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Seismic behaviour of steel plate shear walls by shake table testing Rezai, Mahmoud 1999

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SEISMIC BEHAVIOUR OF STEEL PLATE SHEAR WALLS B Y SHAKE TABLE TESTING BY MAHMOUD REZAI B.A.SC. Iran University of Science and Technology, 1990 MA.Sc. University of Ottawa, 1993 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY OF GRADUATE STUDIES Department of Civil Engineering We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA April, 1999 ©Mahmoud Rezai, 1999  In presenting this thesis in partial fulfilment  of the requirements for an advanced  degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department  or  by  his or  her  representatives.  It  is understood that  copying or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department of The University of British Columbia Vancouver, Canada Date  DE-6 (2/88)  Apr,'/ 1 % . < \ < \  ABSTRACT This dissertation describes an experimental and analytical study on the behaviour of steel plate shear walls with thin unstiffened webs when used as primary lateral load resisting system in medium- and high-rise buildings. The steel plate shear wall system resembles a vertical plate girder where the theoretical buckling strength of the plate panels is negligible and lateral loads are carried through post-buckling strength of the plate panels in combination with the frame action of the surrounding beams and columns. The theory that governs the design of steel plate shear wall structures is essentially the same as that of plate girders developed by Basler in 1961, although the relatively high bending strength and stiffness of the beams and columns have a significant effect on the overall behaviour, especially when high axial forces and overturning effects dominate the behaviour of the system. To verify the guidelines and design principles provided in the latest version of Canada's National Standard on Limit States Design of Steel Structures, CAN/CSA-S16.1-94 (1994), and to broaden the scope of the code, an experimental testing program accompanied by numerical investigation was conducted at the University of British Columbia. This effort was in collaboration with researchers at the University of Alberta and a team of consulting engineers. During the first phase of the experimental program two single storey single bay specimens were tested cyclically to gain information on the general behaviour of the system and verify the adequacy of fabrication procedures. In the second phase, a single bay four-storey 25% scale specimen was tested under a quasi-static cyclic testing protocol. As the third phase of testing, a similar four-storey specimen was tested on the shake table under low, medium and intense dynamic horizontal base motions. The two single storey and one four-storey test specimens were loaded to maximum displacement ductilities of 7 x 8^, 6 x 8^ and 1.6 x 8^, during the first and second phases of testing, respectively. The single storey specimens proved to be very stiff, compared to the bare frame, showed good ductility and energy dissipation characteristics, and exhibited stable  ii  ABSTRACT  behaviour at very large deformations following many cycles of loading. Sufficient data was gathered to establish the overall performance of these structural systems under lateral loading. For the third phase of testing the dynamically tested four-storey specimen was subjected to a number of site-recorded and synthetically generated ground motions with varying intensities. Even though each test gave important information about the dynamic behaviour of the scaled steel plate shear wall specimen, the limited capacity of the shake table prevented the attainment of significant inelastic response in the specimen. Results from the scaled steel plate shear wall tests were used to verify numerical models and to gain an understanding of how the various methods of modelling the shear resistance of thin infill plates would affect the predicted results. In general, the code prescribed strip models overpredicted the elastic stiffness of the test specimens, while the yield and ultimate strength were reasonably well predicted. The load-deformation behaviour of the specimens was considerably affected by small variations of the angle of inclination of the tension struts representing tension field development. The discrepancies between the analytical and experimental results was more dramatic for the four-storey specimen than the single storey specimens. This was deemed to be a function of the overall aspect ratio (total height over panel width) of the specimen. For the four-storey specimens the higher moment to base shear ratio emphasized flexural deformations compared to storey shear behaviour. An improved numerical model was proposed that utilizes discrete strips placed at different angles. A semi-empirical equation was proposed to determine the effective width of the steel panels in resisting storey shears. The proposed model predictions were in good agreement with the envelope of cyclic and dynamic time-history test results obtained from experimental studies at the University of British Columbia and University of Alberta.  TABLE OF CONTENTS ABSTRACT  ii  LIST OF TABLES  xii  LIST OF FIGURES  xiv  LIST OF SYMBOLS  xxiv  ACKNOWLEDGEMENTS  xxvi  CHAPTER 1 . INTRODUCTION  CHAPTER 2.  1  1.1. GENERAL  1  1.2. S C O P E AND OBJECTIVES OF THIS STUDY  3  1.3. THESIS OUTLINE  6  LITERATURE REVIEW  8  2.1. OVERVIEW  8  2.2. TAKAHASHI et al. (1973)  8  2.3. MIMURA AND AKIYANA (1977)  11  2.4. AGELIDIS AND MANSELL (1982). . . -.  14  2.5. THORBURN, KULAK AND MONTGOMERY (1983)  15  2.6. TIMLER AND KULAK (1983)  19  2.7. TROMPOSCH AND KULAK (1987)  21  2.8. ROBERTS AND SABOURI-GHOMI (1991)  23  2.9. YAMADA (1992)  27  2.10. ELGAALY, CACCESE, CHEN AND DU (1993)  28  2.11. XUE AND LU (1994)  32  2.12. SUGII AND YAMADA (1996)  36  2.13. DRIVER (1997)  37  2.14. ELGAALY AND LIU (1997)  40  2.15. SUMMARY  41  iv  TABLE OF CONTENTS  CHAPTER 3.  DESIGN OF TEST SPECIMENS  42  3.1. GENERAL  42  3.2. DYNAMIC MODELLING THEORY  43  3.2.1. Overview  43  3.2.2. Dimensions and Dimensional Analysis  44  3.2.3. Similitude Relationships and Types of Models  46  3.2.4. Development of a Scale Model for Shake Table Studies . . . . 47 3.2.5. Dynamic Properties of Steel Structures  52  3.3. DESIGN OF THE STEEL PLATE SHEAR WALL TEST SPECIMEN. 53 3.3.1. Computer Modelling  56  3.3.2. Analytical Method and Design Criteria  57  3.3.2.1. Selection of Design Earthquakes for Shake Table Tests . . . . 58 3.3.3. Results of Analyses  CHAPTER 4-  61  3.4. SPECIFICATION OF TEST SPECIMENS  78  3.5. SUMMARY  78  QUASI-STATIC TEST PROGRAM  81  4.1. INTRODUCTION  81  4.2. FIRST SINGLE STOREY TEST SPECIMEN  82  4.2.1. Specimen Characteristics  82  4.2.2. Loading Configuration  83  4.2.3. Instrumentation Layout  84  4.2.4. Hysteretic Behaviour  86  4.2.5. Test Results and Observation  87  4.2.5.1. Behaviour of Infill Plate  88  4.2.5.2. Behaviour of Storey Beam  90  4.2.5.3. Behaviour of Columns  90  4.2.5.4. Behaviour of Beam-to-Column Connections  92  4.3. SECOND SINGLE STOREY TEST SPECIMEN  93  v  TABLE OF CONTENTS  4.3.1. Specimen Characteristics  93  4.3.2. Loading Configuration  94  4.3.3. Instrumentation Layout  95  4.3.4. Hysteretic Behaviour  95  4.3.5. Test Results and Observation  98  4.3.5.1. Behaviour of Infill Plate  98  4.3.5.2. Behaviour of Storey Beam  99  4.3.5.3. Behaviour of Columns  100  4.3.5.4. Behaviour of Beam-to-Column Connections  100  4.4. FOUR-STOREY TEST SPECIMEN 4.4.1. Specimen Characteristics  100  4.4.2. Loading Configuration  104  4.4.3. Instrumentation Layout  105  4.4.4. Hysteretic Behaviour  108  4.4.5. Test Results and Observation  111  4.4.5.1. Behaviour of Infill Plate  111  4.4.5.2. Behaviour of Storey Beams  114  4.4.5.3. Behaviour of Columns  115  4.4.5.4. Behaviour of Beam-to-Column Connections  116  4.5. SUMMARY  CHAPTER 5.  100  SHAKE TABLE TEST PROGRAM  116  118  5.1. INTRODUCTION  118  5.2. UBC EARTHQUAKE SIMULATOR FACILITY  119  5.3. SHAKE TABLE TEST SPECIMEN  121  5.3.1. Lateral Bracing System  125  5.3.2. Mass Blocks  127  5.3.3. Instrumentation Layout  128  5.4. SHAKE TABLE TESTING PROCEDURE  131  5.4.1. Shake Table Input Motions  131 vi  TABLE OF CONTENTS  5.4.2. Shake Table Control System  133  5.4.3. Shake Table Loading History  135  5.5. DESCRIPTION OF SHAKE TABLE TEST SEQUENCE  CHAPTER 6-  LOW-AMPLITUDE VIBRATION TESTS  137  148  6.1. INTRODUCTION  148  6.2. VIBRATION TESTS  150  6.2.1. Ambient Vibration Test  150  6.2.2. Impact Vibration Test  153  6.3. VIBRATION DATA ACQUISITION SYSTEM  154  6.4. VIBRATION ANALYSIS SOFTWARE PROGRAMS  155  6.5. UNIVERSITY OF ALBERTA VIBRATION TESTS  157  6.5.1. Specimen Characteristics  158  6.5.2. Loading History  158  6.5.3. Ambient Vibration Test  159  6.5.4. Impact Tests.  160  6.5.5. Natural Frequencies and Mode Shapes of the Specimen . . 162 6.5.5.1. Ambient Vibration Results  162  6.5.5.2. Impact Test Results  165  6.5.5.3. Computer Model Results  167  6.5.6. Evaluation of Viscous Damping Ratio  169  6.5.6.1. Free Vibration Decay  170  6.5.6.2. Hysteretic Damping  171  6.6. VIBRATION TESTS OF THE UBC QUASI-STATIC SPECIMEN. . . 172 6.6.1. Ambient Vibration Tests  172  6.6.2. Impact Tests  173  6.6.3. Natural Frequencies of the Specimen  174  6.6.3.1. Ambient Vibration Results 6.6.3.2. Impact Test Results  174 174  6.6.3.3. Computer Model Results  177 vii  TABLE OF CONTENTS 6.7. VIBRATION TESTS OF THE UBC SHAKE TABLE SPECIMEN . . . 180 6.7.1. Ambient Vibration Tests  181  6.7.2. Impact Tests  181  6.7.3. Natural Frequencies of the Specimen  183  6.7.3.1. Ambient Vibration Results  183  6.7.3.2. Impact Test Results  183  6.7.3.3. Computer Model Results  186  6.8. SUMMARY  CHAPTER 7-  SHAKE TABLE TEST RESULTS  187  190  7.1. GENERAL  190  7.2. DATA REDUCTION METHOD  190  7.3. COMPUTATION OF VARIOUS RESPONSE QUANTITIES  192  7.3.1. Displacements and Interstorey Drifts  193  7.3.2. Storey Shear Forces  193  7.3.3. Overturning Moment  194  7.3.4. Column Axial Force and Bending Moment. . ^  195  7.3.5. Infill Panel Stresses  195  7.3.6. Energy Input and Dissipation  196  7.3.6.1. Input Energy  196  7.3.6.2. Dissipated Energy  197  7.4. BEHAVIOUR OF THE SPECIMEN DURING TESTS 7.4.1. Joshua Tree Record  197 198  7.4.1.1. Acceleration and Displacement Responses  198  7.4.1.2. Natural Frequency  198  7.4.1.3. Maximum Response Envelopes  201  7.4.1.4. Storey Shear versus Storey Drift  203  7.4.1.5. Energy Dissipation Mechanism  204  7.4.1.6. Column Axial Force and Bending Moment  205  7.4.1.7. Infill Panel Strains  208  7.4.2. Tarzana Hill Record  210 viii  TABLE OF CONTENTS 7.4.2.1. Acceleration and Displacement Responses  210  7.4.2.2. Natural Frequency  213  7.4.2.3. Maximum Response Envelopes  215  7.4.2.4. Storey Shear versus Storey Drift  220  7.4.2.5. Energy Dissipation Mechanism  221  7.4.2.6. Column Axial Force and Bending Moment  222  7.4.2.7. Infill Panel Strains  225  7.4.3. VERTEQII Record 7.4.3.1. Acceleration and Displacement Responses  228  7.4.3.2. Natural Frequency  228  7.4.3.3. Maximum Response Envelopes  230  7.4.3.4. Storey Shear versus Storey Drift  232  7.4.3.5. Energy Dissipation Mechanism  234  7.4.3.6. Infill Panel Strains  234  7.4.4. Sinusoidal Excitation  236  7.4.4.1. Acceleration and Displacement Responses  236  7.4.4.2. Maximum Response Envelopes  236  7.4.4.3. Storey Shear versus Storey Drift  239  7.4.4.4. Column Axial Force and Bending Moment  241  7.5. SUMMARY CHAPTER 8-  CHAPTER 9-  228  STRIP MODEL PARAMETERS  243 246  8.1. INTRODUCTION  246  8.2. PANEL THICKNESS  250  8.3. PANEL WIDTH  254  8.4. PANEL HEIGHT  255  8.5. BEAM CROSS-SECTIONAL AREA  256  8.6. COLUMN CROSS-SECTIONAL AREA  258  8.7. COLUMN MOMENT OF INERTIA  259  8.8. SUMMARY  260  NUMERICAL MODELLING  262 ix  TABLE OF CONTENTS  9.1. INTRODUCTION  262  9.2. ANALYSIS METHOD  263  9.3. COMPUTER SOFTWARE  264  9.3.1. ANSYS Program  264  9.3.2. SAP90 Program  265  9.3.2.1. Elements  265  9.3.2.2. Solution Technique  266  9.3.3. CANNY-E Program  268  9.3.3.1. Elements  269  9.3.3.2. Hysteresis Models  270  9.3.3.3. Solution Technique  272  9.4. STEEL PLATE SHEAR WALL MODELS  272  9.4.1. Geometry  273  9.4.2. Material Properties  273  9.4.3. SAP90 Models  275  9.4.4. CANNY-E Models  276  9.5. RESULTS OF PUSHOVER ANALYSES  276  9.5.1. First Single Storey Specimen  276  9.5.2. Second Single Storey Specimen  281  9.5.3. Four-Storey Test Specimen  285  9.5.4. UofA Driver's Four-Storey Test Specimen  293  9.6. RESULTS OF CYCLIC ANALYSES  296  9.6.1. First Single Storey Specimen  296  9.6.2. Second Single Storey Specimen  298  9.6.3. Four-Storey Test Specimen  300  9.7. RESULTS OF DYNAMIC TIME-HISTORY ANALYSIS  303  9.7.1. Results of SAP90 SHELL Element Model  305  9.7.2. Results of SAP90 45° Strip Model  311  9.7.3. Results of CANNY-E 37° Strip Model  315  x  TABLE OF CONTENTS  9.8. DISCUSSION ON STRIP MODEL PHILOSOPHY  322  9.8.1. Proposed Model  323  9.8.2. Analytical Investigation  326  9.9. GENERAL DISCUSSION ON STRIP MODELS  335  9.10. SUMMARY  338  CHAPTER 1 0-  SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS. 340  10.1. INTRODUCTION  340  10.2. SUMMARY AND CONCLUSIONS  341  10.2.1. Performance of Cyclic Test Specimens  342  10.2.2. Performance of Shake Table Test Specimen  344  10.2.3. Dynamic Characteristics of the Models  346  10.2.4. Strip Model Parameters  348  10.2.5. Analytical Predictions  348  10.3. RECOMMENDATIONS FOR FURTHER RESEARCH  351  REFERENCES  356  APPENDIX A  362 . SAMPLE SAP90 INPUT FILE  362  . 45° Strip Model:  362  . SHELL element Model:  364  . SAMPLE CANNY-E INPUT FILE  365  xi  LIST OF TABLES CHAPTER 1 CHAPTER 2 CHAPTER 3 Table 3.1: Summary of scale factors for seismic response analysis (after Moncarz and Krawinkler, 1981)  51  Table 3.2: Similitude scaling relationships for the selected model  62  Table 3.3: Steel sections chosen from the CISC Handbook of Steel Construction for numerical analyses Table 3.4: Computed natural frequencies of the SAP90 models  64 73  CHAPTER 4 CHAPTER 5 Table 5.1: Measured member properties of the shake table specimen  122  Table 5.2: Sequence of input records  135  CHAPTER 6 Table 6.1: Comparison of the measured and calculated natural frequencies for the two phases of damaged and undamaged (— Not identified) 167 Table 6.2: Comparison of the measured and computed natural frequencies of the infill plates for the UofA test frame 168 Table 6.3: Comparison of the measured and calculated natural frequencies of the UBC quasistatic unbraced frame with no applied masses (— Not identified) 177 Table 6.4: Comparison of the measured and calculated natural frequencies of the UBC quasistatic laterally braced frame with applied masses (— Not identified) 178 Table 6.5: Comparison of the measured and calculated natural frequencies of the UBC shake table test specimen with masses attached and lateral support system mounted . 185 Table 6:6: Comparison of the measured and computed natural frequencies of the first storey infill plate for the UBC shake table test specimen 186  xii  LIST OF TABLES  CHAPTER 7 Table 7.1: Comparison between shake table peak acceleration before and after digital filtering for the selected earthquake inputs 192 Table 7.2: Maximum response of the test specimen for Joshua Tree 80% run  200  Table 7.3: Maximum response of the test specimen for Tarzana Hill runs  216  Table 7.4: Maximum response of the test specimen for VERTEQII runs  231  Table 7.5: Maximum response of the test specimen for sinusoidal excitations  238  CHAPTER 8 Table 8.1: Details of the steel plate shear wall specimen case studies  247  Table 8.2: Structural properties of the steel plate shear wall specimens  248  CHAPTER 9 CHAPTER 10  xiii  LIST OF FIGURES CHAPTER 1 CHAPTER 2 Figure 2.1: Hysteresis behaviour of a) an unstiffened and b) a heavily stiffened steel plate shear walls (after Takahashi et al, 1973) 10 Figure 2.2: Monotonic load-deflection behaviour (after Mimura and Akiyana, 1977)... 12 Figure 2.3: Hysteresis curves proposed by Mimura and Akiyana (1977)  13  Figure 2.4: Strip model representation of a typical steel panel developed by Thorburn et al. (1983) a) complete tension field b) partial tension field 17 Figure 2.5: Hysteresis model proposed by Tromposch and Kulak (1987)  23  Figure 2.6: Hysteresis loops for a shear panel with pin jointed frame (after Sabouri-Ghomi and Roberts, 1991) 25 Figure 2.7: Hysteresis loops for a shear panel with fixed beam-to-column connections (after Sabouri-Ghomi and Roberts, 1991) 26 Figure 2.8: Trilinear stress-strain relationship for strip model (after Elgaaly et al, 1993) 32 Figure 2.9: Behaviour of a steel plate shear wall frame (after Xue and Lu, 1994a)  34  Figure 2.10: Hysteresis model proposed by Driver et al. (1997)  40  CHAPTER 3 Figure 3.1: Stress-strain similitude requirements for a completely similar model  49  Figure 3.2: Effect of the strain rate on the stress-strain characteristic for steel structures (after Mirzaef al, 1984) 52 Figure 3.3: Increase in static yield point of steel material with strain rate (after Mirza etal., 1984) 53 Figure 3.4: Typical fish plate to frame and infill plate to fish plate connections  56  Figure 3.5: Time-histories and corresponding elastic response spectra and frequency content of the selected input earthquake records 61 Figure 3.6: SAP90 computer models of the four-storey steel plate shear wall model a) Shrunken SHELL elements b) 45° inclined pin-ended FRAME elements . . . 63 Figure 3.7: Normal stresses in the base of the columns and bottom storey infill panel versus  xiv  LIST OF FIGURES column cross-sectional area for the SAP90 strip model  66  Figure 3.8: Normal stresses in the base of the columns and bottom storey infill panel versus column cross-sectional area for the SAP90 SHELL element model 66 Figure 3.9: Normal stresses in the base of the columns and bottom storey infill panel versus column moment of inertia for the SAP90 strip model 67 Figure 3.10: Normal stresses in the base of the columns and bottom storey infill panel versus column moment of inertia for the SAP90 SHELL element model 67 Figure 3.11: Tensile force in the column versus column cross-sectional area  69  Figure 3.12: Column bending moment (left axis) and maximum strip tensile force (right axis) versus column moment of inertia 69 Figure 3.13: Shear distribution in bottom storey columns and panel versus column crosssectional area for the strip model 71 Figure 3.14: Shear distribution in bottom storey columns and panel versus column moment of inertia for the strip model 71 Figure 3.15: Shear distribution in bottom storey columns and panel versus column crosssectional area for the SHELL element model 72 Figure 3.16: Shear distribution in bottom storey columns and panel versus column moment of inertia for the SHELL element model 72 Figure 3.17: Computed response of the four-storey steel plate shear wall specimen for the strip (dotted line) and SHELL element models (solid line) 74 Figure 3.18: Computed relative displacement response of the four-storey steel plate shear wall specimen for the strip (dotted line) and SHELL element models (solid line) 75 Figure 3.19: Computed dynamic response of the bottom storey column and infill panel. 77 Figure 3.20: Four-storey steel plate shear wall specimen  78  CHAPTER 4 Figure 4.1: First single storey specimen with instrumentation layout  83  Figure 4.2: Overview of the first single storey test set-up  84  Figure 4.3: Hysteresis curves of the first single storey shear wall specimen  85  Figure 4.4: A view of the first single storey specimen at the end of cyclic test  87  Figure 4.5: Angle of the resultant strain at the top corner of infill plate  88 xv  LIST OF FIGURES  Figure 4.6: Displaced profile of the column  90  Figure 4.7: Measured column axial force and bending moment  91  Figure 4.8: A view of the second single storey specimen  93  Figure 4.9: Overview of the second single storey test set-up  94  Figure 4.10: Hysteresis curves of the second single storey shear wall specimen  95  Figure 4.11: Comparison of the and cycles in the first single storey specimen with the corresponding cycles in the second single storey specimen  96  Figure 4.12: A view of the second single storey specimen at the end of cyclic test  97  Figure 4.13: A view of the infill plate buckling and tearing during final cycle of loading 98 Figure 4.14: Four-storey test specimen bolted to the base of the loading frame  101  Figure 4.15: Four-storey steel plate shear wall specimen inside the support frame . . . . 102 Figure 4.16: Overview of quasi-static test set-up for the four-storey shear wall frame . 105 Figure 4.17: Instrumentation layout of the four-storey specimen  106  Figure 4.18: Storey shear versus interstorey deflections 109 Figure 4.19: State of damage to the first storey panel and columns of the quasi-static fourstorey shear wall frame at the termination of test Ill Figure 4.20: Variation of magnitude and angle of principal stresses for the first storey infill plate with storey shear 112 Figure 4.21: Displaced shape of the column under various base shear loadings  114  CHAPTER 5 Figure 5.1: UBC earthquake simulator  119  Figure 5.2: Four-storey steel plate shear wall specimen tested on the shake table  121  Figure 5.3: Steel plate shear wall specimen mounted on the shake table  123  Figure 5.4: Plan view of lateral support system  125  Figure 5.5: Pin connection at the base of lateral support columns  125  Figure 5.6: Shake table four-storey specimen inside lateral support system  126  Figure 5.7: A photo of the shake table four-storey specimen with lateral support frames, storey masses, and X-bracing rods installed 128 Figure 5.8: Time-histories and corresponding Fourier Transforms of the input motions 133  xvi  LIST OF FIGURES Figure 5.9: The installation of foam pads to dampen out the infill panel vibrations. . . . 141 Figure 5.10: Time-histories of the top floor acceleration (dashed line) and added mass acceleration (solid line) 142 Figure 5.11: Cracks in column flange whitewash appeared at the end of Tarzana Hill 120% run 144  CHAPTER 6 Figure 6.1: Typical recording setup for vibration measurements  153  Figure 6.2: Location of sensors and direction of measurements for the UofA test specimen . 159 Figure 6.3: Longitudinal, transverse and torsional ANPSDs for the UofA steel plate shear wall specimen a) undamaged b) damaged 162 Figure 6.4: First and second longitudinal mode shapes of the UofA specimen a) undamaged ) specimen b) damaged specimen 163 Figure 6.5: Typical input and output response of the shear wall frame due to the hammer impacts a) undamaged specimen b) damaged specimen 164 Figure 6.6: Amplitude and phase of the FRFs for the UofA test specimen a) undamaged specimen b) damaged specimen Figure 6.7: Sensor locations and directions for the quasi-static test specimen  165 172  Figure 6.8: A N P S D of the quasi-static unbraced frame-wall specimen with no masses. 174 Figure 6.9: Typical response of the quasi-static frame-wall specimen to hammer blows with masses attached and support system mounted 175 Figure 6.10: Amplitude and phase of the FRFs for the U B C quasi-static test specimen a) specimen alone b) specimen with masses attached and lateral support system mounted 176 Figure 6.11: Sensor locations and directions for the shake table test specimen  181  Figure 6.12: A N P S D of the shake table steel plate shear wall specimen with storey masses and lateral support system mounted 183 Figure 6.13: Amplitude and phase of the FRFs for the U B C shake table test specimen a) specimen alone b) specimen with masses attached and lateral support system mounted prior to testing c) at the end of shake table testing 184  xvii  LIST OF FIGURES  CHAPTER 7 Figure 7.1: Effects of digital filtering on a recorded signal  191  Figure 7.2: Time-histories of floor acceleration and displacement for Joshua Tree 80% run. 198 Figure 7.3: FRF of the test structure for Joshua Tree 80% run  199  Figure 7.4: Maximum response envelopes of the test specimen for Joshua Tree 80% run . . . 201 Figure 7.5: Storey shear versus interstorey drift relationships for Joshua Tree 80% run 202 Figure 7.6: Input energy together with the first and second floors dissipated energy timehistories for Joshua Tree 80% test 204 Figure 7.7: Variation of axial force and bending moment at the column bases for Joshua Tree 80% run 205 Figure 7.8: Variation of column axial force and bending moment for Joshua Tree 80% run . 206 Figure 7.9: Maximum bending moment and axial force along the height of instrumented column during Joshua Tree 80% run 207 Figure 7.10: Magnitude and angle of principal strains at the centre and near the base of the first storey infill plate for Joshua Tree 80% run 208 Figure 7.11: Time-histories of the table and floor accelerations, table displacement and floor relative displacements for Tarzana Hill 80% run 210 Figure 7.12: Time-histories of the table and floor accelerations, table displacement and floor relative displacements for Tarzana Hill 140% run 211 Figure 7.13: Interstorey Drift for Tarzana Hill shake table runs  213  Figure 7.14: FRF of the test structure for Tarzana Hill 140% run  214  Figure 7.15: Maximum response envelopes of the test specimen for Tarzana Hill runs. 215 Figure 7.16: Profile of storey accelerations and relative displacements for Tarzana Hill 140% test during one of the strong shaking cycles 218 Figure 7.17: Storey shear versus interstorey drift relationships for Tarzana Hill 140% run . . 219 Figure 7.18: Input energy together with the first and second floors dissipated energy timehistories for Tarzana Hill 140% test 221 xviii  LIST OF FIGURES Figure 7.19: Variation of columns axial forces and bending moments at the base with base shear for Tarzana Hill 140% run 222 Figure 7.20: Variation of column axial force and bending moment for Tarzana Hill 140% run 223 Figure 7.21: Schematic representation of the first storey column bending moment diagram during one cycle of loading 224 Figure 7.22: Magnitude and angle of principal strains at the centre and near the base of the first storey infill plate for Tarzana 140% run 225 Figure 7.23: Time-histories of the table and floor accelerations, table displacement and floor interstorey drifts for VERTEQII 70% run 228 Figure 7.24: FRF of the test structure for VERTEQII 70% run  229  Figure 7.25: Maximum response envelopes of the test specimen for VERTEQII runs. . 230 Figure 7.26: Storey shear versus interstorey drift relationships for VERTEQII 70% run 232 Figure 7.27: Energy time-histories at each floor for VERTEQII 70% test  233  Figure 7.28: Magnitude and angle of principal strains at the centre and near the base of the first storey infill plate for VERTEQII 70% run 234 Figure 7.29: Time-histories of the table, second and fourth floor accelerations and displacements for 0.2g sinusoidal run  236  Figure 7.30: Interstorey Drift for 0.2g sinusoidal excitation  236  Figure 7.31: Maximum response envelopes of the test specimen subjected to sinusoidal input excitations 237 Figure 7.32: Storey shear versus interstorey drift relationships for 0.2g sinusoidal waveform 239 Figure 7.33: Variation of axial forces and bending moments in the columns at the base with base shear for 0.2g sinusoidal excitation 240 Figure 7.34: Variation of column axial force and bending moment for 0.2g sinusoidal test. . 241 Figure 7.35: Maximum bending moment and axial force along the height of instrumented column during 0.2g sinusoidal input excitation 242  CHAPTER 8 Figure 8.1: Variation of angle of inclination, a, versus web plate thickness  249 xix  LIST OF FIGURES F i g u r e 8.2: T h e effect o f a r i g i d storey b e a m versus a f l e x i b l e storey b e a m o n the angle o f i n c l i n a t i o n o f p r i n i p a l tensile stresses  251  F i g u r e 8.3: V a r i a t i o n o f angle o f i n c l i n a t i o n , a , versus p a n e l w i d t h  252  F i g u r e 8.4: V a r i a t i o n o f angle o f i n c l i n a t i o n , a , versus p a n e l height  254  F i g u r e 8.5: E f f e c t o f b e a m c r o s s - s e c t i o n a l area o n the angle o f i n c l i n a t i o n , a  255  F i g u r e 8.6: E f f e c t o f c o l u m n c r o s s - s e c t i o n a l area o n the angle o f i n c l i n a t i o n , a  256  F i g u r e 8.7: E f f e c t o f c o l u m n m o m e n t o f inertia o n the angle o f i n c l i n a t i o n , a  258  CHAPTER 9  F i g u r e 9.1: S c h e m a t i c representation o f a thin i n f i l l plate shear b u c k l i n g t e n s i o n fields  262  F i g u r e 9.2: T y p i c a l S A P 9 0 S H E L L element m o d e l a n d forces  265  F i g u r e 9.3: C o l u m n i d e a l i z e d as a m u l t i - s p r i n g m o d e l  268  F i g u r e 9.4: B i l i n e a r a n d trilinear skeleton c u r v e s for i n f i l l plate a n d b o u n d a r y f r a m e . .  269  F i g u r e 9.5: T y p i c a l stress-strain relationships for a) i n f i l l p a n e l b) b o u n d a r y m e m b e r s .  272  F i g u r e 9.6: N u m e r i c a l m o d e l s o f the first s i n g l e storey s p e c i m e n  275  F i g u r e 9.7: C o m p a r i s o n o f elastic stiffness part o f the e x p e r i m e n t a l v e r s u s S A P 9 0 a n a l y t i c a l results for the first s i n g l e storey s p e c i m e n  277  F i g u r e 9.8: C o m p a r i s o n o f a n a l y t i c a l m o n o t o n i c l o a d - d e f l e c t i o n c u r v e s o f C A N N Y - E m o d e l s w i t h test results for the first single storey s p e c i m e n  278  F i g u r e 9.9: C o m p a r i s o n o f elastic stiffness part o f the e x p e r i m e n t a l versus S A P 9 0 a n a l y t i c a l results f o r the s e c o n d single storey s p e c i m e n  280  F i g u r e 9.10: C o m p a r i s o n o f a n a l y t i c a l m o n o t o n i c l o a d - d e f l e c t i o n c u r v e s o f C A N N Y - E m o d e l s w i t h test results for the s e c o n d s i n g l e storey s p e c i m e n F i g u r e 9.11: F r a m e m o d e l s o f the f o u r - s t o r e y s p e c i m e n  282 285  F i g u r e 9.12: C o m p a r i s o n o f S A P 9 0 s i n g l e truss element and m u l t i - s t r i p m o d e l analyses w i t h test results for the 1st storey p a n e l o f the f o u r - s t o r e y s p e c i m e n  286  F i g u r e 9.13: C o m p a r i s o n o f C A N N Y - E s i n g l e truss element a n d m u l t i - s t r i p m o d e l analyses w i t h test results for the 1st storey p a n e l o f the f o u r - s t o r e y s p e c i m e n  286  F i g u r e 9.14: C o m p a r i s o n o f S A P 9 0 s i n g l e truss element and m u l t i - s t r i p m o d e l analyses w i t h test results f o r the 2 n d storey p a n e l o f the f o u r - s t o r e y s p e c i m e n  287  F i g u r e 9.15: C o m p a r i s o n o f C A N N Y - E s i n g l e truss element a n d m u l t i - s t r i p m o d e l analyses xx  LIST OF FIGURES with test results for the 2nd storey panel of the four-storey specimen  287  Figure 9.16: Comparison of SAP90 single truss element and multi-strip model analyses with test results for the 3rd storey panel of the four-storey specimen 288 Figure 9.17: Comparison of CANNY-E single truss element and multi-strip model analyses with test results for the 3rd storey panel of the four-storey specimen 288 Figure 9.18: Comparison of SAP90 single truss element and multi-strip model analyses with test results for the 4th storey panel of the four-storey specimen 289 Figure 9.19: Comparison of CANNY-E single truss element and multi-strip model analyses with test results for the 4th storey panel of the four-storey specimen 289 Figure 9.20: Comparison of SAP90 single truss element and multi-strip model analyses with test results for the overall response of the four-storey specimen 290 Figure 9.21: Comparison of CANNY-E single truss element and multi-strip model analyses with test results for the overall response of the four-storey specimen 290 Figure 9.22: Strip model representation of Driver's test specimen  292  Figure 9.23: Strip model analysis for Driver's test specimen  293  Figure 9.24: Comparison of numerical cyclic analysis with test results for the first single storey specimen 295 Figure 9.25: Results of numerical cyclic analysis for the second single storey specimen 297 Figure 9.26: Comparison of numerical cyclic analysis with test results for the second single storey specimen for ductility ratio of 297 Figure 9.27: Prediction of the cyclic behaviour of the first storey panel for the four-storey specimen using 37° strip model '. 300 Figure 9.28: Prediction of the cyclic behaviour of the second storey panel for the four-storey specimen using 37° strip model 300 Figure 9.29: Prediction of the cyclic behaviour of the third storey panel for the four-storey specimen using 37° strip model 301 Figure 9.30: Prediction of the cyclic behaviour of the fourth storey panel for the four-storey specimen using 37° strip model 301 Figure 9.31: SAP90 computer models of the four-storey shear wall model a) SHELL element model b) 45° inclined pin-ended cross-truss element model 302 Figure 9.32: Comparison of absolute acceleration response of the shake table steel plate shear wall specimen subjected to VERTEQII 70% input motion (SHELL element model) 304  xxi  LIST OF FIGURES  Figure 9.33: Comparison of lateral displacement response of the shake table steel plate shear wall specimen subjected to VERTEQII 70% input motion (SHELL element model) 305 Figure 9.34: Comparison of the analytical (SHELL element) and experimental base shear for VERTEQII 70% input motion 306 Figure 9.35: Comparison of the analytical (SHELL element) and experimental axial force and bending moment time-histories at the base of the column for VERTEQII 70% input motion 307 Figure 9.36: Comparison of fourth floor absolute acceleration and relative displacement response together with the column axial load and bending moment at the base and the base shear time-histories of the shake table steel plate shear wall specimen subjected to VERTEQII 70% input motion (SHELL element model, 1.5mm thick elements)  308  Figure 9.37: Comparison of absolute acceleration response of the shake table steel plate shear wall specimen subjected to VERTEQII 70% input motion (S AP90,45° strip model) 310 Figure 9.38: Comparison of lateral displacement response of the shake table steel plate shear wall specimen subjected to VERTEQII 70% input motion (S AP90,45° strip model) 311 Figure 9.39: Comparison of the analytical (strip model) and experimental axial force and bending moment time-histories at the base of the column for VERTEQII 70% input motion 312 Figure 9.40: Comparison of shake table test specimen and CANNY-E 37° strip model floor absolute acceleration and base shear response (VERTEQII 70% input motion) 314 Figure 9.41: Comparison of shake table test specimen and CANNY-E 37° strip model lateral displacement response (VERTEQII 70% input motion) 315 Figure 9.42: Frequency response amplitude and phase angle of the CANNY-E strip model . 317 Figure 9.43: Comparison of shake table test specimen and modified CANNY-E 37° strip model floor absolute acceleration and base shear response (VERTEQII 70% input motion) 318 Figure 9.44: Comparison of shake table test specimen and modified CANNY-E 37° strip model lateral displacement response (VERTEQII 70% input motion) 319 Figure 9.45: Comparison of shake table test specimen and CANNY-E 37° strip model axial  xxii  LIST OF FIGURES force and bending moment response at the column base (VERTEQII 70% input motion)  320  Figure 9.46: Schematic representation of an infilled frame with discrete strips  322  Figure 9.47: Comparison of experimental and proposed analytical model load-deformation results for the first single storey specimen 324 Figure 9.48: Comparison of experimental and proposed analytical model load-deformation results for the second single storey specimen 324 Figure 9.49: Predicted load versus panel deflection of Timler's specimen  325  Figure 9.50: Predicted Load versus 1st storey panel deflection of Driver's specimen . . 326 Figure 9.51: Comparison of the proposed analytical and experimental storey shear versus interstorey drift envelopes of the UBC quasi-static test specimen 327 Figure 9.52: Proposed numerical model of the UBC shake table specimen  329  Figure 9.53: Comparison of shake table test specimen and proposed numerical model floor absolute acceleration and base shear response (VERTEQII 70% input motion)  330  Figure 9.54: Comparison of shake table test specimen and proposed numerical model lateral displacement response (VERTEQII 70% input motion) 331 Figure 9.55: Comparison of shake table test specimen and proposed analytical model axial force and bending moment response at the column base (VERTEQII 70% input motion) 332 Figure 9.56: Comparison of the displaced shapes of Driver's four-storey specimen with a similar eight-storey specimen 334  xxiii  LIST OF SYMBOLS  a  = acceleration  A  = cross-sectional area of an equivalent truss element  A  = cross-sectional area of beam  b  A  = cross-sectional area of column  E  = elastic modulus for steel  c  E  = post-yield modulus for steel  2  /  = frequency  F  = force  F(co)  = Fourier Transform of the hammer impact force  g  = gravitational acceleration  h  = storey height  l  = moment of inertia of beam  b  I  = moment of inertia of column  L  = width of shear wall panel  M  = moment  c  M  L  = moment magnitude  P  = axial force  Q  = storey shear  q  = physical quantity  t  = time  l  Xi(co) = Fourier Transform of the acceleration record at location i w  = infill panel thickness  V  = Storey shear  y  = distance between the outer surface of column flange to the neutral axis xxiv  LIST  a  = angle of inclination of tension strips from the vertical  8  = storey deflection  A  = flexural deformation  £  = strain  . 9  = tan 7  .  