Applied Science, Faculty of
Civil Engineering, Department of
DSpace
UBCV
Bakhtavar, Mark S.
Master of Applied Science - MASc
University of British Columbia
Recorded motion of structures during recent earthquakes provide valuable information on the performance of various types of the buildings under seismic loading. This information can be used to evaluate the accuracy of structural analysis techniques and the efficiency of the current design methods. The objective of the first part of this study was to extract as much information as possible from the recorded motion of 11 well instrumented low-rise steel frame buildings in California, which experienced the 1987 Whittier, 1989 Loma Prieta, 1992 Landers and 1994 Northridge Earthquakes. The results showed that, in most cases, the periods of the buildings were significantly higher that those estimated by the code empirical formulae. Three of the buildings which had fundamental periods of greater than 1.0 second (with six to seven stories), behaved in a way that is usually expected from high-rise buildings. The second part of this research included computer modeling of one of the above mentioned structures, the Burbank 6-story office building, and comparing the anticipated response of the building using various analysis methods to the actual response, measured during the Whittier and Northridge earthquakes. The results indicated that proper modeling of the structure for a dynamic time-history analysis may predict the seismic response of the structures very accurately. A comparative study was performed to evaluate the accuracy and the efficiency of the various analysis techniques. At the end, Non-Linear Time-History Analysis was used to predict the performance of the Burbank 6-story office building, under higher levels of ground motion.
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SEISMIC BEHAVIOR & COMPUTER MODELING OF LOW-RISE STEEL FRAME STRUCTURES by Mark S. Bakhtavar B.Sc, Sharif University of Technology, 1991 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE D E G R E E OF MASTER OF APPLIED SCIENCE in T H E F A C U L T Y OF G R A D U A T E STUDIES Department of Civil Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA July, 2000 © Mark Bakhtavar, 2000 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 The University of British Columbia Vancouver, Canada DE-6 (2/88) ABSTRACT Recorded motion of structures during recent earthquakes provide valuable information on the performance of various types of the buildings under seismic loading. This information can be used to evaluate the accuracy of structural analysis techniques and the efficiency of the current design methods. The objective of the first part of this study was to extract as much information as possible from the recorded motion of 11 well instrumented low-rise steel frame buildings in California, which experienced the 1987 Whittier, 1989 Loma Prieta, 1992 Landers and 1994 Northridge Earth-quakes. The results showed that, in most cases, the periods of the buildings were significantly higher that those estimated by the code empirical formulae. Three of the buildings which had fundamental periods of greater than 1.0 second (with six to seven stories), behaved in a way that is usually expected from high-rise buildings. The second part of this research included computer modeling of one of the above mentioned structures, the Burbank 6-story office building, and comparing the anticipated response of the building using various analysis methods to the actual response, measured during the Whittier and Northridge earthquakes. The results indicated that proper modeling of the structure for a dynam-ic time-history analysis may predict the seismic response of the structures very accurately. A comparative study was performed to evaluate the accuracy and the efficiency of the various analysis techniques. At the end, Non-Linear Time-History Analysis was used to predict the performance of the Bur-bank 6-story office building, under higher levels of ground motion. i i T A B L E O F C O N T E N T S A B S T R A C T ii T A B L E O F C O N T E N T S iii LIST O F T A B L E S viii LIST O F FIGURES xii A C N O W L E D G E M E N T S xxvi D E D I C A T I O N xxvii Chapter 1 Introduction 1 1.1 General Remarks 1 1.2 Objectives 2 1.3 Scope of Work 2 Chapter 2 Background of the Project 4 2.1 Strong Motion Data 4 2.2 Previous Work 4 2.3 Demand for Further Studies 10 2.4 Selection of the Buildings »». 10 2.5 Earthquakes Considered in this Study 11 Chapter 3 Review of System Identification Techniques Used in the Project 12 3.1 Natural Vibration Frequencies 12 3.2 Mode shapes 14 3.3 Estimating Damping 14 3.4 Sources of Error and Reliability of the Results 15 3.5 Program "ME'scope" 17 iii 3.6 Verification of the Results of ME'scope 21 3.7 Three Dimensional Animation of the Mode Shapes 24 3.8 Introducing the Concept of "Spectral Response Function" 24 Chapter 4 Description of the Buildings Under Study 26 4.1 General 26 4.2 Burbank, 6-Story Office Building 29 4.3 San Bernardino 5-Story Hospital 31 4.4 Pasadena 6-Story Office Building 33 4.5 San Jose 3-Story Office Building 35 4.6 San Francisco 4-Story Hospital 37 4.7 Berkeley 2-Story Hospital 39 4.8 Richmond 3-Story Office Building 41 4.9 Redlands 7-Story Commercial Building 43 4.10 San Bernardino 3-Story Office Building 45 4.11 Los Angeles 2-Story Fire Command Control Building (Base-Isolated) 47 4.12 Los Angeles 7-Story University Hospital (Base-Isolated) 49 Chapter 5 Detailed Study Of The Recorded Response Of The Buildings 51 5.1 General 51 5.2 Burbank, 6-Story Office Building 53 5.2a Whittier Earthquake Records 53 5.2b Northridg Earthquake Records 68 5.3 San Bernardino 5-Story Hospital 84 5.4 Pasadena 6-Story Office Building 101 iv 5.5 San Jose 3-Story Office Building 117 5.6 San Francisco 4-Story Hospital 134 5.7 Berkeley 2-Story Hospital 149 5.8 Richmond 3-Story Office Building 162 5.9 Redlands 7-Story Commercial Building 177 5.10 San Bernardino 3-Story Office Building 193 5.11 Los Angeles 2-Story Fire Command Control Building 208 5.12 Los Angeles 7-Story University Hospital 221 Chapter 6 Discussion Of The Information Obtained From Strong Motion Data 237 6.1 General 237 6.2 Properties of the Ground Motions 237 6.3 Three-Dimensional Nature of the Ground Motion and the Response of the Buildings 238 6.4 Rotational Ground Motion 238 6.5 Vertical Ground Motion 239 6.6 Amplification of the Motion 241 6.7 Comparison of Measured Periods to those Estimated by Code Empirical Formulae 242 6.8 Periods Measured by Other Researchers 244 6.9 Contribution of the Higher Modes 246 6.10 Error Due to Manipulation of the Data 247 6.11 Mode Shapes 248 6.12 Base-Isolated Buildings 249 6.13 Damping Ratios 250 6.14 Modal Acceleration Amplification Factors 250 Chapter 7 Computer Modeling of the Burbank 6-Story Office Building 251 7.1 Introduction 251 7.2 Structural System 251 7.3 Estimated Weight of the Building 256 7.4 Description of the Structural Model 257 7.5 Description of the Structural Analysis Program C A N N Y - E 258 7.6 Analysis Parameters used in the CANNY-E Model 259 7.7 Modified Linear Elastic Model (ETABS Model) 260 Chapter 8 Dynamic Analysis of the Burbank 6-Story Office Building 262 8.1 General 262 8.2 Definition of the Structural Models used for the Analyses 262 8.3 Results of Analysis Based on Whittier Earthquake Records . 263 8.4 Results of Analysis Based on Northridge Earthquake Records 272 8.5 Comparison of the Results of Various-Linear Elastic Analysis Methods 289 8.6 Non-Linear Analysis Using Ground Motions Stronger than those Recorded during the Northridge Earthquake 301 Chapter 9 Discussion of the Results of the Analysis of the Burbank 6-story office Building 308 9.1 General Remarks 308 9.2 Possible Structural Damage during the Northridge Earthquake 309 9.3 Effect of the Higher Modes on the Response 310 9.4 Response Spectrum Analysis versus Time-history Analysis . . . . . . . 310 9.5 Spectral Analysis with Code Design Response Spectra 310 vi 9.6 Non-Linear Time-History Analysis 311 9.7 Effect of Damping Value 311 9.8 Non-Linear Static (Push-over) Analysis 312 Chapter 10 Conclusions 313 10.1 Behaviour of the Buildings 313 10.2 Analysis Techniques 314 R E F E R E N C E S 316 Appendix A Separated floor acceleration plots of selected Building 320 Appendix B Samples of ME'scope outputs 327 Appendix C Selected parts of the Canny-e input file for Model A 337 Appendix D C D - R O M Including input and out put files of Canny-e and Etabs, spread sheets of the figures and text files 349 vii LIST OF TABLES Table 3.1 Comparison of the vibration properties of the SAP90 model and the values estimated based on the output time histories using the ME'scope 23 Table 4.1 List of buildings under study 26 Table 4.2 General description of the buildings under study 27 Table 5.2a.1 Results of Frequency Response Functions for the Burbank 6-story bldg., obtained from the 1987 Whittier EQ records : . 66 Table 5.2a.l Results of Spectral Response Functions for the Burbank 6-story bldg., obtained from the 1987 Whittier EQ records 67 Table 5.2b.l Results of Frequency Response Functions for the Burbank 6-story bldg., obtained from the 1987 Northridge E Q records 81 Table 5.2b.l Results of Spectral Response Functions for the Burbank 6-story bldg., obtained from the 1987 Northridge EQ records 82 Table 5.2.3 Estimated natural frequencies (and periods) of the Burbank 6-story bldg. based on the results of FRF results, SRF results and visual inspection of the three dimensional mode shapes obtained from analysis of 1987 Whittier and 1994 Northridge EQ data 83 Table 5.3.1 Results of Frequency Response Functions for the San Bernardino 5-story hospital, obtained from the 1994 Northridge EQ records 98 Table 5.3.2 Results of Spectral Response Functions for the San Bernardino 5-story hospital, ob-tained from the 1994 Northridge EQ records 99 Table 5.3.3 Estimated natural frequencies (and periods) of the San Bernardino 5-story hospital based on the results of FRF results, SRF results and visual inspection of the three dimensional mode shapes obtained from analysis of 1994 Northridge EQ data 100 Table 5.4.1 Results of Frequency Response Functions for the San Bernardino 5-story hospital, obtained from the 1994 Northridge EQ records 114 Table 5.4.2 Results of Spectral Response Functions for the San Bernardino 5-story hospital, ob-tained from the 1994 Northridge EQ records 115 Table 5.4.3 Estimated natural frequencies (and periods) of the Pasadena 6-story office building based on the results of FRF results, SRF results and visual inspection of the three dimensional mode shapes obtained from analysis of 1994 Northridge EQ data 116 Vlll Table 5.5.1 Results of Frequency Response Functions for the San Jose 3-story office bldg., obtained from the 1989 Loma Prieta EQ records 131 Table 5.5.2 Results of Spectral Response Functions for the San Jose 3-story office bldg., ob-tained from the 1989 Loma Prieta EQ records 132 Table 5.5.3 Estimated natural frequencies (and periods) of the San Jose 3-story office bldg. based on the results of FRF results, SRF results and visual inspection of the three dimensional mode shapes obtained from analysis of 1989 Loma Prieta EQ data 133 Table 5.6.1 Results of Frequency Response Functions for the San Francisco 4-story hospital, ob-tained from the 1989 Loma Prieta EQ records 146 Table 5.6.2 Results of Spectral Response Functions for the San Francisco 4-story hospital, ob-tained from the 1989 Loma Prieta EQ records 147 Table 5.6.3 Estimated natural frequencies (and periods) of the San Francisco 4-story hospital, based on the results of FRF results, SRF results and visual inspection of the three dimensional mode shapes obtained from analysis of 1989 Loma Prieta EQ data 148 Table 5.7.1 Results of Spectral Response Functions for the Berkeley 2-story hospital, obtained from the 1989 Loma Prieta EQ records 161 Table 5.7.2 Estimated natural frequencies (and periods) of the Berkeley 2-story hospital, based on the results of FRF results and visual inspection of the three dimensional mode shapes obtained from analysis of 1989 Loma Prieta EQ data 161 Table 5.8.1 Results of Frequency Response Functions for the Richmond 3-story office bldg., ob-tained from the 1989 Loma Prieta EQ records 175 Table 5.8.2 Results of Spectral Response Functions for the Richmond 3-story office bldg., ob-tained from the 1989 Loma Prieta EQ records 175 Table 5.8.3 Estimated natural frequencies (and periods) of the Richmond 3-story office bldg. based on the results of FRF results, SRF results and visual inspection of the three dimensional mode shapes obtained from analysis of 1989 Loma Prieta EQ data 176 Table 5.9.1 Results of Frequency Response Functions for the Redlands 7-story commercial bldg., obtained from the 1992 Landers EQ records 191 Table 5.9.2 Results of Spectral Response Functions for the Redlands 7-story commercial bldg., obtained from the 1992 Landers EQ records 191 Table 5.9.3 Estimated natural frequencies (and periods) of the Redlands 7-story commercial bldg., based on the results of FRF results, SRF results and visual inspection of the three dimen-sional mode shapes obtained from analysis of 1992 Landers EQ data 192 I X Table 5.10.1 Estimated natural frequencies (and periods) of the San Bernardino 3-story office bldg., based on the results of FRF results, SRF results and visual inspection of the three dimen-sional mode shapes obtained from analysis of 1992 Landers EQ data 207 Table 5.11.1 Estimated natural frequencies (and periods) of the L A 2-story fire control bldg., based on the FRF results and visual inspection of the three dimensional mode shapes obtained from analysis of 1994 Northridge EQ data 220 Table 5.12.1 Estimated natural frequencies (and periods) of the L A 7-story university hospital, based on the of FRF results and visual inspection of the three dimensional mode shapes obtained from analysis of 1994 Northridge EQ data 236 Table 6.1 Comparison of the peak ground accelerations of the buildings in various directions and heir epicentral distances 240 Table 6.2 Comparison of the measured periods to those estimated by code empirical formulae . 243 Table 6.3 Measured periods for steel moment frame buildings (after Goel and Chopra 1997) . . 244 Table 6.4 Measured periods for the San Francisco 4-story hospital (after Fenves 1990) . . 245 Table 6.5 Measured frequencies for the Richmond 3-story office building (after De la LLera and Chopra 1991) 245 Table 6.6 Periods measured for the Richmond 3-story bldg. and the San Jose 3-story bldg. (after De la Llera and Chopra 1992) 245 Table 6.7 Measured periods from forced vibration measurements for a two story office bldg. (with no basement) in Oakland (after McClure, 1991) 246 Table 6.8 Measured periods for steel moment frame buildings (after Cole et al. 1992) . . . 246 Table 7.3.1 Estimated floor weights and rotational moments of inertia of Burbank 6-story build-ing 257 Table 8.3.1 Natural frequencies and periods of model B 264 Table 8.3.2 Maximum story shears and overturning moments, time-history analysis of Model B with the ground accelerations obtained from the Whittier E Q records 269 Table 8.3.3 Maximum floor displacements and story drift ratios, time-history analysis of model B with the ground accelerations obtained from the Whittier EQ records 269 Table 8.3.4 Maximum Forces in the South-West corner column and the beams connected to it in E-W (X-dir), time-history analysis of Model B with the ground accelerations obtained from the Whittier E Q records . . 270 Table 8.4.1 Natural frequencies and periods of Model A 273 Table 8.4.2 Maximum story shears and overturning moments, time-history analysis of Model A with the ground accelerations obtained from the Northridge EQ data 282 Table 8.4.3 Maximum floor displacements and story drift ratios, time-history analysis of Model A with the ground accelerations obtained from the Northridge E Q data 282 Table 8.4.4 Maximum forces in the South-West corner column and the beams connected to it in E-W (X-dir), time-history analysis of Model A with the ground accelerations obtained from the Northridge E Q data 283 Table 8.5.1 Vertical distribution of seismic loads for Static Analysis 293 Table 8.5.2 Natural frequencies and periods of Model C 294 Table 8.5.3 Effective mass factors of Model C 294 Table 8.5.4 Dynamic response spectrum base shears of individual (X direction) modes of Mod-els C2 to C5 295 Table 8.5.5 Comparison of maximum story shears of Models CI to C6 296 Table 8.5.6 Comparison of maximum floor overturning moments of Models CI to C6 . . 296 Table 8.5.7 Comparison of maximum floor displacements of Models C I to C6 298 Table 8.5.8 Comparison of maximum inter-story drift ratios of Models CI to C6 298 Table 8.5.9 Comparison of maximum forces in the South-West corner column, obtained from the analyses of Models CI to C6 299 Table 8.5.10 Comparison of Maximum Forces in the perimeter beams of the first span from West at the South edge of the building 300 Table 8.6.1 Comparison of maximum floor displacements and base shears of non-linear and lin-ear models 303 Table 8.6.2 Comparison of maximum inter-story drifts of non-linear and linear models. . 303 Table 8.6.3 Comparison of ductility factors of dynamic and static analyses 304 Table 8.6.4 The vertical distribution factors of the lateral loads, used for nonlinear static (Push-Over) analysis of model PL-A-ST 307 X I LIST OF FIGURES Figure 3.1 Displacement Response factor and phase angle for a damped system excited by har-monic force (after Chopra, 1995) 13 Figure 3.2 Definition of half-power bandwidth (After Chopra, 1995) 14 Figure 3.3 Example of recorded time-histories, Record length T = 60sec, At = 0.02sec, N = 3000 19 Figure 3.4 Fourier Spectra of example Records A & B computed using a Hanning window, a block size N= 2048, 5 averages and 88% segment overlap 19 Figure 3.5 Example of Frequency Response Function (B / A) calculated with 5 averages. . 20 Figure 3.6 Example of Frequency Response Function (B / A) calculated without averaging20 Figure 3.7 The SAP90 model used to verify the accuracy of the results of ME'scope 22 Figure 3.8 An example of the FRF's calculated from the time histories generated by SAP9022 Figure 3.9 An example Spectral Response Function obtained from 0 % and 1 % damping re-sponse spectra 25 Figure 4.1 Location of the buildings and the epicenter of the earthquakes 28 Figure 4.2 Overview of Burbank 6-Story Building and Sensor layout, (After Shakal, et al., 1987) 30 Figure 4.3 Overview of San Bernardino 5-Story Hospital and Sensor layout, (After Shakal, et al., 1994) 32 Figure 4.4 Overview of Pasadena 6-Story Office Building and Sensor layout, (After Shakal, et al., 1994) 34 Figure 4.5 Overview of San Jose 3-Story Office Building and Sensor layout, (After Shakal, et al , 1989) 36 Figure 4.6 Overviewof SanFrancisco4-Story Hospital and Sensorlayout, (After Shakal, etal ,1989) 38 Figure 4.7 Overview of Berkeley 2-Story Hospital and Sensor layout, (After Shakal, et al , 1989) 40 Figure 4.8 Overview of Richmond 3-Story Office Building and Sensor layout, (After Shakal, et al , 1989) 42 xn Figure 4.9 Overview of Redlands 7-Story Commercial Building and Sensor layout, (After Shakal, et al., 1992) 44 Figure 4.10 Overview of San Bernardino 3-Story Office Building and Sensor layout, (After Shakal, et al., 1992) 46 Figure 4.11 Overview of L A 2-Story Fire Control Building and Sensor layout, (After Shakal, et al, 1994) 48 Figure 4.12 Overview of L A 7-Story University Hospital and Sensor layout, (After Shakal, et al, 1994) 50 Figure 5.2a.l Accelerations recorded at the Burbank 6-story bldg, during the 1987 Whittier Earthquake (After Shakal, et al , 1987) 54 Figure 5.2a.2 Time-history and spectral characteristics of E-W (X) component of the ground motion recorded at the Burbank 6-story bldg, during the 1978 Whittier E Q 55 Figure 5.2a.3 Time-history and spectral characteristics of N-S (Y) component of the ground mo-tion recorded at the Burbank 6-story bldg, during the 1978 Whittier EQ 56 Figure 5.2a.4 Time-history and spectral characteristics of rotational (R) component of the ground motion recorded at the Burbank 6-story bldg, during the 1978 Whittier E Q 57 Figure 5 E-W (X-direction) & N-S (Y-direction) absolute accelerations of the instrumented up-per floors of the Burbank 6-story bldg, during the 1987 Whittier EQ 58 Figure 5.2a.6 E-W (X-direction) & N-S (Y-direction) relative displacements of the instrument-ed upper floors of the Burbank 6-story bldg, during the 1987 Whittier E Q 59 Figure 5.2a.7 Torsional response of the instrumented upper floors of the Burbank 6-story bldg, during 1987 Whittier EQ. (See section 5.1 for explanation on obtaining the rotational data.)60 Figure 5.2a.8 Orbital displacements at the center of the instrumented floors of the Burbank 6-story bldg, during the 1987 Whittier EQ 61 Figure 5.2a.9 Representation of Hysteretic behaviour at the instrumented floors of the Burbank 6-story bldg, during the 1987 Whittier EQ 62 Figure 5.2a.l0 Frequency Response Functions of the instrumented floors of the Burbank 6-Sto-ry Bldg, obtained from the 1987 Whittier EQ records 63 Figure5.2a.llModeshapesoftheBurbank6-storybldg,obtainedfromthel987WhittierEQrecords 64 xiii Figure 5.2a.l2 Spectral Response Functions of the Burbank 6-story bldg, obtained from the 1987 Whittier E Q records 65 Figure 5.2b.l Accelerations recorded at the Burbank 6-story bldg, during the 1994 Northridge EQ. (After Shakal, et al, 1994) 69 Figure 5.2b.2 Time-history and spectral characteristics of E-W (X) component of the ground motion recorded at the Burbank 6-story bldg, during the 1994 Northridge E Q 70 Figure 5.2b.3 Time-history and spectral characteristics of N-S (Y) component of the ground mo-tion recorded at the Burbank 6-story bldg, during the 1994 Northridge E Q 71 Figure 5.2b.4 Time-history and spectral characteristics of rotational (R) component of the ground motion recorded at the Burbank 6-story bldg, during the 1994 Northridge E Q . . . . 72 Figure 5.2b.5 E-W (X-direction) & N-S (Y-direction) absolute accelerations of the instrumented upper floors of the Burbank 6-story bldg, during the 1994 Northridge EQ 73 Figure 5.2b.6 E-W (X-direction) & N-S (Y-direction) relative displacements of the instrument-ed upper floors of the Burbank 6-story bldg, during the 1994 Northridge E Q 74 Figure 5.2b.7 Torsional response of the instrumented upper floors of the Burbank 6-story bldg, during the 1994 Northridge EQ 75 Figure 5.2b.8 Orbital displacements at the center of the instrumented floors of the Burbank 6-story bldg, during the 1994 Northridge EQ 76 Figure 5.2b.9 Representation of hysteretic behaviour at the instrumented floors of the Burbank 6-story bldg, during the 1994 Northridge EQ 77 Figure 5.2b.l0 Frequency Response Functions of the instrumented floors of the Burbank 6-story bldg, obtained from the 1994 Northridge EQ records 78 Figure 5.2b.ll Mode shapes of the Burbank 6-story bldg, obtained from the 1994 Northridge EQ records 79 Figure 5.2a.l2 Spectral Response Functions of the Burbank 6-story bldg, obtained from the 1994 Northridge E Q records 80 Figure 5.3.1 Accelerations recorded at the San Bernardino 5-story hospital during the 1994 Northridge Earthquake. (After Shakal, et al , 1994) 85 Figure 5.3.2 Ground motion properties, E-W (X-direction), San Bernardino 5-story hospital, Northridge EQ 86 xiv Figure 5.3.3 Time-history and spectral characteristics of N-S (Y) component of the ground mo-tion recorded at the San Bernardino 5-story hospital during the 1994 Northridge E Q 87 Figure 5.3.4 Time-history and spectral characteristics of rotational (R) component of the ground motion recorded at the San Bernardino 5-story hospital during the 1994 Northridge E Q . . . 88 Figure 5.3.5 Absolute accelerations of the instrumented upper floors of the San Bernardino 5-story hospital during the 1994 Northridge EQ 89 Figure 5.3.6 Relative displacements of the instrumented upper floors of the San Bernardino 5-story hospital during the 1994 Northridg EQ 91 Figure 5.3.7 Orbital displacements at the center of the instrumented floors of the San Bernardino 5-story hospital during the 1994 Northridge EQ 93 Figure 5.3.8 Representation of hysteretic behaviour at the instrumented floors of the San Ber-nardino 5-story hospital during the 1994 Northridge EQ 94 Figure 5.3.9 Frequency Response Functions of the instrumented floors of the San Bernardino 5-story hospital, obtained from the 1994 Northridge EQ records 95 Figure 5.3.10 Mode shapes of (L-shape presentation of) the San Bernardino 5-story hospital, ob-tained from the 1994 Northridge EQ records 96 Figure 5.3.11 Spectral Response Functions of the San Bernardino 5-story hospital, obtained from the 1994 Northridge EQ records 97 Figure 5.4.1 Accelerations recorded at the Pasadena 6-story office building during the 1994 Northridge Earthquake, (After Shakal, etal, 1994) 102 Figure 5.4.2 Time-history and spectral characteristics of E-W (X) component of the ground mo-tion recorded at the Pasadena 6-story office bldg. during the 1994 Northridge EQ 103 Figure 5.4.3 Time-history and spectral characteristics of N-S (Y) component of the ground mo-tion recorded at the Pasadena 6-story office bldg. during the 1994 Northridge EQ 104 Figure 5.4.4 Time-history and spectral characteristics of rotational (R) component of the ground motion recorded at the Pasadena 6-story office bldg. during the 1994 Northridge E Q . . . . 105 Figure 5.4.5 Absolute accelerations of the instrumented upper floors of the Pasadena 6-story of-fice bldg, during the 1994 Northridge EQ 106 Figure 5.4.6 Relative displacements of the instrumented upper floors of the Pasadena 6-story of-fice bldg. during the 1994 Northridge EQ 107 X V Figure 5.4.7 Orbital displacements at the center of the instrumented floors of the Pasadena 6-story office bldg. during the 1994 Northridge EQ 108 Figure 5.4.8 Representation of hysteretic behaviour at the instrumented floors of the Pasadena 6-story office bldg, during the 1994 Northridge EQ 109 Figure 5.4.9a Frequency Response Functions of the instrumented floors of the Pasadena 6-story office bldg, obtained from the 1994 Northridge E Q Records. (With 5 averages) 110 Figure 5.4.9b Frequency Response Functions of the instrumented floors of the Pasadena 6-story office bldg, obtained from the 1994 Northridge EQ records. (With 20 averages) I l l Figure 5.4.10 Mode shapes of the Pasadena 6-story office bldg, obtained from the 1994 Northridge E Q records 112 Figure 5.4.11 Spectral Response Functions of the Pasadena 6-story office bldg, obtained from the 1994 Northridge EQ records 113 Figure 5.5.1 Accelerations recorded at the San Jose 3-story office building during the 1989 Loma Prieta EQ. (After Shakal, et al, 1989) 118 Figure 5.5.2 Time-history and spectral characteristics of E-W (X) component of the free field motion recorded at the Sari Jose 3-story office bldg, during the 1989 Loma Prieta EQ . . . 119 Figure 5.5.3 Time-history and spectral characteristics of N-S (Y) component of the free field motion recorded at the San Jose 3-story office bldg, during the 1989 Loma Prieta EQ . . . 120 Figure 5.5.4 Time-history and spectral characteristics of E-W (X) component of the ground mo-tion recorded at the San Jose 3-story office bldg, during the 1989 Loma Prieta E Q 121 Figure 5.5.5 Time-history and spectral characteristics of N-S (Y) component of the ground mo-tion recorded at the San Jose 3-story office bldg, during the 1989 Loma Prieta E Q 122 Figure 5.5.6 Time-history and spectral characteristics of rotational (R) component of the ground motion recorded at the San Jose 3-story office bldg, during the 1989 Loma Prieta E Q . . . 123 Figure 5.5.7 Absolute accelerations of the instrumented upper floors of the San Jose 3-story of-fice bldg, during the 1989 Loma Prieta EQ 124 Figure 5.5.8 Relative displacements of the instrumented upper floors of the San Jose 3-story of-fice bldg, during the 1989 Loma Prieta EQ 125 Figure 5.5.9 Orbital displacements at the center of the instrumented floors of the San Jose 3-story office bldg, during the 1989 Loma Prieta EQ 126 XV I Figure 5.5.10 Representation of hysteretic behaviour at the instrumented floors of the San Jose 3- story office bldg, during the 1989 Loma Prieta EQ 127 Figure 5.5.11 Frequency Response Functions of the instrumented floors of the San Jose 3-story office bldg, obtained from the 1989 Loma Prieta EQ records 128 Figure 5.5.12 Mode shapes of the San Jose 3-story office bldg, obtained from the 1989 Loma Prieta EQ records 129 Figure 5.5.13 Spectral Response Functions of the San Jose 3-story office bldg, obtained from the 1989 Loma Prieta EQ records 130 Figure 5.6.1 Accelerations recorded at the San Francisco 4-story hospital during the 1989 Lo-maPrieta EQ. (After Shakal, et al, 1989) 135 Figure 5.6.2 Time-history and spectral characteristics of E-W (X) component of the ground mo-tion recorded at the San Francisco 4-story hospital, during the 1989 Loma Prieta E Q . . . . 136 Figure 5.6.3 Time-history and spectral characteristics of N-S (Y) component of the ground mo-tion recorded at the San Francisco 4-story hospital, during the 1989 Loma Prieta E Q . : . . 137 Figure 5.6.4 Time-history and spectral characteristics of rotational (R) component of the ground motion recorded at the San Francisco 4-story hospital, during the 1989 Loma Prieta E Q .138 Figure 5.6.5 Absolute accelerations of the instrumented upper floors of the San Francisco 4-sto-ry hospital, during the 1989 Loma Prieta EQ 139 Figure 5.6.6 Relative displacements of the instrumented upper floors of the San Francisco 4-sto-ry hospital, during the 1989 Loma Prieta EQ 140 Figure 5.6.7 Orbital displacements at the center of the instrumented floors of the San Francisco 4- story hospital, during the 1989 Loma Prieta EQ 141 Figure 5.6.8 Representation of hysteretic behaviour at the instrumented floors of the San Fran-cisco 4-story hospital, during the 1989 Loma Prieta EQ 142 Figure 5.6.9 Frequency Response Functions of the instrumented floors of the San Francisco 4-story hospital, obtained from the 1989 Loma Prieta EQ records 143 Figure 5.6.10 Mode shapes of the San Francisco 4-story hospital, obtained from the 1989 Loma Prieta EQ records 144 Figure 5.6.11 Spectral Response Functions of the San Francisco 4-story hospital, obtained from the 1989 Loma Prieta EQ records 145 xvii Figure 5.7.1 Accelerations recorded at the Berkeley 2-story hospital during the 1989 Loma Pri-eta EQ. (After Shakal, et al , 1989) 150 Figure 5.7.2 Time-history and spectral characteristics of E-W (X) component of the ground mo-tion recorded at the Berkeley 2-story hospital, during the 1989 Loma Prieta EQ 151 Figure 5.7.3 Time-history and spectral characteristics of N-S (Y) component of the ground mo-tion recorded at the Berkeley 2-story hospital, during the 1989 Loma Prieta EQ 152 Figure 5.7.4 Time-history and spectral characteristics of rotational (R) component of the ground motion recorded at the Berkeley 2-story hospital, during the 1989 Loma Prieta EQ 153 Figure 5.7.5 Absolute accelerations of the upper floors of the Berkeley 2-story hospital, during the 1989 Loma Prieta EQ 154 Figure 5.7.6 Relative displacements of the upper floors of the Berkeley 2-story hospital, during the 1989 Loma Prieta EQ 155 Figure 5.7.7 Orbital displacements at the center of the floors of the Berkeley 2-story hospital, during the 1989 Loma Prieta EQ 156 Figure 5.7.8 Representation of hysteretic behaviour at the instrumented floors of the Berkeley 2-story hospital, during the 1989 Loma Prieta EQ 157 Figure 5.7.9 Frequency Response Functions of the Berkeley 2-story hospital, obtained from the 1989 Loma Prieta EQ records 158 Figure 5.7.10 Mode shapes of the Berkeley 2-story hospital, obtained from the 1989 Loma Pri-eta EQ records 159 Figure 5.7.11 Spectral Response Functions of the Berkeley 2-story hospital, obtained from the 1989 Loma Prieta E Q records 160 Figure 5.8.1 Accelerations recorded at the Richmond 3-story office building, during the 1989 Loma Prieta EQ. (After Shakal, et al, 1989) 163 Figure 5.8.2 Time-history and spectral characteristics of E-W (X) component of the ground mo-tion recorded at the Richmond 3-story office building, during the 1989 Loma Prieta EQ. . 