Assessment of the Behaviour Factor for the Seismic Design ... · Assessment of the Behaviour Factor for the Seismic Design of Reinforced Concrete Structural Walls according to SANS

Assessment of the Behaviour Factor for the Seismic

Design of Reinforced Concrete Structural Walls according to SANS 10160: Part 4

by

Christian Alexander Spathelf

Thesis presented in partial fulfillment of the requirements for the degree

Master of Science at Stellenbosch University

Supervisor:

Professor J. A. Wium

December, 2008

i

DECLARATION By submitting this thesis electronically, I declare that the entirety of the work contained

therein is my own, original work, that I am the owner of the copyright thereof (unless to

the extent explicitly otherwise stated) and that I have not previously in its entirety or in

part submitted it for obtaining any qualification.

Date: December 2008

Copyright 2008 Stellenbosch University

All rights reserved

ii

SYNOPSIS

The South African code for the design loading of building structures, namely SABS

0160 (1989), was revised with the requirements for seismic design prescribed in SANS

10160: Part 4: Seismic actions and general requirements for buildings. SANS 10160:

Part 4 incorporates the seismic design provisions of several seismic codes of practice,

however, the influence of the value prescribed for the behaviour factor has not been

established with regard to South African conditions.

The behaviour factor is used by most seismic design codes to account for the energy

dissipating effects of plastification in structural systems when subjected to earthquake

ground motion, to reduce the elastically determined forces to be designed for. However,

a considerable difference is observed in the values of the behaviour factor prescribed for

the design of reinforced concrete walls between the leading international seismic codes.

The aim of this study is to assess the value of the behaviour factor prescribed in SANS

10160: Part 4 for reinforced concrete structural walls under the influence of South

African seismic conditions and code requirements.

A method of quantifying the value of the behaviour factor was developed and

implemented in the study by Ceccotti (2008). This method entails estimation of the

maximum analytical behaviour factor as the ratio of seismic intensity at failure of the

structure to the seismic intensity prescribed by the design code. Such a method is

adopted for this study where the lateral force resisting systems of six-, eight- and ten-

storey buildings are investigated with nonlinear static analysis to quantify the maximum

computationally-determined value of the behaviour factor.

Firstly, it is observed that it is possible to quantify the value of the behaviour factor

through the use of a computational study. The nonlinear static method of analysis is

shown to provide reliable results in the estimation of the behaviour factor for a six-

storey building, however, does not perform well for taller buildings. Further

SYNOPSIS iii

C. A. Spathelf University of Stellenbosch

investigation with the use of dynamic time-history analysis is proposed to evaluate the

influence of the factors identified in this study.

The behaviour of structural walls, designed for reduced forces with the prescribed

behaviour factor of 5.0, exhibits high yield strengths and resists the design seismic

action entirely elastically. This high strength is found to be due to the

reliability/redundancy factor prescribed by SANS 10160: Part 4 and because of the high

values of structural overstrength. Similar studies observed high values of structural

overstrength for buildings designed for low seismic intensity, which were shown to

result from the fact that the resistance required to gravity loading became more critical

than the seismic loads in the design of the structural system.

This study identifies several factors that influence the value of the behaviour factor,

such as the number of walls in the lateral force resisting system; the number of storeys

of the buildings; available displacement ductility of the structural system; and the

ground type designed for.

iv

SINOPSIS

Die Suid-Afrikaanse kode vir die bepaling van die ontwerp belasting van strukture,

naamlik SABS 0160 (1989), word tans hersien met die voorskrifte vir seismiese

ontwerp voorsien in SANS 10160: Part 4: Seismic actions and general requirements for

buildings. SANS 10160: Part 4 bevat die seismiese ontwerp riglyne van verskeie

seismiese ontwerp kodes, sonder dat die invloed van die voorgestelde waarde van die

gedragsfactor (behaviour factor) hersien is vir Suid-Afrikaanse omstandighede.

Die gedragsfaktor word gebruik in die meeste seismiese ontwerp kodes om die energie

dissiperende effek van plastifisering van struktuur elemente in berekening te bring,

sodat die elastiese kragte verminder kan word. Verskille is waargeneem tussen die

voorgestelde waardes van die gedragsfaktor tussen internasionale seismiese ontwerp

kodes.

Die doel van hierdie studie is om die waarde van die gedragsfaktor, soos voorgeskryf in

SANS 10160: Part 4, te evalueer onder die invloed van Suid-Afrikaanse seismiese

kondisies en kode voorskrifte.

Metode is ontwikkel in die studie van Ceccotti (2008) om die gedragsfaktor te

kwantifiseer as die verhouding van die seismiese intensiteit wat faling van die struktuur

veroorsaak tot die seismiese intensiteit wat die kode voorskryf. Soortgelyke metode is

aanvaar vir hierdie studie waar die seismiese gedrag van skuif-mure in ses-, agt- en tien-

verdieping strukture ondersoek is met nie-linere statiese analise om die gedragsfaktor

te kwantifiseer.

Eerstens is daar bevind dat dit moontlik is om die maksimum grootte van die

gedragsfaktor te bereken deur die gebruik van numeriese analise. Dit is bevind dat die

nie-linere statiese analise metode betroubare resultate bied vir die berekening van die

gedragsfaktor vir ses-verdieping struktuur. Hierdie metode het wel nie so goed gevaar

met hor strukture nie en dinamiese tyd-stap analise word voorgestel vir verdere

ondersoek.

SINOPSIS v


Die strukturele gedrag van skuif-mure, ontwerp vir die verlaagde kragte soos bepaal met

die voorgeskrewe gedragsfaktor van 5.0, toon ho swig-sterktes en bied weerstand teen

die ontwerp aardbewing binne die elastiese bereik van die mure. Dit is bevind dat die

ho swig-sterktes veroorsaak word deur die betroubaarheid/oortolligheidsfaktor

(reliability/redundancy factor) voorgeskryf deur SANS 10160: Part 4 en as gevolg

van ho addisionele kapasiteit (overstrength). Soortgelyke navorsing het ook ho

waardes van addisionele kapasiteit (overstrength) bevind vir strukture wat ontwerp is

vir relatiewe lae seismiese intensiteit. Die oorsaak is bewys as die relatiewe invloed van

strukturele gewig wat meer bydra tot die ontwerp van struktuur elemente as die effekte

van seismiese belasting.

Hierdie studie identifiseer aantal faktore wat die grootte van die gedragsfaktor

benvloed, naamlik die aantal skuif-mure in die strukturele sisteem; die aantal

verdiepings van die struktuur; die beskikbare verplasingsduktiliteit van die struktuur; en

die grond tipe waarvoor ontwerp is.

vi

ACKNOWLEDGEMENTS

I would like to acknowledge the contribution of the following people. Without their

support, technical knowledge and encouragement this study would not have been

completed.

Professor J. A. Wium, who always knew when to return to basics and has the

incredible talent of simplifying even the most complex problem into the behaviour

of a beam.

Professor A. Dazio, for accommodating me at the Swiss Federal Institute of

Technology (ETH Zrich, Switzerland) and for providing much insight into the

problem of assessing the behaviour factor.

My fellow students in the Masters office, Chantal, Graeme, Marius and Wibke who

supported me throughout the two years of postgraduate studies and became lifelong

friends during the late nights and many coffee breaks.