OF  SYMBOLS  -iL h  K  = factor for increasing the static yield point  X  = panel effective width  Y  = shear strain  ftj  = dimensionless physical quantity  p  = mass density  a  = stress  G  = stress  G  = yield stress  o  = normal yield stress  x  = in-plane shear yield stress  1)  = Poisson's ratio  tyl  ty2  y  corresponding to the load at which the infill plate yields of infill plate material  xxv  ACKNOWLEDGEMENTS There have been many people who have helped me during the various tasks associated with the completion of this thesis. Their assistance is very much appreciated, and I would not have been able to accomplish as much without their assistance. I would like to first thank my supervisors, Dr. Carlos Ventura and Dr. Helmut Prion, for the guidance and technical advice they have given me over the years. I am personally indebted to Dr. Carlos Ventura and Professor Liam Finn for financing me and my family throughout the course of my study at UBC, as well as their personal advice and assistance during some difficult times. The experimental section of this thesis would not have been possible without the assistance of the Laboratory technicians. Special thanks goes to Dick Postgate, Howard Nichol and Guy Kirsch for their help with machining, electronics and shake table test setup, and welding. Vincent Latendresse, Adam Lubell, Reza Anjam and Peyman Rahmatian are among the many graduate students who helped with various discussions and during the shake table test setup. This project was conducted under a collaborative research grant from the Natural Sciences and Engineering Research Council of Canada. Financial and in-kind assistance by the Department of Civil Engineering, UBC, is gratefully acknowledged. Discussions with and advice from collaborating researchers at the University of Alberta and the consulting community, especially Mr. Peter Timler from Sandwell, are appreciated with thanks. I would also like to thank Dr. Kang-Ning Li for providing his program CANNY-E and helping me by explaining its various features. Finally, but certainly not least, I would like to thank my family. My father has always been my greatest motivation in life and is thanked for his support throughout my graduate career. My wife, Aliyeh, is given special thanks for the patience, care and encouragement she has given me over the course of my study at UBC. xxvi  1  INTRODUCTION  1.1 GENERAL The use of steel plate shear walls as a primary lateral load resisting system in medium- and high-rise buildings largely remains a challenge for structural engineers and has been used in only a few cases so far. The concept of using steel plate shear panels was developed decades ago, especially in the aircraft engineering and shipbuilding industry where shear panels have been used in stiffened and unstiffened applications. A steel plate shear wall frame can be idealized as a vertical cantilever plate girder, in which the steel plates act as the web, the columns act as the flanges and the storey beams represent the transverse stiffeners. The theory that governs the design of steel plate shear wall structures is essentially the same as that of plate girders developed by Basler in 1961, although the relatively high bending strength and stiffness of the beams and columns are expected to have a significant effect on the overall behaviour for the application in buildings. Also, the presence of relatively thick floor slabs (i.e. large rotational stiffness) may favour domination of shear deformations over the height of the shear wall relative to the overall bending deformations. In comparison with moment resistant frames or reinforced concrete shear wall systems, the use of steel plate shear panels has shown (Troy & Richard, 1979 and Timler, 1998) to be more costeffective by: c  Reducing the amount of steel needed.  c  Increasing the available floor space.  c  Increasing the rate of structural steel erection.  c  Reducing foundation costs.  c  Decreasing dead weight while increasing the overall stiffness and reducing the drift index of the structure. 1  CHAPTER 1 INTRODUCTION Timler (1998) selected an eight-storey office building constructed in Toronto for a comparative design study for both steel plate shear wall and reinforced concrete shear wall systems in Vancouver. Quantity take-offs and cost estimations for each building in steel and concrete were performed in order to economically evaluate the steel plate shear wall system against the concrete shear core method. These included fire-proofing for the steel, reshoring of the floors for the concrete alternative as well as design costs and comparison of construction completion schedules. Cost estimation was verified independently by selected industry representatives. The total cost of the steel building was shown to be 74% of the cost for the concrete alternative. The cost of foundation for the steel alternative was 63% of the concrete shear wall building foundation cost. The thickness of the steel panels at the bottom storey floor was selected as 8 mm compared to the 400 mm thick shear walls for the concrete alternative. In comparison with conventional bracing systems, the steel panels have the advantage of being a redundant continuous system exhibiting relatively stable and ductile behaviour under severe cyclic loading (Driver, 1997 & Lubell, 1997). This beneficial behaviour of steel panels along with the high stiffness contributed by the infill plates acting like tension braces greatly qualifies steel plate shear walls as an ideal energy dissipator system in high risk seismic regions, while providing an efficient system to reduce lateral drift. Since the late 1960's, steel plate shear wall systems have been incorporated in several buildings around the world (Troy and Richard, 1979 and Journal of Commerce, 1984). The selection of this structural system has typically been influenced by architectural, construction and economic considerations. In most cases, design of the plates was based on the assumption that the plates do not buckle prior to attainment of their shear yield strength. This resulted in relatively thick plates or, alternatively, generous use of stiffeners in both the vertical and horizontal directions, which often negated the beneficial cost savings of the system. Current design practice in the United States requires steel plate shear walls to be able to carry  2  CHAPTER 1 INTRODUCTION  both vertical and horizontal loads simultaneously. Consequently, both vertical and horizontal stiffeners are used to provide restraint against out-of-plane buckling of the panels. Japanese designers typically design the shear walls to resist horizontal loads only and leave the vertical loads to be carried by the columns of the building. The latter method results in heavy columns while it greatly reduces the thickness of the plates. To prevent the thinner plates from buckling, however, more plate stiffeners are needed, the installation of which is very labour intensive. As a consequence, the construction costs increase. At the beginning of the 1980's, the idea of utilizing the post-buckling strength of the infill shear plates was introduced by researchers at the University of Alberta who conducted extensive experimental and theoretical studies of the quasi-static cyclic behaviour of unstiffened steel plate shear wall panels. The latest version of Canada's national standard on Limit States Design of Steel Structures, CAN/CSA-S16.1-94 (1994), contains an appendix describing the Canadian approach for the analysis and design of thin unstiffened steel plate shear walls. These design requirements are primarily based on the analytical model developed by Thorburn etal. (1983), which has been substantiated by experimental tests of two single storey shear wall panels utilizing fixed beam-to-column connections and true pinned connections between exterior beam and column connections (Timler and Kulak, 1983) or standard bolted shear-type connections at the beam-to-column joints (Tromposch and Kulak, 1987). It is noted that the extrapolation of code provisions for medium- and high-rise buildings is based on computer analysis and engineering judgement. Therefore, there existed a definite need to further study the behaviour of multi-storey steel plate shear walls under cyclic and simulated earthquake loadings. The research described herein includes quasi-static and shake table testing of fourstorey reduced-scale steel plate shear wall models. 1.2  SCOPE AND OBJECTIVES OF THIS STUDY  To verify the guidelines and design principles provided in the latest version of Canada's  3  CHAPTER 1 INTRODUCTION  National Standard on Limit States Design of Steel Structures, CAN/CSA-S16.1-94 (1994), and to broaden the scope of the code provisions, a collaborative study between researchers at the Universities of British Columbia and Alberta was initiated to investigate the performance of steel plate shear walls as the primary lateral load resisting system for medium to high rise buildings located in regions of high seismic risk. The objective of the UBC research program was to investigate the behaviour of steel plate infill panels and boundary frames under simulated earthquake motions and slow quasi-static cyclic loading. Earthquake simulator testing of structural models has the following advantages over subassemblage or pseudo-dynamic testing: (i) the models are subjected to realistic earthquake excitation, and (ii) the strain rate effect is implicitly accounted for and the problems associated with stress relaxation are nonexistent. In the experimental phase, two one-bay four-storey specimens were tested under quasi-static cyclic loading and shake table earthquake loading, respectively. Parallel analytical studies were conducted to aid in the design of specimens and to compare with test results and produce design recommendations. An important part of the experimental studies was to monitor the formation of diagonal tension field action combined with diagonal compression buckling and frame action, with the aim of assessing their influence on the overall behaviour of the steel plate shear panels under dynamic load reversals. The stability of the panel hysteresis curves under intense seismic and quasi-static cyclic loadings was of primary concern. The effects of the full moment resistant frame along with the presence of steel plate shear panels to minimize the influence of pinching in the hysteresis loops and to ensure satisfactory seismic performance was also studied. Low-amplitude vibration tests (ambient and impact tests) were carried out before and after the application of loading sequences to determine the dynamic properties (i.e. natural frequencies, mode shapes and damping ratio) of the specimens. This provided information needed for the 4  CHAPTER 1 INTRODUCTION  calibration of the analytical models of the steel plate shear wall specimens. The effects of plate buckling, steel yielding and weld cracking or tearing on the dynamic characteristics of the infilled frame specimens were studied. The intent was to show that any damage in the infill plates or the frame, such as buckling or cracking, is reflected as a shift of modal frequencies in the frequency response function (FRF) of the system. The sensitivity of natural frequencies and damping ratio to the structural damage was also investigated. In the shake table study, the effects of the storey masses and their distribution along the height of the frame on the overall response of the steel plate shear wall specimen under intense seismic shaking was studied. The variation of inertia forces generated at each storey level was determined and analysed. The results of a simplified equivalent linear elastic analysis and drift index limitation proposed in the National Building Code of Canada (NBCC, 1995) were compared with the experimental results. The ultimate load achieved in the quasi-static cyclic and shake table tests together with the yield strength of the specimens were compared and discussed. Other objectives of the tests were to assess the amount of energy absorption, ductility, redundancy, stiffness decay and strength degradation on the seismic design of steel plate shear wall systems. The observed structural characteristics of a typical steel plate shear wall frame model under earthquake motions such as: initial stiffness, post-buckling stiffness, yield strength, drift limitation and stable resistance under repeated and reversed loads were evaluated. The effect of the ductility factor on the performance of a structure during an earthquake in conjunction with appropriate detailing and proper inspection during the construction work to reduce the overall base shear delivered to the structure is as much a consideration as of the strength. The major parameters involved in enhancing the hysteresis curves and consequently increasing the energy dissipation capability were identified. The effects of the fixed beam-to-  5  CHAPTER 1 INTRODUCTION  column connections and the frame action in general, on the overall behaviour of the loaddeformation curves were studied. A simplified method of analysis to reasonably predict the overall load-deformation behaviour of steel plate shear wall frames and the internal forces was considered to be important. Therefore, a further objective was to critically assess the strip model representation of infill panels and to verify the observed behaviour with the numerical results. The shortcomings and inconsistencies of the strip model in predicting the overall load-deformation relationship of steel plate shear wall frames were addressed. A simple numerical model that is based on the effective panel width and with strips defined at different directions is proposed. The dynamic shake table and quasi-static test results provided the means of verifying the validity of the proposed analytical model. 1.3 THESIS OUTLINE This section of the thesis provides a description of the manner in which the remainder of the manuscript is organized. A detailed study of the available literature on steel plate shear wall behaviour was essential. Chapter 2 provides a comprehensive chronological review of previously published research results on steel plate shear wall structures. Summaries of both analytical and experimental, unstiffened and stiffened shear panels are presented. Chapter 3 describes the scaling laws and an appropriate procedure to decide upon the scaling factor for the test specimens. The determination of the scale that best suited the dimensions and capacity of the shake table is explained. The results of parametric studies for two different finite element models to design the various components of the steel plate shear wall specimens are presented. In Chapter 4, a brief summary of the cyclic results obtained from two single storey and one  6  CHAPTER 1 INTRODUCTION  four-storey steel plate shear wall specimens is provided. Chapter 5 presents the description of shake table tests that were conducted on a four-storey steel plate shear wall specimen. Both the test set-up and the manner in which the test was conducted are discussed. Observations made during the test about the behaviour of the main test specimen are also presented. In Chapter 6, the ambient and impact vibration tests and the results obtained from the analysis of the collected data on a large-scale four-storey steel plate shear wall frame at the University of Alberta and on two reduced-scale four-storey frame-wall panels at the University of British Columbia are described. The results of shake table tests on the four-storey specimen are presented in Chapter 7. This includes the data collected from accelerometers, displacement transducers and strain gauges. Chapter 8 contains a review of the parameters affecting the angle of principal tensile stresses proposed in Appendix M of the latest Canada's National Standard on Limit States Design of Steel Structures, CAN/CSA-S16.1-94 (1994). Chapter 9 describes a simplified method of analysing steel plate shear wall frames. Monotonic, cyclic and time-history analyses are described and the predicted results are presented. A comparison between the numerical analyses and experimental results is described. The shortcomings of the simplified analytical models are revealed and the areas of concern are identified. A numerical model using a semi-empirical equation to estimate the effective panel width was developed. Following the derivation of the numerical model, the procedures used and the correlation of results with experimentation was verified. Chapter 10 provides a summary of the research and a discussion of the conclusions drawn. The need for further studies, both analytical and experimental, is outlined.  7  2 2.1  LITERATURE  REVIEW  OVERVIEW  During the past two decades, the body of research on steel plate shear walls has been divided into two distinct categories: those in which the infill plates are prevented from buckling and those that rely on the post-buckling strength of the steel panels. A number of case studies in Japan and the United States have been conducted on infill steel plate shear walls that were designed not to buckle under extreme lateral loading. In recent years, however, the idea of utilizing the post-buckling strength of the infill steel plates has gained wide attention from researchers in Canada, the United States and England. A limited amount of information is currently available regarding the post-buckling behaviour of steel plate shear walls for the purpose of developing a set of simple expressions for the analysis and design of this structural system. A number of static and quasi-static cyclic tests performed on large and small scale models have been reported since 1983. These studies have examined the behaviour of steel plates throughout the entire range of loading, from elastic to plastic and from pre-buckling to post-buckling stages. The results obtained from the studies unanimously support the rationale of using the post-buckling strength, tension field action, and the stable energy absorption capacity of the steel panels in designing the primary lateral load resisting system for buildings. A brief review of studies conducted on steel plate shear walls around the world is presented in the following. 2.2 TAKAHASHI et al. (1973) In the early 1970's, Takahashi, et al. (1973) conducted a series of experimental and finite element analytical studies on stiffened thin steel plate shear walls. The objective of the tests was to investigate the behaviour of thin stiffened steel plate shear wall systems as an alternative solution to the stiff concrete shear walls commonly designed as lateral load resisting elements  8  CHAPTER 2  LITERATURE REVIEW  in structures. In the first series of tests, twelve one-storey specimens with overall dimensions of 2100 mm width by 900 mm height were tested. The spacing and width of stiffeners on both sides or one side of the steel panels together with the strength, hysteresis curve and post-buckling behaviour of steel panels were the parameters investigated. Three different plate thicknesses, 2.3, 3.2 and 4.5 mm, and three different stiffener arrangements coded type G (six vertical stiffeners), type M l (two vertical and one horizontal stiffeners) and type M2 (six vertical and two horizontal stiffeners) were studied. Two specimens were made of 2.3 mm thick steel plate, one with no stiffeners and the other with stiffener arrangement type M2 and height of 60 mm. Four specimens had infill plate thicknesses of 3.2 mm with stiffener arrangement type M l and heights of 15, 25, 40 and 60 mm. Three specimens had infill plates of 4.5 mm thick with stiffener arrangement type G and heights of 10, 30 and 50 mm. Three more specimens were constructed from 4.5 mm thick steel plate which had stiffener arrangement type M l with heights of 15, 35, and 55 mm. Each shear panel was surrounded by a very stiff rectangular pin jointed frame attached thereto with high-strength bolts. A compressive force was applied in one diagonal direction of the frame producing a state of pure shear stresses on the specimens. The first test results showed that all the specimens underwent large deformations exhibiting a very stable and ductile behaviour. Some of the panels buckled elastically because the height of the transverse stiffeners were small. Partial buckling also occurred in the specimens that had relatively large spacing between stiffeners. In some other specimens, plastic buckling occurred. The yielding shear stresses of the infill panels conformed well to the Von Mises yield criterion, namely T = o^/V^ • After buckling, the rigidity of panels gradually decreased as the plates developed tension field action. The specimens with stiffeners on both sides of the panels showed more stable behaviour than those with stiffeners on one side of the panels only. In general, the hysteresis curves were S-shaped for most specimens, except in a few cases where  9  CHAPTER2.  LITERATURE  REVIEW  the specimens were heavily reinforced (stiffener arrangement type M2) with wide stiffeners. Shear deformations in excess of 0.1 radians were reported for heavily stiffened specimens. Figure 2.1 shows the hysteretic curves of the two specimens made out of 2.3 mm thick steel plate, one with no stiffeners and the other heavily reinforced with horizontal and vertical stiffeners (type M2).  CO  cu CO  Yx 10" (rad) 2  Yx 10" (rad) 2  Figure 2.1: Hysteresis behaviour of a) an unstiffened and b) a heavily stiffened steel plate shear walls (after Takahashi et ai, 1973) In the second series of tests, two full-scale one-bay two-storey steel plate shear wall specimens, taken from a proposed 32-storey building design, were tested under cyclic horizontal load. The test specimens differed from one another in that one was built without openings and the other with an opening in each storey. To provide similar shear rigidity and strength, the specimen with openings was made of 6 mm thick steel plate while the specimen without opening was made of 4.5 mm thick panels. The design of the test specimens which had fixed bases was primarily based on the design principles obtained through the first series of tests. The design criterion ensured that the shear yield strength of the web plates was achieved before out-ofplane plate buckling. However, once elastic limit of the infill panels was exceeded, only local buckling of the web was allowed between the horizontal and vertical stiffeners. 10  CHAPTER2.  LITERATURE  REVIEW  Both full-scale specimens demonstrated robust and stable hysteresis loops and large energy absorption capacity. As the applied lateral load approached the yielding strength of the specimens partial buckling of the infill plates was observed at several points. The influence of these partial buckles on the rigidity of the specimens was very small, however. A theoretical finite element analysis of the specimens was carried out under the assumptions of no out-ofplane buckling for infill plates and bi-linear stress-strain relationship for the steel material. The experimental load-deflection graphs agreed reasonably well with analytical results. The yielding shear stress obtained from the Von Mises equation was in good agreement with experimental results. Tearing of the welds at the base of the columns occurred at the final stage of loading. The authors concluded that the equations presented for the design of stiffeners for thin steel shear walls are satisfactory provided that plate buckling would not occur until the plates develop their shear yield strength. Moreover, they concluded that the conventional shear theory, wherein the horizontal shear is transferred by beam action alone, can be conveniently used to calculate the stiffness and yield strength of the stiffened shear panels. 2.3  MIMURA AND AKIYANA (1977)  A few years after the work by Takahashi et al, Mimura and Akiyana followed their work by developing general expressions for predicting the monotonic and cyclic behaviour of steel plate shear walls. Their main objective was to study the load-deflection behaviour of a steel plate shear wall frame in which the shear buckling load of the plates was considerably less than their shear yield strength. In their derivation, they assumed that the overall strength of a steel shear wall frame is determined by a load required to induce elastic buckling of the infill panels plus the post-buckling strength of the shear panels and boundary frame. To compute the shear buckling load of an infill plate, the well-established elastic buckling theory of plates assuming simply supported boundary conditions was utilized. At loads beyond the elastic buckling load  11  CHAPTER 2  LITERATURE REVIEW  they assumed that the steel panels would develop a tension field to resist the applied loads. The angle of inclination of tension field was computed with the derivation provided by Wagner (1931). The envelope of load-deflection curves was established by the sum of the contributions from the panel and the surrounding frame. Figure 2.2 illustrates the proposed monotonic loaddeflection behaviour of a steel plate shear wall frame. An elastic-plastic behaviour was assumed to establish the monotonic load-deflection curve of the frame.  Q t  8 Figure 2.2: Monotonic load-deflection behaviour (after Mimura and Akiyana, 1977) Mimura and Akiyana then developed a theoretical hysteresis model shown in Figure 2.3. The line OA represents the initial response of a steel plate shear wall structure. Thereafter, global yielding occurs and the post-yield stiffness follows the line AH. If the load is then removed at an arbitrary point B in the post-yield region, the unloading path remains parallel to the elastic line OA until the load is completely removed (point C). As the load is applied in the opposite (negative) direction, the steel panel continues to resist the load elastically until its elastic shear buckling capacity is reached at point D. Beyond this point, the applied shear is to be carried by the tension field action of the steel panel. However, as the infill panel was stretched and shortened diagonally during the deformation AB, a residual deformation DE is required before the tension field could be developed. Because the authors assumed that the surrounding frame 12  CHAPTER2  LITERATURE REVIEW  has zero stiffness prior to the formation of tension field, the line DE is horizontal. The residual deformation DE was taken as one half of the permanent plastic deformation during the previous loading cycle. This was based on the assumption of a tension field angle of 45°, Poisson's ratio of 0.5 and an initially unbuckled panel. From point E, the load-deformation curve follows a linear path EA' where point A ' is equal and opposite to that of point A. Increasing the load further tracks the path A T T which is parallel to the path AH. Unloading at point B' follows the curve B ' C which is parallel to initial elastic stiffness path OA. Once the load is brought back to a zero level, a residual deformation of O C is observed. As loading commences again in the positive direction, the panel resists the load up to its shear buckling capacity (point D')- The steel panel then deforms horizontally to point E ' where redevelopment of tension field begins. A linear transition returns the loading path back to the point of last maximum load (point B). It is noted that the distance D'E' is taken as the average of the distances O C and OF. Additional hysteresis curves would follow in a similar manner. This load-deflection pattern was the basis of the models that were later proposed by the researchers at the University of Alberta.  Figure 2.3: Hysteresis curves proposed by Mimura and Akiyana (1977)  13  CHAPTER 2  LITERATURE REVIEW  2.4 AGELIDIS AND MANSELL (1982) A feasibility study of analysis and design of tall service cores for multi-storey buildings constructed from orthotropically stiffened steel plate shear walls was performed by Agelidis and Mansell (1982). The investigation also included cost estimation of details for stiffeners, plate and stiffener splices, floor beam and slab supporting systems, core corners and connections between core panels and connecting beams. A 20-storey office building was chosen for investigation. The building was 30 m square in plan with a 10 m square central services core. The core consisted of steel plates with vertical stiffeners in each orthogonal direction. The stiffened steel plates were coupled with connecting beams in one direction and acted as two cantilevers in the other direction. The relatively rigid core was assumed to carry the lateral loads plus all the tributary gravity loads. The infill plate thicknesses ranged from 16 mm at the bottom to 8 mm at the top of the building. The thickness of vertical stiffeners varied from 10 mm at the lower levels to 4 mm at the top. The service core panels were assumed to be fabricated and transported in units of four storey lifts. A two-dimensional linear plane-stress finite element analysis was carried out to acquire stresses and maximum deflections of the core under dead, live and wind load combinations. The geometric orthotropy of the stiffened steel plates was modelled by material orthotropy, so that the stiffeners were assumed to be "smeared" throughout the panels' width, giving different elastic moduli in the two principal directions. The cross walls forming the flanges of the core were modelled by beam elements with the same cross-sectional area and material properties. The maximum lateral deflection of the core computed from finite element analysis agreed well with the results obtained by a manual method used first for a preliminary design. The distribution of compressive stresses in the web of the core at the lower storey levels was used for the design of the infill plate elements. The calculated lateral deflection index under wind load was in the order of 1/620. The bending moments in connecting beams were critical for  14  CHAPTER 2  LITERATURE REVIEW  wind loading. The effects of connecting beam stiffness and plate cross-section on the maximum longitudinal stresses in the flange walls and web walls as well as maximum bending moments in the beams and maximum lateral deflection of the core were also investigated. A set of details for transverse stiffening, plate and stiffener splices, floor beam and slab seating, core corners and for the connections between core panels and the connecting beams were drawn. The aim was a) to demonstrate that practical details for steel plate shear wall cores can be conceived, b) to identify the problems requiring further investigation, and c) to enable a comprehensive cost analysis to be performed. The cost of a steel core was estimated to be twice as expensive as a concrete core. This included the price for steel panels, fabrication, erection and sprayed fire-proofing compared to the price for concrete, reinforcement steel, reusable framework and embedded predrilled plates to connect the floor beams. The authors concluded that even though the estimated steel core was twice as expensive as a concrete core, there could be sufficient benefits to offset the extra cost. Some of these important benefits were cited as: a) the time needed to extend the core in each construction cycle is significantly reduced, thus providing savings in holding charges, b) there would be a considerable reduction in the weight of the building and therefore size of the foundations, c) Many of the details can be built in the shop rather than on site, d) demolition of the structure may proceed by dismantling rather than by destruction, and e) the extra cost of the service core is negligible when compared with the total cost of the completed structure. If this new construction technique opens the way to changes in construction methods and procedures that bring other benefits, the extra cost may prove to be worthwhile. 2.5  THORBURN, KULAK AND MONTGOMERY (1983)  Thorburn et al. (1983) developed an analytical method to study the shear resistance of thin unstiffened steel plate shear walls. The model was based on the theory of pure diagonal tension by Wagner (1931) which did not account for any shear carried by the infill plates prior to shear  15  CHAPTER 2  LITERATURE REVIEW  buckling. The so-called strip model represented the shear panels as a series of inclined strip members, capable of transmitting tension forces only, and oriented in the same direction as the principal tensile stresses in the panel. Each strip was assigned an area equal to the product of the strip width and the plate thickness. The derivation of the angle of inclination of the tension strips was based on the Principle of Least Work. A one-storey one-bay steel panel, surrounded by beams and columns, was subjected to pure shear. The columns were assumed to be continuous while the beam-tocolumn connections were considered to be pinned. This assumption ensured that no moment was transferred from the rigid joints to the beams. The effects of column bending was also excluded from the derivation. The storey beams were assumed to be infinitely rigid in bending. This was due to the assumption that tension field forces for any two adjacent storeys differ very little and oppose one another, therefore the net vertical forces acting on the beam would be negligible. Two extreme cases were considered for the column elements: 1) columns with infinite bending stiffness ensuring a uniformly distributed tension zone over the entire panel, and 2) completely flexible columns where no anchorage to the inclined strip tensile forces through the columns was considered. Even though the angle of inclination was derived without considering the bending stiffness of the columns, actual column stiffnesses were used in modelling a steel panel to account for the influence of column bending in response to the horizontal components of the tension field forces. Figure 2.4 shows the strip model representation of a typical steel plate shear panel for the two cases of infinitely stiff and completely flexible columns. The resulting expressions for the inclination of the tensile stresses that would develop in a buckled shear wall panel for the two cases of infinitely stiff columns, Equation (2.1), and completely flexible columns, Equation (2.2), were derived as:  16  CHAPTER2.  LITERATURE  REVIEW  h  Infinitely rigid beam  Tension element  Column  Pinned connection  Figure 2.4: Strip model representation of a typical steel panel developed by Thorburn et al. (1983) a) complete tension field b) partial tension field 1 +  Lw  2A„  tan a =  for infinitely stiff columns  (2.1)  for completely flexible columns  (2.2)  1+^ A  tan 2 a = -  b  where, a = Angle between columns and tension strips w = Thickness of infill plate L = Width of panel h - Height of panel A  c  = Cross-sectional area of column  A  b  = Cross-sectional area of beam 17  CHAPTER £.  LITERATURE REVIEW  To most easily model the stiffness characteristics of a given thin unstiffened steel plate shear panel, an equivalent truss model was also adopted to replace the tension zone of the steel panel with an equivalent truss element having the same storey stiffness as the strip model. The area of an equivalent truss member was derived as:  2 A = 7 7 - • . ? —r^rr 2 sin<|> • sin2<() S  n  •sin4pjl tan  A =  2  for infinitely stiff boundary members J  J  for completely flexible columns  (2.3) '  v  K  (2.4) J  in which all parameters have been defined previously except: A = Area of equivalent truss member tan(|) = 7  h  and  tan2B = 7 h  Thorburn et al. (1983) also conducted a parametric study to investigate the effects of infill plate thickness, storey height, storey width and column stiffness on the strength and stiffness characteristics of a thin unstiffened steel plate shear panel. Their findings for each parameter can be summarized as follows: c  The panel stiffness increased linearly with increasing infill plate thickness. The slope of the line was a function of the panel geometry.  c  The relationships between storey height and panel stiffness was linear on a semi-log scale. As the storey height was increased, the lateral stiffness of the panel decreased.  c  On a log-log scale for panel width and panel stiffness, for certain column properties, the panel stiffness dropped as the panel width was increased. This trend continued until a certain limiting value was reached (the limiting value was for panel aspect ratio, L/h, of less than 1.0). After this point the panel stiffness increased with increasing panel width.  c  A linear relationship was observed between the panel stiffness and the log of column stiffness. The slope of the line varied slightly for different panel aspect ratios.  18  CHAPTER2.  LITERATURE  REVIEW  2.6 TIMLER AND KULAK (1983) To investigate the adequacy of the strip model proposed by Thorburn et al. in 1983, Timler and Kulak (1983) tested a large scale, single storey steel plate shear wall specimen under cyclic loading to the serviceability limit and pushover loading to failure. The test specimen consisted of two panels, 3750 mm wide with a storey height of 2500 mm arranged so that opposing tension fields would form. The thickness of the infill plate was 5 mm. Built-in connections were incorporated at the interior beam-to-column connections while true pin-connections were placed at the exterior beam-to-column connections. No external axial pre-load was induced to the columns prior to the test. The specimen was cycled three times to the maximum permissible serviceability drift limit according to CSA-S16.1-M78 (Canadian Standard Association, 1978). At the service load stage, the angle of inclination of the tensile in-plane principal stresses within the web plate, as derived from the strain readings, varied between 44° and 56° along the centreline of the infill plate. Following this, a final loading excursion was applied until failure of the structural system was reached. At the yield load level, the overall magnitude and distribution of principal stresses along the centreline of the infill plate were uniform and in good agreement with analytical results. The ultimate load attained in the test was governed by the failure of details (weld tear occurred at the web plate to fish plate connection) and did not reflect the ultimate load that can be carried by the web plate and surrounding frame members. Much higher principal tensile stresses were observed in the web plate at ultimate load compared to the yield load. The difference in angle of inclination of the principal stresses along the centreline of the plate became quite significant as the ultimate shear capacity was reached. The derivation of the angle of inclination for diagonal tension strips developed by Thorburn et. al, (1983) was re-evaluated. A revised formula for calculating the angle of inclination of tension strips in multi-storey buildings considering the bending effects of columns, Equation  19  CHAPTER 4.  LITERATURE REVIEW  (2.5), was derived. It is noted that Equation (2.5) has been implemented in the Appendix M of Canada's national standard on Limit States Design of Steel Structures, CAN/CSA-S16.1-94 (1994) for determining the angle of inclination of tension strips in multi-storey buildings. .  Lw  tan a =  4 I  +  hw  +  A  (2.5)  h w  360/ L  b  c  where, I = Column moment of inertia c  As the exterior beam of Timler's specimen was free to bend, the additional bending strain energy of the beam was also included in the total work equation. Also, as the base of the columns were pinned the strain energy term for the column bending was modified. Following the same procedure as outlined by Thorburn et al. (1983), the solution for a was derived as:  tan a =  (2.6) \+hw  (  -^ +320/ —5— L 1  h  3  [2A  b  A  c  y  where, I = Beam moment of inertia b  The second entry in the parenthesis for the numerator is the additional contribution due to bending of the exterior beam member. The predicted angle of inclination for tensile stresses was computed as 51°. The measured angle of inclination of the principal stresses, which is a key parameter in the model, was found to be within 10% of that predicted by the Equation (2.6). The discrepancies between the Thorburn's original derivation and the revised expression, Equation (2.6), was found to be of minor significance. The simplified analytical model, strip 20  __  CHAPTERZ LITERATURE REVIEW  model, developed by Thorburn et al. (1983) was found to be satisfactory in predicting the overall load-deflection response of the specimen, although the predicted elastic stiffness of the specimen was slightly stiffer than the measured value. The measured axial strains in the columns were in good agreement with the predicted values. Less satisfactory correlation was obtained between measured and computed bending strains. In each case, the measured strains were lower than those predicted. 