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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 4.35 Steel assembly modelling parameters ....................................................................... 146





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Table 4.40 Maximum response quantities – DBE 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 4.41 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 4.46 Configuration E core wall plans .............................................................................. 142

Figure 4.47 SLE performance ..................................................................................................... 143



Figure 4.50 Configuration F schematic core wall plans ............................................................. 146

Figure 4.51 SLE performance ..................................................................................................... 147

Figure 4.52 MCE performance ................................................................................................... 148


Figure 4.54 Summary of parametric study ................................................................................. 151

Figure 4.55 VCD design ............................................................................................................. 152


Figure 4.57 Global performance – DBE level ............................................................................ 153


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



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



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



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



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



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


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.)



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



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.



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:



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



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



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



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.



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



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



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)



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



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



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



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



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



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).



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)


Emperical fragility function (MoR-3)




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



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



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



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



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



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.



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



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



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


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)




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



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



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



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



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


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.



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



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



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)



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



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



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



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.



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.



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

)



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

(%

)



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

)



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



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



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


Late

ral

Loa

d (

kip

)

−12 −6 0 6 12−200

−100

0

100

200


Late

ral

Loa

d (

kip

)



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



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



(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.



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



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



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)



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



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)



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



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:



�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)



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



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



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



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



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



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



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



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



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.



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



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



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



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



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.



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



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



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

)



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.)



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.



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



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

)


max. = 4,550 kN

max. = 3,160 kN



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



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

)


δpeak

Vb*

Vb



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



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



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



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



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-



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



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



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).

CHAPTER 4: Case Study 96


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)



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:



• 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



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



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



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



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.



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



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

)



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



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



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



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.



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



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



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



East-West Direction

North-South Direction

Figure 4.14 Reference structure SLE performance

East-West 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

)


0 0.2 0.4 0.6 0.8 1

0

20

40

60

80

100

120


He

igh

t (m

)


0 0.5 1 1.5 20

20

40

60

80

100

120


He

igh

t (m

)


0 10 20 30 40 50

0

20

40

60

80

100

120


He

igh

t (m

)


0 0.5 1 1.5 2

0

20

40

60

80

100

120


He

igh

t (m

)


0 1 2 3 4 50

20

40

60

80

100

120


He

igh

t (m

)


0 20 40 60 80 100

0

20

40

60

80

100

120


He

igh

t (m

)


0 0.5 1 1.5 2

0

20

40

60

80

100

120


He

igh

t (m

)


0 1 2 3 4 50

20

40

60

80

100

120


He

igh

t (m

)


0 20 40 60 80 100

0

20

40

60

80

100

120


He

igh

t (m

)




East-West 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


He

igh

t (m

)


0 1 2 3 4 5 60

20

40

60

80

100

120


He

igh

t (m

)


0 20 40 60 80 100

0

20

40

60

80

100

120


He

igh

t (m

)


0 0.5 1 1.5 2

0

20

40

60

80

100

120


He

igh

t (m

)


0 1 2 3 4 5 60

20

40

60

80

100

120


He

igh

t (m

)


0 20 40 60 80 100

0

20

40

60

80

100

120


He

igh

t (m

)




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 (%)


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 (%)


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



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



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)



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

)




0 0.05 0.1 0.15 0.2

0

20

40

60

80

100

120


He

igh

t (m

)



0 0.05 0.1 0.15 0.2

0

20

40

60

80

100

120


He

igh

t (m

)



0 0.05 0.1 0.15 0.2

0

20

40

60

80

100

120

He

igh

t (m

)






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



a) East-West Direction b) North-South Direction

Figure 4.19 Deformed shape under NBCC SLS wind loads


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


He

igh

t (m

)



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



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



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.



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



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



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



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


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


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




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



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



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.)



