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PERFORMANCE-BASED DESIGN OF RC COUPLED WALL HIGH-RISE BUILDINGS WITH VISCOELASTIC
COUPLING DAMPERS
by
Renée MacKay-Lyons
A thesis submitted in conformity with the requirements for the degree of Master’s of Applied Science
Graduate Department of Civil Engineering University of Toronto
© Copyright by Renée MacKay-Lyons (2013)
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PERFORMANCE-BASED DESIGN OF RC COUPLED WALL HIGH-RISE BUILDINGS WITH VISCOELASTIC
COUPLING DAMPERS
Renée MacKay-Lyons
Master’s of Applied Science
Department of Civil Engineering University of Toronto
2013
ABSTRACT
A new damping technology, the Viscoelastic Coupling Damper (VCD), has been
developed at the University of Toronto for reinforced concrete (RC) coupled wall high-rise
buildings. These dampers are introduced in place of coupling beams to provide distributed
supplemental damping in all lateral modes of vibration. This thesis presents an analytical
investigation of the application of VCDs in a high-rise case study building located in a region of
high seismicity. A parametric study has been conducted to determine the optimal number and
placement of the dampers to achieve enhanced seismic performance without compromising the
wind response of the structure. Nonlinear time history analyses have been carried out in order to
compare the seismic performance of a conventional coupled wall building to alternative designs
incorporating VCDs. Results highlight the improved performance of VCDs over RC coupling
beams at all levels of seismic hazard. A design procedure for seismic-critical buildings is
proposed.
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ACKNOWLEDGMENTS
First and foremost I would like to thank my supervisor, Professor Constantin
Christopoulos, for his guidance and support throughout this thesis project. His commitment to
advancing the field of structural engineering through research is an inspiration. I feel very
fortunate to have been given the opportunity to work with him and to learn from him.
I am also indebted to Doctor Michael Montgomery, whose PhD work has enabled this
project and who kindly and patiently shared with me his experience and expertise on countless
occasions.
Thank you to Professor Oh-Sung Kwon for his thoughtful review of this thesis.
Financial support for this project, provided by the Natural Sciences and Engineering
Research Council of Canada and by the Ontario Graduate Scholarship Program, is gratefully
acknowledged.
I would also like to thank Professor Evan Bentz for generously taking the time to answer
my questions and to provide clear explanations of challenging concepts.
Thank you to Doctor Graham Powell, Professor Emeritus at the University of California
at Berkeley, for his technical assistance with the Perform-3D software.
Additionally, I would like to thank my colleagues and friends at the University of
Toronto. Thank you for sharing your wisdom and for making this experience more fun.
Finally, I would like to thank my family for their love and support. In particular, thank
you to my parents for teaching me about integrity and hard work and for always being there for
me.
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TABLE OF CONTENTS
1 INTRODUCTION...................................................................................................................... 1
2 BACKGROUND........................................................................................................................ 7
2.1 Introduction to Reinforced Concrete Coupled Wall High-Rise Structures ........................ 7
2.2 Design of Reinforced Concrete Coupled Wall High-Rise Structures ................................. 9
2.2.1 Wind Design ........................................................................................................... 9
2.2.2 Seismic Design ...................................................................................................... 19
2.3 Viscoelastic Coupling Damper Concept for RC Coupled Wall High-Rise Buildings ...... 33
3 MODEL VERIFICATION ....................................................................................................... 39
3.1 Introduction ....................................................................................................................... 39
3.2 Element Calibration .......................................................................................................... 40
3.2.1 Reinforced Concrete Shear Wall Elements ........................................................... 40
3.2.2 Diagonally-Reinforced Concrete Coupling Beam Elements ................................ 48
3.2.3 Steel Coupling Beam Elements ............................................................................ 54
3.2.4 Viscoelastic Coupling Damper Elements ............................................................. 59
3.3 System Behaviour Validation ........................................................................................... 77
3.3.1 Description of Nonlinear Model ........................................................................... 78
3.3.2 Model Verification ................................................................................................ 83
3.4 Nonlinear Modelling Assumptions and Limitations ......................................................... 88
3.4.1 Component Models ............................................................................................... 88
3.4.2 System Modelling ................................................................................................. 92
4 CASE STUDY ......................................................................................................................... 96
4.1 Introduction ....................................................................................................................... 96
4.2 Analysis Models .............................................................................................................. 100
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4.2.1 General Building Properties ................................................................................ 100
4.2.2 Component Models ............................................................................................. 102
4.2.3 Loading Criteria .................................................................................................. 106
4.3 Ground Motion Scaling ................................................................................................... 108
4.4 Performance of Reference Structure ............................................................................... 111
4.4.1 Seismic Performance of Reference Structure ..................................................... 111
4.4.2 Response of Reference Structure to Wind Loading ............................................ 116
4.5 Development of Alternative Design Solution ................................................................. 118
4.5.1 Design and Modelling of VCDs ......................................................................... 120
4.5.2 Parametric Study ................................................................................................. 125
4.6 Results and Discussion ................................................................................................... 150
4.6.1 Seismic Performance of Alternative Design ....................................................... 152
4.6.2 Wind Performance of Alternative Design ........................................................... 163
4.6.3 Discussion of Results .......................................................................................... 166
5 CONCLUSIONS AND RECOMMENDATIONS ................................................................ 176
5.1 Summary ......................................................................................................................... 176
5.2 Design of Seismic-Critical and Wind-Critical High-Rise Structures ............................. 179
5.2.1 Seismic-Critical Structures ................................................................................. 179
5.2.2 Wind-Critical Structures ..................................................................................... 185
5.3 Recommendations for Further Research ......................................................................... 188
6 REFERENCES ....................................................................................................................... 193
APPENDIX A: RESPONSE-2000 RESULTS ........................................................................... 205
APPENDIX B: COUPLING BEAM SCHEDULE .................................................................... 208
APPENDIX C: CORE WALL REINFORCEMENT SCHEDULE ........................................... 211
APPENDIX D: COLUMN SIZES .............................................................................................. 213
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APPENDIX E: GRAVITY LOADS ........................................................................................... 215
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LIST OF TABLES
Table 2.1 Recommended upper and lower bounds for wind design (Montgomery, 2011) .......... 38
Table 3.1 Calibrated material modelling parameters for Test Specimen RW2 ............................ 43
Table 3.2 CB24F material properties (Naish et al., 2009) ............................................................ 49
Table 3.3 Measured steel material properties for specimen 2 (Harries et al., 1993) .................... 57
Table 3.4 ISD:111H material properties for KVM (Montgomery, 2011) .................................... 69
Table 3.5 ISD:111H material properties for GMM (Montgomery, 2011) .................................... 69
Table 3.6 VCD model validation matrix ....................................................................................... 70
Table 3.7 VCD model harmonic test results ................................................................................. 73
Table 3.8 VCD model ultimate dynamic test results .................................................................... 75
Table 3.9 FCD B3 2XNorthridge results ...................................................................................... 76
Table 3.10 Element sizes .............................................................................................................. 79
Table 3.11 Gravity loading ........................................................................................................... 83
Table 3.12 Reduced section properties for cracking ..................................................................... 84
Table 3.13 Lateral periods of vibration (sec) ................................................................................ 84
Table 3.14 Calculation of peak base shear in the EW direction (neglecting P-Delta) .................. 86
Table 3.15 Calculation of peak base shear in the NS direction (neglecting P-Delta) ................... 86
Table 3.16 Calculation of peak base shear in the EW direction (including P-Delta) ................... 87
Table 3.17 Calculation of peak base shear in the NS direction (including P-Delta) .................... 87
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Table 3.18 Reduced section properties for seismic analysis ......................................................... 94
Table 4.1 SLE acceptance criteria ................................................................................................ 98
Table 4.2 MCE acceptance criteria ............................................................................................... 98
Table 4.3 Reference structure properties .................................................................................... 101
Table 4.4 Concrete material properties ....................................................................................... 102
Table 4.5 Reinforcing steel material properties .......................................................................... 102
Table 4.6 Model vertical reinforcement ratios ............................................................................ 104
Table 4.7 Coupling beam modelling parameters – N&S Elevations .......................................... 105
Table 4.8 Coupling beam modelling parameters – E&W Elevations ......................................... 105
Table 4.9 Gravity loads ............................................................................................................... 106
Table 4.10 ASCE 7 wind loading criteria (after PEER/ATC, 2011) .......................................... 107
Table 4.11 Historical ground motion records ............................................................................. 109
Table 4.12 Ground motion scale factors ..................................................................................... 109
Table 4.13 Ground motion component orientations ................................................................... 111
Table 4.14 Maximum response quantities – SLE level .............................................................. 113
Table 4.15 Maximum response quantities – DBE level ............................................................. 114
Table 4.16 Maximum response quantities – MCE level ............................................................. 114
Table 4.17 SLS wind cracked section properties ........................................................................ 117
Table 4.18 NBCC wind loading parameters ............................................................................... 117
Table 4.19 VCD configurations .................................................................................................. 120
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Table 4.20 Elastic bar element properties (T = 24 C) ................................................................ 124
Table 4.21 Fluid damper element properties (T = 24 C) ........................................................... 124
Table 4.22 Steel assembly modelling parameters ....................................................................... 124
Table 4.23 SLE acceptance criteria ............................................................................................ 126
Table 4.24 MCE acceptance criteria ........................................................................................... 126
Table 4.25 Properties of RC coupling beams replaced with steel coupling beams .................... 129
Table 4.26 Properties of steel coupling beams ........................................................................... 129
Table 4.27 Steel coupling beam modelling parameters .............................................................. 129
Table 4.28 SLS wind modal properties ....................................................................................... 134
Table 4.29 Maximum response quantities – SLE level .............................................................. 138
Table 4.30 Maximum response quantities – MCE level ............................................................. 138
Table 4.31 SLS wind modal properties ....................................................................................... 141
Table 4.32 Maximum response quantities – SLE level .............................................................. 143
Table 4.33 Maximum response quantities – MCE level ............................................................. 144
Table 4.34 SLS wind modal properties ....................................................................................... 145
Table 4.35 Steel assembly modelling parameters ....................................................................... 146
Table 4.36 Maximum response quantities – SLE level .............................................................. 148
Table 4.37 Maximum response quantities – MCE level ............................................................. 148
Table 4.38 SLS wind modal properties ....................................................................................... 150
Table 4.39 Maximum response quantities – SLE level .............................................................. 155
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Table 4.40 Maximum response quantities – DBE level ............................................................. 155
Table 4.41 Maximum response quantities – MCE level ............................................................. 155
Table 4.42 NBCC wind loading parameters ............................................................................... 164
Table 4.43 Sample free vibration calculations ............................................................................ 169
Table 4.44 SLS wind base shears ............................................................................................... 174
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LIST OF FIGURES
Figure 1.1 Viscoelastic Coupling Damper Concept ....................................................................... 5
Figure 2.1 Lateral load-resisting mechanism in coupled wall structures ........................................ 7
Figure 2.2 Relative displacements at line of contraflexure (after Smith and Coull, 1991) ............ 8
Figure 2.3 Exaggerated flexural deformed shapes of coupled wall systems .................................. 8
Figure 2.4 Static and dynamic components of response in along-wind direction ........................ 10
Figure 2.5 Vortex-shedding (adapted from Irwin, 2010) .............................................................. 11
Figure 2.6 Response spectral density of a dynamic structure under wind loading ....................... 11
Figure 2.7 RWDI wind tunnel model for Petronas Towers (adapted from Irwin, 2010) ............. 13
Figure 2.8 Two-degree-of-freedom representation of vibration absorber concept ....................... 15
Figure 2.9 a) Viscous fluid damper (adapted from Hwang, 2002) b) Hysteretic behaviour of
linear and nonlinear viscous dampers ........................................................................................... 17
Figure 2.10 Damped outrigger concept (adapted from Smith & Wilford, 2007) ......................... 17
Figure 2.11 a) Viscoelastic damper b) Hysteretic behaviour of viscoelastic damper ................... 18
Figure 2.12 Diagonally-reinforced coupling beams (adapted from Wallace et al., 2009) ........... 20
Figure 2.13 Damage in diagonally-reinforced coupling beams (adapted from Naish et al., 2009)
....................................................................................................................................................... 21
Figure 2.14 Fragility curves for diagonally-reinforced coupling beams ...................................... 21
Figure 2.15 Damage from Concepcion Earthquake (adapted from LATBSDC, 2010) ................ 22
Figure 2.16 Steel coupling beams (adapted from El-Tawil et al., 2010) ...................................... 22
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Figure 2.17 Fragility curves for shear-critical EBF links (adapted from Gulec et al., 2011) ....... 24
Figure 2.18 Damage states of EBF links (adapted from Galvez, 2004) ....................................... 25
Figure 2.19 Wall damage in embedment region (adapted from Harries et al., 1993) .................. 26
Figure 2.20 Replaceable fuse concept for steel coupling beams .................................................. 26
Figure 2.21 Vision 2000 performance objectives (after Porter, 2003) ......................................... 27
Figure 2.22 Non-structural damage from Christchurch Earthquake (adapted from Mayes, 2011)
....................................................................................................................................................... 28
Figure 2.23 a) Low-rise building racking deformation b) High-rise building racking and rigid
body deformation (after CTBUH, 2008) ...................................................................................... 29
Figure 2.24 Toggle brace configuration (after Constantinou et al., 1997) ................................... 31
Figure 2.25 VE damper configurations for shear wall structures ................................................. 31
Figure 2.26 Seismic control measures for RC core wall building (after Munir et al., 2011) ....... 31
Figure 2.27 One Rincon Hill lateral load-resisting system (adapted from Robinson, 2012) ........ 32
Figure 2.28 Effect of VE dampers on critical excitation due to long-period ground motions
(adapted from Takewaki, 2011) .................................................................................................... 33
Figure 2.29 Viscous coupling damper (adapted from Montgomery, 2011) ................................. 34
Figure 2.30 Exaggerated deformed shape (adapted from Montgomery, 2011) ............................ 35
Figure 2.31 Viscous coupling damper prototypes (courtesy of M. Montgomery) ....................... 35
Figure 2.32 VCD design concept (adapted from Montgomery, 2011) ......................................... 37
Figure 3.1 Test Specimen RW2 (adapted from Orakcal, 2004) ................................................... 41
Figure 3.2 Fibre element representation of RC shear wall (adapted from PEER/ATC) ............... 42
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Figure 3.3 Hysteretic model for reinforcing steel (from Orakcal & Wallace, 2006) .................... 43
Figure 3.4 Hysteretic models for #2 and #3 steel reinforcing bars ............................................... 43
Figure 3.5 Cyclic degradation parameters for reinforcing steel ................................................... 44
Figure 3.6 Constitutive models for unconfined and confined concrete in compression ............... 45
Figure 3.7 Applied displacement history ...................................................................................... 47
Figure 3.8 a) Measured lateral load versus top displacement (adapted from Thomsen & Wallace,
2004) b) Model lateral load versus displacement ......................................................................... 48
Figure 3.9 Test Specimen CB24F (after Naish et al., 2009) ......................................................... 49
Figure 3.10 Loading protocols: a) Load-controlled; b) Displacement-controlled (adapted from
Naish et al., 2009) ......................................................................................................................... 49
Figure 3.11 Coupling beam chord rotation ................................................................................... 50
Figure 3.12 Test Specimen CB24F force-deformation response .................................................. 50
Figure 3.13 Schematic of typical models for diagonally-reinforced coupling beams .................. 51
Figure 3.14 Backbone load-deformation relations for full-scale diagonally-reinforced concrete
coupling beams (after Naish et al., 2009) ..................................................................................... 52
Figure 3.15 Cyclic degradation parameters for coupling beam elements ..................................... 53
Figure 3.16 Force-deformation response of analytical models a) Including slip/extension hinges,
b) Reduced stiffness to account for slip/extension ....................................................................... 53
Figure 3.17 ASCE 41-06 EBF link beam modelling parameters .................................................. 55
Figure 3.18 Specimen 2 test schematic (adapted from Harries et al., 1993) ................................ 57
Figure 3.19 Specimen 2 link beam details (after Harries et al., 1993) ......................................... 58
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Figure 3.20 Specimen 2 wall reinforcing details (after Harries et al., 1993) ................................ 58
Figure 3.21 Specimen 2 a) Test hysteresis (Harries et al. 1993) b) Model hysteresis (theoretical
backbone curve shown in red) ...................................................................................................... 59
Figure 3.22 Kelvin-Voigt Model .................................................................................................. 60
Figure 3.23 Generalized Maxwell Model for Viscoelastic Material ............................................ 61
Figure 3.24 Generalized Maxwell Model Parameters .................................................................. 62
Figure 3.25 Kelvin-Voigt models for VE dampers in axial brace configuration .......................... 64
Figure 3.26 Schematic of VCD Model ......................................................................................... 64
Figure 3.27 Kelvin-Voigt material model for viscoelastic material in Perform-3D ..................... 65
Figure 3.28 VCD model with fuse mechanism in Perform-3D .................................................... 66
Figure 3.29 VCD Specimen FCD B (adapted from Montgomery, 2011) ..................................... 66
Figure 3.30 VCD Specimen FCD B (adapted from Montgomery, 2011) ..................................... 67
Figure 3.31 Full-Scale Test Setup (adapted with permission from Montgomery, 2011) ............. 68
Figure 3.32 Full-Scale Test Setup (adapted from Montgomery, 2011) ........................................ 68
Figure 3.33 FCD B2 WSHC2 built-up steel assembly force-displacement response ................... 70
Figure 3.34 FCD B2 WSHC force-displacement results .............................................................. 71
Figure 3.35 FCD B3 HSHC force-displacement results ............................................................... 72
Figure 3.36 FCD B3 USCH force-displacement results ............................................................... 72
Figure 3.37 FCD B3 steel assembly backbone curve ................................................................... 74
Figure 3.38 FCD B3 UD force-displacement results .................................................................... 75
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Figure 3.39 FCD B3 2XNorthridge force-displacement results ................................................... 76
Figure 3.40 CNP 2 bounded analysis ............................................................................................ 76
Figure 3.41 Plan and section of coupled shear wall structure (after CAC, 2006) ........................ 77
Figure 3.42 Typical detail for diagonally reinforced coupling beams (after CAC, 2006) ............ 77
Figure 3.43 Typical details for core wall reinforcing steel (after CAC, 2006) ............................. 78
Figure 3.44 Perform-3D model of core wall structure .................................................................. 79
Figure 3.45 Constitutive models for unconfined and confined concrete in compression ............. 80
Figure 3.46 Backbone curve for reinforcing steel ........................................................................ 81
Figure 3.47 Schematic of fibre wall elements .............................................................................. 82
Figure 3.48 Backbone relation for typical coupling beam ............................................................ 82
Figure 3.49 Embedded beams (schematic) ................................................................................... 82
Figure 3.50 Mode Shapes ............................................................................................................. 84
Figure 3.51 Static pushover plots .................................................................................................. 85
Figure 3.52 Pushover analysis schematic (EW direction) ............................................................ 86
Figure 3.53 a) P-Delta schematic b) Peak base shear ................................................................... 87
Figure 3.54 RC coupling beam backbone curve ........................................................................... 91
Figure 4.1 Isometric view of case study building (adapted from PEER/ATC, 2011) .................. 97
Figure 4.2 Case study building foundation plan (after PEER/ATC, 2011) .................................. 99
Figure 4.3 Case study building tower floor plan (after PEER/ATC, 2011) .................................. 99
Figure 4.4 Isometric of typical nonlinear model ......................................................................... 100
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Figure 4.5 Core wall thickness (adapted from PEER/ATC, 2011) ............................................. 101
Figure 4.6 Typical shear wall element schematic ....................................................................... 103
Figure 4.7 Core wall model schematic ....................................................................................... 103
Figure 4.8 a) Concrete fibre compressive stress-strain relation b) Steel fibre stress-strain relation
..................................................................................................................................................... 104
Figure 4.9 Shear hinge backbone curve ...................................................................................... 105
Figure 4.10 Site specific spectra (5% critically damped) ........................................................... 107
Figure 4.11 SLE scaled ground motion spectra .......................................................................... 109
Figure 4.12 DBE scaled ground motion spectra ......................................................................... 110
Figure 4.13 MCE scaled ground motion spectra ........................................................................ 110
Figure 4.14 Reference structure SLE performance ..................................................................... 112
Figure 4.15 Reference structure DBE performance .................................................................... 112
Figure 4.16 Reference structure MCE performance ................................................................... 113
Figure 4.17 Lintel nomenclature ................................................................................................. 115
Figure 4.18 Coupling beam rotations – MCE level .................................................................... 116
Figure 4.19 Deformed shape under NBCC SLS wind loads ...................................................... 118
Figure 4.20 Interstorey drifts under NBCC SLS wind loads ...................................................... 118
Figure 4.21 Proposed VCD solution for case study building ..................................................... 122
Figure 4.22 Alternative connection detail ................................................................................... 122
Figure 4.23 Boundary region reinforcing steel (after El-Tawil et al., 2010) .............................. 123
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Figure 4.24 VE material model ................................................................................................... 123
Figure 4.25 Shear fuse backbone curve ...................................................................................... 124
Figure 4.26 Scaled ground motion spectra ................................................................................. 125
Figure 4.27 Configuration A core wall plans .............................................................................. 127
Figure 4.28 Configuration A core wall elevations ...................................................................... 128
Figure 4.29 Global performance – SLE level ............................................................................. 130
Figure 4.30 Global performance – MCE level ............................................................................ 131
Figure 4.31 VCD hysteresis ........................................................................................................ 131
Figure 4.32 VCD response – MCE level .................................................................................... 132
Figure 4.33 a) Steel coupling beam hysteresis b) Coupling beam rotations – SLE Level ......... 133
Figure 4.34 a) Steel coupling beam hysteresis b) Coupling beam rotations – MCE Level ........ 133
Figure 4.35 Ramp loading function ............................................................................................ 134
Figure 4.36 Mode shapes ............................................................................................................ 135
Figure 4.37 Free vibration at 30th floor level .............................................................................. 135
Figure 4.38 Configurations B, C & D – Schematic .................................................................... 136
Figure 4.39 Global performance – SLE level ............................................................................. 136
Figure 4.40 Global performance – MCE level ............................................................................ 137
Figure 4.41 VCD response – SLE level ...................................................................................... 139
Figure 4.42 VCD hysteresis – Configuration B .......................................................................... 140
Figure 4.43 VCD hysteresis – Configuration C .......................................................................... 140
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Figure 4.44 VCD hysteresis – Configuration D .......................................................................... 140
Figure 4.45 VCD response – MCE level .................................................................................... 141
Figure 4.46 Configuration E core wall plans .............................................................................. 142
Figure 4.47 SLE performance ..................................................................................................... 143
Figure 4.48 Global performance – MCE level ............................................................................ 144
Figure 4.49 VCD response – MCE level .................................................................................... 145
Figure 4.50 Configuration F schematic core wall plans ............................................................. 146
Figure 4.51 SLE performance ..................................................................................................... 147
Figure 4.52 MCE performance ................................................................................................... 148
Figure 4.53 VCD response – MCE level .................................................................................... 149
Figure 4.54 Summary of parametric study ................................................................................. 151
Figure 4.55 VCD design ............................................................................................................. 152
Figure 4.56 Global performance – SLE level ............................................................................. 153
Figure 4.57 Global performance – DBE level ............................................................................ 153
Figure 4.58 Global performance – MCE level ............................................................................ 154
Figure 4.59 Scaled ground displacement time histories – MCE level ........................................ 156
Figure 4.60 Global performance – Northridge 142 (MCE) ........................................................ 157
Figure 4.61 Roof displacement time histories – MCE level ....................................................... 157
Figure 4.62 Maximum VEM strains – MCE level ...................................................................... 158
Figure 4.63 Maximum shear fuse rotations – MCE level ........................................................... 159
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Figure 4.64 Sample coupling beam hysteresis ............................................................................ 159
Figure 4.65 Sample VCD hysteresis ........................................................................................... 160
Figure 4.66 Roof displacement time histories – SLE level ........................................................ 160
Figure 4.67 Roof displacement time histories – MCE level ....................................................... 161
Figure 4.68 Core wall axial tension strains – MCE level ........................................................... 162
Figure 4.69 Core wall axial compression strains – MCE level ................................................... 162
Figure 4.70 Core wall shear – MCE level ................................................................................... 163
Figure 4.71 Free vibration at 30th floor level .............................................................................. 165
Figure 4.72 Deformed shape due to NBCC SLS wind loads ...................................................... 165
Figure 4.73 Interstorey drifts due to NBCC SLS wind loads ..................................................... 165
Figure 4.74 Effects of period shift and added damping on seismic response ............................. 166
Figure 4.75 Free vibration energy plots – Configuration B, East-West Direction ..................... 169
Figure 4.76 Free vibration energy plots – Configuration D, East-West Direction ..................... 169
Figure 4.77 Sample VCD response ............................................................................................. 169
Figure 4.78 a) Fundamental periods of vibration b) Damping ratios in fundamental mode of
vibration ...................................................................................................................................... 171
Figure 5.1 a) Typical coupled wall structure b) VCD coupled wall structure ............................ 181
Figure 5.2 SLE performance ....................................................................................................... 182
Figure 5.3 MCE performance ..................................................................................................... 183
Figure 5.4 Seismic performance of wind-critical design ............................................................ 187
CHAPTER 1: Introduction 1
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
1 INTRODUCTION
Since the late 19th century, high-rises have constituted an increasingly popular building
typology in cities around the world. Tall buildings allow for high urban density and often serve
as important landmarks and symbols of prosperity. As a result of continuous advancements in
engineering and construction technologies, the tall building typology continues to evolve in form
as well as in height. Specifically, there is a prevailing trend towards increased height and
slenderness, making tall buildings more susceptible to lateral dynamic vibrations.
The design of a tall building’s lateral load-resisting system is often governed by
serviceability criteria relating to wind-induced lateral vibrations. Vibration acceleration limits are
prescribed to ensure occupant comfort. The typical approach to wind design begins with the
development of a preliminary structural scheme based on strength requirements, followed by
modifications to achieve adequate stiffness (Jackson and Scott, 2010). Structural members are
designed to remain elastic when subjected to design wind loads, with the exception of minor
cracking of reinforced concrete elements. Wind tunnel testing is usually carried out on the
preliminary design, in order to assess the building’s dynamic response under realistic wind
loading conditions. Acceleration data from wind tunnel testing often result in the need for
vibration mitigation measures. There are several ways in which excessive accelerations due to
dynamic wind excitation can be controlled. Designers can increase the stiffness of the lateral
load-resisting system, reduce the building height, change the structural layout, or enhance the
damping of the structure using supplemental damping devices.
Seismic design of high-rise buildings is usually considered separately from wind design
and requires a fundamentally different approach. Although it is well-known that structures can
undergo significant inelastic deformations during large seismic events, common practice has
been to account for nonlinear material behaviour implicitly, through the application of force
reduction factors. Reduction factors are selected based on the expected ductility of the structural
system, and are applied to the code-specified design base shear. In order to control inelastic
deformations during a severe event, the principle of capacity design is employed. This approach,
developed in New Zealand in the late 1960’s, acknowledges the inevitability of inelastic
CHAPTER 1: Introduction 2
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
behaviour in the event of a large seismic event and allows the designer to dictate where the
inelastic response should occur. For capacity design, ductile fuse elements are selected and
designed to undergo large plastic deformations without significant loss of strength, while
adjacent members are designed to remain elastic under the loading conditions required to reach
the maximum capacity of the fuse elements. The introduction of ductile fuse elements enforces a
desired yield mechanism and provides a stable means of energy dissipation during a seismic
event. Member strength requirements are usually determined from a three-dimensional elastic
analysis of the primary lateral load-resisting system, and compliance with code-specified drift
limits is then checked. Detailing guidelines are followed to ensure adequate ductility of the fuse
elements (Goel et al., 2010).
Increasingly, a more comprehensive, performance-based methodology is being applied to
the design of high-rise buildings in regions of high seismic risk. The concept of Performance-
Based Design (PBD) was first outlined in the Structural Engineers Association of California’s
Vision 2000 document (SEAOC, 1995). The PBD method enhances building performance, safety
and economy by incorporating multiple performance levels, whereas current building codes
address only life-safety and collapse prevention for the design basis earthquake. The PBD
concept relies on the establishment of appropriate acceptance criteria, such as drift limits and
target yield mechanisms. These design parameters are directly related to the extent of structural
damage expected at different seismic hazard levels. In seismic design, three levels of demand are
typically assessed: Serviceability Earthquake (SLE) – 50 percent probability of exceedance in 50
years; Life-Safety or Design Basis Earthquake (DBE) – 10 percent probability of exceedance in
50 years; and Collapse Prevention or Maximum Considered Earthquake (MCE) – 2 percent
probability of exceedance in 50 years (Christopoulos and Filiatrault, 2006). Performance criteria
are selected based on the importance category of the structure and on the needs of the building’s
owner and occupants.
A typical approach to seismic PBD begins with a linear dynamic analysis using a site-
specific response spectrum corresponding to the DBE. The DBE analysis serves to determine the
basic strength requirement of the structure and to ensure that prescribed drift limits are not
exceeded (Klemencic et al., 2006). The degree of material nonlinearity that is expected during
CHAPTER 1: Introduction 3
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
the maximum credible earthquake precludes the use of a simple elastic analysis procedure at the
MCE hazard level. Nonlinear verification analysis using scaled ground motion response histories
for MCE, and sometimes for the SLE seismic hazard level, has become fairly standard practice
among high-rise designers working in areas of high seismic risk. Several commercially available
analysis programs now include nonlinear modelling capabilities. However, accurate prediction of
inelastic response requires a robust model incorporating complex material and element
behavioural characteristics. These models can be time-consuming and labour intensive to
construct and require a sound understanding of nonlinear dynamic behaviour.
One of the most widely-used lateral load-resisting systems for residential high-rise
buildings is the reinforced concrete (RC) coupled shear wall configuration. This configuration
consists of two or more RC shear walls in series, typically coupled using RC beams at each floor
level. Coupling of shear walls enhances the overall building performance by increasing lateral
stiffness and reducing the moments that must be resisted by each wall, thereby increasing the
efficiency of the system, and by providing a means of seismic energy dissipation over the height
of the building (El-Tawil et al., 2010). The desired yielding mechanism for a coupled wall
system, which can be achieved through a capacity design approach, consists of yielding of the
coupling beams, followed by plastic hinge formation at the bases of the walls. As the coupling
beams undergo unrecoverable inelastic deformations during a seismic event, they dissipate
seismic energy, thus limiting large deformations associated with plastic hinging at the bases of
the walls (Harries and McNeice, 2006).
In regions of moderate to high seismic risk, coupling beams are often designed using
diagonal reinforcement, rather than conventional top and bottom longitudinal reinforcement.
Diagonally-reinforced coupling beams are more ductile and exhibit better energy dissipation
properties than conventionally reinforced coupling beams (Paulay and Priestley, 1992). Despite
these advantages, diagonally-reinforced coupling beams are associated with significant
drawbacks. The large depth and complexity of detailing required to achieve adequate ductility in
the beams results in increased construction costs and time.
For tall and slender coupled core wall buildings and buildings in regions of relatively low
seismic risk, the dynamic effects of wind typically govern the design of the lateral load-resisting
CHAPTER 1: Introduction 4
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
system. Design wind loads are amplified to account for inertia forces caused by dynamic
excitation. These inertia forces can account for a large portion of the design wind forces,
resulting in the need for increased strength. Additionally, lateral accelerations often exceed the
allowable limits specified for occupant comfort. Wind-induced accelerations are a function of the
stiffness, mass, and damping of the structure, in addition to the wind climate at the building site.
A common method of mitigating excessive accelerations is to increase the stiffness of the
building’s lateral load-resisting system. However, as buildings become taller and more slender,
this approach becomes uneconomical. The taller and more slender the structure, the more
additional material is needed to achieve the required stiffness (Jackson and Scott, 2010).
Discounting other costly and undesirable methods of acceleration mitigation such as reducing the
building height or changing the structural layout, providing supplemental damping is an
attractive alternative to increasing lateral stiffness.
The most common supplemental damping devices for high-rise buildings are tuned-mass
or tuned-liquid dampers (TMDs or TLDs). These vibration absorbing devices are typically tuned
to the building’s fundamental period of vibration and are thus effective in reducing resonant
contributions to the wind response. For maximum efficiency, they are typically located at or near
the top of tall buildings, where they unfortunately occupy a considerable amount of otherwise
valuable real-estate. Also, in order to support the relatively large added weight of a TMD or
TLD, the building’s gravity load resisting system must be augmented.
Distributed supplemental viscous or viscoelastic damping has recently been proposed as
an alternative to TMDs or TLDs, especially in areas of high seismic risk. Unlike TMDs and
TLDs, viscous and viscoelastic dampers are not tuned to a single frequency of vibration. These
elements are typically distributed throughout the structure and positioned between structural
elements such that they undergo relative displacement due to lateral loading. Because these
devices provide supplemental damping over a wide range of displacements and in many modes
of vibration, they are suitable for both wind and seismic vibration mitigation. In contrast,
vibration absorbing devices such as TMDs and TLDs are less ineffective in reducing higher
mode vibrations, which are common in high-rise structures subjected to seismic excitation
(Chowdhury and Iwuchukwu, 1987). Additionally, viscous and viscoelastic damping devices are
CHAPTER 1: Introduction 5
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
much less sensitive to variations in building frequency, making them a more reliable and
versatile option.
A new viscoelastic damping device for high-rise buildings has been developed at the
University of Toronto (Montgomery, 2011). This device, known as the Viscoelastic Coupling
Damper (VCD), consists of multiple layers of viscoelastic material, placed between layers of
steel plate which are anchored at alternating ends to built-up structural steel members. The VCD
can be used in place of RC coupling beams to add supplemental distributed damping to a coupled
core wall building. As illustrated in Figure 1.1, in a coupled wall configuration the viscoelastic
(VE) material undergoes shear deformations as the walls displace laterally due to wind or
seismic loading. Through this deformation, the VE material provides both a velocity-dependent
viscous force and a displacement-dependent elastic restoring force. The VCDs undergo
significant shear deformations due to the relative motion of the coupled walls under lateral
loading. This is a significant advantage over the typical axial brace configuration of VE dampers,
in which relative displacements are often insufficient to activate the VE material for effective
energy dissipation.
Figure 1.1 Viscoelastic Coupling Damper Concept
Current best practice for high-rise design involves independent consideration of seismic
and wind performance objectives. The governing lateral loads for strength design, either wind or
Viscoelas�c
Material
Layers
CHAPTER 1: Introduction 6
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
seismic, are determined and a preliminary design is carried out in order to satisfy the relevant
code requirements. In areas of high seismic risk, performance-based design methodologies are
often employed to improve seismic performance and provide a more economical design. The
design is then checked and adapted for compliance with code specifications pertaining to the less
critical lateral load case, sometimes resulting in an inefficient design. In order to address some of
the drawbacks associated with current practice in high-rise design, an integrated approach to
seismic and wind design is investigated in this thesis. The analytical work presented herein aims
to demonstrate that VCDs can be used to achieve a design that enhances both the seismic and
wind performance of an RC coupled wall high-rise building in a region of high seismic risk.
Building on the work of Montgomery (2011), this thesis presents an evaluation of the
seismic and wind performance of an RC coupled wall high-rise structure designed using VCDs.
In the following chapters, an overview of current design practices for RC coupled wall high-rise
structures is provided, followed by an introduction to the Viscoelastic Coupling Damper (VCD).
A comprehensive nonlinear modelling validation study is then presented. Next, a case study is
presented in which the seismic and wind performance of a conventional coupled wall high-rise
structure is compared with that of an alternative design including VCDs. Finally, drawing on the
results from the case study, a design procedure for RC coupled wall high-rise buildings in
regions of high seismic risk is proposed and recommendations for further research are presented.
CHAPTER 2: Background 7
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
2 BACKGROUND
In this chapter, the objectives and current methodologies for the design of RC coupled
wall high-rise buildings are discussed. The mechanics of RC coupled wall buildings are
introduced in Section 2.1. Current best-practice approaches to wind and seismic design are
presented in Section 2.2. Finally, in Section 2.3, the Viscoelastic Coupling Damper is introduced
as a viable solution for both wind and seismic design of tall coupled shear wall buildings.
2.1 Introduction to Reinforced Concrete Coupled Wall High-Rise Structures
Reinforced concrete structural walls provide an efficient lateral load-resisting system for
high-rise buildings. Also referred to as shear walls, structural walls are often perforated with
openings to accommodate windows and doors. These openings are typically aligned, as shown in
Figure 2.1, resulting in two or more walls coupled together by beams at each storey level.
Coupled wall systems resist lateral loads through a combination of cantilever action in the
individual wall piers, and frame action resulting from the transfer of vertical loads through the
coupling beams. The coupling ratio is a measure of the degree of coupling in the system and is
computed as the percentage of the total overturning moment resisted through axial tension and
compression forces transferred through the coupling beams in shear. The benefits of coupled
wall systems are well-known to structural engineers. Coupling action reduces the moments that
must be resisted by the individual wall piers, and increases the lateral stiffness of the system.
Figure 2.1 Lateral load-resisting mechanism in coupled wall structures
M1 M
2
P P
V1
V2
Coupling
Beam
(typ.)
CHAPTER 2: Background 8
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
When a coupled wall structure deforms laterally due to wind or seismic loading, the walls
rotate, causing the coupling beams to deform in double curvature. Assuming that no vertical or
rotational displacements occur in the foundation, the components of relative vertical
displacement along the line of contraflexure of the coupling beams are illustrated in Figure 2.2.
For compatibility, the sum of the components of relative vertical displacement must be zero
(Smith and Coull, 1991):
�� + �� + �� = 0 (2-1)
Rotation of the walls due to flexure results in a relative vertical displacement, ��. This
displacement component is equal and opposite to the sum of the shear and flexural deformations
occurring in the coupling beams, ��, and the axial deformations in the walls, ��. If the coupling
elements are flexible, they undergo large displacements and applied loads are resisted primarily
by the flexural capacity of the individual wall elements, as illustrated in Figure 2.3 a). If the
coupling elements are stiff, larger axial forces and deformations are induced in the wall elements
and the system behaves more like a composite cantilever, as illustrated in Figure 2.3 b).
Figure 2.2 Relative displacements at line of contraflexure (after Smith and Coull, 1991)
a)
b)
Figure 2.3 Exaggerated flexural deformed shapes of coupled wall systems a) Flexible coupling elements b) Stiff coupling elements
δ1
δ2
δ3
P
P
CHAPTER 2: Background 9
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
2.2 Design of Reinforced Concrete Coupled Wall High-Rise Structures
The Council on Tall Buildings and Urban Habitat suggests that a building may be
considered tall if it has 14 or more storeys or if it is over 50 meters in height (CTBUH, 2012).
Another characteristic of most tall or high-rise buildings is slenderness and, consequently,
sensitivity to the dynamic effects of wind loading. Under seismic loading, high-rise buildings are
often subjected to higher mode effects, whereas low- and mid-rise buildings respond primarily in
the first translational mode of vibration. Current building codes and standards are based
primarily on the design of low- to mid-rise structures and do not address many of the design
challenges associated specifically with high-rise buildings. In this Section, current best practices
for the design of high-rise structures are presented, with particular emphasis on the design of RC
coupled wall structures.
2.2.1 Wind Design
The structural design of tall buildings is often driven by the dynamic effects of wind
loading. Wind loading on bluff bodies such as buildings can be approximated as a combination
of a static mean component and a fluctuating dynamic component. The dynamic component of
the response of a structure to wind loading results from a combination of low-frequency
fluctuation of wind pressures, commonly referred to as the background response, to which all
structures are subjected, and a resonant response due to the excitation of one or more of the
predominant modes of vibration of the structure. As buildings become taller and more slender,
resonant contributions to wind loading increase and eventually dominate the response (Holmes,
2007). Figure 2.6 shows a time-history of an along-wind (drag) force acting on a bluff body, as
well as the structural response of a low-rise building with a high fundamental frequency of
vibration and the structural response of a high-rise building with a low fundamental frequency of
vibration. As illustrated in the Figure, the behaviour of the low-rise structure is dominated by the
background fluctuating response, whereas the high-rise structure experiences a significant
dynamic resonant response in addition to the background response.
CHAPTER 2: Background 10
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 2.4 Static and dynamic components of response in along-wind direction (after Holmes, 2007)
The atmospheric boundary layer is defined as the zone in which friction at the earth’s
surface influences wind flow. The boundary layer can extend up to an altitude of 1 km. This
region is characterized by an increase in average wind speeds as height above the ground
increases, and turbulent flow at all heights. In addition to the dynamic effects of fluctuating
pressures and forces due to up-wind turbulence, a vortex-shedding phenomenon occurs when
wind strikes the surface of a bluff body. Wind forces fluctuate in the across-wind direction as
separating shear layers curl towards the wake on alternating sides of the body, creating vortices
as illustrated in Figure 2.5. Vortex shedding can occur whether or not the flow is turbulent,
although turbulence can alter and even increase its effect. If the structure begins to vibrate in the
across-wind direction, the frequency of vortex-shedding may change to match the natural
frequency of vibration of the structure. This is known as the lock-in phenomenon (Holmes,
2007).
The variation of wind velocities, pressures and forces within the boundary layer is
complex and cannot be described or predicted deterministically. Therefore, a statistical approach
Wind Force:
Response of Low-Rise Building:
Response of High-Rise Building:
CHAPTER 2: Background 11
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
using random vibration theory is used to characterize the wind-induced vibration of structures.
Spectra are used to describe the relationship between dynamic response and frequency. This
approach forms the basis of code methods that account for the dynamic effects of wind loading.
Figure 2.6 shows the background and first mode resonant components of the wind response
spectrum for a high-rise structure. As previously mentioned, the along-wind dynamic response of
most structures is dominated by the background component, which is largely made up of low-
frequency contributions. However, high-rise buildings with relatively low fundamental
frequencies of vibration can have significant resonant response contributions.
Figure 2.5 Vortex-shedding (adapted from Irwin, 2010)
Figure 2.6 Response spectral density of a dynamic structure under wind loading (after Holmes, 2007)
Bluff Body
Vor!ces
Sp
ect
ral
De
nsi
ty
Frequency
Resonant
ResponseBackground
Response
fnD
CHAPTER 2: Background 12
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Building codes such as the NBCC (NRCC, 2010) typically apply a gust factor to static
equivalent wind loads to account for the dynamic component of the building response. In the
along-wind direction, the structural response, �(), can be separated into mean and fluctuating
components as follows:
�() = �� + �′() (2-2)
where �� is the mean response and �’() is the fluctuating component. In the Canadian code, the
gust factor, ��, is used to account for the expected peak response of the structure under dynamic
wind loading. The gust factor is a function of building exposure, ground surface roughness,
building height and width, natural frequency, mean wind speed, and inherent damping. Because
this approach is highly simplified, it is not generally relied upon for the design of high-rise
buildings which are highly sensitive to wind-vibrations. Current best practice requires that wind
tunnel testing be carried out for a reliable assessment of dynamic wind forces, drifts, and
accelerations.