2.7 TROMPOSCH AND KULAK (1987) A single-storey full-scale unstiffened steel plate shear wall specimen similar to the one tested by Timler and Kulak (1983) was tested by Tromposch and Kulak in 1987. The objective of the test was to verify the inclined tension bar model proposed by Thorburn et al. under quasi static, fully reversed cyclic loading. The specimen had a storey height of 2200 mm and a panel width of 2750 mm. The infill plate was 3.25 mm thick. The specimen was constructed with typical bolted shear beam-to-column connections and pin connections at the column bases. To simulate the effects of gravity loads applied to a structure, an axial pre-load was applied to the columns through high strength prestressing bars anchored at both ends of the columns. The specimen was loaded with a gradually increasing fully reversed cyclic load up to about 67% of the ultimate load subsequently attained. This was due to a limitation of the loading system causing parts of it to reach their capacity before failure of the specimen. A total of 28 cycles comprising two complete cycles of the same maximum deformation in both tension and compression were applied. Following the application of the 28 cycles of lateral load, the loading arrangement was revised and the specimen was loaded monotonously to its ultimate capacity. To avoid the clearance problem of the prestressing rods at large deformations, the axial pre-load of the columns was removed prior to the final loading of the specimen. The final load attained in the test was governed by the maximum capacity of the hydraulic actuator system and did not reflect the ultimate load that can be carried by the web plate and surrounding 21  CHAPTER 2  LITERATURE REVIEW  frame members. As the final load was reached tearing of the welds was observed in several corners of the panel indicating a robust beam-column joint rotation and slip of the bolts. The inclined tension bar model was found to be adequate in predicting the strength and ultimate capacity of the unstiffened steel plate shear wall specimen. The effects of beam-to-column connections, initial column axial loads and residual stresses induced in the infill plate due to the welding process were found to be significant in predicting the load-deflection response of the steel plate shear wall panel. The hysteresis loops developed in the specimen were pinched, but they were stable. An analytical method based on the model described by Mimura and Akiyana (1977) was proposed to predict the hysteresis behaviour of an unstiffened steel plate shear wall panel. Figure 2.5 illustrates the load-deflection hysteresis model proposed by Tromposch and Kulak (1983). The line OA represents the elastic response of a steel plate shear wall panel neglecting the prebuckling strength and stiffness of the thin infill plate. At point A the panel yields and thereafter it behaves inelastically. When the panel is unloaded at any arbitrary point, e.g. point B, the slope of the unloading line is equal to the elastic stiffness (line OA). As the panel is loaded in the opposite (negative) direction, the stiffness of the steel plate shear wall panel is equal to the stiffness of the boundary frame until the tension field starts developing in this direction. The deflection required to develop the tension field is taken as half of the deflection from previous cycle, OC. This assumption is based on the shortening of the diagonal bars due to effects of the Poisson's ratio when yielding occurs in the panel. Once the tension field has reformed, at point D, a linear transition is assumed to apply up to the point of negative yield, A'. Beyond this point the inelastic path ATT parallel to line AB is followed. Unloading at point B' results the deflection to return to point C . As the loading is applied in the positive direction again, the frame stiffness governs the load-deflection curve until reformation of tension field at point D'. Point D' is assumed to be equal to the permanent deflection from the previous cycle, line OC, 22  CHAPTER 2  LITERATURE REVIEW  Figure 2.5: Hysteresis model proposed by Tromposch and Kulak (1987) plus one-half of the permanent deflection just completed in the previous half cycle, line O C . A linear transition connects the point D' to the point of previous maximum deflection B. Subsequent cycles are derived in a similar manner until the frame forms a mechanism due to excessive inelastic deflection. Beyond this deflection, the load-deflection curve is assumed to have zero stiffness until the tension field in the other direction develops. Cycle EFGHB'ET'G'H'E in Figure 2.5 illustrates a case where a mechanism forms in the boundary frame at points G and G'. Further parametric studies showed that frames with fixed beam-to-column connections can dissipate as much as three times more energy as that dissipated by frames with simple pinned beam-to-column connections. The beneficial post-buckling strength and the relatively stable hysteretic characteristics of unstiffened thin steel panels were amply demonstrated. 2.8 ROBERTS AND SABOURI-GHOMI (1991) A series of small scale quasi-static cyclic tests on slender unstiffened shear plate panels, to  23  CHAPTER 2  LITERATURE REVIEW  investigate their load-displacement characteristics, was conducted by Roberts and SabouriGhomi (1991a) at the University of Wales in England. The panels had width-to-height aspect ratios equal to 1.0 and 1.5. Six different specimens with infill panel dimensions of 300 mm x 300 mm or 450 mm x 300 mm and thicknesses ranging from 0.54 mm, 0.83 mm and 1.23 mm were tested. The thinnest plates were made of aluminium alloy and the remainder were made of steel. Tensile tests were performed to measure the Young's modulus and yield stress (0.2% proof stress) of the plate materials. The edges of the plates were clamped to surrounding frame members by two rows of 8 mm diameter high strength bolts. The boundary elements were connected together with pin joints at the corners. All panels were tested by applying tensile or compressive loads at two diagonally opposite corners in the direction of the panels diagonal. For each specimen, tensile forces were applied along one panel diagonal until the panel was well into the elasto-plastic range. Then, the panel was subjected to a similar compressive load. This process was repeated to obtain at least four complete cycles of load-displacement, with the diagonal displacement being gradually increased. All panels exhibited stable but pinched hysteresis loops. The amount of energy dissipated was increased with increasing peak displacement in each cycle. Since the web plates of the test panels were relatively slender, their shear buckling loads were significantly less than the maximum loads achieved during the tests. An approximate elasto-plastic model for predicting the hysteresis characteristics of a slender shear panel, surrounded by a rigid, pin jointed frame and subjected to predominantly shear loading was proposed. The model shown in Figure 2.6 takes into account the elastic shear buckling load of the panel while it neglects the shear resistance of the frame members. After buckling, an inclined tension field is developed which resists the load until the yield strength of the panel is reached at point A. From A to B the panel strains plastically and from B to C the panel unloads elastically parallel to OA. As the load reverses to the other direction, the loop  24  CHAPTER2.  LITERATURE  REVIEW  continues from C to D to A'. Point A ' is equal and opposite to that of point A. At D the plate buckles and from D to A ' an inclined tension field develops in the plate. The line DDI is parallel to line OA and point DI is proportional to the corresponding plastic deformation of the panel in the previous loading (OD1 = p • OC). The ratio (3 is determined from the flow theory 4  of plasticity and assumed state of stress in the plate. From A ' to B' the panel strains plastically in the opposite direction, after which it unloads from B' to C , parallel to OA. As the load is reapplied in the positive direction, the plate buckles at D' and from D' to B an inclined tension field develops in the plate. The line D'D2 is parallel to line OA. Starting from B, the subsequent cycles are similar to the first cycle. The authors, however, recognized the contribution of fixed beam-to-column connections in resisting part of the applied shear load. Assuming that plastic hinges would form at the tops and  Q ' A  Ultimate shear load  Critical buckling shear load  LSs I fl DT / /D  B'  A'  B  Critical buckling shear load  Ultimate shear load  Figure 2.6: Hysteresis loops for a shear panel with pin jointed frame (after Sabouri-Ghomi and Roberts, 1991) bottoms of columns, an elasto-plastic model was utilized for columns resisting storey shear. The hysteresis loops for a complete panel were defined as a superposition of hysteresis loops 25  CHAPTER 2  LITERATURE REVIEW  for the web plate and the surrounding columns, which incorporated the critical shear buckling and the ultimate plastic yielding of the web plate combined with the ultimate shear resistance of the frame columns. Figure 2.7 shows the hysteresis loops for the complete panel. Q Ultimate shear load  1  A  B  >^  /  D  B'  A'  .-—^  /  ^. 8  Ultimate shear load  Figure 2.7: Hysteresis loops for a shear panel with fixed beam-to-column connections (after Sabouri-Ghomi and Roberts, 1991) The theoretical predictions showed satisfactory agreement with the test results. Sabouri-Ghomi and Roberts (1991b) then implemented their proposed hysteresis models in a nonlinear dynamic time-history analysis of thin steel plate shear walls. The method is based on a finite difference solution of the governing differential equation of motion. A thin steel plate shear wall is idealized as a vertical cantilever plate girder beam with the associated storey masses and the corresponding dynamic loads concentrated at each storey level. Initially, the discrete form of the equation of motion of the cantilever beam considering only shear deformations (it was assumed floor beams and associated slabs remain horizontal) was formulated. A more general form of the equation of motion (Sabouri-Ghomi and Roberts, 1992) that included both bending and shear deformations within each panel was presented afterwards. The dynamic equation of motion was solved using a finite difference time stepping technique.  26  CHAPTER 2  LITERATURE REVIEW  A five-storey single bay steel plate shear wall structure was modelled as a vertical cantilever beam with its mass and associated storey masses concentrated at each storey level. The model was subjected to two different pulse loads, with durations of 2 and 1.8 seconds, applied to each storey. In the first case, the response remained elastic, whereas in the second, the pulse loads were increased to induce a non-linear response. The observed relative shear deformation of the first storey was much greater than that of the other storeys. The effects of higher modes of vibration tended to distort the smooth curve of storey deflections. The model was also subjected to a sinusoidal ground motion input that contained a frequency component close to the fundamental natural frequency of the model. The periodic ground motion induced resonance of the shear wall by a linear increase in the amplitude of vibration during the early response of the structure. The onset of yielding, however, inhibited the resonance and resulted in a reduction in the amplitude of vibration. This was attributed to the energy dissipation during plastic hysteresis cycles which acts as a damper, and to a reduction in the stiffness of the structure due to plastic straining. The results obtained from the nonlinear dynamic analysis showed the ability of the hysteresis model to predict the nonlinear dynamic response of thin steel plate shear walls. No attempt, however, was made to validate the analytical results obtained with any experimental dynamic test results. 2.9 YAMADA (1992) The lateral resisting mechanism of composite seismic elements; i.e., reinforced concrete infilled shear panels, steel band bracing reinforced concrete infilled shear panel and steel panel with and without covering reinforced concrete infilled shear panel was studied by Yamada (1992) at Kansai University in Japan. Only the tests performed on steel shear panels are discussed here. Two 1/5 scale, one storey steel plate shear panels with a span of 1200 mm and a height of 600 mm and infilled thin steel panels of 1.2 mm and 2.3 mm thick were tested. The steel shear panels were completely welded to surrounding steel rigid frames. The surrounding  27  CHAPTER2.  LITERATURE REVIEW  composite unit rigid frames were composed of wide flange steel sections encased in a reinforced concrete cross section. The specimens were subjected to a monotonic loading in the direction of the panel diagonals. The main resisting mechanism of the infill steel shear panels were composed of the diagonal tension field of buckled steel panels. The initial stiffnesses of the specimens until buckling of the steel panels were slightly less than the specimens with encased steel panels. However, after buckling of the infill panels the stiffnesses of steel shear panels became fairly low. There was little reduction in the shear resistance of the specimens beyond the ultimate shear resistance of the steel panels. Buckled steel panels formed a pure diagonal tensile state of stress and experienced very large deformation with minor reduction of resistance. The final fracture occurred at the base of the surrounding composite rigid frames. The relative stiffness of plate panels compared to the surrounding frame was noted to be very significant in the overall behaviour of infilled steel plate shear wall frames. 2.10  ELGAALY, C A C C E S E , CHEN AND DU (1993)  The effective use of the post-buckling strength of plate panels for steel plate shear walls was demonstrated in a series of tests conducted by Caccese etal. (Caccese, Elgaaly and Chen, 1993) at the University of Maine. Five quarter scale three storey steel plate shear wall specimens with different plate thicknesses and beam-to-column connections were tested under cyclic and monotonic loading. The tests were performed with no axial load applied to the columns. The effects of beam-to-column connections and panel slenderness ratio (column spacing over thickness of the plate) on the overall behaviour of unstiffened steel plate shear walls were the two major parameters studied. The thicknesses of steel infill plates were 0.076 mm, 1.90 mm and 2.66 mm, while the centre-to-centre column spacing and storey height were kept constant at 1250 mm and 830 mm, respectively. Three specimens were built with moment resisting beam-to-column connections and infill plate thicknesses of 0.076 mm, 1.90 mm and 2.66 mm.  28  CHAPTER 2  LITERATURE REVIEW  The other two specimens were constructed with shear beam-to-column connections and infill plate thicknesses of 0.076 mm and 1.90 mm. A lateral shear load was applied through a servo-controlled hydraulic actuator mounted at the roof level of the specimens. Each specimen was subjected to a cyclic load history with gradually increasing peak displacements. The peak displacements were increased in eight increments of 6.35 mm each up to a maximum of 2% drift measured at the top of the specimens. Each displacement cycle was repeated three times. The entire loading history included 24 fully reversed cycles that were repeated twice for each specimen. Finally, the specimens were pulled monotonically, if at the end of cyclic loading they were intact, to the displacement limit of the actuator. The cyclic behaviour of the specimens, which is generally characterized by its hysteresis loops, exhibited significant pinching. The fixity of beam-to-column connections was found to have a minor effect on the overall load-displacement curve of the specimens. The reason for this was attributed to continuous welding of infill plates to surrounding beams and columns which act as moment resisting connections even without welding the flanges of beams to columns. The effect of beam-to-column connections was more pronounced for the most slender steel plate specimen. The amount of energy dissipated by the specimens was primarily a function of the infill plate thicknesses. As the specimens underwent large lateral forces, the amount of energy dissipated at each cycle of loading for the same number of peak cycle displacements was significantly higher in the specimen with 2.66 mm infill plate than that with 0.076 mm infill steel plates. The presence of steel plates was shown to be very effective in dissipating the energy, even in the very first cycle due to the out-of-plane bending of the plates. Two analytical computer models were developed (Elgaaly, Caccese and Du, 1993) to study the behaviour of steel plate shear wall specimens up to their ultimate capacity under monotonic  29  CHAPTER2.  LITERATURE  REVIEW  loading. First, a non-linear finite element analysis including both material and geometric nonlinearities was carried out to investigate the post-buckling behaviour of steel plate shear wall specimens. The infill plates were modelled with three-dimensional isoparametric doubly curved shell elements while the beams and columns were modelled with three-node isoparametric beam elements. Second, a simple analytical model replacing the infill plates by diagonal tension members that ignores the compression buckling of infill plates was used. For simplicity and practical use, the strip model proposed by the University of Alberta was employed to calculate the ultimate capacity of thin steel plate shear walls. The failure loads in the finite element models that used shell elements with 1.90 mm and 2.66 mm infill plates were obtained when the structures became unstable due to column yielding. The ultimate loads for both cases were nearly identical. As the ultimate capacities of these specimens were controlled by the column strength, it was concluded that the use of thicker plates would not necessarily enhance the capacity of a steel plate shear wall structure. The use of slender unstiffened plates that can achieve a significant post-yield strength prior to the formation of plastic hinges and instability in the columns, in comparison with less slender plates that tend to become unstable due to column buckling before the plate can develop its full strength, was found to be more desirable. The contribution of global overturning moment caused high tensile and compressive stresses within the plates along the inside flanges of the columns near the base. The ultimate loads predicted by the finite element models were significantly higher than the experimental results. The discrepancies were attributed to the initial out-of-plane deformation of the infill plates and the overall out-of-plane deformations of the specimens. These differences caused the physical specimens to be softer than the corresponding finite element computer models. Also, in order to capture the complex shape of the post-buckling deformation of the steel plates, many more elements were needed in the computer models. This resulted in the central processing unit time to be excessive and not practical for cyclic or dynamic loading analysis. 30  CHAPTER 2  LITERATURE REVIEW  The strip model, which assumed an elastic-perfectly plastic stress versus strain curve for the plate material, was found to be inadequate in predicting the overall load-deflection curves of the steel plate shear wall specimens. A bilinearly elastic-perfectly plastic stress-strain curve, shown in Figure 2.8, with slopes E (elastic modulus for steel) and E (selected in such a way 2  to obtain a good agreement between analytical and experimental results) was proposed for Thorburn's strip model to predict the monotonic behaviour of thin steel plate shear walls. The yield stress r j ^ ' 2  s m  e  plate material yield stress and the stress r j  which the plate in the specimens started to yield. The values of  fyl  corresponds to the load at and E depend on the 2  slenderness ratio of the plate material and was determined empirically. This model predicted the monotonic behaviour of the tested specimens with a very good degree of accuracy. The influence of the number of truss members in Thorburn's model was found to be significant when the magnitude of tension field forces on the columns is high and local bending of the columns due to these forces is not negligible. The variation of the angle of inclination of the truss members had a small effect on the ultimate loads predicted by the model. Stress, a t  e  Strain, 8  Figure 2.8: Trilinear stress-strain relationship for strip model (after Elgaaly et al, 1993)  31  CHAPTER 2  LITERATURE REVIEW  2.11 XUE AND LU (1994) The behaviour of steel plate shear wall frame systems with different connection arrangements was examined analytically by Xue and Lu (1994a) at Lehigh University. A three-bay twelvestorey frame-wall structure with moment resisting beam-to-column connections in the exterior bays and with its middle bay filled by steel panels was used. The frame-wall system was designed to resist the earthquake forces specified in the Uniform Building Code (UBC, 1988) for seismic zone four. The vertical distribution of the lateral loads applied to the structure followed the distribution specified in the UBC code for use in the equivalent static load design. No gravity load was applied to the structure. Four different connection arrangements between the plate panels and the interior bay frame members were considered: 1.  Full moment frame with the steel panels attached to both the girders and columns (F-GC).  2.  Full moment frame with the steel panels connected to the girders only (F-G).  3.  Shear connections in the infilled bay and full moment connections in the other bays; shear panels were connected to both the girders and columns (PGC).  4.  Shear connections in the infilled bay and full moment connections in the other bays; shear panels were connected to the girders only (P-G).  The three-bay frame had exterior bays that were 9144 mm wide and an interior bay 3658 mm wide. The lowest storey was 4572 mm high and the remainder were 3658 mm high. Three different thicknesses were selected for the shear panels. The shear panels in the bottom four storey had a thickness of 2.8 mm. The shear panels in the middle four stories had a thickness of 2.4 mm. In the top four storey, shear panels with a thickness of 2.2 mm were used. The primary concern of this study was focused on the lateral stiffness of frame-wall structures at the load level for which drift control is often a major design consideration. In the analyses performed, the beams and columns were assumed to remain elastic, but the infill panels were allowed to buckle and yield. 4-node shell elements with large deformation capacity were  32  CHAPTER 2  LITERATURE REVIEW  selected for the panels. The shell elements were allowed to become elastic-plastic as yielding occurred in the panels due to combined action of the applied in-plane shear and out-of-plane bending induced by buckling. The results obtained from the relationships between the total applied lateral loads and the top displacements showed a great increase in the lateral stiffness of the frame-wall systems due to the presence of shear panels. The full moment connections in the bay filled with shear panels had a negligible effect on increasing the lateral stiffness. The complete and partial panel connections to the surrounding boundary frame essentially resulted in the same lateral stiffness. The shear panels in the P-G system participated early in absorbing a larger share of the lateral load compared to the panels in the F-GC system. This caused much of the yielding and nonlinear action to occur in the panels rather than in the boundary frame. The storey shear was distributed symmetrically to the four columns in the P-G system while in the F-GC system one of the interior columns alone attracted 60% of the total storey shear. Because of the lack of connection between the shear panels and the columns in the P-G system, the column bending moments were caused primarily by the frame action. In both systems, a large portion of the axial forces, however, was shifted from the exterior columns to the interior columns. In the P-G system, the bending moment on the girders was essentially controlled by the tension field action of the panels, and not by the frame action. The results from the analysis showed that for this system the peak bending moments moved away from the beam-to-column connections forcing the plastic hinges to occur within the beams. Such a system was considered more favourable in enhancing the overall ductility of the steel plate shear wall frames while reducing the deformation demand on the beam-to-column connections. The overall deformation of infill panels was considered a combination of the frame action of beams and columns together with the shear action of the wall panels. The results of this interaction forced the infill panels to undergo shear deformation y as well as flexural  33  CHAPTER 2  LITERATURE REVIEW  deformation A, as shown in Figure 2.9. The combination of the shear and normal stresses causes the panels to buckle initially and to develop the tension field action at or near the ultimate state.  Figure 2.9: Behaviour of a steel plate shear wall frame (after Xue and Lu, 1994a) The results of the finite element analysis showed that the shear buckling strength of the panels in the F-PG system are quite different from those in the P-G system. The normal stresses applied on the edges of the panels in the P-G system were mostly in tension, thereby enhancing the shear buckling of the infill plates. For the F-PG system the normal stresses were in compression, thereby reducing the shear buckling strength of the panels. After the initiation of shear buckling in the panels which happened at a low level of loading, the resistance against further loading was taken by frame action through flexural deformation A. Once the lateral load reached a level, such that the drift of the top beam was large enough to compensate for the effect of flexural deformation, the steel plate infill panels could then become effective in resisting additional load because of the development of the tension field action. It was concluded that the flexural deformation of frame-wall structures should be precluded in order to invoke the tension field action of panels after the initiation of the panel's shear buckling. With regard to the performance of each frame-wall structure, the system with simple beam-tocolumn connections in the infilled bay and shear panels connected to girders only, was 34  CHAPTER 2  LITERATURE REVIEW  considered as the most economical and structurally sound system. The overall resistance of steel plate shear wall structures under earthquake ground motions was divided into two separate load resisting subsystems. The shear panels were the primary system while the frames served as the secondary system. The design philosophy was based on three levels of ground motion shakings: minor, moderate and severe. Under minor earthquake ground motion or service wind loading, the structural response was considered as linear behaviour with some localized buckling and yielding of the infill plates developed in critical areas of buckled panels. For moderate earthquakes, the overall response would become noticeably nonlinear with more of the panels buckling and yielding. The beams and columns would be designed to remain elastic at this level of shaking, so that only a small amount of permanent lateral displacement would be induced in the structure after the removal of earthquake forces. At this stage most of the energy would be dissipated through plastic deformation of the wall panels. During a major earthquake, beams and columns would yield and the structure is pushed to its ultimate state of resistance. Because of the large ductility and stable hysteresis strength, collapse of the structure would be minimized. Xue and Lu (1994b) also conducted a numerical parametric study on a one-bay one-storey steel plate shear wall model to study the load-displacement characteristics of frame-wall systems. The key parameters were width-to-thickness and aspect ratio of the panels. The P-G system was selected as a base structure for the numerical modelling. Large post-buckling deformation and yielding of the infill panel were given full consideration in the finite element analysis. The variation of width-to-thickness ratio had no significant effect on the overall loaddisplacement response of the structure. This was attributed to the very low buckling load capacity of steel panels and the initiation of tension field action which typically dominates the performance of a thin shear panel. The need for further studies on the effects of width-tothickness ratio on the ultimate load capacity of shear panels due to tearing of the plates near  35  CHAPTER2.  LITERATURE  REVIEW  connections was emphasized. The aspect ratio of the panels had a significant effect on the behaviour of frame-wall systems. That is because the development of tension field action depends primarily on the panel aspect ratio. The effect of panel aspect ratio was more pronounced within the aspect ratio of 1 to 2, in which the yield strength capacity of the frame-wall system increased by as much as 30%. Increasing the panel aspect ratio from 2 to 2.5, however, had no apparent effect on enhancing the overall yield capacity of the model. Two empirical simplified equations predicting the yield strength, yield displacement and the post-yield stiffness of the frame-wall structures were proposed. The modified RambergOsgood curve (Collins, 1991) was used in the empirical predictions. Good agreement (conservative results) between the analytical predictions and empirical equations was observed. The numerical cyclic analysis of one of the shear panels used in the three-bay, twelve-storey frame-wall system demonstrated significant energy dissipation capacity with some pinching. Pinching, however, became less important as shear deformation increased. Strength degradation occurred in the analysis for successive cycles of same deformation amplitude. The envelope curve predicted by the proposed equation matched reasonably well with the boundaries of the loop cycles. The validity of the proposed empirical equations to be extended for developing empirical hysteresis models was stated. 2.12 SUGII AND YAMADA (1996) Experimental and analytical results of tests carried out on 23 steel panel shear walls, with and without concrete covering, were presented by Sugii and Yamada (1996). The test specimens consisted of different shear span aspect ratios, steel panel thicknesses and concrete wall thicknesses. Both monotonic and cyclic shear loading cases were investigated. The  36  CHAPTER 2  LITERATURE REVIEW  experimental specimens were 1/10 scale models of a prototype structure with a height of 3000 mm and various shear span aspect ratios from 1:1 to 1:2. The thickness of model infill panels were in the range of 0.4 mm to 1.2 mm. Fourteen unstiffened steel shear panel specimens with no concrete covering were tested. Each specimen consisted of two adjacent identical panels which were separated by a deep beam. The horizontal load was applied along the beam at midspan in a manner similar to the set-up used by Timler and Kulak (1983). The two panels were thus loaded identically. In all cases, the surrounding moment resisting composite frames consisted of wide flange steel sections covered by reinforced concrete. The maximum resistance of steel panel shear walls tested monotonically was achieved at a storey sway angle of 0.01 to 0.03 radians. Only slight reduction in resistance was observed beyond these values up to a storey angle of 0.1 radians. Under cyclic loading, the thickness of infill panels was the main factor contributing to the overall strength of the specimens and affecting the area under hysteresis curves. The pinching in the curves was very pronounced for the thin infill plates. An analytical method replacing an infill steel panel by a tension brace with an equivalent effective width of 2/3 of the storey height was proposed. A trilinear stress-strain relationship was assumed for the brace and an elastic perfectly plastic moment-curvature relationship was considered for the surrounding frame. The computed results, however, significantly overpredicted the elastic stiffness part of the load-deflection curves, but reasonably captured the overall strength achieved in the tests. 2.13 DRIVER (1997) Recommendations for testing a multi-storey structure utilizing full moment connections led to Driver's half scale four storey steel plate shear wall frame (Driver, 1997), which was recently tested under quasi-static cyclic loading. The objective of this test was to study the performance of multi-storey steel plate shear walls under the effect of very severe cyclic loading. Aspects of  37  CHAPTER 2  LITERATURE REVIEW  interest were the elastic stiffness, yield strength, post-yield behaviour, energy absorption, cyclic instability and the influence of a moment resisting frame on the shape of hysteresis loops. The four-storey specimen was 7.5 m high and 3.4 m wide. The typical storey height was 1.83 m. The infill plates for the first and second storey were 4.8 mm thick. The third and fourth storey panels were filled with 3.4 mm thick plates. No stiffeners were provided for the infill panels. All beam and column sections conformed to the Canadian steel code of class 1 sections, that is, they would be considered "compact". Connection of beam flanges to the columns was made using complete penetration groove welds, using a backing bar and run-off tabs that were left in place. A fish plate connection detail was provided at the interface of infill panels and boundary frame. A gravity load simulator was used to apply the vertical loads at the tops of the columns. Equal lateral loads were applied cyclically at each floor level. A total of 35 load cycles were applied to the specimen with a maximum ductility ratio of nine. The specimen proved to be more flexible than predicted by the finite element analytical model. Prior to reaching the yield displacement at the first storey panel, six cycles were conducted to explore the elastic and the initial inelastic behaviour of the specimen. After conducting three cycles with the first storey yield displacement, the displacement was increased in multiples of this displacement in each subsequent deformation step. The first sign of yielding was observed in the first storey panel where fish plates were connected to the boundary members and at the periphery of the infill plates. Slightly after this, tension yield patterns began to form at the top corners of the first storey panel. As the load was increased further, yield lines developed that covered virtually the entire area of the first storey panel. At three times first storey yield displacement weld tearing was detected in the top corner of the first storey panel. Also, first yielding in the beam-to-column joint panels was observed at this loading stage. Local buckling of the column flanges occurred immediately below the  38  CHAPTER 2  LITERATURE REVIEW  beam at the first level, at a storey displacement of four times its yield value. At a storey displacement of six times its yield value, a total of fifteen tears were present in the first storey panel. With all the tears in the plate and severe yielding in the columns and formation of local buckling in the column flanges, the total base shear maintained by the specimen was about 95% of its ultimate strength. As the specimen was unloaded in the opposite direction after reaching a storey deflection of nine times its yield displacement, one of the columns fractured at its base. The fracture began at the toe of the weld connecting the outer flange of the column to the base plate and then propagated completely through the web. During this cycle the base shear was 85% of the maximum base shear achieved at five times first storey yield displacement. The uniformity of the recorded hysteresis curves indicated that the specimen exhibited highly ductile and stable hysteresis behaviour under multiple load cycles with increasing ductility levels of up to nine times initial yield displacement in the bottom storey panel. The moment resisting joints did not significantly contribute to the energy dissipation mechanism of the specimen. This was substantiated with the extent of yielding in the panel zones where only minimal whitewash flaking was observed in the beam-column joint regions. A new hysteretic model based on the previous works of Mimura and Akiyana (1977) and Tromposch and Kulak (1987) was proposed. In this model, the behaviour of the shear wall was divided in two distinct components, boundary frame and panel. Figure 2.10 shows Driver's proposed hysteretic model. Line OA represents the initial elastic stiffness of the frame-wall system using the strip model analysis. As the panel behaves inelastically, line AB, the shear wall stiffness reduces to that of the moment resisting frame. Once the frame yields, the postyield stiffness of the frame-wall system is equal to that of the moment resisting frame. During unloading stage, the elastic stiffness of the shear wall remains similar to the initial elastic stiffness. At point D, the panel contribution becomes zero and moment resisting frame resists the entire remaining load. Reloading in the opposite direction follows the path DE to point F  39  CHAPTER £.  LITERATURE REVIEW  where the moment resisting frame becomes inelastic. Beyond point F, the overall stiffness of the shear wall assembly becomes equal to the post-yield stiffness of the moment resisting frame until the redevelopment of tension field occurs. Similar to the assumption made by Mimura and Akiyana (1977), the residual deformation DG was taken as one half of the permanent plastic deformation during the previous loading cycle. As the tension field becomes active, the overall stiffness of the shear wall is equal to the panel stiffness plus the post-yield frame stiffness. As the strips yield upon further loading, the frame post-yield stiffness takes over. Unloading and reloading follows the path C'D'E'F'G'H' in a manner similar to that described above.  Redevelopment of tension field  Shear yield load  Figure 2.10: Hysteresis model proposed by Driver etal. (1997) 2.14 ELGAALY AND LIU (1997) A new modelling technique for thin steel plate shear walls based on a series of strips in the diagonal tension direction connected to the surrounding beams and columns by gusset plates was presented by Elgaaly and Liu (1997). In the analytical models, the infill plates are replaced by 45° strips having an elastic, elasto-plastic, and perfectly plastic stress-strain relationship.  40  CHAPTER 2  LITERATURE REVIEW  The initial yielding and corresponding elongation of the strip-gusset elements together with post-initial yielding modulus were derived semi-empirically. The side dimensions of the gusset plates are determined by equating the buckling shear stress of the equivalent square plate to the shear yield stress of the plate material. The model was developed for both welded and bolted plate connections. The analytical models were able to predict the pushover envelope and hysteresis curves of the tested specimens to a good degree of accuracy. 