164 Figure 5.8.3 Time-history and spectral characteristics of N-S (Y) component of the ground mo-tion recorded at the Richmond 3-story office building, during the 1989 Loma Prieta E Q . 165 Figure 5.8.4 E-W (X-direction) & N-S (Y-direction) absolute accelerations of the upper floors of the Richmond 3-story office bldg, during the 1989 Loma Prieta EQ 166 XVlll Figure 5.8.5 E-W (X-direction) & N-S (Y-direction) relative displacements of the upper floors of the Richmond 3-story office bldg, during the 1989 Loma Prieta EQ 167 Figure 5.8.6 Torsional response of the Richmond 3-story office bldg, during the 1989 Loma Prieta EQ 168 Figure 5.8.7 Orbital displacements at the center of the floors of the Richmond 3-story office bldg, during the 1989 Loma Prieta EQ 169 Figure 5.8.8 Representation of hysteretic behaviour at the instrumented floors of the Richmond 3-story office bldg, during the 1989 Loma Prieta EQ 170 Figure 5.8.9 Frequency Response Functions of the instrumented floors of the Richmond 3-story office bldg, obtained from the 1989 Loma Prieta EQ records 171 Figure 5.8.10 Mode shapes of the Richmond 3-story office bldg, obtained from the 1989 Loma Prieta EQ records 173 Figure 5.8.11 Spectral Response Functions of the Richmond 3-story office bldg, obtained from the 1989 Loma Prieta EQ records 174 Figure 5.9.1 Accelerations recorded at the Redlands 7-story commercial bldg, during the 1992 Landers Earthquake (After Shakal, et al , 1992) 178 Figure 5.9.2 Time-history and spectral characteristics of E-W (X) component of the ground mo-tion recorded at the Redlands 7-story commercial bldg, during the 1992 Landers E Q . . . . 180 Figure 5.9.3 Time-history and spectral characteristics of N-S (Y) component of the ground mo-tion recorded at the Redlands 7-story commercial bldg, during the 1992 Landers E Q . . . . 181 Figure 5.9.4 Time-history and spectral characteristics of rotational (R) component of the ground motion recorded at the Redlands 7-story commercial bldg, during the 1992 Landers E Q . 182 Figure 5.9.5 E-W (X-direction) & N-S (Y-direction) absolute accelerations of the instrumented upper floors of the Redlands 7-story commercial bldg, during the 1992 Landers E Q . . . . 183 Figure 5.9.6 E-W (X-direction) & N-S (Y-direction) relative displacements of the instrumented upper floors of the Redlands 7-story commercial bldg, during the 1992 Landers EQ . . . . 184 Figure 5.9.7 Torsional response of the instrumented upper floors of the Redlands 7-story com-mercial bldg, during the 1992 Landers EQ 185 Figure 5.9.8 Orbital displacements at the center of the instrumented floors of the Redlands 7-story commercial bldg, during the 1992 Landers EQ 186 xix Figure 5.9.9 Representation of hysteretic behaviour at the instrumented floors of the Redlands 7-story commercial bldg, during the 1992 Landers EQ 187 Figure 5.9.10 Frequency Response Functions of the instrumented floors of the Redlands 7-story commercial bldg, obtained from the 1992 Landers EQ records 188 Figure 5.9.11 Mode shapes of the Redlands 7-story commercial bldg, obtained from the 1992 Landers E Q records 189 Figure 5.9.12 Spectral Response Functions of the Redlands 7-story commercial bldg, obtained from the 1992 Landers EQ records 190 Figure 5.10.1 Accelerations recorded at the San Bernardino 3-story office bldg, during the 1992 Landers Earthquake (After Shakal, et al , 1992) 194 Figure 5.10.2 Time-history and spectral characteristics of E-W (X) component of the ground motion recorded at the San Bernardino 3-story office bldg, during the 1992 Landers E Q . 196 Figure 5.10.3 Time-history and spectral characteristics of N-S (Y) component of the ground mo-tion recorded at the San Bernardino 3-story office bldg, during the 1992 Landers E Q . . . 197 Figure 5.10.4 E-W (X-direction) & N-S (Y-direction) absolute accelerations of the upper floors of the San Bernardino 3-story office bldg, during the 1992 Landers E Q 198 Figure 5.10.5 E-W (X-direction) & N-S (Y-direction) relative displacements of the upper floors of the San Bernardino 3-story office bldg, during the 1992 Landers E Q 199 Figure 5.10.6 Torsional response of the upper floors of the San Bernardino 3-story office bldg, during the 1992 Landers EQ 200 Figure 5.10.7 Orbital displacements at the center of the floors of the San Bernardino 3-story of-fice bldg, during the 1992 Landers EQ 201 Figure 5.10.8 Representation of hysteretic behaviour of the San Bernardino 3-story office bldg, during the 1992 Landers E Q 202 Figure 5.10.9 Frequency Response Functions of the San Bernardino 3-story office bldg, ob-tained from the 1992 Landers EQ records 203 Figure 5.10.10 Mode shapes of the San Bernardino 3-story office bldg, obtained from the 1992 Landers E Q records 205 Figure 5.10.11 Spectral Response Functions of the San Bernardino 3-story office bldg, obtained from the 1992 Landers EQ records . 206 X X Figure 5.11.1 Accelerations recorded at the L A 2-story fire control bldg. during the 1994 Northridge EQ (After Shakal, et al, 1994) 209 Figure 5.11.2 Acceleration time histories of free field, foundation (below isolators) and base (above isolators) at the L A 2-story fire control bldg, during the 1994 Northridge E Q . . . . 210 Figure 5.11.3 Normalized Fourier Spectrum of accelerations of free field, foundation (below isolators) and base (above isolators) at the L A 2-story fire control bldg, during the 1994 Northridge E Q 211 Figure 5.11.4 Pseudo acceleration response spectra of the motion of free field, foundation (be-low isolators) and base (above isolators) at the L A 2-story fire control bldg, during the 1994 Northridge EQ 212 Figure 5.11.5 E-W (X) component of the response of the L A 2-story fire control bldg, during the 1994 Northridge EQ 213 Figure 5.11.6 N-S (Y) component of the response of the L A 2-story fire control bldg, during the 1994 Northridge EQ 214 Figure 5.11.7 Orbital displacements at the center of the instrumented floors of the L A 2-story fire control bldg, during the 1994 Northridge EQ 215 Figure 5.11.8 Frequency Response Functions of the roof with respect to first floor (above isola-tors) of the L A 2-story fire control bldg, obtained from the 1994 Northridge E Q records .216 Figure 5.11.9 Frequency Response Functions of the roof and first floor with respect to the foun-dation (below isolators) of the L A 2-story fire control bldg, obtained from the 1994 Northridge EQ records 217 Figure 5.11.10 Mode shapes of the superstructure the L A 2-story fire control bldg. (without iso-lators), obtained from the 1994 Northridge records 218 Figure 5.11.11 Mode shapes of the L A 2-story fire control bldg. (with an extra story at the bot-tom representing the deformation of the isolators), obtained based on Northridge EQ Records .. 219 Figure 5.12.1 Accelerations recorded at L A 7-story university hospital, during the 1994 Northridge EQ. (After Shakal, et al , 1994) 222 Figure 5.12.2 Acceleration time histories of free field, foundation (below isolators) and base (above isolators) at the L A 7-story university hospital, during the 1994 Northridge E Q . . 224 Figure 5.12.3 Normalized Fourier Spectrum of accelerations of free field, foundation (below isolators) and base (above isolators) at the L A 7-story university hospital, during the 1994 Northridge EQ 225 XXI Figure 5.12.4 Pseudo acceleration response spectra of the motion of free field, foundation (be-low isolators) and base (above isolators) at the L A 7-story university hospital, during the 1994 Northridge EQ 226 Figure 5.12.5 E-W (X-direction) & N-S (Y-direction) absolute accelerations of the instrumented upper floors of the L A 7-story university hospital, during the 1994 Northridge E Q 227 Figure 5.12.6 E-W (X-direction) relative displacements of the instrumented upper floors of the L A 7-story university hospital, during the 1994 Northridge EQ 228 Figure 5.12.7 N-S (Y-direction) relative displacements of the instrumented upper floors of the L A 7-story university hospital, during the 1994 Northridge EQ 229 Figure 5.12.8 Orbital displacements (absolute displacements) at the center of the instrumented floors of the L A 7-story university hospital, during the 1994 Northridge E Q 230 Figure 5.12.9 Orbital displacements (relative displacements) at the center of the instrumented floors of the L A 7-story university hospital, during the 1994 Northridge E Q 231 Figure 5.12.10 Frequency Response Functions of the instrumented upper floors with respect to the first floor (above isolators) of the L A 7-story university hospital, obtained from the 1994 Northridge EQ records 232 Figure 5.12.11 Frequency Response Functions of the instrumented floors (including the first floor) with respect to the foundation (below isolators) of the L A 7-story university hospital, ob-tained from the 1994 Northridge EQ records 233 Figure 5.12.12 Mode shapes of the superstructure the L A 7-story university hospital (without isolators), obtained from the 1994 Northridge records 234 Figure 5.12.13 Mode shapes of the L A 7-story university hospital (with an extra story at the bot-tom representing the deformation of the isolators), obtained based on Northridge EQ Records.. 235 Figure 6.1 Vertical to horizontal PGA ratio versus epicentral distance 241 Figure 7.2.1 Typical floor framing plan of the Burbank 6-story bldg. (after Shen & Astaneh, 1990) 253 Figure 7.2.2 Typical perimeter moment resisting frame of the Burbank 6-story bldg 253 Figure 7.2.3 Typical perimeter column base connection detail of the Burbank 6-story bldg. (after Shen & Astaneh, 1990) 254 Figure 7.2.4 Typical interior column base connection detail of the Burbank 6-story bldg. (after Shen & Astaneh, 1990) 254 xxii Figure 7.2.5 Typical beam to column connection detail of the Burbank 6-story building (after Shen & Astaneh, 1990) 255 Figure 7.6.1 Canny hysteretic model used in nonlinear analysis (Canny-e User's manual, 1996) 261 Figure 8.3.1 Comparison the absolute acceleration time-histories obtained from the analysis of Model B with the Whittier EQ records 265 Figure 8.3.2 Comparison the relative displacement time-histories obtained from the analysis of Model B with the Whittier EQ records 267 Figure 8.3.3 Envelope of maximum story shears and overturning moments obtained from the time-history analysisofModelBwiththegroundaccelerationsobtainedfrom the WhittierEQrecords 271 Figure 8.4.1 Comparison the absolute acceleration time-histories obtained from the analysis of Model A with the Northridge EQ records 274 Figure 8.4.2 Comparison the relative displacement time-histories obtained from the analysis of Model A with the Northridge EQ records 276 Figure 8.4.3 Comparison the absolute acceleration time-histories obtained from the analysis of Model B with the Northridge EQ records 278 Figure 8.4.4 Comparison the relative displacement time-histories obtained from the analysis of Model B with the Northridge EQ records 280 Figure 8.4.5 Envelope of maximum story shears and overturning moments, time-history analy-sis of Model A with the ground accelerations obtained from the Northridge E Q data . . . . 284 Figure 8.4.6 Floor absolute accelerations (X-dir), obtained from the time-history analysis of Model A with the ground accelerations obtained from the Northridge E Q data 285 Figure 8.4.7 Floor absolute accelerations (Y-dir), obtained from the time-history analysis of Model A with the ground accelerations obtained from the Northridge E Q data 286 Figure 8.4.8 Floor relative displacements (X-dir), obtained from the time-history analysis of Model A with the ground accelerations obtained from the Northridge E Q data 287 Figure 8.4.9 Floor relative displacements (Y-dir), obtained from the time-history analysis of Model A with the ground accelerations obtained from the Northridge E Q data 288 Figure 8.5.1 3-D view of Model C (ETABS Model) 289 Figure 8.5.2 Design Response Spectra, Uniform Building Code (UBC 1997) 291 XXlll Figure 8.5.3 Response Spectra used in analyses of Models C2 to C5 291 Figure 8.5.4 Two dimensional view of the mode shapes of Model C in X-direction 292 Figure 8.5.5 Comparison of maximum story shears and floor overturning moments of Models CI toC6 297 Figure 8.6.1 Roof absolute acceleration and relative displacement time-histories obtained from the nonlinear analysis of model BU-A-3N (3.5% damping) 305 Figure 8.6.2 Roof absolute acceleration and relative displacement time-histories obtained from the nonlinear analysis of model BU-A-3N (1.5% damping) 306 Figure 8.6.3 Force-displacement relationship obtained from push-over analysis 307 Figure A l Absolute accelerations of the upper floors of the Burbank 6-story office bldg. in the E-W (X) direction, obtained from the 1987 Whittier EQ records 321 Figure A2 Absolute accelerations of the upper floors of the Burbank 6-story office bldg. in the N-S (Y) direction, obtained from the 1987 Whittier EQ records 322 Figure A3 Absolute accelerations of the upper floors of the Redlands 7-story commercial bldg. in the E-W (X) direction, obtained from the 1992 Landers EQ records 323 Figure A4 Absolute accelerations of the upper floors of the Redlands 7-story commercial bldg. in the N-S (Y) direction, obtained from the 1992 Landers EQ records 324 Figure A5 Absolute accelerations of the upper floors of the San Bernardino 3-story office bldg. in the E-W (X) direction, obtained from the 1992 Landers EQ records 325 Figure A6 Absolute accelerations of the upper floors of the San Bernardino 3-story office bldg. in the N-S (Y) direction, obtained from the 1992 Landers EQ records 326 Figure B l Frequency Response Functions of the instrumented floors of the Burbank 6-Story Bldg, obtainedfrom the 1987WhittierEQrecords.(PlotsoftheImaginarypartofthecomplexvalues) 328 Figure B2 Frequency Response Functions of the instrumented floors of the Burbank 6-Story Bldg, obtained from the 1987 Whittier E Q records. (Plot of the Real part of the complex values) 329 Figure B3 Frequency Response Functions of the instrumented floors of the Burbank 6-Story Bldg, obtained from the 1987 Whittier EQ records. (Plot of the Magnitude of the complex values) 330 xxiv Figure B4 Frequency Response Functions of the instrumented floors of the Burbank 6-Story Bldg, obtained from the 1987 Whittier EQ records. (Plots of the Phase angle) 331 Figure B5 1st translational mode shape of the Burbank 6-story bldg, obtained from the 1987 Whittier E Q records 332 Figure B6 2nd translational mode shape of the Burbank 6TStory bldg, obtained from the 1987 Whittier E Q records 333 Figure B7 3rd translational mode shape of the Burbank 6-story bldg, obtained from the 1987 Whittier E Q records 334 Figure B8 1st torsional mode shape of the Burbank 6-story bldg, obtained from the 1987 Whit-tier EQ records 335 Figure B9 2nd torsional mode shape of the Burbank 6-story bldg, obtained from the 1987 Whit-tier E Q records 336 X X V ACKNOWLEDGEMENTS I would like to thank my supervisor Dr. Carlos E. Ventura for introducing me to the project, guid-ing me in selecting and using the proper techniques and his valuable comments throughout the project. I would also like to thank Professor Donald E. Anderson for his valuable lessons during the course of "Earthquake Resistant Structures". Financial support for this project was provided in part by the Steel Structures Educational Foun-dation. X X V I To my brother who inspired me in becoming an engineer xxvii Chapter 1 INTRODUCTION 1.1 General Remarks Building codes provide guidelines for designing structures in seismically active regions. These guidelines include defining a design level of seismic loading based on an estimated natural pe-riod of the building and a simplified approximate method for distributing the loads along the height of the structure. There are several complex factors that control the response of the struc-tures to a given ground motion, such as the three dimensional nature of loading and response, coupling between modes in different directions, the effect of higher modes, nonlinear behaviour of the structure and its ductility. All of the above mentioned factors have been considered in developing the simplified methods suggested by seismic design codes. However, there is still need for more research on the behav-iour of the structures in earthquakes to evaluate the efficiency of the simplified methods and the accuracy of more sophisticated methods of analysis such as nonlinear static, spectral dynamic, linear and nonlinear time history analysis. Due to this need, several buildings in California have been thoroughly instrumented by the Cal-ifornia Strong Motion Program (CSMIP) and the United States Geological Survey (USGS). The buildings include series of instruments that measure the motion at selected locations of the struc-ture. The instruments have recorded the motions during recent severe earthquakes. In this re-search, the recorded motions of 11 low-rise (two to seven story) steel frame structures were used to evaluate the behavior of this type of buildings under seismic loading. 1.2 Objectives The main objective of this study is to gain a better understanding of the behaviour of low-rise steel frame buildings during earthquakes by: 1 .Conducting a detailed study of the recorded response of 11 low-rise steel frame buildings dur-ing recent earthquakes, 2. Determining the natural vibration frequencies and mode shapes of the buildings based on the recorded data, 3. Comparing the measured fundamental vibration period of the buildings to that estimated uti-lizing code formulae, 4. Developing a refined structural model of one of the buildings for dynamic time-history anal-ysis and comparing the results to the recorded data. 5. Studying the nonlinear response of the structural model when subjected to higher levels of ground motion. 6. Comparing the results of various analysis techniques. 1.3 Scope of Work Throughout the course of this project the following work was done to achieve the above men-tioned objectives. 1. A review of signal processing and system identification techniques was conducted to set up a procedure for determining the vibration properties of the buildings using the strong motion da-ta. 2. Vibration properties of the first two or three modes in each of the three lateral directions (X 2 and Y translational and rotational) were estimated. These properties included natural frequen-cies, mode shapes, damping values and modal amplification factors. 3. The recorded motions of buildings at the locations of the installed accelerometers were pro-cessed to separate the translational and rotational components of the motion. These data were used to obtain a better estimate of the translational and rotational response properties. 4. For each building, the properties of the recorded ground motions and the structural response were presented in the form of a series of graphs and tables. 5. A nonlinear structural model of a six story building in Burbank was developed and dynamic time-history analyses were performed using the ground accelerations recorded during the 1987 Whittier and 1994 Northridge earthquakes. 6. The structural model was refined so that the results of the time-history analyses matched the recorded data. 7 The structural-model was analyzed using various linear elastic-analysis-methods-such as-: Spec-tral dynamic analysis (using true response spectrum and code recommended design response spectra) and equivalent static analysis. The results were compared to those of linear elastic time-history analyses. 8. Nonlinear dynamic time history analyses were performed using two and three times the ground accelerations recorded during the 1994 Northridge earthquake. 9. A nonlinear elastic (push-over) analysis was performed and the results were compared to those of the nonlinear time-history analysis. 3 Chapter 2 BACKGROUND OF THE PROJECT 2.1 Strong Motion Data The California Strong Motion Instrumentation Program (CSMIP) and the United States Geolog-ical Survey (USGS) have installed an extensive array of instruments to measure the motion of a large number of buildings, bridges, dams, and free field vibrations during earthquakes. Many of these instruments have recorded the motions of several earthquakes that have happened in recent years, thus providing an extensive database of valuable information for earthquake engineering research. 2.2 Previous Work The strong motion data have been used to study the behaviour of a large number of structures of various types in recent years. Only a limited portion of this work, however, has focused on low-rise steel frame buildings. A brief review of some of the previous research on the behaviour of this type of structures is described in the following paragraphs. Pardoen (1989) studied the recorded response of three instrumented buildings. This included the study of the response of a four story steel frame hospital building in Palm Springs during the Palm Springs earthquake of 1986. A detailed study was conducted by Shen and Astaneh (1990) on the behaviour of the Burbank 6-story office building during the Whittier earthquake. The study included system identification using the Whittier earthquake records and linear elastic dynamic time-history analysis of a re-4 fined model of the structure. They concluded that proper modeling of connections and floor di-aphragms can lead to accurate predictions of the response. They also concluded that code procedures (at the time of the study) predict a period that usually is significantly smaller than the actual period of the steel structures similar to the one studied in that research. Fenves (1990) studied the behavior a four story (steel frame) hospital in San Francisco during the 1984 Morgan Hill and 1989 Loma Prieta earthquakes and a six story hospital in Sylmar dur-ing the 1987 Whittier earthquake. The Sylmar building had a cruciform shape in plan with con-crete shear walls in the lower two stories and steel frames in the upper four stories. The two buildings were selected for their irregular features. A mathematical model of the San Francisco four story hospital was developed for linear dynamic analysis. Close correlation between the measured and analytical response was obtained when mass eccentricity was included (which cre-ated coupled modal response as apparent in the recorded response). McClure (1991) used a three dimensional model of a two story (steel frame) office building in Oakland to evaluate its response during the Loma Prieta earthquake. The structural model was validated by the periods obtained from forced vibration measurements. Time-history and re-sponse spectrum methods were used in the analyses. The displacements obtained from the time-history analyses were very close to those obtained from strong motion records. Peak accelera-tions of 0.65 g, 0.39 g, and 0.26 g, were observed at the roof, second floor and, ground, respec-tively during the Loma Prieta earthquake.According to the time-history analyses, however, the maximum base shear was 14% of the weight of the building. De laLlera and Chopra (1991 and 1992) studied the response of three nominally symmetric-plan buildings to evaluate the code accidental torsional provisions. Two of these buildings were low-5 rise steel frame buildings (a three story office building in Richmond and a three story office building in San Jose). The recorded response of these buildings during the 1989 Loma Prieta earthquake was studied: Three-dimensional models of the buildings were prepared and static analyses were performed at many time instants. The results demonstrated that the accidental tor-sion specified by the Uniform Building Code (UBC) is adequate in representing the torsion in the recorded motions of these three buildings. Cole et al. (1992) developed a database of fundamental periods of 64 buildings to investigate the efficiency of code period formulas. Only regular buildings contemplated by the 1991 Uniform Building Code were included in the study. The following low-rise steel moment frame buildings were included in the study: 1) Burbank 6-story office building, 2) Palm Springs 4-story hospital, 3) Richmond 3-story office building, 4) San Bernardino 3-story office building, 5) San Jose 3-story office building, 6) San Francisco 4-story hospital. Huang et al. (1993) studied the recorded motion of four base-isolated buildings during the 1992 Landers earthquake. Three of these were steel braced frame buildings including. 1) Rancho Cu-camonga 4-story Law and Justice Center, 2) Los Angeles 2-story fire control building, 3) Los Angeles 7-story University hospital. The peak accelerations measured at the foundation level of the buildings were between 0.04 g and 0.11 g. For each building the drifts between roof and the base of the superstructure and the deformation of the isolators were derived from the strong mo-tion data. The results showed that the two story building responded almost like a rigid superstruc-ture over isolators and had negligible drift in the superstructure. The drifts in the superstructures of the other three buildings were considerable. The deformation of the isolators for these four buildings ranged from 0.8 to 1.6 cm. 6 Shakal et al. (1994) studied the strong motion data recorded in several buildings during the 1994 Northridge earthquake. The buildings included the following low-rise steel frame buildings: the Burbank 6-story office building, the Sylmar 6-story hospital and, the Los Angeles 7-story Uni-versity hospital (base-isolated). The study included a preliminary interpretation of the recorded response of the buildings in terms of the natural vibration periods, peak accelerations, displace-ments and the response spectra of the recorded ground motions. Nagarajaiah and Xiahong (1995) studied the response of the Los Angeles 2-story fire control building and the Los Angeles 7-story University hospital (both base-isolated) during the 1994 Northridge earthquake. The study included system identification, nonlinear analytical modeling, interpretation of structural behaviour during the Northridge earthquake , and evaluation of the effectiveness of seismic isolation. The study concluded that 1) the 7-story University hospital performed very well and the seismic isolation was effective in reducing the response, 2) the 2-story fire control building also performed well. Accidental pounding, however, reduced the ef-fectiveness of seismic isolation (due to lack of sufficient free movement at the seismic isolation gap), 3) the analysis techniques used in the study predicted the response of the base-isolated buildings accurately. De la Llera and Chopra (1995) studied the behaviour of eight instrumented buildings during the 1994 Northridge earthquake to evaluate the UBC seismic design provisions. This study included the following steel frame buildings: 1) Burbank 6-story office building, 2) Los Angeles 2-story fire control building (base-isolated), 3) Los Angeles 3-story commercial building, 4) Los Ange-les 6-story office building, 5) Los Angeles 7-story University hospital (base-isolated), 6) Sylmar 6-story hospital. The study included system identification utilizing signal processing techniques, 7 and comparison of the recorded data with the results of linear and nonlinear dynamic time history analyses. The results were used to discuss issues such as instrumentation, building modeling, ductility of the structures and the performance of the perimeter frame systems. They concluded that thorough instrumentation of all floors of the buildings is not economically feasible. As a re-sult, the records of the instrumented floors must be used to predict the motions of the un-instru-mented floors by system identification and/or record interpretation. A degree of uncertainty exists in the accuracy of the structural models that are prepared based on conventional methods. The study showed that the level of uncertainty is highly correlated with the complexity of the structure. The use of inelastic models for the buildings that are designed-to experience substantial inelastic behaviour was highly recommended. The study concluded that perimeter frame systems violate the redundancy requirement for ductile behaviour in the structure. Perimeter frame sys-tems also have a serious deficiency in their inelastic behaviour. Naeim (1996) conducted an elaborate study of the performance of 20 instrumented buildings during the 1994 Northridge earthquake. This study included the following low-rise steel frame buildings: 1) Sylmar 6-story hospital 2) Los Angeles 3-story commercial building, 3) Burbank 6-story building, 4) Los Angeles 6-story office building. The research included inspection of the buildings, damage assessment, and performance evaluation. The forces, displacements, and dy-namic characteristics were obtained from the strong motion-data and were compared with those suggested by building codes. Some of the results of the study include: 1) Building code estimates are consistently less than observed periods. 2) In most cases, the base shears obtained from in-terpretation of the recorded data were larger than the base shears they had apparently been de-signed for, i.e. in most cases the buildings performed much better than they were expected to by routine design analysis techniques. 3) The ratio of the base shears to design code base shears did 8 not correlate very well with the extent of damage observed. However, the overall drift ratios cor-related rather well. 4) The drift ratios were significantly less than what would have been expected from ordinary design analysis techniques. 5) Evaluation of the deformed shape at the time of maximum lateral displacements showed that, at that instant, the deformed shape is almost always similar to the first mode of vibration. In most cases, however, maximum forces and maximum displacements were not concurrent, and except for the short buildings, the distribution of the forces at the time of maximum base shear were radically different from lateral force profile ob-tained from code suggested static procedure. 6) Except for the buildings with structural damage, the period of the building according to the recorded data did not elongate significantly. When elongation occurred, the period returned to the vicinity of the initial value towards the end of the ground motion. 7) For several buildings, torsion contributed significantly to the seismic re-sponse. Goel and Chopra (1997) investigated the empirical formulae for estimating the periods of mo-ment-resisting frame buildings. They studied the fundamental periods of a large number of struc-tures, including six steel frame buildings with two to six stories, which were obtained from analyzing the strong motion data. The measured periods were used to improve the period formu-lae suggested by the building codes. It was concluded that the code formula for steel moment resisting frame buildings leads to shorter values than measured periods, with the margin between the two being much larger than for concrete moment frame buildings. The research showed that the intensity of ground shaking has little influence in elongating the period. In steel frame build-ings, the period elongates slightly due to stronger shaking but less than that for reinforced con-crete buildings. 