Wind engineers use the High-Frequency Force Balance technique, developed by Tschanz
and Davenport (1983), to test tall buildings under dynamic wind loading conditions. The wind
consultant creates a stiff, lightweight model of the building, typically at a 1:400 scale. Figure 2.7
shows the wind tunnel model created by the Canadian wind engineering firm RWDI for the
Petronas Towers project in Kuala Lumpur. Surrounding buildings, including planned future
projects, and a long upwind corridor are included to accurately capture the turbulence profile
acting on the building. The building model is attached to a force balance which measures shear
forces, overturning moments, and torsion at its base.
The wind tunnel consultant uses a mechanical transfer function to determine the expected
response of the structure to the loads determined from the wind tunnel test. The structural
engineer must provide the wind consultant with building properties including mass, stiffness,
modal periods and critical damping ratios. The modal properties are determined from an elastic
analysis model with reduced section properties to account for the anticipated degree of concrete
cracking at the serviceability limit state (SLS). Because cracking is not evenly distributed over
the height of the structure, engineers may perform an iterative analysis to determine a more
CHAPTER 2: Background 13
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
realistic stiffness distribution of the coupling beams. Code based wind loads are applied to an
elastic analysis model with an initial estimate of reduced section properties. The cracked
properties are adjusted depending on the level of demand computed for the individual coupling
beams. This process is repeated until the results converge on a realistic distribution of cracked
section properties (Montgomery, 2011).
Figure 2.7 RWDI wind tunnel model for Petronas Towers (adapted from Irwin, 2010)
Inherent damping has a significant effect on the dynamic response of a high-rise structure
subjected to wind loading. The critical damping ratio in a given mode of vibration is a measure
of the energy dissipated in a vibration cycle as a percentage of critical damping. This energy
dissipation is the result of the formation and elongation of micro-cracks in construction materials
and of friction between both structural elements and non-structural elements, as well damping
provided by soil-structure interaction. Critical damping represents the amount of energy
dissipation required to damp out the free vibration of a system in a single cycle. There is a high
degree of uncertainty associated with the prediction of inherent damping in high-rise structures.
Building properties such as height, natural frequency, geometry, foundation type, soil properties,
construction materials and non-structural elements influence the degree of damping. Inherent
damping is also a function of the amplitude of vibration experienced by the structure (Jeary,
1986). Damping is generally thought to increase with increased amplitude of vibration. However,
recent studies have shown that a maximum critical damping ratio is reached at a relatively low
amplitude (Tamura, 2012). The “critical tip drift ratio” is defined as the roof drift at which the
maximum critical damping ratio of a structure vibrating in the elastic range is reached. This ratio
CHAPTER 2: Background 14
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
is typically in the order of 10-5 to 10-4. Beyond this amplitude of vibration damping decreases
while the primary structure remains elastic, unless additional sources of damping are engaged
such as damage to non-load bearing walls, partitions, slabs and architectural finishes (Tamura,
2012).
A database of free-vibration measurements from over 200 high-rise buildings in Japan
was compiled in order to characterize inherent damping in steel and concrete structures (Satake,
2003). Analysis of the collected data highlighted trends including a reduction in the first mode
damping as building height increased. Typical estimates of inherent damping for the design of
high-rise structures are between 1.5 and 2 percent for serviceability analysis and between 2 and
2.5 percent at the ultimate limit state (Montgomery, 2011). Existing free vibration data from
high-rise structures suggest that these estimates may be unconservative, particularly for the
design of super tall buildings. By adding a dependable source of supplemental damping, reliance
on inherent damping to mitigate the dynamic effects of wind loading can be significantly
reduced.
The current wind design approach for high-rise buildings begins with the selection and
design of a lateral load-resisting system to resist dynamically-enhanced wind loads at the
ultimate limit state (ULS). Reinforced concrete buildings are typically designed to remain elastic
under ULS wind loading. The lateral system is then stiffened in order to meet SLS criteria
(Jackson and Scott, 2010). The added stiffness required to address SLS wind demands also has
the effect of increasing seismic demands. In Canada, return periods of 10 and 50 years are used
for SLS and ULS design, respectively. Serviceability criteria include drift and acceleration
limits. The NBCC (NRCC, 2010) requires that interstorey drifts resulting from the application of
service level wind and gravity loads do not exceed 1/500. In order to ensure occupant comfort
during service level wind events, peak floor accelerations are limited to predefined thresholds.
Serviceability limits of 10-15 milli-g and 20-25 milli-g are typically specified for residential and
office buildings, respectively, in North-America. For wind-sensitive high-rise buildings, wind
tunnel testing is required to verify compliance with both SLS and ULS criteria. Often, the lateral
stiffness required to meet SLS criteria results in an impractical design. In such cases, the addition
of supplemental damping has become common practice.
CHAPTER 2: Background 15
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
The most common means of addressing excessive accelerations due to dynamic wind
loading is through the use of vibration absorbers, such as tuned mass and tuned liquid dampers.
These devices are typically located near the top of the structure, and tuned to its fundamental
period of vibration. The vibration-absorption concept is illustrated using a two-degree-of-
freedom system in Figure 2.8. Tuned mass dampers (TMDs) are heavy masses which transfer
inertia forces to the structure during lateral vibration, opposing the movement of the building
(den Hartog, 1956). Energy is typically dissipated by viscous dampers connected between the
main structure and the TMD. These devices typically provide added damping between 2 and 4
percent of critical. Tuned mass dampers are generally not relied upon to improve the seismic
response of high-rise buildings because of the de-tuning effect resulting from period elongation
after the onset of yielding in the lateral load-resisting system, and because they are usually tuned
to a single period of vibration (Chowdhury and Iwuchukwu, 1987). Since it is most practical to
provide a single vibration absorber at the top of the building, there is a lack of redundancy
associated with designs using these devices. As a result, designers are reluctant to rely on the
added damping provided to reduce the dynamic component of ULS wind loading and thus the
required strength and stiffness of the lateral load-resisting system (Smith and Wilford, 2007).
Figure 2.8 Two-degree-of-freedom representation of vibration absorber concept (after Holmes, 2007)
Tuned liquid dampers (TLDs) make use of the same principles as TMDs, although the
mass, stiffness, and damping are provided by moving liquid. Tuned sloshing dampers (TSDs)
and tuned liquid column dampers (TLCDs) are two common types of TLDs. Tuned sloshing
dampers consist of large tanks containing shallow liquid that dissipates energy by sloshing back
and forth as the building vibrates (Ibrahim, 2005). The fundamental period of oscillation of TSDs
depends on the size of the tank and the depth of the water. Tuned liquid column dampers are U-
M1
M2
u1(t)
u2(t)K
1
C1
K2
C2
CHAPTER 2: Background 16
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
shaped containers filled with liquid. Energy is dissipated through the flow of liquid through an
orifice located at the base of the container (Sakai et al., 1989).
Supplemental distributed damping systems are an attractive alternative to vibration
absorbers. The most common distributed damping devices are viscous and viscoelastic dampers.
These devices are typically integrated into the lateral load-resisting system such that they
undergo axial deformations when the building deforms laterally. Unlike vibration absorbers, they
do not occupy usable floor space in the building, and do not add significant mass to the structure.
Another important benefit associated with distributed damping systems is that they are not tuned
to a single frequency of vibration and can provide viscous damping over a wide range of
amplitudes and frequencies of vibration. Additionally, these devices are relatively insensitive to
changes in the dynamic properties of the building that occur over time and more significantly
during seismic events. These properties make viscous and viscoelastic dampers suitable for the
mitigation of both wind and earthquake effects.
Typical viscous fluid dampers are cylindrical devices filled with silicone oil which is
forced to flow through orifices in the bronze head of a stainless steel piston, as shown in Figure
2.9 a). These devices are typically used in an axial brace configuration in steel or reinforced
concrete frame construction. In purely viscous dampers, the viscous force generated by the
movement of the fluid is proportional to the amplitude and frequency of vibration. Because the
maximum force in a linear viscous damper occurs at zero displacement, its response is out-of-
phase with the response of the structure. Viscous dampers are usually designed such that they
exhibit nonlinear viscous behaviour (Housner et al., 1997). This is done by adjusting the design
of the orifices such that the viscous force is limited at high velocities, as shown in Figure 2.9 b).
Viscous dampers have been used to control both the wind and seismic response of structures.
The 57-storey Torre Mayor in Mexico City contains 98-fluid viscous dampers in axial brace
configurations (Taylor, 2002).
A team of structural engineers at Arup have developed a damping system for high-rise
buildings using viscous dampers in outrigger locations (Smith and Wilford, 2007). This system
can be used to add supplemental damping to RC coupled wall buildings with outriggers. The
concept involves liquid viscous dampers connected between stiff outrigger elements and
CHAPTER 2: Background 17
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
perimeter columns at a number of floor levels, as illustrated in Figure 2.10. As the building
deforms laterally, the dampers undergo axial deformations, thereby providing added damping.
This system relies on the added damping to offset the losses in static strength and stiffness
associated with inserting viscous dampers between the outriggers and the perimeter columns.
a)
b)
Figure 2.9 a) Viscous fluid damper (adapted from Hwang, 2002) b) Hysteretic behaviour of linear and nonlinear viscous dampers
Figure 2.10 Damped outrigger concept (adapted from Smith and Wilford, 2007)
An application of the damped outrigger system is currently under construction in New
York City. The 37-storey steel-frame office tower designed by Skidmore, Owings and Merrill
has a steel frame with a braced steel core and a braced “hat truss” with outriggers connected to
the core at the top floor mechanical level. Seven viscous dampers are used to connect the
outrigger to the perimeter columns, in order to meet acceleration limits. The damped outrigger
design resulted in the addition of 2 percent added damping in the predominant lateral mode of
vibration. No significant damping was provided in the torsional modes. An estimated savings of
1000 tons of structural steel was achieved by relying on added damping rather than added
stiffness to meet SLS wind criteria. The design also resulted in reduced construction costs and
Piston Rod Cylinder Sylicone Oil
Piston Head
with Orifices
Chamber 1 Chamber 2
Control
Valve
Seal
Displacement
Force
Nonlinear
Linear
Damped
connec�on
Outrigger
wallDoors RC core
Perimeter columns
(beam and floor slabs
omi"ed for clarity)
CHAPTER 2: Background 18
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
projected maintenance, when compared with a more conventional TMD or TLD solution
(Jackson and Scott, 2010).
Unlike purely viscous dampers, viscoelastic dampers generate both a displacement-
dependent elastic restoring force and a velocity-dependent viscous force. These devices generally
consist of two or more layers of viscoelastic (VE) material bonded between layers of steel plate,
as illustrated in Figure 2.11 a). Energy is dissipated in the form of heat when the VE material is
deformed in shear, resulting in a viscoelastic hysteretic response, as shown in Figure 2.11 b). VE
material provides damping at all strain amplitudes, however its properties are sensitive to
temperature and frequency of vibration. Like viscous dampers, VE dampers have been used to
mitigate both wind and seismic effects on high-rise buildings. Approximately 10,000 VE
dampers were installed in both of the 110-storey World Trade Center towers in New York City.
The dampers were located between the steel perimeter columns and the lower chords of the
horizontal floor trusses. A total of between 2.5 and 3 percent of critical damping was measured
in the structure during hurricane Gloria in 1978 (Samali and Kwok, 1995).
a)
b)
Figure 2.11 a) Viscoelastic damper b) Hysteretic behaviour of viscoelastic damper
Montgomery (2011) proposed the following procedure for the wind design of RC coupled
wall high-rise buildings:
1) The structural layout is established in collaboration with the architect.
2) A preliminary lateral load-resisting system is developed, including shear wall and
coupling beam dimensions, concrete strengths and a preliminary reinforcing steel design.
3) SLS and ULS wind analyses are carried out using finite element models with appropriate
cracked concrete section properties.
4) Lateral drifts due to SLS wind loading are checked for compliance with drift limits.
Force
Steel Plate
VE Material
Force
Shear
Strain
Force
Displacement
K
CHAPTER 2: Background 19
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
5) A strength design check of the lateral load-resisting-system is carried out based on
factored ULS wind loads.
6) The SLS modal properties are given to a wind tunnel consultant to determine
accelerations, torsional velocities, and wind loads.
7) Steps 3 to 5 are repeated using the wind loads generated in the wind tunnel.
8) If any of the design requirements are not met, a second design iteration must be carried
out by altering lateral load-resisting system and, when necessary, adding a supplemental
damping system.
2.2.2 Seismic Design
Coupled wall systems are recognized for providing superior seismic performance in high-
rise structures because of their ability to dissipate seismic energy while maintaining a relatively
high degree of lateral stiffness (Saatcioglu et al., 1987). In seismic regions, RC coupled core wall
buildings are designed to form a plastic mechanism in which the coupling beams yield, followed
by yielding at the base of the coupled walls. All other structural members are designed to remain
elastic. The coupling beams behave analogously to link beams in eccentrically braced frames
(EBF). A means of energy dissipation is provided over the height of the building as the coupling
beams undergo inelastic deformations. The coupling beams are designed to yield before the
structural walls, providing a significant amount of hysteretic damping and thereby limiting large
displacements and damage associated with inelastic deformations in the walls during moderate
seismic events (Harries and McNeice, 2006).
Research has shown that increasing the degree of coupling in a coupled wall system
results in increased ductility (Harries et al., 1998). In CSA A23.3 (2004), ductile coupled walls
are defined as resisting at least 66 percent of the base overturning moment through coupling
action. A ductile partially coupled wall system is defined as having a coupling ratio of less than
66 percent. Coupling beams must provide adequate strength, stiffness and ductility to achieve the
desired degree of coupling. In order to improve the performance of coupling beams in regions of
moderate to high seismic risk, diagonal reinforcement is typically provided, as shown in Figure
2.12. Diagonally-reinforced coupling beams have been shown to provide enhanced ductility and
CHAPTER 2: Background 20
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
a stable hysteretic response (Paulay and Priestley, 1992). However, the complexity of diagonal
reinforcing steel details can increase both construction time and costs (El Tawil et al., 2010).
Significant damage is expected in RC coupling beams at high levels of ductility. Figure
2.13 shows damage in a diagonally-reinforced coupling beam at different displacement stages
during a cyclic test. Fragility curves indicating the probability of different damage states as a
function of chord rotation in diagonally-reinforced coupling beams with high aspect ratios
(2 < ��/ℎ < 4) are shown in Figure 2.14. These curves were defined using data from a series of
cyclic tests on ½-scale diagonally-reinforced coupling beams (Naish, 2010). Yielding was
observed at a mean chord rotation of approximately 1 percent. Damage state DS1, occurring at a
mean rotation of 2 percent, was defined as damage requiring repair in the form of epoxy
injection of minor residual cracks. It should also be noted that at this level of rotation the
diagonal reinforcing steel will have yielded and it will be difficult to assess its condition.
Damage state DS2, occurring at a mean rotation of approximately 4 percent, was defined as
damage requiring repair of substantial residual cracks using epoxy injection. Damage state DS3,
occurring at a mean rotation of approximately 6 percent, refers to substantial damage associated
with significant strength degradation due to buckling and/or fracture of reinforcement and
crushing of concrete. Anticipated repairs involve removal and replacement of damaged concrete,
as well as attachment of mechanical couplers to reinforcing steel embedded in the walls and
replacement of damaged reinforcing steel bars.
Figure 2.12 Diagonally-reinforced coupling beams (adapted from Wallace et al., 2009)
Coupling Beams
CHAPTER 2: Background 21
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Reports from the 2010 Concepcion earthquake in Chile revealed that owners of high-rise
RC core wall condominium buildings were dissatisfied with the levels of damaged sustained in
their structures. Figure 2.15 illustrates typical damage observed in coupling beams and shear
walls following the Magnitude 8.8 earthquake. Many owners demanded that the condo builders
demolish their buildings and replace them with “earthquake proof” structures (LATBSDC,
2010).
Figure 2.13 Damage in diagonally-reinforced coupling beams (adapted from Naish et al., 2009)
Figure 2.14 Fragility curves for diagonally-reinforced coupling beams (adapted from Naish, 2010)
Structural steel coupling beams have been proposed as a viable alternative to RC
coupling beams (Harries et al., 1993). Reinforced concrete shear walls coupled using steel link
beams are referred to as hybrid coupled walls (HCW), and a small number of buildings with
HCW lateral load-resisting systems have been constructed in regions of moderate to high seismic
risk around the world. Although none of these buildings have been exposed to a major
Pro
ba
bil
ity
of
da
ma
ge
sta
te o
ccu
rin
g
0
1.0
0.5
Beam chord rota!on (%)
100 2 4 6 8
Yield
DS1
DS2
DS3
CHAPTER 2: Background 22
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
earthquake, there is significant experimental evidence to support the use of HCW systems,
particularly for seismic applications (El-Tawil et al., 2010). For the same degree of coupling as a
conventional RC coupled wall system, HCW systems are expected to experience lower ductility
demands on both the wall piers and on the coupling beams because of added damping resulting
from the improved hysteretic response of the coupling beams (Harries et al., 1998). Additionally,
steel coupling beams provide a significant advantage over diagonally-reinforced coupling beams
when architectural restrictions limit their depth.
a)
b)
Figure 2.15 Damage from Concepcion Earthquake (adapted from LATBSDC, 2010) a) Coupling beam damage b) Shear wall damage
Figure 2.16 Steel coupling beams (adapted from El-Tawil et al., 2010)
There remains a lack of design specifications addressing HCW systems. The AISC
Seismic Provisions for Structural Steel Buildings (AISC, 2005) do, however, include prescriptive
Steel
coupling
beam
CHAPTER 2: Background 23
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
provisions for the design of steel coupling beams. Additionally, recommendations for the seismic
design of HCW systems have been published by the American Society of Civil Engineers (El-
Tawil et al., 2009). Research has shown that steel links in EBFs possess excellent ductility and
energy absorption properties when designed and detailed to yield in shear (Engelhardt and
Popov, 1992). In HCW systems, short coupling beams which dissipate energy through plastic
shear deformations are preferred over longer beams which dissipate energy through the
formation of flexural hinges. Steel coupling beams must be embedded in the RC walls such that
their full capacity is developed. The embedment length must be selected such that bearing failure
is prevented at the expected ultimate shear strength of the coupling beam (El-Tawil et al., 2010).
Marcakis and Mitchell (1980) proposed a design approach for connections involving structural
steel members embedded in reinforced concrete. Measures must be taken to ensure that the
embedded portions of steel coupling beams remain elastic.
Under seismic loading, steel coupling beams are designed to respond in a similar manner
to steel links in EBFs. Fragility curves for shear-critical link beams in EBFs are shown in Figure
2.17. These curves were defined using existing test data from a large number of EBF links
(Gulec et al., 2011). Damage states were grouped according to the appropriate method of repair.
MoR-1, occurring at a mean plastic rotation of approximately 4 percent, corresponds to concrete
replacement due to damage in the slab above the link. MoR-2, occurring at a mean plastic
rotation of approximately 6 percent, corresponds to heat straightening of the link associated with
web or flange local buckling. MoR-3, occurring at a mean plastic rotation of approximately 8
percent, corresponds to link replacement due to web or flange fracture. Figure 2.18 shows
examples of web buckling and web fracture in shear-critical EBF links (Gulec et al., 2011).
In addition to the damage states previously described for EBF links, steel coupling beams
can cause extensive damage in the embedment regions of the RC coupled walls during large
earthquakes (Shahrooz et al., 2007). Figure 2.19 shows damage in the embedment regions of RC
wall panels following a cyclic test in which a displacement ductility of 13.6 was achieved in the
steel coupling beam (Harries et al., 1993). The vertical reinforcing steel in the embedment region
did not reach yield during the test. In an effort to localize damage in the steel coupling beam, the
addition of a replaceable shear fuse at its midspan has been investigated (Fortney et al., 2007).
CHAPTER 2: Background 24
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
The beam is designed such that inelastic deformations are concentrated in the fuse, which can be
replaced following a major seismic event. The embedment regions are designed to remain elastic
at the expected ultimate strength of the fuse element. This concept is illustrated in Figure 2.20.
Fortney et al. (2007) conducted cyclic testing on a built-up shear-critical steel coupling beam
with a replaceable fuse. Slippage of the web splice connections was observed beyond a rotation
of 0.04 radians and weld fractures occurred at the flange-web interface of the main built-up
sections beyond a rotation of 0.05 radians. Mansour (2010) investigated a number of replaceable
details for shear links in EBFs. Further research is required to develop and validate this concept
for use in HCW systems.
Figure 2.17 Fragility curves for shear-critical EBF links (adapted from Gulec et al., 2011)
Current best practice in seismic design of high-rise buildings does not follow the
strength-based prescriptive approaches set out in traditional building codes (CTBUH, 2008).
The seismic provisions in current building codes have been developed for low- and mid-rise
buildings which respond primarily in the first translational mode of vibration, whereas ground
shaking is known to excite multiple modes of lateral vibration in tall buildings. Code provisions
are based on elastic analysis methods which may be inaccurate and unconservative for predicting
the response of high-rise buildings subjected to seismic loading. In order to improve the safety,
economy, performance and resilience of high-rise buildings in regions of high-seismic risk,
Pro
ba
bil
ity
of
da
ma
ge
sta
te o
ccu
rin
g
0
1.0
0.8
0.6
0.4
0.2
Inelastic link rotation (rad)
0 0.150.0750.025 0.05 0.10 0.125
Theoretical fragility function (MoR-1)
Emperical fragility function (MoR-2)
Theoretical fragility function (MoR-2)
Emperical fragility function (MoR-3)
Theoretical fragility function (MoR-3)
CHAPTER 2: Background 25
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
structural engineers have adopted a performance-based design philosophy. This philosophy is
based on the premise that seismic performance, which is characterised by the probability of
losses due to structural and non-structural damage, can be reliably predicted. This allows
stakeholders to make informed decisions based on life-cycle considerations, rather than on up-
front construction costs alone. While current building codes permit the use of performance-based
design procedures, they do not accurately specify appropriate modelling, analysis, and
acceptance criteria for tall buildings. Current guidelines for performance-based design of high-
rise buildings include LATBSDC (2008) and PEER (2010).
a)
b)
Figure 2.18 Damage states of EBF links (adapted from Galvez, 2004) a) Web buckling b) Web fracture
Performance-based design allows the design team to select and verify performance
objectives at various intensities of seismic excitation. This approach also allows for the
circumvention of code limitations on building height, choice of structural system, and application
of innovative materials and technologies. Whereas building codes generally address only a life
safety performance objective at the design basis seismic hazard level, performance-based
approaches involve a multi-level performance assessment. Figure 2.21 illustrates the
performance objectives recommended in the Vision 2000 document (SEAOC, 1995). For the
design of tall buildings, at least two performance objectives are typically addressed. Best practice
requires the following minimum requirements:
• Withstand a maximum credible (very rare) earthquake with low probability of collapse
(collapse prevention objective)
• Withstand a service level (frequent) earthquake with negligible damage to structural and
non-structural components (operational objective)
Web buckling
Web fracture
CHAPTER 2: Background 26
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Superior performance can be achieved by specifying more stringent performance objectives. The
design team works with stakeholders to select the desired level of performance.
Figure 2.19 Wall damage in embedment region (adapted from Harries et al., 1993)
Figure 2.20 Replaceable fuse concept for steel coupling beams (adapted from Fortney et al., 2007)
In order to implement performance-based seismic design, the following steps must be taken:
• Selection of return periods for seismic analysis and corresponding performance
objectives
• Selection and scaling of ground motion records using site specific response spectra
• Nonlinear time history analysis
• Evaluation of seismic performance based on acceptance criteria
Damage to
embedment
region
Wall pier Replaceable shear fuse
CHAPTER 2: Background 27
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
The responsible application of this procedure requires considerable knowledge of seismic
hazards and selection and scaling of ground motion records, nonlinear dynamic response and
analysis, capacity design principles, and detailing of structural elements to provide the required
ductility (PEER, 2010). Building officials typically require that a peer review of the design
process be carried out for high-rise building projects in regions of high seismic risk. The peer
review process should include an independent third party assessment of performance objectives
and acceptance criteria, seismic hazard analysis, ground motion selection and scaling, structural
layout and details, modelling and analysis techniques and interpretation of results.
Figure 2.21 Vision 2000 performance objectives (after Porter, 2003)
As mentioned previously, the seismic performance of a high-rise building is
characterized primarily by the probable extent of damage associated with different levels of
seismic intensity. Performance criteria are intended to limit the risk of structural damage, non-
structural damage, probability of collapse, and probability of fatalities. An ongoing project by the
Applied Technology Council is aimed at developing a practical probabilistic loss estimation
framework that is suitable for use in engineering practice (ATC, 2011; Yang et al., 2009). The
performance assessment is intended to allow designers to quantify the probability of structural
Fully
Opera�onal Opera�onal Life Safety
Collapse
Preven�on
Frequent
Occasional
Rare
Very Rare
Fully
Opera�onal
Earthquake Performance Level
Ea
rth
qu
ak
e D
esi
gn
Le
ve
l
Basic Facili!es
Essen!al/Hazardous Facili!es
Safety Cri!cal Facili!es
CHAPTER 2: Background 28
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
and non-structural damage based on engineering demand parameters obtained from nonlinear
time history analysis. Projected damage quantities are then used to develop a quantitative and
probabilistic description of seismic risk for a given structure, expressed in terms of the three D’s:
deaths, dollars and downtime. This information can assist stakeholders in making risk
management decisions and can assist engineers in achieving an optimal design solution.
The devastation of the city of Christchurch, New Zealand, following a Magnitude 6.3
earthquake in February of 2011, highlights the importance of a performance-based seismic
design approach. Although relatively few people were killed (a total of 181 fatalities reported,
115 of which resulted from the collapse of a single 6-storey building), many more were injured
and a large number lost their homes and businesses. As many as 50 percent of the buildings in
the Central Business District (CBD) have been or will be demolished as a result of structural
damage (Christchurch City Council, 2011). Significant non-structural damage was also observed.
Figure 2.22 shows examples of damage to ceilings and other non-structural contents.
Figure 2.22 Non-structural damage from Christchurch Earthquake (adapted from Mayes, 2011)
Because of recent emphasis on the seismic resilience of structures, the use of
supplemental damping systems to enhance seismic performance is becoming increasingly
common. These systems include the previously mentioned vibration absorbers and viscous and
viscoelastic dampers, as well as metallic dampers and friction dampers (Christopoulos and
Filiatrault, 2006). Base isolation systems offer another effective means of improving seismic
performance, although this technology is more commonly applied to the design of low- to mid-
rise structures. Hysteretic damping provided by coupling beams is commonly relied upon for
seismic design of RC coupled wall high-rise buildings; however, several applications of
CHAPTER 2: Background 29
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
supplemental damping systems have been investigated to improve the seismic resilience of these
structures.
Reinforced concrete high-rise shear wall buildings are characterized by relatively high
lateral stiffness and relatively small lateral displacements. Additionally, whereas low-rise
buildings primarily deform in shear, high-rise buildings deform as a combination of racking and
rigid body deformations. As illustrated in Figure 2.23 a), the racking deformation angle, �, is
approximately equal to the interstorey drift ratio, �, in a low-rise building. In a high-rise
building, the interstorey drift ratio is a result of both racking and rigid body deformations, as
illustrated in Figure 2.23 b). Therefore, the placement and orientation of supplemental damping
devices which rely on large deformations and which are typically used in axial brace
configurations present a design challenge for high-rise coupled wall structures.
a)
b)
Figure 2.23 a) Low-rise building racking deformation b) High-rise building racking and rigid body deformation (after CTBUH, 2008)
The damped outrigger concept described in Section 2.2.1 provides a means of mitigating
both wind and seismic effects on coupled wall structures. Other proposed damping systems
include the “toggle brace” configuration for viscous dampers, developed by Constantinou et al.
(1997). This configuration, illustrated in Figure 2.24, utilizes a mechanism to magnify damper
displacements for applications in structures with high lateral stiffness. Madsen et al. (2003)
βθ
βθ
CHAPTER 2: Background 30
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
carried out an analytical investigation of two configurations for viscoelastic dampers in coupled
wall structures. The first configuration involved two axial VE damping elements placed
diagonally in the coupling beam locations, as illustrated in Figure 2.25 a). This system resulted in
relatively low added damping because of limited relative displacements experienced by the
damper elements. The second configuration involved the placement of VE dampers within
openings cut in the shear walls at the lower levels of the building, as shown in Figure 2.25 b).
Analytical results indicated that significant improvements in seismic performance could be
achieved using this system.
Munir et al. (2011) conducted an analytical study comparing the seismic performance of
a 40-storey RC core wall prototype structure with alternative designs using three different energy
dissipating seismic control measures. The first alternative design relied on the formation of
plastic hinges at several locations in the shear walls to dissipate seismic energy, as shown in
Figure 2.26 a). By allowing for plastic hinge formation in locations of high flexural demand,
higher mode effects were effectively mitigated and significant reductions in seismic force
demands were observed, when compared with the reference structure. The second configuration
included buckling restrained braces (BRBs) in an axial brace configuration, located between the
RC core and the perimeter columns. The braces spanned 3 storeys, passing through openings in
intermediate slabs, as shown in Figure 2.26 b). Buckling restrained braces are designed to
provide hysteretic energy dissipation through inelastic axial deformations in both tension and
compression. Reductions in both seismic force and deformation demands were achieved using
this configuration, although the added stiffness associated with the addition of the braces did
offset the benefits of the added damping. The final alternative configuration included fluid
viscous dampers (FVDs) in the same axial brace configuration as the BRBs. The addition of the
viscous dampers resulted in significant reductions in both seismic force and deformation
demands when compared with the reference structure. Reductions of 33 percent, 22 percent, and
27 percent in inelastic shear demand and 60 percent, 22 percent, and 26 percent in inelastic
flexural demand were achieved using plastic hinges, BRBs, and FVDs, respectively.
Approximate reductions of 30-40 percent in inelastic deformation demands were achieved using
the BRB and FVD solutions.
CHAPTER 2: Background 31
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 2.24 Toggle brace configuration (after Constantinou et al., 1997)
a)
b)
Figure 2.25 VE damper configurations for shear wall structures
a)
b)
Figure 2.26 Seismic control measures for RC core wall building (after Munir et al., 2011) a) Plastic hinge solution b) BRB and FVD brace solutions
Damper
Loca�on 1
Damper
Loca�on 2
Pin
Wall Pier
Viscous
damper
Coupling
beam
Wall Pier
Viscous
damper
Opening
RC core
Plas!c
hinge Perimeter
Column
Slab
RC core
Perimeter
Column
Slab
BRB or FVD
brace
CHAPTER 2: Background 32
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
A recent project in San Francisco highlighted the unique challenges associated with the
design of high-rise buildings in regions of high seismic risk. The structural design of the 61-
storey One Rincon Hill building was carried out by Magnusson Klemencic Associates (MKA).
This RC core wall structure was found to be sensitive to both wind and seismic effects (Cassidy,
2007). Two sources of supplemental damping were used to address wind and seismic challenges
separately. In order to mitigate vibration problems affecting occupant comfort, a tuned liquid
damper was installed at the top of the structure. The performance-based seismic design resulted
in the use of buckling-restrained brace elements to provide supplemental hysteretic damping for
severe seismic loading. The BRBs are attached to the RC core using steel outrigger columns, as
illustrated in Figure 2.27.
Figure 2.27 One Rincon Hill lateral load-resisting system (adapted from Robinson, 2012)
Following the 2011 Magnitude 9.0 Tohoku Earthquake in Japan, significant attention has
been drawn to the effects of high-intensity, long-period ground motions on high-rise buildings
(Takewaki et al., 2012). This earthquake and the subsequent tsunami devastated a large area in
Eastern Japan, killing nearly 20,000 people and resulting in tremendous economic loss. This was
also the first earthquake of its kind to affect super-tall buildings in a major city. The phenomenon
Tuned liquid damper
Concrete core
Buckling restrained
brace
Outrigger columns
CHAPTER 2: Background 33
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
of critical excitation of tall building structures due to long-period ground motions has since come
to the forefront of earthquake engineering research. Critical excitation is described as the
phenomenon of resonance occurring due to the coincidence of the predominant period of ground
motion with the fundamental period of a high-rise structure. A case study carried out on two
prototype high-rise steel frame buildings showed that the addition of viscoelastic dampers was
effective in damping out resonant behaviour due to the ground motions recorded during the
Tohoku earthquake (Takewaki, 2011). Maximum storey displacements and interstorey drifts, as
well as a time-history of top storey displacement for the damped and un-damped 60-storey
prototype structure are shown in Figure 2.28. As illustrated, the dampers were effective in
significantly reducing both the amplitude and the number of cycles of vibration experienced by
the prototype structure.
Figure 2.28 Effect of VE dampers on critical excitation due to long-period ground motions (adapted from Takewaki, 2011)
2.3 Viscoelastic Coupling Damper Concept for RC Coupled Wall High-Rise Buildings
The discussion presented in Section 2.2 highlighted some of the many challenges
associated with the design of RC coupled wall high-rise structures, particularly in regions of high
seismic risk. It has been shown that the design of these structures is primarily driven by the need
to ensure adequate performance under dynamic loading conditions. The Viscoelastic Coupling
Damper offers an elegant means of providing supplemental distributed damping which can be
used to mitigate dynamic effects due to both wind and seismic loading. The VCD, illustrated in
No DamperDamper Double
No DamperDamper Double
Sto
rey
Nu
mb
er
Sto
rey
Nu
mb
er
0
10
20
30
40
50
60
0
10
20
30
40
50
60
0 200 400 600 800 1000
Max. Storey Displacement (mm)
0
Max. Interstorey Dri! (mm)
5 10 15 20 25 30
Top
Sto
rey
Dis
pla
cem
en
t (m
m)
1000
500
0
-500
-10000 100 200 300 400 500 600
Time (s)
No DamperDamper Double
CHAPTER 2: Background 34
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 2.29, is made up of a number of layers of viscoelastic material, bonded to layers of steel
plate. The plates are anchored at alternating ends to built-up steel sections. These dampers can be
used to replace RC or steel coupling beams in a coupled wall high-rise building. Like coupling
beams, the VCDs transfer vertical forces between the two walls, increasing the lateral stiffness of
the system. The VCDs, however, have the added benefit of providing viscous damping in all
ranges of motion. When the building deforms laterally due to either wind or seismic loading, the
VE material deforms in shear, as illustrated in Figure 2.30. Through this deformation, the VE
material exerts both a velocity-dependent viscous force and a displacement-dependent elastic
restoring force. Figure 2.31 shows two of the full-scale VCD specimens tested by Montgomery
(2011).
Figure 2.29 Viscous coupling damper (adapted from Montgomery, 2011)
The VCD concept addresses many of the drawbacks associated with other available
supplemental damping systems. By positioning the dampers in lintel locations above openings in
the structural walls, a significant amount of damping can be added to the structure without
occupying usable floor space or altering the structural layout of the building. The VCDs can be
designed to be cast in place during construction, like steel coupling beams, or they can be bolted
or welded to embedded connection plates after the concrete has been cast. The latter type of
connection detail not only facilitates construction, but also enables replacement of damaged
VCD elements following a major seismic event. Additional connection details are discussed in
Montgomery (2011).
Viscoelas�c
Material Layers
Steel
Plates
Possible
Wall Anchorage
Detail
Built-up
Steel Assembly
CHAPTER 2: Background 35
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 2.30 Exaggerated deformed shape (adapted from Montgomery, 2011)
Figure 2.31 Viscous coupling damper prototypes (courtesy of M. Montgomery)
For seismic applications, Montgomery (2011) proposed including a ductile force-limiting
fuse mechanism in the design of the VCD. By including a fuse in series with the VE material,
large shear deformations can be achieved without subjecting the VE material to excessive strains.
Possible fuses include reduced beam sections (RBS) which yield in flexure, shear-critical fuses,
and friction fuses. In addition to protecting the VE material and limiting forces transferred to the
RC walls, each of these types of fuses provides an additional source of damping once activated.
Another advantage of including a fuse mechanism is the localization of damage in the event of a
major earthquake. Montgomery (2011) proposed a post-tensioned connection detail which would
facilitate the removal and replacement of a damaged damper. Other details could be developed
which would allow for the replacement of the fuse component alone. Mansour (2010)
investigated a number of replaceable details for shear links in EBFs. Similar details could be
used to achieve a replaceable shear fuse in a VCD.
θwall
uVE
VE
Material
θwall
Cast-in-place
RC Wall
Cast-in-place
RC slab
CHAPTER 2: Background 36
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 2.32 illustrates the intended hysteretic behaviour of a VCD designed using an RBS
flexural fuse mechanism. Similar behaviour is expected of VCDs designed using a shear or
friction fuse mechanism. As illustrated in the Figure, the VCD has two distinct response
characteristics. Under wind and service level seismic loading, the fuse components remain elastic
and the VCD exhibits a purely viscoelastic response. The area under the force-displacement
curve is equal to the energy dissipated through shear deformation of the VE material. In the
event of a severe earthquake, the fuse mechanism is activated, limiting the force transmitted
through the VE material. In addition to the viscous damping provided by the VE material, the
ductile fuse components provide hysteretic damping during severe earthquakes.
The VCDs are manufactured by Nippon Steel Engineering Co. (NSEC) in Japan. The VE
material is produced by Sumitomo-3M. This material, called ISD-111H, was selected for its
enhanced stiffness and damping coefficients when compared with other ISD compounds, such as
ISD-100, 110 and 111, which have previously been studied and implemented in structural
applications. Additionally, ISD-111H can sustain high levels of strain without tearing and
maintains stable properties under long-term cyclic loading. The same material has previously
been used for seismic applications in Taiwan and in the United States (Montgomery, 2011). The
most significant challenge associated with the use of this material is its sensitivity to
temperature. The properties of the material also vary as a function of frequency and amplitude of
excitation. The effects of frequency and strain are well-defined and can be accurately captured
using available models, as will be discussed in Chapter 3. Temperature effects are, however,
more difficult to capture and must therefore be addressed using a bounded analysis and careful
consideration of the expected loading conditions of the dampers.
Montgomery (2011) proposed design strains and temperature bounds for different lateral
loading scenarios. The VE material stiffness and damping coefficients increase with increased
frequency of excitation and decrease with increased temperature. An increase in strain amplitude
results in an increase in the stiffness of the VE material, while the damping coefficient remains
approximately constant at a constant temperature and frequency of excitation. For wind analysis,
the VCDs are assumed to respond primarily in the fundamental period of vibration of the
structure. Results from a full-scale testing program suggest that the temperature of the VE
CHAPTER 2: Background 37
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
material would increase by approximately 5 C over the course of a one hour long wind storm
due to along wind-loading. A temperature increase of approximately 7 C was observed due to
one hour of across-wind loading (Montgomery, 2011). Upper bound properties should be used
for capacity design of the built-up steel assembly and adjacent structural members. Drift checks
should be carried out using lower bound properties. In the along-wind direction, a combination
of static and dynamic stiffness coefficients is used, depending on the percentage of the maximum
response that is assumed to be dynamic. The effective stiffness of the VCD, �������, can be
determined as follows:
������� = (%� !"#$%/100%)���� + (%'"$%/100%)����( (2-3)
where ���� is the assumed dynamic stiffness of the VCD and ����( is the assumed static
stiffness. An estimate of the percentage of the peak response caused by dynamic effects is
typically provided by a wind-tunnel consultant. Montgomery (2011) provides static stiffness
coefficients measured at the end of SLS along wind tests. Recommended temperature bounds
and design strains for wind loading are listed in Table 2.1.
Figure 2.32 VCD design concept (adapted from Montgomery, 2011)
SLE
Envelope
MCE
Envelope
Viscoelas!c
Plas!c
Envelope
Viscoelas!c
Envelope
Force
Shear
Displacement
θwall
Viscoelas!c
Material
Layers
θwall
Viscoelas!c
Material
Layers
Shear
Displacement Shear
Displacement
Elasto-Plas!c
Fuse
a) b)
c)
SLS Wind
Envelope
ULS Wind
Envelope
CHAPTER 2: Background 38
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Table 2.1 Recommended upper and lower bounds for wind design (Montgomery, 2011)
Loading
Condition
Design Bound
VE Temp. ) ( C)
Design Strain *++ *,-.
Across-wind Upper 20 ±100
SLS Lower 25 Across-wind Upper 20
±135 ULS Lower 30
Along-wind Upper 20 75±50
SLS Lower 25 Along-wind Upper 20
100±70 ULS Lower 30
Because of the short duration of seismic loading, Montgomery (2011) recommended
using an ambient temperature value for preliminary seismic analysis. Approximate increases in
temperature of less than 2 C, 4 C and 5 C are expected during SLE, DBE, and MCE level
seismic events, respectively. Montgomery (2011) recommended using an average temperature of
23 C or 24 C for preliminary analysis. A maximum design strain of 150 percent is
recommended for service level earthquakes, and an absolute maximum strain of 400 percent is
permissible for DBE and MCE level seismic design. A bounded analysis should also be carried
out to confirm the performance of the final design.
CHAPTER 3: Model Verification 39
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
3 MODEL VERIFICATION
This Chapter presents a comprehensive validation of the nonlinear modelling software
used throughout this thesis. An introduction is provided in Section 3.1. Section 3.2 presents
validation studies for the nonlinear elements included in typical high-rise RC core wall models,
as well as steel coupling beams and VCD elements. The validation of a realistic case study
building, modelled using the elements validated in Section 3.2, is presented in Section 3.3.
Finally, Section 3.4 provides a summary of the modelling techniques and assumptions used
throughout this thesis, as well as a discussion of their limitations.
3.1 Introduction
In order to evaluate the behaviour of coupled shear wall systems for performance-based
seismic design, nonlinear modelling and analysis tools are required. Many commercially
available software programs now have nonlinear modelling and analysis capabilities. The
analyses described in this thesis have been conducted using CSI Perform-3D Nonlinear Analysis
and Performance Assessment software (CSI, 2007), referred to hereafter as Perform-3D.
Relatively simple or coarse models are required to reduce computer run times for
nonlinear time history analysis of tall buildings. Therefore, a balance must be achieved between
element simplicity and the ability of the model to predict both global and local responses with
adequate accuracy. It is not usually feasible or necessary to simulate all potential nonlinear
modes of behaviour in a system. In order to obtain reasonable agreement with the global
response of a structure, element models must be selected to simulate the significant modes of
deformation and deterioration expected during severe seismic loading.
This Chapter will focus on the approaches used to model the primary components of a
typical high rise RC core wall structure, as well as steel coupling beam elements and viscoelastic
coupling dampers. Validation of the response of each element type to cyclic loading has been
carried out using available test data. A nonlinear model of a twelve-storey coupled core wall
system was created for the purpose of global building response validation. A summary of key
modelling techniques used in this thesis and their limitations is presented in Section 3.4.
CHAPTER 3: Model Verification 40
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
3.2 Element Calibration
Before attempting to model the complex behaviour of a structure using any analysis
software, it is essential to acquire an understanding of the modelling assumptions included in the
program and to develop confidence in the software’s ability to adequately capture the behaviour
of the model’s constitutive elements. Prior to generating a nonlinear model, it is also important to
understand the inelastic behaviour of the construction materials used. In order to assess the
ability of the Perform-3D software to capture the nonlinear behaviour of RC shear wall elements,
diagonally-reinforced coupling beams, yielding steel coupling beams, and VCD elements, model
validation studies have been carried out, as described in the following sections.