Barbara Garbers, who spent countless hours editing and correcting my somewhat

limited capabilities in the English language.

Lastly, my family (especially Helne) who kept faith in me and were there every

step of the way when I needed them most.

vii

TABLE OF CONTENTS

Chapter Page

DECLARATION ........................................................................................................................................ i

SYNOPSIS.................................................................................................................................................. ii

SINOPSIS .................................................................................................................................................. iv

ACKNOWLEDGEMENTS ..................................................................................................................... vi

LIST OF FIGURES.................................................................................................................................. xi

LIST OF TABLES................................................................................................................................... xv

NOTATION........................................................................................................................................... xviii

TERMINOLOGY AND ACRONYMS ............................................................................................... xxiii

1 INTRODUCTION ........................................................................................ 1

1.1 Background.................................................................................................................................. 1

1.2 Aim of the study........................................................................................................................... 5

1.3 Methodology of the study............................................................................................................ 6

2 LITERATURE REVIEW .............................................................................. 8

2.1 Background.................................................................................................................................. 9 2.1.1 Seismic codes of practice.......................................................................................................... 9 2.1.2 Philosophy of capacity design ................................................................................................ 10

2.2 Analysis methods for seismic design ........................................................................................ 12 2.2.1 Overview of different seismic analysis methods .................................................................... 12 2.2.2 Equivalent lateral (static) force method.................................................................................. 13 2.2.3 Modal response spectrum method .......................................................................................... 15 2.2.4 Nonlinear static (pushover) analysis ....................................................................................... 15 2.2.5 Dynamic time-history analysis ............................................................................................... 16 2.2.6 Capacity spectrum method...................................................................................................... 17

2.3 Ductility ...................................................................................................................................... 17 2.3.1 Ductile structural response...................................................................................................... 18 2.3.2 Enhancing the ductility capacity of walls ............................................................................... 19

2.4 Structural walls.......................................................................................................................... 20 2.4.1 Behaviour of slender structural walls ..................................................................................... 20

2.5 Behaviour (or Response-reduction) factor .............................................................................. 22 2.5.1 The role of the behaviour factor.............................................................................................. 23 2.5.2 Proposed formulations of the behaviour factor....................................................................... 24

TABLE OF CONTENTS viii


2.6 Confinement of concrete ........................................................................................................... 46 2.6.1 Stress-strain relationship for Confined Concrete .................................................................... 47

2.7 Summary of important concepts .............................................................................................. 48

3 COMPARISON OF SEISMIC PROVISIONS IN INTERNATIONAL DESIGN CODES ............................................................................................................ 51

3.1 Prescribed behaviour factor ..................................................................................................... 52 3.1.1 SANS 10160: Part 4 Seismic actions and general requirements for buildings .................... 53 3.1.2 EN 1998-1: 2004: Design of structures for earthquake resistance.......................................... 53 3.1.3 SIA 261: 2003 Actions on structures ...................................................................................... 55 3.1.4 Uniform Building Code (1997)............................................................................................... 56 3.1.5 NZS 4203 (1992): General Structural Design and Design Loading for Buildings ................. 57 3.1.6 Comparison of behaviour factor of different codes ................................................................ 57

3.2 Representation of ground motion............................................................................................. 59 3.2.1 SANS 10160, EN 1998-1 and SIA 261 .................................................................................. 59 3.2.2 Uniform Building Code (1997)............................................................................................... 61 3.2.3 NZS 4203 (1992) .................................................................................................................... 62 3.2.4 Comparison of response spectra of different codes ................................................................ 64

3.3 Seismic load combination factors ............................................................................................. 72 3.3.1 SANS 10160: Part 4 Seismic actions and general requirements for buildings .................... 72 3.3.2 EN 1998-1: 2004: Design of structures for earthquake resistance.......................................... 73 3.3.3 Uniform Building Code (1997)............................................................................................... 73 3.3.4 NZS 4203 (1992): General Structural Design and Design Loading for Buildings ................. 74

3.4 Material/Force reduction factors ............................................................................................. 74 3.4.1 SANS 10160: Part 4, EN 1998-1 and SIA 262 ....................................................................... 74 3.4.2 Uniform Building Code (1997) and NZS 3103 (1992)........................................................... 75

3.5 Methods of analysis prescribed ................................................................................................ 76 3.5.1 SANS 10160: Part 4................................................................................................................ 76 3.5.2 EN 1998-1: 2004..................................................................................................................... 76 3.5.3 SIA 261: 2003......................................................................................................................... 77 3.5.4 Uniform Building Code (1997)............................................................................................... 77 3.5.5 NZS 4203 (1992) .................................................................................................................... 77

4 NUMERICAL MODELLING...................................................................... 78

4.1 Methodology and objectives of this study................................................................................ 79

4.2 Step 1: Design of the structure ................................................................................................. 82 4.2.1 Identification, description and classification of the example building.................................... 82 4.2.2 Slenderness of structural walls ............................................................................................... 86 4.2.3 Design of structural walls according to SANS 10160: Part 4 ................................................. 89

4.3 Inelastic seismic analysis procedures ....................................................................................... 93 4.3.1 Nonlinear static analysis procedures....................................................................................... 95 4.3.2 Capacity spectrum method...................................................................................................... 96

4.4 Step 2: Numerical modelling .................................................................................................... 99 4.4.1 Modelling requirements for nonlinear static analysis ............................................................. 99 4.4.2 Description of software......................................................................................................... 100 4.4.3 Material models .................................................................................................................... 100 4.4.4 Discretization of the numerical model .................................................................................. 103

TABLE OF CONTENTS ix


4.5 Step 3: Definition of failure criteria ....................................................................................... 104

4.6 Step 4: Analysis........................................................................................................................ 108 4.6.1 Practical implementation of nonlinear static analysis ........................................................... 108

4.7 Step 5: Quantification of the behaviour factor ..................................................................... 111

4.8 Verification of the results of nonlinear static analysis.......................................................... 115 4.8.1 Verification using experimental results from literature ........................................................ 115 4.8.2 Dynamic analysis procedures ............................................................................................... 122

4.9 Parametric study ..................................................................................................................... 123

5 RESULTS AND DISCUSSION ............................................................... 127

5.1 Expected outcome of the analyses .......................................................................................... 128

5.2 Initial investigations ................................................................................................................ 130 5.2.1 Influence of confinement parameters for concrete................................................................ 130 5.2.2 Influence of the redundancy factor ( ) on the value of the behaviour factor ..................... 132

5.3 Nonlinear static investigation on Ground Type 1, q = 5.0.................................................... 134 5.3.1 Investigation of a six-storey building ................................................................................... 135 5.3.2 Investigation of an eight-storey building .............................................................................. 138 5.3.3 Investigation of a ten-storey building ................................................................................... 141

5.4 Nonlinear static investigation on Ground Type 1, q = 1.0.................................................... 145 5.4.1 Investigation of a six-storey building ................................................................................... 146 5.4.2 Investigation of an eight-storey building .............................................................................. 150 5.4.3 Investigation of a ten-storey building ................................................................................... 153 5.4.4 Investigation of a sixteen-storey building............................................................................. 156

5.5 Nonlinear static investigation on Ground Type 4, q = 1.0.................................................... 157 5.5.1 Investigation of a sixstorey building................................................................................... 158 5.5.2 Investigation of an eightstorey building ............................................................................. 159 5.5.3 Investigation of a tenstorey building................................................................................... 161