2.15 SUMMARY From the limited amount of research done on the topic of seismic behaviour of unstiffened steel plate shear walls, it can be noted that some notable variations exist in the static and quasi-static tests results and comments as reported by different researchers around the world. The efficiency of moment resistant beam-to-column connections in enhancing the hysteresis loops and consequently dissipating more energy under earthquake loading, has not yet been fully understood. There have been limited quasi-static tests performed on unstiffened steel plate shear wall frames, but no information is available on experimental tests under earthquake loading. To date, no shake table testing of multi storey steel plate shear wall frames is available for reference.  41  3  DESIGN  3.1  OF TEST  SPECIMENS  GENERAL  As part of a Collaborative effort among academic investigators from the University of British Columbia (UBC) and the University of Alberta (UofA) and industry consultants to study the seismic behaviour of steel plate shear walls, the UBC participants planned to conduct quasistatic and shake table testing of small-scale steel plate shear wall specimens. Two small-scale models of a typical steel plate shear wall frame analogous to the larger scale model tested at the University of Alberta (Driver, 1997) were planned for quasi-static cyclic and shake table studies. Testing two similar steel plate shear wall specimens under slow cyclic load reversals and more realistic shake table earthquake loading would permit the study of several behavioural aspects, including: c  Comparison of the overall load-displacement curves between quasi-static test and more realistic shaking table test.  c  Evaluation of the beneficial properties of redundancy, ductility and robust resistance of hysteresis cycles to degradation under cyclic loading and simulated seismic loads.  c  Assessment of the overall variation of panel shear resistance and overturning moment during slow reverse cycles and sudden dynamic loading.  c  Determination of the deflection history of different floors versus storey shears in quasi-static and full dynamic load environments.  The design of the test specimens was primarily based on the limitations of the shake table facilities. The main restrictions of the UBC shake table facilities were: clearance above the table (4.2 m), maximum weight allowed on the table (15,000 kg) and the stalling force capacity of the actuator that produces horizontal longitudinal motions in either direction (-160 kN). The  42  CHAPTER 3  DESIGN OF TEST SPECIMENS  effects of shear panel aspect ratio, panel thickness, stiffness of the surrounding frame (including moment-resistance and shear-only connections), number of storeys, and storey masses on the overall behaviour of a reduced scale steel plate shear wall specimen were examined using the linear finite element analysis computer program SAP90, ver. 5.4 (Wilson and Habibullah, 1992). To study the behaviour of a prototype structure by means of a scale model, the identification of problems affecting the reliability of prototype response prediction based on the results of scale model testing had to be examined. In the following section, the background information necessary for adequate modelling of structures in a shake table testing environment is reviewed. The fundamentals of modelling theory is explained first, then the development of analytical procedures for the analysis and design of the test specimens is described. The limitation and deficiencies of the UBC scaled down models are also discussed. It is recognized that very few inelastic dynamic response phenomena can be reproduced "precisely" at model scales. The overall goal of the first phase (experimental investigation) of this research was to assess the feasibility of using thin plate shear wall system in seismic zones and to make recommendations for further studies. Due to the limitation of the loading equipment, reduced scale models had to be tested. The main purpose of scaling was to get a realistic representation of structural prototype for the calibration of analytical models. 3.2 DYNAMIC MODELLING THEORY 3.2.1  Overview  Laboratory tests can be performed on either full-scale prototype or small-scale models of a complete structure. In most cases, testing a full-scale structure is not possible considering the limitations associated with laboratory equipments and space, and the high cost of experimentation. The validity of test results is, however, greatly dependent on the selected scale factor. The reliability of experimental results of one-half to one-third scale models has  43  CHAPTER 3  DESIGN OF TEST SPECIMENS  generally been accepted by many researchers. Small-scale models in the order of one-fifth or smaller, however, have often been viewed with considerable skepticism (Moncarz and Krawinkler, 1981). In the case of steel structures, the scale models that can accommodate the use of hot-rolled quality steel material with stress-strain characteristics similar to the prototype material is very desirable. Nevertheless, any structural model must satisfy certain modelling laws in order to reasonably simulate the behaviour of an actual structure. To express the relationship between a scale model and prototype structure, a set of modelling rules describing the geometry, material properties, initial conditions, boundary conditions and loading environment of the model and the prototype structure must be established. The theory that leads to the development of model-prototype correlation is called similitude. These similitude requirements of scale models are largely based on the dimensional analysis of the physical parameters that influence the behaviour of prototype structures. 3.2.2 Dimensions and Dimensional Analysis Any physical phenomenon has general characteristics that are either qualitative or quantitative. The qualitative characteristics express a physical phenomenon in certain measures commonly referred to as dimension. The dimension of any physical phenomenon can be defined as the product or powers of some fundamental measures. The most common sets of fundamental engineering measures are mass (M) or force (F), length (L), time (T) and temperature (0). For example, the dimension of acceleration can be expressed in terms of the basic measures length and time. The quantitative characteristic of a physical phenomenon is made up of a number and a standard unit. Each of the fundamental measures, or dimensions, thus has its associated standard units among several unit systems in use today. To study the dimensional characteristics of a prototype structure and its model, we must first define the physical parameters that influence its behaviour. The relationship between any physical phenomenon and its associated variables can be expressed mathematically in a  44  CHAPTER O  DESIGN OF TEST SPECIMENS  dimensionally homogeneous form. That is, the governing equation must be valid regardless of the choice of dimensional units in which the variables are measured. This mathematical form can be represented by: F{4 q v  >?„)= 0  Y  where <Zj > < 7 ' '  a  2  (3.1)  physical parameters describing a phenomenon.  a r e n n  Dimensional analysis is an analytical method that converts a dimensionally homogeneous equation into an equivalent equation containing only independent dimensionless products or powers of the physical variables and parameters (Moncarz and Krawinkler, 1981). Based on the theory of dimensional analysis it can be shown that any equation of the form (3.1) can be expressed in the form: G(n it , v  2  ,n )= k  0  (3.2)  where the n terms are dimensionless products of the n physical variablestfj> < 7 ' ' 2  n •^  a  n e  number k is equal to the total number of physical variables and parameters involved, n, minus the number of basic quantities (fundamental measures) needed to describe the dimensions of all physical variables and parameters. As an example, the deflection, 8, of a rectangular cantilever beam subjected to load P (including both bending and shear rigidities) is a function of beam length /, beam depth h, beam width b, elastic modulus E and Poisson's ratio v. This function can be expressed as: F{h,b,h,l,E,\,P)  = 0  (3.3)  For the rectangular cantilever beam example all quantities can be expressed in terms of the basic quantities Force (F) and length (L). The number of independent dimensionless products in this case can be computed as  = 7 - 2 = 5. The independent dimensionless form of the  rectangular cantilever beam example can be written as:  45  CHAPTER 3  DESIGN OF TEST SPECIMENS  If Equation (3.2) is written once for a prototype structure and once for its scaled model, the following equality can be established: >V  ( i ' 2p>  G  n  n  P  »y  _  {  ( lm> 2m>> im>> km)  G  K  K  n  n  where the subscripts p and m refer to the prototype structure and its model throughout this section. Since the dimensionless products n  ip  and n  im  are independent of the units of  measurement, a complete similarity between the prototype and its model is achieved if the dimensionless products n and 7 t are equal (n = Tt ). ip  (m  ip  im  3.2.3 Similitude Relationships and Types of Models To relate the measured model response to the prototype behaviour a complete similarity between the prototype and model must be established. This can be achieved by establishing scaling factors for each of the independent dimensionless products, n terms in Equation (3.5), of the prototype and model. These scaling factors are usually expressed as ratios of the numbers of units needed to describe similar quantities in model versus prototype., i.e., the relationship between length measurement in a model and prototype can be written as: (3.6) where 5/ is scale factor for length. l and l denote the length measurement of the model and m  p  prototype, respectively. A length scale factor of  means that one unit of length measurement  in the model corresponds to ten equal units of length measurement in the prototype. It is evident that to describe any model-prototype scaling problem one can select as many arbitrary scales as we need to independently describe the model-prototype relationship. Since the fundamental quantities (length, force and time) are independent of each other, it is clear that the number of arbitrarily selected scales must be equal to the number of basic quantities needed to describe the problem. For structures subjected to dynamic loading it is common to choose  46  CHAPTER 3  DESIGN OF TEST SPECIMENS  the length (L), modulus of elasticity (E) and acceleration due to gravity (g) as fundamental physical quantities instead of the commonly used fundamental quantities of length (L), force (F) and time (T) for static tests. All the scale factors are therefore functions of S/, S and S E  g  which are the scale factors for length, modulus of elasticity and gravitational acceleration, respectively. Since it is not practical for shake table testing that g can be different between model and prototype, it is necessary to select S as unity, S =l, which leaves the choice of the g  g  arbitrary scales only to two scale factors, namely S/ and S . E  To illustrate the determination of scale factors for a model-prototype problem, let us consider the rectangular cantilever beam example, described above, whose dimensionless products were written as Equation (3.4). If we select a length scale, 5/, and a scale for modulus of elasticity, S , the complete similitude requirements of all the other parameters can be written as: E  *  S  = h  = h S  = l S  a  n  d  S  = P  S  E -  S  f  (-) 3  ?  where S§ is the scale factor for the deflection of the beam, S and S are length scales for width b  h  and height of the beam, and S is the scale factor for load P. Clearly, Poisson's ratio v as a p  dimensionless quantity must be equal in the model and prototype. A model that maintains complete similarity with the prototype is called a true model. For most practical applications, the economic and technological constraints preclude a model study that fulfils all similitude requirements. It is therefore up to the designer to isolate those features which may be altered such that model construction becomes feasible while the results obtained from testing the model can still be used to reasonably predict the behaviour of a prototype structure. These types of models are called adequate models. 3.2.4 Development of a Scale Model for Shake Table Studies The most important forces that are applied to a structure with a given geometry during a dynamic loading are: inertia, gravity and restoring forces, denoted as Fj, F , and F , G  R  respectively. The relationship of each one of the aforementioned forces to mass density, p,  47  CHAPTER O  DESIGN OF TEST SPECIMENS  geometrical length, /, applied acceleration, a, and gravitational acceleration, g, may be expressed as: Fj - pi a = Ma F ~pl g  = Mg\  3  G  F ~ al  (3.8)  = Eel  2  2  R  where a and e correspond to the stress and strain measurements at some locations, and M is the F  F  mass of the model. At each instant of a dynamic loading, the ratios of — and — may be G  R  F  written as:  F  I pi a a TT ~ ^ T " = G pl g S F  3  (3.9)  3  F  3  / _ pi a _ pla  R  Eel  F  2  E  (3.10)  e  As the gravity acceleration g is considered to be equal for both model and prototype, S = 1, it can be concluded from Equation (3.9) that the amplitudes of input accelerations for model, a , m  a  and prototype, a , must also be similar, y  8  a  =  8  a  > S = —= 1 . a  "  p  Returning to the model problem, Equation (3.10) can be written once for the prototype and once for the model. Equating the prototype equation and the model equation, One obtains:  Since elastic and plastic strains are dimensionless, they must be equal in the prototype and e model structures at each and every instance of dynamic loading, — = S = 1. Thus, £  E  P  considering S = S = S = 1, the true replication of inertia, gravitational and restoring forces P  a  g  o  is possible if and only if the following equation is satisfied:  48  CHAPTER 3  DESIGN OF TEST SPECIMENS  (3.12)  Equation (3.12) indicates that the ratio of modulus of elasticity to mass density of the material used in a model must be scaled appropriately to maintain a complete similarity between the model and prototype. On the other hand, since true replica modelling requires that S = S = 1, the stress-strain relationship of model and prototype materials should be e  l  identical with a ratio of  being constant in the e-direction, see Figure 3.1.  Prototype  r //Ep  <* = S a m  E  p  / fi  b e =  /  E  P  Model  e 1  •  Figure 3.1: Stress-strain similitude requirements for a completely similar model The above similitude requirements for true replica models for which inertial, gravitational and restoring forces are correctly duplicated are difficult to satisfy because of the severe restrictions on the model material properties. For complete similarity between the model and prototype, Equation (3.12) requires that the model material have a small modulus of elasticity (Figure 3.1) or large mass density or both. For models that use the same materials as the prototype, J = [ - J , Equation (3.12) is clearly violated. To address this problem in testing smallv P )m \ P Jp scale structures and structural components on shake tables it is acceptable to increase the mass (-  49  CHAPTER3  DESIGN OF TEST SPECIMENS  density p by adding additional masses that are structurally ineffective but seismically effective. This can be achieved by adding a series of lumped masses concentrated at the floor levels. Rewriting Equation (3.11) for proper simulation of inertial and restoring forces, one obtains: (3.13) which for S = 1 we get: Q  (3.14) where  represents the mass scale. It is noteworthy that the presence of additional lumped  masses may increase the state of stresses in beams and columns due to increased gravity loading. Nevertheless, when the effects of gravity loads compared to the inertia forces are small, the lumped masses at floor levels can be scaled according to Equation (3.14). Other similitude requirements are the time scale of input acceleration time histories and the frequency of vibration of the scaled and prototype structure. A summary of the scale factors obtained from similitude considerations (Moncarz and Krawinkler, 1981) for earthquake loading is given in Table 3.1. True replica models satisfy the requirements set forth by Equations (3.9) and (3.10) which imply simultaneous duplication of inertial, gravitational and restoring forces. Unfortunately, however, such models are practically impossible to build and test because of the severe restrictions imposed on the model material properties, especially the mass density. Alternate scaling laws shown in column (4) of Table 3.1 have been shown to adequately simulate the behaviour of the structure. Considerable success has been achieved in the testing of small-scale structures (Mirza et ai, 1984 & Uang and Bertero, 1986) on shaking tables where additional material of nonstructural nature has been added to simulate the required scale density of the model.  50  CHAPTER 3  DESIGN OF TEST SPECIMENS  Scale Factors Physical quantity (1)  Dimension  True replica model  Model with additional mass  (2)  (3)  (4)  Length, /  L  Displacement, 5  L  Force, F  SL SL  EL  SL  2  EL  S  EL  S  S  S  2  Acceleration, a  8  1  1  Gravitational acceleration, g  8  1  1  Modulus of Elasticity, E  E  SE  s  Poisson's ratio, v  —  1  1  Specific Stiffness  E E/Lg  SL  Stress, a  E  SE  SE  Strain, e  —  1  1  Mass density, p Time, t Frequency,/  E Lg  Is r 8. L  s s Jh E  E  —  —  L  1  1  JS~L  Table 3.1: Summary of scale factors for seismic response analysis (after Moncarz and Krawinkler, 1981) To examine the reliability of test results obtained from shake table tests of small-scale models researchers at Stanford University tested a \ scale model of a prototype steel frame which was previously tested at U.C. Berkeley (Mills and Krawinkler, 1979). A comparative study was performed for strain measurements, joint distortions, storey displacements and accelerations between model and prototype. A detailed comparison between true prototype response and the response obtained from the model test showed a very good agreement. The study confirmed the  51  CHAPTER 3  DESIGN OF TEST SPECIMENS  possibility of reliable prediction of prototype response with tests performed on small-scale models. Shake table experimentation of a variety of small scale models has also been carried out at the University of Illinoise (Otani and Sozen, 1974 & Aristozabal and Sozen, 1977). Although these model structures did not simulate specific prototypes, they have resulted in a wealth of detailed information on the seismic response of structures.  3.2.5  Dynamic Properties of Steel Structures  Experimental studies have indicated that the strength and behaviour of most structural materials depend on the rate of strain, the number of cycles of load reversals and the level of applied loading stress. The effect of the strain rate change on the stress-strain characteristic of steel structures for the case of ASTM (American Society for Testing and Materials) A36 steel is shown in Figure 3.2 (Norris et al, 1959). 500 Rate of strain 1 mm/mm/sec  400 ca  Q_  300  - . . . \ Dynamic yield I I I ' J stress  fStatic yield  v>  I  co  obtained at ASTM rate of strain  200  100  H  0J 0  1  1  1  1  4  8  12  16  1—I 20  Strain, e(%) Figure 3.2: Effect of the strain rate on the stress-strain characteristic for steel structures (after Mirzaet al, 1984)  52  CHAPTER 3  DESIGN OF TEST SPECIMENS  The effects of increasing rate of strain can be summarized as follows: 1.  The nominal yield stress increases.  2.  The strain at yield point increases.  3.  The elastic stiffness (modulus of elasticity, E) remains constant.  4.  The strain at which strain hardening starts increases.  5.  The ultimate stress increases marginally.  One of the most important parameters that influences the lateral resistance of steel structures is the increase in the static yield stress under sudden load reversals. The percentage increase in yield stress based on the rate of strain for two types of steels with different static yield stress is shown in Figure 3.3 by Norris et al, 1959. It is evident in Figure 3.3 that the increase in static yield point is greater for steels with lower static yield point, as is shown by the high slope of curve A in Figure 3.3.  0  0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 Rate of strain (mm/mm/sec)  Figure 3.3: Increase in static yield point of steel material with strain rate (after Mirza et al, 1984)  3.3 DESIGN OF THE STEEL PLATE SHEAR WALL TEST SPECIMEN The main objective of the experimental program was to study the behaviour of steel plate shear walls when subjected to simulated earthquake loading. To fulfil this objective we were faced 53  CHAPTER 3  DESIGN OF TEST SPECIMENS  with one fundamental question: what is the minimum scale and appropriate dimensions of a steel plate shear wall system that can be tested to reasonably reflect strength and deformational properties of the actual structure. The answer to the above question was an important step in shake table dynamic testing of a steel plate shear wall specimen because there were no shaking tables in Canada that are large enough in platform size, payload capacity and flow rate to test full-scale structural systems. The following is a description of the procedure used to select an appropriate scale factor for the steel plate shear wall test specimen. To alleviate the complexity of the relationship between reduced scale shake table tests and actual size structures, it was decided to do auxiliary tests on a similar specimen under quasistatic load combination. It was recognized that much of the available knowledge regarding seismic performance of structural members and their connections has been derived from simplified, quasi-static tests of structural components and subassemblies. There are well established guidelines for the selection of loading histories that can be employed in most quasistatic experiments whose purpose is to assess the seismic performance of a structure that may be subjected to earthquake ground motions of different severities. Therefore, before an attempt was made to test a specimen on the UBC shake table, it was necessary to test a similar specimen under more traditional slow cyclic loading. Direct comparisons between the results obtained from the quasi-static testing of a steel plate shear wall specimen with the results obtained from the shake table tests of a similar specimen would then reveal effects attributable to loading rate. In the design, the main parameters controlling the configuration of the test specimens were the limitations of the UBC shaking table facilities. The newly upgraded 3 m x 3 m aluminium cellular shake table in the Earthquake Engineering Laboratory at UBC is equipped with five high performance servo-controlled electro-hydraulic seismic simulators that can accurately reproduce earthquake ground motions in the horizontal and vertical directions. The four vertical actuators have a nominal force capacity of about 90 kN each, while one actuator has a  54  CHAPTER 3  DESIGN OF TEST SPECIMENS  nominal force capacity of about 160 kN. The later actuator is permanently installed in a horizontal position in the N-S direction. The maximum input base displacement of the shaking table is ±75 mm. The maximum weight allowed on the table is 150 kN corresponding to about 15000 kg of mass. Input motions are controlled by specialized state-of-the-art Multi Exciter Vibration Control Software. Both quasi-static and shake table test specimens had to be designed in such a way that the yield strength of the specimens did not exceed the available capacity of the shake table horizontal actuator. At the same time, the selected length scale factor,  , for the test specimens was  desired to be of as large a scale as possible. The use of hot-rolled quality steel material, both for infill panels and boundary elements, was of primary concern. It is recognized that the most difficult step in attaining a reduced scale model is satisfying the requirements for the mechanical characteristics of the constituent materials. As noted earlier, a hot-rolled quality steel with elastic part, yield plateau and strain-hardening characteristic was desirable for the individual components of the model. A large number of coupon tests were conducted to verify the mechanical characteristics of the model material (Lubell, 1997). Figure 9.5 in Chapter 9 shows a typical stress-strain characteristic of the infill panel and boundary frame. No direct comparison between the state of strains (elastic and inelastic) in the model and prototype structure, however, can be made. The out-of-plane deviation of thin unstiffened steel plate shear wall structures as a result of heat effect and distribution of residual stresses within the infill plate and boundary frame is a very complex phenomenon. The present study does not intend to address these issues for the scaled down models. It is, however, acknowledged that the initial imperfection of infill plates and the state of residual stresses in the scaled down models may considerably be different than those of the prototype structure. To design test specimens that best suit all the above-mentioned criteria an extensive parametric 55  CHAPTER 3  DESIGN OF TEST SPECIMENS  study was p e r f o r m e d . Infill panel geometry (length and height), panel thickness, b e n d i n g and axial rigidities o f b e a m s and c o l u m n s , b e a m - t o - c o l u m n c o n n e c t i o n s , n u m b e r o f storeys, and storey masses were the major parameters studied.  3.3.1  Computer Modelling  T w o different finite element m o d e l s were d e v e l o p e d u s i n g the c o m m e r c i a l , general purpose c o m p u t e r p r o g r a m S A P 9 0 ver. 5.4 ( W i l s o n and H a b i b u l l a h , 1992). In both m o d e l s , beams and c o l u m n s were m o d e l l e d as a t w o - d i m e n s i o n a l F R A M E element. In the first m o d e l , the shear w a l l i n f i l l plates were m o d e l l e d u s i n g 4 - n o d e S H E L L elements. T h e 4 - n o d e S H E L L element f o r m u l a t i o n is a c o m b i n a t i o n o f m e m b r a n e and plate b e n d i n g behaviour. T h e m e m b r a n e is an isoparametric element i n c l u d i n g translational in-plane stiffness c o m p o n e n t s and  rotational  stiffness c o m p o n e n t in the direction n o r m a l to the plane o f the element. T h e plate b e n d i n g behaviour  includes  two-way  out-of-plane  plate  rotational  stiffness  components  and  a  translational stiffness c o m p o n e n t in the direction n o r m a l to the plane o f the element. In the s e c o n d m o d e l , the i n f i l l shear plate was replaced b y a series o f discrete, p i n - e n d e d F R A M E elements i n c l i n e d in the direction o f the tension f i e l d . T h i s s o - c a l l e d strip m o d e l was originally presented b y T h o r b u r n et al. in 1983. It is noted that the geometric i m p e r f e c t i o n o f the infill shear plates was not incorporated into the finite element f o r m u l a t i o n .  T h e c o n n e c t i o n o f i n f i l l plates to the b o u n d a r y frame m e m b e r s was a c c o m p l i s h e d b y means o f "fish plate" c o n n e c t i o n tabs, as s h o w n in F i g u r e 3.4. T h i s detail, d e v e l o p e d at the U n i v e r s i t y o f A l b e r t a , a l l o w s s o m e tolerances in the size o f an i n f i l l plate, thus a v o i d i n g s o m e p o s s i b l e fitup p r o b l e m s d u r i n g fabrication. T h e bases o f the columns were assumed to be fixed.  In the S A P 9 0 finite element m o d e l s the effects o f fish plates were i g n o r e d and all the panels were assumed to be o f the same thickness. It has been demonstrated ( T i m l e r & K u l a k , 1983  and  T r o m p o s c h & K u l a k , 1987) that neglecting the effects o f f i s h plates in m o d e l l i n g infill plates has very little effect o n the n u m e r i c a l results o f overall l o a d - d i s p l a c e m e n t graphs o f the steel  56  CHAPTER 3  DESIGN OF TEST SPECIMENS  Figure 3.4: Typical fish plate to frame and infill plate to fish plate connections plate shear wall frames. It was also assumed that all edges of the infill plates were directly connected to the centre line of the boundary frame. The experimental tests at the University of Alberta (Timler & Kulak, 1983, Tromposch & Kulak, 1987 and Driver, 1997) have shown that the small eccentricity of the fish plates did not affect the behaviour of the columns through torsion. Since at the time of the development of the computer models no steel material had been tested for the beam and column sections, a 300W steel with yield stress of c = 300 MPa and modulus y  of elasticity E = 200 GPa was assumed. The infill shear panels were chosen as hot-rolled quality steel material with yield stress and modulus of elasticity similar to the beam and column sections. 3.3.2 Analytical Method and Design Criteria Dynamic time-history and push-over static analyses of a number of steel plate shear wall frame models with different configurations (panel aspect ratio, panel thickness, number of storeys, beam and column sections and storey masses) were carried out. Because the SAP90 computer program is only capable of performing elastic analyses, the main focus of this effort was to find a base shear load that would produce yielding in the boundary frame or infill panels. To establish the required base shear at which the bottom panel commenced yielding, the tensile stresses in the tension strips or the principal tensile stresses in the SHELL elements were compared with the static or dynamic yield stress of the plate material. The initiation of yield in 57  CHAPTER 3  DESIGN OF TEST SPECIMENS  the outer flanges of the columns was established by superimposing the computed column axial and bending stresses using the interaction equation: P G = -  My + y<KG  (3.15)  y  where P and M are the column axial force and moment, respectively. A and I are the column c  c  cross-section and column moment of inertia about the major axis, respectively, y is the distance between the outer surface of the column flange to the neutral axis of the section. K is a factor for increasing the static yield point of the steel material (K = 1 for push-over analyses). 3.3.2.1  S e l e c t i o n of D e s i g n Earthquakes for S h a k e Table Tests  For dynamic time-history analyses it was required to select earthquake input motions that would cause significant yielding in the specimen, while remaining within the limitations of the shake table facilities. The input earthquake motions had to be selected in such a way that the study of elastic pre-buckling and post-buckling of infill steel panels and post-yielding behaviour of the boundary frame and shear panels would be achieved. The severity of excitations was controlled by the frequency content and acceleration amplitude, and in turn by the power spectral density of the earthquake records. To select an appropriate design earthquake, various characteristics of an earthquake ground motion such as: peak ground acceleration (PA), peak ground velocity (PV), peak ground displacement (PD), frequency content and duration of the record were examined. At the beginning of the earthquake engineering era, the PA was the most widely used attribute of an earthquake ground motion. Newton's Second Law of mechanics clearly states that the acceleration and inertia forces are directly proportional. However, it was soon realized that using PA alone as an index for evaluating damage potential of an earthquake is a poor judgement. The main reason is that a large-magnitude short-duration impulse-like motion in an earthquake record can usually be associated with high frequency components that are out of the  58  CHAPTER 3  DESIGN OF TEST SPECIMENS  range of the natural frequencies of most structures. Hence, a large-magnitude PA may be absorbed by the inertia of a structure with little power to initiate resonance in the elastic range, or be responsible for large inelastic deformations. On the other hand, more moderate acceleration peaks that occur in a few cycles over a longer period of time could result in significant deformations of the structure. Anderson and Bertero (1987) introduced the maximum incremental velocity and maximum incremental displacement parameters to characterize the damage potential of earthquake motions in the near-fault region. These two parameters represent the area under an acceleration pulse and a velocity pulse, respectively. It can be noted that the larger the change in velocity or displacement, the larger are the acceleration and the velocity pulses, respectively. One of the primary procedures that has been used in the earthquake engineering community to characterize the severity of earthquake ground motions is the elastic response spectrum. In this technique, the response of a single degree of freedom oscillator to an input ground motion at various natural frequencies and equivalent viscous damping ratios is obtained. The maximum values of acceleration, s , velocity, s , and displacement, s , are plotted against each a  y  d  corresponding frequency component to obtain an irregular curve over the frequency range of interest. It is noted that the peaks and valleys in response spectra plots can not be used effectively in design because of the major uncertainties associated with the frequency content of any future motions at the site and the uncertainties associated with the dynamic periods of the structure itself. A smooth elastic response spectrum may be constructed from using the peak parameters of earthquake response by e.g. Newmark's method (Newmark and Hall, 1982). A significant shortcoming of a response spectrum is that it does not by itself account for the duration of input ground motion. It is well documented (Applied Technology Council, ATC 306, 1978) that two motions having different durations but similar response spectra cause different degrees of damage, the damage being less for the shorter duration.  59  CHAPTER 3  DESIGN OF TEST SPECIMENS  To better characterize the intensity and damage potential of design ground shaking, ATC 3-06 (1978) introduced two parameters: Effective Peak Acceleration (EPA) and Effective Peak Velocity (EPV). They were defined as normalizing factors for construction of smoothed elastic response spectra. The EPA is based on average spectral ordinates for periods in the range of 0.1 to 0.5 seconds, while the EPV is proportional to spectral ordinates at a period of about 1 second. The constant of proportionality was set at a value of 2.5 for a 5% viscous damping ratio. The EPA and EPV thus obtained are related to PA and PV but are not necessarily the same as or even proportional to peak acceleration and velocity values. As part of the 1993 NEHRP (National Earthquake Hazard Reduction Program) professional fellowship which was funded by the FEMA (Federal Emergency Management Agency), Naeim and Anderson (1993) produced a report that provides detailed information of a large earthquake database containing about 1500 records of earthquake ground motions from 1933 to 1992. The authors classified the severity and damage potential of 1155 selected horizontal components of earthquake ground motions on the basis of two classes. Firstly, were the parameters that related directly to the recorded data such as peak acceleration, peak velocity, peak displacement, peak incremental velocity, peak incremental displacement and bracketed duration (time between the first and last acceleration level larger than 0.05g). Secondly, parameters such as elastic response spectra, effective peak acceleration, effective peak velocity, inelastic response spectra, elastic input energy spectra and hysteretic energy spectra were included. By careful examination of the report by Naeim and Anderson, and the report on the strong motion records of the 1994 M = 6.6 Northridge earthquake in California (Shakal et ai, 1994), L  as well as a number of computer runs with different earthquake inputs, three earthquake records with somewhat different characteristics were chosen for the dynamic analyses and shake table testing. The E-W component of the Tarzana Cedar Hill Nursery Station record from the 1994 Northridge earthquake, the E-W component of the Joshua Tree Fire Station record from the  60  CHAPTER 3  DESIGN OF TEST SPECIMENS  1992 Landers earthquake and the N-S component of the Petrolia Station record from the 1992 Petrolia earthquake were selected. Figure 3.5 shows the time-histories of the three selected earthquake records together with their respective elastic response spectra and Fourier Transform plots. It is noted that the acceleration amplitudes of the Joshua and Petrolia earthquake records have been doubled to increase their damage potential. As can be seen from Figure 3.5, Tarzana Hill record, a near field record, contains some very high frequency components capable of severely exciting structures with natural frequencies in the range of 2.5 - 10 Hz. The Joshua Tree and Petrolia records contain lower frequency components compared to the Tarzana Hill record and would be more effective in exciting structures with natural frequencies in the range of 1 - 3 Hz. The duration of the main shock in the records is considerably longer in the Joshua Tree record compared to the Tarzana Hill or Petrolia records. This is important as the scaling must be performed in time, which reduces the duration of the input signals and doubles the frequency content. 3.3.3  Results of Analyses  Push-over static analyses of a number of models with various length scale factors were carried out first. The main focus of the analyses was to monitor the tensile and compressive stresses at the base of the columns and within the infill panels. A maximum base shear capacity of 160 kN to initiate yielding within the components of the models ruled out a number of shear wall configurations very quickly. Out of a few possible cases, a four-storey steel plate shear wall model with panel aspect ratio of one and 1.5 mm (16 gauge) thick hot-rolled quality infill panels (thinnest hot-rolled sheets available) was found to be suitable for further studies. The typical storey height was chosen as 900 mm. The selected width and height dimensions of the steel plate shear wall model are representative of a shear wall at length scale factor of S, = \ for an office building with 3600 mm typical storey height or about 5 = 30% for a residential ;  61  CHAPTER 3  DESIGN OF TEST SPECIMENS  Tarzana  15  c o 2 co o o  <  20  25  40  Time (sec)  0.6  Joshua  0.3 0.0 -0.3  j  -0.6 10  20  30  40  50  i  60  i  i  70  i  80  Time (sec) Petrolia  15  20  25  30  35  40  Time (sec) 1.0  Tarzana Joshua Petrolia  D)  Tarzana Joshua Petrolia  E  c to  C  o 2 ©  a)  CO o o  5 0.5  < 2  h  o  CO T3  o CO  CL  CO  E < 0.0  _L  _L  0.5  1.0  Period (sec)  0.0 1.5  2  3  Frequency (Hz)  Figure 3.5: Time-histories and corresponding elastic response spectra and frequency content of the selected input earthquake records 62  CHAPTER 3  DESIGN OF TEST SPECIMENS  building. The scaling relationships for the j -scaled down model is presented in Table 3.2.  