3.2.1 Reinforced Concrete Shear Wall Elements
The behaviour of RC shear walls has been studied extensively, both analytically and
experimentally. However, because no test data on the behaviour of complex core wall systems
exists, we must rely on data from tests carried out on isolated walls with rectangular or T-shaped
cross sections for model validation (Salas, 2008). A suitable shear wall model must realistically
capture load versus deformation responses related to both flexure and shear. Results from a
testing program carried out at the University of California (Thomsen and Wallace, 2004) on the
response of slender RC shear walls subjected to cyclic lateral loading have been used to verify
the behaviour of shear wall elements in Perform-3D. The 102mm thick rectangular shear wall
test specimen RW2 is shown in Figure 3.1. This shear wall element was modelled using
Perform-3D and the response of the analytical model is compared with test data.
Slender shear walls are defined as having an aspect ratio (height/length) greater than 3
(Elwood et al., 2007). Lumped-plasticity beam-column elements and fibre beam-column
elements are two common nonlinear models used to simulate the behaviour of these elements.
Lumped-plasticity elements are comprised of linear elastic elements connected at critical points
by nonlinear springs or hinges. Fibre or distributed-plasticity beam-column elements have cross
sectional geometries comprised of individually defined uniaxial concrete and reinforcing steel
fibres. The flexural stiffness and strength of these wall elements are therefore dependent on the
CHAPTER 3: Model Verification 41
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
uniaxial stress-strain relations defined for the constitutive materials and on the sizes and
locations of the fibres.
Fibre element models offer significant advantages over lumped-plasticity beam-column
models. Unlike lumped-plasticity elements, fiber elements implicitly account for both neutral
axis migration during lateral loading and the effect of axial load variation on wall stiffness and
strength. Shortcomings associated with fiber elements include increased modelling and run time
when compared to lumped-plasticity elements, as well as the high sensitivity of computed
maximum fiber strain values to the selection of fiber sizes and assumed material stress-strain
relations (PEER/ATC, 2010).
Figure 3.1 Test Specimen RW2 (adapted from Orakcal, 2004)
In accordance with recommendations from Powell (2007), nonlinear fibre elements were
used to model the axial and flexural behaviour of the rectangular wall specimen RW2. Shear
deformations were included in the model by assuming linear elastic shear behaviour. Although a
small amount of nonlinear shear behaviour was observed during the test, shear deformations
CHAPTER 3: Model Verification 42
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
accounted for approximately 10 percent of the peak lateral displacement of the test specimen.
Shear failure was not accounted for in the model. A schematic cross-section of the fibre element
used to model the RW2 specimen is shown in Figure 3.2. The constitutive material relations for
the steel and concrete fibres were defined based on parameters calibrated by Orakcal and
Wallace (2006) using material test data, as listed in Table 3.1.
Hysteretic reinforcing steel stress-strain relations are typically defined using the well-
known model developed by Menegotto and Pinto (1973), including modifications by Filippou et
al. (1983) to include strain-hardening effects for bars embedded in concrete (Figure 3.3). This
model accounts for strength degradation during cyclic loading through the use of the curvature
parameter, R. Perform-3D software employs a simplified tri-linear reinforcing steel material
relation which can be modified to include strain-hardening and stiffness degradation on reverse
loading (Figure 3.4). Cyclic degradation of the reinforcing steel can be accounted for by
specifying “Energy Factors”. These factors alter the material backbone curve with each load
excursion, making it dependent on the loading history. Perform-3D allows the user to define the
relationship between the maximum strain in a given hysteresis loop and an associated energy
factor. Energy factors represent the ratio of the area of the degraded hysteresis loop over the area
of the un-degraded loop and are typically calibrated using test data. The energy factors used to
model the reinforcing steel in the RW2 test specimen are the same as those used by Ghodsi and
Ruiz (2010) to model the same specimen, as listed in Figure 3.5.
Figure 3.2 Fibre element representation of shear wall (adapted from PEER/ATC, 2010)
CHAPTER 3: Model Verification 43
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Table 3.1 Calibrated material modelling parameters for Test Specimen RW2
Boundary Web Material Parameter (Confined) (Unconfined) Concrete /′0 (MPa) 47.6 42.8
1′0 0.0033 0.0021 20 (GPa) 31.03 31.03 103 0.0037 0.0022 4 1.90 7.00
#2 Reinforcing /5 (MPa) 395 Steel 2 (GPa) 200
6 0.185 #3 Reinforcing /5 (MPa) 336
Steel 2 (GPa) 200 6 0.350
Figure 3.3 Reinforcing steel hysteretic model (adapted from Orakcal and Wallace, 2006)
Figure 3.4 Hysteretic models for #2 and #3 steel reinforcing bars
Str
ess
, σ
(M
Pa
)
Strain, ε
600
-600
-400
-200
0
200
400
-0.01 -0.005 0 0.005 0.01 0.015 0.02
CHAPTER 3: Model Verification 44
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 3.5 Cyclic degradation parameters for reinforcing steel
There are many common material models which define stress-strain relations for concrete
in compression. One model that can be used to capture confined concrete behaviour is the
envelope model proposed by Mander et al. (1988). Stress-strain curves defined using the Mander
model can be calibrated with measured values of peak stress, strain at peak stress, and elastic
modulus, and by adjusting the parameter r which defines the shape of the curve. Orakcal and
Wallace (2004) calibrated the envelope curve for compression of unconfined concrete in
specimen RW2 using results from monotonic cylinder tests. The constitutive model for confined
concrete described by Orakcal and Wallace (2006) defines a compressive envelope curve using
the empirical relations of the Mander model to calculate values of peak stress and strain at peak
stress, and using a post-peak slope derived from Saatcioglu and Razvi (1992). The same model
was used to define the curves for both confined and unconfined concrete in compression in this
study. It was assumed that the concrete in the wall end zones was confined by the rectangular
transverse reinforcing hoops and that the remaining concrete was effectively unconfined. The
tensile strength of the concrete was neglected for modelling simplicity. In Perform-3D, stress-
strain models for concrete are approximated using multi-linear relations, as shown in Figure 3.6.
Shear and flexural/axial behaviour of wall elements are typically uncoupled in
commercially available analysis software. Slender RC shear walls are capacity designed such
that shear does not control lateral strength or energy dissipation. Therefore, elastic shear
behaviour is typically assumed in these elements, even when nonlinear flexural behaviour is
anticipated (Wallace, 2007). Research, however, has shown that shear-flexure interaction can
CHAPTER 3: Model Verification 45
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
have a detrimental effect on the lateral strength and stiffness of even relatively slender, flexure-
dominated walls (Massone et al., 2009). Shear resistance deteriorates due to cracking at high
flexural ductility demands (Paulay and Priestley, 1992). Models incorporating shear-flexure
interaction exist (Massone, 2006) but are not available in commercial software such as Perform-
3D.
a)
b)
Figure 3.6 Constitutive models for unconfined and confined concrete in compression
Shear strength of RC elements has also been shown to be sensitive to axial load. It is
generally acknowledged that axial compression improves shear response, while axial tension
reduces shear strength and stiffness, although predictions of these effects vary between concrete
design codes. A study carried out at the University of Toronto (Xie et al. 2011) showed that the
modified compression field theory (MCFT), developed by Vecchio and Collins (1986),
effectively predicts the shear strength of RC elements subjected to axial stress. The CSA A23.3
(2004) shear provisions are based on the MCFT and provide reasonably accurate predictions of
the influence of axial stress on shear response, whereas the ACI 318 (2008) provisions
overestimate this influence. Shear demands on individual wall elements must be monitored
during nonlinear time history analyses and the effects of axial stress on shear strength should be
considered for the design of these elements.
The shear modulus of uncracked concrete is computed as follows:
70 = 202(1 + 9) (3-1)
0 0.005 0.01 0.0150
10
20
30
−40
50
Strain
Str
ess
(M
Pa
)
ManderModel
0 0.005 0.01 0.0150
10
20
30
−40
50
Strain
Str
ess
(M
Pa
)
ManderModel
CHAPTER 3: Model Verification 46
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
where ν is Poisson’s ratio and Ec is the elastic modulus of the concrete. Prior to significant
cracking, the Poisson’s ratio can be taken as 0.2, resulting in an effective shear modulus, Gc, of
0.4Ec. As discussed previously, cracking due to cyclic loading significantly reduces the effective
shear stiffness. Unfortunately, test data relating to shear stiffness at shear cracking and at shear
yielding is limited (PEER/ATC, 2010). To account for reductions in shear stiffness due to
cracking, an effective shear stiffness of 0.2Ec has been used in this component verification study.
For the design of core wall buildings, uncertainty related to the effective shear stiffness of wall
elements subjected to cyclic loading should be addressed through the application of upper and
lower bound values.
The RW2 wall specimen was modelled using six nonlinear shear wall elements, as shown
in Figure 3.2. Because inelastic strains tend to concentrate in a single element, an element length
equal to an assumed plastic hinge length of 0.5lw was used, as recommended by Wallace (2007).
Inclusion of modest strain hardening in the steel material model can also help to mitigate
problems associated with localization of inelastic deformations. The overall shear force versus
top displacement relation is relatively insensitive to mesh size and number of material fibres
(Orakcal et al. 2004). However, using a more refined mesh (more elements) has been shown to
improve predictions of peak fibre strains in the wall elements. According to Powell (2007), a
single element over the storey height is generally sufficient to capture the behaviour of a shear
wall above the hinge region.
Rectangular wall specimen RW2 was capacity-designed to allow for flexural hinging at
its base. A prototype structure representing a typical multi-storey office building in an area of
high seismicity was developed by Thomsen and Wallace (2004). The geometry and reinforcing
details of the six wall specimens used in the study, including RW2, were then selected to
represent the shear walls in the prototype building at approximately one quarter scale. An axial
load of approximately 0.07Agfc’ was applied to the specimen and held constant throughout the
duration of the test while cyclic lateral displacements were applied at the top of the wall using a
hydraulic actuator. The drift-controlled test protocol for Specimen RW2 is shown in Figure 3.7.
A displacement-controlled nonlinear analysis was carried out in Perform-3D in order to compare
the model response with the results of the drift-controlled cyclic test.
CHAPTER 3: Model Verification 47
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 3.7 Applied displacement history
The measured lateral force-displacement response of Specimen RW2 is shown in Figure
3.8. The lateral force required to achieve the nominal moment at the base of the wall, calculated
based on nominal material strengths, is indicated in this figure. The force-displacement response
predicted by the analytical model is shown in Figure 3.8. By comparing the hysteretic response
of the test specimen with that of the model, it can be seen that the global behaviour of the test
specimen is reasonably well represented by the model.
The most notable discrepancy between the analytical response and the experimental
response is the exaggerated pinching effect exhibited by the analytical model near zero
displacement. This inconsistency is related to the software’s inability to realistically capture
crack-closing upon load-reversal. The constitutive material model for concrete in Perform-3D
includes the simplifying assumption of smooth crack-closure, which is unrealistic and results in a
pronounced pinching behaviour. However, the effect of this discrepancy on the overall
performance of a high-rise core wall building model is considered to be relatively minor
(PEER/ATC, 2010). It was also noted that the model did not capture the strength degradation
which occurred in the positive loading direction during the final cycle of the test. This
degradation was a result of reinforcing steel buckling in the boundary element of the specimen,
which was not accounted for in the analytical model. In Perform-3D, strain limits can be applied
to the reinforcing steel constitutive model in order to verify that reinforcement buckling and
fracture are not expected to occur (PEER/ATC, 2010). Overall, the analytical model appears to
have adequately captured the flexural response of the test specimen.
CHAPTER 3: Model Verification 48
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
a)
b)
Figure 3.8 a) Measured lateral load versus top displacement (adapted from Thomsen and Wallace, 2004) b) Model lateral load versus displacement
3.2.2 Diagonally-Reinforced Concrete Coupling Beam Elements
The first experimental study on the load-deformation behaviour of diagonally-reinforced
coupling beams with aspect ratios typical of tall building construction was carried out at the
University of California, Los Angeles (Naish et al., 2009). The focus of this study was to
investigate an alternative transverse reinforcing detail for diagonally-reinforced coupling beams.
This study was also the first to investigate the effects of reinforced and post-tensioned slabs on
the behaviour of diagonally-reinforced coupling beams. Cyclic load testing was carried out on
seven half-scale diagonally-reinforced coupling beam specimens, three of which included
reinforced or post-tensioned slabs. The prototype beams were designed based on two common
tall building configurations: residential and office construction. In the present validation study,
modelling guidelines presented by Naish et al. (2009) were used to capture the load-deformation
behaviour of test specimen CB24F (Figure 3.9).
Test specimen CB24F had a span-to-depth ratio of 2.4, which is typical for residential
high-rise construction. It was reinforced with two bundles of six-#7 diagonal bars and confined
using #3 transverse hoops at 12 inch spacing. The steel and concrete material properties of the
test specimen were determined using standard material testing procedures and are listed in Table
−4.0 −2.0 0 2.0 4.0−40
−20 0
20
40
Top Displacement (in)
Late
ral
Loa
d (
kip
)
−4.0 −2.0 0 2.0 4.0−40
−20 0
20
40
Top Displacement (in)
Late
ral
Loa
d (
kip
)
CHAPTER 3: Model Verification 49
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
3.2. The test beam was subjected to a force-controlled loading protocol, followed by a
displacement-controlled loading protocol. Both protocols are shown in Figure 3.10.
Figure 3.9 Test Specimen CB24F (after Naish et al., 2009)
The displacement-controlled protocol was applied in increments of chord-rotation, which
is defined as relative lateral displacement over the clear span of the beam, ∆, divided by the
length of the clear span, L (Figure 3.11). It is of interest to note that the maximum chord-rotation
of 3 percent is specified for the collapse prevention limit state in ASCE 41-06 (ASCE, 2007).
The force-displacement response of Specimen CB24F is shown in Figure 3.12.
Table 3.2 CB24F material properties (Naish et al., 2009)
Concrete fc’ 47.2 MPa Reinforcing Steel fy 483 MPa Reinforcing Steel fu 621 MPa
a)
b)
Figure 3.10 Loading protocols: a) Load-controlled; b) Displacement-controlled (adapted from Naish et al., 2009)
0 3 6 9 12−500
−250 0
250
500
Load Step #
Late
ral
Loa
d (
kN
)
0 5 10 15 20 25−12
−8
−4
0
4
8
12
Load Step #
Ro
ta"
on
(%
)
CHAPTER 3: Model Verification 50
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 3.11 Coupling beam chord rotation
Figure 3.12 Test Specimen CB24F force-deformation response (adapted Naish et al., 2009)
A common macroscopic or lumped-plasticity model for diagonally-reinforced concrete
coupling beam elements incorporates a nonlinear shear displacement hinge to capture the
inelastic behaviour. This model typically consists of an elastic beam cross-section with rotational
hinges at each end to account for reinforcing bar slip and extension (strain) deformations, and a
shear hinge at midspan, as shown schematically in Figure 3.13. The properties of the shear hinge
are defined using backbone strength relations derived from test results. The properties of the
slip/extension rotational springs can be defined using a model developed by Alsiwat and
Saatcioglu (1992). Alternatively, the model can be simplified by eliminating the rotational
springs and accounting for slip/extension deformations through a reduced effective elastic
stiffness. Another common macroscopic model for diagonally-reinforced coupling beams
employs rigid-plastic rotational springs at each end of the beam to account for nonlinear
deformations, rather than a single shear displacement hinge at midspan. Both the shear hinge and
the moment hinge models have been shown to adequately capture the overall load-displacement
behaviour of diagonally-reinforced coupling beam elements (Naish et al., 2009).
θ
−12 −6 0 6 12−200
−100
0
100
200
Beam Chord Rota!on (rad)
Late
ral
Loa
d (
kip
)
CHAPTER 3: Model Verification 51
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 3.13 Schematic of typical models for diagonally-reinforced coupling beams
Nonlinear modelling parameters for diagonally-reinforced coupling beams were
introduced in the FEMA 356 guidelines for Seismic Rehabilitation of Existing Buildings
(FEMA, 2000) and the same parameters are recommended in the ASCE41-06 guidelines (ASCE,
2007). Naish et al. (2009) have suggested improved modelling parameters which have been
calibrated using test data from seven half-scale beam specimens. The linearized backbone shear
strength versus rotation curves recommended by Naish et al. (2009) for modelling coupling
beams with integral post-tensioned slabs, reinforced slabs, and without slabs are shown in Figure
3.14. These modelling parameters are based on test data from beams with aspect ratios of 2.4 and
3.33, and can be extended to model beams with clear span to depth ratios of 2.0 to 4.0 (Naish et
al., 2009). The beam shear strength has been normalized with respect to the nominal shear
capacity, as determined from ACI 318-08 (ACI, 2008). For comparison, the backbone curve
from ASCE-06 is also shown in the Figure. Test results from the half-scale beam specimens are
shown using dashed lines.
Results from the seven half-scale tests described by Naish et al. (2009) were consistent,
indicating a yield chord rotation of approximately 1 percent, initiation of strength degradation at
approximately 8 percent rotation, and a residual ultimate shear strength reached at approximately
12 percent rotation. These values were modified to account for the effects of scale by reducing
CHAPTER 3: Model Verification 52
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
the yield, strength degradation, and residual strength rotations to 0.70 percent, 6.0 percent, and
9.0 percent respectively, in order to generate the backbone curves for full-scale beams. The
effective bending stiffness at yield is higher in larger beams due to a reduced relative
contribution of slip deformations (Naish et al. 2009). The test results indicate a lower effective
yield stiffness and substantially higher deformation capacity prior to strength degradation when
compared to the ACSE 41-06 backbone relation. The inclusion of a reinforced or post-tensioned
slab was found to increase the shear strength significantly while having a negligible effect on the
ductility.
Figure 3.14 Backbone load-deformation relations for full-scale diagonally-reinforced concrete coupling beams (after Naish et al., 2009)
Modelling parameters recommended by Naish et al. (2009) were used to simulate the
cyclic behaviour of test specimen CB24F using Perform-3D software. For comparison, two shear
hinge models were generated: one accounting for the effects of slip/extension deformations using
elastic rotational hinges at each end of the beam element, and the other using a reduced effective
yield stiffness to account for slip/extension. A stiffness of 402(103) kip-in was assigned to the
: − �slip/extension hinges, based on the model developed by Alsiwat and Saatcioglu (1992).
The more simplified model was assigned a reduced effective yield stiffness of 0.15EcIg, where Ec
is the Young’s modulus of the concrete and Ig is the gross second moment of inertia of the
beam’s cross-section. A strength loss interaction factor of 0.25 was used to account for the effect
of strength loss in one loading direction on the loss of strength in the reverse direction. Cyclic
degradation was accounted for using parameters selected by Naish et al. (2009) to fit test data, as
0 2 4 6 8 10 12 140
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Rota on (%)
V/V
n
No Slab
RC Slab
PT Slab
ASCE 41
CHAPTER 3: Model Verification 53
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
listed in Figure 3.15. These parameters have been calibrated using results from a study focused
on the effects of the configuration of transverse reinforcement. Further research is required to
validate the use of these values for beams with different diagonal reinforcement ratios.
Figure 3.15 Cyclic degradation parameters for coupling beam elements
The load-deformation response of each of the models is shown in Figure 3.16. Both
models accurately simulate the overall load-deformation behaviour of the test specimen. The
reduced flexural stiffness of 0.15EcIg captured the effects of slip/extension deformation without
the use of slip/extension hinges. For diagonally-reinforced coupling beams with aspect ratios
typical of high-rise residential and office buildings, flexural and slip/extension deformations
account for approximately 80-85 percent of total deformations (Naish et al., 2009). As
recommended by Naish et al. (2009), a shear area of zero was assigned to the elastic beam cross
section in both models, which is equivalent to assigning infinite shear stiffness in Perform-3D.
a)
b)
Figure 3.16 Force-deformation response of analytical models a) Including slip/extension hinges, b) Reduced stiffness to account for slip/extension
−12 −6 0 6 12−200
−100
0
100
200
Beam Chord Rota!on (rad)
Late
ral
Loa
d (
kip
)
−12 −6 0 6 12−200
−100
0
100
200
Beam Chord Rota!on (rad)
Late
ral
Loa
d (
kip
)
CHAPTER 3: Model Verification 54
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
3.2.3 Steel Coupling Beam Elements
Because steel coupling beams behave similarly to yielding steel links in EBFs, the same
approach can be used to model the behaviour of both element types. Steel link elements are
expected to yield in shear if L < 1.6Mp/Vp, where L is the clear span or the length of the link, Mp
is the nominal plastic moment capacity of the section, and Vp is the nominal plastic shear
capacity of the section (Kasai and Popov, 1986). The cyclic shear force versus deformation
behaviour of both yielding steel links in EBFs and yielding steel coupling beams in HCWs can
be approximated using the Ramberg-Osgood hysteretic model.
Perform-3D modelling recommendations specify the use of a lumped-plasticity model,
similar to that used to model diagonally-reinforced concrete coupling beams, to model the
behaviour of yielding steel link elements (CSI, 2006). A compound element consisting of two
elastic steel beam components with a uniaxial shear hinge at midspan is recommended. Elastic
axial, flexural, and shear deformations are accounted for in the elastic beam segments, and
nonlinear shear deformations occur in the shear hinge. Testing has shown that there is effectively
no moment-shear interaction in steel link elements with stiffened webs (Okazaki et al., 2005).
ASCE 41-06 specifies a generalized force-deformation relation for yielding shear links in
eccentrically braced frames. The ASCE 41-06 backbone curve, normalized by the nominal
plastic shear capacity, Vp, is shown in Figure 3.17. The elastic stiffness of the link beam, ke, is
estimated using Equation (3-2):
�� = <=<><=?<> (3-2)
where
�( =7@AB (3-3)
�C =122DCB� (3-4)
and ks and kb are the shear and flexural stiffness of the beam, respectively, G is the shear
modulus of steel, Aw is the shear area of the section, L is the length of the link element, E is the
CHAPTER 3: Model Verification 55
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Young’s modulus of steel, and Ib is the second moment of inertia of the section. ASCE 41-06
specifies a strain-hardening slope of 6 percent where panel zone yielding occurs, unless a greater
slope is justified by test data. In the absence of test data, an estimated post-yield stiffness of 6
percent may also be reasonable to define the backbone curve for a shear link or steel coupling
beam element. A bounded analysis is recommended for performance-based design of hybrid
coupled wall structures to account for uncertainty related to the post-yield stiffness of steel
coupling beams.
The nominal plastic shear resistance of the link is calculated in accordance with CSA-S16
(2009):
EF = 0.55I�J5 (3-5)
where w is the web thickness, � is the overall depth of the section, and J5 is the yield stress of the
link web. The expected yield strength of the shear hinge is then defined as K5EF, where K5
accounts for material overstrength. Testing has shown that the measured web yield strength is
greater by a factor of approximately 1.2 than the nominal yield strength (Mansour and
Christopoulos, 2011), whereas CSA-S16 (2009) specifies a value of 1.1 for K5 . The ultimate
shear strength, EL, accounting for strain-hardening of the link yielding in shear, is calculated as
1.3K5EF (CSA, 2009).
Figure 3.17 ASCE 41-06 EBF link beam modelling parameters
The limited experimental data which exists for HCW systems indicate that steel coupling
beams are not effectively fixed at the beam-wall interface when subjected to cyclic loading
CHAPTER 3: Model Verification 56
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
(Shahrooz et al., 1993, Harries et al., 1997). The resulting additional flexibility of the beams
must be taken into account when modelling HCW systems. The effective fixed point has been
shown to be approximately one third of the embedment length away from the face of the wall
(Harries et al., 2000). Therefore, one way to account for flexibility in the embedment region is to
use an effective beam length of the clear span plus two thirds of the embedment length.
However, this is not practical when fibre elements are used to model the RC shear walls because
it requires reducing the length of the wall elements in order to accommodate the increased length
of the beams. Alternatively, Harries et al. (1998) recommend using a reduced effective flexural
stiffness for the steel coupling beam elements. An effective stiffness of 0.6kEI has been found to
agree well with experimental data from beams with different embedment details (Harries et al.,
2000). The k factor is used to account for the reduction in flexural stiffness due to shear
deformations:
� = M1 + 122DNB�7@AOP�
(3-6)
where 2 is the Young’s modulus of steel, D is the moment of inertia of the beam, B is the clear
span of the beam, 7 is the shear modulus of steel, @A is the shear area of the beam, and Nis the
shape factor. In models where shear deformations are accounted for explicitly, �= 1.
An experimental and analytical study to investigate the cyclic behaviour of steel coupling
beams was carried out at McGill University (Harries et al., 1993). The steel link beams in the
two test specimens used were designed in accordance with the seismic design requirements for
eccentrically braced frames in CSA-S16 (1989). Both test specimens were designed and detailed
to yield in shear, and to avoid local buckling in both the web and the flanges, as well as lateral
buckling of the beam. The wall reinforcing details are shown in Figure 3.20. During the test, one
wall was moved vertically relative to the other which was fixed in place (Figure 3.18). The walls
remained parallel throughout the duration of the cyclic loading protocol. Displacements were
load-controlled until the link element reached general yielding, and displacement-controlled
loading was applied in multiples of the displacement at general yielding, �5, thereafter. Three
load cycles were completed at each load level up to a displacement ductility of approximately 8.
CHAPTER 3: Model Verification 57
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
For the purpose of model validation, an analytical model of Specimen 2, shown in Figure
3.19, has been generated in Perform-3D. The measured material properties of Specimen 2 are
listed in Table 3.3. The embedded portion of the web had an increased thickness, in order to
restrict inelastic shear behaviour to the exposed portion of the link element. The test specimen
exhibited excellent ductility and hysteretic behaviour, with full shear yielding occurring in the
link beam and no significant inelastic behaviour in the embedded region. The complete hysteretic
response of Specimen 2 is shown in Figure 3.21(a).
Specimen 2 was modelled in Perform-3D based on the modelling recommendations
previously described. The beam was modelled with an increased effective length, Leff, in order to
account for the spalling of cover concrete:
B��� = B + 2% (3-7)
where B is the clear span and % is the concrete cover. A reduced flexural stiffness of 0.62Dwas
used to account for the flexibility at the wall-beam interface. The backbone curve was computed
based on an expected yield strength, E5,�RF, of K5EF, where K5 = 1.2, an expected ultimate
strength, EL,�RF, of 1.3E5,�RF, and a post-yield stiffness of 6 percent of the initial effective
stiffness, S�.
Table 3.3 Measured steel material properties for specimen 2 (Harries et al., 1993)
Fy (MPa) Fu (MPa) Web 309 427
Embedded Web 276 442 Flange 295 499
Figure 3.18 Specimen 2 test schematic (after Harries et al., 1993)
�
F
CHAPTER 3: Model Verification 58
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 3.19 Specimen 2 link beam details (after Harries et al., 1993)
Figure 3.20 Specimen 2 wall reinforcing details (after Harries et al., 1993)
The hysteretic response of the model is shown in Figure 3.21(b). As shown in the Figure,
the model response is in reasonably good agreement with the test results. The assumed effective
1200 mm600 mm 600 mm
Embeded por!onS!ffener plates
AB B
Sec!on A Sec!on B
19.2 mm
135 mm
4.7 mm62x10 mm
S!ffener
8.1 mm
19.2 mm
135 mm
62x10 mm
S!ffener
600 mm1500 mm
18
00
mm
35
0 m
m7
25
mm
8-No. 25 bars
4-No. 10 bars
30
0 m
m
CHAPTER 3: Model Verification 59
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
flexural stiffness of 0.62D, recommended by Harries et al. (2000), resulted in a slight
overestimation of the elastic stiffness of the specimen. The post-yield stiffness value of 6 percent
of the elastic stiffness also appears to be an overestimate. However, this exaggerated stiffness,
combined with the overestimated yield strength, has the effect of accounting for isotropic strain-
hardening indirectly, since the model does not capture this phenomenon explicitly. The
Bauschinger effect is not accounted for in the model. The softening portion of the hysteretic
response was not included in the model because the test was terminated before the specimen
suffered any loss of strength. In the absence of test data, the shear displacement at the onset of
strength loss, the residual strength, and the ultimate shear displacement can be taken from ASCE
41-06 (see Figure 3.17). Further testing is required to validate the broad application of these
parameters for modelling steel coupling beams of different dimensions.
a)
b)
Figure 3.21 Specimen 2 a) Test hysteresis (adapted from Harries et al. 1993) b) Model hysteresis (theoretical backbone curve shown in red)
3.2.4 Viscoelastic Coupling Damper Elements
The shear force-displacement hysteretic behaviour of viscoelastic material subjected to
cyclic loading can be described by a simple Kelvin-Voigt model (KVM). This model consists of
a spring and a dashpot in parallel, as shown in Figure 3.22. The shear force versus displacement
relationship of VE material can be described as follows:
J() = ��T�() +%�T�()U (3-8)
−160 −120 −80 −40 0 40 80 120 160−450
−350
−250
−150
−50
50
150
250
350
450
Displacement (mm)
Be
am
Sh
ea
r (k
N)
−160 −120 −80 −40 0 40 80 120 160−450
−350
−250
−150
−50
50
150
250
350
450
Displacement (mm)
Be
am
Sh
ea
r (k
N)
CHAPTER 3: Model Verification 60
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
where F(t) is the applied force at time t, �() is the shear displacement at time t, �U () is the rate
of shear displacement, ��T is the elastic stiffness coefficient, and %�T is the viscous damping
coefficient. For a VE material with shear area A and thickness h, the elastic stiffness and viscous
damping coefficients are determined as follows:
��T =7T@ℎ (3-9)
%�T =7�@ℎ (3-10)
where GE is the shear storage modulus, GC is the shear loss modulus (Soong and Dargush, 1997).
Both the shear storage and shear loss moduli are functions of temperature, strain amplitude, and
loading frequency. In order to account for variations in these parameters, upper and lower bound
properties may be selected to establish a design envelope for the VE material.
Figure 3.22 Kelvin-Voigt Model
A Maxwell element consists of a spring in series with a dashpot, as shown in Figure
3.23a). A more general alternative to the KVM, the Generalized Maxwell Model (GMM), is
shown in Figure 3.23c). Proposed by Fan (1998), the GMM is comprised of a Kelvin-Voigt
element placed in parallel with a number, !, of Maxwell elements to capture the effects of
variations in temperature, frequency, and strain amplitude on the properties of VE material. This
model requires the calibration of 2(! + 1) parameters using results from VE material
characterization tests carried out at various frequencies and temperatures. The strain amplitude
dependence of the material properties can be accounted for by considering the effect of
temperature rise due to self-heating of the VE material during cyclic loading at large strain
amplitudes (Fan, 1998).
FVE
uVE
kVE
uMax
FMax
VEM Hysteresis
kVE
cVE
FVE
uVE
Kelvin-Voigt
Model Schema!c
b)a) c)
FVE
VEM Deformed Shape
uVE
FVE
CHAPTER 3: Model Verification 61
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 3.23 Generalized Maxwell Model for Viscoelastic Material
The modelling parameters for the GMM are shown in Figure 3.24. For a given VE
material temperature and loading frequency, the shear storage and shear loss moduli can be
calculated as follows:
7T = 7V +WXY (Z[\]^)�1 + (Z[\]^)�_7^`�
^a� (3-11)
7�\ = (Z[\�V)7V +WXY (Z[\]^)1 + (Z[\]^)�_7^`�
^a� (3-12)
where ω is the angular frequency of excitation, 7Vand 7^ are calibrated spring stiffness
coefficients, and �V and ]^ are modelling parameters calibrated at the reference temperature,
b3��. A shifting function, proposed by Kasai et al. (2003) is used to adjust the modelling
parameters to account for changes in the temperature of the VE material:
Z[ = Y bb3��_
F (3-13)
where b is the instantaneous VE material temperature and c is a shifting parameter calibrated
using test data.
As discussed in Chapter 1, when a viscoelastic material is deformed in shear, it dissipates
mechanical energy by transforming it into heat. For short duration loading, the associated
k k0
c0
c
k1
k2
kn
c1
c2
cn
Kelvin-Voigt
Element
Maxwell
Element
Generalized Maxwell
Element
k
c
a) b) c)
CHAPTER 3: Model Verification 62
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
incremental increase in the temperature of the VE material, db, can be estimated using the
following equation developed by Fan (1998):
db = ef�<gV�V7V + ∑ e f�^]^7^i�a� ij' d (3-14)
where f<gVand f^are the stresses in the dashpot of the Kelvin-Voigt element and in the dashpot
of Maxwell element $, respectively, j is the mass density of the VE material, ' is the specific
heat of the VE material, and d is the time increment. This expression assumes uniform
temperature change throughout the VE material and neglects any transfer of heat from the VE
material to the adjacent steel plates. The effects of heat generated during long term loading
should also be considered for wind applications (Montgomery, 2011).
Figure 3.24 Generalized Maxwell Model Parameters
In commercial structural analysis software programs, such as Perform-3D, the properties
of the spring and dashpot components of a KVM or a GMM cannot be adjusted at each time step
to account for the effects of self-heating. A bounded analysis is therefore required in order to
capture the effect of temperature variation in VE material. Recommendations for upper and
lower bound temperatures for different loading scenarios are presented in Chapter 2.3.
Kasai et al. (2006) developed a model to capture the force-displacement behaviour of a
VE damper incorporated into an axial brace member. For harmonic loading, the stiffness of the
β0α
TG
0G
0
G1
G2
Gn
Ψ1α
TG
1Ψ
2α
TG
2Ψ
nα
TG
n
FVE
uVE
CHAPTER 3: Model Verification 63
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
brace element can be accounted for by a spring placed in series with a Kelvin-Voigt element
representing the viscoelastic material, as shown in Figure 3.25(a). Alternatively, Kasai et al.
(2006) suggest that an equivalent Kelvin-Voigt model can be used to capture the total axial
force-displacement behaviour of the brace element, as shown in Figure 3.25(b).
The equivalent elastic stiffness coefficient of the axial damper element is computed as:
�� = �Ck�T��T�C + k�T��T (3-15)
where the factork�Tis a function of the elastic stiffness of the VE material, ��T, the elastic
stiffness of the brace element, �C, and the loss factor of the VE material, l:
k�T = 1 + l�T�e1 + �C��Ti
(3-16)
The equivalent loss factor, l�, is calculated as:
l� = l�T1 + (1 + l�T� ) ��T�C
(3-17)
and the equivalent damping coefficient of the axial damper is expressed as:
%� = l���\ (3-18)
Similarly, the shear force-displacement behaviour of a VCD element subjected to
harmonic loading can be captured using an equivalent Kelvin-Voigt model. In this model, the
equivalent KVM is oriented in the direction of shear deformation at the midspan of a rigid beam
element, as shown in Figure 3.26 (Montgomery, 2011). The total effective stiffness of the built-
up steel assemblies at both ends of the damper element can be accounted for in the equivalent
Kelvin-Voigt model by replacing axial brace stiffness, �C, with the effective steel assembly
stiffness, �m, in Equations (3-11), (3-12), and (3-13). The effective stiffness, �m, can be
determined as follows:
CHAPTER 3: Model Verification 64
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
�m = 1n 1�mo +
1�mpq
(3-19)
where �mo and �mp are the stiffnesses of the assemblies to the left and right of the VE material,
respectively.
Figure 3.25 Kelvin-Voigt models for VE dampers in axial brace configuration
Figure 3.26 Schematic of VCD Model
In Perform-3D, a viscous bar element is equivalent to a Maxwell model, consisting of a
spring and a dashpot in series. In order to create a Kelvin-Voigt model in Perform-3D, a viscous
bar element with a very large (≈infinite) spring stiffness, �C^�, can be placed in parallel with an
elastic bar element, as shown in Figure 3.27. In the same way, an effective Kelvin-Voigt model
can be defined to simulate the force-displacement behaviour of the VCD damper in Perform-3D.
A rigid beam element with an equivalent Kelvin-Voigt element oriented in the shear direction at
kVE
cVE
kb
FD
uD
kD
cD
FD
uD
a) b)
Spring Kelvin-Voigt Model Equivalent Kelvin-Voigt Model
kVCD
cVCD
Equivalent
Kelvin-Voigt
Model
Rigid Beam
ElementBuilt-up Steel
Assembly
θwall
VE Layers
uVCD
uVCD
θwall
Deformed shape of VCD Deformed shape of VCD
model in Perform-3D
a) b)
CHAPTER 3: Model Verification 65
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
mid-span can be used to couple two shear walls, as shown in Figure 3.26. Because Perform-3D
does not allow for coincident nodes, the Kelvin-Voigt element must be assigned a finite length.
This can be achieved by adding rigid beam elements to simulate rigid offsets.
For highly variable loading frequencies and strain amplitudes in the VE material, such as
in the case of seismic time-history analyses, the same approach can be used to implement the
Generalized Maxwell model in structural analysis programs. In Perform-3D, elastic and viscous
bar elements can be used to define the components of the GMM. In this model, however, the
elastic behaviour of the built-up steel assembly elements is defined separately from the
viscoelastic material behaviour. The rigid beam elements are replaced using elastic beam
elements having the same effective stiffness as the assembly, �m. When a fuse mechanism is
included in the design of the VCD, a nonlinear hinge element can be added in series with the
damper element. Figure 3.28 shows a schematic of a VCD model including a rigid-plastic fuse
component (a KVM for the VE material is shown for clarity).
Figure 3.27 Kelvin-Voigt material model for viscoelastic material in Perform-3D
A series of full-scale tests were carried out on 6-VCD specimens in a coupled wall
configuration at École Polytechnique de Montréal (Montgomery, 2011). Two sets of three
identical dampers were provided in kind by Nippon Steel in Japan. Test specimen FCD B was
modelled in Perform-3D in order to investigate the robustness of the GMM4 under different
loading conditions.
kVE
cVE
FVE
uVE
kbig
Viscous Bar
Element
Elas!c Bar
Element
CHAPTER 3: Model Verification 66
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 3.28 VCD model with fuse mechanism in Perform-3D
Test specimen FCD B, shown in Figure 3.29, was designed for a 50-storey case study
building in downtown Vancouver. A fuse mechanism was included in the design of FCD B to
limit the force transferred by the damper during extreme seismic loading. As shown in the
Figure, reduced beam sections (RBS) were provided in the built-up steel assemblies at either end
of the damper. In the RBS regions, the widths of the top and bottom flanges are reduced in order
to localize and control flexural yielding, as is often done in special moment resisting steel frames
(SMRF).
Figure 3.29 VCD Specimen FCD B (adapted from Montgomery, 2011)
Detailed drawings of specimen FCD B are provided in Figure 3.30. The VCD was
designed to replace a 750 mm deep, 800 mm wide, and 2,100 mm long RC coupling beam. The
design included 15 layers of VEM ISD:111H with dimensions 380(W)x520(L)x6.5(t) mm,
kVE
cVE
VE Material
Model
FVCD u
VCD
Elas!c Beam
Element
(Typ.)
Rigid-plas!c
Shear Hinge
Rigid Element
(Typ.)
Viscoelas�c
Material Layers
Steel
Plates
Possible
Wall Anchorage
Detail
Reduced Beam Sec�on
Fuse
CHAPTER 3: Model Verification 67
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
between 14-9 mm thick layers of inner steel plates and two 12 mm thick outer plates. Nine high-
strength post-tensioned bolts were used to connect the VE material layers and steel plate layers
to the built-up steel I-sections. The I-sections were fixed to 50 mm thick end plates using full
penetration welds around their perimeters. The dampers were then cast between two 450 mm
thick reinforced concrete walls and were anchored using weldable half couplers and 35M
reinforcing steel bars.
Figure 3.30 VCD Specimen FCD B (adapted from Montgomery, 2011)
The full-scale test setup is shown in Figure 3.31. This setup was designed to represent the
loading conditions of a VCD in a coupled wall configuration. The RC wall elements were
supported on pins to allow racking, as shown in the Figure. The two walls were coupled using
the VCD and connected using pins to two stiff channels at the height of the actuator to simulate
ELEVATION
PLAN
CHAPTER 3: Model Verification 68
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
the axial stiffness of a floor slab. In this configuration, forces applied by the actuator caused the
walls to rotate about the support pins and the VCD to engage in shear.
Figure 3.31 Full-Scale Test Setup (adapted with permission from Montgomery, 2011)
Figure 3.32 Full-Scale Test Setup (adapted from Montgomery, 2011)
FCD
Lwall
= 3900 Lwall
= 3900LVCD
= 2100
a) Case Study VCD Applica�on
LCL
= 6000
hst
ore
y =
30
00
Wall
CentrelineVCD
CentrelineConcrete
Drop Panel
Cast In-Place
Wall
Cast In-Place
Slab
c) Test Setup c) Exaggerated Deformed Shape
Actuator
Applica�on
Top
Middle Wall
Bo!om
Wall
Axial
Element
FCD B
Base PinDywidag
ThreadbarsPin
Centreline
VCD
Centreline
ha
ct =
40
87
Axial
PinTop Wall
LCL
= 6000
Lwall
= 2200 LVCD
= 2100 Lwall
= 2200
b) Exaggerated Deformed Shape
Axial Wall
Deforma�on
Diaphragm ForceNOTE: Concrete Drop Panel
Not Shown for Clarity
Wall
Rota�on
Pdiaphragm
Pdiaphragm
VEM Shear
Deforma�on
VEM Shear
Deforma�on
θwall
θwall
Pin
Rota�on
Actuator
Displacement
Actuator
Force
Pactuator
θwall
θwall
CHAPTER 3: Model Verification 69
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
The material properties provided by the manufacturer for ISD:111H are listed in Table
3.4. Linear interpolation between these properties can be used to approximate the components of
the KVM for a given temperature, strain amplitude, and frequency of loading. Montgomery
(2011) also carried out a nonlinear least-squared regression, as recommended by Fan (1998), to
calibrate modelling parameters for the GMM. Based on recommendations by Fan (1998), four
Maxwell elements were used. The modelling parameters calibrated using material test data
provided by the VE material manufacturer are listed in Table 3.5. The data used to calibrate these
parameters correspond to a range of VE material temperatures from 10 C to 40 C, and a range
of frequencies between 0.1 Hz and 2.0 Hz. The VE material strain amplitude was 10 percent in
each of the tests. A reference temperature, b3��, of 24 °C was used for calibration. The shifting
parameter, c, was assigned a value of -3.10 for the ISD:111H material.
Table 3.4 ISD:111H material properties for KVM (Montgomery, 2011)
*r = ±50% *r = ±100% *r = ±200% s (Hz) s (Hz) s (Hz) ) (°C) 0.1 0.3 1 2 0.1 0.3 1 2 0.1 0.3 1 2 tu 20 0.126 0.194 0.327 0.443 0.123 0.191 0.327 0.446 0.116 0.183 0.316 0.411
(MPa) 30 0.083 0.115 0.176 0.229 0.078 0.109 0.172 0.227 0.069 0.101 0.165 0.224 v 20 0.81 0.98 1.17 1.24 0.82 0.96 1.12 1.16 0.81 0.92 1.03 1.06 30 0.60 0.75 0.93 1.02 0.61 0.76 0.92 0.98 0.63 0.77 0.91 0.94
Table 3.5 ISD:111H material properties for GMM (Montgomery, 2011)
tr (MPa) 0.0623 wr (s) 9.0181e-4 tx (MPa) 0.2605 yx (s) 0.0996 tz (MPa) 0.5493 yz (s) 0.0172 t{ (MPa) 8.2335 y{ (s) 0.0011 t| (MPa) 0.0870 y| (s) 1.1280
A series of harmonic displacement-controlled tests were carried out on the test specimens
to validate the performance of the coupled wall system. A subset of these tests, including
working strain harmonic characterization tests (WSHC), higher strain harmonic characterization
tests (HSHC), and ultimate strain harmonic characterization tests (USHC) were replicated in
Perform-3D. The characteristics of the harmonic tests are listed in Table 3.6.