5.6 Verification of results .............................................................................................................. 163 5.6.1 Dynamic time-history analysis ............................................................................................. 163 5.6.2 Comparison of nonlinear static and dynamic time-history analyses..................................... 165

5.7 Summary and discussion of results ........................................................................................ 167 5.7.1 Influence of displacement ductility on the value of the behaviour factor ............................. 167 5.7.2 Influence of the number of storeys on the value of the behaviour factor.............................. 167 5.7.3 Influence of ground type on the value of the behaviour factor ............................................. 173 5.7.4 Evaluation of reliability of results......................................................................................... 174

6 CONCLUSIONS AND RECOMMENDATIONS ...................................... 175

6.1 Conclusions .............................................................................................................................. 176 6.1.1 Analytical evaluation of the behaviour factor....................................................................... 176 6.1.2 Factors that influence the value of the behaviour factor ....................................................... 177 6.1.3 Reliability of the nonlinear static analysis method ............................................................... 179

6.2 Recommendations for further investigation.......................................................................... 180

APPENDICES................................................................................................ 187

TABLE OF CONTENTS x


A DESIGN OF STRUCTURAL WALLS ..................................................... 188

A.1 Design procedure implemented for a typical structural wall .............................................. 188 A.1.1 Design with equivalent lateral static force method ............................................................... 188 A.1.2 Nonlinear static analysis ....................................................................................................... 196 A.1.3 Capacity spectrum method.................................................................................................... 197

A.2 Capacity curves obtained from nonlinear static analysis..................................................... 199

B VERIFICATION OF NONLINEAR STATIC ANALYSIS.......................... 201

B.1 Verification using experimental results ................................................................................. 201 B.1.1 Material properties used in analysis...................................................................................... 201 B.1.2 Nonlinear static investigation of test specimen: Wall WSH1............................................... 202

B.2 Dynamic time-history analysis ............................................................................................... 205 B.2.1 Six-storey building................................................................................................................ 206 B.2.2 Eight-storey building ............................................................................................................ 207 B.2.3 Ten-storey building............................................................................................................... 209

xi

LIST OF FIGURES

Figure Page Figure 1.1: Influence of the behaviour factor on the shape of the design response spectrum...................... 3 Figure 1.2: Methodology of the investigation.............................................................................................. 6

Figure 2.1: Methodology of the investigation............................................................................................. 8 Figure 2.2: Schematic representation of the equivalent static lateral load procedure ................................ 15 Figure 2.3: Schematic representation of the Capacity spectrum method [20] ........................................... 17 Figure 2.4: Schematic representation of the playoff between strength and ductility [16].......................... 19 Figure 2.5: Hysteretic response of a structural wall controlled by shear strength [15].............................. 21 Figure 2.6: Stable hysteretic response of a ductile wall [22] ..................................................................... 22 Figure 2.7: Typical global structural response idealised as linearly elastic-perfect plastic curve [28] ...... 25 Figure 2.8: Definition of the behaviour factor according to SIA 261 [16]................................................. 26 Figure 2.9: Period-dependant formulation for the behaviour factor as per Eurocode 8 (1994) ................. 27 Figure 2.10: Ductility reduction factor relation proposed by Newmark and Hall (1982) [23] .................. 34 Figure 2.11: Formulation for the ductility reduction factor proposed by Vidic et al. (1994) [32]............. 34 Figure 2.12: Constant-ductility inelastic response spectrum according to the reduction proposed by Vidic

et al. (1994) [32] .............................................................................................................................. 35 Figure 2.13: Components of structural overstrength [26] .......................................................................... 37 Figure 2.14: Proposal of a period-dependant behaviour factor [23] .......................................................... 42 Figure 2.15: Variation of structural overstrength with seismic zones and number of storeys [28]............ 43 Figure 2.16: Experimental setup used to analyse the seismic behaviour of slender structural walls [37] . 44 Figure 2.17: Compression members with confining reinforcement [40] ................................................... 47 Figure 2.18 Stress-strain model for monotonic loading of confined and unconfined concrete in

compression [15] .............................................................................................................................. 47

Figure 3.1 Methodology of the investigation............................................................................................. 51

Figure 3.2: Definition of factors u and 1 on a typical force-deformation curve [18] ......................... 54

Figure 3.3: Design response spectrum according to UBC (1997) [48] ...................................................... 62 Figure 3.4: Seismic hazard acceleration coefficient for different soil conditions according to NZS4203

[45] ................................................................................................................................................... 63 Figure 3.5: Comparison of the elastic design response spectrum for hard subsoil conditions................... 66 Figure 3.6: Comparison of design response spectra for hard soil conditions, reduced with the code

prescribed value of the behaviour factor for structural walls ........................................................... 68

LIST OF FIGURES xii


Figure 3.7: Comparison of design response spectra for soft soil sites, reduced with the code prescribed

value of the behaviour factor for structural walls............................................................................. 70

Figure 4.1: Methodology of the investigation............................................................................................ 78 Figure 4.2 Summary of methodology and objectives ................................................................................ 81 Figure 4.3: Plan layout of the example structure illustrating the possible positions of structural walls in

the N-S direction .............................................................................................................................. 83 Figure 4.4: The components of shear wall deformation [54] ..................................................................... 87 Figure 4.5: Dimensions of a typical prismatic shear wall .......................................................................... 87 Figure 4.6: Comparison of flexural to shear stiffness for different wall slenderness ratios....................... 88 Figure 4.7: Comparison of the analytical and empirical estimation of the structural period ..................... 90 Figure 4.8: Schematic depiction of inelastic analysis procedures [9] ........................................................ 94 Figure 4.9 Inelastic seismic analysis procedures for various structural models and ground-motion

representations [9] ............................................................................................................................ 95 Figure 4.10: The nonlinear static analysis procedure [9] ........................................................................... 96 Figure 4.11: Schematic representation of the capacity spectrum method .................................................. 98 Figure 4.12: Numerical modelling of the wall section in fibre elements ................................................. 101 Figure 4.13: Schematic representation of the element discretization of the 6-, 8- and 10-storey walls ... 104 Figure 4.14: Building Performance Levels and ranges [7] ...................................................................... 105 Figure 4.15: Determination of idealised force-displacement relation [8] ................................................ 110 Figure 4.16: Proposed computational definition of the maximum value of the behaviour factor............ 112 Figure 4.17 Cumulative distribution of probability of failure.................................................................. 113 Figure 4.18 Schematic illustration of the anticipated influence of the choice of modelling on the

estimation of computationally-determined behaviour factor.......................................................... 114 Figure 4.19: Schematic representation of the experimental testing [59].................................................. 116 Figure 4.20: Testing parameters of the three experimental walls tested by Dazio et al. (1999) [59] and

modelled in this study .................................................................................................................... 116 Figure 4.21: Sectional layout of steel reinforcement provided for wall A) WSH1; B) WSH3; and C)

WSH4............................................................................................................................................. 118 Figure 4.22: Comparison of WSH1 experimental hysteresis curve and nonlinear static results.............. 119 Figure 4.23: Comparison of WSH3 experimental hysteresis curve and nonlinear static results.............. 120 Figure 4.24: Comparison of WSH4 experimental hysteresis curve and nonlinear static results.............. 121 Figure 4.25: Schematic representation of analyses performed on Ground Type 1 .................................. 124 Figure 4.26: Schematic representation of the proposed method of evaluating the behaviour factor ....... 125

