Assessment of the behaviour factor for the seismic design of reinforced concrete structural walls according to SANS 10160 : part 4

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(1)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.

(2) 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. i .

(3) 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 tenstorey 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 sixstorey building, however, does not perform well for taller buildings. Further. ii.

(4) SYNOPSIS. iii. 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.. C. A. Spathelf. University of Stellenbosch.

(5) 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. ŉ 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. ŉ Soortgelyke metode is aanvaar vir hierdie studie waar die seismiese gedrag van skuif-mure in ses-, agt- en tienverdieping strukture ondersoek is met nie-lineêre 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-lineêre statiese analise metode betroubare resultate bied vir die berekening van die gedragsfaktor vir ŉ ses-verdieping struktuur. Hierdie metode het wel nie so goed gevaar met hoër strukture nie en dinamiese tyd-stap analise word voorgestel vir verdere ondersoek.. iv.

(6) SINOPSIS. v. Die strukturele gedrag van skuif-mure, ontwerp vir die verlaagde kragte soos bepaal met die voorgeskrewe gedragsfaktor van 5.0, toon hoë swig-sterktes en bied weerstand teen die ontwerp aardbewing binne die elastiese bereik van die mure. Dit is bevind dat die hoë swig-sterktes veroorsaak word deur die betroubaarheid/oortolligheidsfaktor (“reliability/redundancy factor”) voorgeskryf deur SANS 10160: Part 4 en as gevolg van hoë addisionele kapasiteit (“overstrength”). Soortgelyke navorsing het ook hoë 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 ŉ aantal faktore wat die grootte van die gedragsfaktor beïnvloed, 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.. C. A. Spathelf. University of Stellenbosch.

(7) 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 Zürich, 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 Heléne) who kept faith in me and were there every step of the way when I needed them most.. vi.

(8) 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. vii.

(9) 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 4.1. NUMERICAL MODELLING ...................................................................... 78 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. C. A. Spathelf. University of Stellenbosch.

(10) TABLE OF CONTENTS 4.5. ix. 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. 5 5.1. Parametric study ..................................................................................................................... 123. RESULTS AND DISCUSSION ............................................................... 127 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 ( ρ ) 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 six–storey building................................................................................... 158 5.5.2 Investigation of an eight–storey building ............................................................................. 159 5.5.3 Investigation of a ten–storey 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. C. A. Spathelf. University of Stellenbosch.

(11) TABLE OF CONTENTS A. x. 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. B. Capacity curves obtained from nonlinear static analysis..................................................... 199. 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. C. A. Spathelf. University of Stellenbosch.

(12) 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. αu. and. α1. 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. xi.

(13) 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. C. A. Spathelf. University of Stellenbosch.

(14) 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 qmax 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. C. A. Spathelf. University of Stellenbosch.

(15) 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 computationallydetermined 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. C. A. Spathelf. University of Stellenbosch.

(16) 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. α u / α1. 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. xv.

(17) 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, q = 1.0 ................................... 126 Table 4.8: Lateral force resisting systems designed for Ground Type 4,. q = 1.0 ................................. 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, q = 1.0 ......................... 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, q = 1.0 .......................................... 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 ( µ∆ ) and corresponding qmax 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. C. A. Spathelf. University of Stellenbosch.

(18) 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. C. A. Spathelf. University of Stellenbosch.

(19) NOTATION. CAPITAL LETTERS. Ad. Design value of the accidental or seismic action. C , CT , S. Inelastic seismic coefficient. Ceu. Maximum base shear coefficient. Cy. Base shear coefficient corresponding to actual yielding. Cw. Unfactored design base shear coefficient. D*. Displacement of the equivalent SDOF system. Dy *. Yield displacement of the equivalent SDOF system. D (T ). Elastic spectral displacement. Ed , Em. Design seismic loading. Es. Modulus of elasticity of steel reinforcement. F*. Force in the equivalent SDOF system. Fy*. Yield strength of the equivalent SDOF system. F (T ,1.0 ). Strength of the structural system of period T for elastic behaviour. F (T , µ ). Strength of the structural system of period T and ductility demand equal to µ. Fd. Design base shear strength. Fel. Linear elastic base shear force. Fy. Base shear force at yielding. Gk , j , D. Characteristic value of permanent action j. I , γ1. Importance factor. K. Effective confined strength ratio of concrete. Lu. Limit state factor for the ultimate limit state xviii.