A Generalized Maxwell model with ! = 4 Maxwell elements, defined using the
properties listed in Table 3.5, was used to capture the response of the VE material in Perform-
3D. Two models were created for each of the harmonic tests: one with GMM properties defined
CHAPTER 3: Model Verification 70
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
using the initial VE material temperature, b �^}^~�, and one with properties defined using the final
VE material temperature, b�^�~�. The displacement in the steel assembly, �m, was computed as
follows:
�m() = ����() − ��T�() (3-20)
where ���� is the overall shear displacement applied across the length of the VCD by the
actuator and ��T� is the measured VE material displacement. The effective elastic stiffness of
the built-up assembly, �m, was determined from the test results, as shown in Figure 3.33 for
FCD B2 WSHC2. The effective assembly stiffness varied between tests. This may have been the
result of cracking and loss of stiffness in the RC walls during cyclic loading. Montgomery (2011)
observed a slight reduction in effective stiffness during large-amplitude tests. The effective
elastic stiffness computed for each test is given in Table 3.6.
Table 3.6 VCD model validation matrix
Specimen Test # Cycles f0 (Hz) γ0 (%) T initial ( C) Tfinal ( C) kA (kN/mm)
FCD B2 WSHC1 500 0.1 50 21 24.5 100
WSHC2 500 0.3 50 23.5 29 90
FCD B3 HSHC1 100 0.1 100 24 28 100
HSHC3 100 0.3 100 26.5 31 110
USHC1 10 0.1 200 24 26 90
USHC3 10 0.3 200 23 26 90
Figure 3.33 FCD B2 WSHC2 built-up steel assembly force-displacement response
kA
≈ 90 kN/mm
CHAPTER 3: Model Verification 71
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
The shear force-displacement results for the harmonic tests having target VE material
strains of 50 percent, 100 percent, and 200 percent are shown in Figure 3.34, Figure 3.35, and
Figure 3.36. The first load cycle from the model defined using the initial temperature, as well as
the last load cycle from the model defined using the final temperature are also shown in the
figures. Table 3.7 provides a summary of the modelling results for these tests. In this table, the
peak force and energy dissipated in the VE material during the first and last cycles of the
harmonic tests are compared with the results computed from the models. The energy dissipated
in the VE material, 2�T, is computed as the area under the force-displacement relationship
(Christopoulos and Filiatrault, 2006):
2�T =� J()�U ()�}V
(3-21)
The results indicate good agreement between the GMM and the tests at different loading
frequencies, strain amplitudes, and temperatures. Discrepancies may be attributed to inaccuracy
of temperature measurements as well as non-uniform temperature distribution in the VE
material.
FCD B2 WSHC2 a) Experimental b) Model First Cycle (T = 21 C) c) Model Last Cycle (T = 28 C)
FCD B2 WSHC2 d) Experimental e) Model First Cycle (T = 23.5 C) f) Model Last Cycle (T = 29 C)
Figure 3.34 FCD B2 WSHC force-displacement results
CHAPTER 3: Model Verification 72
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
FCD B3 HSHC1 a) Experimental b) Model First Cycle (T = 26.5 C) c) Model Last Cycle (T = 31 C)
FCD B3 HSHC3
d) Experimental e) Model First Cycle (T = 24 C) f) Model Last Cycle (T = 28 C)
Figure 3.35 FCD B3 HSHC force-displacement results
FCD B3 USHC1 a) Experimental b) Model First Cycle (T = 24 C) c) Model Last Cycle (T = 26 C)
FCD B3 USHC3
d) Experimental e) Model First Cycle (T = 23 C) f) Model Last Cycle (T = 26 C)
Figure 3.36 FCD B3 USCH force-displacement results
CHAPTER 3: Model Verification 73
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Table 3.7 VCD model harmonic test results
γ0 (%) Test f0 (Hz) Cycle
Maximum Force (kN) Energy Dissipat d (J)
Test Model % diff. Test Model % diff.
50
WSHC1 0.1 First (T = 21 C) 194 172 11.3 780 956 22.6
Last (T = 24.5 C) 181 153 15.4 754 717 4.9
WSHC2 0.3 First (T = 23.5 C) 243 211 13.4 992 926 6.7
Last (T = 29 C) 223 193 13.6 1,016 922 9.2
100
HSHC1 0.1 First (T = 24 C) 338 295 12.7 3,130 2,880 7.9
Last (T = 28 C) 314 256 18.6 3,020 2,410 20.0
HSHC3 0.3 First (T = 26.5 C) 429 368 14.2 3,340 3,350 0.4
Last (T = 31 C) 390 337 13.6 3,320 3,280 1.3
200 USHC1 .1
First (T = 24 C) 669 605 9.6 13,580 12,190 10.2
Last (T = 28 C) 620 565 8.9 13,880 11,720 15.6
USHC3 0.3 First (T = 23 C) 871 837 3.9 14,870 15,370 3.3 Last (T = 26 C) 817 796 2.6 15,740 14,990 4.8
Test specimens FCD B2 and FCD B3 were loaded dynamically with the intention of
reaching failure. Figure 3.38 shows the shear force-displacement hysteresis from Ultimate
Dynamic Tests UD3 and UD4 on specimen FCD B3. Both tests consisted of 3 load cycles at a
frequency of 0.2 Hz. Strains of approximately 400 percent and 550 percent were reached in the
VE material during tests UD3 and UD4, respectively. Because the VCD displacement was
limited by the capacity of the actuator, the onset of strength degradation was not reached in
either test specimen.
The tests were replicated in Perform-3D in order to validate the program’s ability to
capture the viscoelastic-plastic response of a VCD element designed to include a fuse
mechanism for extreme seismic loading. A nonlinear shear hinge was placed in series with the
GMM to represent the RBS fuse mechanism, as shown schematically in Figure 3.28. For both
models, the VE material temperature measured prior to testing was used to define the VE
material properties. The results show that the properties did not vary significantly due to material
self-heating during these short-duration tests. A trilinear backbone curve was defined to
represent the shear force-deformation relation of the built-up steel assembly. The assembly
modelling parameters were selected to fit the test data, as shown in Figure 3.37. Strength
degradation was not included in the model.
CHAPTER 3: Model Verification 74
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 3.37 FCD B3 steel assembly backbone curve
In the absence of test data, expected response parameters must be used to define the steel
assembly behaviour. The expected yield moment of an RBS is computed as:
:5p�� = K5J5�p�� (3-22)
where K5J5 is the expected yield strength of the flanges and �p��is the elastic modulus of the
RBS section (CSA, 2009). The expected peak moment capacity of an RBS is calculated as
follows:
:F3p�� = 1.1K5J5�p�� (3-23)
where �p�� is the plastic modulus of the reduced section, and 1.1 is a factor accounting for the
effects of strain hardening (CSA, 2009). PEER/ATC (2011) provides recommendations for the
definition of a moment-curvature backbone relation for beams with RBS connections.
The displacement-controlled loading protocols from UD3 and UD4 were applied to the
VCD element models in Perform-3D. The analytical shear force-displacement results are shown
in Figure 3.38b) and e). The analytical and experimental force-displacement responses of the
steel assembly are shown in Figure 3.38c) and f). Table 3.8 provides a comparison between the
model and the test results. As shown in the table, the computed maximum force and energy
dissipated in the VCD are in good agreement with the experimental results. The most significant
discrepancy is the relative contribution of the viscoelastic response of the VE material and the
yielding response of the steel assembly to the energy dissipated by the damper. This difference
u
V
Vy = 900 kN
Vult
= 1300 kN
uult
= 30 mm
K0 = 90 kN/mm
KH = 25 kN/mm
CHAPTER 3: Model Verification 75
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
can be attributed to the inability of the model to capture the Bauschinger effect and isotropic
strain hardening, resulting in an overestimation of the energy dissipated by the steel assembly.
Additionally, it is noted that the VE material in the ultimate dynamic test UD4 had a slightly
lower stiffness than the stiffness of the VE material captured in the model. This may be a result
of an inaccurate temperature reading during the test.
Table 3.8 VCD model ultimate dynamic test results
Maximum Force (kN) Energy Dissipated in VEM
(kJ) Energy Dissipated in VCD
(kJ)
Test T initial
( C) Test Model % Diff. Test Model % Diff. Test Model % Diff.
UD3 25.7 1,236 1,259 1.9 165 146 12.0 284 285 0.4 UD4 26.3 1,265 1,305 3.2 227 179 21.1 373 390 4.6
FCD B3 UD3 a) Experimental b) Model (T = 25.7 C) c) Steel Assembly
FCD B3 UD4
d) Experimental e) Model (T = 26.3 C) f) Steel Assembly
Figure 3.38 FCD B3 UD force-displacement results
A series of seismic time-histories were applied to specimen FCD B3. The ground motion
records were scaled to represent the expected response of a VCD in a 50-storey RC coupled wall
case study building (Montgomery, 2011). The experimental force-displacement response of the
VCD test specimen subjected to the Northridge record scaled to twice the design level is shown
CHAPTER 3: Model Verification 76
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
in Figure 3.40a). An estimated initial VE material temperature of 22 C was assumed for model
validation. The analytical force-displacement results are shown in Figure 3.39b). Table 3.9
provides a comparison between experimental and analytical results for this record. The analytical
results are in very good agreement with the experimental results.
Table 3.9 FCD B3 2XNorthridge results
Maximum Force (kN) Energy Dissipated (kJ)
Test Model % diff. Test Model % diff.
917 924 0.72 75.1 70.4 6.3
Figure 3.40 shows a time history of the force measured in the VCD specimen throughout
the test. A bounded analysis was also carried out in Perform-3D, using lower and upper bound
temperatures of 20 C and 30 C, respectively, to define the VE material properties. The results
indicate that the experimental force measurements remained within the range of the bounded
analysis results throughout the majority of the time-history. The VE material properties did not
change significantly due to self-heating during the 50 second test.
FCD B3 UD4 a) Experimental b) Model (T = 22 C) c) Steel Assembly
Figure 3.39 FCD B3 2XNorthridge force-displacement results
Figure 3.40 CNP 2 bounded analysis
0 5 10 15 20 25 30 35 40 45 50−1000
−500
0
500
1000
Time (sec)
Fo
rce
(k
N)
ExperimentalT = 20 degCT = 30 degC
CHAPTER 3: Model Verification 77
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
3.3 System Behaviour Validation
Following the completion of the element validation studies described in Section 3.2, a
realistic RC coupled core wall structure was modeled and analyzed using Perform-3D. A detailed
seismic design of the lateral load-resisting system for a twelve-storey RC office building located
in Montréal is presented in the Concrete Design Handbook (CAC, 2006). The design consists of
a RC elevator core with openings spanned by RC coupling beams at each floor in two of the four
walls (see Figure 3.41). The core walls have been designed and detailed in accordance with the
CSA Standard A23.3-04 (CSA, 2004) provisions for ductile shear walls. Diagonally-reinforced
coupling beams have been specified at all floor levels in order to achieve sufficient ductility.
Typical reinforcing steel details are presented in Figure 3.42 and Figure 3.43.
Figure 3.41 Plan and section of coupled shear wall structure (after CAC, 2006)
Figure 3.42 Typical detail for diagonally reinforced coupling beams (after CAC, 2006)
5.5
m5
.5 m
6.0
m6
.0 m
6.0
m
5.5 m5.5 m 6.0 m 6.0 m 6.0 m
8.0 m
6.0
m
A B C D E F
1
2
3
4
5
6
2.0 m
A A
PLAN SECTION A-A1
2 @
3.6
5 m
4.6
5 m
0.9
m
1
1
SECTION 1-1
90
0 m
m
20
0 m
m
400 mm
75 mm
75 mm
40 mm
140 mm
200 mm
10M bars
8-20M diagonal bars
10M typical
10M @ 300 mm
10M @ 100 mm
800 mm
CHAPTER 3: Model Verification 78
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 3.43 Typical details for core wall reinforcing steel (after CAC, 2006)
3.3.1 Description of Nonlinear Model
A three-dimensional nonlinear model of the core wall structure was constructed using
Perform-3D. The modelling techniques described and validated in Section 3.2 were applied to
model all of the elements comprising this structure. The gravity load resisting system was not
included in the model. Rigid diaphragms were applied at each floor level and at fixed supports
were assigned to the wall elements at the ground floor level. Gravity loads and seismic masses
were computed based on loading information provided in CAC (2006). Stability effects were
taken into account by applying gravity loads to a column with zero lateral stiffness, located at the
centre of mass of the structure. The axial loads applied to the P-Delta column were calculated
based on a load combination of 1.0 D + 0.5 L + 0.25 S over the entire floor area at each level.
Element sizes are listed in Table 3.10.
Nonlinear fibre shear wall elements were used to represent the response of the core walls.
Stress-strain relationships for the confined and unconfined concrete were defined using the
Mander model (Mander et al., 1988), based on a nominal concrete compressive strength, /0 ’, of
30 MPa. The expected compressive strength was computed as 1.3/0’, as recommended by
LATBSDC (2008). The elastic modulus of the unconfined concrete was estimated in accordance
with CAN/CSA A23.3, assuming normal density concrete:
27
5 m
m
275 mm
4-25M bars
275 mm
27
5 m
m
4-25M bars
10M hoops @ 150 mm
3200 mm
64
00
mm
400 mm
DETAIL B
DETAIL A
AB
400 mm
10M E.W.E.F.
CHAPTER 3: Model Verification 79
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
20 = 3,300�/0′ + 6,900 (3-24)
The compressive stress-strain curves for the confined and unconfined concrete and the
linear approximations used to define the material properties in Perform 3D are shown in Figure
3.45. Concrete tensile strength was not included in the model.
Figure 3.44 Perform-3D model of core wall structure
Table 3.10 Element sizes
Element Description Core Walls 400 mm thick Columns 550 x 550 mm Slabs 200 mm thick flat plate Coupling Beams 400 mm wide x 900 mm deep, diagonally-reinforced
CHAPTER 3: Model Verification 80
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
The material model for reinforcing steel was defined based on a specified yield stress, /5,
of 400 MPa. A tri-linear stress-strain relationship was developed using an expected yield stress
of 1.17/5 and an expected ultimate stress of 1.5/5(LATBSDC, 2008). A post-yield stiffness ratio
of 0.03 was assumed based on recommendations from PEER (PEER/ATC, 2010). Buckling of
reinforcing bars was not included in the model. Cyclic degradation of the reinforcing steel was
accounted for as described in Section 3.2.1 (see Figure 3.5 for Energy Factors). The backbone
stress-strain curve used to define all reinforcing steel fibres is shown in Figure 3.46.
a)
b)
Figure 3.45 Constitutive models for unconfined and confined concrete in compression
A schematic diagram representing the fibre elements used to capture the response of the
core walls is shown in Figure 3.47. Shear wall elements in Perform-3D can have a maximum of
16 fibres. In order to accommodate additional fibres, the walls were modelled using two shear
wall elements in parallel. The vertical distributed steel was modeled in one fibre element, while
the zone steel and concrete fibres were modelled in a separate element. The two elements were
then applied in parallel by using the same four nodes to define their locations in 3-dimensional
space. The concrete fibres were assigned a smaller area near the ends of the walls in order to
capture concrete crushing. All concrete outside of the end zones was considered unconfined.
An elastic shear modulus of 0.220 was assigned to the shear wall elements in the hinge
region at the base of the core wall. Elsewhere, an elastic shear modulus of 0.320 was assumed.
Based on recommendations from Powell (2007), wall elements outside of the hinge region were
assigned a length equal to the storey height. In the bottom storey, the walls were assigned a
length equal to the estimated plastic hinge length, 0.5�A (see Figure 3.44).
0 0.005 0.01 0.0150
10
20
30
−40
50
Strain
Str
ess
(M
Pa
)
Mander
Model
0 0.005 0.01 0.0150
10
20
30
−40
50
Strain
Str
ess
(M
Pa
)
Mander
Model
CHAPTER 3: Model Verification 81
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 3.46 Backbone curve for reinforcing steel
Coupling beams were modelled using lumped plasticity elements, as described in Section
3.2.2. The elastic beam sections were assigned an infinite shear stiffness and an elastic flexural
stiffness of 0.152D to account for slip/extension deformations. A nonlinear backbone curve was
used to define the shear hinge force-displacement behaviour, based on recommendations from
Naish et al. (2009). The expected yield strength, E5,�RF, was computed as follows:
E5,�RF = 2@(/5,�RF'$!Z (3-25)
where @( is the area of diagonal reinforcing steel, /5,�RF is the expected yield strength of the
steel, and Z is the angle of inclination of the diagonal bars. The backbone curve used to model a
typical coupling beam (Figure 3.42) is shown in Figure 3.48. Strength degradation under cyclic
loading was accounted for using the energy factors listed in Figure 3.15.
The coupling beams were connected to the coupled wall piers using embedded beam
elements, as recommended by Powell (2007). These elements are required in order to generate
moment connections at the beam-wall interface. Without the embedded beams, the coupling
beams would be effectively pinned at the piers. These embedded beams extend across the width
of the pier, as shown in Figure 3.49. They have been assigned a large flexural stiffness (20 times
the stiffness of the coupling beams) and a small axial stiffness. The axial stiffness of these beams
is typically limited to ensure that they do not stiffen the piers. However, in this study the beams
have been modelled at the floor levels where the rigid diaphragms connect the walls. An axial
area of 500 mm2 was used for the embedded beams in this study, based on an example by Powell
(2007).
−0.1 −0.05 0 0.05 0.1−1000
−800
−600
−400
−200
0
200
400
600
800
1000
Strain
Str
ess
(M
Pa
)
CHAPTER 3: Model Verification 82
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 3.47 Schematic of fibre wall elements
Figure 3.48 Backbone relation for typical coupling beam
Figure 3.49 Embedded beams (schematic)
Zone Steel Fibre
A = 800 mm2
(typ.)
Distributed Steel
ρ = 0.25% (typ.)
Unconfined
Concrete Fibre
(typ.)
Confined
Concrete Fibre
(typ.)
0 0.05 0.1 0.150
0.5
1.0
1.5
Chord Rota!on (rad)
Sh
ea
r F
orc
e (
V/V
ye
xp
)
Coupling Beam (Typ.)
Embedded
Beam
(Typ.)
Wall
Pier
(Typ.)
CHAPTER 3: Model Verification 83
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
3.3.2 Model Verification
Gravity loads due to self-weight were computed based on the member sizes listed in
Table 3.10 and an assumed concrete density of 24 kN/m3. Live loads and superimposed dead
loads are presented in Table 3.11, as given in CAC (2006). Cladding loads were not included.
Gravity loads were applied to a P-Delta column in order to take into account stability effects, as
described in Section 3.3.1. In addition, axial loads were applied to the core wall elements based
on tributary areas. Seismic mass was computed using a load combination of 1.0 D + 0.25 S and
was applied to the centre of mass at each floor level.
Table 3.11 Gravity loading
Live Loads Superimposed Dead Loads
Roof 2.2 kPa snow 0.5 kPa roofing 0.5 kPa ceiling + mechanical 1.6 kPa mechanical services over core
Floor 2.4 kPa typical 1.0 kPa partitions 4.8 kPa on corridor bays around core 0.5 kPa ceiling + mechanical
CAC (2006) provides the results of a modal analysis carried out using ETABS. As part of
the present verification study, an elastic model of the structure was created in Perform-3D for
comparison with results from the ETABS model described in CAC (2006). Reduced section
properties were used to account for the effects of concrete cracking, as listed in Table 3.12
(CAC, 2006).
Table 3.13 provides a comparison between the modal periods of the elastic model and
those reported in CAC (2006). The results show good agreement between the elastic models
created in Perform-3D and ETABS. Also listed in the table are the modal periods computed from
the nonlinear Perform-3D model. As expected, the periods computed from the elastic models are
longer because of the reduced section properties of the elastic elements. Perform-3D uses the
initial unloaded elastic stiffness of nonlinear elements for modal analysis. The mode shapes for
the first three modes of vibration in each lateral direction are shown in Figure 3.50.
In order to determine the maximum shear strength and the collapse mechanism of the
structure in both the EW and NS directions, nonlinear static push-over analyses were carried out.
An inverted triangle load distribution was applied in each direction until collapse was reached.
CHAPTER 3: Model Verification 84
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
The resulting pushover plots are shown in Figure 3.51. Also shown in the figure are the pushover
curves computed without the inclusion of P-Delta effects (dashed lines). As expected, by
including P-Delta effects, the lateral capacity of the structure was significantly reduced in both
directions.
Table 3.12 Reduced section properties for cracking
Element I e Ave
Diagonally-Reinforced Coupling Beams 0.25Ig 0.45Ig Shear Walls 0.7Ig 0.7Ig
Table 3.13 Lateral periods of vibration (sec)
E-W Direction Model T1 T2 T3 ETABS 1.72 0.44 0.20 Perform-3D Elastic 1.79 0.46 0.21 Perform-3D Nonlinear 1.60 0.42 0.19 N-S Direction Model T1 T2 T3 ETABS 1.83 0.34 0.14 Perform-3D Elastic 1.88 0.36 0.16 Perform-3D Nonlinear 1.50 0.30 0.13
a) E-W Direction b) N-S Direction
Figure 3.50 Mode Shapes
In order to provide verification for the results of the pushover analysis, the peak base
shear capacities of the structure in both the EW and NS directions were estimated based on the
CHAPTER 3: Model Verification 85
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
assumed plastic mechanisms. In the EW direction, the overturning moment capacity at the base
of the coupled wall system, :�[�, was computed from equilibrium, as illustrated in Figure 3.52:
:�[� = :�� +:�� + BWE�RF (3-26)
where :��and :��are the expected flexural capacities of the coupled walls, B is the distance
between the centres of gravity of the walls, and ∑E�RF is the sum of the expected shear capacities
of the coupling beams (Priestley et al., 2007). The expected moment capacities of the RC walls
were determined using Response 2000 (Bentz, 2000). Axial loads on the wall elements were
computed based on the following load case: 1.0 Dead + 1.0 Earthquake + 0.25 Live. Results
from the Response 2000 analysis are provided in Appendix A.
a) EW Direction b) NS Direction
Figure 3.51 Static pushover plots
The peak base shear of the structure neglecting P-Delta effects, EC∗, is computed as:
EC∗ = :�[����ℎ� (3-27)
where ℎ is the building height. Table 3.14 provides summary calculations for the estimated
lateral capacity of the coupled wall system in the EW direction. In the NS direction, the peak
base shear was determined from the flexural capacity of the RC walls, as given in Table 3.15.
These theoretical capacities are in good agreement with the pushover results excluding the
effects of P-Delta, which indicate a peak base shear of 3,990 kN at a roof drift of 2.2 percent in
0 1.5 3.0 4.50
1000
2000
3000
4000
5000
6000
Roof Dri! (%)
Ba
se S
he
ar
(kN
)
No P−DeltaP−Delta
max. = 3,990 kN
max. = 3,090 kN
0 2.0 4.0 6.0 0
1000
2000
3000
4000
5000
6000
Roof Dri! (%)
Ba
se S
he
ar
(kN
)
No P−DeltaP−Delta
max. = 4,550 kN
max. = 3,160 kN
CHAPTER 3: Model Verification 86
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
the EW direction, and a peak base shear of 4,550 kN at a roof drift of 6.2 percent in the NS
direction. These results are represented by dashed lines in Figure 3.51.
Figure 3.52 Pushover analysis schematic (EW direction)
Table 3.14 Calculation of peak base shear in the EW direction (neglecting P-Delta)
∑E�RF (kN) 6,120 B (m) 6.5 ∑E�RF B (kNm) 79,60
��� (kN) 1,100 :�� (kNm) 18,300 ��� (kN) -23,400 :�� (kNm) 33,200 :�[� (kNm) 131,000 ��,-.∗ (kN) 4,040
Table 3.15 Calculation of peak base shear in the NS direction (neglecting P-Delta)
:�[� (kNm) 140,700 ��,-.∗ (kN) 4,340
Including the effects of P-Delta, the pushover analysis in the EW direction gives a peak
base shear capacity of 3,090 kN at a roof drift of 0.83 percent. In the NS direction, the peak base
shear including the effects of P-Delta was found to be 3,160 kN at a roof drift of 0.94 percent. As
illustrated in Figure 3.53, when the structure deforms due to the applied pushover load, the
gravity loads applied at each floor result in an additional overturning moment, :��,which must
Inverted triangle
pushover load
distribu�on
h
MOTM
MW1
MW2
L
ΣVexp
ΣVexp
Vb*
a) Free body diagram b) Flexural resistance mechanism
CHAPTER 3: Model Verification 87
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
be resisted at the base of the structure. In order to validate the pushover results including P-Delta
effects, :��was computed based on the deformed shape of the structure at the roof drift
corresponding to the peak base shear, �F�~< (see Figure 3.53). The peak base shear including the
effects of P-Delta, EC, was then computed using the following expression:
EC = EC∗ − :��(��ℎ) (3-28)
Table 3.16 and Table 3.17 show calculations for the peak base shear in the EW and NS
directions, respectively. Both results are in good agreement with the results of the pushover
analysis carried out using Perform3D.
a)
b)
Figure 3.53 a) P-Delta schematic b) Peak base shear
Table 3.16 Calculation of peak base shear in the EW direction (including P-Delta)
�F�~< (%) 0.83 EC∗ (kN) 3,620 :�� (kNm) 17,700 ��(kN) 3,070
Table 3.17 Calculation of peak base shear in the NS direction (including P-Delta)
�F�~< (%) 0.94 EC∗ (kN) 3,730 :�� (kNm) 18,800 ��(kN) 3,150
MPΔ
Deformed
shape
P
Δ
Inverted triangle
pushover load
distribu!on
0 1.5 3.0 4.50
1000
2000
3000
4000
5000
6000
Roof Dri! (%)
Ba
se S
he
ar
(kN
)
No P−DeltaP−Delta
δpeak
Vb*
Vb
CHAPTER 3: Model Verification 88
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
3.4 Nonlinear Modelling Assumptions and Limitations
Nonlinear time-history analysis is a powerful tool for predicting building response to
ground motions at varying levels of seismic intensity. However, as discussed throughout this
Chapter, several modelling assumptions are required which can significantly affect the accuracy
of results. This Section provides an overview of the nonlinear modelling assumptions and
techniques applied in the subsequent Chapters of this thesis. Although the techniques described
herein are believed to reflect current best practices for nonlinear modelling of high-rise RC core
wall structures, there are limits to their applicability and accuracy. These limitations are also
addressed in this Section.
3.4.1 Component Models
The nonlinear analysis models described in this thesis are comprised of lumped-plasticity
and fibre elements, as described in Section 3.2.1. Expected material properties, as given in
LATBSDC (2008), are used to define the behaviour of all components, rather than nominal or
minimum specified properties. These properties represent median values derived from laboratory
tests on a large number of specimens and are intended to provide unbiased predictions of
structural performance (PEER/ATC, 2010). Hardening and softening behaviours are included in
all component models, in order to capture the full range of response at all levels of seismic
intensity. Cyclic strength degradation is accounted for based on available guidance.
Reinforced concrete shear walls are typically capacity designed such that flexural
yielding is restricted to the plastic hinge region at the base of the wall. However, studies have
shown that higher mode effects can result in nonlinear behaviour above the hinge region in high-
rise buildings (Salas, 2008). Nonlinear fibre elements are therefore recommended to simulate the
response of slender RC shear walls over the full building height. These elements are comprised
of nonlinear uniaxial concrete and reinforcing steel fibres which capture axial-flexural
interaction. A single element is used over the wall width and storey height for slender walls,
where the assumption that plane sections remain plane is reasonable. In the plastic hinge region
at the base of a core wall structure, wall elements should be assigned a length equal to the
assumed plastic hinge length. ASCE 41 (2007) recommends a hinge length equal to the lesser of
CHAPTER 3: Model Verification 89
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
0.5�A , where �A is the wall length, and the storey height. The out-of-plane flexural behaviour of
shear wall elements is modelled as elastic in Perform-3D, and a reduced stiffness is
recommended to account for concrete cracking. An effective out-of-plane stiffness of 0.2520D� is
used to model RC shear walls in this thesis.
Shear-flexure interaction is not accounted for in fibre element models, although it has
been shown to affect the lateral strength and stiffness of RC walls (Elwood et al., 2007). A
bounded analysis is therefore recommended for performance-based design of coupled wall
structures, in order to account for uncertainty related to the effective shear stiffness of RC walls
subjected to reversed cyclic loading (PEER/ATC, 2010). For the purpose of this thesis, the shear
behaviour of all wall elements is modelled as linear elastic and a reduced effective shear
modulus of 0.220 is assigned to account for concrete cracking. In order to ensure ductile flexural
response, shear stress in the wall elements must be limited to prevent nonlinear shear behaviour.
ACI 318 (2008) specifies an upper limit of 0.83�/′0 (MPa) for the nominal shear strength of an
RC wall. This limit is intended to prevent crushing of concrete due to diagonal compression in
the wall element.
The Mander model (Mander et al., 1988), which includes the effects of confinement on
the strength and ductility of concrete, is used to define the stress-strain envelope curve for
concrete fibres in compression. An expected compressive strength of 1.3/0 ’ is assumed for
concrete (LATBSDC, 2008). Compressive stress-strain curves are approximated using a multi-
linear relation in Perform-3D (See Figure 3.6). For simplicity, tensile strength and cyclic
degradation are neglected in the definition of the concrete fibres. Smooth concrete crack-closure
is assumed in Perform-3D, which results in a pinched component hysteresis. This discrepancy is
considered minor and does not significantly affect the accuracy of structural response predictions
(PEER/ATC, 2010). The effect of concrete spalling is accounted for by subtracting cover
concrete from the thickness of the wall elements.
Reinforcing steel fibres are defined using a tri-linear stress-strain backbone relation. The
expected yield and ultimate stresses are computed as 1.17/5 and 1.5/5, respectively (LATBSDC,
2008). A strain hardening slope of 0.032 is assumed. Rebar buckling is not accounted for in the
CHAPTER 3: Model Verification 90
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
model but can be predicted by monitoring axial strains in the steel fibres. ASCE 41-06 specifies
allowable strain limits of 0.02 in compression and 0.05 in tension for reinforcing steel. Cyclic
degradation of reinforcing steel has a significant effect on the hysteretic behaviour of RC wall
elements at large ductility demands. There is, however, a lack of available guidance on the
selection of strength degradation parameters for reinforcing steel material in Perform-3D. In this
thesis, cyclic strength degradation of reinforcing steel in shear walls is accounted for using
parameters calibrated by Ghodsi and Ruiz (2010) to model the UCLA slender wall specimen
RW2 (see Figure 3.5).
Diagonally-reinforced coupling beams are commonly modelled using a nonlinear shear
hinge at the midspan of an elastic beam element. Naish et al. (2009) calibrated backbone shear
strength-rotation relations for diagonally-reinforced coupling beams using test data. These
relations, shown in Figure 3.14, were developed from test results for beam specimens having
aspect ratios of 2.4 and 3.3, and are recommended for modelling beams with conventional span-
to-depth ratios of 2.0 to 4.0. An effective yield stiffness of 0.1520D� is suggested to account for
concrete cracking and reinforcing bar slip and extension at the beam-wall interface (Naish et al.,
2009).
The backbone curve used to model diagonally-reinforced concrete coupling beam
elements, accounting for the added shear strength provided by an RC slab, is shown in Figure
3.54. Shear-axial interaction is not accounted for in this coupling beam model, although axial
restraint provided by the coupled walls has been shown to induce significant compression in the
beams (Barbachyn et al., 2011). Further testing of axially-restrained coupling beams subjected to
cyclic loading is required in order to quantify this effect on the shear capacity of the beams.
Cyclic degradation is accounted for in Perform-3D using Energy Factors calibrated by Naish et
al. (2009), as given in Figure 3.15. These factors have been calibrated based on limited test data
and may not be applicable for all diagonally-reinforced coupling beams. A strength loss
interaction factor of 0.25 is also included in the model.
Shear-critical steel coupling beams are modelled using a lumped-plasticity model similar
to that used to capture the response of diagonally-reinforced coupling beams. Nonlinear shear
deformations are concentrated in a shear hinge, located at the midspan of an elastic beam
CHAPTER 3: Model Verification 91
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
element. There is a lack of available guidance for nonlinear modelling of hybrid coupled walls.
However, because these beams are designed to perform in a similar manner to shear links in
eccentrically braced frames, they can be modelled according to guidelines intended for EBF
links. ASCE 41 (2006) provides a cyclic backbone shear strength-rotation relation for EBF links
(see Figure 3.17). Element backbone curves specified in ASCE 41 (2006) are modified to
account for cyclic strength deterioration indirectly and are not intended to be used in conjunction
with a cyclic degradation function. These relations are based on a combination of test results and
engineering judgment and tend to be conservative (PEER/ATC, 2010).
Figure 3.54 RC coupling beam backbone curve
Harries et al. (2000) recommend an effective flexural stiffness of 0.6EI to account for
flexibility in the embedment regions. Concrete spalling at the beam-wall interface is accounted
for by using an effective length equal to the clear span plus twice the concrete cover. A post-
yield stiffness of up to 6 percent of the elastic stiffness is assumed for shear panel yielding. The
nominal shear yield strength, EF, and ultimate shear strength, EL, are computed in accordance
with CSA-S16 (2009). For the purpose of this thesis, expected yield and ultimate strengths are
estimated using a material overstrength factor, K5, of 1.2, as recommended by Mansour and
Christopoulos (2011).
The nonlinear shear behaviour of VCD elements can be captured using the GMM4, as
described in Section 3.2.4. This model, which captures the frequency-dependent response of the
VE material, consists of a Kelvin-Voigt element in parallel with four Maxwell elements. The
0 2 4 6 8 10 12 140
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Rota on (%)
V/V
y,e
xp (θy, V
y,exp)
(θ2, V
u,exp) (θ
6, V
u,exp)
(θ10
, Vr,exp
)
Vy,exp
= 2Asf
y,expsinα
Vu,exp
= 1.33Vy,exp
Vr,exp
= 0.25Vu,exp
CHAPTER 3: Model Verification 92
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
parameters used to define these elements have been calibrated by Montgomery (2011) for the
ISD:111H VE material and are listed in Table 3.5. These parameters were calibrated using data
from VE material characterization tests at temperatures between 10 C and 40 C, and harmonic
loading frequencies between 0.1 Hz and 2.0 Hz. The VE material models described in Section
3.2.4 were defined using these parameters and have been shown to be in good agreement with
test data from Montgomery (2011) over a wide range of temperatures, frequencies, and strain
amplitudes. However, the modelling parameters listed in Table 3.5 may not be suitable for
temperatures and frequencies outside of the ranges used for calibration.
In Perform-3D, fluid damper components are used to model Maxwell elements, and an
elastic bar element in parallel with a fluid damper component having a very large spring stiffness
is used to capture the Kelvin-Voigt element. Elastic beam elements in series with a nonlinear
shear hinge are used to simulate the response of the built-up steel assembly when a fuse
mechanism is included for seismic loading (see Figure 3.27). For VCDs designed to yield in
shear, the same backbone relationship used to define the response of shear-critical steel coupling
beams is used to define the nonlinear shear hinge. The effect of changes in temperature on the
VE material properties is not accounted for in the model. A bounded analysis is therefore
recommended for design.
3.4.2 System Modelling
The gravity load resisting system is typically not included in nonlinear models of RC
coupled core wall buildings. As such, the influence of the gravity system on the strength and
stiffness of the lateral load-resisting system are not accounted for. However, coupling between
the core walls and the gravity columns can result in increased axial loads in the columns.
PEER/ATC (2010) recommends including effective slab-beams and columns with plastic hinges
representing flexural strength, in order to assess the impact of slab-coupling on column axial
loads and on interstorey drifts. For the purposes of this thesis, gravity-load resisting systems are
not included in the analysis models. Salas (2008) conducted a parametric study on a building
similar to the case study described in Chapter 1 to assess the impact of the gravity system on the
global response of the structure. The results of this study showed that the inclusion of a slab-
CHAPTER 3: Model Verification 93
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
column gravity frame did not have a significant effect on the maximum interstorey drifts or on
column axial loads.
Rigid diaphragms are typically used to model concrete and composite slabs in
commercial analysis programs. The slabs are assumed to be infinitely rigid and the lateral forces
are distributed based on the relative stiffness of the vertical elements. Torsion is introduced due
to eccentricity between the centres of mass and rigidity. Semi-rigid diaphragms are a more
realistic but a more difficult model to implement. PEER/ATC (2010) recommends the use of
semi-rigid diaphragms to account for backstay effects. For the purposes of this thesis, ground
floor and basement slabs are modelled using semi-rigid elastic shell elements with cracked
section properties. Rigid diaphragms are applied at all floor levels above the podium. This
assumption is not expected to have a significant effect on the accuracy of results for the regular
structures analysed herein (PEER/ATC, 2010).
Various recommendations exist for estimating reduced section properties of cracked
concrete elements. These assumptions are of particular importance for linear elastic analysis
where nonlinearity is not explicitly accounted for. In nonlinear models, elements which are
intended to remain essentially elastic, such as basement walls and transfer slabs, are modelled as
elastic shell elements with reduced stiffness to account for cracking. The effective section
properties used to model elastic elements in this thesis are consistent with those used by
Magnusson Klemencic Associates (MKA) to model the PEER case study building described in
Section 4.1. These properties, as well as the reduced section properties specified for seismic
design in CSA A23.3 (2004), are listed in Table 3.18. The factor ZA is computed as follows:
ZA = 0.6 + �(/′0@� ≤ 1.0 (3-29)
where �( is the factored axial load at the base of the wall corresponding to the seismic load case.
A bounded analysis is recommended to assess the influence of cracked properties on the
response quantities used for performance-based design.
As discussed in Section 3.3.1, coupling elements are modelled using beam compound
elements. For simplicity, these elements are typically located at the floor levels although their
CHAPTER 3: Model Verification 94
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
neutral axes are below the floor levels. Embedded beam elements must be used to connect the
coupling elements to the wall piers (see Figure 3.49). These elements are assigned a large
flexural stiffness, in order to provide rigid connections between the beam and the walls. Powell
(2007) recommends applying a flexural stiffness of approximately 20 times the elastic stiffness
of the adjacent coupling element. A small axial stiffness is assigned to the embedded beams to
avoid stiffening the wall elements. Using this model, the influence of local deformations at the
beam-wall interface on the effective stiffness of the coupling elements must be accounted for
indirectly by applying a reduced elastic stiffness to the beam elements.
Table 3.18 Reduced section properties for seismic analysis
MKA CSA (2004) ��� �� ��� �� Walls 0.8@� 0.8D� ZA@� ZAD� Slabs 0.25@� 0.25D� – 0.2D�
The flexural response of nonlinear fibre wall elements is highly dependent on the axial
stress, unlike that of linear elastic wall elements whose properties are independent of force
demands. Therefore, expected gravity loads must be applied on wall elements for nonlinear time
history analysis. Expected gravity loads are computed as the unfactored dead load plus a portion
of the nominal live load (typically 0.25L). Gravity loads are applied to the wall elements based
on tributary areas at each floor level. Expected gravity loads are also applied to a P-Delta column
to account for global stability effects. P-Delta forces include expected gravity loads acting over
the entire floor area at each storey. P-Delta columns are modelled using linear elastic bar
elements with zero lateral stiffness and are connected to the lateral load-resisting system through
the rigid diaphragms at each floor. Seismic masses are assigned at each floor based on expected
dead loads and associated rotation moments of inertia.
The quantification of damping is an important aspect of dynamic analysis. Nonlinear
analysis models account for hysteretic energy dissipation in elements designed to exhibit
nonlinear behaviour, such as coupling beams and the flexural hinge region at the base of an RC
shear wall. The nonlinear response of these elements is defined explicitly in the model. Energy
dissipation due to yielding and cracking of components modelled using elastic elements is,
however, not captured. Other sources of damping which are not accounted for explicitly include
CHAPTER 3: Model Verification 95
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
cracking and yielding of structural elements not included in the model, damage to non-structural
elements, and soil-structure interaction. Damping resulting from these phenomena is typically
modelled as equivalent viscous damping.
Methods for modelling equivalent viscous damping in commercial software include
Rayleigh and modal damping. These models have been developed in the context of elastic modal
analysis and may not be appropriate for nonlinear seismic applications. In particular, caution
should be exercised when the Rayleigh method is used and the stiffness-proportional damping
matrix is defined based on the initial elastic stiffness of the system. This approach, which is used
in Perform-3D, can result in the generation of artificial damping when the structure yields
(Charney, 2008). In order to avoid this effect, a stiffness-proportional damping multiplier of zero
should be assigned to elements which have an artificially high initial stiffness, such as the “rigid”
elements used to model the VCDs. Further research is required to better understand and more
accurately simulate inherent damping in nonlinear models, since limited data exists from high-
rise buildings subjected to earthquake loading (PEER/ATC, 2010).
In this thesis, the Rayleigh model is used to define equivalent viscous damping. In
Perform-3D, stiffness-proportional damping is assigned based on initial elastic stiffness. In order
to be consistent with the report by PEER/ATC (2011), 2.5 percent of critical damping is assigned
to the case study building at periods of 1 and 5 seconds, for all levels of seismic intensity
considered. This value is typical for nonlinear time history analysis of high-rise RC structures
but may be unconservative for service level earthquake analysis. For performance-based design,
a sensitivity study is recommended to assess the influence of the assumed level of viscous
damping on the global structural response (PEER/ATC, 2010).
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Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
4 CASE STUDY
This Chapter presents a comparative study on the seismic performance of two high-rise
RC core wall structures located in Los Angeles, CA. The reference structure was designed as a
case study for the Pacific Earthquake Engineering Research Center (PEER) Tall Buildings
Initiative (TBI). The alternative design uses VCDs in place of the diagonally-reinforced coupling
beams at each floor level. In addition to the seismic performance, the serviceability level wind
response of the two structures was also investigated. An introduction to the TBI case study
building is provided in Section 4.1. The analysis models, which were developed using the
procedures validated in Chapter 3, are described in Section 4.2. The historical ground motions
and the ground motion scaling procedure used in the nonlinear time history analysis are
presented in Section 4.3. The seismic and SLS wind performance of the reference structure is
reviewed in Section 4.4. Section 4.5 describes the development of the alternative design,
including a parametric study involving the preliminary analysis several different VCD
configurations. Finally, the seismic and wind performance of the alternative design is discussed
and compared with the reference structure in Section 4.6.
