection reports are available due to the short time
between the occurrence of earthquake and the time of this study. Therefore, there is no
evidence of any potential structural damage within the elements of the RC frame system
for this building.
49
3.4 Adequacy of RC Members for Ductile Behavior
In the following sections, the structural capacities of different components of the RC
frames in the case study buildings will be calculated based on the given material
properties, the section dimensions, and reinforcement provided in the structural drawings
using two different approaches for more assurance of the ductile behavior of the analyzed
frame.
The first approach is analyzing the frame behavior by applying the “Building Code
Requirements for Structural Concrete (ACI 318-11)” which is the current code of practice
for concrete seismic construction in most jurisdictions in the U.S. The formulae given by
ACI 318-08 to calculate nominal shear and flexural strengths of concrete members
(beams, columns, and joints) for a special (ductile) moment resisting frame is used as
presented in Appendix (A). The second approach is analyzing the member behavior by
applying the Modified Compression Field Theory (MCFT) which was developed by
Vecchio and Collins in 1986 in order to predict the response of RC members when
subjected to both shear and normal stresses. The MCFT has the advantages of
considering the geometry of the whole member as well as the interaction between shear
and normal stresses. The MCFT was applied using the software RESPONSE-2000 which
was developed by Evan Bentz at the University of Toronto.
Also, the detailing of reinforcement for different structural elements especially at the
critical locations which are expected to experience the maximum straining actions and
deformation, is checked to meet the ACI code requirements in order to ensure ductile
behavior of the RC frame without any kind of anchorage failure prior to the formation of
plastic hinges.
3.4.1 RESPONSE-2000
The modified compression field theory (MCFT) which was developed by Vecchio and
Collins more than 25 years ago at the University of Toronto (Vecchio and Collins, 1986)
in order to explain and predict the response of RC members under various actions
(normal and shear stresses), is implemented into a program called RESPONSE-2000. The
program is a nonlinear sectional analysis program, which allows users to analyze beams
50
and columns subjected to moment, shear, and axial loads. It was developed by Evan
Bentz (2000) as a part of his Ph.D. research at University of Toronto under the
supervision of M.P. Collins.
RESPONSE-2000, although a 2-D program based on MCFT, is also capable of
performing calculations on circular, T-shapes and a varieties of other non-uniform section
shapes, this feature considerably widens its applicability into many other areas. The
program calculates the full member response including the deflection and curvature along
the member length, as well as predicted failure modes. RESPONSE-2000 and its manual
are available free for download at http://www.ecf.utoronto.ca/~bentz/r2k.htm.
The program also provides different levels of user-program interaction, making it easier
to control. The material properties, such as stress-strain relationships, can be easily
monitored upon input. The output, likewise, shown graphically, can be easily understood,
hence making the spotting of the final failure mechanism a straightforward task. The user
interfaces are shown in (Figure 3.21), (Figure 3.22) and (Figure 3.23) which give a
typical overview of how the program may look like during its execution.
During the mode of “member response”, the program first performs a series of sectional
analyses with different combinations among shear and moments to produce the shear vs.
moment interaction relationship. The analysis depends on the geometrical configurations
of the member and the corresponding loading conditions, it can give predictions as to the
crack pattern, load-displacement history, shear strain distribution, curvature and
deflection distribution along the span.
Five plots are shown in (Figure 3.22) the main window with two plots in the left window.
These include the member crack diagram, curvature distribution; shear strain distribution,
deflection, load-max deflection, moment-shear interaction diagram, and the shear-
deflection diagram. Each graph in the main window plots values along the length of the
member.
51
Figure 3.21: Input data in RESPONSE-2000.
Figure 3.22: Member response output in RESPONSE-2000.
52
Figure 3.23: Sectional analysis output in RESPONSE-2000.
However, the information used for this study was from the interaction plots in the left
window in (Figure 3.22) and (Figure 3.23) which are described below:
• Moment-Shear Interaction diagram (M-V): The vertical axis is the shear and the
horizontal axis is the moment. The outer blue line represents the failure envelope,
while the inner red line represents the loading envelope.
• Moment-Curvature diagram (M-Phi): The vertical axis is the moment and the
horizontal axis is the curvature. The corresponding moment and curvature is
based on the maximum values achieved by the loading envelope in the moment-
shear interaction diagram.
All beam and column sections were analyzed using RESPONSE-2000 in order to
calculate the capacity of the member in shear and flexure based on their material
properties and the cross sectional dimensions for each of the components of the moment
resisting RC frame (beams and columns) in the transverse direction.
53
3.4.2 North Hollywood Building
This case study building was reported by professional experts (John A. Blume, 1971 and
John A. Martin, 1997) as a ductile moment resisting RC frame building.
Now, it is important to check the conformance of seismic behavior of different structural
elements (beams, columns, and joints) in the main lateral resisting system with the
concepts of ductile behavior in order to apply the findings of this research to the current
and future construction of ductile RC frames. This study will focus on analyzing the
components of the moment resisting RC frame in the transverse direction.
Table 3.3: Section dimensions for the frame in the transverse direction of North
Hollywood building.
Member Location Type f
c
' (psi) f
y
(ksi) A
s
Col. 22x22 Ground and 2nd floor Interior 4000 60 12#9
Col. 20x20 3rd floor to 10th floor Interior 4000 60 8#9
Col. 18x20/15 3rd floor to 10th floor Exterior 4000 60 8#9
Col. 18x20/15 11th floor to roof Exterior 3000 40 8#9
Col. 18x20 11th floor to roof Interior 3000 40 8#9
Beam 12x18 All floors ------ 3000 40
4#9 (Top)
2#7 (Bot.)
3.4.2.a Beam Design and Detailing
The shear and flexural capacities of the floor beam in the transverse RC frame are shown
in (Table 3.4). The frame has a beam of a typical cross section 12x18 inches in all floor
levels. The beam is considered as a T-section taking into account the contribution of the
RC slab as compression flange of a width equal to eight times the slab thickness. The
clear cover for the beam is taken as 1.5 inches as provided in the available structural
54
drawings. The beam has a concrete strength f
c
'=3000 psi (lightweight concrete) and a
yield strength f
y
= 40 ksi for both longitudinal and transverse reinforcements.
As shown in (Table 3.4), the shear force “V
e
” is compared to the nominal shear capacity
of the beam “V
n
” based on the vales of the probable flexural strength “M
p
” for both
positive and negative moments. The modification factor for lightweight concrete “λ” was
applied when calculating the shear strength of the frame beam. It is clear that the analysis
based on the ACI approach shows adequate ductile beam design with less over-strength
than the estimate given by the analysis based on the MCFT approach which represents
the member behavior in a more realistic manner. Both approaches assure that the plastic
hinge in frame beams will occur prior to the shear failure of the beam.
Table 3.4: Beam analysis values.
Approach
ACI 318-11 MCFT (RESPONSE-2000)
Positive Negative Positive Negative
M
p
(kip.in) 930 2296 1268 2053
V
e
(kips) 14.31 14.74
V
n
(kips) 16.78 20.2
V
e
/ V
n
0.85 0.73
Ductile Yes Yes
Based on the available structural drawings, the floor beams have transverse reinforcement
of #3@4” at beam ends and #3@8” at the middle part of the beam. The code limits for
the reinforcement ratio “ρ”, stirrup spacing in the plastic hinge zone “S
1
”, stirrups
spacing along the beam length “S
2
”, and the developed length for a hooked bar “L
dh
” are
checked in the following table. The actual values shown in (Table 3.5) provide a good
agreement with code limits which ensure that anchorage failure is prevented prior the
formation of the plastic hinge in the floor beam.
55
Table 3.5: Beam detailing check.
Values Actual Max. limit Min. limit
Reinforcement ratio “ρ” (%)
0.63% (Bot.)
2.08% (Top)
2.5% 0.5%
S
1
(in) 4 4 -----
S
2
(in) 8 8 -----
L
dh
(in) 15.5 ----- 12.6
3.4.2.b Column Design and Detailing
The shear capacities of the columns in the transverse RC frame are shown in (Table 3.6).
The cross section dimensions, reinforcement, concrete strength and yield strength of
longitudinal steel of all columns are given in (Table 3.3). The clear cover for the beam is
taken as 1.5 inches as provided in the available structural drawings.
Table 3.6: Column analysis values.
Column
C 22x22 C 20x20 C 18x20/15 C 18x20/15 C 18x20
Interior Interior Exterior Exterior Interior
ACI MCFT ACI MCFT ACI MCFT ACI MCFT ACI MCFT
V
e
(kips) 19.2 19.9 30.7 31.6 21.9 19.6 21.9 19.6 30.7 31.6
V
n
(kips) 37.5 53 33.8 64.5 30 42.2 30 39.3 33.8 47.5
V
e
/ V
n
0.51 0.38 0.91 0.49 0.73 0.46 0.73 0.50 0.91 0.67
Ductile Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
As shown in the above table, the shear force “V
e
” is compared to the nominal shear
capacity of the column “V
n
” based on the vales of the probable flexural strength “M
p
” for
both positive and negative moments of the floor beams. The modification factor for
lightweight concrete “λ” was applied when calculating the shear strength of the frame
columns when applicable. It is clear that the analysis based on the ACI approach shows
56
that all columns are adequate in terms of shear capacity as well the analysis based on the
MCFT approach. As for beam shear design, both approaches assure that the plastic hinge
in the frame columns will occur prior to the shear failure of the column.
Table 3.7: Column detailing check.
Value Max. Min. C 22x22 C 20x20 C 18x20/15 C 18x20/15 C 18x20
ρ (%) 1% 6% 2.5% 2% 2.22% 2.22% 2.22%
S
1
(in) 4.5 ---- 4 4 4 4 4
S
2
(in)
6 ---- 8 8 8 8 8
A
sh
(in
2
) ---- 0.39 0.44
0.44 0.44 0.44 0.44
L
o
---- 14.33 20
20 20 20 20
Based on the details of reinforcement for the frame columns provided by the structural
drawings, the code limits are checked in (Table 3.7). The actual values shown in (Table
3.7) provide a good agreement with code limits except for the maximum spacing of the
stirrups where the confinement reinforcement is not required “S
2
”.
3.4.2.c Joint Design and Detailing
Generally, the concept of weak beam-strong column design is one of the basics for
ductile moment resisting frame in seismic design. The summation of the flexural
capacities of the columns at a certain frame joint should be at least 20% larger the
summation of the flexural capacities of the beams at the same joint. As shown in (Table
3.8), this condition is satisfied at all the joints of the moment resisting RC frame in the
transverse direction. The flexural capacities of the columns were calculated using the
MCFT approach only in order to account for the interaction between axial force and
flexure.
57
Table 3.8: Strong column-weak beam check.
Type Beam Column ∑M
c
∑M
b
∑M
c
/∑M
b
Interior B 12x18 C 22x22 10557 3321 3.18
Exterior B 12x18 C 22x22 10557 2053 5.14
Interior B 12x18 C 20x20 9115 3321 2.74
Exterior B 12x18 C 18x20 8932 2053 4.35
Interior B 12x18 C 18x20 7262 3321 2.19
Exterior B 12x18 C 18x20 7262 2053 3.54
As shown in (Table 3.9), the shear force acting through the joint “V
e
” is compared to the
nominal shear capacity of the joint “V
n
” based on the values of the probable flexural
strength “M
p
” for both positive and negative moments of the floor beams. The
modification factor for lightweight concrete “λ” was applied when calculating the shear
strength of the frame joints when applicable. It is clear that all joints are adequate for
shear capacity which assures the ductile behavior of the frame joints.
Table 3.9: Joint shear check.
Type Beam Column V
e
(kips) A
j
(in
2
) V
n
(kips) V
e
/ V
n
Ductile
Interior B 12x18 C 22x22 240 484 612 0.39 Yes
Exterior B 12x18 C 22x22 188 484 459 0.41
Yes
Interior B 12x18 C 20x20 228 400 506 0.45
Yes
Exterior B 12x18 C 18x20 180 360 341 0.53
Yes
Interior
B 12x18 C 18x20
228 360 296 0.77
Yes
Exterior B 12x18 C 18x20
180 360 221 0.81
Yes
The detailing of reinforcement for the frame joint in the available structural drawings
shows that column's stirrups are provided through joint region which prevents shear
failure of the joint prior to the formation of the plastic hinges.
58
3.4.2.d Adequacy
According to the analysis using the ACI code formulae, the RC moment resisting frame
in the transverse direction is found to have adequate shear capacities for the beam floor
and all columns. Also, the analysis using the MCFT approach resulted in adequate shear
capacities for all the components of the RC frame but with a higher over-strength than
the ACI approach for ductile behavior. This difference is attributed to the conservatism
in calculating the probable flexural strength “M
p
” due to the use of a strain hardening
factor of 1.25 for reinforcement steel as specified by the ACI code which results in high
values of “M
p
” and then increases the shear force “V
e
”. The code of practice at the time
of design of the building didn't include strain hardening factor when calculating the
probable flexural strength “M
p
” (Uniform Building Code, 1970) which resulted in less
shear strength of the RC members. On the other hand, applying the MCFT using the
software RESPONSE-2000 which uses the stress-strain relationship for steel in
calculating the section capacity gives more realistic values for shear and flexural
capacities of frame members.
The RC frame in the transverse direction was found to meet all the requirements for
detailing of beams, columns, and joints except for the transverse reinforcement of the
column outside the hinge region (middle part of the column) where the spacing of the
stirrups is 8 inches which is larger than the maximum spacing of 6 inches given in the
ACI 318-11. Since, the primary goal of the transverse steel in columns is to provide the
required shear capacity which is satisfied with a spacing of 8 inches according to (Table
3.6), then the secondary goal which is providing the required confinement. It was found
in (Table 3.7) that the confinement steel required by the code is less than the provided
amount, so the detailing of the columns satisfies both shear and confinement
requirements.
Based on the previous analysis, the transverse frame is considered to satisfy the basic
conditions of the moment resisting RC frames for ductile response under earthquake
loading such as adequate shear strength of beams, columns and joints; weak beam-strong
59
column design; and adequate anchorage of longitudinal bars as well as sufficient
confinement steel for beams and columns.
3.4.3 San Bruno Building
This case study building was designed to have ductile RC moment frames for lateral
resistance. Since the building was constructed in 1978, the seismic design requirement at
that time were inspired by the consequences of the 1971 San Fernando earthquake which
led to significant changes in the design practice. In this section, the RC frame is checked
to make sure that the frame satisfies the seismic design requirements of the current design
codes. The RC frame in the longitudinal (N-S) direction is selected for the analysis in this
study. After this check, it can be determined if the frame is capable of providing the
desired ductile response during earthquakes.
The structural capacities of the components of the RC frame will be calculated based on
the information provided in the available structural drawings and previous studies that
were performed on the same building (Anderson and Bertero, 1997). This building was
constructed using light weight concrete with strength of 5000 psi and reinforcing steel of
Grade 60. The dimensions of the cross sections for each structural element are provided
in the structural drawing and are summarized in (Table 3.10).
The detailed procedure to check the conformance of the different structural components
of the RC frame in the longitudinal (N-S) direction is following the same steps as shown
in sections ( 3.4.2.a) to ( 3.4.2.c) for the North Hollywood building. The tables including
all the calculated values for the design checks are presented in Appendix (D).
According to the analysis using the using the MCFT approach, the RC moment resisting
frame in the transverse direction is found to have adequate shear capacities for the beam
floor and all columns. Also, the analysis resulted in adequate shear capacities for all the
components of the RC frame but with a higher over-strength than the ACI approach for
ductile behavior.
The RC frame in the longitudinal (N-S) direction was found to meet all the requirements
for detailing of beams, columns, and joints. Based on the previous analysis, the frame is
considered to satisfy the basic conditions of the moment resisting RC frames for ductile
60
response under earthquake loading such as adequate shear strength of beams, columns
and joints; weak beam-strong column design; and adequate anchorage of longitudinal
bars as well as sufficient confinement steel for beams and columns.
Table 3.10: Section dimensions for the frame in the longitudinal (N-S) direction of San
Bruno building.
Member Location
Reinforcement
Exterior Interior
Beam 22x30 6th
2#9 (Top) 2#9 (Top)
2#8+1#7 (Bot.) 2#8+1#7 (Bot.)
Beam 22x29 5th
2#9+1#5 (Top) 2#9 (Top)
2#8+1#7 (Bot.) 2#8+1#7 (Bot.)
Beam 22x29 4th
2#9+1#5 (Top) 2#9 (Top)
2#8+1#7 (Bot.) 2#8+1#7 (Bot.)
Beam 22x29 3rd
3#9 (Top) 2#9+1#5 (Top)
2#8+1#7 (Bot.) 2#8+1#7 (Bot.)
Beam 22x29 2nd
2#9+2#8 (Top) 2#9+1#7 (Top)
2#8+2#7 (Bot.) 2#8+1#7 (Bot.)
Beam 22x30 1st
2#9+3#8 (Top) 2#9+2#8 (Top)
4#8+1#7 (Bot.) 2#8+2#7 (Bot.)
Col. 22x24
Axes (A&F)
with axis (8)
------
6#9
Col. 23x24.5 Axes (A&F)
------
8#10
Col. 26x33 Axes (A&F) 8#9 8#9
3.4.4 Avalon Building
The building design practice in New Zealand follows the “NZS 4203: Code of Practice
for General Structural Design and Design Loadings for Buildings”. The NZS-4203:1976
was the first edition to include seismic provisions that provide reasonable protection to
the designed buildings. It included design requirements for both strength and ductility.
61
Since the Avalon building was built prior to 1976 (Uma and Baguley, 2010), it has to be
checked to make sure that it satisfies the current seismic design requirements.
In this section, the RC frame is checked to make sure it satisfies the seismic design
requirements of the current design codes. The RC frame in the transverse (N-S) direction
is selected for the analysis in this study. After this check, it can be determined if the
frame is capable of providing the desired ductile response during earthquakes.
The structural capacities of the components of the RC frame will be calculated based on
the information provided in the available structural drawings for (Unit-2) of the GNS
Science complex and previous studies that were performed on the same building (Uma
and Baguley, 2010). Due to the lack of information, this building was assumed to be
constructed using normal weight concrete with strength of 5000 psi and reinforcing steel
of Grade 60. All beams and columns for the RC frame in the transverse direction have the
same cross section of 24x24”as provided in the structural drawing.
The detailed procedure to check the conformance of the different structural components
of the RC frame in the transverse (N-S) direction is following the same steps as shown in
sections ( 3.4.2.a) to ( 3.4.2.c) for the North Hollywood building. The tables including all
the calculated values for the design checks are presented in Appendix (D).
According to the analysis using the ACI code formulae, the RC moment resisting frame
in the transverse direction is found to have adequate shear capacities for the beam floor
and all columns. Also, the analysis using the MCFT approach resulted in adequate shear
capacities for all the components of the RC frame but with a higher over-strength than the
ACI approach for ductile behavior.
The RC frame in the transverse direction was found to meet all the requirements for
detailing of beams, columns, and joints. Based on the previous analysis, the frame is
considered to satisfy the basic conditions of the moment resisting RC frames for ductile
response under earthquake loading such as adequate shear strength of beams, columns
and joints; weak beam-strong column design; and adequate anchorage of longitudinal
bars as well as sufficient confinement steel for beams and columns.
62
4 CHAPTER (4): MODELING OF THE CASE STUDY
BUILDINGS
This chapter presents the concepts, assumptions and details of the process of modeling
the selected case study buildings which are located in a highly seismic regions in the
United States and New Zealand. The selected buildings have recorded histories of several
earthquakes measured by accelerometers located at different floor levels which are used
to calibrate the numerical models developed in this chapter. The structural software
package PERFORM-3D from Computers and Structures, Inc (CSI, 2007) was used for
the modeling process then series of “Nonlinear Time History Analyses” were done using
recorded base accelerations as input for the models.
This chapter also includes a detailed description of the elements used in modeling the RC
frame as well as the backbone curves defined in PERFORM-3D in order to simulate the
inelastic response of different RC components of the frame. The effect of cyclic loading
on the behavior of the frame components is considered while defining their response
parameters in the analysis software. The influence of joint model in an RC frame
structure is considered to obtain the most realistic building model that could represent the
performance of ductile RC frame buildings under earthquake loading.
Finally, comparisons between the actual and the calculated responses of the case study
buildings are presented in terms of fundamental periods, maximum roof displacement and
displacement histories in order to calibrate the developed models before any further use
in this study.
4.1 Analysis Software (PERFORM-3D)
PERFORM-3D (CSI, 2007) was chosen as the structural analysis software to run
nonlinear time history analysis for the selected ductile RC frames of the case study
buildings. PERFORM-3D is special structural analysis software for nonlinear seismic
analysis and design of structures. Different types of structures with various complexities
63
in the system or the implemented members can be analyzed including a high level of
nonlinearly in the models. A wide variety of deformation-based and strength-based limit
states and nonlinearities are available in the program. A nonlinear time history analysis
could be done for different structural models in PERFORM-3D. The output of these
models includes fundamental periods, as well as mode shapes, deflected shapes, time
history of displacements and forces; and hysteretic loops for different members.
The nonlinear behavior of different elements is defined for plastic hinge models where
PERFORM-3D provides variety of models that could be used after defining their
parameters, such as basic force-deformation relationship, strength loss, deformation
capacity and cyclic degradation.
As mentioned earlier, the nonlinear flexural behavior and the axial-flexural interaction
could be determined for the RC members using RESPONSE-2000 as it is a very powerful
tool in analyzing the behavior of RC sections subject to both normal and shear stresses. It
also provides a very good representation of the material behavior and producing realistic
capacities and deformations of the analyzed members. RESPONSE-2000 is used in this
study for developing the monotonic backbone for the plastic hinge models in PERFORM-
3D. The main characteristics of the monotonic backbone obtained from RESPONSE-
2000 are defined in terms of the yield strength, ultimate strength, deformation at peak
strength and the deformation limit. The monotonic backbone curve obtained by
RESPONSE-2000 should be modified for cyclic behavior. The shape of the hysteresis
loop which is defined by energy dissipation factors at different values of ductility and the
reduction factor for the unloading stiffness.
There are several options available with PERFORM-3D for simulating the cyclic
behavior of RC members under reversed loading. In this study, hysteresis loops with
unloading and reloading stiffness reductions tied to a user-defined energy ratio in relation
to energy dissipated by elasto-plastic systems are defined.
64
4.2 Building Models
Nonlinear time history analyses of the case study buildings were carried out using
PERFORM-3D by applying the recorded base acceleration histories to calibrate the
models of these ductile RC frame buildings. Since, the computational burden (time and
computer memory) of running nonlinear time history analyses in PERFORM-3D for
three-dimensional models is high; the buildings were simplified to be modeled as two-
dimensional frames due to the symmetry and regularity of the case study buildings in the
selected directions as shown in (Figure 3.4, Figure 3.10, and Figure 3.17).
The models are calibrated by comparing the fundamental periods, maximum roof
displacements, and displacement histories with those from the recorded earthquakes
during the life-time of the buildings as described earlier.