Figure 5.1: Methodology of the investigation.......................................................................................... 127 Figure 5.2: Schematic representation of the actual procedure of elastic design ...................................... 129 Figure 5.3 Comparison of force-displacement relation for confined and unconfined concrete models... 131 Figure 5.4: Influence of the Redundancy factor on the capacity curve of a typical RC shear wall ......... 133 Figure 5.5: Design of the 6-storey lateral force resisting system for q = 5.0 (2walls 7500x250mm) ...... 135

LIST OF FIGURES xiii


Figure 5.6: Design of the 6-storey lateral force resisting system for q = 5.0 (2walls 5000x250mm) ...... 136 Figure 5.7: Design of the 8-storey lateral force resisting system for q = 5.0 (2walls 7500x250mm) ...... 139 Figure 5.8: Design of the 8-storey lateral force resisting system for q = 5.0 (4walls 5000x250mm) ...... 140 Figure 5.9: Design of the ten-storey lateral force resisting system for q = 5.0 (4walls 7500x250mm) ... 142 Figure 5.10: Design of the ten-storey lateral force resisting system for q = 5.0 (4walls 5000x250mm) . 143 Figure 5.11: Behaviour factor-displacement ductility relation of the six-storey structures ..................... 148 Figure 5.12: Behaviour factor-plastic hinge rotation relation of the six-storey structures....................... 149 Figure 5.13: Influence of increased wall thickness on the behaviour factor-displacement ductility relation

........................................................................................................................................................ 150 Figure 5.14: Maximum computationally-determined behaviour factor-displacement ductility relation of

the 8 storey walls............................................................................................................................ 152 Figure 5.15: Maximum computationally-determined behaviour factor-plastic hinge rotation relation of the

8 storey walls.................................................................................................................................. 153 Figure 5.16: Maximum computationally-determined value of the behaviour factor-displacement ductility

relation of a 10-storey building ...................................................................................................... 155 Figure 5.17: Maximum computationally-determined behaviour factor-plastic hinge rotation relation of a

10-storey building .......................................................................................................................... 156 Figure 5.18: Maximum computationally-determined value of the behaviour factor-displacement ductility

relation for a 6-storey building....................................................................................................... 158 Figure 5.19: Maximum computationally-determined value of the behaviour factor-displacement ductility

relation of an 8-storey building ...................................................................................................... 160 Figure 5.20: Maximum computationally-determined value of the behaviour factor-displacement ductility

relation of a 10-storey building ...................................................................................................... 161 Figure 5.21: Comparison of maxq results from nonlinear static and dynamic time-history analysis........ 165

Figure 5.22: Summary of the computationally-determined values of the maximum behaviour factor for

Ground Type 1 ............................................................................................................................... 169 Figure 5.23: The maximum computationally-determined behaviour factor as a function of displacement

ductility (Ground Type 1)............................................................................................................... 170 Figure 5.24: Computational values of the maximum behaviour factor obtained for subsoil conditions of

Ground Type 4 ............................................................................................................................... 171 Figure 5.25: Maximum computationally-determined behaviour factor as a function of the displacement

ductility ratio for Ground Type 4 ................................................................................................... 172 Figure 5.26: Schematic representation of the capacity curves and response spectra of Ground Types 1 and

4...................................................................................................................................................... 174

Figure 6.1: Methodology of the investigation.......................................................................................... 175

Figure A.1: Detail of steel reinforcement for the plastic hinge region of the six-storey RC structural wall

(7500 x 300 mm) ............................................................................................................................ 195

LIST OF FIGURES xiv


Figure A.2: Equivalent SDOF capacity curve of the structural wall, obtained with nonlinear static analysis

........................................................................................................................................................ 197 Figure A.3: Implementation of the proposed procedure for estimating the maximum computationally-

determined behaviour factor........................................................................................................... 198 Figure A.4: Capacity curves obtained for the six-storey structural walls ................................................ 199 Figure A.5: Capacity curves obtained for the eight-storey RC structural walls....................................... 200 Figure A.6: Capacity curves obtained for the ten-storey RC structural walls.......................................... 200

Figure B.1 Schematic representation of the boundary region transverse reinforcement of wall WSH1.. 204 Figure B.2 Equivalent SDOF pushover curve obtained from the computational investigation of wall

WSH1 with bilinear approximation................................................................................................ 205 Figure B.3: Total base shear-time relation for the 6-storey wall subjected to the Loma Prieta earthquake

........................................................................................................................................................ 206 Figure B.4: Total base shear-time relation for the 6-storey wall subjected to the Kocaeli earthquake.... 207 Figure B.5: Total base shear-time relation for the 6-storey wall subjected to the Friuli earthquake ....... 207 Figure B.6: Total base shear-time relation for the 8-storey wall subjected to the Loma Prieta earthquake

........................................................................................................................................................ 208 Figure B.7: Total base shear-time relation for the 8-storey wall subjected to the Kocaeli earthquake.... 208 Figure B.8: Total base shear-time relation for the 8-storey wall subjected to the Friuli earthquake ....... 209 Figure B.9: Total base shear-time relation for the 10-storey wall subjected to the Loma Prieta earthquake

........................................................................................................................................................ 209 Figure B.10: Total base shear-time relation for the 10-storey wall subjected to the Kocaeli earthquake 210 Figure B.11: Total base shear-time relation for the 10-storey wall subjected to the Friuli earthquake ... 210

xv

LIST OF TABLES

Table Page Table 1.1: Seismic history of the south western Cape Province [4]............................................................. 2 Table 1.2: Difference of the behaviour factor values between seismic design codes .................................. 5

Table 2.1: Historic development of seismic requirements [12] ................................................................... 9 Table 2.2: Comparison of structural performance between conventional and capacity design under seismic

excitation [16] .................................................................................................................................. 12 Table 2.3: Comparison of the different methods of seismic analysis [16]................................................. 13 Table 2.4: Summary of formulations for the behaviour factor of different seismic codes and standards .. 29 Table 2.5: Summary of behaviour factors and design and detailing requirements for RC shear wall

structural force resisting systems [30].............................................................................................. 30 Table 2.6: Summary of proposed formulations on the ductility reduction factor ...................................... 32 Table 2.7: Summary of investigations on the ductility reduction factor .................................................... 33 Table 2.8: Typical range of overstrength for various structural systems [26]............................................ 37 Table 2.9: Overstrength-related force modification factors of NBCC (2005) ........................................... 38 Table 2.10: Summary of seismic code requirements [14].......................................................................... 40

Table 3.1: Summary of the behaviour factors prescribed by design codes ................................................ 52 Table 3.2: Values of the behaviour factor for building frame systems [3]................................................. 53 Table 3.3: Basic values of the behaviour factor for uncoupled wall system [11] ...................................... 53

Table 3.4 Default values of the ratio 1/u for different structural systems [18] .................................. 54

Table 3.5: Behaviour factor q for structures with non-ductile behaviour [40]........................................... 56 Table 3.6: Behaviour factor q for structures with ductile behaviour [40] .................................................. 56 Table 3.7: Maximum values of the structural ductility factor for reinforced concrete structural walls

according to NZS 3101 [49]............................................................................................................. 57 Table 3.8: Comparison of design horizontal ground accelerations in seismic codes ................................. 60 Table 3.9: Partial safety factors for the design strength determination of reinforced concrete.................. 75 Table 3.10: Summary of strength-reduction factors for different design actions, prescribed in UBC (1997)