9 2.3 Demand for Further Studies In many of the previous studies, the extent of the research was to determine the periods of the first one or two translational modes of vibration in each direction, acceleration amplifications, displacements and inter-story drift ratios. Structural models of some of the buildings were ana-lyzed using linear static or dynamic methods in most cases. Nonlinear analysis for these build-ings was rarely performed. This project was inspired by the need for a better understanding of the behaviour of structures (in particular, low-rise steel frame structures) during earthquakes and the effectiveness of the various analysis techniques currently available for seismic design of structures. This can be ac-complished through more detailed analysis of the recorded data, investigating the higher modes of vibrations of the buildings using system identification techniques, and a comparative study of the results from various analysis techniques. 2.4 Selection of the Buildings The criteria for selecting the buildings from the strong motion data archives for this study were: • Steel moment resisting or braced frames for lateral load resisting system, • Seven or fewer stories, • Preferably recorded peak ground accelerations (PGA) of greater than 0.2 g. Eleven buildings were selected for this study. The peak ground accelerations measured at the foundations of the selected buildings were within 0.06 g to 0.37 g. Description of the buildings and the layout of the recording instrumentation are presented in Chapter 4. This research includes data processing of two base-isolated structures. The Los Angeles 2-story 10 fire control building and the Los Angeles 7-story University hospital were chosen for this pur-pose. 2.5 Earthquakes Considered in this Study The strong motion data used in this research was selected from the database of the recorded mo-tions of the following four earthquakes: 1) Northridge earthquake of January 17, 1994 Hypocenter: 34.215 ° N , 118.538 ° W Depth: 18 km Magnitude: 6.7 2) Landers earthquake of June 28, 1992 Hypocenter: 34.217 ° N , 116.433 ° W Depth: 9 km Magnitude: 7.5 3) Santa Cruz Mountains (Loma Prieta) earthquake of October 17, 1989 Hypocenter: 37.037 ° N , 121.883 0 W Depth: 18 km Magnitude: 7.1 4) Whittier earthquake of October 1, 1987 Hypocenter: 34.062 ° N , 116.433 ° W Depth: 9 km Magnitude: 7.5 11 Chapter 3 REVIEW OF SYSTEM IDENTIFICATION TECHNIQUES USED IN THE PROJECT 3.1 Natural Vibration Frequencies One of the main objectives of this project was to determine the natural frequencies and mode shapes of the buildings using the strong motion data. To achieve this, the concept of resonance was used. We know from structural dynamics that the response of a vibrating system to harmonic loading is harmonic and the amplitude of the response depends on the ratio of the rotational frequency of the loading (co) to the natural frequency of the system (<»„). The response is at a maximum when the frequency of excitation is equal to the natural frequency of the system. This is known as the resonance condition. This means that if we have a plot of response versus the frequency of the loading, the peak of the graph will correspond to the natural frequency of the system (Fig-ure 3.1). In the resonance condition the response has a 90° phase lag with respect to the excita-tion. For practical purposes this property can be used as a tool to verify that the peak of the plot truly indicates a natural frequency (see Figure 3.1). Ground motion during an earthquake is not harmonic, so the strong motion data cannot be used directly to determine the natural frequencies. To solve this problem, the Fourier Transform of the time history of ground motion and the response of the system are used. The Fourier Transform is a mathematical tool used to represent a time variable function as the summation of a series of sinusoidal functions with different frequencies. A plot of these ampli-tudes vs. frequency is called a Fourier Spectrum. Processing the data using their Fourier Spec-12 tra is usually called Frequency Domain Analysis. After calculating the Fourier Spectra of the input (ground motion) and the output (response of the system), a plot of the ratio of output to input vs. frequency can be prepared. This is called Frequency Response Function (FRF). The FRF is a measure of amplification of the motion by the vibrating system, and it can be used to determine the natural frequencies by locating the peaks of the FRF plot. This procedure should be carried out with caution, because not every maximum point on a FRF plot indicates a natural frequency and there are several factors which induce errors in this proce-dure. The sources of errors will be discussed in Section 3.4. o 180°r £ = 0.01 0.1 CO c 0 2 3 Frequency ratio co / (0„ Figure 3.1 Displacement Response factor and phase angle for a damped system excited by harmonic force (after Chopra, 1995). 13 3.2 Mode Shapes After finding a natural frequency, a deformed shape of the building can be plotted according to the amplitudes of FRF's at the natural frequency. This will be a good approximation of the correspond-ing mode shape. If the plotted shape resembles one of the expected mode shapes of the structure, it may confirm that the calculated frequency is a true natural frequency of the system. 3.3 Estimating Damping The method used to estimate damping is based on the concept of Half Power Band Width. On the frequency response curve, if © a andcoij are frequencies on two sides of the resonant frequency where the amplitude is 2*-"1/'2-) of the resonant amplitude (Figure 3.2), the damping value can be cal-culated using the following equation: CO - CO b 2.co 2-c; n (Equation 3.3.1) This method was used in this study to estimate the modal damping values. 5 4 •o 3 u Q 0 0 2 3 4 Frequency ratio to / to. Figure 3.2 Definition of half-power bandwidth (After Chopra, 1995). 14 3.4 Sources of Error and Reliability of the Results There were several factors that seemed to induce errors in the results of the system identification and data processing in this research and influence the reliability of the results. This section in-cludes a brief review of the important issues that seem to be a source of error in this project. These sources of error are as follows. 1. The measuring instruments have a certain level of accuracy and their sensitivity is not neces-sarily the same for all frequencies. There is also a measure of electronic noise being recorded by the instrumentation. 2. The original recorded data usually are not usable directly. The data are usually undergone a series of signal processing stages to be filtered (removing the frequencies that are lower or higher than certain values which could only indicate noise not meaningful data) and base-line corrected. A more realistic data are retrieved from the original data. Although this process improves the accuracy of the data, a measure of noise and error still re-mains in them. Also some of the information may deteriorate or altered during this process. 3. The concept of Fourier Transform has been mathematically proven to be correct for periodic functions with infinite time window length. Applying this technique to strong motion data, which are transient (non-periodic with limited time domain) includes a measure of error. This is called Leakage (see ME'Scope, Operating manual, 1998, Appendix note # 1). To minimize leakage, the data are usually multiplied by a function which takes a value of zero at the beginning and at the end, and is one in the middle, so that the product will be zero at the beginning and the end, and it will have characteristics closer to a periodic function. Experience shows that a sinusoidal function which is commonly known as the Hanning window is one of 15 the most efficient windows to be used in this type of analysis. Using Hanning window results in more accuracy in frequencies, but increases the error in the amplitudes. This may be one of the main reasons that the estimated damping values using the Half-Power Bandwidth method were not as reliable as the estimated natural frequencies. 4. The FRF's of strong motion data usually contain several sharp peaks, which may not represent meaningful information. This usually happens when, at a data point, the denominator of the FRF is close to zero. In such cases a small error in the value of-the-Fourier Spectrum can result in a large error in the FRF. To overcome this, an averaging technique is usually used. The original data are broken into a series of shorter data blocks which have a length of order of 2 n (see Section 3.5) and are overlapped by 50 to 90 percent. The Fourier Transform is applied to these blocks and the average of the results are used as the final FRF. This makes the FRF smoother and de-creases the random error. Figure 3.3 shows an example of two time-history records measured in an actual earthquake (Record A as Input and Record B as Output). Figures 3.4 and 3.5 show Fou-rier Spectra of A & B, and the Frequency Response Function (B/A) which are calculated with averaging. Figure 3.6 shows the FRF obtained without averaging. It can be observed from Figure 3.6 that the FRF calculated without averaging is not providing a realistic representation of the behaviour of the system. 5. The results for the higher modes typically include a higher level error. This is due to the fact that the response has a higher amplitude in the frequency range closer to the fundamental mode, the signal to noise ratio is larger in this range and the results are more reliable for lower modes. On the other hand, the signal to noise ratio decreases in higher frequencies so that, beyond a cer-tain limit, the data become meaningless and determining the higher natural frequencies becomes impossible. 16 As an example, Figure 3.4 shows that the amplitudes of records A and B are close to zero for the frequencies above 15 Ffz. This shows that the large amplitude of the FRF at this frequency range (Figure 3.5) is not a true representation of the behavior of the system since it is the result of a zero-over-zero condition. 6. The buildings have distributed mass in all the elements which result in local vibration modes, which may be present in the computed FRF. 7. Flexibility of the diaphragms and nonlinear behaviour of the structures may also induce a mea-sure of error in the system identification results. 8. When the location of a sensor is close to a nodal point of one of the higher modes of vibration (which theoretically has zero displacement at that mode), the corresponding FRF will not show any amplification of motion at the frequency of that mode of vibration. This may cause confusion in interpreting the results. In such cases FRF's corresponding to other floors can be used to de-termine the natural frequency. 3.5 Program "ME'scope" A signal processing program called ME'scope (ME'Scope Operating Manual, 1998) was used in the first part of this research to evaluate the vibration properties of the buildings selected for data analysis. ME'scope calculates the Fourier spectra using the Fast Fourier Transform (FFT) technique. This is a numerical method to efficiently calculateJheTourier Transform of a time variable function. To use the FFT efficiently, the number of data points in time domain should be a power of 2, i.e. N=2n. Frequency resolution of the results depends on the total time length of the data T=N.dt (where N is the number of data points) Af= 1 /N.At (Equation 3.5.1) 17 and the maximum frequency depends on the time increment (At) f m a x = 1 / 2 At (Equation 3.5.2) Since the number of data points in practical experiments is not of the order of 2n, only a portion of data can be used in each FFT calculation. The user has the option of using the averaging tech-nique explained in item 5 of Section 3.4. This results in smoother FFT and FRF plots and the results are usually more reliable. The number of segments used in this averaging process can be increased by reducing the length of the segments but the trade-off will be a reduction in frequen-cy resolution. The program uses FRF functions to evaluate the natural frequencies and damping values of the system as explained in Sections 3.1 and 3.3. Since the FRF's do not have a smooth shape like the response function shown in Figure 3.1, a curve fitting technique is used by ME'scope to im-prove the results. The user can optimize the curve fitting results by visually inspecting the FRF plot and selecting a narrower band of the FRF where a natural frequency seems to exist. Multi Input Multi Output (MEMO) analysis allows the user to define a series of data as input (ground motion data in this case) and a set of output data (motions of the upper floors) resulting in a ma-trix of FRF's rather than a single function. The user has the option of selecting some of the FRF functions and conducting the curve fitting process. For example, to determine the natural periods in the X direction, only FRF's with input and outputs in that direction may be used. The results for frequencies and damping are the average of the values obtained from all the selected FRF's. The magnitude of each FRF at a natural frequency indicates the corresponding component of the natural mode shape of the building at that frequency. ME'scope also has the option of drawing a structure as a combination of nodes, lines, and sur-18 faces. The user can animate the motion of the structure in both time and frequency domains. „„. M#l (cm/s2) i i / ^ ^ ^ ' i i l y - ' V V Y n 0.00 5.00 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 Seconds M#2 (cm/s*) Z7> • 1 148 Real 22.2 -104 -23 a 0.00 5.00 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 Seconds Figure 3.3 Example of recorded time-histories, Record length T = 60sec, At = 0.02sec, N = 3000. l 5 n M# 1 (cm/s1) Figure 3.4 Fourier Spectra of example Records A & B computed using a Hanning window, a block size N= 2048, 5 averages and 88% segment overlap. 19 5 . 6 0 4 . 8 0 8 0 1 « J O . O O -O . O O 5 . 0 0 Figure 3.5 Example of Frequency Response Function (B / A) calculated with 5 averages. o.oo 25. o Figure 3.6 Example of Frequency Response Function (B / A) calculated without averaging. 20 3.6 Verification of the Results of ME'scope To investigate the accuracy of the results of ME'scope, a series of artificial records were pro-cessed with ME'scope to evaluate the natural frequencies, mode shapes and damping values of a linear elastic structural model. The response data for this model was generated utilizing the pro-gram SAP90 (SAP90 Users Manual, 1989). The model is a 6-story 3-D rigid frame and its mass and stiffness properties were selected so that its fundamental natural frequency was close to that of the Burbank 6-story office building, which was considered in this study. The model had 2.5-5.0% mass eccentricity at each floor to create some degree of coupling between modes in differ-ent directions. The actual ground motion recorded at this building during the Northridge earth-quake was used for a linear time history analysis of the model. The response time histories of the second, third and roof levels were used in ME'scope to determine vibration properties of the sys-tem. Due to limitations of the version of SAP90 used in this project, no rotational ground motion was considered in the analysis. A damping value of 5% was applied to all modes. The SAP90 model is shown in Figure 3.7 and Figure 3.8 shows an example of FRF's calculated using the output time-histories of the dynamic analysis. This represents the true response of a linear multi-degree of freedom system to dynamic loading. A comparison of the vibration properties of the model and the values estimated by ME'scope is presented in Table 3.1. The results show that if an accurate set of records are used, ME'scope can estimate all the natural frequencies of a linear system with an error of less than 1 percent. However, the estimated damping values were not as accurate. The results showed that the error in estimated damping values varied randomly. This suggests that the reliability of the damping values estimated from strong motion data in this research is questionable. 21 Y f X veritl UNDEFORHED SHAPE OPTIONS HIRE FRAME SAP90 Figure 3.7 The SAP90 model used to verify the accuracy of the results of ME'scope. M#l <2x/lx> 0.00 5.00 10.0 Hertz 15.0 20.0 25.0 Figure 3.8 An example of the FRF's calculated from the time histories generated by SAP90. 22 Table 3.1 Comparison of the vibration properties of the SAP90 model and the values estimated based on the output time histories using the ME'scope. Properties of the SAP90 model Values estimated by ME'scope Mode number Modal direction Period (sec) Frequency (Hz) Estimated frequency (Hz) Estimated damping (%) 1 Y(l) 1.263 0.792 0.798 4.59 2 X(l) 1.157 0.864 0.861 3.27 3 ROT(l) 0.782 1.279 1.278 3.05 4 Y(2) 0.461 2.169 2.178 4.33 5 X(2) 0.391 2.557 2.563 4.10 6 ROT(2) 0.288 3.467 3.369 0.68 7 Y(3) 0.255 3.927 3.949 4.02 8 X(3) 0.237 4.226 4.239 3.87 9 Y(4) 0.192 5.211 5.213 3.32 10 X(4) 0.170 5.887 5.822 4.40 11 ROT(3) 0.162 6.188 6.015 3.20 12 Y(5) 0.145 6.900 6.907 4.35 13 X(5) 0.129 7.741 7.735 3.08 14 ROT(4) 0.119 8.407 7.897 5.08 15 - 0.116 8.624 8.508 2.03 16 - 0.113 8.850 8.768 3.68 17 - 0.092 10.819 10.793 3.10 18 - 0.0757 13.2152 13.184 0.13 Note: The SAP90 model had a damping value of 5.00 % for all modes. 23 3.7 Three-Dimensional Animation of the Mode Shapes To visualize the mode shapes, simple prismatic structural models have been prepared as de-scribed in Section 3.5. The X and Y displacements of the corners of the models were required for animation. Since these data were not measured directly, the recorded data were used to gen-erate the required data based on the assumption that all floors behave as rigid diaphragms and the displacements are small. ME'scope uses interpolated displacements for the floors that have no assigned data. So when investigating the mode shapes presented in the following chapters, it is important to take into account that only some of the floors represent actual data. 3.8 Introducing the Concept of "Spectral Response Function" As explained in the previous sections, the FRF's of actual data contain several sharp peaks close to each other which may make it difficult to identify the natural frequencies. For this reason the author was looking for another function with similar properties to the FRF but with smoother curves and better distinguished peaks. For this purpose, the author developed a plot of the ratio of response spectrum of output data to that of the input motion versus frequency. This function will be referred to as Spectral Response Function (SRF) in this study. The advantage of the SRF plots to FRF's is that when the Fourier spectrum of an acceleration record shows a very low or very high amplitude for a certain frequency (compared to the ampli-tude of the adjacent points), the response spectrum, which is governed by the overall properties of the acceleration record does not show a sudden and sharp change in the amplitude of the re-sponse. Therefore the SRF plots are smoother and reflect the overall properties of the recorded data and, in some cases, make it easier to identify a peak, which indicates a natural frequency. 24 The SRF plots appear to give reliable results for the lower modes of vibration, which have a rel-atively higher amplification factor. In this study the SRF's were used to verify the results ob-tained using ME'scope. The programs used to calculate the response spectra were: a) NONLIN, developed by Charney A. Finley, Ph.D., P.E., Advanced Structural Concepts, In-corporated, under a contract with the Federal Emergency Management Agency (FEMA) b) S P E C E Q , programmed by N.C. Nigam & P C . Jennings, California Institute of Technology, Pasadena, California, modified by C.E. Ventura (1992), University of British Columbia, Van-couver, British Columbia To compare the SRF's and FRF's, the Spectral Response Functions were calculated from the zero damping and 1% damping response spectra of the same input and output time histories that were used to obtain the Frequency Response Function of Figure 3.8. These SRF plots are pre-sented in Figure 3.9. Spectral Response Function A 2x/1 x - 0%dmpg I fi\ 2x/1x- 1%dmpg / i f\ A / I J-A A , A X A H / ^ N % A / 0 1 2 3 4 5 6 7 8 9 10 Frequency (Hz) Figure 3.9 An example Spectral Response Function obtained from 0 % and 1 % damping response spectra. 25 Chapter 4 DESCRIPTION OF THE BUILDINGS UNDER STUDY 4.1 General This chapter includes the description of the buildings under study, their location, and figures showing their shape, major dimensions, and the layout of the accelerometers installed on the buildings to record their motion during earthquakes. The arrows in the figures represent the direction of the sensors. The dots represent the sensors measuring the accelerations in the direction perpendicular to the plane of the paper. Table 4.1 shows a list of these buildings. A summary of general information on the buildings is presented in Table 4.2. The location of the buildings and the epicenter of the earthquakes are shown in Figure 4.1. Sections 4.2 to 4.12 describe each building in more detail. Table 4.1 List of buildings under study. Building CSMTP Station # Earthquake studied 1) Burbank, 6-Story Office Building 24370 Whittier Northridge 2) San Bernardino 5-Story Hospital 23634 Northridge 3) Pasadena 6-Story Office Building 24541 Northridge 4) San Jose 3-Story Office Building 57562 Loma Prieta 5) San Francisco 4-Story Hospital 58261 Loma Prieta 6) Berkeley 2-Story Hospital 58496 Loma Prieta 7) Richmond 3-Story Office Building 58506 Loma Prieta 8) Redlands 7-Story Commercial Building 23481 Landers 9) San Bernardino 3-Story Office Building 23516 Landers 10) Los Angeles 2-Story Fire Control Building 24580 Northridge 11) Los Angeles 7-Story University Hospital 24605 Northridge 26 Table 4.2 General description of the buildings under study. Building Plan Shape Major dimensions (m) Lateral Load Resisting System E-W N-S height 1) Burbank, 6-story office bldg. Square 36.6 36.6 25.2 Perimeter moment resisting frames 2) San Bernardino 5-story hptl. L-Shape 45.7 55.2 21.0 Moment resisting frames 3) Pasadena 6-story office bldg. Rectan-gular 35.7 38.1 25.0 Moment resisting frames 4) San Jose 3-story office bldg. Rectan-gular 76.2 28.3 15.1 Moment resisting frames 5) San Francisco 4-story hptl. Rectan-gular 35.7 66.8 16.0 Moment resisting frames (concrete walls at first floor) 6) Berkeley 2-story hptl. Rectan-gular 43.0 35.7 7.7 Eccentrically braced frames 7) Richmond 3-story office bldg. Rectan-gular 24.4 50.3 13.4 Perimeter moment resisting frames 8) Redlands 7-story bldg. Rectan-gular 42.7 28.3 28.8 Perimeter moment resisting frames 9) San Bernardino 3-story bldg. Rectan-gular 40.2 43.9 12.6 Perimeter moment resisting frames 10) L A 2-story fire cntrl bldg. Rectan-gular 25.6 57.3 9,8 Perimeter braced (chevron) frames (Base Isolated) 11) L A 7-story University hptl. S-shape 77.1 92.4 35.7 Diagonally braced perimeter frames (Base Isolated) 27 Figure 4.1 Location of the buildings and the epicenter of the earthquakes. Note: The numbers represent the last 3 digits of CSMIP station numbers. * indicates the location of the earthquakes. 28 4.2 B u r b a n k , 6-Story Office Bui lding Building Description: Location: Burbank, C A Zip Code: 91502 Coordinates: 34.185 ° N , 118.308 ° W CSMIP Station number: 24370 Earthquake records studied: Northridge (1994), Whittier (1987) Height & Number of Stories above ground: 25.2m (82.5ft), 6 stories Plan Shape: Rectangular Typical floor plan dimensions: N-S direction: 36.6m (120ft), E-W direction: 36.6m (120ft) Vertical force resisting system: Steel beams & columns, 3 1/4" concrete slab over metal deck Lateral force resisting system: Perimeter Moment Resisting Steel Frames Design/Construction date: 1976/1977 Foundation type: Concrete Caissons (approx. 9.8m deep) Number of stories below ground: 0 Site Geology: Alluvium . Epicentral distance: 22km W est of bldg. (Northridge EQ) ' 26km South-East of bldg. (Whittier EQ) Note: The above information was obtained from "Shakal et al , 1987" 29 SENSOR LAYOUT 3 "V, N ROOF 6 5 4 3 2 -rf-GROUND 775 S/N ELEVATION Structure Reference Orientation: N : 3 1 0 ° ROOF 2ND FLOOR 3RD FLOOR GROUND Figure 4.2 Overview of Burbank 6-Story Building and Sensor layout, (After Shakal, et al, 1987) 30 4.3 San Bernardino 5-Story Hospital Building Description: Location: San Bernardino, C A Zip Code: — Coordinates: 34.132 ° N , 117.321 ° W CSMIP Station number: 23634 Earthquake record studied: Northridge (1994) Height & Number of Stories above ground: 21m (69ft), 5 stories Plan Shape: L-shape Typical floor plan dimensions: N-S direction: 55.2m (181ft), E-W direction: 45.7m (150ft) Vertical force resisting system: Steel beams & columns Lateral force resisting system: Moment Resisting Steel Frames Design/Construction date: 1986/— Foundation type: Concrete piles Number of stories below ground: 0 Site Geology: Deep Alluvium Epicentral distance: 113km West of building Note: The above information was obtained from "Shakal et al , 1994" 31 Figure 4.3 Overview of San Bernardino 5-Story Hospital and Sensor layout, (After Shakal, et al, 1994) 32 4.4 Pasadena 6-Story Office Bui ld ing Building Description: Location: Pasadena, C A Zip Code: — Coordinates: 34.146 ° N , 118.147 ° W CSMIP Station number: 24541 Earthquake record studied: Northridge (1994) Height & Number of Stories above ground: 25m (82ft), 6 stories + attic Plan Shape: Rectangular Typical floor plan dimensions: N-S direction: 38.1m (125ft), E-W direction: 35.7m (117ft) Vertical force resisting system: Steel beams & columns Lateral force resisting system: Steel frames with U R M infill walls Design/Construction date: 1906/— Foundation type: — Number of stories below ground: 1 Site Geology: Deep Alluvium Epicentral distance: 37km West of the building Note: The above information was obtained from "Shakal et al, 1994" 33 ,5Zl c _cC 0. i_ o _o LL CO ,21 J CO 2 ? O 'co r— < U o CC o CO z L U CO c CO c CO E © w co OQ =/ CO 5 ca a> o o o — o ~ cr < .c .c £ T J T > § IO O < O N C5 Iff (I ,01 •* < •» . .V-.L .9-,11 e> fr "* . I - .28 .6-,81 + . 1 1 O c 2 .2 1 3 CO > © LU LU O CO > < "2 oor c CO o o DC CO c _CC D_ V. O _o U -c CM C O O o O N 3 en r-i CD f—1 0) CO e s CO -H C H 1H M t l C d CJ TH 0) co o .E-.01 Figure 4.4 Overview of Pasadena 6-Story Office Building and Sensor layout, (After Shakal, et al., 1994) 34 4.5 San Jose 3-Story Office Building Building Description: Location: Santa Teresa Hills, San Jose, C A Zip Code: — Coordinates: 37.212 ° N , 121.803 ° W CSMIP Station number: 57562 Earthquake record studied: Loma Prieta (1989) Height & Number of Stories above ground: 15.1m (49.5ft), 3 stories Plan Shape: Rectangular Typical floor plan dimensions: N-S direction: 28.3m (92.7ft), E-W direction: 76.2m (250ft) Vertical force resisting system: Concrete slab on steel deck supported by steel frame Lateral force resisting system: Moment resistant steel frames with exterior cladding Design/Construction date: 1983/1984 Foundation type: Spread footing Number of stories below ground: 0 Site Geology: Alluvium over serpentine Epicentral distance: 21km South-West of the building Note: The above information was obtained from "Shakal et al, 1989" 35 o Figure 4.5 Overview of San Jose 3-Story Office Building and Sensor layout, (After Shakal, et al, 1989) 36 4.6 San Francisco 4-Story Hospital Building Description: Location: San Francisco, C A Zip Code: — Coordinates: 37.66 ° N , 122.439 0 W CSMIP Station number: 58261 Earthquake record studied: Loma Prieta (1989) Height & Number of Stories above ground: 16m (52.5ft), 4 stories Plan Shape: Rectangular Typical floor plan dimensions: N-S direction: 66.8m (219ft), E-W direction: 35.7m (117ft) Vertical force resisting system: 3.5" light-weight concrete fill over metal deck supported by steel frame Lateral force resisting system: Moment-resistant steel frames (Concrete shear walls at 1st floor) Design/Constructiondate: 1972/1973-75 Foundation type: Piles (15 - 21m deep); 8" concrete slab on grade Number of stories below ground: 0 Site Geology: Fill over Sandstone Epicentral distance: 85km South-East of the building Note: The above information was obtained from "Shakal et al, 1989" 37 J' .III '' J Figure 4.6 Overview of San Francisco 4-Story Hospital and Sensor layout, (After Shakal, et al , 1989) 38 4.7 Berkeley 2-Story Hospital Building Description: Location: Berkeley, C A Zip Code: — Coordinates: 37:855 & N , 122.256 S W CSMEP Station number: 58496 Earthquake record studied: Loma Prieta (1989) Height & Number of Stories above ground: 7.7m (25.2ft), 2 stories Plan Shape: Rectangular Typical floor plan dimensions: N-S direction: 35.7m (117ft), E-W direction: 43m (141ft) Vertical force resisting system: Steel frames Lateral force resisting system: Eccentrically braced Steel frames Design/Construction date: 1984/— Foundation type:— Number of stories below ground: 1 Site Geology: Alluvium Epicentral distance: 97km South of the building Note: The above information was obtained from "Shakal et al , 1989" 39 CM CO z o < o o _ I cr O co z 111 CO , 1. I 1. c o co > 1X1 z CO c CO CN 5 1 C co c CD E CD 0) CO CD o CC 01 " 0 3 2 55 O c o -a-u oo to — —i -a i-l c to a tj •H U Ul 4J 1* C -H 01 U-t o B F i g u r e 4.7 Overview of Berkeley 2-Story Hospital and Sensor layout, (After Shakal, et al, 1 40 4.8 Richmond 3-Story Office Building Building Description: Location: Richmond, C A Zip Code: — Coordinates: 37.979 0 N, 122.329 0 W CSMIP Station number: 58506 Earthquake record studied: Loma Prieta (1989) Height & Number of Stories above ground: 13.4m (44.1ft), 3 stories Plan Shape: Rectangular Typical floor plan dimensions: N-S direction: 50.3m (165ft), E-W direction: 24.4m (80ft) Vertical force resisting system: Steel frames with concrete-slab over steel deeking Lateral force resisting system: Perimeter Moment-Resistant Steel Frames Design/Construction date: 1984/1985 Foundation type: Concrete pile caps at each column (Precast-Prestressed piles) - Grade beams Number of stories below ground: 0 Site Geology: Approx. 15 meter of fill Epicentral distance: 112km South of the building Note: The above information was obtained from "Shakal et al, 1989" 41 p o o F T B A C l - 01 B. e 1 £ f>T6ei_ fc£AM S«u>uJ B«?F % II H ii II *> •b » II II i i Z 4- £ STEt i - B^A^A 6 £ L O L 0 -S«W) 6 5 e 5 11 l> I* l l M !• It l l -7 E. .STEEL. B E A M © 6 1 0 * 1 2w D 0 6 I I » " » <=» 5 II •• II II 10 & G&ouuO P L O O ft S L A B I I UP •• n a 12. 5 II •• ii SLA&, KoBlZ. STAH.re.lt AT &0oP p ® 4 I Figure 4.8 Overview of Richmond 3-Story Office Building and Sensor layout, (After Shakal, et al, 1989) 42 4.9 Redlands 7-Story Commercial Building Building Description: Location: Redlands, C A Zip Code: — Coordinates: 34.056 ° N , 117.178 ° W CSMD? Station number: 23481 Earthquake record studied: Landers (1992) Height & Number of Stories above ground: 28.8m (94.4ft), 7 stories Plan Shape: Rectangular Typical floor plan dimensions: N-S direction: 28.3m (93ft), E-W direction: 42.7m (140ft) Vertical force resisting system: Concrete encased Steel columns Lateral force resisting system: Perimeter Moment-Resistant Steel Frames Design/Construction date: 1988/— Foundation type: — Number of stories below ground: 1 Site Geology: Alluvium Epicentral distance: 72km East of the building Note: The above information was obtained from "Shakal et al , 1992" 43 CO O i CN c CO o o DC i i c « i— o o LL xz o c I B •> to * • O O 2 5 CNf C a. o _o u_ •o c CM - O CO z o r -< o o -J cc o CO 2 LU CO r-l O U CJ 0 0 C CJ O N « u H S 0) o S oo CJ C u u ^ m CJ 4-t U W CJ - H C S CO 0 0 • H 0) - H 1-1 CJ o o tx 5 •a c C M s=.6-.ei<3)fr j ; N C S ! '— «— CJ c 1 s ( J CO. c o CO > a> LU LU o o c S II O 2 CC C • 5 = 2 II CO O 0 S 2 Figure 4.9 Overview of Redlands 7-Story Commercial Building and Sensor layout, (After Shakal, et al , 1992) 44 4.10 San Bernardino 3-Story Office Building Building Description: Location: San Bernardino, CA Zip Code: — Coordinates: 34.056 ° N , 117.289 ° W CSMIP Station number: 23516 Earthquake record studied: Landers (1992) Height & Number of Stories above ground: 12.6m (41.3ft), 3 stories Plan Shape: Rectangular Typical floor plan dimensions: N-S direction: 43.9m (144ft), E-W direction: 40.2m (132ft) Vertical force resisting system: Steel frames Lateral force resisting system: Perimeter Moment-Resistant Steel Frames Design/Construction date: 1983/— Foundation type: — Number of stories below ground: 0 Site Geology: Deep Alluvium Epicentral distance: 83km East of the building Note: The above information was obtained from "Shakal et al , 1992" 45 o o CC o or Plan CO or Plan «o or Plan Flo 3rd 3rd CN -2JT 1 _L (fi z g h-< O o _ l CC o (7) z LLt (7) c CO o o TJ c CM 0 9 O O £ ° S II Sz 0 3 . . 