Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Hussain, Nadeem
Doctor of Philosophy - PhD
University of British Columbia
Despite the recent initiatives and developments in building design provisions using performance-based design, practicing engineers frequently adopt force-based design approaches irrespective of the structural system or building irregularity. Modern seismic building codes adopt the concept of simplifying the complex nonlinear response of a structure under seismic loading to an equivalent linear response through elastic analytical procedures using seismic design response factors. Previous studies also adopted different methodologies for quantifying the seismic response factors. This study initially presents a systematic review of the response factors used with linear analytical procedures recommended by modern building design provisions using SDOF and MDOF systems covering previous analytical, experimental and hybrid works. Limitations and gaps are identified from the previous works with 94% on 2D analysis, 92% on regular low-rise buildings and a mere 15.4% of earlier research on shear walls considering mostly unidirectional seismic loading. This comparative review highlighted the need for future research to calibrate seismic response factors to achieve more economical designs with consistent safety margins for different structural systems and irregularities using 3D bidirectional seismic loading. This study thus assessed the force-based seismic design approach of building codes in which the elastic seismic forces and deformation demands are adjusted through the response modification coefficients to arrive at an economical design under the design earthquake. Toward this objective, four multi-storey steel buildings of 8 to 20 storeys are designed using different standards. Additionally, nine high-rise (RC) structures of 40 to 60 storeys are designed in detail to ensure fair assessment of code-recommended coefficients. Three-dimensional (3D) inelastic analyses are performed for the 13 benchmark buildings using detailed fibre-based models. ISAs and MBIDAs under 26 strong ground motions are conducted to assess the seismic design coefficients. For MSBs, the results revealed a safety margin of 42% to 54% on the R coefficients specified in the design codes. For RC high-rise buildings, the observed overstrength factors for regular and irregular buildings range between 2.62 and 2.98, reflecting the code conservative value of 2.5. The deflection amplification coefficients (Cd) exhibit a 14% to 25% safety margin and validate the design code approach for assigning equal or lower Cd factors than the response modification coefficients (R). The safety margins for the R coefficients ranged from 42% to 63% for the bearing wall buildings and between 7% to 21% for dual structures. The fragility functions derived using MBIDA results and damage state probabilities confirmed the satisfactory seismic performance of the 13 benchmark structures at different intensity levels. The outcomes of the current study suggest the potential of increasing the R coefficients for MSBs and RC-bearing wall buildings initially by 10% and by 5% for dual RC buildings, resulting in more cost-effective designs for steel and RC high-rise buildings without compromising safety.
Seismic Response Factors of Code-designed High-rise Buildings using 3D Non-linear Analysis by Nadeem Hussain B.E., Bangalore University, 1992 M.Sc., United Arab Emirates University, 2013 A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSPHY in THE COLLEGE OF GRADUATE STUDIES (Civil Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan) June 2024 © Nadeem Hussain, 2024 ii The following individuals certify that they have read, and recommend to the College of Graduate Studies for acceptance, a dissertation entitled: Seismic Response Factors of Code-designed High-rise Buildings using 3D Non-linear Analysis submitted by Nadeem Hussain in partial fulfillment of the requirements of the degree of Doctor of Philosophy . Dr. Shahria Alam, School of Engineering Supervisor Dr. Sumi Siddiqua, School of Engineering Supervisory Committee Member Dr. Ahmad Rteil, School of Engineering Supervisory Committee Member Dr. Stephen OâLeary, School of Engineering University Examiner Dr. Anjan Bhowmick, Concordia University External Examiner Additional Committee Members include: Dr. Aman Mwafy, United Arab Emirates University Co-Supervisor iii Abstract Despite the recent initiatives and developments in building design provisions using performance-based design, practicing engineers frequently adopt force-based design approaches irrespective of the structural system or building irregularity. Modern seismic building codes adopt the concept of simplifying the complex nonlinear response of a structure under seismic loading to an equivalent linear response through elastic analytical procedures using seismic design response factors. Previous studies also adopted different methodologies for quantifying the seismic response factors. This study initially presents a systematic review of the response factors used with linear analytical procedures recommended by modern building design provisions using SDOF and MDOF systems covering previous analytical, experimental and hybrid works. Limitations and gaps were identified from the previous works with 94% on 2D analysis, 92% on regular low-rise buildings and a mere 15.4% of earlier research on shear walls considering mostly unidirectional seismic loading. This comparative review highlighted the need for future research to calibrate seismic response factors to achieve more economical designs with consistent safety margins for different structural systems and irregularities using 3D bidirectional seismic loading. This study thus assessed the force-based seismic design approach of building codes in which the elastic seismic forces and deformation demands are adjusted through the response modification coefficients to arrive at an economical design under the design earthquake. Toward this objective, four multi-storey steel buildings (MSBs) with heights ranging between eight to twenty storeys are designed using different standards. Additionally, nine high-rise reinforced concrete (RC) structures of 40 to 60 storeys are designed in detail to ensure optimized design, detailing, and fair assessment of code-recommended coefficients. Three-dimensional (3D) inelastic analyses are performed for the thirteen benchmark buildings using detailed fibre-based models. Incremental static analyses (ISAs) and multi-record bidirectional incremental dynamic analyses (MBIDAs) under twenty-six strong ground motions are conducted to assess the seismic design coefficients. For MSBs, the results of the inelastic analyses revealed a safety margin of 42% to 54% on the response modification coefficients specified in the design codes. For RC high-rise buildings, the observed overstrength factors for regular and irregular buildings range iv between 2.62 and 2.98, reflecting the code conservative value of 2.5. The deflection amplification coefficients (Cd) exhibit a 14% to 25% safety margin and validate the design code approach for assigning equal or lower Cd factors than the response modification coefficients (R). The safety margins for the R coefficients ranged from 42% to 63% for the bearing wall buildings and between 7% to 21% for dual structures. The fragility functions derived using MBIDA results, and damage state probabilities confirmed the satisfactory seismic performance of the thirteen benchmark structures at different intensity levels. The outcomes of the current study thus suggest the potential of increasing the R coefficients for MSBs and RC bearing wall buildings initially by 10%, and by 5% for dual RC buildings, resulting in more cost-effective designs for steel and RC high-rise buildings without compromising safety. v Lay Summary The safety of tall buildings is of great concern in earthquake-prone regions. Our study addresses this concern by using advanced 3D non-linear analysis to investigate the seismic response coefficients of code-designed high-rise buildings. Earthquakes dictate the design of high-rise buildings. It is important to design tall structures to resist seismic forces based on the code recommendations. To visualize the response of these tall structures against seismic forces, we created virtual models of high-rise buildings to simulate real earthquake scenarios, utilizing 3D non-linear analysis techniques, and gained deeper insights. Our research sheds crucial light on behaviour of high-rise buildings during earthquakes. Our research outcome provided important information to practicing architects and designers in refining their designs to make the structures more resilient to earthquake events. Our findings provided room for further research to ensure the safety of urban life while facing natural disasters in improving the seismic resistance of high-rise buildings. vi Preface This dissertation is an original, independent work by the author, Nadeem Hussain. The dissertation is based on comprehensive analytical work investigating seismic response factors of code-designed high-rise buildings using 3D non-linear analysis. A version of Chapter 2 has been published [Hussain N, Alam M.S, Mwafy A.M. Developments in quantifying the response factors required for linear analytical and seismic design procedures. Buildings 14(1):247, 2024. doi: 10.3390/buildings14010247]. I was responsible for conceptualization, methodology, investigation, resources, data curation, visualization, and writing the original draft, review, and editing the manuscript. M. Shahria Alam and Aman Mwafy were responsible for the supervision and project administration and were involved in the conceptualization, review, and editing of the manuscript. Selected parts of Chapters 3 to 7 have been submitted to a journal [Hussain N, Alam M.S, Mwafy A.M. Verification of design coefficients of multi-storey steel buildings considering bidirectional earthquake loading. Journal of Constructional Steel Research, 2024]. I was responsible for conceptualization, methodology, investigation, resources, data curation, visualization, and writing the original draft, review, and editing the manuscript. M. Shahria Alam and Aman Mwafy were responsible for the supervision and project administration and were involved in the conceptualization, review, and editing of the manuscript. Other parts of Chapters 3 to 7 have been also submitted to a journal [Hussain N, Alam M.S, Mwafy A.M. Seismic design coefficients verification of regular and vertically irregular RC high-rise buildings using bidirectional horizontal ground motions and 3D modeling. Structures, 2024]. I was responsible for conceptualization, methodology, investigation, resources, data curation, visualization, and writing the original draft, review, and editing the manuscript. M. Shahria Alam and Aman Mwafy were responsible for the supervision and project administration and were involved in the conceptualization, review, and editing of the manuscript. vii Table of Contents Abstract ............................................................................................................................ iii Lay Summary ..................................................................................................................... v Preface ............................................................................................................................... vi Table of Contents ............................................................................................................. vii List of Tables .................................................................................................................... xii List of Figures ................................................................................................................. xiv Notations ....................................................................................................................... xviii Acknowledgements ......................................................................................................... xxi Dedication ....................................................................................................................... xxii 1 Introduction .................................................................................................................... 1 1.1. Introduction.............................................................................................................. 1 1.2. Scope and Objective ................................................................................................ 2 1.3. Report Organization................................................................................................. 5 2 Literature Review ........................................................................................................... 7 2.1. Introduction.............................................................................................................. 7 2.2. Scope and Literature Review Approach .................................................................. 7 2.3. Overview of Seismic Design Response Factors ...................................................... 8 2.3.1. Historical Perspective of Seismic Response Factors ................................... 9 2.3.2. Seismic Response Factors in Various Codes ............................................. 10 2.4. Methods of assessing seismic Response Factors ................................................... 11 2.4.1. Single Degree of Freedom (SDOF) Systems: Assessing the Demands ..... 11 2.4.2. Multi-Degree of Freedom (MDOF Systems): Assessing the Capacities ... 19 2.4.2.1. Steel braced structures ................................................................... 19 2.4.2.2. Steel frame structures ..................................................................... 22 2.4.2.3. Steel wall and other structures ....................................................... 27 2.4.2.4. RC frame structures ....................................................................... 30 viii 2.4.2.5. RC shear wall structures ................................................................ 37 2.5. Limitations, Gaps and Future Research ................................................................. 41 2.5.1. Limitations and gaps .................................................................................. 42 2.5.2. Areas for future research ........................................................................... 44 2.6. Concluding Remarks ............................................................................................. 45 3 Selection and Design of Buildings ............................................................................... 47 3.1. Selection of Benchmark Buildings ........................................................................ 47 3.1.1. Architectural Details and Description of MSBs ........................................ 47 3.1.2. Architectural Details and Description of RC High-rise Buildings ............ 49 3.2. Structural Design of Benchmark Buildings ........................................................... 52 3.2.1 Design of Benchmark MSBs ..................................................................... 53 3.2.2 RC High-rise Buildings ............................................................................. 55 3.3. Concluding Remarks ............................................................................................. 61 4 Three-Dimensional Structural Modelling and Selection of Records ....................... 62 4.1 Three-dimensional Fibre-based Structural Modelling ........................................... 62 4.2 Material Models ..................................................................................................... 65 4.3 Representing Bidirectional Earthquake Loads for MBIDA .................................. 66 4.4 Concluding Remarks ............................................................................................. 72 5 Inelastic Static and Bidirectional Dynamic Analyses ................................................ 73 5.1. Introduction............................................................................................................ 73 5.2. Free Vibration Analysis ......................................................................................... 73 5.3. Inelastic Lateral Response of Benchmark Structures using ISA ........................... 75 5.3.1. Estimation of lateral capacity of benchmark structures ............................. 75 5.3.1.1. Multi-storey Steel Buildings .......................................................... 76 5.3.1.2. RC High-rise Buildings .................................................................. 79 5.3.2. Estimation of Overstrength ........................................................................ 83 5.3.2.1. Multi-storey Steel Buildings .......................................................... 83 ix 5.3.2.2. RC High-rise Buildings .................................................................. 84 5.3.3. Estimation of Lateral Stiffness of Buildings ............................................. 85 5.3.3.1. Multi-storey Steel Buildings .......................................................... 85 5.3.3.2. RC High-rise Buildings .................................................................. 86 5.3.4. Observation of Plastic Hinges ................................................................... 88 5.3.4.1. Multi-storey Steel Buildings .......................................................... 89 5.3.4.1. RC High-rise buildings .................................................................. 89 5.4. Multi-record Bidirectional Incremental Dynamic Analysis (MBIDA) ................. 94 5.4.1. Seismic Response Prediction of MSBs through 3D MBIDA .................... 95 5.4.2. Seismic Response Prediction of RC buildings through 3D MBIDA ......... 96 5.5. Concluding Remarks ............................................................................................. 98 5.5.1. Preliminary and Detailed Assessment of MSBs ........................................ 98 5.5.2. Preliminary and Detailed Assessment of RC high-rise buildings ............. 99 6 Verification of Seismic Response Factors ................................................................. 100 6.1. Seismic Design Coefficients ................................................................................ 100 6.2. Evaluation of Overstrength Factors (Ω) using ISAs and MBIDAs ..................... 100 6.2.1. First Yield Overstrength of MSBs ........................................................... 100 6.2.2. First Yield Overstrength of RC High-rise Buildings ............................... 101 6.3. Intensity and Damage Measures (IM and DM) at Yield and Collapse................ 102 6.4. Evaluation of Seismic Design Coefficients (R and Cd) ....................................... 103 6.4.1. Multi-storey Steel Buildings .................................................................... 104 6.4.2. RC High-rise Buildings ........................................................................... 106 6.5. Concluding Remarks ........................................................................................... 112 6.5.1. Multi-storey Steel Buildings .................................................................... 112 6.5.2. RC High-rise Buildings ........................................................................... 113 7 Seismic Fragility Assessment ..................................................................................... 114 7.1. Fragility Assessment ............................................................................................ 114 x 7.2. Definition of Limit States .................................................................................... 115 7.2.1. Multi-storey Steel Buildings .................................................................... 115 7.2.2. RC High-rise Buildings ........................................................................... 116 7.3. Derivation of Fragility Relationships using MBIDAs ......................................... 117 7.3.1. Multi-storey Steel Buildings .................................................................... 118 7.3.2. RC High-rise Buildings ........................................................................... 121 7.4. Damage State Probabilities (DSP) of the Benchmark Buildings......................... 125 7.4.1. Multi-storey Steel Buildings .................................................................... 125 7.4.2. RC High-rise Buildings ........................................................................... 129 7.5. Concluding Remarks ........................................................................................... 133 7.5.1. Multi-storey Steel Buildings .................................................................... 133 7.5.2. RC High-rise Buildings ........................................................................... 134 8 Comparison of High-rise Buildings Structural Systems ......................................... 135 8.1. Introduction.......................................................................................................... 135 8.2. Comparison of Inelastic Lateral Response .......................................................... 136 8.2.1. Lateral Capacity ....................................................................................... 136 8.2.2. Overstrength Estimation .......................................................................... 136 8.2.3. Stiffness Estimation ................................................................................. 137 8.2.4. Local Damage Development ................................................................... 138 8.3. Comparison of Seismic Design Coefficients ....................................................... 140 8.4. Comparison of Structural Systemsâ Fragilities and Damage State Probabilities 141 8.5. Cost Benefit Analysis .......................................................................................... 144 8.6. Concluding Remarks ........................................................................................... 145 9 Conclusions .................................................................................................................. 147 9.1. Synopsis ............................................................................................................... 147 9.2. Conclusions and Recommendations .................................................................... 149 9.3. Future Research ................................................................................................... 153 xi Bibliography ................................................................................................................... 155 Appendices ..................................................................................................................... 166 Appendix A: Design Summary of Selected Buildings .......................................... 166 Appendix B: ISAs and MBIDAs Results .......................................................................... 197 xii List of Tables Table 2.1: Comparison of Seismic Design Coefficients. .................................................. 10 Table 2.2: List of equations employed for computing seismic response factors using SDOF. ................................................................................................................................ 17 Table 2.3: Summary of the literature work on SDOF systems ......................................... 18 Table 2.4: Summary of the literature on MDOF models â steel braced structures .......... 23 Table 2.5: Summary of the literature work on MDOF models â steel frame structures .. 27 Table 2.6: Summary of the literature work on MDOF models â steel wall and other structures ............................................................................................................................ 30 Table 2.7: Summary of the literature work on MDOF models â RC frame structures .... 37 Table 2.8: Summary of the literature work on MDOF models â RC shear wall structures ........................................................................................................................................... 41 Table 3.1: Selection of benchmark RC buildings. ............................................................ 50 Table 3.2: Elastic periods of the sample MSBs along the longitudinal axis. ................... 53 Table 3.3: Sample design summary showing beams of 20-storey MSB. ......................... 53 Table 3.4: Sample design summary showing columns of 20-storey MSB. ...................... 53 Table 3.5: Design summary of shear walls of 60S-B-R reinforced concrete building. .... 57 Table 3.6: Design summary of core walls of 60S-B-R reinforced concrete building. ..... 59 Table 3.7: Design summary of coupling beams of 60S-B-R reinforced concrete building. ........................................................................................................................................... 60 Table 4.1: Summary of twenty-six input ground motions showing the considered two horizontal components in bidirectional incremental dynamic analyses. ........................... 69 Table 5.1: Comparison of uncracked periods obtained from design and assessment models for benchmark RC high-rise Regular buildings. ................................................................ 74 Table 6.1: Summary of seismic design coefficients of MSBs and 40S-B, 60S-B, and 60-D RC buildings. ................................................................................................................... 112 Table 7.1: Performance limit states of MSBs. ................................................................ 116 Table 7.2: Performance limit states of the three sets of high-rise buildings conceding different structural systems and irregularities.................................................................. 117 Table 7.3: Limit state probabilities and damage state probabilities of MSBs at various intensity levels. ................................................................................................................ 129 Table 7.4: Limit state and damage state probabilities of 40S-B RC buildings at various intensity levels. ................................................................................................................ 130 Table 7.5: Limit state and damage state probabilities of 60S-B RC buildings at various intensity levels. ................................................................................................................ 131 Table 7.6: Limit state and damage state probabilities of 60S-D RC buildings at various intensity levels. ................................................................................................................ 133 Table A.1: Design summary vibration modes in longitudinal direction of the MSBs. .. 166 Table A.2: Design summary showing structural elements of 8 storey steel building. ... 167 xiii Table A.3: Design summary showing structural elements of 12 storey steel building. . 167 Table A.4: Design summary showing structural elements of 16 storey steel building. . 168 Table A.5: Design justification for dual structural system â contribution of frame ....... 168 Table A.6: Design justification for governing lateral force direction. ............................ 169 Table A.7: Design summary of shear walls of 40 storey (40S-B-R) reinforced concrete building. ........................................................................................................................... 170 Table A.8: Design summary of shear walls of 40 storey (40S-B-GI) reinforced concrete building. ........................................................................................................................... 173 Table A.9: Design summary of shear walls of 40 storey (40S-B-SS) reinforced concrete building. ........................................................................................................................... 176 Table A.10: Design summary of shear walls of 60 storey (60S-B-GI) reinforced concrete building. ........................................................................................................................... 180 Table A.11: Design summary of shear walls of 60 storey (60S-B-SS) reinforced concrete building. ........................................................................................................................... 183 Table A.12: Design summary of shear walls of 60 storey (60S-D-R) reinforced concrete building. ........................................................................................................................... 187 Table A.13: Design summary of shear walls of 60 storey (60S-D-GI) reinforced concrete building. ........................................................................................................................... 190 Table A.14: Design summary of shear walls of 60 storey (60S-D-SS) reinforced concrete building. ........................................................................................................................... 193 Table A.15: Rebar schedule for typical floor slab of 60S-B-R building Table A.16: Rebar schedule for typical thick/transfer floor slabâ¦â¦â¦â¦.. .................. 196 Table B.1: Comparison of elastic periods obtained from design and assessment models for MSBs. .............................................................................................................................. 197 Table B.2: Comparison of uncracked periods obtained from design and assessment models for benchmark RC high-rise geometric irregular buildings (vertical irregularity). ......... 197 Table B.3: Comparison of uncracked periods obtained from design and assessment models for benchmark RC high-rise soft storey irregular buildings (vertical irregularity). ........ 197 Table B.4: Comparison on observation of global yield point using confined concrete crushing............................................................................................................................ 198 Table B.5: Overstrength at first yield, global yield, collapse, and ultimate strength for the steel buildings. ................................................................................................................. 198 Table B.6: Overstrength at first yield, global yield, collapse, and ultimate strength for the RC buildings. ................................................................................................................... 199 Table B.7: Stiffness at first yield, global yield, collapse, and ultimate strength for the steel buildings. ......................................................................................................................... 200 Table B.8: Stiffness at first yield, global yield, collapse, and ultimate strength for RC buildings. ......................................................................................................................... 201 xiv List of Figures Figure 1.1: Framework for verifying seismic design coefficients of MSBs. ..................... 3 Figure 1.2: Framework for verifying seismic design coefficients of high-rise buildings, including deflection amplification (Cd), design overstrength (â¦), and response modification (R) factors. ...................................................................................................... 4 Figure 2.1: Summary of review methodology. .................................................................. 8 Figure 2.2: Seismic design coefficients and their relationships ....................................... 10 Figure 2.3: Summary of previous studies related to seismic design response factors as reviewed from the text and tables (a) Type of systems considered, (b) Analysis type, (c) Irregularity, (d) Structural systems. ................................................................................... 44 Figure 3. 1: Typical layout of MSBs representing 8, 12, 16 and 20 storeys with 3D models. ........................................................................................................................................... 48 Figure 3.2: Natural period range of MSBs and 5% damped design response spectra of Eurocode (EN), international building code (IBC), Canadian design provisions (NBCC), New Zealand design standards (NZS), and uniform building design code (UBC). .......... 49 Figure 3.3: Description of 40 and 60-storey benchmark structures showing floor footprints and 3D models: (a) floor footprints of regular structure, (b) reduced floor footprints of geometrically irregular structure, (c) floor footprints of soft storey structure, (d) 3D models of regular structure, (e) 3D models of geometrically irregular structure, and (f) 3D models of soft storey structure. ...................................................................................................... 51 Figure 3.4: Design base shear coefficient of benchmark MSBs considering various design codes. ................................................................................................................................. 54 Figure 3.5: Design inter-storey drift ratios (IDRs) of sample MSBs in the two horizontal orthogonal directions, H1 and H2. ..................................................................................... 55 Figure 3.6: Typical reinforcement details of the core walls showing rebar schedule. ..... 55 Figure 3.7: Typical reinforcement details of the shear walls showing rebar schedule. .... 56 Figure 3.8: Typical reinforcement details for the floor slabs with rebar schedule. .......... 56 Figure 4.1: Fibre-based modelling concept of benchmark high-rise buildings: (a) & (b) modelling approach of different structural members, (c) & (d) typical details of beam and column discretization, and material model. ....................................................................... 63 Figure 4.2: Fibre-based modelling concept of benchmark high-rise buildings: (a) & (b) modelling approach of different structural members, (c) & (d) typical RC cross-section discretization, and material modelling. .............................................................................. 64 Figure 4.3: Material models utilized in the benchmark buildings: (a) steel model used in MSB (b) rebar model used in RC high-rise buildings (c) & (d) concrete material models used in inelastic analyses. .................................................................................................. 65 Figure 4.4: Distribution of PGA showing the seismicity levels around the globe [118]. 67 Figure 4.6: Response spectra of far-field natural earthquake records along with design code spectra for site classes C and D showing the period range of the benchmark buildings. .. 68 Figure 4.7: Acceleration time-history of natural records selected representing large distant earthquakes of magnitude 6.93 to 7·62 with epicentral distance of 96km to 158km along H1 direction. ...................................................................................................................... 70 Figure 4.8: Acceleration time-history of natural records selected representing large distant earthquakes of magnitude 6.93 to 7·62 with epicentral distance of 96km to 158km along H2 direction. ...................................................................................................................... 71 xv Figure 5.1: Lateral response of MSBs with varying heights along with the sequence of yielding considering two lateral load distributions. ........................................................... 77 Figure 5.2: Comparison of lateral response of MSBs considering unidirectional ISA and bidirectional ISA (BISA) in the two orthogonal directions. .............................................. 78 Figure 5.3: IDRs of MSBs with varying heights from incremental static analysis (ISA) employing ULL and TLL patterns. .................................................................................... 79 Figure 5.4: Lateral response of regular and irregular 40S-B RC buildings set showing rebar yielding sequence and confined concrete crushing considering two lateral load distributions. ...................................................................................................................... 80 Figure 5.5: Lateral response of regular and irregular 60S-B RC buildings set showing rebar yielding sequence and confined concrete crushing considering two lateral load distributions. ...................................................................................................................... 80 Figure 5.6: Lateral response of regular and irregular 60S-D RC buildings set showing rebar yielding sequence and confined concrete crushing considering two lateral load distributions. ...................................................................................................................... 81 Figure 5.7: Incremental static analysis (ISA) results of the inter-storey drift ratios (IDRs) distributions for 40S-B RC buildings set using ULL and TLL. ........................................ 81 Figure 5.8: Incremental static analysis (ISA) results of the inter-storey drift ratios (IDRs) distributions for 60S-B RC buildings set using ULL and TLL. ........................................ 82 Figure 5.9: Incremental static analysis (ISA) results of the inter-storey drift ratios (IDRs) distributions for 60S-D RC buildings set using ULL and TLL. ........................................ 82 Figure 5.10: Overstrength factors at first yield, global yield, collapse, and ultimate base shear for the benchmark MSBs.......................................................................................... 83 Figure 5.11: Overstrength factors at first yield, global yield, collapse, and ultimate base shear: (a) 40S-B, (b) 60S-B, and (c) 60S-D RC building sets. ......................................... 84 Figure 5.12: Comparison between initial stiffness and those at global yield, collapse, and ultimate strength of MSBs. ................................................................................................ 85 Figure 5.13: Stiffness modifiers relative to initial stiffness at global yield, ultimate strength, and collapse for the MSBs. ................................................................................. 86 Figure 5.14: Comparison between initial stiffness and those at global yield, collapse, and ultimate strength for 40S-B, 60S-B, and 60S-D RC building sets. ................................... 86 Figure 5.14: Comparison between initial stiffness and those at global yield, collapse, and ultimate strength for 40S-B, 60S-B, and 60S-D RC building sets. ................................... 87 Figure 5.15: Stiffness modifiers relative to initial stiffness at global yield, ultimate strength, and collapse for 40S-B, 60S-B, and 60S-D RC building sets. ........................... 88 Figure 5.16: Comparison between effective stiffness of nine high-rise buildings (R: regular, GI: geometric irregular, SS: soft storey) at global yielding and collapse with recommended uncracked and cracked walls effective stiffness by design standards (ACI: American concrete institute, CSA: Canadian standard association, EN: Eurocode). ........ 88 Figure 5.17: Development of plastic hinge formation for the 8S, 12S, 16S and 20S MSBs at various performance levels. ........................................................................................... 90 Figure 5.18: Development of plastic hinge formation and local damage for 40S-B RC buildings at various performance levels. ........................................................................... 91 Figure 5.19: Development of plastic hinge formation and local damage for 60S-B RC buildings at various performance levels. ........................................................................... 92 Figure 5.20: Development of plastic hinge formation and local damage for 60S-D RC buildings at various performance levels. ........................................................................... 93 Figure 5.21: MBIDA curves of MSBs from 3D dynamic response simulation ............... 96 Figure 5.22: MBIDA curves of 40S-B benchmark buildings set obtained from 3D dynamic response simulation. .......................................................................................................... 97 xvi Figure 5.23: MBIDA curves of 60S-B benchmark buildings set obtained from 3D dynamic response simulation. .......................................................................................................... 97 Figure 5.24: MBIDA curves of 60S-D benchmark buildings set obtained from 3D dynamic response simulation. .......................................................................................................... 98 Figure 6.1: Comparison of structural overstrength at first yield (â¦fy) of MSBs from ISA, BISA, and MBIDA. ......................................................................................................... 101 Figure 6.2: Comparison of structural overstrength at first yield (â¦fy): (a) 40S-B, (b) 60S-B, and (c) 60S-D RC building sets from ISA and MBIDA. ............................................ 102 Figure 6.3: MBIDA results of MSBs showing collapse-to-yield ratios obtained from twenty-six bidirectional input earthquake records: (a) PGA, and (b) IDR. ..................... 105 Figure 6.4: Response modification coefficients of MSBs obtained from 3D MBIDAs using twenty-six bidirectional earthquake records. ................................................................... 106 Figure 6.5: Response modification coefficients (R, Cd and Ω) of MSBs obtained from 3D-MBIDAs. ......................................................................................................................... 106 Figure 6.6: MBIDA results of 40S-B RC building sets showing PGA and IDR ratios at collapse and first yield obtained from 26 bidirectional earthquake records. ................... 107 Figure 6.7: MBIDA results of 60S-B RC building sets showing PGA and IDR ratios at collapse and first yield obtained from 26 bidirectional earthquake records. ................... 108 Figure 6.8: MBIDA results of 60S-D RC building sets showing PGA and IDR ratios at collapse and first yield obtained from 26 bidirectional earthquake records. ................... 109 Figure 6.9: Response modification coefficients (R) of 40S-B, 60S-B and 60S-D sets of high-rise buildings based on 3D-MBIDAs. ..................................................................... 110 Figure 6.10: Seismic design coefficients (R, Cd and Ω) of 40S-B, 60S-B and 60S-D sets of high-rise buildings based on 3D-MBIDAs. ................................................................. 111 Figure 7.1: Regression analysis results of MBIDA from twenty-six input ground motions and performance limit states of MSBs............................................................................. 119 Figure 7.2: Fragility relationships of MSBs obtained from MBIDAs. ........................... 119 Figure 7.3: Fragility curve comparisons of limit states of MSBs: IO (top), LS (middle) and CP (bottom). .................................................................................................................... 120 Figure 7.4: Regression analysis results of MBIDA from twenty-six input ground motions and performance limit states of 40S-B building set......................................................... 121 Figure 7.5: Regression analysis results of MBIDA from twenty-six input ground motions and performance limit states of 60S-B building set......................................................... 122 Figure 7.6: Regression analysis results of MBIDA from twenty-six input ground motions and performance limit states of 60S-D building set. ....................................................... 122 Figure 7.7: Fragility relationships of 40S-B building set obtained from MBIDAs. ....... 123 Figure 7.8: Fragility relationships of 60S-B building set obtained from MBIDAs. ....... 124 Figure 7.9: Fragility relationships of 60S-D building set obtained from MBIDAs. ...... 124 Figure 7.10: Fragility curve comparisons of limit states of 40S-B RC high-rise buildings: IO (top), LS (middle) and CP (bottom). .......................................................................... 126 Figure 7.11: Fragility curve comparisons of limit states of 60S-B RC high-rise buildings: IO (top), LS (middle) and CP (bottom). .......................................................................... 127 Figure 7.12: Fragility curve comparisons of limit states of 60S-D RC high-rise buildings: IO (top), LS (middle) and CP (bottom). .......................................................................... 128 Figure 7.13: Damage state probabilities of MSBs at two intensity levels. ..................... 129 Figure 7.14: Damage state probabilities of 40S-B RC building set at two intensity levels. ......................................................................................................................................... 130 xvii Figure 7.15: Damage state probabilities of 60S-B RC building set at two intensity levels. ......................................................................................................................................... 132 Figure 7.16: Damage state probabilities of 60S-D RC building set at two intensity levels. ......................................................................................................................................... 133 Figure 8.1: Comparison of lateral response of regular and irregular 60S-B and 60S-D RC building sets showing rebar yielding sequence and confined concrete crushing. ........... 137 Figure 8.2: Comparison of IDRs of regular and irregular 60S-B and 60S-D RC building sets at first yield and global yield levels. ......................................................................... 137 Figure 8.3: Comparison of overstrength factors between 60S-B and 60S-D building sets at: (a) first yield, (b) global yield, and (c) ultimate base shear. ....................................... 138 Figure 8.4: Comparison of structural stiffness at different levels between 60S-B and 60S-D building sets at: (a) initial stiffness, (b) global yield, and (c) ultimate base shear. ..... 139 Figure 8.5: Comparison of stiffness modifiers relative to initial stiffness at global yield, ultimate strength, and collapse for 60S-B, and 60S-D RC building sets. ........................ 139 Figure 8.6: Development of plastic hinge formation and local damage for 60S-B and 60S-D RC buildings at global yield and collapse performance levels. ................................... 140 Figure 8.7: Comparison of safety margins of the seismic design coefficients between two structural system building sets. ........................................................................................ 141 Figure 8.9: Comparison of fragility relationships of 60S-B and 60S-D buildings set obtained from MBIDAs for R: regular, GI: geometric irregular, and SS: soft storey irregular buildings. ......................................................................................................................... 142 Figure 8.10: Damage state probabilities at UOC, IOC, SD, and SC of 60S-B and 60S-D RC building sets at two intensity levels. .......................................................................... 143 Figure 8.11: Cost benefit of the 60S-B-R building relative to 60S-D-R building.......... 145 Figure 8.12: Cost benefit of the 60S-B-GI building relative to 60S-D-GI building. ..... 145 Figure A.1: Design inter-storey drift ratios (IDRs) of sample MSBs in the two horizontal orthogonal directions, H1 and H2. ................................................................................... 166 xviii Notations SDOF : Single degree of freedom MDOF : Multi degree of freedom Vs : Design base shear Ve : Elastic base shear Vy : Yield base shear R : Response modification factor Rμ : Ductility reduction factor Cd : Deflection amplification factor Ωo : Structural overstrength factor µ : Ductility T : Fundamental period Tag : Characteristic period GM : Ground motion EQ : Earthquake α : Strain hardening coefficient EPP : Elastic perfectly plastic SSP : Shear-slipped BILE : bilinear elastic R : Strength reduction factor q : Strength reduction factor (behaviour factor in European standards) RD : Damage based strength reduction factor RR : Redundancy factor Rd : Ductility-related modification factor Ro : Overstrength-related modification factor ASCE : American society of civil engineers AISC : American institute of steel construction NZS : New Zealand standard UBC : Universal building code IBC : International building code EN : European Norms (Eurocode) FEMA : Federal emergency management agency MCBC : Mexico City building code xix NBCC : National building code of Canada PEER : Pacific earthquake engineering research centre ATC : Applied technology council CBF : Concentrically braced frame BRBF : Buckling restrained braced frame CKB : Chevron knee brace MRF : Moment resisting frame CMR : Collapse margin ratio ACMR : Adjusted collapse margin ratio ELFA : Equivalent lateral force analysis MRSA : Modal response spectrum analysis PGA : Peak ground acceleration IPA : Inelastic pushover analysis IDA : Incremental dynamic analysis SAC : SAC steel project RC : Reinforced concrete THA : Time history analysis APA : Adaptive pushover analysis DAPA : Displacement based adaptive pushover analysis FAPA : Force based adaptive pushover analysis ISDR : Inter-storey drift ratio SDC : Seismic design category SMA : Shape memory alloy 3D : Three-dimensional RC : Reinforced concrete ISA : Incremental static analysis MBIDA : Multi-record bidirectional incremental dynamic analysis MBTHA : Multi-record bidirectional time history analysis ACI : American concrete institute CSA : Canadian standards association EN : Eurocode 40S-B-R : 40-storey bearing wall regular 60S-B-R : 60-storey bearing wall regular 60S-D-R : 60-storey dual regular xx 40S-B-GI : 40-storey bearing wall geometric irregular 60S-B-GI : 60-storey bearing wall geometric irregular 60S-D-GI : 60-storey dual geometric irregular 40S-B-SS : 40-storey bearing wall soft storey 60S-B-SS : 60-storey bearing wall soft storey 60S-D-SS : 60-storey dual soft storey ELFA : Equivalent lateral force analysis MRSA : Modal response spectrum analysis CAD : Computed aided design FB : Force-based PGA : Peak ground acceleration PGV : Peak ground velocity UAE : United Arab Emirates ULL : Uniform lateral load TLL : Triangular lateral load IDR : Inter-storey drift ratio SCWB : Strong column-weak beam â¦fy : First yield overstrength IM : Intensity measure DM : Damage measure SD : Spectral displacement SA : Spectral acceleration PGA,y : Peak ground acceleration at yield PGA,c : Peak ground acceleration at collapse IDR,y : Inter-storey drift ratio at yield IDR,c : Inter-storey drift ratio at collapse xxi Acknowledgements I wish to express my sincere gratitude to my supervisor, Dr. Shahria Alam, Professor of Structural Engineering, for his technical guidance and valuable suggestions provided throughout the duration of this work. His continuous advice and constant encouragement were a great motivation to complete this study. His esteemed support, both at the academic and personal levels, has been of paramount importance to my life. I would like to thank all those who made possible my studies at UBC. In particular, I would like to thank my co-supervisor, Dr. Aman Mwafy, Professor of Structural Engineering at UAEU, for advising me in my research subjects. I would like to express my infinite love and thanks to all my family members for their love and support during this long period. I deeply appreciate the encouragement given to me by my wife, who made innumerable sacrifices to enable me to concentrate on my studies. The final and highest appreciation goes to my parents without whom this would have not been possible. All that I have accomplished in life is the result of their love and years of sacrifice. xxii Dedication I would like to dedicate this thesis to my father who has been my mentor and my true guide throughout my life. 1 1 Introduction 1.1. Introduction The scarcity of land and its high cost in the major metropolitans shifted the concept of horizontal development to vertical growth, resulting in the need for high-rise buildings. These tall buildings are essential for efficient land use and accommodating growing urban populations. They serve as economic hubs and landmarks and promote sustainability by reducing sprawl and encouraging less disturbance to Mother Nature. The design of these buildings is typically governed by the effect of the lateral loads due to natural hazards, primarily earthquakes or wind. These hazards may impose remarkable damage, resulting in loss of life and property. Despite adhering to seismic design guidelines laid down by various international codes, recent earthquakes have caused devastation in countries where these guidelines were considered sufficient. For instance, the 2010 Maule Earthquake in Chile resulted in an estimated loss of economy of $30 billion [1, 2]. The 2011 Christchurch Earthquake in New Zealand incurred about $20 billion in direct financial losses. The extensive damage included the loss of several downtown buildings and heritage structures, the closure of a central business district for several months, and the outmigration of thousands of residents [3]. Recently, the damage observed from the 2023 earthquake doublets of Kahramanmaras in Turkey affected 11 provinces in the Eastern and South-Eastern Anatolia regions, causing an economic loss of $110 billion, resulting in severe damage or collapse to nearly 25% of the buildings in the affected area [2, 4-7]. These devastations underscore the need for further investigation into current seismic design code-recommended coefficients to ensure structurally sound and safe buildings. Buildings are designed to respond nonlinearly under the design earthquake to achieve optimized design. Thus, inelastic analysis methods are necessary to address this behaviour and account for the earthquake loads on buildings. Because of economic reasons or a lack of competence in implementing inelastic analysis, practicing engineers prefer code-permitted elastic analysis procedures in seismic design. Modern seismic provisions provide the design coefficients needed for the elastic analysis-based design method, implicitly allowing for safe building designs with optimized costs. These design coefficients decrease the seismic forces through the response modification coefficient (R) and magnify deformations using the deflection amplification factor (Cd). Even a slight increase in the R 2 factor reduces the seismic design forces and the overall structural system cost without jeopardizing the buildingâs safety. The damage observed in global seismic events has witnessed several advancements in various international seismic design standards. Seismic design modification coefficients provided in these international design codes cover little information on providing cost-effective structures with a uniform safety margin [8-11]. Further, the response modification coefficient is explained as an empirical factor designed to consider the combined effects of both ductility and damping within a structural system at the maximum displacement of the structure[12]. Building codes or design guidelines have identified a minor technical basis to evaluate these factors. For instance, FEMA [8] established a procedure to evaluate and document a systematic framework for assessing the response of structural systems and evaluating the design coefficients for linear analysis procedures. The latter study was primarily focused on low to medium-rise regular RC frames and low-rise wood and steel buildings and adopted two-dimensional (2D) analysis using different seismic design categories (SDC). Regular building configurations were adopted in deriving most seismic provisions, whereas buildings with irregular configurations witnessed greater damage due to earthquakes despite good design and quality construction. This emphasizes the need for verifying the code provided seismic design approach for high-rise buildings with various structural systems and irregularity features using reliable assessment methodologies. 