.......................................................................................................................................................... 75

Table 4.1: Calculation of gravity loads per storey ..................................................................................... 84 Table 4.2: Ground classes and soil parameters used [3] ............................................................................ 93 Table 4.3: Material parameters for steel reinforcement ........................................................................... 101 Table 4.4: Material parameters for unconfined concrete ......................................................................... 102

LIST OF TABLES xvi


Table 4.5: Material parameters for confined concrete ............................................................................. 102 Table 4.6: Modelling parameters and numerical acceptance criteria for nonlinear procedures in members

controlled by flexure [7]................................................................................................................. 106 Table 4.7: Lateral force resisting system designed for Ground Type 1, 1.0q = ................................... 126

Table 4.8: Lateral force resisting systems designed for Ground Type 4, 1.0q = ................................. 126

Table 5.1: Influence of the redundancy factor on the value of the maximum behaviour factor .............. 133 Table 5.2 Comparison of the design parameters of the six-storey walls.................................................. 137 Table 5.3 Comparison of the design parameters of the eight-storey walls .............................................. 140 Table 5.4 Comparison of the design parameters for the ten-storey walls ................................................ 143 Table 5.5: Summary of buildings designed and analysed for Ground Type 1, 1.0q = ......................... 145

Table 5.6 Summary of walls designed for the 6-storey example building............................................... 146 Table 5.7: Summary of the computationally-determined behaviour factors obtained from failure limits for

the 6-storey buildings ..................................................................................................................... 147 Table 5.8: Summary of structural walls designed for the 8-storey building, q = 1.0 ............................... 151 Table 5.9: Summary of the computationally-determined behaviour factor obtained from failure limits for

the 8-storey building....................................................................................................................... 151 Table 5.10: Summary of walls designed for the 10-storey building, 1.0q = .......................................... 154

Table 5.11: Summary of the computationally-determined behaviour factor obtained from failure limits for

the 10-storey building..................................................................................................................... 154 Table 5.12: Summary of walls designed and analyzed for Ground Type 4, q = 1.0 ................................ 157 Table 5.13: Maximum computationally-determined behaviour factor obtained from failure limits for the

6-storey building ............................................................................................................................ 159 Table 5.14: Maximum computationally-determined behaviour factor obtained from failure limits for the

8-storey building ............................................................................................................................ 161 Table 5.15: Summary of the computationally-determined behaviour factor obtained from failure limits for

the 10-storey building..................................................................................................................... 162 Table 5.16: Historic earthquake accelerograms ....................................................................................... 163 Table 5.17: Three lateral force resisting systems analysed with dynamic time-history analysis ............. 164 Table 5.18: Summary of results obtained from dynamic time-history analysis....................................... 165 Table 5.19: Summary of the displacement ductilities ( ) and corresponding maxq values for buildings

with varying number of storeys, designed for Ground Types 1 and 4............................................ 168

Table A.1: Spreadsheet for the design of RC structural walls under seismic loading, according to SANS

10160: Part 4 .................................................................................................................................. 188 Table A.2: Seismic intensity obtained from the Capacity Spectrum method........................................... 198

Table B.1: Material properties adopted in the numerical analysis of wall WSH1 ................................... 201 Table B.2: Material properties assumed in the numerical analysis of wall WSH 3 ................................. 202

LIST OF TABLES xvii


Table B.3: Material properties assumed for the numerical analysis of wall WSH4 ................................ 202 Table B.4: Summary of loading on experimental test specimen: wall WSH1......................................... 202 Table B.5 Measured material properties for the concrete and steel reinforcement of wall WSH1.......... 203

xviii

NOTATION

CAPITAL LETTERS

dA Design value of the accidental or seismic action

C , ,T SC Inelastic seismic coefficient

euC Maximum base shear coefficient

yC Base shear coefficient corresponding to actual yielding

wC Unfactored design base shear coefficient

*D Displacement of the equivalent SDOF system *

yD Yield displacement of the equivalent SDOF system

( )D T Elastic spectral displacement

dE , mE Design seismic loading

sE Modulus of elasticity of steel reinforcement

*F Force in the equivalent SDOF system *

yF Yield strength of the equivalent SDOF system

( ),1.0F T Strength of the structural system of period T for elastic

behaviour

( ),F T Strength of the structural system of period T and ductility

demand equal to

dF Design base shear strength

elF Linear elastic base shear force

yF Base shear force at yielding

,k jG , D Characteristic value of permanent action j

I , 1 Importance factor

K Effective confined strength ratio of concrete

uL Limit state factor for the ultimate limit state

NOTATION xix


RM Design moment resistance

RdM+ Moment resistance at overstrength

P Vector of applied incremental load during pushover analysis 0P Vector of the pattern of applied nominal loads

iP Equivalent lateral static force applied at the i th DOF in nonlinear

static analysis

,u codePGA Peak ground acceleration prescribed by the code for the ultimate

limit state

,u effPGA Observed peak ground acceleration leading to failure of the

structural element

Q Quantity (force or displacement) of the MDOF system *Q Quantify (force or displacement) of the equivalent SDOF system

R Behaviour factor, response reduction factor of force modification

factor

R , dR , q Ductility reduction factor

sR , oR , sq Strength reduction factor

R Damping reduction factor

sizeR Overstrength factor arising from rounding up of element and

member sizes

R Overstrength factor accounting for difference between nominal

and factored resistances

yieldR Overstrength factor accounting for difference in actual yield

strength to minimum specified yield strength

shR Overstrength factor arising due to strain-hardening

mechR Overstrength factor arising from mobilizing the full capacity of

the structure

S Ground class parameter defining the elastic response spectrum

,a dS Design value of the spectral acceleration

,a OSS Spectral acceleration at overstrength

NOTATION xx


( )dS T Non-dimensional value from the normalized design response

spectra

pS Structural performance factor

nS Nominal strength

*T Elastic period of the idealised equivalent SDOF system

1T Fundamental structural period of vibration

BT , CT , DT Period ranges describing the design response spectra

gT Dominant period of earthquake ground motion

effT Fundamental period determined from the effective cracked

stiffness of the structural member

dV Design value of seismic base shear

,1dV Design base shear for subsoil conditions of Ground Type 1

,4dV Design base shear for subsoil conditions of Ground Type 4

dV+ Design seismic base shear at overstrength

EV Elastic force demand

nV Nominal value of the design seismic base shear

yV Yield strength

nW Nominal value of the sustained vertical load acting on the

structure

tW Total weight of the structure

,k iQ Characteristic value of the accompanying variable action i

Z Zone factor

LOWER-CASE LETTERS

ga , gda Horizontal peak ground acceleration

sd , du Horizontal drift of the structure

NOTATION xxi


ed , elu Displacement obtained from static, elastic analysis

rd Interstorey drift

'ccf Compressive strength of confined concrete

'cf Compressive strength of unconfined concrete

',c medianf Median value of the concrete compressive strength

'lf Effective confining stresses of transverse reinforcement

,y df Design tensile yield strength of reinforcement steel

,y medianf Median value of the yield strength of reinforcement steel

tf Design tensile strength of concrete

g Gravitational constant of acceleration (taken as 9.81 m/s2)