4.1 Introduction
As part of the PEER Tall Buildings Initiative, a high-rise coupled RC core wall structure
was designed by Magnusson Klemencic Associates (PEER/ATC, 2011). Three variations of this
seismic-critical prototype structure, shown in Figure 4.1, were designed in accordance with three
different sets of seismic design guidelines. The study aimed to evaluate and improve on current
design provisions for high-rise buildings located in seismically-active regions. The following
guidelines were considered:
• The prescriptive provisions of the International Building Code (IBC, 2006)
• The performance-based guidelines published by the Los Angeles Tall Building
Structural Design Council (LATBSDC, 2008)
• The performance-based guidelines set out for the PEER Tall Buildings Initiative
(TBI, 2010)
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Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 4.1 Isometric view of case study building (adapted from PEER/ATC, 2011)
The focus of the present thesis is to investigate the performance of a seismic-critical RC
core wall structure designed using VCDs. The reference structure for this study is based on the
prototype building designed by Magnusson Klemencic Associates in accordance with the state-
of-the-art performance-based guidelines set out by the LATBDSC (2008). The building is a 42-
storey hotel located in Los Angeles. The lateral system consists of an RC core with openings
spanned by diagonally-reinforced coupling beams. The gravity system is comprised of flat slabs
supported on perimeter columns. Foundation and tower floor plans are shown in Figure 4.2 and
Figure 4.3, respectively. An alternative design has been developed by introducing VCDs and
yielding steel links in the coupling beam locations of the RC core, as described in Section 4.5. A
parametric study was carried out in order to determine the optimal placement and number of
VCDs to enhance the seismic performance of the alternative design. Several VCD configurations
have been investigated and their seismic performance has been compared with that of the
reference structure using nonlinear time history analysis. Based on the results from the
parametric study, an optimal alternative design configuration was selected. A detailed analysis
was then carried out in order to compare the seismic and wind performance of the reference and
alternative structures.
The reference structure was optimized by the designers for seismic performance using the
procedure outlined by the LATBSDC (2008), with the following exceptions:
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Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
• The serviceability analysis was carried out based on a 25-year mean return
period, rather than the prescribed 43-year return period
• Less than 20 percent of the ductile elements were allowed to reach 150 percent of
their nominal capacity under service level seismic loading
• The minimum base shear requirement was not observed
Required member strengths were determined from an elastic response spectrum analysis
using the 2.5 percent critically damped serviceability spectrum. The design was then checked for
compliance with Collapse Prevention (CP) performance criteria at the maximum credible
earthquake level (MCE) using nonlinear time history analysis. Acceptance criteria for the
performance objectives at the SLE and MCE hazard levels are listed in Table 4.1 and Table 4.2,
respectively (PEER/ATC, 2011). Shear walls are assumed to remain elastic in shear when the
peak shear stress is below the allowable limit of 0.83�/0′ (MPa) set out in ACI (2008). The
effect of slab-column coupling was accounted for in the elastic serviceability analysis using slab
outrigger beams and columns. Acceptance criteria were not specified for the gravity system at
the MCE hazard level.
Table 4.1 SLE acceptance criteria
Demand Parameter Limit Interstorey Drift 0.5% Coupling Beam Rotations Essentially Elastic Core Wall Flexure Essentially Elastic Core Wall Shear Elastic Slab Outrigger Beams Essentially Elastic (Flexure) Columns Elastic
Table 4.2 MCE acceptance criteria
Demand Parameter Limit Interstorey Drift 3.0% Coupling Beam Rotations 0.06 rad. Core Wall Reinforcement Axial Strain
0.05 tension 0.02 compression
Core Wall Concrete Axial Strain
0.015 compression (confined)
Core Wall Shear Elastic
CHAPTER 4: Case Study 99
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 4.2 Case study building foundation plan (after PEER/ATC, 2011)
Figure 4.3 Case study building tower floor plan (after PEER/ATC, 2011)
A
B
C
D
E
F
B.2
D.8
48
’- 0
’’
10’- 0’’
10’- 0’’
23
’- 0
’’2
3’-
0’’
23
’- 0
’’2
3’-
0’’
15
’- 0
’’
15’- 6’’ 15’- 6’’24’- 0’’ 24’- 0’’14’- 6’’14’- 6’’
32’- 0’’
3’- 0’’
3’- 0’’
2.9 4.1
1 2 3 3.5 4 5 6
X1 X2 X4 X6 X8 X9
Y1
Y2
Y5
Y4
Y6
Y8
Y9
30’- 0’’ 30’- 0’’ 30’- 0’’ 30’- 0’’ 30’- 0’’ 30’- 0’’24’- 0’’ 24’- 0’’
228’- 0’’
30
’- 0
’’3
0’-
0’’
30
’- 0
’’3
0’-
0’’
30
’- 0
’’3
0’-
0’’
23
’- 6
’’2
3’-
6’’
22
7’-
0’’
A
B
C
D
E
F
B.2
D.8
48
’- 0
’’
10’- 0’’
10’- 0’’
23
’- 0
’’2
3’-
0’’
23
’- 0
’’2
3’-
0’’
15
’- 0
’’15’- 6’’ 15’- 6’’24’- 0’’ 24’- 0’’14’- 6’’14’- 6’’
32’- 0’’
3’- 0’’
10’- 0’’
10’- 0’’
3’- 0’’
2.9 4.1
1 2 3 3.5 4 5 6
CHAPTER 4: Case Study 100
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
4.2 Analysis Models
In order to evaluate the seismic performance of the reference structure and alternative
design configurations, nonlinear models of the lateral load-resisting systems have been created in
Perform-3D. The modelling assumptions and procedures followed are consistent with those
outlined in Section 3.4. Figure 4.4 shows an isometric view of a typical nonlinear model. The
models include the RC core walls and coupling elements, as well as the foundation walls and
slabs at the podium and parking levels. Gravity columns and slabs are not included in the
nonlinear models because they have been shown to have a negligible effect on the structural
response (Salas, 2008). Nonlinear properties are assigned to elements which are expected to
undergo inelastic deformations and effective elastic properties are assigned to elements which
are designed to remain elastic.
Figure 4.4 Isometric of typical nonlinear model
4.2.1 General Building Properties
The general properties of the reference structure are listed in Table 4.3. Core wall
thicknesses are given in Figure 4.5. A reinforcement schedule for the core walls is provided in
Appendix C. Boundary reinforcement details were not included in the report by Magnusson
CHAPTER 4: Case Study 101
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Klemencic (PEER/ATC, 2011). The diagonally-reinforced coupling beams have a typical depth
of 762 mm (30 in) and a width equal to the core wall thickness. Coupling beam reinforcement
details are provided in Appendix B. A column schedule is also provided in Appendix D.
Construction material properties are listed in Table 4.4 and Table 4.5. Grade 60 reinforcing steel
is used in the core walls and Grade 75 reinforcing steel is used in the coupling beams.
Figure 4.5 Core wall thickness (adapted from PEER/ATC, 2011)
Table 4.3 Reference structure properties
Element Description Number of Storeys 42 above ground
4 below ground Storey Height 3.2 m below ground
4.2 m ground floor level 3.2 m typical tower level 3.5 m 42nd floor level 6.1 m penthouse level
Foundation Mat foundation with variable thickness under tower footprint Slab Construction 254 mm thick RC flat slabs below grade
305 mm thick RC flat podium slab 203 mm post-tensioned flat tower slabs 254 mm thick RC roof slabs
Basement Walls 406 mm thick RC walls around perimeter of basement Core Walls RC walls, 533 mm to 813 mm thick Coupling Beams Diagonally-reinforced, 762 mm deep (typical) Columns Square RC columns, 457x457 mm to 914x914 mm
Core Wall
Thickness:
L31-R:
530 mm
L13-L31:
610 mm
B4-L13:
813 mm EW
914 mm NS
N
E
CHAPTER 4: Case Study 102
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Table 4.4 Concrete material properties
Element
Nominal f’ c (MPa)
Expected f’c (MPa)
Nominal Ec (MPa)
Expected Ec (MPa)
Basement Walls 34.5 44.8 26,400 29,100 Foundation Mat 41.4 53.8 28,300 31,200 Non-Post-Tensioned Beams and Slabs
37.9 49.3 27,400 30,300
Post-Tensioned Slabs 37.9 49.3 27,400 30,300 Columns 55.2 71.8 31,600 35,000 Core Walls 55.2 71.8 31,600 35,000
Table 4.5 Reinforcing steel material properties
Standard
Nominal fy (MPa) Expected fy
(MPa) Expected fu
(MPa) ASTM A615 Grade 60 414 (non-seismic) N/A N/A ASTM A706 Grade 60 414 (seismic) 483 724 ASTM A615 Grade 75 517 586 896
4.2.2 Component Models
The axial-flexural interaction of the core walls was captured using nonlinear fibre
elements, as described in Section 3.2.1 and Section 3.4.1. The shear response was modelled as
elastic with an effective shear modulus of 0.220. For simplicity, “Auto Size” shear wall elements
were used, meaning that each wall element, regardless of its length, was assigned a fixed number
of concrete and steel fibres with fixed relative sizes. Each element was modelled using a total of
16 fibres. A schematic of the cross-section of a typical shear wall fibre element is shown in
Figure 4.6. Smaller fibres were used near the ends of the walls in order to capture concrete
crushing. A simplified vertical reinforcing steel schedule, given in Table 4.6, was used to model
the core wall elements (see the complete shear wall reinforcing steel schedule in Appendix C). A
constant reinforcement ratio, j, was used for each wall thickness, . An assumed concrete cover
of 25 mm was subtracted from the wall thickness on both sides, in order to account for concrete
spalling. The reinforcement ratio was adjusted accordingly. A schematic plan view of the shear
wall elements at a typical tower floor level is shown in Figure 4.7. Rigid diaphragm constraints
were applied at each floor level.
CHAPTER 4: Case Study 103
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 4.6 Typical shear wall element schematic
The Mander model (Mander et al., 1988) was used to define the stress-strain relation for
the concrete fibres in compression. For simplicity, all concrete fibres were modelled using the
multi-linear stress-strain curve shown in Figure 4.8 a). A confined strength ratio of 1.3 was
assumed for all shear wall concrete. The tensile strength of concrete was not included in the
models. The reinforcing steel fibres were defined using the trilinear stress-strain curve shown in
Figure 4.8 b). A strain hardening slope of 0.032 was assumed. Buckling of reinforcing steel was
not included in the models. Cyclic degradation of reinforcing steel was defined using the same
parameters that were calibrated by Ghodsi and Ruiz (2010). The Energy factors are summarized
in Figure 3.5.
Figure 4.7 Core wall model schematic
Steel
Fibre
(typ.)
Concrete
Fibre
(typ.)
Subtracted
Cover
(typ.)
Rigid
Diaphragm
Fibre
Element
(typ.)
Centre
of Mass
W32
W30
W34
W22
W20
W24
W01 W03
W11 W13
CHAPTER 4: Case Study 104
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Table 4.6 Model vertical reinforcement ratios
N&S Elevations E&W Elevations
Floors �
(mm) W01&W10 � (%)
W03&W13 � (%) �
(mm) W20&W34 � (%)
W22&W32 � (%) W24&W30 � (%)
L31-R 533 0.79 1.01 533 1.01 0.63 0.79 L13-L31 610 1.39 1.76 610 1.76 0.83 1.39 L1-L13 813 1.32 1.32 711 1.51 0.94 1.51 B4-L1 813 1.62 1.62 711 1.86 1.86 1.86
a)
b)
Figure 4.8 a) Concrete fibre compressive stress-strain relation b) Steel fibre stress-strain relation
The nonlinear model for the diagonally-reinforced coupling beams consisted of an elastic
beam element with a nonlinear shear hinge at midspan, as described in Section 3.2.2 and Section
3.4.1. The elastic beam sections were assigned an effective stiffness of 0.152D, based on
recommendations from Naish et al. (2009). Figure 4.9 shows the backbone curve for a nonlinear
shear hinge in Perform-3D. The yield force and ultimate force are denoted J� and J�,
respectively. The variable �� represents the shear displacement when the coupling beam reaches
the ultimate strength; �B represents the shear displacement at the onset of strength loss; �K
represents the shear displacement when the residual strength is reached; and �� represents the
ultimate shear displacement capacity of the member. The analysis terminates when a
displacement of �� is reached in any member. The modelling parameters used to simulate the
behaviour of the coupling beams on the north and south elevations and east and west elevations
are given in Table 4.7 and Table 4.8, respectively. Embedded beams were used to provide
moment connections between the coupling beams and adjacent walls (see Figure 3.49). The
properties of the embedded beams were selected to provide large flexural stiffness (20 times
0 0.005 0.01 0.015 0.02 0.025 0.030
20
40
60
80
100
120
Strain
Str
ess
(M
Pa
)
ManderModel
−0.1 −0.05 0 0.05 0.1−1000
−500
0
500
1000
Strain
Str
ess
(M
Pa
)
CHAPTER 4: Case Study 105
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
more stiff than the coupling beams) and small axial stiffness (100 times less stiff than the
coupling beams).
Figure 4.9 Shear hinge backbone curve
Table 4.7 Coupling beam modelling parameters – N&S Elevations
Designation
� (mm)
(mm)
¡r(kN/mm)
¢£(kN)
¢¤(kN)
¢¥(kN)
¤(mm)
¦(mm)
¥(mm)
§(mm)
1B 533 762 586 871 1159 290 23.9 75.7 129.0 193.8 3B 533 762 586 1307 1738 434 22.9 74.8 128.8 193.6 4B 533 762 586 2100 2800 700 21.1 73.0 128.3 193.1 5B 610 762 670 2100 2800 700 21.7 73.5 128.5 193.3 7B 610 762 670 2590 3440 860 20.8 72.6 128.3 193.0 11B 813 762 893 3180 4220 1055 21.2 73.0 128.4 193.1 13B 813 762 893 3450 4590 1150 20.8 72.6 128.3 193.0
Table 4.8 Coupling beam modelling parameters – E&W Elevations
Designation
� (mm)
(mm)
¡r(kN/mm)
¢£(kN)
¢¤(kN)
¢¥(kN)
¤(mm)
¦(mm)
¥(mm)
§(mm)
1B 533 762 311 722 960 240 28.9 92.9 159.2 239.3 2B 711 762 414 722 960 240 29.7 93.7 159.4 249.5 3B 533 762 311 1083 1440 360 27.4 91.4 158.9 238.9 4B 533 762 311 1743 2320 580 24.5 88.6 158.2 238.2 6B 711 762 414 1743 2320 580 26.4 90.4 158.6 238.6 7B 610 762 355 2130 2830 707 24.0 88.1 158.0 238.0 8B 711 762 414 2130 2830 707 25.2 89.2 158.3 238.3 9B 610 762 355 2610 3470 868 22.2 86.2 157.6 237.6 10B 711 762 414 2610 3470 868 23.6 87.6 157.9 237.9 12B 711 762 414 2840 3770 943 22.9 86.9 157.7 237.8 14B 711 762 414 3480 4630 1158 20.8 84.8 157.2 2387.2
Sh
ea
r Fo
rce
Shear Displacement
FY
FU
DU DL DR DX
CHAPTER 4: Case Study 106
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
The perimeter basement walls were modelled using elastic shear wall elements with a
reduction factor of 0.8 to account for concrete cracking. The floor diaphragms at the podium and
basement levels were modelled using elastic shell elements with a reduction factor of 0.25 to
account for concrete cracking. Pin connections were assigned to all nodes at the level at the top
of the foundation mat. Soil-structure interaction was neglected in all models.
4.2.3 Loading Criteria
The specified gravity loads for the reference structure are listed in Table 4.9, as given in
the PEER/ATC report (2011). The self-weight of the structure was also accounted for in the
analysis models. A single load combination was used for all nonlinear time history analyses:
1.0D + 0.25L + 1.0E. Accidental torsion was not considered in the analyses. Gravity loads were
applied as point loads on the core walls at each floor based. P-Delta loads were applied to a P-
Delta column located at the centre of mass. The seismic mass at each floor was computed as the
specified dead load and an associated rotational moment of inertia. Masses were applied at the
centre of gravity at each floor level above grade. Gravity loads and seismic masses are given in
Appendix D.
Table 4.9 Gravity loads
Use Live Loads Superimposed Dead Loads Parking 1.9 kPa 0.1 kPa Level 1 Retail 4.8 kPa 5.3 kPa Level 1 Podium 4.8 kPa 16.8 kPa Tower Core 4.8 kPa 1.3 kPa Residential/hotel 1.9 kPa 1.3 kPa Mechanical/Electrical 445 kN at roof level Roof 1.2 kPa 1.3 kPa External Cladding 0.7 kPa (wall area)
The PEER/ATC design team were provided with seven sets of ground motions whose
spectra were matched to a site-specific SLE design spectrum for the case study building. The
target design spectrum was based on a return period of 25-years for 2.5 percent critical damping.
The historical records were modified in both the frequency and time domains to match the design
spectrum for periods between 0.01 seconds and 15.0 seconds. For the performance assessment
phase of the PEER/ATC study, historical ground motion records were scaled in amplitude to
CHAPTER 4: Case Study 107
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
match the 5 percent critically damped site specific spectra at five hazard levels: OVE (4975 year
return period), MCE (2475 year return period), DBE (475 year return period), SLE43 (43 year
return period), and SLE25 (25 year return period). A combination of synthetic and historical
records was used at the very rare OVE hazard level. Only the SLE43, DBE, and MCE hazard
levels were investigated in the present thesis. The target design spectra are shown in Figure 4.10.
The historical ground motions and scaling procedure used in the present study are presented in
Section 4.3.
Wind loading criteria were also considered in the PEER/TBI study but did not govern any
aspect of the design (PEER/ATC, 2011). The ASCE 7 wind design parameters are listed in Table
4.10. The alternative designs presented in this thesis have been checked for compliance with drift
criteria set out in the NBCC (NRCC, 2010).
Figure 4.10 Site specific spectra (5% critically damped)
Table 4.10 ASCE 7 wind loading criteria (after PEER/ATC, 2011)
Parameter Value Basic wind speed, 3 second gust (50 year return) (E V) 139 km/h Basic wind speed, 3 second gust (10 year return) (E�V) 108 km/h Exposure Category B Occupancy Category II Importance Factor (DA) 1.0 Topographic Factor (S©}) 1.0 Enclosure Classification Enclosed Internal Pressure Coefficient (7�F^) 0.18 Mean Roof Height (h) 124.9 m
0 1 2 3 4 5 6 7 80
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
T (sec)
Sa
(g
)
SLE SpectrumDBE SpectrumMCE Spectrum
CHAPTER 4: Case Study 108
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
4.3 Ground Motion Scaling
The case study building site is located in Los Angeles and is surrounded by active faults.
Thus, the seismic hazard includes both near-field and far-field contributions. Seven pairs of
horizontal ground motion records were used to assess the seismic performance of the reference
structure and the alternative designs. The historical records, listed in Table 4.11, were procured
from the PEER Ground Motion Database (PEER, 2010b). The ground motions were amplitude-
scaled to match the 5 percent critically damped target spectra at the SLE, DBE and MCE hazard
levels in accordance with the scaling requirements of ASCE 7 (2010). The basic steps of the
scaling procedure used are as follows:
• The square root of the sum of the squares (SRSS) of the two horizontal components is
computed for each record
• A unique scale factor (J��^) is applied to each of the records such that the SRSS of
the two horizontal components has the same spectral acceleration as the design
spectrum at the fundamental period of vibration of the structure, b
• A second scale factor (��) is applied to the entire suite of records such that the mean
of the SRSS of the seven records is not less than 1.17 times the design spectrum for
periods ranging from 0.2b to 1.5b
The records were scaled using a preliminary estimate of the fundamental period of
vibration of the structure, b, of 4.8 seconds. Because the fundamental periods are different in the
North-South (bª� = 3.7 seconds) and East-West (bT� = 4.8 seconds) directions, the second scale
factor, ��, was computed using a scaling range of 0.2bª� to 1.5bT�. The scaling factors for the
SLE, DBE, and MCE hazard levels are listed in Table 4.12. The scaled spectra are shown in
Figure 4.11, Figure 4.12, and Figure 4.13. In order to reduce analysis time, a time step of 0.04
seconds was used for all analyses, regardless of the original sampling rate of the individual
record.
CHAPTER 4: Case Study 109
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Table 4.11 Historical ground motion records
Record Name Region Station Magnitude R (km) Superstition Hills California Parachute Site Test 6.54 0.9
Denali Alaska Pump Station #9 7.90 54.8 Northridge California Sylmar Converter Station 6.69 5.3
Kocaeli Turkey Izmit 7.51 7.2 Landers California Yermo 7.28 23.6 Duzce Turkey Duzce 7.14 6.6
Loma Prieta California Saratoga Aloha 6.93 8.5
Table 4.12 Ground motion scale factors
Scale Factors Record Name SLE DBE MCE
Superstition Hills 0.30 1.02 1.24 Denali 0.75 2.54 3.09
Northridge 0.30 1.02 1.24 Kocaeli 0.58 1.98 2.41 Landers 0.41 1.38 1.68 Duzce 0.21 0.73 0.89
Loma Prieta 0.72 2.46 2.99
Figure 4.11 SLE scaled ground motion spectra
0 2 4 6 80
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
T (sec)
Sa
(g
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean SpectrumSLE 5% Damped Spectrum
CHAPTER 4: Case Study 110
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 4.12 DBE scaled ground motion spectra
Figure 4.13 MCE scaled ground motion spectra
0 2 4 6 80
0.5
1
1.5
2
2.5
3
T (sec)
Sa
(g
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean SpectrumDBE 5% Damped Spectrum
0 2 4 6 80
0.5
1
1.5
2
2.5
3
3.5
T (sec)
Sa
(g
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean SpectrumMCE 5% Damped Spectrum
CHAPTER 4: Case Study 111
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
4.4 Performance of Reference Structure
In this Section, the results from nonlinear time history analyses of the reference structure
using seven ground motions at the SLE, DBE, and MCE hazard levels are presented. Drift levels
under SLS wind loading, calculated using the dynamic procedure set out in the NBCC (NRCC,
2010) are also presented.
4.4.1 Seismic Performance of Reference Structure
The seismic performance of the reference structure was investigated using nonlinear time
history analysis at the SLE, DBE, and MCE hazard levels. Each pair of scaled ground motion
components was applied simultaneously in orthogonal directions and then rotated by 90 degrees,
for a total of 14 analyses at each hazard level. The results from the ground motion orientation
which produced the most severe response were taken for each record. The performance of the
structure was defined based on mean response quantities from the seven ground motion records.
The direction of the ground motion records was selected arbitrarily, in order to avoid any bias in
the results. The component orientations are summarized in Table 4.13. Three engineering
demand parameters were selected as a basis for evaluating the seismic performance at each
hazard level – peak floor accelerations, maximum interstorey drifts, and maximum core wall
shears. Maximum response quantities at the SLE, DBE, and MCE hazard levels are summarized
in Figure 4.14, Figure 4.15, and Figure 4.16, respectively.
Table 4.13 Ground motion component orientations
Orientation 1 Orientation 2 East-West
Component North-South Component
East-West Component*
North-South Component
Superstition Hills 225 315 315 225 Denali 013 103 103 013
Northridge SCS 052 142 142 052 Loma Prieta 000 090 090 000
Duzce 180 270 270 180 Landers 270 360 360 270 Kocaeli 090 180 180 090
*The East-West component was applied in the negative X-Direction in Orientation 2
CHAPTER 4: Case Study 112
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
East-West Direction
North-South Direction
Figure 4.14 Reference structure SLE performance
East-West Direction
North-South Direction
Figure 4.15 Reference structure DBE performance
0 0.2 0.4 0.6 0.8 1
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 0.5 1 1.5 20
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Supers""on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 10 20 30 40 50
0
20
40
60
80
100
120
Maximum Core Wall Shear (MN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 0.2 0.4 0.6 0.8 1
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 0.5 1 1.5 20
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Supers""on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 10 20 30 40 50
0
20
40
60
80
100
120
Maximum Core Wall Shear (MN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 0.5 1 1.5 2
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 1 2 3 4 50
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Supers""on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 20 40 60 80 100
0
20
40
60
80
100
120
Maximum Core Wall Shear (MN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 0.5 1 1.5 2
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 1 2 3 4 50
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Supers""on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 20 40 60 80 100
0
20
40
60
80
100
120
Maximum Core Wall Shear (MN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
CHAPTER 4: Case Study 113
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
East-West Direction
North-South Direction
Figure 4.16 Reference structure MCE performance
The maximum response quantities at the SLE hazard level, taken as the mean of the
seven ground motion records, are listen in Table 4.14. As shown in Figure 4.14, the interstorey
drift limit of 0.5 percent was exceeded in the East-West direction at the SLE hazard level. A
maximum interstorey drift of 0.63 percent was observed. However, this analysis was based on a
43-year return period, whereas the design team used a 25-year return period for the serviceability
analysis. The design team computed maximum interstorey drifts of 0.25 percent and 0.20 percent
in the East-West and North-South directions, respectively, from an elastic serviceability analysis.
Table 4.14 Maximum response quantities – SLE level
Direction
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
East-West 0.33 27,600 0.63 North-South 0.33 32,500 0.49
The maximum response quantities at the DBE hazard level, taken as the mean of the
seven ground motion records, are listen in Table 4.15. It can be seen from the results that the
0 0.5 1 1.5 2
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 1 2 3 4 5 60
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Supers""on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 20 40 60 80 100
0
20
40
60
80
100
120
Maximum Core Wall Shear (MN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 0.5 1 1.5 2
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 1 2 3 4 5 60
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Supers""on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 20 40 60 80 100
0
20
40
60
80
100
120
Maximum Core Wall Shear (MN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
CHAPTER 4: Case Study 114
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
core wall shear demands at the DBE hazard level are approximately twice as large as the core
wall shear demands at the SLE hazard level. No specific performance objectives were set for the
DBE hazard level.
Table 4.15 Maximum response quantities – DBE level
Direction
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
East-West 0.86 56,200 1.95 North-South 0.72 56,400 1.46
The maximum response quantities at the MCE hazard level, taken as the mean of the
seven ground motion records, are listen in Table 4.16. The interstorey drifts shown in Figure
4.16 indicate that the Collapse Prevention acceptance criterion of 3 percent was met at the MCE
hazard level. Maximum interstorey drifts of 2.5 percent and 1.8 percent were observed in the
East-West and North-South directions, respectively. The design team from MKA computed
maximum interstorey drifts of 2.0 percent and 1.3 percent in the East-West and North-South
directions, respectively, at the MCE hazard level. This discrepancy may be a result of the
differences between the ground motion records and scaling techniques used.
Table 4.16 Maximum response quantities – MCE level
Direction
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
East-West 1.04 66,100 2.50 North-South 0.81 62,000 1.78
It was reported that the shear walls were designed for approximately 3 to 3.5 times the
shear demands computed from the elastic serviceability (SLE) analysis conducted in ETABS
(PEER/ATC, 2011). The service-level shear demands are larger in this case study, as a result of
the longer return period used. The MCE level shear demands shown in Figure 4.16 are between 2
and 3 times larger than the service level demands shown in Figure 4.14. Core wall shear
demands at the MCE hazard level governed the selection of wall thickness (PEER/ATC, 2011).
The maximum wall shear stresses approached the allowable limit set out in ACI (2008). The
CHAPTER 4: Case Study 115
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
design team computed maximum core wall shears of approximately 57,800 kN in the East-West
direction and 55,600 kN in the North-South direction at the MCE hazard level.
Figure 4.17 shows a schematic plan of the RC core indicating the nomenclature assigned
to the lintel locations. The maximum coupling beam rotations at the MCE level in each of the six
lintel locations are shown in Figure 4.18. As shown in the Figure, none of the coupling beams
surpassed the allowable rotation limit of 0.06 radians (indicated by the solid red line). Based on
the fragility curves developed by Naish (2010) for diagonally reinforced coupling beams with
high aspect ratios (2.0 < ��/ℎ < 4.0), the need for repair is anticipated beyond a rotation of 0.02
radians. The number of coupling beams expected to require repair at the MCE hazard level is
indicated in Figure 4.18. As shown in the Figure, the majority of the coupling beams are
expected to require repair following an MCE level event.
Figure 4.17 Lintel nomenclature
The results from the nonlinear time-history analyses of the reference structure are in
reasonable agreement with the analysis results reported by MKA (PEER/ATC, 2011). At the
SLE hazard level, the peak demand parameters were found to be significantly higher than those
computed by MKA. This can be explained by the difference in return periods used for the SLE
level analyses. The design team used a return period of 25 years and a 43-year return period is
used in this study. Additional discrepancies may be a result of the differences between the
N
L32
L30
L22
L20
L10
L01
CHAPTER 4: Case Study 116
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
ground motion records, scaling methods, and modelling assumptions used. Although the same
return period (2,475-years) was used for the MCE analyses, interstorey drifts and core wall shear
demands were found to be somewhat higher than those reported by MKA. This may be a result
of the differences between the ground motion records and scaling methods, as well as the
modelling assumptions used. This result highlights the sensitivity of the analysis results to the
selection and scaling of ground motion records and to the selection of nonlinear modelling
assumptions.
a) L01 b) L20 c) L22
d) L10 e) L30 f) L32
Figure 4.18 Coupling beam rotations – MCE level
4.4.2 Response of Reference Structure to Wind Loading
Service level wind loads were computed in accordance with the dynamic procedure set
out in NBCC (NRCC, 2010). An elastic analysis model of the reference structure was created in
Perform-3D using the cracked section properties listed in Table 4.17. A damping ratio, �, of 1.5
percent was assumed for both the East-West and North-South directions. The fundamental
periods of vibration, b, were computed using Perform-3D as 4.39 seconds and 2.29 seconds in
the East-West and North-South directions, respectively. The gust effect factors, ��, which
0 0.05 0.1 0.15 0.2
0
20
40
60
80
100
120
Maximum Coupling Beam Rota!ons (rad)
He
igh
t (m
)
37 Beams Require Repair
Supers!!on HillsDenaliNorthridgeLoma PrietaDuzceLandersKocaeliMeanRepair Required
0 0.05 0.1 0.15 0.2
0
20
40
60
80
100
120H
eig
ht
(m)
36 Beams Require Repair
Supers!!on HillsDenaliNorthridgeLoma PrietaDuzceLandersKocaeliMeanRepair Required
Maximum Coupling Beam Rota!ons (rad)0 0.05 0.1 0.15 0.2
0
20
40
60
80
100
120
He
igh
t (m
)
37 Beams Require Repair
Supers!!on HillsDenaliNorthridgeLoma PrietaDuzceLandersKocaeliMeanRepair Required
Maximum Coupling Beam Rota!ons (rad)
0 0.05 0.1 0.15 0.2
0
20
40
60
80
100
120
Maximum Coupling Beam Rota!ons (rad)
He
igh
t (m
)
37 Beams Require Repair
Supers!!on HillsDenaliNorthridgeLoma PrietaDuzceLandersKocaeliMeanRepair Required
0 0.05 0.1 0.15 0.2
0
20
40
60
80
100
120
Maximum Coupling Beam Rota!ons (rad)
He
igh
t (m
)
36 Beams Require Repair
Supers!!on HillsDenaliNorthridgeLoma PrietaDuzceLandersKocaeliMeanRepair Required
0 0.05 0.1 0.15 0.2
0
20
40
60
80
100
120
He
igh
t (m
)
36 Beams Require Repair
Supers!!on HillsDenaliNorthridgeLoma PrietaDuzceLandersKocaeliMeanRepair Required
Maximum Coupling Beam Rota!ons (rad)
CHAPTER 4: Case Study 117
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
account for the dynamic component of wind loading, were computed as 2.36 and 2.15 in the
East-West and North-South directions, respectively. As expected, the structure was found to be
more dynamically sensitive in the less stiff East-West direction. The NBCC (NRCC, 2010)
specifies a gust effect factor of 2.0 for rigid or non-dynamically-sensitive structures. The wind
loading parameters are listed in Table 4.18.
The service-level base shears were computed as 4,030 kN and 3,670 kN in the East-West
and North-South directions, respectively. The deformed shapes of the RC core in the East-West
and North-South directions when subjected to static equivalent SLS wind loads and gravity loads
are shown in Figure 4.19. Interstorey drifts are plotted in Figure 4.20. As shown in the Figure,
the interstorey drifts were significantly lower than the NBCC allowable limit of 0.2 percent
(1/500) in both the East-West and North-South directions.
Table 4.17 SLS wind cracked section properties
��� �� Core Walls 1.0@� 0.9D�
Coupling Beams 1.0@� 0.5D� Basement Walls 1.0@� 1.0D�
Floor Slabs 0.8@� 0.5D�
Table 4.18 NBCC wind loading parameters
Parameter Value Mean height 124.9 m �« 0.75 (SLS) ¬ 0.378 kPa w 0.015
Exposure B (rough terrain) s (EW) 0.228 Hz s (NS) 0.435 Hz ®¯ (EW) 2.36 ®¯ (NS) 2.15
CHAPTER 4: Case Study 118
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
a) East-West Direction b) North-South Direction
Figure 4.19 Deformed shape under NBCC SLS wind loads
a) East-West Direction b) North-South Direction
Figure 4.20 Interstorey drifts under NBCC SLS wind loads
4.5 Development of Alternative Design Solution
As discussed in Section 4.4, the reference structure meets the performance objectives set
out by the designers for the SLE and MCE hazard levels. In order to investigate the performance
of a seismic-critical structure designed using VCDs, an alternative design of the case study
building was developed by introducing VCDs and steel coupling beams in lieu of the RC
coupling beams. A case study was carried out in which a series of design configurations were
analyzed, in order to better understand the complex effects of the VCDs on the nonlinear
0 50 100 150 200
0
20
40
60
80
100
120
Displacement (mm)
He
igh
t (m
)
0 50 100 150 200
0
20
40
60
80
100
120
Displacement (mm)
He
igh
t (m
)
0 0.05 0.1 0.15 0.2
0
20
40
60
80
100
120
Interstorey Dri! (%)
He
igh
t (m
)
0 0.05 0.1 0.15 0.2
0
20
40
60
80
100
120
Interstorey Dri! (%)
He
igh
t (m
)
CHAPTER 4: Case Study 119
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
dynamic response of a high-rise RC core wall structure subjected to seismic loading at different
hazard levels.
It is well understood from the work of Montgomery (2011) that the replacement of RC
coupling beams with VCDs can affect both the damping and the stiffness of a high-rise structure.
If the VCDs are less stiff than RC coupling beams, the degree of coupling between the core walls
is decreased when the coupling beams are replaced by VCDs. This results in a reduction in the
lateral stiffness of the structure and therefore an elongation of the fundamental periods of
vibration. This period elongation has a similar effect to that of installing isolators at the base of a
structure. In a base-isolated system, the isolators have a much lower lateral stiffness than the
superstructure which causes a shift in the natural period of the system beyond the predominant
periods of typical earthquakes (Christopoulos and Filiatrault, 2006). The other key component of
an isolated system is the added damping provided by an energy-dissipation mechanism. This
added damping limits the forces transmitted to the superstructure and controls excessive
displacements. A similar phenomenon is observed in high-rise buildings designed using VCDs.
The increase in period results in lower forces and accelerations, and the lateral drifts are
controlled by the added damping provided by the VCDs. Elongation of the fundamental periods
of vibration also causes an increase in the dynamic response of the structure to wind loading
which must be counteracted by the added viscous damping.
In this Section, the wind and seismic performance of six VCD configurations
implemented in the case study building are investigated. The VCD configurations are listed in
Table 4.19. In Configuration A, four of the RC coupling beams at each floor were replaced with
4-VCDs placed in parallel. This design was intended to add damping to the structure without
significantly affecting the fundamental periods of vibration of the building. In order to facilitate
construction and repair in the event of a severe earthquake, the two RC coupling beams not
replaced by VCDs at each floor level were replaced by shear-critical steel coupling beams. In
Configuration B, four of the RC coupling beams at each floor were replaced with 3-VCDs in
parallel. In Configuration C 2-VCDs were used to replace the coupling beams in each of four
lintel locations, and in Configuration D a single VCD was used to replace the coupling beams in
each of four lintel locations. As discussed in Section 4.6, as the lateral stiffness of the structure
CHAPTER 4: Case Study 120
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
was reduced by reducing the number of VCDs in each lintel location the seismic performance
was improved at both the SLE and MCE hazard levels.
Although Configuration D resulted in the largest improvements in seismic performance,
the VE material reached shear strains surpassing the allowable limit set by the material
manufacturer. In order to reduce the VE material strains, Configuration E was developed. In
Configuration E, four of the coupling beams at floors 1-14 were replaced with 2-VCDs placed in
parallel, and four of the coupling beams at floors 15-41 were replaced with a single VCD.
Although the VE material shear strains were effectively reduced in Configuration E, the seismic
performance was somewhat compromised due to the added stiffness in the lower portion of the
building. A final Configuration, Configuration F, was investigated in which all of the RC
coupling beams were replaced with a single VCD. In order to reduce the strain in the VE
material, the shear fuse activation force was reduced and the thickness of the VE material was
increased. This Configuration yielded the best seismic performance at both the SLE and MCE
hazard levels, while meeting the SLS wind drift criteria set out in NBCC (NRCC, 2010).
Table 4.19 VCD configurations
Configuration Description A 4-VCDs x 4 lintel locations per storey B 3-VCDs x 4 lintel locations per storey C 2-VCDs x 4 lintel locations per storey D 1-VCDs x 4 lintel locations per storey E 2-VCDs x 4 lintel locations per storey in bottom 1/3 of building,
1-VCD x 4 lintel locations per storey in top 2/3 of building F 1-VCDs x 6 lintel locations per storey
4.5.1 Design and Modelling of VCDs
A custom VCD design was provided by Kinetica Dynamics for the case study building.
In order to accommodate the relatively short spans of the coupling beams in the case study
building, the VCD was designed using a shear-critical seismic fuse detail. The proposed design is
illustrated in Figure 4.21. Since global structural performance was the primary focus of the case
study, a detailed VCD design was not carried out. The cast-in-place detail shown in the Figure
CHAPTER 4: Case Study 121
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
was selected because of architectural constraints, although other connection details are available
as discussed in Montgomery (2011). A possible alternative connection detail is shown in Figure
4.22. In this design, a post-tensioned connection detail is introduced at one end of the VCD. This
detail would facilitate the replacement of the shear fuse component if it were damaged during a
major seismic event. The VCD design philosophy requires that any potential damage be
restricted to the shear fuse.
The VCD was designed using 30 layers of ISD:111H VE material, with dimensions of
460(W)x350(L)x5(t) mm. The VE material layers are bonded to 9 mm thick layers of steel plate,
anchored at alternating ends to built-up steel sections. The two outermost plates have a thickness
of 12 mm. The steel plates are connected to the built-up sections using filler plates and high-
strength pre-tensioned bolts. A slip-critical bolted connection is required for all design loading
conditions. The shear-critical fuse was designed using two built-up I-sections in parallel. In the
preliminary VCD design, the built-up sections had a web thickness of 12 mm, 35 mm thick
flanges, and an overall depth of 590 mm. The VCDs have clearspans of 1295 mm in the East-
West direction and 1600 mm in the North-South direction. The fuse section has a span of 585
mm in the East-West direction and 885 mm in the North-South direction. The I-beam cross-
sections, VE material dimensions, and bolted sections are identical in both VCD designs.
If an embedded connection detail is used, special transverse and longitudinal reinforcing
steel details are required in the boundary regions of the RC walls. El Tawil et al. (2010) provide
recommendations for boundary reinforcement detailing of hybrid coupled walls. A typical
embedded connection detail is shown in Figure 4.23. Additionally, vertical transfer bars are
typically welded to the steel beams to improve the embedment capacity. The transfer bars may
be connected to the flanges of the embedded beam using mechanical half-couplers or they may
pass through the flanges and be welded to the web. In the plastic hinge region, transverse
confinement reinforcement must be detailed to pass through the web of the embedded steel
beams. For the purpose of the case study, the core wall reinforcement was not altered to
accommodate the replacement of the coupling beams with VCDs. For a practical application, the
RC slabs must also be detailed to allow for significant shear deformations in the VCDs.
Montgomery (2011) provides recommendations for slab connection details.
CHAPTER 4: Case Study 122
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 4.21 Proposed VCD solution for case study building
Figure 4.22 Alternative connection detail
VEM: ISD111H
460(W)x350(L)x5(t)x30 layers
Shear Fuse
Detail
PLAN VIEW
ELEVATION VIEW
Web
S!ffeners
Embedded
Por!on
RC Wall
End Plate
Post-
Tensioning
Embedded
Por!on
CHAPTER 4: Case Study 123
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 4.23 Boundary region reinforcing steel (after El-Tawil et al., 2010)
As shown in Section 3.2.4, the Generalized Maxwell Model can be implemented in
Perform-3D to accurately capture the nonlinear response of the VE material. For the purpose of
this case study, nonlinear models of the VCD elements were developed as described in Section
3.2.4 and Section 3.4.1. For the purpose of the case study, a constant VE material temperature of
24 C was assumed. The Generalized Maxwell Model was comprised of elastic bar elements and
fluid damper elements, as shown in Figure 4.24. The modelling parameters were determined
based on the ISD:111H material properties given in Table 3.5. The parameters used to define the
elastic bar and fluid damper elements are listed in Table 4.20 and Table 4.21, respectively. The
steel assembly, including the shear-critical fuse, was modelled as an elastic beam element in
series with a nonlinear shear hinge. The elastic stiffness of the steel assembly, SV, was provided
by Kinetica Dynamics. The backbone curve for the shear fuse, shown in Figure 4.25, was
defined based on available guidance for shear links in EBFs (see Section 3.2.3). A post-yield
stiffness of 0.06SV was assumed. The modelling parameters used to define the shear force-
displacement backbone curves for the steel assemblies in the North-South and East-West
directions are listed in Table 4.22.
Figure 4.24 VE material model
A A
B BSec�on A Sec�on B
K0
K1
K2
K3
K4
C1
C2
C3
C4
FVE
Kbig
C0
uVE Fluid Damper
Element
Elastic Bar
Element
CHAPTER 4: Case Study 124
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Table 4.20 Elastic bar element properties (T = 24 C)
Element ¡ (kN/mm) ¦ (mm) � (mm2) u (kN/mm2) K0 60.2 100 100 60.2 K1 251.6 50 100 125.8 K2 530.6 50 100 265.3 K3 7954.6 50 100 3976.8 K4 84.0 50 100 42.0 Kbig 106 50 100 500x103
Table 4.21 Fluid damper element properties (T = 24 C)
Element C (kNs/mm) L (mm) C0 0.0543 50 C1 25.1 50 C2 9.13 50 C3 8.75 50 C4 94.8 50
Figure 4.25 Shear fuse backbone curve
Table 4.22 Steel assembly modelling parameters
Direction
¡r(kN/mm)
¢£(kN)
¢¤(kN)
¢¥(kN)
¤(mm)
¦(mm)
¥(mm)
§(mm)
EW 592 2880 3750 2300 21.8 96.9 105 111 NS 331 2880 3750 2300 39.9 150 163 172
0 5 10 15 20 250
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Rota on (%)
V/V
y,e
xp
(θy, V
y,exp)
(θu, V
u,exp) (θ
l, V
u,exp)
(θr, V
r,exp)
Vy,exp
= 1.2Vp
Vu,exp
= 1.3Vy,exp
Vr,exp
= 0.8Vy,exp
K0
CHAPTER 4: Case Study 125
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
4.5.2 Parametric Study
Several VCD configurations were investigated in order to determine the optimal number
and placement of the VCDs for the alternative design. In order to reduce analysis time during the
preliminary design phase, three representative ground motion pairs were selected. The
displacement and acceleration spectra of the selected records are shown in Figure 4.26. This
subset of the seven scaled pairs of records was used to develop trends in the seismic performance
of the structure as the VCD configuration changed. Only the SLE and MCE hazard levels were
investigated during the preliminary design phase. A complete nonlinear time history analysis was
then carried out to assess the performance of the final design solution, Configuration F, at the
SLE, DBE, and MCE hazard levels. Equivalent viscous damping was defined as 2.5 percent
Rayleigh mass and stiffness proportional damping at periods of 1 and 5 seconds in all analysis
models.