1.2. Scope and Objective This study aims to address the limitations in the earlier research by verifying the response modification coefficients of code-compliant regular moment-resisting MSBs with increasing heights using 3D nonlinear analysis. Numerical models of the benchmark MSBs, ranging from 8 to 20 storeys and representing typical footprints built in a medium seismic region, are modeled, designed, and detailed using finite element software. The study objective is attained through developing fibre-based detailed simulation models for MSBs through which their response modification coefficients are evaluated, and the vulnerability relationships are derived by conducting several 3D incremental static analyses (ISAs) and multi-record bidirectional incremental dynamic analyses (MBIDAs). The framework suggested in this study to verify the code-provided seismic design coefficients of MSBs is summarized in Figure 1.1 and discussed in the following sections. 3 Figure 1.1: Framework for verifying seismic design coefficients of MSBs. Moreover, the current study is thus directed to address the limitations identified in previous studies related to assessing the seismic design coefficients for RC high-rise buildings, considering different heights, structural systems, and irregularities using 3D dynamic response simulation and bidirectional earthquake records. Nine high-rise reinforced concrete (RC) buildings of 40 to 60 storeys placed in a medium seismicity zone are designed and detailed using a verified finite element analysis platform using code-recommended seismic design coefficients. Detailed 3D fibre-based simulation models are subsequently developed to evaluate the design coefficients. Over 3800 incremental static Assessment methodologies SDOF System Assessing demand MDOF System Assessing capacities Analytical Areas of future research Conclusions o Steel braced structures o Steel frame structures o Steel wall & other structures o R.C. frame structures o R.C. shear wall structures o Analytical o IPA o IDA o Experimental o Hybrid Limitations gaps Evaluation of Seismic Response Factors oResponse Modification Factor oOverstrength oDeflection Amplification Factor Derivation of Fragility Relationships oLimit States o Fragility Relationships oDamage State Probabilities End of Frame or for Seismic Assessment Start of Evaluation of Seismic Assessment Multi story Steel Buildings (MSBs) o 8 Story o 12 Story o 16 Story o 20 Story Selection of MSBs o European Code (EN) o International Building Code (ICC) o Canadian Code (NBCC) o New Zealand Code (NZS) o Uniform Building Code (UBC) StoryDesign of MSBs Free ibration Analyses Detailed 3D Fibre based Modeling of MSBs Incremental Static Analyses (ISA) Verification of Lateral Response oLateral Capacity oOverstrength o Stiffness o Plastic Hinges Multi-record Bi-directional Incremental Dynamic Analyses (MBIDA) Bi-directional Seismic Loading oBase Shear oDisplacement o Inter-story drift o Plastic Hinges Verification of Lateral Response 4 analyses (ISAs) and multi-record bidirectional dynamic analyses (MBIDAs) using 3D computationally demanding simulation models are conducted under the effect of 26 earthquake records to meet the study objective. Figure 1.2 illustrates the present study's framework and depicts the relationships among the various seismic design coefficients, as discussed in the following sections. Figure 1.2: Framework for verifying seismic design coefficients of high-rise buildings, including deflection amplification (Cd), design overstrength (â¦), and response modification (R) factors. Evaluation of Seismic Design Coefficients End of Frame or for Evaluation of Seismic Design Coefficients Start of Evaluation of Seismic Design Coefficients of igh rise Buildings Selection and Design of RC Buildings Bearing all (40S B, 0S B) Dual ( 0S D) Structural System Free ibration Analyses Detailed 3D Fiber based Modeling of RC Buildings Incremental Static Analyses (ISA) erification of Lateral Response Lateral Capacity Overstrength Stiffness Plastic inges Multi record Bi directional Incremental Dynamic Analyses (MBIDA) Bi directional Seismic Loading st ield Overstrength o Limit States o Inter story drift o Plastic inges erification of Seismic Response ype of System Buildings Design Regular (R) eometric Irregular ( I) Soft Story (SS) 40S B R 40S B I 40S B SS 0S B R 0S B I 0S B SS 0S D R 0S D I 0S D SS 5 The specific objectives of the study are as follows: â¢ Systematically review the response factors recommended by contemporary building design codes and to compare the methodologies adopted in previous studies to evaluate these factors. â¢ Verify the response modification coefficients of code-compliant MSBs with increasing heights using 3D MBIDA nonlinear analysis. â¢ Assess the seismic design coefficients for high-rise buildings, considering different heights, structural systems, and irregularities using 3D dynamic response simulation and bidirectional earthquake records. â¢ Evaluate probabilistically the seismic performance of code-compliant MSBs and high-rise buildings representing various structural systems with different building irregularities. â¢ Provide necessary recommendations on the code-recommended design coefficients and safety margins for various structural systems with different building irregularities. 1.3. Report Organization Following this introductory chapter, Chapter 2 covers the state-of-the-art review of the seismic design response factors addressing the literature of over five decades on steel and RC buildings with varying heights, irregularities, and structural systems. Limitations and gaps were presented from the previous reviews considering the type of systems, type of analysis, components of seismic design factors, type of buildings, structural systems, input ground motions and the seismic loading applied on the structures. Chapter 3 discusses the selection and design of the four regular multi-storey steel buildings (MSBs) of varying heights and three RC high-rise buildings covering varying structural systems and irregularities. The structural design of the thirteen benchmark buildings is finally summarized in this chapter and appendices. Chapter 4 describes the 3D structural modelling of the selected steel and RC high-rise buildings for inelastic static and dynamic analysis. The analysis platform employed in the 6 present study is introduced. The selection of a diverse set of input ground motions to realistically represent the seismicity of the medium seismic zone is discussed in detail. Chapter 5 presents the inelastic static and dynamic analysis of the thirteen benchmark buildings. The free vibration analyses performed to identify the periods of vibrations are described. The lateral capacities of the various buildings, their overstrength, formation of plastic hinges and stiffness is discussed. Results of the incremental dynamic analysis is discussed and summarized in this chapter. Chapter 6 discusses in detail the assessment of seismic design coefficients of the steel and RC buildings. Seismic response factors are compared with respect to the various irregularities in the range of the high-rise buildings and the results are summarized. Recommendations are presented and compared with the code specified design coefficients. Chapter 7 deals with the assessment of the seismic fragility of the selected buildings. This chapter describes the adopted methodology for developing fragility relationships. The limit states required to assess the performance of the reference buildings are also explained. Damage states are defined to assess the performance of the reference buildings. Chapter 8 provides the overall comparison between two structural systems in terms of seismic performance, design coefficients and costs. Results and recommendations are provided. Chapter 9 summarizes the adopted methodologies, main findings and recommendations of the study. Suggestions for future work are also provided. 7 2 Literature Review 2.1. Introduction Rapid urbanization in major metropolitan areas around the globe has witnessed scarcity and a high cost of land, giving rise to a remarkable increase in the number of multi-storey building constructions. These multi-storey buildings, if not acceptably designed, can be under significant threat from natural hazards that can cause potential damage to the structures, resulting in substantial economic losses. Lateral loads, particularly in wind or earthquake-prone regions, usually govern the design of a multi-storey building. Inelastic analysis is required to capture the seismic behaviour realistically since buildings are expected to experience large deformations under the design of an earthquake. Practicing engineers adopt elastic analysis methods in the design of structures instead of nonlinear analysis, either due to economic reasons or a lack of required knowledge to utilize nonlinear analysis procedures. The inelastic response of a structure is accounted for in the elastic analysis methods by reducing seismic forces and amplifying deformations to arrive at safe designs with optimized costs. Thus, seismic design response factors play an essential part in the safety and economy of structures. Seismic response factors prescribed in various design codes and guidelines covering different regions, structural systems, and constructional practices may not provide cost-effective designs for different structures and seismic zones with a uniform margin of safety [13-18]. Accurately calibrating these factors optimizes the seismic design forces, reducing costs for the overall structural system without compromising structural safety. This highlights the need for verifying the code-provided seismic design response factors of multi-storey buildings with various structural systems using well-founded assessment methodologies. Thus, it becomes important to systematically review the response factors recommended by contemporary building design codes and compare the methodologies adopted in previous studies to evaluate these factors, aiming to provide insights into the need for future research to achieve more cost-effective designs with consistent safety margins for different structural systems. 2.2. Scope and Literature Review Approach The existing literature on the development, assessment, and verification of the seismic response factors of multi-storey buildings is studied systematically in this research, as 8 shown in Figure 2.1. A brief overview of the seismic design response factors in various seismic codes is discussed. The historical perspective showing the evolution of the seismic design factors is presented, followed by an overview of the strength reduction factor defining its various components. The literature is then summarized by providing the available methodologies adopted by various researchers in evaluating the seismic design factors. Finally, the comparative review is followed by a description of the limitations and gaps in the literature, highlighting the need to consistently quantify the seismic design factors for multi-storey buildings. Figure 2.1: Summary of review methodology. 2.3. Overview of Seismic Design Response Factors The seismic design forces of structures are derived in design codes by reducing the anticipated elastic seismic forces with a force reduction factor. The factors used to reduce seismic forces and amplify deformations to arrive at a safe design with optimized cost are termed seismic design response factors. Seismic design response factors may be based on engineering judgment and have a limited analytical basis [13]. The values of these seismic Overvie of seismic design response factors istorical perspectives Factors in various codes Assessment methodologies SDOF System Assessing demand MDOF System Assessing capacities Analytical Areas of future research Conclusions o Steel braced structures o Steel frame structures o Steel wall & other structures o R.C. frame structures o R.C. shear wall structures o Analytical o IPA o IDA o Experimental o Hybrid Limitations gaps 9 design factors adopted in seismic design codes do not provide uniform safety margins covering various structural systems, although they dictate the performance of buildings and the seismic design process. This presses the need for the proper selection of appropriate values of the seismic design factors for building structures, which has been a debatable issue in the development of seismic design provisions and highlighted in several previous studies. The shortcomings in seismic design factors are particularly evident at various performance levels and under bidirectional input ground motions [19-22]. Hence, the accurate evaluation of seismic design factors and the interrelationships between the different design parameters are essential components in the seismic design of multi-storey buildings. The reserve strength and the ductility levels in a structure are utilized to reduce the seismic forces through the response modification factor [13-18]. Lateral load-resisting systems are designed to be deflection-controlled and possess adequate inelastic deformation capacity. The ductile detailing is essential to ensure that the components of these systems achieve a desirable behaviour. Some previous studies highlighted the significance of redundancy in the structure to the seismic design response factors [23-26]. Figure 2.2 illustrates a typical lateral forceâdeformation relationship defining the components of seismic response factors, including the response modification factor (R), ductility reduction factor (Rµ), deflection amplification factor (Cd), and structural overstrength factor (â¦o), as recommended in various building codes [13, 14]. The values of the R, Cd, and â¦o factors depend on the structural system and material. 2.3.1. Historical Perspective of Seismic Response Factors The evolution of seismic-resistant designed buildings can be traced several decades after the San Francisco earthquake of 1906 and classified into three phases [27, 28]. The first phase adopted the application of the prescribed percentage of building weight as an applied load to the structure [29]. This was published under the first seismic code provisions of the Uniform Building Code (UBC) presented by SEAOC in 1927. The second phase used the concept of the seismic base shear (V) related to zone factor (Z), building system type (K), building period (C), and building weight (W) [30]. The response modification factor was introduced under this phase for the first time in the late 1970s to calculate the design base shear (Vs) of the structure by reducing the elastic base shear (Ve) with the reduction factor (R) using 5% damped acceleration for different systems. The present phase, also defined 10 as the third phase, is based on applying the equivalent lateral force on the structure and employing spectral acceleration maps representing the site seismicity, importance factors, the natural building period, factors affecting the site, and the response modification factors [31]. Figure 2.2: Seismic design coefficients and their relationships 2.3.2. Seismic Response Factors in Various Codes Seismic design factors serve a similar function basically in all the seismic design codes. These factors introduced in the seismic codes are denoted in different terms and assigned with different numerical values. Brief comparisons of these factors practiced in various seismic codes are illustrated in Table 2.1. Table 2.1: Comparison of Seismic Design Coefficients. Seismic Provisions Applicable Region / Country Response Modification Factor Deflection Amplification Factor Deflection Amplification Factor / Response Modification Factor ASCE 7-22 [32] U.S. and other Countries R Cd 0.50 - 1.00 Eurocode 8 [16] Europe qi q 1.00c NZS 1170.4 [33] New Zealand µb µ 1.00c NBCC [34] Canada Rd/Ro Rd/Ro MCBC [18] Mexico Qau Q 1.00c UBC UBC (1994) [35] U.S. and other Countries Rew (3/8)Rw 0.375 UBC (1997) [36] R 0.7R 0.70 a reduces to 1.0 at T = 0 sec, and period-dependent in short period range, b does not reduce to 1.0 at T = 0 sec, and period-dependent in 0.45 â 0.7 sec range, and c greater than 1.0 in short period range Base shear (V)VyR = Rµ â¦oElastic strengthLateral displacement (â)Design strengthVfyVsVeâeElastic displacement Cd = âd /âsYield strengthFirst yield strengthof a real systemRµ = Ve / Vyâ¦o = Vy / VsâdDesign displacement âs = âe / RDisplacement under reduced design forcedisplacement â¦fy = Vfy / VsPlastic hinge development11 2.4. Methods of assessing seismic Response Factors The literature review of previous assessment studies on seismic response factors is grouped under the following two categories: o Single degree of freedom (SDOF) systems assessing the demands o Multi-degree of freedom (MDOF) systems assessing the capacities Methodologies adopting SDOF systems for computing the reduction factor âdemandâ are derived based on the ratio between the elastic strength demand (Ve) and the inelastic strength demand (Vy), corresponding to a defined constant ductility µ [37]. They can also be related to the ratio between the elastic and inelastic response spectral ordinate (Sa, elastic and Sa, inelastic, respectively) related to a specific natural period T [38]. On the other hand, approaches adopting MDOF systems are focused on realistic buildings and actual structures [22, 39, 40]. Previous studies covering the above two methodologies by various researchers in evaluating the seismic design factors are reviewed and described briefly in the following sections. 2.4.1. Single Degree of Freedom (SDOF) Systems: Assessing the Demands Newmark and Hall [41, 42] parameterized the reduction factor as a function of ductility. The concept proposed by Newmark focused on SDOF structures covering long period and short period ranges. The strength reduction factor (termed as behaviour factor, q in European standards) was considered as equal to the displacement ductility factor for long elastic period and ductile systems with similar initial stiffness and equal displacement. An equal energy approach was proposed in computing the reduction factor for the short period elastic and inelastic structures. For short period structures, ductility reduction factor (Rμ) was considered equal to unity. Three period zones covering the short period (< 0.2s), intermediate period (0.2 to 0.5s) and the long period (> 1s) were considered in the study. Newmark & Hall established a relationship with Rμ factor and verified it as a function of ductility (µ) and period dependent (T) and proposed the equations to evaluate the behaviour factor (Rμ) as shown in Table 2.2. Krawinkler and Nassar [43] established a relationship to evaluate the force reduction factor using the nonlinear response of SDOF systems. Fifteen ground motions were selected for statistical analysis representing alluvium soil and rock sites with an earthquake magnitude of 5.7 to 7.7 representing the Western USA region. The structural system parameters were 12 examined using the fundamental period (T), strain-hardening coefficient (α), the level of yield and type of inelastic behaviour of material (bilinear versus stiffness degrading) apart from the epicentral distance in estimating the sensitivity of strength reduction factors. Estimations of the strength reduction factors were proposed using the equations shown in Table 2.2, by giving importance to the site conditions showing negligible influence on epi-central distance and stiffness degradation under 5% damping. The study was limited to alluvium soil and rock sites under moderate seismicity regions, and other site classes and seismicity regions were not investigated. Miranda and Bertero [44] evaluated the strength reduction factors using the elastic strength demands under 124 recorded ground motions over different conditions of soil, representing low shear wave velocity. The study was based on different soil conditions representing rock, very soft, and alluvium sites. The average strength reduction factors were evaluated for SDOF systems on each soil group, assuming 5% critical damping under the influence of magnitude and epicentral distance. Soil conditions significantly influenced the strength reduction factors, whereas the earthquake magnitude and its epicentral distance had a negligible effect. Simplified expressions were proposed to compute the period dependent force reduction factors (Rµ) with a 5% maximum damping based on the mean strength reduction factors covering different soil types, as shown in Table 2.2. Vidic et al. [45] considered SDOF systems using a bilinear response model along with a stiffness degrading model (Q-model) to compute the ductility reduction factor (Rµ) by approximating a bilinear curve. Twenty standard records were selected from seismic events, with moderate epicentral distances and predominant periods in estimating the strength reduction factors. Simplified expressions were proposed in estimating the reduction factor for strong motions, considering two linear segments depending on the hysteretic behaviour of the system and its respective damping, as shown in Table 2.2. The physical boundary conditions of R = µ and = â were not satisfied with the value of constants other than unity, and structures with very long periods are affected, and hence, the study is limited to short-period structures only. Borzi and Elnashai [37] derived the response modification factors by evaluating the ratio between the elastic and the inelastic acceleration spectra using regression analysis utilizing a broad range of input ground motion data. The influence of ductility on response factors was assessed using a hysteretic model of elastic perfectly plastic (EPP) nature on the input 13 ground motion parameters like the magnitude of an earthquake, the distance from the epicentre, and soil conditions. The study concluded that ductility played a significant role in evaluating the response modification factor under the influence of the input ground motion parameters. Analyses were conducted on all the selected SDOF systems considering various ductility levels to define functions of the period-dependent response factor for earthquake sets with different ground motion parameters, as shown in Table 2.2. The study was limited to earthquake magnitudes between 5.5 and 7.9, while investigations on other magnitude ranges were not considered. The isoductile yield strengths and the corresponding strength reduction factors were studied on elastoplastic SDOF systems by Cuesta and Aschheim [46] using inelastic response subjected to waveforms containing linear, triangular, sinusoidal, and quadratic acceleration components. The SDOF systems were studied under twenty-four simple waveforms characterized by only a few cycles of repetitions, and the response characteristics were compared to assess their similarities and differences under an organized characteristic period. The strength reduction factor (R) was expressed as the ratio of the strength to isoductile yield strength (Vy) under constant ductility (µ = 1), as shown in Table 2.2. The inelastic response data of the systems due to gradual and shock loading pulses are compared with the expected results based on the concepts of preserved force, equal displacement, and equal energy to estimate the isoductile strengths and the strength reduction factors under constant ductility response. For all pulses, the R factor value increases with an increase in the ductility value and tends to be equal to unity for µ =1 and reaches asymptotic limits in the short- and long-period systems. Only one SDOF system (elastoplastic) with simple waveforms of not more than a few cycles was considered to assess the R factor. This study did not cover the investigation with other systems investigated under realistic ground motions representing both long-period and short-period systems. Cuesta et al. [47] presented a relationship to simplify the R factor with strong ground motions by modifying the original coefficients based on the characteristic period from the previous studies [37, 45]. Models representing the bilinear load deformation and stiffness-degrading load deformation with varying amounts of viscous damping were considered with different ratios of post-yield stiffness to initial stiffness. Ground motions were selected to represent both short- and long-duration frequencies. The inelastic spectra obtained for a set of 14 ground motions were compared using several bilinear models; load-deformation 14 relationships were studied, and the errors were compared. The bilinear and stiffness degradation systems performed well with the simplified R factor model, indicating limited stiffness degradation under the selected ground motions with a fair amount of accuracy of the strength estimates, except for the nearly harmonic motions generated at soft soil sites. However, an additional study was recommended to confirm their findings with a single bilinear R factor representing both near and far fault ground motions. Chakraborti and Gupta [48] studied the dependence of force reduction factors on the input parameters for strength and stiffness degrading structural systems. Two models with different input parameters under a scaled spectrum representing strong ground motions were considered. The input parameters considered for the first model were based on geological site conditions, the magnitude of the earthquake and its duration, the period of the structure, ductility supply, and the ductility demand ratio. In contrast, the second model was characterized by the input based on the normalized design spectrum, the ductility demand ratio, and ductility supply. Lower values of the force reduction factors were identified in the case of high ductility demand ratios with flexible oscillators, making a slight difference to the degradation factors. The study was conducted to estimate the lateral yield strength of the structural system with known ductility demand and supply, which may not apply to existing structures due to underestimating the maximum displacement. The study did not consider structures under high-magnitude earthquakes and other seismic regions, including near source records. Genshu and Yongfeng [49] analyzed the R factor for the modified Clough hysteretic model. The study compared it with elastic perfectly plastic (EPP), bilinear elastic (BILE), and shear slipped (SSP) models to separate the effects of ductility, energy dissipation, and stiffness degradation with different soil types on R spectra. The above models were analyzed with varying damping and post-yield stiffness ratios by normalizing the system periods for different earthquake records to maintain the peak characteristic (T) of R spectra near the characteristic period (Tg) for better correlation. An equation for R spectra was proposed as a product of functions representing mean ductility coefficient (Rµ), mean post yield stiffness coefficient (Rα), and mean damping coefficient (Rξ ) by maintaining the peak characteristics of R spectra to unity, as shown in Table 2.2. Ductility was the most prominent factor for determining R, which increased with an increase in ductility value compared with post-yield stiffness and damping, which had a minor effect on the structures with a short period range. The study was conducted with a maximum acceleration of 0.2 g 15 by scaling all the records for easier comparison. The seismic behaviour of the structures and the influence of the R factor with varying accelerations representing other ranges of seismic events need to be investigated to validate the studyâs recommendation. Jalali and Trifunac [50] analyzed the force reduction factors for structures near earthquake faults, such as near-fault, fault-parallel, and fault-normal strong motion displacements. A simple two-column structure with the strength reduction factors under different earthquake faults was considered for the study, and the results were summarized. For the structures designed close to near-fault or active-fault regions, the study recommended the use of constant strength reduction factors equal to â2ð â 1 for all elements of motion for both long and short periods. The structures designed for fault-parallel motions in the study presented smaller values of the R factor than the design R values representing non-conservatism and recommended change. However, the structures designed for fault-normal pulses had higher values of R factors than the selected R values, showing a conservative design and describing the reduction amplitudes properly near strong earthquake faults. The study used only a simplified form of ground motions using smooth pulses representing strong motions for peak amplitudes, which may not provide realistic results, as real scaled records were not employed in their analysis. Hatzigeorgiou [51] developed a procedure to evaluate the ductility demands of structures under multiple near-fault earthquakes using the appropriate strength reduction factor (q) considering the viscous damping, period of vibration, and post-yield stiffness ratio. Empirical expressions were derived through nonlinear regression analysis to propose the estimation of mean strength reduction factors satisfying the basic principles of dynamic inelastic analysis. The results provided a good similarity between the analysis and model results. The study was focused on ideal structures where smaller earthquakes are expected to have similar behaviour factors and similar ductility demands under the design earthquake. In contrast, seismic sequences provide smaller behaviour factors requiring greater ductility demands, possibly resulting in more significant structural damage. The study recommended a performance-based design to overcome the above drawback for actual structures with the design earthquake. Zhang et al. [52] investigated the strength reduction factor of SDOF systems for sequence-type records of mainshockâaftershock events classified under site classes B and C, considering the respective displacement ductility and cumulative damage. A SDOF 16 systems series of elastic plastic type scaled to five relative intensity levels of ductility factor and the damage index were studied using nonlinear time history analysis under different site conditions to determine the strength demands and the aftershock effects of the natural period and proposed expressions as a function of the damage index, period, and the ductility factor. The study indicated that the damage-based force reduction factor (RD) was influenced strongly by the period for short-period structures compared to the long period. Furthermore, the ductility-based force reduction factor (Rµ) was more than the damage-based force reduction factor (RD) for long-period structures. The proposed study was limited to only two types of soil class, and investigation of other soil types was not considered. Molazadeh and Saffari [53] considered the effects of ground motion duration on different hysteretic models to study the structural behaviour and assess the effects on ductility and energy dissipation. Two sets of seismic records representing long and short-duration events were considered in conducting nonlinear response history analysis (NLRHA) on five SDOF models. The behaviour of the elastic perfectly plastic, stiffness deterioration and degradation under two sets of ground motion with different values of Rµ was evaluated. The behaviour of structures with pinching-degradation models compared to EPP models was more severe under long periods than under short periods, with lower effects of Rµ on hysteretic energy dissipation and ductility. The regression equations proposed were limited to the structures with the ductility values considered in the study to ensure a satisfactory structural performance, where the required ductility capacity needs to be greater than the ductility demand of the structure obtained by the nonlinear analysis. Feng Wang et al. [54] developed a spectra of damage-based strength reduction factor for systems subject to bidirectional input ground motions more suitable for 2D analyses. The study presented an inelastic system of single-mass bi-degree-of-freedom (SMBDOF) for orthogonal bidirectional input ground motions, where the x-component constructs damage-based force reduction factor spectra (Rb spectra) with a constant damage index from the park-ang model. Utilizing 178 input ground motion records across site classes, the study established mean Rb spectra based on ductility capacity and damage level. Comparative analysis with SDOF system R spectra indicated increased strength demand in specific cases when coupling two-component responses in SMBDOF systems. Rb spectra trends remain generally consistent across site classes, reflecting site condition characteristics. Consideration of the period ratio is crucial, as significant differences may worsen seismic 17 damage. The study derives curves of Rb spectra with a period ratio of 1 through regression analysis, incorporating correction factors. Validation against actual mean spectra demonstrates a good match, confirming the proposed procedure's effectiveness. It is clear from the literature review of over five decades that the previous studies conducted on seismic response factors on SDOF systems were mainly based on hypothetical systems with hysteresis relationships and not on real structures. Most of the earlier work was based on ductility reduction factors without accounting for the contribution of overstrength factors. Several studies based their analytical work with seismic scenarios representing moderate to severe earthquakes and simple wave forms, while studies covering multiple seismic scenarios including aftershock events were hardly considered. For the sake of brevity, the review of the equations employed in the SDOF models is summarized in Table 2.2, whereas the review summary of the SDOF systems is presented in Table 2.3. Table 2.2: List of equations employed for computing seismic response factors using SDOF. Author Equations Remarks Newmark & Hall [41, 42] Rμ = 1 Rμ = â2ð â 1 Rμ = ð T < 0.2 s 0.2s < T < 0.5 s T > 1 s Krawinkler & Nassar [43] Rμ = [ð (ð â 1) + 1]1ðâ c ( , α) = ð»ðð+ ð»ð + ðð» Hardening alue α Model Parameters a b 0% 1.00 0.42 2% 1.01 0.37 10% 0.80 0.29 Miranda & Bertero [44] ð = 1 + ðððð»âð ð» - ððð» exp [ - 1.5 (ln T - 0.6)2 ] ð = 1 + ðððð»âð ð» - ððð» exp [ - 2.0 (ln T - 0.2)2 ] ð = 1 + ð»ððð» - ðð»ððð» exp [(ð¥ð§ ð»ð»ð â ðð)ð] Rμ = ðâ1Ï + 1 â¥ 1 Rock sites Alluvium sites Soft soil sites ð»ð, is the predominant period of ground motion corresponding to the relative velocity of linear elastic system with 5% maximum damping for the entire period range. Vidic et al [45] Rμ â ð Rμ = c1 (ð â 1)ð¶ð ððð + 1 Rμ = c1 (ð â 1)ð¶ð + 1 To = c2 ððð T1 To, is the period range in the two segments related to the predominant period of the ground motion T1 T â¤ To T â¥ To c1, c2, cR and cT depend on hysteretic behaviour and damping. Borzi & Elnashai [37] q = (q1 - 1) ð»ð»ð + 1 q = q1 + (q2 - q1) ð»â ð»ðð»ðâ ð»ð q = q2 T â¤ T1 T1 < T â¤ T2 T > T2 Cuesta & Aschheim [46] R = R(µ,T) = ðð¦(ð=1,ð)ðð¦(ð,ð) Genshu & Yongfeng [49] R = Rμ Rα Rξ 18 Table 2.3: Summary of the literature work on SDOF systems Author Analysis type, Methodology Type of structures & structural systems Seismic design factors Seismic factor dependencies Soil site class Features of input ground motions Newmark & Hall [41, 42] 2D Analytical Long & short period range structures Rµ T, µ Alluvium, very soft and rock sites Elastic response spectra for long and short periods Krawinkler & Nassar [43] 2D Analytical Short period range structures Rµ , µ, α Alluvium soil and rock sites 15 GM with 5.7 to 7.7 EQ magnitude Miranda & Bertero [44] 2D Analytical Short period range structures Rµ T, Tg, µ Alluvium, very soft and rock sites 124 GM with low shear velocity Vidic et al [45] 2D Analytical Short period range structures Rµ T, µ, c Alluvium and stiff soil sites 20 strong motion EQ records Borzi & Elnashai [37] 2D Analytical Low rise structures R (q) T, µ Soft, stiff and rock sites 43 GM with 5.5 to 7.7 EQ magnitude Cuesta & Aschheim [46] 2D Analytical Elasto-plastic structures R T, µ, Tg Alluvium and stiff soil sites 24 simple wave form linear, triangular, sinusoidal, quadratic Cuesta et al [47] 2D Analytical Bilinear and stiffness degrading models R T, µ, Tg Alluvium and stiff soil sites 14 GM of short and long duration frequencies Chakraborti & Gupta [48] 2D Analytical Short period range structures R T, µ, Tg Alluvium, Intermediate, hard rock sites Several accelerograms of 3 to 8 EQ magnitude Genshu & Yongfeng [49] 2D Analytical Modified-Clough hysteretic model R T, µ, Tg Site class A, B, C & D 370 seismic records, different site class, 0.2g acceleration Jalali & Trifunac [50] 2D Analytical Short period range structures R T, µ Stiff and soft soil sites Near field EQ with EQ magnitude ranging from 4 to 8 Hatzigeorgiou [51] 2D Analytical RC structures R (q) T, µ Soft, stiff, dense and rock sites 110 near-fault Eqn. with 5.5 to 7.8 magnitude Zhang et al [52] 2D Analytical Elasto-plastic structures Rµ , RD T, µ Site class B & C Mainshock > 0.10g PGA and aftershock > 0.05g Molazadeh & Saffari [53] 2D Analytical Short period range structures Rµ T, µ Site class D Short & long duration records of varying magnitude Feng Wang et al [54] 2D Analytical Short period range structures Rb, R T, µ All Site classes 178 ground motion records with bidirectional loading 19 2.4.2. Multi-Degree of Freedom (MDOF Systems): Assessing the Capacities The review of the seismic response factors under the MDOF systems is classified based on the different structural systems and presented in the following five categories: o Steel braced structures. o Steel frame structures. o Steel walls and other structures. o RC frame structures. o RC shear wall structures. 2.4.2.1. Steel braced structures Calado et al. [55] evaluated the strength reduction factor (q) of low-rise steel buildings by analysing three structural systems using a simple steel frame, cantilever, and diagonally braced cantilever buildings. The analysis used a single-storey frame to study the cantilever buildings with and without braces, whereas two and three storeys were used for frame buildings. Natural and artificial accelerograms represented various seismic loading conditions with 15 to 25 s. durations. The study characterized the failure of the structures using a numerical index based on the damage accumulation. The study concluded that the q factors were very conservative based on their parametric results influenced by different natural frequencies. The study was limited to regular 2D ideal structures with limited accelerograms, and other structural systems were not investigated. Balendra and Huang [56] explored overstrength and ductility factors in low seismic conditions for three steel frame types: moment-resisting frames (MRFs), concentrically braced frames (CBFs), and semi-rigid frames. They designed three, six, and ten-storey symmetric office buildings following BS 5950 guidelines, addressing P-â effects. As the study region (Singapore) lacked seismic provisions, seismic performance was evaluated using inelastic pushover analysis (IPA) and the N2 method for the design earthquake. MRFs exhibited significant overstrength and ductility, with overstrength decreasing by up to 50% and ductility increasing by over 25% when rigid connections were replaced with semi-rigid ones. Response modification factor values ranged from 16 to 6 for MRFs, 8.5 to 3.5 for CBF, and 15 to 3.5 for semi-rigid frames. The obtained R factors varied widely, and the study, confined to regular structures and pushover analysis, did not assess seismic performance through nonlinear dynamic analysis. 20 Asgarian and Shokrgozar [57] investigated ductility, overstrength, and response modification factors for the Buckling Restrained Braced Frames (BRBFs) in four to fourteen-storey buildings with split X, diagonal, chevron (V and inverted V) bracing configurations. Employing the Iranian National Building Code (2006) and seismic parameters from Iranian Earthquake Resistant Design Codes (2005), the study used two-dimensional IPA, linear dynamic, and nonlinear inelastic dynamic analysis (IDA) with three natural ground motion records. Seismic parameters for BRBF in various configurations were evaluated using the ultimate limit state and the allowable stress methods. The study found conservative seismic response values compared to design codes, indicating decreased overstrength and ductility factors with increased storey height. o ever, the studyâs reliance on a limited number of seismic records may not fully capture the variability in input ground motions. Mahmoudi and Zaree [58] assessed response modification factors using conventional steel CBFs and BRBFs, selecting thirty conventional steel CBFs and twenty BRBFs ranging from three to twelve storeys. For conventional CBFs, chevron V, X-type bracings, and chevron-inverted V were considered, while BRBFs were studied with chevron-inverted V and chevron V bracing types. The response modification factor and ductility values of CBFs and BRBFs were assessed considering the life safety structural performance levels using IPA to evaluate the factors on ductility, overstrength, and force reduction. Overstrength and R factors increased with the number of braced bays, decreasing slightly for taller BRBFs due to increased ductility. The study identified conservative response modification factors in Iranian seismic codes, recommending necessary modifications. The analysis was based on IDA for ideal structures up to 12 storeys without investigating seismic response with real seismic records. Farahi and Mofid [59] evaluated the Rµ, â¦o, and R factors of chevron knee bracing (CKB) frames adopting the FEMA P695 approach involving inelastic static and dynamic analyses. The IPAs were conducted to evaluate the overstrength and ductility, while IDA was conducted to obtain the selected buildingsâ collapse margin ratios (CMRs). he CMR values were modified to derive adjusted collapse margin ratios (ACMRs) for each frame type. These values exceeded the acceptable collapse margins of FEMA P695. The R factor values considered were conservative, and the collapse margins decreased with the increase in structure height. The ductility and stiffness were higher in the CKB frames with more 21 spans than with fewer bays. The study was limited to a few 2D CKB frames, and further investigation with a wider range of structures was recommended. Moni et al. [60] employed twelve regular BRBF buildings with four, six, and eight storeys using split X and chevron-inverted V braces to evaluate the seismic design factors. The buildings were analyzed and designed using the NBCC [15] to match the response spectrum of Vancouver, Canada. Two-dimensional nonlinear dynamic time history analysis (THA) was performed using nine natural records and one artificial record to evaluate the seismic performance and estimate the response modification, overstrength, and ductility factors. The response modification factors, ductility, and overstrength met the code limits and were conservative, decreasing with increased building height and span length. The study was limited to regular structures with limited bracing systems. Kheyroddin and Mashhadiali [61] proposed the R factor of steel concentrically braced frames (CBFs) forming a hexagonal pattern using the V and inverted V bracings. They quantified the R factor through FEMA P695 methodology, conducting nonlinear static and dynamic analyses on four, ten, and 20-storey buildings. The proposed hexa-braced buildings, designed with an assumed value of R factor complying with ASCE standards, were compared with similar buildings braced by X braces as a benchmark. Two-dimensional IPA and IDA, employing two sets of near-field and far-field scaled ground motion records, were performed. The CMR based on FEMA P695 methodology obtained until collapse demonstrates adequate safety margins for both X-braced and hexa-braced frame models. The study was limited to regular buildings and recommended further investigation covering other codes with experimental verification. Masood Yakhchalian et al. [62] evaluated the deflection amplification factor (Cd) of steel buckling restrained braced frames (BRBFs) using six regular low-to-midrise structures ranging from two to twelve storeys under the design earthquake. The study compared the adequacy of the ASCE recommended Cd value of 5.0 for estimating inelastic maximum drift ratios (IMIDRs) in steel BRBFs. They conducted 2D inelastic analyses using 78 seismic records and observed that the Cd underestimates the IMIDR of lower storeys while overestimating for taller structures. A more realistic approach was proposed to estimate the Cd using the particle swarm optimization (PSO) algorithm. The influence of the strain hardening ratio on Cd and Cd Roof relative to the response modification coefficient (R) with the ductility reduction factor (Rµ) was also investigated. 22 Shen Li et al. [63] assessed the seismic response factors of regular Y-shaped eccentrically braced high-strength steel frames ranging from four to sixteen storeys. The study employed ordinary steel in links and high-strength steel in beams and columns. The high-strength steel in beams and columns was used to reduce the cross-section, maintaining good ductility with excellent plastic deformation ability during seismic events. The study assessed R and Cd by conducting 2D performance-based design, static elastic plastic, and incremental dynamic analyses utilizing ten ground motion records. The R and Cd were calculated considering the number of storeys and the link lengths and established linear relationships between the seismic design response factors. Mahdi Mokhtari and Ali Imanpour [64] verified the overstrength and the ductility related force modification and deflection amplification factors for 14 prototype steel resisting braced frames (MKFs) in Vancouver, Canada. Regular buildings ranging from six to fifteen storeys were designed, and 2D numerical models were developed to assess the seismic design factors. The IDAs were conducted using three sets of ten seismic records, each representing subduction intraslab, shallow crustal, and subduction interface events. The study suggested designing the proposed MKF system as a moderately ductile system in high seismicity regions, with a maximum height of 40 m using 1.60 as the overstrength factor and 3.0 as the ductility factor. The presented review of the seismic response factors of MDOF systems for steel-braced structures in the present study covered investigations published since 1995. Most of the earlier work was based on 2D analytical work with unidirectional seismic loading. Regular low-rise- to medium-rise-braced frames were analyzed using IPA and IDA with limited research on relatively tall buildings. In earlier studies, irregular structures under the effect of bi-directional loading representing real buildings with varying heights employing 3D inelastic analysis were not considered. The review of the MDOF systems representing steel-braced structures is summarized and presented in Table 2.4 for a better understanding. 2.4.2.2. Steel frame structures Mohammadi [65] considered elastoplastic MDOF models with various dynamic characteristics to evaluate the effect of the deflection amplification factor of steel frame buildings. Buildings with five to fifteen storeys were selected and designed, as per AISC design procedures. A two-dimensional nonlinear dynamic analysis assessed the seismic performance under twenty-one accelerograms from ten different earthquakes. The study 23 proposed an approximate approach to evaluate maximum inelastic deformation in a structure using given strengths and deflection amplification factors. The study concluded that the values of the deflection amplification factor for the MDOF systems obtained were more significant than the theoretical values. The study was limited to regular structures with a specific structural system, while other structural systems were not investigated. Table 2.4: Summary of the literature on MDOF models â steel braced structures Author Analysis type, Methodology Type of Structures & Structural Systems No. of storeys Seismic Design Factors Remarks Calado et al [55] 2D Analytical Regular MRF, cantilever & braced 1, 2 & 3 R(q) Adequate margin of safety Balendra & Huang [56] 2D Analytical, IPA Regular MRF, CBF & semi-rigid 3, 6 & 10 Rï­ and Ωo Adequate margin of safety Asgarian & Shokrgozar [57] 2D Analytical, IPA & IDA BRBF with diagonal, split X, Chevron V & inverted V bracings 4, 6, 8, 10, 12 & 14 Rï­, Ωo, and R Adequate margin of safety Mahmoudi & Zaree [58] 2D Analytical, IPA Regular CBF & BRBF with X, Chevron V & inverted V bracings 3, 5, 7, 10 & 12 R Adequate margin of safety Farahi & Mofid [59] 2D Analytical, IPA & IDA Regular Chevron Knee Bracings 2, 4, 6, 10 & 14 Rï­, Ωo, and R Adequate margin of safety Moni et al [60] 2D Analytical, IPA & THA Regular BRBF with Chevron inverted V and split X bracings 4, 6 & 8 Rï­, Ωo, and R Adequate margin of safety Kheyroddin & Mashhadiali [61] 2D Analytical, IPA & IDA Regular CBF with hexagonal pattern & X frames 4, 10 & 20 R Adequate margin of safety Masood Yakhchalian et al [62] 2D Analytical, IPA & IDA Regular BRBF 2,4,6,8,10 & 12 R, Cd Adequate margin of safety Shen Li et al [63] 2D Analytical, IPA & IDA Y-shaped eccentrically braced high-strength 4 to 16 R, Cd Adequate margin of safety Mahdi Mokhtari and Ali Imanpour [64] 2D Analytical, IPA & IDA Moment resisting knee brace (MKF) 6 to 15 Rd, Rï¯, Adequate margin of safety Foutch and Wilcoski [66] proposed an approach for determining R factors of steel MRFs using both analytical and previous experimental work. Steel regular buildings were designed and detailed per the International Building Code (IBC). The IDA was performed on each building under 20 near-fault input ground motions to suit the Los Angeles site. The R factors evaluated were conservative, indicating that the values can be reduced considerably. The demand and capacity for the proposed study were based on storey drift, which may not be effective on stiff systems, like steel-braced frames and shear walls. The study was limited to the moment-resisting frames, while other structural systems were not investigated. 