wh Height of the structural wall

wl Length of the structural wall

*m Mass of the equivalent SDOF system

im Mass on storey i

q , R Behaviour factor, response reduction factor of force modification

factor

q Period-dependant behaviour factor

maxq Computationally-determined maximum value of the behaviour

factor as obtained in the investigation of this study

nw Nominal value of the distributed floor load

GREEK CAPITAL LETTERS

y Yield displacement of the structural system

u , Ultimate lateral displacement of top node of the structural system

Vector of modal displacements

i Modal displacement at the i th DOF

Modal participation factor

NOTATION xxii


, 0 , O Structural overstrength factor

D Design overstrength

M Material overstrength

S System overstrength

GREEK LOWER-CASE LETTERS

1/u Seismic action causing development of a full plastic hinge

mechanism to the seismic action at the formation of the first

plastic hinge

0 Acceleration amplification factor

t Time step used for time-history analysis

su Tensile fracture strain of reinforcement steel

cu , cc Concrete strain at peak stress and collapse strain of confined

concrete, respectively

Strength-reduction factor

m Partial material factor

s Partial factor for steel reinforcement

c Partial factor for concrete

Parameter accounting for equivalent viscous damping

Load factor for incrementing

Ductility ratio

Displacement ductility ratio

m Maximum interstorey ductility ratio

Reliability/redundancy factor

c , s Specific weight of concrete and steel reinforcement

t Total ratio of reinforcement content to concrete area

Viscous damping ratio

, i Action combination factor

xxiii

TERMINOLOGY AND ACRONYMS

Accelerogram Earthquake ground motion data set (usually presented as

acceleration-time)

ADRS Acceleration-Displacement Response Spectrum

ATC Applied Technology Council

Behaviour factor, force-reduction

factor or response modification

factor

Factor responsible for reducing the elastically determined

seismic loading due to the effects of inelastic deformation,

ductility and structural overstrength.

Capacity curve Force-lateral deformation relation of a structure, determined

from pushover analysis, and presented in acceleration-

displacement format.

Capacity design General design philosophy ensuring that brittle structural failure

is prevented by proper design so the full capacity of ductile,

yielding elements can be utilized.

Confinement of concrete Special detailing of transverse reinforcement steel to effectively

confine the core concrete and increase compressive strength

and strain capacity.

Ductility Defined as the ratio of the ultimate response (such as

displacement or rotation) to the yield response.

FEMA Federal Emergency Management Agency

MDOF Multi-degree-of-freedom

Nonlinear static analysis Method of seismic evaluation of building structures using

nonlinear material law with static application of the lateral

loading (refer to pushover analysis)

Overstrength ratio Ratio of the actual strength of a structural element to the

strength assumed for design.

PBE Performance based engineering

RC Reinforced concrete

SDOF Single-degree-of-freedom

Seismic intensity Measure of the magnitude of the demand earthquake, quantified

by the peak horizontal ground acceleration in this thesis.

SLS Serviceability limit state

Static pushover analysis Analysis method to determine the force-lateral deformation

relation with static loading, monotonically increased until

failure of the structure.

Structural wall Normally referred to as shear walls in practice, these are wall

TERMINOLOGY AND ACRONYMS xxiv


elements that provide lateral stiffness in buildings through

flexure and shear mechanisms.

ULS Ultimate limit state

Wall boundary elements Regions at the ends of a structural wall, designed for high

compressive forces through stringent detailing of the

confinement reinforcement.

1

Chapter 1

1 INTRODUCTION

1.1 Background

In 2004 a decision was made to revise the current South African loading code, SABS

0160-1989 [1]: The general procedures and loadings to be adopted in the design of

buildings [2]. Due to objections and a lack of confidence in the existing codes section

for the seismic design of structures among designers in the Western Cape region, it was

decided to establish a local seismic load subcommittee in 2004 for revision of the

seismic requirements [2]. The subcommittee consisted of academic staff from the

University of Stellenbosch and representatives from consulting engineering firms in the

region [2]. The seismic design section of the revised code incorporates the requirements

of the existing SABS 0160 (1989). Clause 5.6 (Earthquake loads) in SABS 0160 [1]

was revised in the draft form as SANS 10160: Part 4: Seismic actions and general

requirements for buildings [3].

SANS 10160: Part 4 [3] inherited the seismic design philosophy as developed in areas

of moderate to high seismicity, such as Southern Europe, California, New Zealand and

Japan. The aspects inherited from the leading seismic design codes of these areas in

SANS 10160: Part 4 [3] include implementation of the philosophy of Capacity design

(as developed in the 1970s by Priestley and Paulay in New Zealand); definition of the

design peak ground acceleration; structural requirements to ensure seismic resistance;

definition of the design response spectrum for elastic analysis with parameters for the

various soil conditions; and use of empirically-determined behaviour factors to account

for ductile response of structures and the inherent structural overstrength.

CHAPTER 1: Introduction 2


The southern part of Africa is thought to be relatively stable in terms of seismic activity,

however it has experienced a small number of medium intensity earthquakes since the

seventeenth century. Thus, South Africa is defined as a country with areas of moderate

seismic activity. Some of the more significant seismic events of the south western Cape

Province, as published by the Council for Geoscience [4] are shown in Table 1.1.

Table 1.1: Seismic history of the south western Cape Province [4]

Date Local Time

(GMT)

Summarised description of observations

Deduced magnitude (Richter

scale)

Source

4-12 Dec 1809

22:08 "Three strong quakes""all buildings suffered numerous cracks"

6.1 Von BuchernRoder, 1830

2 Jun 1811 11:00 "Walls cracked, some unsafe" 5.5 6.0

Von BuchernRoder, 1830; Burchell, 1822

20 Feb 1912 15:04

"felt all over South Africa, many farm buildings completely destroyed."

6 Finsen, 1950; Gutenberg and Richter, 1965

4 Dec 1920 07:52

"Very strong quake in the sea felt in Cape Town, George and Port Elizabeth"

6.2 Finsen, 1950; Gutenberg and Richter, 1965

29 Sept 1969

22:03 "Marked tremor all over Western Cape""extensive damage, deaths""extensive cracks"

6.3

Magnetic observatory, Hermanus; Die Burger; The Argus; USCGS Bulletin

14 Apr 1970

21:10 "Marked tremor at Ceres/Tulbagh""damage" 5.7

Magnetic observatory, Hermanus; The Argus; USCGS Bulletin

The code prescribes expected peak ground accelerations in the order of 0.1g to 0.15g

for design purposes in the Western Cape. The south Western Cape, especially around

Cape Town, is heavily populated and much of the existing infrastructure is vulnerable to

earthquake ground shaking.

The design seismic action of SANS 10160: Part 4 is represented by an elastic ground

acceleration response spectrum, defined for different soil conditions and 5 per cent

critical damping. The code allows definition of the design seismic base shear force from

elastic analysis (Equivalent lateral static force method), reduced by a constant factor to



include the effects of ductile, non-linear behaviour of the structural system. This

constant reduction factor is defined as the behaviour factor ( q ) that accounts for the

capacity of the structure to dissipate hysteretic energy by ductile behaviour,

overstrength and redundancy of the structural system. The influence of the behaviour

factor in the code formulation SANS 10160: Part 4 for determining the nominal base

shear force ( nV ) via the equivalent lateral static force method [3] is illustrated by

equation 1.1.