0C C co .2 w 3 CO o c 3 CO £: ~ CO O O © E 2 © C 0) E ~ CP I S 2 Q. > • • • J i 1 i c o CO > HI z CO • • • D • - B -• • - B -• • - B -D • • • • C « Cu > CD _ l TJ C D O T CD K- «•> » Figure 4.10 Overview of San Bernardino 3-Story Office Building and Sensor layout, (After Shakal, et al , 1992) 46 4.11 Los Angeles 2-Story Fire Command Control Building (Base-Isolated) Building Description: Location: Los Angeles, C A Zip Code: 90063 Coordinates: 34.053 ° N , 118.171 ° W CSMTP Station number: 24580 Earthquake record studied: Northridge (1994) Height & Number of Stories above ground: 9.8m (32ft), 2 stories Plan Shape: Rectangular Typical floor plan dimensions: N-S direction: 57.3m (188ft), E-W direction: 25.6m (84ft) Vertical force resisting system: Steel vented roof decking and steel decking with 3-4" concrete fill supported by steel frames and rubber bearings Lateral force resisting system: Perimeter braced (Chevron) steel frames isolated by elasto-meric bearings (under all 32 columns) Design/Construction date: 1988/1989-90 Foundation type: Spread footings Number of stories below ground: 0 Site Geology: Rock Sedimentary Epicentral distance: 38km North-West of the building Note: The above information was obtained from "Shakal et al, 1994" 47 c CL o _o u. C O | CO | c co o o LL r r o CO LU CO < e> — « £ 2 — w o . 91 dz Figure 4.11 Overview of L A 2-Story Fire Control Building and Sensor layout, (After Shakal, et al, 1994) 48 4.12 Los Angeles 7-Story University Hospital (Base-Isolated) Building Description: Location: Los Angeles, CA Zip Code: 90033 Coordinates: 34.062 ° N , 118.198 ° W CSMIP Station number: 24605 Earthquake record studied: Northridge (1994) Height & Number of Stories above ground: 31.1m (102ft), 7 stories Height & Number of Stories above isolated base: 35.7m (117ft), 8stories Plan Shape: S-shape Typical floor plan dimensions: N-S direction: 92.4m (303ft), E-W direction: 77.1m (253ft) Vertical force resisting system: Concrete slabs over steel deck supported by steel frames and rubber isolators Lateral force resisting system: Diagonally braced perimeter steel frames isolated by lead-rubber and elastomeric isolators Design/Construction date: 1988/1989-91 Foundation type: Continuous Spread footings under perimeter isolators and spread footings un-der interior isolators Site Geology: Rock Sedimentary Epicentral distance: 36km North-West of the building Note: The above information was obtained from "Shakal et al , 1994" 49 Figure 4.12 Overview of L A 7-Story University Hospital and Sensor layout, (After Shakal, et al, 1994) 50 Chapter 5 DETAILED STUDY OF THE RECORDED RESPONSE OF THE BUILDINGS 5.1 General The information obtained by processing the strong motion data recorded at each of the buildings is presented by a series of graphs and tables in Sections 5.2 to 5.11 of this chapter. These results will be discussed in Chapter 6. Sections 5.2 to 5.11 include the following: 1. Time-history of the accelerations recorded at the base of the buildings, which show the mag-nitude and the duration of the ground motions. 2. Pseudo acceleration response spectra of the ground motions, which show the expected level of seismically induced loads on the buildings, given their natural periods. 3. Relative displacement response spectra, which indicate the expected level of displacements in the buildings. 4. The Fourier spectra of the ground motion time histories are presented in a normalized form to show the frequency content of the ground vibrations. 5. The response of the buildings to the ground motions are presented as time-histories of absolute accelerations and relative displacements of the upper floors. 6. Rotational motions are computed as half the difference between the translations (or accelera-tions) of the two ends of each building. The summation of the translation at the center of the building and the rotation (as presented in this report) will result in the measured translation at the end of the building. The calculation of the rotational motions presented in the figures 51 is explained for each building in the beginning of the sections 5.2 to 5.12. The rotational data presented in the figures have the same units as the translational data. 7. Plots of orthogonal (X vs. Y) displacements (floor orbital motion) show the magnitude and direction of the displacements at the center of each floor. 8. Plots of absolute accelerations vs. relative displacements represent an estimate of the hyster-etic behaviour of the buildings. 9. Frequency response functions of the recorded accelerations show a measure of the accelera-tion amplification vs. frequency. These plots are used to determine the natural frequencies as explained in Chapter 3. The better distinguished and more relevant peaks on the FRF plots provide a higher level of accuracy in the estimation of the natural frequencies. 10. Spectral Response Functions are used to verify the results obtained from FRF's. 11. Tables of acceleration amplification factors associated with the potential modes are used to compare the amplification factors of the various modes. These values provide information that is similar to the modal participation factors in dynamic analysis. Note that in some cases two frequencies were associated with a single potential mode where there were two very close peaks on a FRF, or the peaks of the FRF's of two different floors corresponding the same potential mode did not occur at the same frequency. These cases represent a limitation of the accuracy of the system identification method. 12. The value of the Spectral Response Functions are presented for comparison with those of the FRF's. 52 5.2 Burbank 6-Story Office Building 5.2a Whittier Earthquake Records Properties of the Strong Motion Data Record Length: 40 sec Time interval: 0.02 sec No. of data points for each channel: 2000 Usable frequency range: 0.5 Hz to 23.0 Hz Assuming a rigid diaphragm at each floor, the accelerations, velocities and displacements at the center of the building in three directions, E-W (or X-directions) , N-S (or Y-directions) and ro-tation about vertical axis (or R-component) at levels 1, 2, 3 and 7 (roof) were obtained by ma-nipulating the recorded data of channels 1 to 13 as follows: IX = (Chan9 + Chan8)/2, 1Y = -Chan 13 + (Chan9-Chan8)/2 , 1R = (Chan9-Chan8)/2 2X = (Chan7 + Chan6)/2,2Y = -Chan 12 + (Chan7-Chan6)/2 , 2R = (Chan7-Chan6)/2 3X = (Chan5 + Chan4)/2 , 3Y = -Chanll + (Chan5-Chan4)/2 , 3R = (Chan5-Chan4)/2 7X = (Chan3 + Chan2)/2,7Y = -ChanlO + (Chan3-Chan2)/2 , 7R = (Chan3-Chan2)/2 A similar procedure was used to infer data for the corners of the buildings (assuming that dia-phragms are rigid and the displacements are small). These data were used to animate a 3-D rep-resentation of the buildings in order to evaluate the mode shapes. 53 Figure 5.2a.l Accelerations recorded at the Burbank 6-story bldg, during the 1987 Whittier Earthquake (After Shakal, et al , 1987) 54 Ground Acceleration in E-W direction (X-dir), (g's) 0.2 0.1 0 -0.1 -0.2 . l .«hJ l»r t ,WJ i 2£L _3Q_ Time (sec) JP Pseudo Acceleration Response Spectrum (g's) 0.8 0.6 0.4 0.2 0 -f'v. - 2.5% Dmpg 5% Dmpg -| 1 1 1 , I 0.5 1.5 Period (sec) 2.5 Relative Displacement Response Spectrum (mm) 0.5 1.5 2 Period (sec) 2.5 3.5 1 0.8 0.6 0.4 0.2 0 Normalized Fourier Spectrum I I J III 1 1 IVUii,Lkl -L. i.. 10 15 Frequency (Hz) 20 25 Figure 5.2a.2 Time-history and spectral characteristics of E-W (X) component of the ground motion recorded at the Burbank 6-story bldg, during the 1978 Whittier EQ. 55 Ground Acceleration in N-S direction (Y-dir), (g's) to- " 2 0 - - 3 0 " -4D Time (sec) Pseudo Acceleration Response Spectrum (g's) -2.5% Dmpg 5% Dmpg 0.5 1.5 Period (sec) —r-2.5 Relative Displacement Response Spectrum (mm) 50 40 30 20 10 0 2.5% Dmpg 5% Dmpg • . 0.5 Period (sec) 3.5 Normalized Fourier Spectrum 10 15 Frequency (Hz) 20 25 F i g u r e 5.2a.3 T ime-h is tory and spectral characterist ics o f N - S ( Y ) component o f the g round t ion recorded at the B u r b a n k 6-story b l d g , dur ing the 1978 Whi t t i e r E Q . 56 Ground Acceleration, Rotational (North acc-South acc)/2, (g's) -45- -20- -25- -30- -35- -40 Time (sec) Pseudo Acceleration Response Spectrum (g's) 1 1.5 Period (sec) 5 4 3 2 1 0 Relative Displacement Response. Spectrum (mm] 2.5% Dmpg 5% Dmpg y^-\ ^ / 0.5 1-5 a-2, x 2.5 Perioa (sec) 3.5 Normalized Fourier Spectrum T 10 15 Frequency (HZ) 20 25 F i g u r e 5.2a.4 T ime-h is tory and spectral characterist ics o f rotat ional (R) component o f the ground mot ion recorded at the Bu rbank 6-story b l d g , dur ing the 1978 Wh i t t i e r E Q . 57 0.2 Time (sec) Figure 5.2a.5 E-W (X-direction) & N-S (Y-direction) absolute accelerations of the instrumented upper floors of the Burbank 6-story bldg, during the 1987 Whittier EQ. Note: See Appendix A for individual plots of the absolute accelerations. 58 40 30 20 10 0 -10 -20 -30 -40 i Floor Relative Displacements (mm) Time (sec) 2x 3x 7x 60 50 40 30 20 10 0 -10 -20 -30 -40 -50 -60 Floor Relative Displacements (mm) 2y 3y 7y Time (sec) Figure 5.2a.6 E-W (X-direction) & N-S (Y-direction) relative displacements of the instrument-ed upper floors of the Burbank 6-story bldg, during the 1987 Whittier EQ. 59 0.04 0.03 0.02 0.01 -0.01 -0.02 -0.03 -0.04 4 3 2 1 0 -1 -2 -3 -4 Floor Absolute Rotational Acc (North acc -South acc) 12, (g's) Time (sec) Floor Relative Rotations (North dis -South dis)/2 (mm) Time (sec) 2r 3r 7r 2r 3r 7r Figure 5.2a.7 Torsional response of the instrumented upper floors of the Burbank 6-story bldg, during 1987 Whittier EQ. (See section 5.1 for explanation on obtaining the rotational data.) 60 Absolute Displ. Relative Displ. base u A •f 5 -4 -2 V< 2 4 1 •"t 6-1x(cm) E o 2nd floor —6--6-2x(cm) E o I A 5 -4 - 2 ^ K , uij i i V)U 2 4 1 A H 6 -3x(cm) Roof / 4 1 ^~^6'L.;__> E o 2nd floor A 5 -4 -2 ^ r 2 4 ( /f 6 -2x(cm) Roof 7x(cm) o— 3 -4 V-2/ /CjSM ) 4 ( V V Figure 5.2a.8 Orbital displacements at the center of the instrumented floors of the Burbank 6-story bldg, during the 1987 Whittier EQ. 61 F i g u r e 5.2a.9 Representat ion o f Hysteret ic behaviour at the instrumented f loors o f the B u r b a n k 6-story b l d g , dur ing the 1987 Whi t t ie r E Q . 62 M#l <2x/lx> 0.00 10.0 Hertz , t M#4 <2y/ly> './In 0.00 10.0 Hertz M#7 <2r/lr> 0.00 10.0 Hertz F I G 5 - 2 A . B L K M#2 <3x/lx> M#3 <7x/lx> 9.98 0.00 10.0 Hertz M#S<3yAy> Hertz 2 3 . 4 , ^ < 7 ^ 9.48 Mag 4.74 0.00 10.0 Hertz M#8 <3r/lr> 0.00 10.0 Hertz M#9 <7r/lr> 0.00 10.0 Hertz 0.00 10.0 Hertz Figure 5.2a.l0 Frequency Response Functions of the instrumented floors of the Burbank 6-Sto-ry Bldg, obtained from the 1987 Whittier EQ records. Note: The FRF's are computed by ME'scope using a Harming window, a block size N=1024,10 averages and 89% segment overlap. 63 IX 1Y IR Figure 5.2a.ll Mode shapes of the Burbank 6-story bldg, obtained from the 1987 Whittier E Q records. Note: The displacements of levels 2,3 and 7 (roof) are obtained from measured data. Displacements of the other floors are based on ME'scope's interpolation algorithm. 64 Figure 5.2a.l2 Spectral Response Functions of the Burbank 6-story bldg, obtained from the 1987 Whittier E Q records. 65 Table 5.2a. 1 Resu l ts o f Frequency Response Func t ions for the B u r b a n k 6-story b l d g , obtained f r om the 1987 Wh i t t i e r E Q records. X-direction Potential Mode # Frequency (Hz) Amplification Factor (2X/1X) Amplification Factor (3X/1X) Amplification Factor (7X/1X) 1 0.82 2.58 4.80 13.0 2a 2.34 3.03 4.27 3.81 2b 2.39 3.35 4.99 4.58 3 4.25 1.67 1.13 1.60 Damping Ratio estimated by M E ' s c o p e for mode I X : 4 . 5 4 % Y-direction Potential Mode# Frequency (Hz) Amplification Factor (2Y/1Y) Amplification Factor (3 Y/1Y) Amplification Factor (7 Y/1Y) l a 0.73 6.22 9.99 23.4 l b 0.78 4.19 7.83 22.2 2 a 2.25 4.20 5.31 4.43 2b 2.29 2.38 3.19 3.11 3a 4.05 1.66 0.94 1.42 3b 4.25 1.72 1.51 1.06 Damping Ratio estimated by M E ' s c o p e for mode 1Y: 3.00% R-direction Potential Mode# Frequency (Hz) Amplification Factor (2R/1R) Amplification Factor (3R/1R) Amplification Factor (7R/1R) 1 1.08 5.80 9.49 21.8 2 3.17 6.11 8.29 7.08 3a 5.62 3.85 1.48 2.68 3b 5.91 1.95 1.55 1.51 Damping Ratio estimated by M E ' s c o p e for mode 1R: 1.66% 66 Table 5.2a.2 Resu l t s o f Spectral Response Funct ions fo r the B u r b a n k 6-story b l d g , obtained f r om the 1987 Wh i t t i e r E Q records. X-direction Potential Mode# Frequency (Hz) SRF 0% damping (2X/1X) SRF 0% damping (3X/1X) SRF 0% damping (7X/1X) l a 0:77 3.05 4.83 11.3 l b 0.80 2.65 4.52 11.6 2 2.38 3.50 5.08 4.51 3 4.35 1:55 1.12 1.40 Y-direction Potential Mode* Frequency (Hz) SRF 0% damping (2Y/1Y) SRF 0% damping (3Y/1Y) SRF 0% damping (7Y/1Y) 1 0.77 5.17 8.45 21.4 2 2.27 3.56 4.64 3.78 3a 4.17 1.08 0.96 1.01 3b 4.35 0.99 0.91 1.14 R-direction Potential Mode# Frequency (Hz) SRF 0% damping (2R/1R) SRF 0% damping (3R/1R) SRF 0% damping (7R/1R) 1 1.11 5.33 8.70 20.0 2 3.23 5.88 8.71 7.44 3a 5.88 1.98 1.56 1.66 3b 6.25 1.86 1.59 1.32 67 Burbank 6-Story Office Building 5.2b Northridge Earthquake Records Properties of the Strong Motion Data Record Length: 60 sec Time interval: 0.02 sec No. of data points for each channel: 3000 Usable frequency range: 0.2 Hz to 23.0 Hz Manipulating the data to obtain the motion of the center of the building in the 3 directions, E-W (or X-directions), N-S (or Y-directions) and rotation about vertical axis (or R-component) . IX = (Chan9 + Chan8)/2 , 1Y = -Chanl3 + (Chan9-Chan8)/2 , IR = (Chan9-Chan8)/2 2X = (Chan7 + Chan6)/2 , 2Y = -Chanl2 + (Chan7-Chan6)/2 , 2R = (Chan7-Chan6)/2 7X = (Chan3 + Chan2)/2 , 7Y = -ChanlO + (Chan3-Chan2)/2 , 7R = (Chan3-Chan2)/2 68 Figure 5.2b.l Accelerations recorded at the Burbank 6-story bldg, during the 1994 Northridj EQ. (After Shakal, et al, 1994) 69 Ground Acceleration in E-W direction (X-dir), g's Time (sec) Pseudo Acceleration Response Spectrum (g's) -2.5% Dmpg 5% Dmpg 0.5 1.5 Period (sec) 2.5 Relative Displacement Response Spectrum (mm 3 4 Period (sec) 1 -0.8 -0.6 -0.4 -0.2 -0 -Normalized Fourier Spectrum I J III.,I ll I 1 l i l i l i i i U I ' M J M ! , 10 15 Frequency (Hz) 20 25 Figure 5.2b.2 Time-history and spectral characteristics of E-W (X) component of the ground motion recorded at the Burbank 6-story bldg, during the 1994 Northridge EQ. 70 Ground Acceleration in N-S direction (Y-dir), g's - 3 0 - " 4 0 -Time (sec) Pseudo Acceleration Response Spectrum (g's) — 1 - 5 0 " -90 -2.5% Dmpg 5% Dmpg 150 100 50 1.5 Period (sec) Relative Displacement Response Spectrum (mm) 2.5 2.5% Dmpg 5% Dmpg 1 0.8 0.6 0.4 0.2 3 4 Period (sec) Normalized Fourier Spectrum 1 i l l j ] ,!if1ffll l lHH 10 15 Frequency (Hz) 20 25 Figure 5.2b.3 Time-history and spectral characteristics of N-S (Y) component of the ground tion recorded at the Burbank 6-story bldg, during the 1994 Northridge EQ. 71 Ground Acceleration, Rotational (North Acc- South Acc)/2, (g's) 0.15 -i .0.15 J Time (sec) Pseudo Acceleration Response Spectrum (g's) 1.5 Period (sec) -2.5% Dmpg •5% Dmpg 2.5 20 15 10 0 Relative displacement Response Spectrum (mm) -2.5% Dmpg 5% Dmpg 7.5 Normalized Fourier Spectrum 10 15 Frequency (Hz) 20 25 Figure 5.2b.4 Time-history and spectral characteristics of rotational (R) component of the ground motion recorded at the Burbank 6-story bldg, during the 1994 Northridge EQ. 72 Figure 5.2b.5 E-W (X-direction) & N-S (Y-direction) absolute accelerations of the instrumented upper floors of the Burbank 6-story bldg, during the 1994 Northridge EQ. 73 100 T Floor Relative Displacements (mm) Time (sec) 2x-| 7x 100 80 60 40 20 0 -20 -40 -60 -80 -100 -120 Floor Relative Displacements (mm) Time (sec) Figure 5.2b.6 E-W (X-direction) & N-S (Y-direction) relative displacements of the instrument-ed upper floors of the Burbank 6-story bldg, during the 1994 Northridge EQ. 74 0.05 Floor Absolute Rotational Acc . (North acc-South acc)/2,(g's) 2r 7r Time (sec) 10 -10 Floor Relative Rotations (North dis-South dis)/2, (mm) 2 r 7 r Time (sec) F i g u r e 5.2b.7 Tors iona l response o f the instrumented upper f loors o f the B u r b a n k 6-story b l d g , dur ing the 1994 Nor th r idge E Q . 75 Absolute Displ. Relative Displ. base dx(cm) 2nd floor 9 1E dx(cm) 2nd floor -4f 2 -9 -6 -3^5y 3 6 9 1|2 dx(cm) R o o f E •a dx(cm) oRpof dx(cm) F i g u r e 5.2b.8 Orbital displacements at the center of the instrumented floors of the Burbank 6-story bldg, during the 1994 Northridge E Q . 76 Figure 5.2b.9 Representation of hysteretic behaviour at the instrumented floors of the Burbank 6-story bldg, during the 1994 Northridge EQ. 77 FG5-2B.BLK M#l <2x/lx> 0.00 M#5 <2r/lr> 5.00 10.0 Hertz M#2 <7x/lx> 0.00 M#4 <7y/ly> 5.00 10.0 Hertz 0.00 M#6 <7r/lr> 5.00 10.0 Hertz 5.00 10.0 Hertz 5.00 10.0 Hertz Figure 5.2b.l0 Frequency Response Functions of the instrumented floors of the Burbank 6-story bldg, obtained from the 1994 Northridge EQ records. Note: The FRF's are computed by ME'scope using a Harming window, a block size N=2048, 5 averages and 88% segment overlap. 78 IX 1Y 1R 3X 3Y 3R Figure 5.2b.ll Mode shapes of the Burbank 6-story bldg, obtained from the 1994 Northridge EQ records. Note: The displacements of levels 2 and 7 (roof) are obtained from measured data. Displacements of the other floors are based on ME'scope's interpolation algorithm. 79 -2x/1x-0%dmpg - i : — - r 1 2 3 4 Frequency (Hz) 8 6 4 2 0 16 14 12 10 8 6 4 2 0 -I I 7x/1x-0%dmpg - 1 1 1 ! •—, ; ,— 1 2 3 4 Frequency (Hz) 2y/1 y-0%dmpg I A V 1 2 3 4 5 Frequency (Hz) 22.5 20 17.5 15 12.5 10 7.5 5 2.5 0 1 2 3 4 Frequency (Hz) -2r/1r-0%dmpg 20 17.5 15 12.5 10 7.5 5 2.5 0 7r/1r-0%dmpg I 1 1 . A i 1 1 1 1 1 2 3 4 5 Frequency (Hz) Figure 5.2a.l2 Spectral Response Functions of the Burbank 6-story bldg, obtained from the 1994 Northridge EQ records. 80 Table 5.2b.l Resu l ts o f Frequency Response Funct ions fo r the B u r b a n k 6-story b l d g , obtained f r o m the 1994 Nor th r idge E Q records X-direction Potential Mode# Frequency (Hz) Amplification Factor (2X/1X) Amplification Factor (3X/1X) Amplification Factor (7X/1X) 1 0.71 5.09 - 21.9 2 2.00 4.89 - 6.03 3 3.71 3.00 - 3.71 4 4.86 0.98 - 1.96 Damping Ratio estimated by M E ' s c o p e for mode IX: 3.28% Y-direction Potential Mode# Frequency (Hz) Amplification Factor (2Y/1Y) Amplification Factor (3 Y/1Y) Amplification Factor (7 Y/1Y) 1 0.71 5.60 - 19.8 2 2.05 6.99 - 8.42 3 3.42 3.70 - 6.74 Damping Ratio estimated by M E ' s c o p e for mode 1Y: 2.00% R-direction Potential Mode* Frequency (Hz) Amplification Factor (2R/1R) Amplification Factor (3R/1R) Amplification Factor (7R/1R) 1 1.09 5.06 - 15.3 2 3.10 7.00 - 9.30 3 5.15 4.41 - 2.42 Damping Ratio estimated by M E ' s c o p e for mode IR: 1.10% 81 Table 5.2b.2 Resu l ts o f Spectral Response Funct ions for the B u r b a n k 6-story b l d g , obtained f r om the 1994 Nor th r idge E Q records. X-direction Potential Mode # Frequency (Hz) SRF 0% damping (2X/1X) SRF 0% damping (3X/1X) SRF 0% damping (7X/1X) 1 0.714 3.84 .- 15.4 2 2.04 2.14 - 2.55 3 3.70 1.20 - 1.15 Y-direction Potential Mode# Frequency (Hz) SRF 0% damping (2Y/1Y) SRF 0% damping (3Y/1Y) SRF 0% damping (7Y/1Y) 1 0.72 5.34 - 20.4 2 2.13 2.74 - 3.84 3 3.85 1.50 - 1.45 R-direction Potential Mode# Frequency (Hz) SRF 0% damping (2R/1R) SRF 0% damping (3R/1R) SRF 0% damping (7R/1R) 1 1.11 4.5 - 19.1 2 2.94 2.97 - 3.68 3 5.88 1.05 - 0.83 82 Table 5.2.3 Estimated natural frequencies (and periods) of the Burbank 6-story bldg. based on the results of FRF results, SRF results and visual inspection of the three dimensional mode shapes obtained from analysis of 1987 Whittier and 1994 Northridge EQ data. WHITTIER E A R T H Q U A K E DATA X-Direction (E-W) Y-Direction (E-W) Rotation Frequency (Hz) Period (S) Frequency (Hz) Period (S) Frequency (Hz) Period (S) Model 0.80 1.25 0.76 1.32 1.10 0.91 Mode 2 2.37 0.42 2.27 0.44 3.20 0.31 Mode 3 4.30 0.23 4.20 0.24 5.70 0.18 N O R T H R I D G E E A R T H Q U A K E DATA X-Direction (E-W) Y-Direction (E-W) Rotation Frequency (Hz) Period (S) Frequency (Hz) Period (S) Frequency (Hz) Period (S) Mode 1 0.71 1.41 0.71 1.41 1.10 0.91 Mode 2 2.02 0.50 2.05 0.49 3.05 0.33 Mode 3 3.70 0.27 3.65 0.27 5.40 0.19 Mode 4 4.86 0.21 - - - -Fundamental Period according to N B C C 1995: T = 0.1 N ==> T = 0.60 sec T = 0.085 (h n ) 3 / 4 = 0.085 (25.15m)3/4 = 0.96 sec Fundamental Period according to U B C 1997: T = 0.035 (h n ) 3 / 4 = 0.035 (82.5 ft) 3 / 4 = 0.96 sec 83 5.3 San Bernardino 5-Story Hospital Properties of the Strong Motion Data: Record Length: 100 sec Time interval: 0.01 sec No. of data points for each channel: 10001 Usable frequency range: 0.3 Hz to 46.0 Hz Manipulating the data to obtain the motion of the center of the building in the 3 directions, E-W (or X-directions) , N-S (or Y-directions) and rotation about vertical axis (or R-component) : IX = (2 .Chan3 + Chan4)/3 , 1Y = Chan2 , 1R = (Chan3-Chan4)/2 3X = (2 .Chan7+Chan8)/3 , 3Y = (2 .Chan5+ Chan6)/3 3R= {[(Chan7-Chan8)/2] + [(Chan6-Chan5)/2] .(140/110) }/ 2 6X = (2 .Chan7+Chan8)/3 , 6Y = (2 .Chan5+ Chan6)/3 6R= {[(Chan7-Chan8)/2] + [(Chan6-Chan5)/2] .(140/110) }/ 2 Note: Rotation of level 3 could be obtained both from the difference of channels 7 & 8 and chan-nels 5 & 6. The average of the two values are used in this study as shown above. This also applies to level 6 data. 84 O J — ' e n r ^ ^ m o a i u D i n c v i Figure 5.3.1 Accelerations recorded at the San Bernardino 5-story hospital during the 1994 Northridge Earthquake. (After Shakal, et al, 1994) 85 Ground Acceleration in E-W direction (X-dir), g's _8a -0.05 Time (sec) 100 0.25 Pseudo Acceleration Response Spectrum (g's) 1.5 Period (sec) Relative Displacement Response Spectrum (mm) 1.5 2 2.5 Period (sec) Normalized Fourier Spectrum 10 Frequency (Hz) Figure 5.3.2 Ground motion properties, E-W (X-direction), San Bernardino 5-story hospital, Northridge EQ. 86 Ground Acceleration in N-S direction (Y-dir), g's Time (sec) 0.25 0.2 0.15 0.1 0.05 0 Pseudo Acceleration Response Spectrum (g's) 2.5% Dmpg 5% Dmpg 17f \ \ rJ -AS X — ""' h * ^ v s \ LS » —-„\ 0.5 1.5 Period (sec) 2.5 50 40 30 20 10 0 Relative Displacement Response Spectrum (mm) -2.5% Dmpg 5% Dmpg 0.5 1.5 2 2.5 Period (sec) Normalized Fourier Spectrum 0.8 0.6 0.4 0.2 04 OT^^ — 10 Frequency (Hz) 15 20 Figure 5.3.3 Time-history and spectral characteristics of N-S (Y) component of the ground motion recorded at the San Bernardino 5-story hospital during the 1994 Northridge EQ. 87 Ground Accelerations, Rotational ( g's) Time (sec) 0.05 0.04 0.03 0.02 0.01 0 Pseudo Acceleration Response Spectrum (g's) 2.5% Dmpg 5% Dmpg 0.5 1.5 Period (sec) 2.5 Relative Displacement Response Spectrum (mm) 1.5 2 2.5 Period (sec) Normalized Fourier Spectrum 10 Frequency (Hz) 15 20 Figure 5.3.4 Time-history and spectral characteristics of rotational (R) component of the ground motion recorded at the San Bernardino 5-story hospital during the 1994 Northridge EQ. 88 0.2 0.15 0.1 0.05 0 -0.05 (jl -0.1 -0.15 -0.2 Floor Absolute Accelerations, (g's) fc. A M J^ftii • Time (sec) Floor Absolute Accelerations, (g's) 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 Floor Absolute Accelerations, (g's) Time (sec) Figure 5.3.5 Absolute accelerations of the instrumented upper floors of the San Bernardino 5-story hospital during the 1994 Northridge EQ. 89 0.2 0.15 0.1 0.05 0 -0.05 3J0--0.1 -0.15 -0.2 Floor Absolute Accelerations, (g's) 3x 6x 50 _2D_ Time (sec) 0.2 0.15 0.1 0.05 0 -0.05: -0.1 -0.15 -0.2 Floor Absolute Accelerations, (g's) AH 3y 6y S0_ _60_ JUL Time (sec) 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 30 Floor Absolute Accelerations, (g's) 40 50 60 70 Time (sec) 3r 6r Figure 5.3.5 Cont'd 90 Floor Relative Displacements (mm) 12.5 -, -8 Floor Relative Displacements (mm) 3r 6r • ill I 0 5 10 15 llJIfll'' I IF M p Time (sec) Figure 5.3.6 Relative displacements of the instrumented upper floors of the San Bernardino 5-story hospital during the 1994 Northridg EQ. 91 12.5 10 7.5 5 2.5 0 -2.5 -5 -7.5 -10 -12.5 Floor Relative Displacements (mm) 3x 6x -40 50 §0 70- 8P Time (sec) 8 6 4 2 0 -2 -4 -6 -8 Floor Relative Displacements (mm) 3y 6y I* 111 11 1 iin ' «;n fin 7n an Time (sec) Floor Relative Displacements (mm) 3r 6r 3TJ 40 50 60 70 Time (sec) Figure 5.3.6 Cont'd 92 Absolute Displ. Relative Displ. « -11 3rd floor -4-5 -1 -0 .5 -4-0.5 1 1 3x(cm) E _ Roof 1 .5 ^ * 4 M ~ ^ l l i 6x(cm) E Roof 1 .5 -1 - - S ^ | | | l | 1 - T 6x(cm) Figure 5.3.7 Orbital displacements at the center of the instrumented floors of the San Bernardino 5-story hospital during the 1994 Northridge EQ. 93 F i g u r e 5.3.8 Representat ion o f hysteretic behaviour at the instrumented f loors o f the San B e r -nard ino 5-story hospi ta l dur ing the 1994 Nor thr idge E Q . 94 F I G - 5 - 3 . B L K M M <3x/lx> M#2 <6x/lx> 0.00 5.00 10.0 15.0 Hertz 0.00 14.6 g 7 i 1 L A , 0.00 5.00 10.0 15.0 Hertz M#5 <3r/lr> 0.00 J 0.00 5.00 10.0 15.0 0.00 5.00 10.0 15.0 Hertz l f t . MM <6y/ly> 1"->1 i 0.00 5.00 10.0 15.0 Hertz M#6 <6r/lr> Hertz 0.00 5.00 10.0 15.0 Hertz Figure 5.3.9 Frequency Response Functions of the instrumented floors of the San Bernardino 5-story hospital, obtained from the 1994 Northridge EQ records. Note: The FRF' s are computed by ME' scope using a Harming window, a block size N=4096, 10 averages and 89% segment overlap. 95 3X 3Y 3R Figure 5.3.10 Mode shapes of (L-shape presentation of) the San Bernardino 5-story hospital, ob-tained from the 1994 Northridge EQ records. Note: The displacements of levels 3 and 6 (roof) are obtained from measured data. Displacements of the other floors are based on ME'scope's interpolation algorithm. 96 Figure 5.3.11 Spectral Response Functions of the San Bernardino 5-story hospital, obtained from the 1994 Northridge E Q records. 97 Table 5.3.1 Resu l ts o f Frequency Response Funct ions fo r the San Berna rd ino 5-story hospi ta l , obtained f r o m the 1994 Nor thr idge E Q records X-direction Potential Mode# Frequency (Hz) Amplification Factor (3X/1X) Amplification Factor (6X/1X) 1 1.98 8.80 16.1 2 5.51 3.84 5.68 3 10.25 3.37 3.16 Damping Ratio estimated by M E ' s c o p e for mode I X : 3.30% Y-direction Potential Mode* Frequency (Hz) Amplification Factor (3 Y/1Y) Amplification Factor (6Y/1Y) 1 2.08 10.5 19.6 2 5.57 3.42 4.60 3 10.37 1.56 3.25 Damping Ratio estimated by M E ' s c o p e for mode 1Y: 2.80% R-direction Potential Mode* Frequency (Hz) Amplification Factor (3R/1R) Amplification Factor (6R/1R) 1 2.56 14.6 28.3 2 6.67 9.64 7.03 3a 11.2 4.91 4.51 3b 13.33 3.52 0.84 Damping Ratio estimated by M E ' s c o p e for mode 1R: 1.00% 98 Table 5.3.2 Results of Spectral Response Functions for the San Bernardino 5-story hospital, ob-tained from the 1994 Northridge EQ records. X-direction Potential Mode# Frequency (Hz) SRF 0% damping (3X/1X) SRF 0% damping (6X/1X) 1 1.96 7.26 13.4 2 5.26 3.19 7.03 3 9.10 3.03 1.41 Y-direction Potential Mode# Frequency (Hz) SRF 0% damping (3Y/1Y) SRF 0% damping (6Y/1Y) 1 2.08 7.14 14.2 2 5.88 2.58 3.07 3 - - -R-direction Potential Mode# Frequency (Hz) SRF 0% damping (3R/1R) SRF 0% damping (6R/1R) 1 2.50 19.6 38.9 2 7.10 8.0 10.9 3 - - -99 Table 5.3.3 Estimated natural frequencies (and periods) of the San Bernardino 5-story hospital based on the results of FRF results, SRF results and visual inspection of the three dimensional mode shapes obtained from analysis of 1994 Northridge EQ data. N O R T H R I D G E E A R T H Q U A K E DATA X-Direction (E-W) Y-Direction (E-W) Rotation Frequency (Hz) Period (S) Frequency (Hz) Period (S) Frequency (Hz) Period (S) Model 2.00 0.50 2.10 0.48 2.50 0.4 Mode 2 5.50 0.18 5.60 0.18 7.00 0.14 Mode 3 10.1 0.10 10.4 0.10 12.5 0.08 * Spectral values at the natural periods in the ground motion response spectra and the re-sponse time-histories suggest that the 1st mode dominated the structural response. Fundamental Period according to N B C C 1995: T = 0 . 1 N = > T - 0 . 5 0 sec T = 0.085 (h n ) 3 / 4 = 0.085 (21.03m)3/4 = 0.84 sec Fundamental Period according to U B C 1997: T = 0.035 (h n ) 3 / 4 = 0.035 (69 ft) 3 / 4 = 0.84 sec 100 5.4 Pasadena 6-Story Office Building Properties of the Strong Motion Data: Record Length: 60sec Time interval: 0.02 sec No. of data points for each channel: 3000 Usable frequency range: 0.24 Hz to 23.0 Hz Manipulating the data to obtain the motion of the center of the building in the 3 directions, E-W (or X-directions), N-S (or Y-directions) and rotation about vertical axis (or R-component): IX - (Chanl4+ Chanl3)/2 , 1Y = Chanl6, IR = (Chanl4-Chanl3)/2 2X = (Chanl2+ Chanl l)/2 , 2Y = (Chan2+Chanl)/2, 2R= {[(Chanl2-Chanll)/2] + [(Chan2-Chan l)/2].( 125/117) }ll 8X = (Chan8+ Chan6)/2 , 8Y - (Chan4+Chan3)/2 , 8R= {[(Chan8-Chan7)/2] .(125/54) + [(Chan4-Chan3)/2] .(125/117) }ll 8X(modified) = Chan7 -{ [(8R) (2/125)]. (8.5) } Note: Rotation of level 2 could be obtained both from the difference of channels 12& 11 and channels 1& 2. The average of the two values are used in this study as shown above. Similar idea has been applied to level 8 (roof). 101 Figure 5.4.1 Accelerations recorded at the Pasadena 6-story office building during the 1994 Northridge Earthquake, (After Shakal, et al, 1994) 102 Ground acceleration in E-W direction (X-dir), g's Time (sec) Pseudo Acceleration Response Spectrum (g's) 0.5 0.4 0.3 0.2 0.1 0 -2.5% Dmpg - - - - - 5% Dmpg 0.5 1.5 Period (sec) 2.5 Relative Displacement Response Spectrum (mm) -2.5% Dmpg 5% Dmpg k Normalized Fourier Spectrum 10 Frequency (Hz) 15 20 Figure 5.4.2 Time-history and spectral characteristics of E-W (X) component of the ground motion recorded at the Pasadena 6-story office bldg. during the 1994 Northridge EQ. 103 Ground acceleration in N-S direction (Y-dir), g's 0.15 T 1 Time (sec) Pseudo Acceleration Response Spectrum (g's) 2.5% Dmpg 5% Dmpg 0 0.5 1 1.5 2 2.5 3 Period (sec) Relative Displacement Response Spectrum (mm) 2 2.5 Period (sec) 2.5% Dmpg 5% Dmpg Normalized Fourier Spectrum 0.8 0.6 0.4 0.2 10 Frequency (Hz) 15 20 F i g u r e 5.4.3 Time-history and spectral characteristics of N-S (Y) component of the ground motion recorded at the Pasadena 6-story of f ice bldg. during the 1994 Northridge E Q . 104 Ground Acceleration, Rotational, g's -20- -30- 40-Time (sec) -50-0.25 0.2 0.15 0.1 0.05 0 Pseudo Acceleration Response Spectrum (g's) 2.5% Dmpg 5% Dmpg 0.5 1 1.5 Period (sec) 2.5 Relative Displacement Response Spectrum (mm) -2.5% Dmpg 5% Dmpg Period (sec) 1 0.8 0.6 0.4 0.2 0 Normalized Fourier Spectrum •L. 1 Illl • M Mi I 10 15 Frequency (Hz) 20 25 Figure 5.4.4 Time-history and spectral characteristics of rotational (R) component of the ground motion recorded at the Pasadena 6-story office bldg. during the 1994 Northridge EQ. 105 Figure 5.4.5 Absolute accelerations of the instrumented upper floors of the Pasadena 6-story office bldg, during the 1994 Northridge EQ. 106 Floor Relative Displacements (mm) 2x 8x Time (sec) Floor Relative Displacements (mm) 2y 8y 50 -20 -30 Time (sec) 15 10 5 0 -5 -10 -15 Floor Relative Displacements (mm) Time (sec) F i g u r e 5.4.6 Re la t i ve displacements o f the instrumented upper f loors o f the Pasadena 6-story o f f ice b ldg . dur ing the 1994 Nor thr idge E Q . 