24 Stefano et al. [67] studied the impact of overstrength in plan-irregular multi-storey steel frame buildings, comparing the inelastic seismic response of a six-storey asymmetric steel building with a single-storey building with negligible overstrength. Single-storey and six-storey asymmetric buildings were designed in two different directions based on Eurocode 8. Two-dimensional IPAs and THAs using 30 artificial accelerograms were employed to assess the ductility demand and the torsional behaviour. The study emphasized the significant role of overstrength, especially in buildings under torsion, and highlighted greater ductility demands in the upper floors of multi-storey asymmetric buildings with higher overstrength, contrary to results from corresponding single-storey buildings. Furthermore, the study was limited to only two ideal buildings investigated with 2D IPA and THA, while 3D nonlinear analysis was not considered to estimate the torsional effects of irregular structures. Karavasilis et al. [68] analyzed a set of 36 regular-plane steel MRFs to evaluate their response in estimating the strength reduction factors (q). The Eurocode was used for frame design, and ground motions were based on the EC8 response spectrum using a PGA of 0.35g for soil class B. Employing two-dimensional IDA with thirty-four natural records from the PEER (2005) database, the study compared results with experimental findings from the nine-storey SAC steel frame (SAC steel project) by Gupta and Krawinkler [69]. The proposed strength reduction factor was independent of sectional dimensions but significantly dependent on the storey height and the capacity factor. The study observed that the conventional strength reduction factor recommended by the seismic design code may or may not be conservative. The study was limited to buildings of 20 storeys and did not account for long durationâhigh amplitude seismic motions. Kang and Choi [70] proposed the evaluation of the response modification factor (R) of steel MRFs as a product of the ductility factor (Rµ) for SDOF systems, the modification factor of MDOF systems (RM), and the strength factor (RS). Regular frames of four to sixteen storeys were designed with varying soil profiles and seismic zone factors, as per UBC standards and the provisions of the AISC code. A two-dimensional IPA was conducted on selected frames to estimate the Rµ, RM, and RS factors, and the failure mechanisms were assessed. The R factor was evaluated for frames with strong columnâweak beam (SCWB) models and weak columnâstrong beam (WCSB) models. The mean value of R factors for the SCWB models exceeded the code-recommended values, while the values for the WCSB models were below the code recommendations. The proposed rule was verified on regular 25 steel MRFs using IPAs only. The study recommended evaluating the seismic performance with other structural systems to ensure a uniform margin of safety. Izadinia et al. [71] derived and compared the seismic response factors using capacity curves from different pushover analysis methods. Three regular steel frames from the SAC project of three to twenty storeys were considered in the study to evaluate the Rµ, â¦o, and R factors. Conventional pushover analysis (CPA) and adaptive pushover analysis (APA) were conducted on each frame, and the results were compared. The study adopted force and displacement-based adaptive pushover analyses (FAPA and DAPA) using various constants and load patterns. The study identified a relative difference of 16% and 17% of R factor and ductility ratios (µ) between CPA and APA (FAPA or DAPA) due to larger results in APA using different seismic records. The study was limited to regular 2D MRFs with static pushover analysis, while dynamic analysis was not considered. Ferraioli et al. [72] assessed redundancy, overstrength, ductility response modification, and strength reduction (q) factors in six regular and six vertical irregular steel MRFs of varying heights (three to nine storeys) and bay configurations. Designed for soil class A as per the Italian seismic code, IPAs and IDAs with 12 ground motions were conducted. The redundancy factor for both regular and irregular frames was conservative compared to that recommended by Eurocode 8 and the Italian seismic code values. The strength reduction factor evaluated was below the code-recommended values for higher storey frames due to the limited rotation capacity of the first-storey columns. The code recommended values of the strength reduction factor were conservative in the case of a fixed connection at the base and recommended a full-strength connection at the column base-to-foundation. The study was limited to 2D frames and recommended further investigation of other types of connections. Reyes-Salazar et al. [73] investigated ductility (µ), ductility reduction factor (Rµ), and energy dissipation (E) in low-rise and medium-rise steel buildings of 3 to 10-storey, designed with strong column-weak beam principle according to IBC. Two-dimensional nonlinear THA was conducted using 20 strong ground motions to assess the µ, Rµ and E, at local, storey, and global structural levels. The values of the local ductility capacity of beams were larger in medium-rise buildings than in low-rise buildings. The study proposed the findings based on the ratios of global ductility to local ductility (Q), local ductility reduction factor to local ductility (QL), storey ductility reduction factor to storey ductility 26 (QS), global reduction ductility factor to global ductility (QG), storey ductility reduction factor to storey energy dissipation (PS) and global ductility reduction factor to global energy dissipation (PG). The values were evaluated as 0.33 for the Q ratio, 0.32 to 0.6 for the QL ratio, 0.60 to 1.10 for the QS ratio, and 0.73 to 0.86 for the QG ratio. The study was limited to medium-rise regular steel buildings with only one structural system, and other structural systems with high-rise buildings were not investigated. The study by Macedo et al. [74] aimed to evaluate the impact of a more logical selection of the behaviour factor (q) of steel moment-resisting frames (MRFs) designed according to Eurocode 8. The seismic design of steel MRFs was conducted on 30 buildings with five frame heights ranging from two to eight storeys, using both code-prescribed q and an improved force-based design (IFBD) approach. The seismic behaviour was assessed using nonlinear static and response history analyses utilizing 40 input ground motions. The IFBD-designed steel frames exhibited inelastic demands evenly distributed along the building height and ductility demands that align better with design assumptions. Fayaz Rofooei and Ali Seyedkazemi [75] determined the seismic performance factors (SPF) for steel diagrid structures spanning six to twenty-four storeys. The study considered the post-buckling behaviour of diagonal compression members, along with variations in span length and diagonal angles. SPF calculations were based on the ATC-19 coefficient method, while FEMA P695 was employed to evaluate accuracy. Seismic collapse capacity was assessed through IDAs with 22 far-field records. Their results indicated that as diagrid structures increased in height, there was a decrease in the response modification factor, overstrength, and median collapse intensity, associated with an increase in the ductility factor. Additionally, the collapse margin ratios of the diagrid structures exceeded FEMA P695 recommended limits. Maysam Samadi and Norouz Jahan [76] examined the impact on seismic design parameters such as the response modification factor (R), overstrength factor (â¦), deflection amplification factor (Cd), and the damping ratios for tall steel buildings. The study examined regular steel buildings with 28 and 56 storeys, featuring steel-braced and reinforced concrete (RC) shear wall cores with outriggers placed at every quarter of the building height, resulting in 44 building models. Seismic parameters were assessed using the modal response spectrum (MRS), pushover, and nonlinear time history (NLTH) 3D analyses. Including the outriggers increased the response modification factor, overstrength, 27 stiffness, and damping ratios, particularly in the buildings with RC core walls, while reducing ductility in both systems. Their study also identified inadequacy in the code-recommended Cd values. The evaluation of the seismic response factors of MDOF systems for steel MRF structures in the past two decades was mainly based on 2D analytical works. Regular low-rise-to medium-rise-braced frames were analyzed using IPAs and IDAs, with little work on relatively tall buildings. In earlier studies, irregular structures under the effect of bi-directional loading representing real buildings with varying heights employing 3D inelastic analysis were not considered. Limited experimental validation was performed to validate the analytical work. For the sake of brevity, the review of the MDOF systems representing steel frame structures is summarized and presented in Table 2.5. Table 2.5: Summary of the literature work on MDOF models â steel frame structures Author Analysis type, Methodology Type of Structures & Structural Systems No. of storeys Seismic Design Factors Remarks Mohammadi [65] 2D Analytical, IDA Regular MRF buildings 5, 10 & 15 Cd Adequate margin of safety Foutch & Wilcoski [66] 2D Analytical, Experimental, IDA Regular MRF buildings 3, 9 & 20 R Adequate margin of safety. Stefano et al [67] 2D Analytical, IPA & THA Plan irregular MRF buildings 1 & 6 Ωo Proposed improvement Karavasilis et al [68] 2D Analytical, Experimental, THA Regular MRF buildings 3, 6, 9, 12, 15 & 20 R (q) Not valid for long duration-high amplitude GMs Kang & Choi [70] 2D Analytical, IPA Regular MRF buildings 4, 8 & 16 R Adequate margin of safety. Izadinia et al [71] 2D Analytical, IPA Regular MRF buildings 3, 9 & 20 Rï­, Ωo, and R Conservative with CPA & APA Ferraioli et al [72] 2D Analytical, IPA & IDA 6 regular & 6 irregular MRF 3,5,7 & 9 Rï­, Ωo, and R (q) Adequate margin of safety. Reyes-salazar et al [73] 2D Analytical, THA Regular MRF buildings 3 & 10 µ, Rï­ and E More conservative in medium rise Macedo et al [74] 2D Analytical, IPA & IDA 5 regular MRF frames 2 to 8 R (q) Adequate margin of safety. Fayaz Rofooei and Ali Seyedkazemi [75] 2D Analytical, IPA & IDA Regular steel diagrid structures 6 to 24 R, Ωo Adequate margin of safety. Maysam Samadi and Norouz Jahan [76] 3D Analytical, MRS, IPA, NLTH 2 Regular steel braced buildings with outriggers 28 & 56 R, Cd, Ωo Adequate margin of safety R, Ωo. Inadequate Cd, 2.4.2.3. Steel wall and other structures Elnashai and Broderick [77] evaluated the strength reduction factors (q) of moment resisting composite frames. Twenty frames from two, three, six, and ten storeys grouped 28 under two sets of ten frames each were analyzed and designed to the member capacity, as per the Eurocodes. The first set represented frames with bare steel columns, while the second set represented partially encased composite columns. Six sets of ground motions with various intensities were employed by performing dynamic analysis to determine the seismic response of the selected frames. The strength reduction factor evaluated for steel moment-resisting and composite frames was exceptionally higher than the code recommendation. The study was conducted on the selected class of structures and recommended further studies on various structures, including braced frames. Moroni et al. [78] evaluated the seismic response factors for confined masonry buildings by comparing the linear and nonlinear analyses of eight Chilean buildings with three and four storeys. Three-dimensional THA was conducted under severe earthquakes representing Chilean and Mexican records to assess the seismic behaviour and evaluate the force reduction factor, ductility reduction factors, displacement amplification factors, and ductility ratios. The wall density of the buildings reflecting the building period and the nature of earthquake intensity influenced the strength reduction factor. Lower damage levels were witnessed in the buildings with higher wall density, resulting in lower values of the strength reduction factor. Furthermore, Chilean seismic records had higher damage levels than Mexican records, which had low to moderate damage. The study was limited to confined masonry buildings with a short to medium epicentral distance from the source of the earthquake; hence, the R values were not compared for other structural systems for different ductility requirements. Mitchell et al. [79] proposed changes in the force modification factors for the 2005 edition of the NBCC by describing the overstrength-related modification factor (Ro) and the ductility-related modification factor (Rd). The proposed values for seismic force-resisting systems (SFRS) were derived from the methodology in the 2005 NBCC, covering steel, concrete, timber, and masonry structures. The Rd was referred to as the force reduction factor (R) used in the 1995 NBCC. Recommendations were based on sub-assemblage tests, nonlinear analyses across structural systems, post-earthquake evaluations, and structural behaviour assessments. The study proposed an increase in the Rd values in the 2005 NBCC, ranging from one for brittle systems (unreinforced masonry) to five for the most ductile systems (ductile steel moment-resisting frames). Ro was introduced by eliminating the calibration factor (U) and proposing values of Ro between 1.00 and 1.70, causing further reduction in the designed base shear considering the reserved strength in the SFRS. 29 Kurban and Topkaya [80] assessed the seismic design factors of shear plate shear wall (SPSW) systems with different geometrical characteristics designed as per AISC seismic provisions. They analyzed forty-four SPSW systems from two, four, six, eight, and ten-storey buildings, considering the storey mass, plate thickness, and plate aspect ratio as the prime variables. Twenty near-field and far-field earthquake records were employed in the 3D finite element analysis to compute the overstrength (â¦o), ductility reduction factor (Rµ), displacement amplification (Cd), and response modification factors (R). Equations were developed for mean values and lower and upper bound ranges, proposing a relationship between the Cd and R factors. Cd increased with an increase in R, which increased with the ISDR values. The study was limited to regular ideal SPSW frames, and further research was recommended on realistic SPSW systems that represent a part of moment-resisting systems. Fiorino et al. [81] performed a numerical study on cold-formed steel (CFS) strap-braced stud walls based on the IDA procedures of FEMA P695 to evaluate the strength reduction factor (q). Fourteen regular ordinary buildings classified under residential and office building categories with varying heights of one, two, three, and four storeys were designed with a PGA of 0.15 g, 0.25 g, and 0.35 g and soil class C, as per the Eurocodes, assuming a trial value of q as 2.5. Three-dimensional IDA was performed in both directions using a set of 44 earthquake records scaled until global collapse. Collapse fragility was evaluated, validating the assumed q value of 2.5 for CFS strap-braced stud walls with acceptable CMR values. Since the study was limited to low-rise regular buildings based on numerical works, buildings with irregular configurations and verification of shake table tests were recommended. Reza Salimbahrami and Majid Gholhaki [82] focused on the ductility reduction factor (Rµ) and inelastic displacement ratio (CR) in SDOF structures. Their study extended to examine the impact of Rµ and CR on the lateral strength adjustment and their role in determining the response modification factor (R) for the MDOF structures. Regular six, twelve, and twenty-storey RC moment-resisting frames with steel plate shear walls were investigated. Nonlinear time history analysis, utilizing seven far- and near-field ground motions on the 2D models was employed to assess CR, hich as then compared ith FEMA 440âs C1 factor. The ratio of Cd to the ultimate response factor (Ru) of the MDOF system was evaluated at various ductility levels. They observed variations in Rµ factors for near- and 30 far-field input ground motions and recommended modifications in MDOF structures, resulting in an increased modification factor with higher periods and ductility demands. The evaluation of the seismic response factors of MDOF models for steel walls and other structures since 1996 included work on steel MRF composite buildings, confined masonry buildings, shear walls, and stud walls. Ideal buildings representing low-rise to mid-rise frames were analyzed using IDA with limited work on relatively tall buildings. In earlier studies, the investigation of irregular structures under the effect of bi-directional loading representing real buildings of varying heights was not considered. For the sake of clarity, the review of the MDOF systems representing steel walls and other structures is summarized and presented in Table 2.6. Table 2.6: Summary of the literature work on MDOF models â steel wall and other structures Author Analysis type, Methodology Type of Structures & Structural Systems No. of storeys Seismic Design Factors Remarks Elnashai & Broderick [77] 2D Analytical, IDA Steel MRF and composite buildings 2, 3, 6 & 10 R (q) Adequate margin of safety Moroni et al [78] 3D Analytical, THA Regular confined masonry buildings 3 & 4 Rï­, Cd, and R Reasonable margin of safety Mitchell et al [79] 2D Analytical, Experimental Steel, Concrete, Timber & Masonry building Buildings up to 12 storeys Rd and Ro Proposed changes by enhancing R values Kurban & Topkaya [80] 3D Analytical, THA SPSW systems 2, 4, 6, 8 & 10 Rï­, â¦o, Cd, and R R increased proportionally with height. Fiorino et al [81] 3D Analytical, IDA CFS strap-braced stud wall 1, 2, 3 & 4 R (q) Adequate margin of safety Reza Salimbahrami and Majid Gholhaki [82] 2D Analytical, IDA Steel MRF with steel plate shear walls 6, 12 & 20 Rï­, CR, Rïµ, Cd, Adequate margin of safety 2.4.2.4. RC frame structures The strength reduction factors (q) of low-rise- to medium-rise reinforced concrete (RC) buildings were evaluated based on the ductility and overstrength by Kappos [83] for earthquake motions in Southern Europe. Five RC buildings with one to five storeys were analyzed using six sets of ground motions representing rock and alluvium sites by scaling the design spectrum to 35%. Two-dimensional IPAs and THAs were employed to evaluate the strength reduction factor dependent on overstrength. They observed that the calculated ductility-dependent part of the strength reduction factor exceeded the code values. The combined reduction factor was reasonably conservative compared to the recommended 31 EC8 values for short and intermediate periods. The study only focused on regular RC buildings, 2D nonlinear analysis, and seismic records representing southern Europe. Chryssanthopoulos et al. [84] proposed a probabilistic assessment methodology of the strength reduction factors (q) of RC frames designed as per Eurocode 8. The study analyzed a three-bay, ten-storey regular RC frame for the medium ductility class, considering various spatial distribution scenarios, failure criteria, random member capacity, and inter-storey drift. Adequate safety margins were estimated for the ultimate limit state compared to the service limit state, which depended mainly on the adopted structural criterion. The strength reduction factors were calibrated based on actual behaviour factors, considering hazard and ultimate limit state vulnerability curves. The study focused on a 2D regular frame with limited input ground motions. Elnashai and Mwafy [85] calibrated the overstrength (â¦o) to investigate the relationship with force reduction factors (R) by undertaking a comprehensive study on RC buildings designed with modern seismic codes. The R factors were evaluated using refined expressions, and the âsupplyâ values ere verified ith âdesignâ and âdemandâ on the selected medium-rise RC buildings. Twelve RC buildings with eight and twelve storeys were classified into three groups based on ductility and PGA, as per EC8. Irregular frame buildings and regular frame wall buildings with eight storeys were classified under Group 1 and Group 3, respectively. Twelve-storey regular frame buildings were classified under Group 2. IPAs and IDAs were performed using eight natural and artificial records to evaluate the â¦o and R factors under different components of ground motions. The calculated R factors were over-conservative compared to the design code and recommended an increase, particularly for regular frame structures with high ductility levels at lower PGA values. The study focused on medium-rise buildings designed to Eurocode standards. Maheri and Akbari [86] investigated the seismic behaviour factor (R) on a dual system with RC frames and steel bracings, braced with steel X and knee-braced systems. Three regular RC buildings with four, eight, and twelve storeys were considered to assess the effect of storey height, load sharing of the bracing system, and the type of bracing on the R factor. The design base shear was obtained using a PGA of 0.3 g for the dual system. The elements of the R factor, including the ductility reduction factor and overstrength factor, were evaluated using the 2D IPA based on a study by Mwafy and Elnashai [87]. The results 32 generated from the numerical IPAs were verified with three similar model results obtained from the experimental pushover results [88]. The results were found to be conservative with the code-recommended values. The study was limited to regular RC-braced buildings investigated with 2D pushover analysis without inelastic dynamic analysis. Husain and Tsopelas [23] provided two measuring indices to quantify the structural redundancy in RC buildings using a 2D IPA. The deterministic redundancy effects were quantified using the redundancy strength index, while probabilistic redundancy effects were quantified using the redundancy variation index. RC frames with three to nine storeys with one to six bays were analyzed using the IPA. Simplified expressions were developed based on the number of structural members, ductility capacity, and strength and stiffness distribution in the members. The results indicated that the structural redundancy increased as the ductility capacity of the member increased. However, the study had a limitation since the time-dependent characteristics of the seismic response, such as frequency content, excitation amplitude, and duration, were not accounted for, which emphasized the need to quantify the impact of structural redundancy using the inelastic time history analysis. FEMA P695 [13] proposed a rational methodology to quantify the seismic response factors of force-resisting systems. Six regular RC frame buildings with one to twenty storeys were developed and designed according to ASCE 7-05 criteria for the B, C, and D seismic design category (SDC) to evaluate the â¦o, Cd, and R factors. Two-dimensional nonlinear IPA was performed to assess the overstrength factor and ductility capacity, while nonlinear dynamic response history analysis was employed to evaluate collapse capacities and CMR. Twenty-two sets of far-field and twenty-eight sets of near-field seismic records were employed by deriving the seismic response factors of the buildings, which were designed with an assumed trail value of R. The CMR values were adjusted depending on the uncertainty of the system and the acceptable limits of collapse probabilities. The trail R value was considered acceptable when the adjusted collapse margin ratio was more significant than the probability of collapse at the maximum considered earthquake (MCE). It was recommended to limit the methodology to 20â30 storeys for MRF structures and 30â40 storeys for shear wall and braced frame structures due to variations in response characteristics of very tall buildings. Further, the study was based on unidirectional seismic loading and the plan, and elevation irregularities were not addressed. 33 Alhamaydeh et al. [89] investigated three RC-framed buildings with four, sixteen, and thirty-two storeys to evaluate the seismic design factors. The buildings were modelled and designed as per the IBC (2009). The study considered two sets of seismic records for a 2% probability of exceedance and a 10% probability of exceedance in 50 years. The seismic design parameters, such as the overstrength factor (â¦o), response modification factor (R), and deflection amplification factor (Cd), were evaluated using 2D THA with inelastic inter-storey drift as a criterion to assess the seismic response. The seismic design factors evaluated depended significantly on the input ground motion. The study indicated that the code values were conservative compared to both exceedance probabilities. The study was limited to regular structures with few case study buildings, and further investigation was recommended on a more extensive range of buildings with different heights. Alam et al. [90] performed a study on three, six, and eight-storey RC framed concrete buildings strengthened with a super elastic shape memory alloy (SMA) rebar to assess the seismic overstrength (Ro) and ductility (µ). The beams of each RC building were reinforced with three different types: (a) regular steel reinforcement (steel), (b) SMA rebar in the plastic hinge region and normal steel in other areas of beams (steel SMA), and (c) SMA rebar as the main reinforcement in beams (SMA RC). The columns representing the frame system of all the buildings were reinforced with normal steel only. The buildings were designed and detailed to suit the high seismic zone in Canada (Vancouver), as per the NBCC. The Ro and µ were evaluated using 2D IPA and THA under the effect of 10 earthquake records. The Ro of the SMA RC frame and normal steel RC frame were similar and in the acceptable range, with a lower ductility in the SMA RC frame due to a lower modulus of elasticity. The study focused on regular frame structures with and without SMA and recommended experimental research and further studies with structures, including slabs and transverse beams. Thuat [91] investigated the strength reduction factor demands of RC buildings designed under different ground motion intensity levels with varying soil types and strength reduction factors (q). Regular RC MRFs with five and nine storeys were designed for earthquake intensities of 0.25 g and 0.50 g, covering soil types from A to D, with strength reduction factors ranging from 1.5 to 5.0. Nonlinear dynamic response analysis was conducted with several scaled records to assess the strength reduction factor demands. The results indicated that the code-recommended strength reduction factor demands were conservative. The study expressed the strength reduction factor for the maximum ground 34 acceleration by a linear relationship. The study was limited to 2D regular frame structures, and further research covering different seismic zones was recommended. Seismic design response factors of the regular RC frames braced with steel chevron braces were evaluated by Akbari and Maheri [92] using the IPA. Overstrength, the response modification factor, and the ductility of four- to twelve-storey RC-braced frames were investigated under different ductility demands. The parameters affecting the strength reduction factor under the applied lateral load, including the bracing system and height of the frame, were investigated. The braced RC frame had a larger ductility capacity than the moment-resisting RC frame, indicating a significant effect on the R factor. Buildings with braced frames of shorter height had a higher ductility than those with taller heights with higher R factors. The study indicated conservative R factor values under different ductility demands for the investigated buildings and recommended tentative R factors for future works. However, the study was limited to pushover analysis on regular 2D frames only, and nonlinear dynamic analysis was not considered. Nine-storey plan-symmetric RC MRF structures were assessed under the effect of higher modes, and their seismic response was investigated by Maniatakis et al. [93]. Using 34 seismic records obtained from the PEER strong motion database, 2D nonlinear response history analyses were conducted on a building designed with the Greek seismic design code EAK 2000. The study concluded that the flexural overstrength and the ground motion characteristics influenced the storey inertial and shear forces, which were attributed to higher modes. The modal reduction factors decreased with the increasing mode order compared to behaviour and ductility factors. The study was limited to only one building and one structural system, and the flexural overstrength was developed based on the deformation of the frame subjected to second and third modes and cannot be generalized to higher modes. Mondal et al. [21] focused on evaluating the actual values of the response reduction factor for realistic RC MRF buildings. The buildings were designed based on Indian standards for seismic requirements, and RC designs were detailed to meet the requirements of ductile detailing. The study was conducted on a ductile (special) RC MRF to verify and validate the code-recommended response reduction factor (R) value. Four typical plan-symmetric RC frame regular office building structures with two, four, eight, and twelve-storey configurations were considered in the seismic zone IV study region, as per Indian 35 standards. The results indicated that the Indian standard recommended a higher R value than the actual value of R. However, the study was limited to one single plan-symmetric configuration and one seismic zone, and nonlinear response time history analysis was not considered. Hossain et al. [94] considered a set of RC buildings with three and eight storeys with varying reinforcement detailing for the horizontal elements of the building systems to estimate the seismic force reduction factors. Vertical elements of the 13 RC frames used in the study were reinforced with normal steel. The beams were reinforced with normal steel in two frames along the height of the buildings, while eleven frames were reinforced at the plastic hinges with super elastic shape memory alloy (SMA) bars as a gradual replacement to the steel from level 1 to the building height. The NBCC was used to perform linear analysis to design the buildings. Twenty records were employed in the nonlinear IDAs to investigate the seismic force reduction factors. The result demonstrated satisfactory performance with sufficient margins for the seismic factors but was limited only to regular frame structures. Vona and Mastroberti [95] investigated the existing RC frame buildings to estimate the strength reduction factor (q) based on the force-based assessment procedure. Existing RC buildings with two, four, and eight storeys were considered, with three sets representing buildings with frames without effective infill, frames retrofitted with masonry infill, and frames with masonry infill at the ground floor level. Structural modelling was performed using IDA with 50 seismic records on each building type. The study proposed the strength reduction factors for the investigated buildings for the existing code, including retrofitting measures, which improved and extended the existing seismic performance. The study recommended further studies on different structural types covering a more comprehensive range of buildings. Seismic response coefficients of tunnel-form RC buildings with horizontal irregularity were investigated on three, five, seven, and-ten-storey buildings by Vahid Mohsenian et al. [96]. IDAs were performed on the 3D models using 10 far-field earthquake records. Response modification factors were calculated at both demand and supply values. The demand response was estimated depending on site seismicity and physical and geometrical specifications, while the supply response was based on the capacity of the building to resist the inelastic deformations to meet the desired performance levels. Their study indicated 36 that an increase in the building height witnessed an increase in ductility-related modification factors and a decrease in those related to overstrength and response modification factors. The seismic response exhibited a good safety margin compared to the code-recommended value of five. Kader Newaj Siddiquee et al. [97] assessed seismic performance using the collapse margin ratio (CMR) for regular concrete-reinforced frames with shape memory alloy (SMA) rebars. Their study, involving 2D nonlinear static pushover and IDA using 20 input ground motion records on three, six, and eight-storey buildings, aimed to evaluate the collapse safety of frames with SMA rebars compared to frames reinforced with conventional steel rebars. Four reinforcement scenarios were considered: steel reinforcement only, SMA rebar in the plastic hinge region in the columns on ground floor and steel rebars in other areas (SMA-CM), SMA rebar in the plastic hinge region in the beams on the ground floor and steel rebars in other areas (SMA-BM), and SMA rebars in the plastic hinges in both beams and columns on the ground floor (SMA-BM-CM). The study concluded that three and eight-storey frames exhibited increased collapse capacity with SMAs, and seismic response modification factors were deemed adequate, as per the FEMA P695 guidelines. Farrokh Fazileh et al. [98] recommended a methodology to evaluate the seismic strength reduction factors for different seismic force-resisting systems (SFRSs) using a performance-based unified (PBU) procedure. This procedure was designed as a performance-based approach used in systematically quantifying the ductility-related modification factor (Rd) and the overstrength-related modification factor (Ro) for diverse SFRSs in the NBCC. Twenty-one concrete moment frame archetypes were utilized with a two-level screening process to optimize the number of archetypes efficiently in assessing the seismic force modification factors. Nonlinear static pushover analysis was used to calculate the Ro as a preliminary screening process before conducting IDA. The proposed methodology enhanced the performance level intensity by 90% in the SFR systems. The evaluation of the seismic response factors of MDOF systems for RC frame structures for three decades was mainly based on 2D analytical works with unidirectional seismic loading. Regular low-rise to medium-rise frame buildings were analysed using IPA and IDA, with limited work on relatively tall buildings. Earlier studies did not consider irregular buildings under the effect of bi-directional loading representing real buildings employing 37 3D inelastic analysis. For the sake of clarity, the review of the MDOF systems representing RC frame structures is summarized and presented in Table 2.7. Table 2.7: Summary of the literature work on MDOF models â RC frame structures Author Analysis type, Methodology Type of Structures & Structural Systems No. of storeys Seismic Design Factors Remarks Kappos [83] 2D Analytical, IPA & THA Regular MRF buildings 1 to 5 R (q) Adequate safety Margins Chryssanthopoulos et al [84] 2D Analytical, THA Regular MRF buildings 10 R (q) Adequate safety Margins Elnashai & Mwafy; Mwafy & Elnashai [85] 2D Analytical, IPA & IDA Regular and irregular MRF buildings 8, 12 â Regular, 8 - Irregular Ωo, and R Adequate safety margins Maheri & Akbari [86] 2D Analytical, Experimental, IPA Regular MRF with steel bracing 4, 8 & 12 R Adequate safety Margins Husain & Tsopelas [23] 2D Analytical, IPA Regular MRF 3, 5, 7 & 9 RR RR increased with increase in ductility capacity FEMA P695 [13] 2D Analytical, IPA & THA Regular MRF 1, 2, 4, 8, 12 & 20 â¦o, Cd, and R R acceptable for ACMR > collapse probability at MCE Alhamaydeh et al [89] 2D Analytical, IPA & THA Regular MRF buildings 4, 16 & 32 â¦o, Cd, and R Adequate margin of safety Alam et al [90] 2D Analytical, IPA & THA Regular MRF buildings with SMA 3, 6 & 8 µ and Ro Adequate margin of safety Thuat [91] 2D Analytical, THA Regular MRF 5 & 9 R (q) Adequate safety Margins Akbari & Maheri [92] 2D Analytical, IPA Dual system (frame with steel bracings) 4, 8 & 12 â¦o, Cd, and R Adequate safety Margins Maniatakis et al [93] 2D Analytical, IPA & THA Regular MRF buildings 9 R Adequate safety Margins Mondal et al [21] 2D Analytical, IPA Regular MRF buildings 2, 4, 8 & 12 R Adequate margin of safety Hossain et al [94] 2D Analytical, IPA & IDA Regular MRF buildings with SMA 3 & 8 R Adequate margin of safety Vona & Mastroberti [95] 2D Analytical, IDA Regular MRF buildings retrofit with masonry infill 2, 4 & 8 R (q) Proposed R values for retrofit building Vahid Mohsenian et al [96] 3D Analytical, IDA Horizontal irregular MRF 3, 5, 7 and 10 R, â¦o, Cd, Adequate margin of safety Kader Newaj Siddiquee et al [97] 2D Analytical, IPA, IDA Regular MRF with normal rebars and SMA bars 3, 6 and 8 R Adequate margin as per FEMA P695 Farrokh Fazileh et al [98] 2D Analytical, IPA, IDA Regular SFRS using PBU procedure 21 SFRS archetypes Rd, Ro, Proposed work enhanced performance level 2.4.2.5. RC shear wall structures Challal and Gauthier [99] evaluated the seismic response of RC-coupled shear walls (CSWs) through nonlinear deformation and ductility response, designed as per the NBCC [15] and Canadian Concrete Standards [100]. Five buildings with six, ten, fifteen, twenty, 38 and thirty storeys were considered in the design using three Canadian seismic zones. Non-linear dynamic analysis under five seismic records verified inter-storey drift and assessed plastic hinges, displacement, and rotational ductility in walls and coupling beams. The code-specified drift limit was conservative, with lower drifts for taller CSWs. Maximum displacement and ductility demand factors were conservative in comparison with the NBCC limit, which decreased with an increase in the storey height. The study was limited to regular structures using 2D analysis with few seismic records and recommended further investigation with different irregularities under a more extensive range of ground motions. Elnashai and Mwafy [85, 87] evaluated â¦o and R on RC wall buildings designed with modern seismic codes. Regular frame-wall buildings with eight storeys were designed according to EC8. The seismic design factors were evaluated using IPAs and IDAs with eight natural and artificial records. The calculated R factors were over-conservative compared with the design code, prompting a recommendation to increase R values, especially for structures with high ductility levels at lower PGA values. The study focused on medium-rise buildings designed to Eurocode standards. Seismic design response factors of RC wall buildings were investigated by Mwafy [19] in densely populated areas in the United Arab Emirates (UAE). The study included factors such as the overstrength (â¦o) factor, the force reduction (R) factor, and the deflection amplification (Cd). Five buildings from 20 to 60 storeys, representing various regular concrete wall structures, were designed according to the modern seismic design codes. Nonlinear analyses were conducted under twenty natural and artificial seismic records using IPAs and IDAs to evaluate the seismic design response factors. Under moderate earthquakes, it was observed that the medium-rise buildings had higher seismic risk due to a lower contribution of the building fundamental mode than high-rise buildings. An adequate margin of safety was witnessed in the Cd and R factors. The study confirmed that the evaluated R factors were higher than the code-specified R values and recommended an increase in seismic design response factors for a more cost-efficient design of the buildings. The study focused on regular RC wall buildings with 2D analysis. Mwafy [20] proposed a simple theoretical approach to arrive at a cost-efficient and safe design using actual ductility and first yield overstrength of RC structures. RC wall buildings with ten to sixty storeys and RC frames with eight to twelve storeys were investigated to assess their inelastic structural response. Force demands obtained from the 39 elastic procedures were compared with the inelastic 2D IDA under realistic input ground motions. The study proposed suitable ranges based on the actual ductility and the first yield overstrength to identify the design efficiency. The results indicated an over-conservative design concerning the recommended seismic design factors provided in the seismic design code and recommended using IDA to verify the design for structures with seismic responses outside the acceptable range. The study was focused on regular buildings using 2D nonlinear response history analysis. Mwafy et al. [22] studied five sixty-storey regular RC shear wall buildings with varying concrete strengths designed with similar periods in evaluating the seismic design coefficients. he impact of the varying concrete strengths on â¦o, R, and Cd was investigated using 2D IPAs and IDAs with 20 input ground motions. The increase in concrete strength in high-strength buildings reduced a significant amount of steel reinforcement with a considerable reduction in vertical elementsâ cross-section, resulting in reduced lateral stiffness. igher design overstrength (â¦o) was observed in all the buildings than the code-recommended values with slightly reduced levels of overstrength factors (â¦o and â¦y) for buildings with increased building material strengths. The adequate safety margins of Cd were reflected with a constant increase in the material strength. The median R values were sufficiently higher than the design values of ASCE 7. The study recommended the possibility of increasing the R values to achieve cost-effective building designs and was limited to investigation with 2D inelastic analysis on regular-wall buildings. Mwafy and Khalifa [101] assessed the safety margin of seismic coefficients of realistic reinforced concrete high-rise buildings with vertical irregularities in medium-seismicity regions. Five 50-storey buildings representing typical vertical irregularities were designed employing 3D models, as per international codes and seismic standards. Forty seismic records were chosen to conduct the 2D nonlinear IPAs and IDAs covering far-field and near-source seismic events. The seismic design coefficients evaluated by IPA and IDA with vertical irregularities were found to be conservative with adequate safety margins compared to the seismic code provisions, which can be revised to achieve economical designs. The study focused on unidirectional seismic loading using 2D IDA for irregular shear wall buildings. Zerbin et al. [102] recommended an alternative formulation to evaluate the ductility reduction factor of RC wall and frame structures. Two sets of frame and wall buildings 40 ranging from three to twelve storeys were designed with medium ductility class requirements, as per Eurocode 8, to investigate three levels of sectional ductility. Simplified analytical models of frame and wall structures were proposed to resemble an equivalent SDOF system to evaluate the ductility reduction factor. Pushover and THA were performed with 34 natural ground motions to estimate the ductility reduction and modification factors. The ductility reduction factors of the frame and wall models derived from the proposed formulation provided good results with the numerical analysis from the Eurocode 8 design approach. The ductility reduction and modification factors of the frame and wall systems for MDOF models decreased with an increase in the number of storeys. The code recommended force reduction factors were more conservative than those evaluated with the proposed formulation method and depended mainly on structural ductility and overstrength. The study was limited to ideal structures, and further studies on overstrength factors and real structures were recommended. Matteo Zerbin et al. [103] proposed a numerical formulation to evaluate the ductility force reduction factors for regular RC wall and RC frame structures compared to Eurocode 8. Simple four, eight, and twelve storeys representing both wall and frame structures were investigated using 2D pushover and inelastic time history analysis models, employing thirty-four natural ground motions. Their study revealed that in both wall and frame systems, the ductility reduction factors for the MDOF systems decreased with the increase in the number of storeys, indicating a reduced system capability to utilize base sectional ductility and an increased importance and impact of the higher mode effects. Maysam Samadi and Norouz Jahan [76] examined the impact on seismic design parameters such as (a) the response modification factor (R), (b) the deflection amplification factor (Cd), (c) the overstrength factor (â¦), and (d) the damping ratios for tall steel buildings. he study examined regular steel buildings with 28 and 56 storeys, featuring steel-braced and RC shear wall cores with outriggers placed at every quarter of the building height, resulting in forty-four building models. Seismic parameters were assessed using the modal response spectrum (MRS), pushover, and nonlinear time history (NLTH) 3D analyses. Including the outriggers increased the response modification factor, overstrength, stiffness, and damping ratios, particularly in the buildings with RC core walls, while reducing ductility in both systems. Their study also identified inadequacy in the code-recommended Cd values. 41 The previous studies conducted since 2001 on assessing the seismic response factors of MDOF systems for RC shear wall structures were based on 2D analytical works using IPAs and IDAs. Earlier studies were based on regular shear wall buildings, and the evaluations of seismic response factors were based on unidirectional seismic loading. In earlier studies, irregular shear wall buildings under the effect of bi-directional loading employing 3D inelastic analysis were not considered. For the sake of brevity, the review of the MDOF systems representing RC shear wall structures is summarized and presented in Table 2.8. Table 2.8: Summary of the literature work on MDOF models â RC shear wall structures Author Analysis type, Methodology Type of Structures & Structural Systems No. of storeys Seismic Design Factors Remarks Challal & Gauthier [99] 2D Analytical, IDA Regular Coupled shear wall (CSW) system 6, 10, 15, 20 & 30 µd Adequate margin of safety Elnashai & Mwafy; Mwafy & Elnashai [85, 87] 2D Analytical, IPA & IDA Regular shear wall building 8 Ωo, and R Adequate safety margins Mwafy [19] 2D Analytical, IPA & IDA Regular Shear wall buildings 20 to 60 â¦o, Cd, and R Adequate margin of safety Mwafy [20] 2D Analytical, IPA & IDA Regular Shear wall buildings 10 to 60 â¦o, Cd, and R Adequate margin of safety Mwafy et al [22] 2D Analytical, IPA & IDA Regular Shear wall buildings with varying material strengths 60 â¦o, Cd, and R Adequate margin of safety Mwafy & Khalifa [101] 2D Analytical, IPA & IDA Regular Shear wall buildings with varying vertical irregularities 50 â¦o, Cd, and R Adequate margin of safety Zerbin et al [102] 2D Analytical, IPA & THA Regular frame and wall buildings 3 to 12 Cd, and R Adequate margin of safety Matteo Zerbin et al [103] 2D Analytical, IPA & THA Regular RC wall and frame 4, 8 and 12 Rï­, Rï­, decrease with increase in storey height with adequate safety margin Maysam Samadi and Norouz Jahan [76] 3D Analytical, MRS, IPA, NLTH 2 Regular steel braced buildings with outriggers 28 & 56 R, Cd, Ωo Adequate margin of safety R, Ωo. Inadequate Cd, 2.5. Limitations, Gaps and Future Research Based on the detailed review conducted since the early 1970s, it was noticed that the R factor is influenced by ductility, the period of the structure, structural system, construction materials, and the shape of the hysteresis loops used to simplify the response of buildings using SDOF systems. The comprehensive state-of-the-art review of the seismic response factors provided specific findings, which are more fully expressed under the limitations and gaps and the possible areas for future research, as provided in the following sections. 42 2.5.1. Limitations and gaps Seismic response factors were reviewed from previous studies considering the assessment of SDOF and MDOF systems. The MDOF systems contribute 75% of the review compared to 25% of the studies from SDOF systems, as shown in Figure 2.3 (a). Regular and irregular buildings covering RC, steel, masonry, and composite construction with various structural systems were reviewed, and the limitations were identified and described as follows. Type of systems considered: The presented review of seismic response factors is studied under the SDOF and MDOF systems and summarized in Tables 2.3 to 2.8. The SDOF systems were based on hypothetical models with hysteresis relationships, while real structures were not investigated. Most of the earlier work on MDOF systems was limited to regular low-rise to medium-rise buildings, while real buildings with different irregularities and high-rise structures were not investigated. This brings in the need for future exploration and further research on works for high-rise buildings with irregularities. Type of modelling: The previous studies primarily used two-dimensional analysis to evaluate seismic response factors. About 94% of the previous research was based on 2D non-linear analyses, with only 6% of work on 3D analysis, as shown in Figure 3(b). Since the 2D analysis approach is based on unidirectional seismic loading, it will not capture the realistic 3D behaviour of the structures. The impact of bi-directional input ground motions is not accounted for in this approach, particularly with the irregular buildings. Since only 6% of work was carried out in 3D analysis from the earlier researchers, there is a big gap emphasizing the need for investigation of 3D seismic behaviour of buildings employing bi-directional seismic loading. Type of analysis: Several studies employed only IPA in evaluating the R factors, while IDA was not utilized in assessing the seismic performance, as shown in Tables 2.4 to 2.8. About 30% of the previous studies on steel braced structures, steel frame structures and RC framed structures employed 2D IPA in evaluating R factors, while 70% of the work was based on the IDAs. The reliance on the former system may not yield good results for high-rise structures, which were scantly covered in earlier investigations. IDAs were mainly using unidirectional seismic loading and bidirectional seismic loading was hardly considered in the previous research. This emphasizes the need for future investigation on the 3D high-rise buildings with bidirectional loading using IDAs to have a realistic seismic performance and assessment of seismic response factors. 43 Components of seismic design factors: In the previous studies, the seismic response factors investigated using SDOF systems were based on ductility reduction factors. The contribution of the system overstrength in evaluating the strength reduction factors of SDOF models was not considered. Similarly, structural overstrength was not evaluated in most of the previous studies conducted on MDOF models, as shown in Tables 2.4 to 2.8. This brings in the need to evaluate structural overstrength in future works as it plays a vital role in the evaluation of the strength reduction factors. Type of buildings: The earlier studies primarily covered simple regular buildings in evaluating seismic response factors. About 92% of the previous research was based on regular buildings, compared with 8% on irregular buildings, as illustrated in Figure 3(c). Most of the previous work was limited to ideal buildings of regular configuration with limited heights, while buildings with varying heights and irregular configurations were not investigated. Since modern buildings are mostly irregular in configuration and with only 8% of earlier research on these irregularities, there is a greater room to assess the seismic performance of irregular buildings. Structural systems: Seismic response factors were primarily evaluated on frame systems comprising RC, steel, and steel braced frame buildings. It is noteworthy to state that from this review, one-third of the research was made on RC frame buildings, 20.5% on steel frame buildings, 17.9% on steel braced buildings, followed by 15.4% on shear wall buildings and 12.87% on steel wall and other structural systems, respectively as shown in Figure 3(d). Furthermore, most of the modern structures are irregular and high-rise buildings, and investigation of buildings using bi-directional seismic loading on shear walls and other structural systems becomes quite predominant for future researchers. Input ground motions and seismic loading: Previous studies on seismic assessment of SDOF systems were based on analytical work considering seismic scenarios representing near-field earthquakes suitable for medium seismic zones. Some SDOF studies employed simple waveforms to evaluate the seismic design factors without employing real earthquake records. The seismic behaviour of structures with aftershock events was hardly considered in the SDOF systems. Several studies were limited to very few seismic records, which do not adequately account for the variability in the input ground motions [43,70], while other studies were limited to near-field records with little investigation on far-field earthquakes [54]. Most structures were employed using unidirectional seismic loading on 44 2D regular frames without considering the effect of bi-directional loading on real structures using 3D inelastic analysis. This emphasizes the need for future research openings on 3D irregular buildings with bi-directional seismic loading to capture the realistic seismic behaviour considering the torsion effects of the buildings. (a) (b) (c) (d) Figure 2.3: Summary of previous studies related to seismic design response factors as reviewed from the text and tables (a) Type of systems considered, (b) Analysis type, (c) Irregularity, (d) Structural systems. 2.5.2. Areas for future research The limitations and gaps identified in the previous studies while evaluating the seismic response factors emphasize the pressing need for further research in the following areas: â¢ Limited research (only 8% of previous studies) was conducted to evaluate the seismic response of irregular buildings. This emphasizes the need to investigate practical buildings covering different types of irregularities with various heights. â¢ Most of the earlier work was based on 2D inelastic analysis with unidirectional seismic loading. Only 6% of research was conducted using 3D inelastic analysis. This presses the need to evaluate the seismic response factors using 3D inelastic analysis under the effect of bi-directional seismic loading. SDOF, 25.0%MDOF, 75.0%2D Analysis, 94%3D Analysis, 6%Regular buildings, 92%Irregular buildings, 8%Steel braced, 17.9%Steel frame, 20.5%Steel wall & other structures, 12.8%RC frame, 33.3%RC shear wall, 15.4%45 â¢ Many previous studies did not account for structural overstrength. This shows the need to consider structural overstrength in assessing the seismic response of buildings. â¢ Studies on regular RC shear wall buildings were limited to 15.4% in the previous investigations. This emphasizes a need to evaluate the seismic behaviour of RC hear wall buildings with varying heights. â¢ Previous studies focused on buildings in seismic zones representing moderate to severe earthquakes. Furthermore, the effects of aftershock events need to be investigated to better evaluate the seismic performance of buildings with post-earthquake events. 2.6. Concluding Remarks The literature review presented a systematic and comparative literature review on seismic response factors over five decades. It provided a brief overview of the use of seismic response factors in various international codes, historical perspectives, and their respective definitions. Seismic response factors were reviewed from the previous studies considering the SDOF and MDOF system assessment. The MDOF systems contributed 3/4 of the review, while the SDOF system contributed 1/4 of the previous research. Regular and irregular buildings covering RC, steel, masonry, and composite construction with various structural systems were reviewed and summarized. The review also identified that the ductility, structural system, natural period, construction materials and shape of the hysteresis loop influenced the R factor. Limitations and gaps in the previous studies were presented considering the type of systems, type of analysis, components of seismic design factors, irregularity, structural systems, input ground motions and the seismic loading applied on the structures. Most previous research in the SDOF system was based on hypothetical models, while MDOF systems were limited to regular low-rise to medium-rise buildings. A significant research contribution was based on 2D inelastic analysis by employing unidirectional seismic loading, while very little work was conducted using 3D inelastic analysis. Only 6% of the work was based on the 3D analysis, while 8% of the work was conducted on irregular buildings with most of the work focused on regular buildings with 2D analysis. Regular RC, steel frame and braced buildings were investigated to 72%, whereas shear walls had only 28% of research in the 46 previous studies. About 30% of the work on steel braced frame and RC frame buildings was conducted using IPA, while 70% of the work was with IDAs employing unidirectional seismic loading. Several studies recommended improving the code-recommended R values for regular buildings due to observed adequate safety margins. Based on the review of seismic response factors and the identified limitations and gaps, the present study provided possible future research covering structural irregularity, 3D inelastic analysis, and investigation of different structural systems related to multi-storey and high-rise buildings under bi-directional seismic loading. Further investigations to evaluate the seismic response of RC shear wall buildings with varying heights and irregularities are emphasized using 3D inelastic analysis covering regions influenced by various seismic scenarios. This would calibrate the seismic design factors recommended in design standards, resulting in more cost-effective designs with consistent safety margins for different structural systems. Accordingly, the scope of this research is based on covering the gaps identified in the literature review. 