Seismic vulnerability and retrofitting of gravity load designed RC buildings

ACKNOWLEDGEMENTS I would like to take this opportunity to express my profound gratitude and sincere appreciation to my erudite supervisors Professor Tan Kiang Hwee and formerly Professor T. Balendra, for their kind and systematic guidance and supervision throughout the course of this study. Their knowledge and experience has been my guiding star throughout this endeavor. I am forever indebted to my supervisor Prof. Tan Kiang Hwee for the enormous amount of patience he has shown during my thesis writing. I would also like to thank the staffs of the Structural Laboratory for their help and advice. Many thanks to Mr. Sit Beng Chiat, Mr. Edgar Lim, Mr. Ang Beng Onn, Ms Annie Tan, Mr. Ow Weng Moon, Mr. Kamsan Bin Rasman, Mr. Yip Kwok Keong, Mr. Ong Teng Chew, Mr. Yong Tat Fah, Mr Wong Kah Wai, Stanley, and Mr. Martin who help in many ways in the experiment. Special acknowledgement is given to Mr. Choo Peng Kin, Mr. Koh Yian Kheng and Mr. Ishak Bin A Rahman who had assisted and guided me tremendously in the experiments. I would also like to acknowledge NUS for providing all necessary financial and academic support without which my Ph.D. would not have been possible. I am grateful to my lecturers, relatives and friends who have supported the study in many ways. Gratitude is extended to my seniors Dr. Tamali Bhowmik, Dr. Du Hongjian for their kind help with my experiments and encouragement throughout the study. I am greatly indebted to my parents and sister who have encouraged me a lot and made many sacrifices during the study. Thank you for all those sleepless nights you have spent praying for me. Thank you for understanding and continuing to be an inseparable part of my life. I am at a loss for words to thank my wife who have suffered a lot and made many sacrifices, especially during the thesis writing. Finally I am grateful to Allah for everything that He has granted me. I II DECLARATION I hereby declare that the thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. _________________ Aziz Ahmed 27th September 2012 III IV TABLE OF CONTENTS ACKNOWLEDGEMENTS I DECLARATION III TABLE OF CONTENTS V SUMMARY . IX LIST OF FIGURES XI LIST OF TABLES XVIII LIST OF SYMBOLS . XIX CHAPTER INTRODUCTION . 1.1 BACKGROUND . 1.2 ULTIMATE SEISMIC CAPACITY OF RC GLD STRUCTURES 1.3 SEISMIC DEMAND AND ADEQUACY EVALUATION FOR BUILDINGS IN SINGAPORE 1.4 SEISMIC RETROFITTING OF RC GLD BUILDINGS IN SINGAPORE 12 1.5 OBJECTIVE AND SCOPE 14 1.6 ORGANIZATION OF THE THESIS . 16 CHAPTER LITERATURE REVIEW . 25 2.1 GENERAL . 25 2.2 SHEAR BEHAVIOR OF LOAD-BEARING ELEMENTS . 26 2.3 TOTAL DISPLACEMENT COMPONENTS OF COLUMNS UNDER LATERAL LOAD . 34 2.3.1 Flexural deformation 34 2.3.2 Bar slip . 37 2.3.3 Shear deformation 38 2.4 SHEAR HINGE MODELS . 39 2.4.1 Sezen‘s shear hinge 39 2.4.2 Patwardhan‘s shear hinge . 42 2.4.3 Drift capacity model . 44 2.4.3.1 Total drift ratio at flexural yielding . 44 2.4.3.2 Drift ratio at shear and subsequent axial failure 45 2.5 DEFICIENT BEAM COLUMN JOINTS . 47 2.5.1 Experimental study on deficient beam column joints 47 2.5.2 Retrofitting of beam column joints using FRP . 48 2.6 FINITE ELEMENT MODELING OF FRP RETROFITTED RC STRUCTURES 49 2.7 DAMAGE INDEX . 50 2.8 MACRO MODELING OF BEAM COLUMN JOINT 52 2.9 SUMMARY . 54 CHAPTER DUCTILE SHEAR BEHAVIOR OF WIDE COLUMNS AND SHEAR WALLS . 71 3.1 GENERAL . 71 3.2 EXPERIMENTAL STUDY ON TYPICAL WIDE COLUMNS . 72 3.2.1 Test Program 73 3.2.2 Material properties . 74 V 3.2.2.1 Internal steel reinforcement . 74 3.2.2.2 Concrete . 75 3.2.3 Fabrication of specimens 75 3.2.4 Test setup 76 3.2.5 Instrumentation . 77 3.2.5.1 Strain gauges . 77 3.2.5.2 Displacement transducers 77 3.2.6 Test procedure 78 3.3 TEST RESULTS AND DISCUSSION . 78 3.4 FINITE ELEMENT ANALYSIS 80 3.4.1 Finite element modeling . 80 3.4.2 Material laws 81 3.4.3 Finite element verification study 82 3.4.4 Effect of axial load ratio . 84 3.5 DEVELOPMENT OF SHEAR HINGE FOR WIDE COLUMNS 84 3.5.1 Results from experiments and finite element analysis . 