Figure 4.26 Scaled ground motion spectra
0 1 2 3 4 5 6 7 80
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
T (sec)
Sd
(g
)
5% Damped Spectral Displacement (MCE)
EW Direc!on
Supers!!on Hills 225Loma Prieta 000Duzce 180Mean of 3 recordsMean of 7 records
0 1 2 3 4 5 6 7 80
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
T (sec)
Sd
(g
)5% Damped Spectral Displacement (MCE)
NS Direc!on
Supers!!on Hills 315Loma Prieta 090Duzce 270Mean of 3 recordsMean of 7 records
0 1 2 3 4 5 6 7 80
0.5
1
1.5
2
2.5
3
3.5
T (sec)
Sa
(g
)
5% Damped Spectral Accelera!on (MCE)
EW Direc!on
Supers!!on Hills 225Loma Prieta 000Duzce 180Mean of 3 recordsMean of 7 records
0 1 2 3 4 5 6 7 80
0.5
1
1.5
2
2.5
3
3.5
T (sec)
Sa
(g
)
5% Damped Spectral Accelera!on (MCE)
NS Direc!on
Supers!!on Hills 315Loma Prieta 090Duzce 270Mean of 3 recordsMean of 7 records
CHAPTER 4: Case Study 126
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Acceptance criteria for the alternative design at the SLE and MCE hazard levels are listed
in Table 4.23 and Table 4.24, respectively. The steel coupling beams and VCD shear fuses are
intended to remain elastic at the SLE level. ASCE 41 (2006) specifies a maximum plastic
rotation of 0.16 radians for shear-critical EBF links at the Collapse Prevention performance
level. However, the more conservative plastic rotation limit of 0.08 radians, set out in CAN/CSA
S16 (2009), was applied to the steel coupling beams and VCD shear fuses in this case study. A
maximum allowable strain of 400 percent is specified by the manufacturers of the ISD:111H VE
material (Montgomery, 2011). Compliance with all acceptance criteria was based on mean
results from the seven ground motion pairs. Additionally, an upper limit of 600 percent strain in
the VE material was set for individual ground motion records at the MCE hazard level.
Table 4.23 SLE acceptance criteria
Demand Parameter Limit Interstorey Drift 0.5% Steel Coupling Beam Rotations Elastic VCD Shear Fuse Rotations Elastic Core Wall Flexure Essentially Elastic Core Wall Shear Elastic
Table 4.24 MCE acceptance criteria
Demand Parameter Limit Interstorey Drift 3.0% Steel Coupling Beam Rotations 0.8 rad. VCD Shear Fuse Rotations 0.8 rad. VE Material Strains (Mean of 7 records) 400% VE Material Strains (Maximum) 600% Core Wall Reinforcement Axial Strain
0.05 tension 0.02 compression
Core Wall Concrete Axial Strain 0.015 compression (confined) Core Wall Shear Elastic
4.5.2.1 Configuration A
The intent of Configuration A was to add damping without significantly affecting the
stiffness of the structure, as is typically the objective for wind-sensitive buildings (Montgomery,
2011). Configuration A involved the addition of four VCDs in parallel at four locations at each
CHAPTER 4: Case Study 127
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
floor level. The coupling beams in lintels L01, L10, L22 and L30 were replaced with VCDs, as
illustrated in Figure 4.27. The placement of 4-VCDs in parallel would require a significant
increase in core wall thickness in the embedment regions. The additional core wall thickness was
not accounted for in this preliminary analysis. A detailed design of the embedment region was
not carried out. Because of architectural constraints and the high cost associated with using a
large number of VCDs, this is not likely to be a practical solution for the case study building. It
was therefore examined as a purely theoretical configuration to gain a better understanding of
how the introduction of VCDs affects the response of a seismic-critical RC coupled wall high-
rise structure. Schematic elevations of the core walls are shown in Figure 4.28.
Figure 4.27 Configuration A core wall plans
As discussed previously, in order to provide a modular construction solution, the RC
coupling beams that were not replaced by VCDs were replaced with steel coupling beams. The
steel coupling beams were selected based on the requirement that they remain elastic under wind
loading and during an SLE level seismic event. This was achieved by selecting I-sections that
approximately matched the yield strength, E5,°±², of the RC coupling beams. The properties of
the RC coupling beams replaced with steel coupling beams are given in Table 4.25. The
properties of the shear-critical steel coupling beams are listed in Table 4.26. The steel coupling
beams are significantly less stiff than the RC coupling beams, resulting in a lower coupling ratio
and a lower lateral stiffness in the North-South direction. The steel coupling beams were
modelled using the same theoretical backbone curve as the shear fuse components of the VCDs
(see Figure 4.25). The steel coupling beam modelling parameters are listed in Table 4.27.
Storeys 1-41
VCD
Steel Link
Storeys B4-GND
N
L32
L30
L22
L20
L10
L01
CHAPTER 4: Case Study 128
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 4.28 Configuration A core wall elevations
B4
B3
B2
B1
GND
L2
L3
L4
L5
L6
L7
L8
L9
L10
L11
L12
L13
L14
L15
L16
L17
L18
L19
L20
L21
L22
L23
L24
L25
L26
L27
L28
L29
L30
L31
L32
L33
L34
L35
L36
L37
L38
L39
L40
L41
L42
PH
TOC
North & South Eleva!ons East & West Eleva!ons
Steel
Coupling
Beam
(typ.)
VCD
(typ.)
CHAPTER 4: Case Study 129
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Table 4.25 Properties of RC coupling beams replaced with steel coupling beams
Designation
Number
¡r(kN/mm)
�³,�.´
(kN) �µ,�.´
(kN) 2B 1 414 722 960 3B 2 311 1080 1440 4B 9 311 1740 2320 6B 2 414 1740 2320 7B 15 355 2130 2830 8B 1 414 2130 2830 9B 3 355 2610 3470 10B 3 414 2610 3470 12B 9 414 2840 3770
Table 4.26 Properties of steel coupling beams
RC Beam Designations
I-Section Designation
¡r(kN/mm)
�³,�.´
(kN) �µ,�.´
(kN) 2B, 3B, 4B, 6B W530x165 178 1770 2300
7B & 8B W530x219 241 2370 3080 9B, 10B, 12B W530x300 334 3120 4060
Table 4.27 Steel coupling beam modelling parameters
Direction
¡r(kN/mm)
¢£(kN)
¢¤(kN)
¢¥(kN)
¤(mm)
¦(mm)
¥(mm)
§(mm)
W530x165 178 1770 2300 1410 46.6 244 261 276 W530x219 241 2370 3080 1890 46.3 244 261 276 W530x300 334 3120 4060 2500 44.0 245 261 276
Mean response values from the three ground motions were used to compare the reference
structure and each of the alternative design configurations, in order to establish trends in global
performance. Configuration A exhibited improved seismic performance at the SLE hazard level
when compared with the reference structure, as shown in Figure 4.29. In the East-West direction,
mean interstorey drifts were reduced by up to 19 percent, core wall shears were reduced by up to
4 percent, and peak floor accelerations were reduced by up to 16 percent. In the North-South
direction, mean interstorey drifts were reduced by up to 33 percent, core wall shears were
reduced by up to 18 percent, and peak floor accelerations were reduced by up to 4 percent. A
decline in seismic performance was observed at the MCE hazard level, with increases of up to 10
percent and 13 percent in core wall shears in the East-West and North-South directions,
respectively. A comparable performance was nonetheless achieved with regard to interstorey
CHAPTER 4: Case Study 130
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
drifts and peak floor accelerations, as shown in Figure 4.30. An increase in core wall shear stress
at the MCE hazard level could result in the need for additional transvers reinforcing steel or even
increased core wall thicknesses. Such a requirement would be considered a major draw-back for
architects and building owners.
Figure 4.31 shows hystereses from lintel location L10 at the 10th floor level, obtained
under the Loma Prieta record scaled to the MCE hazard level. As shown, the shear fuse remained
elastic throughout the MCE level event and the VCDs exhibited a purely viscoelastic response.
Figure 4.32 shows the maximum VE material strains and VCD shear fuse rotations in two lintel
locations at the MCE hazard level. As shown in the Figures, the mean VE material strains in both
the East-West and North-South directions reached a maximum of approximately 200 percent, or
about half of the allowable limit of 400 percent. The shear fuses were not activated in any of the
VCDs.
East-West Direction
North-South Direction
Figure 4.29 Global performance – SLE level
0 0.2 0.4 0.6 0.8 1
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Reference StructureConfigura!on A
0 0.2 0.4 0.6 0.8 10
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Reference StructureConfigura#on A
0 1 2 3 4 5
x 104
0
20
40
60
80
100
120
Maximum Core Wall Shear (kN)
He
igh
t (m
)
Reference StructureConfigura"on A
0 0.2 0.4 0.6 0.8 1
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Reference StructureConfigura!on A
0 0.2 0.4 0.6 0.8 10
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Reference StructureConfigura#on A
0 1 2 3 4 5
x 104
0
20
40
60
80
100
120
Maximum Core Wall Shear (kN)
He
igh
t (m
)
Reference StructureConfigura"on A
CHAPTER 4: Case Study 131
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
East-West Direction
North-South Direction
Figure 4.30 Global performance – MCE level
a) VCD Response b) VEM Response c) Steel Response
Figure 4.31 VCD hysteresis
Figure 4.33 a) shows the force-displacement response of a W530x300 steel coupling
beam located at the 10th floor level. The response shown in the Figure corresponds to the Loma
Prieta record, scaled to the SLE hazard level. The link remained elastic during the SLE level
event, as intended in the design. Figure 4.33 b) shows the maximum steel coupling beam
rotations in one of the lintel locations at the SLE hazard level. As anticipated, all of the coupling
beams remained elastic. Figure 4.34 a) shows the hysteresis of a W530x300 steel coupling beam
located at the 10th floor level, during the Loma Prieta ground motion record scaled to the MCE
0 0.5 1 1.5 2
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Reference StructureConfigura!on A
0 0.5 1 1.5 2 2.5 3 3.50
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Reference StructureConfigura#on A
0 2 4 6 8 10
x 104
0
20
40
60
80
100
120
Maximum Core Wall Shear (kN)
He
igh
t (m
)
Reference StructureConfigura"on A
0 0.5 1 1.5 2
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Reference StructureConfigura!on A
0 0.5 1 1.5 2 2.5 3 3.50
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Reference StructureConfigura#on A
0 2 4 6 8 10
x 104
0
20
40
60
80
100
120
Maximum Core Wall Shear (kN)
He
igh
t (m
)
Reference StructureConfigura"on A
−20 −10 0 10 20−15
−10
−5
0
5
10
15
Displacement (mm)
Fo
rce
(M
N)
−20 −10 0 10 20−15
−10
−5
0
5
10
15
Displacement (mm)
Fo
rce
(M
N)
−20 −10 0 10 20−15
−10
−5
0
5
10
15
Displacement (mm)
Fo
rce
(M
N)
CHAPTER 4: Case Study 132
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
hazard level. Figure 4.34 b) shows the maximum plastic steel coupling beam rotations in one of
the lintel locations at the MCE hazard level. Plastic deformations were observed in all of the
steel coupling beams. Based on the fragility curves developed by Gulec et al. (2011) for shear-
critical EBF links, the need for repair of a shear fuse is anticipated beyond a plastic rotation of
0.04 radians. Therefore, the need for repair of any of the steel coupling beams is not anticipated.
None of the beams surpassed the plastic rotation limit of 0.08 radians. It should also be noted
that the assumption of the requirement for repair of shear fuses having surpassed 0.04 radians of
rotation may be overly conservative. The fragility curves proposed by Gulec et al. (2011) were
developed based on results from cyclic tests of shear links for EBFs. These tests involved a large
number of load cycles, whereas the VCD shear fuses undergo a small number of large
displacement excursions during severe seismic events and are therefore likely to sustain less
cumulative damage at the same maximum level of rotation.
Figure 4.32 VCD response – MCE level
0 100 200 300 400 500
0
20
40
60
80
100
120
Maximum VE Material Shear Strain (%)
He
igh
t (m
)
Supers!!on HillsLoma PrietaDuzceMean of 3 Records
0 0.002 0.004 0.006 0.008 0.01
0
20
40
60
80
100
120
Maximum Shear Fuse Rota!on (rad)
He
igh
t (m
)
Supers!!on HillsLoma PrietaDuzceMean of 3 Records
0 100 200 300 400 500
0
20
40
60
80
100
120
Maximum VE Material Shear Strain (%)
He
igh
t (m
)
Supers!!on HillsLoma PrietaDuzceMean of 3 Records
0 0.002 0.004 0.006 0.008 0.01
0
20
40
60
80
100
120
Maximum Shear Fuse Rota!on (rad)
He
igh
t (m
)
Supers!!on HillsLoma PrietaDuzceMean of 3 Records
CHAPTER 4: Case Study 133
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
a)
b)
Figure 4.33 a) Steel coupling beam hysteresis b) Coupling beam rotations – SLE Level
a)
b)
Figure 4.34 a) Steel coupling beam hysteresis b) Coupling beam rotations – MCE Level
Free vibration analysis was used to assess the added damping provided by the VCDs in
Configuration A for serviceability (SLS) level wind loading. Linear elastic models were created
in Perform-3D, using the cracked concrete section properties listed in Table 4.17. The VCDs
were modelled using Generalized Maxwell elements with the properties listed in Table 4.20 and
Table 4.21. A modal damping ratio of 1.5 percent was assigned to all modes of vibration in the
SLS wind models. Uniformly distributed lateral loads were then applied using the ramp function
shown in Figure 4.35, in order to excite the structure in each of the three predominant modes of
vibration. A logarithmic decrement technique was used to estimate the modal damping ratios.
The logarithmic decrement in the $th mode of vibration, �^, is computed as follows (Chopra,
2001):
−150 −100 −50 0 50 100 150−5000
−4000
−3000
−2000
−1000
0
1000
2000
3000
4000
5000
Displacement (mm)
Fo
rce
(k
N)
0 0.002 0.004 0.006 0.008 0.01
0
20
40
60
80
100
120
Maximum Coupling Beam Rota!on (rad)
He
igh
t (m
)
Supers!!on HillsLoma PrietaDuzceMean of 3 Records
−150 −100 −50 0 50 100 150−5000
−4000
−3000
−2000
−1000
0
1000
2000
3000
4000
5000
Displacement (mm)
Fo
rce
(k
N)
0 0.02 0.04 0.06 0.08 0.1 0.12
0
20
40
60
80
100
120
Maximum Plas!c Coupling Beam Rota!on (rad)
He
igh
t (m
)
Supers!!on HillsLoma PrietaDuzceMean of 3 Records
CHAPTER 4: Case Study 134
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
�^ =1c �! Y(��)^(��?F)^_ (4-1)
where (��)^ and (��?F)^ are peak amplitudes and c is the number of free vibration cycles
between the peaks. Displacements were measured at the 30th floor level, in order to avoid any
influence from higher mode effects.
Figure 4.35 Ramp loading function
The three predominant mode shapes are shown in Figure 4.36. The displacement histories
from the free vibration analyses of both the reference structure and Configuration A are shown in
Figure 4.37. The modal periods and damping ratios are listed in Table 4.28. The results of the
free vibration analysis indicate approximately 2 percent added damping in modes 1 and 2.
Approximately 8 percent damping was added in the torsional mode. A small increase in period
was observed in both modes 1 and 2. The periods were increased by approximately 3 percent and
7 percent in modes 1 and 2, respectively. The period was increased by approximately 24 percent
in the torsional mode of vibration.
Table 4.28 SLS wind modal properties
Configuration
Modal Periods Modal Damping Ratios T1
(sec) T2
(sec) T3
(sec) ξ1
(%) ξ2
(%) ξ3
(%) Reference 4.38 3.31 2.17 1.5 1.5 1.5
A 4.50 3.53 2.68 3.4 3.6 9.4
0 20 40 60 80 100Time (s)
Fo
rce
CHAPTER 4: Case Study 135
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
a) EW Direction b) NS Direction c) Torsion
Figure 4.36 Mode shapes
a) EW Direction b) NS Direction c) Torsion
Figure 4.37 Free vibration at 30th floor level
4.5.2.2 Configurations B, C & D
Although Configuration A offers some performance advantages over the reference
structure, the large number of VCDs required would be costly in comparison with the RC
coupling beams. Additionally, this preliminary design configuration resulted in increased core
wall shears at the MCE level, which is undesirable. In order to assess the performance of more
practical design alternatives, several other configurations were developed using fewer VCDs
than Configuration A. Configurations B is similar to Configuration A, but with 3-VCDs in four
lintel locations at each floor level. Configuration C has 2-VCDs per lintel location, and
Configuration D has a single VCD per lintel location. Figure 4.38 shows schematic core wall
plans of Configurations B, C, and D. All elements are identical in the analysis models for
Configurations A, B, C, and D, with the exception of the number of VCDs in each lintel location.
0 20 40 60 80 100−100
−80
−60
−40
−20
0
20
40
60
80
100
Time (s)
Dis
pla
cem
en
t (m
m)
Reference StructureConfigura#on A
0 20 40 60 80 100−60
−40
−20
0
20
40
60
Time (s)
Dis
pla
cem
en
t (m
m)
Reference StructureConfigura#on A
0 20 40 60 80 100−20
−15
−10
−5
0
5
10
15
20
Time (s)R
ota
"o
n (
rad
x10
3)
Reference StructureConfigura"on A
CHAPTER 4: Case Study 136
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 4.39 and Figure 4.40 show mean response values from the subset of three representative
ground motions, at the SLE and MCE levels, respectively.
Figure 4.38 Configurations B, C & D – Schematic
East-West Direction
North-South Direction
Figure 4.39 Global performance – SLE level
The maximum SLE and MCE response quantities, taken as the mean of the three ground
motion records, for configurations A, B, C, and D are listed in Table 4.29 and Table 4.30. The
results indicate that a smaller number of VCDs results in superior seismic performance at both
the SLE and MCE hazard levels. Configuration D, with 1-VCD in each lintel location, provides
VCD
Steel Link
N
Configura"on B Configura"on DConfigura"on C
L32
L30
L22
L20
L10
L01
L32
L30
L22
L20
L10
L01
L32
L30
L22
L20
L10
L01
0 0.2 0.4 0.6 0.8
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Reference StructureConfigura!on BConfigura!on CConfigura!on D
0 0.2 0.4 0.6 0.8 10
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Reference StructureConfigura#on BConfigura#on CConfigura#on D
0 1 2 3 4
x 104
0
20
40
60
80
100
120
Maximum Core Wall Shear (kN)H
eig
ht
(m)
Reference StructureConfigura"on BConfigura"on CConfigura"on D
0 0.2 0.4 0.6 0.8
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Reference StructureConfigura!on BConfigura!on CConfigura!on D
0 0.2 0.4 0.6 0.8 10
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Reference StructureConfigura#on BConfigura#on CConfigura#on D
0 1 2 3 4
x 104
0
20
40
60
80
100
120
Maximum Core Wall Shear (kN)
He
igh
t (m
)
Reference StructureConfigura"on BConfigura"on CConfigura"on D
CHAPTER 4: Case Study 137
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
the greatest improvement in seismic performance at both hazard levels. In the East-West
direction, mean interstorey drifts were reduced by up to 24 percent, core wall shears were
reduced by up to 25 percent, and peak floor accelerations were reduced by up to 40 percent at the
SLE hazard level. In the North-South direction, mean interstorey drifts were reduced by up to 19
percent, core wall shears were reduced by up to 25 percent, and peak floor accelerations were
reduced by up to 21 percent at the SLE hazard level. At the MCE hazard level, mean interstorey
drifts were reduced by up to 7 percent, core wall shears were reduced by up to 2 percent, and
peak floor accelerations were reduced by up to 22 percent in the East-West direction. In the
North-South direction, mean interstorey drifts were reduced by up to 7 percent, core wall shears
were reduced by up to 19 percent, and peak floor accelerations were reduced by up to 3 percent
at the MCE hazard level.
East-West Direction
North-South Direction
Figure 4.40 Global performance – MCE level
Figure 4.41 shows the maximum VE material strains and VCD shear fuse rotations in two
lintel locations at the SLE hazard level for Configurations B, C, and D. These results represent
mean values from the subset of three ground motions. For each of the three configurations,
yielding is expected to occur in the shear fuse at a rotation of 0.008 radians in the East-West
0 0.5 1 1.5 2 2.5
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Reference StructureConfigura!on BConfigura!on CConfigura!on D
0 1 2 3 40
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Reference StructureConfigura#on BConfigura#on CConfigura#on D
0 2 4 6 8 10
x 104
0
20
40
60
80
100
120
Maximum Core Wall Shear (kN)
He
igh
t (m
)
Reference StructureConfigura"on BConfigura"on CConfigura"on D
0 0.5 1 1.5 2 2.5
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Reference StructureConfigura!on BConfigura!on CConfigura!on D
0 1 2 3 40
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Reference StructureConfigura#on BConfigura#on CConfigura#on D
0 2 4 6 8 10
x 104
0
20
40
60
80
100
120
Maximum Core Wall Shear (kN)
He
igh
t (m
)
Reference StructureConfigura"on BConfigura"on CConfigura"on D
CHAPTER 4: Case Study 138
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
direction, and 0.01 radians in the North-South direction. None of the shear fuses were activated
in any of the three configurations. Configuration D resulted in the highest VE material strains
and shear fuse rotations. Because there is only one VCD in each lintel location in Configuration
D, the coupling elements have a relatively low stiffness and therefore undergo higher shear
deformations than the stiffer lintels in Configurations B and C. The mean VE material strains
reached a maximum of 150 percent in the East-West direction and 175 percent in the North-
South direction at the SLE hazard level.
Table 4.29 Maximum response quantities – SLE level
East-West Direction North-South Direction
Configuration
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
Reference 0.35 29,800 0.55 0.29 27,800 0.47 A 0.30 28,700 0.45 0.28 22,800 0.31 B 0.28 27,800 0.45 0.24 22,700 0.37 C 0.28 25,500 0.42 0.27 22,300 0.37 D 0.25 22,300 0.42 0.23 20,800 0.38
Table 4.30 Maximum response quantities – MCE level
East-West Direction North-South Direction
Configuration
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
Reference 1.07 65,700 2.26 0.72 55,700 1.63 A 0.93 72,100 2.35 0.81 62,600 1.69 B 0.96 71,100 2.47 0.81 60,600 1.70 C 0.87 69,000 2.35 0.72 55,800 1.63 D 0.83 64,200 2.10 0.70 44,900 1.52
Figure 4.42, Figure 4.43, and Figure 4.44 show hystereses from lintel L10 at the 10th
floor level in Configurations B, C, and D, respectively, obtained under the Loma Prieta record
scaled to the MCE hazard level. As shown, the shear fuses were activated in each of the three
configurations and the VCDs exhibited a viscoelastic-plastic response, as intended in the design.
Figure 4.45 shows the maximum VE material strains and plastic shear fuse rotations in two lintel
locations at the MCE hazard level. As expected, Configuration D resulted in the highest VE
material strains and shear fuse rotations at the MCE level. The mean VE material strains
CHAPTER 4: Case Study 139
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
exceeded the limit of 400 percent in several lintel locations in Configuration D. The maximum
VE material shear strain surpassed the allowable limit on 21 floor levels in lintel location L10
and on 10 floor levels in lintel location L22. Because the VE material strains surpassed the
allowable limit specified by the material manufacturer, Configuration D does not meet the
performance objectives set out for the alternative design of the reference structure. A number of
VCD shear fuses in Configuration D surpassed a total rotation of 0.04 radians, whereas no
requirement for repair is anticipated for Configurations B and C.
Figure 4.41 VCD response – SLE level
0 100 200 300 400
0
20
40
60
80
100
120
Maximum VE Material Shear Strain (%)
He
igh
t (m
)
Configura"on BConfigura"on CConfigura"on D
0 0.002 0.004 0.006 0.008 0.01
0
20
40
60
80
100
120
Maximum Shear Fuse Rota!on (rad)
He
igh
t (m
)
Configura!on BConfigura!on CConfigura!on D
0 100 200 300 400
0
20
40
60
80
100
120
Maximum VE Material Shear Strain (%)
He
igh
t (m
)
Configura"on BConfigura"on CConfigura"on D
0 0.002 0.004 0.006 0.008 0.01
0
20
40
60
80
100
120
Maximum Shear Fuse Rota!on (rad)
He
igh
t (m
)
Configura!on BConfigura!on CConfigura!on D
CHAPTER 4: Case Study 140
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
d) VCD Response e) VEM Response f) Steel Response
Figure 4.42 VCD hysteresis – Configuration B
a) VCD Response b) VEM Response c) Steel Response
Figure 4.43 VCD hysteresis – Configuration C
a) VCD Response b) VEM Response c) Steel Response
Figure 4.44 VCD hysteresis – Configuration D
Free vibration analyses were carried out on elastic models of Configurations B, C, and D
in order to assess the added damping provided by the VCDs for SLS wind loading. The
logarithmic decrements were computed using the procedure described in Section 4.5.2.1. The
modal periods and damping ratios are listed in Table 4.31. The results of the free vibration
analysis indicate that a significant amount of damping was provided by the VCDs in each of the
three configurations. Configuration D resulted in the largest amount of added damping, despite
having the smallest number of VCDs. As expected, Configuration D also resulted in the most
−50 0 50−10
−8
−6
−4
−2
0
2
4
6
8
10
Displacement (mm)
Fo
rce
(M
N)
−50 0 50−10
−8
−6
−4
−2
0
2
4
6
8
10
Displacement (mm)
Fo
rce
(M
N)
−50 0 50−10
−8
−6
−4
−2
0
2
4
6
8
10
Displacement (mm)
Fo
rce
(M
N)
−50 0 50−10
−8
−6
−4
−2
0
2
4
6
8
10
Displacement (mm)
Fo
rce
(M
N)
−50 0 50−10
−8
−6
−4
−2
0
2
4
6
8
10
Displacement (mm)
Fo
rce
(M
N)
−50 0 50−10
−8
−6
−4
−2
0
2
4
6
8
10
Displacement (mm)
Fo
rce
(M
N)
−50 0 50−10
−8
−6
−4
−2
0
2
4
6
8
10
Displacement (mm)
Fo
rce
(M
N)
−50 0 50−10
−8
−6
−4
−2
0
2
4
6
8
10
Displacement (mm)
Fo
rce
(M
N)
−50 0 50−10
−8
−6
−4
−2
0
2
4
6
8
10
Displacement (mm)
Fo
rce
(M
N)
CHAPTER 4: Case Study 141
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
significant increase in the predominant periods of vibration. The periods of modes 1, 2, and 3
were increased by approximately 12 percent, 19 percent, and 65 percent, respectively. This is a
result of the low stiffness of the VCDs, relative to the RC coupling beams in the reference
structure. A reduction in the stiffness of the coupling elements reduces the coupling ratio of the
system, resulting in a reduction in lateral stiffness and a longer natural period. The implications
of these observations on the wind performance of the structure are discussed further in Section
4.6. A more detailed investigation of the wind performance was carried out for the final design in
Section 4.6.2.
Figure 4.45 VCD response – MCE level
Table 4.31 SLS wind modal properties
Configuration
Modal Periods Modal Damping Ratios T1
(sec) T2
(sec) T3
(sec) ξ1
(%) ξ2
(%) ξ3
(%) Reference 4.38 3.31 2.17 1.5 1.5 1.5
B 4.55 3.59 2.80 3.9 4.2 10.9 C 4.65 3.69 3.02 4.6 5.0 12.6 D 4.91 3.95 3.57 6.0 6.6 14.2
0 200 400 600 800
0
20
40
60
80
100
120
Maximum VE Material Shear Strain (%)
He
igh
t (m
)
Configura"on BConfigura"on CConfigura"on D
0 0.02 0.04 0.06 0.08 0.1
0
20
40
60
80
100
120
Maximum Plas!c Shear Fuse Rota!on (rad)
He
igh
t (m
)
Configura!on BConfigura!on CConfigura!on D
0 200 400 600 800
0
20
40
60
80
100
120
Maximum VE Material Shear Strain (%)
He
igh
t (m
)
Configura"on BConfigura"on CConfigura"on D
0 0.02 0.04 0.06 0.08 0.1
0
20
40
60
80
100
120
Maximum Plas!c Shear Fuse Rota!on (rad)
He
igh
t (m
)
Configura!on BConfigura!on CConfigura!on D
CHAPTER 4: Case Study 142
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
4.5.2.3 Configuration E
The results presented in Section 4.5.2.2 indicate that the seismic performance of the
structure improved as the number of VCDs was reduced. Configuration D, with 1-VCD in each
lintel location, resulted in a significant improvement in the seismic performance of the case study
building, when compared with the reference structure. However, the VCDs in Configuration D
underwent significant shear deformations, resulting in VE material strains greater than the
allowable 400 percent limit. In order to reduce the VE material strains, a second VCD was added
in lintel locations L01, L10, L22, and L30 at storeys 1-14. Schematic plans of Configuration E
are shown in Figure 4.27. Mean response values from the subset of three ground motions were
used to compare the performance of the reference structure and Configurations D and E. Results
from the nonlinear time history analyses at the SLE and MCE hazard levels are shown in Figure
4.47 and Figure 4.48, respectively.
Figure 4.46 Configuration E core wall plans
As shown in Figure 4.47, the added VCDs did not significantly affect the global
performance at the SLE hazard level. However, at the MCE hazard level, Configuration E
resulted in relatively poor performance when compared with Configuration D. The maximum
SLE and MCE response quantities, taken as the mean of the three ground motion records, for
configurations D and E are listed in Table 4.32 and Table 4.33. In the East-West direction, mean
interstorey drifts were increased by up to 6 percent, core wall shears were increased by up to 8
percent, and peak floor accelerations were increased by up to 6 percent at the MCE hazard level
due to the addition of the VCDs in Configuration E. In the North-South direction, mean
Storeys 1-14
VCD
Steel Link
Storeys B4-GND
N
L32
L30
L22
L20
L10
L01
Storeys 15-41
L32
L30
L22
L20
L10
L01
CHAPTER 4: Case Study 143
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
interstorey drifts were increased by up to 9 percent, core wall shears were increased by up to 15
percent, and peak floor accelerations were increased by up to 7 percent at the MCE hazard level.
The performance of Configuration E was comparable with the performance of the reference
structure at the MCE hazard level.
East-West Direction
North-South Direction
Figure 4.47 SLE performance
Table 4.32 Maximum response quantities – SLE level
East-West Direction North-South Direction
Configuration
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
Reference 0.35 29,800 0.55 0.29 27,800 0.47 D 0.25 22,300 0.42 0.23 20,800 0.38 E 0.26 23,800 0.42 0.24 20,900 0.37
Figure 4.49 shows the maximum VE material strains and plastic shear fuse rotations in
two lintel locations at the MCE hazard level. As expected, Configuration E resulted in lower VE
material strains and shear fuse rotations than Configuration D. By adding additional VCDs, the
VE material strains were reduced to meet the allowable limit of 400 percent. The plastic shear
0 0.2 0.4 0.6 0.8
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Reference StructureConfigura!on DConfigura!on E
0 0.2 0.4 0.6 0.8 10
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Reference StructureConfigura#on DConfigura#on E
0 1 2 3 4
x 104
0
20
40
60
80
100
120
Maximum Core Wall Shear (kN)
He
igh
t (m
)
Reference StructureConfigura"on DConfigura"on E
0 0.2 0.4 0.6 0.8
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Reference StructureConfigura!on DConfigura!on E
0 0.2 0.4 0.6 0.8 10
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Reference StructureConfigura#on DConfigura#on E
0 1 2 3 4
x 104
0
20
40
60
80
100
120
Maximum Core Wall Shear (kN)H
eig
ht
(m)
Reference StructureConfigura"on DConfigura"on E
CHAPTER 4: Case Study 144
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
fuse rotations were also reduced significantly such that no repair would be required at the MCE
hazard level. This is a significant improvement over the reference structure in which the RC
coupling beams undergo significant damage requiring repair at the MCE hazard level (see Figure
4.18). The results presented in Section 4.4.1 indicate that a total of approximately 219 coupling
beams would require repair following an MCE level seismic event.
East-West Direction
North-South Direction
Figure 4.48 Global performance – MCE level
Table 4.33 Maximum response quantities – MCE level
East-West Direction North-South Direction
Configuration
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
Reference 1.07 65,700 2.26 0.72 55,700 1.63 D 0.83 64,200 2.10 0.70 44,900 1.52 E 0.88 69,300 2.23 0.75 51,700 1.65
A free vibration analysis was carried out on an elastic model of Configuration E, in order
to assess the added damping provided by the VCDs for SLS wind loading. The logarithmic
0 0.5 1 1.5 2
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Reference StructureConfigura!on DConfigura!on E
0 1 2 3 40
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Reference StructureConfigura#on DConfigura#on E
0 2 4 6 8 10
x 104
0
20
40
60
80
100
120
Maximum Core Wall Shear (kN)
He
igh
t (m
)
Reference StructureConfigura"on DConfigura"on E
0 0.5 1 1.5 2
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Reference StructureConfigura!on DConfigura!on E
0 1 2 3 40
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Reference StructureConfigura#on DConfigura#on E
0 2 4 6 8 10
x 104
0
20
40
60
80
100
120
Maximum Core Wall Shear (kN)
He
igh
t (m
)
Reference StructureConfigura"on DConfigura"on E
CHAPTER 4: Case Study 145
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
decrements were computed using the procedure described in Section 4.5.2.1. The modal periods
and damping ratios for the three fundamental modes of vibration are listed in Table 4.31. The
modal properties of the reference structure and Configuration D are shown for comparison. As
expected, the additional VCDs included in Configuration E resulted in increased lateral stiffness
and reduced lateral periods of vibration. The results of the free vibration analysis indicate that the
added stiffness also caused a reduction in the modal damping ratios in the lateral modes of
vibration.
Figure 4.49 VCD response – MCE level
Table 4.34 SLS wind modal properties
Configuration
Modal Periods Modal Damping Ratios T1
(sec) T2
(sec) T3
(sec) ξ1
(%) ξ2
(%) ξ3
(%) Reference 4.38 3.31 2.17 1.5 1.5 1.5
D 4.91 3.95 3.57 6.0 6.6 14.2 E 4.81 3.83 3.32 5.7 6.0 14.3
0 200 400 600 800
0
20
40
60
80
100
120
Maximum VE Material Shear Strain (%)
He
igh
t (m
)
Configura"on DConfigura"on E
0 0.02 0.04 0.06 0.08 0.1
0
20
40
60
80
100
120
Maximum Plas!c Shear Fuse Rota!on (rad)H
eig
ht
(m)
Configura!on DConfigura!on E
0 200 400 600 800
0
20
40
60
80
100
120
Maximum VE Material Shear Strain (%)
He
igh
t (m
)
Configura"on DConfigura"on E
0 0.02 0.04 0.06 0.08 0.1
0
20
40
60
80
100
120
Maximum Plas!c Shear Fuse Rota!on (rad)
He
igh
t (m
)
Configura!on DConfigura!on E
CHAPTER 4: Case Study 146
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
4.5.2.4 Configuration F
A final design was evaluated in which all of the coupling beams were replaced by VCDs,
as shown schematically in Figure 4.50. Because the global seismic performance of Configuration
D was found to be superior to that of Configuration E, an alternative means of reducing the VE
material strains was investigated. By reducing the web thickness in the shear fuse from 12mm to
10mm, the fuse activation force was reduced, resulting in more of the shear deformations being
concentrated in the shear fuse at high force levels, as well as a slight reduction in the stiffness of
the built-up steel assembly. The updated shear fuse modelling parameters are listed in Table
4.35. Mean response values from the subset of three ground motions were used to compare the
performance of the reference structure and Configurations D and F. Results from the nonlinear
time history analyses at the SLE and MCE hazard levels are shown in Figure 4.51 and Figure
4.52, respectively.
Figure 4.50 Configuration F schematic core wall plans
Table 4.35 Steel assembly modelling parameters
Direction
¡r(kN/mm)
¢£(kN)
¢¤(kN)
¢¥(kN)
¤(mm)
¦(mm)
¥(mm)
§(mm)
EW 542 2400 3120 1920 20.0 95.4 104 109 NS 307 2400 3120 1920 35.9 147 160 168
As shown in Figure 4.51, the global structural performance at the SLE hazard level was
significantly improved in the North-South direction due to the replacement of the steel coupling
beams in lintel locations L20 and L32 with VCDs. The reduced web thickness of the shear fuses
did not have a significant effect on the global response of the structure in the East-West
Storeys 1-41
VCD
Steel Link
Storeys B4-GND
N
L32
L30
L22
L20
L10
L01
CHAPTER 4: Case Study 147
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
direction. A similar trend was observed at the MCE hazard level. Comparable performance was
observed for Configurations D and F in the East-West direction, whereas a significant
improvement was achieved in the North-South direction with Configuration F. The maximum
SLE and MCE response quantities, taken as the mean of the three ground motion records, for
configurations D and F are listed in Table 4.36 and Table 4.37. Compared with the reference
structure in the East-West direction, mean interstorey drifts were reduced by up to 27 percent,
core wall shears were reduced by up to 25 percent, and peak floor accelerations were reduced by
up to 30 percent at the SLE hazard level. In the North-South direction, mean interstorey drifts
were reduced by up to 37 percent, core wall shears were reduced by up to 33 percent, and peak
floor accelerations were reduced by up to 26 percent at the SLE hazard level. At the MCE hazard
level, mean interstorey drifts were reduced by up to 9 percent, core wall shears were reduced by
up to 6 percent, and peak floor accelerations were reduced by up to 20 percent in the East-West
direction. Mean interstorey drifts were reduced by up to 13 percent, core wall shears were
reduced by up to 27 percent, and peak floor accelerations were reduced by up to 6 percent in the
North-South direction.
East-West Direction
North-South Direction
Figure 4.51 SLE performance
0 0.2 0.4 0.6 0.8
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Reference StructureConfigura!on DConfigura!on F
0 0.2 0.4 0.6 0.8 10
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Reference StructureConfigura#on DConfigura#on F
0 1 2 3 4
x 104
0
20
40
60
80
100
120
Maximum Core Wall Shear (kN)
He
igh
t (m
)
Reference StructureConfigura"on DConfigura"on F
0 0.2 0.4 0.6 0.8
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Reference StructureConfigura!on DConfigura!on F
0 0.2 0.4 0.6 0.8 10
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Reference StructureConfigura#on DConfigura#on F
0 1 2 3 4
x 104
0
20
40
60
80
100
120
Maximum Core Wall Shear (kN)
He
igh
t (m
)
Reference StructureConfigura"on DConfigura"on F
CHAPTER 4: Case Study 148
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
East-West Direction
North-South Direction
Figure 4.52 MCE performance
Table 4.36 Maximum response quantities – SLE level
East-West Direction North-South Direction
Configuration
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
Reference 0.35 29,800 0.55 0.29 27,800 0.47 D 0.25 22,300 0.42 0.23 20,800 0.38 F 0.25 22,500 0.40 0.21 18,500 0.30
Table 4.37 Maximum response quantities – MCE level
East-West Direction North-South Direction
Configuration
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
Reference 1.07 65,700 2.26 0.72 55,700 1.63 D 0.83 64,200 2.10 0.70 44,900 1.52 F 0.85 61,700 2.05 0.67 40,500 1.42
0 0.5 1 1.5 2
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Reference StructureConfigura!on DConfigura!on F
0 1 2 3 40
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Reference StructureConfigura#on DConfigura#on F
0 2 4 6 8 10
x 104
0
20
40
60
80
100
120
Maximum Core Wall Shear (kN)
He
igh
t (m
)
Reference StructureConfigura"on DConfigura"on F
0 0.5 1 1.5 2
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Reference StructureConfigura!on DConfigura!on F
0 1 2 3 40
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Reference StructureConfigura#on DConfigura#on F
0 2 4 6 8 10
x 104
0
20
40
60
80
100
120
Maximum Core Wall Shear (kN)
He
igh
t (m
)
Reference StructureConfigura"on DConfigura"on F
CHAPTER 4: Case Study 149
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 4.53 shows the maximum VE material strains and VCD shear fuse rotations in two
lintel locations at the MCE hazard level. As expected, Configuration F resulted in lower VE
material strains and somewhat higher shear fuse rotations than Configuration D. Although the
VE material strains were effectively reduced by reducing the web thickness of the shear fuse, the
VE material strains surpassed the allowable limit of 400 percent in lintel location L10 at floor
levels 20 to 23. The maximum VE material strain was found to be 425 percent at floor 21.
However, the VE material strain is proportional to 1/ℎ, where ℎ is the VE material thickness. If
the VE material thickness is increased from 5 mm to 5.5 mm, the maximum VE material strain
will be reduced to approximately 386 percent, resulting in a valid design solution. The stiffness
of the VE material is proportional to @/ℎ, where @ is the area of the VE material. By increasing
both the area and the thickness of the VE material by a factor of 5.5/5, the stiffness of the VE
material and thus the shear deformations in the VE material would remain identical to
Configuration F. The final design will therefore include 30 layers of ISD:111H VE material with
dimensions of 506(W)x350(L)x5.5(t) mm. Minor repairs are expected to be required in VCD
locations where the plastic fuse rotations exceed 0.04 radians.
Figure 4.53 VCD response – MCE level
0 200 400 600 800
0
20
40
60
80
100
120
Maximum VE Material Shear Strain (%)
He
igh
t (m
)
Configura"on DConfigura"on F
0 0.02 0.04 0.06 0.08 0.1
0
20
40
60
80
100
120
Maximum Plas!c Shear Fuse Rota!on (rad)
He
igh
t (m
)
Configura!on DConfigura!on F
0 200 400 600 800
0
20
40
60
80
100
120
Maximum VE Material Shear Strain (%)
He
igh
t (m
)
Configura"on DConfigura"on F
0 0.02 0.04 0.06 0.08 0.1
0
20
40
60
80
100
120
Maximum Plas!c Shear Fuse Rota!on (rad)
He
igh
t (m
)
Configura!on DConfigura!on F
CHAPTER 4: Case Study 150
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
A free vibration analysis was carried out on an elastic model of Configuration F, in order
to assess the added damping provided by the VCDs for SLS wind loading. The logarithmic
decrements were computed using the procedure described in Section 4.5.2.1. The modal periods
and damping ratios for the three fundamental modes of vibration are listed in Table 4.38. The
modal properties of the reference structure and Configuration D are shown for comparison. As
shown in the Table, the replacement of the steel coupling beams with VCDs resulted in a
significant elongation of the fundamental period of vibration in the North-South direction, as
well as in the predominant torsional mode of vibration. A significant amount of damping was
added in Configuration F, in all three predominant modes of vibration.
Table 4.38 SLS wind modal properties
Configuration
Modal Periods Modal Damping Ratios T1
(sec) T2
(sec) T3
(sec) ξ1
(%) ξ2
(%) ξ3
(%) Reference 4.38 3.31 2.17 1.5 1.5 1.5
D 4.91 3.95 3.57 6.0 6.6 14.2 F 4.96 4.26 3.83 6.9 8.7 16.9
4.6 Results and Discussion
A summary of the results from the parametric study used to develop an optimal
alternative design for the case study building is presented in Figure 4.54. As described in Section
4.5.2, the parametric study was carried out using a subset of three of the scaled ground motion
pairs at the SLE and MCE hazard levels. Several VCD configurations were investigated and
mean response quantities were compared in order to determine the best design strategy for the
seismic-critical case study building. The results from the parametric study indicate that using
fewer VCDs, resulting in a softer structure, resulted in dramatically improved seismic
performance at the SLE hazard level, and significant improvements in performance at the MCE
hazard level. Configuration F resulted in the best seismic performance. This configuration
consists of the original RC core walls coupled with a single VCD in each lintel location. A total
of 252 VCDs are included in the alternative design.