PARAMETER  SCALING  PROTOTYPE 1/4-SCALED DOWN MODEL  Length  4  Time  2  Mass Displacement  s  2  L  16 4  Acceleration  1  1  Stress  1  1  Strain  1  1  Force  s L s s 2  16  2  16  4  256  Area Moment of Inertia  L  Table 3.2: Similitude scaling relationships for the selected model Figure 3.6 shows the two different SAP90 models (SHELL element formulation and strip model representation) of the four-storey steel plate shear wall structure. For the strip model the infill panel was replaced with a series of tension-compression struts placed diagonally in one direction. The angle of inclination of struts in the strip model configuration was simply considered as 45°. Appendix I contains typical SAP90 input data files of both models. One of the major factors influencing the overall behaviour of a steel plate shear wall frame is the column rigidities. In a frame-wall system, columns have three important tasks: carrying gravity loads, resisting lateral load, and providing boundary supports to the shear panels. To examine the influence of column cross-sectional area and moment of inertia on the distribution of tensile and compressive stresses within the columns and the shear panels, an analytical study was carried out which also aided in the selection of beam and column sizes for the four-storey steel plate shear wall frame. The SAP90 computer models of the four-storey steel plate shear wall frame, shown in Figure 3.6, were analysed for equal lateral forces of 40 kN at each storey 63  CHAPTER.  DESIGN OF TEST SPECIMENS  ^••••••••rt  •••••••••• •••••••••• ••••••••••  •••••••  Storey beams  ••••••••LT Storey masses  »,•••••••••[ -]••••••••  V  SH E LL D O elements 00 IlLl(Shrunken)DD DDuuuuuuDD ] D n  n  n  n D D  Columns  'pin-ended \ FRAME elements  A Figure 3.6: SAP90 computer models of the four-storey steel plate shear wall model a) Shrunken SHELL elements b) 45° inclined pin-ended FRAME elements level resulting in a total base shear of 160 kN. At each storey level, a gravity load of 15 kN was applied at beam-to-column connections for a total of 60 kN vertical load. Various column sizes ranging from very flexible (low axial and bending rigidities) to very stiff were chosen from the CISC Handbook of Steel Construction and incorporated in the computer models. The storey beams were assigned similar properties as column sections. The computer models were run for each column size and the output files were stored in separate files for each computer run. Table 3.3 shows the properties of steel sections chosen for the analytical studies. The following is a description of the results obtained from the lateral load analyses with emphasis on two issues. One is the effectiveness of the bottom storey shear panel in resisting  64  CHAPTER 3  Steel Section  S75x8 HSS76x51x3.8 HSS76x51x6.4 HSS89x64x3.2 HSS64x64x6.4 HSS89x64x4.8 HP200x54 M100xl9 M130x28.1 M200x9.7 S100xl4.1 M250xl3.4 HSS76x76x8 HSS89x89x9.5 SI 50x26 S180x30 HSS127xl27xll W250x49 HSS178xl78xl3 HSS76x51x4.8 HSS76x51x8 HSS127x76x9.5 HSS152xl02xll S200x34 W100xl9 W130x28 W150x37 W200xl5 W200x21  Area (mm ) 2  1070 872 1350 903 1350 1310 6820 2460 3580 1200 1800 1700 2010 2790 3270 3800 4840 6250 7970 1060 1600 3280 4840 4370 2470 3580 4730 1900 2710  DESIGN OF TEST SPECIMENS  Moment of Inertia Distance to neutral x 1 0 (mm ) axis (mm) 6  1.04 0.66 0.92 0.99 0.70 1.36 49.80 5.20 10.00 7.56 2.85 16.10 1.49 2.79 10.90 17.80 10.40 70.60 35.20 0.77 1.01 6.12 13.60 27.00 4.76 10.90 22.20 12.70 19.80  4  38.0 38.0 38.0 44.5 32.0 44.5 102.0 51.0 63.5 101.5 63.5 127.0 38.0 44.5 76.0 89.0 63.5 123.5 89.0 38.0 38.0 63.5 76.0 101.5 53.0 65.5 81.0 100.0 101.5  Table 3.3: Steel sections chosen from the CISC Handbook of Steel Construction for numerical analyses seismic lateral load. The other is the behaviour of column members in terms of flexural, axial and shear resistances. The interaction between the bottom storey panel and the columns were  CHAPTER 3  DESIGN OF TEST SPECIMENS  studied by comparing the stress distribution in the columns and in the panel. It is noted that an understanding of the interaction effect is crucial in establishing rational analysis and design procedures for steel plate shear wall structures. The tensile and compressive stresses in the columns were computed using Equation (3.15). The plots of computed tensile and compressive stresses in the outer flanges of columns at the base together with the maximum principal tensile stresses in the first-storey infill panel versus column area and column moment of inertia for the strip and SHELL element computer models are illustrated in Figures 3.7, 3.8, 3.9 and 3.10. A standard exponential curve fitting was performed on all scattered data. In general, the SAP90 SHELL element model resulted in tensile and compressive stresses for the columns and infill panels (Figures 3.9 and 3.10) that are lower than the results obtained from the strip model (Figures 3.7 and 3.8). This was expected because neglecting the effects of geometric imperfection for the infill plates would represent the four-storey SHELL element model as a frame-wall system with very high elastic stiffness. In the range of flexible columns, both models show that the normal stresses in the outer flanges of the columns are considerably higher than the infill panel principal tensile stresses. As the column cross-sectional area increases the column normal stresses and infill plate principal stresses become closer. For the strip model, the tensile stresses computed for the outer flange of the column in tension is considerably higher than the compressive stresses computed for the outer flange of the column in compression. On the other hand, for the SHELL element model the column compressive stresses are slightly higher than the column tensile stresses. This discrepancy can be attributed to the effect of tensile forces in the discrete strips that are anchored to the columns. The results indicate that for a large number of selected column sections yielding would occur at the bases of the columns before the shear panels, if the yield strength of boundary frame and infill plate material is assumed to be the same.  66  CHAPTER 3 500  —i  i  IN  DESIGN OF TEST SPECIMENS  i  i  i  i  SAP90 Strip Model 400  —  CO  Tensile stress in c o l u m n  Q_  co  C o m p r e s s i v e s t r e s s in c o l u m n  300  —  -«- —  T e n s i l e s t r e s s in p a n e l strip  CO CD 1_  +—>  cn OS  E o  200  • - -'igiT?  •  100 h  u  o  1000  2000  3000  4000  5000  6000  7000  8000  Column Cross-Sectional Area (mm ) 2  Figure 3.7: Normal stresses in the base of the columns and bottom storey infill panel versus column cross-sectional area for the SAP90 strip model  500  pjU— — —i—•—'—'— | 1  1  .  1  I  1 1 1  i  .  .  .  i  .  .  .  , — i — i —  ,  SAP90 SHELL Element Model  •\& 400  r—  -  •  Tensile stress in column  —  CO  — • —  co 300 CO  CD i_* -*—  •A  BS  ^>  C o m p r e s s i v e stress in c o l u m n  •  P r i n c i p a l t e n s i l e s t r e s s in p a n e l  -  C/3  "co 200  E o z  "  -  * * ^ ^ «  100 _l  0 1000  2000  3000  4000  5000  ,  L .  1  .  6000  .  ,  1  .  7000  .  .  8000  Column Cross-Sectional Area (mm ) 2  Figure 3.8: Normal stresses in the base of the columns and bottom storey infill panel versus column cross-sectional area for the SAP90 SHELL element model 67  CHAPTER 3  500  '  • »— T —|  •  1  1  |  1  1  1  J - T — I — 1  1  1  1  •  |  .  • •  _ 400 Q_  .  |  .  |  1 1 1 1 1 1  CD  • ~-- -  Tensile stress in column  •  Compressive stress in column. Tensile stress in panel strip  •  .  , . 1 . , , 1 . , .  0  8  J  &  100  0  1 —  • •  CO  "I 200  | '7—1—1  I  •  — $—  co 300 \_ -I—»  .  SAP90 Strip Model  D  •  CO  .  DESIGN OF TEST SPECIMENS  »  • • —*—'— —•—*—'—* . . i . . 1  12  16  20  24  28  32  36  40  Column Moment of Inertia x 10 (mm ) 6  4  Figure 3.9: Normal stresses in the base of the columns and bottom storey infill panel versus column moment of inertia for the SAP90 strip model  500  i  1  1  1  i  1  1  1  i • • • i  1  1  1  i • • • i * • * i • ••  SAP90 SHELL Element Model 400  •  Q_  •  Tensile stress in column  »  Compressive stress in column Principal tensile stress in panel  •  w to 300 •  CO  CO  |  200 100  0  •  0  •  •  •  '  1  8  12  • • •  16  '  1  20  24  •  28  32  •  36  •  40  Column Moment of Inertia x 10 (mm ) 6  4  Figure 3.10: Normal stresses in the base of the columns and bottom storey infill panel versus column moment of inertia for the SAP90 SHELL element model 68  CHAPTER 3  DESIGN OF TEST SPECIMENS  To better understand the influence of column rigidities on the distribution of lateral forces within the columns and infill panels, the variation of tensile forces and moments at the base of the column that is subjected to uplift with respect to the column area and column moment of inertia is plotted in Figures 3.11 and 3.12, respectively. From Figure 3.11 it can be observed that up to a certain point, both models show a small increase in the column tensile forces with increasing column cross-sectional area. Beyond this point, the axial load in the column is gradually reduced as the column area increases. Also, the SHELL element model generates higher axial tensile forces in the column than the strip model. It is noted that a small variation in the column axial forces are related to the applied overturning moment which remains constant for all column sections. Therefore, the action of coupled tension-compression in the boundary columns would remain almost the same, no matter how big or small the crosssectional area of the columns is. Figure 3.12 exhibits the significant effect of the column moment of inertia on the bending moments generated in the columns. It is evident that an increase in the column moment of inertia causes a large portion of the lateral load to be absorbed by the columns. This can be attributed to the overall bending stiffness of the frame that is significantly higher than the inplane stiffness of the infill plates. On the same figure, the maximum tensile forces generated in the truss elements are also shown. A polynomial decrease in the panel tensile forces versus the column bending moments is evident. It can be observed that substantial flexural behaviour of the boundary frame precludes the infill plates to become effectively involved in resisting the applied lateral loads. Figures 3.13 to 3.16 show the distribution of total storey shear to the columns and panel in the bottom storey of the four-storey shear wall system for different column cross-sectional area and moment of inertia for the strip and SHELL element model representations of the frame-wall system. The results presented are the variation of base shear distributed between the column  69  CHAPTER  340 •  c o  'co cz CD  g  •  Q  • _  o 300  OF TEST  SPECIMENS  i—  320 CD  DESIGN  3  •  t-n.  • •  B •  ••  280  hc 260 h E o O 240  Strip model  —  • —  SHELL element model _i  220 1000  2000  i  i  i_  L  _i  3000  4000  5000  6000  7000  8000  Column Cross-Sectional Area (mm ) 2  Figure 3.11: Tensile force in the column versus column cross-sectional area  •»—1  0  4  8  1  1  1  1—1  12  1  1  1  16  I  I  I  1  20  L_J  1  |  24  |  |  |  | _ J  |  |__|  28  32  .  .  .  I  36  .  .  .  40  Column Moment of Inertia x 10 (mm ) 6  4  Figure 3.12: Column bending moment (left axis) and maximum strip tensile force (right axis) versus column moment of inertia 70  CHAPTER3  DESIGN OF TEST SPECIMENS  sections and infill panel. All graphs confirm that the shear panel takes a small share of the lateral loads when the columns have high axial and bending rigidities. The variation of shear forces in the columns and infill panel increases or decreases exponentially. The data points for column and infill panel shear forces versus column moment of inertia are less scattered compared to the data points for column and infill panel shear forces versus column crosssectional area. The results also indicate that the storey shear is distributed unevenly between the columns. The column in tension takes more than 70% of the total column share of the storey shear. The results, in general, support the premise that increasing the size of the columns would increase the contribution of the boundary frame in attracting a larger percentage of the imposed lateral loads. On the other hand, flexible columns are more susceptible to the horizontal components of the infill panel tensile stresses, thereby increasing the normal tensile stresses in the column outside flanges through bending. From the preceding discussion and plots, the size of the beams and columns was selected. As 160 kN was the limiting base shear load, a column section with a cross-sectional area around 1000 mm and a moment of inertia around l.OxlO mm seemed to be well-suited for the four2  6  4  storey steel plate shear wall frame. A S75x8 section was chosen for the columns. A S75x8 section was also chosen for the first three storeys beams. A deep stiff beam, S200x34, was selected for the top storey panel to anchor the tension field forces generated in the upper storey plate. To further verify the suitability of the designed four-storey steel plate shear wall specimen, a dynamic time-history analysis was carried out. The superimposed mass at each storey level was selected, based on numerous computer runs, to meet the limitation of maximum input base shear on the shake table with a reasonable correspondence to scaled nominal lateral load demand on a full scale steel plate shear wall prototype carrying an area of 10 m x 10 m at each  71  CHAPTER 3  DESIGN OF TEST SPECIMENS  1  1  1000  2000  3000  4000  5000  1  1  I  6000  I  I  I  L.  7000  8000  Column Cross-Sectional Area (mm ) 2  Figure 3.13: Shear distribution in bottom storey columns and panel versus column crosssectional area for the strip model 150  1 ''  1  1  1  i  T -  1 •  I  'T  |  1  1  1  |  .  1—I—!—!—!—I—  • 125  •  •  Z  •  100 rl¥'  D  •  co  75  CD  CO  50 25  ~  •  •  Panel  — •  0  i  0  • •  •  8  i  i  —•— i  ,•  12  i  •  '  16  •-  Column •  •  i  20  •  24  28  32  36  •  •  40  Column Moment of Inertia x 10 (mm ) 6  4  Figure 3.14: Shear distribution in bottom storey columns and panel versus column moment of inertia for the strip model 72  CHAPTER 3  DESIGN OF TEST SPECIMENS  -i—i—i—i—|—i—i—i—r  25  D—  Panel  0 1000  J  i  1  i  2000  L  i  i  Column  i  3000  J  4000  5000  1  1  i  6000  i_  I  7000  8000  Column Cross-Sectional Area (mm ) 2  Figure 3.15: Shear distribution in bottom storey columns and panel versus column crosssectional area for the SHELL element model 150  25  Panel  0  •  0  •  •  '  1  8  •  •  •  1  •-. •  12  •  •  1  •  16  •  Column •  1  20  i  .  .  .  i  24  1  28  32  1  '  1  1  36  •  •  40  Column Moment of Inertia x 10 (mm ) 6  4  Figure 3.16: Shear distribution in bottom storey columns and panel versus column moment of inertia for the SHELL element model 73  CHAPTER 3  DESIGN OF TEST SPECIMENS  floor. Equal storey masses of 1400 kg were attached at each floor level for a total of 5600 kg mass on the specimen. The first three natural frequencies of both the strip and the SHELL element models were identified by eigenvalue analysis. This would help in controlling the severity of the excitation through the spectra of the selected records. Table 3.4 summarizes the first three modes of vibration for both models. Frequency (Hz) Mode shape  Strip model SHELL element model  First longitudinal  6.3  7.7  Second longitudinal  22.2  30.9  Third longitudinal  42.2  61.3  Table 3.4: Computed natural frequencies of the SAP90 models As the natural frequencies of the models were high, Tarzana Hill earthquake record was considered as the most appropriate input excitation for computer analyses. Since the length scale factor was chosen as 4, the time axis of the input record was scaled by a factor of 2 to satisfy the scaling laws shown in Table 3.1. The results of total base shear and absolute acceleration at each storey level for the SAP90 SHELL element and strip models of the fourstorey specimen are shown in Figure 3.17. The results obtained from the strip model predicts amplification factors of 4.8, 3.5, 2.6 and 1.6 for the fourth, third, second and first storey, respectively. On the other hand, the SHELL element model predicts much lower amplification factors of 2.6, 1.9, 1.4 and 1.2 for the fourth, third, second and first storey, respectively. This indicates that the strip model was more severely excited by the Tarzana Hill earthquake record compared to the SHELL element model. The results of the floor relative displacement time-histories are presented in Figure 3.18. A significant difference is observed between the predicted response by the two models. The actual response may be somewhere between these two extremes. The response of the SHELL  74  CHAPTER3  SHELL element model  DESIGN OF TEST SPECIMENS  Strip model  First Floor  c o CC CD  o o <  c o  '•*—> CC 1—  0)  CD O O <  7.0 c g  Third Floor  3.5  "H—»  CO  0) CD O O <  0.0 -3.5 J  -7.0  L  J  I  i  L  J  I  I  9.0 c o  4.5  cc Q)  0.0  '  0 O  o  <  j  L  L  Fourth Floor  -4.5 J  -9.0  L  J  I  J  L  i  i  i_  CO CD  SZ  CO  CD CO CO CD  -300 0  4  5  6  8  10  Time (sec) Figure 3.17: Computed response of the four-storey steel plate shear wall specimen for the strip (dotted line) and SHELL element models (solid line) 75  CHAPTERi  E c  *  DESIGN  OF TEST  SPECIMENS  Strip model  10  First Floor  SHELL element model  5  CD  E CD O _C0 CL CO  0 -5 J  5 -10 20 E c CD  E CD o 05  1  1  1  10 0  Q  'E  34  CD  E CD O _C0 CL CO  Q EP  E, c  — *- >  CD  E 0 O CO CL  (  i  I  Second Floor  !i j: j;; _  ,A'XA'AAAAX-AAAWAA.*ftA'A'A'A^AA  ... —... .^v/V^Y^ I  I  i  I  1  i  r ;' i :  I  1  *•»  **•  ••  ,  \\  Third Floor  17 -Lf"/t/i-/i MM^AK A'A?iVVy\/l :  0  :  -17 •: i  -34 44  1  i  1  j?  i  1  i  1  i  1  i  l  Fourth Floor  22 0 -22 -ii ' i  i  .<2 -44 Q  i  i_i  -10 -20  c  i  , :i ....  CL  co  1  0  4  1 5  i  6  8  9  i  i  10  Time (sec) Figure 3.18: Computed relative displacement response of the four-storey steel plate shear wall specimen for the strip (dotted line) and SHELL element models (solid line) element model may be considered as an upper bound system with high elastic stiffness and high frequency modes. The results obtained from the strip model seems to be unusually high in terms of the degree of amplification for the absolute accelerations and relative floor displacements. 76  CHAPTER O  DESIGN OF TEST SPECIMENS  Figure 3.19 shows the results of the dynamic analyses for the column axial load, column bending moment and the maximum stress in the bottom storey panel. It is observed that the column bending moment is significantly higher for the strip model compared to the SHELL element model. These high in-plane bending moments are produced in the boundary columns due to large in-plane horizontal components of the discrete truss elements replacing the infill shear panel. The column axial load is not affected to the same extent as the column bending moment by the overall behaviour of the panel-column interaction. The maximum stress generated in the panel and experienced by the discrete truss elements are comparable at most instances. It is noted that the stresses in the boundary columns and the bottom storey infill panel are substantially higher than the yield strength of the steel material.  c cu  E o  E?  IS  o O  24 12 0 -12 -24  T3 CO O  600  "cC  300  cog c ~~-  E  _2  o O  CD C CO  e--c?  . £ Q_  0)5 CO CD  CO  i  1  J  I  i  I  '  J  i  I  0 -300 -600 Strip model  600  SHELL element model  300 h 0 -300 -600  J  0  L  J  4  L  5 6 Time (sec)  J  J  L  8  L  10  Figure 3.19: Computed dynamic response of the bottom storey column and infill panel  77  CHAPTER3  3.4  DESIGN OF TEST SPECIMENS  SPECIFICATION OF TEST SPECIMENS  The specimen was comprised of S75x8 columns, kept constant through the height of the frame, and S75x8 beams for the bottom three storeys and a deep stiff beam, S200x34, at the top storey to anchor the tension field forces generated in the upper storey plate. At the bottom panel of the shear wall, the tension field was anchored internally by providing a S75x8 beam. Beam-tocolumn joints were fully welded with web stiffeners in the columns opposite the beam flanges, thus creating full moment connections. Figure 3.20 shows the four-storey steel plate shear wall specimen planned for the quasi-static and shake table studies. 3.5  SUMMARY  Experimental tests are vital to study the behaviour of structures in a controlled environment and to provide a means for calibrating analytical models. Full-scale shake table testing of structural models is generally not a feasible task as the majority of shake tables available in North America are limited for testing of half-scale or smaller scale models. It is, therefore, the responsibility of the analyst to find acceptable alternatives to model a prototype structure in such a way that the behaviour of the model does not differ significantly with that of the prototype. The overall goal of the first phase (experimental investigation) of this research was to assess the feasibility of using thin plate shear wall system in seismic zones and to make recommendations for further studies. Due to the limitation of the loading equipment, reduced scale models had to be tested. The main purpose of scaling was to get a realistic representation of structural prototype for the calibration of analytical models. In studies involving the simultaneous simulation of the gravity and inertia effects, some major discrepancies arise between a prototype and its model. Similitude laws require the use of model materials with specific stiffnesses ^ ^ which scale in the same proportion as the length. An alternative, which permits the use of prototype material for many practical cases, is provided  78  CHAPTER 3  DESIGN OF TEST SPECIMENS  S200X34  PL 8 0 0 x 6 7 6 x 1 , 5 m m Typical  PL 4 4 x 2 7 x 5  900  mm  S75X8  mm  -X-  PL 8 0 0 x 8 0 0 x 1 . 5 m m 900  T y p i c a l 2.5 m m F i s h P L  mm  T y p i c a l 2.5 m m F i s h P L S75X8  PL 8 0 0 x 8 0 0 x 1 . 5 m m 900  mm  976  mm  S75X8  PL 8 0 0 x 8 0 0 x 1 . 5 m m  900  mm c/c  S75X8  Figure 3.20: Four-storey steel plate shear wall specimen 79  CHAPTER 3  DESIGN OF TEST SPECIMENS  by adding lumped masses to the model structure. These lumped masses must be structurally ineffective and distributed in such a way that adequate simulation of all gravitational and inertial effects become possible. The design of the test specimens was primarily based on the limitations of the shake table facilities. Clearance above the table, maximum weight allowed on the table and the stalling force capacity of the actuator that produces the horizontal longitudinal motions, were the main restrictions. The effects of different panel aspect ratios, number of floors and the crosssectional area of the beams and columns on the overall behaviour of the steel plate shear wall specimen were examined with a finite element analysis using the computer program SAP90 ver. 5.4. A four-storey steel plate shear wall model with panel aspect ratio of one and length scale factor of S, = \ was found to be suitable for shake table studies. / 4 The aspect ratio of 1.0 for the steel panels, the 900 mm centre-to-centre column spacing and floor-to-floor height, the 1.5 mm thick infill steel panels and the number of floors along with the specified beam and column cross-sections were selected such that the test objectives could be achieved using available resources. Because the material properties of the plate for the test specimens are extremely important for applicability of the test results, the thinnest available commercial quality, hot-rolled steel plate was selected.  80  4  QUASI-STATIC  4.1  TEST  PROGRAM  INTRODUCTION  Slow cyclic quasi-static tests of two single storey steel plate shear wall specimens and one fourstorey specimen were carried out prior to a more realistic shake table testing of a four-storey specimen. These tests were carried out as part of a Master thesis (Lubell, 1997) and only information relevant to this study is included in this chapter. The main objectives for the quasi-static tests were: c  To study the influence of fabrication techniques and distortion due to welding on test results.  o  To investigate the effects of a stiff top beam versus a flexible beam.  c  To compare and validate the overall shape of the load-deformation graphs of the UBC small-scale specimens with the results obtained from testing the larger scale models at the University of Alberta.  c  To determine the experimental base shear required to reach the yield point of the four-storey specimen and compare with analytical predictions and with the stalling force capacity of the shake table horizontal actuator.  c  To identify problems associated with assembly and cyclic loading of the fourstorey steel plate shear wall specimen, so that the problems could be addressed before testing a similar specimen on the shake table.  The overall strength, elastic post-buckling stiffness, interaction between frame action and shear panel behaviour, effects of beam and column rigidities, the formation of diagonal tension field action combined with diagonal compression buckling of the infill plate and the stability of panel hysteresis curves were the main issues investigated during quasi-static testing.  81  CHAPTER H  1  QUASI-STA TIC TEST PROGRAM  The guidelines outlined in ATC-24 (Applied Technology Council, 1992) for cyclic testing of structural components were followed for the second single storey and four-storey steel plate shear wall tests. ATC-24 requires that a "displacement control parameter" be selected for controlling the test. It recommends a load control method to be adopted prior to achieving the global yield displacement of the selected control parameter. It is left to the researcher's judgment to select a point on the load-deflection plot at which significant yielding occurs. Beyond the global yield point, ATC-24 suggests a displacement control method to be followed at multiples of the global yield displacement of the control parameter. Three cycles of loaddisplacement are to be completed at each load step. A minimum of three load levels should be applied prior to reaching global yield, with one of these load levels applied above 75% of the force required to achieve the global yield displacement. In this chapter the quasi-static experimental program conducted in the Structures Laboratory at the University of British Columbia is reviewed. More details of the tests can be found in Lubell, 1997. 4.2 FIRST SINGLE STOREY TEST SPECIMEN To better understand the load-deflection behaviour of the four-storey steel plate shear wall specimen and to examine the effects of weld distortion on the behaviour of thin infill panels and the surrounding frame, a single panel specimen representative of the bottom storey panel of the four-storey specimens that were planned for quasi-static and shake table testing was constructed and tested. 4.2.1  Specimen Characteristics  The single storey test specimen, shown in Figure 4.1, was fabricated in a steel shop with no special precaution to eliminate frame and plate distortion due to welding. As a result, initial out-of-plane deformations of up to 26 mm (fifteen times the thickness of the plate) were measured for the infill plate. The surrounding frame was composed of S shape sections  82  CHAPTER 1  QUASI-STATIC TEST PROGRAM  (S75x8). The infill panel was 1.5 mm thick. No measure was taken to provide special anchorage to the plate tension field at the top beam. This was done intentionally to study the effects of bending and axial rigidities of the top storey beam on the overall behaviour of a steel plate shear wall system. Full moment connections at beam-to-column joints were provided by a continuous fillet weld of the entire beam section to the column flanges, with column web stiffeners added opposite to the beam flanges. The infill panel was connected to the surrounding frame members using a fish plate connection, as shown in Figure 3.4 in Chapter 3. Continuous fish plates of 2.5 mm thick and 25 mm wide were fillet-welded to the inside flanges of the beams and columns. A 45° cut was performed at all corners where the column fish plates and beam fish plates met. The infill panels were positioned in the plane of the beam and column webs and were continuously welded to one side of the fish plates along the edge on both sides. The bases of the columns were also fully welded to the bottom base plate. To prevent premature cracking of the fillet welds at the base of the columns, triangular stiffeners were welded to the flanges of the columns at the base. This was done to better distribute the column web and column outer flange tension forces. The specimen was braced in the out-of-plane direction and was free to move in the in-plane direction. The bracing system consisted of two support arms, 3.0 m long, attached to the tops of the columns through pin connections, as shown in Figure 4.1. This system was very easy to setup, but it had the disadvantage of imposing some out-of-plane deformation to the frame, due to the racking behaviour, at large in-plane displacements. 4.2.2 Loading Configuration A horizontal lateral load was applied to the test specimen by means of an MTS 445 kN capacity double-acting hydraulic jack lined up at the beam mid-height elevation. The stroke of hydraulic jack was limited to ±305 mm. As the predicted ultimate base shear capacity of the specimen  83  CHAPTER 4  QUASI-STATIC TEST PROGRAM  Out-of-plane support arms-  •  Load Cell  String-pod •fj  Displacement Transducer  =|  LVDT Uniaxial  Strain Gauge  9 0 0 c/c  ill—  —Arc Support Arms „  Section A - A Figure 4.1: First single storey specimen with instrumentation layout was high and the required welding length for the loading tab (during "pull back" mode) was computed to be longer than the height of the storey beam, a load transfer mechanism was devised based on the concept of applying compression against column flanges. Two loading plates were installed at each end of the storey beam using four 25 mm threaded rods running parallel to the beam, as shown in Figure 4.1. The rods were tightened to make sure that the end loading plates were completely seated against the specimen. The hydraulic jack was attached to one of the loading plates through a pin connection unit which was free to rotate in the vertical direction.  4.2.3  Instrumentation Layout  The specimen was instrumented with displacement transducers and LVDTs (Linear Variable 84  CHAPTER 1  QUASI-STATIC TEST PROGRAM  Displacement Transducers) at the top beam mid-height, column mid-height and diagonally from the bottom left corner of the infill plate to the opposite top corner, as shown in Figure 4.1. The applied lateral load was recorded by an integral MTS load cell attached to the actuator. Pairs of uniaxial strain gauges were mounted at two locations (bottom left corner and upper right corner) on the infill plate to measure the state of strain and onset of yielding in the plate in both orthogonal directions. The strain gauges were placed on each side of the plate to cancel out the effects of out-of-plane bending. Two uniaxial strain gauges were affixed near the base of the left column on the inner and outer flanges to monitor the strain variations in the column. All strain gauges were mounted a distance away from the joints to reduce the effects of stress concentration and distortion on the recorded data. Figure 4.2 shows a photograph of the first single storey shear wall test set-up with loading system, lateral support mechanism and instrumentation devices mounted.  Figure 4.2: Overview of the first single storey test set-up 85  CHAPTER**  4.2.4  QUASI-STATIC  TEST  PROGRAM  Hysteretic Behaviour  Figure 4.3 shows the load-deformation behaviour of the specimen under slow cyclic loading.  -40  -30 -20 -10  0  10  20  30  40  50  60  70  80  In-plane Longitudinal Displacement of Top Beam (mm) Figure 4.3: Hysteresis curves of the first single storey shear wall specimen The specimen was subjected to a horizontal in-plane load history with gradually increasing cycles with one or two cycles at each load level until global yielding was observed. Thereafter, displacement amplitudes were increased incrementally by multiples of the yield displacement ±o\y. As the storey displacement reached 2 x 8^, yielding of the various components of the shear wall resulted in a significant decrease in the stiffness of the specimen in the post-yield region. Once the load was removed, the unloading curve showed a very small elastic stiffness decay for the panel. As the load reversed to the opposite (negative) direction, the stiffness of the steel plate shear wall specimen reduced substantially to approximately 30% of the initial elastic stiffness. The loss of stiffness can be attributed to the permanent stretching of the plate in the previous loading. The redevelopment of the tension field increased the stiffness until the  86  CHAPTER  QUASI-STATIC TEST PROGRAM  load approached the yield strength achieved in the negative direction. As the displacement ductility was increased to -2 x 8^, yielding of various structural elements resulted in another substantial decrease in the stiffness of the specimen in the negative post-yield region. Unloading the specimen followed the elastic stiffness curve very closely. Shortly after the load increased in the positive direction, the stiffness dropped rapidly. The initiation of the infill plate tension field contributed greatly to the increase in stiffness, until the maximum force achieved in the previous loading was attained. The subsequent reloading and unloading resulted in a similar hysteresis curves described above, only more expanded. One cycle of load-deformation was conducted at each post-yield deformation step until a displacement of 4x8^ was achieved. Before finishing the first cycle of 4 x 8^, one complete cycle of ±100 kN lateral load was applied and then the load was increased to reach the top displacement of 4 x 8 . This was y  done to examine the behaviour of the specimen to a low level input excitation after going through a few cycles of high load intensities. It can be noted from the Figure 4.3 that the overall strength of the specimen started to drop after reaching top displacement of 4 x 8^. Beyond this point, the specimen was subjected to a pushover loading to failure up to a maximum displacement of 7 x 8^. The test was stopped at this point due to excessive twist and deformation of one of the out-of-plane support arms at its far end connection. It is noted that the overall strength of the specimen at each displacement ductility level would have been lower than the tabulated results had we executed three cycles of loading. 4.2.5  Test Results and Observation  The overall shape of the hysteresis curves, Figure 4.3, indicates that the behaviour of the smallscale single storey steel plate shear wall specimen under cyclic loading was very robust and stable. The degradation of strength at high ductility levels was primarily related to severe plate tearing and weld cracking. Even though the specimen experienced ductility demand of seven times the yield displacement, no sudden loss in stiffness or strength occurred in the specimen. In any case, current earthquake engineering practice (NBCC, 1995 and FEMA, 1994) limit the 87  CHAPTER *l  QUASI-STATIC TEST PROGRAM  ductility demand of building structures to storey deflections of lesser magnitude than was applied to the specimen. Figure 4.4 shows the extent of damage at the end of the experiment. The overall behaviour of individual components of the steel plate shear wall specimen shown in Figure 4.4 is discussed in the following sections.  Figure 4.4: A view of the first single storey specimen at the end of cyclic test 4.2.5.1  Behaviour of Infill Plate  One of the interesting characteristics of this test was a very audible popping noise of the infill plate once the reorientation of the tension field and compression plate buckling would occur. This was attributed to the large initial out-of-plane imperfection of the infill plate which made it biased to the reversing action of the plate. These popping sounds were typically heard at low levels of applied load when the hydraulic jack was reversing from the positive direction to the negative direction and vice versa.  88  CHAPTER  *f QUASI-STATIC TEST PROGRAM  The relationship between the horizontal and vertical components of strains generated in the  infill plate and the level of horizontal load at which the infill panel started yielding was studied through strain gauges affixed to the plate in the two orthogonal directions. Figure 4.5 shows the angle of inclination of resultant strain from the vertical line computed for the strains measured at top corner of the infill plate. It can be observed that the angle remained almost constant between 55° and 75° for the load causing tension in the adjacent column. As the tension field reoriented in the opposite direction, the angle decreased steadily with increasing load intensity. The angle of resultant strain varied between 80° to 45° as the storey shear approached the yield strength of the specimen. It was generally observed that the infill plate membrane forces were anchored between the top and bottom of the columns, and between column bases and beam-tocolumn connections as the load intensity approached the ultimate. The inclination of the line of action of infill plate tension field towards the columns could be attributed to the flexibility of the top beam causing a redistribution of the strains to some degree.  90 -200  -100) 0 100 Storey shear (kN)  200  Figure 4.5: Angle of the resultant strain at the top corner of infill plate  89  CHAPTER *t 4.2.5.2  QUASI-STATIC TEST PROGRAM  B e h a v i o u r of Storey B e a m  The top beam was extensively damaged at the end of the test. The formation of plastic hinges was evident from substantial whitewash flaking at both ends and in the middle of the beam. The low flexural stiffness of the beam had a visible effect on the angle of inclination of the tension field and overall in-plane deformation of the specimen. It is noted that in a multi-storey structure the angle of inclination, a, does not, generally, depend on the flexural behaviour of the storey beam because the presence of an additional infill panel above under similar tension field action from horizontal shears approximately balances the vertical component of the tension field below. A stiff top beam may be utilized for the top floor to properly anchor the tension field forces. 