For modeling, lumped plasticity approach was employed through using rotational plastic
hinges for the RC frame components. In lumped plasticity models, nonlinear behavior is
concentrated at certain locations according to user definitions where flexure is governing
the behavior. Plastic hinges are assigned at the ends of a frame member where maximum
seismic moments are expected; otherwise elastic properties are assigned to the remaining
portion of the element. Nonlinear behavior at these plastic hinges is defined by using the
cyclic backbone moment-curvature curves.
The required information for the frame members in PERFORM-3D is defined by
assigning cross sectional properties to the elastic component and by defining the cyclic
backbone relationship for the plastic hinges. For modeling cyclic behavior under
earthquake loading, PERFORM-3D uses energy dissipation ratios and unloading stiffness
reduction factor to define the hysteresis loop rules. Beam and column sections are both
assumed to be elastic for shear and torsion.
The beam-column connections of the RC frame are modeled using joint panel zone
element; which is defined by the relationship between the moment at the hinge and the
shear angle deformation within the panel zone as will be illustrated later. A Schematic of
the frame structural analysis model which is recommended by the ATC 72-1 report for
the nonlinear analysis of RC frame systems subjected to earthquake loading is shown in
65
(Figure 4.1). It shows the fixed base supports, hinges at column bases, lumped plasticity
elements and beam-column joint model which is used in this study. The output results of
the model in PERFORM-3D can be obtained in any terms such as displacement history,
force history, moment-curvature and moment-rotation responses etc.
Figure 4.1: A frame model for nonlinear analysis as recommended by ATC 72-1.
4.2.1 Geometry
As mentioned before, the case study buildings are modeled as two dimensional frames in
PERFORM-3D. For these models, structural dimensions were considered through the
centerlines of the components of the modeled frame. Three degrees of freedom (two
translational and one rotational) are considered at each node. Rigid end zones were taken
into account to reflect the effect of the joint rigidity and to prevent plastic hinges from
occurring within the joints and shifts the inelastic behavior outside the joint region where
it is expected to occur. As shown in (Figure 4.2), rigid elements were placed at every
beam-column joint. According to the common engineering practice, T-sections were
utilized for beam sections for both North Hollywood and Avalon buildings with an
effective flange width to be equal to the beam width plus four times the slab thickness on
both sides of the web (ACI 318-11).
66
Figure 4.2: Rigid offsets within a beam-column joint (Pampanin et al., 2003).
4.2.1.a North Hollywood Building
As shown in the plan of this building in (Figure 3.4), it has a symmetrical configuration
in the longitudinal direction so torsional effects are neglected. Since the building has no
irregularities in plan, a two-dimensional model of an intermediate RC frame in the
transverse (N-S) direction is considered sufficient to simulate the structural response
under earthquake excitations in the (N-S) direction. Only the part of the building above
the ground was included in the model because the basement was surrounded by concrete
walls around its perimeter which are 12-inches thick to resist lateral loads. These walls
make the part of the building below the ground level very stiff, so the columns are
considered fixed at the ground level. A view of the frame model in PERFORM-3D is
shown in (Figure 4.3).
4.2.1.b San Bruno Building
As shown in the plan of this building in (Figure 3.10), it has two RC frames on its two
longitudinal edges to resist the lateral forces in the longitudinal (N-S) direction. It also
has three RC frames in the transverse directions, two on the transverse edges and one
near the middle of the building. In order to minimize the torsional effects of the structural
response, one of the two RC frames on the longitudinal edges of the buildings is
considered to be sufficient to simulate the structural response in the longitudinal (N-S)
67
direction under earthquake excitations. A view of the frame model in PERFORM-3D is
shown in (Figure 4.4).
Figure 4.3: A view of the model for North Hollywood building.
68
Figure 4.4: A view of the model for San Bruno building.
Figure 4.5: A view of the model for Avalon building.
69
4.2.1.c Avalon Building
As shown in the plan of this building in (Figure 3.17), it has a symmetrical configuration
in the longitudinal direction so torsional effects are neglected. Since the building has no
irregularities in plan, a two-dimensional model of an intermediate RC frame in the
transverse (N-S) direction is considered sufficient to simulate the structural response
under earthquake excitations. The roof level has a steel truss carried by the perimeter
columns which will be modeled as a bar element with moment release at the ends. The
axial stiffness of this bar element is calculated by considering the area of both the top and
bottom chords of the truss. The basement of the building is considered as a part of the
model. A view of the frame model in PERFORM-3D is shown in (Figure 4.5).
4.2.2 Stiffness
The properties of the construction materials for each of the case study buildings are used
in the modeling as provided in chapter (3). The values of the moment of inertia of
different members are calculated based on cracked section properties. The stiffness of
each structural member in the RC frame models is taken as the average slope of the
elastic portion in the moment curvature curve obtained from RESPONSE-2000 after
modification for bar-slip effect as illustrated in section ( 4.3.2). This slope was considered
as the effective stiffness “EI
eff
” for members prior to inelastic range.
4.2.3 Mass
Since nonlinear dynamic analysis is significantly dependent on the mass of the system,
the applied gravity load should be close to the expected values during the building service
life as a combination of both dead and live loads. The applied dead load (D) includes
structure self-weight, partitions and ceiling finishes while the applied live load (L)
includes all the movable occupancies in the building. A combination of (1.0D + 0.2L)
was applied to each floor as recommended by the ATC-72-1 report in order to consider
the low probabilities of having the nominal live load and the earthquake to occur
simultaneously. Masses were lumped at the frame joints and at mid-span of the beams.
The effective weight and mass of each floor is shown in (Table 4.1) to (Table 4.3).
70
Table 4.1: Effective seismic weights and masses for North Hollywood building.
Floor
Gravity Weight
(Kips)
Weight per frame
(Kips)
Floor Mass
(Kip.s
2
/in)
1st 1408 100.6 0.2604
2nd 1200 85.7 0.2228
3rd to 17th 736 52.6 0.1361
18th 728 52 0.1346
19th 616 44 0.1139
20th 704 50.3 0.1302
Table 4.2: Effective seismic weights and masses for San Bruno building.
Floor
Gravity Weight
(Kips)
Weight per frame
(Kips)
Floor Mass
(Kip.s
2
/in)
1st to 6th 1850 925 2.394
6th 1944 972 2.516
Table 4.3: Effective seismic weights and masses for Avalon building.
Floor
Gravity Weight
(Kips)
Weight per frame
(Kips)
Floor Mass
(Kip.s
2
/in)
Ground to 2nd 990 141.57 0.3664
Roof 352 50.3 0.1302
4.2.4 Damping
Most researchers suggested a damping ratio between 5 and 7 percent of the critical
damping for RC structures subjected to moderate ground motions. An average value of
6.0 percent of the critical damping will be used based on the previous research done by
several groups after studying the response of instrumented building during earthquakes
(Maragakis and Saiidi, 1993).
71
4.3 Modeling Parameters for Inelastic Behavior
In order have a good representation of the building behavior under earthquake loading;
attention should be paid toward several modeling parameters. The model includes a
variety of elements with different types of behavior, such as elastic frame members,
rotational plastic hinges and joint panel zones that requires identifying many parameters
to control their behavior.
A typical lumped plasticity model where plastic hinges are defined at the ends of frame
component is shown in (Figure 4.6). This frame component consists of three main
features, (1) an elastic beam segment, (b) rotational plastic hinges at the ends, and (c)
rigid end zones at both ends just before and after the plastic hinges inside the joint region.
The frame element has a uniform elastic cross-section for which cracked stiffness is
considered based on the average slope of the elastic portion of the monotonic moment-
curvature relationship developed using RESPONSE-2000. The rigid end zone has the
length of one half of the column width or beam depth (depending on the orientation of the
frame element), and the stiffness of this zone is assumed to 10 times larger than the
stiffness of the elastic frame element. Rotational plastic hinges are the basic elements that
represent the inelastic behavior of the frame component taking place throughout the
hinges by defining the backbone curve.
Figure 4.6: A typical frame component with lumped plasticity model (PERFORM-3D,
User Manual, 2007).
4.3.1 Monotonic Backbone Curve
In order to get this backbone curve, the monotonic moment-curvature relationships of the
frame elements are obtained by RESPONSE-2000 then they will be modified to account
72
for bar-slip and the cyclic degradation. While computing the moment-curvature curve of
the frame elements, a stress-strain relationship with strain hardening was used for
reinforcing steel and concrete was represented using Mander model (Mander and
Priestly, 1988) for stress-strain relationship considering the effect of the existing
confinement steel. Afterwards, the rotation values are obtained by multiplying the
curvature values by the plastic hinge length according to the equation developed by
Priestly et. al, 1996:
b y p
d F L L 15 . 0 08 . 0 + =
where “L” is the member length between points of contra-flexure in inches, “F
y
” is the
yield strength of the longitudinal steel in ksi, and “d
b
” is the diameter if the longitudinal
reinforcing bars in inches.
4.3.2 Bar-Slip effect
Additional rotations are developed in an RC member due to the extension of reinforcing
bars relative to the adjacent concrete which result the bar-slip deformation. This effect
should be considered when developing the backbone curve for the rotational plastic
hinges as it could add up to an additional 50% to the monotonic rotation values. The
additional rotation due to bar-slip “θ
s
” at the plastic hinge is calculated using the model
developed by Sezen and Moehle (2003) and Sezen and Setzler (2008) according to the
following equations:
) ( 8 c d u
d f
b
b s s
s
−
=
ε
θ for ε
s
< ε
y
( )( ) [ ]
y s y s y y
b
b
s
f f f
c d u
d
− + +
−
= ε ε ε θ 2
) ( 8
for ε
s
> ε
y
where “ε
y
” is the yield strain of the longitudinal bars, “f
y
” is the yield strength of the
longitudinal bars, “d” is the section depth, and “c” is the compression zone depth. The
bond stress “u
b
” is taken as ' 12
c
f for the elastic range and ' 6
c
f for the inelastic range.
The difference between the monotonic and modified moment-rotation relationships for a
typical floor beam in North Hollywood building is shown in (Figure 4.7) which indicates
a significant increase in the inelastic rotation.
73
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
-0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06
Rot. (rad.)
M (kip.in)
Monotonic with bar-slip
Monotonic
Figure 4.7: The effect of bar-slip on the monotonic moment-rotation relationship for the
beam component of the RC frame model for North Hollywood building.
After modifying the monotonic backbone curve obtained from RESPONSE-2000 using
the previous equations to account for bar-slip deformations, the modified curve is
linearized into a multi-linear backbone curve as shown in (Figure 4.8) in order match the
force-deformation (F-D) relationship definition for inelastic element in PERFORM-3D
shown in (Figure 4.9). The multi-linear F-D relationship is defined by five points (Y, U,
L, R and X) which represent the different states of inelastic behavior according to the
level of ductility.
74
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
-0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06
Rot. (rad.)
M (kip.in)
Monotonic with bar-slip
Backbone
Figure 4.8: Linearization of the monotonic backbone curve for the beam component of
the RC frame model for North Hollywood building.
Figure 4.9: F-D relationship in PERFORM-3D (PERFORM-3D, User Manual, 2007).
75
4.3.3 Cyclic Backbone Curve
Since the RC frame is subjected to earthquake loading which causes the member to suffer
a certain number of loading cycles during each event, the cyclic deterioration should be
considered in order to achieve a realistic modeling of the hysteretic behavior of the RC
components. If there is no cyclic deterioration, the monotonic backbone curve could be
used as the backbone curve. Once cyclic deterioration occurs, the monotonic backbone
curve should be modified as shown in (Figure 4.10). The cyclic backbone curve is
defined as a backbone curve that is continuously updated to account for cyclic
deterioration. The branches of a cyclic backbone curve translate towards the origin or
rotate relative to the monotonic backbone curve. It is dependent on the loading history
and changes continuously after each excursion that causes damage in the component.
Figure 4.10: Difference between monotonic and cyclic backbone curves (ATC 72-1,
2010)
The ATC 72-1 report recommends different options for modifying the monotonic
backbone curve in order to obtain the cyclic backbone curve. One of the options is to use
of factors for modification of the monotonic backbone curve; then the shape of the
backbone curve is modified to account for cyclic deterioration effects. Some numerical
values of the modification factors are introduced based on an evaluation of experimental
database information for reinforced concrete components (Haselton et al., 2008).
76
The following values for the parameters of a modified backbone curve are recommended:
• Capping Strength: F
c
* = 0.9F
c
• Pre-capping plastic deformation: Δ
p
* =0.7 Δ
p
• Post-capping plastic deformation: Δ
pc
* =0.5 Δ
pc
• Residual Strength: F
r
* = 0.9F
r
Using the above factors, the monotonic moment-rotation curve can be modified for cyclic
behavior as shown in (Figure 4.11):
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
-0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06
Rot. (rad.)
M (kip.in)
Cyclic Backbone
Monotonic Backbone
Figure 4.11: The difference between the monotonic and the cyclic backbone curves for
the beam component of the RC frame for North Hollywood building.
77
4.3.4 Cyclic Degradation:
Most structural members undergo stiffness and strength degradation under cyclic loading.
Appling reversed loading cycles; the effective backbone curve will degrade, with smaller
stiffness, strength, energy dissipation and/or ductility.
The modified backbone curve in the previous section is considered to account for
strength and ductility degradation, so both stiffness and energy degradation are still
needed to be considered in modeling the behavior of an RC frame component.
To model stiffness and energy degrading hysteresis loops in PERFORM-3D, the program
uses the degradation energy factor “e”, defined as the ratio of the area of degraded
hysteresis loops divided by the area non-degraded loop (PERFORM-3D, User Manual,
2007). Also, the unloading stiffness factor is used to represent the variation in the
stiffness during the unloading process in the loop and it also controls the elastic range of
the hysteretic loop as shown in (Figure 4.12).
The value of the energy degradation factor ranges between 0.3 and 0.6 for ductile RC
members while the unloading stiffness factor is taken as 0.5 (Naish et al., 2009).
Figure 4.12: Control of unloading stiffness in the hysteresis loops (PERFORM-3D, User
Manual, 2007).
78
4.3.5 Joint Model
The behavior of the joint region in the RC frame is represented by an inelastic connection
panel zone element in PERFORM-3D. This element is a one node element which is
assigned at the intersection of beam and column centerlines. The rigid end zones at the
ends of the frame beams and columns are connected with a connection panel zone
element. The behavior of the connection panel zone element is defined by a rotational
spring attached to it which has a nonlinear moment rotation relationship that enables the
definition of the inelastic behavior. The panel zone model is shown in (Figure 4.13).
Figure 4.13: Connection panel zone element (PERFORM-3D, User Manual, 2007).
The inelastic behavior of joint region can is defined by the relationship between the joint
shear deformation and the joint moment which has been established by several parametric
studies. The equations developed by (Unal, 2010) generate the inelastic joint shear
strength “v
j
” versus shear strain “γ
j
” relationship for connection regions in RC frames
based on the available experimental database.
The formula for calculating the joint shear stress includes the main contributing
parameters such as concrete compressive strength “f
c
'” in the connection region and joint
dimensions. Considering the effects of these parameters on the joint behavior, a tri-linear
model of joint shear stress versus strain behavior was developed. The critical points in the
joint model are the cracking point (v
cr
, γ
cr
), the yielding point (v
y
, γ
y
), and the ultimate
79
point (v
u
, γ
u
). Parametric equations are presented which predict shear stress and shear
strain values at the critical points. The equations are summarized below:
c j c u
h b f JT v ' = (MPa)
v
y
= 0.9 v
j,u
(MPa)
v
cr
= 0.4 v
j,u
(MPa)
j
c u
y
b
h
JT G
v
.
1
.
= γ
γ
cr
= 0.15γ
y
γ
u
= 2.5γ
y
where “JT” is the joint confinement factor as defined by table (1) in the ACI 352R-02,.
These critical points define the shear stress vs. shear strain relationship are shown in
(Figure 4.14).
Figure 4.14: Shear stress vs. Shear strain for the joint model (Unal, 2010).
Then, shear stress values are converted to moment using the following equation:
M
j
= v
j
. b
j
. h
c
.d*
where “b
j
” is the effective joint width which is computed according to the ACI 352R-02
formula as the average width of the beam and the column, “h
c
” is the column depth, and
“d*” is the distance between the top and the bottom reinforcements in the beam.
80
The procedure described above was used to calculate the joint model parameters for
different joints in the RC frames. An example for the RC frame in the transverse direction
of North Hollywood building is shown in (Table 4.4).
Table 4.4: Joint model parameters for the frame in the transverse (N-S) direction of
North Hollywood building.
Type Beam Column v
u
M
cr
M
y
M
u
γ
cr
γ
y
γ
u
Int. B 12x18 C 22x22
0.967 1809 4070 4522 7.4E-05 0.00049 0.00123
Ext. B 12x18 C 22x22
0.651 1217 2739 3043 7.4E-05 0.0005 0.00124
Int. B 12x18 C 20x20
0.987 1580 3554 3949 7.2E-05 0.00048 0.0012
Ext. B 12x18 C 18x20
0.683 1025 2306 2562 7.9E-05 0.00053 0.00132
Int. B 12x18 C 18x20
0.939 1408 3169 3521 8.1E-05 0.00054 0.00136
Ext. B 12x18 C 18x20
0.638 957 2153 2392 8.3E-05 0.00055 0.00138
4.4 Building Model Calibration
The results of the models of the case study buildings are used to evaluate the accuracy
with which the nonlinear modeling procedures predict the responses of the buildings
under earthquake loading in the light of the recorded response during the past recorded
earthquakes. This calibration process is necessary for further extension of the analysis
using the same models in order to achieve the goals of this study.
The results of the analysis are presented in terms of building periods, mode shapes,
maximum roof displacement, and displacement histories. The calculated periods as well
as the maximum roof displacement values are compared to the values obtained from
analyzing the recorded data. Also, the calculated displacement histories are compared
with the actual histories from the recorded response at the roof level.
4.4.1 North Hollywood Building
4.4.1.a Building Period and Mode shapes
The results of the modal analysis are presented in (Figure 4.15) that shows the periods of
the first three modes for the RC frame in the transverse (N-S) direction.
81
Figure 4.15: Mode shapes 1, 2, and 3 for the frame in the transverse direction (T
1
=2.589,
T
2
=0.880, and T
3
=0.524 seconds).
In order to verify the value of the fundamental period (T
1
) of the frame in the light of the
recorded responses of the building, the transfer functions in the transverse direction are
developed for each of the three recorded earthquakes. The transfer function is defined as
the ratio of absolute value of the Fast Fourier Transform (FFT) of the output acceleration
which is usually selected as that recorded at the roof level, and of the input acceleration
which selected as that recorded at the building base. The lowest frequency at the first
peak in the transfer function curve approximately represents the value of the fundamental
frequency.
The recorded acceleration histories are divided into two segments in order to differentiate
between the initial behavior of the building with less cracking (mostly an elastic
behavior) in the RC members of the frame due to weak ground motions and the behavior
with significant cracking during relatively strong ground motions.
The transfer functions in the transverse direction are presented in (Figure 4.16). The
identified fundamental period in the transverse direction from the initial segment of the
recorded motions during the all the three earthquakes, is about 2.05 sec. The period
changes to 2.56 sec for the later segment of the recorded response. This might be
82
attributed to a reduction in the initial stiffness of the RC members due to crack growth.
This could be also related to the lower contribution of the non-structural elements to the
structural system during the strong shaking phase of the ground motion which reduces the
global stiffness of the building.
When comparing the values of the fundamental period in the transverse direction (2.05
and 2.56 seconds) which are obtained from the transfer functions with the calculated
fundamental period (2.589 seconds) from the PERFORM-3D model, it could be found
that the model is capable of simulating the response during the relatively strong ground
motion better than the weak ground motion. This could be attributed to the definitions of
effective stiffness values for the RC members as the average slope of the elastic part in
the moment-curvature curves developed by RESPONSE-2000 after modification for bar-
slip effect. This average slope could be considered as a better representation of the
behavior during a strong ground motion than the initial slope due to the effect of the
crack growth inside the RC members.
4.4.1.b Displacement Histories
Based on the previous finding about the capability of the model of predicting the
fundamental period of the building in the transverse direction during relatively strong
ground motions with a good level of acceptance, nonlinear time history analyses were
executed using PERFORM-3D. The recorded acceleration histories for the first three
earthquakes (San Fernando 1971, Whittier 1987, and Northridge 1994) at the basement
level in the transverse (N-S) direction were used for the analysis of the RC frame. Each
earthquake was applied individually to the frame model.
The displacement histories of the roof are calculated and compared with the recorded
roof displacement histories for each of these earthquakes as shown in (Figure 4.17).
The best agreement between the calculated and the recorded roof displacement histories
is found to be for the Northridge earthquake relative to the agreement for San Fernando
and Whittier earthquakes. The recorded and calculated maximum roof displacements in
the transverse direction for each earthquake is also found to be very close for Northridge
earthquake as compared to the other two earthquakes as listed in (Table 4.5).
83
Figure 4.16: Transfer functions of the recorded earthquakes for North Hollywood
building.
Table 4.5: Recorded and calculated maximum roof displacements for North Hollywood
building.
Earthquake Year
Max. roof displacement
(Recorded)
Max. roof displacement
(Calculated)
San Fernando 1971 2.68 2.17
Whittier 1987 0.78 0.62
Northridge 1994 8.79 8.27
84
Based on the previous comparison, it was found that the model gives the best agreement
between the recorded and calculated values for Northridge earthquake in terms of
fundamental period, displacement histories, and maximum roof displacements. There is
less agreement for both San Fernando and Whittier earthquakes in terms of the same
characteristics. This might be related to the relatively high PGA for Northridge
earthquake (0.317g), which might result in more cracking and damage in the members of
the RC frame. This condition matches the assumption of using the average stiffness value
for the elastic part of the moment-curvature curves for each member.
85
Figure 4.17: Comparison between recorded and calculated displacement histories at the
roof in the transverse (N-S) direction of North Hollywood building.
86
4.4.2 San Bruno Building
4.4.2.a Building Period and Mode shapes
The modal analysis gives the periods of the first three modes for the RC frame in the
longitudinal (N-S) direction as shown in (Figure 4.18).
Figure 4.18: Mode shapes 1, 2, and 3 for the frame in the longitudinal direction
(T
1
=0.951, T
2
=0.309, and T
3
=0.173 seconds).
87
A verification of the calculated fundamental period (T
1
) of the frame is performed using
the transfer function of the recorded response during the Loma Prieta earthquake. The
recorded acceleration history was also divided into two segments to evaluate the response
during both weak shaking in the first few seconds of the earthquake and the strong
shaking in the later seconds of the earthquake. The transfer function in the longitudinal
(N-S) direction is presented in (Figure 4.19).
Figure 4.19: Transfer functions of the Loma-Prieta earthquake for San Bruno building.
According to these transfer functions, the identified fundamental period in the
longitudinal direction from the initial segment of the recorded motions during the Loma-
Prieta earthquake is 0.788 seconds. The period changes to 0.931 seconds for the later
segment of the recorded response which might be attributed to the reduction in the
stiffness of the RC frame members due to crack growth during strong earthquake shaking
as well as the higher contribution of the non-structural elements to the structural response
during the weak earthquake shaking.