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



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


Figure 4.29 Global performance – SLE level

0 0.2 0.4 0.6 0.8 1

0

20

40

60

80

100

120


He

igh

t (m

)

Reference StructureConfigura!on A

0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120


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


He

igh

t (m

)


0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120


He

igh

t (m

)


0 1 2 3 4 5

x 104

0

20

40

60

80

100

120


He

igh

t (m

)




East-West 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


He

igh

t (m

)


0 0.5 1 1.5 2 2.5 3 3.50

20

40

60

80

100

120


He

igh

t (m

)


0 2 4 6 8 10

x 104

0

20

40

60

80

100

120


He

igh

t (m

)


0 0.5 1 1.5 2

0

20

40

60

80

100

120


He

igh

t (m

)


0 0.5 1 1.5 2 2.5 3 3.50

20

40

60

80

100

120


He

igh

t (m

)


0 2 4 6 8 10

x 104

0

20

40

60

80

100

120


He

igh

t (m

)


−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)



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

)


0 100 200 300 400 500

0

20

40

60

80

100

120


He

igh

t (m

)


0 0.002 0.004 0.006 0.008 0.01

0

20

40

60

80

100

120


He

igh

t (m

)




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

)


−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

)




�^ =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



a) EW Direction b) NS Direction c) Torsion

Figure 4.36 Mode shapes


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)


0 20 40 60 80 100−60

−40

−20

0

20

40

60

Time (s)

Dis

pla

cem

en

t (m

m)


0 20 40 60 80 100−20

−15

−10

−5

0

5

10

15

20

Time (s)R

ota

"o

n (

rad

x10

3)




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



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


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


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


He

igh

t (m

)


0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120


He

igh

t (m

)


0 1 2 3 4

x 104

0

20

40

60

80

100

120


He

igh

t (m

)




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



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


He

igh

t (m

)


0 1 2 3 40

20

40

60

80

100

120


He

igh

t (m

)


0 2 4 6 8 10

x 104

0

20

40

60

80

100

120


He

igh

t (m

)


0 0.5 1 1.5 2 2.5

0

20

40

60

80

100

120


He

igh

t (m

)


0 1 2 3 40

20

40

60

80

100

120


He

igh

t (m

)


0 2 4 6 8 10

x 104

0

20

40

60

80

100

120


He

igh

t (m

)




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.


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



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



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


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


He

igh

t (m

)

Configura!on BConfigura!on CConfigura!on D

0 100 200 300 400

0

20

40

60

80

100

120


He

igh

t (m

)


0 0.002 0.004 0.006 0.008 0.01

0

20

40

60

80

100

120


He

igh

t (m

)




d) VCD Response e) VEM Response f) Steel Response

Figure 4.42 VCD hysteresis – Configuration B


Figure 4.43 VCD hysteresis – Configuration C


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)



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.



Configuration


(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


He

igh

t (m

)


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

)


0 200 400 600 800

0

20

40

60

80

100

120


He

igh

t (m

)


0 0.02 0.04 0.06 0.08 0.1

0

20

40

60

80

100

120


He

igh

t (m

)




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



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


Figure 4.47 SLE performance



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


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


He

igh

t (m

)

Reference StructureConfigura#on DConfigura#on E

0 1 2 3 4

x 104

0

20

40

60

80

100

120


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


He

igh

t (m

)


0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120


He

igh

t (m

)


0 1 2 3 4

x 104

0

20

40

60

80

100

120

Maximum Core Wall Shear (kN)H

eig

ht

(m)




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





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


He

igh

t (m

)


0 1 2 3 40

20

40

60

80

100

120


He

igh

t (m

)


0 2 4 6 8 10

x 104

0

20

40

60

80

100

120


He

igh

t (m

)


0 0.5 1 1.5 2

0

20

40

60

80

100

120


He

igh

t (m

)


0 1 2 3 40

20

40

60

80

100

120


He

igh

t (m

)


0 2 4 6 8 10

x 104

0

20

40

60

80

100

120


He

igh

t (m

)




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.