84 3.5.2 Proposed shear hinge 86 3.6 DEVELOPMENT OF SHEAR HINGE FOR SHEAR WALLS 90 3.7 SUMMARY 91 CHAPTER STUDY ON T-BEAM-WIDE-COLUMN JOINTS 121 4.1 GENERAL . 121 4.2 DESCRIPTION OF T-BEAM-WIDE-COLUMN JOINTS . 121 4.3 FABRICATION OF SPECIMENS . 122 4.3.1 Overview of specimens and reinforcement details . 122 4.3.2 Materials . 122 4.3.3 Fabrication of joints 123 4.3.3.1 Non-retrofitted joints . 123 4.3.3.2 FRP retrofitted joints . 125 4.4 TEST SETUP 126 4.5 INSTRUMENTATION 127 4.5.1 Strain gauges 127 4.5.2 Displacement transducers . 127 4.6 TEST PROCEDURE 128 4.7 TEST RESULTS AND DISCUSSION . 129 4.7.1 General behavior 129 4.7.1.1 Non-retrofitted joints . 129 4.7.1.2 FRP retrofitted joints . 131 4.7.2 Effectiveness of applied retrofit . 134 4.8 FINITE ELEMENT ANALYSIS 136 4.8.1 Finite element modeling . 136 4.8.1.1 FRP-retrofitted joints . 136 4.8.2 Analysis of results 137 4.8.2.1 Effect of boundary modelling 140 4.8.2.2 Effect of inherent slip 141 4.8.2.3 Effect of difference in cube strength . 142 4.9 FURTHER ENHANCEMENT IN JOINT PERFORMANCE 142 4.10 SUMMARY 144 VI CHAPTER SEISMIC DEMAND AND PERFORMANCE EVALUATION . 197 5.1 GENERAL . 197 5.2 SELECTED HIGHRISE RC BUILDINGS FOR STUDY . 197 5.3 FUNDAMENTAL FREQUENCIES OF BUILDINGS 198 5.4 SEISMIC DEMAND ENVELOPE FOR SINGAPORE SOIL SITES . 200 5.4.1 Singapore soil types . 200 5.4.2 Generation of response spectra 201 5.4.2.1 Conversion of NSPT value to value 205 5.4.2.2 Calibration of empirical constant 207 5.4.2.3 Effect of new empirical constant . 208 5.4.3 Combined response spectrum 209 5.5 MODELING OF THE STRUCTURES 211 5.5.1 25 Story reinforced concrete point block . 211 5.5.2 15 Story reinforced concrete point block . 212 5.5.3 Basic modeling features . 212 5.5.4 Modeling non-linear hinges . 213 5.5.4.1 Shear hinge 214 5.5.4.2 Axial hinge 215 5.5.4.3 Flexural hinge . 215 5.5.5 Verification of non-linear hinges . 215 5.6 EVALUATION OF CAPACITY 217 5.7 POST LOCAL SHEAR FAILURE BEHAVIOR . 218 5.8 PROPOSED DAMAGE INDEX . 219 5.9 PERFORMANCE OF THE STRUCTURE 223 5.10 PERFORMANCE OF THE RETROFITTED STRUCTURE . 225 5.10.1 Macro modelling of T-beam-wide-column joint 225 5.10.2 Macro modeling of retrofitted components 229 5.10.2.1 T-beam-wide-column joint 229 5.10.2.2 Shear wall 230 5.10.2.3 Wide column . 231 5.10.3 Capacity evaluation using proposed T-beam-wide-column joint model 232 5.10.3.1 Non-retrofitted structures 232 5.10.3.2 Retrofitted structures . 233 5.10.4 Performance of retrofitted structure . 235 5.11 SUMMARY . 236 CHAPTER CONCLUSIONS AND RECOMMENDATIONS 295 6.1 REVIEW OF WORK . 295 6.2 CONCLUSIONS . 296 6.3 RECOMMENDATIONS FOR FURTHER RESEARCH 300 REFERENCES 301 APPENDIX 311 VII VIII SUMMARY Buildings in Singapore were designed according to the British Standard without any seismic provision. However, due to the far-field effects of earthquakes in Sumatra, these buildings are occasionally subjected to tremors. Previous studies showed that some buildings may suffer damage due to the worst possible earthquake. Continuing from past studies, two different types of residential buildings have been selected for further analysis because of unique components they comprise, such as wide columns and T-beam-wide-column joints. Moreover, past researches on such buildings have been primarily focused on estimation of the maximum lateral load capacity rather than the displacement capacity. On the other hand, this study aims to estimate the ultimate seismic capacity of these buildings based on displacement capacity. For this purpose shear hinges are proposed based on existing literature and new experiments to model the ductile shear behavior of typical columns and shear walls found in Singapore. Shear behavior becomes more significant for wide columns because of low shear span/depth ratio and high length/width ratio. Tests on wide columns provided evidence of ductile shear behavior. Test results were used to verify the micro FEA models of the columns which were also used to study the effect of axial load ratio which were