When comparing the values of the fundamental period in the longitudinal direction
(0.788 and 0.931 seconds) which are obtained from the transfer function with the
calculated fundamental period (0.951 seconds) from the PERFORM-3D model, it could
be found that the model is capable of simulating the response during the relatively strong
ground motion better than the weak ground motion. This could be attributed to the
definitions of effective stiffness values for the RC members as the average slope as
mentioned before.
88
4.4.2.b Displacement Histories
Based on the previous finding, the developed model of the RC frame in the longitudinal
direction is capable of predicting the structural response and the fundamental period
during relatively strong ground motions. Nonlinear time history analysis is performed in
order to calculate the structural response in terms of the roof displacement using the
recorded accelerations at the ground level during the Loma-Prieta earthquake as input for
the model of the RC frame.
The displacement history of the roof is calculated and compared with the actual
displacement history from the recorded response as shown in (Figure 4.20). This
comparison shows a good agreement between the recorded and the calculated
displacement history at the roof level in the longitudinal direction. The recorded
maximum roof displacement is found to be 2.50 inches while the calculated value is 2.37
inches which represents an acceptable error in predicting the structural response using the
developed model.
The calculated response shows also a permanent displacement after the end of the
duration of the input acceleration record which agrees with the inspection that was
performed for the building after the Loma-Prieta earthquake where signs of inelastic
response were found in several locations in the RC frame beams.
Figure 4.20: Comparison between recorded and calculated displacement histories at the
roof in the longitudinal (N-S) direction of San Bruno building.
89
4.4.3 Avalon Building
4.4.3.a Building Period and Mode shapes
The modal analysis gives the periods of the first three modes for the RC frame in the
transverse (N-S) direction as shown in (Figure 4.21).
Figure 4.21: Mode shapes 1, 2, and 3 for the frame in the transverse direction (T
1
=0.407,
T
2
=0.143, and T
3
=0.079 seconds).
A verification of the calculated fundamental period (T
1
) of the frame is performed using
the transfer function of the recorded response during the Lake Grassmere earthquake. The
recorded acceleration history was also divided into two segments to evaluate the response
during both weak shaking in the first few seconds of the earthquake and the strong
shaking in the later seconds of the earthquake. The transfer function in the transverse (N-
S) direction is presented in (Figure 4.22).
Figure 4.22: Transfer functions of the Lake Grassmere earthquake for Avalon building.
90
According to these transfer functions, the identified fundamental transverse vibration
period from the segment between 10 to 15 seconds of the recorded motions during the
Lake Grassmere earthquake is 0.341 seconds. The period changes to 0.393 seconds for
the later segment between 15 to 25 seconds of the recorded response which might be
attributed to the reduction in the stiffness of the RC frame members due to crack growth
during strong earthquake shaking and the higher contribution of the non-structural
elements to the structural response during the weak earthquake shaking.
When comparing the values of the fundamental period in the transverse direction (0.341
and 0.393 seconds) which are obtained from the transfer function with the calculated
fundamental period (0.407 seconds) from the PERFORM-3D model, it could be found
that the model is capable of simulating the response during the relatively strong ground
motion better than the weak ground motion. This could be attributed to the definitions of
effective stiffness values for the RC members as the average slope as mentioned before.
4.4.3.b Displacement Histories
Similarly the previous finding shows that the developed model of the RC frame in the
transverse direction is capable of predicting the structural response and the fundamental
period during relatively strong ground motions. Nonlinear time history analysis is
performed in order to calculate the structural response in terms of the roof displacement
using the recorded accelerations at the basement level during the Lake Grassmere
earthquake as input for the model of the RC frame.
The displacement history of the roof is calculated and compared with the recorded
displacement history as shown in (Figure 4.23). This comparison shows a good
agreement between the recorded and the calculated displacement history at the roof level
in the transverse direction. The recorded maximum roof displacement is found to be 0.24
inches while the calculated value is 0.246 inches which represents an acceptable error in
predicting the structural response using the developed model.
91
Figure 4.23: Comparison between recorded and calculated displacement histories at the
roof in the transverse (N-S) direction of Avalon building.
4.4.4 Conclusion
According to the previous sections, the three models for the selected case study buildings
showed good simulated response in the light of the recorded responses during the
recorded earthquake response for each building. The comparison was performed in terms
of the fundamental period of vibration in a specific direction, the maximum displacement
at the roof level, and comparison between the recorded and the calculated roof
displacement histories. Hence, the level of agreement between the recorded and the
calculated values is considered satisfactory to represent the behavior of the RC frame
buildings in these specific directions if they are subjected to relatively strong ground
motions.
Based on the previous conclusion of the calibration process, the developed models for the
case study buildings in PERFORM-3D can be used for further study using different
earthquake scenarios to investigate the effect of multiple earthquakes on the ductile RC
frame systems which is the primary goal of this study.
92
5 CHAPTER (5): SELECTED EARTHQUAKE SCENARIOS
In order to achieve the goals of the current study, the analysis of the three case study
buildings which started in the previous chapter should be extended using multiple
earthquake scenarios which represent real cases from past events. Locations from all over
the world suffered from different earthquake scenarios either by combination of main-
shocks with their fore- and after-shocks or by multiple earthquakes that occur over a
relatively short period of time (from several days to several months).
In this chapter, different multiple earthquake scenarios are selected to be applied to the
case study buildings after calibrating the numerical models in order to study the behavior
of different structural elements (beams, columns and joints) of the ductile RC frame as a
lateral resisting system. Earthquake scenarios were selected from the available
earthquake databases to represent real cases of different ground motion characteristics in
terms of frequency contents, durations and peak ground accelerations (PGA). Three main
categories of earthquake scenarios including short to medium duration, long duration and
multiple earthquakes are presented by selecting 18 real cases of earthquake sequences.
This chapter presents the selected earthquake scenarios by describing the sequence as
well as the ground motion parameters for each. The spectral accelerations of each
earthquake scenario is calculated to show the frequency content and give an idea about
the expected behavior of the three case study buildings which represent a wide range of
fundamental frequencies (from 0.40 to 2.60 seconds) as it was calculated in the previous
chapter.
5.1 Selection Criteria
Since the objective of this study is to investigate the effects of applying multiple
earthquakes in a sequence on the structural response of ductile RC frame buildings, it is
important to select ground motion records that provide a realistic representation of
earthquake magnitudes, frequency contents, and durations which creates a variety of real
93
scenarios of earthquakes (main, fore-, and after-shocks). The selected ground motions
include at least one main shock (MS), after-shocks (AS), and fore-shocks (FS) if existed
which create different loading scenarios. Some of the recorded after-shocks are described
as strong after-shock (SA) if they have PGA value close or larger than the value for the
main-shock.
These real ground motion records were downloaded from the available large strong
motion databases via the internet such as “Pacific Earthquake Engineering Research
Center (PEER)”, “COSMOS Virtual Data Center”, “Center of Engineering Strong-
Motion Data”, and “GeoNet”. These databases include acceleration, velocity, and
displacement time histories for most of the stations where the ground motions were
recorded. The acceleration histories used in this study were selected from these databases
to be recorded by the same station, in the same direction (angle from the global north)
within periods ranging from several days to several months.
The selection criteria were established to provide variety in the ground motion
characteristics for the acceleration time histories. The basic selection criteria can be
summarized as follows:
1- A ground motion should have a magnitude of at least 5.0 on Richter scale.
2- A ground motion should have a minimum value for the PGA of 0.05g.
3- A ground motion should have a minimum value for the spectral acceleration of
0.05g for each of the selected cases study buildings using 6% damping ratio (This
criterion is for the main shock in a certain earthquake scenario)
4- A ground motion should have duration of at least 10 seconds.
The selected earthquake scenarios represent real cases of multiple ground motions that
affected a certain location within a certain period of time that could range from a few
minutes to a few weeks to a few months. All the selected ground motion originated from
the same location at the fault line as the tectonic plates release the seismic energy
gradually in the form of several ground motions after the initial rupture till a stable
condition is reached. The magnitudes of the after-shocks cannot be predicted as it may
occur anywhere along the highly stressed fault rupture zone. It is also difficult to predict
94
when the after-shocks may stop as the rupture plane needs to relive all the accumulated
strains through the movement along the fault line.
The selected earthquake scenarios were divided into three major categories, two
categories according to the duration of the main shock and one category for independent
earthquakes that occurred over a relatively long period of time with their fore- and after-
shocks. The developed numerical models for the case study buildings will be analyzed
under the effects of these earthquake scenarios from all three categories in order to study
the behavior of ductile RC frame systems when subjected to multiple earthquakes.
5.2 Short to Medium Duration Earthquakes with a Series of Fore- and
After-shocks
In this category, nine real scenarios of short to medium duration earthquakes (duration
from 10 to 100 seconds) were selected which represent different combinations of fore-
shocks and after-shocks with the main shock. These ground motions originated mostly
from the same fault rupture but occurred over few days to few weeks period which may
not provide enough time for a repair or rehabilitation plans to take place which increase
the possibility of damage accumulation through the whole earthquake scenario.
These selected earthquake scenarios are namely:
• Ground motion sequences in California: the 1992 Cape-Mendocino (3 shocks)
from two stations, the 1986 Chalflant Valley (4 shocks), the 1980 Mammoth
Lakes (6 shocks), and the 1983 Coalinga (3 shocks) earthquakes.
• Ground motion sequences from the 1999 Chi-Chi earthquake in Taiwan from two
stations (4 shocks) and (5 shocks).
• Ground motion sequence from the 1985 Mexico earthquake (2 shocks).
• Ground motion sequence from the 1997 Kyushu earthquake in Japan (2 shocks).
The characteristics of each ground motion from these earthquake scenarios are presented
in (Table 5.1).
95
Table 5.1: List of short to medium duration earthquakes with their fore- and after-shocks.
Ground
Motion
Station Type Date Angle Magnitude PGA(g)
Duration
(Seconds)
Cape-
Mendocino
1583
MS 04/25/1992
90
7.0 0.334 28
SA 04/26/1992 6.6 0.395 28
AS 04/26/1992 6.6 0.249 28
89156
MS 04/25/1992
00
7.0 -0.589 60
SA 04/26/1992 6.6 0.598 40
AS 04/26/1992 6.6 -0.323 40
Chalflant
Valley
54428
FS 07/20/1986
00
5.9 0.232 40
MS 07/21/1986 6.4 0.402 40
AS 07/21/1986 5.6 -0.104 40
AS 07/31/1986 5.8 -0.065 40
Mammoth
Lakes
54099
MS 05/25/1980
90
6.1 0.410 65
AS 05/25/1980 6.0 -0.161 58
AS 05/25/1980 6.1 -0.277 65
SA 05/25/1980 5.7 -0.345 56
AS 05/26/1980 5.7 -0.133 65
AS 05/27/1980 6.2 0.253 65
Chi-Chi
TCU079
MS 09/20/1999
00
7.6 -0.393 70
AS 09/20/1999 5.9 -0.212 45
AS 09/20/1999 6.2 -0.263 73
SA 09/25/1999 6.3 0.622 55
CHY036
MA 09/20/1999
90
7.6 0.294 80
AS 09/20/1999 5.9 -0.076 58
AS 09/20/1999 6.2 0.104 108
AS 09/20/1999 6.2 0.092 114
SA 09/25/1999 6.3 0.201 78
Kyushu KSG005
MS 03/26/1997
00
6.3 0.441 57
SA 05/13/1997 6.2 0.920 42
96
Table 5.1: List of short to medium duration earthquakes with their fore- and after-shocks
(cont’d).
Ground
Motion
Station Type Date Angle Magnitude PGA(g)
Duration
(Seconds)
Coalinga 1162
MS 05/02/1983
45
6.7 0.313 60
AS 05/09/1983 5.3 -0.054 12
SA 07/22/1983 6.0 0.439 20
Mexico AZIH
MS 09/19/1985
00
8.1 -0.100 72
SA 09/21/1985 7.5 -0.162 55
The acceleration histories of the selected ground motions including the main, fore- and
after-shocks are shown in (Figure 5.1). Also, the spectral acceleration for each ground
motion record is calculated based on damping ratio of 6.0% which is the same value used
in the numerical models for the case study buildings. The curves of the spectral
acceleration versus the period of vibration are presented in (Figure 5.2).
The spectral acceleration curves show that for San Bruno building which has a
fundamental period of 0.931 seconds, several after-shocks give higher values than the
values from the main shocks such as Cape-Mendocino (1583 and 89156), Mammoth
Lakes, Kyushu, and Mexico. For Avalon building which has a fundamental period of
0.393, there are also several after-shocks that give higher values for the spectral
acceleration than the main shocks such as Cape-Mendocino (1583 and 89156), Chalflant
Valley, Chi-Chi (CHY036), and Mexico. These after-shocks can be more damaging to
these two buildings than the main shocks or they can lead to damage accumulation within
the frame components that experienced prior damage for the main shock.
97
0 10 20 30 40 50 60 70 80 90 100
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Cape-Mendocino 1992 (Station 1583)
Time (Seconds)
Acceleration (g)
MS-04/25/1992 SA-04/26/1992 AS-04/26/1992
0 20 40 60 80 100 120 140 160
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Cape-Mendocino 1992 (Station 89156)
Time (Seconds)
Acceleration (g)
MS-04/25/1992 SA-04/26/1992 AS-04/26/1992
0 20 40 60 80 100 120 140 160 180 200
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Chalflant Valley 1986 (Station 54428)
Time (Seconds)
Acceleration (g)
FS-07/20/1986 MS-07/21/1986 AS-07/21/1986 AS-07/31/1986
Figure 5.1: Sequences for short to medium duration earthquakes.
98
0 50 100 150 200 250 300 350 400
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Mammoth Lakes (Station 54099)
Time (Seconds)
Acceleration (g)
MS-05/25/1980 AS-05/25/1980 AS-05/25/1980 SA-05/25/1980 AS-05/26/1980 AS-05/27/1980
0 50 100 150 200 250
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Chi-Chi 1999 (Station TCU079)
Time (Seconds)
Acceleration (g)
MS-09/20/1999 AS-09/20/1999 AS-09/20/1999 SA-09/25/1999
0 50 100 150 200 250 300 350 400 450
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Chi-Chi 1999 (Station CHY036)
Time (Seconds)
Acceleration (g)
MS-09/20/1999 AS-09/20/1999 AS-09/20/1999 AS-09/20/1999 SA-09/25/1999
Figure 5.1: Sequences for short to medium duration earthquakes (cont’d).
99
0 20 40 60 80 100
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Kyushu 1997 (Station KSG005)
Time (Seconds)
Acceleration (g)
MS-03/26/1997 SA-05/13/1997
0 20 40 60 80 100
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Coalinga 1983 (Station 1162)
Time (Seconds)
Acceleration (g)
MS-05/02/1983 AS-05/09/1983 SA-07/22/1983
0 20 40 60 80 100 120 140
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
Mexico 1985 (Station AZIH)
Time (Seconds)
Acceleration (g)
MS-09/19/1985 SA-09/21/1985
Figure 5.1: Sequences for short to medium duration earthquakes (cont’d).
100
0 0.5 1 1.5 2 2.5 3
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Cape-Mendocino 1992 (Station 1583)
Period (Seconds)
Spectral Acceleration (g)
MS-04/25/1992
SA-04/26/1992
AS-04/26/1992
0 0.5 1 1.5 2 2.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Cape-Mendocino 1992 (Station 89156)
Period (Seconds)
Spectral Acceleration (g)
MS-04/25/1992
SA-04/26/1992
AS-04/26/1992
0 0.5 1 1.5 2 2.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Chalflant Valley 1986 (Station 54428)
Period (Seconds)
Spectral Acceleration (g)
FS-07/20/1986
MS-07/21/1986
AS-07/21/1986
AS-07/31/1986
Figure 5.2: Spectral Acceleration for short to medium duration earthquakes.
101
0 0.5 1 1.5 2 2.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Mammoth Lakes 1980 (Station 54099)
Period (Seconds)
Spectral Acceleration (g)
MS-05/25/1980
AS-05/25/1980
AS-05/25/1980
SA-05/25/1980
AS-05/26/1980
AS-05/27/1980
0 0.5 1 1.5 2 2.5 3
0
0.5
1
1.5
2
2.5
Chi-Chi 1999 (Station TCU079)
Period (Seconds)
Spectral Acceleration (g)
MS-09/20/1999
AS-09/20/1999
AS-09/20/1999
SA-09/25/1999
0 0.5 1 1.5 2 2.5 3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Chi-Chi 1999 (Station CHY036)
Period (Seconds)
Spectral Acceleration (g)
MA-09/20/1999
AS-09/20/1999
AS-09/20/1999
AS-09/20/1999
SA-09/25/1999
Figure 5.2: Spectral Acceleration for short to medium duration earthquakes (cont’d).
102
0 0.5 1 1.5 2 2.5
0
0.5
1
1.5
2
2.5
3
3.5
Kyushu 1997 (Station KSG005)
Period (Seconds)
Spectral Acceleration (g)
MS-03/26/1997
SA-05/13/1997
0 0.5 1 1.5 2 2.5 3
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Coalinga 1983 (Station 1162)
Period (Seconds)
Spectral Acceleration (g)
MS-05/02/1983
AS-05/09/1983
SA-07/22/1983
0 0.5 1 1.5 2 2.5
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Mexico 1985 (Station AZIH)
Period (Seconds)
Spectral Acceleration (g)
MS-09/19/1985
SA-09/21/1985
Figure 5.2: Spectral Acceleration for short to medium duration earthquakes (cont’d).
103
5.3 Long Duration Earthquakes with their After-shocks
In this category, six recorded earthquakes of long duration (between 100 to 300 seconds)
and their after-shocks were selected which represent different earthquake scenarios.
These ground motions originated mostly from the same fault source but occurred over a
period of a few days to a few weeks period.
These selected earthquake scenarios are namely:
• Ground motion sequences from the 2011 Tohoku earthquake in Japan from two
stations (3 shocks each).
• Ground motion sequence from the 1985 Valparaiso earthquake in Chile (3
shocks).
• Ground motion sequence from the 2007 Honshu earthquake in Japan (2 shocks).
• Ground motion sequence from the 2003 Tokachi earthquake in Japan (2 shocks).
• Ground motion sequence from the 2010 Maule earthquake in Chile (2 shocks).
The characteristics of each ground motion from these earthquake scenarios are presented
in (Table 5.2).
The acceleration histories of the selected long duration ground motions and their after-
shocks are shown in (Figure 5.3). The curves of the spectral acceleration versus the
period of vibration based on damping ratio of 6.0% are presented in (Figure 5.5).
104
Table 5.2: List of long-duration earthquakes with their after-shocks.
Ground
Motion
Station Type Date Angle Magnitude PGA(g)
Duration
(Seconds)
Tohoku
FKS012
MS 03/11/2011
90
9.0 -0.359 288
SA 04/07/2011 7.1 0.502 245
AS 04/11/2011 6.6 -0.090 135
IBR013
MS 03/11/2011
00
9.0 1.375 240
SA 04/07/2011 7.1 -0.547 158
AS 04/11/2011 6.6 -0.135 154
Valparaiso LLO
MS 03/03/1985
10
7.8 0.712 120
AS 03/03/1985 7.2 -0.186 43
AS 04/08/1985 7.5 0.204 40
Honshu ISK005
MS 03/25/2007
00
6.9 0.481 126
AS 03/25/2007 5.3 0.134 90
Tokachi HKD109
MS 09/26/2003
90
8.0 0.245 150
SA 09/26/2003 7.1 -0.417 120
Maule 499
MS 02/27/2010
90
8.8 0.413 180
AS 02/28/2010 6.6 0.147 49
105
0 100 200 300 400 500 600 700
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Tohoku 2011 (Station FKS012)
Time (Seconds)
Acceleration (g)
MS-03/11/2011 SA-04/07/2011 AS-04/11/2011
0 100 200 300 400 500
-1.5
-1
-0.5
0
0.5
1
1.5
Tohoku 2011 (Station IBR013)
Time (Seconds)
Acceleration (g)
MS-03/11/2011 SA-04/07/2011 AS-04/11/2011
0 50 100 150 200
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Valprasio 1985 (Station LLO)
Time (Seconds)
Acceleration (g)
MS-03/03/1985 AS-03/03/1985 AS-04/08/1985
Figure 5.3: Sequences for long-duration earthquakes.
106
0 50 100 150 200
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Honshu 2007 (Station ISK005)
Time (Seconds)
Acceleration (g)
MS-03/25/2007 AS-03/25/2007
0 50 100 150 200 250
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Tokachi 2003 (Station HKD109)
Time (Seconds)
Acceleration (g)
MS-09/26/2003 SA-09/26/2003
0 50 100 150 200 250
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Maule 2010 (Station 499)
Time (Seconds)
Acceleration (g)
MS-02/27/2010 AS-02/28/2010
Figure 5.4: Sequences for long-duration earthquakes (cont’d).
107
0 0.5 1 1.5 2 2.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Tohoku 2011 (Station FKS012)
Period (Seconds)
Spectral Acceleration (g)
MS-03/11/2011
SA-04/07/2011
AS-04/11/2011
0 0.5 1 1.5 2 2.5
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Tohoku 2011 (Station IBR013)
Period (Seconds)
Spectral Acceleration (g)
MS-03/11/2011
SA-04/07/2011
AS-04/11/2011
0 0.5 1 1.5 2 2.5 3
0
0.5
1
1.5
2
2.5
Valprasio 1985 (Station LLO)
Period (Seconds)
Spectral Acceleration (g)
MS-03/03/1985
AS-03/03/1985
AS-04/08/1985
Figure 5.5: Spectral Acceleration for long- duration earthquakes.
108
0 0.5 1 1.5 2 2.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Honshu 2007 (Station ISK005)
Period (Seconds)
Spectral Acceleration (g)
MS-03/25/2007
AS-03/25/2007
0 0.5 1 1.5 2 2.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Tokachi 2003 (Station HKD109)
Period (Seconds)
Spectral Acceleration (g)
MS-09/26/2003
SA-09/26/2003
0 0.5 1 1.5 2 2.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Maule 2010 (Station 499)
Period (Seconds)
Spectral Acceleration (g)
MS-02/27/2010
AS-02/28/2010
Figure 5.6: Spectral Acceleration for long- duration earthquakes (cont’d).
109
5.4 Multiple Earthquakes with their Fore- and After-shocks
In this category, three real sets of earthquakes were selected which represent different
combinations of multiple earthquakes with their fore and after-shocks. These ground
motions are all measured at the same station over a period of few months which is longer
than the previous categories. This category simulates the case of a certain location that
recently suffered from multiple earthquakes over several months which can lead to
serious damage if no repair or rehabilitation efforts were made due to any delays as was
discussed in chapter (1) when the catastrophes of both the CTV building and the PGC
building were presented.