4.2.5.3  B e h a v i o u r of C o l u m n s  Both columns were permanently deformed to the inside, due to the horizontal components of the infill plate tensile stresses. To investigate the degree of interaction between an infill panel and surrounding column elements, one LVDT was installed at the mid-height level of one of the columns (see Figure 4.1) to monitor the displaced shape of the column at this point under cyclic loadings. Figure 4.6 illustrates the displacement profile of the instrumented column under alternate in-plane shear loadings. It can be seen that when the column was subjected to compression due to the applied overturning moment, the top storey displaced more outwards relative to the mid-height of the column. This indicates that a flexural type behaviour was exhibited by the column. However, when the applied in-plane shear reversed, the column underwent tension and was pulled inward by the plate indicating a shear type behaviour for the column. The behaviour of the columns alternated from flexure to shear as the applied horizontal load reversed cyclically. The columns played an important role in anchoring the tension field. Plastic hinges occurred in the columns in the top and bottom, as the tension field pulled the member inward. This effect  90  CHAPTER H  QUASI-STA TIC TEST PROGRAM  In-plane Displacement, mm Figure 4.6: Displaced profile of the column alternated once the loading reversed. As the storey height and width of the specimen were the same, the measured column axial load and the applied storey shear were expected to be very close (column moments were considered to be negligible). The relationship between the column axial force and bending moment, measured through uniaxial strain gauges mounted on column flanges, with the storey shear is presented in Figure 4.7. A near linear relationship between the column axial load and storey shear is observed. Figure 4.7 indicates that the column in compression was effective in anchoring the significant proportion of the infill plate tension field. The axial load of the column in tension, however, slightly digressed from the 45° reference indicating that some portion of the tension field was partially anchored to the bottom beam. It is noted that some portion of the fish plates and the adjacent panel act with the column in resisting the tension as a result of overturning moments, thereby reducing the theoretical axial demand on the column in tension. The interaction of column axial force and bending  91  CHAPTER *f  -200  -100  0  100  200  -6  Column axial load (kN)  -3  QUASI-STA TIC TEST PROGRAM  0  3  6  Column bending moment (kN.m)  Figure 4.7: Measured column axial force and bending moment moment with the column shear at ultimate limit states in a steel plate shear wall frame is extremely important for the development of plastic moment capacity and stability of the boundary columns. The interaction of column axial load and bending moment indicated that the outer fibres of the column cross-section had exceeded the actual yield strength of the steel.  4.2.5.4  Behaviour of Beam-to-Column Connections  The beam-to-column connections were fully welded moment-resisting joints and remained intact throughout the entire load sequence. Toward the end of the test and with severe yielding of the storey beam at both ends, the beam-to-column joint regions remained relatively square with only some flaking of the whitewash and limited yielding was detected in those regions. It is noted that, other than flange continuity stiffener plates, no doubler plates or other forms of panel stiffening were used. It was evident that the infill plate significantly reduced the demand on the beam-to-column joints by transferring the energy dissipating mechanism to the formation of diagonal tension field and compression buckling in the infill panel. This confirms the primary reason of using 92  CHAPTER *t  QUASI-STATIC TEST PROGRAM  infill steel panels to minimize the reliance on the moment-resisting frames for dissipating the seismic demand. 4.3 SECOND SINGLE STOREY TEST SPECIMEN The second single storey test specimen was fabricated in the machine shop laboratory at UBC with extreme precautions to reduce the effects of weld distortion on the infill plate and surrounding frame. The specimen was built in such a way to address the shortcomings of the first single storey cyclic test specimen with regard to the low flexural stiffness of the storey beam and excessive initial out-of-plane deviation of the infill plate at the end of the welding process. 4.3.1  Specimen Characteristics  To better anchor the tension field forces in the infill plate an additional top beam was added on top of the storey beam. A stiffer storey beam would better represent the effect of an additional infill panel above, as would be the case in multi-storey steel plate shear wall structures. Welding of the infill panel was conducted in short lengths and chill bars were used to reduce the effect of excessive heat on distorting the plate. The measured initial out-of-plane deviation of the infill panel at the end of the welding process was 3 mm to 4 mm which indicated a significant reduction from the previous test configuration. As before, full moment connections were developed by a continuous fillet weld of the entire beam section to the column flanges. Column web stiffeners were provided at beam-to-column connection joints to prevent the crippling of column webs or distortion of column flanges. The infill panels were connected to the boundary frame using the fish plate configuration shown in Figure 3.4. The bases of the columns were fully welded to a base plate. As extensive weld cracking was observed at the base of the columns at the end of the first single storey test, longer gusset plates were welded to the outer flanges of the columns. Figure 4.8 shows a view of the second single storey test specimen. Similar to the first single storey test, support arms extending 3.0 m from the plane of the 93  CHAPTER Loading Tab ^^Out-of-p\ane tt  support a r m s ^ ^  *r  QUASI-STATIC TEST PROGRAM  Figure 4.8: A view of the second single storey specimen specimen were attached to the tops of the columns to support the specimen in the out-of-plane direction. The support arms were connected to the tops of the columns and top flange of the support beam via pin connection units. The beam supporting the far ends of the support arms was adequately strengthened to prevent premature failing.  4.3.2 Loading Configuration The horizontal load was applied to the specimen through a 25 mm thick loading tab. The tab was fillet welded on the flange of the left column, over the full height of the top beam, positioned in the plane of the column web. The actuator was pin-connected to both the reaction frame and the loading tab. The pin units allowed the actuator to rotate freely in the vertical direction. Horizontal loading started with low intensity cycles and progressed to increasingly higher intensities. The recommendations laid out by the Applied Technology Council (ATC-24) were followed in terms of loading histories, presentation of the test results and other experimental aspects pertaining to slow cyclic load application. 94  CHAPTER H  QUASI-STATIC TEST PROGRAM  4.3.3 Instrumentation Layout Only a few channels of data were collected for the second single storey steel plate shear wall specimen. The storey displacement at the mid-height level of the top beam together with the diagonal extension of the infill panel were measured using a string-pod displacement transducer and a LVDT, respectively. The input horizontal load was also measured by an integral MTS load cell. Figure 4.9 shows a photograph of the second single storey shear wall test set-up with loading system, lateral support mechanism and instrumentation devices mounted.  Figure 4.9: Overview of the second single storey test set-up 4.3.4 Hysteretic Behaviour The specimen was loaded with increasing force magnitude cyclically, until the evidence of global yielding was observed. After the on-set of yielding, load was increased by multiples of the observed global yield displacement. The load-deformation curves, shown in Figure 4.10,  95  CHAPTER  H  QUASI-STATIC TEST PROGRAM  exhibit similar behaviour to that observed in the first single storey specimen.  -50  -40  -30  -20  -10  0  10  20  30  40  50  In-plane Longitudinal Displacement of Top Beam (mm) Figure 4.10: Hysteresis curves of the second single storey shear wall specimen The overall hysteretic behaviour was robust and stable. Immediately after yield, the post-yield stiffness of the specimen dropped to approximately 10% of the elastic value. A maximum displacement of 6x5^ was reached prior to the termination of the test. The loading and unloading sequences in the alternate directions produced a consistent and characteristic pattern. As recommended by the ATC-24, each loading cycle was repeated three times for each displacement ductility level. The maximum load achieved in each cycle of an equal storey displacement dropped slightly for the first few displacement ductility levels. However, at higher displacement levels, a more noticeable strength degradation was observed between the first and third cycles of an equal displacement. The slope of unloading curves tended to decrease gradually with increasing storey displacements. A comparison between the load-displacement graphs of the first and second single storey test specimens was conducted to compare the parameters influenced the overall behaviour of each 96  CHAPTER'  QUASI-STATIC TEST PROGRAM  specimen. The representative cycles of 2 x 8 and 4 x 8^ for the first single storey specimen y  and the first cycle of 2 x 8^ and 4x8^ in the second single storey specimen are shown in Figure 4.11. Both initial and post-yield stiffnesses of the second single storey specimen were considerably higher than the initial and post-yield stiffnesses of the first single storey specimen. The yield displacement of the second single storey test was recorded as 6 mm compared to about 8.5 mm for the first single storey test. The corresponding yield loads were 180 kN and 190 kN for the first and second single storey specimens, respectively. The maximum storey shear achieved in the second single storey test was 260 kN for a displacement ductility level of 4 x d as opposed y  to 200 kN for the first single storey test. The significant improvement in the overall loaddeformation behaviour of the second single storey specimen was primarily attributed to the stiffer storey beam and the lessening of initial out-of-plane imperfections.  270  I  1 I  1  I  1  I  180 T3 CO  90  CO CD -C  0  -  o  1  •  to  <D  15.  -90  i i  ~  C L  <  1  -180  o ' ^ r *  s— i  i  i  i  '  1  i  •  /  1  /  '  /  1  -35  I /  I j 1  i  -1---/  -270 -45  1 ' -i  /  ,  •  yr  6  ,  -25  1  </  -15  1  1  *H  1  /  /  1  ' 1  ' 1  7 2nd  ; .  J  -  5  j/--jy 1  7 T T  I I 1 J,o  a i  i  1  A ft  1  I**T°Y*  - -o- -  1st  single storey specimen single storey specimen  1  -5  5  15  25  35  45  In-plane Longitudinal Displacement of Top Beam (mm) Figure 4.11: Comparison of the 2 x 8^ and 4 x 8^ cycles in the first single storey specimen with the corresponding cycles in the second single storey specimen  97  CHAPTER t  QUASI-STATIC TEST PROGRAM  Test Results and Observation  4.3.5  Figure 4.12 shows the overall shape of the second single storey specimen at the end of cyclic testing. The test was stopped due to an extensive column fracture just above the stiffener gusset plate at the base of the left column. In the following, the behaviour of each component of the one storey shear wall frame is discussed.  Figure 4.12: A view of the second single storey specimen at the end of cyclic test 4.3.5.1  Behaviour of Infill Plate  Contrary to the first single storey test, the popping sound of the plate reorientation during reversed cycles was minimal. The first sign of infill panel yielding was observed at a storey shear of 180 kN. Most of the yielding occurred at the top and bottom corners of the infill plate to fish plate connection. Some cracking of fillet welds joining the fish plate to columns was observed at a displacement ductility of 2 x 8^, and increased in size in subsequent cycles. At a storey shear of 200 kN a visible diagonal tension yield pattern began to form at the top corners 98  CHAPTER H  1  QUASI-STATIC TEST PROGRAM  of the infill panel. Tearing at the quarter points of the infill plate was observed at the displacement ductility level of 4 x 5 ^ , mainly due to the folding of the stretched plate during load reversals. The plate tended to kink and straighten cyclically as the buckles reoriented themselves. Figure 4.13 shows a photo of the infill panels with one such tear at the peak displacement. The photograph presented in Figure 4.13 shows the plate buckled into three halfwaves at an angle of about 45°.  Figure 4.13: A view of the infill plate buckling and tearing during final cycle of loading  4.3.5.2  Behaviour of Storey Beam  The addition of a S75x8 section on top of the storey beam provided much improved anchorage for the tension field generated in the infill plate. It also enhanced the rigidity of the surrounding frame and therefore expanded the hysteresis loops during revered cycles, as shown in Figures 4.10 and 4.11. No sign of yielding or distress was observed at any location in the beam.  99  CHAPTER H 4.3.5.3  QUASI-STATIC TEST PROGRAM  Behaviour of Columns  In the second single storey specimen longer stiffener gusset plates were utilized to force the formation of the plastic hinges in the columns away from the column bases. As a result, plastic hinges were developed immediately above the tip of the tapered stiffeners. Figure 4.12 shows the condition of the columns at the end of the test. The overall shape of the columns is similar to that observed at the end of the first single storey test. Both columns were deformed inwards as a result of horizontal components of the tension field forces. Significant yielding was also observed at the top of the columns, just below the beam-column connections. Evidence of column shear yielding was visible near beam-to-column joints. 4.3.5.4  Behaviour of Beam-to-Column Connections  All beam-to-column connections were strengthened with stiffeners to prevent nonlinearity within the joint panel zones. As a result, no yielding was observed in these regions throughout the test, which supports the hypothesis that the primary ductile energy absorbing element of the steel plate shear wall systems is the infill plate. The results of the test clearly demonstrated that the infill steel plate significantly reduced demand on the moment-resisting frame by producing redundant diagonal storey bracing which alleviates the demand on the beam-to-column connections. 4.4  FOUR-STOREY TEST SPECIMEN  After testing two single storey steel plate shear wall specimens, one four-storey specimen with storey dimensions and beam and column sizes similar to the first single storey specimen was constructed and tested under quasi-static cyclic loading. 4.4.1  Specimen Characteristics  The specimen, shown in Figure 3.20 in Chapter 3, consisted of a one-bay frame with typical storey height of 900 mm and overall width of 976 mm (the columns were 900 mm centre-to-  100  CHAPTER *t  QUASI-STATIC TEST PROGRAM  centre). The infill steel panels were 1.5 mm (16 gauge) thick in all four storeys. They were connected to the surrounding frame members using the fish plate connection, as shown in Figure 3.4 in Chapter 3. The fish plates were 25 mm wide and 2.5 mm thick and were welded to the inside flanges of the beams and columns by means of fillet welds on both sides. The drawback of this detail is that the ultimate strength of the system may be governed at the fillet welds connecting the infill plates to the fish plates or at the fillet welds connecting the fish plates to the surrounding frame members. It is, however, noted that fillet welds have much higher capacity than the fish plates or the infill panel. The four-storey test specimen was fabricated in the machine shop at UBC. Special precautions were taken to maintain welding distortions at a minimum. At the end of fabrication, a maximum out-of-plane deviation of 3 mm was measured for the infill panels. Once the specimen was bolted to the base of the support frame, out-of-plumbness of the columns in the two principal directions was measured. A clear twist in the columns indicated that the columns were out-of-plumb perpendicular to the plane of the specimen in opposite directions. The lateral displacement at the tip of the columns with respect to the base of the specimen was measured about 80 mm. This was mainly attributed to the fabrication procedure. Figure 4.14 shows a photo of the specimen erected inside the support frame. To simulate the effects of column axial loads on the overall behaviour of a steel plate shear wall frame under the action of cyclic horizontal loading, gravity loads were applied to the storey floors of the test specimen through large steel plates (Figure 4.15). The interaction of applied overturning moment and column axial loads on reducing the tension uplift on one column while increasing the compressive load on the other column as well as the P-A effects were the parameters investigated during the course of this study. Steel plate masses of 1.5 m x 0.6 m with various thicknesses were attached to the specimen through the centre of each beam-tocolumn connection. Doubler plates, 6 mm thick, were welded inside the beam-column joints on 101  CHAPTER  QUASI-STATIC TEST PROGRAM  Figure 4.14: Four-storey test specimen bolted to the base of the loading frame both sides of the column web to accommodate the attachment of the masses. The vertical load at each storey level corresponded to 13.5 kN, providing a total of 54 kN of gravity load. The stress at the base of the columns was 25 MPa with no horizontal load applied. The steel plates on the upper three stories were bolted to the centre of each beam-column joint such that the plane of the plates was parallel to the plane of the specimen. The gravity load on the first storey was transferred by channel sections welded to the outside flanges of the columns at the joint locations.  102  CHAPTER *t  QUASI-STATIC TEST PROGRAM  The steel plates were fixed on the top flanges of the channels with their planes perpendicular to the plane of steel plate shear wall specimen. This was done to expose the entire first storey panel of the frame for visual observation of the formation of diagonal tension field and compression buckling of the infill panel under cyclic lateral loading. Figure 4.15 shows a schematic view of the four-storey steel plate shear wall specimen, inside the support frame, together with the hydraulic actuators and storey masses attached.  Figure 4.15: Four-storey steel plate shear wall specimen inside the support frame The steel plate shear wall specimen had to be braced laterally to reduce the out-of-plane unbraced length of the columns. It was required to devise a lateral restraint system that resisted any out-of-plane motion, but allowed in-plane movement. The lateral support system that was  103  CHAPTER t  QUASI-STATIC TEST PROGRAM  selected consisted of 100 mm diameter steel wheels mounted on a central pin unit and stiff external support beams. For the fourth and second storey floors, the base of the steel rollers were bolted to the support beams, running on each side of the specimen, while the wheels were positioned against the mass steel plates. At the first floor level, the rollers were bolted through the columns, using spacers, and were allowed to rotate against the flanges of the support beams. The external support beams were connected to the support frame using bolted connections. Once the installation of lateral restraint system was completed, the initial twist in the steel plate shear wall specimen due to welding had been corrected. As a result, residual stresses would develop throughout the specimen.  4.4.2  Loading Configuration  The load was applied at each storey floor through a computer controlled hydraulic actuator capable of producing up to 200 kN horizontal force. The actuators have a stroke of ±150 mm. Each actuator was connected to a very stiff support frame through pin units that were free to rotate in the vertical direction. The actuators were connected to the column flanges at the level of storey beams via loading tabs. The tabs were welded to the column flanges over the full height of the floor beams. At the fourth floor the loading tab was welded over the top 75 mm of the deep beam. Pin units that were free to rotate vertically were used to connect the loading tabs to the actuators. An attempt was made to linearly vary the actuator forces at each storey level as per shear distribution according to the National Building Code of Canada (NBCC, 1995). As the load was increased to a total base shear of 50 kN, excessive vibrations of actuators resulting from feedback instability in the control system made it very difficult to maintain the load. Because of control problems, it was decided to continue the test by connecting all four actuators to a common manifold, thereby providing equal hydraulic pressure to each actuator. However, small variations in the applied forces on each storey level were expected due to friction losses  104  CHAPTER 1  QUASI-STA TIC TEST PROGRAM  in the hydraulic hoses and tolerances in the actuator components. In reality, the lateral forces exerted to a structure by an earthquake are functions of time and are generally amplified as the earthquake motion travels through the height of the structure. The magnitudes of these lateral forces at each storey floor depend on a number of factors including frequency content of the input motion versus the natural frequencies of the structure, storey masses, modal vibration and the damping ratios. It was felt therefore that the assumption of equal storey forces is no better or worse than any other rational configuration. A photograph of the specimen installed inside the support frame with lateral support, storey masses and hydraulic actuators attached is shown in Figure 4.16.  4.4.3 Instrumentation Layout Extensive instrumentation layout was used for the four-storey shear wall specimen to measure performance of columns, storey beams, infill panels and beam-to-column connections together with interstorey drifts and overall load-deformation behaviour. The specimen was instrumented accordingly with load cells, string-pod displacement transducers, LVDTs, uniaxial and rosette strain gauges. Figure 4.17 shows the instrumentation layout of the specimen. In the following the details of the measuring devices are described. Lateral loads were measured at all four actuators using load cells capable of measuring loads in both tension and compression. The first, second and third storey actuators were hooked to 89 kN capacity load cells, while a 222 kN load cell was used on the fourth floor actuator. In-plane horizontal deflections were measured by string-pod displacement transducers located at storey beams mid-height elevations. To better capture the effects of shear and bending deformations of the frame under intense lateral loading, displacement sensors were placed along the first storey column to measure the deformed profile of the column. Also, one additional string-pod displacement transducer was installed at a short distance above the first storey floor. 105  CHAPTER *t  QUASI-STATIC TEST PROGRAM  Figure 4.16: Overview of quasi-static test set-up for the four-storey shear wall frame As the behaviour of the first storey panel was expected to be the most critical, rosette strain gauges were mounted extensively on the infill plate. The aim was to measure the principal strains and their associated directions within the web plate. Nine strain rosettes were placed on both sides of the first storey plate in the horizontal and vertical directions, parallel to the storey beam and column, to continuously monitor the degree of change in the distribution of stresses and strains in the panel with increasing load intensities. Two strain rosettes were also placed on  106  CHAPTER *t  QUASI-STATIC TEST PROGRAM  1  +  +  a  P  —c= ^  +  Load Cell  M—•  String -pod Displacement Transducer  1  LVDT Strain Gauge Rosette  {  |r  r  r  r  F  Uniaxial Strain Gauge  +  H  j  —i  JF  i  iF  |  -  —i •  Figure 4.17:  Instrumentation layout of the four-storey specimen  107  CHAPTER 1  QUASI-STA TIC TEST PROGRAM  the opposite corners of the second storey panel on either side of the plate. The duplication of the gauges was done in order to account for the bending stresses expected to occur within the plate as a result of buckling. Uniaxial strain gauges were placed longitudinally on the flanges of beams and columns near the column bases and the first storey beam-to-column connection where strains were expected to be the highest. From these strains the participation of the frame elements in resisting the applied loading was assessed. A total of 68 data acquisition channels were recorded during the test. The data acquisition software allowed the load-displacement graphs of each storey to be displayed on a PC monitor during the test. 4.4.4 Hysteretic Behaviour The specimen proved to be somewhat more flexible than the one-storey specimens tested before. This was expected because the influence of overturning moment becomes more significant as the height of a structure increases. The yield deflection in the first storey panel was determined as 9 mm at a storey shear of about 150 kN. Prior to reaching this value, three cycles each of ±25 kN, ±50 kN, ±80 kN, ±100 kN and ±125 kN were conducted to explore the elastic and initial inelastic behaviour of the specimen. During these cycles marginal stretching of the load-deformation hysteresis loops and a small permanent horizontal drift of about 1.5 mm for the first panel was observed. After three cycles of ±150 kN with a yield deflection of &\y = 9 mm, the deflection in the first storey was increased in multiples of the global yield deflection. As the deflection was increased to about 1.6 times of the yield value the post-yield stiffness of the specimen decreased significantly and the load reversed at a storey deflection of about 15 mm. As the load reversed, the unloading stiffness was parallel to the initial elastic stiffness. Increasing the load to the opposite (negative) direction caused some pinching in the hysteresis curve with moderate reduction in the stiffness. This was also observed in the previous tests because the first storey infill plate was stretched and buckled inelastically during  108  CHAPTER H  QUASI-STATIC TEST PROGRAM  the previous loading direction. It would thus not be fully effective in the reversed loading until the load would be increased enough to compensate for the effects of Poisson's ratio. Once the tension field started to form in the web plate, the stiffness increased. The load was brought up to the negative yield strength of the specimen and increased by a manually adjusted control valve. As the first storey deflection reached -15 mm, the compression column buckled in the out-of-plane direction. The test was terminated at this point. It should be noted here that the test was conducted under load control by manually operating the pressure control valve on the hydraulic supply. It was, thus, not possible to control the specimen displacements when the specimen resistance decreased at the point of buckling. One of the primary reasons for testing a multi-storey shear wall frame was to study the relationship between the base shear and interstorey deflections. This relationship is crucial evidence in determining the overall behaviour of these structural systems. Figure 4.18 shows the storey shear plotted against the interstorey drifts at all floors. It should be noted that these are not storey shear displacements since they also include the overturning component. The first storey panel showed stable hysteresis curves. A significant portion of the input energy was dissipated by the first storey panel through column yielding and infill panel diagonal buckling and yielding. As no evidence of yielding was observed above the first storey level, the load-deformation hysteresis loops of the upper storey floors did not reflect the significant contribution of these floors to the overall energy dissipation mechanism through shear yielding or plate buckling. The load-deformation hysteresis loops of the upper stories reflected a rigid body rotation due to the column shortening or plastic hinging in the first storey. This may be verified by the similarity between the load-deformation plots of the upper storey levels with the pattern observed for the first storey panel. A comparison was made between lateral deflections obtained from the experimental program with seismic drift limitations prescribed by the N B C C (1995). The N B C C states that the  109  CHAPTER *t 200  1  i  r  176  |  200  —i  QUASI-STATIC TEST PROGRAM  1  I  132 100  -  -  CD  co >-  Q  /  CD O  15  —  100  CO CD SI  co W  z  •  V  0  CD  14  i_  CO  o  2 -100  — t- ' 03 X3  <N -100  1  -200 -20  •  -10  0  i  10  I  -200 -20  20  -10  1 st storey drift (mm) 200  1  |  T  1  i  0  10  20  2nd storey drift (mm) 200  1  I  ,  '  1  1  1  -  100  88"  CO CD .C  -  45  CD  .c  C/3  >i CD  ^  o  03 ><  ' 14  14.6  03 »  O -t— ' 03  C/3  T3 00  z 100 1 CO  •100  -200 -20  -100  1  i  -10  0  10  -200 -20  20  i 10  i 0  10  20  4th storey drift (mm)  3rd storey drift (mm)  Figure 4.18: Storey shear versus interstorey deflections interstorey deflections shall be limited to 0.01 h for post-disaster buildings and Q.Q2h for all s  $  other buildings, where h is the storey height. For the four-storey steel plate shear wall $  specimen, this is equivalent to a deflection of 9 mm (1 x 5^) for post-disaster buildings and 18 mm (2 x 8p for other buildings. From the load-deformation relationships it can be observed that the NBCC (1995) limiting drift ratios would govern the design of the specimen. The computed interstorey drift limitations are, however, small enough that would not lead to any 110  CHAPTER *t  QUASI-STATIC TEST PROGRAM  strength degradation in the structure. It was demonstrated in the single storey tests that the steel plate shear walls can undergo severe storey deflections without any significant loss to the strength. It is noted that in a prototype steel plate shear wall structure it is not desirable to let the interstorey drift ratios govern the design. The infilled frames must be stiff enough to allow significant yielding while limiting the overall drift index of the structure.  4.4.5 Test Results and Observation The test specimen failed as a result of global out-of-plane buckling of the first storey column. Prior to column buckling, the first storey infill panel had undergone considerable inelastic buckling and yielding. Figure 4.19 illustrates the state of damage to the first storey column and infill panel at the termination of the test. Even though a premature failure mechanism occurred when the specimen was experiencing inelastic deformations, useful data regarding initial elastic stiffness, post-yield stiffness, storey drifts, overall deformed column profile, variation of principal tensile stresses in the plate and the interaction of the boundary frame with the steel panels was collected from the test. The overall behaviour of each component of the four-storey shear wall specimen is described in the subsequent sections.  4.4.5.1  Behaviour of Infill Plate  Similar to the second single storey specimen and contrary to the first test specimen very little infill plate popping sound was detected during cyclic testing. This confirmed the rationale that the initial out-of-plane deformation of thin unstiffened plates could significantly bias the response of steel plate shear wall systems subjected to low level of cyclic loading. This is mainly related to the tendency of thin infill plates buckling in one favourable direction. As the load reverses, the formation of tension field and thus the diagonal buckling mode of the infill plates would alternate. During this reversed cycle the energy is stored in the plate until the reversed tension field forces the plate to buckle in the opposite direction wherein the plate pops 111  CHAPTER 1  QUASI-STATIC TEST PROGRAM  Figure 4.19: State of damage to the first storey panel and columns of the quasi-static fourstorey shear wall frame at the termination of test with a loud noise. The out-of-plane deviation of the buckled first storey panel was minor until the specimen was loaded beyond its yield strength. The magnitude and direction of principal stresses (tensile and compressive) measured at three locations on the bottom storey infill panel for three cycles of loading up to the global yield strength of the specimen is illustrated in Figure 4.20. It can be observed that the infill plate  112  CHAPTER H  1  QUASI-STA TIC TEST PROGRAM  principal stresses were below 300 MPa indicating that the global yielding of the panel had not been reached. It is, however, noted that localized yielding at the connection of fish plates to the boundary members and at the periphery of the first storey infill plate was detected as a result of white wash flaking. It is noteworthy that the strain rosettes were mounted about 100 mm away from the inside edge of the beam-to-column connections to avoid stress disturbances, and this might result in lower stress values. Residual stresses might also have had an effect on the results.  -300 -180 -60 60 180 300 -45 -30 -15 0 15 30 45 Principal stress / mm length (MPa) Angle of principal stress from vertical, deg Figure 4.20: Variation of magnitude and angle of principal stresses for the first storey infill plate with storey shear Although the stress distribution in the infill plate of the test specimen could not be uniquely determined, certain qualitative statements can be made. Figure 4.20 illustrates that the magnitude of infill plate principal stresses were greater at the vicinity of beam-to-column connections than near the base of the columns. This could be attributed to the continuous welding of the infill plate at the base which would cause some distribution of the stresses. On the other hand, built-in beam-to-column connections were stiffer than the storey beam and boundary columns, thus anchoring a significant portion of the infill plate tension field. The test  113  CHAPTER 1  QUASI-STATIC TEST PROGRAM  results also show that the minor principal stresses (in this case, compressive) were significant, in particular near the beam-to-column joints. This may provide an additional load path that contributes to the shear resistance and stiffness of the panel. A significant difference between the measured principal stresses near the beam-to-column joints undergoing a "closing" and "opening" type action is also evident. This observation indicates that for each cycle of loading the formation of tension field action was primarily effective over a certain diagonal width of plate concentrated at the centre of panel. As load reversed, because the plate had been stretched in the previous cycle, considerable storey deflection was required to redevelop the tension field action in the opposite direction. This is the main reason why the strain gauge recordings at the centre of the plate did not change their signs as soon as the load was changed from "pull" to "push" and vice versa. The redevelopment of the tension field seems to have occurred as soon as the specimen passed its neutral position and was loaded in the opposite direction. The angle of inclination of the infill plate principal stresses, a, varied between ±42°. As the horizontal loads decreased from positive to negative, the angle a varied differently from the location of rosette 1 to 3. The variation of the angle a was rather abrupt at the corners, but gradual at the center of the infill panel. The steeper angle of inclination at the center may lead to a lower proportion of the internal forces generated by the tension field resisting the applied storey shear. 4.4.5.2  B e h a v i o u r of Storey B e a m s  Evaluation of bending and axial strains in the first storey beam revealed that there was very small flexure and axial stresses generated in the beam. Higher flexural stresses were recorded near the columns than at the beam mid-span. The test results supported the assumption of flexurally rigid beams for determining the angle of inclination of infill plate tensile stresses recommended in Appendix M of CAN/CSA-S16-94. 114  CHAPTER' 4.4.5.3  QUASI-STATIC TEST PROGRAM  B e h a v i o u r of C o l u m n s  In general, the columns of a steel plate shear wall frame are subjected to a significant amount of in-plane forces which in turn influence the overall performance of the columns and the steel plate shear wall frame. To better understand the degree of interaction between the first storey infill panel and surrounding column elements, displacement instrumentation was arrayed along the first storey column (see Figure 4.17) to monitor the displaced shape of the column under cyclic loadings. Figure 4.21 illustrates the column profile obtained under alternate cyclic inplane shear loadings. It can be observed that under each cycle of loading the column in tension was pulled inward by the infill plate tension field exhibiting a shear type behaviour. For the column in compression, the displaced profile exhibited a near linear trend indicating that the overall behaviour of the column was governed by superposition of a shear and flexural type  3.6  2.7 h 25 kN 50 kN CT 'CD I  75 kN  1.8 h  >. CD  100 kN  i—  O CO  125 kN 150 kN  0.9 h  175 kN  0.0 -60  -45  -30 -15 0 15 30 Floor Displacement (mm)  45  60  Figure 4.21: Displaced shape of the column under various base shear loadings 115  CHAPTER *f QUASI-STATIC TEST PROGRAM behaviour. The interaction of infill plate horizontal tension forces influenced the shear beam behaviour of the column in compression. The displaced shape of the column above first storey level resembled a straight line for all load intensities. This denotes that the second, third and fourth storey levels, in principle, rotated as a rigid body above the first floor. This observation signifies an important attribute of a steel plate shear wall frame in which the bottom storey panel dissipates a major portion of the input energy. Under intense lateral loading, plastic hinges are mainly concentrated at the top and bottom of columns and in the infill plates of the lower storey levels. This is contrary to the seismic behaviour of a steel moment frame structure where plastic hinges are distributed throughout the structure. It is, therefore, quite important that in a steel plate shear wall structure the base of the columns be detailed carefully to ensure a robust ductile behaviour. It is, however, noted that in a multi-storey steel plate shear wall structure the thickness of the infill panels and the properties of the boundary column may be assigned in such a way to develop some degree of nonlinearity within the plate and boundary elements for the upper floors. 4.4.5.4  Behaviour of Beam-to-Column Connections  The uniaxial strain gauges attached near the first storey beam-column joints indicated very little flexural response in the beam and column members at the joint. Beam-to-column connections were fully welded moment-resisting joints and remained intact throughout the entire load cycles. This implies that the joint panel zone remained rigid, in part due to the presence of infill plates. As the infill plates substantially reduced the lateral load demand on the beam-column joints, the influence of moment-resisting beam-to-column connections in contrast to simply supported beam-to-column connections in enhancing the overall hysteretic behaviour of the shear wall frames should be investigated in greater detail.  