107 Absolute Displ. Relative Displ. base a— A • r •\ o o £. A A. 1 1 1 i@9 pK7i i . I . I j -4 .3 -2 -vx o 1 1 2 3 4 !i •> - O A • f -L — >— 09 1x(cm) 2nd floor A H *> O £. 4 I f 1 ? s 4 ! " *t - 5 -2x(cm) 2nd floor CM A H o £. 1 I i i i ^ppP 5 -4 _3 _ 2 -1 -j ( ) 1 ° 3 A ' - z i •o /I *t 6-2x(cm) I A 1 o «_ ^ -A ^ T ^ a ^ r ^ A ••f 5 -8x(cm) Roof 1 *1 A *T •Q <3 <L f \ \ J 1 1 \. \. U \ l A H 5 -8x(cm) Figure 5.4.7 Orbital displacements at the center of the instrumented floors of the Pasadena 6-story office bldg. during the 1994 Northridge EQ. 108 F i g u r e 5.4.8 Representat ion o f hysteretic behaviour at the instrumented f loors o f the Pasadena 6-story o f f ice b l d g , dur ing the 1994 Nor thr idge E Q . 109 F I G 5 - 4 A . B L K M#l <2x/lx> 0.00 5.00 10.0 15.0 Hertz J g 7 0.00 5.00 10.0 15.0 Hertz 0 M#5 <2r/lr> M#2 <8x/lx> 0.00 5.00 10.0 15.0 Hertz M#6 <8r/lr> 0.00 5.00 10.0 15.0 Hertz 5.00 10.0 15.0 Hertz F i g u r e 5 .4.9a Frequency Response Funct ions o f the instrumented f loors o f the Pasadena 6-story o f f ice b l d g , obtained f r om the 1994 Nor thr idge E Q Records . ( W i t h 5 averages). Note: The FRF's are computed by ME'scope using a Harming window, a block size N=2048 and 88% segment overlap. 110 F I G 5 - 4 B . B L K M#l <2x/lx> M#2 <8x/lx> 0.00 5.00 10.0 15.0 Hertz , M # 3 <2y/ly> 1.45-n J -^~ 0.00 5.00 10.0 15.0 Hertz M#4 <8y/ly> 0.00 5.00 10.0 15.0 Hertz M#5 <2r/lr> 0.00 5.00 10.0 15.0 Hertz M#6 <8r/lr> 0.00 5.00 10.0 15.0 Hertz 0.00 5.00 10.0 15.0 Hertz Figure 5.4.9b Frequency Response Functions of the instrumented floors of the Pasadena 6-story office bldg, obtained from the 1994 Northridge EQ records. (With 20 averages). Note: The FRF's are computed by ME'scope using a Harming window, a block size N=1024 and 90% segment overlap. I l l IX 1R Not obtained 3X 3R Figure 5.4.10 Mode shapes of the Pasadena 6-story office bldg, obtained from the 1994 Northridge E Q records. Note: The displacements of levels 2 and 8 are obtained from measured data. Displacements of the other floors are based on ME'scope's interpolation algorithm. 112 30 25 20 15 10 5 0 -2x/1x-0%dmpg -i r 2 4 6 8 10 Frequency (Hz) -2y/1y-0%dmpg 2 4 6 8 Frequency (Hz) 2r/1r-0%dmpg n L 1 1 1 1 2 4 6 8 10 Frequency (Hz) 12 10 8 6 -8x/1x-0%dmpg - i 1 1 1 1 2 4 6 8 10 Frequency (Hz) 10 8 6 4 2 0 8y/1 y-0%dmpg 1 1 1 1 2 4 6 8 10 Frequency (Hz) 50 45 40 35 30 25 20 15 10 5 0 -8r/1r-0%dmpg ~i r 2 4 6 8 Frequency (Hz) 10 Figure 5.4.11 Spectral Response Functions of the Pasadena 6-story office bldg, obtained from the 1994 Northridge EQ records. 113 Table 5.4.1 Resu l t s o f Frequency Response Funct ions fo r the San Berna rd ino 5-story hospi ta l , obta ined f r o m the 1994 Nor thr idge E Q records X-direction Potential Mode # Frequency (Hz) Amplification Factor (2X/1X) Amplification Factor (8X71X) .1 0.45 5.32 14.7 2 1.81 2.82 4.42 3 3.32 2.00 4.09 Damping Ratio estimated by M E ' s c o p e for mode I X : 3.90% Y-direction Potential Mode # Frequency (Hz) Amplification Factor (2 Y/1Y) Amplification Factor (8Y/1Y) 1 0.59 3.22 7.08 2 2.22 2.07 2.00 3 3.89 1.96 1.62 Damping Ratio estimated by M E ' s c o p e for mode 1Y: 3.40% R-direction Potential Mode# Frequency (Hz) Amplification Factor (2R/1R) Amplification Factor (8R/1R) 1 0.84 12.85 47.6 2 2.47 6.01 7.32 3a 4.8 8.46 5.65 3b 5.2 9.75 1.43 Damping Ratio estimated by M E ' s c o p e for mode 1R: 2.00% 114 Table 5.4.2 Resu l ts o f Spectral Response Funct ions fo r the San Berna rd ino 5-story hosp i ta l , ob-tained f r o m the 1994 Nor thr idge E Q records. X-direction Potential Mode # Frequency (Hz) SRF 0% damping (2X/1X) SRF 0% damping (8X/1X) 1 0.45 4.0 11.1 2 1.89 1.6 2.9 3 3.57 1.4 2.5 Y-direction Potential Mode# Frequency (Hz) SRF 0% damping (2Y/1Y) SRF 0% damping (8Y/1Y) 1 0.55 3.6 7.0 2 2.13 1.1 1.4 3 - - -R-direction Potential Mode* Frequency (Hz) SRF 0% damping (2R/1R) SRF 0% damping (8R/1R) 1 0.72 17.6 46.2 2 2.56 10.5 11.5 3 - - -115 Table 5.4.3 Estimated natural frequencies (and periods) of the Pasadena 6-story office building based on the results of FRF results, SRF results and visual inspection of the three dimensional mode shapes obtained from analysis of 1994 Northridge EQ data. NORTHRIDGE E A R T H Q U A K E DATA X-Direction (E-W) Y-Direction (E-W) Rotation Frequency (Hz) Period (S) Frequency (Hz) Period (S) Frequency (Hz) Period (S) Model 0.45 2.22 0.58 1.72 0.82 1.22 Mode 2 1.85 0.54 2.20 0.45 2.50 0.40 Mode 3 3.40 0.29 3.9 0.26 - -* Spectral values at the natural periods in the ground motion response spectra and the re-sponse time-histories suggest that the 2nd & 3rd modes had a significant contribution in the structural response. Fundamental Period according to N B C C 1995: T = 0.1 N ==> T = 0.70 sec T = 0.085 (h n ) 3 / 4 = 0.085 (25.0m)3/4 = 0.95 sec Fundamental Period according to U B C 1997: T = 0.035 (h n ) 3 / 4 = 0.035 (82 ft) 3 / 4 = 0.95 sec 116 5.5 San Jose 3-Story Office Building Properties of the Strong Motion Data: Record Length: 50 sec Time interval: 0.02 sec No. of data points for each channel: 2500 Usable frequency range: 0.16 Hz to 23.0 Hz Manipulating the data to obtain the motion of the center of the building in the 3 directions, E-W (or X-directions) , N-S (or Y-directions) and rotation about vertical axis (or R-component): IX = - Chan2 , 1Y = (Chan3 + Chan4)/2 , 1R = (Chan3-Chan4)/2 3X = - Chan5 , 3 Y = (Chan6 + Chan7)/2, 3R = (Chan6-Chan7)/2 4X = - Chan8 , 4Y = (Chan9 + Chanl0)/2, 4R = (Chan9-Chanl0)/2 117 Free Field Acceleration, E-W direction (X-dir), g's 1.2 1 0.8 0.6 0.4 0.2 0 200 150 100 50 0 Pseudo Acceleration Response Spectrum (g's) 2.5% Dmpg f i ( V l II | \ fail lu / 5% Dmpg 0.5 1.5 priod (sec) 2.5 Relative Displacement Response Spectrum (mm) / v ^ — ^~z~ ~* 2.5% Dmpg -5% Dmpg 2.5 period (sec) 7.5 10 Normalized Fourier Spectrum 10 15 Frequency (Hz) 20 25 Figure 5.5.2 Time-history and spectral characteristics of E-W (X) component of the free field motion recorded at the San Jose 3-story office bldg, during the 1989 Loma Prieta EQ. 119 Free Field Acceleration, N-S direction (Y-dir), g's Pseudo Acceleration Response Spectrum (g's) •2.5% Dmpg 5% Dmpg 0.5 1 1.5 2 priod (sec) 2.5 400 300 200 100 0 Relative Displacement Response Spectrum (mm) ~ — *-' 2.5% Dmpg \j /o u 111 \J y 2.5 period (sec) 7.5 10 Normalized Fourier Spectrum 10 15 Frequency (Hz) 20 25 Figure 5.5.3 Time-history and spectral characteristics of N-S (Y) component of the free field motion recorded at the San Jose 3-story office bldg, during the 1989 Loma Prieta EQ. 120 0.2 0.1 0 -0.1 -0.2 Ground Acceleration, E-W direction (X-dir), g's 30 4b Time (sec) Pseudo Acceleration Response Spectrum (g's) •2.5% Dmpg 5% Dmpg 0.5 1.5 Period (sec) 2.5 Relative Displacement Response Spectrum (mm) 2.5% Dmpg 5% Dmpg 4 5 Period (sec) 1 0.8 0.6 0.4 0.2 0 Normalized Fourier Spectrum •-Hi 10 15 Frequency (Hz) 20 25 Figure 5.5.4 Time-history and spectral characteristics of E-W (X) component of the ground motion recorded at the San Jose 3-story office bldg, during the 1989 Loma Prieta EQ. 121 0.2 0.15 0.1 0 . 0 5 0 - 0 . 0 5 -0.1 -0.15 - 0 . 2 Ground Acceleration, N-S direction (Y-dir), g's I -20 30- -40-Time (sec) Pseudo Acceleration Response Spectrum (g's) 0.5 1.5 Period (sec) •2.5% Dmpg 5% Dmpg 2.5 300 250 200 150 100 50 0 Relative Displacement Response Spectrum (mm) "" "— s*^Z.~*~~ ' " • • ^ r 2.5% Dmpg 5% Dmpg 4 5 6 Period (sec) 10 Normalized Fourier Spectrum 10 15 Frequency (Hz) 20 25 Figure 5.5.5 Time-history and spectral characteristics of N-S (Y) component of the ground motion recorded at the San Jose 3-story office bldg, during the 1989 Loma Prieta EQ. 122 Ground Acceleration, Rotational, g's 0.25 0.2 0.15 0.1 0.05 0 Pseudo Acceleration Response Spectrum (g's) O CO/. r V m n n -£ . . \ J /O LTTipy 5% Dmpg 0.5 1 1.5 Period (sec) 2.5 10 8 6 4 2 0 Relative Dispacement Response Spectrum (mm) » |1 ". -2.5% Dmpg 5% Dmpg 2.5 7.5 10 Period (sec) 1 0.8 0.6 0.4 0.2 0 Normalized Fourier Spectrum I i J litfrrh—i P 10 15 Frequency (Hz) 20 25 F i g u r e 5.5.6 T ime-h is tory and spectral characterist ics o f rotational (R) component o f the ground mo t ion recorded at the San Jose 3-story of f ice b l d g , dur ing the 1989 L o m a Pr ie ta E Q . 123 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 F loor Abso lu te Acce le ra t ions (g's) Time (sec) 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 F loor Abso lu te Acce le ra t ions (g's) Time (sec) 0.2 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 F loor Abso lu te Acce le ra t ions (g's) 3r 4r 20 25 30 Time (sec) F i g u r e 5.5.7 Abso lu te accelerat ions o f the instrumented upper f loors o f the San Jose 3-story of f ice b l d g , dur ing the 1989 L o m a Pr ie ta E Q . 124 60 40 20 0 -20 -40 -60 Floor Relat ive Disp lacements (mm) 3x 4x 3b Time (sec) 60 40 20 0 -20 -40 -60 Floor Relative Displacements (mm) 3y 4y 25 3b Time (sec) 30 20 10 0 -10 -20 -30 Floor Relative Displacements (mm) 3r 4r •?^ ->Ay<V-20 25 3b Time (sec) F i g u r e 5.5.8 Re la t i ve displacements o f the instrumented upper f loors o f the San Jose 3-story of f ice b l d g , dur ing the 1989 L o m a Pr ie ta E Q . 125 A b s o l u t e D i s p l . R e l a t i v e D i s p l . F i g u r e 5.5.9 Orb i ta l d isplacements at the center o f the instrumented f loors o f the San Jose 3-story o f f ice b l d g , dur ing the 1989 L o m a Pr ie ta E Q . 126 Figure 5.5.10 Representation of hysteretic behaviour at the instrumented floors of the San Jose 3-story office bldg, during the 1989 Loma Prieta EQ. 127 Figure 5.5.11 Frequency Response Functions of the instrumented floors of the San Jose 3-story office bldg, obtained from the 1989 Loma Prieta EQ records. Note: The FRF's are computed by ME'scope using a Hanning window, a block size N=2048, 3 averages and 89% segment overlap. 128 I X 1 Y 1 R 3 X _3_Y_ 3 R F i g u r e 5.5.12 M o d e shapes o f the San Jose 3-story of f ice b l d g , obtained f rom the 1989 L o m a Pr ie ta E Q records. Note: The displacements of levels 3 and 4 (roof) are obtained from measured data. Displacements of the other floors are based on ME'scope's interpolation algorithm. 129 Figure 5.5.13 Spectral Response Functions of the San Jose 3-story office bldg, obtained from the 1989 Loma Prieta EQ records. 130 Table 5.5.1 Resu l t s o f Frequency Response Funct ions for the San Jose 3-story o f f ice b l d g , ob-ta ined f r o m the 1989 L o m a Pr ie ta EQ records X-direction Potential Mode # Frequency (Hz) Amplification Factor (3X/1X) Amplification Factor (4X/1X) 1 1.5.62 13.1 16.9 2 4.69 1.12 2.51 3 7.81 2.16 3.10 Damping Ratio estimated by M E ' s c o p e fo r mode IX: 4.70% Y-direction Potential Mode# Frequency (Hz) Amplification Factor (3Y/1Y) Amplification Factor (4 Y/1Y) 1 1.37 10.3 14.5 2 4.15 1.64 3.74 3 6.68 0.67 1.27 Damping Ratio estimated by M E ' s c o p e for mode 1Y: 2.10% R-direction Potential Mode# Frequency (Hz) Amplification Factor (3R/1R) Amplification Factor (4R/1R) 1 2.05 4.45 7.07 2 - - -Damping Ratio estimated by M E ' s c o p e fo r mode IR: 0.40% 131 T a b l e 5.5.2 Resu l ts o f Spectral Response Funct ions for the San Jose 3-story o f f ice b l d g , ob-tained f r o m the 1989 L o m a Pr ie ta E Q records. X - d i r e c t i o n Potential Mode* Frequency (Hz) SRF 0% damping (3X/1X) SRF 0% damping (4X/1X) 1 1.453 8.02 9.93 2 5.17 1.31 4.55 3 - - -Y - d i r e c t i o n Potential Mode* Frequency (Hz) SRF 0% damping (3Y/1Y) SRF 0% damping (4Y/1Y) 1 1.39 8.5 12.0 2 4.06 1.5 3.60 3a 6.73 0.9 1.60 3b 7.55 1.0 1.60 N o t e : The S R F ' s d id not prov ide usable in format ion for torsional modes. 132 Table 5.5.3 Estimated natural frequencies (and periods) of the San Jose 3-story office bldg. based on the results of FRF results, SRF results and visual inspection of the three dimensional mode shapes obtained from analysis of 1989 Loma Prieta EQ data. L O M A PRIETA E A R T H Q U A K E DATA X-Direction (E-W) Y-Direction (E-W) Rotation Frequency (Hz) Period (S) Frequency (Hz) Period (S) Frequency (Hz) Period (S) Model 1.56 0.64 1.37 0.73 2.05 0.49 Mode 2 4.80 0.21 4.15 0.24 - -Mode 3 7.80 0.13 6.70 0.15 - -* Spectral values at the natural periods in the ground motion response spectra and the re-sponse time-histories suggest that the 1st mode dominated the structural response. Fundamental Period according to N B C C 1995: T = 0.1 N = > T = 0.30 sec T = 0.085 (h n ) 3 / 4 = 0.085 (15.09m)3/4 = 0.65 sec Fundamental Period according to U B C 1997: T = 0.035 (h n ) 3 / 4 = 0.035 (49.5 ft) 3 / 4 = 0.65 sec 133 5.6 San Francisco 4-Story Hospital Properties of the Strong Motion Data: Record Length: 40 sec Time interval: 0.02 sec No. of data points for each channel: 2000 Usable frequency range: 0.16 Hz to 23.0 Hz Manipulating the data to obtain the motion of the center of the building in the 3 directions, E-W (or X-directions), N-S (or Y-directions) and rotation about vertical axis (or R-component): 0X = -Chanl , 0 Y = Chan3 IX = - (Chan5 + Chan4)/2 , 1R = (Chan5-Chan4)/2 2X = - Chan6 , 2 Y = Chan7, 2R = (Chan8-Chan6) 5X = - Chan9 , 5Y = ChanlO , 5R = (Chanl 1-Chan9) 134 Figure 5.6.1 Accelerations recorded at the San Francisco 4-story hospital during the 1989 Loma Prieta EQ. (After Shakal, et al, 1989) 135 Ground acceleration in E-W direction (X-dir), g's Pseudo Acceleration Response Spectrum (g's) 0.5 1 1.5 Period (sec) 2.5 Relative Displacement Response Spectrum (mm) 1.5 2 2.5 Period (sec) 1 0.8 0.6 0.4 0.2 0 Normalized Fourier Spectrum k • • if 10 Frequency (Hz) 15 20 Figure 5.6.2 Time-history and spectral characteristics of E-W (X) component of the ground motion recorded at the San Francisco 4-story hospital, during the 1989 Loma Prieta EQ. 136 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 Ground acceleration in N-S direction (Y-dir), g's II llillllHiL n 1 1 1 Mm • (itij i ' i I UI 11 1 ' Time (sec) Pseudo Acceleration Response Spectrum (g's) 1.2 1 0.8 0.6 0.4 0.2 2.5% Dmpg 5% Dmpg ^/'' ^ 0 4 0.5 1.5 Period (sec) 2.5 Relative Displacement Response Spectrum (mm) 4 5 6 Period (sec) 1 0.8 0.6 0.4 0.2 0 Normalized Fourier Spectrum 10 Frequency (Hz) 15 20 F i g u r e 5.6.3 Time-history and spectral characteristics of N-S (Y) component of the ground motion recorded at the San Francisco 4-story hospital, during the 1989 Loma Prieta EQ. 137 F i g u r e 5.6.4 T ime-h is to ry and spectral characterist ics o f rotational (R ) component o f the ground mot ion recorded at the San Franc isco 4-story hospi tal , dur ing the 1989 L o m a Pr ie ta E Q 138 Floor Absolute Accelerations, (g's) 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 Time (sec) 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 Floor Absolute Accelerations, (g's) Time (sec) 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 Floor Absolute Accelerations, (g's) F i g u r e 5.6.5 Abso lu te accelerat ions o f the instrumented upper f loors o f the San F r a n c i s c o 4-story hospi ta l , dur ing the 1989 L o m a Pr ie ta E Q . 139 80 Floor Relative Displacements (mm) 2x 5x Time (sec) 60 40 20 0 -20 -40 -60 Floor Relative Displacements (mm) Time (sec) 40 Floor Relative Displacements (mm) 40 F i g u r e 5.6.6 Re la t i ve displacements o f the instrumented upper f loors o f the San F ranc i sco 4-story hospi ta l , dur ing the 1989 L o m a Pr ie ta E Q . 140 Absolute Displ. Relative Displ. Base Ox(cm) 2nd floor 2x(cm) 2nd floor CM 2x(cm) Roof u> 5x(cm) E "5* 8 1P Sx(cm) Figure 5.6.7 Orbital displacements at the center of the instrumented floors of the San Francisco 4-story hospital, during the 1989 Loma Prieta EQ. 141 Figure 5.6.8 Representation of hysteretic behaviour at the instrumented floors of the San Francisco 4-story hospital, during the 1989 Loma Prieta EQ. 142 F I G 5 - 6 . B L K M#l <2x/lx> M#2 <5x/lx> 5.00 10.0 Hertz 5.00 10.0 Hertz 3 6 . 7 , ^ < 2 ^ Mag 18.3 0.00 1 4 M#4 <5y/0y> 0.00 M#5 <2r/lr> 5.00 10.0 Hertz 5.00 10.0 Hertz 5.00 Hertz 5.00 Hertz F i g u r e 5.6.9 Frequency Response Funct ions o f the instrumented f loors o f the San F ranc i sco 4-story hospi ta l , obtained f rom the 1989 L o m a Pr ie ta E Q records. Note: The FRF's are computed by ME'scope using a Harming window, a block size N=1024,10 averages and 89% segment overlap. 143 Not obtained Not obtained 3X 3Y 3R Figure 5.6.10 Mode shapes of the San Francisco 4-story hospital, obtained from the 1989 Loma Prieta EQ records. Note: The displacements of levels 2 and 5 (roof) are obtained from measured data. Displacements of the other floors are based on ME'scope's interpolation algorithm. 144 10 8 6 4 2 0 16 14 12 10 8 6 4 2 0 30 T 25 20 15 10 -2x/1x-0%dmpg 2 4 6 8 10 Frequency (Hz) •2y/0y-0%dmpg 2 4 6 8 Frequency (Hz) 10 -2r/1r-0%dmpg 2 4 6 8 10 Frequency (Hz) 10 8 6 4 2 0 5x/1x-0%dmpg 2 C 4 6 . 8 10 Frequency (Hz) 16 14 12 10 8 6 4 2 0 •5y/1y-0%dmpg 2 4 6 8 Frequency(Hz) 10 30 25 20 15 10 5r/1 r-0%dmpg 2 4 6 Frequency (Hz) 8 10 F i g u r e 5.6.11 Spectral Response Funct ions o f the San Franc isco 4-story hosp i ta l , obtained f r om the 1989 L o m a Pr ie ta E Q records. 145 Table 5.6.1 Resu l t s o f Frequency Response Funct ions for the San F ranc i sco 4-story hospi ta l , obtained f r o m the 1989 L o m a Pr ie ta E Q records. X-direction Potential Mode # Frequency (Hz) Amplification Factor (2X/1X) Amplification Factor (5X/1X) 1 1.46 30.13 110.4 2 4.39 3.02 9.68 3 - - -Damping Ratio estimated by M E ' s c o p e for mode IX: 1.20% Y-direction Potential Mode# Frequency (Hz) Amplification Factor (2Y/0Y) Amplification Factor (5Y/0Y) 1 1.42 3.98 14.3 2 4.15 6.04 7.60 3 7.23 5.89 4.75 Damping Ratio estimated by M E ' s c o p e for mode 1Y: 0.07% R-direction Potential Mode* Frequency (Hz) Amplification Factor (2R/1R) Amplification Factor (5R/1R) 1 1.72 10.11 40.9 2 4.89 27.5 21.2 Damping Ratio estimated by M E ' s c o p e for mode IR: 0.47% 146 Table 5.6.2 Results of Spectral Response Functions for the San Francisco 4-story hospital, obtained from the 1989 Loma Prieta EQ records. X-direction Potential Mode# Frequency (Hz) SRF 0% damping (2X71X) SRF 0% damping (5X/1X) la 1.41 3.05 8.56 lb 1.65 2.58 10.0 2a 4.97 2.34 4.14 2b 5.17 3.64 3.9 Y-direction Potential Mode* Frequency (Hz) SRF 0% damping (2Y/0Y) SRF 0% damping (5Y/0Y) 1 1.40 5.07 15.7 2a 4.51 3.39 3.77 2b 5.07 3.43 6.55 3 8.04 4.18 4.13 R-direction Potential Mode* Frequency (Hz) SRF..0% damping (2R/1R) SRF 0% damping (5R/1R) 1 1.64 6.82 27.4 147 Table 5.6.3 Estimated natural frequencies (and periods) of the San Francisco 4-story hospital, based on the results of FRF results, SRF results and visual inspection of the three dimensional mode shapes obtained from analysis of 1989 Loma Prieta EQ data. L O M A PRIETA E A R T H Q U A K E DATA X-Direction (E-W) Y-Direction (E-W) Rotation Frequency (Hz) Period (S) Frequency (Hz) Period (S) Frequency (Hz) Period (S) Model 1.50 0.67 1.42 0.70 1.70 0.59 Mode 2 4.40 0.23 4.20 0.24 5.00 0.20 Mode 3 - ' - 7.20 0.14 - -* Spectral values at the natural periods in the ground motion response spectra and the re-sponse time-histories suggest that the 1st mode dominated the structural response. Fundamental Period according to N B C C 1995: T = 0.1 N = > T = 0.40 sec T = 0.085 (h n ) 3 / 4 = 0.085 (16.0m)3/4 = 0.68 sec Fundamental Period according to U B C 1997: T = 0.035 (h n ) 3 / 4 = 0.035 (52.5 ft) 3 / 4 = 0.68 sec 148 5.7 Berkeley 2-Story Hospital Properties of the Strong Motion Data: Record Length: 40 sec Time interval: 0.02 sec No. of data points for each channel: 2000 Usable frequency range: 0.24 Hz to 23.0 Hz Manipulating the data to obtain the motion of the center of the building in the 3 directions, E-W (or X-directions) , N-S (or Y-directions) and rotation about vertical axis (or R-component): IX = - (Chan3 + 2 . Chan6)/3 , 1Y = Chan9 - {[(Chan6-Chan3)/2] .(70/87)} 1R = [(Chan6-Chan3)/2] .(117/87) 2X = - (Chan4 + 2 . Chan7)/3 , 2Y = ChanlO - {[(Chan7-Chan4)/2] .(70/87)} 2R = [(Chan7-Chan4)/2] .(117/87) 3X = - (Chan5 + 2 . Chan8)/3 , 3Y = Chanl 1 - {[(Chan8-Chan5)/2] .(70/87)} 3R= [(Chan8-Chan5)/2] .(117/87) 149 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 Ground Acceleration in E-W direction (X-dir), g's 20- -30-Time (sec) 0.5 0.4 0.3 0.2 0.1 0 Pseudo Acceleration Response Spectrum (g's) 2.5% Dmpg 5% Dmpg rf\f '."V \ — i 1 i i 1 0.5 1.5 Period (sec) 2.5 125 100 75 50 25 0 Relative Displacement Response Spectrum (mm) Period (sec) Normalized Fourier Spectrum 10 Frequency (Hz) 15 20 Figure 5.7.2 Time-history and spectral characteristics of E-W (X) component of the ground motion recorded at the Berkeley 2-story hospital, during the 1989 Loma Prieta EQ. 151 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 Ground Acceleration in N-S direction (Y-dir), g's 20_ _3Q_ J O Time (sec) Pseudo Acceleration Response Spectrum (g's) •2.5% Dmpg 5% Dmpg 0.5 1.5 Period (sec) 2.5 Relative Displacement Response Spectrum (mm) 3 4 Period (sec) 2.5% Dmpg |~, 5% Dmpg 1 0.8 0.6 0.4 0.2 0 Normalized Fourier Spectrum itl I H t MM^M^ — 10 Frequency (Hz) 15 20 Figure 5.7.3 Time-history and spectral characteristics of N-S (Y) component of the ground motion recorded at the Berkeley 2-story hospital, during the 1989 Loma Prieta EQ. 152 0.06 0.04 0.02 0 -0.02 -0.04 -0.06 Ground Acceleration, Rotational, g's 30-Time (sec) ^ 0 0.2 0.15 0.1 0.05 0 15 10 5 0 Pseudo Acceleration Response Spectrum (g's) 2.5% Dmpg 5% Dmpg 0.5 1.5 Period (sec) 2.5 Relative Displacement Response Spectrum (mm) 2.5% Dmpg ~ 5% Dmpg ~ - 1 1 1 — — i 1 , ; 3 4 Period (sec) 1 0.8 0.6 0.4 0.2 Normalized Fourier Spectrum 10 Frequency (Hz) 15 20 Figure 5.7.4 Time-history and spectral characteristics of rotational (R) component of the ground motion recorded at the Berkeley 2-story hospital, during the 1989 Loma Prieta EQ. 153 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 Floor Absolute Accelerations, (g's) 0.3 0.2 0.1 2x 3x Time (sec) Floor Absolute Accelerations, (g's) 25 30 2y 3y 25 3b 0.15 0.1 0.05 Floor Absolute Accelerations, (g's) 3b Figure 5.7.5 Absolute accelerations of the upper floors of the Berkeley 2-story hospital, during the 1989 Loma Prieta EQ. 154 8 6 4 2 0 -2 J -4 -6 -8 -10 Floor Relative Displacements (mm) -4P 8 6 4 2 0 -2 -4 -6 -8 Floor Relative Displacements (mm) Time (sec) 4 3 2 1 0 -1 -2 -3 -4 Floor Relative Displacements (mm) Time (sec) Figure 5.7.6 Relative displacements of the upper floors of the Berkeley 2-story hospital, during the 1989 Loma Prieta EQ. 155 Absolute Displ. Relative Displ. Base u 1 1 ; a— 1x(cm) E CM 2nd floor o— 1 1 i 1 ^ 2 : 1 1 2x(cm) >< CM 2nd floor r— 1 I fe-2 -1 ( l l -i 1 : -1 2x(cm) Roof E "5 1 i .3 1 i i -1 «iPP> 1 1 I 1 R 3x(cm) Figure 5.7.7 Orbital displacements at the center of the floors of the Berkeley 2-story hospital, during the 1989 Loma Prieta EQ. 156 Figure 5.7.8 Representat ion o f hysteretic behaviour at the instrumented f loors o f the B e r k e l e y 2-story hospi ta l , dur ing the 1989 L o m a Pr ie ta E Q . 157 F I G 5 - 7 . B L K M#l <2x/lx> „ , M#2 <3x/lx> Hertz Hertz Figure 5.7.9 Frequency Response Functions of the Berkeley 2-story hospital, obtained from the 1989 Loma Prieta E Q records. Note: The FRF' s are computed by ME 'scope using a Hanning window, a block size N=1024,10 averages and 89% segment overlap. 158 IX z 2X 1Y z Z Y^X IR Figure 5.7.10 Mode shapes of the Berkeley 2-story hospital, obtained from the 1989 Loma Prieta E Q records. 159 2 4 6 8 Frequency (Hz) 10 2 4 6 8 10 Frequency (Hz) 2 4 6 8 10 Frequency (Hz) 10 8 6 3x/1 x-0%dmpg j I t I A . J - : 1 1 1 1 12.5 10 7.5 5 2.5 0 10 8 6 4 2 2 4 6 8 Frequency (Hz) 10 3y/1 y-0%dmpg 4 6 8 Frequency (Hz) 10 3r/1 r-0%dmpg I, ll k 2 4 6 8 10 Frequency (Hz) Figure 5.7.11 Spectral Response Functions of the Berkeley 2-story hospital, obtained from the 1989 Loma Prieta EQ records. 160 Table 5.7.1 Results of Spectral Response Functions for the Berkeley 2-story hospital, obtained from the 1989 Loma Prieta EQ records. Mode# Frequency (Hz) AmplificationFactor (2nd floor / base) AmplificationFactor (3rd floor / base) IX 2.86 12.9 23.1 1Y 3.00 7.33 13.2 1R 4.55 11.5 19.4 Table 5.7.2 Estimated natural frequencies (and periods) of the Berkeley 2-story hospital, based on the results of FRF results and visual inspection of the three dimensional mode shapes obtained from analysis of 1989 Loma Prieta EQ data. 1 Mode* Frequenc y(Hz) Period (sec) AmplificationFactor (2nd floor / base) Ampl ification F actor (3rd floor / base) Damping ratio IX 2.88 0.35 12.9 23.1 0.81% 1Y 3.07 0.33 7.33 13.2 0.66% 1R 4.63 0.22 11.5 19.4 0.75% * Spectral values at the natural periods in the ground motion response spectra and the re-sponse time-histories suggest that the 1st mode dominated the structural response. Fundamental Period according to N B C C 1995: T = 0.1 N = > T = 0.20 sec T = 0.09 h n / (D s ) 1 / 2 = 0.09 x (7.67 m) / (18.30 m) 1 / 2 = 0.16 sec (for both directions) Fundamental Period according to U B C 1997: T = 0.020 (h n ) 3 / 4 = 0.020 (25.17 ft) 3 / 4 = 0.23 sec 161 5.8 Richmond 3-Story Office Building Properties of the Strong Motion Data: Record Length: 80 sec Time interval: 0.02 sec No. of data points for each channel: 4000 Usable frequency range: 0.2 Hz to 23.0 Hz Manipulating the data to obtain the motion of the center of the building in the 3 directions, E-W (or X-directions) , N-S (or Y-directions) and rotation about vertical axis (or R-component): l X = C h a n l 0 , 1Y = -Chanl2 2X = (Chan8+Chan7)/2 , 2Y = -Chan9 , 2R = (Chan8-Chan7)/2 3X = (Chan5+Chan4)/2 , 3 Y = -Chan6 , 3R = (Chan5-Chan4)/2 4X = (Chan2+Chanl)/2 , 4Y = -Chan3 , 4R = (Chan2-Chanl)/2 162 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 Ground acceleration in E-W direction (X-dir), g's A O L M L -50_ -eb Time (sec) 0.5 0.4 0.3 0.2 0.1 0 Pseudo Acceleration Response Spectrum, g's —2.5% Dmpg 5% Dmpg i 1 1 1 1 0.5 1.5 Period (sec) 2.5 Relative Displacement Response Spectrum (mm) •2.5% Dmpg 5% Dmpg 3 4 Period (sec) ~~r~ 6 Normalized Fourier Spectrum 4 6 Frequency (Hz) 10 Figure 5.8.2 Time-history and spectral characteristics of E-W (X) component of the ground motion recorded at the Richmond 3-story office building, during the 1989 Loma Prieta EQ. 164 Ground acceleration in N-S direction (Y-dir), g's Pseudo Acceleration Response Spectrum (g's) 2.5% Dmpg 5% Dmpg 0.5 1.5 Period (sec) 2.5 250 200 150 100 50 0 Relative Displacement Response Spectrum (mm) 2 5% Dmpg 5% Dmpg - — 1 1 1 1 1 3 4 Period (sec) 1 0.8 0.6 0.4 0.2 0 Normalized Fourier Spectrum Al 1 1 I I w In 1 V v W W w W w V ^ " ^ ' " • «"i •• •• 4 6 Frequency (Hz) 10 Figure 5.8.3 Time-history and spectral characteristics of N-S (Y) component of the ground motion recorded at the Richmond 3-story office building, during the 1989 Loma Prieta EQ. 165 0.3 0.2 Floor Absolute Accelerations, g's -0.3 Time (sec) 0.3 Floor Absolute Accelerations, g's Time (sec) Figure 5.8.4 E-W (X-direction) & N-S (Y-direction) absolute accelerations of the upper floors of the Richmond 3-story office bldg, during the 1989 Loma Prieta EQ. 166 35 30 25 20 15 10 5 0 -5 -10 -15 -20 -25 -30 Floor Reative Displacements (mm) Time (sec) Floor Reative Displacements (mm) Time (sec) Figure 5.8.5 E-W (X-direction) & N-S (Y-direction) relative displacements of the upper floors of the Richmond 3-story office bldg, during the 1989 Loma Prieta EQ. 167 0.1 0.08 0.06 0.04 0.02 0 -0.02 -0.04 -0.06 -0.08 Floor Absolute Rotational Accelerations, g's Time (sec) Floor Absolute Rotations (East dis-West dis)/2 (mm) 1b" -4 -6 -I Time (sec) Figure 5.8.6 Torsional response of the Richmond 3-story office bldg, during the 1989 Loma Prieta EQ. 168 Absolute Displ. Relative Displ. E u A 2nd floor •t *> £. 1 1 UaH 3 -4 -2 & 4 (» A *T , C -zx(cm) E >« CO E "5 Figure 5.8.7 Orbital displacements at the center of the floors of the Richmond 3-story office bldg, during the 1989 Loma Prieta EQ. 169 " T O u o < o in J3 <0 i o o 2nd floor Relative Disp., X (mm) X d o < a) o </) .Q < i O o I T : TJ k_ CO 3rd floor Relative Disp., X (mm) in "TO o o < o in X2 < 4— O o a: Roof Relative Disp., X (mm) in "en o u < o in . a < o o c 2nd floor Relative Disp., Y (mm) in " T O o o < CD .O < 1 o o q= 3rd floor Relative Disp., Y (mm) in " T O o o < o m si < o o or -40 -30 Roof Relative Disp., Y (mm) Figure 5.8.8 Representation of hysteretic behaviour at the instrumented floors of the Richmond 3-story office bldg, during the 1989 Loma Prieta EQ. 170 F I G - 5 - 8 A . B L K M#l <2x/lx> 2 4 2 M#2 <2y/ly> 0.00 M#3 <3x/lx> 5.00 Hertz 0.00 M#5 <4x/lx> 5.00 Hertz 5.00 Hertz 10.3 M M < 3 ^ 5.00 10.0 Hertz 0.00 M#6 <4y/ly> 5.00 10.0 Hertz 5.00 Hertz F i g u r e 5.8.9 Frequency Response Funct ions o f the instrumented f loors o f the R i c h m o n d 3-story of f ice b l d g , obtained f rom the 1989 L o m a Pr ie ta E Q records. Note: The FRF's are computed by ME'scope using a Hanning window, a block size N=2048, 3 averages and 89% segment overlap. 171 F I G - 5 - 8 B . B L K M#l <2r/lx> 1 A 0 M#2 <2r/ly> Hertz Hertz Figure 5.8.9 Cont'd 172 173 Figure 5.8.11 Spectral Response Functions of the Richmond 3-story office bldg, obtained from the 1989 Loma Prieta EQ records. 174 Table 5.8.1 Resu l t s o f Frequency Response Funct ions for the R i c h m o n d 3-story of f ice b l d g , obta ined f r o m the 1989 L o m a Pr ie ta E Q records. X-direction Potential Mode# Frequency (Hz) Amplification Factor (2X71X) Amplification Factor (3X/1X) Amplification Factor (4X/1X) 1 1.42 3.72 6.62 9.24 2 4.13 2.18 1.17 3.28 3. 7.00 2.10 3.45 3.24 Damping Ratio estimated by M E ' s c o p e for mode I X : 4 . 5 5 % Y-direction Potential Mode# Frequency (Hz) Amplification Factor (2 Y/1Y) Amplification Factor (3Y/1Y) Amplification Factor (4Y/1Y) 1 1.59 4.65 8.64 12.4 2 4.83 6.29 4.42 19.7 3 7.20 6.71 3.75 9.18 Damping Ratio estimated by M E ' s c o p e for mode 1Y: 2 . 4 0 % Table 5.8.2 Resu l t s o f Spectral Response Funct ions for the R i c h m o n d 3-story o f f ice b l d g , obta ined f r o m the 1989 L o m a Pr ie ta E Q records. X-direction Potential Mode # Frequency (Hz) SRF 0% dmpg (2X/1X) SRF 0% dmpg (4X/1X) 1 1.33 3.33 7.37 2a 3.76 2.32 2.38 2b 4.43 1.12 2.83 Y-direction Potential Mode # Frequency (Hz) SRF 0% dmpg (2Y/1Y) SRF0%dmpg(4Y/lY) la 1.58 3.54 9.19 lb 1.67 3.27 9.49 2 4.87 3.00 8.40 175 Table 5.8.3 Estimated natural frequencies (and periods) of the Richmond 3-story office bldg. based on the results of FRF results, SRF results and visual inspection of the three dimensional mode shapes obtained from analysis of 1989 Loma Prieta EQ data. L O M A PRIETA E A R T H Q U A K E DATA X-Direction (E-W) Y-Direction (E-W) Rotation Frequency (Hz) Period (S) Frequency (Hz) Period (S) Frequency (Hz) Period (S) Model 1.43 0.70 1.57 0.64 2.1 0.48 Mode 2 4.17 0.24 4.80 0.21 5.4 0.19 Mode 3 7.01 0.14 7.28 0.14 9.9 0.10 * Spectral values at the natural periods in the ground motion response spectra and the response time-histories suggest that the 1st mode dominated the structural response. Fundamental Period according to N B C C 1995: T = 0.1 N = > T = 0.30 sec T = 0.085 (h n ) 3 / 4 = 0.085 (13.44m)3/4 = 0.60 sec Fundamental Period according to U B C 1997: T = 0.035 (h n ) 3 / 4 = 0.035 (44.08 ft) 3 7 4 = 0.60 sec 176 5.9 Redlands 7-Story Commercial Building Properties of the Strong Motion Data: Record Length: 60 sec Time interval: 0.02 sec No. of data points for each channel: 3000 Usable frequency range: 0.2 Hz to 23.0 Hz Manipulating the data to obtain the motion of the center of the building in the 3 directions, E-W (or X-directions) , N-S (or Y-directions) and rotation about vertical axis (or R-component): IX = - Chanl3 + {[(Chan9-Chan8)/2] .(93/140)} 1Y = - (Chan9+Chan8)/2 , 1R = (Chan9-Chan8)/2 3X = - Chanl2 + {[(Chan7-Chan6)/2] .(93/140)} 3 Y = - (Chan7+Chan6)/2 , 3R = (Chan7-Chan6)/2 5X= - Chanll + {[(Chan5-Chan4)/2] .(93/140)} 5Y = - (Chan5+Chan4)/2 , 5R = (Chan5-Chan4)/2 8X = - ChanlO + {[(Chan3-Chan2)/2] .