47 3 Selection and Design of Buildings 3.1. Selection of Benchmark Buildings In the current study, thirteen buildings categorised into four sets of steel and RC high-rise buildings, considered benchmark buildings are selected and investigated to verify the seismic response factors of code-designed high-rise buildings using 3D non-linear analysis. These selected benchmark buildings comprise a set of regular multi-storey steel buildings (MSBs) with varying heights ranging from 8 to 20-storeys, and three sets of RC high-rise buildings with varying heights of 40 to 60-storeys using different structural systems and irregularities. The benchmark buildings are designed and detailed as per the code-recommended provisions. The building footprints of the benchmark buildings represent typical floor layouts adopted in major cosmopolitan cities employing state-of-the-art prevailing construction practices. The architectural features, layout details and design approach of these benchmark buildings are discussed in the following subsequent sections under the respective steel and RC high-rise buildings, separately. 3.1.1. Architectural Details and Description of MSBs Four moment-resisting MSBs are selected and designed in a region with medium seismicity, such as Sacramento-California, Dubai-UAE, or Izmir-Turkey, which represents a vast part of the globe [104, 105]. These MSBs of 8, 12, 16, and 20 storeys of regular structural configuration are designed and detailed using the structural analysis and design system ETABS [106]. The floor footprint measures 35m x 27m, as shown in Figure 3.1(a). Each selected MSB comprises a ground storey of 4.5m and a typical upper storey of 3.3m height, making the total heights of each of the four MSBs, as shown in Figure 3.1(b). The 3D building models are developed considering the framing system formed with structural steel columns and beams using W-sections with elevators and staircases placed within the centre of the building. The steel yield strength considered in the current study is 350 MPa. To resist the lateral actions efficiently and prevent undesirable failure modes in the buildings, a deck floor slab system is designed to account for the lateral actions from environmental loads. The deck floor system on each floor is a 0.16m thick RC deck slab using a concrete cube strength of 40 MPa and rebar yield strength of 420 MPa, respectively. Shear studs are fixed over the structural steel beams to provide a diaphragm effect, facilitating the effective transfer of lateral forces to the moment-resisting frame. 48 (a) Typical building floor layout of MSBs 8 Storey 12 Storey 16 Storey 20 Storey (b) 3D models of steel building Figure 3. 1: Typical layout of MSBs representing 8, 12, 16 and 20 storeys with 3D models. Permanent dead and live loads represent gravitational loads, whereas wind and seismic effects contribute to the lateral loads. Superimposed dead load is applied on all floor slabs with a uniform load of 4.0 kN/m2 to account for the weight of partitions, floors, etc., in addition to the weight of the structure. Uniform distributed live loads are applied on staircases and floor slabs on each selected MSB with a uniform load of 4.8 kN/m2 and 2.0 kN/m2, respectively. A wind speed of 45m/s over an exposure category C is considered in estimating the wind loads. The MSBs are considered on very dense soil, representing soil C1 C1C1 C1C2C2C2C2 C2 C2C2 C2C3C3C3C3 C3 C3C2C2C2C2 C2 C2C2 C2C3C3C3C3 C3 C3C2 C2C3C4C5C3 C4 C5C4 C4C2 C2C3C4C5C3 C4 C5C4 C4C2 C2C3C4C5C3 C4 C5C4 C4B1 B1 B1 B1 B1 B1 B1B2 B2 B2 B2 B2 B2 B2B2 B2B5B2B5B2 B2B5 B5B5 B5B5 B5B5 B5B5 B5B2B2B2 B2 B2 B2B2 B2 B2 B2B2 B2 B2 B2 B2 B2 B2B1 B1 B1 B1 B1 B1 B1B1B1B3B1B1B3B3B3B3B3B3B3B4B4B4B4B4B4B4B4B4B4B4B4B2B2B2B2B2B2B2B2B2B2B2B2B2B2B2B2B2B2B2B2B2B2B2B2B2B2B1B1B1B15.0 X 7.0 = 35.0 m27.0 m3.5 m3.5 mColumnBeamDeck Slab LiftShaft LiftShaft LiftShaft LiftShaft 49 class C. Seismic loads are calculated using the seismic design coefficients selected from the mapped spectral accelerations based on a design peak ground acceleration (PGA) of 0.16g with a 10% probability of exceedance in 50 years. Equivalent lateral force and modal response spectrum analyses are employed to estimate seismic loads. To consider the effects of the higher modes, the modal response spectrum analysis approach is adopted in the design of the MSBs. Since a minimum modal base shear value of 85% obtained from ELFA must be used in the MRSA, a combination of multi-modes is employed to fulfil the minimum design code-specified mass participation requirement. The design PGA is 0.16g, and the seismic coefficients at 0.2 and 1.0 seconds are 0.80 and 0.32, respectively, with a long-period transition of 8.0 seconds. The selected seismic design criteria represent regions of medium seismicity (e.g. Dubai-UAE). Detailed 3D numerical models of MSBs are developed considering five design standards [107-114]. Figure 3.2 depicts a comparison between the 5% damped design response spectra of the selected design standards. Figure 3.2: Natural period range of MSBs and 5% damped design response spectra of Eurocode (EN), international building code (IBC), Canadian design provisions (NBCC), New Zealand design standards (NZS), and uniform building design code (UBC). 3.1.2. Architectural Details and Description of RC High-rise Buildings Nine RC high-rise buildings with varying heights, irregularities, and structural systems are designed and detailed to ensure the optimized design and fair assessment of seismic design coefficients [115]. The bearing wall structural system is considered for both 40 and 60-storey building sets, whereas the dual structural system is considered for 60-storey building sets, as shown in Table 3. . he selected structural systems are based on the design codesâ classification and recommendations of previous studies for high-rise buildings, as they 00.10.20.30.40.50.60.70 2 4 6 8 10Acceleration, m/sec2Period, secsDesign resonse spectra ENIBCNBCCNZSUBCPeriod range for MSBs50 provide better control of drift than moment-resisting frames under horizontal loads from earthquake and wind effects [32, 116]. In these structural systems, shear walls act as deep beams that carry the shear effects with lesser lateral deformation than frame structures, and floor slabs connecting vertical structural elements increase the effectiveness of the lateral force-resisting system. All the selected benchmark RC buildings are laid on a footprint measuring 42.00m x 29.20m, which is conceptualized on a typical architectural building floor layout representing major cosmopolitan cities in medium seismicity regions that cover a major part of the world [117, 118]. The considered irregularities in the present study are defined per ASCE/SEI [32]. Table 3.1: Selection of benchmark RC buildings. Building Set Structural System Configuration Type of Irregularity Building Reference 40 Storey Bearing Wall System Regular None 40S-B-R Vertical Irregularity Geometric Irregularity (GI) 40S-B-GI Vertical Irregularity Stiffness - Soft Storey (SS) 40S-B-SS 60 Storey Dual System Regular None 60S-D-R Vertical Irregularity Geometric Irregularity (GI) 60S-D-GI Vertical Irregularity Stiffness - Soft Storey (SS) 60S-D-SS 60 Storey Bearing Wall System Regular None 60S-B-R Vertical Irregularity Geometric Irregularity (GI) 60S-B-GI Vertical Irregularity Stiffness - Soft Storey (SS) 60S-B-SS The nine benchmark buildings comprise two basement storeys, a ground storey, and typical upper storeys. The height of the typical storey is 3.3m, including the basement storey, while that of the ground storey is 4.5m. The total height of the respective buildings is estimated as 133.2m and 199.2m for 40 and 60-storey building sets, respectively, as illustrated in Figure 3.3. The floor slab system consists of flat slabs in the bearing wall structures. For the dual structural system, the flat slabs are supported on peripheral beams, which connect external shear walls. Apart from the regular benchmark structures, two types of vertical irregularities are addressed in the present study, including the geometric and soft storey irregularities. The geometric irregularity is introduced by reducing the floor footprint, as illustrated in Figure 2(b) and Figure 2(e). The footprint dimension at lower storeys is more than 130% at upper storeys, hence exceeding the design code limit for vertical geometric irregularity [32]. The soft storey irregularity is introduced by reducing the stiffness of the lower three storeys by 30% to 34% compared with the upper storeys, as depicted in Figure 2(c) and Figure 2 (f) [32]. 51 Note: (a*), (b*), and (c*) are floor footprints of the corresponding layouts with peripheral beams for dual structures. Figure 3.3: Description of 40 and 60-storey benchmark structures showing floor footprints and 3D models: (a) floor footprints of regular structure, (b) reduced floor footprints of geometrically irregular structure, (c) floor footprints of soft storey structure, (d) 3D models of regular structure, (e) 3D models of geometrically irregular structure, and (f) 3D models of soft storey structure. Detailed 3D models are developed for the design of all benchmark structures by employing shell elements to model shear walls, central cores, and floor slabs, while coupling beams are modelled as spandrels within the core walls, as illustrated in Figure 3.3. For the bearing wall and dual structural systems, the R factor is 4.0 and 5.5, respectively, per the design code [32]. The vertical structural members, namely shear walls and core walls, of the benchmark buildings are designed and detailed following various load combinations specified by the ACI 318M Building Code [119]. The cross-sectional dimensions of the P1 P5 P6 P6 P5 P1P1 P5 P6 P6 P5 P1P2P2CORE 1 CORE 2 CORE 1CORE 2 P2P2UPUP8.40 m 8.40 m 8.40 m 8.40 m 8.40 m42.00 m10.90 m7.40 m10.90 m29.20 mCB1CB2CB3CB1CB3CB2 8.4 x 5.0 = 42.00m 10.9 m 10.9 m 7.4 m 29.20m (a) a a a* P5 P6 P6 P5P5 P6 P6 P5CORE 1 CORE 2 CORE 1CORE 2UPUP8.40 m 8.40 m 8.40 m 8.40 m 8.40 m42.00 m10.90 m7.40 m10.90 m29.20 mCB1CB2CB3CB1CB3CB2 8.4 x 3.0 = 25.20m 14.6 m 29.20m 14.6 m (b) b a a b a* b* 10.9 m 10.9 m 7.4 m 29.20m 8.4 x 5.0 = 42.00m (c) a a a* c c c (e) (d) (f) 52 vertical structural elements are slightly reduced every four floors for 40-storey buildings and every five floors for 60-storey structures, avoiding introducing any additional irregularities. Varying cylinder concrete strength, ranging from 35 MPa to 65MPa, is used throughout the benchmark building height for the core walls and shear walls. Reinforced cast-in-situ flat slabs of 0.30m thickness with a concrete cylinder strength of 35MPa. The yield strength of reinforcing steel is 420 MPa in all structural members of the benchmark buildings. Stiffness modifiers are employed in the design of floor slabs, beams, shear walls and columns per the ACI design requirements [119]. Gravitational loads represent permanent loads, including the weight of structural and non-structural elements and live loads, while lateral loads represent earthquake and wind forces [32]. The non-structural element dead load of 4.0 kN/m2 is applied as a uniform load on all floor slabs. The uniform live load is 2.0 kN/m2 and 4.8 kN/m2 for floor slabs and staircases, respectively. Lateral load due to wind is applied on the buildings in both orthogonal directions using a basic wind speed of 45 m/s with an exposure category C. The benchmark buildings rest on class C soil, representing very dense soil [32]. The design response spectral acceleration at the short and long periods is 0.80g and 0.32g, respectively, with a long-period transition of 8.0 seconds. The selected seismic design criteria represent a medium seismicity region such as Dubai (United Arab Emirates), Izmir (Turkey), or Sacramento (California). The seismic loads of the benchmark buildings are estimated using the equivalent lateral force analysis (ELFA) and modal response spectrum analysis (MRSA). Since high-rise buildings are dictated by higher modes of vibration, the MRSA analysis is adopted in the design to meet the code recommendation of utilizing 100% of the base shear obtained from ELFA [32]. The considered number of vibration modes is per the design code to achieve at least 90% of the mass participation in both the orthogonal directions. 3.2. Structural Design of Benchmark Buildings A comprehensive analysis of the selected MSB and RC high-rise building sets, varying in height, and structural systems irregularities are conducted using a verified finite element analysis platform [115]. This analysis is performed in accordance with the respective code-recommended seismic design coefficients for both MSBs and RC high-rise buildings. The findings are presented separately for both the MSB set and RC high-rise building sets in the following sections. 53 3.2.1 Design of Benchmark MSBs The elastic analytical process of the MSBs is further facilitated by an automated design approach, employing ETABS and Excel spreadsheets. The results from the ETABS 3D idealizations are summarized, and comparative assessments are made, focusing on elastic response parameters like the periods of vibration, base shear, and inter-storey drift ratio (IDR). The period of vibration of samples of MSBs concerning the various codes is presented in Table 3.2. For brevity, sample design information of both horizontal and vertical structural steel elements of a 20-storey building designed using IBC is summarized in Tables 3.3 and 3.4, and additional design results of the remaining MSBs are presented in Appendix A. Table 3.2: Elastic periods of the sample MSBs along the longitudinal axis. MSBs Code Vibration mode in longitudinal direction Period T1 (sec) Period T2 (sec) Period T3 (sec) 8 Storey EN 2.63 0.88 0.43 IBC 2.91 0.96 0.45 NBCC 2.78 0.88 0.41 NZS 2.99 0.98 0.45 UBC 2.52 0.8 0.32 20 Storey EN 4.83 1.83 0.96 IBC 5.91 2.09 1.04 NBCC 4.65 1.9 0.98 NZS 5.71 2.05 1.02 UBC 5.03 1.91 0.98 Table 3.3: Sample design summary showing beams of 20-storey MSB. Horizontal elements - Beams Storey B1 B2 B3 B4 B5 1 to 20 W12X58 W12X58 W12X30 W12X30 W12X40 Table 3.4: Sample design summary showing columns of 20-storey MSB. Vertical elements - Columns Storey C1 C2 C3 C4 C5 19-20 W21X44 W21X44 W21X44 W21X44 W21X44 13-16 W21X83 W21X83 W21X83 W21X73 W21X55 9-10 W21X93 W21X101 W21X101 W21X93 W21X62 7-8 W21X101 W21X101 W21X101 W21X101 W21X68 3-6 W21X101 W21X111 W21X111 W21X101 W21X83 1-2 W21X111 W24X162 W24X162 W21X111 W21X111 54 Figure 3.4 compares the base shear coefficient of the selected MSBs when designed using different international codes. The selected seismic codes exhibited a lower base shear coefficient (V/W) for all buildings with increased height. Notably, in the current study, for MSBs up to 12 storeys, the design was governed by EN and NZS codes, with EN code being the more critical among the two codes, as depicted in Figure 3.4. In contrast, for MSBs exceeding 12 storeys in height, the IBC and NBCC codes dictated the design, with the IBC code being the more critical, as indicated in Figure 3.4. Table 3.2 and Figure 3.4 shows that 20 MSBs with different heights and design standards are considered. The computationally demanding approach adopted in the present study to assess the seismic design coefficients and the response of benchmark structures using ISAs and MBIDAs considering 26 earthquake records requires 420 3D inelastic analyses for each building. Consequently, to reduce the number of analysis and following a conservative approach, inelastic analyses are performed on MSBs designed with governing codes to assess the seismic performance across various building heights, employing inelastic static analyses (ISAs) and multi-record bidirectional incremental dynamic analyses (MBIDAs) for further in-depth examination. Around 1700 multi-step 3D inelastic analyses are conducted for the four selected MSBs with varying heights using the developed fibre-based numerical models. Notably, the IDRs of the sample of the selected MSBs, depicted in Figure 3.5 satisfy the allowable criteria of the design codes. Information on the remaining MSBs is available in Appendix A. Figure 3.4: Design base shear coefficient of benchmark MSBs considering various design codes. 0.000.200.400.600.801.001.208 Storey 12 Storey 16 Storey 20 StoreyBase Shear Coefficient, V/WEN IBC NBCC NZS UBC55 Figure 3.5: Design inter-storey drift ratios (IDRs) of sample MSBs in the two horizontal orthogonal directions, H1 and H2. 3.2.2 RC High-rise Buildings An automated approach is used in the design process of the nine benchmark RC high-rise buildings, which is validated using Excel spreadsheets [115]. The core walls and all shear walls are designed per ACI 318 provisions [119]. Typical reinforcement details of the core walls and shear walls are illustrated in Figures 3.6 and 3.7, respectively. Sample design information on the shear walls and the core walls for a 60S-B-R building are shown in Tables 3.5 and 3.6, respectively. Information on other remaining benchmark buildings are shown in Appendix A. Figure 3.6: Typical reinforcement details of the core walls showing rebar schedule. 01234567890.0 0.5 1.0 1.5 2.0 2.5Storey (Nos)Interstorey Drift (%)8S H1 H20481216200.0 0.5 1.0 1.5 2.0 2.5Storey (Nos)Interstorey Drift (%)20S H1 H256 Figure 3.7: Typical reinforcement details of the shear walls showing rebar schedule. Floor slabs are designed considering the effects of the seismic loads to avoid premature yielding limiting the risk to the overall structural integrity of the buildings. Details of the placement of reinforcement and the typical rebar schedule of floor slab placement are shown with details in Figure 3.8. A summary of the rebar schedule and design details for both typical normal floor slabs in all benchmark buildings and transfer slabs in soft-storey buildings are provided in Appendix A. To dissipate the energy efficiently and provide the required stiffness to the building, the shear wall openings are interconnected with each other with the coupling beams. The coupling beams are designed per the ACI code provisions based on the ratio of the beam length to its height. Sample design information of the coupling beams for a 60S-B-R building is shown in Tables 3.7 and 3.6 and the remaining information on other benchmark buildings is presented in Appendix A. Figure 3.8: Typical reinforcement details for the floor slabs with rebar schedule. 57 Table 3.5: Design summary of shear walls of 60S-B-R reinforced concrete building. REINFORCEMENT SCHEDULE OF PIER, P1 Location of section Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.54 Length, L (mm) 2750 2750 2750 2750 2750 2750 2750 2750 2750 2750 2750 2750 Breadth, B (mm) 550 550 450 450 350 350 275 275 250 250 225 225 Vertical steel ratio required (µ,%) 1.25% 1.25% 1.54% 1.54% 3.25% 3.29% 2.52% 0.67% 1.77% 0.47% 0.68% 2.09% Vertical steel ratio provided (%) 1.29% 1.29% 1.58% 1.58% 3.38% 3.38% 2.62% 0.69% 1.84% 0.59% 0.73% 2.21% Design/Capacity (D/C) Ratio 0.97 0.97 0.97 0.97 0.96 0.97 0.96 0.97 0.96 0.80 0.93 0.95 Reinforcement Vertical AS1 + AS2 (end) 16T32mm 16T32mm 16T32mm 16T32mm 16T32mm 16T32mm 16T25mm 18T12mm 16T20mm 16T12mm 16T12mm 18T20mm AS3 (middle) 40T25mm 40T25mm 40T25mm 40T25mm 40T25mm 40T25mm 38T20mm 28T12mm 38T16mm 20T12mm 24T12mm 26T20mm Horizontal AS4 T12-150mm T12-150mm T12-200mm T12-200mm T12-200mm T12-200mm T12-200mm T12-200mm T12-200mm T12-200mm T12-200mm T12-200mm AS5 T10-150mm T10-150mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm Length of Boundary elements, mm 600 600 600 600 600 600 600 600 600 600 600 600 Concrete strength (fcu) MPa 80 80 70 70 60 60 60 60 50 50 45 45 Concrete strength (fc') MPa 65 65 57 57 50 50 50 50 40 40 35 35 REINFORCEMENT SCHEDULE OF PIER P2 Location of section Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.54 Length, L (mm) 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750 Breadth, B (mm) 600 550 500 500 450 400 325 325 250 250 225 225 Vertical steel ratio required (µ,%) 4.36% 3.80% 4.15% 4.21% 2.86% 4.12% 2.17% 0.72% 2.39% 0.97% 1.03% 1.62% Vertical steel ratio provided (%) 4.41% 3.96% 4.23% 4.23% 2.93% 4.23% 2.23% 0.75% 2.48% 1.02% 1.05% 1.68% Design/Capacity (D/C) Ratio 0.99 0.96 0.98 1.00 0.98 0.97 0.97 0.96 0.96 0.95 0.98 0.96 Reinforcement Vertical AS1 + AS2 (end) 40T40mm 32T40mm 32T40mm 32T40mm 32T32mm 26T40mm 28T25mm 24T16mm 24T25mm 24T16mm 22T16mm 24T20mm AS3 (middle) 60T40mm 48T32mm 48T40mm 48T40mm 46T32mm 38T40mm 42T25mm 36T16mm 36T25mm 36T16mm 36T16mm 36T20mm Horizontal AS4 T12-150mm T12-150mm T12-150mm T12-150mm T12-200mm T12-200mm T12-200mm T12-200mm T12-200mm T12-200mm T12-200mm T12-200mm AS5 T10-150mm T10-150mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm Length of Boundary elements, mm 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 Concrete strength (fcu) MPa 80 80 70 70 60 60 60 60 50 50 45 45 Concrete strength (fc') MPa 65 65 57 57 50 50 50 50 40 40 35 35 58 Table 3.5: Design summary of shear walls of 60S-B-R reinforced concrete building (cont... d) REINFORCEMENT SCHEDULE OF PIER P5 Location of section Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.54 Length, L (mm) 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750 Breadth, B (mm) 550 550 500 500 450 400 325 325 250 250 225 225 Vertical steel ratio required (µ,%) 4.61% 3.53% 4.57% 4.48% 3.91% 3.70% 3.79% 1.24% 3.47% 0.72% 0.65% 0.82% Vertical steel ratio provided (%) 4.71% 3.58% 4.66% 4.55% 4.00% 3.81% 3.86% 1.30% 3.55% 0.74% 0.68% 0.85% Design/Capacity (D/C) Ratio 0.98 0.99 0.98 0.98 0.98 0.97 0.98 0.95 0.98 0.97 0.96 0.96 Reinforcement Vertical AS1 + AS2 (end) 40T40mm 36T40mm 36T40mm 34T40mm 28T40mm 36T32mm 30T32mm 26T20mm 34T25mm 32T12mm 26T12mm 32T12mm AS3 (middle) 58T40mm 52T40mm 52T40mm 52T40mm 40T40mm 54T32mm 44T32mm 38T20mm 52T25mm 46T12mm 38T12mm 48T12mm Horizontal AS4 T12-150mm T12-150mm T12-150mm T12-150mm T12-200mm T12-200mm T12-200mm T12-200mm T12-200mm T12-200mm T12-200mm T12-200mm AS5 T10-150mm T10-150mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm Length of Boundary elements, mm 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 Concrete strength (fcu) MPa 80 80 70 70 60 60 60 60 50 50 45 45 Concrete strength (fc') MPa 65 65 57 57 50 50 50 50 40 40 35 35 REINFORCEMENT SCHEDULE OF PIER P6 Location of section Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.54 Length, L (mm) 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750 Breadth, B (mm) 550 550 500 500 450 400 325 325 250 250 225 225 Vertical steel ratio required (µ,%) 4.29% 2.80% 4.36% 2.68% 3.73% 3.21% 3.59% 1.17% 3.49% 1.10% 0.98% 1.14% Vertical steel ratio provided (%) 4.33% 2.88% 4.44% 2.71% 3.88% 3.30% 3.65% 1.22% 3.55% 1.12% 0.99% 1.20% Design/Capacity (D/C) Ratio 0.99 0.97 0.98 0.99 0.96 0.97 0.98 0.96 0.98 0.98 0.99 0.95 Reinforcement Vertical AS1 + AS2 (end) 36T40mm 24T40mm 34T40mm 32T32mm 26T40mm 32T32mm 28T32mm 24T20mm 34T25mm 26T16mm 22T16mm 26T16mm AS3 (middle) 54T40mm 56T32mm 50T40mm 48T32mm 40T40mm 46T32mm 42T32mm 36T20mm 52T25mm 40T16mm 36T16mm 38T16mm Horizontal AS4 T12-150mm T12-150mm T12-150mm T12-150mm T12-200mm T12-200mm T12-200mm T12-200mm T12-200mm T12-200mm T12-200mm T12-200mm AS5 T10-150mm T10-150mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm T10-200mm Length of Boundary elements, mm 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 Concrete strength (fcu) MPa 80 80 70 70 60 60 60 60 50 50 45 45 Concrete strength (fc') MPa 65 65 57 57 50 50 50 50 40 40 35 35 59 Table 3.6: Design summary of core walls of 60S-B-R reinforced concrete building. REINFORCEMENT SCHEDULE OF CORE C1 Location of section Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.54 Core thickness (mm) 500 450 350 350 275 275 250 250 225 225 225 225 Vertical steel ratio required (µ,%) 3.81% 1.08% 1.24% 0.25% 0.48% 0.25% 0.71% 0.25% 0.25% 0.25% 0.25% 0.25% Vertical steel ratio provided (%) 3.83% 1.08% 1.25% 0.27% 0.49% 0.35% 0.72% 0.38% 0.42% 0.42% 0.42% 0.42% Design/Capacity (D/C) Ratio 0.99 1.00 0.99 0.93 0.98 0.71 0.99 0.66 0.60 0.60 0.60 0.60 Reinforcement Vertical AS1: AS6 (end) 92T40mm 46T40mm 40T40mm 48T12mm 40T12mm 40T12mm 56T12mm 36T12mm 36T12mm 36T12mm 54T12mm 54T12mm AS7: AS11 (middle) 280T40mm 164T32mm 144T32mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm Horizontal AS12 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm AS13 T10-100mm T10-100mm T10-100mm T10-100mm T10-100mm T10-100mm T10-100mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm Concrete strength (fcu) MPa 80 70 60 60 60 60 50 50 50 50 45 45 Concrete strength (fc') MPa 65 57 50 50 50 50 40 40 40 40 35 35 REINFORCEMENT SCHEDULE OF CORE C2 Location of section Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.54 Core thickness (mm) 550 500 400 400 300 300 275 275 250 250 225 225 Vertical steel ratio required (µ,%) 4.70% 1.73% 1.62% 0.25% 0.70% 0.25% 0.37% 0.25% 0.25% 0.40% 0.52% 0.48% Vertical steel ratio provided (%) 4.72% 1.75% 1.79% 0.26% 0.71% 0.32% 0.37% 0.34% 0.37% 0.41% 0.73% 0.48% Design/Capacity (D/C) Ratio 1.00 0.99 0.91 0.96 0.99 0.78 1.00 0.74 0.68 0.98 0.71 1.00 Reinforcement Vertical AS1: AS6 (end) 104T40mm 54T40mm 72T32mm 58T20mm 40T12mm 40T12mm 40T12mm 40T12mm 40T12mm 40T12mm 40T12mm 40T12mm AS7: AS11 (middle) 242T40mm 194T32mm 166T32mm 132T20mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm Horizontal AS12 T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T12-100mm T12-100mm T12-100mm T12-150mm AS13 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm Concrete strength (fcu) MPa 80 70 60 60 60 60 50 50 50 50 45 45 Concrete strength (fc') MPa 65 57 50 50 50 50 40 40 40 40 35 35 60 Table 3.7: Design summary of coupling beams of 60S-B-R reinforced concrete building. REINFORCEMENT SCHEDULE OF COUPLING BEAM CB1 Location of section Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.54 Clear span, L (mm) 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 Breadth, b (mm) 500 450 350 350 275 275 250 250 225 225 225 225 Overall depth, h (mm) 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 Coupling beam depth, c (mm) 250 250 250 250 250 250 250 250 250 250 250 250 Reinforcement Main Beam Horizontal bars 6T32mm 10T32mm 10T32mm 10T32mm 8T32mm 8T32mm 10T25mm 8T25mm 10T20mm 8T20mm 6T20mm 8T16mm Vertical ties 4L-12T100 4L-12T100 4L-12T100 4L-12T100 4L-10T100 4L-10T100 4L-10T100 4L-10T100 4L-10T100 4L-10T100 4L-10T100 4L-10T100 Coupling Diagonal bars 8T20mm 8T20mm 8T20mm 8T20mm 8T16mm 8T16mm 8T16mm 8T16mm 6T16mm 6T16mm 6T16mm 6T16mm Beam Diagonal ties 2L-12T100 2L-12T100 2L-12T100 2L-12T100 2L-10T100 2L-10T100 2L-10T100 2L-10T100 2L-10T100 2L-10T100 2L-10T100 2L-10T100 Side Bars at each face 4T16mm 4T16mm 4T16mm 4T16mm 4T16mm 4T16mm 4T16mm 4T16mm 4T12mm 4T12mm 4T12mm 4T12mm REINFORCEMENT SCHEDULE OF COUPLING BEAM CB2 Location of section Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.54 Clear span, L (mm) 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 Breadth, b (mm) 550 500 400 400 300 300 275 275 250 250 225 225 Overall depth, h (mm) 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 Coupling beam depth, c (mm) 250 250 250 250 250 250 250 250 250 250 250 250 Reinforcement Main Beam Horizontal bars 8T32mm 10T32mm 8T32mm 8T32mm 6T32mm 6T32mm 8T25mm 6T25mm 8T20mm 6T20mm 8T16mm 8T16mm Vertical ties 4L-12T100 4L-12T100 4L-12T100 4L-12T100 4L-10T100 4L-10T100 4L-10T100 4L-10T100 4L-10T100 4L-10T100 4L-10T100 4L-10T100 Coupling Diagonal bars 8T20mm 8T20mm 8T20mm 8T20mm 8T16mm 8T16mm 8T16mm 8T16mm 6T16mm 6T16mm 6T16mm 6T16mm Beam Diagonal ties 2L-12T100 2L-12T100 2L-12T100 2L-12T100 2L-10T100 2L-10T100 2L-10T100 2L-10T100 2L-10T100 2L-10T100 2L-10T100 2L-10T100 Side Bars at each face 4T12mm 4T12mm 4T12mm 4T12mm 4T12mm 4T12mm 4T12mm 4T12mm 4T12mm 4T12mm 4T12mm 4T12mm REINFORCEMENT SCHEDULE OF COUPLING BEAM CB3 Location of section Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.54 Clear span, L (mm) 2800 2800 2800 2800 2800 2800 2800 2800 2800 2800 2800 2800 Breadth, b (mm) 550 500 400 400 300 300 275 275 250 250 225 225 Overall depth, h (mm) 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 Coupling beam depth, c (mm) 250 250 250 250 250 250 250 250 250 250 250 250 Reinforcement Main Beam Horizontal bars 16T40mm 20T40mm 14T40mm 14T40mm 12T40mm 10T40mm 10T40mm 8T40mm 10T32mm 8T32mm 10T20mm 8T20mm Vertical ties 4L-12T100 4L-12T100 4L-12T100 4L-12T100 4L-10T100 4L-10T100 4L-10T100 4L-10T100 4L-10T100 4L-10T100 4L-10T100 4L-10T100 Coupling Diagonal bars 8T20mm 8T20mm 8T20mm 8T20mm 8T16mm 8T16mm 8T16mm 8T16mm 6T16mm 6T16mm 6T16mm 6T16mm Beam Diagonal ties 4L-12T100 4L-12T100 2L-12T100 2L-12T100 2L-10T100 2L-10T100 2L-10T100 2L-10T100 2L-10T100 2L-10T100 2L-10T100 2L-10T100 Side Bars at each face 4T12mm 4T12mm 4T12mm 4T12mm 4T12mm 4T12mm 4T12mm 4T12mm 4T12mm 4T12mm 4T12mm 4T12mm 61 3.3. Concluding Remarks Steel buildings of varying heights were designed and compared under five international standards. The selected seismic codes exhibited a lower base shear coefficient (V/W) for all buildings with increased height. Notably, in the current study, for MSBs up to 12 storeys, the design was governed by EN and NZS codes, with EN code being the more critical among the two codes. In contrast, for MSBs exceeding 12 storeys in height, the IBC and NBCC codes dictated the design, with the IBC code being the more critical. Consequently, following a conservative approach, inelastic analyses are performed on MSBs designed with governing codes to assess the seismic performance across various building heights, employing ISAs and MBIDAs. The design of deck floor slabs with shear studs was investigated in the design of steel buildings considering all load cases. The incorporation of shear studs over the steel beams was instrumental in efficiently accounting for the diaphragm effect in the design of horizontal elements, especially in addressing the lateral loads. The RC high-rise building sets were meticulously designed, each representing different structural systems and irregularities. Walls were designed using boundary wall elements in the lower storeys, while the need for these boundary elements at the upper storeys was negligible as the reinforcement reduced significantly. The shear walls were designed following the ACI provision, which recommends the utilization of boundary wall elements. However, the design code doesnât require the boundary elements for ordinary shear alls, this approach not only helps in reducing the amount of required steel reinforcement but also enhances the bending moment-to-axial force ratio. The RC slabs and the transfer slabs in the RC buildings were designed considering the effect of seismic loads. It was observed that under seismic load combinations, the reinforcement at the support region between the slabs and the vertical elements saw an increase exceeding 100%. This may cause potential cracks due to the large bending moment, an aspect that is sometimes overlooked by practicing engineers. Failure to adequately consider lateral loads during slab design could result in the premature yielding of slabs and pose a risk to the overall structural integrity of the building, especially in the context of design earthquakes. 62 4 Three-Dimensional Structural Modelling and Selection of Records 4.1 Three-dimensional Fibre-based Structural Modelling The seismic assessment of the selected benchmark MSB set and three RC high-rise building sets involves several inelastic analyses [120]. The seismic response of these buildings is evaluated by carrying out several 3D ISAs and MBIDAs on fibre-based analytical models of the selected benchmark building using the adopted nonlinear analysis platform [120]. This analysis program has the capability to predict the seismic behaviour of large space frames under diverse static and dynamic loading conditions. Both material inelasticity and geometric nonlinearities are considered in this analysis platform, enabling the prediction of substantial deformations in the frame elements subject to severe loading conditions such as strong earthquakes. This analysis platform is globally used for its reliability as it has been validated through multiple experimental tests [121-123]. The current study utilizes the fibre-modelling technique to monitor the behaviour of individual fibres in both confined and unconfined concrete regions, including reinforcing steel. Extensive 3D ISAs and MBIDAs are performed on benchmark buildings using the developed thirteen fibre-based simulation models representing both the MSB set and three RC high-rise building sets. The modelling concept employed for the MSBs showing the typical steel cross-section discretization of the horizontal and vertical members including the utilized steel model are shown in Figure 4.1. Furthermore, Figure 4.2 illustrates the modelling technique adopted for the RC high-rise benchmark buildings showing different components of the numerical model along with the cross-section discretization of beams and walls and utilized material models. The fibre-based idealization technique provides several benefits, such as eliminating the requirement for initial moment-curvature analysis, using material constitutive models in determining the element hysteresis automatically, and considering the interaction between bending moment and axial loads directly. The inelastic force-based (FB) elements are used in the current study to capture the inelasticity of different structural members. This modelling approach maintains the equilibrium of the inelastic analysis without limitations on the inelastic deformations, particularly when addressing the material inelasticity. By using the FB concept, the need 63 for element discretization is eliminated, leading to more simplified 3D models and quicker analysis when compared to other alternatives, such as inelastic displacement-based elements. To achieve accurate numerical integration, four integration sections are considered in the current study for each structural member [124]. The FB element enables the representation of each structural member using a single element, creating a direct linkage between vertical and horizontal structural members, and other model elements in the numerical model. This eliminates the need for meshing within each element, even when dealing with varying cross-sections. (a) Elements of inelastic model 0.15 L0.15 LLNode ANode BAB ABNode B0.15 H0.15 HHNode A (c) Detail A: Fibre-based modelling of beam (d) Detail B: Fibre-based modelling of column Figure 4.1: Fibre-based modelling concept of benchmark high-rise buildings: (a) & (b) modelling approach of different structural members, (c) & (d) typical details of beam and column discretization, and material model. Beam Column Slab Detail B Detail A (b) Floor Plan Beam Floor ColumnGauss section Gauss section Structural steel model 64 (a) Elements of inelastic model ABLNode ANode B0.15 L0.15 L0.50 L0.50 L ABNode ANode B0.15 H0.15 HHL Figure 4.2: Fibre-based modelling concept of benchmark high-rise buildings: (a) & (b) modelling approach of different structural members, (c) & (d) typical RC cross-section discretization, and material modelling. The extensive results from the design phase and related elastic analysis are used in developing the 3D inelastic fibre-based models of MSBs and RC high-rise benchmark buildings covering different structural systems and irregularities. Gravity loads are applied to the 3D fibre-based numerical models of the benchmark structures as permanent loads at the nodes of the horizontal frame elements while conducting the ISAs and MBIDAs. Likewise, mass is assigned to different elements and distributed in a similar pattern as the gravity loads. Beam Wall Slab Detail A Detail C Detail B (b) Detail A: Floor slab modelling approach Rigid link Beam Floor openings Wall Gauss section Gauss section(c) Detail B: Fibre-based modelling of beam element (d) Detail C: Fibre-based modelling of wall element Confined concrete model Unconfined concrete model Rebar model Floor slab constraints 65 4.2 Material Models Various cross-sections from the analysis platform library are used to model structural elements, such as columns and beams for the MSBs; and slabs, connecting beams, shear walls, core walls, and rigid arms for the RC high-rise benchmark buildings. A kinematic hardening steel model recognized for its accuracy and efficient computational performance is adopted to idealize structural steel members of the MSBs. A uniaxial steel model known for better numerical stability and accuracy due to its efficient stress-strain relationship during transient seismic loading is used to idealize the rebars of the RC members [125, 126]. A uniaxial nonlinear constant confinement model is considered for concrete cylinder strength below 50 MPa as it considers the effects of lateral transverse reinforcement, assuming a consistent confining pressure over the whole stress-strain field [127, 128]. For concrete cylinder strength above 50 MPa, a uniaxial constant confinement model for high-strength concrete is adopted as it accounts for the reduced ductility in post-peak behaviour [129-131]. Figure 4.3 shows the material models utilized in the fibre-based models of the benchmark buildings. (a) Bilinear steel model (stl bl) (b) Menegotto-Pinto steel model (stl mp) (c) Mandel et al. concrete model (con ma) (d) Kappos and Konstantinidis concrete model (con hs) Figure 4.3: Material models utilized in the benchmark buildings: (a) steel model used in MSB (b) rebar model used in RC high-rise buildings (c) & (d) concrete material models used in inelastic analyses. 66 4.3 Representing Bidirectional Earthquake Loads for MBIDA The response of a structure during an earthquake is significantly influenced by the selection of earthquake records. Hence, this selection plays a vital role in evaluating the seismic performance of the buildings. Several parameters, such as the peak ground acceleration (PGA), the class of soil, the magnitude of the earthquake, the ratio between PGA and peak ground velocity (PGV) (a/v), and the distance from the epicentre, are considered while selecting the earthquake records [132, 133]. The current study selects a set of real earthquake records to assess the seismic response modification coefficients of the benchmark MSBs and RC high-rise building sets. The benchmark MSBs and RC high-rise building sets are considered in a medium seismicity region, such as Izmir-Turkey, Sacramento-California, or Dubai-UAE. These seismic regions cover a major part of the geographical area in the globe as depicted in Figure 4.4 [118]. Further, earthquake-prone regions may be vulnerable to multiple seismic scenarios such as a far-field scenario, which replicates strong earthquakes occurring at a significant distance from the epicentre, and a near-source scenario, which encompasses moderate events within a close distance between the seismic source and the building location. The far-field earthquakes, in comparison with the latter ones, exhibit greater spectral accelerations in the medium to long period range, resulting in amplifying the seismic response of higher modes for the benchmark high-rise buildings. This effect can have a substantial impact on the response of the selected set of benchmark buildings and, consequently, on the evaluation of seismic design coefficients. Moreover, several previous studies confirmed that the far-field events impose significant seismic demands on high-rise buildings as compared with the near-source events [13, 134-136]. Henceforth, the current study incorporates distant earthquakes to evaluate the seismic design coefficients and assess the seismic behaviour and response of the four MSBs and nine benchmark RC buildings. Based on the above considerations, 26 far-field natural earthquake records representing the medium seismicity region are selected for nonlinear dynamic simulations. A comprehensive search was conducted from two reliable databases to select 26 natural records representing earthquake scenarios relevant to the study region (i.e., Dubai, UAE), specifically far-field source events [137, 138]. The type of soil, magnitude of the earthquake and the distance from the source were considered while selecting these 67 earthquake records. The selected records represent the fair-field events with a distance from the source to the structure measuring between 95 km to 161 km and earthquake magnitudes ranging between 6.5 to 7.62. Earthquakes with larger magnitudes typically exhibit more extended effective durations and prominent peaks, significantly influencing dynamic structural behaviour. Figure 4.4: Distribution of PGA showing the seismicity levels around the globe [118]. Ground motion duration significantly impacts maximum seismic responses [139]. To address this issue, the most important earthquake duration is considered between 5% and 95% of the total integral of acceleration [140]. This consideration notably reduces analysis time, particularly for distant ground motions characterized by prolonged durations. The selection process involved initial filtering and final selection based on recommended design response spectra. To narrow down the selection of records, they are initially filtered based on the criteria established for the selection of records, including the distance from the epicentre to the source, the magnitude of the earthquake, the soil class type, PGA, and the a/v ratio. In the final stage, the initially filtered records are compared against the design code spectra, scaled to match the selected design intensity of the study region [32, 141]. In the current study, a total of 26 natural earthquake records, denoted R1-R26, as shown in Table 4.1, are selected to encompass uncertainties in seismic events. Figure 4.6 illustrates response spectra of far-field natural earthquake records along with design code spectra for site classes C and D, including the period range of the selected benchmark buildings. Two horizontal components of each earthquake record employed in the MBIDAs, denoted H1 and H2, are shown in Figures 4.7 and 4.8, respectively. The selected earthquake records 68 are normalized to the recommended PGA of 0.16 g for the case study area for a 10% likelihood of occurrence in 50 years [142]. Figure 4.5: Response spectra of far-field natural earthquake records along with design code spectra for site classes C and D showing the period range of the benchmark buildings. The ratio of PGA to peak ground velocity (PGV) (a/v) serves as a valuable metric for describing ground motion characteristics concerning earthquake magnitude, frequency, and distance from the epicentre [143]. The a/v ratios less than 0.8 g/ms-1 indicate input ground motions with predominantly lower frequencies covering a broad range of response spectra representing medium-to-high earthquakes, longer distance to source, and extended durations. The selected seismic records align with this classification, as detailed in Table 4.1 and Figures 4.7 and 4.8 illustrating pictorial information of both horizontal orthogonal directions. The spectral accelerations of the selected 26 input ground motions cover the wide period range related to the benchmark MSBs and RC high-rise, demonstrating expected significant seismic response across different frequency ranges as shown in Figure 4.6. This ensures that the selected benchmark MSBs and RC high-rise buildings are rigorously evaluated under diverse seismic records capable of amplifying their seismic response, particularly by employing MBIDA to utilize 3D analysis capabilities. The simultaneous application of the earthquake records in both horizontal directions in the MBIDAs on the selected benchmark RC high-rise buildings may have the potential to effectively account for torsional effects in the irregular buildings. 00.10.20.30.40.50.60.70.80 1 2 3 4 5 6 7 8Spectral Acc. (g)Period (s)Mean spectrumSevere distant recordsDesign Code Spectrum (C)Design Code Spectrum (D) Period range for benchmark buildings 69 Table 4.1: Summary of twenty-six input ground motions showing the considered two horizontal components in bidirectional incremental dynamic analyses. Record No. Earthquake Site Class Epicentral distance, KM PEER Record Information Recorded Motions Duration (s) PGA/PGV g/ms-1 PGA/ PGV class Name Recording Station M Year PGA max (g) PGV max (m/s) Component H1 Component H2 R1 Imperial Valley Delta 6.50 1979 stiff 96.0 IMPVALL/H-DLT262 IMPVALL/H-DLT352 0.30 0.43 20.0 0.70 <0.8 low R2 El Mayor-Cucapah Chihuahua, Mexico 7.20 2010 stiff 98.0 SIERRA.MEX CHI000 SIERRA.MEX CHI090 0.40 0.52 90.0 0.77 R3 Izmit, Turkey Amerli-Termik 7.60 1999 stiff 110.0 IZM/AT000 IZM/AT090 0.52 0.68 40.0 0.76 R4 Hector Mine Hector 7.13 1999 v. dense 98.0 HECTOR/HEC000 HECTOR/HEC090 0.34 0.46 70.0 0.74 R5 Peldehue, Chile Near coast of central Chile 6.70 2012 stiff 96.0 EMSC.HNE.D EMSC.HNN.D 0.31 0.56 70.0 0.31 R6 Imperial Valley El Centro, Array #11 6.50 1979 stiff 110.0 IMPVALL/H-E11140 IMPVALL/H-E11230 0.38 0.48 100.0 0.79 R7 Chi-Chi, Taiwan CWB 99999 ILA013 7.62 1995 v. dense 135.0 CHICHI/CWBILA013-E CHICHI/CWBILA013-N 0.51 0.80 60.0 0.64 R8 Kocaeli, Turkey Bursa Tofas 7.51 1995 stiff 95.0 KOCAELI/BRC000 KOCAELI/BRC090 0.24 0.38 130.0 0.63 R9 Kocaeli, Turkey Hava Alani 7.51 1999 v. dense 102.0 KOCAELI/HAV180 KOCAELI/HAV270 0.36 0.59 106.6 0.61 R10 Kocaeli, Turkey Arcelik 7.51 1999 v. dense 96.2 KOCAELI/ARC000 KOCAELI/ARC090 0.22 0.40 60.0 0.55 R11 Landers Yermo Fire Station 7.30 1992 stiff 131.0 LANDERS/YER270 LANDERS/YER360 0.24 0.52 56.5 0.46 R12 Landers Coolwater 7.30 1992 stiff 115.0 LANDERS/CLW-LN LANDERS/CLW-TR 0.31 0.42 60.0 0.74 R13 Loma Prieta Emeryville 6.93 1989 v. dense 96.5 LOMAP/EMR000 LOMAP/EMR090 0.53 0.81 40.0 0.65 R14 Loma Prieta Gilroy Array #3 6.93 1989 stiff 100.0 LOMAP/G03000 LOMAP/G03090 0.56 0.85 40.0 0.66 R15 Manjil, Iran Abbar 7.42 1990 v. dense 131.0 MANJIL/ABBAR-L MANJIL/ABBAR-T 0.51 0.92 35.4 0.55 R16 Superstition Hills El Centro Imp. Co. 6.50 1987 stiff 100.0 SUPERST/B-ICC000 SUPERST/B-1CC090 0.36 0.46 60.0 0.78 R17 Superstition Hills Poe Road (temp) 6.50 1987 stiff 105.0 SUPERST/B-POE270 SUPERST/B-POE360 0.27 0.36 60.0 0.75 R18 Cape Mendocino Rio Dell Overpass 7.00 1992 stiff 98.0 CAPEMEND/RIO270 CAPEMEND/RIO0360 0.55 0.94 44.0 0.59 R19 Chi-Chi, Taiwan CHY101 7.62 1999 stiff 135.0 CHICHI/CHY101-E CHICHI/CHY101-N 0.44 1.15 35.0 0.38 R20 Chi-Chi, Taiwan TCU045 7.62 1999 v. dense 142.0 CHICHI/TCU045-E CHICHI/TCU045-N 0.51 0.89 60.0 0.57 R21 San Fernando LA - Hollywood Stor 6.60 1971 stiff 97.0 SFERN/PEL090 SFERN/PEL180 0.21 0.49 60.0 0.43 R22 Friuli, Italy Tolmezzo 6.50 1976 v. dense 90.0 FRIULI/A-TMZ000 FRIULI/A-TM270 0.35 0.51 40.0 0.69 R23 Izmit AL 088 CNK 7.64 1999 v. dense 113.0 TK.1701.HNE.D TK.1701.HNN.D 0.32 0.53 40.0 0.60 R24 Bucharest Bucharest Res. Inst. 6.90 1990 stiff 161.0 ROA39.HNE.D ROA39.HNN.D 0.30 0.55 20.0 0.55 R25 Kern County LA - Hollywood Stor FF 7.30 1952 stiff 117.0 KERN.PEL090 KERN.PEL180 0.21 0.45 60.0 0.47 R26 Peldehue, Chile Offshore Valparaiso 6.90 2017 stiff 130.0 G.PEL.HNE.D G.PEL.HNN.D 0.31 0.56 52.5 0.31 70 Figure 4.6: Acceleration time-history of natural records selected representing large distant earthquakes of magnitude 6.93 to 7·62 with epicentral distance of 96km to 158km along H1 direction. 0.16 0.16 0.00 0.16 0.16 0.00 0.16 0.16 0.00 0.16 0.16 0.00 0.16 0.16 0.00 0.16 0.16 0.00 0.16 0.16 0.00 0.16 0.16 0.00 0.16 0.16 0.00 0.16 0.16 0.00 0 120 60 90 30 0 120 60 90 30 0 120 60 90 30 R2-H1 R1-H1 R3-H1 R4-H1 R5-H1 R6-H1 R7-H1 R8-H1 R9-H1 R10-H1 R11-H1 R12-H1 R13-H1 R14-H1 R15-H1 R16-H1 R17-H1 R18-H1 R19-H1 R20-H1 R21-H1 R22-H1 R23-H1 R24-H1 R25-H1 R26-H1 71 Figure 4.7: Acceleration time-history of natural records selected representing large distant earthquakes of magnitude 6.93 to 7·62 with epicentral distance of 96km to 158km along H2 direction. 0.16 0.16 0.00 0.16 0.16 0.00 0.16 0.16 0.00 0.16 0.16 0.00 0.16 0.16 0.00 0.16 0.16 0.00 0.16 0.16 0.00 0.16 0.16 0.00 0.16 0.16 0.00 0.16 0.16 0.00 0 120 60 90 30 0 120 60 90 30 0 120 60 90 30 R2-H2 R1-H2 R3-H2 R4-H2 R5-H2 R6-H2 R7-H2 R8-H2 R9-H2 R10-H2 R11-H2 R12-H2 R13-H2 R14-H2 R15-H2 R16-H2 R17-H2 R18-H2 R19-H2 R20-H2 R21-H2 R22-H2 R23-H2 R24-H2 R25-H2 R26-H2 72 It is important to note that the two horizontal components of each of the selected 26 input ground motions include a primary and a secondary component. The input ground motion component with higher intensity is considered the primary component, which is incrementally scaled based on the scaling approach subsequently discussed in MBIDA. The secondary component of the earthquake record is scaled using the same normalization factor as the primary component. Hence, the ratio between the primary and secondary input ground motion accelerations and the number of peaks are preserved as the naturally recorded earthquake. In MBIDA, the primary and secondary components of input ground motions are applied in the longitudinal (main) and transverse (slave) directions, respectively. As subsequently emphasized from ISA results, the longitudinal direction of MSBs controls their lateral response. Hence, the primary component with higher intensity is applied in this direction. 4.4 Concluding Remarks A nonlinear analysis platform was employed to conduct inelastic fibre-based modelling on the selected set of MSB and three sets of RC high-rise buildings, aiming to evaluate their seismic performance. A comprehensive study was undertaken to understand the advantages of the fibre-based modelling approach used in the analysis platform, along with the fibre-based modelling techniques for both MSBs and RC high-rise buildings. The selection of material models for the study was carried out considering various strengths of steel and concrete. To assess the seismic response of both the regular and irregular sets of selected buildings, a 3D idealization approach was utilized for comprehensive inelastic analyses, employing both the ISAs and MBIDAs. To comprehensively address ground motion uncertainties, a total of 26 natural earthquake records, representing the medium seismicity region was considered. These selections were made based on a case study with a PGA of 0.16g with a 10% probability of exceedance in 50 years, for Class C and Class D soil. Application of the bidirectional earthquake loads using 26 input ground motions ensured a thorough evaluation of the seismic design coefficients of the benchmark high-rise buildings by employing the capabilities of 3D MBIDA. 73 5 Inelastic Static and Bidirectional Dynamic Analyses 5.1. Introduction Inelastic analyses are critical in earthquake engineering, studying how structures behave beyond their elastic range, particularly in seismic events causing substantial inelastic deformations. These analyses consider material and geometric nonlinearity, encompassing changes in stiffness, strength, and deformation characteristics. In the current study, a comprehensive assessment of the seismic performance of the selected set of MSBs and three sets of RC high-rise buildings with varying heights, structural systems and irregularities is conducted using the following 3D inelastic analyses: â¢ Free vibration analyses or Eigenvalue analyses. â¢ Inelastic static pushover analyses (ISAs), employing both uniform and triangular load patterns. â¢ Multi-record bidirectional incremental dynamic analyses (MBIDA), employing bidirectional loading along both horizontal orthogonal directions using 26 natural earthquake records, as outlined in Table 4.1 and Figures 4.7 and 4.8. Over 5500 multi-step 3D inelastic analyses are conducted on both sets of MSBs of varying heights and three sets of RC high-rise benchmark buildings with varying heights, structural systems and irregularities. The extensive output data files are meticulously processed and stored in spreadsheets. The results of these thorough analyses are then utilized to provide insight into the seismic performance of the thirteen benchmark MSB and RC high-rise buildings under 26 realistic bidirectional earthquake records. The comprehensive analysis results are utilized to evaluate seismic design response factors and establish fragility relationships for the different sets of MSBs and benchmark RC buildings, as discussed hereafter. 5.2. Free Vibration Analysis Free vibration analysis is a fundamental step to comprehend the dynamic characteristics of structures and detect any issues in their numerical models. This analysis is conducted prior to ISAs and MBIDAs to ascertain the undamped free vibration mode shapes and natural 74 periods of reference buildings. The free vibration analysis relies on the structure's stiffness and mass distribution. It offers valuable insights into a structure's dynamic behaviour concerning vibration frequencies and mode shapes, a crucial aspect prior to evaluating the inelastic structure performance against lateral force-induced vibrations. Furthermore, this straightforward analysis serves as an initial validation tool for the inelastic analysis models, as discussed in detail below. The design and modelling process of the reference buildings, as elaborated in Chapters 3 and 4, are used to obtain the fundamental periods of the selected thirteen MSBs and RC benchmark buildings. Comparative analysis of the elastic and uncracked periods obtained from assessment simulation models and the initial design models are conducted, and the results are tabulated. A sample comparison of the uncracked periods between the 3D design and assessment models of benchmark bearing wall RC building set is shown in Table 5.1, while comparisons between the other benchmark buildings are presented in Appendix B. Table 5.1: Comparison of uncracked periods obtained from design and assessment models for benchmark RC high-rise Regular buildings. Mode 40S-B-R building Period, (Secs) 60S-B-R building Period, (Secs) 60S-D-R building Period, (Secs) Design Model Assessment Model Design Model Assessment Model Design Model Assessment Model 1 4.12 3.79 6.62 6.03 6.28 5.84 2 4.01 3.69 6.46 5.88 5.96 5.55 3 3.75 3.45 5.74 5.22 4.62 4.30 4 1.27 1.17 2.04 1.85 1.93 1.80 5 1.16 1.06 1.84 1.67 1.76 1.64 6 1.08 0.99 1.74 1.58 1.55 1.44 7 0.65 0.60 1.07 0.97 1.03 0.95 8 0.61 0.56 0.95 0.87 0.87 0.80 9 0.48 0.45 0.85 0.78 0.83 0.77 10 0.41 0.38 0.68 0.62 0.67 0.62 11 0.39 0.35 0.62 0.57 0.57 0.53 12 0.28 0.26 0.50 0.45 0.50 0.46 The difference between the fundamental uncracked periods of design and assessment models for the regular RC high-rise buildings range between 7% to 9%; while this difference ranges between 5% to 9% for geometric irregular buildings and 6% to 10% for the soft storey irregular buildings, respectively. This difference between the design and assessment models is due to the presence of re-bars in the inelastic simulation models, which enhances the stiffness of the members in the assessment models, unlike the case with the RC members of the design models. Further, the improvement in concrete confinement contributes to higher compressive strength, subsequently increasing the stiffness of the structural elements, resulting in shorter vibration periods. 