4.5  SUMMARY  Two different fabrication configurations for the single storey steel plate shear wall specimens 116  CHAPTER * T  QUASI-STATIC TEST PROGRAM  were attempted; a flexible and a stiff top beam. The maximum storey shear achieved in the second single storey test was 260 kN for a displacement ductility level of 4 x 8^ as opposed to 200 kN for the first single storey test. The significant improvement in the overall loaddeformation behaviour of the second single storey specimen was primarily attributed to the stiffer storey beam and to some effect the reduction in the out-of-plane deviation of infill panel. The results of both tests demonstrated that the infill steel plate significantly reduced demand on the moment-resisting frame by producing redundant diagonal storey bracing which alleviates the demand on fixed beam-to-column connections. The four-storey specimen proved to be somewhat more flexible than the one-storey specimens. This was expected because the influence of overturning moment becomes more significant as the height of a structure increases. A premature column buckling prevented the continuation of testing for ductility ratios above twice established yield displacement of the first storey panel. The displaced shape of the column above the first storey level resembled a straight line for all load intensities indicating that the second, third and fourth storey levels, in principle, rotated as a rigid body above the first floor. This observation signifies an important attribute of a tall multi-storey steel plate shear wall frame in which the bottom storey panel attracts a major portion of the input energy. The demand on the column bases were shown to be extremely high, thus, it is of utmost importance that in a steel plate shear wall structure, the base of the column be detailed carefully to ensure a robust ductile behaviour.  117  5 5.1  SHAKE  TABLE  TEST  PROGRAM  INTRODUCTION  Shaking table tests are increasingly being used to evaluate seismic performance of structures, especially since advances in servo-hydraulic technology and computer control hardware and software enable the experimentalist to accurately reproduce earthquake motions. The newly upgraded shake table facility in the Earthquake Engineering Laboratory at U B C provided a unique opportunity to conduct dynamic testing of a scaled multi-storey steel plate shear wall specimen. While there have been a limited number of static and quasi-static tests performed on unstiffened steel plate shear wall frames, no information is available on the behaviour of these structural systems under earthquake loading. To date, no shake table testing of a multi-storey steel plate shear wall frame is available for reference. The objective of the shake table testing program was to provide some information regarding the seismic performance of multi-storey steel plate shear walls under the effect of intense seismic loading. To evaluate this behaviour, the first ever shake table test was conducted on a reduced-scale multi-storey steel plate shear wall with thin unstiffened panels. The structural characteristics of a typical steel plate shear wall frame model under earthquake motions such as initial stiffness, post-buckling stiffness, yield strength, displaced profile of the columns, drift limitation and stable resistance under repeated and reversed loads were of primary concern. Furthermore, the effects of the storey masses and their distribution along the height of the frame on the overall response of the steel plate shear wall specimen was monitored. The efficiency of moment-resisting beam-to-column connections in enhancing the hysteresis loops and consequently dissipating more energy under earthquake loading was also of primary interest. The input motions were intended to simulate as closely as feasible the effects of real earthquakes recorded around the world on a prototype steel plate shear wall frame.  118  CHAPTER  D  SHAKE TABLE TEST PROGRAM  The shake table test program described herein includes a quarter-scale four-storey steel plate shear wall specimen. This test was performed in conjunction with a slow cyclic test of a similar specimen to provide important additional evidence supporting the qualification of thin unstiffened steel plate shear models as seismic lateral load resisting systems. The specimen was subjected to low, intermediate and high intensity simulated earthquake motions.  5.2 UBC EARTHQUAKE SIMULATOR FACILITY The U B C Earthquake Engineering Laboratory is equipped with an advanced, closed-loop, servo-controlled hydraulic seismic simulator or shake table. It can accurately reproduce earthquake ground motions in one or more directions. The key element of the U B C earthquake simulator is a 3 m x 3 m platform, which consists of a 0.4 m thick aluminium cellular structure with a weight of about 20 kN. The table has a grid of 38 mm diameter holes that are used to attach test specimens. The aluminium platform and attached hardware were designed to have a fundamental vibration frequency around 40 Hz, so that it can be considered rigid within the usual operating frequency range (0 - 20 Hz) of the shaking table. At present, the shaking table can provide two component input motions in the two horizontal directions. In order to allow such input motions, the table is supported by four vertical rigid links located in a square pattern, 1.5 m apart, and three horizontal actuators, as shown in Figure 5.1. The actuator in the N-S direction has a main stage area of 80.9 cm , while the two actuators in 2  the E-W direction have an effective piston area of 45.2 cm . Oil supplied at 2000 N/cm by a 2  2  265 lit/min pump. The two translational and one rotational degrees of freedom of the table can be programmed to produce any type of waveform within the limits of the displacement, velocity and force capacity and the frequency bandwidth of the table. The displacement of the table is limited by the stroke of actuators, ±76 mm in both directions. The flowrate in the servovalves limits the maximum velocities produced in the N-S and E-W actuators to about 100 cm/sec. The maximum acceleration is limited by the force limits of the actuators together with  119  CHAPTER O  SHAKE TABLE TEST  Actuator  N  165 kN  Attachment a n c h o r holes  t  Pit  4 o  PROGRAM  o  o  o  o  o  Shake Table  A  A  1  Ji o  o  o  o  o  Actuator 90 kN  o  PLAN  Fixed links Jf  hinged at the  X  top and bottom  O / / / / ; / / / / / /  S E C T I O N A-A  Figure 5.1: UBC earthquake simulator the mass of the table-specimen system. The stalling force capacity of the horizontal actuator that produces earthquake motions in the N-S direction is 165 kN, while the other two actuators in the E-W direction each have a capacity of 90 kN. As an example, the table is able to produce motions recorded at Tarzana Hill station during the Northridge earthquake of 1994 with time 120  CHAPTER  O SHAKE TABLE TEST PROGRAM  increment At reduced to 0.01 sec, including both the N-S and E-W components combined. The reduced time increment alleviates the displacement demand on the actuators. The actuator force reactions are resisted by a massive pit. The pit is a reinforced concrete foundation extending all around the table in the form of an open box, 1.5 m thick on the sides where the actuators are installed. The outside dimensions of the wall are 6 m x 5.5 m x 2.5 m, and the inside dimensions are 3.6 m x 3.6 m x 2 m. Input motions are controlled by specialized state-of-the-art Multi Exciter Vibration Control Software. The digital computer control system allows a closed-loop control of the input excitations (acceleration) and is capable of reproducing recorded earthquake motions with high accuracy. The high performance digital control system can easily replicate earthquake motions for models with different mass-stiffness characteristics. This is very desirable for comparative studies of different models or equipment under the same loading conditions. It is noteworthy that the horizontal actuator in the N-S direction had not been utilized to its ultimate payload capacity in the past. Thus, the performance of this actuator in terms of its capability of reproducing the desired input motion at very high input base shear had to be examined during the course of this study.  5.3  SHAKE TABLE TEST SPECIMEN  The model, shown in Figure 5.2, consisted of a four storey one bay frame with typical storey height of 900 mm and overall width of 1016 mm (the columns were 920 mm centre-to-centre). The specimen was built in the machine shop at UBC. All connections and details were fabricated using fillet welding. Extreme caution was taken during welding of the structural members to reduce the effects of input heat, which would cause distortion and warping of the infill panels and surrounding frames. The specimen comprised of B 100x9 columns, kept constant through the height of the frame, S75x8 beams for the bottom three storeys and a deep  121  CHAPTER  5  SHAKE  TABLE  TEST  PROGRAM  S200x34 L 675x800x1.5 mm o o  Accelerometer  CD  String-pod Displacement Transducer  •X-  LVDT  S75x8  1—P  Strain Gauge Rosette  L 800x800x1.5 mm  Uniaxial Strain Gauge  o o cn  S75x8  •—d  L 800x800x1.5 mm  Typical 2.5 mm Fish P L o o CO  -X-  S75x8  •  §  r  L  L 800x800x1.5 mm  Figure 5.2: Four-storey steel plate shear wall specimen tested on the shake table 122  CHAPTER D  SHAKE TABLE TEST PROGRAM  stiff beam, S200x34, at the top storey to anchor the tension field forces generated in the upper storey plate. The column sizes differed slightly from the quasi-static test specimen to increase the out-of-plane buckling strength of the columns, and to effectively accommodate the installation of a lateral support system (see section 5.3.1). The measured structural properties of the shake table test specimen are given in Table 5.1. Full moment connections at all beamto-column joints were provided by a continuous fillet weld of the entire beam section to the column flanges. No continuity plates were added to the beam-column joints. Steel plate infill panels of 800 mm square with 1.5 mm nominal thickness were connected to the boundary members using the fish plate connection shown in Figure 3.4 (Chapter 3). At the bottom panel of the shear wall, the tension field was anchored to a W100xl9 beam. The bases of the columns together with the bottom flange of the base beam were fillet welded to a 1.3 m x 0.2 m x 25 mm steel plate. The plate was anchored to a 1.5 m x 1.5 m x 30 mm base plate using fourteen 16 mm diameter A325 bolts, as shown in Figure 5.2. The base plate in turn was bolted to the shake table by means of nine 30 mm high strength threaded rods. A photo of the four-storey steel plate shear wall specimen mounted on the U B C shake table is illustrated in Figure 5.3. Property Cross-sectional area (mm ), A 2  Moment of inertia about ^-direction (mm ), /  B100x9  S75x8  1130  1076  1.97x10  4  s  1.06X10  6  0.65X10  0.18X10  Width of flange (mm), b  98  56  Depth of section (mm), d  96  76  Flange thickness (mm),  3.5  6.8  3.7  4.2  Moment of inertia about y-direction (mm ), /  6  4  Web thickness (mm), t  w  y  6  Table 5.1: Measured member properties of the shake table specimen Once the fabrication of the four-storey steel plate shear wall specimen was completed, several other items had to be specifically designed to facilitate testing of the specimen: the attachment  123  CHAPTER O  SHAKE TABLE TEST PROGRAM  Figure 5.3: Steel plate shear wall specimen mounted on the shake table of the mass plates to the specimens to simulate gravity and inertia forces; the bracing system for out-of-plane deformation of the storey masses; the connection details of the lateral support system to the specimen; and the pin connection detail of the lateral support system to the table were the major elements that had to be designed and implemented. It can be observed from Figure 5.3 that the unsupported specimen had a noticeable twist distortion due to the welding process. As the torsional stiffness of the shear wall assembly was very low, however, only a small force exerted against the lateral support frame was adequate to  124  CHAPTER D  SHAKE TABLE TEST PROGRAM  provide alignment.  5.3.1 Lateral Bracing System As the four-storey steel plate shear wall model was designed to resist a uni-directional motion, it was necessary to restrain it from out-of-plane movement. Several ideas for a configuration of lateral support system were examined. The important issues that had to be considered in implementing a lateral support system were the installation of storey masses, elimination of twist in the columns and bracing of the columns in the out-of-plane direction at each storey level. To fulfil the aforementioned tasks, the lateral bracing system had to be attached at each storey level so that gravity and inertia loads could be transferred to the test specimen, while the columns were restrained in the out-of-plane direction. The unbraced length of the columns was then limited to the storey heights. The lateral support assembly that was chosen consisted of two parallel frames mounted on the shake table on each side of the steel plate shear wall specimen (Black, etal., 1996). The support frames were also four-storey steel framing systems with storey width and height similar to the frame-wall specimen. Steel cross beams of S75xll were used to connect the test specimen to the parallel support frames at each storey level, as shown in Figure 5.4. Each S75xl 1 beam was bolted firmly to the column webs through an end plate and four 12 mm A325 bolts. Also, all storey beams connecting the two columns of the support frames were bolted to the column flanges through a pin unit connection. This was to reduce the amount of energy dissipated within the support frame beam-to-column connections. The support frames were connected to the shake table with hinged connections. Each hinge was made from two separate halves which rotated around a 20 mm diameter central pin, see Figure 5.5. The top half of the hinge unit was bolted to an end plate that was welded to the base of each support column. The bottom half of the hinge was bolted to a 16 mm base plate that was bolted directly on top of the shake table.  125  CHAPTER!  SHAKE TABLE TEST PROGRAM  B100X9  B100x9  B100x9  B100x9  B100x9  B100x9  Figure 5.4: Plan view of lateral support system  4r -up-  CO-  -4n ;  i  Figure 5.5: Pin connection at the base of lateral support columns It is noted that by connecting the bases of the lateral support frames to the table, they would get excited together with the specimen when subjected to table motions. To minimize the amount of energy dissipated by the lateral support frames, extreme care was taken to provide hinge connections where appropriate. Upon complete installation of the out-of-plane bracing system, the out-of-plumbness of the columns in the direction perpendicular to the plane of shear wall frame was removed for all intents and purposes. Figure 5.6 illustrates the shake table fourstorey specimen inside the lateral support system.  126  CHAPTER O  SHAKE TABLE TEST PROGRAM  Figure 5.6: Shake table four-storey specimen inside lateral support system  5.3.2  Mass Blocks  The storey dead loads were modelled through stacks of steel plates attached to the specimen at each storey level. Three different sets of steel plates with overall dimensions of 1.5 m x 0.6 m and varying thicknesses were used. The configuration of storey masses involved installing two stacks of steel plates on either side of the specimen. Each stack comprised of three steel plates with thicknesses of 63.5 mm, 31.75 mm and 15.875 mm. This resulted in a 1700 kg mass at  127  CHAPTER D  SHAKE TABLE TEST PROGRAM  each storey floor and a total of 6800 kg mass on the specimen. The connection of the mass plates to the specimen was achieved through S75xll beams connecting the support frames to the specimen. First, all the plates were stacked on the top flanges of the beams. Then, 1.5 m long C100x8 channel sections were clamped against the underside of the beams by threaded rods which passed through patterned holes in the plates. The rods were securely tightened to avoid slippage of the mass and to provide in-plane racking stiffness to the support frame. There were four threaded rods and two channel sections attached to each stack of plates. To increase the stability and stiffness of the 3-dimensional shear wall-frame assembly and to maximize the degree of confidence in supporting the steel plate shear wall specimen during strong shaking in the out-of-plane direction, threaded rod X-bracing was attached to the support frames in a direction perpendicular to the plane of specimen. The rods were tightened to about 50% of their yield capacity to prevent them from flopping during the strong motion shaking. Figure 5.7 shows a photograph of the steel plate shear wall specimen mounted on the table with lateral support frames, storey masses, and X-bracing rods installed.  5.3.3  Instrumentation Layout  The specimen was instrumented with accelerometers, string-pod displacement transducers, LVDTs, 3-element 45° single-plane strain rosettes and uniaxial strain gauges. The total number of recorded measurements was limited by the number of data acquisition channels available. The UBC Earthquake Laboratory is equipped with two sets of data collection banks. One is a 16- channel data acquisition system for controlling and monitoring the table, the other is a 32channel Sample/Hold 128 Multiplexed data acquisition system that is used for recording specimen measurements. The 32-channel Sample/Hold can be amplified and filtered to improve the quality of the signals by increasing their amplitude and removing undesired frequency contents (noise level). Beyond 32 channels and up to 128 channels, data can be  128  CHAPTER O  SHAKE  TABLE  TEST  PROGRAM  Figure 5.7: A photo of the shake table four-storey specimen with lateral support frames, storey masses, and X-bracing rods installed collected with amplifiers but no filters. Based on the number of channels available, with and without filtering, an instrumentation scheme was planned for the steel plate shear wall model. Figure 5.2 shows the layout of the accelerometers, displacement transducers and strain gauges affixed to the shake table test specimen. The input absolute acceleration of the table was recorded using 8304A(X) K - B E A M capacitive  129  CHAPTER O  SHAKE TABLE TEST PROGRAM  accelerometer with an acceleration range of ±10g and frequency response of zero to 400 Hz. The output absolute acceleration of all four storey levels was recorded using model 3140 ICSENSORS PizoRESISTIVE accelerometers capable of measuring accelerations in the range of either ±2g, ±5g or ±10g and in the frequency range of zero to 250 Hz. Four PizoBEAM accelerometers, model 8628, with acceleration range of ±5g and frequency threshold of zero to 1000 Hz were also installed at the fourth floor of the specimen to monitor the response of the specimen in the transverse direction and to check the relative motion of the storey masses with respect to the specimen. The accelerometers were mounted in the longitudinal and transverse directions on the mass plates and on the storey columns. The in-plane displaced shape of the specimen was monitored at all four floor levels using C E L E S C O model PT101 string-pod displacement transducers with an accuracy of 0.2 mm. The displacement transducers were mounted to a steel frame, fixed to the base, on the north side of the table. Three T R A N S - T E K D C - D C series 240 LVDTs with an accuracy of 0.01 mm were also mounted at three intermediate points between the base and first storey column. The supporting frame of the LVDTs was firmly attached to the table. The absolute displacement of the table was recorded with a L V D T that is part of the actuator control component. The strain gauges were put in the locations where large deformations were expected. A total of ten, 45° rosettes were placed on the infill plates, five on the front and the other five directly opposite on the other side of the plates. This was done to cancel the effects of through-thickness bending strains that were present within the plates and to determine the state of strains in the panels as they stretched in one direction. The flanges of the columns near the base level were instrumented with strain gauges oriented in the axial direction. One of the beam-to-column connections in the first storey was also instrumented with axial strain gauges on both flanges of the beam and columns. Axial strain gauges were also placed on the flanges of one of the firststorey columns at mid-height level to monitor the effects of horizontal components of the  130  CHAPTER O  SHAKE TABLE TEST PROGRAM  tension field forces on the column bending moment diagram. Furthermore, four axial strain gauges were placed at each column location on the inside and outside flanges. This was done to eliminate the effects of local bending in the flanges of the columns.  5.4  SHAKE TABLE TESTING PROCEDURE  Before the start of the shake table test, it was essential to have a good estimate on the fundamental natural frequencies of the shear wall frame assembly in both directions. The natural frequencies predicted by the SAP90 computer models (discussed in Chapter 3) had to be verified before a shake table testing scheme was planned. A detailed description of the lowamplitude vibration test investigations performed on the quasi-static and shake table test specimens is presented in Chapter 6. In short summary, the hammer test results showed that the first fundamental natural frequency of the shake table specimen with surrounding support frame was 6.1 Hz in the longitudinal (parallel to the plane of shear wall frame) direction. In the transverse direction the first fundamental natural frequency was measured as 8.97 Hz. The first torsional mode of the frame-wall structure was estimated as 6.2 Hz.  5.4.1  Shake Table Input Motions  It was desirable to select earthquake input motions that would cause some nonlinearity to the specimen, while still satisfying the constraints imposed by the U B C Earthquake Laboratory shake table facilities. During the design stage of the shake table test specimen (Chapter 3), three different earthquake records that had the potential of causing some damage to a multi-storey steel plate shear wall building were chosen. These were records from the 1992 Landers, 1992 Petrolia and 1994 Northridge earthquakes. The actual time-histories, elastic spectra and power spectral density plots of the three selected records are shown in Figure 3.5 in Chapter 3. It should be noted, however, that a variety of earthquake ground motions with different intensities and damage potential may exist that could lead to significant damage in a prototype structure. The general behaviour of a prototype structure is influenced by the characteristics of the 131  CHAPTER O  SHAKE TABLE TEST PROGRAM  earthquake ground motion anticipated at a site. Since earthquakes are random in nature, it is unlikely that the same earthquake ground motion would be repeated at some future time at the given site. Individual earthquake motions at a given location are dependent on a set of parameters such as magnitude, focal depth, attenuation characteristics, frequency content and duration that makes them unique in a sense that they will likely never occur again. This shortcoming in the use of recorded strong motion data for testing the frame-wall specimen was addressed by the use of an artificially generated earthquake that has similar characteristics as the past observed earthquakes. A synthetically generated acceleration time-history waveform from Bell Communications Research (Bellcore, 1995), the so called "VERTEQII" record, that had been synthesized from several typical earthquakes and for different building and soil site conditions, was selected. This waveform was designed for the shake table tests of telecommunications equipment located in the areas with the highest risk of ground shaking. The record has a maximum acceleration level of about 1.65g and a strong motion duration of 16 seconds. The sampling frequency of the VERTEQII is 200 Hz with an effective frequency band of 2 Hz to 10 Hz. To run the VERTEQII waveform, a shaking table system with actuators having a stroke of ±127 mm peak-to-peak would be needed. Because the displacement operation range of the UBC shaker is limited to ±76 mm peak-to-peak, some modifications had to be made. Firstly, the low frequency components (< 0.01 Hz) of the record were filtered out using digital filtering techniques. Secondly, the input base acceleration record was scaled to 95% of the amplitude of the original record. The severity of the excitations was controlled by the acceleration amplitude and in turn by the power spectral density of the earthquake records. For the most severe excitation, a specimen should be excited with an earthquake record, the spectrum of which has a relatively large peak around the first natural frequency of vibration of the structure. Figure 5.8 shows the scaled  132  CHAPTER O  SHAKE TABLE TEST PROGRAM  versions of the Joshua Tree, Petrolia, Tarzana Hill and modified VERTEQII earthquake records together with their respective power spectral density plots. It is noted that the time parameter of the accelerations was scaled by a factor of 2 to satisfy the similitude laws. With regard to the first fundamental natural frequency of the system, it was expected that the Tarzana Hill and VERTEQII records would have the most damaging effect on the specimen. This deduction can be readily observed from the Fourier Transform plots of the records in Figure 5.8 illustrating that the Tarzana Hill and VERTEQII records contain large frequency components that are in the vicinity of the specimen's first natural frequency.  5.4.2  Shake Table Control System  Once the input time-histories were selected, they had to be fed to the shake table system in a special format. In general, shake table actuators are driven by displacement time-history signals. Therefore, the input acceleration records had to be integrated twice to give values for displacements. This was done by a Mathcad® calculation sheet that was developed at U B C (Latendresse, 1998). The program conditions the records, sets the required cut off levels for the lowpass filters and uses a recursive integration routine to find the displacement results. The control system of the table then determines whether the desired displacement or acceleration demand can be achieved. The use of lowpass filters ensures the removal of low frequency components that result in excessive displacement, which may surpass the available stroke limit of the table, scaled for increased intensity. One of the main challenges of shake table testing is to ensure that the system can accurately replicate the desired motions. The main cause of distortion in an input signal can be attributed to the limited hydraulic power of a system and the mass of the specimen compared to the mass of the shake table, which affects the interaction between the two systems. The shaking tablespecimen interaction is a complex phenomenon that has been studied by many researchers in the past (Rea, et al, 1977 & Rinawi and Clough, 1991). The degree of interaction becomes  133  CHAPTER O  Time (sec)  SHAKE TABLE TEST PROGRAM  Frequency (Hz)  Figure 5.8: Time-histories and corresponding Fourier Transforms of the input motions more severe, when the masses are attached to a specimen at higher floors, so that the effect of overturning inertia forces become significant. Sophisticated control systems use automatic tuning features that optimize the input signals, based on low level shaking of the specimen. When a specimen undergoes severe plastic deformations during a strong motion test, however, the natural frequency of the system changes and the divergence between a desired signal and a  134  CHAPTER D  SHAKE  TABLE  TEST  PROGRAM  measured signal typically increases. The capability of a table to reproduce earthquake records greatly depends on the control system. To minimize the effect of table-structure interaction on distorting the input signals, the U B C seismic simulator uses control software (MEVCS) that closely monitors feedback signals from the transducers during the preliminary runs. It then corrects the feedback signals through an iterative process that compares the measured frequency response function with the desired frequency band of the reference acceleration, velocity and displacement traces. Based on the degree of error  obtained from each time-history  signal (acceleration,  velocity  and  displacement), a modified drive signal is generated and used to drive the next test run. Since it is not feasible to run the table at high acceleration levels, because of the potential of damaging the model, the effectiveness of the iterative procedure used by the M E V C S to generate corrected signals, may be affected as the specimen is subjected to severe excitation in the actual test run. To generate an appropriate set of compensated drive signal histories for testing the steel plate shear wall specimen, all the masses (about 7000 kg) were first attached to the table. The table was run for each reference earthquake record individually, and the error signals between the measured time-histories and the desired signals were obtained. The process was repeated a few times until satisfactory results regarding the effectiveness of the table in reproducing the desired motions was achieved.  5.4.3 Shake Table Loading History The steel plate shear wall specimen was subjected to all four earthquakes in a sequential order. Initially, a very low level run was performed to determine whether the instruments were functioning properly. Also, the measured table acceleration and displacement were compared with the desired input values to ensure that the generated drive histories produced for the tablemass system were properly set up. Before running the table with a maximum intensity of the  135  CHAPTER  O  SHAKE TABLE TEST PROGRAM  selected earthquake records, a number of runs with low to intermediate intensity levels were tried. To simulate a low or an intermediate intensity level, shake table earthquake runs were taken as a percentage of the Peak Ground Acceleration (PGA) of the selected reference earthquakes. Each test run was related to the selected reference earthquake by its acceleration amplitude. This meant that a 20% run would be a run where the peak acceleration of the desired input earthquake motion was 20% of the recorded PGA of the reference earthquake. Table 5.2 presents the sequence and amplitude of the input records. It is noted from Table 5.2 that the desired peak accelerations were in some cases quite different than the measured table accelerations. This was mainly due to the interaction of the specimen with the table in a sense that the local vibrations of the structural elements of the specimen would significantly affect the table motions. In the following section the behaviour of the specimen under each loading is described.  Reference % of PGA of the Desired Peak Test Run Earthquake Record Reference Earthquake Acceleration (g)  1  loshua Tree  10  0.028  2  loshua Tree  10  0.028  3  loshua Tree  10  0.028  4  Joshua Tree  10  0.028  5  Joshua Tree  20  0.057  6  Joshua Tree  40  0.114  7  Tarzana Hill  10  0.179  8  Tarzana Hill  20  0.357  9  Tarzana Hill  20  0.357  10  Tarzana Hill  40  0.714  11  Tarzana Hill  40  0.714  12  Petrolia  10  0.059  13  Petrolia  20  0.118  Table 5.2: Sequence of input records 136  CHAPTER O  SHAKE TABLE TEST PROGRAM  14  Petrolia  40  0.236  15  Petrolia  80  0.472  16  Joshua Tree  80  0.228  17  Tarzana Hill  80  1.428  19  Tarzana Hill  80  1.428  20  VERTEQII  10  0.165  21  VERTEQII  20  0.330  22  VERTEQII  40  0.660  23  Tarzana Hill  120  2.142  24  VERTEQII  80  1.320  25  VERTEQII  60  0.984  26  Tarzana Hill  140  2.499  27  VERTEQII  50  0.825  28  VERTEQII  60  0.984  29  VERTEQII  70  1.155  30  VERTEQII  80  1.320  31  Tarzana Hill  150  2.678  32  VERTEQII  50 (6 times)  0.825  33  Tarzana Hill  120 (6 times)  2.142  34  Sine (5.5 Hz)  5%g  0.05  35  Sine (5.5 Hz)  10%g  0.10  36  Sine (5.5 Hz)  15%g  0.15  37  Sine (5.5 Hz)  20%g  0.20  Table 5.2: Sequence of input records (cont.)  5.5 DESCRIPTION OF SHAKE TABLE TEST SEQUENCE The specimen was first subjected to the Joshua Tree record with 10% intensity. The duration of strong shaking was about 12 seconds. To examine the adequacy of the control system parameters, errors between the desired and produced motions (acceleration and displacement) were checked and considered to be unacceptable. The errors were adjusted by the  137  CHAPTER O  SHAKE TABLE TEST PROGRAM  compensation algorithm of the control system and the test was repeated. No improvement in the errors between input and output accelerations was apparent. It was obvious that the initial drive history files obtained by attaching the masses alone to the table were not good enough to accurately reproduce the required input motion. A new impedance matrix for the history drives taking into account the flexibility of the specimen and the height at which the masses were fixed was required. Before continuing the test, the frequency control band of the table was set at frequencies below 15 Hz. The specimen was subjected to a low-amplitude chirp function in a frequency range of 0.5 Hz -15 Hz. By performing a Frequency Response Function (FRF) analysis of the produced table outputs (acceleration, velocity and displacement), new drive history files were generated for the control system. The Joshua Tree 10% run was repeated with new drive history files to determine the effect on the errors. Errors were within tolerable limits (5% difference between the input and output accelerations), but slightly high. The compensation process was called to further reduce the errors. The Joshua Tree 10% input record was then run for the fourth time to check the state of the input-output response. The errors were reasonably small, therefore it was decided to continue the test with higher loading level. To gain better results at higher input accelerations, the errors were again compensated. The amplitude of the table input excitation was increased to 20% of Joshua Tree record. While running the table, the out-of-plane vibration of infill plates caused an audible noise. The sound heard during the test was comparable to a sound produced when a thin piece of plate is held in someone's hand and excited perpendicular to its plane like a cantilever object. The errors in both acceleration and displacement continued to decrease further, as was expected, so a 40% level run of Joshua Tree record was executed. During this test, the vibration of the infill plates became more pronounced. Visual observation detected a combination of first longitudinal and  138  CHAPTER  O  SHAKE TABLE TEST  PROGRAM  torsional response for the frame during excitation. This was due to the fact that the Joshua Tree record did not have enough energy (see the Fourier Transform amplitude in Figure 5.8) to effectively excite the structure in its first longitudinal mode. In the next run, it was decided to try the Tarzana Hill record which contains high frequency components that were in the vicinity of the first longitudinal natural frequency of the specimen. A 10% run was executed first. The expected strong motion shaking was 4 to 5 seconds. During the excitation, the vibration of the plates was more severe than during the Joshua Tree runs. The input-output errors were low, but the system was further compensated for the errors. The next run was the Tarzana Hill record at 20%. While running the test, vibration of the infill plates was quite visible and accompanied by very audible noise. The reorientation of the plates' tension field and the corresponding buckling of the plates was very pronounced. Torsional vibration was not noticeable. Upon visual inspection of the recorded data, it was noticed that the first and second floor accelerometers contained unusually high peaks that were not present in the third or fourth floor acceleration outputs. The accelerometers were checked, and no defect was found. The same test was repeated to see if the problem would be solved by itself. At the end of the test, the results showed that the first and second floor accelerometers were still drifted for the strong shaking part. At this point, it was thought that the high frequency vibration of the infill plates was interfering with the instrumentation devices causing the ±2g accelerometers to saturate. To filter out the high frequency noise, soft rubber pads were installed underneath the accelerometers to dampen out the effects of local infill plate vibrations. Next, a 40% level of Tarzana Hill record was tried. The local vibration of plates was quite severe. The same problem with the first and second floor accelerometers was still present. The accelerometers were not following the traces of the input excitation during the strong shaking part. It was decided to replace the third floor accelerometer (±5g) with the first floor accelerometer and run the same test to find out if the problem was related to the  139  CHAPTER O  SHAKE TABLE TEST PROGRAM  instramentation. After the shake table run, the results were checked and it was found that the third floor acceleration drifted instead of the first floor. It was obvious that the ±2g accelerometers had to be replaced before the test could be continued. Next, the Petrolia earthquake record was applied to the test specimen at 10%, 20%, 40% and 80% intensities, respectively. All instrumentation worked properly. The effects of plate vibration was very minimal compared to the vibration during the Tarzana Hill record. By visual observation during the tests, the specimen was responding to the input excitations mainly in a torsional mode. The longitudinal relative motion of the steel plate shear wall specimen at the top was not noticeable indicating that the specimen was mainly riding on the table like a rigid body. It was apparent that the Petrolia record did not have enough energy to cause any damage to the specimen because of its amplitude and frequency content, so no further testing was planned using the Petrolia earthquake as the input motion. To examine the effect of the Joshua Tree record on the steel plate shear wall specimen at high acceleration level, the next test was carried out using this record with 80% intensity. Similar conclusions as the Petrolia 80% run were drawn. Even though the Joshua Tree record had a long duration of strong motion shaking, it did not contain the required level of energy around the frequency range of interest. The Tarzana 80% run was tried next. The table, however, was not able to function properly and had to be shut down manually. The problem arose towards the end of the test when the table began vibrating with a loud noise and at a high frequency rate. This was attributed to the severe out-of-plane vibration of thin infill panels which influenced the sensitive control accelerometer of the table. As a result, the feedback signal to the control hardware unit was contaminated with large high-frequency components that caused the control panel to believe that the table was undergoing extreme motions that were quite different from the compensated drive history files and therefore the whole system became instable. During high frequency vibration, the recorded  140  CHAPTER O  SHAKE TABLE TEST PROGRAM  acceleration amplitudes were several times more than the desired input acceleration amplitudes. To gain some more information regarding the nature of the infill plate vibrations, the first few fundamental natural frequencies of the infill panels were measured using an instrumented hammer and a pizoelectric accelerometer mounted on one of the plates. This was done to compare the dominant frequency of measured table acceleration with the natural frequency of vibration of plates. The first and second fundamental natural frequencies of the infill panel were computed as 22.2 Hz and 38.5 Hz. To verify that the source of energy in exciting the infill panels was the result of structural behaviour and not the input excitations, a sine sweep waveform in the frequency range of 2 to 10 Hz (well below the frequency input required to excite the plates) was applied to the specimen. As was expected, the vibration of the infill panels was quite severe. The table was not able to produce the motion and the system became instable so that the table had to be shut down manually. It was concluded that the vibration of infill panels could be related to the formation of diagonal tension action combined with diagonal compression buckling of the infill plates. As the infill plates were subjected to diagonal compression stresses during sudden load reversals, they popped and produced a high frequency signal that traveled through the specimen into the table. To continue the test, it was necessary to reduce the out-of-plane vibration of the plates. Several ideas of installing a damping device were examined. The main consideration was to minimize the interference of the damping device with the structural action of the plates, that is, the plates had to be allowed to buckle in and out once the device was in place. After examining a few different methods of damping the plate vibration, it was decided to restrain the plates in the out-of-plane direction by means of rubber pads. Rubber composite pads together with high density foam pads were installed at opposite faces of the infill plates using 2x4 timber studs. The timber studs were tightened against the edges of the column  141  CHAPTER O  SHAKE TABLE TEST  PROGRAM  flanges, as shown in Figure 5.9. This was done for the second, third and fourth storey plates as no interference with the structural behaviour of the first storey infill plate was intended. Also, the cut-off frequency of the lowpass filter used as part of the signal conditioning system was lowered which caused the frequency band of the control parameter to be limited to a narrow band. These changes were intended to bring the focus of the control system on the frequency band of interest and to permit the system to function in an optimal manner.  