(93/140)} 8Y = - (Chan3+Chan2)/2 , 8R = (Chan3-Chan2)/2 177 Figure 5.9.1 Accelerations recorded at the Redlands 7-story commercial bldg, during the 1992 Landers Earthquake (After Shakal, et al , 1992) 178 Figure 5.9.1 Continued 179 0.1 0.05 Ground Acceleration in E-W direction (X-dir), g's Time (sec) Pseudo Acceleration Response Spectrum( g's) -2.5% Dmpg 5% Dmpg Relative Displacement Response Spectrum (mm) Period (sec) -2.5% Dmpg 5% Dmpg Normalized Fourier Spectrum Frequency (Hz) 10 15 Figure 5.9.2 Time-history and spectral characteristics of E-W (X) component of the ground motion recorded at the Redlands 7-story commercial bldg, during the 1992 Landers EQ. 180 0.3 0.2 0.1 0 Pseudo Acceleration Response Spectrum(g,s) A A 2.5% Dmpg 5% Dmpg /fa A. 0.5 1 1.5 2 Period (sec) 2.5 Relative Displacement Response Spectrum (mm) -2.5% Dmpg 5% Dmpg Period (sec) 1 0.8 0.6 0.4 0.2 Normalized Fourier Spectrum Frequency (Hz) 10 15 Figure 5.9.3 T ime-h is tory and spectral characterist ics o f N-S (Y) component o f the ground mot ion recorded at the Red lands 7-story commerc ia l b l d g , dur ing the 1992 Lande rs EQ. 181 Pseudo Acceleration Response Spectrum(g,s) 0.5 1 1.5 Period (sec) 2.5 Relative Displacement Response Spectrum (mm) 100 •2.5% Dmpg 5% Dmpg Period (sec) Normalized Fourier Spectrum Frequency (Hz) 10 15 F i g u r e 5.9.4 T ime-h is to ry and spectral characterist ics o f rotational (R) component o f the ground mot ion recorded at the Red lands 7-story commerc ia l b l d g , dur ing the 1992 Landers E Q . 182 Floor Absolute Accelerations, g's Time (sec) Floor Absolute Accelerations, g's Time (sec) Figure 5.9.5 E-W (X-direction) & N-S (Y-direction) absolute accelerations of the instrumented upper floors of the Redlands 7-story commercial bldg, during the 1992 Landers EQ. Note: See Appendix A for individual plots of the absolute accelerations. 183 Figure 5.9.6 E - W (X-d i rec t ion) & N - S (Y-d i rect ion) relat ive d isplacements o f the instrumented upper f loors o f the Red lands 7-story commerc ia l b l d g , dur ing the 1992 Lande rs E Q . 184 0.04 Figure 5.9.7 Torsional response of the instrumented upper floors of the Redlands 7-story commercial bldg, during the 1992 Landers EQ. Absolute Displ. Relative Displ. Base E "5* u A •j t i i i t / ^ tfc, 1 1 1 1 5 - 4 - 3 - 2 -tl ( l ^ ^ 2 3 4 i " Z 1 5 -1x(cm) 3x(cm) 5th floor u A *T ( 1 — 1 — 1 — i /f*i ^598 5 -4 -3 - 2 p ^ S ^ 1 q A *r I 6- 1 5x(cm) 8x(cm) 3rd floor 3 6 3x(cm) 5th floor 1 5-1 *t q o ) -z -c*Hc z o * ; q " O /I ~*t 5x(cm) , —5° of 00 if 3 3 6 8x(cm) Figure 5.9.8 Orbital displacements at the center of the instrumented floors of the Redlands 7-story commercial bldg, during the 1992 Landers EQ. 186 in u o CO o in ro L _ o o <^ T 3 i CO 3rd floor rel: displacement X, (mm) in "en u o ca a> -*-« _2 o ( 0 . o (0 L o o 5th floor rel. displacement X, (mm) Q Roof rel. displacement X, (mm) in o o ro o in .o ro k_ o o 3rd floor rel. displacement Y, (mm) in "bi o o ro o V) ro i o o 5th floor rel. displacement Y, (mm) -946 _Q-j g Roof rel. displacement Y, (mm) Figure 5.9.9 Representation of hysteretic behaviour at the instrumented floors of the Redlands 7-story commercial bldg, during the 1992 Landers EQ. 187 M#l <3x/lx> F I G 5 - 9 . B L K M#2 <5x/lx> M#3 <8x/lx> Hertz M#4 <3y/ly> Hertz Hertz i 2 4 , 9 r 41.UT1 Mag Mag 12.4 20.8 " 0.00f 1 o . o J 0.00 10.0 Hertz M#7 <3r/lr> 0.00 10.0 Hertz M#8 <5r/lr> 0.00 Hertz M#9 <8r/lr> 0.00 10.0 Hertz 0.00 10.0 Hertz Hertz Figure 5.9.10 Frequency Response Functions of the instrumented floors of the Redlands 7-story commercial bldg, obtained from the 1992 Landers E Q records. Note: The FRF's are computed by ME'scope using a Harming window, a block size N=1024,20 averages and 90% segment overlap. 188 z Not obtained 3X 3Y 3R Figure 5.9.11 M o d e shapes o f the Red lands 7-story commerc ia l b l d g , obta ined f r om the 1992 Landers E Q records. Note: The displacements of levels 3, 5 and 8 (roof) are obtained from measured data. Displacements of the other floors are based on ME'scope's interpolation algorithm. 189 1 3x/1 x-0%dmpg 1 Jli A 2 4 6 8 10 Frequency (Hz) -3y/1y-0%dmpg 0 2 4 6 8 10 Frequency (Hz) 3r/1 r-0%dmpg A WJ 0 2 4 6 8 10 Frequency (Hz) 17.5 15 12.5 10 7.5 5 2.5 0 3 2 1 2 _ 4 6 U 8 10 Frequency(Hz) 8y/1 y-0%dmpg Mk \ A ^ > — — 2 4 6 8 10 Frequency(Hz) -8r/1r-0%dmpg 2 4 6 8 10 Frequency (Hz) Figure 5.9.12 Spectral Response Functions of the Redlands 7-story commercial bldg, obtained from the 1992 Landers EQ records. 190 Table 5.9.1 Results of Frequency Response Functions for the Redlands 7-story commercial bldg, obtained from the 1992 Landers EQ records. X-direction Potential Mode# Frequency (Hz) Amplification Factor (3X/1X) Amplification Factor (5X/1X) Amplification Factor (8X/1X) 1 0.73 6.40 16.4 29.1 2 2.10 3.27 2.35 3.00 3 5.52 3.24 1.84 2.53 Damping Ratio estimated by ME'scope for the first mode: 3.94% Y-direction Potential Mode# Frequency (Hz) Amplification Factor (3 Y/1Y) Amplification Factor (5Y/1Y) Amplification Factor (8 Y/1Y) 1 0.59 10.8 24.9 41.7 2 1.76 3.81 3.75 3.51 Damping Ratio estimated by ME'scope for the first mode: 3.53% R-direction Potential Mode* Frequency (Hz) Amplification Factor (3R/1R) Amplification Factor (5R/1R) Amplification Factor (8R/1R) 1 0.93 0.80 1.70 3.10 2 3.17 0.89 1.58 1.28 Damping Ratio estimated by ME'scope for the first mode: 4.18% Table 5.9.2 Results of Spectral Response Functions for the Redlands 7-story commercial bldg, obtained from the 1992 Landers EQ records Potential Mode # Frequency (Hz) SRF 0% dmpg (3rd floor/base) SRF 0% dmpg (8th floor/base) IX 0.66 3.55 12.4 1Y 0.63 4.37 17.2 IR 0.94 0.90 3.05 191 Table 5.9.3 Estimated natural frequencies (and periods) of the Redlands 7-story commercial bldg, based on the results of FRF results, SRF results and visual inspection of the three dimen-sional mode shapes obtained from analysis of 1992 Landers EQ data. L A N D E R S E A R T H Q U A K E DATA X-Direction (E-W) Y-Direction (E-W) Rotation Frequency (Hz) Period (S) Frequency (Hz) Period (S) Frequency (Hz) Period (S) Model 0.73 1.37 0.63 1.59 0.95 1.05 Mode 2 2.10 0.48 1.90 0.53 3.30 0.30 Mode 3 3.50 0.29 - - - -* Spectral values at the natural periods in the ground motion response spectra and the re-sponse time-histories suggest that the 2nd & 3rd modes had a significant contribution in the structural response. Fundamental Period according to N B C C 1995: T = 0.1 N = > T = 0.70 sec T = 0.085 ( h „ ) 3 / 4 = 0.085 (31.83m)3/4 =1.14 sec Fundamental Period according to U B C 1997: T = 0.035 (h n ) 3 / 4 = 0.035 (104.42ft)3/4 = 1.14 sec 192 5.10 San Bernardino 3-Story Office Building Properties of the Strong Motion Data: Record Length: 80 sec Time interval: 0.02 sec No. of data points for each channel: 4000 Usable frequency range: 0.16 Hz to 23.0 Hz Manipulating the data to obtain the motion of the center of the building in the 3 directions, E-W (or X-directions) , N-S (or Y-directions) and rotation about vertical axis (or R-component): IX = -(Chan9) , 1Y = (Chanl3) 2X = -(Chan7 + Chan8)/2 , 2Y = (Chan 12) , 2R = (Chan6-Chan4)/2 3X = -(Chan4 + 2 .Chan5 + Chan6)/4 , 3 Y = (Chanl 1), 3R = (Chan8-Chan7)/2 4X = -(Chan3 + Chan2)/2 , 4Y = (ChanlO) , 4R = (Chan3-Chan2)/2 193 Figure 5.10.1 Accelerations recorded at the San Bernardino 3-story office bldg, during the 1992 Landers Earthquake (After Shakal, et al, 1992) 194 Figure 5.10.1 Continued 195 Pseudo Acceleration Response Spectrum (g's) -2.5% Dmpg 5% Dmpg 0.5 1.5 Period (sec) 2.5 Relative Displacement Response Spectrum (mm) 3 4 Period (sec) •2.5% Dmpg 5% Dmpg Normalized Fourier Spectrum I • 1 t i l i ± l 1 v V \ M f > ^ M A ^ ^ ^ — I ... . O.i 0 , o.: 4 6 Frequency (Hz) 10 Figure 5.10.2 Time-history and spectral characteristics of E-W (X) component of the ground motion recorded at the San Bernardino 3-story office bldg, during the 1992 Landers EQ. 196 0.1 0.05 0 -0.05 -0.1 Ground Acceleration in N-S direction (Y-dir), g's Pseudo Acceleration Response Spectrum (g's) -2.5% Dmpg 5% Dmpg Relative Displacement Response Spectrum (mm) 2.5% Dmpg 5% Dmpg 3 4 Period (sec) 1 0.8 0.6 0.4 0.2 0 Normalized Fourier Spectrum I 1 III A . J L 1. Ilk . u i 1 . J 4 6 Frequency (Hz) 10 Figure 5.10.3 T ime-h is to ry and spectral characterist ics o f N -S (Y) component o f the ground mo t ion recorded at the San Bernard ino 3-story of f ice b l d g , dur ing the 1992 Landers E Q . 197 0.3 -0.3 0.3 -0.3 Floor Absolute Accelerations, g's Time (sec) Floor Absolute Accelerations, g's Time (sec) Figure 5.10.4 E-W (X-direction) & N-S (Y-direction) absolute accelerations of the upper floors of the San Bernardino 3-story office bldg, during the 1992 Landers EQ. Note: See Appendix A for individual plots of the absolute accelerations. 198 Figure 5.10.5 E-W (X-direction) & N-S (Y-direction) relative displacements of the upper floors of the San Bernardino 3-story office bldg, during the 1992 Landers EQ. 199 0.05 -0.05 J Figure 5.10.6 Torsional response of the upper floors of the San Bernardino 3-story office bldg, during the 1992 Landers EQ. 200 Absolute Displ. Relative Displ. E >« n Base 1 5 -10 - 5 ^ ^ M -1x(cm) 2nd floor 2x(cm) 3rd floor •40-3x(cm) E o 4x(cm) I 5 -10 -SvStS *e-2nd floor u < 3 -3 ( •> W ) 3 f 6 -2x(cm) 3rd floor 3x(cm) 4x(cm) *3 3 -3 I 3 ( 6-Figure 5.10.7 Orbital displacements at the center of the floors of the San Bernardino 3-story-office bldg, during the 1992 Landers EQ. 201 in X" 8 o in .o ro L_ o o q= TJ C CM 2nd floor rel. displacement X, (mm) in 'at u o ro o in ro i _ o o c= TJ c CN 2nd floor rel. displacement Y, (mm) 8 CO a) o in co o o i= X3 i CO 30 43 "en o o ro ro k_ o o 5= "O 3rd floor rel. displacement X, (mm) 3rd floor rel. displacement Y, (mm) Roof rel. displacement X, (mm) in u o ro o in _Q ro o o a. Roof rel. displacement Y, (mm) Figure 5.10.8 Representation of hysteretic behaviour of the San Bernardino 3-story office bldg, during the 1992 Landers EQ. 202 F I G 5 - 1 0 A . B L K M#l <2x/lx> ^ AM#2 <2y/ly> Hertz Hertz Figure 5.10.9 Frequency Response Functions of the San Bernardino 3-story office bldg, obtained from the 1992 Landers EQ records. Note: The FRF's are computed by ME'scope using a Harming window, a block size N=2048, 10 averages and 89% segment overlap. 203 F I G 5 - 1 0 B . B L K M#l <2r/lx> 5.00 10.0 Hertz 3.9a M#3 <3r/lx> o.oa 4.19 o.oa M#2 <2r/ly> g 5 0.00 5.00 10.0 Hertz n M#5 <4r/lx> g 9 | 0.00 5.00 10.0 5.00 10.0 Hertz , e<1 M#6 <4r/ly> J . J Z T Hertz 5.00 10.0 Hertz Figure 5.10.9 Cont'd 204 0 4 -2x/1x-0%dmpg —i 1 1 i 2 4 6 8 Frequency (Hz) 10 0 A -4x/1x-0%dmpg - | r 2 4 6 8 10 Frequency (Hz) 2y/1 y-0%dmpg i , i k W h J r 2 4 6 8 10 Frequency (Hz) 10 -4y/1y-0%dmpg - i r 2 4 6 8 10 Frequency (Hz) Figure 5.10.11 Spectral Response Functions of the San Bernardino 3-story office bldg, obtained from the 1992 Landers EQ records. 206 Table 5.10.1 Estimated natural frequencies (and periods) of the San Bernardino 3-story office bldg, based on the results of FRF results, SRF results and visual inspection of the three dimen-V sional mode shapes obtained from analysis of 1992 Landers EQ data. L A N D E R S E A R T H Q U A K E DATA X-Direction (E-W) Y-Direction (E-W) Rotation Frequency (Hz) Period (S) Frequency (Hz) Period (S) Frequency (Hz) Period (S) Model 1.83 0.55 1.77 0.56 2.4 0.42 Mode 2 5.9 0.17 5.9 0.17 - -Damping ratio of fundamental mode estimated by ME'scope: 7.7% * Spectral values at the natural periods in the ground motion response spectra and the re-sponse time-histories suggest that the 1st mode dominated the structural response. Fundamental Period according to N B C C 1995: T = 0.1 N = > T = 0.30 sec T = 0.085 (h n ) 3 / 4 = 0.085 (12.60m)3/4 = 0.57 sec Fundamental Period according to U B C 1997: T = 0.035 (h n ) 3 / 4 = 0.035 (41.34ft)3/4 = 0.57 sec 207 5.11 Los Angeles 2-Story Fire Command Control Building Properties of the Strong Motion Data: Record Length: 60 sec Time interval: 0.01 sec No. of data points for each channel: 6001 Usable frequency range: 0.2 Hz to 46.0Hz Manipulating the data to obtain the motion of the center of the building in the 3 directions, E-W (or X-directions) , N-S (or Y-directions) and rotation about vertical axis (or R-component): FF = Free Field Level 0 = Foundation (below isolators) Level 1 = Base (above isolators) F F - X = [(FF90°) * SIN(50°)] + [(FF1800) * COS(50°)] F F - Y = [(FF90°) * COS(50°)] - [(FF1800) * SIN(50°)] OX = - (Chan7 + Chan6)/2 , 0Y = Chan5 - [(Chan7-Chan6) . (14/188)], OR = (Chan7-Chan6)/2 l X = -(Chanll +Chan9)/2, l Y = Chan8 -[(Chanll-Chan9).(14/188)], lR = (Chanll-Chan9)/2 3X = - (Chanl6 + Chanl4)/2 , 3Y = Chanl3 - [(Chanl6-Chanl4).(14/188)], 3R = (Chanl6-Chanl4)/2 208 o i n u 3 0 J c n o * - > u D i ^ r n c o i r > o j - < r r n « - ' o o . ' o ^ - i i 0 3 C D Figure 5.11.1 Accelerations recorded at the L A 2-story fire control bldg. during the 1994 Northridge EQ (After Shakal, et al, 1994) 209 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 Ground Acceleration (Free Field), g's FF-x 25 30 35 40 415 Time (sec) 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 Ground Acceleration (Free Field), g's FF-y 30 35 40 _4B Time (sec) 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 Ground Acceleration, Foundation (Below Isolators), g's Ox 1 0 15 20 25 30 35 40 4)5 Time(sec) 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 Ground Acceleration, Foundation (Below Isolators), g's T O — f b l ' 2U Oy "25" "3TT "35" "415 Time(sec) 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 Ground Acceleration, Base (Above Isolators), g's 1x A3. 20_ _25_ _30_ 33. AO. 45 Time (sec) 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 Ground Acceleration, Base (Above Isolators), g's — r •1y 10 15 20 25 30 35 40 46 Time (sec) Figure 5.11.2 Acceleration time histories of free field, foundation (below isolators) and base (above isolators) at the L A 2-story fire control bldg, during the 1994 Northridge EQ. 210 F I G - 5 - 1 1 . B L K Hertz Hertz Figure 5.11.3 Normalized Fourier Spectrum of accelerations of free field, foundation (below isolators) and base (above isolators) at the L A 2-story fire control bldg, during the 1994 Northridge EQ. 211 P s e u d o Acce le ra t ion R e s p o n s e Spec t ra , 2 . 5 % damp ing 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 ll ! f ree f ield (X-dir) foundat ion (X-dir) b a s e (X-dir) h i \ " j ! * • ' v y \ A t t w \ \ / .iii - \ /At r •• 0.5 1.5 Per iod (sec) 2 .5 P s e u d o Acce le ra t ion R e s p o n s e Spec t ra , 2 . 5 % damp ing •free f ield (Y-dir) foundat ion (Y-dir) b a s e (Y-dir) 2 .5 Figure 5.11.4 Pseudo acceleration response spectra of the motion of free field, foundation (be low isolators) and base (above isolators) at the L A 2-story fire control bldg, during the 1994 Northridge EQ. 212 40 30 20 10 0 -10 £ -20 -30 -40 Roof Relative to Ground Displacement mm) 3x-0x -30- -35- ^ 0 -Time (sec) 40 30 20 10 0 -10 -20 -30 -40 Deformation of the Isolators (mm) 1x-0x ~3TT "35" ~4tr "45 Time (sec) 20 10 0 -10 -20 Roof Relative to base Displacement mm) 3x-1x v~i~v^v— -^r —f " i r" 10 15 20 25 30 35 40 4J5 Time (sec) Figure 5.11.5 E-W (X) component of the response of the L A 2-story fire control bldg, during the 1994 Northridge EQ. 213 0.2 0.1 0 -0.1 -0.2 Roof Absolute Acceleration (g's) 20 10 0 -10 -20 Roof Relative to base Displacement mm) 3y-1y 10 15 20 25 30 Time (sec) 35 40 45 Figure 5.11.6 N-S (Y) component of the response of the L A 2-story fire control bldg, during the 1994 Northridge EQ. 214 Absolute Displ. Relative Displ. Free field -4-ff-x(cm) Foundation -4-Ox(cm) E "3K •a 1" ' 2 . . A 1 1x(cm) E u . 3x(cm) Isolators' deformation 9 I 4 | 3-2-^ v x / t 2 ( r ^ ^ ^ ^ ^ ^ • ^•—.^"-2 -3-4-1x-0x (cm) Roof (relative to ground) >< 3-^ 3^ — ^ — — i N-a -2( - f ^ t F— -3-3x-0x(cm) Roof (relative to base) 1 *~1 q 1 n 4 1 1 i u ^ ^ l -1 -3 -2 - I ' M i I 1 2 o J *_ "> 3x-1x (cm) Figure 5.11.7 Orbital displacements at the center of the instrumented floors of the L A 2-story fire control bldg, during the 1994 Northridge EQ 215 F G 5 - 1 1 - 8 . B L K M#l <3x/lx> o.oo-0.00 2.50 5.00 7.50 10.0 12.5 15.0 17.5 20.0 22.5 25.0 Hertz M#2 <3y/ly> 0.00 2.50 5.00 7.50 10.0 12.5 15.0 17.5 20.0 22.5 25.0 Hertz M#3 <3r/lr> o.oa 0.00 2.50 5.00 7.50 10.0 12.5 15.0 17.5 20.0 22.5 25.0 Hertz Figure 5.11.8 Frequency Response Functions of the roof with respect to first floor (above isola-tors) of the L A 2-story fire control bldg, obtained from the 1994 Northridge E Q records. Note: The FRF's are computed by ME'scope using a Hanning window, a block size N=2048,15 averages and 86% segment overlap. 216 F G 5 - 1 1 - 9 . B L K M#l <lx/Ox> M#2 <3x/0x> 0.00 5.00 10.0 15.0 Hertz „ M#3 <ly/0y> j / i 0.00 M#5 <lr/0r> 5.00 10.0 15.0 Hertz 0.00 5.00 10.0 Hertz 15.0 , M#4 <3y/0y> j g 6 0.00 5.00 10.0 15.0 Hertz MU <3r/0r> 0.00 5.00 10.0 15.0 Hertz 0.00 5.00 10.0 15.0 Hertz Figure 5.11.9 Frequency Response Functions of the roof and first floor with respect to the foun-dation (below isolators) of the L A 2-story fire control bldg, obtained from the 1994 Northridge EQ records. Note: The FRF's were computed by ME'scope using the same parameters as noted for figure 5.11.8 217 z IX z 1Y z IR Figure 5.11.10 Mode shapes of the superstructure the L A 2-story fire control bldg. (without iso-lators), obtained from the 1994 Northridge records. Note: The displacements of roof are obtained from measured data. Displacements of the 2nd floor are based on ME'scope's interpolation algorithm. 218 IX 2 X Figure 5.11.11 M o d e shapes o f the L A 2-story fire control b ldg . (wi th an extra story at the bot-tom represent ing the deformat ion o f the isolators), obtained based on Nor th r idge E Q Records . Note: The displacements of 1 st floor and roof are obtained from measured data. Displacements of the 2nd floor are based on ME'scope's interpolation algorithm. 219 Table 5.11.1 Estimated natural frequencies (and periods) of the L A 2-story fire control bldg, based on the FRF results and visual inspection of the three dimensional mode shapes obtained from analysis of 1994 Northridge EQ data. SUPERSTRUCTURE (obtained from the FRF's of Figure 5.11.8) X-Direction (E-W) Y-Direction (E-W) Rotation Frequency (Hz) Period (S) Frequency (Hz) Period (S) Frequency (Hz) Period (S) Model 2.9 0.34 2.9 0.34 4.1 0.24 Mode 2 - - - - - -BASE-ISOLATED (obtained from the FRF's of Figure 5.11.9) X-Direction (E-W) Y-Direction (E-W) Rotation Frequency (Hz) Period (S) Frequency (Hz) Period (S) Frequency (Hz) Period (S) Mode 1 0.9 1.1 0.9 1.1 1.2 0.8 Mode 2 6.0 0.17 6.0 0.17 9.0 0.11 Fundamental Period of the building without Base Isolation: a) N B C C 1995: T = 0.1 N = > T = 0.20 sec T =0.09 h n / (D s ) 1 / 2 = 0.09 (9.75m) / (25.6m)1/2 - 0.17 b^ U B C 1997; T = 0.020 (h n ) 3 / 4 = 0.020 (32ft)3/4 = 0.27 sec 220 5.12 Los Angeles 7-Story University Hospital Properties of the Strong Motion Data: Record Length: 60 sec Time interval: 0.01 sec No. of data points for each channel: 6001 Usable frequency range: 0.2 Hz to 46.0 Hz Manipulating the data to obtain the motion of the center of the building in the 3 directions, E-W (or X-directions) , N-S (or Y-directions) and rotation about vertical axis (or R-component): FF = Free Field Level 0 = Foundation (below isolators) Level 1 = Base (above isolators) FF-X = [(Chan27) * COS(50)] - [(Chan25) * SIN(50)] F F - Y = [(Chan25) * COS(50)] + [(Chan27) * SIN(50)] OX = Chan7, 0Y = Chan5 , OR = (Chan8 - Chan6)/2 IX = Chanl 1 , 1Y = Chan9 , 1R = (Chanl2 - Chanl0)/2 4X = Chanl5 , 4Y = Chanl3 , 4R = (Chanl6 - Chanl4)/2 6X = Chanl9, 6Y = Chanl7, 6R = (Chan20 - Chanl8)/2 8X = Chan23 , 8Y - Chan21, 8R = (Chan24 - Chan22)/2 221 223 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 Ground Acceleration, Foundation (Below Isolators), g's Ox "TO "35" "45 20 25 "30" Time(sec) Ground Acceleration, Foundation (Below Isolators), g's 2 0 2 5 : -30- -35- -40-0y -45 Time(sec) 0.2 1 0.1 0 -0.1 $ -0.2 Ground Acceleration, Base (Above Isolators), g's — r e ts 20— 1x — 2 5 Time (sec) - 3 0 - - 3 5 - "45 0.2 0.1 0 -0.1 £ -0.2 Ground Acceleration, Base (Above Isolators), g's • — r ~ - 4 0 -iyH -to T5- - 2 0 - —25 Time (sec) - 3 0 - - 3 5 - -45 Figure 5.12.2 Acceleration time histories of free field, foundation (below isolators) and base (above isolators) at the L A 7-story university hospital, during the 1994 Northridge EQ. 224 F I G - 5 - 1 2 . B L K Hertz Hertz M#3 <0x> , lnW4 <0y> Hertz Hertz Figure 5.12.3 Normalized Fourier Spectrum of accelerations of free field, foundation (below isolators) and base (above isolators) at the L A 7-story university hospital, during the 1994 Northridge EQ. 225 P s e u d o Acce le ra t ion R e s p o n s e Spec t ra , 2 . 5 % damp ing 1.2 1 0.8 0.6 0.4 0.2 - f r e e f ield (X-dir) - foundat ion (X-dir) - b a s e (X-dir) 0.5 1 1.5 Period (sec) 2.5 P s e u d o Acce le ra t ion R e s p o n s e Spec t ra , 2 . 5 % damp ing • free f ield (Y-dir) foundat ion (Y-dir) b a s e (Y-dir) I T I " * -"-*-iH 0.5 1.5 2 2.5 Period (sec) 3.5 Figure 5.12.4 Pseudo acceleration response spectra of the motion of free field, foundation (below isolators) and base (above isolators) at the L A 7-story university hospital, during the 1994 Northridge EQ. 226 0.2 0.1 0 -0.1 -0.2 Floor Abso lu te Acce le ra t ions (g's) | 8x ^ . . h . l . k J-I..J\II Min IPI M J \ #V\ /ill A / H M r / A r t A / A J A / ^ i-^l cA/^ n fA / \ s\ A r - >**Ww*^*mT9 111) III Hi !i IcF 115 f 1 1 20 V 25 30 35 40 45 0.2 0.1 0 -0.1 -0.2 -6x 10 20 25 30 35 40 46 0.2 0.1 0 -0.1 -0.2 4x 10 15 7 A 0 r s v ^ ^ v n 20 25 30 35 v ' V 40 4|5 0.2 0.1 0 -0.1 -0.2 6y J, LA iff 111 "I ^ " ' - 3 0 V ' " i " ' "40 " 45 0.2 0.1 0 -0.1 -0.2 4y .............. AMJIMMI,, 15 Time (sec) Figure 5.12.5 E-W (X-direction) & N-S (Y-direction) absolute accelerations of the instrumented upper floors of the L A 7-story university hospital, during the 1994 Northridge EQ. 227 20 10 0 -10 -20 J Floor Relative Displacement (mm) Time (sec) Floor Relative Displacement (mm) Time (sec) Deformation of the Isolators (mm) Time (sec) 4x-1x 10 15 / v 20 25 30 35 40 45 5p Figure 5.12.6 E-W (X-direction) relative displacements of the instrumented upper floors of the L A 7-story university hospital, during the 1994 Northridge EQ. 228 30 20 10 0 -10 -20 -30 20 10 -10 -20 Floor Relative Displacement (mm) 8y-1y 35 40 45 50 Time (sec) Floor Relative Displacement (mm) Time (sec) Floor Relative Displacement (mm) - 4y-1 y 10 15 30 35 40 45 5b Time (sec) Figure 5.12.7 N-S (Y-direction) relative displacements of the instrumented upper floors of the L A 7-story university hospital, during the 1994 Northridge EQ. 229 Absolute Displacements free field >» i t 1 &-A H ** •J O A. 1 lW| ? 3 4 * ff-x cm) Base *r o— /I 1 / 1 I / / 1 -*t s-1x(cm) Foundation i n A H O o 5 • 1 3 ^ ffl ° 3 4 ' ,1 5 -Ox(cm) 4th floor - 5 -4x(cm) 6x(cm) Roof 8x(cm) Figure 5.12.8 Orbital displacements (absolute displacements) at the center of the instrumented floors of the L A 7-story university hospital, during the 1994 Northridge E Q 230 Relative Displacements Figure 5.12.9 Orbital displacements (relative displacements) at the center of the instrumented floors of the L A 7-story university hospital, during the 1994 Northridge E Q 231 M#l <4x/lx> FG5-1210 .BLK , f t M#2 <4y/ly> JUi i M#3 <4r/lr> 0.00 M#4 <6x/lx> 10.0 Hertz 0.00 10.0 Hertz M#5 <6y/ly> 0.00 M#6 <6r/lr> 10.0 Hertz 0.00 M#7 <8x/lx> 10.0 Hertz 10.0 Hertz 0 1 M#8 <8y/ly> 0.00 M#9 <8r/lr> 10.0 Hertz 10.0 Hertz 10.0 Hertz Figure 5.12.10 Frequency Response Functions of the instrumented upper floors with respect to the first floor (above isolators) of the L A 7-story university hospital, obtained from the 1994 Northridge EQ records. Note: FRF's are computed using a Harming window, a block size N=2048, 20 averages and 90% segment overlap. 232 M#l <lx/Ox> F G 5 - 1 2 1 1 . B L K . 0 1 M#2 <ly/Oy> I.61-n M#3 <lr/Or> 0.00 10.0 Hertz M#4 <4x/0x> 0.00 10.0 Hertz M#5 <4y/0y> 0.00 10.0 Hertz M#6 <4r/0r> 0.00 10.0 Hertz M#7 <6x/0x> 0.00 10.0 Hertz M#8 <6y/0y> 0.00 10.0 Hertz M#9 <6r/0r> 0.00 10.0 Hertz 0.00 10.0 Hertz M#10 <8x/0x> , . 0 M l <8y/0y> n 1 4.58n 0.00 10.0 Hertz M#12 <8r/0r> 0.00 10.0 Hertz 0.00 10.0 Hertz 0.00 10.0 Hertz F i g u r e 5.12.11 Frequency Response Funct ions o f the instrumented f loors ( inc lud ing the first f loor ) w i t h respect to the foundat ion (be low isolators) o f the L A 7-story un ivers i ty hospi ta l , ob-ta ined f r o m the 1994 Nor th r idge E Q records. Note: FRF's are computed using a Harming window, a block size N=2048, 20 averages and 90% segment overlap. 233 3X 3Y 3R Figure 5.12.12 Mode shapes of the superstructure the L A 7-story university hospital (without isolators), obtained from the 1994 Northridge records. Note: The displacements of 4th, 6th and 8th floors are obtained from measured data. Displacements of the other floors are based on ME'scope's interpolation algorithm. 234 \ F i g u r e 5.12.13 M o d e shapes o f the L A 7-story universi ty hospital (wi th an extra story at the bot tom represent ing the deformat ion o f the isolators), obtained based on Nor th r idge E Q Reco rds . Note: The displacements of 1 st, 4th, 6th and 8th floors are obtained from measured data. Displacements of the other floors are based on ME'scope's interpolation algorithm. 235 Table 5.12.1 Estimated natural frequencies (and periods) of the L A 7-story university hospital, based on the of FRF results and visual inspection of the three dimensional mode shapes obtained from analysis of 1994 Northridge EQ data. SUPERSTRUCTURE (obtained from the FRF's of Figure 5.12.10) X-Direction (E-W) Y-Direction (E-W) Rotation Frequency (Hz) Period (S) Frequency (Hz) Period (S) Frequency (Hz) Period (S) Model 1.10 0.91 1.39 0.72 1.65 0.61 Mode 2 2.8 0.36 3.33 0.30 3.9 0.26 Mode 3 5.5 0.18 6.4 0.16 - -BASE-ISOLATED (obtained from the FRF's of Figure 5.12.11) X-Direction (E-W) Y-Direction (E-W) Rotation Frequency (Hz) Period (S) Frequency (Hz) Period (S) Frequency (Hz) Period (S) Mode 1 0.73 1.37 0.7 1.43 0.8 1.25 Mode 2 1.7 0.59 1.9 0.53 2.1 0.48 Fundamental Period of the building without Base Isolation: a) N B C C 1995: T = 0.1 N ==> T = 0.80 sec T x =0.09 h n / ( D s x ) 1 / 2 = 0.09 (35.66m) / (77.1 lm) 1 / 2 = 0.37 T y =0.09 h n / ( D s y ) 1 / 2 = 0.09 (35.66m) / (92.35.1 lm) 1 / 2 = 0.33 h^ U B C 1997: T = 0.020 (h n ) 3 / 4 = 0.020 (117ft)3/4 = 0.71 sec 236 Chapter 6 DISCUSSION OF THE INFORMATION OBTAINED FROM STRONG MOTION DATA 6.1 General A detailed discussion of all the information presented in Chapter 5 is beyond the scope of this thesis due to time and space constraints. However, the following important observations could be made from the analyses performed. 6.2 Properties of the Ground Motions The time-history plots of the ground motions indicated that, although the instruments recorded motions with durations of 40 to 100 seconds, the strong portion of the shaking in most cases start-ed after 5 to 10 seconds with durations of 10 to 20 seconds. The Normalized Fourier Spectra of the ground motions indicated that the frequency content of the records were mainly within the range of 0.5 to 15 Hz with peak values typically occurring in the range of 1.0 to 2.0 Hz. The Pseudo Acceleraton Response Spectra provided the most critical information about the ground motions where seismic response of buildings is concerned. The peaks of the acceleraton response spectra in most cases were within a period range of 0.2 to 0.4 seconds and a significant drop was observed in the spectral values for periods greater than 1.0 second. This implies that the participation of the first mode in the response of buildings with a fundamental period of greater than 1.0 second will be relatively small under such seismic loading. There were also cas-es where the peaks of the acceleraton response spectra were within a period range of 0.5 to 1.0 seconds and the drop in the spectral value started after a period of 1.5 seconds. 237 The variation in the shape of the Relative Displacement Response Spectra was much greater than that of the acceleration response spectra. The periods corresponding to the peak displace-ment spectral values were always greater than those of the acceleration spectral values, ranging from 1.2 to 9.0 seconds. 6.3 Three-Dimensional Nature of the Ground Motion and the Response of the Buildings In addition to the vertical motions recorded in the earthquakes, it can be observed from the or-bital motion plots presented in Chapter 5 that the horizontal ground motion has a two dimension-al nature and the X and Y components of the motion presented in the time history plots are not the two components of a unidirectional motion. The two translational components of the ground motion seem to be uncorrelated and their peaks do not occur simultaneously. The response of the buildings has also a three dimensional nature. This is both due to the 3-D ground motions and the 3-D properties of the structure. This issue becomes more critical when the structure is non-symmetrical and has mass eccentric-ity which results in coupling of the translational and torsional modes of vibrations of the struc-ture. 6.4 Rotational Ground Motion The ground motion time-history plots show that the portion of the ground accelerations at the ends of the buildings due to pure rotation were 10 to 35 percent of the magnitude of the transla-tional accelerations at the center of the buildings. This affects the 3-D response of the structures. Further research has to be done to evaluate the significance of this effect and whether there is 238 need for including a torsional seismic design load in addition to the torsion due to accidental mass eccentricity introduced by building codes. De la Llera and Chopra (1991 and 1992) studied the response of three low-rise nominally sym-metric buildings (including the Richmond 3-story office building and the San Jose 3-story office building) to evaluate the code accidental torsional provisions. The study showed that U B C acci-dental eccentricity (5 percent of the building dimension) seems to be satisfactory in representing the torsional motion of the Richmond 3-story office building during the 1989 Loma Prieta Earth-quake. It was also concluded that accidental eccentricity may not be necessary in designing these three buildings. However, "extrapolating these observations to other situations is somewhat speculative" [De la Llera and Chopra, 1992]. 6 . 5 Vertical Ground Motion The ratio of vertical to horizontal peak ground accelerations (PGA) measured in the buildings is summarized in Table 6.1. This ratio is mainly within the range of 30% to 50%. The response of the buildings to vertical ground motion depends on the vertical vibration prop-erties of the structure. These properties, which are determined by the distribution of the mass and the stiffness of the vertical load resisting system, are independent from the lateral vibration prop-erties and may vary for the different parts of the structure. A plot of vertical to horizontal PGA ratio versus epicentral distance for the buildings under study does not show a clear relationship between these two parameters (Fig 6.1). 