(20) NOTATION. xix. MR. Design moment resistance. + M Rd. Moment resistance at overstrength. P. Vector of applied incremental load during pushover analysis. P0. Vector of the pattern of applied nominal loads. Pi. Equivalent lateral static force applied at the i th DOF in nonlinear static analysis. PGAu ,code. Peak ground acceleration prescribed by the code for the ultimate limit state. PGAu ,eff. 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. Rµ , Rd , qµ. Ductility reduction factor. Rs , Ro , qs. Strength reduction factor. Rξ. Damping reduction factor. Rsize. Overstrength factor arising from rounding up of element and member sizes. Rφ. Overstrength factor accounting for difference between nominal and factored resistances. Ryield. Overstrength factor accounting for difference in actual yield strength to minimum specified yield strength. Rsh. Overstrength factor arising due to strain-hardening. Rmech. Overstrength factor arising from mobilizing the full capacity of the structure. S. Ground class parameter defining the elastic response spectrum. S a ,d. Design value of the spectral acceleration. Sa ,OS. Spectral acceleration at overstrength. C. A. Spathelf. University of Stellenbosch.

(21) NOTATION S d (T ). xx Non-dimensional value from the normalized design response spectra. Sp. Structural performance factor. Sn. Nominal strength. T*. Elastic period of the idealised equivalent SDOF system. T1. Fundamental structural period of vibration. TB , TC , TD. Period ranges describing the design response spectra. Tg. Dominant period of earthquake ground motion. Teff. Fundamental period determined from the effective cracked stiffness of the structural member. Vd. Design value of seismic base shear. Vd ,1. Design base shear for subsoil conditions of Ground Type 1. Vd ,4. Design base shear for subsoil conditions of Ground Type 4. Vd+. Design seismic base shear at overstrength. VE. Elastic force demand. Vn. Nominal value of the design seismic base shear. Vy. Yield strength. Wn. Nominal value of the sustained vertical load acting on the structure. Wt. Total weight of the structure. Qk ,i. Characteristic value of the accompanying variable action i. Z. Zone factor. LOWER-CASE LETTERS. ag , agd. Horizontal peak ground acceleration. d s , ud. Horizontal drift of the structure. C. A. Spathelf. University of Stellenbosch.

(22) NOTATION. xxi. d e , uel. Displacement obtained from static, elastic analysis. dr. Interstorey drift. f cc'. Compressive strength of confined concrete. f c'. Compressive strength of unconfined concrete. f c', median. Median value of the concrete compressive strength. fl '. Effective confining stresses of transverse reinforcement. f y ,d. Design tensile yield strength of reinforcement steel. f y , median. Median value of the yield strength of reinforcement steel. ft. Design tensile strength of concrete. g. Gravitational constant of acceleration (taken as 9.81 m/s2). hw. Height of the structural wall. lw. Length of the structural wall. m*. Mass of the equivalent SDOF system. mi. Mass on storey i. q, R. Behaviour factor, response reduction factor of force modification factor. q. Period-dependant behaviour factor. qmax. Computationally-determined maximum value of the behaviour factor as obtained in the investigation of this study. wn. 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. Φ. Vector of modal displacements. Φi. Modal displacement at the i th DOF. Γ. Modal participation factor. C. A. Spathelf. University of Stellenbosch.

(23) NOTATION. xxii. Ω , Ω0 , Φ O. Structural overstrength factor. ΩD. Design overstrength. ΩM. Material overstrength. ΩS. System overstrength. GREEK LOWER-CASE LETTERS. α u / α1. Seismic action causing development of a full plastic hinge mechanism to the seismic action at the formation of the first plastic hinge. β0. Acceleration amplification factor. δt. Time step used for time-history analysis. ε su. Tensile fracture strain of reinforcement steel. ε cu , ε cc. Concrete strain at peak stress and collapse strain of confined concrete, respectively. φ. Strength-reduction factor. γm. Partial material factor. γs. Partial factor for steel reinforcement. γc. Partial factor for concrete. η. Parameter accounting for equivalent viscous damping. λ. Load factor for incrementing. µ. Ductility ratio. µ∆. Displacement ductility ratio. µm. Maximum interstorey ductility ratio. ρ. Reliability/redundancy factor. ρc , ρ s. Specific weight of concrete and steel reinforcement. ρt. Total ratio of reinforcement content to concrete area. ζ. Viscous damping ratio. ψ , ϕi. Action combination factor. C. A. Spathelf. University of Stellenbosch.

(24) 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 responsible for reducing the elastically determined. factor or response modification. seismic loading due to the effects of inelastic deformation,. factor. ductility and structural overstrength.. Capacity curve. Force-lateral deformation relation of a structure, determined from pushover analysis, and presented in accelerationdisplacement 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. xxiii.

(25) 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.. C. A. Spathelf. University of Stellenbosch.

(26) 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 code’s 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.. 1.