Figure 5.9: The installation of foam pads to dampen out the infill panel vibrations  142  CHAPTER O  SHAKE TABLE TEST PROGRAM  Once the installation of dampers was completed, the Tarzana Hill 80% run was repeated. The test was successfully carried out. The presence of high density foam pads damped out the high frequency plate vibration significantly, while the plates were allowed to buckle in and out with very little resistance from the foam pads. The table acceleration was still contaminated by the high frequency peaks that were superimposed on top of the signal, but the noise level was not as prevalent. At the end of the test, it was realized that the top storey masses had been moved relative to the S75xll support beams. Upon further examination, it was found out that a number of nuts were loose, and therefore the friction between the plates and the support beams was not sufficient to hold the mass plates in place. It is noted that high frequency vibration of bolted structural elements could have been the main reason for the loose nuts. The nuts were tightened securely and the test was continued. A  comparison of time-histories  of  accelerometers mounted on the top mass plates and attached to the top floor is shown in Figure 5.10. This comparison was essential, because a difference between the two readings would mean that the mass was not rigidly connected to the floor diaphragm. Figure 5.10 shows small differences between the two accelerations indicating that some energy had been dissipated by slipping of the mass plates.  6  7  8  10  11  12  Time (sec) Figure 5.10: Time-histories of the top floor acceleration (dashed line) and added mass acceleration (solid line) 143  CHAPTER  O  SHAKE TABLE TEST PROGRAM  Before an attempt was made to push the table to its ultimate payload capacity and possibly the specimen to its nonlinear behaviour using the Tarzana Hill record, the response of the specimen to the modified VERTEQII earthquake was investigated. The first run was performed with 10% severity. The strong motion shaking lasted for about 8 seconds. Plate vibrations were present, but at low intensity. In the next runs, the amplitude of input excitation was increased to 20% and 40% of the reference VERTEQII earthquake, respectively. The tests were completed successfully. It is noted that a considerable reduction in the unwanted noise level generated by the vibration of infill panels was crucial in the execution of high intensity earthquake records. The Tarzana Hill 120% run was tried next. It was expected that the test might cause some nonlinearity to the specimen. After running the test, the specimen was checked for any sign of yielding. Upon visual inspection, a number of horizontal cracks in the whitewash on the outer flange of one of the columns was observed. The cracks were distributed fairly uniformly along the first storey height. Figure 5.11 illustrates the extent and location of whitewash cracks at the end of Tarzana Hill 120% run. It can be observed that the cracks initiated from the tip of the column flange and extended toward the column web. The VERTEQII record with 80% intensity was tried next. The test, however, was not successful. The control system shut down the table right at the start of the strong motion part of the record. It was concluded that the system underwent a severe enough jolt to cause the TAPS unit of the actuators to override the input signal and cause a controlled stoppage of the test. The intensity of input record was reduced to a 60% level and the test was run again. During the strong motion part, the plate vibration problem again became apparent causing the table to become instable and the technician had to shut down the table. The out-of-plane buckling of the second storey infill plate was quite visible between the storey beams and mid-panel rubber pads accompanied by a popping like sound. This was believed to be the main contributor to the noise in the system. Therefore, the second storey infill panel was reinforced with another set of  144  CHAPTER  O  SHAKE TABLE TEST  PROGRAM  Figure 5.11: Cracks in column flange whitewash appeared at the end of Tarzana Hill 120% run rubber pads and foam to further limit the buckling length of the infill panel and therefore, dampen out the out-of-plane motion of the panel. The specimen was then subjected to the Tarzana Hill 140% run. The test was performed completely. The previous yield lines on one of the column outer flange grew a little bit more toward the column web. Also, a few more whitewash cracks developed between the previous crack lines. At the base of the yielded column, whitewash cracking was observed in the weld 145  CHAPTER 5  SHAKE TABLE TEST PROGRAM  location both outside the column flange and inside the web. In the next run, the VERTEQII 50% record was tried. The test was completed successfully. In the subsequent tests, the VERTEQII 60% and 70% runs were applied to the specimen, respectively. The plate vibration and very audible noise were the main characteristics of the specimen in all three runs. Plate buckling was quite visible even as far as the third storey panel. As the severity of the VERTEQII was increased to 80%, TAPS shutdown occurred indicating that the capacity of the horizontal actuator was surpassed. The test was continued with the Tarzana Hill record at 150% intensity. The table control system was not able to perform the test and therefore, the 140% Tarzana Hill and 70% VERTEQII runs were considered as the final stage of loading. To complement the shake table runs, the specimen was subjected to six times 50% VERTEQII run, consecutively. It was then subjected to six times 120% Tarzana Hill run, consecutively. The main reason for these tests was to see if there was any degradation in the recorded motion as a result of repeated earthquake loading. No adverse effect on the behaviour of the test specimen or recorded motions was evident. Before the termination of shake table tests, it was decided to study the behaviour of the shear wall specimen under simulated sinusoidal motions with an input frequency component close to the longitudinal fundamental natural frequency of the specimen. An input sinewave motion with a frequency component of 5.5 Hz and a built-up ramp to gradually increase the amplitude of the waveform to the required level, was generated by the control software of the shake table system. The specimen was first subjected to an input amplitude of 0.05g. The response of the specimen to the input excitation was severely amplified. The effect of resonance on exciting the specimen was evident. Upon checking the recorded acceleration at the top storey of the specimen, a peak acceleration of 0.6g was recorded. The test was continued by increasing the amplitude of the input motion to O.lg. The specimen was severely shaken during the test. Plate vibration and buckling of the infill panels, which was accompanied by a loud noise, was  146  CHAPTER D  SHAKE TABLE TEST PROGRAM  present. In the next run, the amplitude of input motion was increased to 0.15g. Similar behaviour as in the previous runs was observed. Once the amplitude of the input motion was increased to 0.2g, some uplift was observed at the base of the columns. The shaking table seemed to be rocking with the specimen. Once the test set-up was dismantled, the pins at the base of the supporting frame columns were severely bent indicating that a substantial amount of up-ward or down-ward forces had been exerted on the stabilizing frames. No further testing was carried out as it was possible to induce some damage to the table due to bending.  147  6  LOW-AMPLITUDE  VIBRATION  TESTS 6.1 INTRODUCTION The results from low-amplitude vibration tests on the University of British Columbia (UBC) and University of Alberta (UofA) test specimens are presented in this chapter. Experimental dynamic tests of full and small scale civil engineering structures have been conducted by many researchers and practitioners for several decades. Structural damage identification through vibration testing has already been proven to be a useful tool for the purpose of structural inspection and retrofit. Considerable effort has been undertaken in the past few decades to investigate the relationship between the damage location, the damage type and its severity with the corresponding modal parameters. It is a growing field of research since invisible defects in structures, such as offshore rigs or buildings where structural members are covered with cladding, can pose severe risk of collapse if not identified and repaired in time. Inspection methods can be very expensive and great benefit can be gained by narrowing the potential damage area with analytical and non-destructive measuring systems. The method of modal testing has been used in many cases in an attempt to detect and characterize damage that a structure has endured as a result of earthquakes, wave forces or corrosion. Often, serious structural damage may be virtually invisible, as was the case with many steel framed buildings following the Northridge and Hyogoken-Nanbu earthquakes in 1994 and 1995, respectively. A large number of moment resisting frames sustained severe damage in the beam-to-column moment connection regions, which only became evident after expensive inspection procedures that required the removal of wall cladding and fire proofing. Footprint recordings made of buildings and bridges in a seismic region, can be used as a basis for comparison with similar measurements after an earthquake. The discrepancies between the  148  CHAPTER 6  LOW-AMPLITUDE VIBRATION TESTS  results (pre- and post-earthquake measurements) may reveal important information regarding the existence of potential damage in the structures, and possibly an indication of the approximate location for damaged regions. Therefore, structural damage identification through ambient or forced vibration signature may be a practical method of preliminary damage assessment. Although the technique of damage detection appears very promising, in practice it still remains very difficult to characterize damage in complex structures in all but the most severe cases. For this project the purpose of vibration testing was to provide information needed for the calibration of analytical models of the steel plate shear wall specimens. Generally, finite element computer models are based on geometric information of prototype structures taken from drawings and nominal material properties specified for use in structures. Various assumptions regarding the type of finite elements, the effects of boundary conditions and the complex behaviour of a structure at some key points are also made. It is thus evident that the effectiveness of computer models to represent the behaviour of the real structure can be highly questionable and uncertain. To overcome this limitation, the results from vibration tests can be used to verify such models and, therefore, increase the level of confidence on the results obtained from various analyses using these models. The results of a modal testing program (ambient and impact tests) conducted on a half-scale four-storey steel plate shear wall specimen at the UofA and two quarter-scale four-storey steel plate shear wall specimens at the U B C are presented. The low level vibration measurements performed at the Centre for Frontier Engineering Research (C-FER) in Edmonton, Alberta and at the U B C Structural and Earthquake Laboratories were used to determine the dynamic characteristics (i.e. natural frequencies, mode shapes and damping ratios) of the steel plate shear wall frames. These results were then compared with those obtained from finite element models representing the elastic behaviour of the structures at low levels of motion. The  149  CHAPTER 6  LOW-AMPLITUDE VIBRATION TESTS  experimental results may also be used for refining the linear-elastic analytical models of the frame-wall structures. After verifying various computer models, the linear and nonlinear behaviour of the models for significant levels of loading (cyclic storey load or input base motion) may be computed with good confidence in the output results.  6.2  VIBRATION TESTS  There are two commonly used types of low-amplitude vibration tests, namely ambient and forced methods. In the ambient vibration method, vibration responses are measured due to unknown forces (e.g. wind, machine operation, etc.). In the forced vibration method, a controlled excitation is applied at one or more points on a structure. It has been demonstrated in the early seventies (Trifunac, 1972) that both of these methods lead to similar results if they are applied correctly. In general, the ambient vibration method is most suitable for testing long span bridges and tall buildings, while the forced vibration approach is commonly used for small to medium size structures. The forced vibration test is generally conducted under more closelycontrolled conditions than the former and consequently yields more accurate and detailed information (Ewins, 1992). Impact tests are one type of forced vibration method that has been used to measure the dynamic response of small structures. The location and direction of impacts have to be determined carefully, however, so that the required modes of vibration are excited sufficiently for accurate measurements. The basic concepts of ambient and impact vibration techniques are described in the following sections.  6.2.1  Ambient Vibration Test  During ambient vibration testing, a structure is presumed to be excited by wind, micro tremors, machinery or in the case of bridges, traffic loading. The input motion to the structure is assumed to resemble "white noise" with a full frequency spectrum. Contrary to forced or impact vibration testing, one does not control the force that is applied to vibrate the structure and measurements are taken over a relatively long time duration to capture a broad band of  150  CHAPTER 6  LOW-AMPLITUDE VIBRATION TESTS  input excitation. Natural frequencies and mode shapes of the structure are obtained by measuring the vibrations, usually accelerations, at selected locations which will capture the desired independent degrees of freedom of the structure. The peaks of the power spectral density functions of ambient vibration records determine the potential natural frequencies of the structure. To estimate natural frequencies more accurately and to ensure that all the natural frequencies of a structure are identified, one can take averages of the power spectral density functions over a number of time-histories recorded at different locations on the structure. The power spectral density function of a time series x(t) is defined as: FSD(co) = lx(co) • X(oS)|  (6.1)  2  where X(co) is the Fourier Transform of x(t) and X(co) is the complex conjugate of X((o). PSD(co) corresponds to the square of the magnitude of the Fourier Transform of the response. For successful ambient vibration measurement, the structural system under consideration must have certain attributes. A reliable estimate of modal characteristics can be achieved, if the following conditions are met: o  The process being measured is stationary. This means that the measurements are independent of time. Thus, they can be recorded at any point of time, and the results obtained from analysing these measurements will be the same.  o  All the significant modes of vibration are excited equally. This means that the power spectrum of the excitation has white noise characteristics (the PSD of the excitation is a horizontal line over the frequency range of interest).  c  The modes of interest are well separated and lightly damped (less than 5% of critical damping).  c  The excitation does not induce any non-linearity  in the system (the  superposition principle is valid).  151  CHAPTER 6  LOW-AMPLITUDE VIBRATION TESTS  The ambient vibrations can be measured at any location i of a multi-degree of freedom structure as a displacement, x-(r), velocity,  jc.(f),  or acceleration x-(r). The geometric response  (displacement) of a multi-degree of freedom structure at location i subjected to arbitrary loading can be expressed in the time domain as a superposition of mode shapes and generalized modal responses in a form of: + <P2,  *,•(') = ^ 1 , «  where cp  fc i  i  +  +  (6.2)  <P*,; y (t) k  is the ith component of the kth mode shape of the structure, and y (t) k  is the time-  history of kth generalized modal response. The Equation (6.2) can be converted into the frequency domain using the Fourier Transform: + <P ,• *2(<B) +  X .(ul) = <Pi, i (  (6.3)  + <Pjk, i  2)  where X-(co) is the Fourier Transform of x - ( f ) and Y (cd) is the Fourier Transform of the k  modal response of the structure corresponding to mode k. The modal responses can be expressed as the product of the modal forcing function, P (u>), and the frequency response k  function, H ((£>): k  Y (a>) = H (a>)P ((0) = [-<Q M + i<aC + K ]~ P (<o) 2  k  k  k  l  k  k  k  k  (6.4)  H ((i)) represents the modal response of a structure in the kth mode when it is subjected to a k  unit dynamic load of e . im  M, k  C  k  and K~ are modal mass, modal damping and modal k  stiffness of the structure for thefcthmode, respectively. In practice, acceleration time-histories of structural elements are generally recorded. Thus, it is desirable to work with these records directly rather than using integrated displacements. The acceleration data recorded during an ambient vibration test for a structure in frequency domain can be expressed as: i,-(a>) = © [q>i, ^(co)+cp . y (a>) + 2  2>  2  + (?  k i  y^©)]  (6.5)  where X;(co) is the Fourier Transform of the acceleration record at location i. The response of  152  CHAPTER 6  LOW-AMPLITUDE VIBRATION TESTS  an individual record measured at location i at a natural frequency co. can be expressed as:  Xi((0.)  = co[cpy,(co) + (p . y(co.) + 2 ;  1(  y  2>  2  + cp ^(co.)]  (6.6)  M  On the basis that the modes are well separated and that modal damping is small, it can be deduced that the response of the system at a natural frequency of co. is dominated by the corresponding mode of vibration. Hence, the following approximation can be made.  X,-(co.) = cocp,- iYj«Oj) 2  cocp- iHjiapPjitoj) 2  =  (6.7)  ;  To estimate the mode shapes of a structure experimentally, one can use the ratios of the Fourier Transforms of the time series collected at each node of vibration with respect to a reference sensor location. It is important to note that this estimate can only be made if the response of the structure at a natural frequency is indeed dominated by the corresponding mode shape. On the basis of this, one can estimate the modal amplitude ratio of a particular mode at two locations a and b if the two records were collected simultaneously at these locations. The modal amplitude ratio of the jth mode can be estimated for the two locations a and b using: i  ( c o )  a  ]_ _ X ((Oj) b  coV-  i (Oj  a  HA(o.)P.((o.)  ha CP;,  j  j  cp. j—i  ^ (CO.)P.(CO )  fc  /  /  =  ^  (  6  g  )  Vj, b  This equation indicates that the ratio of the Fourier amplitudes of two acceleration records at locations a and b and at the;'th natural frequency of a structure is equal to the modal amplitude ratio of the jth mode at those locations. The detailed mathematical development of these procedures can be found in most structural dynamics text books or in the dissertation by Felber (1993).  6.2.2  Impact Vibration Test  Impact testing is a relatively simple means of exciting a structure into vibration. The structure is instrumented with accelerometers and is struck with a hammer that is equipped with a force transducer. The magnitude of the impact is determined by the mass of the hammer head and its  153  CHAPTER D  LOW-AMPLITUDE VIBRATION TESTS  velocity when it hits the structure. The impact force and acceleration response time-histories are then used to compute frequency response functions. As mentioned earlier, one can estimate the natural frequencies, mode shapes and damping values of the structure from these frequency response functions. The frequency response function (FRF) of a structure is defined as the ratio between an output (displacement, velocity or acceleration) and an input (hammer force) signal. //(co) =  (6.9)  F(co)  where F(co) is the Fourier Transform of the hammer impact force. The ratio is complex valued as there is an amplitude ratio, |//(co)|, and a phase angle between the two components. 6.3 VIBRATION DATA ACQUISITION SYSTEM Figure 6.1 shows a typical UBC ambient and impact vibration test setup with all the necessary measurement hardware equipment. Analog to Digital Converter  Sensor  Spectrum Analyzer  V^---^  Data Acquisition Computer Data Analysis Computer  Figure 6.1: Typical recording setup for vibration measurements  154  CHAPTER 6  LOW-AMPLITUDE VIBRATION TESTS  Components of the vibration measurement hardware are as follows: c  Sensors and Cables; Sensors convert the physical excitation into electrical signals. The current hardware measurement system has eight sensor connections capable of measuring eight different signals from eight different sensor locations or directions. These sensors are capable of measuring accelerations of up to ±0.5g with resolution of 0.2pg. Cables are used to transmit the electronic signals from sensors to the signal conditioner.  c  Signal Conditioner; The signal conditioner unit is used to improve the quality of the signals by removing undesired frequency contents (filtering) and amplifying the signals.  c  Analog/Digital Converter; The amplified and filtered analog signals are converted to digital data using an analog to digital converter before they are stored on the data acquisition computer. The analog to digital converter is controlled by the data acquisition computer using a custom program called A V D A (Ambient Vibration Data Acquisition), (Schuster, 1994). The analog to digital converter is capable of sampling up to eight channels at sampling frequencies between 0.2 Hz to 2000 Hz.  c  Data Acquisition Computer; Signals converted to digital form are stored on the hard disk of the data acquisition computer in binary form. The data can then be transferred to the data analysis computer where the numerical analyses of measured data can be carried out independently of the data acquisition processes.  6.4  VIBRATION ANALYSIS SOFTWARE PROGRAMS  The custom data acquisition program A V D A was used to record ambient and impact vibrations. The computer programs P2, U2, V2 (EDI, 1995) and FRF (Ventura and Horyna, 1995) were used to identify the natural frequencies and mode shapes of the steel plate shear wall specimens.  CHAPTER D  LOW-AMPLITUDE VIBRATION TESTS  The program P2 was developed to compute the Averaged Normalized Power Spectral Density (ANPSD) for a series of ambient vibration records. This function, ANPSD, is defined as the average of a group of / normalized power spectral densities (Felber 1993): i= l  ANPSDifj) = | X  i(fp  NPSD  (- ) 6  10  i=l  where NPSD(f-) is defined as:  PSD.(f.) NPSDty)  =  A  '  J  (6.11)  j= k where A = £ PSDftj), and f. is they'th discrete frequency, GLV = 2 TC/J., and & is the number  j=  1  of discrete frequencies. The index i refers to the ith power spectral density out of the total /. The peaks of the ANPSD were used to determine the natural frequency estimates, f., of the tested steel plate shear wall specimens. The program U2 was developed to analyse one or two sets of data obtained from vibration tests. U2 can compute the individual power spectral densities, cross spectrum, transfer function, phase angle, coherence function and the potential modal ratio function. It has a graphical display capability which enables the user to check the data very quickly during measurements and repeat data recordings if the signals are not satisfactory. The program V2 was developed in conjunction with the program U2 to illustrate and animate mode shapes obtained from ambient vibration data. Once all the potential modal ratio functions, Equation (6.8), have been computed, with respect to a reference sensor location, one can assemble and animate the mode shapes using the program V2. To accomplish this, the program uses two types of files: a structure file (*.str) defining the geometry of the structure and locations of all the measurements and a measurement file (*.mes) containing the potential modal ratio files and the direction of the modes (i.e. longitudinal, transverse or vertical). The program can then be used to assemble the potential modal ratios at a selected frequency into a  156  CHAPTER 6  LOW-AMPLITUDE VIBRATION TESTS  shape which can be displayed and animated. At the frequencies corresponding to the natural frequencies of the structure these animated shapes correspond to mode shapes. The mode shapes can then be printed or stored in a file. Peaks of the ANPSD which do not correspond to natural frequencies of the structure will fail to meet the appropriate phase and coherence cut off criteria placed upon them in the potential modal ratio functions and generate shapes that look very unnatural, quite unlike a mode shape. By verifying the modes associated with the natural frequencies of the structure visually, one can eliminate the abnormal peaks in the ANPSD and gain better understanding of the dynamic behaviour of the structure. The FRF program computes the frequency response function (magnitude and phase) along with the coherence function of an input and an output signal. The coherence function is a measure of how well correlated the input and output signals are. Clearly, if the quality of the measurements is ideal, for a linear system, the coherence should be unity unless there is unwanted noise present on either of the two signals which could degrade the calculated power spectra density functions.  6.5 UNIVERSITY OF ALBERTA VIBRATION TESTS The UofA vibration tests were performed in two phases. The first phase was performed at the early stage of the testing program before the specimen was attached to the loading and support mechanisms. This led to the information regarding the dynamic characteristics of the steel plate shear wall specimen alone, with no damage due to the application of external loading. After the shear wall specimen was loaded to failure in a gradually increasing load cycle history, the second phase of vibration tests was carried out to capture the effects of plate buckling, steel yielding and weld cracking or tearing on the dynamic characteristics of the shear wall frame specimen. The intent was to investigate whether any damage in the infill plates or the frame, such as buckling, tearing or cracking, would be reflected as a shift of modal frequencies in the frequency response function (FRF) of the system. Since the specimen was not loaded with  157  CHAPTER 6  LOW-AMPLITUDE VIBRATION TESTS  realistic storey masses and natural frequencies would thus be disproportionately high, the modal test results should be considered for comparative purposes only and should not be interpreted as absolute values. The sensitivity of natural frequencies and damping ratio to the structural damage was also investigated as part of the modal testing program.  6.5.1  Specimen Characteristics  The test specimen was a 50% scale model representing one bay of the lower four storeys of an office building. The typical storey height was 1.83 m for the top three storeys. The first storey was 1.94 m high. The columns, which were made of W310x118 wide flange sections of grade 300W steel, were kept constant throughout the frame. Medium depth wide flange beams, W310x60, were used for the bottom three storeys while a deep stiff beam, W530x82, was used above the top storey to anchor the tension field forces generated in the shear plate. The thicknesses of the shear wall infill panels were 4.54 mm, 4.65 mm, 3.35 mm and 3.40 mm in panels 1 to 4 from the bottom storey to the top storey, respectively. All the beam to column connections were fully welded to create fixed moment connections. The shear panels were continuously welded to the surrounding beams and columns by means of a fish plate connection detail.  6.5.2  Loading History  A load distribution beam was attached to the top of the columns, to apply a constant gravity load of 720 kN to each column throughout the test. Equal horizontal loads were applied at each storey level by means of hydraulic actuators, cycling between predetermined displacements of increasing amplitude. At the final stage of loading, the bottom shear plate sustained the most severe damage from buckling and yielding. Repeated folding caused several small tears in the plate which resulted in a gradual degradation of load carrying capacity and stiffness with increasing load cycles. Tears also developed in the corners where the shear panels were attached to the beams and  158  CHAPTER 6  LOW-AMPLITUDE VIBRATION TESTS  columns. All of the tears propagated very slowly as loads were redistributed to adjacent parts of the frame. A crack developed in the west column starting from the toe of the weld to the base plate during the 30th load cycle, resulting in a sudden load drop and termination of the test. Before this occurrence, the remaining load capacity of the frame was about 85% of the ultimate load and the unloading stiffness was about 88% of the initial elastic stiffness. More details on the test setup, the cyclic loading sequences and the load-deflection curves are available in Driver (1997).  6.5.3 Ambient Vibration Test Eight strong motion accelerometers were used for measurements of motions in each test, which required 4 setups for the ambient vibration tests. Figure 6.2 shows the location and direction of the ambient vibration measurements along the height of the shear wall frame. Three reference sensors were used during the ambient vibration tests, in the longitudinal, transverse and vertical directions. The remaining 5 accelerometers were moved to different locations for each test setup. Since the reference sensors were to be used to normalize the entire data set, it was important to have them located at a position of large relative motion. Furthermore, their location was assigned based on the approximate mode shapes of the structure and to ensure that the structure would exhibit motion at that particular location for all the natural frequencies of interest. The top left corner of the specimen was selected as the location for the reference sensors, as shown in Figure 6.2. The data was collected for a total of 11 stations (numbered 0 to 10 in Figure 6.2) in the longitudinal, transverse and vertical directions. Sensor 10 was attached to the floor about 10 m away from the specimen to measure the free field vibrations. It is noted that the number of recorded segments and length of each segment have an important effect on the quality of ambient vibration measurements. Thus, time-histories of length 8192x(16 segments) = 128k were recorded for each accelerometer. At each station, the 159  CHAPTER  D  LOW-AMPLITUDE  VIBRATION  TESTS  Location of the reference sensorsV 00 00  f • .. ."S <  . • .•.;. • I ;•'•"•' : j"* . ? 1 3  1  .C  '«  • -•  .03  1  00 CO  • i  :'"^vC,  Q •  '* •  i  CD V<s: g ^"^ •'• c o cs 9 : *  CO  00 00  I  -»—»  . . " • , • 3  ••  a  f • -. cs * i  .7  .;p.,«a  '• - ft: O s:,.  CD CO  cs **•: * •  • 1  OUT-OF-PLANE (Transverse)  10  - IN-PLANE (Longitudinal)  t IN-PLANE (Vertical)  Figure 6.2: Location of sensors and direction of measurements for the UofA test specimen •calibrations of the accelerometers were verified before each test. More details on the test can be found in Rezai et al. (1996). As mentioned earlier, because of the light mass of the test frame itself and no added external masses, the corresponding natural frequencies of the frame were expected to be high in the longitudinal direction. The sampling frequency was set at 1000 Hz meaning that for each one second of recording 1000, sample points were taken.  6.5.4  Impact Tests  Impact tests were performed by an impulse hammer that was instrumented with an integral  160  CHAPTER  6  LOW-AMPLITUDE  VIBRATION  TESTS  piezoelectric force sensor to measure the applied force. Two sets of hammer impacts were applied on the specimen at two different locations (at locations 2 and 4 in Figure 6.2) restricted to the longitudinal direction. Four consecutive hammer blows were struck at each location within an approximately 16 second time interval for a total of 64 seconds. The impacts at the top storey of the frame were applied to excite the frame mainly in the first mode, while impacts at the second storey were meant to induce some energy for the second mode of vibration. In both cases, however, it was expected that the first mode would be dominant. To capture the peaks of the hammer blows very accurately, the sampling time interval of the impact force transducer had to be very small, therefore the sampling frequency was selected at 1000 Hz. Time-histories of length 16384x(4 segments) = 64k were recorded for each hammer test setup. To investigate the effects of local cracking and diagonal buckling of the infill steel plates on the overall dynamic behaviour of the shear wall frame, impact tests were performed on the bottom storey shear plate during the first phase of the vibration measurements. After the frame was loaded to failure, severe damage was observed in the bottom storey plate and the surrounding columns. Thus, for the second phase of testing, the impact measurements were taken at the second storey plate. It is noted that evidence of yielding and buckling in the second storey infill plate together with cracking of welds at discrete points was observed. The plate was instrumented with accelerometers on a quarter point grid to determine the out-of-plane natural frequencies and mode shapes. Because of the small thicknesses of the plates, even a very slight strike of the hammer was found to saturate some of the accelerometers. The double sided tape that was used to fix the accelerometers to the plate proved to be less than satisfactory where the surface of the plate was rough, due to welding splatter or white wash. Nevertheless, three setups of hammer impacts were successfully performed on the plate during the first phase of testing. Only one setup was performed during the second phase of impact testing. More details on the testing procedure and  161  CHAPTER 6  LOW-AMPLITUDE VIBRATION TESTS  experimental and analytical results can be found in Rezai et al. (1996).  6.5.5 Natural Frequencies and Mode Shapes of the Specimen Response of the steel plate shear wall specimen for both impact and ambient vibration tests was measured in the two orthogonal directions: longitudinal and transverse. The natural frequencies and mode shapes of the specimen were obtained from the Fourier Transform of the time domain signals for the two stages of undamaged and damaged specimen. Since natural frequencies are proportional to the square root of stiffness, any structural degradation would result in a global decrease in natural frequencies. The frequency-domain relationships of the acceleration data recorded at each phase of the vibration tests are studied in the following.  6.5.5.1 Ambient Vibration Results The ANPSD plots of the acceleration time series were computed using the program P2. The longitudinal records were used to compute the longitudinal ANPSD while the transverse ANPSD was evaluated using the transverse records. The torsional ANPSD was computed by subtracting the time-histories of two accelerometers in the same horizontal level but at different sides of the frame. This was done because, if the motions of the two sides of the frame are in the opposite direction, then subtracting the signals will amplify the resulting signal as well as the corresponding torsional ANPSD peaks of the potential natural frequencies. The longitudinal, transverse and torsional ANPSD plots of the undamaged and damaged steel plate shear wall specimen are presented in Figure 6.3. As can be observed from the ANPSD plots, there are many peaks in each plot that have the potential of being one of the longitudinal, transverse, torsional or a combined natural frequency of the frame. In order to evaluate the relevancy of each peak in terms of the probable natural frequency and at the same time evaluate the corresponding mode shape, the programs U2 and V2 were employed. The potential modal ratio functions were calculated with the program U2 for the longitudinal and transverse directions. For a natural frequency, all the nodes should 162  CHAPTER 6  LOW-AMPLITUDE VIBRATION TESTS  Longitudinal Transverse Torsional  "1— —I— —I— —I— —I— —I— —I 1  60  70  80  90  1  1  1  1  1  100 110 120 130 140 150  Frequency (Hz) 1E + 3  -a  -1—I  0  10  20  30  I  I  40  1  I  50  1  I  1  60  I  1  70  I  1  80  I  1  90  I  100 110 120 130 140 150  Frequency(Hz) Figure 6.3: Longitudinal, transverse and torsional ANPSDs for the Uof A steel plate shear wall specimen a) undamaged b) damaged 163  CHAPTER 6  LOW-AMPLITUDE VIBRATION TESTS  move e