75 5.3. Inelastic Lateral Response of Benchmark Structures using ISA Inelastic analysis is performed to understand the seismic behaviour of the benchmark set of MSBs and the three sets of RC high-rise buildings beyond their elastic range, encompassing the changes in stiffness, strength, and deformation characteristics. The extensive output data files from the structural design phase, processed and stored in spreadsheets, are utilized to develop the 3D inelastic models of the set of MSBs of varying heights, and the three sets of RC high-rise benchmark buildings with varying heights, structural systems and irregularities. These models are used for ISAs and MBIDAs. Over 5500 multi-step 3D inelastic analyses are conducted on the detailed fibre-based numerical models representing the benchmark buildings. The inelastic analysis results are then utilized to provide insight into the seismic behaviour of the thirteen benchmark buildings under realistic bidirectional earthquake records. These analysis results evaluate seismic design response factors and establish fragility relationships for the selected sets of benchmark buildings. Due to the nonlinear behaviour of high-rise buildings, the benchmark buildings exhibit changes in their strength, stiffness, and deformation nature beyond the elastic range. To provide insights into the lateral response of benchmark structures beyond the elastic range, ISA is conducted on the 3D fibre-based simulation models of the benchmark MSB and RC high-rise building sets. The developed 3D fibre-based models of the regular benchmark MSBs of varying heights and RC high-rise buildings covering varying heights, structural systems and irregularities are used to perform multi-step ISAs. It is important to note that although the ISA procedure is used in this study as an initial assessment tool for the lateral capacity, stiffness, and local damage development, the comprehensive frameworks shown in Figures 1.1 and 1.2, which involve using the computationally demanding MBIDAs, is employed in the present study to assess the seismic design coefficients, as discussed in subsequent sections. 5.3.1. Estimation of lateral capacity of benchmark structures In the current study, 3D ISAs are conducted using a verified inelastic analysis platform to predict the lateral response, sequence of yielding, and stiffness degradation of the benchmark MSBs set and three RC high-rise building sets [144]. A plot is generated in this analysis showing the total base shear of each building versus its respective top displacement, helping identify any premature failures or weaknesses in the MSBs set and 76 high-rise benchmark building sets. The study explores the response of these benchmark buildings by employing the following load distributions: (i) uniform lateral load (ULL) representing the uniform mass distribution along the building height, and (ii) triangular lateral load (TLL) expressing the fundamental mode. Previous studies identified that the former lateral load distribution provides a conservative approach in estimating structural strength and stiffness compared to the latter load pattern due to the effect of higher modes contribution to the response of multi-storey and high-rise benchmark buildings [22, 71, 101, 145]. Lateral loads are incrementally applied along the building height until the structure reaches all limit states, as subsequently discussed. The analysis is also used to monitor the strength of each MSB at the first plastic hinge formation, global yield, and ultimate failure of the structure. Additionally, the formation of the plastic hinges at the first indication of yielding at both horizontal and vertical elements, unconfined and confined concrete crushing, global yielding, and the ultimate base shear are monitored. The IDR of each of the benchmark buildings is also captured at different levels of base shear to relate it to different local performance indicators. It is noteworthy that the estimation of seismic demands using ISAs may not be realistic in the case of high-rise buildings, which are influenced by higher modes. Nevertheless, this analysis tool facilitates the assessment of the lateral capacity of the structure and provides valuable information on the sequence of plastic hinge formation and the development of local failure modes. The more detailed MBIDAs are adopted to evaluate the seismic design coefficients realistically, as subsequently discussed. 5.3.1.1. Multi-storey Steel Buildings In the current study, the seismic response of the MSBs is monitored for different events and at various performance levels, including those at yield and collapse. The initial sign of local yielding is detected in beams followed by columns, as depicted in Figure 5.1. This observation substantiates the strong column-weak beam (SCWB) principle, emphasizing concentrating energy dissipation in the horizontal elements. To identify the global yield, two models: the equal energy model and the elasto-plastic model were considered. Adopting a conservative approach, recommendation on earlier studies and observing the development of the hinges in the vertical elements, the elasto-plastic model is employed in the current study [146, 147]. 77 The capacity envelopes of MSBs are linearized to determine the global yield, which is evaluated based on a comparable elasto-plastic model considering reduced initial stiffness represented by a secant stiffness at first yield in vertical structural members [146, 148]. Moreover, the ultimate structural capacity of all the MSBs was ascertained at the respective points of maximum base shear. he benchmar MSBsâ IDRs are monitored and presented at the first yield in beams and columns, followed by system yielding, collapse, and the ultimate levels. The IDRs are consistent among all MSBs, with lower storeys experiencing higher IDRs under ULL than the TLL due to load distribution differences [71, 136]. The collapse level is considered at the IDR of the buckling strain of MSBs. Figure 5.3 summarizes the IDRs of the benchmark MSBs for both ULL and TLL patterns. Figure 5.1: Lateral response of MSBs with varying heights along with the sequence of yielding considering two lateral load distributions. 0246810120.0 0.2 0.4 0.6 0.8 1.0 1.2Base Shear (MN)Top Displacement (m)8S ULL & TLLUltimate =10349 KN1.45% IDR 0.76% IDR 3.68% IDR Overstrength =3.70Design =2675 KN0246810120.0 0.5 1.0 1.5Base Shear (MN)Top Displacement (m)12S ULL & TLLDesign =3162 KNUltimate =11415 KNOverstrength =3.610.86% IDR 1.44% IDR 3.77% IDR 024681012140.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1Base Shear (MN)Top Displacement (m)16S ULL & TLL1.48% IDR Overstrength =3.46Design =3810 KNUltimate =13200 KN0.88% IDR 3.70% IDR 02468101214160.0 0.5 1.0 1.5 2.0 2.5Base Shear (MN)Top Displacement (m)20S ULL & TLLUltimate =14947 KNDesign =4426 KN0.90% IDR 1.48% IDR 3.75% IDR Overstrength =3.3878 Moreover, to investigate the structural response of the benchmark buildings in the two orthogonal directions, ISA is conducted in the longitudinal and transverse directions. The impact of considering bidirectional lateral load on the response of the benchmark buildings is also investigated and compared with unidirectional lateral load patterns [149]. The results of 3D bidirectional ISA (BISA) in the two orthogonal directions of the four benchmark buildings are depicted in Figure 5.2. It is shown from the presented results in Figure 5.2, that the longitudinal (X) direction has a lower lateral capacity than the transverse (Y) direction. Hence, the most conservative direction (i.e., X direction) is considered in the present study to assess the lateral capacity of the MSBs. Additionally, it is shown from the comparison of the ISA and BISA results that the unidirectional lateral load distribution has a marginal impact on lateral capacity envelopes and the first indication of yielding in the most conservative direction (i.e., X direction). It is noteworthy, that the considered MSBs represent regular steel buildings and do not exhibit several horizontal irregularities, which are likely to be affected by BISA. Therefore, based on the presented results in Figure 5.2, the BISA results are considered in calculating the seismic design coefficients, as subsequently discussed. Figure 5.2: Comparison of lateral response of MSBs considering unidirectional ISA and bidirectional ISA (BISA) in the two orthogonal directions. 024681012140.0 0.2 0.4 0.6 0.8 1.0 1.2Base Shear (MN)Top Displacement (m)8S ISA & BISAISA-X Dir Yield ISA X DirBISA-X Dir Yield BISA X DirBISA-Y Dir Yield BISA Y DirISA-Y Dir0.76% IDR Design =2675 KN0.70% IDR 02468101214160.0 0.5 1.0 1.5Base Shear (MN)Top Displacement (m)12S ISA & BISAISA-X Dir Yield ISA X DirBISA-X Dir Yield BISA - X DirBISA-Y Dir Yield BISA Y DirISA-Y DirDesign =3162 KN0.80% IDR 0.86% IDR 024681012140.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1Base Shear (MN)Top Displacement (m)16S ISA & BISAISA-X Dir Yield ISA X DirBISA-X Dir Yield BISA X DIrBISA-Y Dir Yield BISA Y DirISA-Y Dir0.82% IDR Design =3810 KN0.88% IDR 0246810121416180.0 0.5 1.0 1.5 2.0 2.5Base Shear (MN)Top Displacement (m)20S ISA & BISAISA-X Dir Yield ISA X DirBISA-X Dir Yield BISA X DirBISA-Y DirDesign =4426 KN0.90% IDR 0.83% IDR 79 Figure 5.3: IDRs of MSBs with varying heights from incremental static analysis (ISA) employing ULL and TLL patterns. 5.3.1.2. RC High-rise Buildings The Lateral capacity envelopes estimate the lateral response of the benchmark high-rise buildings at different performance levels, starting from initial yielding until the building reaches collapse. Figures 5.4 to 5.6 show the lateral response curves for the 40S-B, 60S-B and 60S-D sets, including mapping of rebar yielding sequence and confined concrete crushing considering two lateral load distributions. The initial sign of the local yielding is identified first in horizontal elements, followed by vertical elements, as shown in Figures 5.4 to 5.6. The observed yielding sequence validates the strong column-weak beam (SCWB) concept of design codes [119]. The global yield of benchmark buildings is identified by evaluating the initial stiffness using a secant stiffness that passes through 75% of the ultimate strength [146, 150]. Based on monitoring the unconfined concrete and the confined concrete crushing of the benchmark buildings, it is observed that the confined concrete crushing correlated to the onset of global yielding, as shown in Figures 5.4 to 5.6. For brevity, the details of these observations are tabulated in Appendix B. The ultimate strength of the selected buildings is evaluated based on the corresponding base shear obtained from their respective capacity envelopes. The distribution of the IDRs for RC high-rise building sets for both loading patterns, namely ULL and TLL, are shown in Figures 5.7 to 5.9. The presented results for the 40S-B, 60S-B and 60S-D RC building sets show higher IDRs in the lower storeys under the ULL than the TLL due to the lower location of the lateral force resultant for the former load than the TLL load pattern [22, 136]. 02468100 2 4Storey (Nos)Interstorey Drift (%)8S ULL & TLL TLLULL024681012140 2 4Storey (Nos)Interstorey Drift (%)12S ULL & TLL TLLULL0246810121416180 2 4Storey (Nos)Interstorey Drift (%)16S ULL & TLL TLLULL0481216200 2 4Storey (Nos)Interstorey Drift (%)20S ULL & TLL TLLULL80 Figure 5.4: Lateral response of regular and irregular 40S-B RC buildings set showing rebar yielding sequence and confined concrete crushing considering two lateral load distributions. Figure 5.5: Lateral response of regular and irregular 60S-B RC buildings set showing rebar yielding sequence and confined concrete crushing considering two lateral load distributions. 0153045600.0 0.5 1.0 1.5 2.0 2.5Base Shear (MN)Top Displacement (m)40S-B-R ULL & TLL1.82% IDR Ultimate =52227 KN0.61% IDR 0.97% IDR Overstrength =2.83Design =18691 KN01530450.0 0.5 1.0 1.5 2.0 2.5Base Shear (MN)Top Displacement (m)40S-R-GI ULL & TLL0.97% IDR 0.60% IDR Overstrength =2.76Ultimate =43888 KNDesign =16150 KN1.74% IDR 0153045600.0 0.5 1.0 1.5 2.0 2.5Base Shear (MN)Top Displacement (m)40S-B-SS ULL & TLL Ultimate =53084 KNDesign =19031 KNOverstrength =2.790.55% IDR 1.00% IDR 1.86% IDR 01530456075900.0 1.0 2.0 3.0 4.0Base Shear (MN)Top Displacement (m)60S-B-R ULL & TLLUltimate =80269 KNDesign =29125 KNOverstrength =2.831.22% IDR 0.63% IDR 1.89% IDR 015304560750.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0Base Shear (MN)Top Displacement (m)60S-B-GI ULL & TLL0.58% IDR 1.16% IDR Ultimate =67011 KNDesign =25541 KNOverstrength =2.621.99% IDR 01530456075900.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0Base Shear (MN)Top Displacement (m)60S-B-SS ULL & TLL Ultimate =79882 KNDesign =29807 KNOverstrength =2.680.52% IDR 1.08% IDR 1.84% IDR 81 Figure 5.6: Lateral response of regular and irregular 60S-D RC buildings set showing rebar yielding sequence and confined concrete crushing considering two lateral load distributions. Figure 5.7: Incremental static analysis (ISA) results of the inter-storey drift ratios (IDRs) distributions for 40S-B RC buildings set using ULL and TLL. 01530456075901050.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0Base Shear (MN)Top Displacement (m)60S-D-R ULL & TLL0.88% IDR 0.50% IDR 1.95% IDR Ultimate =94638 KNOverstrength =2.91Design =32512 KN01530456075900.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0Base Shear (MN)Top Displacement (m)60S-D-GI ULL & TLL0.79% IDR 0.48% IDR Overstrength =2.89Design =28664 KNUltimate =82921 KN1.76% IDR 01530456075901050.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0Base Shear (MN)Top Displacement (m)60S-D-SS ULL & TLL Ultimate =94177 KNDesign =32951 KNOverstrength =2.860.76% IDR 0.48% IDR 1.72% IDR 0510152025303540450 1 2 3 4Storey (Nos)Interstorey Drift (%)40S-B-R ULLTLL0510152025303540450 1 2 3 4Storey (Nos)Interstorey Drift (%)40S-R-GI ULLTLL0510152025303540450 1 2 3 4Storey (Nos)Interstorey Drift (%)40S-B-SS ULLTLL 82 Figure 5.8: Incremental static analysis (ISA) results of the inter-storey drift ratios (IDRs) distributions for 60S-B RC buildings set using ULL and TLL. Figure 5.9: Incremental static analysis (ISA) results of the inter-storey drift ratios (IDRs) distributions for 60S-D RC buildings set using ULL and TLL. 051015202530354045505560650 1 2 3 4Storey (Nos)Interstorey Drift (%)60S-B-R ULLTLL051015202530354045505560650 1 2 3 4Storey (Nos)Interstorey Drift (%)60S-B-GI ULLTLL051015202530354045505560650 1 2 3 4Storey (Nos)Interstorey Drift (%)60S-B-SS ULLTLL051015202530354045505560650 1 2 3 4Storey (Nos)Interstorey Drift (%)60S-D-R ULLTLL051015202530354045505560650 1 2 3 4Storey (Nos)Interstorey Drift (%)60S-D-GI ULLTLL051015202530354045505560650 1 2 3 4Storey (Nos)Interstorey Drift (%)60S-D-SS ULLTLL83 5.3.2. Estimation of Overstrength The reserve strength of the structural system plays a vital role in evaluating the seismic design coefficients by assuring the buildingâs safety ith optimized cost. he overstrength factor (Ω) is a ratio of the actual to the design structural strength [13, 85, 90]. Seismic design codes account for the reserve strength when the elastic seismic force (Ve) is modified to estimate the design base shear (Vs), as shown in Figure 2.2. Usually, well-designed buildings exhibit a substantial degree of overstrength at different performance levels, including initial yield (Ωfy) and ultimate strength (Ω). he indication of the Ωfy is detected at a higher intensity than that adopted in the design. The structural reserve strength of the benchmark MSBs and the RC high-rise buildings is explained in the following sections. 5.3.2.1. Multi-storey Steel Buildings The overstrength factor for the chosen sets of MSBs is assessed at various lateral strength stages. These stages encompass the strength at the beginning of initial yielding in beams and columns and the points of system yielding, collapse, and maximum strength relative to the design value of the respective MSB. Figure 5.10 visually illustrates the overstrength coefficients at the various strength levels. A marginal decrease in the overstrength at the points of first yield, global yield, collapse, and ultimate base shear is observed with the increase in the building height. This reduction in overstrength factors results from the reduced V/W design forces associated with taller buildings, as illustrated in Figure 3.4. It is also shown that using the ULL pattern, the overstrength factors at first yield and ultimate strength are, on average, 2.0 and more than 3.55, respectively. These values reflect the adequate overstrength exhibited by the buildings, as recommended by the design codes. For brevity, the overstrength of the MSBs is tabulated and presented in Appendix B. Figure 5.10: Overstrength factors at first yield, global yield, collapse, and ultimate base shear for the benchmark MSBs. 0.001.002.003.004.00ULL TLL ULL TLL ULL TLL ULL TLL8S 12S 16S 20SOverstrength Factor1st Yield Overstrength-Horizontal Elements 1st Yield Overstrength-Vertical ElementsGlobal Yield Overstrength Ultimate OverstrengthOverstrength at Collapse84 5.3.2.2. RC High-rise Buildings The structural overstrength factors for benchmark RC high-rise buildings are thus evaluated at multiple lateral strength levels. These levels include the strength at the commencement of the initial yielding in horizontal elements followed by the vertical elements, global yielding, ultimate strength, and collapse. It is noteworthy that different limit states are defined based on the extensive ISA and MBIDA results, as discussed in subsequent sections. Figure 5.11 shows the structural overstrength coefficients at different strength levels for the nine benchmark buildings categorised under three sets. The results in Figures 5.4 to 5.6 and Figure 5.11 confirm that the benchmark RC high-rise buildings exhibit comparable overstrength values at various strength levels in the regular and irregular buildings. The results reflect the insignificance of the geometric and soft storey irregularities on the overstrength factors. Notably, the design code does not require increasing seismic loads for these two irregularities [32, 101]. It is also observed that the overstrength values estimated based on the ULL lateral load in all the benchmark buildings at the initial yield and ultimate strength range between 1.33 to 1.89, and 2.62 to 2.98, respectively, demonstrating adequacy over the design code recommended values [32]. Comprehensive results of these evaluations are tabulated and presented in Appendix B. (a) Overstrength factors for 40S-B buildings (b) Overstrength factors for 60S-B buildings (c) Overstrength factors for 60S-D buildings Figure 5.11: Overstrength factors at first yield, global yield, collapse, and ultimate base shear: (a) 40S-B, (b) 60S-B, and (c) 60S-D RC building sets. 0.001.002.003.00ULL TLL ULL TLL ULL TLL40S-B-R 40S-B-GI 40S-B-SSOverstrength Factor1st Yield Overstrength-Hor Elements 1st Yield Overstrength-Ver ElementsGlobal Yield Overstrength Ultimate OverstrengthOverstrength at Collapse0.001.002.003.00ULL TLL ULL TLL ULL TLL60S-B-R 60S-B-GI 60S-B-SSOverstrength Factor1st Yield Overstrength-Horizontal Elements 1st Yield Overstrength-Vertical ElementsGlobal Yield Overstrength Ultimate OverstrengthOverstrength at Collapse0.001.002.003.00ULL TLL ULL TLL ULL TLL60S-D-R 60S-D-GI 60S-D-SSOverstrength Factor1st Yield Overstrength-Horizontal Elements 1st Yield Overstrength-Vertical ElementsGlobal Yield Overstrength Ultimate OverstrengthOverstrength at Collapse85 5.3.3. Estimation of Lateral Stiffness of Buildings During an earthquake, rigid structures experience more significant seismic forces than flexible ones. The design of MSBs and RC buildings is based on the strict drift requirements of the design code to ensure that a minimum level of stiffness is maintained under normal service conditions by limiting IDRs and lateral displacement. Before yielding occurs in the MSBs, the structure retains a consistent stiffness based on the stiffness of its original cross-section. However, if external loads lead to yielding, the structure's stiffness reduces. Similarly, before the occurrence of concrete cracking, the structure maintains a constant stiffness based on the uncracked cross-section. This stiffness reduces at the onset of concrete cracking due to the large deformations caused by external loads, reducing the structure's stiffness. Henceforth, evaluating the effective stiffness is vital, particularly for the MSBs and RC buildings that are governed by lateral drift requirements, considering factors contributing to reduced structure stiffness, mainly due to yielding and fracture in MSBs and concrete cracking in RC buildings. The lateral stiffness of the respective MSBs and 40S-B, 60S-B, and 60S-D RC building sets is discussed in the following sections. 5.3.3.1. Multi-storey Steel Buildings In the current study, stiffness and related modifiers are determined by analyzing the capacity curves of the MSBs at various stages, including first yield, global yield, ultimate strength, and collapse, as illustrated in Figures 5.12 and 5.13. The MSBs exhibited a decrease in stiffness at different stages, including the initial yield, global yield, and collapse stages. Figure 12 shows that the average stiffness modifiers of MSBs relative to initial stiffness at global yield, ultimate strength and collapse are 0.82, 0.37, and 0.34. These stiffness modifiers can be used in the elastic analysis of comparable MSBs. Detailed results of the stiffness evaluation for all the MSBs are tabulated and presented in Appendix B. Figure 5.12: Comparison between initial stiffness and those at global yield, collapse, and ultimate strength of MSBs. 051015202530ULL TLL ULL TLL ULL TLL ULL TLL8S 12S 16S 20SStiffness, kN/mmInitial Stiffness Global Yield Stiffness Ultimate Stiffness Stiffness at Collapse86 Figure 5.13: Stiffness modifiers relative to initial stiffness at global yield, ultimate strength, and collapse for the MSBs. 5.3.3.2. RC High-rise Buildings In the current study, the capacity curves from the ISAs are used to determine the stiffness and the associated modifiers at various performance levels. Figure 5.14 shows the stiffness of the nine RC buildings divided into three sets at the initial yielding, global yielding, ultimate strength, and collapse limit state. Stiffness modifiers of the 40S-B, 60S-B, and 60S-D RC high-rise buildings at different levels relative to initial stiffness are illustrated in Figure 5.15. The three RC building sets exhibited a continuous decrease in stiffness with increasing lateral load. The higher initial stiffness is due to the absence of cracks in concrete cross-sections in the elastic range before initial yielding, as illustrated in Figure 5.14. Among all the RC buildings, the initial stiffness in the soft-storey buildings is higher than that of regular structures, followed by geometric vertical irregular buildings. (a) Lateral stiffness of 40S-B RC buildings (b) Lateral stiffness of 60S-B RC buildings (c) Lateral stiffness of 60S-D RC buildings Figure 5.14: Comparison between initial stiffness and those at global yield, collapse, and ultimate strength for 40S-B, 60S-B, and 60S-D RC building sets. 0.00.20.40.60.81.08S 12S 16S 20S0.84 0.81 0.82 0.820.340.39 0.37 0.360.30 0.340.350.34Stiffness Modifier Global Yield Ultimate Strength Collapse01020304050ULL TLL ULL TLL ULL TLL40S-B-R 40S-B-GI 40S-B-SSStiffness, kN/mmInitial Stiffness Global Yield Stiffness Ultimate Stiffness Stiffness at Collapse01020304050ULL TLL ULL TLL ULL TLL60S-B-R 60S-B-GI 60S-B-SSStiffness, kN/mmInitial Stiffness Global Yield Stiffness Ultimate Stiffness Stiffness at Collapse020406080ULL TLL ULL TLL ULL TLL60S-D-R 60S-D-GI 60S-D-SSStiffness, kN/mmInitial Stiffness Global Yield Stiffness Ultimate Stiffness Stiffness at Collapse87 Effective stiffness values of the RC high-rise buildings at different levels relative to initial stiffness obtained from the ULL distribution are illustrated in Figure 5.15. The average effective stiffness relative to initial stiffness at global yield, ultimate strength, and collapse levels among all the two RC bearing wall building sets (40S-B, 60S-B) are 0.82, 0.56, and 0.49, while those for the RC dual building set (60S-D) are 0.83, 0.44, and 0.36, respectively. The effective stiffness of all the benchmark RC buildings representing varying heights, structural systems, and irregularities at global yield and collapse are compared in Figure 5.16 with the recommended values for uncracked and cracked walls by different design standards [16, 100, 119]. The results confirm that the recommended uncracked and cracked wall effective stiffness by ACI and CSA of 0.70 and 0.35, respectively, are conservative when compared with the observed effective stiffness of the nine benchmark high-rise buildings at global yield and collapse of 0.82 and 0.45, respectively. On the other hand, the recommended unified effective stiffness by Eurocode of 0.5 is over-conservative for uncracked walls and unconservative for cracked walls. Complete information on the stiffness of the benchmark RC buildings is tabulated and presented in Appendix B. (a) Lateral stiffness of 40S-B RC buildings (b) Lateral stiffness of 60S-B RC buildings (c) Lateral stiffness of 60S-D RC buildings Figure 5.15: Comparison between initial stiffness and those at global yield, collapse, and ultimate strength for 40S-B, 60S-B, and 60S-D RC building sets. 01020304050ULL TLL ULL TLL ULL TLL40S-B-R 40S-B-GI 40S-B-SSStiffness, kN/mmInitial Stiffness Global Yield Stiffness Ultimate Stiffness Stiffness at Collapse01020304050ULL TLL ULL TLL ULL TLL60S-B-R 60S-B-GI 60S-B-SSStiffness, kN/mmInitial Stiffness Global Yield Stiffness Ultimate Stiffness Stiffness at Collapse020406080ULL TLL ULL TLL ULL TLL60S-D-R 60S-D-GI 60S-D-SSStiffness, kN/mmInitial Stiffness Global Yield Stiffness Ultimate Stiffness Stiffness at Collapse88 (a) Stiffness modifiers of 40S-B RC buildings (b) Stiffness modifiers of 60S-B RC buildings (c) Stiffness modifiers of 60S-D RC buildings Figure 5.16: Stiffness modifiers relative to initial stiffness at global yield, ultimate strength, and collapse for 40S-B, 60S-B, and 60S-D RC building sets. Figure 5.17: Comparison between effective stiffness of nine high-rise buildings (R: regular, GI: geometric irregular, SS: soft storey) at global yielding and collapse with recommended uncracked and cracked walls effective stiffness by design standards (ACI: American concrete institute, CSA: Canadian standard association, EN: Eurocode). 5.3.4. Observation of Plastic Hinges The formation of the plastic hinges depends on the exceedance of the yield strain limit in the outermost flexural reinforcing steel. Monitoring the development of these plastic hinges at various stages, specifically under seismic events, is very important in assessing the 0.00.20.40.60.81.040S-B-R 40S-B-GI 40S-B-SS0.81 0.810.850.50 0.530.550.46 0.470.53Stiffness Modifier Global Yield Ultimate Strength Collapse0.00.20.40.60.81.060S-B-R 60S-B-GI 60S-B-SS0.81 0.80 0.820.59 0.59 0.570.550.48 0.48Stiffness Modifier Global Yield Ultimate Strength Collapse0.00.20.40.60.81.060S-D-R 60S-D-GI 60S-D-SS0.80 0.810.880.44 0.470.400.37 0.36 0.34Stiffness Modifier Global Yield Ultimate Strength Collapse0.00.20.40.60.81.0R GI SS ACI CSA EN0.81 0.810.850.70 0.700.500.46 0.44 0.460.35 0.350.50Effective StiffnessRC High-rise Buildings Standards89 damage propagation and possible collapse mechanisms. The plastic hinges in this study are evaluated, and their development is monitored in ISAs under the lateral loading patterns as discussed earlier. The formation of the plastic hinges in the MSBs and the development of different member damages in the 40S-B, 60S-B, and 60S-D RC building sets are discussed in the following sections. 5.3.4.1. Multi-storey Steel Buildings In the current study, ULL and TLL patterns are employed to evaluate and monitor the development of yielding in MSBs at the global yield and collapse. As depicted in Figure 5.1, the initial yielding occurs in the horizontal components of the benchmark MSBs before affecting the vertical members. Figure 5.17 shows the development of the plastic hinge formation for the MSBs at various performance levels: global yielding and collapse levels. Larger plastic hinges are formed in horizontal members at global yield and collapse than their vertical counterparts, as depicted in Figure 5.17. This reflects that energy dissipation is primarily witnessed in the horizontal elements of all the selected benchmark MSBs, thereby supporting the principles of the SCWB concept. The developments of plastic hinges initiated at beam ends on lower storeys and progressively propagated to upper storeys. Plastic hinges at the lower part of the building are formed later. It is observed that taller buildings tend to develop more plastic hinges than shorter ones due to the increased number of structural members with increasing the building height. 5.3.4.1. RC High-rise buildings In the current study, the formation of plastic hinges is evaluated and the development of different member damage modes in the RC high-rise benchmark buildings is monitored in the ISAs under the ULL loading pattern. The formation of the first hinging is observed in the horizontal elements, followed by the vertical elements in all the benchmark buildings, as shown in Figures 5.18 to 5.20. This reflects that energy dissipation is primarily witnessed in the horizontal elements of all three selected benchmark RC buildings, thereby supporting the principles of the SCWB concept. In addition to plastic hinges, the developments of concrete crushing in unconfined and confined concrete are also monitored for the nine benchmark buildings divided into three sets (40S-B, 60S-B and 60S-D) at global yield and collapse levels. The complete results related to member damage developments in the 40S-B, 60S-B and 60S-D RC high-rise building sets are presented in Figures 5.18 to 5.20, respectively. 90 (a) Plastic hinges at global yielding (b) Plastic hinges at collapse Figure 5.18: Development of plastic hinge formation for the 8S, 12S, 16S and 20S MSBs at various performance levels. 0150300450600ULL TLL ULL TLL ULL TLL ULL TLL8S 12S 16S 20SNo. of Plastic HingesPlastic Hinges-Horizontal Elements Plastic Hinges-Vertical Elements03006009001200ULL TLL ULL TLL ULL TLL ULL TLL8S 12S 16S 20SNo. of Plastic HingesPlastic Hinges-Horizontal Elements Plastic Hinges-Vertical Elements 8S 12S 16S 20S 8S 12S 16S 20S 91 (a) Plastic hinges at global yielding (b) Plastic hinges at collapse Figure 5.19: Development of plastic hinge formation and local damage for 40S-B RC buildings at various performance levels. 010020040S-B-R 40S-B-GI 40S-B-SSNo. of Plastic HingesYield: Hor elements Yield: Ver elementsUnconf conc crushing: Hor elements Unconf conc crushing: Ver elementsConf conc crushing: Hor elements Conf conc crushing: Ver elements010020030040040S-B-R 40S-B-GI 40S-B-SSNo. of Plastic HingesYield: Hor elements Yield: Ver elementsUnconf conc crushing: Hor elements Unconf conc crushing: Ver elementsConf conc crushing: Hor elements Conf conc crushing: Ver elements 40S-B-R 40S-B-R 40S-B-SS 40S-B-SS 92 (a) Plastic hinges at global yielding (b) Plastic hinges at collapse Figure 5.20: Development of plastic hinge formation and local damage for 60S-B RC buildings at various performance levels. 010020030040050060S-B-R 60S-B-GI 60S-B-SSNo. of Plastic HingesYield: Hor elements Yield: Ver elementsUnconf conc crushing: Hor elements Unconf conc crushing: Ver elementsConf conc crushing: Hor elements Conf conc crushing: Ver elements020040060080060S-B-R 60S-B-GI 60S-B-SSNo. of Plastic HingesYield: Hor elements Yield: Ver elementsUnconf conc crushing: Hor elements Unconf conc crushing: Ver elementsConf conc crushing: Hor elements Conf conc crushing: Ver elements 60S-B-SS 60S-B-SS 60S-B-GI 60S-B-GI 93 (a) Plastic hinges at global yielding (b) Plastic hinges at collapse Figure 5.21: Development of plastic hinge formation and local damage for 60S-D RC buildings at various performance levels. 0200400600800100060S-D-R 60S-D-GI 60S-D-SSNo. of Plastic HingesYield: Hor elements Yield: Ver elementsUnconf conc crushing: Hor elements Unconf conc crushing: Ver elementsConf conc crushing: Hor elements Conf conc crushing: Ver elements03006009001200150060S-D-R 60S-D-GI 60S-D-SSNo. of Plastic HingesYield: Hor elements Yield: Ver elementsUnconf conc crushing: Hor elements Unconf conc crushing: Ver elementsConf conc crushing: Hor elements Conf conc crushing: Ver elements 60S-D-GI 60S-D-GI 60S-D-SS 60S-D-SS 94 Figure 5.18 depicts the development of different damage modes for 40S-B set of benchmark buildings at both global and collapse limit states. While Figures 5.19 and 5.20, illustrate the different damage modes for 60S-B and 60S-D, respectively. In all sets of 40S-B, 60S-B and 60S-D RC buildings, the formation of various local damage modes initiated at lower storeys and then progressed towards the upper storeys. Detailed information on the formation of yielding in rebars and the development of damage in the unconfined and confined concrete due to concrete crushing is presented in Appendix B. As shown in Figure 5.19, the buildings with vertical geometric irregularity exhibited less member damage than the regular and soft storey structures. This is due to the fewer structural members in the vertical geometric irregularity buildings due to the reduced floor footprint compared to other buildings. For the buildings with soft storey irregularity, comparable member damage to the regular structures was observed at the global yield and collapse levels, with only more extensive unconfined concrete crushing in the former structures at the collapse limit state. The presented results for the local damage assessment of regular and irregular high-rise buildings support the design code provisions, which do not mandate additional seismic loads for the geometric and soft storey irregularities, unlike other types of severe vertical irregularities. 5.4. Multi-record Bidirectional Incremental Dynamic Analysis (MBIDA) Due to its inherent limitations, the ISA procedure may be unreliable in capturing the seismic response precisely, particularly for complex and long-period structures such as high-rise buildings when subjected to severe seismic events. Additionally, this approach may not adequately account for the various vibration modes of high-rise buildings, particularly in the post-elastic range. To address the ISA shortfalls, a comprehensive inelastic dynamic analysis approach is adopted to accurately assess the seismic response of the high-rise structures. The time history analysis evaluates the inelastic response of the structure over time using the time histories at a specific seismic intensity. The incremental dynamic analysis evaluates the comprehensive response of the structure till it reaches the collapse. It involves conducting multi-step inelastic response history analysis on a chosen set of seismic records, scaled to different intensity levels till the structure approaches global dynamic instability potentially leading to the collapse. To address the limitations associated with ISA, a comprehensive framework shown in Figure 1.2, which involves the computationally demanding MBIDA, is employed in the 95 present study to assess the seismic design coefficients. The MBIDA procedure realistically assesses the response of the high-rise structures to the earthquake records, considering an incremental increase in intensity. Extensive 3D-MBIDAs are performed on the benchmark building sets. The 26 bidirectional natural records shown in Figures 4.7 and 4.8 are used in the 3D-MBIDAs. Both horizontal orthogonal components of the selected earthquake records are scaled with a uniform increment of 0.08g, starting from a PGA of 0.08g until 1.28g. The IDRs of the selected benchmark buildings at the first yielding, system yield level, and structural collapse level are monitored using the MBIDA curves. These curves cover the structural response till collapse with proper records scaling [151-153]. Selecting an appropriate intensity measure (IM) is essential for developing the MBIDA curves. Several IMs have been proposed in earlier studies [152-156]. The PGA measures the maximum ground acceleration at a specific location during an earthquake, offering essential information about ground shaking intensity, typically expressed in gravity units. On the other hand, spectral displacement (SD) assesses a structure's displacement response at specific periods or frequencies during seismic activity derived from the spectral acceleration response spectrum. It elucidates how a structure's displacement varies with differing ground motion frequencies. Lastly, spectral acceleration (SA) quantifies a structure's maximum acceleration response during earthquake motion at specific periods or frequencies. Several previous studies employed PGA as the IM in determining the seismic response of buildings at various intensity levels [101, 123, 136, 157-161]. Accordingly, PGA is employed as the IM in this study to evaluate the seismic behaviour of the selected set of MSBs and three sets of RC high-rise buildings [162, 163]. The prediction of bidirectional seismic response of these nine buildings is discussed in the following sections. 5.4.1. Seismic Response Prediction of MSBs through 3D MBIDA Over 1700 3D-MBIDAs are conducted using PGA as the IM and the IDR as the primary global damage measures (DM) to generate the MBIDA curves of the benchmark MSBs. The primary objective of this extensive analysis is to monitor and record the seismic response across various limit states until each of the selected benchmark MSBs reaches the onset of collapse. Critical global response parameters are derived from this comprehensive analysis. These parameters include base shear, top displacement, and IDR. Figure 5.21 illustrates the MBIDA curves for all four MSBs generated from the selected 26 input 96 ground motions. These curves are further utilized to identify the limit states and evaluate the seismic response factors, as subsequently discussed. Figure 5.22: MBIDA curves of MSBs from 3D dynamic response simulation 5.4.2. Seismic Response Prediction of RC buildings through 3D MBIDA In the current study, over 3800 3D-MBIDAs are performed to generate the MBIDA curves of the benchmark high-rise buildings, with varying heights, different structural systems and irregularities, using PGA as the IM and the IDR as the global damage measure (DM). This comprehensive analysis facilitates monitoring and recording the seismic behaviour of each set of the 40S-B, 60S-B and 60S-D benchmark RC high-rise buildings at different limit states till they reach the point of collapse. Several vital global structural response parameters are obtained using MBIDAs, which include base shear, IDR, and roof displacement. The initial yield and structural collapse performance criteria obtained from the incremental dynamic analysis are mapped on MBIDA curves, which are obtained from the selected 26 natural earthquake records, as shown in Figures 5.22 to 5.24. The complete results of these extensive MBIDAs are processed, tabulated, and documented elsewhere. The MBIDA curves are used to evaluate and verify the seismic design coefficients, as discussed in the following sections.0.00.20.30.50.60.81.01.11.30.0 1.0 2.0 3.0 4.0Peak Ground Acceleration (g)Maximum Interstorey Drift (%)8S MBIDA Curves16% IDA Fractile50% IDA Fractile84% IDA FractileMBIDA CurvesCollapse PointsYielding Points0.00.20.30.50.60.81.01.11.30.0 1.0 2.0 3.0 4.0Peak Ground Acceleration (g)Maximum Interstorey Drift (%)12S MBIDA Curves16% IDA Fractile50% IDA Fractile84% IDA FractileMBIDA CurvesCollapse PointsYielding Points0.00.20.30.50.60.81.01.11.30.0 1.0 2.0 3.0 4.0Peak Ground Acceleration (g)Maximum Interstorey Drift (%)16S MBIDA Curves16% IDA Fractile50% IDA Fractile84% IDA FractileMBIDA CurvesYielding PointsCollapse Points0.00.20.30.50.60.81.01.11.30.0 1.0 2.0 3.0 4.0Peak Ground Acceleration (g)Maximum Interstorey Drift (%)20S MBIDA Curves16% IDA Fractile50% IDA Fractile84% IDA FractileMBIDA CurvesYielding PointsCollapse Points97 Figure 5.23: MBIDA curves of 40S-B benchmark buildings set obtained from 3D dynamic response simulation. Figure 5.24: MBIDA curves of 60S-B benchmark buildings set obtained from 3D dynamic response simulation.0.000.160.320.480.640.800.961.121.280.0 0.5 1.0 1.5 2.0 2.5 3.0Peak Ground Acceleration (g)Maximum Interstorey Drift (%)40S-B-R MBIDA Curves16% IDA Fractile50% IDA Fractile84% IDA FractileMBIDA CurvesCollapse PointsYielding Points0.000.160.320.480.640.800.961.121.280.0 0.5 1.0 1.5 2.0 2.5 3.0Peak Ground Acceleration (g)Maximum Interstorey Drift (%)40S-B-GI MBIDA Curves16% IDA Fractile50% IDA Fractile84% IDA FractileMBIDA CurvesCollapse PointsYielding Points0.000.160.320.480.640.800.961.121.280.0 0.5 1.0 1.5 2.0 2.5 3.0Peak Ground Acceleration (g)Maximum Interstorey Drift (%)40S-B-SS MBIDA Curves16% IDA Fractile50% IDA Fractile84% IDA FractileMBIDA CurvesCollapse PointsYielding Points0.000.160.320.480.640.800.961.121.280.0 0.5 1.0 1.5 2.0 2.5 3.0Peak Ground Acceleration (g)Maximum Interstorey Drift (%)60S-B-R MBIDA Curves16% IDA Fractile50% IDA Fractile84% IDA FractileMBIDA CurvesCollapse PointsYielding Points0.000.160.320.480.640.800.961.121.280.0 0.5 1.0 1.5 2.0 2.5 3.0Peak Ground Acceleration (g)Maximum Interstorey Drift (%)60S-B-GI MBIDA Curves16% IDA Fractile50% IDA Fractile84% IDA FractileMBIDA CurvesCollapse PointsYielding Points0.000.160.320.480.640.800.961.121.280.0 0.5 1.0 1.5 2.0 2.5 3.0Peak Ground Acceleration (g)Maximum Interstorey Drift (%)60S-B-SS MBIDA Curves16% IDA Fractile50% IDA Fractile84% IDA FractileMBIDA CurvesCollapse PointsYielding Points98 Figure 5.25: MBIDA curves of 60S-D benchmark buildings set obtained from 3D dynamic response simulation. 5.5. Concluding Remarks 5.5.1. Preliminary and Detailed Assessment of MSBs The MSBs exhibited a reduction in stiffness at different damage stages, including the global yield, ultimate strength, and collapse. The average stiffness modifiers relative to initial stiffness at these three stages were 0.82, 0.37, and 0.34. These stiffness modifiers can be used in the elastic analysis of comparable MSBs. Plastic hinges were developed at beam ends of the lower storey levels, then propagated to upper levels, and observed later at the base of vertical elements. This strong-column weak-beam mechanism agreed with the design code principles of having the dissipation of the energy mainly in horizontal structural members. The MBIDA provided key insights into the nonlinear seismic performance of the benchmark MSBs, enabling assessing design modification coefficients. These curves are utilized for identifying the limit states. 0.000.160.320.480.640.800.961.121.280.0 0.5 1.0 1.5 2.0 2.5 3.0Peak Ground Acceleration (g)Maximum Interstorey Drift (%)60S-D-R MBIDA Curves16% IDA Fractile50% IDA Fractile84% IDA FractileMBIDA CurvesCollapse PointsYielding Points0.000.160.320.480.640.800.961.121.280.0 0.5 1.0 1.5 2.0 2.5 3.0Peak Ground Acceleration (g)Maximum Interstorey Drift (%)60S-D-GI MBIDA Curves16% IDA Fractile50% IDA Fractile84% IDA FractileMBIDA CurvesCollapse PointsYielding Points0.000.160.320.480.640.800.961.121.280.0 0.5 1.0 1.5 2.0 2.5 3.0Peak Ground Acceleration (g)Maximum Interstorey Drift (%)60S-D-SS MBIDA Curves16% IDA Fractile50% IDA Fractile84% IDA FractileMBIDA CurvesCollapse PointsYielding Points99 5.5.2. Preliminary and Detailed Assessment of RC high-rise buildings he benchmar structuresâ rebar yielding sequence indicated initial signs of first local yielding in horizontal elements, followed by vertical elements, validating the design code strong column-weak beam concept. The first yield overstrength factors from ISA were more conservative than those from MBIDA due to the influence of higher mode effects of high-rise buildings. The confined concrete crushing correlated to the onset of global yielding. The local damage assessment of regular and irregular high-rise buildings supported the design code provisions for not mandating additional seismic loads for the geometric and soft storey irregularities. The benchmark buildings exhibited continuous stiffness reduction at different performance levels due to the development of steel yielding and concrete cracking. The average stiffness modifiers relative to initial stiffness at global yield, ultimate strength, and collapse levels were 0.83, 0.50, and 0.43, respectively. The recommended uncracked and cracked wall effective stiffness by ACI and CSA of 0.70 and 0.35, respectively, are conservative when compared with the observed effective stiffness of the nine benchmark high-rise buildings at global yield and collapse of 0.82 and 0.45, respectively. The results confirm that the benchmark RC high-rise buildings exhibit comparable overstrength values at various strength levels in the regular and irregular buildings. The results reflect the insignificance of the geometric and soft storey irregularities on the overstrength factors. The observed overstrength values estimated at the ultimate strength ranged between 2.62 to 2.98, confirming adequacy over the design code recommended value of 2.5. 100 6 Verification of Seismic Response Factors 6.1. Seismic Design Coefficients In the current study, seismic design coefficients of a set of MSB and three sets of RC high-rise buildings, namely: overstrength factor (Ω), response modification coefficient (R), and deflection amplification coefficient (Cd) are evaluated using the results from MBIDAs. The PGA and IDR at the yield and collapse are monitored from the MBIDA curves for the set of 26 natural earthquake records. The R coefficient is defined as the ratio of PGA at collapse (PGA,c) to PGA at yield (PGA,y) when combined with the first yield overstrength (Ωfy). Similarly, the Cd coefficient is expressed as the ratio of the IDR at collapse (IDR,c) to IDR at yield (IDR,y) in the current study [13, 87]. The seismic design coefficients for the set of MSBs with varying heights, and three sets of RC high-rise benchmark buildings with varying heights, structural systems and irregularities are discussed in the following sections. It is noteworthy that the methodologies adopted in this study to assess the seismic design coefficients for MSBs, and RC high-rise buildings are depicted in Figures 1.1 and 1.2, respectively [164]. 6.2. Evaluation of Overstrength Factors (Ω) using ISAs and MBIDAs The reserve strength of the thirteen-benchmark steel and RC buildings is evaluated in the current study using the ISAs and MBIDAs. he Ω factor is defined as a ratio of yield strength (Vy) to the design strength (Vs), and Ωfy factor is expressed as a ratio of the first yield strength (Vfy) to the design strength (Vs), as depicted in Figure 2.3 [13, 20, 136]. Figures 5.1 and 5.4 to 5.6, illustrate that the selected MSBs and RC high-rise benchmark buildings, experienced the lateral load levels at the initial yielding and the ultimate strength confirming adequacy over the design code recommended values. The assessment of these coefficients for the MSBs and RC benchmark buildings is discussed in the subsequent sections. 6.2.1. First Yield Overstrength of MSBs The design modification coefficients of MSBs are evaluated based on the results obtained from MBIDAs. In the case of adequately designed MSBs, a structure made of steel elements is considered to reach a state of yielding when any of the structureâs most stressed elements attains the yield capacity. To estimate the structural overstrength at the initial 101 indication of yielding (Ωfy) for the benchmark MSBs, a comprehensive comparison is made between the results of ISAs and MBIDAs of the MSBs [20]. Figure 6.1 compares the first yield overstrength from ISAs and MBIDAs of the benchmark MSBs. It is evident from Figure 4 that the Ωfy values obtained for benchmark MSBs employing ISA are observed lo er than the Ωfy values determined from the MBIDA results. This difference is primarily attributed to the impact of higher mode effects on taller steel buildings, which lead to significant amplification of the base shear of the MSBs during MBIDAs. This discrepancy highlights a notable contrast between ISA and MBIDA analysis outcomes, as established in previous studies [101, 136]. It is noteworthy that a marginal change in the first yield overstrength is observed between BISA and ISA. Due to the bidirectional loading, the first significant yield occurs slightly earlier than the ISA, as shown in Figure 6.1. Consequently, for a conservative assessment of the R factors, the Ωfy values calculated from ISAs are employed for the MSBs. Figure 6.1: Comparison of structural overstrength at first yield (â¦fy) of MSBs from ISA, BISA, and MBIDA. 6.2.2. First Yield Overstrength of RC High-rise Buildings The results obtained from MBIDAs are used to evaluate the seismic design coefficients of the three selected high-rise buildings. As previously discussed in the ISA results, in a well-designed RC building, the first observation of yielding (Ωfy) usually occurs at a higher intensity level in comparison to the design intensity. A structure is considered to have reached the state of significant yielding when one of its most stressed elements reaches its yield strength. This criterion is assumed when the strain in the longitudinal tensile reinforcement exceeds the yield strain of steel. An extensive comparison between the results of ISAs and MBIDAs is made to evaluate the structural overstrength at first significant yielding (Ωfy) [20, 90]. Figure 6.2 compares the initial yield overstrength obtained from ISA and MBIDA for the RC high-rise benchmar buildings. he Ωfy values from the ISA are lower than those obtained from MBIDA. The primary reason for this 0.01.02.03.08 Storey 12 Storey 16 Storey 20 Storey2.01 2.04 2.012.142.09 2.12 2.192.212.61 2.682.75 2.79First Yield OverstrengthBISA ISA MBIDA102 difference is the influence of higher mode effects of high-rise buildings accounted for in MBIDA, as discussed earlier, resulting in a considerable increase in the base shear of the benchmark buildings during dynamic response simulation. This variation between ISA and MBIDA analysis outcomes underscores a significant contrast, which was also concluded in earlier studies [101, 136]. Accordingly, in the current study, the Ωfy values obtained from ISAs are used to provide a conservative evaluation of the seismic design coefficients. (a) First yield overstrength of 40S-B buildings (b) First yield overstrength of 60S-B buildings (c) First yield overstrength of 60S-D buildings Figure 6.2: Comparison of structural overstrength at first yield (â¦fy): (a) 40S-B, (b) 60S-B, and (c) 60S-D RC building sets from ISA and MBIDA. 6.3. Intensity and Damage Measures (IM and DM) at Yield and Collapse Intensity measures (IM) and damage measures (DM) are important to evaluate the seismic design coefficients, R and Cd. The MBIDAs results obtained from 26 natural earthquake records are used in the monitoring of these measures. The PGAs at first significant yield and collapse levels are monitored as the IMs for evaluating the R coefficients, while IDRs at first significant yield and collapse are considered as the DMs for evaluating the Cd coefficients of the benchmark buildings. Further details on the IMs and DMs for both the MSBs and the benchmark RC high-rise buildings are discussed in the following sections. 0.00.51.01.52.02.53.040S-B-R 40S-B-GI 40S-B-SS1.89 1.841.482.70 2.652.12First Yield OverstrengthISA MBIDA0.00.51.01.52.02.560S-B-R 60S-B-GI 60S-B-SS1.571.45 1.421.971.80 1.79First Yield OverstrengthISA MBIDA0.00.51.01.52.02.53.060S-D-R 60S-D-GI 60S-D-SS1.661.751.472.632.512.01First Yield OverstrengthISA MBIDA103 The MBIDAs conducted for MSBs and RC high-rise buildings under the influence of twenty-six natural seismic records are monitored until both the first yielding point and collapse limit states are satisfied. The IM and DM from different input ground motions are closely observed to monitor the initial yield and collapse and related PGAs to establish the ground motion-dependent component of the response modification coefficient for all MSBs. Simultaneously, the respective IDRs corresponding to the yield and collapse are recorded to evaluate the deflection amplification factors. Establishing a reliable criterion that aligns with the collapse prevention limit state is paramount to assessing the structure's seismic response and determining the R coefficient [69, 165-167]. The collapse performance criterion, among other limit states, is selected based on the current study's findings obtained from ISA and MBIDA, as presented in Table 7.1. The primary collapse criterion in this study is selected based on IDR, as elaborated in subsequent sections. Beyond the selected collapse limit, the effects of P-delta (P-Î) become significant and contribute to a reduction in lateral resistance, potentially leading to structural collapse. The MBIDAs performed on the RC building sets using 26 natural earthquake records applied simultaneously in both orthogonal directions are underta en until all buildingsâ initial yield and collapse limits are identified. The seismic performance is monitored carefully by observing the IM and DM from various earthquake records. The PGA values representing the IM at yield and collapse are recorded to identify the ground motion-dependent component of the R coefficient for all the benchmark buildings. Similarly, the respective IDR values representing the DM at yield and collapse are monitored to evaluate the Cd coefficient for all the benchmark buildings. Moreover, it is paramount to establish dependable criteria corresponding to the limit state for identifying different structural performance levels of high-rise buildings while assessing the seismic response to evaluate the R coefficients [166]. The selection of the limit states is based on the findings in the current study results obtained from the ISAs and MBIDAs supported by the code recommendation, as illustrated in Table 7.2. IDRs are used in the current study to establish the collapse criterion. 