Configuration


(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


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


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


He

igh

t (m

)

Configura!on DConfigura!on E



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



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



0 0.2 0.4 0.6 0.8

0

20

40

60

80

100

120


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


He

igh

t (m

)

Reference StructureConfigura#on DConfigura#on F

0 1 2 3 4

x 104

0

20

40

60

80

100

120


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


He

igh

t (m

)


0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120


He

igh

t (m

)


0 1 2 3 4

x 104

0

20

40

60

80

100

120


He

igh

t (m

)




East-West Direction


Figure 4.52 MCE performance



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



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


He

igh

t (m

)


0 1 2 3 40

20

40

60

80

100

120


He

igh

t (m

)


0 2 4 6 8 10

x 104

0

20

40

60

80

100

120


He

igh

t (m

)


0 0.5 1 1.5 2

0

20

40

60

80

100

120


He

igh

t (m

)


0 1 2 3 40

20

40

60

80

100

120


He

igh

t (m

)


0 2 4 6 8 10

x 104

0

20

40

60

80

100

120


He

igh

t (m

)




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.


0 200 400 600 800

0

20

40

60

80

100

120


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


He

igh

t (m

)

Configura!on DConfigura!on F

0 200 400 600 800

0

20

40

60

80

100

120


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


He

igh

t (m

)

Configura!on DConfigura!on F



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.


Configuration


(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



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


- Modest improvement at SLE

-Poor performance at MCE

-Modest loss of lateral s"ffness

Configura"on B


- 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



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



East-West Direction



East-West 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


He

igh

t (m

)

Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanReference Structure Mean

0 0.5 1 1.5 20

20

40

60

80

100

120


He

igh

t (m

)

Supers""on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanReference Structure Mean

0 10 20 30 40 50

0

20

40

60

80

100

120


He

igh

t (m

)


0 0.2 0.4 0.6 0.8 1

0

20

40

60

80

100

120


He

igh

t (m

)


0 0.5 1 1.5 20

20

40

60

80

100

120


He

igh

t (m

)


0 10 20 30 40 50

0

20

40

60

80

100

120


He

igh

t (m

)


0 0.5 1 1.5 2

0

20

40

60

80

100

120


He

igh

t (m

)


0 1 2 3 4 50

20

40

60

80

100

120


He

igh

t (m

)


0 20 40 60 80 100

0

20

40

60

80

100

120


He

igh

t (m

)


0 0.5 1 1.5 2

0

20

40

60

80

100

120


He

igh

t (m

)


0 1 2 3 4 50

20

40

60

80

100

120


He

igh

t (m

)


0 20 40 60 80 100

0

20

40

60

80

100

120


He

igh

t (m

)




East-West Direction



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


He

igh

t (m

)


0 1 2 3 4 5 6 70

20

40

60

80

100

120


He

igh

t (m

)


0 20 40 60 80 100 120

0

20

40

60

80

100

120

Maximum Storey Shear (MN)

He

igh

t (m

)


0 0.5 1 1.5 2 2.5

0

20

40

60

80

100

120


He

igh

t (m

)


0 1 2 3 4 5 6 70

20

40

60

80

100

120


He

igh

t (m

)


0 20 40 60 80 100 120

0

20

40

60

80

100

120

Maximum Storey Shear (MN)

He

igh

t (m

)




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.



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


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 (%)




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 (%)


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



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



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


He

igh

t (m

)

Reference StructureAlterna!ve Design

0 1 2 3 40

20

40

60

80

100

120


He

igh

t (m

)

Reference StructureAlterna"ve Design

0 20 40 60 80 100

0

20

40

60

80

100

120


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

)


peak = 1.23 mpeak = 1.22 m



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

)


0 200 400 600 800 1000

0

20

40

60

80

100

120


He

igh

t (m

)


0 200 400 600 800 1000

0

20

40

60

80

100

120


He

igh

t (m

)


0 200 400 600 800 1000

0

20

40

60

80

100

120


He

igh

t (m

)


0 200 400 600 800 1000

0

20

40

60

80

100

120


He

igh

t (m

)


0 200 400 600 800 1000

0

20

40

60

80

100

120


He

igh

t (m

)




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


He

igh

t (m

)

Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanRepair Required

0 0.05 0.1 0.15

0

20

40

60

80

100

120


He

igh

t (m

)


0 0.05 0.1 0.15

0

20

40

60

80

100

120


He

igh

t (m

)


0 0.05 0.1 0.15

0

20

40

60

80

100

120

11 Fuses Require Repair


He

igh

t (m

)

Supers!!on HillsDenaliNorthridge SCSLoma PrietaDuzceLandersKocaeliMeanRepair Required

0 0.05 0.1 0.15

0

20

40

60

80

100

120


He

igh

t (m

)


0 0.05 0.1 0.15

0

20

40

60

80

100

120


He

igh

t (m

)


−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)



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



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

)


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)


peak = 263 mmpeak = 240 mm



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.