239 Table 6.1 Comparison of the peak ground accelerations of the buildings in various directions and their epicentral distances. Building EQ Epicentral distance (km) Peak Ground Acceleration (g's) E-W N-S Absolute Horiz. Vertical Vertical to Hoz. Ratio Burbank, 6-Story Office Building Whittier 25 0.16 0.22 0.24 0.09 36% Northridge 22 0.30 0.26 0.31 0.12 40% San Bernardino 5-Story Hospital Northridge 113 0.05 0.06 0.06 0.03 51% Pasadena 6-Story Office Building Northridge 37 0.10 0.15 0.15 0.07 45% San Jose 3-Story Office Building Loma Prieta 21 0.20 0.17 0.20 0.12 57% San Francisco 4-Story Hospital Loma Prieta 85 0.15 0.14 0.16 0.08 52% Berkeley 2-Story Hospital Loma Prieta 97 0.12 0.11 0.12 0.04 33% Richmond 3-Story Office Building Loma Prieta 112 0.11 0.08 0.12 0.04 35% Redlands 7-Story Commercial Bldg. Landers 72 0.05 0.05 0.07 0.06 95% San Bernardino 3-Story Office Bldg. Landers 83 0.11 0.10 0.11 0.06 53% L A 2-Story Fire Control Building Northridge 38 0.16 0.19 0.24 0.11 44% L A 7-Story University Hospital Northridge 36 0.16 0.37 0.37 0.07 18% 240 Ratio of Vertical to Horizontal PGA (%) 100 80 60 40 20 • • 20 40 60 80 100 120 Epicentral Distance (km) Figure 6.1 Vertical to horizontal PGA ratio versus epicentral distance 6.6 Amplification of the Motion The time history plots show that peak accelerations were amplified in the upper floors in most cases. However, the variation in these results was significant. For example, the peak accelera-tions recorded at the roof level of the San Bernardino 5-story hospital during the Northridge earthquake were about three times the recorded PGA's, whereas the peak acceleration recorded at the roof level of the Pasadena 6-story office building in the N-S direction during the same earthquake was about 15 % less than the recorded PGA in that direction. This significant differ-ence is mainly due to the large difference between the fundamental periods of these buildings (see Table 6.2). In the Burbank 6-story office building during the Whittier earthquake an increase of approxi-mately 30 % (with respect to the PGA) was observed in the roof peak acceleration in the N-S direction whereas no amplification was recorded in the E-W direction. During the Northridge 241 earthquake, the results for this building were the opposite, i.e. there was about a 50 % increase in peak acceleration in the E-W direction and only approximately 10 % increase in N-S direction. 6.7 Comparison of Measured Periods to those Estimated by Code Empirical Formulae The results of this study, which are summarized in Table 6.2 show that the fundamental period of buildings in most cases are 50% to 100% higher than the values estimated by empirical for-mulae. The equation T= 0.1N significantly under-estimates the fundamental period for the type of build-ings of this research, which are mainly office buildings and their floor to floor heights are usually greater than residential buildings. The height dependent formula for steel moment frame build-ings, T = 0.085 (h n ) 3 / 4 shows a better agreement with the results of this research. Even though the latter formula provides a relatively better estimate of the fundamental period in many cases, it shows a significant error in some cases and the reliability of such empirical formulae in calcu-lating the seismic base shear becomes questionable. Another important observation is that the results of the Burbank 6-story office building indicate a higher period during the 1994 Northridge earthquake than the 1987 Whittier earthquake (which had a lower peak ground acceleration). This issue, which will be discussed in more detail in Chapters 8 & 9, indicates a non-linear behaviour of the building. The non-linearity can be due to yielding of the main structural and/or non-structural elements or nonlinear elastic behavior of the system (which results in lower global stiffness at higher levels of displacement). 242 T a b l e 6.2 Comparison of the measured periods to those estimated by code empirical formulae. Building P.G.A.(g) 0.1N 0.085. ( h „ ) 3 / 4 0.09 h n / (D s ) 1 / 2 Measured Period (sec) E-W N-S E-W N-S E-W N-S Burbank 6-st bldg. (Whittier EQ records) 0.16 0.22 0.6 0.96 - - 1.25 1.32 Burbank 6-st bldg. (Northridge EQ records) 0.30 0.26 0.6 0.96 - - 1.41 1.41 San Bernardino 5-Story Hospital 0.05 0.06 0.5 0.84 - - 0.50 0.48 Pasadena 6-Story Office Building 0.10 0.15 0.7 0.95 - - 2.22 1.72 San Jose 3-Story Office Building 0.20 0.17 0.3 0.65 - - 0.64 0.73 SanFrancisco 4-Story Hospital 0.15 0.14 0.4 0.68 - - 0.67 0.70 Berkeley 2-Story Hospital 0.12 0.11 0.2 - 0.16 0.16 0.35 0.33 Richmond 3-Story Office Building 0.11 0.08 0.3 0.60 - - 0.70 0.64 Redlands 7-Story Commercial Building 0.05 0.05 0.7 1.14 - - 1.37 1.59 San Bernardino 3-Story Office Building 0.11 0.10 0.3 0.57 - - 0.55 0.56 L A 2-Story Fire Con-trol Building 0.16 0.19 0.2 - 0.17 0.17 0.34 0.34 L A 7-Story University Hospital 0.16 0.37 0.8 - 0.37 0.33 0.91 0.72 243 6.8 Periods Measured by Other Researchers. A summary of the periods measured for low-rise steel structures by other researchers (extracted from the reports that were mentioned in Chapter 2) is included in this section for additional in-formation and for comparison with the results of this thesis. These values are presented in Tables 6.3 to 6.8. Table 6.3 Measured periods for steel moment frame buildings (after Goel and Chopra 1997). Building ID Number of Height EQ Measured Period (sec) Location1 Number2 Stories (m) Name Longitudinal Transverse Burbank* C24370 6 24.2 Northridge 1.36 1.38 Whittier 1.32 1.30 Long Beach C14323 7 27.7 Whittier 1.19 1.50 Los Angeles U5208 6 31.7 Northridge 0.94 0.96 Norwalk U5239 7 29.3 Whittier 1.54 1.54 Norwalk U5239 7 29.9 Whittier 1.30 1.22 Palm Springs C12299 4 15.7 Palm Springs 0.71 0.63 Pasadena* C24541 6 28.1 Northridge 2.19 1.79 Richmond * C58506 3 13.7 Loma Prieta 0.63 0.74 0.60 0.76 San Bernardino* C23516 3 12.6 Whittier 0.50 0.46 San Jose* C57562 3 13.7 Loma Prieta 0.67 0.69 0.69 0.69 Note 1: * Denotes that the building is the same as studied in this thesis. Note 2: The letters C and U denote the CSMIP (California Strong Motion Instrumentation Plan) and USGS (United States Geological Survey) station numbers. 244 Table 6.4 M e a s u r e d periods fo r the San Franc isco 4-story hospi tal (after Fenves 1990). Ear thquake N a m e Peak G r o u n d Acce le ra t ion (g 's) T ime W i n d o w M e a s u r e d Pe r i od (sec) Longitudinal Transverse Longitudinal Transverse M o r g a n H i l l 0.02 0.03 0-15 sec 0.54 0.54 15-40 sec 0.56 0.57 L o m a Pr ie ta 0.14 0.16 0-9 sec 0.61 0.65 9-26 sec 0.71 0.71 Table 6.5 M e a s u r e d frequencies fo r the R i c h m o n d 3-story of f ice bu i l d ing (after D e l a L L e r a and C h o p r a 1991). Ear thquake N a m e Measured Frequency for the F i rs t M o d e s (Hz ) X- la tera l Y - la te ra l Tors iona l L o m a Pr ie ta 1.317 1.672 2.242 Table 6.6 Per iods measured for the R i c h m o n d 3-story b ldg . and the San Jose 3-story b ldg . (after D e l a L l e r a and C h o p r a 1992). Earthquake N a m e Measured Per iods for the F i rs t M o d e s (sec) X- la te ra l Y - la te ra l Tors iona l R i c h m o n d 3-story o f f ice bu i l d ing L o m a Pr ie ta 0.63 0.74 0.46 San Jose 3-story of f ice bu i l d ing L o m a Pr ie ta 0.67 0.69 0.65-0.69 245 Table 6.7 M e a s u r e d per iods f rom forced v ibrat ion measurements fo r a two story o f f ice b ldg . (wi th no basement) i n Oak land (after M c C l u r e , 1991). M o d e # Measured Per iod (sec) 1 0.426 2 1.672 B u i l d i n g D imens ions : 49 .7m x 46.6m , he igh t : 8.5m Table 6.8 M e a s u r e d per iods for steel moment f rame bui ld ings (after C o l e et a l . 1992). Building L ocation CSMIP Station Number Number of Height EQ Measured Period (sec) Stories (m) Name Transverse Longitudinal Burbank* 24370 6 24.2 Whittier 1.30 1.32 Long Beach 14323 7 27.7 Whittier 1.50 1.19 Palm Springs 12299 4 15.7 Palm Springs 0.63 0.71 Richmond* 58506 3 13.7 Loma Prieta 0.76 0.60 San Bernardino* 23516 3 12.6 Whittier 0.46 0.50 San Jose* 57562 3 15.1 Loma Prieta 0.69 0.69 San Francisco* 58261 4 16.0 Loma Prieta 0.71 0.71 Note: * Denotes that the building is the same as studied in this thesis. 6.9 Contribution of the Higher Modes Cont r ibu t ion o f the h igher modes o f v ibrat ion i n the overal l response o f the bu i ld ings to ground mot ion ma in l y depends on the natural frequencies o f the structure and the shape o f ground m o -t ion response spectra. T h e first mode usual ly contains 70 % to 80 % o f the ef fect ive mass o f the structure. (The higher moda l accelerat ion ampl i f ica t ion factors fo r the first modes presented i n 246 the tables of Chapter 5 are due to this fact). However, the periods of the higher modes usually are in the region of higher amplitude in the ground motion response spectra. In this study, the significance of the contribution of the higher modes in the structural response were evaluated by locating the natural periods of the buildings in the ground motion response spectra and investigating the out of phase accelerations and displacements on the time-history plots. A fundamental period in the low amplitude range of the acceleration response spectra indicates a small contribution of the first mode in the seismic response of the building. It was observed that for the buildings with the above mentioned situation, time history plots showed out of phase accelerations and displacements for the various floors, indicating the significance of the effect of the higher modes in the overall response of these buildings. The results of this study showed significant higher mode effects for the buildings with a funda-mental period of greater than 1.0 second. In the buildings with a period of less than 0.5 seconds the first mode seemed to dominate the overall response. It is important to note that the periods of some of the buildings in this study were significantly higher than what is usually expected for low-rise buildings, and their response was highly affect-ed by the second and third modes. In other words, these buildings behaved more like typical high-rise buildings. 6.10 Error Due to Manipulation of the Data At this point it is important to note that in order to identify the translational and rotational vibra-tion properties of the buildings, the X, Y, and Rotational components of the ground motion and the structural response at the center of the buildings were calculated by manipulating the record-247 ed data. This calculation, which was done based on the assumption of rigid floors and small dis-placements, may have introduced a measure of error to the analysis results. This error may be of larger magnitude for the time histories calculated for the center of the buildings at the foundation level of the buildings with spread footings (where there is no concrete diaphragm at that level). The rotational data, which are obtained by subtracting the two translational time-history data, have a smaller magnitude than the translational data whereas their random error and noise is of the same order of magnitude. This results in a significantly higher percentage of error for rota-tional data which should be considered when using those data. 6.11 Mode Shapes The existing data and the techniques used to determine the mode shapes were not precise enough to clearly distinguish between the modes in the X and Y direction when their periods were very close to each other. As a special case, the Burbank 6-story office building has almost identical structural properties in the X and Y directions with no mass eccentricity and no coupling between the modes. For such a structure, theoretically, there are no separate modes of vibration in the X and Y directions. The X and Y mode shapes are the same with the same period. In such cases any linear combination of the two mode shapes can also be a mode shape and will satisfy the properties of a mode shape in the dynamic equilibrium equations. 248 6.12 Base-Isolated Buildings Two of the buildings considered in this study were base-isolated. The response of both buildings (Los Angeles 2-story fire control building and Los Angeles 7-story University hospital) has been studied in detail by Huang et al. (1993) and Nagarajaiah and Xiahong (1995). The parameters that control the response of this type of building are more complicated than for rigid base build-ings. In particular, the use of a classical (Rayleigh's) damping matrix for structural analysis and the concept of equivalent linear damping has limited meaning for these structures. The effect of damping mechanisms on the response of base isolated buildings has been studied by Chang and Markis (1999). The theoretical basis of seismic isolation and energy dissipation has been studied by Kelly, (1997). More detailed study of the behaviour of the base-isolated structures was not within the scope of work of this research. However, a brief review of the information obtained from the strong mo-tion data (presented in Chapter 5) shows that base isolation mainly affects the seismic response of the buildings in the following two ways: 1) The fundamental period of the structure increases due to base isolation (a 50% increase was observed in the Los Angeles 7-story hospital and 200% in the Los Angeles 2-story fire control building). This places the fundamental period of the building in the low amplitude part of the ground motion response spectra and is very beneficial for low-rise buildings where their relative-ly low periods are usually in the high amplitude part of the ground motion response spectra. 2) A significant portion of the deformation of the building due to seismic loads happens in the isolators, which are capable of undergoing several circles of large deformations without signifi-cant damage. As a result, the elastic deformation of the rest of the building is significantly less than ordinary buildings. 249 6.13 Damping Ratios The estimated damping ratios were mainly within the range of 2 to 5 %. The data has undergone several stages of processing and curve fitting before estimating the damping values. The analysis results indicated that the method used in this project to estimate the damping values from the strong motion data does not always yield reliable results. Specifically, the results for higher modes did not seem to be reliable and were excluded from the final report. The damping val-ues estimated for the first modes in each direction were included in the report for information. How-ever, the accuracy of these results is questionable. 6.14 Modal Acceleration Amplification Factors The modal acceleration amplification factors obtained from the FRF and SRF analyses (presented in Chapter 5) were mainly used for estimating the natural frequencies of the buildings. However, they can also represent the dynamic response properties of these buildings. The amplification factors calculated for the fundamental modes were significantly higher than those of the higher modes. As noted in Section 6.9, this is due to the fact that for low-rise and mid-rise buildings, the first mode usually contains 70 % to 80 % of the effective dynamic mass of the system. 250 Chapter 7 COMPUTER MODELING OF THE BURBANK 6-STORY OFFICE BUILDING 7.1 I n t r o d u c t i o n The B u r b a n k 6-story of f ice bu i ld ing was chosen for a detai led computer mode l i ng and structural analys is . T h e bu i l d ing has a symmetr ica l p lan w i th no irregulari t ies. The mo t i on o f the bu i l d ing was recorded dur ing the 1994 Nor thr idge and the 1987 Whi t t ie r earthquakes. The bu i l d i ng ex-per ienced a peak ground accelerat ion o f 0.3g dur ing the Nor th r idge earthquake. These facts made the B u r b a n k bu i ld ing a desirable choice for this part o f the research, where invest igat ing the accuracy o f var ious analysis techniques was the ma in object ive. 7.2 S t r u c t u r a l Sys tem Genera l in fo rmat ion on the Bu rbank 6-story of f ice bu i ld ing is inc luded i n Chapter 4. In addi t ion, the f o l l o w i n g in format ion was also used in computer mode l ing o f the bu i l d ing . T h e bu i l d ing does not have a basement and the 4 inch concrete slab on grade prov ides grounds fo r assumpt ion o f a rigid d iaphragm at the first f loor. Th is assumption was used to generate data fo r the ground accelerat ions at the center o f the bu i ld ing . Typ i ca l f loors consist o f a 3 i nch l ight -weight concrete slab over corrugated metal decks supported by steel girders, w h i c h transfer the f l oo r loads to the co lumns. Shear studs, 19 m m (3/4 inch) in diameter and 114 m m (4.5 inch) i n length, we lded to the steel girders at 305 m m c/c (12 inch) provide composi te act ion between the concrete slabs and the steel girders i n the E - W direct ion. The composi te act ion o f the beams in the E - W direct ion may be a reason fo r the h igher stiffness 251 ( lower per iod) observed in the bu i ld ing dur ing the 1987 Whi t t ie r earthquake. The f r ic t ion be-tween concrete and steel components o f the composi te beam may be one o f the reasons for the h igher damp ing va lues estimated for the bu i ld ing in this direct ion. The co lumns are made o f wide- f lange, hot ro l led structural steel sect ions, w h i c h are sp l iced at 3 feet above the th i rd and f i f th f loors (where the co lumn sections are reduced i n s ize). The exterior co lumns, w h i c h f o rm the moment-resist ing frames, are we lded to steel grade beams. These beams are encased in re inforced concrete and supported by 9.75 m (32 feet) l ong , 762 m m (30 inch) diameter re inforced concrete pi les. A pair o f p i les under each c o l u m n is expected to pro-v i de moment resist ing supports at the base o f the co lumn in the plane o f the per imeter f rames (F igure 7.2.3). The f lex ib i l i t y o f the steel grade beams, however , makes the assumpt ion o f f i xed supports quest ionable (Shen and Astaneh, 1990). The inter ior co lumns are supported on base plates anchored to concrete grade beams. These co lumns are also supported on 30 i n c h diameter concrete pi les w i th a length o f 10.0 t o l 2 .2 meters (33 to 40 feet). T w o types o f beam to co lumn connect ions are used in the structural system. P i n connect ions are used for the inter ior beams and moment resist ing connect ions for the per imeter beams. F igures 7.2.1 to 7.2.5 show the typ ica l f raming, r ig id and p in connect ions, and c o l u m n base connect ion detai ls. 252 c d f g h 2 3 4 5 6 7 8 9 10 11 12 13 , i r- \W I I 1 i I N i ij L-rn i i — P I r 1 1 t 1 1 i —3 i r • 1 1 —1 p T 1 E — 1 1 1 1 1 1 -1 1 1 E ~ -F i_ _ i j P L J i r 1 r - |-per-JL r ; 1 t _ J _ 1 1 1 i ii i — 1 " • i i'. i i I'l 1 . . . i r i I I ni ' ! i 1 o O CM 30 ft f r Figure 7.2.1 Typical floor framing plan of the Burbank 6-story bldg. (after Shen & Astaneh, 1990). W21x68 to CD X CO 23 s co W24x81 W21x84 W27x84 M27xl02 W27xll6 i in CO g ra t • Q) i n CD i 6 Q 20'-0 - 120-0 Figure 7.2.2 Typical perimeter moment resisting frame of the Burbank 6-story bldg. 253 f WHx184 i \ Figure 7.2.3 Typical perimeter column base connection detail of the Burbank 6-story bldg. (after Shen & Astaneh, 1990). 1 in. Dia. • r • • Figure 7.2.4 Typical interior column base connection detail of the Burbank 6-story bldg. (after Shen & Astaneh, 1990). 254 D o u b l e r P l a t e S t i f f e n e r Moment Connection flange web Shear Connection Figure 7.2.5 Typical beam to column connection detail of the Burbank 6-story building (after Shen & Astaneh, 1990). The building drawings indicate the following material properties of the structural elements: • Structural steel: A S T M A-36 • Reinforcing Steel: Grade 40 or 60 • Lightweight Concrete: 17.3 kN/m 3 (110 pel) with f'c = 20.7 MPa (3000 psi) (for fill in metal decks) • Normal weight Concrete: P c = 13.8 MPa (2000 psi) for slabs on grade, f' c = 20.7 MPa (3000 psi) for all others. 255 7.3 Estimated Weight of the Building The f l oo r weights were calculated based on the in format ion prov ided in the structural drawings and the f o l l o w i n g assumptions: 3 i nch deep metal deck 3:0 ps f Concre te fill + 3.5 inch topping (l ight weight concrete, 1 lOpcf ) 44.0 p s f Steel beams and co lumns (2nd f loor) 14.0 ps f Steel beams and co lumns (3rd f loor) 12.0 ps f Steel beams and co lumns (typical f loor) 10.0 p s f Steel beams and co lumns (roof) 8.0 ps f Par t i t ion wa l l s 5.0 ps f Per imeter glass wa l l s (wal l area) 8.5psf(wall) C e i l i n g + M e c h a n i c a l 6.0 ps f R o o f i n g 7.0 ps f Penthouse roo f 30.0 ps f E leva to r mach ine room, concrete slab & wa l l s 150.0 p c f R o o f parapet (per uni t length) 135.0 p l f W i t h this in format ion, the f loor weights and corresponding rotat ional moments o f inert ia were calculated to be used in the dynamic analysis. Tab le 7.2.1 shows the f loor weights and the moments o f inert ia used in the computer mode ls o f the B u r b a n k bu i ld ing . 256 T a b l e 7.3.1 Es t imated f loo r weights and rotational moments o f inert ia o f B u r b a n k 6-story bu i ld ing . F l o o r D imens ions ft Total F l o o r Weight kips (kN) M o m e n t o f Inert ia kips . ft2 (KN . m 2) 2nd 1 3 0 x 1 3 0 1367 (6085) 4 3 5 2 0 0 0 ( 1 8 0 0 0 0 0 ) 3 rd 121.5 x 121.5 1115 (4965) 3022000 (1250000) 4th 121.5 x 121.5 1087(4839) 2 9 0 1 0 0 0 ( 1 2 0 0 0 0 0 ) 5th 121.5 x 121.5 1082(4817) 2780000 (1150000 ) 6th 121.5 x 121.5 1082(4817) 2780000 (1150000 ) R o o f + P . H . 133 x 1 3 3 1477(6577) 4 5 9 4 0 0 0 ( 1 9 0 0 0 0 0 ) Total - 7210 (32100) -7.4 Description of the Structural Model The structure was modeled as 3 -D frame structure w i th fu l ly rigid connect ions for per imeter f rames and a l l co l umn bases. The interior beams were mode led i n two ways . In the f irst model they were mode led w i t h p in connect ions so that they w o u l d not contr ibute to the lateral stiffness o f the structure. In the second mode l the interior beams were mode led as cont inuous beams w i th rigid connect ions to the co lumns. The object ive was to account fo r the compos i te act ion o f the beams in E - W (X-d i rec t ion) , the interaction o f the concrete slabs and the co lumns , and part ial f i x i t y o f the shear connect ions. The section properties o f the inter ior beams in the second model were mod i f i ed to prov ide the overal l lateral stiffness such that the natural f requencies o f the structural mode l matched those obtained f rom the Whi t t ie r earthquake data. P-de l ta effects, rotat ional and vert ical ground accelerations were considered. A l l f loors were assumed to be r ig id diaphragms and the f loor masses were l umped at the center 257 o f gravi ty o f the diaphragms. S ince a l l the inter ior beams were p in connected to the other elements, the ver t ica l loads on these beams w o u l d not affect the behaviour o f the perimeter moment resist ing f rames. The gravi ty loads and ver t ica l se ismic loads were only appl ied to the perimeter f rame members i n the mode l . T o apply the ver t ica l se ismic loads, the distr ibuted loads on the per imeter beams were l umped in the m id -span and the two ends o f each beam (2/3 o f the total distr ibuted load l umped as a con -centrated load at mid-span so that it wou ld result i n the same f i xed end moment as a un i fo rm ly distr ibuted load). In mode l i ng the spl iced co lumns, where the top 3/4 (approximately) o f the length o f the co l umn had a smal le r cross sect ion, s ingle elements w i th approximately equivalent sect ion propert ies were used. 7.5 D e s c r i p t i o n o f the S t r u c t u r a l A n a l y s i s P r o g r a m C A N N Y - E The p rogram C A N N Y - E ( C A N N Y - E U s e r ' s M a n u a l , 1996) was used for the nonl inear analyses i n this study. C A N N Y - E is capable o f per forming 3-d imensional non- l inear dynam ic t ime-h is -tory structural analys is. The nonl ineari ty o f C A N N Y - E ' s structural elements is based on a l umped plast ic i ty mode l , w h i c h assumes that y ie ld ing on ly occurs at the two ends o f the element. C A N N Y - E inc ludes a l ibrary o f var ious types o f hysteresis models that can be assigned to each element based on its mater ial and structural properties. The program does not consider geometr ic nonl ineari ty (wh ich is due to large deformat ions). H o w e v e r , P-del ta effects can be considered in the analysis. The user has the opt ion o f i nc lud ing rotat ional and ver t ica l ground accelerations. The lateral se ismic loads are app l ied to the centroid o f the r ig id f l oo r d iaphragms accord ing to the lumped masses assigned to each d iaphragm. V e r -258 t ica l se ismic loads can be appl ied to the structural mode l ( loca l ly ) by ass ign ing l umped masses to selected nodes. 7.6 Analysis Parameters used in the C A N N Y - E Model The f o l l o w i n g parameters were used i n the C A N N Y - E model o f the structure. 1) Damping: The program C A N N Y - E uses a R a y l e i g h type damping , where the damp ing matr ix is a l inear combinat ion o f the mass and stiffness matrices. In this method the damp ing ratio o f on ly two modes can be def ined by the user. Th is d id not a l l ow assigning dif ferent damp ing v a l -ues to var ious modes in the X and Y direct ions. Because o f this l imi ta t ion o f the p rogram, the analyses were per formed w i th different damping values unt i l the best match w i t h the recorded data i n two direct ions was obtained. The analyses showed that the damp ing va lue, w h i c h gave a better match w i th N - S (Y-d i rec t ion) data was lower than that o f the E - W (X-d i rec t ion ) data. H o w e v e r , a cr i t ica l damping ratio o f 3 .0% assigned to the first two modes (wh i ch showed rea-sonable results fo r both direct ions) was used in the final mode l . 2) Time step method: C A N N Y - E has the opt ion o f us ing var ious t ime step integrat ion tech-niques. The N e w m a r k ' s method w i th a Be ta value o f 0.25 was used for the t ime step analys is in this project (see Chop ra , 1995). 3) Hysteresis model: B i - l i nea r Degrad ing E las to-P las t ic hysteresis loops were used to mode l the bend ing stiffness propert ies o f the beams and co lumns and axia l stiffness o f the co lumns . F i gu re 7.6.1 shows the C A N N Y - E hysteretic model used for the nonl inear analys is i n this project. 259 The f o l l o w i n g parameters were used i n def in ing the hysteretic models : • P o s t y i e l d i n g stiffness factor o f 0.02 ( w i t h reference to S A C 95-04, 1995) • U n l o a d i n g stiffness degradat ion factor y = 0.3 • Strength degradat ion factor 0.75 The factor y is used determine the un load ing stiffness as f o l l ow ing : V max max/ W h e r e K u , K 0 , dy, d ' y , c L ^ and d ' m a x , are shown i n F igu re 7.5.1. The factor is used to determine the re loading y i e l d strength as fo l l ows (where dm and d y are shown in F igu re 7.5 .1 ,u = d m / d y represents duct i l i ty and F y represents the in i t ia l y i e l d strength): F , - F , - ( l - X . - ( l - 5 ) ) F o r example , X 1 1= 0.75 w i l l result i n a 5 0 % reduct ion i n strength at duct i l i ty u = 3. 4) Material Strength: The expected y ie ld stress o f the structural steel was cons idered to be 1.05Fy = 260 M P a based on the recommendat ions o f the Inter im Gu ide l ines ( F E M A 1 9 9 5 ) . F o r plast ic moment , M p = Z . F y (where Z is the plast ic modulus o f the steel sect ion) was used i n the b i - l inear Hysteret ic models for beam & co lumn bending properties. 5) Shear: Shear stiffness properties were modeled as l inear elastic. 7.7 Modified Linear Elastic Model (ETABS Model) The program C A N N Y - E does not inc lude an opt ion for per forming a response spectrum analy-sis. S ince spectral dynamic analysis is w ide ly used in the se ismic design o f the structures, it was 260 desirable to inc lude in this study a compar ison o f results f rom t ime-history and response spec-t rum analyses. F o r this reason a s impler model o f the bu i l d ing was prepared to be analyzed w i th the program E T A B S ( E T A B S U s e r ' s M a n u a l , 1995). The propert ies o f the E T A B S mode l , w h i c h was also 3-d imens iona l , were as fo l l ows : • L i n e a r elastic behaviour • N o inter ior beams (interior co lumns were lateral ly supported by the rigid d iaphragms) • Un id i rec t i ona l input ground mot ion (only the E - W (X -d i r ) component o f the ground mot ion recorded dur ing the Nor th r idge E Q ) was app l ied to the mode l . • T h e per iod o f the f irst mode in the X d i rect ion was very c lose to that o f mode l A (the C A N N Y - E model w h i c h matched the Nor th r idge earthquake records, as descr ibed in the next chapter). F i g u r e 7.6.1 C A N N Y - E hysteretic mode l used i n nonl inear analys is ( C A N N Y - E U s e r ' s manual , 1996). 261 Chapter 8 DYNAMIC ANALYSIS OF THE BURBANK 6-STORY OFFICE BUILDING 8.1 General In this chapter, a summary o f the results o f the analyses per formed on the structural mode ls o f the B u r b a n k 6-story of f ice bu i ld ing , and a compar ison o f the results o f var ious analys is methods, w i l l be presented i n the format o f tables and diagrams. A more detai led d iscuss ion o f the results w i l l be inc luded i n Chapter 9. 8.2 Definition of the Structural Models used for the Analyses Three dif ferent structural models o f the bu i ld ing were used in this study. These are: Model A : C A N N Y - E non- l inear model w i th p in connected inter ior beams, no compos i te act ion between beams and concrete slabs, fu l ly f i xed co lumn bases and exter ior b e a m - c o l u m n connec-t ions. T h e f loor weights were mod i f i ed so that the mode l had the same natural f requencies as those obtained f rom the measurements dur ing the Nor thr idge earthquake. T ime-h is to ry outputs o f this mode l matched the Nor thr idge earthquake Records . M o d e l A was a lso used fo r the non-l inear analyses w i t h h igher levels o f input ground mot ion. Model B : C A N N Y - E non- l inear model w i th fixed end inter ior beams i n the E - W ( X ) di rect ion and increased stiffness properties for al l the elements. The stiffness o f this mode l was scaled so that i ts natural f requencies matched the higher frequencies obtained f r om measurements dur ing the Wh i t t i e r earthquake. 262 T h e addi t ional stiffness i n this model may be just i f ied by part ial f i x i ty o f the inter ior connect ions, interact ion o f concrete slabs w i th the steel beams and co lumns, and the sti f fness o f the non-struc-tural elements. Model C : E T A B S l inear elastic mode l (as descr ibed in Chapter 7) fo r compar ison o f the results f r o m the f o l l o w i n g analysis methods: 1) T ime-h is to ry analys is 2) Response spectrum analysis based on true response spectra o f the recorded g round mot ion 3) Response spectrum analysis based on code def ined response spectra 4) Equ i va len t Stat ic analysis. 8.3 Results of Analysis Based on Whittier Earthquake Records A s exp la ined i n Sect ion 8.2, the stiffness o f M o d e l B was scaled to match the Wh i t t i e r E Q data. A dynam ic t ime-history analysis was performed on this mode l , us ing the ground accelerat ions obtained f r om the Whi t t ie r earthquake records. Th is sect ion inc ludes a summary o f the results o f this analys is . The natural f requencies and periods o f M o d e l B are l isted in Tab le 8.3.1. A compar ison o f the f loor accelerat ion and displacement t ime-histor ies obtained f r om dynamic analys is o f M o d e l B w i th those obtained f rom the Whi t t ie r earthquake records is presented i n F igu res 8.3.1 and 8.3.2. The m a x i m u m values o f story shears, overturning moments, inter-story dr i f t rat ios, f l oo r d is-p lacements and the forces i n selected structural members, obtained f rom t ime-h is tory analysis are presented i n Tables 8.3.2 to 8.3.4. 