6.4. Evaluation of Seismic Design Coefficients (R and Cd) The seismic design coefficients, R and Cd, of both MSBs and benchmark RC high-rise buildings are computed based on the results obtained over 5500 MBIDAs. The PGAs and 104 the IDRs of the respective MSB and RC benchmark buildings at both the first significant yield and the collapse levels are monitored for each record from the MBIDAs. The overstrength at the first yield is computed as explained earlier using the results of ISAs and MBIDAs. The assessment of the seismic design coefficients for the MSBs and the three sets of RC benchmark buildings are discussed in the following sections. 6.4.1. Multi-storey Steel Buildings The MBIDA results for the MSBs subjected to twenty-six natural bidirectional seismic records are presented in Figure 6.3. Additionally, these figures include the ratios of collapse P A and IDRs to those at yield. hen combined ith the Ωfy, the presented ratios in Figure 15 are employed to evaluate the R and Cd factors. The first formation of significant yield and indication of collapse for the MSBs are summarized elsewhere. The ratios of IDR at collapse to that of yield consistently exhibited lower values than the corresponding PGA ratios for the benchmark MSBs, as depicted in Figure 6.3. Notably, the average difference between these ratios falls within the range of 3.5% to 7.3%, with the difference increasing as the building height witnessed an increase. This trend reflects the appropriate level of conservatism in equating the Cd with the R factor. The presented results in Figure 6.3 validate the recommended design code approach for Cd factors, which are lower than the R coefficients [32]. The code-recommended response modification coefficient (R Code EN/IBC) considered for MSBs is presented along with the median R values in Figure 6.4. These R median values obtained from the twenty-six bidirectional natural seismic records are calculated from the median PGA values at collapse and those at yield, as shown in Figure 6.4. It is evident from Figure 6.4 that the evaluated median values of the response modification coefficient for the MSBs are conservative when compared with the code coefficients [107, 111]. The summarized information on the seismic modification coefficients (R, Cd, and Ω) for the selected set of MSBs is depicted in Figure 6.5. The results shown in Figures 6.4 and 6.5 highlight that as building height increases from 8 to 20 storeys, the safety margin associated with the R coefficient grows, ranging from 34% to 45%. The response modification and deflection amplification coefficients show the adequate safety and conservatism of the design codes for MSBs of varying heights. The presented results in Figures 6.4 and 6.5 also suggest the possibility of increasing R factors, potentially leading to more cost-effective 105 designs. For brevity, the results of the seismic design coefficients of the MSBs are summarised in Table 6.1. (a) Yield and collapse PGAs ratios of MSBs (b) Yield and collapse IDRs of MSBs Figure 6.3: MBIDA results of MSBs showing collapse-to-yield ratios obtained from twenty-six bidirectional input earthquake records: (a) PGA, and (b) IDR. 0.00.20.30.50.60.81.01.11.31.41.6R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26PGA (g)Records8 Storey PGA,y PGA,c1.120.40 PGAc/y= 2.880.01.02.03.04.05.0R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26IDR (%)Records8 Storey IDR,y IDR,c3.521.28IDRc/y= 2.740.00.20.30.50.60.81.01.11.31.41.6R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26PGA (g)Records12 Storey PGA,y PGA,c1.160.40 PGAc/y= 2.900.01.02.03.04.05.0R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26IDR (%)Records12 Storey IDR,y IDR,c3.661.30IDRc/y= 2.820.00.20.30.50.60.81.01.11.31.41.6R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26PGA (g)Records16 Storey PGA,y PGA,c1.160.40PGAc/y= 2.900.01.02.03.04.05.0R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26IDR (%)Records16 Storey IDR,y IDR,c3.661.27IDRc/y= 2.860.00.20.30.50.60.81.01.11.31.41.6R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26PGA (g)Records20 Storey PGA,y PGA,c1.200.40PGAc/y= 3.000.01.02.03.04.05.0R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26IDR (%)Records20 Storey IDR,y IDR,c3.551.28IDRc/y= 2.77 106 Figure 6.4: Response modification coefficients of MSBs obtained from 3D MBIDAs using twenty-six bidirectional earthquake records. Figure 6.5: Response modification coefficients (R, Cd and Ω) of MSBs obtained from 3D-MBIDAs. 6.4.2. RC High-rise Buildings Figures 6.6 to 6.8 illustrate the MBIDA results of the three RC high-rise benchmark building sets showing PGA and IDR ratios at their first yield (PGA,y and IDR,y, respectively) and collapse (PGA,c and IDR,c, respectively) obtained from 26 bidirectional earthquake records. The PGA ratios of the collapse to yield (i.e., PGA,c/PGA,y) shown in Figures 6.6 to 6.8 hen combined ith the Ωfy shown in Figure 6.2 are employed to evaluate the R coefficient. Similarly, the IDR ratios of the collapse to yield (i.e., 5.64 5.816.06 6.2302468101214168S 12S 16S 20SR FactorsRecordsRecords Median R Median C/Y R Code EN R Code IBC012345678 Storey 12 Storey 16 Storey 20 Storey3.133.413.023.393.685.593.44 3.385.64 5.816.06 6.23Seismic Response Factors of MSBsR - code: 4.0 (EN) and 4.5 (IBC), Cd - code: 4.0, â¦ - code: 3.0 Cd â¦ R107 IDR,c/IDR,y) shown in Figures 6.6 to 6.8 are employed to evaluate the Cd coefficients [117]. The IDR,c/IDR,y ratios consistently displayed lower values than the corresponding PGA,c/PGA,y ratios, as depicted in Figures 6.6 to 6.8. The average difference between these ratios for the 40 and 60-storey bearing wall building sets ranged between 6.7% to 16.7%. The average difference for the 60-storey dual building set ranged between 7.4% and 11.4%, respectively. The presented results in Figures 6.6 to 6.8 validate the design code approach for Cd factors, which are equal to or lower than the R coefficients [32]. (a) Yield and collapse PGAs ratios of MSBs (b) Yield and collapse IDRs of MSBs Figure 6.6: MBIDA results of 40S-B RC building sets showing PGA and IDR ratios at collapse and first yield obtained from 26 bidirectional earthquake records. 0.00.20.30.50.60.81.01.11.31.41.6R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26PGA (g)Records40S-B-R PGA,y PGA,c1.120.32 PGAc/y= 3.500.00.51.01.52.02.53.03.54.0R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26IDR (%)Records40S-B-R IDR,y IDR,c2.380.78IDRc/y= 3.050.00.20.30.50.60.81.01.11.31.41.6R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26PGA (g)Records40S-B-GIPGA,y PGA,c1.120.32 PGAc/y= 3.500.00.51.01.52.02.53.03.54.0R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26IDR (%)Records40S-B-GI IDR,y IDR,c2.300.74IDRc/y= 3.130.00.20.30.50.60.81.01.11.31.41.6R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26PGA (g)Records40S-B-SS PGA,y PGA,c1.120.32PGAc/y= 3.500.00.51.01.52.02.53.03.54.0R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26IDR (%)Records40S-B-SS IDR,y IDR,c2.200.69IDRc/y= 3.19 108 The median R coefficients derived from 26 bidirectional natural earthquake records estimated PGA,c/PGA,y ratios for all three sets of high-rise benchmark buildings are shown in Figure 6.9. The presented results in Figure 6.9 indicate that the median values evaluated for the response modification coefficients are higher than the code-recommended values, confirming an adequate margin of safety in all three sets of benchmark buildings [32]. The summarized seismic design coefficients (R, Cd, and Ω) for all three sets of RC buildings are illustrated in Figure 6.10. (a) Yield and collapse PGAs ratios of MSBs (b) Yield and collapse IDRs of MSBs Figure 6.7: MBIDA results of 60S-B RC building sets showing PGA and IDR ratios at collapse and first yield obtained from 26 bidirectional earthquake records. 0.00.20.30.50.60.81.01.11.31.41.6R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26PGA (g)Records60S-B-R PGA,y PGA,c1.150.32 PGAc/y= 3.580.00.51.01.52.02.53.03.54.0R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26IDR (%)Records60S-B-R IDR,y IDR,c2.400.80IDRc/y= 3.000.00.20.30.50.60.81.01.11.31.41.6R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26PGA (g)Records60S-B-GI PGA,y PGA,c1.120.32 PGAc/y= 3.500.00.51.01.52.02.53.03.54.0R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26IDR (%)Records60S-B-GI IDR,y IDR,c2.400.73IDRc/y= 3.280.00.20.30.50.60.81.01.11.31.41.6R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26PGA (g)Records60S-B-SS PGA,y PGA,c1.240.32PGAc/y= 3.880.00.51.01.52.02.53.03.54.0R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26IDR (%)Records60S-B-SS IDR,y IDR,c2.180.62 IDRc/y= 3.54 109 (a) Yield and collapse PGAs ratios of MSBs (b) Yield and collapse IDRs of MSBs Figure 6.8: MBIDA results of 60S-D RC building sets showing PGA and IDR ratios at collapse and first yield obtained from 26 bidirectional earthquake records. Based on the results shown in Figure 6.9, the safety margins for the R coefficients, calculated as median R to R code ratios, range from 42% to 63% for the bearing wall building sets, while this range is between 7% to 21% for the 60-storey dual RC building set. The margin of safety is reduced for irregular buildings compared to their regular counterpart. Similarly, the deflection amplification coefficients exhibit a safety margin, calculated as median Cd to Cd code ratios, ranging between 14% to 25% for the bearing wall building sets, while this range is between 15% to 23% for the dual building set. The 0.00.20.30.50.60.81.01.11.31.41.6R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26PGA (g)Records60S-D-R PGA,y PGA,c1.200.32PGAc/y= 3.750.00.51.01.52.02.53.03.54.0R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26IDR (%)Records60S-D-R IDR,y IDR,c2.240.65IDRc/y= 3.450.00.20.30.50.60.81.01.11.31.41.6R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26PGA (g)Records60S-D-GI PGA,y PGA,c1.130.32PGAc/y= 3.530.00.51.01.52.02.53.03.54.0R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26IDR (%)Records60S-D-GI IDR,y IDR,c2.220.70IDRc/y= 3.170.00.20.30.50.60.81.01.11.31.41.6R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26PGA (g)Records60S-D-SS PGA,y PGA,c1.240.32PGAc/y= 3.930.00.51.01.52.02.53.03.54.0R1R2R3R4R5R6R7R8R9R10R11R12R13R14R15R16R17R18R19R20R21R22R23R24R25R26IDR (%)Records60S-D-SS IDR,y IDR,c2.200.60IDRc/y= 3.66 110 R and the Cd coefficients demonstrate considerable conservatism and safety compared to the code-recommended values. The results depicted in Figures 6.9 and 6.10 confirm the potential for increasing the design R coefficients, resulting in more cost-effective designs without compromising the safety of regular and irregular high-rise buildings. For brevity, the results of the seismic design coefficients are summarised in Table 6.1. Figure 6.9: Response modification coefficients (R) of 40S-B, 60S-B and 60S-D sets of high-rise buildings based on 3D-MBIDAs. 6.52 6.445.92024681012141640S-B-R 40S-B-GI 40S-B-SSR FactorsRecordsRecords Median R Median C/Y R Code6.08 5.80 5.68024681012141660S-B-R 60S-B-GI 60S-B-SSR FactorsRecordsRecords Median R Median C/Y R Code6.646.185.88024681012141660S-D-R 60S-D-GI 60S-D-SSR FactorsRecordsRecords Median R Median C/Y R Code111 Figure 6.10: Seismic design coefficients (R, Cd and Ω) of 40S-B, 60S-B and 60S-D sets of high-rise buildings based on 3D-MBIDAs. 024640S-B-R 40S-B-GI 40S-B-SS2.83 2.76 2.793.09 3.01 3.156.52 6.445.92Seismic Response Coefficients BuildingsR - code: 4.0 Cd - code: 4.0 â¦ - code: 2.5 â¦ Cd R024660S-B-R 60S-B-GI 60S-B-SS2.83 2.62 2.683.05 3.253.446.085.80 5.68Seismic Response Coefficeints BuildingsR - code: 4.0 Cd - code:4.0 â¦ - code: 2.5 â¦ Cd R024660S-D-R 60S-D-GI 60S-D-SS2.91 2.89 2.863.483.203.826.646.185.88Seismic Response Coefficients BuildingsR - code: 5.5 Cd - code: 4.5 â¦ - code: 2.5 â¦ Cd R112 Table 6.1: Summary of seismic design coefficients of MSBs and 40S-B, 60S-B, and 60-D RC buildings. Ref Building Information Reference Structures Frame System Wall System Dual System R Cd â¦ R Cd â¦ R Cd â¦ Code EN 2004 ASCE/SEI 7-22 4.00* 4.50# 4.00 4.00 3.00 3.00 4.00 4.00 2.50 5.50 4.50 2.50 Steel Structure (MSBs) 8 Storey 6.00 3.13 3.70 12 Storey 6.15 3.41 3.61 16 Storey 6.40 3.02 3.46 20 Storey 6.63 3.39 3.38 40S Bearing Wall System 40S-B-R 6.52 3.09 2.83 40S-B-GI 6.44 3.01 2.76 40S-B-SS 5.92 3.15 2.79 60S Bearing Wall System 60S-B-R 6.08 3.05 2.83 60S-B-GI 5.80 3.25 2.62 60S-B-SS 5.68 3.44 2.68 60S Dual Wall System 60S-D-R 6.64 3.48 2.91 60S-D-GI 6.18 3.20 2.89 60S-D-SS 5.88 3.82 2.86 Note: Overstrength values are calculated from IPAs. *Behaviour factor for 8 and 12 S # R factor for 16 and 20S 6.5. Concluding Remarks The code-recommended seismic design modification coefficients of the MSBs and the three sets of RC high-rise buildings were verified by conducting over 5500 3D ISAs and MBIDAs using 26 natural earthquake records. The most important conclusions are summarized under the following: 6.5.1. Multi-storey Steel Buildings The MBIDA provided key insights into the nonlinear seismic performance of the benchmark MSBs, enabling assessing design modification coefficients. The ratios of IDR at collapse to that at yield were consistently lower than corresponding PGA ratios. This verified the design code approach in adopting a lower deflection amplification factor, Cd, than the response modification coefficient, R. The calculated design modification coefficients confirm the satisfactory factors adopted by the design codes for MSBs of varying heights. The median R coefficients of the benchmark MSBs were higher than the values adopted by the design codes, indicating a substantial safety margin in these structures. The safety margin associated with the R factor ranged from 34% to 45%. The 113 calculated overstrength factor, â¦, as conservative, on average, 8% higher than the design values. The Cd factor was also conservative as it was, on average, 19% lower than the code deflection amplification factors. The outcomes of this study suggest the possibility of increasing R factors initially by at least 10%, potentially leading to more cost-effective designs. 6.5.2. RC High-rise Buildings The IDR,c/IDR,y ratios consistently displayed lower values than the corresponding PGA,c/PGA,y ratios, ranging between 6.7% to 16.7%, which validated the design code approach for assigning equal or lower Cd factors than the R coefficients. The deflection amplification coefficients exhibited a 14% to 25% safety margin. The safety margins for the R coefficients ranged from 42% to 63% for the bearing wall buildings and between 7% to 21% for dual buildings. The margin of safety was lower for vertically irregular buildings compared to their regular counterpart. The current study suggests the potential for increasing the R coefficients initially by 10% for bearing wall buildings and by 5% for dual RC structures, resulting in more cost-effective designs for regular and irregular high-rise buildings. 114 7 Seismic Fragility Assessment 7.1. Fragility Assessment Fragility curves are vital in addressing the uncertainties and variabilities associated with the structureâs capacity and seismic demand. hese curves are essential for estimating potential physical and related financial losses and guiding decisions regarding seismic retrofitting measures. Such seismic losses carry both direct and indirect consequences. In the context of multi-storey and high-rise buildings, structural damage can lead to significant loss of life and injuries stemming from factors such as structural collapses and fires. Therefore, it is crucial to undertake fragility assessments for multi-storey and high-rise buildings to predict and mitigate these risks effectively. Fragility curves are developed by gathering the damage information using four possible approaches: observational, experimental, analytical, and hybrid techniques [169]. The current study employs the analytical approach as it is the most precise and economical option, which involves developing the damage data through MBIDAs of 3D fibre-based simulation models. Several previous studies adopted various analytical methods in deriving vulnerability relationships, applying simulation of various analysis methods and structural idealizations using structural response either with inter-storey drifts, floor accelerations or floor velocities [154, 158, 170-174]. The current study employs IDRs as the DM in deriving the fragility relationships of the selected MSBs and benchmark RC high-rise buildings. The development of fragility relationships is greatly influenced by the nature of the uncertainties, which are either deterministic or probabilistic. For instance, the uncertainties due to ground motions are probabilistic in nature. These are addressed by selecting a diverse set of input ground motions. Additionally, previous studies concluded the significance of the input ground motion uncertainty over other sources of uncertainties [140, 152]. Whereas the modelling uncertainty is deterministic, which is addressed with the fibre-based modelling approach. In the current study, the inelastic modelling approach and MBIDA use twenty-six bidirectional natural seismic records to address the uncertainties. 115 7.2. Definition of Limit States Limit states play a vital role in the development of fragility curves, as they directly affect the evaluation of building performance levels. In the current study, the fragility relationships of the thirteen benchmark buildings divided further into one set of regular MSBs of varying heights and three sets of RC high-rise buildings of varying heights, structural systems and irregularities are established using three distinct limit states [111]. These limit states represent minor yielding, referred to as immediate occupancy (IO); extensive damage, referred to as life safety (LS); and extensive fracture with buckling for the MSBs and extensive confined concrete crushing in the case of the RC buildings, referred to as collapse prevention (CP). These performance levels are determined using ISAs, multi-record bidirectional time history analysis (MBTHA) and MBIDA obtained from the diverse set of 26 natural earthquake records. The respective limit states for the benchmark regular MSBs ranging from 8 storeys to 20 storeys and three sets of RC high-rise buildings (40S-B, 60S-B, and 60S-D) with different heights, structural systems and irregularities are explained in the following sections. 7.2.1. Multi-storey Steel Buildings The different performance levels, namely immediate occupancy (IO), life safety (LS), and collapse prevention (CP) for the benchmark MSBs are determined using ISAs, MBTHA, and MBIDA at 16%, 50% and 84% fractile values employing PGA as the IM and IDR as the DM. The MBTHA evaluates the inelastic response of the regular MSBs ranging from 8 storeys to 20 storeys using the selected 26 bidirectional time histories at different seismic intensities. Regression analyses are conducted for MBTHA analysis results of the 26 earthquake records to arrive at the 16%, 50%, and 84% fractile values shown in Table 7.1. The incremental dynamic analysis evaluates the response of the structure till it reaches collapse. The 16%, 50%, and 84% IDA curves are derived from MBIDA results of the benchmark MSBs, as shown in Figure 5.21. Based on the slope of the 16%, 50% and 84% of the IDA curves, the IO and CP are identified [101, 135]. The values of the three performance limit states, IO, LS, and CP, are evaluated and compared with those recommended in seismic provisions and earlier research [168, 169], as illustrated in Table 7.1. Accordingly, the below-mentioned three performance limit states (IO, LS, and CP) employed for the regular benchmark MSBs of varying heights ranging from 8 to 20 storeys are selected as 0.76%, 1.44% and 3.48%, respectively. 116 Table 7.1: Performance limit states of MSBs. MSBs Selection Approach Performance limit state (Inter-storey drift ratio, %) IO LS CP 8-storey to 20-storey ISA 0.76 â 0.90 1.44 â 1.58 3.70 â 3.92 MBTHA â 16% 0.80 â 0.92 3.48 â 3.66 MBTHA â 50% 0.89 â 1.22 3.51 â 3.71 MBTHA â 84% 0.91 â 1.24 3.55 â 3.88 MBIDA â 16% 0.82 â 0.83 3.50 â 3.70 MBIDA â 50% 0.89 â 1.28 3.55 â 3.74 MBIDA â 84% 0.93 â 1.34 3.58 â 3.90 Selected performance limit states 0.76 1.44 3.48 7.2.2. RC High-rise Buildings It is paramount to establish dependable criteria corresponding to the limit state for identifying different structural performance levels of benchmark RC high-rise buildings while assessing the seismic response to evaluate the R coefficients [166]. The selection of the limit states is based on the findings in the current study, which were obtained from the ISAs, MBTHAs, and MBIDAs and supported by the code recommendation, as illustrated in Table 7.2. The MBTHA evaluates the inelastic response of the RC high-rise building sets using the selected 26 bidirectional time histories at different seismic intensities. Regression analyses are conducted for MBTHA analysis results of the 26 earthquake records to arrive at the 16%, 50%, and 84% fractile values shown in Table 7.2. The incremental dynamic analysis evaluates the response of the structure till it reaches collapse. The 16%, 50%, and 84% IDA curves are derived from MBIDA results, as shown in Figures 5.22 to 5.24. Based on the slope of the 16%, 50% and 84% of the MBIDA curves, the IO and CP are identified [101, 135]. The values of immediate occupancy, life safety, and collapse prevention are evaluated based on the 16%, 50% and 84% fractile values employing PGA as the IM and IDR as the DM from the above analyses. The respective IDR values at different levels are compared with those recommended in seismic provisions and earlier research [168, 169], as illustrated in Tables 7.2. Accordingly, the three performance limit states, namely: IO, LS and CP, employed for the benchmark RC high-rise bearing wall building sets (40S-B and 60S-B) are 0.52, 0.97, and 2.00, respectively. Similarly, for the benchmark RC high-rise dual building set (60S-D), the three performance limit states employed in the current study are 0.48, 0.76, and 2.00, respectively as shown in Table 7.2. 117 Table 7.2: Performance limit states of the three sets of high-rise buildings conceding different structural systems and irregularities. Ref Selection Approach Reference Structures Limit State â Inter-storey Drift (%) IO LS CP IO LS CP IO LS CP Code ASCE 41 (2007) 0.50 1.00 2.00 0.50 1.00 2.00 0.50 1.00 2.00 Current Study 40 S Reg 40 S VI 40 S SS 40 Storey Bearing Wall System IPA 0.61 0.97 2.50 0.60 0.97 2.50 0.55 1.02 2.50 THA - 16% 0.60 2.20 0.61 2.12 0.53 2.00 THA - 50% 0.72 2.38 0.76 2.17 0.61 2.09 THA - 84% 0.81 2.46 0.83 2.49 0.76 2.20 IDA - 16% 0.65 2.24 0.63 2.28 0.57 2.05 IDA - 50% 0.76 2.42 0.74 2.39 0.65 2.12 IDA - 84% 0.91 2.54 0.97 2.43 0.81 2.24 Selected Limit State 0.60 0.97 2.20 0.60 0.97 2.12 0.53 1.02 2.00 Current Study 60 S Reg 60 S VI 60 S SS 60 Storey Bearing Wall System IPA 0.63 1.22 2.50 0.58 1.16 2.50 0.52 1.08 2.50 THA - 16% 0.62 2.30 0.56 2.18 0.53 2.00 THA - 50% 0.72 2.49 0.70 2.25 0.65 2.14 THA - 84% 0.83 2.65 0.74 2.52 0.71 2.31 IDA - 16% 0.66 2.35 0.69 2.24 0.69 2.07 IDA - 50% 0.74 2.46 0.74 2.33 0.74 2.17 IDA - 84% 0.85 2.58 0.81 2.42 0.81 2.24 Selected Limit State 0.60 1.22 2.30 0.56 1.16 2.18 0.52 1.08 2.00 Current Study 60 S D Reg 60 S D VI 60 S D SS 60 Storey Dual Structural System IPA 0.50 0.86 2.50 0.48 0.79 2.50 0.48 0.76 2.50 THA - 16% 0.51 2.09 0.48 2.04 0.49 2.00 THA - 50% 0.73 2.17 0.72 2.15 0.61 2.15 THA - 84% 0.92 2.24 0.90 2.19 0.89 2.20 IDA - 16% 0.54 2.13 0.52 2.11 0.51 2.03 IDA - 50% 0.91 2.21 0.89 2.18 0.68 2.14 IDA - 84% 0.96 2.28 0.95 2.25 0.98 2.21 Selected Limit State 0.50 0.86 2.09 0.48 0.79 2.04 0.48 0.76 2.00 7.3. Derivation of Fragility Relationships using MBIDAs Over 5500 ISAs and MBIDAs are conducted using twenty-six natural earthquake records to derive the fragility relationships of both benchmark MSBs and RC high-rise buildings. In addition to tracking global response parameters such as IDR, top displacement, and base shear, the formation of plastic hinges is examined in various structural members of all the buildings under investigation to gain a deeper understanding of structural damage levels. For each reference building, 416 data points are plotted, each representing the PGA-IDR values obtained from the inelastic response history analysis. The fragility relationships are 118 expressed graphically with PGAs versus the exceedance probabilities. The power-law equation generated with the trend line of these plots is used in the equation of fragility curves to derive the fragility relationships of the selected MSBs and RC high-rise buildings [170]. The fragility relationships for the benchmark MSBs and the RC buildings are explained in the following sections. 7.3.1. Multi-storey Steel Buildings Figure 7.1 displays the MBIDA results for the regular MSBs with varying heights ranging from 8 to 20 storeys, visually representing their seismic performance. The horizontal lines in these plots serve as the indicators for the adopted three performance criteria (IO, LS, and CP) based on the recommendations outlined in Table 7.1 for each MSB. The seismic response of MSBs with height ranging from 8 storeys to 20 storeys, obtained from the selected diverse set of twenty-six natural records is comparable between the regular moment-resisting MSBs of the respective heights. The MBIDA results from the bidirectional seismic loading yielded consistent outcomes at various PGA levels, from 0.08g to 1.28g. Over sixteen inelastic analyses are performed for each combination of MSB and natural seismic record, starting with an intensity representing half the design PGA of 0.08g and concluding with 1.28g to reach all performance limit states, which ensures equal probability distribution across these intervals. For each benchmark MSB, a total of 416 data points is plotted, with every single point representing the values of PGA-IDR derived from the MBIDAs. The regression equation generated with the trend line of these plots is employed to develop the fragility functions of MSBs, considering the demand, drift capacity, and modelling uncertainties. The latter two uncertainties are considered deterministic, as recommended in previous studies [135, 152, 171, 172]. The fragility relationships of the benchmark MSBs are expressed graphically with PGAs versus the exceedance probabilities of each of the selected MSBs, as illustrated in Figure 7.2. To provide insights into the derived fragility relationships and the differences between MSBs, the results are visualized at different increments of PGAs of 0.16g, 0.32g, 0.64g, and 1.12g. Figure 7.3 illustrates the fragility functions of MSBs for various performance limit states. For the IO and LS performance limit states, the curves illustrate steeper slopes, and the exceedance probability is higher for taller MSBs compared to their shorter counterparts. For the last performance limit state, the curves are represented with flatter slopes due to the loss of stiffness. 119 Figure 7.1: Regression analysis results of MBIDA from twenty-six input ground motions and performance limit states of MSBs. UOC: Undisturbed occupancy, IOC: Impaired occupancy, SD: Structural damage, SC: Structural collapse Figure 7.2: Fragility relationships of MSBs obtained from MBIDAs. y = 4.1058x1.1651R² = 0.78170.02.04.06.08.010.00.00 0.16 0.32 0.48 0.64 0.80 0.96 1.12 1.28Maximum Interstorey Drift (%)Peak Ground Acceleration (g)8SCP: 3.48%LS: 1.44%IO: 0.76%y = 4.3129x0.9478R² = 0.80920.02.04.06.08.010.00.00 0.16 0.32 0.48 0.64 0.80 0.96 1.12 1.28Maximum Interstorey Drift (%)Peak Ground Acceleration (g)12SCP: 3.48%LS: 1.44%IO: 0.76%y = 4.4118x0.9683R² = 0.84230.02.04.06.08.010.00.00 0.16 0.32 0.48 0.64 0.80 0.96 1.12 1.28Maximum Interstorey Drift (%)Peak Ground Acceleration (g)16SCP: 3.48%LS: 1.44%IO: 0.76%y = 4.4209x1.0349R² = 0.82340.02.04.06.08.00.00 0.16 0.32 0.48 0.64 0.80 0.96 1.12 1.28Maximum Interstorey Drift (%)Peak Ground Acceleration (g)20SCP: 3.48%LS: 1.44%IO: 0.76%00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)8 SIO LS CPUOCIOCSDSC00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)12 SIO LS CPUOC IOCSDSC00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)16 SIO LS CPUOC IOCSDSC00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)20 SIO LS CPUOC IOCSDSC120 Figure 7.3: Fragility curve comparisons of limit states of MSBs: IO (top), LS (middle) and CP (bottom). 00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)All Steel Buildings IO @ 1.28 PGA8 S12 S16 S20 SIOCUOC00.10.20.30.40 0.04 0.08 0.12 0.16P(Limit State|GMI)Peak Ground Acceleration (g)All Steel Buildings IO @ 0.16 PGA8 S12 S16 S20 SIOCUOC8S20S00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)All Steel Buildings LS @ 1.28 PGA8 S12 S16 S20 SSDIOC00.10.20.30.40.50.60 0.08 0.16 0.24 0.32P(Limit State|GMI)Peak Ground Acceleration (g)All Steel Buildings LS @ 0.32 PGA8 S12 S16 S20 SSDIOC8S20S00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)All Steel Buildings CP @ 1.28 PGA8 S12 S16 S20 SSDSC00.20.40.60.80 0.16 0.32 0.48 0.64P(Limit State|GMI)Peak Ground Acceleration (g)All Steel Buildings CP @ 0.64 PGA8 S12 S16 S20 SSDSC8S20S121 7.3.2. RC High-rise Buildings The MBIDA results for the three sets of RC high-rise buildings with different structural systems and irregularities, illustrating their seismic performance, are shown in Figures 7.4 to 7.6. The adopted IO, LS, and CP performance criteria for each RC high-rise benchmark building are shown in these Figures by the horizontal lines based on the recommendations provided in Table 7.2. Figures 7.4 to 7.6 indicate comparable seismic responses between the three sets of RC high-rise buildings obtained from the 26 bidirectional natural earthquake records. The MBIDA results of the benchmark RC high-rise buildings obtained from the 26 bidirectional seismic loadings yielded consistent outcomes at various PGA levels, from 0.08g to 1.28g. It is shown in Figures 7.4 to 7.6 that the scatter of the response points obtained from MBIDA increases significantly with increasing ground motion intensity. Therefore, unlike multi-storey buildings which have an average high correlation coefficient (R2) of 0.81, as shown in Figure 7.1, the average R2 for the high-rise bearing wall and dual buildings is 0.655 and 0.61, respectively [164]. The difference in the R2 coefficients is mainly due to the impact of the higher modes on high-rise buildings. Figure 7.4: Regression analysis results of MBIDA from twenty-six input ground motions and performance limit states of 40S-B building set. y = 3.054x0.9777R² = 0.64740.01.02.03.04.05.06.07.00.00 0.16 0.32 0.48 0.64 0.80 0.96 1.12 1.28Maximum Interstorey Drift (%)Peak Ground Acceleration (g)40S-B-RCP: 2.00%LS: 0.97%IO: 0.52%y = 3.4976x0.9702R² = 0.64440.01.02.03.04.05.06.07.00.00 0.16 0.32 0.48 0.64 0.80 0.96 1.12 1.28Maximum Interstorey Drift (%)Peak Ground Acceleration (g)40S-B-GICP: 2.00%LS: 0.97%IO: 0.52%y = 3.5292x0.9686R² = 0.69330.01.02.03.04.05.06.07.00.00 0.16 0.32 0.48 0.64 0.80 0.96 1.12 1.28Maximum Interstorey Drift (%)Peak Ground Acceleration (g)40S-B-SSCP: 2.00%LS: 0.97%IO: 0.52%122 Figure 7.5: Regression analysis results of MBIDA from twenty-six input ground motions and performance limit states of 60S-B building set. Figure 7.6: Regression analysis results of MBIDA from twenty-six input ground motions and performance limit states of 60S-D building set.y = 2.6308x0.9788R² = 0.64290.01.02.03.04.05.06.07.00.00 0.16 0.32 0.48 0.64 0.80 0.96 1.12 1.28Maximum Interstorey Drift (%)Peak Ground Acceleration (g)60S-B-RCP: 2.00%LS: 0.97%IO: 0.52%y = 3.0127x0.9808R² = 0.6390.01.02.03.04.05.06.07.00.00 0.16 0.32 0.48 0.64 0.80 0.96 1.12 1.28Maximum Interstorey Drift (%)Peak Ground Acceleration (g)60S-B-GICP: 2.00%LS: 0.97%IO: 0.52%y = 3.0395x0.9721R² = 0.68310.01.02.03.04.05.06.07.00.00 0.16 0.32 0.48 0.64 0.80 0.96 1.12 1.28Maximum Interstorey Drift (%)Peak Ground Acceleration (g)60S-B-SSCP: 2.00%LS: 0.97%IO: 0.52%y = 2.4031x0.9811R² = 0.63070.01.02.03.04.05.06.07.00.00 0.16 0.32 0.48 0.64 0.80 0.96 1.12 1.28Maximum Interstorey Drift (%)Peak Ground Acceleration (g)60S-D-RCP: 1.99%LS: 0.76%IO: 0.48%y = 2.5333x0.9789R² = 0.62620.01.02.03.04.05.06.07.00.00 0.16 0.32 0.48 0.64 0.80 0.96 1.12 1.28Maximum Interstorey Drift (%)Peak Ground Acceleration (g)60S-D-GICP: 1.99%LS: 0.76%IO: 0.48%y = 2.544x1.0432R² = 0.57620.01.02.03.04.05.06.07.00.00 0.16 0.32 0.48 0.64 0.80 0.96 1.12 1.28Maximum Interstorey Drift (%)Peak Ground Acceleration (g)60S-D-SSCP: 1.99%LS: 0.76%IO: 0.48%123 To ensure equal probability distribution across the scaling intervals, over sixteen inelastic analyses are performed for each high-rise building and natural seismic record combination, starting with an intensity representing half the design PGA of 0.08g and concluding with 1.28g to reach all performance limit states. For each benchmark high-rise building, a total of 416 data points are plotted, with every single point representing the values of IM-DM derived from the MBIDAs. The plots shown in Figures 7.4 to 7.6 generate a regression equation, which is employed to develop the fragility functions of the RC high-rise buildings. These functions are developed considering the demand, drift capacity, and modelling uncertainties. The latter two uncertainties are considered deterministic based on the recommendation of the previous studies [135, 152, 171, 172]. The fragility relationships are expressed graphically with IMs versus the exceedance probabilities, as illustrated in Figures 7.7 to 7.9. Figure 7.7: Fragility relationships of 40S-B building set obtained from MBIDAs. 00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)40S-B-RIO LS CPUOCIOCSDSC00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)40S-B-GIIO LS CPUOCIOCSDSC00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)40S-B-SSIO LS CPUOCIOCSDSC124 Figure 7.8: Fragility relationships of 60S-B building set obtained from MBIDAs. Figure 7.9: Fragility relationships of 60S-D building set obtained from MBIDAs.00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)60S-B-RIO LS CPUOCIOCSDSC00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)60S-B-GIIO LS CPUOCIOCSDSC00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)60S-B-SSIO LS CPUOCIOCSDSC00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)60S-D-RIO LS CPUOCIOCSDSC00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)60S-D-GIIO LS CPUOCIOCSDSC00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)60S-D-SSIO LS CPUOCIOCSDSC125 To provide insights into the derived fragility relationships and the differences between benchmark buildings, the results are visualized at four input ground motion intensities of PGAs of 0.16g, 0.32g, 0.64g, and 1.12g. Figures 7.10 to 7.12 illustrate the fragility functions of benchmark RC high-rise buildings for various performance limit states. For the IO and LS performance criteria, the fragilities illustrate steeper slopes. For the collapse performance limit state, the fragilities have flatter slopes due to the gradual loss of stiffness and strength. The fragility analysis results show that the exceedance probabilities of performance criteria (P[Limit Stateï½GMI], EPPC) is higher for soft storey RC buildings compared with the geometric irregularity structure followed by the regular RC buildings. This observation is confirmed at different ground motion intensities (GMI) starting from 0.16g to 0.64g for the three building sets (40S-B, 60S-B, and 60S-D). 7.4. Damage State Probabilities (DSP) of the Benchmark Buildings Based on the employed three performance limit states, the fragility relationships developed for the benchmark MSBs, and RC buildings are correlated with the damage state of the MSBs and RC high-rise buildings and categorized under four states of damage. These damage state probabilities (DSP) for the benchmark buildings at different PGA levels are obtained by computing the differences between the three performance limit state probabilities. Accordingly, the following DSPs are considered in the current study: (a) undisturbed occupancy (UOC), (b) impaired occupancy (IOC), (c) structural damage (SD), (d) structural collapse (SC) [135, 173]. Furthermore, based on damage state definitions employed in earlier research, UOC can be referred to as âno damageâ, IOC can be referred to as âslight-to-moderate damageâ, SD can be referred to as âextensive damageâ, and SC can be referred to as âcomplete damageâ, respectively [173, 174]. 7.4.1. Multi-storey Steel Buildings The DSPs of the benchmark MSPs are evaluated at various PGA levels and presented as shown in Table 7.3. The benchmark MSBs global DSPs are compared at different intensity levels, as depicted in Figure 7.13. At the design PGA, the likelihood of experiencing IOC falls within the 15% to 26% range, with a very low probability of SD. Typically, buildings are engineered to withstand a certain degree of damage at the design PGA. The notably high probability of UOC at the designed PGA confirms the adequate seismic performance of the benchmark MSBs under far-field earthquake records representing a conservative 126 seismic scenario for the specific seismicity zone. At a higher intensity represented by twice the design PGA, the probabilities of IOC and SD are below 51% and 38%, respectively, while the likelihood of SC is insignificantly small. Taller buildings are slightly more vulnerable than their shorter counterparts due to lower overstrength and stiffness, as shown in Figures 5.12 and 5.13. Hence, taller buildings exhibit slightly higher IDRs than shorter MSBs, as confirmed by the MBIDA results in Figure 7.1. The presented results are consistent with the observations of previous studies [165, 175]. Figure 7.10: Fragility curve comparisons of limit states of 40S-B RC high-rise buildings: IO (top), LS (middle) and CP (bottom). 00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)40S-B Buildings IO @ 1.28 PGA40S-B-R40S-B-GI40S-B-SSIOCUOC00.10.20.30.40 0.04 0.08 0.12 0.16P(Limit State|GMI)Peak Ground Acceleration (g)40S-B Buildings IO @ 0.16 PGA40S-B-R40S-B-GI40S-B-SSIOCUOC40S R40S SS00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)40S-B Buildings LS @ 1.28 PGA40S-B-R40S-B-GI40S-B-SSSDIOC00.10.20.30.40.50.60 0.08 0.16 0.24 0.32P(Limit State|GMI)Peak Ground Acceleration (g)40S-B Buildings LS @ 0.32 PGA40S-B-R40S-B-GI40S-B-SSSDIOC 40S R40S SS00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)40S-B Buildings CP @ 1.28 PGA40S-B-R40S-B-GI40S-B-SSSDSC00.20.40.60.80 0.16 0.32 0.48 0.64P(Limit State|GMI)Peak Ground Acceleration (g)40S-B Buildings CP @ 0.64 PGA40S-B-R40S-B-GI40S-B-SSSDSC40S R40S SS127 Figure 7.11: Fragility curve comparisons of limit states of 60S-B RC high-rise buildings: IO (top), LS (middle) and CP (bottom). 00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)60S-B Buildings IO @ 1.28 PGA60S-B-R60S-B-GI60S-B-SSIOCUOC00.10.20.30.40 0.04 0.08 0.12 0.16P(Limit State|GMI)Peak Ground Acceleration (g)60S-B Buildings IO @ 0.16 PGA60S-B-R60S-B-GI60S-B-SSIOCUOC60S R60S SS00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)60S-B Buildings LS @ 1.28 PGA60S-B-R60S-B-GI60S-B-SSSDIOC00.10.20.30.40.50.60 0.08 0.16 0.24 0.32P(Limit State|GMI)Peak Ground Acceleration (g)60S-B Buildings LS @ 0.32 PGA60S-B-R60S-B-GI60S-B-SSSDIOC60S R60S SS00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)60S-B Buildings CP @ 1.28 PGA60S-B-R60S-B-GI60S-B-SSSDSC00.20.40.60.80 0.16 0.32 0.48 0.64P(Limit State|GMI)Peak Ground Acceleration (g)60S-B Buildings CP @ 0.64 PGA60S-B-R60S-B-GI60S-B-SSSDSC60S R60S SS128 Figure 7.12: Fragility curve comparisons of limit states of 60S-D RC high-rise buildings: IO (top), LS (middle) and CP (bottom). 00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)60S-D Buildings IO @ 1.28 PGA60S-D-R60S-D-GI60S-D-SSIOCUOC00.10.20.30.40 0.04 0.08 0.12 0.16P(Limit State|GMI)Peak Ground Acceleration (g)60S-D Buildings IO @ 0.16 PGA60S-D-R60S-D-GI60S-D-SSIOCUOC60S D R60S D SS00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)60S-D Buildings LS @ 1.28 PGA60S-D-R60S-D-GI60S-D-SSSDIOC00.10.20.30.40.50.60 0.08 0.16 0.24 0.32P(Limit State|GMI)Peak Ground Acceleration (g)60S-D Buildings LS @ 0.32 PGA60S-D-R60S-D-GI60S-D-SSSDIOC 60S D R60S D SS00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)60S-D Buildings CP @ 1.28 PGA60S-D-R60S-D-GI60S-D-SSSDSC00.20.40.60.80 0.16 0.32 0.48 0.64P(Limit State|GMI)Peak Ground Acceleration (g)60S-D Buildings CP @ 0.64 PGA60S-D-R60S-D-GI60S-D-SSSDSC60S D R60S D SS129 UOC: Undisturbed occupancy, IOC: Impaired occupancy, SD: Structural damage, SC: Structural collapse. Figure 7.13: Damage state probabilities of MSBs at two intensity levels. Table 7.3: Limit state probabilities and damage state probabilities of MSBs at various intensity levels. Steel Buildings Periods TE (s) Ground Motion Intensities PGA (g) Limit State Probability of Exceedance Damage State Probability of Exceedance IO LS CP UOC IOC SD SC 8 S 2.35 0.16 0.156 0.001 0.000 0.844 0.155 0.001 0.000 0.32 0.817 0.305 0.011 0.183 0.512 0.294 0.011 0.64 0.997 0.872 0.259 0.003 0.125 0.613 0.259 1.12 0.999 0.993 0.754 0.001 0.006 0.239 0.754 12 S 3.95 0.16 0.206 0.002 0.000 0.794 0.204 0.002 0.000 0.32 0.857 0.332 0.006 0.143 0.525 0.326 0.006 0.64 0.998 0.927 0.267 0.002 0.071 0.660 0.267 1.12 0.999 0.998 0.816 0.001 0.001 0.182 0.816 16 S 4.49 0.16 0.246 0.002 0.001 0.754 0.244 0.001 0.001 0.32 0.867 0.365 0.009 0.133 0.502 0.356 0.009 0.64 0.998 0.927 0.289 0.002 0.071 0.638 0.289 1.12 0.999 0.998 0.815 0.001 0.001 0.183 0.815 20 S 5.26 0.16 0.283 0.020 0.001 0.717 0.263 0.019 0.001 0.32 0.887 0.398 0.011 0.113 0.489 0.387 0.011 0.64 0.998 0.937 0.308 0.002 0.061 0.629 0.308 1.12 0.999 0.998 0.826 0.001 0.001 0.172 0.826 7.4.2. RC High-rise Buildings The DSPs of the three sets of benchmark RC high-rise buildings are evaluated and presented in Tables 7.4 to 7.6 and Figures 7.14 to 7.16, respectively. The global DSPs of the benchmark RC bearing wall building sets (40S-B and 60S-B) and the RC dual building set (60S-D) are compared at different intensity levels, as depicted in Figures 7.14 to 7.16. The discussion related to the DSPs of each RC high-rise building set is provided below. The global DSPs of the 40S-B RC building set are compared at different intensity levels as shown in Table 7.4 and Figure 7.14. At the design PGA, the likelihood of experiencing UOC falls within the range of 77% to 66%, with lower values for geometric irregularity structure followed by soft storey high-rise buildings. Also, IOC values are acceptable 0.00.20.40.60.81.01.28 S 12 S 16 S 20 SProbability of ExceedanceDamage State Probability of Exceedance - 0.16gUOC IOC SD SC0.00.20.40.60.81.01.28 S 12 S 16 S 20 SProbability of ExceedanceDamage State Probability of Exceedance - 0.32gUOC IOC SD SC130 ranging between 19% to 28%, and a very low probability of SD values is observed at this intensity level. The results confirm that well designed regular and vertically irregular high-rise buildings to modern design standards withstand low levels of damage at the design PGA [32, 119]. Unlike, the notable high probability of UOC at the design intensity observed in steel moment resisting frames with different heights, the benchmark high-rise buildings have a much lower level of damage due to the effectiveness of the shear wall in controlling lateral deformation demands [164]. The fragility analysis results confirm the adequate seismic performance of the benchmark 40S-B RC buildings under far-field earthquake records representing a conservative seismic scenario for the multiple earthquake prone regions. At a higher intensity represented by twice the design PGA, the probabilities of SD and SC range between 21% to 31% and 3% to 6%, respectively, which increase for geometric irregularity followed by the soft storey irregularity. The irregular buildings exhibit higher IDRs than the regular high-rise structures, as confirmed by the MBIDA results in Figure 7.4. Table 7.4: Limit state and damage state probabilities of 40S-B RC buildings at various intensity levels. Reference Buildings Periods (s) Ground Motion Intensities (g) Limit State Probability of Exceedance Damage State Probability of Exceedance TE IO LS CP UOC IOC SD SC 40S-B-R 3.79 0.16 0.226 0.035 0.000 0.774 0.191 0.035 0.000 0.32 0.728 0.240 0.030 0.272 0.488 0.210 0.030 0.64 0.960 0.853 0.395 0.040 0.107 0.458 0.395 1.12 0.997 0.980 0.774 0.003 0.017 0.206 0.774 40S-B-GI 3.34 0.16 0.306 0.050 0.002 0.694 0.256 0.048 0.002 0.32 0.770 0.310 0.050 0.230 0.460 0.260 0.050 0.64 0.981 0.871 0.509 0.019 0.110 0.362 0.509 1.12 0.999 0.984 0.863 0.001 0.015 0.121 0.863 40S-B-SS 3.76 0.16 0.338 0.061 0.003 0.662 0.277 0.058 0.003 0.32 0.810 0.370 0.060 0.190 0.440 0.310 0.060 0.64 0.988 0.884 0.525 0.012 0.104 0.359 0.525 1.12 0.999 0.987 0.869 0.001 0.012 0.118 0.869 UOC: Undisturbed occupancy, IOC: Impaired occupancy, SD: Structural damage, SC: Structural collapse. Figure 7.14: Damage state probabilities of 40S-B RC building set at two intensity levels. 0.00.20.40.60.81.040S-B-R 40S-B-GI 40S-B-SSProbability of ExceedanceDamage State Probability of Exceedance - 0.16gUOCIOCSDSC0.00.20.40.60.81.040S-B-R 40S-B-GI 40S-B-SSProbability of ExceedanceDamage State Probability of Exceedance - 0.32gUOCIOCSDSC131 Similarly, the global DSPs of the 60S-B RC building set are compared at different intensity levels as shown in Table 7.5 and Figure 7.15. At the design PGA, the likelihood of experiencing UOC falls within the range of 79% to 68%, with lower values for geometric irregularity structure followed by soft storey high-rise buildings. Also, IOC values are acceptable ranging between 18% to 23%, and a very low probability of SD values is observed at this intensity level. The results confirm that well designed regular and vertically irregular high-rise buildings to modern design standards withstand low levels of damage at the design PGA [32, 119]. Unlike, the notable high probability of UOC at the design intensity observed in steel moment resisting frames with different heights, the benchmark high-rise buildings have a much lower level of damage due to the effectiveness of the shear wall in controlling lateral deformation demands [164]. The fragility analysis results confirm the adequate seismic performance of the benchmark 60S-B RC buildings under far-field earthquake records representing a conservative seismic scenario for the multiple earthquake prone regions. At a higher intensity represented by twice the design PGA, the probabilities of SD and SC range between 19% to 26% and 5% to 9%, respectively, which increase for geometric irregularity followed by the soft storey irregularity. The irregular buildings exhibit higher IDRs than the regular high-rise structures, as confirmed by the MBIDA results in Figure 7.5. The results also indicate that the DSPs are lower for the higher building set (i.e., 60S-B) as compared to the lower building set (i.e., 40S-B). Table 7.5: Limit state and damage state probabilities of 60S-B RC buildings at various intensity levels. Reference Buildings Periods (s) Ground Motion Intensities (g) Limit State Probability of Exceedance Damage State Probability of Exceedance TE IO LS CP UOC IOC SD SC 60S-B-R 6.03 0.16 0.215 0.038 0.000 0.750 0.210 0.038 0.000 0.32 0.677 0.237 0.045 0.323 0.440 0.192 0.049 0.64 0.946 0.701 0.296 0.054 0.245 0.405 0.296 1.12 0.994 0.927 0.653 0.006 0.067 0.274 0.653 60S-B-GI 5.42 0.16 0.290 0.073 0.002 0.710 0.217 0.071 0.002 0.32 0.739 0.338 0.078 0.251 0.401 0.260 0.078 0.64 0.966 0.796 0.417 0.034 0.170 0.379 0.417 1.12 0.997 0.959 0.761 0.003 0.038 0.198 0.761 60S-B-SS 5.87 0.16 0.319 0.090 0.003 0.681 0.229 0.087 0.003 0.32 0.738 0.350 0.087 0.262 0.388 0.263 0.087 0.64 0.974 0.850 0.453 0.026 0.124 0.397 0.453 1.12 0.998 0.977 0.797 0.002 0.021 0.180 0.797 132 UOC: Undisturbed occupancy, IOC: Impaired occupancy, SD: Structural damage, SC: Structural collapse. Figure 7.15: Damage state probabilities of 60S-B RC building set at two intensity levels. Finally, the global DSPs of the 60S-D RC building set is compared at different intensity levels as shown in Table 7.6 and Figure 7.16. At the design PGA, the likelihood of experiencing UOC falls within the range of 75% to 72%, with lower values for geometric irregularity structure followed by soft storey high-rise buildings. Also, IOC values are acceptable ranging between 21% to 18%, and a very low probability of SD values is observed at this intensity level. The results confirm that well designed regular and vertically irregular high-rise buildings to modern design standards withstand low levels of damage at the design PGA [32, 119]. Unlike, the notable high probability of UOC at the design intensity observed in steel moment resisting frames with different heights, the benchmark high-rise buildings have a much lower level of damage due to the effectiveness of the shear wall in controlling lateral deformation demands [164]. The fragility analysis results confirm the adequate seismic performance of the benchmark 60S-D RC buildings under far-field earthquake records representing a conservative seismic scenario for the multiple earthquake prone regions. At a higher intensity represented by twice the design PGA, the probabilities of SD and SC range between 18% to 23% and 5% to 7%, respectively, which increase for geometric irregularity followed by the soft storey irregularity. The irregular buildings exhibit higher IDRs than the regular high-rise structures, as confirmed by the MBIDA results in Figure 7.6. The results also indicate that the DSPs are slightly lower for the dual building set (i.e., 60S-D) as compared to bearing wall building sets (i.e., 40S-B and 60S-B). 0.00.20.40.60.81.060S-B-R 60S-B-GI 60S-B-SSProbability of ExceedanceDamage State Probability of Exceedance - 0.16gUOCIOCSDSC0.00.20.40.60.81.060S-B-R 60S-B-GI 60S-B-SSProbability of ExceedanceDamage State Probability of Exceedance - 0.32gUOCIOCSDSC133 Table 7.6: Limit state and damage state probabilities of 60S-D RC buildings at various intensity levels. Reference Buildings Periods (s) Ground Motion Intensities (g) Limit State Probability of Exceedance Damage State Probability of Exceedance TE IO LS CP UOC IOC SD SC 60S-D-R 5.84 0.16 0.255 0.048 0.000 0.790 0.180 0.048 0.000 0.32 0.726 0.230 0.049 0.274 0.496 0.181 0.045 0.64 0.961 0.839 0.305 0.039 0.122 0.534 0.305 1.12 0.996 0.972 0.660 0.004 0.024 0.312 0.660 60S-D-GI 5.04 0.16 0.263 0.075 0.001 0.737 0.188 0.074 0.001 0.32 0.768 0.280 0.064 0.232 0.488 0.216 0.064 0.64 0.969 0.879 0.344 0.031 0.090 0.535 0.344 1.12 0.997 0.981 0.690 0.003 0.016 0.291 0.690 60S-D-SS 5.74 0.16 0.280 0.100 0.002 0.720 0.180 0.098 0.002 0.32 0.742 0.290 0.062 0.258 0.452 0.228 0.068 0.64 0.968 0.886 0.357 0.032 0.082 0.529 0.357 1.12 0.998 0.984 0.719 0.002 0.014 0.265 0.719 UOC: Undisturbed occupancy, IOC: Impaired occupancy, SD: Structural damage, SC: Structural collapse. Figure 7.16: Damage state probabilities of 60S-D RC building set at two intensity levels. 7.5. Concluding Remarks 7.5.1. Multi-storey Steel Buildings The fragility analysis of the benchmark MSBs indicated that at the design intensity, the likelihood of experiencing impaired occupancy (IOC) fell within the 15% to 26% range, with a very low probability of structural damage (SD). The notably high probability of unimpaired occupancy (UOC) at the designed PGA of 72% to 85% reflected the adequate seismic performance of the benchmark MSBs under a conservative far-field seismic scenario. At twice the design intensity, the probabilities of IOC and SD were below 51% and 38%, respectively, while the likelihood of SC was insignificantly small. The results confirmed the satisfactory seismic performance of the MSBs at the design intensity and 0.00.20.40.60.81.060S-D-R 60S-D-GI 60S-D-SSProbability of ExceedanceDamage State Probability of Exceedance - 0.16gUOCIOCSDSC0.00.20.40.60.81.060S-D-R 60S-D-GI 60S-D-SSProbability of ExceedanceDamage State Probability of Exceedance - 0.32gUOCIOCSDSC134 twice the design PGA. The results also lent weight to the proposed adjustment in the response modification coefficients. 7.5.2. RC High-rise Buildings Well-designed regular and vertically irregular bearing wall high-rise buildings to modern design standards withstand low levels of damage at the design PGA, where the likelihood of experiencing UOC falls within the average range of 78% to 67% and 75% to 72% for bearing wall and dual building sets, respectively, with lower values for geometric irregularity structure followed by soft storey high-rise building. Also, IOC values are acceptable ranging between 19% to 26%, and 21% to 18% for bearing wall and dual building sets, respectively, and a very low probability of SD values is observed at this intensity level. Unlike, the relatively higher probability of UOC at the design intensity observed in steel moment resisting frames with different heights, the benchmark high-rise buildings have a much lower level of damage due to the effectiveness of the shear wall in controlling lateral deformation demands. At a higher intensity represented by twice the design PGA, the probabilities of SD and SC range between 19% to 25% and 4% to 8%, respectively, which increase for geometric irregularity followed by the soft storey irregularity. The irregular buildings exhibit higher IDRs than the regular high-rise structures. The DSPs are lower for the higher building set (60S-B) as compared to the lower building set (40S-B). The results also indicate that the DSPs are slightly lower for the dual building set (i.e., 60S-D) as compared to the bearing wall building sets (i.e., 40S-B and 60S-B). The fragility analysis results confirm the adequate seismic performance of all the benchmark RC high-rise buildings under far-field earthquake records representing a conservative seismic scenario for the multiple earthquake prone regions. 