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

)


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)


peak = 669 mm

peak = 861 mm



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


0 0.004 0.008 0.012 0.016B4

GND

L5 L10 L15 L20 L25 L30 L35 L40 R

Tensile Strain

Sto

rey


0 0.004 0.008 0.012 0.016B4

GND

L5 L10 L15 L20 L25 L30 L35 L40 R

Tensile Strain

Sto

rey


0 0.004 0.008 0.012 0.016B4

GND

L5 L10 L15 L20 L25 L30 L35 L40 R

Tensile StrainS

tore

y


0 0.001 0.002 0.003 0.004B4

GND

L5 L10 L15 L20 L25 L30 L35 L40 R

Compressive Strain

Sto

rey


0 0.001 0.002 0.003 0.004B4

GND

L5 L10 L15 L20 L25 L30 L35 L40 R

Compressive Strain

Sto

rey


0 0.001 0.002 0.003 0.004B4

GND

L5 L10 L15 L20 L25 L30 L35 L40 R

Compressive Strain

Sto

rey


0 0.001 0.002 0.003 0.004B4

GND

L5 L10 L15 L20 L25 L30 L35 L40 R

Compressive Strain

Sto

rey




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

)


c’

0 2 4 6 8

x 104

0

20

40

60

80

100

120

Shear (kN)

He

igh

t (m

)


c’

0 5000 10000 150000

20

40

60

80

100

120

Shear (kN)

He

igh

t (m

)


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

)


c’

0 1 2 3 4

x 104

0

20

40

60

80

100

120

Shear (kN)

He

igh

t (m

)


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

)


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

)


c’

0 1 2 3 4

x 104

0

20

40

60

80

100

120

Shear (kN)

He

igh

t (m

)


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

)


c’



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




Figure 4.71 Free vibration at 30th floor level


Figure 4.72 Deformed shape due to NBCC SLS wind loads


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)


0 20 40 60 80 100−80

−60

−40

−20

0

20

40

60

80

Time (s)

Dis

pla

cem

en

t (m

m)


0 20 40 60 80 100−40

−30

−20

−10

0

10

20

30

40

Time (s)

Ro

ta"

on

(ra

dx1

03)


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


He

igh

t (m

)


0 0.05 0.1 0.15 0.2

0

20

40

60

80

100

120


He

igh

t (m

)




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



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[ÁSÂ¾¿^À (4-4)

where ¾¿^À is the mode shape in mode $ and ÁSÂ 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



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, 2Ã�, 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.



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



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



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



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



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



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 = DAÄ��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



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


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



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



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.



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



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,



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



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.


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



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

)


Period

shi!

Typical

design

Alterna�ve

design

T (sec)

SD

(m

m)


Period

shi!

Typical

design

Alterna�ve

design



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.



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.


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



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



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

)


Added

damping

Typical

design

Alterna�ve

design

T (sec)

SD

(m

m)


Added

damping

Typical

design

Alterna�ve

design



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.


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.



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.



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



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



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.

CHAPTER 6: References 193


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205


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


Geometry and Material Properties

207


Sectional Response

208


APPENDIX B: COUPLING BEAM SCHEDULE

This appendix includes a coupling beam schedule for the case study reference structure.

209


(adapted from PEER/ATC, 2011)

210


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

211


APPENDIX C: CORE WALL REINFORCEMENT SCHEDULE

This appendix includes the core wall reinforcement schedule for the case study reference

structure.

212


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






























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









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



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




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

213


APPENDIX D: COLUMN SIZES

This appendix includes the column sizes for the case study reference structure.

214


(adapted from PEER/ATC, 2011)

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

215


APPENDIX E: GRAVITY LOADS

This appendix includes the gravity loads and seismic masses for the case study reference

structure.

216


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