Three locations from the recent series of earthquakes that struck New Zealand between
September 2010 and December 2011 were selected for this category. These locations are
the Christchurch Botanical Gardens (CBGS), Riccarton High School (RHSC), and
Templeton School (TPLC) in the city of Christchurch, which experienced scenarios of
eight major ground motions. These ground motions are four main-shocks with their fore
and after-shocks as described in (Table 5.3).
These selected stations have acceleration histories from all the eight ground motions as
provided via the online database “GeoNet”. The (CBGS) station was selected as it is one
of the closest stations to the location of the CTV building as shown in (Figure 5.7). It is
important to investigate this particular site as the recent catastrophe of can be understood
in the light of the damage accumulation phenomena which is the main scope of this
study. The other stations (RHSC) and (TPLC) were selected based on the values of the
PGA during the 4 September 2010 and the 22 February 2011 earthquakes as the (RHSC)
station experience higher PGA during the second earthquake where the (TPLC) station
experience higher PGA during the first earthquake.
The acceleration histories of the selected ground motion scenarios and are shown in
(Figure 5.8). The curves of the spectral acceleration versus the period of vibration based
on damping ratio of 6.0% are presented in (Figure 5.9).
110
Figure 5.7: Locations of the strong motion recording stations near the location of the
CTV building (Canterbury Earthquakes Royal Commission, 2012).
Table 5.3: List of multiple earthquake scenarios at selected locations in Christchurch, NZ.
Type Date Mag.
CBGS (S01W) RHSC (S04W) TPLC (N27W)
PGA Duration PGA Duration PGA Duration
MS 09/03/2010 7.1 0.185 148 0.232 136 0.282 138
MS 02/22/2011 6.3 -0.430 85 0.250 56 0.122 52
AS 02/23/2011 5.8 0.003 50 0.184 36 0.069 42
AS 02/23/2011 5.9 0.353 67 -0.215 60 0.132 63
FS 06/13/2011 5.9 0.168 67 -0.091 68 0.040 38
MS 06/13/2011 6.4 0.172 87 0.188 85 0.068 50
FS 12/23/2011 5.9 0.161 57 -0.173 58 -0.077 42
MS 12/23/2011 6.0 0.170 57 -0.153 58 0.111 42
111
0 100 200 300 400 500 600
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Christchurch Botanical Gardens (CBGS)
Time (Seconds)
Acceleration (g)
Major 8 Ground Motions between 09/04/2010 and 12/23/2011
0 100 200 300 400 500 600
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
Riccarton High School (RHSC)
Time (Seconds)
Acceleration (g)
Major 8 Ground Motions between 09/04/2010 and 12/23/2011
0 50 100 150 200 250 300 350 400 450 500
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Templeton School (TPLC)
Time (Seconds)
Acceleration (g)
Major 8 Ground Motions between 09/04/2010 and 12/23/2011
Figure 5.8: Sequences for multiple earthquakes from Christchurch, New Zealand.
112
0 0.5 1 1.5 2 2.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Christchurch Botanic Gardens (CBGS)
Period (Seconds)
Spectral Acceleration (g)
CBGS-1
CBGS-2
CBGS-3
CBGS-4
CBGS-5
CBGS-6
CBGS-7
CBGS-8
0 0.5 1 1.5 2 2.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Riccarton High School (RHSC)
Period (Seconds)
Spectral Acceleration (g)
RHSC-1
RHSC-2
RHSC-3
RHSC-4
RHSC-5
RHSC-6
RHSC-7
RHSC-8
0 0.5 1 1.5 2 2.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Templeton School (TPLC)
Period (Seconds)
Spectral Acceleration (g)
TPLC-1
TPLC
TPLC-3
TPLC-4
TPLC-5
TPLC-6
TPLC-7
TPLC-8
Figure 5.9: Spectral Acceleration for multiple earthquakes from Christchurch, New
Zealand.
113
5.5 Nonlinear Time History Analysis
By applying the acceleration records from the selected earthquake scenarios to the
numerical models of case study RC ductile frame buildings using PERFROM-3D, the
structural response can be evaluated. The selected ground motions represent real
earthquake loading scenarios with a wide spectrum of characteristics which can lead to a
huge variety in the output results considering that each building has its unique dynamic
characteristics that affect the structural response. There are different response parameters
such as displacements, distribution of plastic hinges, and hysteretic behavior that can help
understanding the structural performance of the ductile RC frame buildings under the
effect of multiple earthquake scenarios.
The models of the three case study buildings are analyzed twice in order to compare the
results of each ground motion when applied as part of a sequence (Train) and when
applied separately (Single). When applying the ground motions in a sequence, a time gap
with zero acceleration is applied between each two consecutive ground motions. This
time gap ranges between 8 to 20 seconds according to the original duration of prior
ground motion in order to allow for the free vibration phase of the building motion to
decay. The model is almost brought back to rest before the next ground motion is applied.
The analysis was performed considering the geometric nonlinearity of the RC frame
columns due to the second order moments under the assigned gravity loads as defined in
chapter (4). The model of San Bruno building has additional vertical loads from the
gravity columns at the centerline of the building where the other two buildings don’t have
any gravity columns, so no additional vertical loads are assigned in the their models.
The major results of nonlinear time history analysis are presented in the following
chapters along with remarks and conclusions.
114
6 CHAPTER (6): ANALYSIS RESULTS
The analyses of numerical models of the case study buildings which represent different
configurations of the ductile RC frame system as the main lateral force resisting system
were completed using PERFRORM-3D. The selected scenarios of multiple earthquakes
as presented in the previous chapter were applied to the building models where no
collapse during the main shock of any scenario was observed. This assures that the
capacities of the structural members in these buildings provide good levels of ductile
response especially the strong column-weak beam criterion as checked in chapter (3).
Inelastic deformations were developed within several components of the frame models
for at least one ground motion in each earthquake scenario where in few cases the models
behaved elastically during all the applied ground motions. This reflects the efficiency of
the selection criteria that was adopted in selecting the earthquake scenarios in order to
represent different ground motion characteristics and achieve inelastic deformation which
is desired to study the behavior of the analyzed models.
Mostly, the largest values of plastic deformations were developed during the main-shock
of each scenario except for a few scenarios where the deformations were higher during
the later ground motions.
In most of the analyses, the RC frame models experienced plastic deformations which
indicate certain levels of damage that can be assessed in terms of changes in the ductility
demands and changes in the fundamental periods of the frame models due to the
reduction in stiffness due to the large number of loading cycles in each earthquake
scenario.
The global behavior of the ductile RC frame models is evaluated in terms of lateral
displacements, development of plastic hinges and hysteretic behavior. Comparisons
between the analysis of the multiple earthquake sequence (Train) and the analysis of
individual earthquakes (Single) are performed in order to highlight the effect of multiple
ground motions on the structural response of the ductile RC frames.
115
The results of the nonlinear dynamic history analyses that were performed on the
numerical models of the case study buildings under the selected multiple earthquake
scenarios are presented in this chapter.
6.1 Displacement Time Histories
The time histories of the lateral displacements at the roof levels of the case study
buildings in the specified directions which resulted from the nonlinear analysis under the
selected earthquake scenarios are presented in (Figure 6.1) to (Figure 6.18). Each figure
shows the displacement time histories for the three case study buildings under the effect a
certain earthquake scenario that was analyzed using two approaches. First, the ground
motions of each scenario were applied in a sequence (Train) where the initial conditions
for each ground motion after the first one are assumed to be captured from the last time
step of the previous analysis. Secondly, each ground motion in a certain scenario is
applied to the numerical models separately (Single) where the initial conditions of each
one is set to zero regardless of the response of the building during the prior ground
motion.
In order to highlight the difference between these two approaches, each graph represents
the time history for one of the case study buildings during the whole duration of the
earthquake scenario including all ground motions with a time gap between each two
successive ground motions. The displacement time histories from both approaches are
plotted together to show the difference in the behavior where the sequence analysis is
plotted in solid black lines and the individual analysis is plotted in a solid grey line.
Two general observations can be concluded from the presented displacement histories in
these figures which can characterize the structural response of the analyzed ductile RC
frame models. The first observation from these figures is the vertical shift in the
displacement time histories for most of the earthquake scenarios due to the plastic
deformation that occurred within the frame components usually during the first ground
motion. This shift can be defined as the permanent (residual) deformation which also
reflects the formation of plastic hinges within the frame components. The formation of
116
plastic hinges is usually associated with yielding of the main flexural reinforcement of
the frame components as well as the formation of visual cracks.
The second observation is the change in the density of each of the time histories
according to each case study building as each has its unique dynamic characteristics such
as the fundamental period which affect the vibrational response of the building. The
fundamental period of the numerical model for North Hollywood building is 2.589
seconds which resulted in less cycles of vibration that those of both San Bruno and
Avalon buildings whose numerical models have fundamental periods of 0.951 and 0.407
seconds respectively. The number of cycles of vibration is an important factor in the low-
cycle fatigue behavior of different structural components as it will be discussed in more
detail in chapter (7). It also affects the deterioration of the stiffness of the frame
components due to the increase of the number of loading and unloading cycles.
There are also few specific observations for San Bruno building which depend on the
assigned loads and the structural properties of the frame components. For example, the
nonlinear analysis of the building model stopped due to failure of frame components
during both Cape-Mendocino earthquake scenarios. The individual analyses of the model
during the first after-shock of Cape-Mendocino (1583) and the second after-shock of
Cape-Mendocino (89156) scenarios lead to structural failure as indicated by the analysis.
On the other hand, both scenarios were analyzed in a sequence analysis and the analysis
was completed without any sign of failure of the model. This might be attributed to the
reduction of the stiffness of the frame components due to the inelastic response which
might lead to change in the dynamic properties of the frame and change the seismic
demand accordingly.
Another specific observation was the failure of the model of San Bruno building during
the Sequence (Train) analysis of the Christchurch (CBGS) scenario during the sixth
ground motion while the Individual (Single) analysis of model under the same ground
motion didn’t show any structural failure and was completed successfully. This might be
due to the damage accumulation from the previous five ground motions of that scenario
that possibly led to the failure of the building in the model.
117
0 10 20 30 40 50 60 70 80 90 100
-15
-10
-5
0
5
10
15
North Hollywood Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 10 20 30 40 50 60 70 80 90 100
-6
-4
-2
0
2
4
6
San Bruno Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 10 20 30 40 50 60 70 80 90 100
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Avalon Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
Figure 6.1 Displacement histories at the roof level for Cape-Mendocino (1583) scenario.
118
0 20 40 60 80 100 120 140 160
-10
-5
0
5
10
15
North Hollywood Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 20 40 60 80 100 120 140 160
-6
-4
-2
0
2
4
6
8
San Bruno Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 20 40 60 80 100 120 140 160
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
Avalon Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
Figure 6.2: Displacement histories at the roof level for Cape-Mendocino (89156)
scenario.
119
0 20 40 60 80 100 120 140 160 180 200
-6
-4
-2
0
2
4
6
North Hollywood Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 20 40 60 80 100 120 140 160 180 200
-6
-5
-4
-3
-2
-1
0
1
2
3
San Bruno Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 20 40 60 80 100 120 140 160 180 200
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Avalon Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
Figure 6.3: Displacement histories at the roof level for Chalflant Valley scenario.
120
0 50 100 150 200 250 300 350 400
-6
-4
-2
0
2
4
6
North Hollywood Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 50 100 150 200 250 300 350 400
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
San Bruno Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 50 100 150 200 250 300 350 400
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Avalon Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
Figure 6.4: Displacement histories at the roof level for Mammoth Lakes scenario.
121
0 50 100 150 200 250
-10
-8
-6
-4
-2
0
2
4
6
8
10
North Hollywood Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 50 100 150 200 250
-4
-3
-2
-1
0
1
2
3
4
5
6
San Bruno Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 50 100 150 200 250
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Avalon Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
Figure 6.5: Displacement histories at the roof level for Chi-Chi (TCU079) scenario.
122
0 50 100 150 200 250 300 350 400 450
-15
-10
-5
0
5
10
15
North Hollywood Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 50 100 150 200 250 300 350 400 450
-5
-4
-3
-2
-1
0
1
2
3
4
San Bruno Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 50 100 150 200 250 300 350 400 450
-1.5
-1
-0.5
0
0.5
1
1.5
Avalon Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
Figure 6.6: Displacement histories at the roof level for Chi-Chi (CHY036) scenario.
123
0 20 40 60 80 100
-10
-8
-6
-4
-2
0
2
4
6
8
North Hollywood Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 20 40 60 80 100
-4
-3
-2
-1
0
1
2
3
San Bruno Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 20 40 60 80 100
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Avalon Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
Figure 6.7: Displacement histories at the roof level for Kyushu scenario.
124
0 20 40 60 80 100
-8
-6
-4
-2
0
2
4
6
8
North Hollywood Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 20 40 60 80 100
-4
-3
-2
-1
0
1
2
3
4
San Bruno Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 20 40 60 80 100
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Avalon Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
Figure 6.8: Displacement histories at the roof level for Coalinga scenario.
125
0 20 40 60 80 100 120 140
-8
-6
-4
-2
0
2
4
6
8
North Hollywood Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 20 40 60 80 100 120 140
-3
-2
-1
0
1
2
3
San Bruno Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 20 40 60 80 100 120 140
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Avalon Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
Figure 6.9: Displacement histories at the roof level for Mexico scenario.
126
0 100 200 300 400 500 600 700
-20
-15
-10
-5
0
5
10
15
North Hollywood Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 100 200 300 400 500 600 700
-4
-3
-2
-1
0
1
2
3
4
5
San Bruno Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 100 200 300 400 500 600 700
-1.5
-1
-0.5
0
0.5
1
1.5
Avalon Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
Figure 6.10: Displacement histories at the roof level for Tohoku (FKS012) scenario.
127
0 100 200 300 400 500
-15
-10
-5
0
5
10
North Hollywood Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 100 200 300 400 500
-4
-3
-2
-1
0
1
2
3
San Bruno Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 100 200 300 400 500
-5
-4
-3
-2
-1
0
1
2
3
4
Avalon Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
Figure 6.11: Displacement histories at the roof level for Tohoku (IBR013) scenario.
128
0 50 100 150 200
-8
-6
-4
-2
0
2
4
6
8
North Hollywood Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 50 100 150 200
-4
-3
-2
-1
0
1
2
3
4
5
San Bruno Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 50 100 150 200
-3
-2
-1
0
1
2
3
Avalon Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
Figure 6.12: Displacement histories at the roof level for Valparaiso scenario.
129
0 50 100 150 200
-6
-4
-2
0
2
4
6
8
North Hollywood Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 50 100 150 200
-6
-4
-2
0
2
4
6
San Bruno Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 50 100 150 200
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Avalon Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
Figure 6.13: Displacement histories at the roof level for Honshu scenario.
130
0 50 100 150 200 250
-15
-10
-5
0
5
10
15
North Hollywood Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 50 100 150 200 250
-3
-2
-1
0
1
2
3
4
5
6
San Bruno Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 50 100 150 200 250
-3
-2
-1
0
1
2
3
4
Avalon Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
Figure 6.14: Displacement histories at the roof level for Tokachi scenario.
131
0 50 100 150 200 250
-8
-6
-4
-2
0
2
4
6
8
North Hollywood Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 50 100 150 200 250
-3
-2
-1
0
1
2
3
4
5
San Bruno Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 50 100 150 200 250
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Avalon Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
Figure 6.15: Displacement histories at the roof level for Maule scenario.
132
0 100 200 300 400 500 600
-20
-15
-10
-5
0
5
10
15
20
North Hollywood Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 100 200 300 400 500 600
-6
-4
-2
0
2
4
6
San Bruno Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 100 200 300 400 500 600
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Avalon Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
Figure 6.16: Displacement histories at the roof level for Christchurch (CBGS) scenario.
133
0 100 200 300 400 500 600
-20
-15
-10
-5
0
5
10
15
North Hollywood Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 100 200 300 400 500 600
-3
-2
-1
0
1
2
3
San Bruno Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 100 200 300 400 500 600
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Avalon Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
Figure 6.17: Displacement histories at the roof level for Christchurch (RHSC) scenario.
134
0 50 100 150 200 250 300 350 400 450 500
-20
-15
-10
-5
0
5
10
15
North Hollywood Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 50 100 150 200 250 300 350 400 450 500
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
San Bruno Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
0 50 100 150 200 250 300 350 400 450 500
-1.5
-1
-0.5
0
0.5
1
1.5
Avalon Building
Time (Seconds)
Displacement (in.)
Individual Analysis (Single)
Sequence Analysis (Train)
Figure 6.18: Displacement histories at the roof level for Christchurch (TPLC) scenario.
135
6.2 Story Displacements
The values of the lateral displacements at the roof levels for the case study buildings are
presented in (Table 6.1) to (Table 6.9). These tables include the absolute values of the
maximum lateral displacement in each direction and the permanent lateral deformation at
the end of ground motion in every earthquake scenario using the Sequence (Train)
analysis approach as well as the maximum values from the individual analysis of each
ground motion.
Also, the envelopes for lateral displacements at each floor level of the three case study
buildings during the last ground motion of each scenario are presented in (Figure 6.19) to
(Figure 6.36). Using the same approach of both Sequence (Train) and Individual (Single)
analyses, the displacement envelopes for each approach are plotted using solid black and
grey lines respectively. It can be observed from these figures that the envelopes for the
Sequence (Train) analysis approach have higher maximum displacements than the
Individual (Single) analysis approach for most of the earthquake scenarios. The
difference between both approaches might be due to the accumulation of plastic
deformations during the prior ground motions which was reflected in the response during
the last ground motion of each scenario. For several scenarios, no difference is observed
between both approaches which is most probably due to the elastic response of such a
building model during a specific earthquake scenario.
For few cases, the maximum displacement envelopes are in the same direction to the
right or to the left of the buildings vertical axes such as the case of San Bruno and Avalon
buildings during the Tohoku (IBR013) scenario which means that these two buildings
became tilted vertically due to the accumulation of plastic deformations which resulted in
lateral displacements in one direction. This permanent displacement might influence the
second order effect in the frame column especially for San Bruno buildings where the
moment frame columns are loaded with additional loads from the gravity columns.
Based on this comparison of both analysis approaches, it becomes clear that the
permanent lateral displacements from the prior ground motions of each scenario affect
the way the building vibrates when the next ground motion occurs.
136
Table 6.1: Roof displacements of North Hollywood building (Short to medium duration).
Earthquake
Scenario
Station Type PGA(g)
Train Single
Perm. (in) Max. (in) Max. (in)
Cape-
Mendocino
1583
MS 0.334 -0.229 13.5 13.5
SA 0.395 -0.142 8.04 8.08
AS 0.249 -0.173 10.7 10.9
89156
MS -0.589 -0.0116 12 12
SA 0.598 0.644 9.85 10.1
AS -0.323 0.652 5.95 5.36
Chalflant
Valley
54428
FS 0.232 -0.0869 2.5 2.5
MS 0.402 -0.103 5.02 5.12
AS -0.104 -0.111 0.565 0.512
AS -0.065 -0.115 0.566 0.486
Mammoth
Lakes
54099
MS 0.410 -0.0275 5.45 5.45
AS -0.161 -0.0356 1.52 1.51
AS -0.277 -0.0326 5.27 5.26
SA -0.345 -0.0353 1.24 1.23
AS -0.133 -0.0282 0.804 0.806
AS 0.253 -0.0288 1.44 1.43
Chi-Chi
TCU079
MS -0.393 0.0127 9.35 9.35
AS -0.212 0.0106 0.772 0.732
AS -0.263 0.0114 0.872 0.827
SA 0.622 0.00835 3.64 3.6
CHY036
MS 0.294 -0.0496 8.13 8.13
AS -0.076 -0.0141 0.25 0.287
AS 0.104 -0.0136 5.24 5.25
AS 0.092 -0.0114 4.56 4.54
SA 0.201 0.116 11.8 11.8
Kyushu KSG005
MS 0.441 -0.0132 4.77 4.77
SA 0.920 -0.142 8.97 9.01
137
Table 6.1: Roof displacements of North Hollywood building (Short to medium duration).
(cont’d).
Earthquake
Scenario
Station Type PGA(g)
Train Single
Perm. (in) Max. (in) Max. (in)
Coalinga 1162
MS 0.313 -0.0844 6.87 6.87
AS -0.054 -0.0776 0.554 0.473
SA 0.439 -0.0796 5.91 5.88
Mexico AZIH
MS -0.100 -0.0546 7.44 7.44
SA -0.162 -0.04 6.41 6.4
Table 6.2: Roof displacements of North Hollywood building (Long duration).
Earthquake
Scenario
Station Type PGA(g)
Train Single
Perm. (in) Max. (in) Max. (in)
Tohoku
FKS012
MS -0.359 -0.163 15.6 15.6
SA 0.502 -0.143 12.8 13.1
AS -0.090 -0.15 1.09 0.937
IBR013
MS 1.375 -0.411 11.4 11.4
SA -0.547 -0.389 3.74 3.33
AS -0.135 -0.392 1.36 0.994
Valparaiso LLO
MS 0.712 0.271 7.37 7.37
AS -0.186 0.269 1.83 1.53
AS 0.204 0.257 2.61 2.48
Honshu ISK005
MS 0.481 -0.0374 7.81 7.81
AS 0.134 -0.0394 1.81 1.8
Tokachi HKD109
MS 0.245 0.44 13.1 13.1
SA -0.417 0.488 6.88 6.46
Maule 499
MS 0.413 -0.0361 7.52 7.52
AS 0.147 -0.038 1.55 1.56
138
Table 6.3: Roof displacements for North Hollywood building (Christchurch scenarios).
Station Type PGA(g)
Train Single
Perm. (in) Max. (in) Max. (in)
CBGS
MS 0.185 -0.644 18.4 18.4
MS -0.430 -0.56 15.9 15.4
AS 0.003 -0.583 0.701 0.0481
AS 0.353 -0.586 3.65 3.21
FS 0.168 -0.583 1.89 1.47
MS 0.172 -0.644 11.5 11.9
FS 0.161 -0.666 7.71 7.06
MS 0.170 -0.638 5.25 4.64
RHSC
MS 0.232 -0.514 16.2 16.2
MS 0.250 -0.481 9.62 9.89
AS 0.184 -0.475 1.71 1.32
AS -0.215 -0.477 1.57 1.15
FS -0.091 -0.479 1.6 1.12
MS 0.188 -0.487 5.89 5.25
FS -0.173 -0.491 4.34 3.58
MS -0.153 -0.48 2.41 2.37
TPLC
MS 0.282 -0.268 15.9 15.9
MS 0.122 -0.262 4.18 3.98
AS 0.069 -0.261 1.13 0.968
AS 0.132 -0.263 1.5 1.48
FS 0.040 -0.256 0.831 0.667
MS 0.068 -0.279 3.01 3.04
FS -0.077 -0.277 1.43 1.27
MS 0.111 -0.255 1.22 0.948
139
Table 6.4: Roof displacements of San Bruno building (Short to medium duration).