Minor changes were made to the original VCD design provided by Kinetica Dynamics.
The web thickness in the shear-critical fuse region was reduced from 12 mm to 10mm, in order
CHAPTER 4: Case Study 151
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
to lower the fuse activation force and to limit the deformation in the VE material. Additionally,
the VE material thickness was increased from 5 mm to 5.5 mm in order to satisfy the
manufacturer’s requirement for a maximum strain of 400 percent. In order to maintain the
stiffness of the VE material, the area was increased by a factor of 5.5/5. The final VCD design is
shown in Figure 4.55. A detailed design of the VCD-wall connections was not carried out in this
study. Because a single VCD is used in each lintel location, it is not likely that the core wall
thickness would need to be increased in order to accommodate the width of the damper.
In this Section, the results from nonlinear time history analysis of the optimal alternative
design configuration using seven ground motions at the SLE, DBE, and MCE hazard levels are
presented. The seismic performance of the alternative design is compared with that of the
reference structure. Drift levels under SLS wind loading are also compared. Finally, a discussion
of the results from the case study is presented.
Figure 4.54 Summary of parametric study
Reference Structure
(PEER Case Study Building 1B)
Configura"on C
2-VCDs X 4 Lintels / Floor
- Improved performance at SLE
-Slightly reduced performance
at MCE
Configura"on E
2-VCDs X 4 Lintels / Floor in
bo!om 1/3 of building,
1-VCD X 4 Lintels / Floor above
- Good performance at SLE
-Slightly reduced performance
at MCE
-No VEM tearing at MCE
Configura"on A
4-VCDs X 4 Lintels / Floor
- Modest improvement at SLE
-Poor performance at MCE
-Modest loss of lateral s"ffness
Configura"on B
3-VCDs X 4 Lintels / Floor
- Mondest improvement at SLE
-Poor performance at MCE
Configura"on D
1-VCD X 4 Lintels / Floor
- Excellent performance at
MCE and SLE
-High VEM strains and link
rota"ons
Add damping without
decreasing s"ffness
Reduce s"ffness to increase
VEM ac"va"on
Configura"on F
1-VCD X 6 Lintels / Floor
Fuse web thickness
reduced to 10 mm, VEM
thickness increased to 5.5 mm
- Excellent performance at SLE
-Improved performance at MCE
- No VEM tearing at MCE
Prevent tearing in VEM at
MCE by adding s"ffness
Prevent tearing in VEM
by reducing fuse ac"va"on force
+
Provide addi"onal damping
in NS direc"on
CHAPTER 4: Case Study 152
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 4.55 VCD design
4.6.1 Seismic Performance of Alternative Design
The seismic performance of the optimal proposed alternative design was investigated
using nonlinear time history analysis at the SLE, DBE, and MCE hazard levels. The entire suite
of scaled ground motion pairs were applied to the model as discussed in Section 4.4.1.
Performance was measured based on mean response quantities from the seven ground motion
records and compared with the mean values from the reference structure at each hazard level.
Mean peak global response quantities from the seven ground motion records at the SLE, DBE,
and MCE hazard levels are summarized in Figure 4.56, Figure 4.57, and Figure 4.58,
respectively.
VEM: ISD111H
506(W)x350(L)x5.5(t)x30 layers
Shear Fuse
Detail
PLAN VIEW
ELEVATION VIEW
Web
S!ffeners
Embedded
Por!on
RC Wall
CHAPTER 4: Case Study 153
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
East-West Direction
North-South Direction
Figure 4.56 Global performance – SLE level
East-West Direction
North-South Direction
Figure 4.57 Global performance – DBE level
0 0.2 0.4 0.6 0.8 1
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanReference Structure Mean
0 0.5 1 1.5 20
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Supers""on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanReference Structure Mean
0 10 20 30 40 50
0
20
40
60
80
100
120
Maximum Core Wall Shear (MN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanReference Structure Mean
0 0.2 0.4 0.6 0.8 1
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanReference Structure Mean
0 0.5 1 1.5 20
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Supers""on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanReference Structure Mean
0 10 20 30 40 50
0
20
40
60
80
100
120
Maximum Core Wall Shear (MN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanReference Structure Mean
0 0.5 1 1.5 2
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanReference Structure Mean
0 1 2 3 4 50
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Supers""on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanReference Structure Mean
0 20 40 60 80 100
0
20
40
60
80
100
120
Maximum Core Wall Shear (MN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanReference Structure Mean
0 0.5 1 1.5 2
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanReference Structure Mean
0 1 2 3 4 50
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Supers""on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanReference Structure Mean
0 20 40 60 80 100
0
20
40
60
80
100
120
Maximum Core Wall Shear (MN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanReference Structure Mean
CHAPTER 4: Case Study 154
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
East-West Direction
North-South Direction
Figure 4.58 Global performance – MCE level
As shown in Figure 4.56, a significant improvement in seismic performance was
achieved with the alternative design at the SLE hazard level. By replacing the diagonally-
reinforced coupling beams with VCDs, the mean interstorey drifts were reduced by up to 29
percent, core wall shears were reduced by up to 31 percent, and peak floor accelerations were
reduced by up to 31 percent in the East-West direction. In the North-South direction mean
interstorey drifts were reduced by up to 35 percent, core wall shears were reduced by up to 47
percent, and peak floor accelerations were reduced by up to 38 percent. The results shown in
Figure 4.57 highlight the improvements in seismic performance achieved at the DBE hazard
level. The mean interstorey drifts were reduced by up to 15 percent, core wall shears were
reduced by up to 8 percent, and peak floor accelerations were reduced by up to 18 percent in the
East-West direction. In the North-South direction mean interstorey drifts were reduced by up to
21 percent, core wall shears were reduced by up to 18 percent, and peak floor accelerations were
reduced by up to 15 percent. As shown in Figure 4.58, reductions in all response quantities were
observed at all three hazard levels. At the MCE hazard level, mean interstorey drifts were
reduced by up to 14 percent, core wall shears were reduced by up to 12 percent, and peak floor
0 0.5 1 1.5 2 2.5
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanReference Structure Mean
0 1 2 3 4 5 6 70
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Supers""on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanReference Structure Mean
0 20 40 60 80 100 120
0
20
40
60
80
100
120
Maximum Storey Shear (MN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanReference Structure Mean
0 0.5 1 1.5 2 2.5
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanReference Structure Mean
0 1 2 3 4 5 6 70
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Supers""on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanReference Structure Mean
0 20 40 60 80 100 120
0
20
40
60
80
100
120
Maximum Storey Shear (MN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanReference Structure Mean
CHAPTER 4: Case Study 155
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
accelerations were reduced by up to 19 percent in the East-West direction. The mean interstorey
drifts were reduced by up to 18 percent, core wall shears were reduced by up to 17 percent, and
peak floor accelerations were reduced by up to 12 percent in the North-South direction. The
maximum response quantities, taken as the mean values from the seven scaled ground motions,
are listed in Table 4.39, Table 4.40, and Table 4.41, for the SLE, DBE, and MCE hazard levels,
respectively.
Table 4.39 Maximum response quantities – SLE level
East-West Direction North-South Direction
Configuration
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
Reference 0.33 27,600 0.63 0.33 32,500 0.49 Alternative 0.23 18,900 0.45 0.21 17,200 0.32
Table 4.40 Maximum response quantities – DBE level
East-West Direction North-South Direction
Configuration
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
Reference 0.86 56,200 1.95 0.72 56,400 1.46 Alternative 0.71 51,600 1.67 0.62 46,300 1.16
Table 4.41 Maximum response quantities – MCE level
East-West Direction North-South Direction
Configuration
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
Maximum Floor
Acceleration (g)
Maximum Core Wall
Shear (kN)
Maximum Interstorey
Drift (%)
Reference 1.04 66,100 2.50 0.81 62,000 1.78 Alternative 0.84 58,500 2.14 0.71 51,700 1.47
Strong near-fault ground motion records often contain distinct high-amplitude, short-
duration pulses which subject structures to large amounts of seismic energy. These pulse-type
events have been shown to induce increased higher mode effects in RC cantilever wall high-rise
buildings when compared with far-field records (Calugaru and Panagiotou, 2012). Because
higher mode effects contribute significantly to the inelastic response of high-rise RC wall
CHAPTER 4: Case Study 156
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
structures, it is important to consider pulse type events for the design of buildings in the vicinity
of active faults. Figure 4.59 shows the scaled input acceleration and velocity time histories
corresponding to the near-field Northridge SCS 142 ground motion record which contains a
distinct velocity pulse. As shown in Figure 4.56, Figure 4.57, and Figure 4.58, the Northridge
record resulted in relatively large response quantities when compared with the mean of the seven
ground motion records used in this study. Maximum response quantities for the reference and
alternative structures in the East-West direction corresponding to the Northridge record
(Orientation 2) scaled to the MCE hazard level are shown in Figure 4.60. As shown in the
Figure, the added damping provided by the VCDs was effective in reducing the response of the
alternative structure to this pulse type event. Time-histories of the roof displacement in the East-
West direction are shown in Figure 4.61. Although the peak roof accelerations and displacements
of both the reference and alternative structures were approximately equal, the added damping
provided by the VCDs in the alternative design resulted in a reduced number of large amplitude
cycles.
a) Ground acceleration – Northridge SCS 142
b) Ground Velocity – Northridge SCS 142
Figure 4.59 Scaled ground displacement time histories – MCE level
0 5 10 15 20 25 30 35 40−2
−1
0
1
2
Time (s)
Gro
un
d A
cce
lera
"o
n (
g)
peak = -1.11 g
0 5 10 15 20 25 30 35 40−2
−1
0
1
2
Time (s)
Gro
un
d V
elo
city
(m
/s)
peak = 1.27 m/s
Velocity pulse
CHAPTER 4: Case Study 157
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
East-West Direction
Figure 4.60 Global performance – Northridge 142 (MCE)
a) Roof acceleration (East-West direction)
b) Roof displacement (East-West direction)
Figure 4.61 Roof displacement time histories – MCE level
Figure 4.62 shows the mean of the maximum VE material shear strains in each of the
lintel locations for the seven ground motion records scaled to the MCE hazard level. As shown,
by increasing the thickness of the VE material thickness to 5.5 mm, the shear strains were
reduced enough to satisfy the MCE acceptance criterion of a maximum shear strain of 400
percent. None of the scaled ground motion records resulted in maximum strains greater than the
upper limit of 600 percent. As shown in Figure 4.63, the maximum shear fuse rotations were
0 0.5 1 1.5 2
0
20
40
60
80
100
120
Peak Floor Accelera!on (g)
He
igh
t (m
)
Reference StructureAlterna!ve Design
0 1 2 3 40
20
40
60
80
100
120
Maximum Interstorey Dri! (%)
He
igh
t (m
)
Reference StructureAlterna"ve Design
0 20 40 60 80 100
0
20
40
60
80
100
120
Maximum Core Wall Shear (MN)
He
igh
t (m
)
Reference StructureAlterna!ve Design
0 5 10 15 20 25 30 35 40−2
−1
0
1
2
Time (s)
Ro
of
Acc
ele
ra"
on
(g
)
Alterna"ve DesignReference Structure
peak = 1.38gpeak = 1.31 g
0 5 10 15 20 25 30 35 40−2
−1
0
1
2
Time (s)
Re
la"
ve
Ro
of
Dis
pla
cem
en
t (m
)
Alterna"ve DesignReference Structure
peak = 1.23 mpeak = 1.22 m
CHAPTER 4: Case Study 158
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
significantly lower than the allowable limit of 0.08 radians at the MCE hazard level. In the East-
West direction, a number of shear fuses reached rotations of more than 0.04 radians, indicating
that minor repairs may be required in these locations following an MCE level event.
a) L01 b) L20 c) L22
d) L10 e) L30 f) L32
Figure 4.62 Maximum VEM strains – MCE level
Sample hysteretic responses of an RC coupling beam and a VCD are shown in Figure
4.64 and Figure 4.65, respectively. The hysteretic responses illustrated in the Figures correspond
to the Loma Prieta ground motion record (Orientation 1), scaled to the SLE, DBE and MCE
hazard levels. Both the coupling beam and the VCD are located in lintel position L10 at the 10th
floor of the structure. The expected yield forces of the coupling beam and the VCD shear-critical
fuse, /5,�RF, are indicated using dashed lines. As highlighted in the Figures, the coupling beam
transfers significantly larger shear forces than the less stiff VCD. The coupling beam reached
yielding at the SLE hazard level, while the VCD exhibited a purely viscoelastic response. Both
the RC coupling beam and the VCD exhibited inelastic deformations at the DBE and MCE
hazard levels. At all three hazard levels, the VCD exhibited a fuller hysteresis, resulting in the
dissipation of more energy than in the RC coupling beam.
0 200 400 600 800 1000
0
20
40
60
80
100
120
Maximum VE Shear Strain Strain (%)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 200 400 600 800 1000
0
20
40
60
80
100
120
Maximum VE Shear Strain Strain (%)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 200 400 600 800 1000
0
20
40
60
80
100
120
Maximum VE Shear Strain Strain (%)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 200 400 600 800 1000
0
20
40
60
80
100
120
Maximum VE Shear Strain Strain (%)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 200 400 600 800 1000
0
20
40
60
80
100
120
Maximum VE Shear Strain Strain (%)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 200 400 600 800 1000
0
20
40
60
80
100
120
Maximum VE Shear Strain Strain (%)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
CHAPTER 4: Case Study 159
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
a) L01 b) L20 c) L22
d) L10 e) L30 f) L32
Figure 4.63 Maximum shear fuse rotations – MCE level
a) SLE b) DBE c) MCE
Figure 4.64 Sample coupling beam hysteresis
Figure 4.66 shows the time-histories of the roof acceleration and relative displacement
during the SLE Loma Prieta ground motion record (Orientation 1) in the East-West direction. As
shown in the Figure, the added damping provided by the VCDs is effective in reducing the
resonant response at the top of the structure during the SLE level event. Figure 4.67 shows the
time-histories of the roof acceleration and relative displacement during the MCE Loma Prieta
ground motion record (Orientation 1) in the East-West direction. The added damping provided
by the VCDs is less effective in reducing the resonant response at the top of the structure during
the MCE level event, because the hysteretic damping provided by the diagonally-reinforced
0 0.05 0.1 0.15
0
20
40
60
80
100
120
8 Fuses Require Repair
Maximum Plas!c Shear Fuse Rota!on (rad)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanRepair Required
0 0.05 0.1 0.15
0
20
40
60
80
100
120
Maximum Plas!c Shear Fuse Rota!on (rad)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 0.05 0.1 0.15
0
20
40
60
80
100
120
Maximum Plas!c Shear Fuse Rota!on (rad)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 0.05 0.1 0.15
0
20
40
60
80
100
120
11 Fuses Require Repair
Maximum Plas!c Shear Fuse Rota!on (rad)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanRepair Required
0 0.05 0.1 0.15
0
20
40
60
80
100
120
Maximum Plas!c Shear Fuse Rota!on (rad)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 0.05 0.1 0.15
0
20
40
60
80
100
120
Maximum Plas!c Shear Fuse Rota!on (rad)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
−100 −50 0 50 100−5000
0
5000
Displacement (mm)
Fo
rce
(k
N)
−100 −50 0 50 100−5000
0
5000
Displacement (mm)
Fo
rce
(k
N)
−100 −50 0 50 100−5000
0
5000
Displacement (mm)
Fo
rce
(k
N)
CHAPTER 4: Case Study 160
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
coupling beams in the reference structure is comparable to the damping provided by the VCDs in
the alternative design.
a) SLE b) DBE c) MCE
Figure 4.65 Sample VCD hysteresis
a) Roof acceleration (East-West direction)
b) Roof displacement (East-West direction)
Figure 4.66 Roof displacement time histories – SLE level
Figure 4.68 shows the maximum axial tensile strains in the extreme corners of the RC
core of the alternative design at the MCE hazard level. As shown in the Figure, the peak tensile
strains were significantly less than the allowable limit of 0.05. A small amount of yielding was
observed over much of the building height, and strain concentrations occurred at the ground floor
−100 −50 0 50 100−5000
0
5000
Displacement (mm)
Fo
rce
(k
N)
−100 −50 0 50 100−5000
0
5000
Displacement (mm)F
orc
e (
kN
)
−100 −50 0 50 100−5000
0
5000
Displacement (mm)
Fo
rce
(k
N)
0 5 10 15 20 25 30 35 40−0.5
0
0.5
Time (s)
Ro
of
Acc
ele
ra"
on
(g
)
Alterna"ve DesignReference Structure
peak = 0.48 g
peak = 0.39 g
0 5 10 15 20 25 30 35 40−1000
−500
0
500
1000
Time (s)Re
la"
ve
Ro
of
Dis
pla
cem
en
t (m
m)
Alterna"ve DesignReference Structure
peak = 263 mmpeak = 240 mm
CHAPTER 4: Case Study 161
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
level and at the 31st floor level where there is a change in core wall thickness. As shown in
Figure 4.69, the core wall concrete remained elastic in compression at the MCE hazard level.
The compressive strains remained below the assumed crushing strain limit of 0.03 over the
height of the building. This result suggests that the assumed confined strength ratio of 1.3 is
sufficient for the design of the core wall boundary regions. It should also be noted that although
the axial strains in the core walls did not surpass allowable limits at the MCE hazard level,
damage due to yielding of longitudinal reinforcing steel and concrete spalling is anticipated in
the event of a severe earthquake. While the alternative design solution using VCDs does
significantly reduce the degree of damage expected in the coupling elements, it does not address
the level of damage expected in the plastic hinge regions of the RC walls.
a) Roof acceleration (East-West direction)
b) Roof displacement (East-West direction)
Figure 4.67 Roof displacement time histories – MCE level
Figure 4.70 shows the shear force in each wall panel of the alternative design, at the MCE
hazard level. As shown in the figure, the panel shear stresses remain below the ACI limit of
0.83�/′0 (MPa) over the height of the building. This result indicates that the wall thickness is
sufficient to prevent diagonal compression failure at the MCE hazard level. Because of the
reduction in core wall shear forces achieved in the alternative design, it may also be possible to
reduce the core wall thickness.
0 5 10 15 20 25 30 35 40−1.5
−1
−0.5
0
0.5
1
1.5
Time (s)
Ro
of
Acc
ele
ra"
on
(g
)
Alterna"ve DesignReference Structure
peak = 1.30 gpeak = 1.12 g
0 5 10 15 20 25 30 35 40
−2000
−1000
0
1000
2000
Time (s)Re
la"
ve
Ro
of
Dis
pla
cem
en
t (m
m)
Alterna"ve DesignReference Structure
peak = 669 mm
peak = 861 mm
CHAPTER 4: Case Study 162
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 4.68 Core wall axial tension strains – MCE level
Figure 4.69 Core wall axial compression strains – MCE level
0 0.004 0.008 0.012 0.016B4
GND
L5 L10 L15 L20 L25 L30 L35 L40 R
Tensile Strain
Sto
rey
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 0.004 0.008 0.012 0.016B4
GND
L5 L10 L15 L20 L25 L30 L35 L40 R
Tensile Strain
Sto
rey
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 0.004 0.008 0.012 0.016B4
GND
L5 L10 L15 L20 L25 L30 L35 L40 R
Tensile Strain
Sto
rey
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 0.004 0.008 0.012 0.016B4
GND
L5 L10 L15 L20 L25 L30 L35 L40 R
Tensile StrainS
tore
y
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 0.001 0.002 0.003 0.004B4
GND
L5 L10 L15 L20 L25 L30 L35 L40 R
Compressive Strain
Sto
rey
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 0.001 0.002 0.003 0.004B4
GND
L5 L10 L15 L20 L25 L30 L35 L40 R
Compressive Strain
Sto
rey
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 0.001 0.002 0.003 0.004B4
GND
L5 L10 L15 L20 L25 L30 L35 L40 R
Compressive Strain
Sto
rey
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
0 0.001 0.002 0.003 0.004B4
GND
L5 L10 L15 L20 L25 L30 L35 L40 R
Compressive Strain
Sto
rey
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean
CHAPTER 4: Case Study 163
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 4.70 Core wall shear – MCE level
4.6.2 Wind Performance of Alternative Design
Service level static equivalent wind loads were computed in accordance with the dynamic
procedure set out in NBCC (NRCC, 2010). An elastic analysis model of the alternative design
was created in Perform-3D using the cracked section properties listed in Table 4.17. The VCDs
were modelled as elastic beam elements with a conservative estimate of the VE material stiffness
0 5000 10000 150000
20
40
60
80
100
120
Shear (kN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean0.83√f
c’
0 2 4 6 8
x 104
0
20
40
60
80
100
120
Shear (kN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean0.83√f
c’
0 2 4 6 8
x 104
0
20
40
60
80
100
120
Shear (kN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean0.83√f
c’
0 5000 10000 150000
20
40
60
80
100
120
Shear (kN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean0.83√f
c’
0 0.5 1 1.5 2 2.5 3
x 104
0
20
40
60
80
100
120
Shear (kN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean0.83√f
c’
0 1 2 3 4
x 104
0
20
40
60
80
100
120
Shear (kN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean0.83√f
c’
0 0.5 1 1.5 2 2.5 3
x 104
0
20
40
60
80
100
120
Shear (kN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean0.83√f
c’
0 0.5 1 1.5 2 2.5 3
x 104
0
20
40
60
80
100
120
Shear (kN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean0.83√f
c’
0 1 2 3 4
x 104
0
20
40
60
80
100
120
Shear (kN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean0.83√f
c’
0 0.5 1 1.5 2 2.5 3
x 104
0
20
40
60
80
100
120
Shear (kN)
He
igh
t (m
)
Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMean0.83√f
c’
CHAPTER 4: Case Study 164
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
based on a static storage modulus, 7(, of 0.018. This value is a recommended by Montgomery
(2011) as a lower bound static stiffness for SLS wind loading. Because the static equivalent wind
loads computed using the NBCC dynamic procedure are intended to account for both the static
and dynamic contributions to wind loading, the use of the static storage modulus to model the
VE material is conservative.
The natural frequencies of vibration,/��, and associated damping ratios, �, for the two
predominant lateral modes of vibration were determined using a logarithmic decrement
procedure, as described in Section 4.5.2.4. The displacement histories from the free vibration
analyses of both the reference structure and alternative design are shown in Figure 4.71. The
modal properties and are presented in Table 4.42. The gust effect factors, ��, were computed as
1.95 and 1.88 in the East-West and North-South directions, respectively. The gust factors, which
account for the dynamic contributions to structural response in the NBCC dynamic procedure,
are significantly lower for the alternative structure than for the reference structure. This result
indicates that the added damping provided by the VCDs effectively reduced the resonant
dynamic response of the structure under SLS wind loading.
The service-level base shears were computed as 3,340 kN and 3,200 kN in the East-West
and North-South directions, respectively. Figure 4.72 shows the displaced shapes of both the
reference structure and the alternative design when subjected to static equivalent SLS wind loads
and gravity loads. As shown in the Figure, the alternative structure was displaced significantly
more than the reference structure because of the loss of lateral stiffness associated with replacing
the RC coupling beams with VCDs. Interstorey drifts are shown in Figure 4.73. As shown in the
Figure, the interstorey drifts were lower than the NBCC allowable limit of 1/500 for the
alternative structure, despite the conservative assumption used to model the VE material
stiffness.
Table 4.42 NBCC wind loading parameters
Parameter East-West Direction North-South Direction w 0.069 0.087 s 0.202 Hz 0.235 Hz ®¯ 1.96 1.88
CHAPTER 4: Case Study 165
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
a) EW Direction b) NS Direction c) Torsion
Figure 4.71 Free vibration at 30th floor level
a) East-West Direction b) North-South Direction
Figure 4.72 Deformed shape due to NBCC SLS wind loads
a) East-West Direction b) North-South Direction
Figure 4.73 Interstorey drifts due to NBCC SLS wind loads
0 20 40 60 80 100−100
−80
−60
−40
−20
0
20
40
60
80
100
Time (s)
Dis
pla
cem
en
t (m
m)
Reference StructureAlterna"ve Design
0 20 40 60 80 100−80
−60
−40
−20
0
20
40
60
80
Time (s)
Dis
pla
cem
en
t (m
m)
Reference StructureAlterna"ve Design
0 20 40 60 80 100−40
−30
−20
−10
0
10
20
30
40
Time (s)
Ro
ta"
on
(ra
dx1
03)
Reference StructureAlterna"ve Design
0 50 100 150 200
0
20
40
60
80
100
120
Displacement (mm)
He
igh
t (m
)
Alterna!ve DesignReference Structure
0 50 100 150 200
0
20
40
60
80
100
120
Displacement (mm)
He
igh
t (m
)
Alterna!ve DesignReference Structure
0 0.05 0.1 0.15 0.2
0
20
40
60
80
100
120
Interstorey Dri! (%)
He
igh
t (m
)
Alterna"ve DesignReference Structure
0 0.05 0.1 0.15 0.2
0
20
40
60
80
100
120
Interstorey Dri! (%)
He
igh
t (m
)
Alterna"ve DesignReference Structure
CHAPTER 4: Case Study 166
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
4.6.3 Discussion of Results
The results presented in Section 4.6.1 show that the seismic performance of the case
study building was significantly enhanced by adding VCDs in place of diagonally reinforced
coupling beams. Several VCD configurations were examined in Section 4.5. The results of the
preliminary analyses revealed that the seismic performance was improved as the number of
VCDs in each lintel location was reduced. It was determined that reducing the stiffness of the
structure and adding a significant amount of distributed viscous damping to the system by
replacing the RC coupling beams with VCDs was an effective design strategy for this seismic-
critical high-rise structure. This concept is illustrated in Figure 4.74. By reducing the lateral
stiffness of the structure, the fundamental period of vibration is elongated and spectral
accelerations are reduced. The added damping provided by the VCDs further reduces the spectral
accelerations, while counteracting the detrimental effect of the elongated period on the spectral
displacements.
Figure 4.74 Effects of period shift and added damping on seismic response (after Christopoulos and Filiatrault, 2006)
In Configurations A, B, C, and D, four coupling beams were replaced with VCDs at each
floor level. Identical damper properties were used in each of the four configurations, although the
number of VCDs placed in parallel in each lintel location varied. Four VCDs were placed in
parallel in each lintel location in Configuration A, 3 in Configuration B, 2 in Configuration C,
and a single VCD was used in each lintel location in Configuration D. The results from free
vibration analyses in the predominant modes of vibration for wind response indicate that the
T (sec)
SA (g)
Period
shi!
Added
damping
Typical
design
Alterna"ve
design
T (sec)
SD (mm)
Period
shi!
Added
damping
Typical
design
Alterna"ve
design
CHAPTER 4: Case Study 167
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
equivalent viscous damping in the system increased as the number of VCDs per lintel location
was reduced from four to one.
The equivalent viscous damping in the $}¶ mode of vibration of a system containing
VCDs, ·�¸^, can be expressed as follows:
·�¸^ = 14º
2�^2(^ (4-2)
where 2�^ is the total energy dissipated in the system and 2(^ is the total strain energy stored in
the system at the maximum displacement. The energy dissipated by the VCDs in a single cycle
in the $}¶ mode of vibration can be expressed as follows:
2���^ = W%º\^�V^»�ª
»a� (4-3)
where ¼ is the number of identical dampers in the system, % is the VCD damping constant, \^ is
the rotational frequency of vibration in the $}¶mode, and �V^» is the displacement amplitude of
damper ½ in mode $. The total recoverable strain energy in the system is expressed as follows:
2(^ = ��¾¿^À[ÁS¾¿^À (4-4)
where ¾¿^À is the mode shape in mode $ and ÁS is the stiffness matrix of the system.
By reducing the number of dampers in each lintel location, the degree of coupling of the
walls is reduced. As discussed in Section 2.1, reducing the stiffness of the coupling elements has
the effects of reducing the lateral stiffness of the system and increasing the deformations in the
coupling elements. Because the energy dissipated by VCD ½ in mode $ is proportional to the
square of the displacement amplitude, �V^», as shown in Equation (4-3), the dampers are more
effective when displacement amplitude is maximized. Therefore, although the damping constant,
%, decreases as the number of dampers in each lintel location is reduced, the damper
displacements increase, resulting in a net increase in energy dissipation. Additionally, by
examining Equation (4-4) it can be seen that for a given lateral displacement, the strain energy
stored in the system decreases with decreased lateral stiffness. This effect, combined with the
CHAPTER 4: Case Study 168
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
increase in energy dissipation in the VCDs, can result in a significant increase in equivalent
viscous damping, as shown in the results presented in Section 4.5.2.2.
In order to illustrate this concept, energy plots from the first-mode free vibration analyses
of Configurations B and D are shown in Figure 4.75 and Figure 4.76, respectively. These plots
show the variation of strain energy in the system with respect to time, and the energy dissipated
through a combination of modal damping, 2�, and viscous damping in the VCDs, 2����.
Sample calculations were carried out to estimate the equivalent viscous damping in both
configurations based on one quarter of a free vibration cycle. The strain energy stored in the
system at the maximum displacement in a given cycle, 2(�, occurs at a peak in the strain energy
plot at time �. When the strain energy returns to zero after one quarter of a free vibration cycle,
the structure is at zero displacement. This point occurs at time �, as shown in the Figures. The
energy dissipated between time � and time � corresponds approximately to the energy
dissipated in one quarter of a cycle. However, because the amplitude of vibration is reduced due
to damping in each half cycle of free vibration, Equation (4-4) provides only an estimate of the
equivalent viscous damping in the system. A sample VCD response is shown in Figure 4.77.
Sample calculations estimating the equivalent viscous damping in Configurations B and
D are presented in Table 4.43. As shown in the Table, the VCDs in Configuration D, which
employed a single VCD per lintel location, dissipated significantly more energy than the VCDs
in Configuration B, which employed three VCDs per lintel location. Additionally, more strain
energy was stored in the stiffer Configuration B, resulting in a lower equivalent viscous damping
ratio. In both configurations modal damping of 1.5 percent was used to account for the assumed
inherent damping in the system. The results from this approximate calculation are in reasonably
good agreement with the equivalent viscous damping computed using the logarithmic decrement
technique described in Section 4.5.2.1. The logarithmic decrement analysis yielded estimates of
3.9 and 6.0 percent equivalent viscous damping in Mode 1 for Configurations B and D,
respectively.
CHAPTER 4: Case Study 169
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 4.75 Free vibration energy plots – Configuration B, East-West Direction
Figure 4.76 Free vibration energy plots – Configuration D, East-West Direction
Figure 4.77 Sample VCD response
Table 4.43 Sample free vibration calculations
Configuration B (Three VCDs/Lintel)
Configuration D (Single VCD/Lintel)
t1 24.6 sec. 24.8 sec. t2 25.7 sec. 26.1 sec. Es1 63.0 KJ 57.9 KJ Em1 11.0 KJ 11.0 KJ EVCD1 16.8 KJ 33.8 KJ ξ1 3.5 % 6.2 %
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
Time (s)
Str
ain
En
erg
y (
KJ)
t1
t2
Es1
0 20 40 60 80 1000
50
100
150
Time (s)
Dis
sip
ate
d E
ne
rgy
(K
J)
t1
t2
ED1/4
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
Time (s)
Str
ain
En
erg
y (
KJ)
t1
t2
Es1
0 20 40 60 80 1000
50
100
150
Time (s)
Dis
sip
ate
d E
ne
rgy
(K
J)
t1
t2
ED1/4
Displacement
Fo
rce
t1
t2
CHAPTER 4: Case Study 170
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Figure 4.78 a) shows the increase in the fundamental period of vibration for wind loading
in the East-West direction as the number of VCDs was reduced from four VCDs per lintel
location in Configuration A to a single VCD per lintel location in Configuration D. The
fundamental periods corresponding to the theoretical configurations employing one half, one
quarter and one eighth of the stiffness and damping coefficients of a single VCD in each lintel
location, as well as the case in which the walls were completely uncoupled in the East-West
direction are also plotted. As shown in the Figure, the period continues to increase as the
stiffness and damping coefficients of the coupling elements decrease.
Figure 4.78 b) shows the increase in equivalent viscous damping in the predominant
mode of vibration in the East-West direction as the number of VCDs was reduced from four to a
single VCD per lintel location. Also shown in the Figure are the equivalent viscous damping
ratios for the configurations employing one half, one quarter, and one eighth of a VCD per lintel
location. As shown in the plot, the equivalent viscous damping reaches a maximum when
approximately one half of a damper is provided in each lintel location. Beyond this point the
increased VCD deformations and reduced stiffness associated with reducing the number of
dampers are no longer sufficient to offset the reduction in the damping coefficient, %. Only the
assumed inherent modal damping ratio of 1.5% was provided in the uncoupled model. These
results indicate that reducing the size of the VCD used in the alternative design to about half of
its original size would result in optimal damping. However, this option was not investigated in
the present study because of concerns pertaining to excessive wind drifts resulting from any
further reduction in the lateral stiffness of the structure.
As shown in the results from Section 4.5.2, the added damping associated with a lower
number of VCDs effectively counteracted the unfavourable effect of the period shift on the
lateral displacements of the structure due to seismic loading. At both the SLE and MCE hazard
levels, the VCDs underwent greater deformations when fewer dampers were provided in each
lintel location. Several of the VCDs in Configuration D underwent VE material strains greater
than the allowable limit of 400 percent at the MCE seismic hazard level. In order to reduce the
VE material strains, VCD Configuration E was investigated. This Configuration included 2-
VCDs in four lintel locations in the bottom third of the RC core, and a single VCD in four lintel
CHAPTER 4: Case Study 171
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
locations in the top two thirds. The addition of the VCDs in the lower part of the structure
effectively reduced the VE material strains while having a detrimental effect on the seismic
performance at both the SLE and MCE hazard levels due to an increase in lateral stiffness and a
reduction in modal damping.
a)
b)
Figure 4.78 a) Fundamental periods of vibration b) Damping ratios in fundamental mode of vibration
An alternative means of protecting the VE material from excessive strain was
investigated in Configuration F. This Configuration, which exhibited the best seismic
performance overall, involved the replacement of all of the coupling beams with VCDs at every
floor level. In order to achieve the required reduction in VE material strain, the shear fuse
activation force was decreased by reducing the web thickness and the VE material thickness was
increased from 5 mm to 5.5 mm. In order to maintain the stiffness of the VE material, the area
was increased by a factor of 5.5/5. The global response of the structure in the East-West direction
was not significantly affected by the change in the VCD design. However, the addition of two
extra VCDs in the North-South direction resulted in a significant improvement in global seismic
response. By replacing the steel coupling beams with VCDs, the lateral stiffness of the structure
was reduced and additional damping was added to the structure.
Because of its superior seismic performance, Configuration F was selected for the
alternative design of the case study building. Complete nonlinear time history analysis results for
the alternative structure are presented in Section 4.6.1. Three engineering demand parameters
were used to assess the seismic performance at the SLE, DBE and MCE hazard levels. In order
012344
4.5
5
5.5
6
6.5
7
Number of VCDs per Lintel
T (
s)
T = 6.5 sec
with no
dampers
012340
1
2
3
4
5
6
7
8
9
10
Number of VCDs per Lintel
Mo
da
l D
am
pin
g R
a!
o (
%)
Assumed 1.5 %
inherent
damping
CHAPTER 4: Case Study 172
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
to be consistent with the PEER/ATC report (2011), peak floor accelerations, maximum
interstorey drifts, and maximum core wall shear forces were examined. Peak floor accelerations
are associated with damage to non-structural contents, such as elevators, ceilings, HVAC
systems, shelving, etc. Losses at the SLE hazard level are predominantly associated with non-
structural damage due to accelerations. Interstorey drifts are associated with both structural
damage and damage to non-structural drift-sensitive components, such as partitions. As seismic
intensity increases, a larger portion of losses becomes associated with damage to structural and
non-structural drift-sensitive subsystems (PEER/ATC, 2011). Maximum interstorey drifts are
also associated with structural collapse due to P-Delta effects. Maximum core wall shears are
another important demand parameter. The thickness of the core walls is determined based on the
maximum shear demands at the MCE hazard level. If shear demands on the core walls are
reduced, the core wall thicknesses may be reduced. A reduction in core wall thickness is an
attractive incentive for designers because of the associated savings in construction materials,
costs, and space.
As shown in the results presented in Section 4.6.1, the acceptance criteria for the
performance objectives set out in Section 4.5, have been met in the alternative design. At the
SLE hazard level, the structure remained essentially elastic and maximum interstorey drifts were
below the allowable limit of 0.5 percent. At the MCE hazard level, maximum interstorey drifts
were below the allowable limit of 3 percent and maximum core wall axial strains and shear
stresses satisfied the requirements set out by the designers. The VCD rotation and shear strain
demands were also within allowable limits.
The improvements in seismic performance highlighted in the results presented in Section
4.6.1 are associated with potential savings in both initial costs and projected repair costs resulting
from damage due to seismic events during the life of the structure. At the SLE hazard level,
which has a return period of 43 years, maximum interstorey drifts were reduced by up to 36
percent and peak floor accelerations were reduced by up to 31 percent. These results are
associated with a significant reduction in projected losses due to non-structural damage in the
event of an earthquake which has a high probability of occurring during the life of the building.
At the DBE hazard level, maximum interstorey drifts were reduced by up to 21 percent, peak
CHAPTER 4: Case Study 173
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
floor accelerations were reduced by up to 18 percent and maximum core wall shears were
reduced by up to 18 percent. These reductions in seismic demand are associated with significant
reductions in losses associated with both structural and non-structural damage. At the MCE
hazard level, maximum interstorey drifts were reduced by up to 17 percent, peak floor
accelerations were reduced by up to 19 percent, and maximum core wall shears were reduced by
up to 17 percent. These reductions are associated with reduced potential for casualties as well as
losses associated with damage and downtime in the event of a rare earthquake. Decreased
maximum interstorey drifts and storey shears are directly related to reductions in expected
structural damage and in the probability of collapse of the structure. Additionally, the non-trivial
reductions in storey shears observed at the MCE level may allow for reductions in core wall
thicknesses, resulting in significant savings in the initial cost of the building.
Another indication of expected losses due to distributed structural damage at the MCE
hazard level is the maximum coupling beam rotations observed in the reference structure, shown
in Figure 4.18. As shown in the Figure, almost all of the coupling beams would require repair
following a rare earthquake. A total of 219 coupling beams surpassed a chord rotation of 0.02
radians, resulting in the expectation of minor damage requiring epoxy injection repair. However,
none of the coupling beams reached the chord rotation of 0.04 radians which is associated with
the expected need for major repair. Losses associated with damage to the VCDs in the alternative
design are expected to be significantly less than losses associated with damage to the coupling
beams in the reference structure. As shown in Figure 4.62, shear strains in the VE material were
effectively limited to less than 400 percent, indicating that no tearing of the material is expected
at the MCE hazard level. Figure 4.63 shows that only 19 VCD shear fuses exceeded rotations of
0.04 radians in the East-West direction. Minor damage requiring repair of the surrounding
concrete is expected in these locations following a rare seismic event. It should also be noted that
the alternative design using VCDs does not explicitly address damage in the plastic hinge region
at the base of the RC core.
Although the advantages of the improved seismic performance of the alternative structure
are considerable, the reduced lateral stiffness associated with the replacement of the RC coupling
beams with VCDs has been shown to have a detrimental effect on lateral drifts due to the static
CHAPTER 4: Case Study 174
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
component of SLS wind loading. As shown in Figure 4.73, a significant increase in interstorey
drifts was observed in the alternative design when compared with the reference structure. In the
NBCC (NRCC, 2010), the specified external wind pressure acting on a structure, c, is computed
as:
c = DA�����F (4-5)
where DA is the importance factor (0.75 for SLS wind loading), Ä is the reference velocity
pressure, �� is the exposure factor, �� is the gust factor, and �F is the external pressure
coefficient. In comparing the gust factors computed for the reference and alternative structures, it
can be observed that the dynamic response of the structure was significantly reduced due to the
added damping provided by the VCDs in the alternative design, despite the considerable increase
in the predominant lateral periods of vibration. Modal damping was increased by 5.4 percent in
the East-West direction and 7.2 percent in the North-South direction, as compared to the
assumed modal damping ratio of 1.5 percent in the reference structure. As a result, the static
equivalent SLS wind loads for the alternative design are significantly lower than the SLS wind
loads computed for the reference structure. The SLS static equivalent base shears are listed in
Table 4.44.
Table 4.44 SLS wind base shears
Structure
East-West Direction (kN)
North-South Direction (kN)
Reference 4,030 3,670 Alternative 3,340 3,200
The increase in interstorey drifts in the alternative design can be attributed to the reduced
stiffness of the alternative design relative to the stiffness of the reference structure, since the
added damping was effective in reducing the dynamic component of the wind loading in both the
East-West and North-South directions. Montgomery recommended computing the effective
stiffness of the VCDs in the along-wind direction using an estimate of the static contribution to
the maximum wind response, as provided by the wind tunnel consultant (see Equation (2-2)). For
the purpose of this study, the VE material properties were defined based on the conservative
assumption that the static component of wind loading contributed 100 percent of the maximum
CHAPTER 4: Case Study 175
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
wind response. Using this conservative approach, the maximum interstorey drift limit of 1/500
was satisfied for the alternative design.
CHAPTER 5: Conclusions and Recommendations 176
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
5 CONCLUSIONS AND RECOMMENDATIONS
The motivation for this thesis project was the development of an integrated, performance-
based approach to the seismic and wind design of high-rise structures using a new distributed
damping technology, the Viscoelastic Coupling Damper (VCD). This system has previously
been shown analytically to reduce the dynamic resonant response of slender high-rise buildings
subjected to wind loading (Montgomery, 2011). The present thesis describes the results from a
case study in which the seismic performance of an RC coupled wall high-rise building designed
using VCDs was investigated. The results from this study demonstrate that substantial
improvements in seismic performance can be achieved when RC coupling beams are replaced
using VCDs. Whereas current approaches to high-rise design address seismic and wind
considerations separately, the results from this study indicate that VCDs can be used to enhance
both seismic and wind performance. The findings from this study are intended to contribute to
the development of an innovative and integrated approach to the seismic and wind design of
high-rise coupled wall buildings, improving both the safety and economy of this common
structural system.
This Chapter provides an overview of the thesis, the final conclusions, and
recommendations for further work. A summary of the work is presented in Section 5.1. Section
5.2 presents the conclusions drawn from the case study and outlines a proposed design strategy
for seismic-critical high-rise RC core wall structures using VCDs. The design procedure
proposed by Montgomery (2011) for wind-critical high-rise structures is also presented for
comparison purposes. In Section 5.3, recommendations for further research are discussed.