used together with the test results to propose the shear hinge for these columns. Experiments were carried out on 2/5-scale T-beam-wide-column joints. Tests were performed to investigate the behavior of exterior and interior joints. A practical FRP retrofit model was applied on two other specimens to determine the effectiveness of FRP retrofit on such joints. All these specimens were used to verify micro FEA models. Using the verified retrofit modelling approach an enhanced FRP retrofit scheme was proposed. IX Using the joint test data, constitutive relationship for flexure was proposed for both non-retrofitted and retrofitted T-beam-wide-column-joints which can be used in macro finite element analysis. Using previous experimental studies, constitutive relationships for retrofitted wide columns and shear walls were proposed. With these proposed constitutive relationships FE models of the selected two buildings were generated and non-linear pushover analysis was performed using the macro finite element analysis software SAP2000. To develop a demand envelope, formulae to calculate shear wave velocity of soil layers was calibrated for Singapore soils. Based on response spectra developed for 10 soil sites, a demand curve was proposed for Kallang soil formation for the expected worst case scenario of earthquake of moment magnitude at 600 km from Singapore. Furthermore, a comprehensive procedure to determine a new damage index for the analysed structures was proposed in this study which accounts for ductile shear behavior and the role of frame and wall in a structure in providing the overall stability of the structure. The performance state of the analysed structure was thus derived based on the damage index at the performance point. The improved performance due to the application of FRP retrofit was also derived using the same approach. The approach developed in this study can be adapted to accurately estimate the ultimate seismic capacity and the effectiveness of similar retrofit techniques on similar nonseismically designed buildings. X Appendix D.1.5 15-storey building without infill and loaded along Y direction 0.16 Spectral acceleration, Sa , g 0.14 0.12 0.1 0.08 0.06 0.04 Demand envelope Capacity 0.02 10 Damage Index 1st Storey Damage index 0.8 Damage index 5th storey 0.6 0.4 0.2 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Spectral displacement, Sd , m 0.16 0.18 0.2 Figure D.1.5: Performance of the 15-storey structure without infill loaded along Y direction 335 Appendix D.1.6 15-storey building with infill and loaded along X direction 0.25 Spectral acceleration, Sa , g 0.2 0.15 0.1 Demand envelope 0.05 Capacity 10 Damage index 0.8 0.6 0.4 Damage Index 1st Storey 0.2 Damage Index 6th Storey 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Spectral displacement, Sd , m 0.16 0.18 0.2 Figure D.1.6: Performance of the 15-storey structure with infill loaded along X direction 336 Appendix D.1.10 15-storey building with infill and loaded along Y direction 0.35 0.3 Spectral acceleration, Sa , g 0.25 0.2 0.15 0.1 Demand envelope Capacity 0.05 01 Damage index 0.8 0.6 0.4 Damage Index 1st Storey 0.2 Damage Index 6th Storey 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Spectral displacement, Sd , m 0.16 0.18 0.2 Figure D.1.7: Performance of the 15 storey structure with infill loaded along Y direction 337 Appendix D.2 Performance of Retrofitted Structures Figures D.2.1 to D.2.7 present the performance evaluation of the retrofitted structures. In the upper portion of the figures, capacity curve for both non-retrofitted and retrofitted structure are superimposed on the proposed demand curve. And the lower portion of the figures plots the damage indices at the most damaged storey against spectral displacement. Table D.2 summarizes the findings from these figures in terms of respective performance point, most damaged storey, damage index and performance state for both non-retrofitted and retrofitted structure for each case. 338 Table D.2 Summary of performance of retrofitted structures