Earthquake
Scenario
Station Type PGA(g)
Train Single
Perm. (in) Max. (in) Max. (in)
Cape-
Mendocino
1583
MS 0.334 0.542 3.46 3.46
SA 0.395 0.298 4.25 4.53
AS 0.249 -1.13 5.18 5.36
89156
MS -0.589 -1.32 5.84 5.84
SA 0.598 1.13 7.73 7.13
AS -0.323 0.737 3.37 3.48
Chalflant
Valley
54428
FS 0.232 -0.0185 1.39 1.39
MS 0.402 -0.848 5.23 5.22
AS -0.104 -0.849 1.15 0.293
AS -0.065 -0.853 1.34 0.576
Mammoth
Lakes
54099
MS 0.410 -0.143 2.08 2.08
AS -0.161 -0.109 1.75 1.91
AS -0.277 0.0529 2.07 2.15
SA -0.345 -0.0204 1.64 1.69
AS -0.133 -0.0202 0.753 0.789
AS 0.253 -0.00656 1.7 1.64
Chi-Chi
TCU079
MS -0.393 0.296 2.97 2.97
AS -0.212 0.296 0.663 0.388
AS -0.263 0.37 2.49 2.12
SA 0.622 0.586 3.14 2.91
CHY036
MS 0.294 0.312 4.75 4.75
AS -0.076 0.312 0.579 0.344
AS 0.104 0.308 1.42 1.13
AS 0.092 0.308 1.28 1.16
SA 0.201 0.211 2.72 2.38
Kyushu KSG005
MS 0.441 -0.823 3.83 3.83
SA 0.920 -0.493 3.58 2.95
140
Table 6.4: Roof displacements of San Bruno building (Short to medium duration).
(cont’d).
Earthquake
Scenario
Station Type PGA(g)
Train Single
Perm. (in) Max. (in) Max. (in)
Coalinga 1162
MS 0.313 -0.285 3.37 3.37
AS -0.054 -0.286 0.882 0.625
SA 0.439 -0.375 1.72 1.13
Mexico AZIH
MS -0.100 -0.00178 1.72 1.72
SA -0.162 -0.126 2.99 2.99
Table 6.5: Roof displacements of San Bruno building (Long duration).
Earthquake
Scenario
Station Type PGA(g)
Train Single
Perm. (in) Max. (in) Max. (in)
Tohoku
FKS012
MS -0.359 -0.225 3.06 3.06
SA 0.502 0.969 4.51 4.76
AS -0.090 0.969 1.76 0.631
IBR013
MS 1.375 -0.498 3.16 3.16
SA -0.547 -0.551 2.03 2.1
AS -0.135 -0.551 0.793 0.25
Valparaiso LLO
MS 0.712 0.784 4.34 4.34
AS -0.186 0.756 2.31 1.31
AS 0.204 0.69 2.33 2.03
Honshu ISK005
MS 0.481 -1.07 5.66 5.66
AS 0.134 -0.834 3.02 2.57
Tokachi HKD109
MS 0.245 -0.228 2.54 2.54
SA -0.417 1.28 5.66 5.89
Maule 499
MS 0.413 0.665 4.08 4.08
AS 0.147 0.557 1.91 1.43
141
Table 6.6: Roof displacements for San Bruno building (Christchurch scenarios).
Station Type PGA(g)
Train Single
Perm. (in) Max. (in) Max. (in)
CBGS
MS 0.185 0.425 3.26 3.26
MS -0.430 -0.432 4.79 4.89
AS 0.003 -0.433 0.436 0.00253
AS 0.353 -0.177 3.34 2.73
FS 0.168 -0.177 1.38 1.51
MS 0.172
Failure
5.03
FS 0.161 1.95
MS 0.170 2.09
RHSC
MS 0.232 -0.308 2.76 2.76
MS 0.250 -0.314 2.64 2.42
AS 0.184 -0.27 1.31 1.19
AS -0.215 -0.121 1.59 1.56
FS -0.091 -0.121 0.785 0.711
MS 0.188 -0.133 1.53 1.54
FS -0.173 -0.113 0.913 0.82
MS -0.153 -0.198 2.48 2.36
TPLC
MS 0.282 -0.592 2.95 2.95
MS 0.122 -0.54 1.69 1.36
AS 0.069 -0.54 0.905 0.447
AS 0.132 -0.54 1.08 0.583
FS 0.040 -0.541 0.753 0.208
MS 0.068 -0.544 1.57 1.01
FS -0.077 -0.544 0.856 0.307
MS 0.111 -0.545 1.35 0.802
142
Table 6.7: Roof displacements of Avalon building (Short to medium duration).
Earthquake
Scenario
Station Type PGA(g)
Train Single
Perm. (in) Max. (in) Max. (in)
Cape-
Mendocino
1583
MS 0.334 0.0378 2.47 2.47
SA 0.395 0.0573 2.19 2.34
AS 0.249 0.0551 1.07 1.02
89156
MS -0.589 -0.0441 1.95 1.95
SA 0.598 0.174 2.64 2.67
AS -0.323 0.178 1.18 1.05
Chalflant
Valley
54428
FS 0.232 0.0441 1.88 1.88
MS 0.402 0.0714 2.02 1.99
AS -0.104 0.0714 0.424 0.357
AS -0.065 0.0715 0.43 0.365
Mammoth
Lakes
54099
MS 0.410 0.011 1.68 1.68
AS -0.161 0.011 0.746 0.743
AS -0.277 0.0119 1.08 1.08
SA -0.345 0.0118 0.807 0.806
AS -0.133 0.0118 0.545 0.543
AS 0.253 0.0119 0.767 0.763
Chi-Chi
TCU079
MS -0.393 -0.0986 2.2 2.2
AS -0.212 -0.0987 0.65 0.613
AS -0.263 -0.0992 0.986 0.87
SA 0.622 -0.101 1.7 1.78
CHY036
MS 0.294 0.0131 1.28 1.28
AS -0.076 0.0131 0.492 0.49
AS 0.104 0.0131 0.551 0.553
AS 0.092 0.0131 0.323 0.321
SA 0.201 0.0118 1.39 1.39
Kyushu KSG005
MS 0.441 -0.0315 1.83 1.83
SA 0.920 -0.0266 1.53 1.56
143
Table 6.7: Roof displacements of Avalon building (Short to medium duration) (cont’d).
Earthquake
Scenario
Station Type PGA(g)
Train Single
Perm. (in) Max. (in) Max. (in)
Coalinga 1162
MS 0.313 -0.0504 2.09 2.09
AS -0.054 -0.0502 0.336 0.285
SA 0.439 -0.0535 1.64 1.6
Mexico AZIH
MS -0.100 0.0109 0.612 0.612
SA -0.162 0.0107 0.699 0.699
Table 6.8: Roof displacements of Avalon building (Long duration).
Earthquake
Scenario
Station Type PGA(g)
Train Single
Perm. (in) Max. (in) Max. (in)
Tohoku
FKS012
MS -0.359 0.0138 1.32 1.32
SA 0.502 0.0124 1.36 1.36
AS -0.090 0.0124 0.29 0.288
IBR013
MS 1.375 -0.341 4.37 4.37
SA -0.547 -0.373 1.78 1.62
AS -0.135 -0.373 0.575 0.216
Valparaiso LLO
MS 0.712 0.0637 2.77 2.77
AS -0.186 0.0636 1.25 1.13
AS 0.204 0.064 0.817 0.823
Honshu ISK005
MS 0.481 0.03773 1.8319 1.8319
AS 0.134 0.037747 0.73552 0.76118
Tokachi HKD109
MS 0.245 0.0142 1.62 1.62
SA -0.417 0.206 3 3
Maule 499
MS 0.413 0.00619 2.16 2.16
AS 0.147 0.0062 0.497 0.514
144
Table 6.9: Roof displacements for Avalon building (Christchurch scenarios).
Station Type PGA(g)
Train Single
Perm. (in) Max. (in) Max. (in)
CBGS
MS 0.185 0.0107 0.816 0.816
MS -0.430 0.0748 2.08 2.08
AS 0.003 0.0748 0.0785 0.0145
AS 0.353 0.087 1.74 1.73
FS 0.168 0.079 1.39 1.3
MS 0.172 0.0789 1.12 1.02
FS 0.161 0.0793 1.16 1.1
MS 0.170 0.0795 1.16 1.07
RHSC
MS 0.232 0.0127 1.48 1.48
MS 0.250 -0.0149 1.87 1.87
AS 0.184 -0.0147 0.892 0.907
AS -0.215 -0.0144 1.42 1.47
FS -0.091 -0.0144 0.517 0.49
MS 0.188 -0.0144 0.997 0.975
FS -0.173 -0.0144 0.889 0.908
MS -0.153 -0.0144 0.686 0.682
TPLC
MS 0.282 0.0139 1.44 1.44
MS 0.122 0.0139 0.788 0.792
AS 0.069 0.0139 0.232 0.229
AS 0.132 0.0139 0.601 0.598
FS 0.040 0.0139 0.21 0.207
MS 0.068 0.0139 0.323 0.326
FS -0.077 0.0139 0.563 0.566
MS 0.111 0.0139 0.601 0.604
145
-15 -10 -5 0 5 10
0
2
4
6
8
10
12
14
16
18
20
North Hollywood Building
Displacement (in.)
Story
Max. (Train)
Min. (Train)
Max. (Single)
Min. (Single)
-6 -4 -2 0 2
0
1
2
3
4
5
6
San Bruno Building
Displacement (in.)
Story
-3 -2 -1 0 1 2 3
0
1
2
3
4
Avalon Building
Displacement (in.)
Story
Figure 6.19: Envelopes of lateral displacement for Cape-Mendocino (1583) scenario.
-6 -4 -2 0 2 4 6 8
0
2
4
6
8
10
12
14
16
18
20
North Hollywood Building
Displacement (in.)
Story
Max. (Train)
Min. (Train)
Max. (Single)
Min. (Single)
-3 -2 -1 0 1 2 3 4
0
1
2
3
4
5
6
San Bruno Building
Displacement (in.)
Story
-1 -0.5 0 0.5 1 1.5
0
1
2
3
4
Avalon Building
Displacement (in.)
Story
Figure 6.20: Envelopes of lateral displacement for Cape-Mendocino (89156) scenario.
146
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6
0
2
4
6
8
10
12
14
16
18
20
North Hollywood Building
Displacement (in.)
Story
Max. (Train)
Min. (Train)
Max. (Single)
Min. (Single)
-1.5 -1 -0.5 0 0.5 1
0
1
2
3
4
5
6
San Bruno Building
Displacement (in.)
Story
-0.4 -0.2 0 0.2 0.4 0.6
0
1
2
3
4
Avalon Building
Displacement (in.)
Story
Figure 6.21: Envelopes of lateral displacement for Chalflant Valley scenario.
-1.5 -1 -0.5 0 0.5 1 1.5
0
2
4
6
8
10
12
14
16
18
20
North Hollywood Building
Displacement (in.)
Story
Max. (Train)
Min. (Train)
Max. (Single)
Min. (Single)
-2 -1 0 1 2
0
1
2
3
4
5
6
San Bruno Building
Displacement (in.)
Story
-1 -0.5 0 0.5 1
0
1
2
3
4
Avalon Building
Displacement (in.)
Story
Figure 6.22: Envelopes of lateral displacement for Mammoth Lakes scenario.
147
-3 -2 -1 0 1 2 3 4
0
2
4
6
8
10
12
14
16
18
20
North Hollywood Building
Displacement (in.)
Story
Max. (Train)
Min. (Train)
Max. (Single)
Min. (Single)
-3 -2 -1 0 1 2 3 4
0
1
2
3
4
5
6
San Bruno Building
Displacement (in.)
Story
-2 -1 0 1 2
0
1
2
3
4
Avalon Building
Displacement (in.)
Story
Figure 6.23: Envelopes of lateral displacement for Chi-Chi (TCU079) scenario.
-15 -10 -5 0 5 10 15
0
2
4
6
8
10
12
14
16
18
20
North Hollywood Building
Displacement (in.)
Story
Max. (Train)
Min. (Train)
Max. (Single)
Min. (Single)
-3 -2 -1 0 1 2 3
0
1
2
3
4
5
6
San Bruno Building
Displacement (in.)
Story
-1.5 -1 -0.5 0 0.5 1 1.5
0
1
2
3
4
Avalon Building
Displacement (in.)
Story
Figure 6.24: Envelopes of lateral displacement for Chi-Chi (CHY036) scenario.
148
-10 -5 0 5 10
0
2
4
6
8
10
12
14
16
18
20
North Hollywood Building
Displacement (in.)
Story
Max. (Train)
Min. (Train)
Max. (Single)
Min. (Single)
-4 -3 -2 -1 0 1 2 3
0
1
2
3
4
5
6
San Bruno Building
Displacement (in.)
Story
-1.5 -1 -0.5 0 0.5 1 1.5 2
0
1
2
3
4
Avalon Building
Displacement (in.)
Story
Figure 6.25: Envelopes of lateral displacement for Kyushu scenario.
-6 -4 -2 0 2 4 6
0
2
4
6
8
10
12
14
16
18
20
North Hollywood Building
Displacement (in.)
Story
Max. (Train)
Min. (Train)
Max. (Single)
Min. (Single)
-2 -1.5 -1 -0.5 0 0.5 1 1.5
0
1
2
3
4
5
6
San Bruno Building
Displacement (in.)
Story
-2 -1.5 -1 -0.5 0 0.5 1 1.5
0
1
2
3
4
Avalon Building
Displacement (in.)
Story
Figure 6.26: Envelopes of lateral displacement for Coalinga scenario.
149
-8 -6 -4 -2 0 2 4 6
0
2
4
6
8
10
12
14
16
18
20
North Hollywood Building
Displacement (in.)
Story
Max. (Train)
Min. (Train)
Max. (Single)
Min. (Single)
-3 -2 -1 0 1 2 3
0
1
2
3
4
5
6
San Bruno Building
Displacement (in.)
Story
-1 -0.5 0 0.5 1
0
1
2
3
4
Avalon Building
Displacement (in.)
Story
Figure 6.27: Envelopes of lateral displacement for Mexico scenario.
-1.5 -1 -0.5 0 0.5 1
0
2
4
6
8
10
12
14
16
18
20
North Hollywood Building
Displacement (in.)
Story
Max. (Train)
Min. (Train)
Max. (Single)
Min. (Single)
-1 -0.5 0 0.5 1 1.5 2
0
1
2
3
4
5
6
San Bruno Building
Displacement (in.)
Story
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3
0
1
2
3
4
Avalon Building
Displacement (in.)
Story
Figure 6.28: Envelopes of lateral displacement for Tohoku (FKS012) scenario.
150
-1.5 -1 -0.5 0 0.5 1
0
2
4
6
8
10
12
14
16
18
20
North Hollywood Building
Displacement (in.)
Story
Max. (Train)
Min. (Train)
Max. (Single)
Min. (Single)
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6
0
1
2
3
4
5
6
San Bruno Building
Displacement (in.)
Story
-0.6 -0.4 -0.2 0 0.2 0.4
0
1
2
3
4
Avalon Building
Displacement (in.)
Story
Figure 6.29: Envelopes of lateral displacement for Tohoku (IBR013) scenario.
-3 -2 -1 0 1 2 3
0
2
4
6
8
10
12
14
16
18
20
North Hollywood Building
Displacement (in.)
Story
Max. (Train)
Min. (Train)
Max. (Single)
Min. (Single)
-2 -1 0 1 2 3
0
1
2
3
4
5
6
San Bruno Building
Displacement (in.)
Story
-1 -0.5 0 0.5 1
0
1
2
3
4
Avalon Building
Displacement (in.)
Story
Figure 6.30: Envelopes of lateral displacement for Valparaiso scenario.
151
-2 -1.5 -1 -0.5 0 0.5 1 1.5
0
2
4
6
8
10
12
14
16
18
20
North Hollywood Building
Displacement (in.)
Story
Max. (Train)
Min. (Train)
Max. (Single)
Min. (Single)
-4 -3 -2 -1 0 1 2 3
0
1
2
3
4
5
6
San Bruno Building
Displacement (in.)
Story
-1 -0.5 0 0.5 1
0
1
2
3
4
Avalon Building
Displacement (in.)
Story
Figure 6.31: Envelopes of lateral displacement for Honshu scenario.
-6 -4 -2 0 2 4 6 8
0
2
4
6
8
10
12
14
16
18
20
North Hollywood Building
Displacement (in.)
Story
Max. (Train)
Min. (Train)
Max. (Single)
Min. (Single)
-4 -2 0 2 4 6
0
1
2
3
4
5
6
San Bruno Building
Displacement (in.)
Story
-3 -2 -1 0 1 2 3 4
0
1
2
3
4
Avalon Building
Displacement (in.)
Story
Figure 6.32: Envelopes of lateral displacement for Tokachi scenario.
152
-1.5 -1 -0.5 0 0.5 1 1.5 2
0
2
4
6
8
10
12
14
16
18
20
North Hollywood Building
Displacement (in.)
Story
Max. (Train)
Min. (Train)
Max. (Single)
Min. (Single)
-1.5 -1 -0.5 0 0.5 1 1.5 2
0
1
2
3
4
5
6
San Bruno Building
Displacement (in.)
Story
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6
0
1
2
3
4
Avalon Building
Displacement (in.)
Story
Figure 6.33: Envelopes of lateral displacement for Maule scenario.
-6 -4 -2 0 2 4
0
2
4
6
8
10
12
14
16
18
20
North Hollywood Building
Displacement (in.)
Story
Max. (Train)
Min. (Train)
Max. (Single)
Min. (Single)
-4 -2 0 2 4 6
0
1
2
3
4
5
6
San Bruno Building
Displacement (in.)
Story
-1.5 -1 -0.5 0 0.5 1 1.5
0
1
2
3
4
Avalon Building
Displacement (in.)
Story
Figure 6.34: Envelopes of lateral displacement for Christchurch (CBGS) scenario.
153
-3 -2 -1 0 1 2 3
0
2
4
6
8
10
12
14
16
18
20
North Hollywood Building
Displacement (in.)
Story
Max. (Train)
Min. (Train)
Max. (Single)
Min. (Single)
-3 -2 -1 0 1 2 3
0
1
2
3
4
5
6
San Bruno Building
Displacement (in.)
Story
-1 -0.5 0 0.5 1
0
1
2
3
4
Avalon Building
Displacement (in.)
Story
Figure 6.35: Envelopes of lateral displacement for Christchurch (RHSC) scenario.
-1.5 -1 -0.5 0 0.5 1
0
2
4
6
8
10
12
14
16
18
20
North Hollywood Building
Displacement (in.)
Story
Max. (Train)
Min. (Train)
Max. (Single)
Min. (Single)
-1.5 -1 -0.5 0 0.5 1
0
1
2
3
4
5
6
San Bruno Building
Displacement (in.)
Story
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6
0
1
2
3
4
Avalon Building
Displacement (in.)
Story
Figure 6.36: Envelopes of lateral displacement for Christchurch (TPLC) scenario.
154
6.3 Development of Plastic Hinges
As it was mentioned before, the formation of plastic hinges within the components of a
ductile RC frame is an indication of significant deformation. This deformation is
associated with yield of flexural reinforcement and the occurrence of relatively wide
cracks on the face of the concrete component which might not be visible after the
earthquake due to the architectural installation on the inside and the outside of the
buildings. Since visual inspection is one of the most important techniques of post-
earthquake evaluation of existing buildings, it is important to have a good idea about the
possible location of plastic hinges before the inspection in order to reduce the effort of
removing the architectural fixtures and lead to more effective inspection.
The analysis results of the case study buildings show formation of plastic hinges for most
of the applied earthquake scenarios either during the main shock or the after-shocks. The
number of plastic hinges are provided in (Table 6.10) to (Table 6.18) which are classified
according to each analysis approach. For the Sequence (Train) analysis approach, plastic
hinges are defined as newly formed hinges which are the hinges formed at specific
locations during the main shock of an earthquake scenario or during an after-shock where
there was no plastic hinges in the prior ground motions. For the Individual (Single)
analysis approach, only new hinges are provided as it is assumed that the analysis for
each ground motion doesn’t depend on the previous ones.
For most the earthquake scenarios, the formation of plastic hinges occurred during the
main-shock accompanied with permanent deformation within the structural elements of
the RC frame. After the main shock, further plastic deformations occurred within the
frame components during the following aftershocks except for several scenarios where
the building models didn’t show more plastic deformations within any component. For
example, Chi-Chi (TCU079) scenario didn’t result in any further plastic deformation for
North Hollywood building after the main shock where plastic deformations where
detected at 14 locations. On the other hand, the model of San Bruno building
experienced plastic deformation during seven ground motions out of eight during the
Christchurch (RHSC) scenario.
155
An important observation is the plastic deformation that occurred at seven locations
within North Hollywood building during the after-shock of Kyushu scenario while there
was no plastic deformation during the main shock. This indicates the possibility of the
unexpected damage during an after-shock based on a false conclusion from the behavior
of the building during the main shock. In this case, it is recommended that buildings
should be inspected after the after-shocks as well as the main shocks.
Another observation comes from the analysis of San Bruno during the Chalflant Valley
scenario which led to plastic deformations at 11 locations during the fore-shock which
was increased to a total of 109 during the main shock. The Individual (Single) analysis of
the main shock showed the same numbers of plastic hinges when the main shock was
applied separately but higher plastic deformations are observed from the Sequence
(Train) analysis approach.
The general observation is that the total number of plastic hinges with the frame models
of the case study buildings is higher for the Sequence (Train) analysis than the Individual
(Single) analysis.
The distribution of plastic hinges during Cape-Mendocino (89156) scenario for the three
case study buildings are shown in (Figure 6.37) to (Figure 6.39). These figures provide a
good example of the development of new plastic hinges during the after-shocks as well as
the increase in plastic deformation at plastic hinges that were formed during the main
shock. The newly developed plastic hinges are indicated with the small solid circle which
increases in size with the more developed plastic deformation during the next ground
motion. Another example is from the Christchurch (CBGS) scenario for San Bruno
building which is shown in (Figure 6.40) which developed large number of plastic hinges
during first, second and fourth ground motions before the building model fails during the
sixth ground motion.
In order to show the difference between the Sequence (Train) and Individual (Single)
analysis approaches, (Figure 6.41) to (Figure 6.43) show the distribution of plastic hinges
in the three cases study buildings during the last after-shock of three different earthquake
scenarios. These figures show that the models experienced larger plastic deformations
156
during the aftershocks when analyzed as a part of a Sequence (Train) than the analysis of
Individual (Single) ground motions in terms of both the number of plastic hinges and the
extent of plastic deformation. This is attributed to the formation of plastic hinges due to
prior ground motions which led to higher number of plastic hinges with more plastic
deformations during the last aftershock of each of the selected earthquake scenarios.
An important observation from the previously mentioned figures is the identification of
the locations of plastic hinges which are developed at the ends of the floor beam. For the
first floor columns of San Bruno building and the basement floor columns of Avalon
building, several additional plastic hinges were formed at the foundation level. This
complies with the strong column-weak beam approach that as described in chapter (2)
which is one of the main concepts of the current seismic design criteria. It also indicates
that the original designs of the case study buildings were performed considering a good
level of ductile response during earthquake. Despite this conclusion, most probably these
designs were against one major earthquake while the ductile response during multiple
earthquakes becomes a critical aspect of the design after the recent collapses from the
Christchurch earthquakes.