1, . =

n a nV S T Wq (1.1)

where

( )aS T Non-dimensional value from the normalized design response spectrum

nW Nominal sustained vertical load acting on the structure

q Behaviour factor, defined for different structural systems on the basis of

its ductility capacity

T Fundamental period of the structure

0

0.5

1

1.5

2

2.5

3

0.1 1.0 10.0Structural Period

T [s]

Acc

eler

atio

n S a

[m/s

2]

q = 1.0

q = 2.0

q = 4.0q = 6.0

Figure 1.1: Influence of the behaviour factor on the shape of the design response spectrum



The reduced design seismic loading, obtained in this manner, has a much smaller lateral

force, which allows for more economic design solutions. The influence of the behaviour

factor on the shape of the design response spectrum, and subsequently on the spectral

acceleration ( ( )aS T ), is illustrated in Figure 1.1.

The behaviour factor of unity describes the behaviour of a single-degree-of-freedom

(SDOF) oscillator that exhibits an ideal elastic response to earthquake ground motion.

Subsequent increases in the value of the behaviour factor result in lower pseudo-

accelerations as indicated in the response spectrum shown in Figure 1.1. The design

spectral acceleration, and therefore the design force, is sensitive to the numerical value

of the behaviour factor, which may result in the design for either too high or too low

structural resistance, as illustrated by the following two cases. If the numerical value of

q is too low, a high seismic loading on the structural system is obtained from the

response spectrum, which may result in uneconomic design. Conversely, if the value of

q is too high, very large reductions in seismic loads are obtained, which could lead to

unconservative design.

The problem faced by code-drafting committees worldwide is the quantification of the

behaviour or force-reduction factor. In 1991, Uang [5] stated that the most controversial

part of the development of seismic design provisions for building structures is the

development of the behaviour factors. According to Lee et al. [6], determination of the

strength reduction factors, R (or behaviour factor q ), for various structural systems has

been based mainly on engineering judgment and accumulated experiences from the past

earthquakes, rather than theoretical background. Recent research results regarding the

assigned value for the behaviour factor have raised concerns regarding the scientific

basis of their determination (Applied Technology Council, ATC-19 and ATC-34).

The behaviour factor is used by most seismic design codes to include the effects of

plastification in structural systems when subjected to ground motions. There is,

however, considerable difference in the value of the behaviour factor prescribed for the

design of reinforced concrete walls by the leading international seismic codes and

guidelines (Table 1.2).



Table 1.2: Difference of the behaviour factor values between seismic design codes

Behaviour factor Seismic design code Symbol Structural Wall

EN 1998-1 (2004) q 1 3.0 4.4

UBC (1997) R 2 5.5

NZS 4203 (1992) 3 2.0 - 4.0

SIA 261 (2003) q 4.0

SANS 10160: 4 q 5.0 1 Values are given for Medium (DCM) to High ductility structural walls (DCH) 2 Includes a reliability/redundancy factor () in addition to a load factor of 1.1 for seismic action 3 Includes the structural performance factor ( pS ) of 0.67

1.2 Aim of the study

The behaviour factor is used by most seismic design codes to consider the effects of

plastification in structural systems when subjected to ground motions. There is,

however, considerable difference in the value of the behaviour factor prescribed for the

design of reinforced concrete walls by the leading international seismic codes and

guidelines (Table 1.2).

The difference in the values of the behaviour factor creates uncertainty as to the

appropriate value that should be adopted by the revised SANS 10160. The reduction in

elastic forces, obtained from the behaviour factor, should be compatible with the SANS

level of reliability. Little is known regarding the sensitivity of the behaviour factor to

local conditions and, due to its empirical nature, this investigation proposes to assess the

suitability of the current behaviour factor for the revised South African code: SANS

10160. In order to achieve this, a method is required to assess the compatibility of the

current seismic behaviour factor within the safety limit required by the code.

This investigation aims to assess the value of the behaviour factor, for structural walls

under the influence of South African seismic conditions and code requirements.



1.3 Methodology of the study

In order to achieve the aim of this project, namely to assess a computationally-

determined value of the behaviour factor, a methodology for investigation is defined.

The methodology of this study is illustrated in Figure 1.2.

Compare seismic provisions in international

codes

Chpt.2 -LITERATURE REVIEW

Investigate proposals for the behaviour factor

Investigate numerical analysis methods for

seismic design

Construct numerical model

Investigate value of the behaviour factor with

nonlinear static analysis

Discuss results

Provide conclusions and recommendations for

further study

Verification of results1) Experimental results2) Dynamic time-history

analysis

Chpt. 3 COMPARISON OF BEHAVIOUR FACTOR IN DESIGN CODES

Chpt. 4 NUMERICAL MODELLING

Chpt. 5 RESULTS AND DISCUSSION

Chpt. 6 CONCLUSIONS AND RECOMMENDATIONS

Figure 1.2: Methodology of the investigation

Chapter 2 provides background to the investigation, defines important concepts of

seismic design and gives a brief review of analysis methods for seismic design. A

review of literature on the behaviour factor is presented to compare different proposals

and investigate the methods employed to determine the range of values specified for the

behaviour factor.



Following the review of analysis methods in literature, current seismic design

provisions for various international codes of practice are compared. Such a comparison

is made in chapter 3, which aims to establish possible reasons for the difference in

values of the behaviour factor, prescribed by the different codes of practice.

Chapter 4 provides the methodology for the computational investigation of this study.

The methodology is described in five steps namely: (1) design of the structure; (2)

numerical modelling; (3) definition of failure criteria; (4) analysis; and (5)

quantification of the behaviour factor. Each of these steps is subsequently discussed in

more detail in this chapter. Section 4.3 is concerned with the different computational

methods of analysis prescribed by international standards such as the Federal

Emergency Management Agency (FEMA) [7-9] , the Swiss Standard (SIA 2018) [10]

and Eurocode [11]. The nonlinear static method of analysis, in particular, is investigated

with the aim of implementing such a method in the computational determination of the

behaviour factor in this study. The verification of the results obtained from nonlinear

static analysis is presented with two different methods. Finally, a layout of the

parametric study is presented.

Nonlinear static analysis is selected to evaluate the behaviour factor required for

structural walls. Following the computational analyses, a parameter study is performed,

using the proposed method, to estimate the influence of a range of factors on the

inelastic behaviour of a number of structural walls. The sensitivity of the behaviour

factor to various parameters, such as number of storeys, number of structural walls in

the lateral force resisting system and confinement of concrete, is investigated. The

results obtained from the computational analysis, parameter study and verification with

experimental result from literature and dynamic time-history analysis, are provided and

discussed in chapter 5.

Finally, chapter 6 provides conclusions on the results obtained in this study and

recommendations for future study are proposed.

8

Chapter 2

2 LITERATURE REVIEW

Compare seismic provisions in international

codes

Chpt.2 -LITERATURE REVIEW

Investigate proposals for the behaviour factor

Investigate numerical analysis methods for

seismic design

Construct numerical model

Investigate value of the behaviour factor with

nonlinear static analysis

Discuss results

Provide conclusions and recommendations for

further study

Verification of results1) Experimental results2) Dynamic time-history

analysis

Chpt. 3 COMPARISON OF BEHAVIOUR FACTOR IN DESIGN CODES

Chpt. 4 NUMERICAL MODELLING

Chpt. 5 RESULTS AND DISCUSSION

Chpt. 6 CONCLUSIONS AND RECOMMENDATIONS

Figure 2.1: Methodology of the investigation

CHAPTER 2: Literature Review 9


2.1 Background

2.1.1 Seismic codes of practice

In most seismically active areas, building construction is subject to a legally enforceable

code, which establishes minimum requirements [12]. Structural design codes, however,

describe minimum rules for standard conditions and cannot cover every eventuality.