Appendix 339 Appendix D.2.1 25-storey building without infill and loaded along X direction 0.16 0.14 Spectral acceleration, Sa , g 0.12 0.1 0.08 0.06 Demand envelope 0.04 Capacity non-retrofitted Capacity retrofitted 0.02 10 1st storey non-retrofitted Damage index 0.8 15th storey retrofitted 0.6 0.4 0.2 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Figure D.2.1: Comparison of performance of the retrofitted and non-retrofitted 25storey without infill structure loaded along X direction 340 Appendix D.2.2 25-storey building without infill and loaded along Y direction 0.16 0.14 Spectral acceleration, Sa , g 0.12 0.1 0.08 0.06 Demand envelope Capacity non-retrofitted 0.04 Capacity retrofitted 0.02 10 Damage index 0.8 0.6 0.4 1st storey non-retrofitted 0.2 4th storey retrofitted 0 0.05 0.1 0.15 0.2 0.25 Spectral displacement, Sd , m 0.3 0.35 0.4 Figure D.2.2: Comparison of performance of the retrofitted and non-retrofitted 25storey without infill structure loaded along Y direction 341 Appendix D.2.3 25-storey building with infill and loaded along X direction 0.3 Spectral acceleration, Sa , g 0.25 0.2 0.15 0.1 Demand envelope Capacity non-retrofitted Capacity retrofitted 0.05 01 Damage index 0.8 0.6 0.4 1st storey non-retrofitted 0.2 1st storey retrofitted 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Spectral displacement, Sd , m 0.16 0.18 0.2 Figure D.2.3: Comparison of performance of the retrofitted and non-retrofitted 25storey structure with infill loaded along X direction 342 Appendix D.2.4 15-storey building without infill and loaded along X direction 0.16 0.14 Spectral acceleration, Sa , g 0.12 0.1 0.08 0.06 Demand envelope 0.04 Capacity non-retrofitted Capacity retrofitted 0.02 10 Damage index 0.8 0.6 0.4 4th storey retrofitted 0.2 1st storey non-retrofitted 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Spectral displacement, Sd , m 0.16 0.18 0.2 Figure D.2.4: Comparison of performance of the retrofitted and non-retrofitted 15storey without infill structure loaded along X direction 343 Appendix D.2.5 15-storey building without infill and loaded along Y direction 0.16 0.14 Spectral acceleration, Sa , g 0.12 0.1 0.08 0.06 Demand envelope 0.04 Capacity non-retrofitted Capacity retrofitted 0.02 01 Damage index 0.8 0.6 0.4 1st storey non-retrofitted 0.2 4th storey retrofitted 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Spectral displacement, Sd , m 0.16 0.18 0.2 Figure D.2.5: Comparison of performance of the retrofitted and non-retrofitted 15storey without infill structure loaded along Y direction 344 Appendix D.2.6 15-storey building with infill and loaded along X direction 0.3 Spectral acceleration, Sa , g 0.25 0.2 0.15 0.1 Demand envelope Capacity non-retrofitted 0.05 Capacity retrofitted 01 Damage index 0.8 0.6 0.4 Damage Index 1st storey nonretrofitted Damage index 1st storey retrofitted 0.2 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Spectral displacement, Sd , m 0.16 0.18 0.2 Figure D.2.6: Comparison of performance of the retrofitted and non-retrofitted 15storey with infill structure loaded along X direction 345 Appendix D.2.7 15-storey building with infill and loaded along Y direction 0.45 0.4 Spectral acceleration, Sa , g 0.35 0.3 0.25 0.2 0.15 0.1 Demand envelope Capacity non-retrofitted Capacity retrofitted 0.05 10 Damage index 0.8 0.6 0.4 Damage Index 1st storey nonretrofitted Damage index 1st storey retrofitted 0.2 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Spectral displacement, Sd , m 0.16 0.18 0.2 Figure D.2.7: Comparison of performance of the retrofitted and non-retrofitted 15storey with infill structure loaded along Y direction 346 Appendix APPENDIX E Calculation of Capacity of a Beam Section Figure E.1 shows a T-beam section under sagging (positive) moment when the first yielding in tension reinforcing bars occurs. The corresponding concrete strain at the compression side can be found by assuming the height of neutral axis c and performing trial and error procedure until the compression force equals tensile force for the