The failure of San Bruno model during the sixth ground motion of the Christchurch
(CBGS) scenario might be due to excessive plastic deformations that were accumulated
throughout the prior five earthquakes. This case highlights the need to consider multiple
earthquake scenarios for both the analysis and design of ductile RC frame building as it
might be a critical case for a specific building based on its loading conditions and
dynamic properties as well as the characteristics of the ground motions.
157
Table 6.10: Plastic hinges in North Hollywood building (Short to medium duration).
Earthquake
Scenario
Station Type
Train Single
New Accumulated Total New
Cape-
Mendocino
1583
MS
60 ---- 60 60
SA
5 35 65 10
AS
---- 51 65 20
89156
MS
63 ---- 63 63
SA
28 51 91 61
AS
---- 33 91 4
Chalflant
Valley
54428
FS
---- ---- ---- ----
MS
11 ---- 11 11
AS
---- ---- 11 ----
AS
---- ---- 11 ----
Mammoth
Lakes
54099
MS
1 ---- 1 1
AS
---- ---- 1 ----
AS
---- ---- 1 ----
SA
---- ---- 1 ----
AS
---- ---- 1 ----
AS
---- ---- 1 ----
Chi-Chi
TCU079
MS
14 ---- 14 14
AS
---- ---- 14 ----
AS
---- ---- 14 ----
SA
---- ---- 14 ----
CHY036
MS
6 ---- 6 6
AS
---- ---- 6 ----
AS
---- ---- 6 1
AS
---- ---- 6 ----
SA
25 6 31 31
Kyushu KSG005
MS
---- ---- ---- ----
SA
7 ---- 7 7
158
Table 6.10: Plastic hinges in North Hollywood building (Short to medium duration).
(cont’d).
Earthquake
Scenario
Station Type
Train Single
New Accumulated Total New
Coalinga 1162
MS
4 ---- 4 4
AS
---- 4 4 ----
SA
---- 4 4 3
Mexico AZIH
MS
4 ---- 4 4
SA
---- ---- 4 3
Table 6.11: Plastic hinges in North Hollywood building (Long duration).
Earthquake
Scenario
Station Type
Train Single
New Accumulated Total New
Tohoku
FKS012
MS
67 ---- 67 67
SA
4 57 71 43
AS
---- ---- 71 ----
IBR013
MS
57 ---- 57 57
SA
---- ---- 57 ----
AS
---- ---- 57 ----
Valparaiso LLO
MS
40 ---- 40 40
AS
---- ---- 40 ----
AS
---- ---- 40 ----
Honshu ISK005
MS
7 ---- 7 7
AS
---- ---- ---- ----
Tokachi HKD109
MS
40 ---- 40 40
SA
9 17 49 14
Maule 499
MS
4 ---- 4 4
AS
---- ---- 4 ----
159
Table 6.12: Plastic hinges in North Hollywood building (Christchurch scenarios).
Station Type
Train Single
New Accumulated Total New
CBGS
MS
74 ---- 74 74
MS
1 64 75 65
AS
---- ---- 75 ----
AS
---- ---- 75 ----
FS
---- ---- 75 ----
MS
---- 66 75 41
FS
---- 4 75 4
MS
---- ---- 75 1
RHSC
MS
70 ---- 70 70
MS
---- 61 70 21
AS
---- ---- 70 ----
AS
---- ---- 70 ----
FS
---- ---- 70 ----
MS
---- ---- 70 1
FS
---- ---- 70 ----
MS
---- ---- 70 ----
TPLC
MS
68 ---- 68 68
MS
---- ---- 68 ----
AS
---- ---- 68 ----
AS
---- ---- 68 ----
FS
---- ---- 68 ----
MS
---- ---- 68 ----
FS
---- ---- 68 ----
MS
---- ---- 68 ----
160
Table 6.13: Plastic hinges in San Bruno building (Short to medium duration).
Earthquake
Scenario
Station Type
Train Single
New Accumulated Total New
Cape-
Mendocino
1583
MS
89 ---- 89 89
SA
31 89 120 119
AS
---- 120 120 Failure
89156
MS
120 ---- 120 120
SA
---- 120 120 Failure
AS
---- 105 120 105
Chalflant
Valley
54428
FS
11 ---- 11 11
MS
98 11 109 109
AS
---- ---- ---- ----
AS
---- ---- ---- ----
Mammoth
Lakes
54099
MS
72 ---- 72 72
AS
2 71 74 28
AS
1 73 75 70
SA
1 74 76 29
AS
---- ---- 76 ----
AS
---- 74 76 15
Chi-Chi
TCU079
MS
107 ---- 107 107
AS
---- ---- 107 ----
AS
---- 105 107 87
SA
3 107 110 107
CHY036
MS
106 ---- 106 106
AS
---- ---- 106 ----
AS
---- ---- 106 ----
AS
---- ---- 106 ----
SA
---- 96 106 59
Kyushu KSG005
MS
107 ---- 107 107
SA
11 97 118 113
161
Table 6.13: Plastic hinges in San Bruno building (Short to medium duration). (cont’d).
Earthquake
Scenario
Station Type
Train Single
New Accumulated Total New
Coalinga 1162
MS
108 ---- 108 108
AS
---- ---- 108 ----
SA
---- 86 108 14
Mexico AZIH
MS
24 ---- 24 24
SA
71 24 95 94
Table 6.14: Plastic hinges in San Bruno building (Long duration).
Earthquake
Scenario
Station Type
Train Single
New Accumulated Total New
Tohoku
FKS012
MS
97 ---- 97 97
SA
21 97 118 118
AS
---- ---- 118 ----
IBR013
MS
142 ---- 142 142
SA
---- 120 142 96
AS
---- ---- 142 ----
Valparaiso LLO
MS
120 ---- 120 120
AS
---- 76 120 1
AS
---- 94 120 81
Honshu ISK005
MS
110 ---- 110 110
AS
---- 74 110 74
Tokachi HKD109
MS
108 ---- 108 108
SA
---- 108 108 119
Maule 499
MS
109 ---- 109 109
AS
---- 87 109 1
162
Table 6.15: Plastic hinges in San Bruno building (Christchurch scenarios).
Station Type
Train Single
New Accumulated Total New
CBGS
MS
97 ---- 97 97
MS
21 95 118 115
AS
---- ---- 118 ----
AS
---- 117 118 77
FS
---- 6 118 2
MS
Failure
96
FS
51
MS
72
RHSC
MS
107 ---- 107 107
MS
1 107 108 95
AS
---- 86 108 19
AS
---- 74 108 51
FS
---- ---- 108 ----
MS
---- 107 108 3
FS
---- 26 108 1
MS
1 107 109 75
TPLC
MS
95 ---- 95 95
MS
---- 72 95 ----
AS
---- ---- 95 ----
AS
---- ---- 95 ----
FS
---- ---- 95 ----
MS
---- 12 95 ----
FS
---- ---- 95 ----
MS
---- ---- 95 ----
163
Table 6.16: Plastic hinges in Avalon building (Short to medium duration).
Earthquake
Scenario
Station Type
Train Single
New Accumulated Total New
Cape-
Mendocino
1583
MS
9 ---- 9 9
SA
---- 7 9 7
AS
---- ---- 9 ----
89156
MS
4 ---- 4 4
SA
4 5 9 7
AS
---- 2 9 ----
Chalflant
Valley
54428
FS
6 ---- 6 6
MS
---- 6 6 5
AS
---- ---- 6 ----
AS
---- ---- 6 ----
Mammoth
Lakes
54099
MS
4 ---- 4 4
AS
---- ---- 4 ----
AS
---- ---- 4 ----
SA
---- ---- 4 ----
AS
---- ---- 4 ----
AS
---- ---- 4 ----
Chi-Chi
TCU079
MS
5 ---- 5 5
AS
---- ---- 5 ----
AS
---- ---- 5 ----
SA
1 5 6 4
CHY036
MS
---- ---- ---- ----
AS
---- ---- ---- ----
AS
---- ---- ---- ----
AS
---- ---- ---- ----
SA
---- ---- ---- ----
Kyushu KSG005
MS
4 ---- 4 4
SA
1 4 5 1
164
Table 6.16: Plastic hinges in Avalon building (Short to medium duration). (cont’d).
Earthquake
Scenario
Station Type
Train Single
New Accumulated Total New
Coalinga 1162
MS
7 ---- 7 7
AS
---- ---- 7 ----
SA
---- 4 7 1
Mexico AZIH
MS
---- ---- ---- ----
SA
---- ---- ---- ----
Table 6.17: Plastic hinges in Avalon building (Long duration).
Earthquake
Scenario
Station Type
Train Single
New Accumulated Total New
Tohoku
FKS012
MS
---- ---- ---- ----
SA
---- ---- ---- ----
AS
---- ---- ---- ----
IBR013
MS
12 ---- 12 12
SA
---- 4 12 2
AS
---- ---- 12 ----
Valparaiso LLO
MS
10 ---- 10 10
AS
---- ---- 10 ----
AS
---- ---- 10 ----
Honshu ISK005
MS
5 ---- 5 5
AS
---- ---- 5 ----
Tokachi HKD109
MS
3 ---- 3 3
SA
6 3 9 9
Maule 499
MS
9 ---- 9 9
AS
---- ---- 9 ----
165
Table 6.18: Plastic hinges in Avalon building (Christchurch scenarios).
Station Type
Train Single
New Accumulated Total New
CBGS
MS
---- ---- ---- ----
MS
7 ---- 7 7
AS
---- ---- 7 ----
AS
---- 6 7 2
FS
---- 1 7 ----
MS
---- ---- 7 ----
FS
---- ---- 7 ----
MS
---- ---- 7 ----
RHSC
MS
---- ---- ---- ----
MS
6 ---- 6 6
AS
---- ---- 6 ----
AS
---- 4 6 ----
FS
---- ---- 6 ----
MS
---- ---- 6 ----
FS
---- ---- 6 ----
MS
---- ---- 6 ----
TPLC
MS
---- ---- ---- ----
MS
---- ---- ---- ----
AS
---- ---- ---- ----
AS
---- ---- ---- ----
FS
---- ---- ---- ----
MS
---- ---- ---- ----
FS
---- ---- ---- ----
MS
---- ---- ---- ----
166
Figure 6.37: Development of plastic hinges in San Bruno building during Cape-
Mendocino (89156) scenario.
Figure 6.37: Development of plastic hinges in North Hollywood building during Cape-Mendocino (89156)
scenario.
167
Figure 6.38: Development of plastic hinges in San Bruno building during Cape-
Mendocino (89156) scenario.
168
Figure 6.39: Development of plastic hinges in Avalon building during Cape-Mendocino
(89156) scenario.
169
Figure 6.40: Development of plastic hinges in San Bruno building during Christchurch
(CBGS) scenario.
170
Figure 6.41: Comparison between the Sequence Analysis (Train) and the Individual
Analysis (Single) for North Hollywood building during the last after-shock of Tokachi
scenario.
171
Figure 6.42: Comparison between the Sequence Analysis (Train) and the Individual
Analysis (Single) for San Bruno building during the last after-shock of Valparaiso
scenario.
172
Figure 6.43: Comparison between the Sequence Analysis (Train) and the Individual
Analysis (Single) for Avalon building during the last after-shock of Chi-Chi (TCU079)
scenario.
173
6.4 Hysteretic Behavior
According to the plastic hinge distributions for the selected earthquake scenarios, plastic
hinges occurred mainly at the ends of the floor beams with several additional plastic
hinges in the bottom floor columns at the foundation level. For the plastic hinges at the
ends of the floor beams, the moment-curvature relationships showed hysteresis loops
while for rest of the beams, no hysteresis loops were observed where the relationship is
just a straight line indicating an elastic behavior.
During both Coalinga and Cape-Mendocino (89156) scenarios, inelastic deformation
started during the main-shock (first ground motion) which affected the shape of the
hysteretic behavior during the following ground motions as shown in (Figure 6.44) and
(Figure 6.45). It shows the hysteresis loops of sample floor beam elements from each of
the case study buildings during the last after-shock in comparison with a prior ground
motion. The plot of the hysteresis loops for the last after-shock also shows the difference
between the two analysis approaches as indicated by solid black line for Sequence (Train)
analysis approach versus Individual (Single) analysis approach.
Significant change in the shape of the hysteresis loops is observed by comparing both
analysis approaches which led to an increase in the curvature values for the analysis as a
part of a sequence (Train). This can be translated to an increase in the ductility demand
which is required to provide a more ductile response during multiple earthquakes than
only a single major earthquake.
Sample beam elements were selected from each building model where the hysteresis
loops from three different earthquakes scenario are presented in (Figure 6.46) to (Figure
6.48) for the first and last ground motions. These figures indicates the difference in the
hysteresis loops between the two analysis approaches such as the difference between
linear behavior and the hysteretic behavior of element #6 in Avalon building during the
last ground motion of the Kyushu scenario. This kind of behavior neglects the stiffness
deterioration due to the previously applied ground motions which may lead to inaccurate
analysis due to the change of the dynamic properties of the frame model which affects the
seismic demand accordingly.
174
In order to show the effect of multiple earthquakes on the hysteretic behavior at plastic
hinges, the results from Christchurch (CBGS) scenario for three sample beam elements
form the case study buildings are shown in (Figure 6.49) to (Figure 6.51). These figures
show the change in the shape of the hysteresis loops due to the damage accumulations
during three ground motions out of eight in this scenario. For each building, plastic
hinges were formed during the first ground motion then continued to experience both
increase in their numbers and more plastic deformations at previously developed plastic
hinges. The prior plastic deformation affected the size of the hysteresis loops which
represents the dissipated energy during the structural response as well as the inclination
of the loop which reflects the deterioration in the stiffness of the beam element due to
several loading and unloading cycles.
The previous discussion highlights the need to analyze the RC ductile frame buildings by
applying all the ground motions that affected the building during relatively short period
of time as long as no repair or rehabilitation plan is applied to the building which can
change the structural properties of the building. This is mostly required for the case of
main shocks with their after-shocks or it might be also valid for earthquakes that occurred
over a longer period without any change in the structural system of the building.
175
-3 -2 -1 0 1 2 3
x 10
-4
-1000
-500
0
500
1000
North Hollywood Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
x 10
-4
-1000
-500
0
500
1000
North Hollywood Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
a) Element #110 in North Hollywood building
-3 -2 -1 0 1 2 3
x 10
-4
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
San Bruno Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
-8 -6 -4 -2 0 2 4 6 8
x 10
-5
-3000
-2000
-1000
0
1000
2000
3000
San Bruno Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
b) Element #83 in San Bruno building
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
x 10
-4
-6000
-4000
-2000
0
2000
4000
6000
Avalon Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
-2 -1 0 1 2
x 10
-4
-6000
-4000
-2000
0
2000
4000
6000
Avalon Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
c) Element #6 in Avalon building
Figure 6.44: Hysteretic behavior at sample beam elements during the first (to the left) and
the last (to the right) ground motions in the Coalinga scenario.
176
-4 -3 -2 -1 0 1 2 3 4
x 10
-4
-1500
-1000
-500
0
500
1000
1500
North Hollywood Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
x 10
-4
-1500
-1000
-500
0
500
1000
1500
North Hollywood Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
a) Element #115 in North Hollywood building
-8 -6 -4 -2 0 2 4 6 8
x 10
-4
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
San Bruno Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
-3 -2 -1 0 1 2 3
x 10
-4
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
San Bruno Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
b) Element #94 in San Bruno building
-2 -1 0 1 2
x 10
-4
-6000
-4000
-2000
0
2000
4000
6000
Avalon Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
-1 0 1
x 10
-4
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
Avalon Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
c) Element #6 in Avalon building
Figure 6.45: Hysteretic behavior at sample beam elements during the second (to the left)
and the third (to the right) ground motions in the Cape Mendocino (89156) scenario.
177
-4 -3 -2 -1 0 1 2 3 4
x 10
-4
-2000
-1500
-1000
-500
0
500
1000
1500
2000
North Hollywood Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
x 10
-4
-1500
-1000
-500
0
500
1000
1500
North Hollywood Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
a) Cape Mendocino (1583) scenario.
-2 -1 0 1 2
x 10
-4
-1500
-1000
-500
0
500
1000
1500
North Hollywood Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
-2 -1 0 1 2
x 10
-4
-1500
-1000
-500
0
500
1000
1500
North Hollywood Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
b) Chi-Chi (CHY036) scenario.
-4 -3 -2 -1 0 1 2 3 4
x 10
-4
-1500
-1000
-500
0
500
1000
1500
North Hollywood Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
x 10
-4
-1500
-1000
-500
0
500
1000
1500
North Hollywood Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
c) Tokachi scenario.
Figure 6.46: Hysteretic behavior at beam element #115 in North Hollywood building
during the first and the last ground motions of three different scenarios.
178
-5 -4 -3 -2 -1 0 1 2 3 4 5
x 10
-4
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
San Bruno Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
-3 -2 -1 0 1 2 3
x 10
-4
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
San Bruno Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
a) Chi-Chi (TCU079) scenario.
-4 -3 -2 -1 0 1 2 3 4
x 10
-4
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
San Bruno Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
-3 -2 -1 0 1 2 3
x 10
-4
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
San Bruno Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
b) Kyushu scenario.
-2 -1 0 1 2
x 10
-4
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
San Bruno Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
-5 -4 -3 -2 -1 0 1 2 3 4 5
x 10
-4
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
San Bruno Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
c) Tokachi scenario.
Figure 6.47: Hysteretic behavior at beam element #86 in San Bruno building during the
first and the last ground motions of three different scenarios.
179
-3 -2 -1 0 1 2 3
x 10
-4
-6000
-4000
-2000
0
2000
4000
6000
Avalon Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
-2 -1 0 1 2
x 10
-4
-6000
-4000
-2000
0
2000
4000
6000
Avalon Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
a) Chi-Chi (TCU079) scenario.
-2 -1 0 1 2
x 10
-4
-6000
-4000
-2000
0
2000
4000
6000
Avalon Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
-1.5 -1 -0.5 0 0.5 1 1.5
x 10
-4
-6000
-4000
-2000
0
2000
4000
6000
Avalon Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
b) Kyushu scenario.
-1.5 -1 -0.5 0 0.5 1 1.5
x 10
-4
-6000
-4000
-2000
0
2000
4000
6000
Avalon Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
-3 -2 -1 0 1 2 3
x 10
-4
-6000
-4000
-2000
0
2000
4000
6000
Avalon Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
c) Tokachi scenario.
Figure 6.48: Hysteretic behavior at beam element #6 in Avalon building during the first
and the last ground motions of three different scenarios.
180
-6 -4 -2 0 2 4 6
x 10
-4
-2000
-1500
-1000
-500
0
500
1000
1500
2000
North Hollywood Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
a) Second ground motion
-6 -4 -2 0 2 4 6
x 10
-4
-2000
-1500
-1000
-500
0
500
1000
1500
2000
North Hollywood Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
b) Sixth ground motion.
-3 -2 -1 0 1 2 3
x 10
-4
-1500
-1000
-500
0
500
1000
1500
North Hollywood Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
c) Seventh ground motion
Figure 6.49: Hysteretic behavior at beam element #109 in North Hollywood building
during three ground motions of the Christchurch (CBGS) scenario.
181
-4 -3 -2 -1 0 1 2 3 4
x 10
-4
-5000
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
5000
San Bruno Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
a) Second ground motion
-3 -2 -1 0 1 2 3
x 10
-4
-5000
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
5000
San Bruno Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
b) Fourth ground motion.
-4 -3 -2 -1 0 1 2 3 4
x 10
-4
-5000
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
5000
San Bruno Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
c) Sixth ground motion (before failure).
Figure 6.50: Hysteretic behavior at beam element #9 in San Bruno building during three
ground motions of the Christchurch (CBGS) scenario.
182
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
x 10
-4
-6000
-4000
-2000
0
2000
4000
6000
Avalon Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
a) Second ground motion
-2 -1 0 1 2
x 10
-4
-6000
-4000
-2000
0
2000
4000
6000
Avalon Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
b) Fourth ground motion.
-1.5 -1 -0.5 0 0.5 1 1.5
x 10
-4
-6000
-4000
-2000
0
2000
4000
6000
Avalon Building
Curvature (1/in)
Moment (kip.in)
Individual Analysis (Single)
Sequence Analysis (Train)
c) Fifth ground motion.
Figure 6.51: Hysteretic behavior at beam element #7 in Avalon building during three
ground motions of the Christchurch (CBGS) scenario.
183
6.5 Ductility Demand
The ductility demand due to a certain ground motion is one of the basic concepts for
ductile design of structures in general. For ductile RC frames, ductility is considered as
an important damage indicator as it defines the yielding of the main reinforcing bars at
plastic hinge locations as well as significant cracking and spalling of concrete. It
represents the state of damage at plastic hinges while the rest of the RC element is
assumed to have minimal damage or remain elastic.
The ductility demand can be defined in terms curvature as,
y
m
ϕ
ϕ
μ =
where “φ
y
” is the curvature of the RC section at the first yield of longitudinal reinforcing
bars and “φ
m
” is the maximum curvature along the RC element which usually happens at
plastic hinges (Banon et al., 1981).
The ductility demands were calculated for all the floor beams in the case study buildings
during the selected earthquake scenarios as shown in (Figure 6.52) to (Figure 6.69) for
both Sequence (Train) analysis and Individual (Single) analysis approaches. These
figures show the ductility demands for the ground motions after the first ground motion
in each earthquake scenario in the first and second category while for Christchurch
scenarios; it shows the ductility demands after the second ground motion. Each figure is
in the form of a bar chart where the grey portion of the bar represents the maximum
ductility for the Individual (Single) analysis approach while the black portion represent
the increase in the maximum ductility due to the damage accumulation from the
Sequence (Train) analysis approach.
The model for North Hollywood building reached maximum ductility demand of almost
6.5 during Christchurch (CBGS) scenario and experienced high ductility demands
between 4 and 5 during Cape-Mendocino (1583), Cape-Mendocino (89516), Chalflant
Valley, Chi-Chi (TCU079), Chi-Chi (CHY036), Kyushu, Tohoku (FKS012), and
Christchurch (RHSC) scenarios. It is clear that the effect of previously developed plastic
184
deformation from the first ground motion increased the ductility demand during the later
ground motions for most of the selected earthquake scenarios.
On the other hand, the model for San Bruno building reached maximum ductility demand
of almost 13 during Cape-Mendocino (89156) scenario and experienced very high
ductility demands between 5 and 10 during Cape-Mendocino (1583), Chalflant Valley,
Chi-Chi (TCU079), Kyushu, Tohoku (FKS012), Tokachi, and Christchurch (CBGS)
scenarios. Similarly, the effect of previous plastic damage is obvious for most of the
earthquake scenarios. For several scenarios, this effect was minimal such as Chalflant
Valley, Mexcio, and Tohoku (FKS012) which might be due to the significant plastic
deformation that happened during the later ground motions by themselves (Individual
Analysis) which was larger than the plastic deformation during the first ground motion.