5.1 Summary
The application of viscoelastic coupling dampers (VCDs) in the performance-based
design of a seismic-critical high-rise RC core wall structure has been investigated using
nonlinear time-history analysis. The results from a case study indicate that by introducing the
VCDs in place of diagonally-reinforced coupling beams in a conventional RC core wall
structure, significant improvements in seismic performance can be achieved. Improved seismic
performance was observed at the SLE, DBE, and MCE hazard levels, resulting in the potential
CHAPTER 5: Conclusions and Recommendations 177
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
for savings in both the initial cost of the building and in the repair costs associated with damage
due to seismic events occurring throughout the life of the building.
The results from the case study suggest that the most effective design strategy for a
seismic-critical high-rise structure with VCDs is to allow for elongation of the natural period of
the structure. By replacing the diagonally-reinforced coupling beams with less stiff VCDs, the
lateral stiffness of the structure is reduced and the natural period is shifted beyond the
predominant periods of typical earthquakes. The added damping provided by the VCDs
dissipates seismic energy and effectively controls excessive drifts. The results from a basic wind
serviceability analysis indicate that the added damping provided by the VCDs effectively reduces
the dynamic response of the structure under service level wind loading, even in the presence of
period elongation. However, a reduction in lateral stiffness can result in a significant increase in
along-wind drifts. The application of this design approach is therefore restricted to seismic-
critical high-rise structures which are not highly sensitive to wind loading.
Although performance-based design offers a rational means of improving the resilience
of buildings located in regions of high seismic risk, this approach relies heavily on nonlinear
modelling and analysis of structures. Whereas current prescriptive code-based approaches
employ highly simplified linear elastic models, performance-based design requires the use of
advanced models capable of capturing all significant modes of deformation and deterioration
anticipated during a severe earthquake. Therefore, before undertaking the case study, a
comprehensive model validation study was carried out. All analyses in this study were carried
out using Perform-3D Nonlinear Analysis and Performance Assessment software.
In order to validate the accuracy of the software, the hysteretic responses of the primary
components of a typical RC core wall structure were verified using test data. Models were also
developed to realistically capture the hysteretic responses of steel coupling beams and VCDs.
The Generalized Maxwell Model (GMM), which accounts for the frequency-dependence of
viscoelastic material properties, was implemented in Perform-3D and validated using test data. It
was demonstrated that the GMM accurately captures the viscoelastic response of the VCD at a
given temperature. An ambient temperature of 24 C was used to define the VE material
properties in the case study since the temperature of the VE material is not expected to increase
CHAPTER 5: Conclusions and Recommendations 178
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
significantly during a seismic event. In addition, a pushover analysis was carried out on a
nonlinear model of a twelve-storey coupled core wall structure, in order to validate the nonlinear
response of a coupled wall system.
The reference structure for the case study was based on a prototype building designed by
Magnusson Klemencic Associates for the PEER Tall Buildings Initiative. The 42-storey RC core
wall structure was designed in accordance with the state-of-the-art performance-based design
criteria published by the Los Angeles Tall Buildings Design Council. The seismic performance
of the reference structure was assessed at the SLE, DBE, and MCE hazard levels. An alternative
design using VCDs in place of the diagonally-reinforced coupling beams was then proposed. A
custom VCD design was provided by Kinetica Dynamics for the purpose of the case study. A
parametric study was carried out in which several VCD configurations were investigated in order
to determine the most effective design strategy. Three engineering demand parameters were used
as a basis for comparison between the various VCD configurations and the reference structure –
maximum interstorey drifts, peak floor accelerations, and maximum core wall shears. The results
from the preliminary analysis showed that using a single damper in each lintel location resulted
in the greatest reduction in all of the engineering demand parameters at the SLE and MCE hazard
levels when compared with the reference structure.
A seismic performance assessment was carried out on the optimal design of the
alternative structure at the SLE, DBE and MCE hazard levels. The results showed that the
interstorey drifts, peak floor accelerations, and core wall shears were effectively reduced at all
hazard levels when compared with the reference structure. The most significant performance
enhancement was observed at the SLE hazard level due to the distributed viscoelastic damping
provided by the VCDs at this hazard level. All of the acceptance criteria were met for
serviceability at the SLE hazard level and collapse prevention at the MCE hazard level. By
improving the seismic performance of the structure, the application of VCDs enhances seismic
resilience. Losses associated with both structural and non-structural damage following a seismic
event are expected to be lower in the alternative design. In addition, core wall thicknesses may
be reduced because of the reduced shear stresses at the MCE hazard level, resulting in a savings
in construction materials and costs.
CHAPTER 5: Conclusions and Recommendations 179
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Because the ultimate wind force demands on the case study building were known to be
insignificant when compared with the seismic design forces, only the service level wind response
was investigated. The NBCC (NRCC, 2010) dynamic procedure was used to compute service
level wind loads for the reference and alternative structures. The added damping provided by the
VCDs was effective in reducing the dynamic contributions to the peak loading effect. The
reduced lateral stiffness of the alternative structure resulted in increased drifts, however drift
limits were satisfied.
5.2 Design of Seismic-Critical and Wind-Critical High-Rise Structures
The results of the case study provide an improved understanding of the complex
nonlinear response of seismic-critical high-rise structures designed using VCDs. By examining
the effects of various VCD configurations on the seismic and wind performance of the structure,
a design strategy for seismic-critical high-rise structures was developed. This strategy is only
applicable, however, to buildings which are not highly sensitive to wind vibrations. An 85-storey
wind-critical case study carried out by Montgomery (2011) concluded that the optimal
performance of a wind-critical structure is achieved by adding damping without significantly
affecting the stiffness of the structure. In this Section, the results from both case studies are
discussed in the context of general design strategies for seismically-governed and wind-governed
high-rise coupled wall structures using VCDs. The benefits of using VCDs over conventional
construction methods for an integrated approach to both wind and seismic design are also
discussed.
5.2.1 Seismic-Critical Structures
The focus of the present thesis is the performance of seismic-critical high-rise structures
designed using VCDs. The results of the case study described in Chapter 4 show that significant
improvements in seismic performance can be achieved by substituting VCDs in lieu of RC
concrete coupling beams in a conventional coupled wall structure. The function of typical
coupling beams is to transfer vertical forces between adjacent wall piers, resulting in increased
the lateral stiffness and a reduction in the moments that must be resisted by the individual piers.
The degree of coupling is a function of the relative stiffness and strength of the coupling beams
CHAPTER 5: Conclusions and Recommendations 180
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
and the wall piers. Coupled wall structures are designed using a capacity-design procedure in
which plastic hinges are allowed to form in the coupling beams and at the base of each wall
during a large seismic event. The resulting plastic mechanism limits the forces transferred to the
structure and provides a means of seismic energy dissipation over the height of the building as
the coupling beams undergo inelastic deformations. For conventional coupled wall systems, it
has been shown that the ductility of the system increases as the degree of coupling is increased
(Harries et al., 1997).
In areas of moderate to high seismic risk, diagonal reinforcement is provided in order to
increase the ductility and energy-absorption of the coupling beams. The use of diagonally-
reinforced coupling beams has become common practice, despite the added costs and
construction time associated with the complexity of the reinforcing details. Furthermore, a
significant amount of damage is associated with the high degree of ductility required in the
coupling beams during large seismic events. In some cases, the extent of structural damage
following a major seismic event can be so great that the most economical solution may be to
decommission the building.
The results of the case study show that the use of VCDs in place of diagonally-reinforced
RC coupling beams can address many of the drawbacks associated with the conventional design
strategy. In order to effectively apply this new technology in the design of seismic-critical
structures, the adoption of a new design philosophy is required. Whereas the intent with
conventional coupled wall structures is to provide a moderate to high degree of coupling,
resulting in a stiffer lateral system, the results from the present thesis show that allowing for a
reduction in the lateral stiffness of the structure results in a more economical design when VCDs
are employed. By replacing the diagonally-reinforced coupling beams with less stiff VCDs, the
degree of coupling of the wall piers is reduced, as illustrated in Figure 5.1. Although the VCDs
do provide some degree of coupling, a larger portion of the base moment is resisted by the
individual wall piers. The resulting reduction in lateral stiffness causes an elongation of the
natural period of the structure.
In a coupled wall configuration, the VCDs undergo shear deformations due to the relative
displacement of the wall piers under lateral loading. Under wind and SLE level seismic loading,
CHAPTER 5: Conclusions and Recommendations 181
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
the VCDs exhibit viscoelastic behaviour, imparting both damping and stiffness to the structure.
Conversely, in a conventional coupled wall system, the coupling beams are designed to remain
elastic under wind and SLE level seismic loads and therefore do not provide damping. The
effects of the period shift and the added damping associated with replacing conventional
coupling beams with VCDs on the SLE level seismic response are illustrated in Figure 5.2. As
shown in the Figure, the period shift results in lower spectral accelerations and somewhat higher
spectral displacements. However, the significant amount of added damping provided by the
VCDs controls displacements and further reduces seismic forces and accelerations. These effects
are confirmed in the results from the case study presented in Chapter 4.
a)
b)
Figure 5.1 a) Typical coupled wall structure b) VCD coupled wall structure
At the DBE and MCE hazard levels, conventional coupling beams are expected to
undergo inelastic deformations, imparting hysteretic damping to the structure and limiting the
transfer of forces to the adjacent walls. As the coupling beams deform inelastically, the degree of
coupling is reduced and the effective period of the structure is elongated. For seismic
applications, a ductile fuse is included in design of the VCDs. In the event of a large earthquake,
the fuse yields or activates, limiting the transfer of forces and protecting the VE material from
excessive shear strains. At the DBE and MCE hazard levels, the VCDs exhibit a viscoelastic-
plastic response. At high levels of seismic demand, the distinctions between the global structural
responses of conventional coupled wall structures and VCD coupled wall structures are less
Vb
Diagonally-
reinforced
coupling beam
M1
M2
P P
M1
M2
Vb
VCD
CHAPTER 5: Conclusions and Recommendations 182
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
significant than for wind and SLE level seismic loading. The period shift associated with the
reduced stiffness of the VCDs compared with RC coupling beams, if any, is expected to be
smaller. Also, the hysteretic damping provided by the coupling beams becomes comparable with
the combined viscoelastic and hysteretic damping provided by the VCDs at high levels of
seismic demand. This concept is illustrated in Figure 5.3. The results from the case study showed
a considerable reduction in seismic response at both the DBE and MCE hazard levels.
Figure 5.2 SLE performance
Although the benefits of using VCDs to improve global seismic performance are less
pronounced at the DBE and MCE hazard levels than at the SLE hazard level, the level of
damaged sustained following a major seismic event is expected to be significantly reduced at all
hazard levels. While diagonally-reinforced coupling beams exhibit good energy dissipation
characteristics, significant damage is expected due to the high ductility demands associated with
large seismic events. The VCDs, however, are able to undergo considerable shear deformations
without sustaining significant damage. As shown in the results from the case study, damage
requiring repair is expected in a relatively small number of VCDs at the MCE hazard level,
whereas almost all of the RC coupling beams in the reference structure underwent chord
rotations sufficient to cause damage requiring repair. Additionally, because the VCD design
philosophy requires that any potential damage is restricted to the seismic fuse, VCDs are easier
to inspect and repair than diagonally-reinforced coupling beams. The development of a
replaceable fuse mechanism would allow for the expedient replacement of severely damaged
FCB
uCB
Elas�c Coupling Beam
Response
FCB
kCB
FVCD
uVCD
Viscoelas�c VCD
Response
kVCD
T (sec)
SA
(g
)
Spectral Accelera�on
Period
shi!
Added
damping
Typical
design
Alterna�ve
design
T (sec)
SD
(m
m)
Spectral Displacement
Period
shi!
Added
damping
Typical
design
Alterna�ve
design
CHAPTER 5: Conclusions and Recommendations 183
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
VCDs in the event of a severe earthquake, whereas the replacement of severely damaged RC
coupling beams is comparatively costly and time-consuming.
Figure 5.3 MCE performance
Even when the design of a high-rise building is governed by seismic loading, the effects
of wind loading on the structure must be considered. Force demands associated with ultimate
wind loads are not expected to govern any aspect of the strength design; however, wind
serviceability considerations may affect the design. In a seismic-critical structure, sufficient
lateral stiffness is typically provided such that wind-induced drifts and accelerations are within
the allowable limits. However, the period shift associated with the application of VCDs can have
a detrimental effect on the dynamic wind response of the structure. As buildings become more
slender or less stiff, resonant contributions to the wind response become more significant
(Holmes, 2007). Therefore, while reducing the seismic response of the structure, the period shift
can increase the resonant dynamic component of the wind response. However, as shown in the
results from the case study, the added damping provided by the VCDs offsets the negative effect
of the period shift and can reduce the resonant response of the structure, when compared with a
conventional system. The resonant contribution to the peak wind response was effectively
reduced as a result of the added damping provided by the VCDs in the alternative design.
However, the reduction in lateral stiffness associated with the replacement of the RC coupling
beams with VCDs resulted in increased lateral drifts in the along-wind direction. Typically, a
wind tunnel test would be carried out to verify the wind performance of the structure.
uCB
Hystere�c Coupling
Beam Response
FCB
FVCD
uVCD
Viscoelas�c-plas�c
VCD Response
T (sec)
SA
(g
)
Spectral Accelera�on
Period
shi!
Typical
design
Alterna�ve
design
T (sec)
SD
(m
m)
Spectral Displacement
Period
shi!
Typical
design
Alterna�ve
design
CHAPTER 5: Conclusions and Recommendations 184
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Based on the results from the case study, the following performance-based design
procedure is proposed for seismic-critical high-rise RC core wall structures:
1) The structural layout is developed in collaboration with the architect.
2) Seismic performance objectives and corresponding acceptance criteria are established
by the design team.
3) A preliminary lateral load-resisting system is designed using conventional
construction methods (i.e. reinforced concrete coupling beams). This design will
serve as a basis for comparison with the alternative VCD design.
4) The VCD design consultant produces a damper design to suit the architectural
requirements of the structure. A ductile fuse mechanism is included in the design for
severe seismic loading. The activation load is selected such that no yielding occurs
under wind or SLE loading.
5) A preliminary VCD configuration is developed in which RC coupling beams are
replaced with dampers. In the initial design, a large number of coupling beams are
replaced using VCDs to provide a relatively flexible structure with a large amount of
added viscous damping. The remaining RC coupling beams may be replaced using
steel coupling beams in order to further soften the structure and to provide a modular
construction solution.
6) Nonlinear analysis models of the reference and VCD designs are created. The
Generalized Maxwell model is used to capture the frequency-dependent response of
the VE material at an assumed ambient temperature.
7) A nonlinear time-history analysis is carried out at both the SLE and MCE hazard
levels. The structural response is checked for compliance with the acceptance criteria,
including maximum VE material strains.
8) An optimization study is carried out. The number and location of the VCDs is varied
to determine the most economic configuration. Less effective dampers may be
removed and replaced with steel coupling beams to provide a more economical
design solution. Since the strength design is governed by the force demand at the
MCE hazard level, the configuration which provides the greatest improvement in
seismic performance at this hazard level is selected.
CHAPTER 5: Conclusions and Recommendations 185
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
9) Nonlinear time-history analyses are carried out using upper and lower bound VE
material properties to confirm that acceptance criteria are met for all seismic loading
conditions.
10) If the maximum design forces are effectively reduced at the MCE hazard level, the
structural member sizes may be reduced and Step 9 repeated.
11) An SLS finite element model is created using lower bound properties of the VE
material and cracked concrete section properties.
12) Lateral drifts due to SLS wind loading are checked for compliance with drift limits.
13) The SLS modal and upper and lower bound VE material properties are given to a
wind tunnel consultant to determine accelerations, torsional velocities, and wind
loads.
14) Strength and serviceability checks for wind are carried out using the loads generated
in the wind tunnel.
15) If any of the design requirements are not met, a second design iteration must be
carried out by altering the number, placement, and/or design properties of the VCDs
or the lateral load-resisting system.
5.2.2 Wind-Critical Structures
As buildings become taller or more slender, resonant contributions to wind loading
increase and eventually dominate the response. Montgomery (2011) developed guidelines for the
wind design of high-rise structures using VCDs. These guidelines were then applied to a realistic
85-storey case study building located in downtown Toronto. The primary design consideration
for high-rise buildings in Toronto is the dynamic response due to wind loading. In order to
increase the height of the building from 75 storeys to 85 storeys, the building was designed using
two tuned mass dampers located at the top storey level. Montgomery recommended an
alternative design using VCDs instead of the proposed vibration absorbers. Two VCD design
configurations were considered for the case study. Option 1 had 2-VCDs placed in parallel at 122
locations in the tower. Because of the relatively low stiffness of the VCDs, the RC coupling
beams above and below the VCDs were replaced using steel coupling beams. The steel coupling
beams were less stiff than the RC beams and therefore promoted more VE material deformations
CHAPTER 5: Conclusions and Recommendations 186
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
in the adjacent VCDs. Option 2 had a single large VCD in a total of 104 lintel locations. The
architectural requirement limiting the depth of the coupling beams was not met in this
configuration. Because of the increased stiffness of the VCDs in Option 2, the adjacent RC
coupling beams were not replaced with steel coupling beams.
The results from the case study showed that both VCD configurations provided
approximately the same amount of added damping as the proposed vibration absorbers in each of
the three predominant modes of vibration. The natural periods in the three predominant modes of
vibration were increased by less than five percent due to the addition of the VCDs in Option 1.
No period shift was observed for Option 2. Modal properties determined from an elastic analysis
model and upper and lower bound VE material properties were provided to a wind tunnel
laboratory to determine the wind loads, accelerations, and torsional velocities. The results from
the wind tunnel indicated that the human perception criteria for accelerations were met in both
Options 1 and 2. The reduced stiffness associated with the addition of the steel coupling beams
and VCDs in place of the RC coupling beams in Option 1 resulted in increased drifts due to SLS
wind loading. Only a small increase in drifts was observed for Option 2. In both cases the NBCC
(NRCC, 2010) drift limit of 1/500 was met. The wind forces determined by the wind tunnel
consultants indicated that the base moments and base shears for both VCD configurations were
comparable to the results from the proposed TMD solution.
A historical ground motion record, scaled to the Toronto design spectrum (MCE hazard
level), was applied to the case study building. Because buildings in Toronto are typically
designed for only nominal ductility, a linear elastic model was used for the time history analysis.
The results indicated a small reduction in the seismic response of the damped structure.
For a wind-sensitive structure, the primary objective of the VCD design is to minimize
loss of stiffness while maximizing added damping. Seismic design considerations are typically
taken into account after the wind design is complete. In regions of low seismic risk, seismic
design checks are typically carried out using a linear elastic response spectrum analysis
approach. The added damping provided by the VCDs is expected to have a beneficial effect on
the seismic response of the structure, as illustrated in Figure 5.4. In cases where seismic demands
on the structure are also a significant design concern, the seismic performance may be evaluated
CHAPTER 5: Conclusions and Recommendations 187
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
using nonlinear time history analysis at multiple hazard levels. In such cases, the seismic
performance is expected to be enhanced at the SLE hazard level, when compared with a
conventional coupled wall design. Comparable or slightly improved performance is anticipated
for the VCD design under more severe earthquake loading.
The VCD offers several advantages over conventional solutions using vibration absorbers
for wind-sensitive structures. The primary advantage is the distributed viscous damping provided
by the VCDs in all lateral modes of vibration, whereas typical vibration absorbers are tuned to
provide damping in one or two modes of vibration only. In the event of an earthquake, vibration
absorbers become ineffective, whereas VCDs continue to provide damping resulting in improved
seismic performance. Vibration absorbers require considerable maintenance and monitoring as
the properties of the structure change overtime. Conversely, VCDs require little to no
maintenance over the life of the building. Additionally, the VCDs are integrated into the lateral
load-resisting system and therefore do not occupy usable floor space. The added damping
provided by the VCDs leads to a reduction in the dynamic component of wind loading, resulting
in reduced design loads and potential savings in construction materials and costs.
Figure 5.4 Seismic performance of wind-critical design
The wind design procedure recommended by Montgomery (2011) is as follows:
1) The structural layout is developed in collaboration with the architect.
2) A preliminary lateral load-resisting system is designed, including a preliminary VCD
configuration. A target level of added damping is established and the number and
FCB
uCB
Elas�c Coupling Beam
Response
FCB
kCB
FVCD
uVCD
Viscoelas�c VCD
Response
kVCD
T (sec)
SA
(g
)
Spectral Accelera�on
Added
damping
Typical
design
Alterna�ve
design
T (sec)
SD
(m
m)
Spectral Displacement
Added
damping
Typical
design
Alterna�ve
design
CHAPTER 5: Conclusions and Recommendations 188
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
placement of VCDs required to achieve the target is determined through an
optimization process.
3) SLS and ULS finite element models are created using upper and lower bound
properties of the VE material and cracked concrete section properties.
4) Lateral drifts due to SLS wind loading are checked for compliance with drift limits.
5) A strength design check is carried out based on factored ULS wind loads, including
the VCD strain limits.
6) The SLS modal and upper and lower bound VE material properties are given to a
wind tunnel consultant to determine accelerations, torsional velocities, and wind
loads.
7) Steps 3 to 5 are repeated using the wind loads generated in the wind tunnel.
8) If any of the design requirements are not met, a second design iteration must be
carried out by altering the number, placement, and/or design properties of the VCDs
or the lateral load-resisting system.
5.3 Recommendations for Further Research
The analytical work presented in this thesis is intended to complement the research and
development work of Montgomery (2011). A number of opportunities exist to expand upon both
the present work and the work of Montgomery. In this Section, recommendations for further
research are discussed.
As nonlinear modelling of tall buildings for performance-based design becomes
increasingly common in regions of high seismic risk, there is a need for the development of
standardized guidelines for nonlinear modelling of structural elements. Because current codes are
based on the design of low and mid-rise structures, there remains a lack of provisions addressing
the dynamic behaviour of high-rise structures. Definitive modelling, analysis, and acceptance
criteria that address the specific design challenges associated with high-rise structures are
required. Existing test data could be used and expanded upon to develop improved relations for
the cyclic response of typical structural components which can be accessed and applied by
consulting engineers using commercially available analysis software.
CHAPTER 5: Conclusions and Recommendations 189
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
Several recommendations for further laboratory testing of VCDs are presented by
Montgomery (2011). These include:
• Alternative connection details such as cast-in-place connections, bolted or post-
tensioned connection details, splice-plate connection details, and welded
connection details;
• Alternative fuse mechanisms such as a shear-critical fuse, axial force-limiting
anchor details, and friction-fuse mechanisms;
• Replaceable connection details;
• Applications for different lateral load-resisting systems such as outrigger systems
and tube systems;
• Testing of VCD specimens including RC slabs.
The shear-critical fuse mechanism used in the VCD design for the case study presented in
Chapter 4 has not been validated through testing. A complete full-scale testing program is
recommended to characterize the response of the shear fuse in series with the VE material, prior
to the application of this kind of fuse mechanism in the design of a real building. Different
replaceable connection details could be developed and tested to facilitate the replacement of
damaged shear fuses following a major seismic event. Reinforced concrete slabs should be
included in a full-scale test setup in order to investigate the effects of slab stiffness on the VCD
response, and to assess the level of damage in the slab associated with VCD shear deformations.
The development of fragility curves for different VCD fuse details would be of great benefit to
designers working in regions of high seismic risk.
The results from the case study presented in this thesis indicate that the replacement of
conventional RC coupling beams with VCDs in an RC coupled wall high-rise building reduces
the degree of distributed damage anticipated in the event of a severe earthquake. However,
damage in the plastic hinge region at the base of the RC core is not expected to be significantly
reduced when compared with a conventional structure. The development of a design solution
incorporating both VCDs as well as a means of mitigating structural damage at the base of the
core walls would further improve the seismic resilience of these structures.
CHAPTER 5: Conclusions and Recommendations 190
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
A significant challenge associated with the use of VE material is the temperature-
dependence of the material properties. As the VE material deforms in shear, energy is dissipated
in the form of heat, causing the temperature of the material to rise. Although changes in material
properties associated with changes in temperature can be accounted for through using a bounded
analysis, the development of an empirical relationship for the rate of change of VE material
temperature as a function of frequency, strain and duration of loading would be useful. Research
on this topic is currently underway at the University of Toronto.
The alternative design proposed for the case study building in this thesis involved
replacing all of the RC coupling beams in the reference structure with VCDs. Two similar VCD
designs were used over the entire height of the building – one in the East-West direction where
the coupling beam spans were 1295 mm, and one in the North-South direction where the
coupling beam spans were 1600 mm. The VE material and built-up steel assembly dimensions
were identical in the two designs, with the exception of the span of the shear-critical fuse
component. No attempts were made to improve the global response of the structure by using two
different VCD designs in the two orthogonal directions. Further optimization of the structural
response may also be possible by using multiple VCD designs in each core wall elevation. The
effects of tapering the VE material area and/or the shear fuse activation force up the height of the
structure on wall axial demands and higher mode behaviour could be investigated. Additionally,
a friction force-limiting fuse could be used in place of a shear-critical fuse to allow for
decoupling of the stiffness from the fuse force in the VCD design.
As discussed in Section 4.6.3, the added damping for wind provided by the VCDs
increases as the number of VCDs per lintel location is reduced. Although counterintuitive, this
trend can be understood by examining Equation (4-2), in which the equivalent viscous damping
in the system is expressed as a function of energy dissipated divided by the elastic energy stored
in the system at maximum displacement. By reducing the number of VCDs in each lintel
location, thereby reducing the degree of coupling between the wall piers, the energy dissipated
increases due to increased activation of the VCDs. Also, by reducing the lateral stiffness of the
system, the strain energy stored at a given displacement amplitude is reduced, resulting in a
further reduction in equivalent viscous damping. However, the results from this study show that
CHAPTER 5: Conclusions and Recommendations 191
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
there is an optimal number or size of VCDs, beyond which the equivalent viscous damping is
reduced when the number of VCDs is reduced. The development of an optimization tool to
determine the number and size of VCDs required to provide the largest amount of equivalent
viscous damping would enable designers to maximize design efficiency.
Cost analysis is an important aspect of performance-based seismic design. A thorough
assessment comparing the initial and life cycle costs of a conventional seismic-critical RC
coupled core wall high-rise structure with an alternative design using VCDs could be used to
inform stakeholders considering the application of this new technology. A probabilistic
estimation of repair costs, loss of operability, and the potential for casualties and structural
collapse associated with different seismic return periods could be carried out to provide a
measure of expected performance over the life of the structure.
The selection of appropriate ground motions to represent the seismic hazard at a given
site is a critical step in the performance-based design approach for high-rise buildings. Long-
period ground motions, such as those observed during the Tohoku Earthquake in 2011, have
been found to excite resonance in the predominant period of vibration of high-rise structures.
Distributed damping has been shown to be effective in reducing the duration and magnitude of
resonant vibration of high-rise buildings caused by long-period ground motions (Takewaki,
2011). Near-fault, high-intensity ground motions often contain severe velocity pulses which can
excite higher modes of vibration in high-rise structures (Calugaru and Panagiotou, 2012). The
results from the case study presented in Section 4.6.1 suggest that the distributed viscous
damping provided by VCDs may be effective in improving the response of RC coupled wall
high-rise structures to near-field pulse type events. Further studies examining the effectiveness of
VCDs in improving the response of RC coupled wall high-rise structures to long-period and
pulse type ground motions are recommended.
The case study described in this thesis provides an improved understanding of the seismic
and wind performance of a seismic-critical high-rise structure designed using VCDs. Based on
the results from the case study, an integrated design procedure for seismic-critical structures was
proposed. Montgomery (2011) proposed a design approach for wind-critical high-rise structures
using VCDs. However, in some cases the design of a high-rise structure may be controlled by a
CHAPTER 5: Conclusions and Recommendations 192
Performance-Based Design of RC Coupled Wall High-Rise Buildings with Viscoelastic Coupling Dampers
combination of seismic and wind effects. More research is required in order to develop a general
design strategy for high-rise structures that are both seismic-critical and wind-critical.
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APPENDIX A: RESPONSE-2000 RESULTS
This appendix includes screen captures from Response-2000. Input parameters and
sectional response analysis results for the RC core walls in the Case Study building described in
Section 3.4.2 are presented.
206
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Geometry and Material Properties
207
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Sectional Response
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APPENDIX B: COUPLING BEAM SCHEDULE
This appendix includes a coupling beam schedule for the case study reference structure.
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Coupling Beam Schedule
N&S Elevations
Storey L01 & L10 L20 & L32 L22 & L30
R
B124
41 1B 1B 3B
40 3B 3B 3B
39 4B 4B 4B
38 4B 4B 4B
37 4B 4B 4B
36 4B 4B 4B
35 4B 4B 4B
34 4B 4B 4B
33 4B 4B 4B
32 4B 4B 4B
31 4B 4B 4B
30 5B 7B 7B
29 5B 7B 7B
28 5B 7B 7B
27 5B 7B 7B
26 5B 7B 7B
25 5B 7B 7B
24 5B 7B 7B
23 5B 7B 7B
22 5B 7B 7B
21 5B 7B 7B
20 7B 7B 7B
19 7B 7B 7B
18 7B 7B 7B
17 7B 7B 7B
16 7B 9B 7B
15 7B 9B 9B
14 7B 9B 9B
13 7B 9B 9B
12 11B 12B 10B
11 11B 12B 10B
10 11B 12B 12B
9 11B 14B 12B
8 13B 14B 12B
7 13B 14B 12B
6 13B 14B 12B
5 13B 14B 12B
4 13B 14B 12B
3 13B 14B 12B
2 11B 14B 12B
1 11B 12B 10B
B81B
B62B
B63B
B24B
E&W Elevations
N
L32
L30
L22
L20
L10
L01
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APPENDIX C: CORE WALL REINFORCEMENT SCHEDULE
This appendix includes the core wall reinforcement schedule for the case study reference
structure.
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Core Wall Reinforcement Schedule
Storey
Horizontal Vertical Horizontal Vertical Horizontal Vertical Horizontal Vertical Horizontal Vertical
R #6 @ 12'' EF #5 @ 12'' EF #6 @ 12'' EF #5 @ 12'' EF #6 @ 12'' EF #5 @ 12'' EF #6 @ 12'' EF #5 @ 12'' EF #6 @ 12'' EF #5 @ 12'' EF
42 #5 @ 4'' EF #8 @ 12'' EF #8 @ 12'' EF #7 @ 12'' EF #6 @ 12'' EF #8 @ 12'' EF #6 @ 12'' EF #7 @ 12'' EF #7 @ 12'' EF #7 @ 12'' EF
41 #5 @ 4'' EF #8 @ 12'' EF #8 @ 12'' EF #7 @ 12'' EF #6 @ 12'' EF #8 @ 12'' EF #7 @ 12'' EF #7 @ 12'' EF #7 @ 12'' EF #7 @ 12'' EF
40 #5 @ 4'' EF #8 @ 12'' EF #8 @ 12'' EF #7 @ 12'' EF #6 @ 12'' EF #8 @ 12'' EF #7 @ 12'' EF #7 @ 12'' EF #7 @ 12'' EF #7 @ 12'' EF
39 #5 @ 4'' EF #8 @ 12'' EF #8 @ 12'' EF #7 @ 12'' EF #6 @ 12'' EF #8 @ 12'' EF #7 @ 12'' EF #7 @ 12'' EF #7 @ 12'' EF #7 @ 12'' EF
38 #5 @ 4'' EF #8 @ 12'' EF #8 @ 12'' EF #7 @ 12'' EF #6 @ 12'' EF #8 @ 12'' EF #7 @ 12'' EF #7 @ 12'' EF #7 @ 12'' EF #7 @ 12'' EF
37 #5 @ 4'' EF #8 @ 12'' EF #8 @ 12'' EF #7 @ 12'' EF #6 @ 12'' EF #8 @ 12'' EF #7 @ 12'' EF #7 @ 12'' EF #7 @ 12'' EF #7 @ 12'' EF
36 #5 @ 4'' EF #10 @ 12'' EF #6 @ 6'' EF #9 @ 12'' EF #7 @ 12'' EF #10 @ 12'' EF #6 @ 12'' EF #8 @ 12'' EF #8 @ 12'' EF #9 @ 12'' EF
35 #5 @ 4'' EF #10 @ 12'' EF #6 @ 6'' EF #9 @ 12'' EF #7 @ 12'' EF #10 @ 12'' EF #6 @ 12'' EF #8 @ 12'' EF #8 @ 12'' EF #9 @ 12'' EF
34 #5 @ 4'' EF #10 @ 12'' EF #6 @ 6'' EF #9 @ 12'' EF #7 @ 12'' EF #10 @ 12'' EF #6 @ 12'' EF #8 @ 12'' EF #8 @ 12'' EF #9 @ 12'' EF
33 #5 @ 4'' EF #10 @ 12'' EF #6 @ 6'' EF #9 @ 12'' EF #7 @ 12'' EF #10 @ 12'' EF #6 @ 12'' EF #8 @ 12'' EF #8 @ 12'' EF #9 @ 12'' EF
32 #5 @ 4'' EF #10 @ 12'' EF #6 @ 6'' EF #9 @ 12'' EF #7 @ 12'' EF #10 @ 12'' EF #6 @ 12'' EF #8 @ 12'' EF #8 @ 12'' EF #9 @ 12'' EF
31 #5 @ 4'' EF #10 @ 12'' EF #6 @ 6'' EF #9 @ 12'' EF #7 @ 12'' EF #10 @ 12'' EF #6 @ 12'' EF #8 @ 12'' EF #8 @ 12'' EF #9 @ 12'' EF
30 #5 @ 4'' EF #9 @ 6'' EF #6 @ 6'' EF #8 @ 6'' EF #8 @ 12'' EF #9 @ 6'' EF #6 @ 12'' EF #9 @ 12'' EF #8 @ 12'' EF #8 @ 6'' EF
29 #5 @ 4'' EF #9 @ 6'' EF #6 @ 6'' EF #8 @ 6'' EF #8 @ 12'' EF #9 @ 6'' EF #6 @ 12'' EF #9 @ 12'' EF #8 @ 12'' EF #8 @ 6'' EF
28 #5 @ 4'' EF #9 @ 6'' EF #6 @ 6'' EF #8 @ 6'' EF #8 @ 12'' EF #9 @ 6'' EF #6 @ 12'' EF #9 @ 12'' EF #8 @ 12'' EF #8 @ 6'' EF
27 #5 @ 4'' EF #9 @ 6'' EF #6 @ 6'' EF #8 @ 6'' EF #8 @ 12'' EF #9 @ 6'' EF #6 @ 12'' EF #9 @ 12'' EF #8 @ 12'' EF #8 @ 6'' EF
26 #5 @ 4'' EF #9 @ 6'' EF #6 @ 6'' EF #8 @ 6'' EF #8 @ 12'' EF #9 @ 6'' EF #6 @ 12'' EF #9 @ 12'' EF #8 @ 12'' EF #8 @ 6'' EF
25 #5 @ 4'' EF #9 @ 6'' EF #6 @ 6'' EF #8 @ 6'' EF #8 @ 12'' EF #9 @ 6'' EF #6 @ 12'' EF #9 @ 12'' EF #8 @ 12'' EF #8 @ 6'' EF
24 #5 @ 4'' EF #9 @ 6'' EF #7 @ 6'' EF #8 @ 6'' EF #8 @ 12'' EF #9 @ 6'' EF #6 @ 12'' EF #9 @ 12'' EF #8 @ 12'' EF #8 @ 6'' EF
23 #5 @ 4'' EF #9 @ 6'' EF #7 @ 6'' EF #8 @ 6'' EF #8 @ 12'' EF #9 @ 6'' EF #6 @ 12'' EF #9 @ 12'' EF #8 @ 12'' EF #8 @ 6'' EF
22 #5 @ 4'' EF #9 @ 6'' EF #7 @ 6'' EF #8 @ 6'' EF #8 @ 12'' EF #9 @ 6'' EF #6 @ 12'' EF #9 @ 12'' EF #8 @ 12'' EF #8 @ 6'' EF
21 #5 @ 4'' EF #9 @ 6'' EF #7 @ 6'' EF #8 @ 6'' EF #8 @ 12'' EF #9 @ 6'' EF #6 @ 12'' EF #9 @ 12'' EF #8 @ 12'' EF #8 @ 6'' EF
20 #5 @ 4'' EF #9 @ 6'' EF #7 @ 6'' EF #8 @ 6'' EF #8 @ 12'' EF #9 @ 6'' EF #6 @ 12'' EF #9 @ 12'' EF #8 @ 12'' EF #8 @ 6'' EF
19 #5 @ 4'' EF #9 @ 6'' EF #7 @ 6'' EF #8 @ 6'' EF #8 @ 12'' EF #9 @ 6'' EF #6 @ 12'' EF #9 @ 12'' EF #8 @ 12'' EF #8 @ 6'' EF
18 #5 @ 4'' EF #10 @ 6'' EF #7 @ 6'' EF #9 @ 6'' EF #8 @ 12'' EF #10 @ 6'' EF #7 @ 12'' EF #7 @ 6'' EF #7 @ 6'' EF #9 @ 6'' EF
17 #5 @ 4'' EF #10 @ 6'' EF #7 @ 6'' EF #9 @ 6'' EF #8 @ 12'' EF #10 @ 6'' EF #7 @ 12'' EF #7 @ 6'' EF #7 @ 6'' EF #9 @ 6'' EF
16 #5 @ 4'' EF #10 @ 6'' EF #7 @ 6'' EF #9 @ 6'' EF #8 @ 12'' EF #10 @ 6'' EF #7 @ 12'' EF #7 @ 6'' EF #7 @ 6'' EF #9 @ 6'' EF
15 #5 @ 4'' EF #10 @ 6'' EF #7 @ 6'' EF #9 @ 6'' EF #8 @ 12'' EF #10 @ 6'' EF #7 @ 12'' EF #7 @ 6'' EF #7 @ 6'' EF #9 @ 6'' EF
14 #5 @ 4'' EF #10 @ 6'' EF #7 @ 6'' EF #9 @ 6'' EF #8 @ 12'' EF #10 @ 6'' EF #7 @ 12'' EF #7 @ 6'' EF #7 @ 6'' EF #9 @ 6'' EF
13 #5 @ 4'' EF #10 @ 6'' EF #7 @ 6'' EF #9 @ 6'' EF #8 @ 12'' EF #10 @ 6'' EF #7 @ 12'' EF #7 @ 6'' EF #7 @ 6'' EF #9 @ 6'' EF
12 #5 @ 4'' 3 layers #10 @ 6'' EF #8 @ 6'' EF #10 @ 6'' EF #6 @ 6'' EF #10 @ 6'' EF #8 @ 6'' EF #8 @ 6'' EF #7 @ 6'' EF #10 @ 6'' EF
11 #5 @ 4'' 3 layers #10 @ 6'' EF #8 @ 6'' EF #10 @ 6'' EF #6 @ 6'' EF #10 @ 6'' EF #8 @ 6'' EF #8 @ 6'' EF #7 @ 6'' EF #10 @ 6'' EF
10 #5 @ 4'' 3 layers #10 @ 6'' EF #8 @ 6'' EF #10 @ 6'' EF #6 @ 6'' EF #10 @ 6'' EF #8 @ 6'' EF #8 @ 6'' EF #7 @ 6'' EF #10 @ 6'' EF
9 #5 @ 4'' 3 layers #10 @ 6'' EF #8 @ 6'' EF #10 @ 6'' EF #6 @ 6'' EF #10 @ 6'' EF #8 @ 6'' EF #8 @ 6'' EF #7 @ 6'' EF #10 @ 6'' EF
8 #5 @ 4'' 3 layers #10 @ 6'' EF #8 @ 6'' EF #10 @ 6'' EF #6 @ 6'' EF #10 @ 6'' EF #8 @ 6'' EF #8 @ 6'' EF #7 @ 6'' EF #10 @ 6'' EF
7 #5 @ 4'' 3 layers #10 @ 6'' EF #8 @ 6'' EF #10 @ 6'' EF #6 @ 6'' EF #10 @ 6'' EF #8 @ 6'' EF #8 @ 6'' EF #7 @ 6'' EF #10 @ 6'' EF
6 #5 @ 4'' 3 layers #10 @ 6'' EF #9 @ 6'' EF #10 @ 6'' EF #7 @ 6'' EF #10 @ 6'' EF #9 @ 6'' EF #8 @ 6'' EF #8 @ 6'' EF #10 @ 6'' EF
5 #5 @ 4'' 3 layers #10 @ 6'' EF #9 @ 6'' EF #10 @ 6'' EF #7 @ 6'' EF #10 @ 6'' EF #9 @ 6'' EF #8 @ 6'' EF #8 @ 6'' EF #10 @ 6'' EF
4 #5 @ 4'' 3 layers #10 @ 6'' EF #9 @ 6'' EF #10 @ 6'' EF #7 @ 6'' EF #10 @ 6'' EF #9 @ 6'' EF #8 @ 6'' EF #8 @ 6'' EF #10 @ 6'' EF
3 #5 @ 4'' 3 layers #10 @ 6'' EF #8 @ 6'' 3 layers #10 @ 6'' EF #8 @ 6'' EF #10 @ 6'' EF #8 @ 6'' 3 layers #8 @ 6'' EF #9 @ 6'' EF #10 @ 6'' EF
2 #5 @ 4'' 3 layers #10 @ 6'' EF #8 @ 6'' 3 layers #10 @ 6'' EF #8 @ 6'' EF #10 @ 6'' EF #8 @ 6'' 3 layers #8 @ 6'' EF #9 @ 6'' EF #10 @ 6'' EF
1 #5 @ 4'' 3 layers #10 @ 6'' EF #8 @ 6'' 3 layers #10 @ 6'' EF #8 @ 6'' EF #10 @ 6'' EF #8 @ 6'' 3 layers #8 @ 6'' EF #9 @ 6'' EF #10 @ 6'' EF
B1 #6 @ 6'' EF # 11 @ 6'' EF #6 @ 6'' EF # 11 @ 6'' EF #7 @ 6'' EF #11 @ 6'' EF #7 @ 6'' EF #11 @ 6'' EF #7 @ 6'' EF #11 @ 6'' EF
B2 #6 @ 6'' EF # 11 @ 6'' EF #6 @ 6'' EF # 11 @ 6'' EF #7 @ 6'' EF #11 @ 6'' EF #7 @ 6'' EF #11 @ 6'' EF #7 @ 6'' EF #11 @ 6'' EF
B3 #6 @ 6'' EF # 11 @ 6'' EF #6 @ 6'' EF # 11 @ 6'' EF #7 @ 6'' EF #11 @ 6'' EF #7 @ 6'' EF #11 @ 6'' EF #7 @ 6'' EF #11 @ 6'' EF
B4 #6 @ 6'' EF # 11 @ 6'' EF #6 @ 6'' EF # 11 @ 6'' EF #7 @ 6'' EF #11 @ 6'' EF #7 @ 6'' EF #11 @ 6'' EF #7 @ 6'' EF #11 @ 6'' EF
W20&W34 W22&W32 W24&W30
E&W Elevations
W01&W13 W03&W11
N&S Elevations
W32
W30
W34
W22
W20
W24
W01 W03
W11 W13
N
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APPENDIX D: COLUMN SIZES
This appendix includes the column sizes for the case study reference structure.
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A
B
C
D
E
F
1 2 3 3.5 4 5 6
F/4 F/5
E/6E/5
D/6D/5D/3.5
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APPENDIX E: GRAVITY LOADS
This appendix includes the gravity loads and seismic masses for the case study reference
structure.
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