section. This equilibrium neutral axis height is used to calculate the corresponding forces and flexural capacity of the section. This is the capacity of the beam section at first yield. Figure E.1: Beam section when the tension reinforcing bars reach the yield strength where, = strain in concrete = strain in bars in slab = strain in top beam bars = strain in bottom beam bars = strain in concrete = stress in bars in slab = stress in top beam bars = strain in bottom beam bars 347 Appendix = yield strength of steel = Elastic modulus of steel Since the compressive concrete stress is generally small when the first yielding of reinforcement occurs, the distribution of concrete stress can be assumed as linear while calculating the compressive force in concrete. The compressive stress in concrete is calculated as below based on the recommendation by Macgregor (2005).   Ec c     f c   f c '[ c  ( c ) ] 0.02 0.02  f '  c  c  0.4 f c ' Ec 0.4 f c '   c  0.002 Ec E.1 0.002   c   cu where, = concrete compressive cylinder strength = Elastic modulus of concrete = strain in concrete Curvature of the section at yield is obtained by following Equation E.2 On the other hand Figure E.2 shows a T-beam section under positive moment when the concrete at extreme compression Fibre reaches ultimate strain. Figure E.2: Beam section when concrete at extreme compression fibre reaches ultimate strain 348 Appendix where, . For this case the maximum compression strain of concrete is assumed to be , as suggested by Paulay et al.(1992). The parabolic stress distribution of concrete is simplified to rectangular distribution according to ACI code (ACI318 2011). And the bilinear stress-strain relationship of steel is assumed with no steel hardening. Similar to the procedure to calculate yield capacity, the corresponding steel strain at all locations are found by assuming the height of neutral axis c and performing trial and error procedure until the compression force equals tensile force for the section. The corresponding moment capacity is taken as the ultimate capacity of the section. To calculate the hogging (negative) moment capacity, the section is rotated 180 degree and the same procedure is repeated. However, in this case the yield capacity corresponds to the yielding of top beam bars. 349 Appendix APPENDIX F Shear Capacity of FRP Retrofitted RC Components The total shear capacity of the FRP wrapped component consists of shear capacity of reinforced concrete and FRP. The equation of shear capacity of FRP wrap is derived following ACI Committee 440 (2002) code on FRP which leads to a design equation in EURO code format, ENV 1992-1-1 (1991). VR = Vc + Vs + VF (F.1) Vf = Ef εf ρf ( h) t (F.2) where, VT = total shear capacity due to reinforced concrete and FRP Vc = shear capacity due to concrete calculated based on ACI 318(2011) (Eq. 3.3) Vs = shear capacity due to steel calculated based on ACI 318(2011) (Eq. 3.3) Vf = shear capacity due to FRP wrap Ef Young‘s modulus of Fibre (69 GPa for GFRP and 240 GPa for CFRP) ρf = FRP shear reinforcement ratio is 2tf/t for continuously bonded shear reinforcement of thickness tf εf = effective FRP strain at failure which is 0.0025 for GFRP (Kong 2004) and 0.004 for CFRP (from experiments, as shown in Figure 4.56 ) tf = thickness of the carbon Fibre t = thickness of retrofitted section h = height of the retrofitted section h b Figure F.1: Planar Cross section of a component 350 [...]... ultimate seismic capacity of these buildings accurately and compare the performance of such buildings against the worst case scenario earthquake demand and to propose a practical retrofit solution if necessary 1.2 Ultimate Seismic Capacity of RC GLD Structures Besides buildings in Singapore, old RC structures built in other non -seismic or low -seismic regions, like the eastern and central United States and. .. reinforced polymer g Acceleration of gravity G Shear modulus GFRP Glass fibre reinforced polymer XX Gmax initial shear modulus GLD Gravity load designed h Height of the storey Height of the