Finally, the model for Avalon building reached maximum ductility demand of almost 3.5
during Tokachi scenario and experienced moderate ductility demands between 2 and 3
during Cape-Mendocino (89156) and Tohoku (IBR013) scenarios. The ductility demands
during the later ground motions were less than those of the first ground motion during 6
of the selected earthquake scenarios as no further plastic deformation occurred. For the
rest 9 scenarios, the plastic deformations due to the first ground motion of each
earthquake scenario increased the ductility demands during the later ground motion.
The general conclusion from the presented ductility demand graphs is the significant
effect of initial plastic deformation during the first ground motion on the behavior of the
ductile RC frame buildings which resulted in higher ductility demands for most of the
earthquake scenarios. This effect was highlighted by comparing the results from both
Sequence (Train) analysis and Individual (Single) analysis approaches.
185
1 2 3 4 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Ductility
Story
Train
Single
1 3 5 7 9 11 13 15
0
1
2
3
4
5
6
San Bruno Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
Avalon Building
Ductility
Story
Train
Single
Figure 6.52: Maximum ductility in floor beams for Cape-Mendocino (1583) scenario.
1 2 3 4 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Ductility
Story
Train
Single
1 3 5 7 9 11 13 15
0
1
2
3
4
5
6
San Bruno Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
Avalon Building
Ductility
Story
Train
Single
Figure 6.53: Maximum ductility in floor beams for Cape-Mendocino (89156) scenario.
186
1 2 3 4 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Ductility
Story
Train
Single
1 3 5 7 9
0
1
2
3
4
5
6
San Bruno Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
Avalon Building
Ductility
Story
Train
Single
Figure 6.54: Maximum ductility in floor beams for Chalflant Valley scenario.
1 2 3 4 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
5
6
San Bruno Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
Avalon Building
Ductility
Story
Train
Single
Figure 6.55: Maximum ductility in floor beams for Mammoth Lakes scenario.
187
1 2 3 4 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Ductility
Story
Train
Single
1 3 5 7 9
0
1
2
3
4
5
6
San Bruno Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
Avalon Building
Ductility
Story
Train
Single
Figure 6.56: Maximum ductility in floor beams for Chi-Chi (TCU079) scenario.
1 2 3 4 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
5
6
San Bruno Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
Avalon Building
Ductility
Story
Train
Single
Figure 6.57: Maximum ductility in floor beams for Chi-Chi (CHY036) scenario.
188
1 2 3 4 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Ductility
Story
Train
Single
1 3 5 7 9
0
1
2
3
4
5
6
San Bruno Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
Avalon Building
Ductility
Story
Train
Single
Figure 6.58: Maximum ductility in floor beams for Kyushu scenario.
1 2 3 4 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
5
6
San Bruno Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
Avalon Building
Ductility
Story
Train
Single
Figure 6.59: Maximum ductility in floor beams for Coalinga scenario.
189
1 2 3 4 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
5
6
San Bruno Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
Avalon Building
Ductility
Story
Train
Single
Figure 6.60: Maximum ductility in floor beams for Mexico scenario.
1 2 3 4 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Ductility
Story
Train
Single
1 3 5 7 9
0
1
2
3
4
5
6
San Bruno Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
Avalon Building
Ductility
Story
Train
Single
Figure 6.61: Maximum ductility in floor beams for Tohoku (FKS012) scenario.
190
1 2 3 4 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
5
6
San Bruno Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
Avalon Building
Ductility
Story
Train
Single
Figure 6.62: Maximum ductility in floor beams for Tohoku (IBR013) scenario.
1 2 3 4 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
5
6
San Bruno Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
Avalon Building
Ductility
Story
Train
Single
Figure 6.63: Maximum ductility in floor beams for Valparaiso scenario.
191
1 2 3 4 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
5
6
San Bruno Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
Avalon Building
Ductility
Story
Train
Single
Figure 6.64: Maximum ductility in floor beams for Honshu scenario.
1 2 3 4 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Ductility
Story
Train
Single
1 3 5 7 9 11 13 15
0
1
2
3
4
5
6
San Bruno Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
Avalon Building
Ductility
Story
Train
Single
Figure 6.65: Maximum ductility in floor beams for Tokachi scenario.
192
1 2 3 4 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
5
6
San Bruno Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
Avalon Building
Ductility
Story
Train
Single
Figure 6.66: Maximum ductility in floor beams for Maule scenario.
1 3 5 7 9
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Ductility
Story
Train
Single
1 3 5 7 9 11 13 15
0
1
2
3
4
5
6
San Bruno Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
Avalon Building
Ductility
Story
Train
Single
Figure 6.67: Maximum ductility in floor beams for Christchurch (CBGS) scenario.
193
1 2 3 4 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
5
6
San Bruno Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
Avalon Building
Ductility
Story
Train
Single
Figure 6.68: Maximum ductility in floor beams for Christchurch (RHSC) scenario.
1 2 3 4 5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
5
6
San Bruno Building
Ductility
Story
Train
Single
1 2 3 4 5
0
1
2
3
4
Avalon Building
Ductility
Story
Train
Single
Figure 6.69: Maximum ductility in floor beams for Christchurch (TPLC) scenario.
194
7 CHAPTER (7): LOW-CYCLE FATIGUE OF
REINFORCING BARS
As discussed in Chapter (2), the seismic provisions for the ductile design of RC frames
depends mainly on preventing brittle failure modes such as shear and anchorage failures
by applying proper design and detailing requirements at the plastic hinge locations. Each
earthquake affecting an RC building could induce both elastic and inelastic cycles which
might cause some damage at plastic hinge locations depending on the number and the
amplitudes of these cycles. In order for the building to be able to dissipate energy,
inelastic deformations are allowed to happen at plastic hinges which should be able to
withstand the multiple loading cycles without premature brittle failure or significant
accumulated damage.
Low-cycle fatigue of longitudinal reinforcing bars which is mainly controlled by high
amplitude cycles in the inelastic range is one of the main sources of damage
accumulation at plastic hinge locations. So, it is important to understand the low-cycle
fatigue behavior of reinforcing bars in order to estimate the cumulative damage and the
reduction in the fatigue life of steel reinforcement used in a ductile RC frame building.
In this chapter, the analysis results from chapter (6) for various multiple earthquakes
scenarios will be used to estimate the cumulative fatigue damage at the plastic hinge
locations in the analyzed frame models for the case study buildings. The fatigue damage
at plastic hinges depend on the low-cycle fatigue behavior of the main reinforcing bars
that can be estimated using the fatigue life relationships that were developed for different
grades of reinforcing steel.
7.1 Fatigue Life Relationships
Based on the available literature, several fatigue life relationships were developed
through cyclic testing of reinforcing bars under constant amplitude loading. The existing
relationships predict the number of cycles to failure at certain strain amplitude. These
195
relationships are in an exponential form though when they are plotted on a log-scale, they
become linear. The constants of the fatigue formulae are obtained from test results
performed by many researchers including various types of reinforcing steel. The equation
developed by Koh and Stephens (1991) has two major fatigue parameters. The equation
is presented in terms of the total strain amplitude “ε
a
” and the number of cycles to failures
“N
f
”. The Koh Stephens equation is presented below where the constants “ε
f
” and “m”
are determined for the results of cyclic testing of individual bars. These constants are
defining linear relationship in log-scale as shown in the equation below.
m
f f a
N ) 2 (
2
ε
ε
ε =
Δ
=
7.1.1 Mander et al. (1994)
This research studied the low-cycle fatigue behavior of reinforcing and pre-stressing steel
bars used in both structural building and bridge construction. Mander et al. tested both
Grade 40 (A615) reinforcing steel and (A722) high strength pre-stressing steel rebar
under constant strain amplitudes up to 6%. The buckling of bars was prevented by using a
spacing between the testing machine grips of six times the diameter of the bar assuming
fixed end conditions.
Different fatigue life relationships were provided out of this research for both types of
steel as presented below:
For Grade 40:
448 . 0
) 2 ( 0795 . 0
2
−
=
Δ
=
f a
N
ε
ε
For A722:
381 . 0
) 2 ( 0791 . 0
2
−
=
Δ
=
f a
N
ε
ε
Also, a general formula was proposed that can be used for any type of reinforcing steel in
order to define a single line which could be used in estimating the approximate number of
cycles to failure under constant amplitude strain.
5 . 0
) 2 ( 08 . 0
2
−
=
Δ
=
f a
N
ε
ε
196
7.1.2 Brown and Kunnath (2004)
This research carried out a comprehensive study to examine the low-cycle fatigue
behavior of Grade 60 (A615) reinforcing steel bars ranging from bar size No. 6 to No. 9.
The bars were tested under constant amplitude cyclic loading with minimum strain
amplitude of 1.5% and maximum of 3%. Also, buckling of reinforcing bars was
prevented by setting the spacing between the grips of the machine to six times the bar
diameter.
The research emphasized that low-cycle fatigue should be considered when designing RC
members subjected to seismic loading cycles. It was also found that the fatigue life is
affected by the bar size and the geometry of the rolled on deformations. Several fatigue
life relationships were developed for each bar size, as follows:
No. 6 bars
45 . 0
) 2 ( 09 . 0
2
−
=
Δ
=
f a
N
ε
ε
No. 7 bars
44 . 0
) 2 ( 11 . 0
2
−
=
Δ
=
f a
N
ε
ε
No. 8 bars
36 . 0
) 2 ( 08 . 0
2
−
=
Δ
=
f a
N
ε
ε
No. 9 bars
31 . 0
) 2 ( 07 . 0
2
−
=
Δ
=
f a
N
ε
ε
7.1.3 Kunnath and Xiao (2009)
The goal of this research was to study the low-cycle fatigue behavior of large diameter
bars which are used as longitudinal reinforcement for bridge piers. The primary goal of
the research was test Grade 60 (A706) reinforcing steel bars of bar size No. 14 and No.
18 but due to some experimental difficulties only No. 14 bars were tested. Also, a few
tests on No.11 bars were done in order to check the adequacy of the test setup. The
imposed strain amplitudes were between 1% and 4% at intervals of 1%. Only one fatigue
life relationship was developed for No. 14 bar as follows:
493 . 0
) 2 ( 099 . 0
2
−
=
Δ
=
f a
N
ε
ε
197
7.1.4 Hawileh et al. (2010)
This study was performed to examine the low-cycle fatigue behavior of reinforcing bars
used in precast hybrid frame connections but it could be used also for other reinforcement
applications. Two types of commercial Grade 60 reinforcing steel bars which are (A615)
and (A706) were tested under constant amplitude non-zero mean strain cyclic loading in
a range between 2% to 8%. Fatigue life relationships were developed for non-zero mean
strain amplitudes with strain ration (R=0) as follows:
For A706 bars
409 . 0
) 2 ( 09 . 0
2
−
=
Δ
=
f a
N
ε
ε
For A615 bars
428 . 0
) 2 ( 101 . 0
2
−
=
Δ
=
f a
N
ε
ε
These relationships were compared to those developed by Mander et al. after
modification to account for the effect of non-zero strain to become as follows:
Modified Mander et al.:
448 . 0
) 7 . 3 4 ( 0795 . 0
2
−
+ =
Δ
=
f a
N
ε
ε
7.2 Strain Histories
The curvature histories are obtained from the analysis of the numerical models of the case
study buildings in chapter (6) for each of the selected earthquake scenarios using
PERFORM-3D. Then, strain values are calculated from curvature values using the results
obtained from the section analysis of each RC frame component using RESPONSE-2000,
which provides strain vs. curvature relationships for all the RC members especially for
beams where high inelastic defamations were developed at plastic hinges. Two equations
are developed for each beam section in both positive and negative curvature. An example
of the strain-curvature relationships for the 12x18 typical beam section in North
Hollywood building is presented below:
For positive curvature: 001 . 0 756 . 14 1776 86895
2 3
+ + + = ϕ ϕ ϕ ε
For negative curvature: ϕ ϕ ϕ ε 6 9113 5665761
2 3
+ − =
where “φ” refers to the curvature of the beam section in flexure.
198
Similar relationships were developed for the beam sections in both San Bruno building
and Avalon building, then were used to obtain the strain time histories from the curvature
time history at each plastic hinge.
According to the results from chapter (6), the case study buildings experienced
significant inelastic deformation during most of the selected earthquake scenarios.
Sample strain histories for Cape-Mendocino (89156) scenario at plastic hinge locations in
sample floor beams in the three frame models are shown in (Figure 7.1). It is clear that
beams experienced significant plastic strains at the plastic hinge locations during the
main shock of this scenario. These plastic strains remain existing during the next after-
shocks until more plastic strain is experienced during any of the following ground
motions which can increase or decrease the plastic deformation. This is considered as a
non-zero mean strain cyclic loading affecting the low-cycle fatigue behavior of the main
reinforcing bars at plastic hinges. The fatigue damage due to a non-zero mean strain
loading is usually more than the cyclic loading with zero mean strain which leads to less
number of cycles to failure or shorter fatigue life.
7.3 Rain-flow Counting Method
The strain histories at each plastic hinge location are highly irregular containing large
number of random cycles of varying amplitudes so, the rain-flow counting method is
used to extract the stress or strain cycles at constant amplitudes. The rain-flow method is
a well-known approach in fatigue analysis for structural applications which defines the
corresponding number of cycles at each stress or strain amplitude. It was developed in
1968 by Professor T. Endo and since then it has been widely used in many structural
engineering applications.
The obtained strain histories are analyzed by applying the rain-flow counting method
using MATLAB at strain increments of 0.0005 above the value of 50% the yield strain
for the longitudinal reinforcing steel for beams which is Grade 40 steel for North
Hollywood building and Grade 60 for both San Bruno and Avalon buildings.
199
0 20 40 60 80 100 120 140 160
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
North Hollywood Building
Time (Seconds)
Strain (%)
Element #107
0 20 40 60 80 100 120 140 160
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
San Bruno Building
Time (Seconds)
Strain (%)
Element #97
0 20 40 60 80 100 120 140 160
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
Avalon Building
Time (Seconds)
Strain (%)
Element #9
Figure 7.1: Sample strain histories for floor beams in the case study buildings during the
Cape-Mendocino (89156) scenario.
200
7.4 Palmgen-Miner Damage Rule
In 1924, A. Palmgen developed a rule for calculating the cumulative damage in structures
then, in 1945 M. A. Miner modified that rule and since then it became a widely used rule
in damage assessment of structures subjected to fatigue type loading. It was assumed that
the damage due to fatigue type loading (in terms of stress or strain cycles) is
accumulating linearly according to the number of loading cycles. It simply states that the
fatigue life of a structure or an element is exhausted when the sum of all the fatigue
fractions at different loading amplitudes from a random fatigue loading is equal to unity
as shown below.
∑
≤ = + + + 1 ........
3
3
2
2
1
1
fi
i
f f f
N
N
N
N
N
N
N
N
For the strain histories obtained from the analysis of the case study buildings, the number
of strain cycles at each strain increment “N
i
” is determined using the rain-flow counting
method then, the available fatigue life relationships are used to calculate the number of
cycles to failure at each strain level “N
f
”. Hence, the Palmgen-Miner damage rule is used
to calculate the cumulative fatigue damage in the longitudinal reinforcing bars. The
increase in the cumulative fatigue damage is corresponding to the reduction in the fatigue
life of the structural member subjected to fatigue type loading.
7.5 Cumulative Fatigue Damage
As shown in chapter (6), all plastic hinges occurred at the ends of the floor beams of the
case study buildings for the selected earthquake scenarios with several additional plastic
hinges occurred within the bottom floor columns at the foundation level in both San
Bruno and Avalon buildings. As mentioned in chapter (3), the available information for
North Hollywood and San Bruno buildings show than Grade 40 and Grade 60 reinforcing
steel bars, respectively were used for the longitudinal reinforcement for the floor beams.
For Avalon building, no information is available about the grade of steel used for the
main reinforcement of the RC frame component so, it was assumed that Grade 60 steel is
used.
201
Hence, the available expressions for the fatigue life for both Grade 40 and Grade 60
reinforcing steel bars are used to calculate the number of cycles to failure at each strain
level as determined through the rain-flow counting. Since, low-cycle fatigue is associated
with high strain amplitudes due to large inelastic deformations at plastic hinges during
each earthquake scenario, only strain amplitudes beyond the 50% of the yield strain of
each type of steel are considered.
It was clear from the strain histories that large plastic deformations occur during early
ground motions of each earthquake scenario (usually during the main shock) which
influences the fatigue damage during the later loading cycles. In order to account for the
effect of the non-zero mean strain loading due to permanent plastic strains, a modification
suggested by Collins (2003) is applied to the previous equation as follows:
[ ]
a
a a
f
f
a
R N
R
/ 1
) 2 ( ) 1 )( 1 4 (
' ) 1 (
2
+ − −
−
=
Δ
=
ε
ε
ε
where “R” is the strain ration = ε
max
/ε
min
, “ε’
f
” and “a” are determined based on the
fatigue life relationship of each type of steel. After calculating the number of cycles at
each strain level using the rain-flow method and the number of cycles to failure using the
previous equation, the Palmgen-Miner rule is used to calculate the cumulative fatigue
damage within the main reinforcement at critical locations.
Cumulative fatigue damage was calculated at each critical section (beam ends) in the
floor beams in the case study buildings by summing up the resulting fatigue damage from
all ground motions in each earthquake scenario. The maximum values for the cumulative
damage at each floor level are shown in in (Figure 7.2) to (Figure 7.19) for both
Sequence (Train) analysis and Individual (Single) analysis approaches. The figures show
the percentage of fatigue damage in the form of bar charts where grey portion of the bar
represents the sum of the damage for the individual analysis approach while the black
portion represent the increase in the fatigue damage due to the damage accumulation
from the sequence analysis approach.
It is clear that the Sequence (Train) analysis results in higher values than the Individual
(Single) analysis for most of the selected earthquake scenarios. This might be attributed
202
to the effect of plastic deformations that usually occurs during the early ground motions
(main shocks) which reduces the fatigue life significantly. In other words, the plastic
hinge locations are more likely to experience more reduction in the fatigue life of the
main reinforcing due to the high plastic strains associated with the large rotations during
the strong ground motions within each earthquake scenario. For example, North
Hollywood building didn’t experience any plastic deformations during the main shock of
the Kyushu scenario then seven plastic hinges where formed during the after-shock which
didn’t result in any difference between the two analysis approaches. On the other hand,
the same building experienced plastic deformations during only the first main shock out
of the eight ground motions of the Christchurch (TPLC) scenario but a significant
increase in the fatigue damage during the rest of the scenario.
It is also clear that the cumulative damage exceeded 100% for San Bruno building during
Tohoku (FKS012), Tohoku (IBR013), and Christchurch (RHSC) scenarios. This might be
attributed to the relatively long total duration of these scenarios with respect to the
fundamental period of the building and the plastic deformations at plastic hinges. Avalon
building also experienced cumulative damage more than 100% during Tohoku (IBR013)
scenario. Generally, the fatigue life was reduced by significant amounts during most of
the case especially for the buildings of the shorter fundamental periods which vibrate in
higher number of cycles.
Another observation is about Avalon building where no fatigue damage was observed
during Chi-Chi (CHY036), Mexico, Tohoku (FKS012), and Christchurch (TPLC)
scenarios. As presented in chapter (6), the building didn’t experience any plastic
deformation during these scenarios which reflects low strain values which might be lower
than the threshold of 50% of the yield strain that was specified earlier. Even though these
scenarios are of long durations but the resulting strains were very low that might belong
to the high cycle fatigue range which has fatigue life up to thousands of cycles.
This concludes that the effect of multiple earthquake scenarios is significantly increasing
the cumulative fatigue damage for reinforcing bars which means shorter fatigue life for
next earthquakes which could lead to failure RC frame members.
203
0 20 40 60 80 100
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
5
6
San Bruno Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
Avalon Building
Fatigue Damage (%)
Story
Train
Single
Figure 7.2: Maximum cumulative fatigue damage for Cape-Mendocino (1583) scenario.
0 20 40 60 80 100
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
5
6
San Bruno Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
Avalon Building
Fatigue Damage (%)
Story
Train
Single
Figure 7.3: Maximum cumulative fatigue damage for Cape-Mendocino (89156) scenario.
204
0 20 40 60 80 100
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
5
6
San Bruno Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
Avalon Building
Fatigue Damage (%)
Story
Train
Single
Figure 7.4: Maximum cumulative fatigue damage for Chalflant Valley scenario.
0 20 40 60 80 100
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
5
6
San Bruno Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
Avalon Building
Fatigue Damage (%)
Story
Train
Single
Figure 7.5: Maximum cumulative fatigue damage for Mammoth Lakes scenario.
205
0 20 40 60 80 100
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
5
6
San Bruno Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
Avalon Building
Fatigue Damage (%)
Story
Train
Single
Figure 7.6: Maximum cumulative fatigue damage for Chi-Chi (TCU079) scenario.
0 20 40 60 80 100
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
5
6
San Bruno Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
Avalon Building
Fatigue Damage (%)
Story
Train
Single
Figure 7.7: Maximum cumulative fatigue damage for Chi-Chi (CHY036) scenario.
206
0 20 40 60 80 100
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
5
6
San Bruno Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
Avalon Building
Fatigue Damage (%)
Story
Train
Single
Figure 7.8: Maximum cumulative fatigue damage for Kyushu scenario.
0 20 40 60 80 100
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
5
6
San Bruno Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
Avalon Building
Fatigue Damage (%)
Story
Train
Single
Figure 7.9: Maximum cumulative fatigue damage for Coalinga scenario.
207
0 20 40 60 80 100
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
5
6
San Bruno Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
Avalon Building
Fatigue Damage (%)
Story
Train
Single
Figure 7.10: Maximum cumulative fatigue damage for Mexico scenario.
0 20 40 60 80 100
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100 120 140 160 180 200
0
1
2
3
4
5
6
San Bruno Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
Avalon Building
Fatigue Damage (%)
Story
Train
Single
Figure 7.11: Maximum cumulative fatigue damage for Tohoku (FKS012) scenario.
208
0 20 40 60 80 100
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Fatigue Damage (%)
Story
Train
Single
0 50 100 150 200 250 300 350
0
1
2
3
4
5
6
San Bruno Building
Fatigue Damage (%)
Story
Train
Single
0 50 100 150 200 250 300 350
0
1
2
3
4
Avalon Building
Fatigue Damage (%)
Story
Train
Single
Figure 7.12: Maximum cumulative fatigue damage for Tohoku (IBR013) scenario.
0 20 40 60 80 100
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
5
6
San Bruno Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
Avalon Building
Fatigue Damage (%)
Story
Train
Single
Figure 7.13: Maximum cumulative fatigue damage for Valparaiso scenario.
209
0 20 40 60 80 100
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
5
6
San Bruno Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
Avalon Building
Fatigue Damage (%)
Story
Train
Single
Figure 7.14: Maximum cumulative fatigue damage for Honshu scenario.
0 20 40 60 80 100
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
5
6
San Bruno Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
Avalon Building
Fatigue Damage (%)
Story
Train
Single
Figure 7.15: Maximum cumulative fatigue damage for Tokachi scenario.
210
0 20 40 60 80 100
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
5
6
San Bruno Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
Avalon Building
Fatigue Damage (%)
Story
Train
Single
Figure 7.16: Maximum cumulative fatigue damage for Maule scenario.