135 8 Comparison of High-rise Buildings Structural Systems 8.1. Introduction The selection of the structural system of a high-rise building plays a vital role in the design and seismic performance of the structure. This selection is based on the design codesâ classification and previous studiesâ recommendations for high-rise buildings. The structural system of high-rise buildings should provide better control of lateral drift under horizontal loads from earthquake and wind effects than systems used in low and medium-rise structures such as moment-resisting frames [32, 116]. Previous studies suggested limits on the height for different structural systems of high-rise buildings [116]. On the other hand, design codes do not provide clear limits on the use of different structural systems. For instance, the bearing wall and dual systems are allowed for unlimited height for seismic design categories B and C [32]. This may result in costly or unsafe designs for certain structural systems if adopted for buildings of short or tall heights. To address this issue for the two structural systems investigated in the present study, namely the bearing walls and dual systems, their seismic performance and cost are compared and discussed in the following sections [32, 116]. Two RC high-rise building sets representing 60-storey bearing wall (60S-B) and 60-storey dual system (60-D) are selected to compare their seismic performance under the diverse set of bidirectional natural earthquake records. Each building set represents a regular, geometric irregular, and soft-storey irregular buildings. Similar architectural features between the 60-B and 60-D sets are selected to draw a fair comparison, as illustrated in Figure 3.3. As previously indicated, each of the selected RC high-rise buildings is carefully designed and detailed per the code-recommended seismic design requirements [32]. The lateral response of the two selected benchmark RC high-rise buildings is estimated using the ISAs, as discussed in Chapter 5. The MBIDA results of the selected two sets of benchmark high-rise buildings with varying heights, different structural systems, and irregularities are discussed in Chapter 6. The comparisons of the seismic performance of the two sets and cost-benefit analysis results are subsequently presented 136 8.2. Comparison of Inelastic Lateral Response The seismic behaviour of the selected two benchmark RC high-rise building sets beyond their elastic range, encompassing the changes in stiffness, strength, and deformation characteristics is assessed using the ISAs. The ISAs are conducted on the 3D fibre-based simulation models of the two RC high-rise building sets as an initial assessment tool for lateral capacity, stiffness, and local damage development. Comparisons are drawn between their lateral capacities, strength, stiffness and local damage developments and presented in the subsequent sections. 8.2.1. Lateral Capacity Figures 5.5 and 5.6 and Figures 5.8 and 5.9 depict the lateral capacities and the IDRs of the selected building sets, respectively. Comparisons are made between the lateral capacity curves of the two structural systems for regular and vertically irregular buildings, as illustrated in Figure 8.1. Figure 8.2 also compares the IDRs at the first significant and global yield levels for both structural systems. The first yield in horizontal structural elements and the global yield are observed at lower IDRs in the dual system than in the bearing wall system. The capacity curves shown in Figure 8.1 are utilized further to compare the strength, stiffness and local damage developments for the two investigated systems, as explained in the following sections. 8.2.2. Overstrength Estimation The first yield indication is detected at a higher intensity than that adopted in the design among the 60S-B and 60S-D building sets, as shown in Figure 5.11. The results in Figure 8.3 confirm that both the benchmark RC high-rise systems exhibit comparable overstrength values at various strength levels for the regular and irregular buildings. The results reflect the insignificance of the geometric and soft storey irregularities on the overstrength factors. Notably, the design code does not require increasing seismic loads for these two irregularities [32, 101]. It is also observed that the overstrength values estimated based on the ULL distribution in the benchmark building sets of 60S-B and 60S-D at the initial yield and ultimate strength range between 1.42 to 1.75, and 2.62 to 2.91, respectively, demonstrating adequacy over the design code recommended values [32]. The 60S-D buildings indicate higher overstrength values than the 60S-B buildings, as shown in Figure 8.3. The higher overstrength of the dual structural system is due to the additional stiffness provided by the perimeter frames as compared with the 60S-B buildings set. 137 Figure 8.1: Comparison of lateral response of regular and irregular 60S-B and 60S-D RC building sets showing rebar yielding sequence and confined concrete crushing. (a) IDR at first yield (b) IDR at the global yield Figure 8.2: Comparison of IDRs of regular and irregular 60S-B and 60S-D RC building sets at first yield and global yield levels. 8.2.3. Stiffness Estimation Figure 5.14 shows the stiffness of the selected RC buildings at the initial yielding, global yielding, ultimate strength, and collapse limit state. The effective stiffness of the 60S-B and 60S-D RC high-rise buildings at different strength levels relative to initial stiffness is illustrated earlier in Figure 5.15. Figure 8.4 draws comparisons between the 60S-B and 60S-D RC building sets, which exhibit a continuous decrease in stiffness with increasing lateral load. The higher initial stiffness is due to the absence of cracks in concrete cross-01530456075901050.0 1.0 2.0 3.0 4.0Base Shear (MN)Top Displacement (m)60S-D-R and 60S-B-R0.88% IDR 0.50% IDR 1.22% IDR 0.63% IDR 01530456075900.0 1.0 2.0 3.0 4.0Base Shear (MN)Top Displacement (m)60S-D-GI and 60S-B-GI0.79% IDR 0.48% IDR 1.16% IDR 0.58% IDR 01530456075901050.0 1.0 2.0 3.0 4.0Base Shear (MN)Top Displacement (m)60S-D-SS and 60S-B-SS0.76% IDR 0.48% IDR 1.08% IDR 0.52% IDR 0.000.150.300.450.600.75R GI SS0.630.580.520.50 0.48 0.48IDR at First Yield, % Bearing Wall System Dual Structural System0.000.250.500.751.001.251.50R GI SS1.221.161.080.880.79 0.76IDR at Global Yield, % Bearing Wall System Dual Structural System 1st Yield IDR 60S-D 1st Yield IDR 60S-BGlobal Yield IDR 60S-D Global Yield IDR 60S-B138 sections in the elastic range before initial yielding, as illustrated in Figure 8.4. Effective stiffness values of the RC high-rise buildings at different levels relative to initial stiffness obtained from the ULL distribution are illustrated in Figure 8.5. The average effective stiffness values relative to initial stiffness at global yield, ultimate strength, and collapse levels for RC bearing wall building sets (60S-B) are 0.81, 0.58, and 0.52, while those for the RC dual building set (60S-D) are 0.83, 0.44, and 0.36, respectively. The effective stiffness of all the benchmark RC buildings representing varying heights, structural systems, and irregularities at global yield and collapse are compared in Figure 5.16 with the recommended values for uncracked and cracked walls by different design standards [16, 100, 119]. (a) First yield overstrength (b) Overstrength at global yield (a) Ultimate overstrength Figure 8.3: Comparison of overstrength factors between 60S-B and 60S-D building sets at: (a) first yield, (b) global yield, and (c) ultimate base shear. 8.2.4. Local Damage Development The formation of plastic hinges is evaluated and the development of different member damage modes in the high-rise RC benchmark buildings is monitored in the ISAs under the ULL loading pattern as discussed in Chapter 5 and illustrated in Figures 5.18 to 5.20. Figure 8.6 illustrates the local damage development at global yielding and collapse levels. As shown in Figure 8.6, the 60S-D system exhibits more yielding and unconfined concrete crushing in horizontal members than the 60S-B buildings, which is primarily due to the 0.00.51.01.52.0R GI SS1.571.45 1.421.661.751.47First Yield OverstrengthBearing Wall System Dual Structural System0.01.02.03.0R GI SS2.452.62 2.632.492.76 2.86Global Yield OverstrengthBearing Wall System Dual Structural System0.01.02.03.0R GI SS2.762.62 2.682.91 2.89 2.98Ultimate OverstrengthBearing Wall System Dual Structural System139 additional perimeter beams in the dual system. Furthermore, within each set of the benchmark buildings, the vertical geometric irregularity exhibited less member damage than the regular and soft storey structures. This is due to the fewer structural members in the vertical geometric irregularity buildings due to the reduced floor footprint compared to other buildings. For the buildings with soft storey irregularity, comparable member damage to the regular structures is observed at the global yield and collapse levels, with only more extensive unconfined concrete crushing in the former structures at the collapse limit state. (a) Initial stiffness (b) Stiffness at global yield (b) Ultimate stiffness Figure 8.4: Comparison of structural stiffness at different levels between 60S-B and 60S-D building sets at: (a) initial stiffness, (b) global yield, and (c) ultimate base shear. Figure 8.5: Comparison of stiffness modifiers relative to initial stiffness at global yield, ultimate strength, and collapse for 60S-B, and 60S-D RC building sets. 0.020.040.060.080.0R GI SS37.52 35.0041.0063.5159.1070.69Initial Stiffness, kN/mmBearing Wall System Dual Structural System0.015.030.045.060.075.0R GI SS30.3828.0033.5051.0047.7062.00Stiffness at Global Yield, kN/mmBearing Wall System Dual Structural System0.010.020.030.0R GI SS22.0020.5023.5026.0024.0028.00Ultimate Stiffness, kN/mmBearing Wall System Dual Structural System 0.00.20.40.60.81.060S-B-R 60S-B-GI 60S-B-SS0.81 0.80 0.820.59 0.59 0.570.550.48 0.48Stiffness Modifier Global Yield Ultimate Strength Collapse0.00.20.40.60.81.060S-D-R 60S-D-GI 60S-D-SS0.80 0.810.880.44 0.470.400.37 0.36 0.34Stiffness Modifier Global Yield Ultimate Strength Collapse140 (a) Plastic hinge formation and local damage for 60S-B RC buildings. (b) Plastic hinge formation and local damage for 60S-D RC buildings. Figure 8.6: Development of plastic hinge formation and local damage for 60S-B and 60S-D RC buildings at global yield and collapse performance levels. 8.3. Comparison of Seismic Design Coefficients The MBIDA results of the 60S-B and 60S-D RC building sets showing the PGA and IDR ratios at their first yield (PGA,y and IDR,y, respectively) and collapse (PGA,c and IDR,c, respectively) obtained from 26 bidirectional earthquake records are shown in Figures 6.7 to 6.8. The R coefficients of the two structural systems are evaluated by combining the Ωfy with PGA ratios of the collapse to yield (i.e., PGA,c/PGA,y) shown in Figures 6.7 to 6.8. Likewise, Cd coefficients are evaluated by using the IDR ratios of the collapse to yield (i.e., IDR,c/IDR,y) shown in Figures 6.7 to 6.8. Figure 8.7 compares the 60S-B and 60S-D structural systems illustrating the safety margins of all the seismic design coefficients (R, Cd, and â¦). The safety margins for the R coefficients range from 42% to 52% for the bearing wall buildings and between 7% to 21% for dual buildings. Notably, the higher safety margins for the 60S-B system are due to the conservative factors adopted by the design code (i.e., 4.0), while the low R coefficients for 020040060080060S-B-R 60S-B-GI 60S-B-SS 60S-B-R 60S-B-GI 60S-B-SSMember Damage at Global Yielding Member Damage at CollapseNo. of Plastic Hinges60S-BYield: Hor elements Yield: Ver elements Unconf conc crushing: Hor elementsUnconf conc crushing: Ver elements Conf conc crushing: Hor elements Conf conc crushing: Ver elements030060090012001500180060S-D-R 60S-D-GI 60S-D-SS 60S-D-R 60S-D-GI 60S-D-SSMember Damage at Global Yielding Member Damage at CollapseNo. of Plastic Hinges60S-DYield: Hor elements Yield: Ver elements Unconf conc crushing: Hor elementsUnconf conc crushing: Ver elements Conf conc crushing: Hor elements Conf conc crushing: Ver elements141 the 60S-D structural system are attributed to the high design factors recommended by the code (i.e., 5.5). The Cd coefficients exhibit comparable safety margins of 14% to 24% for bearing wall buildings and 15% to 28% for dual buildings. The calculated Cd coefficients are, on average, 19% lower than the code deflection amplification factors, as shown in Figure 8.7. The safety margins of the â¦ coefficient are higher for 60S-D building sets than the 60S-B building sets, as depicted in Figure 8.7. (a) Safety margins of R coefficients (b) Safety margins of Cd coefficients (b) Safety margins of â¦ factor Figure 8.7: Comparison of safety margins of the seismic design coefficients between two structural system building sets. 8.4. Comparison of Structural Systemsâ Fragilities and Damage State Probabilities Fragility relationships of the two considered structural systems were derived as explained in Chapter 7. Figures 7.5 to 7.6 indicate comparable seismic responses between the two sets of benchmark buildings. Figure 8.9 compares the fragility functions of the two structural systems at various performance limit states. The DSPs of the two benchmark RC high-rise buildings representing the bearing wall and dual structural systems are evaluated and presented in Tables 7.5 to 7.6 and Figures 7.15 to 7.16, respectively. The global DSPs of the benchmark RC bearing wall building set (60S-B) and the RC dual building set (60S-D) are compared at different intensity levels, as depicted in Figures 7.15 to 7.16. The UOC, IOC, SD and SC are compared between the two building sets at the design PGA of 0.16g and twice the design PGA of 0.32g, as shown in Figure 8.10. The results show that the seismic performance of the bearing wall and dual building sets is comparable. 0102030405060R GI SS52454221137Safety Margins in R Coefficients, % Bearing Wall System Dual Structural System010203040R GI SS241914252815Safety Margins in CdCoefficient, % Bearing Wall System Dual Structural System01020R GI SS1357171615Safety Margins in â¦Factors, % Bearing Wall System Dual Structural System142 Figure 8.8: Comparison of fragility relationships of 60S-B and 60S-D buildings set obtained from MBIDAs for R: regular, GI: geometric irregular, and SS: soft storey irregular buildings. At the design intensity, the likelihood of experiencing UOC falls within the average range of 75% to 68% and 79% to 72% for bearing wall and dual building sets, respectively, with lower values for geometric irregularity structure followed by soft storey high-rise building. Also, at IOC values are acceptable, ranging between 21% to 23%, and 18% to 19% for bearing wall and dual building sets, respectively. A very low probability of SD values is observed at this intensity level. Moreover, at a higher intensity represented by twice the design PGA, the probabilities of SD and SC range between 19% to 25% and 4% to 8%, respectively, which increase for geometric irregularity followed by soft storey irregularity. The irregular buildings exhibit higher IDRs than the regular high-rise structures. The results also indicate that the DSPs are slightly lower for the dual building set (60S-D) as compared to bearing wall building sets (60S-B). The fragility analysis results confirm better adequacy in the seismic performance of the dual building set (60S-D) than the bearing wall building set (60S-B) under far-field earthquake records representing a conservative seismic scenario for the multiple earthquake-prone regions. 00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)RIO 60S-B IO 60S-DLS 60S-B LS 60S-DCP 60S-B LS 60S-DUOCIOCSDSC00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)GIIO 60S-B IO 60S-DLS 60S-B LS-60S-DCP 60S-B CP 60S-DUOCIOCSDSC00.20.40.60.810 0.16 0.32 0.48 0.64 0.8 0.96 1.12 1.28P(Limit State|GMI)Peak Ground Acceleration (g)SSIO 60S-B IO 60S-DLS 60S-B LS 60S-DCP 60S-B CP 60S-DUOCIOCSDSC143 (a) Damage state probabilities at undisturbed occupancy (UOC) of 60S-B and 60S-D RC building sets at two intensity levels. (b) Damage state probabilities at impaired occupancy (IOC) of 60S-B and 60S-D RC building sets at two intensity levels. (c) Damage state probabilities at structural damage (SD) of 60S-B and 60S-D RC building sets at two intensity levels. (d) Damage state probabilities at structural collapse (SC) of 60S-B and 60S-D RC building sets at two intensity levels. Figure 8.9: Damage state probabilities at UOC, IOC, SD, and SC of 60S-B and 60S-D RC building sets at two intensity levels. 0.00.30.50.81.0R GI SS0.750.71 0.680.790.74 0.72Probability of ExceedanceDamage State Probability of Exceedance - 0.16gBearing Wall System Dual Structural SystemUOC0.00.20.30.5R GI SS0.320.250.270.270.230.26Probability of ExceedanceDamage State Probability of Exceedance - 0.32gBearing Wall System Dual Structural SystemUOC0.00.10.20.3R GI SS0.21 0.220.230.18 0.19 0.18Probability of ExceedanceDamage State Probability of Exceedance - 0.16gBearing Wall System Dual Structural SystemIOC0.00.20.40.6R GI SS0.440.40 0.390.50 0.490.45Probability of ExceedanceDamage State Probability of Exceedance - 0.32gBearing Wall System Dual Structural SystemIOC0.000.030.060.090.120.15R GI SS0.040.070.090.050.070.10Probability of ExceedanceDamage State Probability of Exceedance - 0.16gBearing Wall System Dual Structural SystemSD0.00.10.20.30.4R GI SS0.190.26 0.260.180.22 0.23Probability of ExceedanceDamage State Probability of Exceedance - 0.32gBearing Wall System Dual Structural SystemSD0.0000.0020.0040.0060.0080.010R GI SS0.0000.0020.0030.0000.0010.002Probability of ExceedanceDamage State Probability of Exceedance - 0.16gBearing Wall System Dual Structural SystemSC0.0000.0200.0400.0600.0800.100R GI SS0.0490.0780.0870.0450.0640.068Probability of ExceedanceDamage State Probability of Exceedance - 0.32gBearing Wall System Dual Structural SystemSC144 8.5. Cost Benefit Analysis Following the satisfactory seismic performance of both the bearing wall and dual structural building sets, it is vital to understand the cost benefit analysis of the two systems. Significant ease in construction is observed in the bearing wall buildings due to the absence of peripheral beams as compared with the dual system. This construction ease accounts for the additional cost and time involved in the construction of the peripheral beams of the dual buildings. Accordingly, the bearing wall and dual structural system buildings are assessed with respect to the cost incurred and the relative additional time needed to complete the construction of the two building systems. For brevity, Dubai, United Arab Emirates, is considered as the study region as discussed earlier. In the current study, the cost benefit analysis considers the hard cost and the soft cost evaluation approach. Under the hard cost evaluation, the cost component needed for the construction of the peripheral beams of each of the dual building sets, which includes the cost of the formwork, reinforcing steel, and concrete, is estimated. The soft costs are estimated based on the probable returns from each building incurred due to the delay in handing over the dual buildings. The combination of both hard cost and soft cost is assessed in arriving at the cost benefit analysis, as subsequently explained. Figures 8.11 and 8.12 depict the cost benefits obtained from the regular and geometric irregular bearing wall buildings, respectively, relative to the respective dual building counterparts. Figures 8.11 and 8.12 indicate the hard cost grouped under the cost of formwork, rebars, and the quantity of concrete needed to cast the peripheral beams in the dual wall systems. The soft cost is estimated from the additional number of days needed to construct the peripheral beams in the respective high-rise buildings. These extra days are equated to the potential net rental return after deducting the maintenance charges assumed from the residential use. The overall cost benefit is thus termed as the total cost, which is the summation of the hard and the soft cost. The cost analysis in the current study is estimated by considering the present construction market and rental demand in Dubai. For brevity, the cost benefit from the regular bearing wall building (60S-B-R) over the regular dual building (60S-D-R) shown in Figure 8.11 is approximately $17M. Similarly, the cost benefit from the geometric irregular bearing wall building (60S-B-GI) over the geometric irregular dual building (60S-D-GI) shown in Figure 8.12 is approximately $15.7M. The differences in the cost benefits between the regular and geometric irregular structures are 145 due to the reduced floor area of the geometric irregular building. Finally, it is important to note that similar cost benefits for the soft storey bearing wall building (60S-B-SS) are expected as calculated for the regular structure (60S-B-R). Figure 8.10: Cost benefit of the 60S-B-R building relative to 60S-D-R building. Figure 8.11: Cost benefit of the 60S-B-GI building relative to 60S-D-GI building. 8.6. Concluding Remarks The performance of the bearing wall buildings was on par with the dual structural system. The safety margins for the R coefficients ranged from 42% to 52% for the bearing wall buildings and between 7% to 21% for dual buildings. Notably, the higher safety margins for the bearing wall system are due to the conservative factors adopted by the design code, while the low R coefficients for the dual structural system are attributed to the high design factors recommended by the code. The Cd coefficients exhibited comparable safety margins 1$1,055,165.00$4,140,000.00$358,400.00$5,553,565.00$11,413,043.48$16,966,608.48CHART TITLETotal Cost Total Soft Cost Total Hard CostConcrete Rebars Formwork1$949,648.50$3,690,000.00$315,000.00$4,954,648.50$10,733,695.65$15,688,344.15CHART TITLETotal Cost Total Soft Cost Total Hard CostConcrete Rebars Formwork146 for bearing all buildings and dual buildings. he safety margins of the â¦ coefficient were higher for the dual building set than the bearing wall building set. The cost benefits from the regular and geometric irregular bearing wall building over the dual building counterparts were approximately $17M and $15.7M, respectively. Similar cost benefits for the soft storey bearing wall building are expected as calculated for the regular structure. 147 9 Conclusions 9.1. Synopsis This study presented a comprehensive investigation of seismic design coefficients for multi-storey steel and RC high-rise buildings designed according to current building codes using 3D inelastic analysis. The research covered thirteen benchmark buildings with varying construction materials, heights, structural systems and irregularities in medium seismicity regions. The study focused on four regular moment-resisting multi-storey steel buildings (MSBs) ranging from 8 to 20 storeys and nine RC high-rise buildings of 40 to 60 storeys, divided into four sets. The MSB set included steel buildings with varying heights. The three RC high-rise building sets comprised a regular building and two vertical irregular buildings of geometric irregularity and soft storey irregularity. The study initiated with a comprehensive literature review to identify the limitations and gaps in the previous works on seismic response factors over five decades. It provided a brief overview of the use of seismic response factors in various international codes, historical perspectives, and their respective definitions. Seismic response factors were reviewed from the previous studies considering the SDOF and MDOF system assessment. The review also identified that the ductility, structural system, natural period, construction materials and shape of the hysteresis loop influenced the R factor. Limitations and gaps in the previous studies were presented considering the type of systems, type of analysis, components of seismic design factors, irregularity, structural systems, input ground motions and the seismic loading applied on the structures. The study then addressed the limitations and gaps identified by the comprehensive literature review. Systematic frameworks were adopted for verifying seismic design coefficients, including selecting and designing thirteen benchmark structures, detailed 3D fibre-based modelling, evaluating inelastic lateral response, and predicting bidirectional seismic behaviour through 3D MBIDA. All benchmark buildings were designed carefully, avoiding unwanted overstrength to ensure a fair assessment of design coefficients. The study involved over 5500 3D ISAs and MBIDAs employing 26 bidirectional natural earthquake records. For MSBs, the study verified code-recommended seismic design coefficients and assessed the vulnerability of four benchmark structures ranging from 8 to 20 storeys to represent well-designed steel structures. For RC high-rise buildings, the study 148 also verified the seismic design coefficients recommended by building codes and assessed the vulnerability for nine structures, ranging from 40 to 60 storeys divided into three sets. The study addressed three structural systems: steel moment-resisting frames, RC bearing walls and RC dual systems. Vertical geometric and soft storey irregularities were accounted for apart from regular structures. The following tasks were undertaken meticulously while verifying and validating the seismic design coefficients of the benchmark steel and RC high-rise buildings: Structural Design and 3D Fibre-based modelling of Benchmark Buildings â¢ Following the literature review, thirteen buildings were selected and designed in a region with medium seismicity, which represents a vast part of the globe. The selected benchmark buildings comprised of a set of regular MSBs with varying heights ranging from 8 to 20-storey, and three sets of RC high-rise buildings with varying heights of 40 to 60-storey using different structural systems and irregularities. A fully automated design process was executed using 3D finite element models adhering to current design steel and concrete standards. The comprehensive design results were summarized in spread sheets and design drawings. â¢ A verified nonlinear analysis platform was employed to idealize the thirteen benchmark MSB and RC high-rise buildings, aiming to evaluate their seismic performance and assessed the design coefficients. To comprehensively address ground motion uncertainties, a total of 26 natural earthquake records, representing medium seismicity regions were considered. Application of the bidirectional earthquake loads using the selected 26 input ground motions ensured a thorough evaluation of the seismic design coefficients of the benchmark buildings by employing the capabilities of 3D MBIDA. Prediction of Lateral Response using ISAs and MBIDAs â¢ Over 5500 multi-step 3D ISAs and MBIDAs were conducted on both set of MSBs of varying heights and three sets of RC high-rise benchmark buildings with varying heights, structural systems and irregularities. The primary objective of this extensive analysis was to monitor and record the seismic response across various limit states until each of the selected benchmark buildings reaches the onset of 149 collapse. Critical global response parameters were derived from this comprehensive analysis. The MBIDA curves for all benchmark buildings were generated from the selected 26 input ground motions. The comprehensive analysis results were utilized to evaluate seismic design response factors and establish fragility relationships for the different sets of MSBs and benchmark RC buildings. Evaluation of Seismic Design Coefficients and Assessment of Seismic Response â¢ Seismic design coefficients of set of MSB and three sets of RC high-rise buildings, namely overstrength factor (Ω), response modification coefficient (R), and deflection amplification coefficient (Cd) were evaluated using the results from MBIDAs. The PGA and IDR at the yield and collapse are monitored from the MBIDA curves for the set of 26 natural earthquake records for evaluating the R and Cd coefficients. â¢ Fragility relationships of the thirteen benchmark buildings were established using three distinct limit states, IO, LS, and CP. These limit states were determined using ISAs, MBTHA and MBIDA. For each reference building, 416 data points were plotted, each representing the PGA-IDR values obtained from the inelastic response history analysis. The fragility relationships were expressed graphically with PGAs versus the exceedance probabilities. The fragility relationships developed for the benchmark MSBs, and RC buildings were correlated with the damage state of the MSBs and RC high-rise buildings and categorized under four states of damage. â¢ Comparisons were made between the seismic response, design coefficients and cost of two lateral force resisting systems for RC high-rise buildings, namely the bearing wall and the dual system. The seismic performance, safety margins and the design coefficients of the two building sets were evaluated. A cost benefit analysis between the two structural systems was compared. 9.2. Conclusions and Recommendations The most important conclusions of the present study are summarized below: Literature Review â¢ The MDOF systems contributed 3/4 of the review, while the SDOF system contributed 1/4 of the previous research. Regular and irregular buildings covering 150 RC, steel, masonry, and composite construction with various structural systems were reviewed and summarized. â¢ Most previous research in the SDOF system was based on hypothetical models, while MDOF systems were limited to regular low-rise to medium-rise buildings. A significant research contribution was based on 2D inelastic analysis by employing unidirectional seismic loading, while very little work was conducted using 3D inelastic analysis. Only 6% of work was based on the 3D analysis, while 8% of work was conducted on irregular buildings with most of the work focused on regular buildings with 2D analysis. Regular RC, steel frame and braced buildings were investigated to 72%, whereas shear walls had only 28% of research in the previous studies. About 30% of the work on Steel braced, framed and RC framed buildings was conducted using IPA, while 70% of the work was with IDAs employing unidirectional seismic loading. Several studies recommended improving the code-recommended R values for regular buildings due to observed adequate safety margins. â¢ The review provided directions for possible future research covering structural irregularity, 3D inelastic analysis, and investigation of different structural systems related to multi-storey and high-rise buildings under bi-directional seismic loading. Further investigations to evaluate the seismic response of RC shear wall buildings with varying heights and irregularities were emphasized using 3D inelastic analysis covering regions influenced by various seismic scenarios. Mult-storey Steel Buildings (MSBs) â¢ The MSBs exhibited a reduction in stiffness at different damage stages, including the global yield, ultimate strength, and collapse. The average stiffness modifiers relative to initial stiffness at these three stages were 0.82, 0.37, and 0.34. These stiffness modifiers can be used in the elastic analysis of comparable MSBs. Plastic hinges were developed at beam ends of the lower story levels, then propagated to upper levels, and observed later at the base of vertical elements. This strong-column weak-beam mechanism agreed with the design code principles of having the dissipation of the energy mainly in horizontal structural members. â¢ The MBIDA provided key insights into the nonlinear seismic performance of the benchmark MSBs, enabling assessing design modification coefficients. The ratios 151 of IDR at collapse to that at yield were consistently lower than corresponding PGA ratios. This verified the design code approach in adopting a lower deflection amplification factor, Cd, than the response modification coefficient, R. â¢ The calculated design modification coefficients confirm the satisfactory factors adopted by the design codes for MSBs of varying heights. The median R coefficients of the benchmark MSBs were higher than the values adopted by the design codes, indicating a substantial safety margin in these structures. The safety margin associated with the R factor ranged from 42% to 54%. The calculated overstrength factor, â¦, as conservative, on average, 8% higher than the design values. The Cd factor was also conservative as it was, on average, 19% lower than the code deflection amplification factors. The outcomes of this study suggest the possibility of increasing R factors initially by at least 10%, potentially leading to more cost-effective designs. â¢ The fragility analysis of the benchmark MSBs indicated that at the design intensity, the likelihood of experiencing impaired occupancy (IOC) fell within the 15% to 26% range, with a very low probability of structural damage (SD). The notably high probability of unimpaired occupancy (UOC) at the designed PGA of 72% to 85% reflected the adequate seismic performance of the benchmark MSBs under a conservative far-field seismic scenario. At twice the design intensity, the probabilities of IOC and SD were below 51% and 38%, respectively, while the likelihood of SC was insignificantly small. The results confirmed the satisfactory seismic performance of the MSBs at the design intensity and twice the design PGA. The results also lent weight to the proposed adjustment in the response modification coefficients. RC High-rise Buildings â¢ he benchmar structuresâ rebar yielding sequence indicated initial signs of first local yielding in horizontal elements, followed by vertical elements, validating the design code strong column-weak beam concept. The first yield overstrength factors from ISA were more conservative than those from MBIDA due to the influence of higher mode effects of high-rise buildings. The confined concrete crushing correlated to the onset of global yielding. The local damage assessment of regular 152 and irregular high-rise buildings supported the design code provisions for not mandating additional seismic loads for the geometric and soft storey irregularities. â¢ The results reflected the insignificance of the geometric and soft storey irregularities on the reserve strength factors. The observed overstrength factors at the ultimate strength ranged between 2.62 to 2.98, confirming adequacy over the design code recommended value of 2.5. â¢ The benchmark buildings exhibited continuous stiffness reduction at different performance levels due to the development of steel yielding and concrete cracking. The average stiffness modifiers relative to initial stiffness at global yield, ultimate strength, and collapse levels were 0.83, 0.50, and 0.43, respectively. The recommended design stiffness modifier for vertical shear walls elastic analysis by Eurocode is over-conservative, while the most realistic value of 0.8 observed in the current study was recommended by FEMA 356. â¢ The IDR,c/IDR,y ratios consistently displayed lower values than the corresponding PGA,c/PGA,y ratios, ranging between 6.7% to 16.7%, which validated the design code approach for assigning equal or lower Cd factors than the R coefficients. The deflection amplification coefficients exhibited a 14% to 25% safety margin. â¢ The safety margins for the R coefficients ranged from 42% to 63% for the bearing wall buildings and between 7% to 21% for dual buildings. The margin of safety was lower for vertically irregular buildings compared to their regular counterpart. The current study suggests the potential for increasing the R coefficients initially by 10% for bearing wall buildings and by 5% for dual RC structures, resulting in more cost-effective designs for regular and irregular high-rise buildings. â¢ Unlike, the relatively higher probability of UOC at the design intensity observed in steel moment resisting frames with different heights, the benchmark high-rise buildings have much low level of damage due to the effectiveness of shear wall in controlling lateral deformation demands. At the design PGA, the likelihood of experiencing UOC fell within the average range of 78% to 67% and 75% to 72% for bearing wall and dual building sets, respectively, with lower values for geometric irregularity structure followed by soft storey high-rise building. IOC values were acceptable ranging between 19% to 26%, and 21% to 18% for bearing wall and dual building sets, respectively, and a very low probability of SD values were observed at this intensity level. At a higher intensity represented by twice the 153 design PGA, the probabilities of SD and SC ranged between 19% to 25% and 4% to 8%, respectively, which increased for geometric irregularity followed by the soft storey irregularity. â¢ The irregular buildings exhibited higher IDRs than the regular high-rise structures. The DSPs were lower for higher building set (60S-B) as compared lower building set (40S-B). The results indicated that the DSPs were slightly lower for dual building set (i.e., 60S-D) as compared bearing wall building sets (i.e., 40S-B and 60S-B). The fragility analysis results confirmed the adequate seismic performance of the all the benchmark RC high-rise buildings under far-field earthquake records representing a conservative seismic scenario for the multiple earthquake prone regions. Comparison of the two building structural systems â¢ The seismic performance of the bearing wall buildings was on par with the dual structural system. The safety margins for the R coefficients ranged from 42% to 52% for the bearing wall buildings and between 7% to 21% for dual buildings. The higher safety margins for the bearing wall system are due to the conservative factors adopted by the design code, while the low R coefficients for the dual structural system are attributed to the high design factors recommended by the code. The Cd coefficients exhibited comparable safety margins for bearing wall buildings and dual buildings. he safety margins of the â¦ coefficient ere higher for the dual building set than the bearing wall building set. â¢ The cost benefits from the regular and geometric irregular bearing wall building over the dual building counterparts were approximately $17M and $15.7M, respectively. Similar cost benefits for the soft storey bearing wall building are expected as calculated for the regular structure. The study emphasized the cost benefits of the bearing wall structural system over the dual system without compromising safety. 9.3. Future Research While the conclusions of this comprehensive study were based on thirteen MSBs and RC high-rise buildings with varying construction materials, heights, structural systems, and vertical irregularities and detailed assessment frameworks, the research can be extended as follows: 154 â¢ Further studies are needed for MSBs, and high-rise buildings designed using the proposed increase in the R coefficients to confirm the possibility for additional adjustments. â¢ Investigate vertical and horizontal irregularities other than those covered in this study. â¢ Assess other structural systems of high-rise and super tall buildings. â¢ The present study focussed on medium seismic zones, while further investigations are recommended for high seismic areas. â¢ Impact on the vertical component of the ground motions need to be studied particularly for high-irregular buildings, as the study focussed on horizontal components of earthquake records. 155 Bibliography [1] Salazar K., McNutt M. 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Building Code Vibration mode in longitudinal direction Mode 1 Mode 2 Mode 3 Period T1 (sec) Mass Participation (%) Period T2 (sec) Mass Participation (%) Period T3 (sec) Mass Participation (%) 8 Storey EN 2.63 73.72 0.88 19.02 0.43 4.46 IBC 2.91 74.21 0.96 18.29 0.45 4.44 NBCC 2.78 81.99 0.88 11.64 0.41 3.53 NZS 2.99 73.72 0.98 18.46 0.45 4.68 UBC 2.52 76.01 0.80 17.35 0.32 4.32 12 Storey EN 3.37 72.87 1.21 17.18 0.62 5.43 IBC 4.11 70.85 1.37 19.17 0.66 5.43 NBCC 3.98 79.36 1.23 12.43 0.58 3.88 NZS 4.07 70.69 1.36 19.29 0.66 5.43 UBC 3.41 76.32 1.16 15.22 0.53 4.62 16 Storey EN 4.04 72.35 1.52 15.73 0.78 5.69 IBC 5.07 71.57 1.74 17.81 0.86 5.36 NBCC 4.92 76.16 1.66 14.42 0.80 4.52 NZS 4.90 71.10 1.71 17.60 0.85 5.10 UBC 4.19 74.15 1.53 16.00 0.77 4.97 20 Storey EN 4.83 70.85 1.83 16.56 0.96 5.96 IBC 5.91 70.17 2.09 17.88 1.04 5.79 NBCC 4.65 74.71 1.90 14.88 0.98 4.69 NZS 5.71 74.93 2.05 15.04 1.02 4.71 UBC 5.03 73.20 1.91 16.41 0.98 4.69 024681012140.0 0.5 1.0 1.5 2.0 2.5Storey (Nos)Interstorey Drift (%)12S H1 H20246810121416180.0 0.5 1.0 1.5 2.0 2.5Storey (Nos)Interstorey Drift (%)16S H1 H2167 Table A.2: Design summary showing structural elements of 8-storey steel building. Vertical elements - Columns Storey C1 C2 C3 C4 C5 8 W16X26 W16X26 W16X26 W16X26 W16X26 7 W16X26 W16X26 W16X31 W16X26 W16X26 6 W16X26 W16X36 W16X36 W16X36 W16X26 5 W16X26 W16X36 W18X50 W16X36 W16X31 4 W16X26 W16X40 W21X55 W16X40 W18X35 3 W16X31 W16X45 W21X62 W16X45 W18X35 2 W16X36 W16X45 W21X62 W18X50 W16X40 1 W16X40 W16x67 W18X86 W18X76 W18X50 Horizontal elements - Beams Storey B1 B2 B3 B4 B5 All storeys W12X58 W12X58 W12X58 W12X30 W12X40 Table A.3: Design summary showing structural elements of 12-storey steel building. Vertical elements - Columns Storey C1 C2 C3 C4 C5 12 W16X26 W16X36 W16X26 W16X26 W16X26 11 W16X26 W16X36 W16X36 W16X40 W16X36 10 W16X36 W16X36 W16X40 W21X57 W16X40 9 W16X36 W16X40 W21X57 W21X57 W16X45 8 W16X36 W18X50 W18X60 W18X50 W18X50 7 W16X40 W18X50 W18X76 W18X50 W18X50 6 W16X40 W21X62 W16X67 W21X57 W18X50 5 W16X40 W21X62 W18X76 W16X67 W16X67 4 W16X36 W16X67 W18X76 W16X67 W16X67 3 W16X45 W16X67 W18X86 W16X67 W16X67 2 W16X45 W16X67 W18X86 W16X67 W16X67 1 W16X67 W18X76 W21X111 W18X86 W18X97 Horizontal elements - Beams Storey B1 B2 B3 B4 B5 168 All storeys W12X58 W12X58 W12X58 W12X30 W12X40 Table A.4: Design summary showing structural elements of 16-storey steel building. Vertical elements - Columns Storey C1 C2 C3 C4 C5 16 W16X26 W16X26 W16X26 W16X26 W16X26 15 W16X26 W16X26 W16X31 W16X36 W16X26 14 W16X26 W16X36 W18X35 W16X40 W16X31 13 W16X26 W16X40 W16X45 W18X50 W16X36 12 W16X36 W16X45 W18X50 W21X55 W16X40 11 W16X36 W21X55 W21X55 W21X55 W16X40 10 W16X36 W21X55 W21X62 W16X67 W18X35 9 W16X36 W21X55 W21X62 W16X67 W18X50 8 W16X36 W21X55 W16X67 W16X67 W18X50 7 W16X40 W21X55 W18X76 W16X67 W21X55 6 W16X40 W21X55 W18X76 W16X67 W18X50 5 W16X45 W16X67 W18X76 W18X50 W16X67 4 W16X45 W16X67 W18X86 W18X50 W16X67 3 W18X50 W16X67 W18X86 W18X50 W16X67 2 W18X50 W16X67 W18X97 W21X55 W16X67 1 W18X67 W18X86 W21X122 W18X86 W18X76 Horizontal elements - Beams Storey B1 B2 B3 B4 B5 All storeys W12X58 W12X58 W12X58 W12X30 W12X40 Table A.5: Design justification for dual structural system â contribution of frame Building Element Type Base Shear, KN X- Direction Y-Direction 60S-D-R Core Walls 21412 24776 Pier Walls 11099 10312 Contribution (%) 34% 29% 60S-D-GI Core Walls 19665 23432 Pier Walls 8599 8232 Contribution (%) 30% 26% 60S-D-SS Core Walls 22077 25884 Pier Walls 10873 10066 Contribution (%) 33% 28% 169 Table A.6: Design justification for governing lateral force direction. Building Earthquake Load (kN) Wind Load (kN) FX FY FX FY 40S-B-R 18691.12 20171.90 5528.61 8659.85 40S-B-GI 16150.03 17429.49 4776.99 7482.53 40S-B-SS 20776.21 22306.02 6072.18 9446.39 60S-B-R 29125.05 31432.44 8614.84 13494.03 60S-B-GI 25541.00 27564.45 7554.72 11833.49 60S-B-SS 29807.56 32002.37 8711.74 13552.70 60S-D-R 32512.10 35087.82 9616.69 15063.30 60S-D-GI 28664.46 30935.36 8478.60 13280.64 60S-D-SS 32951.13 35377.41 9630.50 14982.00 170 Table A.7: Design summary of shear walls of 40-storey (40S-B-R) reinforced concrete building. Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.340.50% 0.58% 1.09% 0.82% 0.57% 0.25% 0.39% 1.79%0.51% 0.59% 1.13% 0.82% 0.63% 0.59% 0.66% 1.88%20T12mm 20T12mm 22T16mm 24T12mm 16T12mm 16T12mm 16T12mm 24T16mm30T12mm 30T12mm 32T16mm 36T12mm 22T12mm 20T12mm 20T12mm 34T16mm600 600 600 600 600 600 600 600T10-150mm T10-150mm T10-150mm T10-150mm T10-200mm T10-200mm T10-200mm T10-200mmT10-150mm T10-150mm T10-150mm T10-150mm T10-200mm T10-200mm T10-200mm T10-200mm0.98 0.98 0.96 1.00 0.90 0.42 0.59 0.95400x2750 350x2750 350x2750 300x2750 250x2750 250x2750 225x2750 225x275060 60 50 50 50 50 50 4550 50 40 40 40 40 40 35Vertical steel ratio required (µ,%)Location of sectionPIER P1 Vertical steel ratio provided (%)Vertical reinforcement, endsVertical reinforcement, middleLength of Boundary elements,mmHorizontal reinforcement/m heightExtra Horizontal reinforcementDesign/Capacity (D/C) RatioPeir section (mm x mm)Concrete strength (fcu) MPaConcrete strength (fc') MPaBase 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.343.28% 1.73% 3.07% 2.21% 1.48% 0.43% 0.57% 1.14%3.39% 1.81% 3.19% 2.27% 1.52% 0.53% 0.59% 1.20%36T32mm 28T25mm 26T32mm 26T25mm 36T16mm 20T12mm 20T12mm 26T16mm54T32mm 42T25mm 40T32mm 40T25mm 54T16mm 36T12mm 36T12mm 38T16mm1000 1000 1000 1000 1000 1000 1000 1000T12-150mm T12-150mm T12-150mm T12-150mm T12-200mm T12-200mm T12-200mm T12-200mmT10-150mm T10-150mm T10-150mm T10-150mm T10-200mm T10-200mm T10-200mm T10-200mm0.97 0.96 0.96 0.97 0.97 0.81 0.97 0.95450x4750 400x4750 350x4750 300x4750 250x4750 250x4750 225x4750 225x475060 60 50 50 50 50 50 4550 50 40 40 40 40 40 35PIER P2Concrete strength (fc') MPaLocation of sectionVertical steel ratio required (µ,%)Vertical steel ratio provided (%)Vertical reinforcement, endsVertical reinforcement, middleLength of Boundary elements,mmHorizontal reinforcement/m heightExtra Horizontal reinforcementDesign/Capacity (D/C) RatioPeir section (mm x mm)Concrete strength (fcu) MPa171 Table A.7: Design summary of shear walls of 40-storey (40S-B-R) reinforced concrete building (contâ¦d). Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.342.79% 2.37% 3.93% 3.41% 2.73% 0.25% 0.25% 0.51%2.86% 2.43% 4.06% 3.44% 2.81% 0.53% 0.59% 0.59%30T32mm 38T25mm 34T32mm 40T25mm 28T25mm 20T12mm 20T12mm 20T12mm46T32mm 56T25mm 50T32mm 60T25mm 40T25mm 36T12mm 36T12mm 36T12mm1000 1000 1000 1000 1000 1000 1000 1000T12-150mm T12-150mm T12-150mm T12-150mm T12-200mm T12-200mm T12-200mm T12-200mmT10-150mm T10-150mm T10-150mm T10-150mm T10-200mm T10-200mm T10-200mm T10-200mm0.98 0.98 0.97 0.99 0.97 0.47 0.42 0.86450x4750 400x4750 350x4750 300x4750 250x4750 250x4750 225x4750 225x475060 60 50 50 50 50 50 4550 50 40 40 40 40 40 35Peir section (mm x mm)Location of sectionVertical steel ratio required (µ,%)Vertical steel ratio provided (%)Vertical reinforcement, endsVertical reinforcement, middleLength of Boundary elements,mmHorizontal reinforcement/m heightExtra Horizontal reinforcementDesign/Capacity (D/C) RatioPIER P5 Concrete strength (fcu) MPaConcrete strength (fc') MPaBase 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.342.45% 2.10% 3.70% 3.18% 2.51% 0.25% 0.33% 0.68%2.56% 2.17% 3.77% 3.24% 2.54% 0.53% 0.59% 0.70%28T32mm 34T25mm 32T32mm 38T25mm 38T20mm 20T12mm 20T12mm 26T12mm40T32mm 50T25mm 46T32mm 56T25mm 58T20mm 36T12mm 36T12mm 40T12mm1000 1000 1000 1000 1000 1000 1000 1000T12-150mm T12-150mm T12-150mm T12-150mm T12-200mm T12-200mm T12-200mm T12-200mmT10-150mm T10-150mm T10-150mm T10-150mm T10-200mm T10-200mm T10-200mm T10-200mm0.96 0.97 0.98 0.98 0.99 0.47 0.56 0.97450x4750 400x4750 350x4750 300x4750 250x4750 250x4750 225x4750 225x475060 60 50 50 50 50 50 4550 50 40 40 40 40 40 35Extra Horizontal reinforcementLocation of sectionVertical steel ratio required (µ,%)Vertical steel ratio provided (%)Vertical reinforcement, endsVertical reinforcement, middleLength of Boundary elements,mmHorizontal reinforcement/m heightPIER P6 Design/Capacity (D/C) RatioPeir section (mm x mm)Concrete strength (fcu) MPaConcrete strength (fc') MPa172 Table A.7: Design summary of core walls of 40-storey (40S-B-R) reinforced concrete building (contâ¦d). Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.343.78% 1.51% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25%3.85% 1.53% 0.38% 0.38% 0.42% 0.42% 0.42% 0.42%56T40mm 74T20mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm128T40mm 170T20mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mmT12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mmT10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm0.98 0.99 0.66 0.66 0.60 0.60 0.60 0.60300 250 250 250 225 225 225 22550 50 50 50 50 50 45 4540 40 40 40 40 40 35 35Vertical reinforcement, middleLocation of sectionVertical steel ratio required (µ,%)Vertical steel ratio provided (%)Vertical reinforcement, endsCORE C1Horizontal reinforcement/m heightExtra Horizontal reinforcementDesign/Capacity (D/C) RatioCore thickness (mm)Concrete strength (fcu) MPaConcrete strength (fc') MPaBase 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.343.16% 1.02% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25%3.20% 1.04% 0.38% 0.38% 0.42% 0.42% 0.42% 0.42%54T40mm 60T20mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm128T40mm 138T20mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mmT12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mmT10-100mm T10-100mm T10-100mm T10-100mm T10-100mm T10-150mm T10-150mm T10-150mm0.99 0.98 0.66 0.66 0.60 0.60 0.60 0.60350 300 250 250 225 225 225 22550 50 50 50 50 50 45 4540 40 40 40 40 40 35 35Vertical reinforcement, endsLocation of sectionVertical steel ratio required (µ,%)Vertical steel ratio provided (%)CORE C2 Concrete strength (fc') MPaVertical reinforcement, middleHorizontal reinforcement/m heightExtra Horizontal reinforcementDesign/Capacity (D/C) RatioCore thickness (mm)Concrete strength (fcu) MPa173 Table A.8: Design summary of shear walls of 40-storey (40S-B-GI) reinforced concrete building. Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.242750 2750 2750 2750 2750 2750300 250 250 250 225 2251.93% 2.16% 0.52% 0.25% 0.25% 2.17%2.06% 2.28% 0.59% 0.59% 0.66% 2.23%0.94 0.95 0.88 0.42 0.38 0.97AS1 + AS2 (end) 22T20mm 20T20mm 16T12mm 16T12mm 16T12mm 18T20mmAS3 (middle) 32T20mm 30T20mm 20T12mm 20T12mm 20T12mm 26T20mmAS4 T10-150mm T10-150mm T10-150mm T10-150mm T10-200mm T10-200mmAS5 T10-150mm T10-150mm T10-150mm T10-150mm T10-200mm T10-200mm600 600 600 600 600 60050 50 50 50 50 4540 40 40 40 40 35Vertical steel ratio required (µ,%)Location of sectionLength, L (mm)Breadth, B (mm)PIER P1 Vertical steel ratio provided (%)Length of boundary elements, mmConcrete strength (fcu) MPaConcrete strength (fc') MPaDesign/Capacity (D/C) RatioReinforcementVerticalHorizontal Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.244750 4750 4750 4750 4750 4750450 400 350 300 225 2251.41% 0.48% 0.91% 0.27% 0.60% 1.54%1.47% 0.50% 0.94% 0.41% 0.63% 1.58%0.96 0.96 0.97 0.66 0.95 0.97AS1 + AS2 (end) 26T25mm 34T12mm 32T16mm 20T12mm 24T12mm 34T16mmAS3 (middle) 38T25mm 50T12mm 46T16mm 36T12mm 36T12mm 50T16mmAS4 T12-150mm T12-150mm T12-150mm T12-150mm T12-200mm T12-200mmAS5 T10-150mm T10-150mm T10-150mm T10-150mm T10-200mm T10-200mm1000 1000 1000 1000 1000 100060 60 50 50 50 4550 50 40 40 40 35PIER P2Concrete strength (fc') MPaLocation of sectionVertical steel ratio required (µ,%)Vertical steel ratio provided (%)Length of boundary elements, mmConcrete strength (fcu) MPaLength, L (mm)Breadth, B (mm)Design/Capacity (D/C) RatioReinforcementVerticalHorizontal 174 Table A.8: Design summary of shear walls of 40-storey (40S-B-GI) reinforced concrete building (contâ¦d). Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.344750 4750 4750 4750 4750 4750 4750 4750450 400 350 300 250 225 225 2252.12% 1.35% 2.74% 1.89% 1.73% 0.25% 0.33% 1.57%2.16% 1.39% 2.78% 1.94% 1.77% 0.59% 0.59% 1.62%0.98 0.97 0.99 0.97 0.98 0.42 0.56 0.97AS1 + AS2 (end) 38T25mm 34T20mm 38T25mm 36T20mm 38T16mm 20T12mm 20T12mm 34T16mmAS3 (middle) 56T25mm 50T20mm 56T25mm 52T20mm 56T16mm 36T12mm 36T12mm 52T16mmAS4 T12-150mm T12-150mm T12-150mm T12-150mm T12-200mm T12-200mm T12-200mm T12-200mmAS5 T10-150mm T10-150mm T10-150mm T10-150mm T10-200mm T10-200mm T10-200mm T10-200mm1000 1000 1000 1000 1000 1000 1000 100060 60 50 50 50 45 45 4550 50 40 40 40 35 35 35Length of boundary elements, mmLocation of sectionLength, L (mm)Breadth, B (mm)Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)Design/Capacity (D/C) RatioReinforcementVerticalHorizontal PIER P5Concrete strength (fcu) MPaConcrete strength (fc') MPaBase 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.344750 4750 4750 4750 4750 4750 4750 4750450 400 350 300 250 225 225 2252.65% 2.26% 3.85% 3.32% 2.64% 1.66% 0.25% 0.49%2.78% 2.33% 3.87% 3.38% 2.65% 1.69% 0.59% 0.59%0.95 0.97 0.99 0.98 1.00 0.98 0.42 0.83AS1 + AS2 (end) 30T32mm 36T25mm 32T32mm 40T25mm 40T20mm 36T16mm 20T12mm 20T12mmAS3 (middle) 44T32mm 54T25mm 48T32mm 58T25mm 60T20mm 54T16mm 36T12mm 36T12mmAS4 T12-150mm T12-150mm T12-150mm T12-150mm T12-200mm T12-200mm T12-200mm T12-200mmAS5 T10-150mm T10-150mm T10-150mm T10-150mm T10-200mm T10-200mm T10-200mm T10-200mm1000 1000 1000 1000 1000 1000 1000 100060 60 50 50 50 45 45 4550 50 40 40 40 35 35 35Breadth, B (mm)Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)Design/Capacity (D/C) RatioLength of boundary elements, mmLocation of sectionLength, L (mm)PIER P6ReinforcementVerticalHorizontal Concrete strength (fcu) MPaConcrete strength (fc') MPa175 Table A.8: Design summary of core walls of 40-storey (40S-B-GI) reinforced concrete building (contâ¦d). Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34300 250 250 250 225 225 225 2251.96% 0.56% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25%1.96% 0.57% 0.38% 0.38% 0.42% 0.42% 0.42% 0.42%1.00 0.98 0.66 0.66 0.60 0.60 0.60 0.60AS1: AS6 (end) 72T25mm 76T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mmAS7: AS11 (middle) 168T25mm 174T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mmAS12 T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mmAS13 T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm50 50 50 50 50 50 45 4540 40 40 40 40 40 35 35Concrete strength (fcu) MPaConcrete strength (fc') MPaVertical steel ratio required (µ,%)Vertical steel ratio provided (%)Core thickness (mm)Location of sectionCORE C1Design/Capacity (D/C) RatioReinforcementVerticalHorizontal Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34350 300 250 250 225 225 225 2251.11% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25%1.12% 0.32% 0.38% 0.38% 0.42% 0.42% 0.42% 0.42%0.99 0.78 0.66 0.66 0.60 0.60 0.60 0.60AS1: AS6 (end) 76T20mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mmAS7: AS11 (middle) 174T20mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mmAS12 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mmAS13 T10-100mm T10-100mm T10-100mm T10-100mm T10-100mm T10-150mm T10-150mm T10-150mm50 50 50 50 50 50 45 4540 40 40 40 40 40 35 35Concrete strength (fcu) MPaConcrete strength (fc') MPaLocation of sectionCore thickness (mm)Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)ReinforcementVerticalHorizontal CORE C2 Design/Capacity (D/C) Ratio176 Table A.9: Design summary of shear walls of 40-storey (40S-B-SS) reinforced concrete building. Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.342750 2750 2750 2750 2750 2750 2750 2750400 350 350 300 250 250 225 2250.72% 0.73% 1.22% 4.60% 0.82% 0.25% 0.25% 2.21%0.73% 0.79% 1.25% 4.87% 0.82% 0.59% 0.66% 2.34%0.99 0.92 0.98 0.94 1.00 0.42 0.38 0.94AS1 + AS2 (end) 16T16mm 16T16mm 24T16mm 20T32mm 20T12mm 16T12mm 16T12mm 18T20mmAS3 (middle) 24T16mm 22T16mm 36T16mm 30T32mm 30T12mm 20T12mm 20T12mm 28T20mmAS4 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mmAS5 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm600 600 600 600 600 600 600 60060 60 50 50 50 50 50 4550 50 40 40 40 40 40 35Vertical steel ratio required (µ,%)Location of sectionLength, L (mm)Breadth, B (mm)PIER P1 Vertical steel ratio provided (%)Length of boundary elements, mmConcrete strength (fcu) MPaConcrete strength (fc') MPaDesign/Capacity (D/C) RatioReinforcementVerticalHorizontal Floor no.2 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.344750 4750 4750 4750 4750 4750 4750 4750450 400 350 300 250 250 225 2252.75% 2.44% 3.60% 2.72% 1.63% 0.26% 0.49% 1.23%2.78% 2.54% 3.68% 2.76% 1.69% 0.53% 0.59% 1.28%0.99 0.96 0.98 0.99 0.96 0.49 0.83 0.96AS1 + AS2 (end) 30T32mm 24T32mm 30T32mm 32T25mm 26T20mm 20T12mm 20T12mm 28T16mmAS3 (middle) 44T32mm 36T32mm 46T32mm 48T25mm 38T20mm 36T12mm 36T12mm 40T16mmAS4 T16-100mm T16-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mmAS5 T16-100mm T16-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm1000 1000 1000 1000 1000 1000 1000 100060 60 50 50 50 50 50 4550 50 40 40 40 40 40 35PIER P2Concrete strength (fc') MPaLocation of sectionVertical steel ratio required (µ,%)Vertical steel ratio provided (%)Length of boundary elements, mmConcrete strength (fcu) MPaLength, L (mm)Breadth, B (mm)Design/Capacity (D/C) RatioReinforcementVerticalHorizontal 177 Table A.9: Design summary of shear walls of 40-storey (40S-B-SS) reinforced concrete building (contâ¦d). Floor no.2 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.344750 4750 4750 4750 4750 4750 4750 4750450 400 350 300 250 250 225 2252.93% 2.52% 4.11% 3.61% 2.93% 0.25% 0.25% 0.50%3.01% 2.54% 4.16% 3.72% 3.06% 0.53% 0.59% 0.59%0.97 0.99 0.99 0.97 0.96 0.47 0.42 0.85AS1 + AS2 (end) 32T32mm 24T32mm 34T32mm 26T32mm 30T25mm 20T12mm 20T12mm 20T12mmAS3 (middle) 48T32mm 36T32mm 52T32mm 40T32mm 44T25mm 36T12mm 36T12mm 36T12mmAS4 T16-100mm T16-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mmAS5 T16-100mm T16-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm1000 1000 1000 1000 1000 1000 1000 100060 60 50 50 50 50 50 4550 50 40 40 40 40 40 35Length of boundary elements, mmLocation of sectionLength, L (mm)Breadth, B (mm)Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)Design/Capacity (D/C) RatioReinforcementVerticalHorizontal PIER P5Concrete strength (fcu) MPaConcrete strength (fc') MPaFloor no.2 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.344750 4750 4750 4750 4750 4750 4750 4750450 400 350 300 250 250 225 2252.25% 2.28% 3.90% 3.39% 2.71% 0.25% 0.25% 0.61%2.26% 2.37% 4.06% 3.61% 2.81% 0.53% 0.59% 0.63%1.00 0.96 0.96 0.94 0.96 0.47 0.42 0.97AS1 + AS2 (end) 24T32mm 22T32mm 34T32mm 26T32mm 28T25mm 20T12mm 20T12mm 24T12mmAS3 (middle) 36T32mm 34T32mm 50T32mm 38T32mm 40T25mm 36T12mm 36T12mm 36T12mmAS4 T16-100mm T16-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mmAS5 T16-100mm T16-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm1000 1000 1000 1000 1000 1000 1000 100060 60 50 50 50 50 50 4550 50 40 40 40 40 40 35Breadth, B (mm)Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)Design/Capacity (D/C) RatioLength of boundary elements, mmLocation of sectionLength, L (mm)PIER P6ReinforcementVerticalHorizontal Concrete strength (fcu) MPaConcrete strength (fc') MPa178 Table A.9: Design summary of core walls of 40-storey (40S-B-SS) reinforced concrete building (contâ¦d). Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34300 250 250 250 225 225 225 2250.54% 1.15% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25%0.61% 1.16% 0.38% 0.38% 0.42% 0.42% 0.42% 0.42%0.89 0.99 0.66 0.66 0.60 0.60 0.60 0.60AS1: AS6 (end) 50T16mm 86T16mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mmAS7: AS11 (middle) 132T16mm 202T16mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mmAS12 T16-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mmAS13 T16-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm50 50 50 50 50 50 45 4540 40 40 40 40 40 35 35Concrete strength (fcu) MPaConcrete strength (fc') MPaVertical steel ratio required (µ,%)Vertical steel ratio provided (%)Core thickness (mm)Location of sectionCORE C1Design/Capacity (D/C) RatioReinforcementVerticalHorizontal Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34350 300 250 250 225 225 225 2250.63% 0.61% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25%0.63% 0.63% 0.38% 0.38% 0.42% 0.42% 0.42% 0.42%1.00 0.97 0.66 0.66 0.60 0.60 0.60 0.60AS1: AS6 (end) 66T16mm 56T16mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mmAS7: AS11 (middle) 154T16mm 132T16mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mmAS12 T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mmAS13 T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm50 50 50 50 50 50 45 4540 40 40 40 40 40 35 35Concrete strength (fcu) MPaConcrete strength (fc') MPaLocation of sectionCore thickness (mm)Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)ReinforcementVerticalHorizontal CORE C2Design/Capacity (D/C) Ratio179 Table A.9: Design summary of columns of 40-storey (40S-B-SS) reinforced concrete building in lower floors (contâ¦d). AS1 AS2AS3AS4Breadth, B (mm)C6B, C7B, C14B, C15B1600120016001200 1600Columns between Base 1 to Floor 1Location of sectionLength, L (mm)C5B, C8B, C13B, C16B1600C2A, C3A, C10A, C11A C5A, C8A, C13A, C16A C6A, C7A, C14A, C15A C2B, C3B, C10B, C11B1600Concrete strength (fcu) MPaConcrete strength (fc') MPa 50Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)Design/Capacity (D/C) RatioReinforcementVerticalHorizontal 2.22%2.36%600.9414T40mm22T40mm6LT16-100mm2LT12-100mm 2LT12-100mm6050160012001.78%1.84%0.9718T32mm26T32mm2.03%2.23%0.9114T40mm20T40mm6LT16-100mm 6LT16-100mm2LT12-100mm60500.80%0.84%0.9520T25mm160016000.80%0.84%0.9520T25mm5024T25mm6LT12-150mm2LT12-100mm605024T25mm6LT12-150mm2LT12-100mm606LT12-150mm2LT12-100mm605016000.80%0.84%0.9520T25mm24T25mm180 Table A.10: Design summary of shear walls of 60 storey (60S-B-GI) reinforced concrete building. Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.342750 2750 2750 2750 2750 2750 2750 2750350 350 300 275 250 250 225 2253.30% 1.82% 3.07% 1.38% 2.25% 0.91% 1.27% 3.00%3.34% 1.94% 3.21% 1.44% 2.28% 1.05% 1.30% 3.17%0.99 0.94 0.96 0.96 0.99 0.87 0.98 0.95AS1 + AS2 (end) 16T32mm 16T25mm 22T25mm 22T16mm 20T20mm 16T16mm 16T16mm 16T25mmAS3 (middle) 24T32mm 22T25mm 32T25mm 32T16mm 30T20mm 20T16mm 24T16mm 24T25mmAS4 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mmAS5 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm600 600 600 600 600 600 600 60060 60 60 60 50 50 45 4550 50 50 50 40 40 35 35Vertical steel ratio provided (%)Length of boundary elements, mmConcrete strength (fcu) MPaConcrete strength (fc') MPaDesign/Capacity (D/C) RatioReinforcementVerticalHorizontal Vertical steel ratio required (µ,%)Location of sectionLength, L (mm)Breadth, B (mm)REINFORCEMENT SCHEDULE OF PIER P1Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.344750 4750 4750 4750 4750 4750 4750 4750450 400 350 325 250 250 225 2255.31% 4.41% 5.13% 2.64% 4.74% 1.51% 1.52% 2.38%5.53% 4.63% 5.29% 2.81% 4.74% 1.59% 1.70% 2.66%0.96 0.95 0.97 0.94 1.00 0.95 0.89 0.89AS1 + AS2 (end) 38T40mm 28T40mm 28T40mm 22T32mm 28T32mm 24T20mm 22T20mm 22T25mmAS3 (middle) 56T40mm 42T40mm 42T40mm 32T32mm 42T32mm 36T20mm 36T20mm 36T25mmAS4 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mmAS5 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm1000 1000 1000 1000 1000 1000 1000 100060 60 60 60 50 50 45 4550 50 50 50 40 40 35 35Concrete strength (fc') MPaLocation of sectionVertical steel ratio required (µ,%)Vertical steel ratio provided (%)Length of boundary elements, mmConcrete strength (fcu) MPaLength, L (mm)Breadth, B (mm)Design/Capacity (D/C) RatioReinforcementVerticalHorizontal REINFORCEMENT SCHEDULE OF PIER P2181 Table A.10: Design summary of shear walls of 60 storey (60S-B-GI) reinforced concrete building (contâ¦d). Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.544750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750550 550 500 500 450 400 325 325 250 250 225 2252.49% 0.99% 2.44% 0.74% 1.56% 0.79% 0.56% 0.47% 0.25% 0.25% 0.50% 2.06%2.59% 1.01% 2.51% 0.79% 1.61% 0.80% 0.57% 0.48% 0.53% 0.53% 0.59% 2.18%0.96 0.98 0.97 0.94 0.97 0.99 0.98 0.98 0.47 0.47 0.85 0.94AS1 + AS2 (end) 34T32mm 34T20mm 30T32mm 24T20mm 28T25mm 30T16mm 32T12mm 26T12mm 20T12mm 20T12mm 20T12mm 30T20mmAS3 (middle) 50T32mm 50T20mm 44T32mm 36T20mm 42T25mm 46T16mm 46T12mm 40T12mm 36T12mm 36T12mm 36T12mm 44T20mmAS4 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mmAS5 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 100080 80 70 70 60 60 60 60 50 50 45 4565 65 57 57 50 50 50 50 40 40 35 35Concrete strength (fcu) MPaConcrete strength (fc') MPaLength of boundary elements, mmREINFORCEMENT SCHEDULE OF PIER P5Location of sectionLength, L (mm)Breadth, B (mm)Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)Design/Capacity (D/C) RatioReinforcementVerticalHorizontal Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.544750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750550 550 500 500 450 400 325 325 250 250 225 2253.30% 1.93% 3.52% 1.89% 2.94% 2.49% 2.89% 0.46% 2.58% 0.96% 0.37% 0.87%3.37% 1.97% 3.60% 2.03% 3.01% 2.54% 3.13% 0.47% 2.65% 1.02% 0.59% 0.89%0.98 0.98 0.98 0.93 0.98 0.98 0.92 0.98 0.97 0.94 0.63 0.98AS1 + AS2 (end) 28T40mm 26T32mm 28T40mm 24T32mm 32T32mm 24T32mm 24T32mm 26T12mm 26T25mm 24T16mm 20T12mm 34T12mmAS3 (middle) 42T40mm 38T32mm 40T40mm 36T32mm 48T32mm 36T32mm 36T32mm 38T12mm 38T25mm 36T16mm 36T12mm 50T12mmAS4 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mmAS5 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 100080 80 70 70 60 60 60 60 50 50 45 4565 65 57 57 50 50 50 50 40 40 35 35ReinforcementVerticalHorizontal Concrete strength (fcu) MPaConcrete strength (fc') MPaREINFORCEMENT SCHEDULE OF PIER P6Location of sectionLength, L (mm)Breadth, B (mm)Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)Design/Capacity (D/C) RatioLength of boundary elements, mm182 Table A.10: Design summary of core walls of 60 storey (60S-B-GI) reinforced concrete building (contâ¦d). Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.54500 450 350 350 275 275 250 250 225 225 225 2251.05% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.31% 0.48% 0.52% 0.48%1.06% 0.25% 0.29% 0.29% 0.35% 0.35% 0.38% 0.38% 0.43% 0.48% 0.53% 0.48%0.99 1.00 0.86 0.86 0.71 0.71 0.66 0.66 0.72 1.00 0.98 1.00AS1: AS6 (end) 66T25mm 60T12mm 48T12mm 48T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 58T12mm 64T12mm 58T12mmAS7: AS11 (middle) 150T25mm 140T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 134T12mm 146T12mm 134T12mmAS12 T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mmAS13 T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm80 70 60 60 60 60 50 50 50 50 45 4565 57 50 50 50 50 40 40 40 40 35 35Design/Capacity (D/C) RatioReinforcementVerticalHorizontal Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)Core thickness (mm)REINFORCEMENT SCHEDULE OF CORE C1Location of sectionConcrete strength (fcu) MPaConcrete strength (fc') MPaBase 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.54550 500 400 400 300 300 275 275 250 250 225 2251.93% 1.06% 0.44% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.43% 0.43%1.94% 1.07% 0.47% 0.26% 0.32% 0.32% 0.35% 0.35% 0.38% 0.38% 0.46% 0.46%0.99 0.99 0.94 0.96 0.78 0.78 0.71 0.71 0.66 0.66 0.93 0.93AS1: AS6 (end) 80T32mm 66T25mm 54T16mm 54T12mm 40T12mm 40T12mm 36T12mm 36T12mm 36T12mm 36T12mm 52T12mm 52T12mmAS7: AS11 (middle) 186T32mm 152T25mm 132T16mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mmAS12 T16-100mm T16-100mm T16-100mm T16-100mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T12-150mm T12-150mm T12-150mmAS13 T16-100mm T16-100mm T16-100mm T16-100mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T12-150mm T12-150mm T12-150mm80 70 60 60 60 60 50 50 50 50 45 4565 57 50 50 50 50 40 40 40 40 35 35Design/Capacity (D/C) RatioConcrete strength (fcu) MPaConcrete strength (fc') MPaREINFORCEMENT SCHEDULE OF CORE C2Location of sectionCore thickness (mm)Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)ReinforcementVerticalHorizontal 183 Table A.11: Design summary of shear walls of 60 storey (60S-B-SS) reinforced concrete building. Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.542750 2750 2750 2750 2750 2750 2750 2750 2750 2750 2750 2750550 550 450 450 350 350 275 275 250 250 225 2250.63% 0.25% 2.48% 0.98% 3.94% 2.07% 3.03% 1.07% 1.89% 0.44% 0.79% 2.16%0.66% 0.48% 2.54% 1.02% 4.18% 2.24% 3.25% 1.17% 2.01% 0.59% 0.80% 2.23%0.95 0.52 0.98 0.96 0.94 0.92 0.93 0.91 0.94 0.75 0.99 0.97AS1 + AS2 (end) 20T16mm 16T16mm 26T25mm 16T20mm 20T32mm 18T25mm 20T25mm 18T16mm 18T20mm 16T12mm 18T12mm 18T20mmAS3 (middle) 30T16mm 20T16mm 38T25mm 24T20mm 30T32mm 26T25mm 30T25mm 26T16mm 26T20mm 20T12mm 26T12mm 26T20mmAS4 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mmAS5 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm600 600 600 600 600 600 600 600 600 600 600 60080 80 70 70 60 60 60 60 50 50 45 4565 65 57 57 50 50 50 50 40 40 35 35Vertical steel ratio required (µ,%)REINFORCEMENT SCHEDULE OF PIER P1Location of sectionLength, L (mm)Breadth, B (mm)Vertical steel ratio provided (%)Length of boundary elements, mmConcrete strength (fcu) MPaConcrete strength (fc') MPaDesign/Capacity (D/C) RatioReinforcementVerticalHorizontal Floor no.2 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.544750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750600 550 500 500 450 400 325 325 250 250 225 2254.02% 4.02% 4.89% 2.96% 3.61% 2.69% 2.54% 0.50% 1.22% 0.75% 0.83% 1.75%4.14% 4.14% 4.97% 3.05% 3.69% 2.79% 2.54% 0.51% 1.25% 0.76% 0.85% 1.77%0.97 0.97 0.98 0.97 0.98 0.96 1.00 0.98 0.98 0.99 0.98 0.99AS1 + AS2 (end) 38T40mm 34T40mm 38T40mm 36T32mm 40T32mm 26T32mm 32T25mm 28T12mm 30T16mm 32T12mm 32T12mm 38T16mmAS3 (middle) 56T40mm 52T40mm 56T40mm 54T32mm 58T32mm 40T32mm 48T25mm 42T12mm 44T16mm 48T12mm 48T12mm 56T16mmAS4 T16-100mm T16-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mmAS5 T16-100mm T16-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 100080 80 70 70 60 60 60 60 50 50 45 4565 65 57 57 50 50 50 50 40 40 35 35REINFORCEMENT SCHEDULE OF PIER P2Concrete strength (fc') MPaLocation of sectionVertical steel ratio required (µ,%)Vertical steel ratio provided (%)Length of boundary elements, mmConcrete strength (fcu) MPaLength, L (mm)Breadth, B (mm)Design/Capacity (D/C) RatioReinforcementVerticalHorizontal 184 Table A.11: Design summary of shear walls of 60 storey (60S-B-SS) reinforced concrete building (contâ¦d). Floor no.2 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.544750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750550 550 500 500 450 400 325 325 250 250 225 2254.08% 3.35% 4.86% 3.23% 4.23% 3.77% 4.17% 1.47% 3.49% 0.45% 0.40% 0.85%4.14% 3.37% 4.97% 3.39% 4.35% 3.81% 4.38% 1.51% 3.55% 0.53% 0.59% 0.89%0.99 0.99 0.98 0.95 0.97 0.99 0.95 0.97 0.98 0.85 0.68 0.96AS1 + AS2 (end) 34T40mm 28T40mm 38T40mm 26T40mm 30T40mm 36T32mm 34T32mm 30T20mm 34T25mm 20T12mm 20T12mm 34T12mmAS3 (middle) 52T40mm 42T40mm 56T40mm 38T40mm 44T40mm 54T32mm 50T32mm 44T20mm 52T25mm 36T12mm 36T12mm 50T12mmAS4 T16-100mm T16-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mmAS5 T16-100mm T16-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 100080 80 70 70 60 60 60 60 50 50 45 4565 65 57 57 50 50 50 50 40 40 35 35Length of boundary elements, mmREINFORCEMENT SCHEDULE OF PIER P5Location of sectionLength, L (mm)Breadth, B (mm)Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)Design/Capacity (D/C) RatioReinforcementVerticalHorizontal Concrete strength (fcu) MPaConcrete strength (fc') MPaFloor no.2 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.544750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750550 550 500 500 450 400 325 325 250 250 225 2253.66% 3.07% 4.63% 2.97% 3.98% 3.50% 3.88% 1.19% 3.19% 0.40% 0.49% 1.06%3.75% 3.17% 4.76% 3.05% 4.12% 3.56% 3.96% 1.22% 3.31% 0.53% 0.59% 1.13%0.98 0.97 0.97 0.97 0.97 0.98 0.98 0.98 0.96 0.75 0.83 0.94AS1 + AS2 (end) 32T40mm 26T40mm 36T40mm 36T32mm 28T40mm 34T32mm 30T32mm 24T20mm 32T25mm 20T12mm 20T12mm 24T16mmAS3 (middle) 46T40mm 40T40mm 54T40mm 54T32mm 42T40mm 50T32mm 46T32mm 36T20mm 48T25mm 36T12mm 36T12mm 36T16mmAS4 T16-100mm T16-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mmAS5 T16-100mm T16-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 100080 80 70 70 60 60 60 60 50 50 45 4565 65 57 57 50 50 50 50 40 40 35 35Breadth, B (mm)Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)Design/Capacity (D/C) RatioLength of boundary elements, mmREINFORCEMENT SCHEDULE OF PIER P6Location of sectionLength, L (mm)ReinforcementVerticalHorizontal Concrete strength (fcu) MPaConcrete strength (fc') MPa185 Table A.11: Design summary of core walls of 60 storey (60S-B-SS) reinforced concrete building (contâ¦d). Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.54500 450 350 350 275 275 250 250 225 225 225 2250.63% 0.63% 1.36% 0.25% 0.25% 0.25% 0.32% 0.25% 0.25% 0.26% 0.46% 0.45%0.64% 0.64% 1.37% 0.29% 0.35% 0.35% 0.39% 0.38% 0.42% 0.42% 0.46% 0.46%0.98 0.98 0.99 0.86 0.71 0.71 0.82 0.66 0.60 0.62 1.00 0.98AS1: AS6 (end) 62T20mm 56T20mm 60T25mm 48T12mm 38T12mm 38T12mm 40T12mm 36T12mm 36T12mm 36T12mm 52T12mm 50T12mmAS7: AS11 (middle) 142T20mm 132T20mm 136T25mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mmAS12 T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T12-150mm T12-150mm T12-150mm T12-150mmAS13 T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T12-150mm T12-150mm T12-150mm T12-150mm80 70 60 60 60 60 50 50 50 50 45 4565 57 50 50 50 50 40 40 40 40 35 35Concrete strength (fcu) MPaConcrete strength (fc') MPaVertical steel ratio required (µ,%)Vertical steel ratio provided (%)Core thickness (mm)REINFORCEMENT SCHEDULE OF CORE C1Location of sectionDesign/Capacity (D/C) RatioReinforcementVerticalHorizontal Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.54550 500 400 400 300 300 275 275 250 250 225 2251.59% 1.58% 0.85% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.46% 0.45%1.61% 1.59% 0.86% 0.26% 0.32% 0.32% 0.35% 0.35% 0.38% 0.38% 0.42% 0.46%0.99 0.99 0.99 0.96 0.78 0.78 0.71 0.71 0.66 0.66 1.10 0.98AS1: AS6 (end) 66T32mm 60T32mm 66T20mm 50T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 50T12mmAS7: AS11 (middle) 154T32mm 138T32mm 152T20mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mmAS12 T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T12-150mm T12-150mm T12-150mm T12-150mmAS13 T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T12-150mm T12-150mm T12-150mm T12-150mm80 70 60 60 60 60 50 50 50 50 45 4565 57 50 50 50 50 40 40 40 40 35 35Concrete strength (fcu) MPaConcrete strength (fc') MPaREINFORCEMENT SCHEDULE OF CORE C2Location of sectionCore thickness (mm)Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)ReinforcementVerticalHorizontal Design/Capacity (D/C) Ratio186 Table A.11: Design summary of columns of 60 storey (60S-B-SS) reinforced concrete building (contâ¦d). AS1 AS2AS3AS4Breadth, B (mm)C6B, C7B, C14B, C15B1600120016001200 1600Columns between Base 1 to Floor 1Location of sectionLength, L (mm)C5B, C8B, C13B, C16B1600C2A, C3A, C10A, C11A C5A, C8A, C13A, C16A C6A, C7A, C14A, C15A C2B, C3B, C10B, C11B1600Concrete strength (fcu) MPaConcrete strength (fc') MPa 65Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)Design/Capacity (D/C) RatioReinforcementVerticalHorizontal 3.97%4.19%800.9526T40mm38T40mm6LT16-100mm6LT16-100mm 6LT16-100mm8065160012002.40%2.51%0.9624T32mm36T32mm2.92%3.01%0.9718T40mm28T40mm6LT16-100mm 6LT16-100mm6LT16-100mm80650.80%0.84%0.9522T25mm160016000.80%0.84%0.9522T25mm6522T25mm6LT12-100mm6LT12-100mm806522T25mm6LT12-100mm6LT12-100mm806LT12-100mm6LT12-100mm806516000.80%0.84%0.9522T25mm22T25mm187 Table A.12: Design summary of shear walls of 60 storey (60S-D-R) reinforced concrete building. P1A P1B P1C P1D P1E P1F P1G P1H P1J P1K P1L P1MBase 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.545.21% 4.43% 4.30% 3.98% 4.55% 3.94% 2.53% 1.64% 1.00% 0.47% 0.45% 1.34%5.33% 4.57% 4.49% 4.15% 4.65% 4.09% 2.60% 1.78% 1.04% 0.52% 0.59% 1.43%28T40mm 24T40mm 22T40mm 20T40mm 22T40mm 28T32mm 16T32mm 24T20mm 20T16mm 16T12mm 16T12mm 18T16mm42T40mm 36T40mm 32T40mm 30T40mm 34T40mm 42T32mm 24T32mm 36T20mm 30T16mm 22T12mm 20T12mm 26T16mm600 600 600 600 600 600 600 600 600 600 600 600T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-200mm T12-200mm T12-200mm T12-200mmT10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-200mm T10-200mm T10-200mm T10-200mm0.98 0.97 0.96 0.96 0.98 0.96 0.97 0.92 0.96 0.90 0.76 0.94600x2750 600x2750 550x2750 550x2750 550x2750 500x2750 450x2750 400x2750 350x2750 300x2750 250x2750 225x275080 70 70 60 50 50 50 50 50 50 45 4565 57 57 m 40 40 40 40 40 40 35 35Vertical steel ratio required (µ,%)PIER P1 P4 P9 P12Model of section [P1, P4, P9, P12]Location of sectionVertical steel ratio provided (%)Vertical reinforcement, endsVertical reinforcement, middleLength of Boundary elements,mmHorizontal reinforcement/m heightExtra Horizontal reinforcementDesign/Capacity (D/C) RatioPeir section (mm x mm)Concrete strength (fcu) MPaConcrete strength (fc') MPaBase 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.543.86% 4.44% 2.85% 2.69% 2.90% 2.23% 1.60% 1.23% 0.92% 0.88% 0.91% 1.40%3.97% 4.59% 2.89% 2.79% 2.96% 2.30% 1.61% 1.26% 0.94% 0.90% 0.95% 1.47%36T40mm 42T40mm 24T40mm 24T40mm 38T32mm 38T32mm 28T25mm 30T20mm 32T16mm 26T16mm 22T16mm 20T20mm54T40mm 62T40mm 36T40mm 36T40mm 58T32mm 40T32mm 42T25mm 46T20mm 46T16mm 38T16mm 34T16mm 30T20mm1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-200mm T12-200mm T12-200mm T12-200mmT10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-200mm T10-200mm T10-200mm T10-200mm0.97 0.97 0.99 0.96 0.98 0.97 0.99 0.98 0.98 0.98 0.96 0.95600x4750 600x4750 550x4750 550x4750 550x4750 500x4750 450x4750 400x4750 350x4750 300x4750 250x4750 225x475080 70 70 60 50 50 50 50 50 50 45 4565 57 57 50 40 40 40 40 40 40 35 35PIER P2 Concrete strength (fc') MPaLocation of sectionVertical steel ratio required (µ,%)Vertical steel ratio provided (%)Vertical reinforcement, endsVertical reinforcement, middleLength of Boundary elements,mmHorizontal reinforcement/m heightExtra Horizontal reinforcementDesign/Capacity (D/C) RatioPeir section (mm x mm)Concrete strength (fcu) MPa188 Table A.12: Design summary of shear walls of 60 storey (60S-D-R) reinforced concrete building (contâ¦d). Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.543.78% 3.87% 3.78% 3.65% 3.96% 3.31% 2.54% 1.87% 0.98% 0.53% 0.48% 0.58%3.88% 3.97% 3.85% 3.75% 4.04% 3.39% 2.63% 1.91% 1.02% 0.56% 0.55% 0.59%36T40mm 36T40mm 32T40mm 32T40mm 34T40mm 40T32mm 28T32mm 30T25mm 34T16mm 28T12mm 22T12mm 22T12mm52T40mm 54T40mm 48T40mm 46T40mm 50T40mm 60T32mm 42T32mm 44T25mm 50T16mm 42T12mm 36T12mm 36T12mm1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-200mm T12-200mm T12-200mm T12-200mmT10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-200mm T10-200mm T10-200mm T10-200mm0.97 0.97 0.98 0.97 0.98 0.98 0.97 0.98 0.96 0.95 0.87 0.98600x4750 600x4750 550x4750 550x4750 550x4750 500x4750 450x4750 400x4750 350x4750 300x4750 250x4750 225x475080 70 70 60 50 50 50 50 50 50 45 4565 57 57 50 40 40 40 40 40 40 35 35Peir section (mm x mm)PIER P5 Location of sectionVertical steel ratio required (µ,%)Vertical steel ratio provided (%)Vertical reinforcement, endsVertical reinforcement, middleLength of Boundary elements,mmHorizontal reinforcement/m heightExtra Horizontal reinforcementDesign/Capacity (D/C) RatioConcrete strength (fcu) MPaConcrete strength (fc') MPaP6A P6B P6C P6D P6E P6F P6G P6H P6J P6K P6L P6MBase 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.543.54% 3.69% 3.63% 3.52% 4.76% 3.24% 2.54% 1.94% 1.36% 1.03% 0.94% 1.15%3.70% 3.79% 3.75% 3.56% 4.81% 3.32% 2.63% 2.02% 1.40% 1.04% 0.98% 1.20%34T40mm 34T40mm 32T40mm 30T40mm 40T40mm 40T32mm 28T32mm 32T25mm 30T20mm 30T16mm 24T16mm 26T16mm50T40mm 52T40mm 46T40mm 44T40mm 60T40mm 58T32mm 42T32mm 46T25mm 44T20mm 44T16mm 34T16mm 38T16mm1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-200mm T12-200mm T12-200mm T12-200mmT10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-200mm T10-200mm T10-200mm T10-200mm0.96 0.97 0.97 0.99 0.99 0.98 0.97 0.96 0.97 0.99 0.96 0.96600x4750 600x4750 550x4750 550x4750 550x4750 500x4750 450x4750 400x4750 350x4750 300x4750 250x4750 225x475080 70 70 60 50 50 50 50 50 50 45 4565 57 57 50 40 40 40 40 40 40 35 35Extra Horizontal reinforcementPIER P6Model of section [P6, P7, P14, P15] Location of sectionVertical steel ratio required (µ,%)Vertical steel ratio provided (%)Vertical reinforcement, endsVertical reinforcement, middleLength of Boundary elements,mmHorizontal reinforcement/m heightDesign/Capacity (D/C) RatioPeir section (mm x mm)Concrete strength (fcu) MPaConcrete strength (fc') MPa189 Table A.12: Design summary of core walls of 60 storey (60S-D-R) reinforced concrete building (contâ¦d). Core1A Core1B Core1C Core1D Core1E Core1F Core1G Core1H Core1J Core1K Core1L Core1MBase 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.543.59% 0.83% 0.25% 0.25% 2.16% 0.94% 0.25% 0.25% 0.25% 0.25% 0.33% 0.35%3.60% 0.83% 0.29% 0.32% 2.20% 0.95% 0.38% 0.42% 0.42% 0.42% 0.43% 0.44%78T40mm 64T20mm 48T16mm 40T16mm 68T25mm 72T16mm 36T12mm 36T12mm 36T12mm 36T12mm 40T12mm 42T12mm180T40mm 148T20mm 132T16mm 132T16mm 156T25mm 164T16mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mmT12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-200mm T12-200mm T12-200mm T12-200mmT10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-150mm T10-200mm T10-200mm T10-200mm T10-200mm1.00 1.00 0.86 0.78 0.98 0.99 0.66 0.60 0.60 0.60 0.77 0.80450 400 350 300 250 250 250 225 225 225 225 22580 70 60 60 50 50 50 50 50 45 45 4565 57 50 50 40 40 40 40 40 35 35 35Vertical reinforcement, middleCORE C1Model of section [Core 1, Core4] Location of sectionVertical steel ratio required (µ,%)Vertical steel ratio provided (%)Vertical reinforcement, endsHorizontal reinforcement/m heightExtra Horizontal reinforcementDesign/Capacity (D/C) RatioCore thickness (mm)Concrete strength (fcu) MPaConcrete strength (fc') MPaCore2A Core2B Core2C Core2D Core2E Core2F Core2G Core2H Core2J Core2K Core2L Core2MBase 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.543.09% 1.54% 0.80% 0.25% 0.99% 0.83% 0.25% 0.25% 0.25% 0.25% 0.33% 0.35%3.12% 1.55% 0.81% 0.29% 1.01% 0.84% 0.38% 0.42% 0.42% 0.42% 0.42% 0.44%74T40mm 86T25mm 62T20mm 48T12mm 58T20mm 62T16mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 42T12mm174T40mm 198T25mm 144T20mm 132T12mm 134T20mm 146T16mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mmT16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T12-150mm T12-150mm T12-150mmT16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T12-150mm T12-150mm T12-150mm0.99 0.99 0.99 0.86 0.98 0.99 0.66 0.60 0.60 0.60 0.79 0.80500 450 400 350 300 250 250 225 225 225 225 22580 70 60 60 50 50 50 50 50 45 45 4565 57 50 50 40 40 40 40 40 35 35 35Vertical reinforcement, endsCORE C2Model of section [Core 2, Core3]Location of sectionVertical steel ratio required (µ,%)Vertical steel ratio provided (%)Concrete strength (fc') MPaVertical reinforcement, middleHorizontal reinforcement/m heightExtra Horizontal reinforcementDesign/Capacity (D/C) RatioCore thickness (mm)Concrete strength (fcu) MPa190 Table A.13: Design summary of shear walls of 60 storey (60S-D-GI) reinforced concrete building. Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.342750 2750 2750 2750 2750 2750 2750 2750550 500 450 400 350 300 250 2255.10% 4.89% 4.33% 3.58% 2.79% 2.15% 2.49% 3.22%5.32% 5.12% 4.47% 3.66% 2.86% 2.21% 2.56% 3.49%0.96 0.96 0.97 0.98 0.98 0.97 0.97 0.92AS1 + AS2 (end) 26T40mm 22T40mm 18T40mm 20T32mm 22T25mm 24T20mm 22T20mm 18T25mmAS3 (middle) 38T40mm 34T40mm 26T40mm 30T32mm 34T25mm 34T20mm 34T20mm 26T25mmAS4 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mmAS5 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm600 600 600 600 600 600 600 60050 50 50 50 50 50 45 4540 40 40 40 40 40 35 35Vertical steel ratio required (µ,%)Location of sectionLength, L (mm)Breadth, B (mm)PIER P1 Vertical steel ratio provided (%)Length of boundary elements, mmConcrete strength (fcu) MPaConcrete strength (fc') MPaDesign/Capacity (D/C) RatioReinforcementVerticalHorizontal Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.344750 4750 4750 4750 4750 4750 4750 4750550 500 450 400 350 300 250 2254.67% 3.53% 3.05% 2.38% 1.59% 1.25% 1.45% 2.02%4.81% 3.70% 3.16% 2.43% 1.65% 1.32% 1.48% 2.06%0.97 0.95 0.97 0.98 0.96 0.95 0.98 0.98AS1 + AS2 (end) 40T40mm 28T40mm 34T32mm 38T25mm 22T25mm 24T20mm 22T20mm 28T20mmAS3 (middle) 60T40mm 42T40mm 50T32mm 56T25mm 34T25mm 36T20mm 34T20mm 42T20mmAS4 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mmAS5 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm1000 1000 1000 1000 1000 1000 1000 100050 50 50 50 50 50 45 4540 40 40 40 40 40 35 35PIER P2Concrete strength (fc') MPaLocation of sectionVertical steel ratio required (µ,%)Vertical steel ratio provided (%)Length of boundary elements, mmConcrete strength (fcu) MPaLength, L (mm)Breadth, B (mm)Design/Capacity (D/C) RatioReinforcementVerticalHorizontal 191 Table A.13: Design summary of shear walls of 60 storey (60S-D-GI) reinforced concrete building (contâ¦d). Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.544750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750600 600 550 550 550 500 450 400 350 300 250 2252.46% 2.70% 2.49% 2.34% 2.72% 2.02% 1.19% 0.90% 1.19% 0.82% 0.96% 1.87%2.65% 2.82% 2.59% 2.40% 2.77% 2.03% 1.23% 0.93% 1.21% 0.85% 1.02% 1.94%0.93 0.96 0.96 0.98 0.98 1.00 0.97 0.97 0.98 0.96 0.94 0.96AS1 + AS2 (end) 24T40mm 26T40mm 34T32mm 32T32mm 36T32mm 24T32mm 34T20mm 22T20mm 26T20mm 24T16mm 24T16mm 26T20mmAS3 (middle) 36T40mm 38T40mm 50T32mm 46T32mm 54T32mm 36T32mm 50T20mm 34T20mm 38T20mm 36T16mm 36T16mm 40T20mmAS4 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mmAS5 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 100080 70 70 60 50 50 50 50 50 50 45 4565 57 57 50 40 40 40 40 40 40 35 35Length of boundary elements, mmPIER P5Location of sectionLength, L (mm)Breadth, B (mm)Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)Design/Capacity (D/C) RatioReinforcementVerticalHorizontal Concrete strength (fcu) MPaConcrete strength (fc') MPaBase 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.544750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750600 600 550 550 550 500 450 400 350 300 250 2252.43% 2.73% 2.55% 2.42% 2.85% 2.22% 1.47% 0.60% 0.25% 0.42% 0.47% 0.88%2.56% 2.82% 2.59% 2.46% 2.89% 2.30% 1.52% 0.63% 0.38% 0.46% 0.53% 1.05%0.95 0.97 0.98 0.98 0.99 0.97 0.97 0.95 0.66 0.91 0.89 0.84AS1 + AS2 (end) 24T40mm 26T40mm 34T32mm 32T32mm 38T32mm 28T32mm 26T25mm 24T16mm 20T12mm 22T12mm 20T12mm 20T16mmAS3 (middle) 34T40mm 38T40mm 50T32mm 48T32mm 56T32mm 40T32mm 40T25mm 36T16mm 36T12mm 36T12mm 36T12mm 36T16mmAS4 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mmAS5 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 100080 70 70 60 50 50 50 50 50 50 45 4565 57 57 50 40 40 40 40 40 40 35 35Breadth, B (mm)Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)Design/Capacity (D/C) RatioLength of boundary elements, mmPIER P6 Location of sectionLength, L (mm)ReinforcementVerticalHorizontal Concrete strength (fcu) MPaConcrete strength (fc') MPa192 Table A.13: Design summary of core walls of 60 storey (60S-D-GI) reinforced concrete building (contâ¦d). Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.54450 400 350 300 250 250 250 225 225 225 225 2250.52% 0.25% 0.25% 0.25% 1.38% 0.26% 0.25% 0.25% 0.25% 0.25% 0.38% 0.37%0.52% 0.26% 0.29% 0.32% 1.38% 0.38% 0.38% 0.42% 0.42% 0.42% 0.42% 0.42%1.00 0.96 0.86 0.78 1.00 0.68 0.66 0.60 0.60 0.60 0.90 0.88AS1: AS6 (end) 70T16mm 54T12mm 48T12mm 40T12mm 66T20mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mmAS7: AS11 (middle) 164T16mm 132T12mm 132T12mm 132T12mm 154T20mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mmAS12 T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mmAS13 T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm80 70 60 60 50 50 50 50 50 45 45 4565 57 50 50 40 40 40 40 40 35 35 35Concrete strength (fcu) MPaConcrete strength (fc') MPaVertical steel ratio required (µ,%)Vertical steel ratio provided (%)Core thickness (mm)CORE C1Location of sectionDesign/Capacity (D/C) RatioReinforcementVerticalHorizontal Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.54500 450 400 350 300 250 250 225 225 225 225 2251.51% 0.47% 0.25% 0.25% 0.42% 0.32% 0.25% 0.25% 0.25% 0.25% 0.30% 0.33%1.53% 0.47% 0.26% 0.29% 0.42% 0.40% 0.38% 0.42% 0.42% 0.42% 0.42% 0.42%0.99 1.00 0.96 0.86 1.00 0.80 0.66 0.60 0.60 0.60 0.71 0.79AS1: AS6 (end) 58T32mm 64T16mm 54T12mm 48T12mm 68T12mm 44T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mmAS7: AS11 (middle) 132T32mm 148T16mm 132T12mm 132T12mm 156T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mmAS12 T16-100mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T12-150mm T12-150mm T12-150mm T12-150mmAS13 T16-100mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T12-150mm T12-150mm T12-150mm T12-150mm80 70 60 60 50 50 50 50 50 45 45 4565 57 50 50 40 40 40 40 40 35 35 35Concrete strength (fcu) MPaConcrete strength (fc') MPaCORE C2 Location of sectionCore thickness (mm)Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)ReinforcementVerticalHorizontal Design/Capacity (D/C) Ratio193 Table A.14: Design summary of shear walls of 60 storey (60S-D-SS) reinforced concrete building. Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.542750 2750 2750 2750 2750 2750 2750 2750 2750 2750 2750 2750700 700 600 550 500 450 400 325 250 250 225 2255.56% 4.43% 5.29% 4.60% 4.91% 4.91% 3.63% 3.05% 4.46% 1.98% 0.85% 1.32%5.74% 4.57% 5.33% 4.82% 5.12% 5.08% 3.66% 3.19% 4.57% 2.01% 0.88% 1.43%0.97 0.97 0.99 0.95 0.96 0.97 0.99 0.96 0.98 0.99 0.97 0.92AS1 + AS2 (end) 36T40mm 28T40mm 28T40mm 24T40mm 22T40mm 20T40mm 20T32mm 24T25mm 26T25mm 18T20mm 20T12mm 18T16mmAS3 (middle) 52T40mm 42T40mm 42T40mm 34T40mm 34T40mm 30T40mm 30T32mm 34T25mm 38T25mm 26T20mm 28T12mm 26T16mmAS4 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mmAS5 T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm600 600 600 600 600 600 600 600 600 600 600 60080 80 80 80 70 60 60 60 50 50 45 4565 65 65 65 57 50 50 50 40 40 35 35Vertical steel ratio provided (%)Length of boundary elements, mmConcrete strength (fcu) MPaConcrete strength (fc') MPaDesign/Capacity (D/C) RatioReinforcementVerticalHorizontal Vertical steel ratio required (µ,%)PIER P1Location of sectionLength, L (mm)Breadth, B (mm)Floor no.2 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.544750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750600 550 500 500 450 400 325 325 250 250 225 2252.22% 1.68% 3.08% 1.48% 2.46% 1.93% 2.16% 1.23% 1.87% 1.14% 1.04% 1.53%2.26% 1.69% 3.18% 1.53% 2.56% 1.96% 2.23% 1.30% 1.96% 1.19% 1.09% 1.58%0.98 0.99 0.97 0.97 0.96 0.98 0.97 0.95 0.95 0.96 0.95 0.97AS1 + AS2 (end) 32T32mm 36T25mm 38T32mm 30T25mm 28T32mm 30T25mm 28T25mm 26T20mm 30T20mm 28T16mm 24T16mm 34T16mmAS3 (middle) 48T32mm 54T25mm 56T32mm 44T25mm 40T32mm 46T25mm 42T25mm 38T20mm 44T20mm 42T16mm 34T16mm 50T16mmAS4 T16-100mm T16-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mmAS5 T16-100mm T16-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 100080 80 70 70 60 60 60 60 50 50 45 4565 65 57 57 50 50 50 50 40 40 35 35Concrete strength (fc') MPaLocation of sectionVertical steel ratio required (µ,%)Vertical steel ratio provided (%)Length of boundary elements, mmConcrete strength (fcu) MPaLength, L (mm)Breadth, B (mm)Design/Capacity (D/C) RatioReinforcementVerticalHorizontal PIER P2194 Table A.14: Design summary of shear walls of 60 storey (60S-D-SS) reinforced concrete building (contâ¦d). Floor no.2 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.544750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750550 550 500 500 450 400 325 325 250 250 225 2253.95% 3.33% 4.79% 3.16% 4.18% 3.77% 4.24% 1.65% 3.78% 0.84% 0.25% 0.49%4.04% 3.37% 4.97% 3.17% 4.35% 3.81% 4.38% 1.71% 3.89% 0.86% 0.59% 0.59%0.98 0.99 0.96 1.00 0.96 0.99 0.97 0.96 0.97 0.98 0.42 0.83AS1 + AS2 (end) 34T40mm 28T40mm 38T40mm 24T40mm 30T40mm 36T32mm 34T32mm 34T20mm 38T25mm 36T12mm 20T12mm 20T12mmAS3 (middle) 50T40mm 42T40mm 56T40mm 36T40mm 44T40mm 54T32mm 50T32mm 50T20mm 56T25mm 54T12mm 36T12mm 36T12mmAS4 T16-100mm T16-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mmAS5 T16-100mm T16-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 100080 80 70 70 60 60 60 60 50 50 45 4565 65 57 57 50 50 50 50 40 40 35 35Concrete strength (fcu) MPaConcrete strength (fc') MPaLength of boundary elements, mmPIER P5Location of sectionLength, L (mm)Breadth, B (mm)Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)Design/Capacity (D/C) RatioReinforcementVerticalHorizontal Floor no.2 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.544750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750 4750550 550 500 500 450 400 325 325 250 250 225 2253.49% 2.90% 4.44% 2.79% 3.80% 3.34% 3.78% 1.29% 3.33% 1.05% 0.80% 1.14%3.56% 3.08% 4.55% 2.84% 3.88% 3.39% 3.86% 1.34% 3.47% 1.08% 0.83% 1.20%0.98 0.94 0.98 0.98 0.98 0.99 0.98 0.96 0.96 0.97 0.96 0.95AS1 + AS2 (end) 30T40mm 26T40mm 34T40mm 34T32mm 26T40mm 32T32mm 30T32mm 26T20mm 34T25mm 26T16mm 32T12mm 26T16mmAS3 (middle) 44T40mm 38T40mm 52T40mm 50T32mm 40T40mm 48T32mm 44T32mm 40T20mm 50T25mm 38T16mm 46T12mm 38T16mmAS4 T16-100mm T16-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mmAS5 T16-100mm T16-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-100mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 100080 80 70 70 60 60 60 60 50 50 45 4565 65 57 57 50 50 50 50 40 40 35 35ReinforcementVerticalHorizontal PIER P6 Location of sectionLength, L (mm)Breadth, B (mm)Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)Design/Capacity (D/C) RatioLength of boundary elements, mmConcrete strength (fcu) MPaConcrete strength (fc') MPa195 Table A.14: Design summary of core walls of 60 storey (60S-D-SS) reinforced concrete building (contâ¦d). Base 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.54500 450 350 350 275 275 250 250 225 225 225 2250.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.36% 0.37%0.34% 0.38% 0.27% 0.27% 0.35% 0.35% 0.38% 0.38% 0.42% 0.42% 0.42% 0.42%0.74 0.66 0.93 0.93 0.71 0.71 0.66 0.66 0.60 0.60 0.86 0.88AS1: AS6 (end) 36T16mm 36T16mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mmAS7: AS11 (middle) 132T16mm 132T16mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mmAS12 T16-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mmAS13 T16-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm T12-150mm80 70 60 60 60 60 50 50 50 50 45 4565 57 50 50 50 50 40 40 40 40 35 35Design/Capacity (D/C) RatioReinforcementVerticalHorizontal Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)Concrete strength (fcu) MPaConcrete strength (fc') MPaCore thickness (mm)CORE C1 Location of sectionBase 1 Floor no.4 Floor no.9 Floor no.14 Floor no.19 Floor no.24 Floor no.29 Floor no.34 Floor no.39 Floor no.44 Floor no.49 Floor no.54550 500 400 400 300 300 275 275 250 250 225 2250.88% 0.50% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.25% 0.35% 0.35%0.89% 0.51% 0.26% 0.26% 0.32% 0.32% 0.35% 0.35% 0.38% 0.38% 0.42% 0.42%0.99 0.98 0.96 0.96 0.78 0.78 0.71 0.71 0.66 0.66 0.83 0.83AS1: AS6 (end) 60T25mm 76T16mm 54T12mm 54T12mm 40T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mm 36T12mmAS7: AS11 (middle) 140T25mm 176T16mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mm 132T12mmAS12 T16-100mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T12-150mm T12-150mm T12-150mm T12-150mmAS13 T16-100mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T16-150mm T12-150mm T12-150mm T12-150mm T12-150mm80 70 60 60 60 60 50 50 50 50 45 4565 57 50 50 50 50 40 40 40 40 35 35Design/Capacity (D/C) RatioConcrete strength (fcu) MPaConcrete strength (fc') MPaCORE C2Location of sectionCore thickness (mm)Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)ReinforcementVerticalHorizontal 196 Table A.14: Design summary of columns of 60 storey (60S-D-SS) reinforced concrete building below the transfer slab(contâ¦d). Table A.15: Rebar schedule for typical floor slab of 60S-B-R building Table A.16 : Rebar schedule for typical thick/transfer floor slab AS1 AS2AS3AS46LT12-150mm2LT12-100mm806516000.80%0.84%0.9518T25mm26T25mm6526T25mm6LT12-150mm2LT12-100mm806526T25mm6LT12-150mm2LT12-100mm800.80%0.84%0.9518T25mm160016000.80%0.84%0.9518T25mm6LT16-100mm 6LT16-100mm2LT12-100mm80652LT12-100mm 2LT12-100mm8065160012001.81%1.84%0.9818T32mm26T32mm2.40%2.62%0.9216T40mm24T40mmConcrete strength (fcu) MPaConcrete strength (fc') MPa 65Vertical steel ratio required (µ,%)Vertical steel ratio provided (%)Design/Capacity (D/C) RatioReinforcementVerticalHorizontal 2.36%2.49%800.9516T40mm22T40mm6LT16-100mmColumns between Base 1 to Floor 1Location of sectionLength, L (mm)C5B, C8B, C13B, C16B1600C2A, C3A, C10A, C11A C5A, C8A, C13A, C16A C6A, C7A, C14A, C15A C2B, C3B, C10B, C11B1600Breadth, B (mm)C6B, C7B, C14B, C15B1600120016001200 1600197 Appendix B: ISAs and MBIDAs Results Table B.1: Comparison of elastic periods obtained from design and assessment models for MSBs. Mode 8 Storey building (8S) Period, Secs 12 Storey building (12S), Period, Secs 16 Storey building (16S), Period, Secs 20 Storey building (20S) Period, Secs Design Model Assessment Model Design Model Assessment Model Design Model Assessment Model Design Model Assessment Model 1 2.52 2.35 4.07 3.95 4.90 4.49 5.91 5.26 2 1.76 1.45 2.67 2.87 3.52 3.21 4.43 4.24 3 1.61 1.30 2.64 2.64 3.27 3.00 4.15 4.09 4 0.80 0.87 1.36 1.52 1.71 1.72 2.05 2.18 5 0.56 0.52 0.86 1.00 1.15 1.12 1.45 1.49 6 0.51 0.50 0.85 0.90 1.06 1.04 1.35 1.38 7 0.47 0.44 0.78 0.90 0.94 1.02 1.17 1.30 8 0.32 0.37 0.53 0.64 0.85 0.73 1.02 0.97 9 0.31 0.29 0.49 0.58 0.66 0.66 0.83 0.87 10 0.27 0.29 0.48 0.52 0.60 0.59 0.77 0.81 11 0.25 0.25 0.42 0.49 0.50 0.56 0.64 0.72 12 0.20 0.24 0.33 0.40 0.45 0.46 0.58 0.61 Table B.2: Comparison of uncracked periods obtained from design and assessment models for benchmark RC high-rise geometric irregular buildings (vertical irregularity). Mode 40S-B-GI building Period, (Secs) 60S-B-GI building Period, (Secs) 60S-D-GI building Period, (Secs) Design Model Assessment Model Design Model Assessment Model Design Model Assessment Model 1 3.67 3.34 5.77 5.42 5.48 5.04 2 3.56 3.24 5.74 5.40 5.41 4.98 3 3.02 2.75 4.16 3.91 3.88 3.57 4 1.22 1.11 2.07 1.94 2.00 1.84 5 1.03 0.94 1.78 1.68 1.68 1.54 6 0.98 0.89 1.45 1.36 1.38 1.27 7 0.67 0.61 1.11 1.04 1.09 1.00 8 0.56 0.51 0.85 0.8 0.82 0.76 9 0.47 0.43 0.81 0.76 0.79 0.73 10 0.41 0.37 0.68 0.64 0.68 0.62 11 0.36 0.32 0.53 0.50 0.52 0.48 Table B.3: Comparison of uncracked periods obtained from design and assessment models for benchmark RC high-rise soft storey irregular buildings (vertical irregularity). Mode 40S-B-SS building Period, (Secs) 60S-B-SS building Period, (Secs) 60S-D-SS building Period, (sec) Design Model Assessment Model Design Model Assessment Model Design Model Assessment Model 1 4.05 3.76 6.53 5.87 6.24 5.74 2 4.00 3.72 6.33 5.70 5.89 5.42 3 3.68 3.42 5.64 5.08 4.58 4.21 4 1.22 1.13 1.98 1.78 1.89 1.74 5 1.13 1.05 1.80 1.62 1.73 1.59 6 1.04 0.97 1.71 1.54 1.53 1.41 7 0.63 0.59 1.04 0.93 1.00 0.92 8 0.60 0.56 0.94 0.85 0.86 0.79 9 0.48 0.44 0.84 0.75 0.82 0.75 10 0.40 0.37 0.67 0.60 0.65 0.60 11 0.38 0.35 0.61 0.55 0.57 0.52 12 0.28 0.26 0.49 0.44 0.49 0.45 198 Table B.4: Comparison on observation of global yield point using confined concrete crushing. RC Buildings Observation of IDR at Global Yield (%) IDR at Global Yield by Park's approach using secant stiffness with 75% of Ultimate strength Type of concrete crushing Type Reference 1st Unconfined concrete crushing* (secant stiffness of Ultimate strength) % IDR at 1st Confined concrete crushing in horizontal elements 40 Storey Bearing Wall Buildings 40S-B-R 0.97% 75.00 0.97% 40S-B-GI 0.97% 75.00 0.97% 40S-B-SS 1.02% 75.00 1.02% 60 Storey Bearing Wall Buildings 60S-B-R 1.22% 72.00 1.22% 60S-B-GI 1.16% 75.00 1.16% 60S-B-SS 1.08% 72.00 1.08% 60 Storey Dual Buildings 60S-D-R 0.88% 73.00 0.88% 60S-D-GI 0.79% 72.00 0.79% 60S-D-SS 0.76% 75.00 0.76% *Park's recommendation: Initial stiffness point passing through 75% of ultimate strength as secant stiffness Table B.5: Overstrength at first yield, global yield, collapse, and ultimate strength for the steel buildings. Steel Buildings Base Shear, kN 1st Yield Overstrength in Horizontal Elements, â¦y, 1h Type Reference 1st Yield, Vy, 1h - Horizontal elements Design Base Shear, Vd TLL ULL TLL ULL Steel Buildings 8 S 3231.63 3771.35 2245.00 1.44 1.68 12 S 4605.50 4964.00 3162.00 1.46 1.57 16 S 4458.00 6050.00 3810.00 1.17 1.59 20 S 4507.34 6656.26 4426.00 1.02 1.50 Steel Buildings Base Shear, kN 1st Yield Overstrength in Vertical Elements, â¦y, 1v Type Reference 1st Yield, Vy, 1v - Vertical elements Design Base Shear, Vd TLL ULL TLL ULL Steel Buildings 8 S 4066.92 4923.38 2245.00 1.81 2.19 12 S 5887.08 6672.40 3162.00 1.86 2.11 16 S 5291.00 7105.00 3810.00 1.39 1.86 20 S 5601.22 8441.42 4426.00 1.27 1.91 Steel Buildings Base Shear, kN Overstrength at Global Yield, â¦g Type Reference Global Yield Base Shear, Vg Design Base Shear, Vd TLL ULL TLL ULL Steel Buildings 8 S 4630.00 5800.00 2245.00 2.06 2.58 12 S 7230.00 8490.00 3162.00 2.29 2.69 16 S 7560.00 9560.00 3810.00 1.98 2.51 20 S 8890.00 11260.00 4426.00 2.01 2.54 Steel Buildings Base Shear, kN Overstrength at Collapse, â¦c Type Reference Base Shear at Collapse, Vc Design Base Shear, Vd TLL ULL TLL ULL Steel Buildings 8 S 5210.00 6521.00 2245.00 2.32 2.90 12 S 7290.00 8831.00 3162.00 2.31 2.79 16 S 8470.00 10810.00 3810.00 2.22 2.84 20 S 10000.00 12680.00 4426.00 2.26 2.86 Steel Buildings Base Shear, kN Ultimate Overstrength, â¦u Type Reference Ultimate Base Shear, Vu Design Base Shear, Vd TLL ULL TLL ULL Steel Buildings 8 S 5298.39 6619.54 2245.00 2.36 2.95 12 S 7469.00 9171.00 3162.00 2.36 2.90 16 S 8491.00 10863.00 3810.00 2.23 2.85 20 S 10056.00 12691.00 4426.00 2.27 2.87 199 Table B.6: Overstrength at first yield, global yield, collapse, and ultimate strength for the RC buildings. RC Buildings Base Shear, kN 1st Yield Overstrength in Horizontal Elements, â¦y, 1h Type Reference 1st Yield, Vy, 1h â Hor. elements Design Base Shear, Vd TLL ULL TLL ULL 40 Storey Bearing Wall Buildings 40S-B-R 26174.22 35270.32 18691.00 1.40 1.89 40S-B-GI 20882.50 29638.90 16150.00 1.29 1.84 40S-B-SS 26693.72 30711.81 20776.00 1.28 1.48 60 Storey Bearing Wall Buildings 60S-B-R 37065.50 45770.77 29125.00 1.27 1.57 60S-B-GI 31894.96 37020.88 25541.00 1.25 1.45 60S-B-SS 39753.34 42320.31 29807.00 1.33 1.42 60 Storey Dual Structural System Buildings 60S-D-R 41475.37 53984.44 32512.00 1.28 1.66 60S-D-GI 41236.45 50240.58 28664.00 1.44 1.75 60S-D-SS 43759.00 43726.13 32951.00 1.33 1.33 RC Buildings Base Shear, kN 1st Unconf. Conc. Crushing Overstrength, â¦uc, 1uc Type Reference 1st Crushing Unconf, Vy, 1uc Design Base Shear, Vd TLL ULL TLL ULL 40 Storey Bearing Wall Buildings 40S-B-R 33163.71 37397.86 18691.00 1.77 2.00 40S-B-GI 26459.00 33456.60 16150.00 1.64 2.07 40S-B-SS 30596.29 39758.55 20776.00 1.47 1.91 60 Storey Bearing Wall Buildings 60S-B-R 43008.34 52183.65 29125.00 1.48 1.79 60S-B-GI 39030.14 45843.90 25541.00 1.53 1.79 60S-B-SS 42369.10 58981.88 29807.00 1.42 1.98 60 Storey Dual Structural System Buildings 60S-D-R 52949.89 60672.00 32512.00 1.63 1.87 60S-D-GI 53637.35 60356.67 28664.00 1.87 2.11 60S-D-SS 59099.87 75549.49 32951.00 1.79 2.29 RC Buildings Base Shear, kN 1st Conf. Conc. Crushing Overstrength, â¦cc, 1cc Type Reference 1st Crushing Conf Conc., Vy, 1cc Design Base Shear, Vd TLL ULL TLL ULL 40 Storey Bearing Wall Buildings 40S-B-R 38740.12 44573.68 18691.00 2.07 2.38 40S-B-GI 30908.00 38351.40 16150.00 1.91 2.37 40S-B-SS 36281.74 49792.91 20776.00 1.75 2.40 60 Storey Bearing Wall Buildings 60S-B-R 60817.43 72772.27 29125.00 2.09 2.50 60S-B-GI 46523.94 56063.95 25541.00 1.82 2.20 60S-B-SS 53039.06 69475.30 29807.00 1.78 2.33 60 Storey Dual Structural System Buildings 60S-D-R 60856.98 69984.45 32512.00 1.87 2.15 60S-D-GI 60422.76 68219.94 28664.00 2.11 2.38 60S-D-SS 64975.29 82925.36 32951.00 1.97 2.52 RC Buildings Base Shear, kN 1st Yield Overstrength in Vertical Elements, â¦y, 1v Type Reference 1st Yield, Vy, 1v - Ver elements Design Base Shear, Vd TLL ULL TLL ULL 40 Storey Bearing Wall Buildings 40S-B-R 29668.97 36334.09 18691.00 1.59 1.94 40S-B-GI 23670.75 31547.75 16150.00 1.47 1.95 40S-B-SS 28645.01 35235.18 20776.00 1.38 1.70 60 Storey Bearing Wall Buildings 60S-B-R 40036.92 48977.21 29125.00 1.37 1.68 60S-B-GI 35462.55 41432.39 25541.00 1.39 1.62 60S-B-SS 41061.22 50651.10 29807.00 1.38 1.70 60 Storey Dual Structural System Buildings 60S-D-R 47212.63 57328.22 32512.00 1.45 1.76 60S-D-GI 47436.90 55298.63 28664.00 1.65 1.93 60S-D-SS 51429.44 59637.81 32951.00 1.56 1.81 200 Table B.6 (contâd) Overstrength at first yield, global yield, collapse, and ultimate strength for RC buildings. RC Buildings Base Shear, kN Overstrength at Collapse, â¦c Type Reference Base Shear at Collapse, Vc Design Base Shear, Vd TLL ULL TLL ULL 40 Storey Bearing Wall Buildings 40S-B-R 41560.00 52900.00 18691.00 2.22 2.83 40S-B-GI 33105.00 44035.00 16150.00 2.05 2.73 40S-B-SS 48010.00 61205.00 20776.00 2.31 2.95 60 Storey Bearing Wall Buildings 60S-B-R 61045.00 80128.00 29125.00 2.10 2.75 60S-B-GI 48990.00 66980.00 25541.00 1.92 2.62 60S-B-SS 61025.00 79125.00 29807.00 2.05 2.65 60 Storey Dual Structural System Buildings 60S-D-R 71800.00 94100.00 32512.00 2.21 2.89 60S-D-GI 66500.00 82900.00 28664.00 2.32 2.89 60S-D-SS 71650.00 93980.00 32951.00 2.17 2.85 RC Buildings Base Shear, kN Ultimate Overstrength, â¦u Type Reference Ultimate Base Shear, Vu Design Base Shear, Vd TLL ULL TLL ULL 40 Storey Bearing Wall Buildings 40S-B-R 41881.90 52983.14 18691.00 2.24 2.83 40S-B-GI 33414.60 44523.60 16150.00 2.07 2.76 40S-B-SS 48128.02 61916.89 20776.00 2.32 2.98 60 Storey Bearing Wall Buildings 60S-B-R 61445.10 80269.48 29125.00 2.11 2.83 60S-B-GI 49022.06 67011.04 25541.00 1.92 2.62 60S-B-SS 61623.38 79882.79 29807.00 2.07 2.68 60 Storey Dual Structural System Buildings 60S-D-R 72638.48 94638.24 32512.00 2.23 2.91 60S-D-GI 66981.74 82921.14 28664.00 2.34 2.89 60S-D-SS 73675.33 94177.50 32951.00 2.24 2.86 Table B.7: Stiffness at first yield, global yield, collapse, and ultimate strength for the steel buildings. Steel Buildings Base Shear at 1st Yield Vy, kN Displacement at 1st Yield ây, mm Stiffness at 1st Yield Ky, kN/mm Type Reference TLL ULL TLL ULL TLL ULL Steel Buildings 8 S 3231.63 3771.35 240.00 210.00 13.47 17.96 12 S 4605.50 4964.00 300.00 240.00 15.35 20.68 16 S 4458.00 6050.00 420.00 420.00 10.61 14.40 20 S 4507.34 6656.26 440.00 480.00 10.24 13.87 Steel Buildings Base Shear at Global Yield Vg, kN Displacement at Global Yield âgy, mm Stiffness at Global Yield Kgy, kN/mm Type Reference TLL ULL TLL ULL TLL ULL Steel Buildings 8 S 4630.00 5800.00 421.00 400.10 11.00 14.50 12 S 7230.00 8490.00 510.00 450.00 14.18 18.87 16 S 7560.00 9560.00 870.00 810.00 8.69 11.80 20 S 8890.00 11260.00 1120.00 990.00 7.94 11.37 Steel Buildings Base Shear at Collapse Vc, kN Displacement at Collapse âc, mm Stiffness at Collapse Kc, kN/mm Type Reference TLL ULL TLL ULL TLL ULL Steel Buildings 8 S 5210.00 6521.00 990.00 1000.00 5.26 6.52 12 S 7290.00 8831.00 990.00 1020.00 7.36 8.66 16 S 8470.00 10810.00 1500.00 1500.00 5.65 7.21 20 S 10000.00 12680.00 1959.00 1959.00 5.10 6.47 Steel Buildings Base Shear at Ultimate Vu, kN Displacement at Ultimate âu, mm Stiffness at Ultimate Ku, kN/mm Type Reference TLL ULL TLL ULL TLL ULL Steel Buildings 8 S 5298.39 6619.54 690.00 720.00 7.68 9.19 12 S 7469.00 9171.00 630.00 630.00 11.86 14.56 16 S 8491.00 10863.00 1350.00 1380.00 6.29 7.87 20 S 10056.00 12691.00 1800.00 1800.00 5.59 7.05 201 Table B.8: Stiffness at first yield, global yield, collapse, and ultimate strength for RC buildings. RC Buildings Base Shear at 1st Yield Vy, kN Displacement at 1st Yield ây, mm Stiffness at 1st Yield Ky, kN/mm Type Reference TLL ULL TLL ULL TLL ULL 40 Storey Bearing Wall Buildings 40 S Reg 26174.22 35270.32 783.36 783.60 33.41 45.01 40 S VI 20882.50 29638.90 773.60 789.16 26.99 37.56 40 S SS 26693.72 30711.81 720.00 560.00 37.07 54.84 60 Storey Bearing Wall Buildings 60 S Reg 37065.50 45770.77 1448.56 1219.84 25.59 37.52 60 S VI 31894.96 37020.88 1440.00 1120.00 22.15 33.05 60 S SS 39753.34 42320.31 1468.32 1004.64 27.07 42.12 60 Storey Dual Structural System Buildings 60 S D Reg 41475.37 53984.44 927.36 850.00 44.72 63.51 60 S D VI 41236.45 50240.58 1081.19 850.08 38.14 59.10 60 S D SS 43759.00 43726.13 927.84 618.56 47.16 70.69 RC Buildings Base Shear at 1st Crush conf Vy, 1cc, kN Displacement at 1st Crush conf ây,1cc, mm Stiffness at 1st Crush conf Ky, 1cc, kN/mm Type Reference TLL ULL TLL ULL TLL ULL 40 Storey Bearing Wall Buildings 40 S Reg 38740.12 44573.68 1462.72 1149.28 26.48 38.78 40 S VI 30908.00 38351.40 1452.00 1253.70 21.29 30.59 40 S SS 36281.74 49792.91 1200.00 1120.00 30.23 44.46 60 Storey Bearing Wall Buildings 60 S Reg 60817.43 72772.27 3354.56 2515.92 18.13 28.92 60 S VI 46523.94 56063.95 3120.00 2240.00 14.91 25.03 60 S SS 53039.06 69475.30 2318.40 2086.56 22.88 33.30 60 Storey Dual Structural System Buildings 60 S D Reg 60856.98 69984.45 1700.16 1236.48 35.79 56.60 60 S D VI 60422.76 68219.94 1932.00 1313.76 31.27 51.93 60 S D SS 64975.29 82925.36 1701.1 1469.08 38.20 56.45 RC Buildings Base Shear at Global Yield Vg, kN Displacement at Global Yield âg, mm Stiffness at Global Yield Kg, kN/mm Type Reference TLL ULL TLL ULL TLL ULL 40 Storey Bearing Wall Buildings 40 S Reg 38740.00 45600.00 1462 1253 26.50 36.39 40 S VI 30908.00 38351.00 1200 1253.7 25.76 30.59 40 S SS 32681.00 53200.00 1200 1330 27.23 40.00 60 Storey Bearing Wall Buildings 60 S Reg 57600.00 71400.00 2890 2350 19.93 30.38 60 S VI 46523.00 67011.00 3120 2240 14.91 29.92 60 S SS 53039.00 79882.00 2318 2080 22.88 38.40 60 Storey Dual Structural System Buildings 60 S D Reg 65800.00 81000.00 2000 1670 32.90 48.50 60 S D VI 56400.00 72500.00 1700 1520 33.18 47.70 60 S D SS 64975.00 94177.00 1700 1469 38.22 64.11 RC Buildings Base Shear at Collapse Vc, kN Displacement at Collapse âc, mm Stiffness at Collapse Kc, kN/mm Type Reference TLL ULL TLL ULL TLL ULL 40 Storey Bearing Wall Buildings 40 S Reg 41560.00 52900.00 2550 2550 16.30 20.75 40 S VI 33105.00 44035.00 2500 2500 13.24 17.61 40 S SS 48010.00 61205.00 2435 2450 19.72 24.98 60 Storey Bearing Wall Buildings 60 S Reg 61045.00 80128.00 3800 3850 16.06 20.81 60 S VI 48990.00 66980.00 3840 3960 12.76 16.91 60 S SS 61025.00 79125.00 3950 3980 15.45 19.88 60 Storey Dual Structural System Buildings 60 S D Reg 71800.00 94100.00 3950 3980 18.18 23.64 60 S D VI 66500.00 82900.00 3850 3860 17.27 21.48 60 S D SS 71650.00 93980.00 3900 3950 18.37 23.79 RC Buildings Ultimate Base Shear Vu, kN Displacement at Ultimaate âu, mm Stiffness at Ultimate Ku, kN/mm Type Reference TLL ULL TLL ULL TLL ULL 40 Storey Bearing Wall Buildings 40 S Reg 41881.90 52983.14 2089.60 2350.80 20.04 22.54 40 S VI 33414.60 44523.60 2146.00 2246.00 15.57 19.82 40 S SS 48128.02 61916.89 2160.00 2380.00 22.28 26.02 60 Storey Bearing Wall Buildings 60 S Reg 61445.10 80269.48 3659.52 3659.52 16.79 21.93 60 S VI 49022.06 67011.04 3980.00 3920.00 12.32 17.09 60 S SS 61623.38 79882.79 3786.72 3554.88 16.27 22.47 60 Storey Dual Structural System Buildings 60 S D Reg 72638.48 94638.24 3245.76 3709.44 22.38 25.51 60 S D VI 66981.74 82921.14 3632.16 3013.82 18.44 27.51 60 S D SS 73675.33 94177.50 3324.76 3711.36 22.16 25.38
Thesis/Dissertation
eng
Civil Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Alam, M. Shahria
Mwafy, Aman
Seismic response factors of code-designed high-rise buildings using 3D non-linear analysis
Text