(27) 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). 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. 4 Dec 1920. 07:52. "Very strong quake in the sea felt in Cape Town, George and Port Elizabeth". 6.2. 29 Sept 1969. 22:03. "Marked tremor all over Western Cape"…"extensive damage, deaths"…"extensive cracks". 6.3. 14 Apr 1970. 21:10. "Marked tremor at Ceres/Tulbagh"…"damage". 5.7. Source. Finsen, 1950; Gutenberg and Richter, 1965 Finsen, 1950; Gutenberg and Richter, 1965 Magnetic observatory, Hermanus; Die Burger; The Argus; USCGS Bulletin Magnetic observatory, Hermanus; The Argus; USCGS Bulletin. The code prescribes expected peak ground accelerations in the order of 0.1g to 0.15 g 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. C. A. Spathelf. University of Stellenbosch.

(28) CHAPTER 1:. Introduction. 3. 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 ( Vn ) via the equivalent lateral static force method [3] is illustrated by equation 1.1. ⎛ 1⎞ Vn = Sa ⎜ T , ⎟ .Wn ⎝ q⎠. (1.1). where S a (T ). Non-dimensional value from the normalized design response spectrum. Wn. Nominal sustained vertical load acting on the structure. q. Behaviour factor, defined for different structural systems on the basis of its ductility capacity Fundamental period of the structure. T. 3. q = 1.0. Acceleration Sa [m/s2]. 2.5. 2. 1.5. q = 2.0. 1. q = 4.0 q = 6.0. 0.5. 0 0.1. 1.0 Structural Period T [s]. 10.0. Figure 1.1: Influence of the behaviour factor on the shape of the design response spectrum. C. A. Spathelf. University of Stellenbosch.

(29) CHAPTER 1:. Introduction. 4. 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 ( S a (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 pseudoaccelerations 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).. C. A. Spathelf. University of Stellenbosch.

(30) CHAPTER 1:. Introduction. 5. Table 1.2: Difference of the behaviour factor values between seismic design codes Seismic design code EN 1998-1 (2004). Behaviour factor Symbol Structural Wall 1 q 3.0 – 4.4. UBC (1997). R2. NZS 4203 (1992). µ. SIA 261 (2003). q. 3. 5.5 2.0 - 4.0 4.0. q SANS 10160: 4 5.0 Values are given for Medium (DCM) to High ductility structural walls (DCH) 2 Includes a reliability/redundancy factor (ρ) in addition to a load factor of 1.1 for seismic action 3 Includes the structural performance factor ( S p ) of 0.67 1. 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.. C. A. Spathelf. University of Stellenbosch.

(31) CHAPTER 1:. Introduction. 6. 1.3 Methodology of the study In order to achieve the aim of this project, namely to assess a computationallydetermined value of the behaviour factor, a methodology for investigation is defined. The methodology of this study is illustrated in Figure 1.2.. Chpt.2 -LITERATURE REVIEW. Investigate proposals for the behaviour factor. Chpt. 3 – COMPARISON OF BEHAVIOUR FACTOR IN DESIGN CODES. Compare seismic provisions in international codes. Investigate numerical analysis methods for seismic design. Construct numerical model. Chpt. 4 – NUMERICAL MODELLING. Verification of results 1) Experimental results 2) Dynamic time-history analysis. Investigate value of the behaviour factor with nonlinear static analysis. Chpt. 5 – RESULTS AND DISCUSSION. Discuss results. Chpt. 6 – CONCLUSIONS AND RECOMMENDATIONS. Provide conclusions and recommendations for further study. 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. C. A. Spathelf. University of Stellenbosch.

(32) CHAPTER 1:. Introduction. 7. 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.. C. A. Spathelf. University of Stellenbosch.

(33) Chapter 2. 2 LITERATURE REVIEW. Investigate proposals for the behaviour factor. Chpt.2 -LITERATURE REVIEW. Chpt. 3 – COMPARISON OF BEHAVIOUR FACTOR IN DESIGN CODES. Compare seismic provisions in international codes. Investigate numerical analysis methods for seismic design. Chpt. 4 – NUMERICAL MODELLING. Construct numerical model. Investigate value of the behaviour factor with nonlinear static analysis. Chpt. 5 – RESULTS AND DISCUSSION. Discuss results. Chpt. 6 – CONCLUSIONS AND RECOMMENDATIONS. Provide conclusions and recommendations for further study. Verification of results 1) Experimental results 2) Dynamic time-history analysis. Figure 2.1: Methodology of the investigation. 8.

(34) 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. C. A. Spathelf. University of Stellenbosch.

(35) CHAPTER 2:. Literature Review. 10. 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 ( Tn ) of the system. Each plot represents the response of a SDOF system having a fixed damping ratio ζ .. 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 ( µ ) 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 C. A. Spathelf. University of Stellenbosch.

(36) CHAPTER 2:. Literature Review. 11. 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.. C. A. Spathelf. University of Stellenbosch.

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