0 20 40 60 80 100
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
5
6
San Bruno Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
Avalon Building
Fatigue Damage (%)
Story
Train
Single
Figure 7.17: Maximum cumulative fatigue damage for Christchurch (CBGS) scenario.
211
0 20 40 60 80 100
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100 120 140 160
0
1
2
3
4
5
6
San Bruno Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
Avalon Building
Fatigue Damage (%)
Story
Train
Single
Figure 7.18: Maximum cumulative fatigue damage for Christchurch (RHSC) scenario.
0 20 40 60 80 100
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
North Hollywood Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
5
6
San Bruno Building
Fatigue Damage (%)
Story
Train
Single
0 20 40 60 80 100
0
1
2
3
4
Avalon Building
Fatigue Damage (%)
Story
Train
Single
Figure 7.19: Maximum cumulative fatigue damage for Christchurch (TPLC) scenario.
212
8 CHAPTER (8): SUMMARY AND CONCLUSIONS
8.1 Summary
Since the ductile RC frame system is one of the most common systems for resisting
lateral loads, it is important to keep improving its design standards in the light of the most
recent earthquakes where incidents of structural failure or collapse were observed.
Therefore, the effect of multiple earthquake scenarios should be examined after the New
Zealand, Chile, and Japan earthquakes where failure due to damage accumulation is
believed by experts to be one of the main reasons of failure.
Three case study buildings that have ductile RC moment resisting frames, were selected
in order to investigate the effect of multiple earthquakes on the structural performance.
These buildings have recorded responses from several earthquakes during their service
lives which were used to calibrate the developed numerical model using PERFORM-3D.
After calibrating the numerical models for the case study buildings, the analysis was
extended by applying selected multiple earthquake scenarios that represent real cases
from all over the world. Eighteen scenarios in three categories were selected then applied
to the numerical models which resulted in different sets of output data.
The output results were in terms of displacement histories, distribution of plastic hinges,
and hysteresis loops at plastic hinges. These results obtained for the three buildings were
then used to analyze the structural response in terms of permanent (residual) lateral
displacement and ductility demands which showed the significant effect of the multiple
earthquake scenarios especially during after-shocks.
Finally, an investigation of the low-cycle fatigue behavior of the main reinforcing bars at
the critical locations was performed. The available fatigue life relationships were
presented then used to estimate the number of cycles to failure under specific amplitudes.
Then, the rain-flow counting method was used to obtain the equivalent constant
amplitude cycles of the strain histories obtained from the analysis in order to apply the
Palmgen-Miner rule to estimate the cumulative fatigue damage.
213
8.2 Conclusion
The occurrence of multiple earthquakes over a relatively short period of time (from
several days to several months) is found to have significant effects of the structural
performance of ductile RC frame buildings. If a building is damaged during the main
shock and the structural properties of the building (in terms of strength and stiffness)
remain constant without any repair or rehabilitation efforts being made, it might be
vulnerable to severe damage during later after-shocks or future earthquakes. In this case,
the effects of a sequence of ground motions can be different than the expected effects due
to a single ground motion. The following conclusions highlight the effects on the
behavior of ductile RC frames during multiple earthquakes.
• The occurrence of permanent displacements at the floor levels during the main
shock of a multiple earthquake scenario due to plastic deformations within the
components of the RC frame could lead to higher displacements during the later
ground motions (after-shocks) or future earthquakes.
• The permanent displacements from the prior ground motions could lead to tilting
the building from its original vertical axis if they are larger than the maximum
displacement experienced in the later ground motion. This tilting increases the
effects of the geometric nonlinearities (Second order moments) especially if the
building has gravity columns in combination with RC moment resisting frames.
• The increased number of loading cycles during multiple earthquake scenarios
results in stiffness deterioration due to the unloading and reloading of the RC
frame components. This reduction of the stiffness of individual members affects
the global stiffness of the frame system which changes the dynamic
characteristics of the structure such as the fundamental period that might lead to a
significant change in the seismic demand during the later ground motions.
• The ductility demands due to the analysis under the effect of multiple earthquakes
are generally higher than the demands due single events which is the current
requirement for seismic design by most building codes. The design for the most
credible earthquake (MCE) results in levels of ductility that might not be
214
sufficient to withstand multiple earthquakes such as relatively strong aftershock.
This requires the designer to provide more ductility capacities for the structural
members to account for the accumulation of plastic deformations which is not
considered in the current seismic design practice.
• The distribution of plastic hinges depends greatly on the formation of plastic
hinges during the prior ground motions (usually the main shock) where the
number of plastic hinges could increase during the later ground motions. The
extent of plastic deformation within the plastic hinge also depends on the
experienced plastic deformation during the prior ground motions. Generally, the
occurrence of multiple earthquakes can lead to more plastic hinges which means
more locations of possible damage (yield of reinforcement and cracking of
concrete) within the RC frame.
• The shape of the hysteresis loops is affected by the prior inelastic behavior at the
plastic hinge locations as it might change the start point of the loop as well as the
initial slope which depends on the reloading stiffness. The area of the loop is also
affected which changes the amount of dissipated energy during the later ground
motions which can also contribute to the occurring damage.
• According to the ground motion characteristics of the after-shocks, they can be
more damaging than the main shock which might not be expected from post-
earthquake inspection if the building didn’t suffer serious damage during the main
shock. In some cases, a building behaves elastically during the main shock but
suffers from plastic deformations during the later ground motions. So, inspection
should be made for the after-shocks as well as the main shock.
• The later ground motions (usually the after-shocks) can even be more harmful
and cause complete collapse of the building as discussed in the examples of both
the CTV building and the PGC building in New Zealand. The results of the
analysis in this study showed possible collapse for one of the case study buildings
(San Bruno building) when subjected to multiple earthquakes in a sequence while
it survived all the ground motions when they were applied individually. This is
215
believed to be the accumulation of seismic damage at plastic hinges as a result of
the increase of plastic deformations.
• Multiple earthquake scenarios usually have overall long duration which increase
the number of loading cycles. The increase in the number of cycles leads to more
deterioration of the stiffness due to the reversed nature of the seismic loading. It
can also lead to higher vulnerability to low-cycle fatigue failure of the main
reinforcing bars as it depends mainly on the number of loading cycles.
• Low and medium rise buildings are found to be more vulnerable to damage
accumulation and stiffness deterioration as they have shorter fundamental periods
that result in more loading cycles. This also reduces the fatigue life of the main
reinforcing bars as mentioned before.
• The low-cycle fatigue behavior of the main reinforcing bars in the RC frame
components affects the remaining service life of the building. It was found that
significant fatigue damage occurs in the main reinforcing bars due to the
increased number of cycles during the whole duration of multiple earthquakes.
Current code provisions don’t account for the low-cycle fatigue in the design for
ductile RC frame system while it could be a major reason of failure of structural
components due the reduction in the fatigue life.
• Permanent strains in the main reinforcing bars that occur at plastic hinges reduce
the fatigue life significantly. This is attributed to the effect of the non-zero mean
strain cycles which lead to more cumulative fatigue damage. If a building suffered
plastic deformations during the main shock it will be more vulnerable to low-
cycle fatigue failure during the later ground motions.
• The individual analysis of each ground motion in the multiple earthquake scenario
underestimates their effects on the structural response of the RC frame as it
neglects the plastic deformations and the change in the dynamic characteristics
due to the stiffness deterioration. It is advised that RC frame buildings should be
analyzed considering its history of response to ground motions as long as no
structural upgrade was made to the building.
216
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Affected Assisi, Central Italy”, Bulletin of Engineering Geology and the
222
Environment, 57, 101-109.
− Priestley, M., Seible, F., Calvi, G., (1996), “Seismic Design and retrofit of
Bridges”, John Wiley & Sons. New York, NY.
− Raghunandan, M., Liel, A., Ryu, H., Luco, N., and Uma, S., (2012), “Aftershock
Fragility Curves and Tagging Assessments for Main-Shock Damaged Buildings”,
Proceedings of the Fifteenth World Conference on Earthquake Engineering,
Lisbon, Portugal.
− Sezen, H., and Moehle, J., (2003), “Bond-slip Behavior of Reinforced Concrete
Members.” Proceedings of FIB Symposium on Concrete Structures in Seismic
Regions, CEB-FIP, Athens, Greece.
− Sezen, H., and Setzler, J., (2008), “Reinforcement Slip in Reinforced Concrete
Columns.” ACI Structural Journal, Vol. 105(3), 280–289.
− Sunasaka, Y., and Kiremidjian A., (1993), “A Method for Structural Safety
Evaluation under Mainshock-Aftershock Earthquake Sequences”, Report No. 105,
The John A. Blume Earthquake Engineering Center, Stanford University
− U.S. Department of Commerce, (1971), “San Fernando, California, Earthquake of
February 9, 1971: Part (A)”.
− Uma S., Cousins, W., and Baguley, D., (2010), “Seismic instrumentation of GNS
Science Building at Avalon”, GNS Science Report 2010/26.
− Unal, M., (2010), “Analytical Modeling of Reinforced Concrete Beam-to-Column
Connections”, Master thesis, Middle East Technical University.
− Uniform Building Code (1970), International Conference of Building Officials.
− Vecchio, F., and Collins, M., (1986), “The Modified Compression Field Theory
for Reinforced Concrete Elements Subjected to Shear”, ACI Structural Journal,
Vol. 83, No. 2, 219-231.
− Wang, B., Jiang, H., and Lu, X., (2011), “Seismic Analysis of RC Structure
Under Multiple Earthquakes”, Proceedings of the Eighth International Conference
on Urban Earthquake Engineering, Tokyo Institute of Technology, Tokyo, Japan.
223
APPENDIX (A): CODE PROVISIONS (ACI 318-11)
Adopted from “Seismic and Wind forces – Structural Design Examples” by Allan
Williams (2006).
The ACI-318-11 introduces the design requirements for ductile (Special) RC moment
resisting frames in “Chapter 21”, providing the necessary design procedure and detailing
techniques to ensure ductile response of the frame components (beam, columns and
joints).
A.1 Beam Design and Detailing
“To ensure ductile flexural failure of a beam and prevent brittle shear failure, ACI
Section 21.3.4 requires the design shear force to be determined from the probable flexural
strength that can be developed at the ends of the beam plus the factored tributary gravity
loads. The probable flexural strength is calculated by assuming that strain hardening
increases the effective tensile strength of the reinforcement by 25 percent and by using a
strength reduction factor of 1.0, as specified in ACI Section 21.3.4.1. The probable
flexural strength is given by:
] ' / ) 25 . 1 ( 59 . 0 1 [ ) 25 . 1 (
c y y s pr
f f d F A M ρ − =
Both the positive and negative probable flexural strengths must be calculated at both ends
of the beam in order to determine the critical shear value. The design shear force at the
end of the beam under seismic loading is:
gl n pr pr e
V L M M V + + =
− +
/ ) (
where “L
n
” is the clear span of the beam and “V
gl
” is the shear force due to acting gravity
loads.
The design shear capacity of the beam is the summation of the design shear capacities of
both concrete and transverse steel as given by ACI Equations (11-1) and (11-2):
s c n
V V V φ φ φ + =
224
In accordance with ACI Section 21.3.4.2, the shear resistance of the concrete shall not be
included in the shear capacity of the beam if the seismic induced shear force represents
one-half or more of the total applied shear or if the factored axial compressive force is
less than (A
g
f
c
'/20).
The reinforcement detailing provisions of ACI “Chapter 21” are intended to produce a
ductile structure capable of withstanding the large inelastic deformations that occur
during a severe earthquake as shown in (Figure A.1).
Figure A.1: Typical reinforcement details of a beam in a special RC moment resisting
frame (Williams, 2006).
In order to allow for the possibility of moment reversals, at least two reinforcing bars
shall be provided at the top and bottom of the beam. Also, at any section, along the beam,
neither the positive nor the negative moment strength shall be less than one-fourth of the
moment strength at the ends of the beam.
Reinforcement splices are not permitted in regions of plastic hinging as splices are
unreliable under inelastic cyclic loading conditions. Hence, ACI Section 21.3.2.3
specifies that splices shall not be used within a beam-to-column joint, within a distance of
twice the beam depth from the face of the joint, and at locations of flexural yielding.
The development length “L
dh
” for a hooked bar in normal weight concrete shall not be
less than the larger of
c b y
f d f ' 65 / , 8d
b
or 6 inches.
225
The hook shall be located within the confined core of a column or boundary element. For
straight bars of sizes 3 through 11 embedded in confined concrete, the development
length is given as L
d
= 2.5L
dh
” (Williams, 2006)
A.2 Column Design and Detailing
“In accordance with ACI Section 21.4.5, the design shear force for columns shall be
calculated using the probable moment strengths at the top and bottom of the column. The
probable flexural strength is calculated by assuming that strain hardening increases the
effective tensile strength of the reinforcement by 25% and by using a strength reduction
factor of 1.0, as specified in ACI Section 21.3.4.1. As shown in Figure 4-11, the probable
moments are assumed to occur at the axial load producing a balanced strain condition that
gives rise to the maximum moments. The design shear force at the top and bottom of the
column is
n prB prT e
H M M V / ) ( + =
where: “H
n
” is the column clear height.
The cyclical nonlinear effects produced by seismic loading necessitate additional shear
requirements to ensure a ductile flexural failure. When the factored compressive force in
a member is less than (A
g
f
c
'/20) and the seismic induced shear represents one half or
more of the total design shear, the shear resistance of the concrete “V
c
” shall be
neglected. Shear reinforcement shall then be provided to resist the total design shear as
required by ACI Section 21.3.4.
Transverse reinforcement, consisting of closed hoops and crossties, shall be provided
throughout the height of the column to furnish shear resistance and confinement. As
specified in ACI Section 21.4.4.3 and shown in Figure 4-8, crossties or legs of
overlapping hoops shall be spaced a maximum distance of 14 inches on center and shall
engage a longitudinal bar at each end.
At the ends of the column, over the length lo specified by ACI Section 21.4.4.4, the area
of the confinement reinforcement required is given by the greater value obtained from:
226
A
sh
= 0.3.s.b
c
(A
g
/A
ch
− 1)/f
y
and A
sh
= 0.09s.b
c
/f
y
where "s" is the spacing of hoop reinforcement, “A
g
” is the gross area of column section,
and “A
ch
” is the area enclosed by the outer of the hoop. Column details are shown in
(Figure A.2). ” (Williams, 2006)
Figure A.2: Typical reinforcement details of a column in a special RC moment resisting
frame (Williams, 2006).
227
A.3 Joint Design and Detailing
“The formation of plastic hinges at both ends of the columns in a given story, due to
seismic loads, may produce a side-sway mechanism that causes the story to collapse. To
prevent this, a strong column- weak beam design is required by ACI Section 21.4.2.2. A
column forming part of the lateral force- resisting system and with factored axial force
exceeding (A
g
f
c
'/10) shall be designed to satisfy ACI Equation (21-1), which is
ΣM
nc
≥ 1.2ΣM
nb
where: “ΣM
nc
” is the summation of the nominal flexural strengths of columns at the face
of a joint calculated for the applicable factored axial force resulting in the lowest flexural
strength and “ΣM
nb
” is the summation of the nominal flexural strengths of beams at the
face of the joint and in the same plane as the columns. In T-beam construction, slab
reinforcement within an effective width of the flange is assumed to contribute to the
negative flexural strength.
Joints are designed on an expected strength basis using the probable strength of the
materials. At a joint in a frame, the horizontal design shear force is determined as
required by ACI Section 21.5.1.1. The net shear acting on the joint is given by
c prB prT sb sT y e
H M M A A f V / ) ( ) ( 25 . 1 + − + =
In accordance with ACI Section 21.5.3 the nominal shear capacity of the joint depends on
the concrete strength and effective area of the joint, and the contribution of hoops to the
shear strength is neglected. The nominal shear strength of the joint is given by
c j
f A ' λ
where “A
j
” is the effective cross-sectional area within the joint. The values of “λ” are 20
for joints confined on four faces, 15 for joints confined on opposite faces or on three
faces, and 12 for other conditions
As specified in ACI Section 21.5.2, hoop reinforcement shall be provided through the
joint. With the exception of the condition where beams frame into all four sides of the
joint, hoop reinforcement “A
sh
”, as specified over the length “L
o
” of the column, shall be
provided throughout the height of the joint.
228
Beam reinforcement terminating in a column shall extend to the far face of the confined
concrete core and be provided with an anchorage length as specified in ACI Section
21.5.4. Typical joint details are shown in (Figure A.3). ” (Williams, 2006)
Figure A.3: Typical reinforcement details of a joint in a special RC moment resisting
frame (Williams, 2006).
Reference:
Williams, A., (2006), “Seismic and Wind Forces Structural Design Examples”, 3
rd
Edition, International Code Council.
229
APPENDIX (B): STRUCTURAL DRAWINGS
B.1 North Hollywood Building
230
231
232
233
B.2 San Bruno Building
234
235
236
B.3 Avalon Building
237
238
239
240
241
242
243
APPENDIX (C): RECODED MOTIONS
244
245
246
APPENDIX (D): CHECK OF DUCTILE BEHAVIOR
D.1 San Bruno Building
Beam analysis values using MCFT (RESPONSE-2000).
Floor Beam
M
p
(kip.in)
V
e
(kips) V
n
(kips) V
e
/V
n
Ductile
Pos. Neg.
6th
Exterior 4809 4406 48.0 51.8 0.93 Yes
Interior 4809 4406 48.0 51.8 0.93 Yes
5th
Exterior 4617 4862 49.4 54.1 0.91 Yes
Interior 4627 4607 48.1 49.9 0.96 Yes
4th
Exterior 4617 4862 49.4 54.1 0.91 Yes
Interior 4627 4607 48.1 49.9 0.96 Yes
3rd
Exterior 4627 6162 56.2 65.4 0.86 Yes
Interior 4617 4862 49.4 54.1 0.91 Yes
2nd
Exterior 5799 7290 68.2 76.6 0.89 Yes
Interior 4622 5412 52.3 55.1 0.95 Yes
1st
Exterior 8038 9225 89.9 94.1 0.96 Yes
Interior 5902 7342 69.0 76.9 0.90 Yes
Column analysis values using MCFT (RESPONSE-2000).
Column Type V
e
V
n
V
e
/V
n
Ductile
C 22x24 Interior 55.83 72.6 0.77 Yes
C 23x24.5 Interior 44.13 74.25 0.59 Yes
C 26x33 Exterior 69.00 99.00 0.70 Yes
247
Strong column-weak beam check.
Floor Type ∑M
c
∑M
b
∑M
c
/∑M
b
> 1.2
6th
Exterior 4809 20700 4.30 Yes
Interior 9215 10614 1.15 No
5th
Exterior 4862 20700 4.26 Yes
Interior 9234 11490 1.24 Yes
4th
Exterior 4862 20700 4.26 Yes
Interior 9234 12364 1.34 Yes
3rd
Exterior 6162 20700 3.36 Yes
Interior 9479 13240 1.40 Yes
2nd
Exterior 7290 20700 2.84 Yes
Interior 10034 14114 1.41 Yes
1st
Exterior 9225 20700 2.24 Yes
Interior 13244 14990 1.13 No
Joint shear check.
Floor Type V
e
(kips) A
j
(in
2
) V
n
(kips) V
e
/V
n
Ductile
6th
Exterior 127.4 726 616 0.21 Yes
Interior 252.1 539 770 0.33 Yes
5th
Exterior 137.6 726 616 0.22 Yes
Interior 251.9 539 770 0.33 Yes
4th
Exterior 137.6 726 616 0.22 Yes
Interior 251.9 539 770 0.33 Yes
3rd
Exterior 163.4 726 616 0.27 Yes
Interior 273.6 539 770 0.36 Yes
2nd
Exterior 199.8 726 616 0.32 Yes
Interior 291.6 539 770 0.38 Yes
1st
Exterior 282.8 726 616 0.46 Yes
Interior 388.7 539 770 0.50 Yes
248
D.2 Avalon Building
Beam analysis values.
Approach
ACI 318-11 MCFT (RESPONSE-2000)
Positive Negative Positive Negative
M
p
(kip.in) 7610 7258 8310 7755
V
e
(kips) 61.95 66.94
V
n
(kips) 112 118.4
V
e
/ V
n
0.55 0.56
Ductile Yes Yes
Column analysis values.
Approach
ACI 318-11 MCFT (RESPONSE-2000)
Exterior Interior Exterior Interior
V
e
(kips) 122.6 154.7 125.2 159.0
V
n
(kips) 387.2 387.2 248.6 248.6
V
e
/ V
n
0.32 0.40 0.50 0.64
Ductile Yes Yes Yes Yes
Strong column-weak beam check.
Floor Type ∑M
c
∑M
b
∑M
c
/∑M
b
> 1.2
Typical
Exterior 26232 8310 3.15 Yes
Interior 27822 16065 1.73 Yes
Joint shear check.
Floor Type V
e
(kips) A
j
(in
2
) V
n
(kips) V
e
/V
n
Ductile
Typical
Exterior 413.8 576 613.0 0.67 Yes
Interior 831.6 576 817.4 1.01 No
Abstract (if available)
Abstract
Since the ductile RC frame system is one of the most common systems for resisting lateral loads, it is important to keep improving its design standards in the light of the most recent earthquakes where incidents of structural failure or collapse were observed. Therefore, the effect of multiple earthquake scenarios should be examined after the earthquakes in New Zealand, Chile, and Japan where failure due to damage accumulation is believed by experts to be one of the major reasons of failure. ❧ Three case study buildings that have ductile RC moment resisting frames were selected in order to investigate the effect of multiple earthquakes on the structural performance. These buildings have recorded responses from several earthquakes during their service lives which were used to calibrate the developed numerical model using PERFORM‐3D. After calibrating the numerical models for the case study buildings, the analysis was extended by applying selected multiple earthquake scenarios that represent real cases from all over the world. Eighteen scenarios in three categories were selected then applied to the numerical models which resulted in different sets of output data. ❧ The output results were in terms of displacement histories, distribution of plastic hinges, and hysteresis loops at plastic hinges. These results, obtained for the three buildings, were then used to analyze the structural response in terms of permanent (residual) lateral displacement and ductility demands which showed the significant effect of the multiple earthquake scenarios especially during after‐shocks. ❧ Finally, an investigation of the low‐cycle fatigue behavior of the main reinforcing bars at the critical locations was performed. The available fatigue life relationships were presented then used to estimate the number of cycles to failure under specific amplitudes. Then, the rain‐flow counting method was used to calculate the equivalent constant amplitude cycles of the strain histories obtained from the analysis in order to apply the Palmgen‐Miner rule to estimate the cumulative fatigue damage. It was found that a significant reduction in the fatigue life is likely to occur due to the longer duration of multiple earthquake scenarios especially for buildings of shorter fundamental periods.
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Asset Metadata
Creator
Mantawy, Ahmed
(author)
Core Title
Behavior of ductile reinforced concrete frames subjected to multiple earthquakes
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Civil Engineering (Structural Engineering)
Publication Date
03/11/2014
Defense Date
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