Buildings, in areas of seismicity, respond to ground shaking in strict accordance with

the laws of physics, not in accordance with rules laid down by a (sometimes fallible)

code-drafting committee [12].

The historical development of the concept of using equivalent static lateral forces for

seismic design is summarized in Table 2.1.

Table 2.1: Historic development of seismic requirements [12]

Date Seismic Area Lateral force as proportion of building weight

1909 Messina (Italy) Italian commission recommended lateral forces 1/12 of the weight.

1923 Tokyo (Japan) A lateral force factor of 1/10 was recommended and a 33 meter height limit imposed.

1933 California (USA) Lateral force requirements adopted by law

1943 Los Angeles (USA) Lateral forces related to fundamental building vibration period

1948 SAEOC (Structural Engineers Association of California)

Recommended the use of base shear related to fundamental period of building.

Early codes were based directly on the practical lessons learnt from historic

earthquakes, relating primarily to types of construction [12]. Advances in the study of

the dynamic response of structures led to the base shear being distributed over the

height of the building according to the shape of the fundamental mode of vibration [12].

The definition of equivalent lateral forces has undergone a revolution from an arbitrary

set of forces based on earthquake damage studies to a set of forces, which, applied as



static loads, reproduce the peak dynamic response of the structure to the design

earthquake.

Structural response to strong earthquake ground motion involves yielding of the

structure so that the response is inelastic. In practice, the cost of elastic design

requirements is unacceptably high and thus it is almost universally accepted that ductile

structural design should apply for major earthquakes [12].

(Design) response spectra

The implementation of structural dynamics in seismic design procedures resulted in the

use of response spectra for the determination of equivalent seismic loading. Most

seismic codes provide design spectra to represent the expected design earthquake

demand. The response spectrum provides a convenient means to summarize the peak

response of all possible linear single-degree-of-freedom (SDOF) systems to a particular

component of ground motion. Furthermore, it allows for practical application of

structural dynamics to the design of structures and development of lateral force

requirements in building codes [13].

The response spectrum is presented as a plot of the peak value of a response quantity

(acceleration or displacement) as a function of the natural period ( nT ) of the system.

Each plot represents the response of a SDOF system having a fixed damping ratio .

The elastic design spectrum provides a basis for calculating the design force and

deformation for SDOF systems to be designed to remain elastic. In contrast, an inelastic

design spectrum for elastoplastic systems for specified ductility factors ( ) can be

constructed by creating the constant ductility response spectrum for many plausible

ground motions for the site. The constant ductility response spectrum is created by

reducing the elastic response spectrum with the specified ductility reduction factor for

each period range [13].

2.1.2 Philosophy of capacity design

Capacity design involves the design of structural elements, susceptible to brittle failure

modes (such as shear in poorly detailed concrete beams), so that the yield capacity is



reached first in ductile elements (such as bending of well-detailed concrete beams) [12].

As such, capacity design is essentially a procedure for imposing the desired hierarchy of

member strengths on a structure to ensure the development of the most appropriate

plastic mechanism in the event of a major earthquake [14]. The capacity design

approach is likely to assure predictable and satisfactory inelastic response under

conditions for which even sophisticated dynamic analysis techniques can yield only

crude estimates [15].

With capacity design of structures for earthquake resistance, distinct elements of the

primary lateral force resisting system are identified and suitably designed and detailed

for energy dissipation under severe imposed deformations [15]. Critical regions of these

members, termed plastic hinges, are detailed for inelastic flexural action, and shear

failure is inhibited by providing adequate strength. All other members of the structure

are designed with adequate strength to remain within the elastic domain of deformation.

Modern earthquake codes take advantage of ductile yielding to reduce the level of

seismic design force, typically to a level two to eight times lower than the strength

required for the structure to remain elastic [12]. Most design codes today recognize and

incorporate the capacity design approach, albeit to varying degrees [14].

Comparison of conventional and capacity design performance under seismic excitation

Table 2.2 provides a comparison between the performances of conventionally and

capacity designed buildings under the influence of seismic excitation. The comparison

illustrates the importance of the capacity design of structures in the prevention of

structural failure in regions of moderate to high seismicity. Capacity design for seismic

application thus plays a major role in the requirements of design codes.



Table 2.2: Comparison of structural performance between conventional and capacity design under

seismic excitation [16]

Conventionally designed structures Capacity designed structures

Plastic hinges could develop anywhere

The plastic mechanism is arbitrary and

not identified.

The local ductility of the plastified

regions varies significantly and the global

ductility of the structure is in general

small and not known.

Performance under seismic excitation is

unpredictable

Plastic deformations are only possible

within clearly identified regions.

The plastic mechanism is identified and

suitably detailed.

The local ductility within the plastic

hinges is adapted to the global ductility

which in turn is chosen in accordance

with the design class.

The behaviour under seismic excitation is

well known.

Full resistance is provided for elements

assumed to remain elastic.

Limited safety against collapse High safety against collapse

2.2 Analysis methods for seismic design

2.2.1 Overview of different seismic analysis methods

A comparison of the main methods of analysis utilized in the seismic design of

structures is provided in Table 2.3. The methods of analysis are presented in increasing

order of complexity and mention the corresponding benefits attained with an increase in

complexity.



Table 2.3: Comparison of the different methods of seismic analysis [16]

Equivalent lateral force method

Response spectrum method Nonlinear static analysis Nonlinear time-history analysis

Dynamic model Linear SDOF system Linear MDOF system Nonlinear SDOF system Nonlinear MDOF system

Geometric model 2D 2D or 3D 2D 2D or 3D

Material model Linear Linear Nonlinear Nonlinear

Damping model Viscous Viscous Viscous Viscous and hysteretic

Modes of vibration considered Fundamental mode only All modes Fundamental mode only -

Consideration of torsion Amplification factor Linear Amplification factor Nonlinear

Consideration of material nonlinearities q-factors q-factors Nonlinear material factor Nonlinear material factor

Seismic action Design spectrum Design spectrum Design spectrum Time history

Output Sectional forces and deformations

Sectional forces and deformations

Local ductility demand, sectional forces and

deformations

Local ductility demand, sectional forces and

deformations

Applicability Regular buildings only All buildings Regular buildings only All buildings

Typical application Design Design Assessment of existing

buildingsAssessment of new and

existing buildings

Effort Low Moderate Moderate Large

The methods of analysis, implemented in this study shall be described in the following

sections.

2.2.2 Equivalent lateral (static) force method

Most design codes specify a procedure whereby the minimum lateral strength required

to resist an earthquake is calculated and applied to the structure as a set of equivalent

static forces applied along the height of the building [12]. This procedure is suited for

low-rise buildings without significant structural irregularities. More complex analyses

are, however, required for other structural types. Nevertheless, static elastic analysis

procedures still remain t

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Assessment of the Behaviour Factor for the Seismic Design ... · Assessment of the Behaviour Factor for the Seismic Design of Reinforced Concrete Structural Walls according to SANS