retrofitted section H Height of a building IO Performance state Immediate occupancy Ig Uncracked moment of inertia of cross section of the column Iyy Moment of inertia of a section in y-y direction Izz Moment of inertia... Moment magnitude of earthquakes My Column moment at yielding of the longitudinal reinforcement Yield moment MW Moment magnitude of earthquake Damage vale of beam Damage vale of column Damage vale of shear wall Damage vale of masonry infills Number of beams in a storey Number of columns in a storey Number of walls in a storey XXI Number of masonry infills in a storey Nspt N value of the standard penetration... analysis of various soil sites to find the worst case scenario for a particular building Furthermore, it is required to develop a process to quantify the degree of damage at the performance point This can be achieved by means of a comprehensive damage index 1.4 Seismic Retrofitting of RC GLD Buildings in Singapore Seismic retrofitting refers to wise modification of the structural properties of an existing... Effect of axial load ratio on lateral load displacement relationship of nonretrofitted exterior joint 190 Figure 4.58: Effect of axial load ratio on lateral load displacement relationship of nonretrofitted interior joint 190 Figure 4.59: Elastic end roller support for exterior joint 191 Figure 4.60: Comparison of lateral load displacement relationship obtained from test and. .. advantage of micro modelling capabilities of ABAQUS, the components such as columns and joints will be modelled in detail by ABAQUS and these models will be used to propose macro models to be used in SAP2000 Thus this study aims to leverage on the accuracy and robustness of ABAQUS and computational efficiency and wide spread usability of SAP2000 1.3 Seismic Demand and Adequacy Evaluation for Buildings. .. world has similar low seismic hazard classification Taking advantage of this, buildings in Singapore are gravity- load designed (GLD) structures, according to BS8110 (1985), which does not have any seismic provision However, due to the far-field effects of earthquakes in Sumatra (Balendra et al 2002, 2003), buildings in Singapore, of which most are reinforced concrete (RC) shear wall and frame structures,... reinforcement and column footing v Shear capacity of a section expressed in terms of stress vc Shear capacity provided by concrete in terms of stress vs Shear capacity provided by transverse reinforcement in terms of stress vf Shear capacity of FRP wrap in terms of stress shear carried by shear wall at ith storey V Shear force Vc Shear force carried by concrete Vcr Shear capacity at cracking Vs Shear force... and ABAQUS (both types of boundary model) for non-retrofitted exterior joint 192 Figure 4.61: Comparison of lateral load displacement relationship obtained from test and ABAQUS (both types of boundary model) for non-retrofitted interior joint 192 Figure 4.62: Comparison of lateral load displacement relationship obtained from test and ABAQUS (both types of boundary model) for retrofitted exterior joint... occur at the Sumatra fault and the subduction of the Indian-Australian plate into the Eurasian Plate Therefore, the need to evaluate the seismic vulnerability of buildings in Singapore in case a larger or nearer earthquake occurs; has been studied to some extent (Balendra et al., 2007) The seismic vulnerability was evaluated by combining the seismic demand and the capacity of the structure in A-D format . SEISMIC CAPACITY OF RC GLD STRUCTURES 4 1.3 SEISMIC DEMAND AND ADEQUACY EVALUATION FOR BUILDINGS IN SINGAPORE 9 1.4 SEISMIC RETROFITTING OF RC GLD BUILDINGS IN SINGAPORE 12 1.5 OBJECTIVE AND. CHAPTER 5 SEISMIC DEMAND AND PERFORMANCE EVALUATION 197 5.1 GENERAL 197 5.2 SELECTED HIGHRISE RC BUILDINGS FOR STUDY 197 5.3 FUNDAMENTAL FREQUENCIES OF BUILDINGS 198 5.4 SEISMIC DEMAND ENVELOPE. ABAQUS for retrofitted interior joint 183 Figure 4.50: Comparison of non-retrofitted and retrofitted exterior joint in ABAQUS 184 Figure 4.51: Comparison of non-retrofitted and retrofitted interior