263 F igu re 8.3.3 inc ludes plots o f the envelopes o f m a x i m u m story shears and over turn ing moments. Important results f r om this t ime-history analysis inc lude: • M a x B a s e Shear i n X direct ion: 2675 k N ( = 0.0833 W ) • M a x B a s e Shear i n Y direct ion: 3567 k N ( = 0.1111 W ) • M a x Abso lu te Hor i zon ta l B a s e Shear : 3599 k N ( = 0.1121 W ) • M a x Duc t i l i t y i n beams : 0.48 • M a x Duc t i l i t y i n co lumns : 0.43 N o t e : The analys is showed no y ie ld ing i n the structure, (i.e. the response was w i t h i n the l inear elast ic range.) T a b l e 8.3.1 Natura l frequencies and per iods o f mode l B X - D i r e c t i o n ( E - W ) Y - D i r e c t i o n ( E - W ) Ro ta t i on Frequency (Hz) Per iod (S) Frequency (Hz) Per iod (S) Frequency (Hz) Per i od (S) M o d e # 1 0.808 1.238 0.774 1.292 1.192 0.834 M o d e 2 2.267 0.441 2.182 0.458 3.257 0.307 M o d e 3 4.037 0.248 3.909 0.256 5.790 0.173 M o d e 4 6.075 0.165 5.935 0.169 8.711 0.115 M o d e 5 8.532 0.117 8.403 0.119 12.136 0.082 M o d e 6 11.377 0.088 11.325 0.088 15.823 0.063 A cr i t ica l damp ing rat io o f 3.5 % assigned to the f irst and the second modes results i n a R a y -le igh ' s damp ing matr ix [C] = 0.0070 [K] + 0.1738 [M ] , i n w h i c h [K ] and [ M ] represent stiffness and mass matr ices. 264 2 1.5 1 0.5 0 -0.5 -1 -1.5 Absolute Accelerations (m/s^2) 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -2.5 J Absolute Accelerations (m/sA2) Time (sec) 7x-recorded 7x 2y-recorded |-| 2y F i g u r e 8.3.1 C o m p a r i s o n the absolute accelerat ion t ime-histor ies obtained f rom the analys is o f M o d e l B w i th the Whi t t ie r E Q records. 265 1.5 1 0.5 0 -0 -1 -1.5 Absolute Accelerations (m/sA2) 2x-recorded 2x 520 -25- -30- -35-Time (sec) 2 1.5 1 0.5 0 -0.520 -1 -1.5 Absolute Accelerations (m/sA2) 7x-recorded 7x -25 39- ^5- -40 Time (sec) 2 1.5 1 0.5 0 -0.5. -1 -1.5 -2 -2.5 Absolute Accelerations (m/sA2) 2y-recorded 2y 2tr "25" ^30" "35" "3G Time (sec) Absolute Accelerations (m/sA2) 7y-recorded 7y -l2Q -25- -30-Time (sec) -35- ^ 0 Figure 8.3.1 Cont'd 266 0.05 0.04 0.03 0.02 0.01 0 -0.01 -0.02 -0.03 -0.04 -0.05 0.08 0.06 0.04 0.02 0 -0.02 -0.04 -0.06 -0.08 Relative Displacements (m) Time (sec Relative Displacements (m) Time (sec) 7x-recorded 7x 7y-recorded 7y F i g u r e 8.3.2 Compar i son the relat ive displacement t ime-histor ies obtained f r om the analys is o f M o d e l B w i th the Whi t t ie r E Q records. 267 0.015 0.01 0.005 0 -0 -0.01 -0.015 00540-Relative Displacements (m) V A A A A / ^ ^ - 2 5 - -3TX - 3 5 -2x-recorded 2x -40 Time (sec) 0.05 0.04 0.03 0.02 0.01 0 235 Relative Displacements (m) 7x-recorded 7x -0.03 -0.04 -0.05 2 5 30 35 4)0 Time (sec) 0.08 0.06 0.04 0.02 0 -0.022fr -0.04 -0.06 -0.08 Relative Displacements (m) 7y-recorded 7y JL - 2 5 " 3 0 " 3 5 - "4(0 Time (sec) F i g u r e 8.3.2 C o n t ' d 268 T a b l e 8.3.2 M a x i m u m story shears and overturning moments, t ime-history analys is o f M o d e l B w i t h the ground accelerat ions obtained f rom the Whi t t ie r E Q records. Overturning Moment (N.m) Story Shear (N) M / V i V A m a x ' v max (m) Mx(max) My(max) Vx(max) Vy(max) X Y 6th story 4.28e6 7.65e6 1.080e6 1.93 l e 6 3.96 3.96 5th story 9.91e6 16.63e6 1.506e6 2.277e6 6.58 7.30 4th story 16.88e6 23.94e6 1.782e6 2.352e6 9.74 10.18 3rd story 24.49e6 32.01e6 2.022e6 2 .25 le6 12.11 14.22 2nd story 32.84e6 39.51e6 2.371e6 2.715e6 13.85 14.55 B a s e 45.61e6 47.57e6 2.675e6 3.567e6 17.05 13.34 Note: The ratios of overturning moments to story shears at each floor represent an equivalent lever arm length in-dicating the hypothetical location where applying a static force equal to the maximum story shear would result in an overturning moment equal to the maximum overturning moment obtained from the time-history analysis at the corresponding floor. T a b l e 8.3.3 M a x i m u m f loor displacements and story drift ratios, t ime-history analys is o f mode l B w i t h the ground accelerat ions obtained f rom the Whi t t ie r E Q records. Floor Displacement (m) Story drift ratio (%) Dx(max) Dy(max) dx(max) dy(max) 7th f loo r 0.046 0.057 6th story 0.15 0.29 6th f loo r 0.040 0.048 5th story 0.20 0.33 5th f loo r 0.034 0.037 4th story 0.20 0.30 4th f loo r 0.026 0.031 3rd story 0.20 0.24 3rd f loo r 0.019 0.024 2nd story 0.20 0.24 2nd f loo r 0.011 0.015 1st story 0.21 0.28 269 T a b l e 8.3.4 M a x i m u m Forces i n the South-West corner co lumn and the beams connected to it i n E - W (X -d i r ) , t ime-history analysis o f M o d e l B w i th the ground accelerat ions obtained f rom the Wh i t t i e r E Q records. Column forces Beam forces M o m e n t ( k N - m ) Shear ( kN) A x i a l ( kN ) M o m e n t ( k N - m ) Shear ( k N ) 6th story 106.3 57.2 118.5 7th f loo r 112.9 57.8 5th story 118.8 70.0 263.8 6th f loo r 208.9 80.6 4th story 141.8 82.3 431.8 5th f loo r 274.5 102.6 3rd story 162.2 94.3 600.3 4th f l oo r 306.3 113.1 2nd story 200.1 91.8 773.0 3rd f loo r 403.0 146.5 1st story 370.9 132.5 979.0 2nd f loor 518.1 187.3 270 25 -i t(m) \ Floor Heigh \ Floor Heigh k Floor Heigh 5 n 0.0E+00 2.0E+06 4.0E+06 Story Shear X-dir (N) 25 20 ? S 15 '5 10 0111 \ O.OE+00 2.0E+06 4.0E+06 Story Shear X-dir (N) Figure 8.3.3 Envelope of maximum story shears and overturning moments obtained from the time-history analysis of Model B with the ground accelerations obtained from the Whittier EQ records. 271 8.4 Results of Analysis Based on Northridge Earthquake Records The natural f requencies and periods o f M o d e l A matched those obtained f rom the Nor th r idge earthquake records. T h i s mode l was used for a dynamic t ime-history analys is w i th the ground mot ions obtained f rom the Nor thr idge earthquake data. The results o f this analys is are presented i n this sect ion. The natural f requencies and periods o f M o d e l A are l isted in Tab le 8.4.1. A compar i son o f the f loo r accelerat ion and displacement t ime-histor ies obtained f r om the dy-namic analys is o f M o d e l A w i th those obtained f rom the Nor th r idge earthquake records is pre-sented i n F igures 8.4.1 and 8.4.2. A l t hough the analysis o f M o d e l B w i t h the Wh i t t i e r earthquake ground mot ions showed good agreement w i th the recorded data, the results o f the analys is o f this mode l w i t h the Nor th r idge earthquake ground mot ions d id not match the recorded data. The re-sults o f t ime-h is tory analys is o f M o d e l B w i th Nor thr idge earthquake ground mot ions are pre-sented i n F igu res 8.4.3 and 8.4.4 fo r compar ison. The m a x i m u m values o f story shears, overturning moments, inter-story dr i f t rat ios, f l oo r d is-p lacements and the forces i n selected structural members, obtained f rom t ime-his tory analys is o f M o d e l A w i t h the ground mot ions obtained f rom the Nor thr idge E Q data are presented i n Tables 8.4.2 to 8.4.4. F igu re 8.4.5 inc ludes plots o f the envelopes o f m a x i m u m story shears and over turn ing moments. In F igu res 8.4.6 to 8.4.9 absolute accelerations and relat ive d isplacements o f a l l upper f loors (second to seventh f loors) are presented i n an over la id format to observe the out-of-phase re-sponse o f the var ious f loors. Th is out-of-phase response, w h i c h is more not iceable i n the acce l -erat ion plots, indicates the s igni f icance o f the effect o f the higher modes i n the structural response. 272 Important results f r o m this t ime-history analysis inc lude: • M a x i m u m B a s e Shear i n X direct ion: 4290 k N ( = 0.1336 W ) • M a x i m u m B a s e Shear i n Y direct ion: 3509 k N ( = 0.1093 W ) • M a x i m u m C o m b i n e d ( X & Y ) Base Shear : 4642 k N ( = 0.1446 W ) • M a x i m u m Duc t i l i t y i n beams : 0.71 • M a x i m u m Duc t i l i t y i n co lumns : 0.78 N o t e : T h e analys is showed no y ie ld ing i n the structure, (i.e. the response was w i t h i n the l inear elast ic range.) T a b l e 8.4.1 Natura l frequencies and per iods o f M o d e l A . X - D i r e c t i o n ( E - W ) Y - D i r e c t i o n ( E - W ) Ro ta t ion Frequency (Hz) Per iod (S) Frequency (Hz) Per iod (S) Frequency (Hz) P e r i o d (S) M o d e l 0.723 1.383 0.725 1.379 1.133 0.882 M o d e 2 2.041 0.490 2.049 0.488 3.110 0.322 M o d e 3 3.678 0.272 3.691 0.271 5.543 0.180 M o d e 4 5.634 0.178 5.653 0.177 8.382 0.119 M o d e 5 8.110 0.123 8.124 0.123 11.779 0.085 M o d e 6 11.025 0.091 11.038 0.091 15.480 0.065 A cr i t ica l damp ing ratio o f 3.5 % assigned to the f irst and the second modes results i n a R a y -le igh ' s damp ing matr ix [C]=0.0077[K]+0.1593[M], in w h i c h [K ] and [ M ] represent st i f fness and mass matr ices. 273 . i A Absolute Accelerations (m/sA2) Time (sec) 2x-recorded 2x - 3 0 F i g u r e 8.4.1 C o m p a r i s o n the absolute accelerat ion t ime-histor ies obtained f r om the analys is o f M o d e l A w i t h the Nor th r idge E Q records. 274 -i3tL Absolute Accelerations (m/sA2) -35- -40- -45- -50-Time (sec) 2x-recorded 2x -55- -00 4 3 2 1 0 -1 -2 -3 -4 -5 30" 35~ Absolute Accelerations (m/sA2) 7x-recorded 7x "4TT ~45~ "50" Time (sec) "55" "6P Absolute Accelerations (m/sA2) 2y-recorded 2y Absolute Accelerations (m/sA2) Time (sec) 7y-recorded 7y -55- -6P F i g u r e 8.4.1 C o n t ' d 275 0.025 0.02 0.015 0.01 0.005 0 -0.005 -0.01 -0.015 -0.02 Relative Displacements (m) 2x-recorded 2x 0.025 0.02 0.015 0.01 0.005 0 -0.005 -0.01 -0.015 -0.02 -0.025 J Relative Displacements (m) 2y-recorded 2y Time (sec 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 Relative Displacements (m) 7y-recorded 7y Time (sec) F i g u r e 8.4.2 Compar i son the relat ive displacement t ime-histor ies obtained f r om the analys is o f M o d e l A w i t h the Nor thr idge E Q records. 276 0 .025 0 .02 0 . 0 1 5 0.01 0 .005 0 -0.00! -0.01 - 0 . 0 1 5 -0 .02 ,53b Relative Displacements (m) "40 45" ~50~ 2x-recorded 2x "55" "35 Time (sec) 0.1 0 . 08 0 .06 0 . 04 0.02 0 -0.023)0? -0 . 04 -0 .06 -0 .08 -0.1 Relative Displacements (m) 7x-recorded 7x 35- -4fr "*5 55- ^ 0 Time (sec) Relative Displacements (m) 7y-recorded 7y - 0 . 1 5 -45 -5a Time (sec) -55- -6P Figure 8.4.2 Cont'd 277 Absolute Accelerations (m/sA2) 2x-recorded 2x -25 -3b Absolute Accelerations (m/sA2) 7x-recorded 7x "25" T i m e (sec ) "30 2 1.5 1 0.5 0 -0.5 -1 -1.5 Absolute Accelerations (m/sA2) 2y-recorded 2y T i m e ( s e c F i g u r e 8.4.3 C o m p a r i s o n the absolute acceleration t ime-histor ies obtained f r om the analys is o f M o d e l B w i th the Nor th r idge E Q records. 278 3 i Absolute Accelerations (m/sA2) 2x-recorded 2x 0 z 1 -v • i3 0 a * 4n 45 'fifi R • I V - Z o Time (sec) -O A , - — — — ; . ; . . < o Absolute Accelerations (m/s A2^ 0 0 o / A I c C U I U c U 7 v Z / X 1 -n i / V s / ^ / N ^\ A A , - / ^ - L ^ / \ -S~*t ^— —- — i — u i •13 o J 3b 4U 4b b U bb b - Z o -o - -A -H - - Time (sec) 2 1.5 1 0.5 -as* -1 -1.5 Absolute Accelerations (m/sA2) 2y-recorded n 2y ^ fy o c / in 4 5 5 0 5 5 R D U O O n U HO OKJ DO D u Time (sec) O Absolute Accelerations (m/sA2) 7y-recorded 7y 0 Z •1 1 u -\ | v 3^ 40 45 50 R -Z • Time (sec) Figure 8.4.3 C o n t ' d 2 7 9 0.025 0.02 0.015 0.01 0.005 0 -0.005 -0.01 -0.015 -0.02 0.025 0.02 0.015 0.01 0.005 0 -0.005 -0.01 -0.015 -0.02 -0.025 -0.15 Relative Displacements (m) Relative Displacements (m) A 2x-recorded 2x 2y-recorded 2y F i g u r e 8.4.4 Compar i son the relat ive displacement t ime-histor ies obtained f r om the analys is o f M o d e l B w i th the Nor th r idge E Q records. 280 0.025 0.02 0.015 0.01 0.005 0 -0.01 -0.015 -0.02 Relative Displacements (m) 45" "50" 2x-recorded 2x "55" "6P "35" ~4U Time (sec) 0.1 0.08 0.06 0.04 0.02 0 -0.023jfj ! -0.04 -0.06 -0.08 -0.1 Relative Displacements (m) 7x-recorded 7x 35 -4Q- -45- -55- -6)0 Time (sec) Relative Displacements (m) 2y-recorded 2y Relative Displacements (m) 7y-recorded 7y -0.15 -4a -45- -50-Time (sec) -55- -6t> Figure 8.4.4 Cont'd 2 8 1 T a b l e 8.4.2 M a x i m u m story shears and overturning moments, t ime-history analys is o f M o d e l A w i t h the ground accelerat ions obtained f rom the Nor thr idge E Q data. Overturning Moment (N.m) Story Shear (N) M / V iy±max' v max (m) Mx(max) M y (max) Vx(max) Vy(max) X Y 6th story 11.90e6 5.45e6 3.002e6 1.375e6 3.96 3.96 5th story 26.53e6 13.75e6 3.751e6 2.106e6 7.07 6.53 4th story 38.94e6 24.16e6 3.347e6 2.73 l e 6 11.63 8.85 3rd story 46.52e6 36.41e6 3.521e6 3.112e6 13.21 11.70 2nd story 56.45e6 49.06e6 3.804e6 3.239e6 14.84 15.15 B a s e 74.87e6 65.55e6 4.290e6 3.509e6 17.45 18.68 Note: The ratios of overturning moments to story shears at each floor represent an equivalent lever arm length in-dicating the hypothetical location where applying a static force equal to the maximum story shear would result in an overturning moment equal to the maximum overturning moment obtained from the time-history analysis at the corresponding floor. T a b l e 8.4.3 M a x i m u m f loor displacements and story drift ratios, t ime-history analys is o f M o d e l A w i t h the ground accelerat ions obtained f rom the Nor th r idge E Q data. Floor Displacement (m) Story drift ratio (%) Dx(max) Dy(max) dx(max) dy(max) 7th f l oo r 0.097 0.084 6th story 0.55 0.26 6th floor 0.085 0.074 5th story 0.62 0.37 5th f loo r 0.068 0.059 4th story 0.47 0.40 4th f loo r 0.052 0.043 3rd story 0.43 0.38 3rd floor 0.036 0.030 2nd story 0.40 0.33 2nd floor 0.020 0.017 1 st story 0.39 0.32 282 Table 8.4.4 Maximum forces in the South-West comer column and the beams connected to it in E-W (X-dir), time-history analysis of Model A with the ground accelerations obtained from the Northridge EQ data. Column forces Beam forces Moment (kN-m) Shear (kN) Axial (kN) Moment (kN-m) Shear (kN) 6th story 305.5 165.2 170.3 7th floor 339.9 106.8 5th story 376.4 209.0 400.7 6th floor 643.0 193.4 4th story 355.0 181.0 638.1 5th floor 674.5 206.9 3rd story 344.5 189.2 835.6 4th floor 651.4 226.8 2nd story 370.9 212.7 1010.0 3rd floor 747.7 261.0 1st story 646.1 222.7 1318.1 2nd floor 891.7 284.8 283 25 20 '(U I 15 10 0.0E+00 2.0E+06 4.0E+06 6.0E+06 Story Shear X-dir (N) 25 T 20 15 'a> I o o LL 10 0.0E+00 2.0E+06 4.0E+06 6.0E+06 Story Shear X-dir (N) Figure 8.4.5 Envelope of maximum story shears and overturning moments, time-history analy-sis of Model A with the ground accelerations obtained from the Northridge EQ data. 284 I 1 1 1 1 o 1 1 1 1 1 ^ C O C N I T - O T J - C N O O ^ I O F i g u r e 8 . 4 . 6 Ove r la id plot o f f loor absolute accelerations o f (X -d i r ) , obtained f r o m the t ime-h is -tory analys is o f M o d e l A w i th the ground accelerations obtained f rom the Nor th r idge E Q data. m c N j i o - r - L o o i O T - i n c N CNJ v~ O O ' rj ' F i g u r e 8.4.7 F l o o r absolute accelerations (Y-d i r ) , obtained f rom the t ime-his tory analys is M o d e l A w i t h the ground accelerat ions obtained f rom the Nor th r idge E Q data. 1 T - 00 CD CN o CN CD 00 o o o o o o o o o d d d d d d d d d I I I I F i g u r e 8.4.8 F l o o r relat ive displacements (X-d i r ) , obtained f r om the t ime-his tory analys is M o d e l A w i t h the ground accelerations obtained f rom the Nor th r idge E Q data. 287 O O C Q ^ - C N O C N ' ^ C O O O O O O O O O O O O O O O O O O O F i g u r e 8.4.9 F l o o r relat ive displacements (Y -d i r ) , obtained f r om the t ime-his tory analys is M o d e l A w i t h the ground accelerations obtained f rom the Nor th r idge E Q data. 288 8.5 C o m p a r i s o n o f the Resu l t s o f V a r i o u s L i n e a r - E l a s t i c A n a l y s i s M e t h o d s In this sect ion, the l inear elastic M o d e l C (the E T A B S expla ined i n Chapter 7) was ana lyzed i n s ix dif ferent ways : C I : T ime -H i s to r y A n a l y s i s ( X - d i r e c t i o n ground accelerat ion o f Nor th r idge E Q records) C 2 : M o d a l Spectral A n a l y s i s w i th true response spectrum calculated for the above record. C 3 : S i m i l a r to C 2 but scaled to the base shear o f C I . C 4 : M o d a l Spectral Ana l ys i s w i t h U B C 9 7 recommended design response spect rum, assum-ing so i l p ro f i le type Srj> (st i f f soi l ) , a n c j scaled to the base shear o f C I . C 5 : S im i l a r to C 4 but assuming soi l prof i le type S g (soft soi l ) . C 6 : Static A n a l y s i s w i th base shear same as C I and code recommended ver t ica l d is t r ibut ion o f lateral loads. A c r i t i c a l d a m p i n g ra t i o o f 3.5 % was used for al l modes o f the mode ls C I to C 5 . F igu re 8.5.1 shows a three d imensional v i e w o f M o d e l C . F i g u r e 8.5.1 3 -D v i e w o f M o d e l C ( E T A B S M o d e l ) 289 The Response Spectra used for the analyses o f M o d e l s C4 and C5 were ca lcu la ted us ing U B C 9 7 gu ide l ines (See F igures 8.5.2 & 8.5.3), based on the f o l l ow ing assumpt ions: M o d e l C4: Se ism ic source distance > l O K m N a = N v = 1.0 So i l P r o f d e Type: S D (St i f f So i l ) Z = 0.4 C a = 0.44 N a = 0.44 C v = 0 . 6 4 N v = 0.64 T s = C v / 2 . 5 C a = 0.582 sec T o = 0 . 2 T s = 0 .116sec M o d e l C5: Se ism ic source distance > l O K m N a , N v > and Z , same as above So i l P ro f i l e Type : S D (St i f f So i l ) So i l p ro f i le type: S E (Soft So i l ) C a = 0.36 N a = 0.36 C v = 0 . 9 6 N v = 0.96 T s = C v / 2 . 5 C a = 1.0667 sec T 0 = 0.2 T s = 0.2133 sec 290 < cr U J o o < < cr Q_ C/) Ca 2-5C„ CONTROL PERIODS Ts = CV2.5Q, To = 0.2r, J I I l l PERIOD (SECONDS) F i g u r e 8.5.2 D e s i g n Response Spectra, U n i f o r m B u i l d i n g C o d e ( U B C 1997) Acce le ra t ion R e s p o n s e Spec r ta (g's) UBC97, S E •UBC97, S D 3.5% dmpg F i g u r e 8.5.3 Response Spectra used in analyses o f M o d e l s C 2 to C 5 . 291 UL Hi LU i-f UL '•-ii LUI H / / / l I 1 \ 1 1 \ f t r n Mode IX Mode 2X z A \ 1? \ Mode 3X Mode 4X Mode 5X Mode 6X F i g u r e 8.5.4 T w o d imensional v i e w o f the mode shapes o f M o d e l C i n X -d i r ec t i on . 292 In M o d e l C 6 , the base shear obtained f rom the t ime history analys is o f mode l C I was appl ied as static lateral loads, distr ibuted in the height o f the bu i l d ing based on code static analys is proce-dure. In this process, the extra concentrated load at top leve l , F t (see U B C 9 7 and/or N B C C 9 5 ) was calcu lated based on a per iod obtained f rom the f o l l ow ing empi r ica l fo rmu la : T = 0.085 ( h n ) 3 / 4 = 0.085 ( 2 5 . 1 5 m ) 3 / 4 = 0.955 sec ==> F t = 0.07 T V = 0.07 x 0.955 x 4256.85 = 284.57 k N The calcu lat ions o f the lateral static loads used in M o d e l C 6 are summar ized in Tab le 8.5.1. T a b l e 8.5.1 Ver t i ca l distr ibut ion o f se ismic loads for Stat ic A n a l y s i s . W i ( k N ) h i (m) W i . h i W i . h i / S u m F t f i F i= f i+F t F i . h i 7th f l oo r 6577 25.000 164425 0.3366 284.57 1337.1 1621.7 40542 6th f l oo r 4817 21.038 101338 0.2075 - 824.1 824.1 17337 5th f l oo r 4817 17.075 82251 0.1684 - 668.9 668.9 11421 4th f l oo r 4839 13.113 63452 0.1299 - 516.0 516.0 6766 3rd f loo r 4965 9.150 45432 0.0930 - 369.5 369.5 3381 2nd f l oo r 6085 5.188 31569 0.0646 - 256.7 256.7 1332 S u m . 32100 488468 1 4256.9 80779 The dynam ic propert ies o f M o d e l C are summar ized in Tables 8.5.2 through 8.5.4. The natural f requencies and per iods o f M o d e l C are inc luded in Tab le 8.5.2. A two d imens iona l v i e w o f the natural mode shapes o f M o d e l C i n the X direct ion is presented i n F i gu re 8.5.4. In Tab le 8.5.3 effect ive masses o f the ind iv idua l modes o f the structure are presented as a per-centage o f the total mass o f the bu i ld ing. Part ic ipat ion o f each mode in the total dynam ic loads 293 appl ied to the structure is determined as the product o f the moda l mass and the spectral va lue at the per iod corresponding to that mode. A compar ison o f the response spectrum base shears o f the X d i rect ion modes o f M o d e l s C I to C 5 is presented i n Tab le 8.5.4 T a b l e 8.5.2 Natura l frequencies and per iods o f M o d e l C X - D i r e c t i o n ( E - W ) Y - D i r e c t i o n ( E - W ) Ro ta t ion Frequency (Hz) Per iod (S) Frequency (Hz) Per iod (S) Frequency (Hz) P e r i o d (S) M o d e l 0.738 1.355 0.738 1.355 1.144 0.874 M o d e 2 2.067 0.484 2.067 0.484 3.148 0.318 M o d e 3 3.639 0.275 3.640 0.275 5.508 0.182 M o d e 4 5.541 0.181 5.544 0.180 8.296 0.121 M o d e 5 7.754 0.129 7.755 0.129 11.454 0.087 M o d e 6 10.316 0.097 10.309 0.097 14.869 0.067 T a b l e 8.5.3 E f fec t i ve mass factors o f M o d e l C X - D i r e c t i o n ( E - W ) Y - D i r e c t i o n ( E - W ) Ro ta t ion %-MASS % - S U M %-MASS % - S U M %-MASS % - S U M M o d e l 81.14 81.1 81.11 81.1 80.82 80.8 M o d e 2 13.17 94.3 13.17 94.3 14.33 95.2 M o d e 3 3.82 98.1 3.83 98.1 3.46 98.6 M o d e 4 1.24 99.4 1.20 99.4 0.89 99.6 M o d e 5 0.45 99.8 0.46 99.8 0.27 99.9 M o d e 6 0.18 100.0 0.18 100.0 0.09 100.0 294 A s is shown i n Tab le 8.5.3, the first mode in each di rect ion inc ludes 8 1 % o f the dynamic re-sponse factor o f the structure. Howeve r , a look at the response spectra o f F i gu re 8.5.3 shows that the h igher modes are i n the higher ampl i tude region o f the spectra. Therefore, the part ic ipat ion o f the f i rst mode i n the total response is less than 8 1 % (Table 8.5.4). Th i s issue becomes more s ign i f icant i n tal ler bu i ld ings w i th larger fundamental periods. A compar i son o f the results o f the different methods o f analysis i n terms o f story shears, over-turn ing moments , d isplacements, inter-story drift ratios and selected element forces is summa-r ized i n Tab les 8.5.5 to 8.5.10. P lo ts o f m a x i m u m story shears and f l oo r over turn ing moments are presented i n F igu re 8.5.5 fo r a more clear compar ison o f the results. T a b l e 8.5.4 D y n a m i c response spectrum base shears o f ind iv idua l ( X di rect ion) modes o f M o d e l s C 2 to C 5 . Modal Base Shears (kN) C2 C3 C4 C5 M o d e 1 3675 3077 3951 4157 M o d e 2 3166 2651 1493 857 M o d e 3 1364 1142 433 249 M o d e 4 422 353 140 73 M o d e 5 . 83 70 51 23 M o d e 6 27 23 18 8 CQC 5084 4257 4257 4257 295 T a b l e 8.5.5 C o m p a r i s o n o f m a x i m u m story shears o f M o d e l s C I to C 6 . Story Shear (kN) CI C2 C3 C4 C5 C6 6th story 3202.1 2749.4 2302.2 1632.1 1426.9 1621.7 5th story 3786.6 3202.1 2681.3 2406.9 2306.8 2445.8 4th story 3473.3 3250.3 2721.7 2926.5 2993.4 3114.7 3rd story 3200.3 3406.6 2852.5 3376.8 3531.1 3630.7 2nd story 3662.4 3937.3 3296.9 3817.6 3940.1 4000.1 B a s e 4256.9 5083.7 4256.9 4256.9 4256.9 4256.9 T a b l e 8.5.6 Compar i son o f m a x i m u m f loor overturning moments o f M o d e l s C I to C 6 . Overturning Moment (kN-m) CI C2 C3 C4 C5 C6 6th f l oo r 12700 10900 9120 6470 5650 6430 5th f l oo r 27500 22800 19100 15800 14700 16100 4th f l oo r 39700 33200 27800 26800 26400 28500 3rd f loo r 47900 42400 35500 39200 40000 42800 2nd f loo r 52200 51600 43200 52800 55200 58700 B a s e 71300 67700 56700 72700 76500 80800 Base Overturning Moment Base Shear Ratio (M b / V b ) 16.75 13.32 13.32 17.08 17.97 18.98 296 Comparison of Story Shears Story Shear (kN) 25 20 Il5 D) ©10 X 5 0 Floor Overturning Moments 1 1 : 1 - H - C 3 - A - C 4 - H - C 5 C6 0.E+00 2.E+04 4.E+04 6.E+04 8.E+04 Overturning Moment (kN-m) 1.E+05 F i g u r e 8.5.5 C o m p a r i s o n o f m a x i m u m story shears and f loor over turn ing moments o f M o d e l s C I to C6. 297 T a b l e 8.5.7 Compar i son o f m a x i m u m f loor displacements o f M o d e l s C I to C 6 . Floor Displacement (mm) CI C2 C3 C4 C5 C6 7th f l oo r 95.8 89.5 74.9 94.1 98.6 105.2 6th f l oo r 84.0 77.2 64.7 82.8 87.1 91.5 5th f l oo r 67.3 64.2 53.7 67.9 71.2 73.7 4th f l oo r 49.6 51.2 42.9 51.5 53.5 54.7 3rd f loo r 33.4 37.3 31.3 34.9 35.7 36.2 2nd f loo r 18.0 21.7 18.1 19.0 19.1 19.3 T a b l e 8.5.8 Compar i son o f m a x i m u m inter-story drift ratios o f M o d e l s C I to C 6 . Inter-Story Drift Ratio (% hi) CI C2 C3 C4 C5 C6 6th story 0.62 0.52 0.44 0.34 0.31 0.35 5th story 0.64 0.54 0.45 0.43 0.42 0.45 4th story 0.51 0.47 0.40 0.44 0.46 0.48 3rd story 0.45 042 0.35 0.43 0.45 0.47 2nd story 0.39 0.41 0.34 0.41 0.42 0.43 1st story 0.35 0.42 0.35 0.37 0.37 0.37 298 T a b l e 8.5.9 Compar i son o f m a x i m u m forces in the South-West corner c o l u m n , obtained f rom the analyses o f M o d e l s C I to C 6 . Max. Moment (kN-m) CI C2 C3 C4 C5 C6 6th story 325 276 231 169 149 167 5th story 361 304 255 233 228 239 4th story 359 323 270 269 274 282 3rd story 327 326 273 309 321 331 2nd story 365 387 324 374 389 396 1st story 627 756 633 645 648 649 Max. Shear (kN) CI C2 C3 C4 C5 C6 6th story 183 158 133 91 77 88 5th story 207 176 147 130 124 131 4th story 189 177 148 158 162 168 3rd story 189 185 155 181 189 194 2nd story 210 229 192 220 226 229 1st story 239 285 239 238 238 234 Axial Force (kN) CI C2 C3 C4 C5 C6 6th story 127 109 91 64 55 62 5th story 345 288 241 191 175 193 4th story 551 456 382 351 340 369 3rd story 707 609 510 540 545 586 2nd story 804 759 636 760 790 843 1st story 1036 955 799 1019 1071 1135 299 T a b l e 8.5.10 Compar i son o f M a x i m u m Forces in the perimeter beams o f the first span f rom W e s t at the South edge o f the bu i ld ing. Max. Moment (kN-m) CI C2 C3 C4 C5 C6 6th story 412 352 294 211 185 209 5th story 696 575 482 410 386 420 4th story 664 587 492 517 522 551 3rd story 655 624 523 624 652 677 2nd story 727 735 615 744 776 793 1st story 860 989 828 900 916 924 Max. Shear (kN) CI C2 C3 C4 C5 C6 6th story 130 i l l 93 67 58 65 5th story 225 186 156 133 125 136 4th story 218 193 161 169 171 181 3rd story 215 205 172 205 214 222 2nd story 240 242 203 245 256 261 1st story 275 316 265 288 293 295 300 8.6 Non-Linear Analysis Using Ground Motions Stronger than those Recorded during the Northridge Earthquake. Since the t ime-history analysis o f the non- l inear mode l w i th recorded ground mot ions indicated no y i e l d i ng i n major structural elements, the analysis was repeated w i th h igher levels o f ground mot ions , w h i c h were obtained by ampl i f y ing those recorded i n Nor th r idge earthquake by factors o f two and three. The object ive was to compare the results o f nonl inear and l inear elast ic dynam-i c t ime-his tory analyses and nonl inear static (push-over) analys is. F o r this purpose the f o l l ow ing analyses were performed: BTJ-A-N: M o d e l A , T ime-H is to ry Ana l ys i s , Nor thr idge E Q ground acc. (same as sect ion 8.4). BU-A-2N: M o d e l A , Non l inear , T ime-H is to ry A n a l y s i s , 2 x (Nor thr idge E Q ground acc.) BU-A-3N: M o d e l A , Non l inear , T ime-H is to ry Ana l ys i s , 3 x (Northr idge E Q ground acc.) EL-A-2N: M o d e l A , L i n e a r E las t i c , T ime-H is to ry A n a l y s i s , 2 x (Northr idge E Q ground acc.) EL-A-3N: M o d e l A , L i n e a r E las t i c , T ime-H is to ry Ana l ys i s , 3 x (Northr idge E Q ground acc.) P L - A - S T : M o d e l A , N o n - L i n e a r Static (Push-Over) A n a l y s i s w i th r o o f m a x i m u m disp lacement set to be equal to that o f t ime-history analysis o f BU-A-3N & EL-A-3N. A critical damping ratio of 3.5 % was assigned to the first two modes i n a l l o f the above m e n -t ioned dynamic analyses. In non- l inear analys is , i n addi t ion to the dissipat ion o f energy due to damping , an extra amount 301 o f energy dissipates due to the plast ic behavior. It is general ly recommended to use smal ler damp ing va lues fo r non- l inear analysis to avo id under-est imat ing the displacements. H o w e v e r , i n this study, the object ive was to compare the results o f var ious analys is methods. Therefore the same damp ing va lues were used for al l analyses. A t the end, to v isua l i ze the impact o f a smal ler damping va lue, the analys is o f mode l BU-A-3N was repeated w i th a damping va lue o f 1.5%. The roo f accelerat ion and d isp lacement t ime-histo-ries obtained f r o m this analysis are presented i n F igu re 8.6.2 to be compared to the results ana l -ys is w i t h 3 . 5 % damping (presented i n F igu re 8.6.1). Vertical distribution of the lateral loads fo r the nonl inear static (push-over) analys is was cho-sen to be the same as the code recommended distr ibut ion for static analys is (same as that o f M o d -el C6 i n Chapter 8). The load factors used to distribute the base shear a long the height o f the bu i l d i ng i n this analys is are shown i n Tab le 8.6.4. A compar ison o f the base shears, m a x i m u m f loor displacements, and inter-story dr i f t ratios ob-tained f r om the l inear and nonl inear analyses o f this sect ion is inc luded i n Tab les 8.6.1 and 8.6.2. In Tab le 8.6.3, m a x i m u m duct i l i ty factors o f selected beams and co lumns obtained f r o m the non -l inear analyses are compared. The results o f the push-over analysis (see Tables 8.6.1 to 8.6.3) are presented fo r the two cases where the structure is pushed unt i l ach iev ing roo f displacements equal to the m a x i m u m roo f d isplacements obtained f rom the analyses o f BU-A-3N and E L - A - 3 N . P lo ts o f f l oo r d isplacements versus base shear obtained f rom the push-over analys is w i t h a max -i m u m r o o f d isplacement o f 2.00 meter is presented i n F igu re 8.6.3 302 T a b l e 8.6.1 Compar i son o f m a x i m u m f loor displacements and base shears o f non- l inear and l inear models , Max. floor displacement in X-dir (mm) B U - A - N B U - A - 2 N B U - A - 3 N E L - A - 2 N E L - A - 3 N P L - A - S T * 7th f l oo r 97 188 252 194 290 252 290 6th f l oo r 85 165 217 169 254 227 264 5th f l oo r 68 130 162 136 204 185 215 4th f l oo r 52 96 111 104 156 137 158 3rd f l oo r 36 66 77 72 108 88 101 2nd f loo r 20 37 42 41 61 46 51 B a s e S h e a r ( k N ) 4290 7842 8668 8576 12860 8709 8973 T a b l e 8.6.2 Compar i son o f m a x i m u m inter-story drifts o f non- l inear and l inear mode ls . Inter-story drift in X-dir (% hi) B U - A - N B U - A - 2 N B U - A - 3 N E L - A - 2 N E L - A - 3 N P L - A S T * 6th story 0.55 1.05 1.65 1.08 1.62 0.66 0.69 5th story 0.62 1.33 2.21 1.23 1.85 1.06 1.22 4th story 0.47 0.97 1.63 0.94 1.41 1.21 1.44 3rd story 0.43 0.77 0.99 0.86 1.30 1.21 1.44 2nd story 0.40 0.73 0.86 0.79 1.18 1.07 1.27 1st story 0.39 0.72 0.82 0.78 1.17 0.89 0.98 * T h e two co lumns inc lude the results o f analysis o f P L - A - S T w i t h the m a x i m u m roo f d is-p lacements o f equal to those obtained f rom the analyses o f B U - A - 3 N and E L - A - 3 N . M a x i m u m beam duct i l i ty factor in the or ig inal analysis was observed at the first span f rom Wes t on Southern edge o f the bu i ld ing . M a x C o l u m n duct i l i ty was observed i n 3rd c o l u m n f r om Wes t on the same side o f the bu i ld ing . In Tab le 8.5.4 duct i l i ty factors o f co lumns and beams at the above ment ioned locat ion are compared. T a b l e 8.6.3 Compar i son o f duct i l i ty factors o f dynamic and static analyses. Column Ductility Factor B U - A - N B U - A - 2 N B U - A - 3 N P L - A - S T * 6th story 0.78 1.94 3.66 0.89 0.93 5th story 0.78 2.63 4.72 1.50 1.87 4th story 0.58 1.17 2.06 1.02 1.21 3rd story 0.46 0.83 1.04 0.92 0.94 2nd story 0.48 0.86 0.94 1.50 1.95 1st story 0.51 0.93 1.04 1.27 1.48 Beam Ductility Factor B U - A - N B U - A - 2 N B U - A - 3 N P L - A - S T * 7th f loo r 0.45 0.82 2.02 0.48 0.49 6th f loo r 0.67 2.69 6.26 0.88 0.95 5th f l oo r 0.71 2.92 6.95 2.68 3.59 4th f l oo r 0.63 1.45 3.28 3.47 4.57 3rd f loo r 0.58 1.11 1.96 3.20 4.28 2nd f loor 0.55 1.10 1.65 2.70 3.54 * T h e two co lumns inc lude the results o f analysis o f P L - A - S T w i t h the m a x i m u m r o o f d is-p lacements o f equal to those obtained f rom the analyses o f B U - A - 3 N and E L - A - 3 N . 304 Roof absolute acceleration, X-direction CM < to £Z CD O O < 10 8 6 4 2 0 -2 -4 -6 -8 -10 — i t r I... — — — w | U | V " V 3 0 40 "So 60 Time (sec) Roof relative displacement, X-direction 0.3 0.25 0.2 0.15 r 0.1 | 0.05 CD n o U | -0-05 Q -0.1 -0.15 -0.2 -0.25 Time (sec) Figure 8.6.1 R o o f absolute accelerat ion and relat ive displacement t ime-histor ies obtained f rom the non l inear analysis o f mode l B U - A - 3 N (3 .5% damping). 305 Roof Absolute acc, 1.5% damping 10 8 ~ 6 CN CO 4 o 0 S -2 < -6 -8 -10 11 Hi—f - j — . j l l f i t I f *m ll MO 4 0 - - ' - i(yV 60 Time (sec) c cu E cu o JS o. CO b 0.3 0.25 0.2 0.15 0.1 0.05 0 •0.05 -0.1 •0.15 -0.2 •0.25 Roof relative dis., 1.5% damping BP Time (sec) Figure 8.6.2 R o o f absolute accelerat ion and relat ive displacement time-histories obtained f rom the nonl inear analysis o f mode l B U - A - 3 N (1 .5% damping). 306 Push-Over Analysis 1 4 0 0 0 t i ^ » » m » m i i ^ » ^ ; Floor displacements (mm) F i g u r e 8.6.3 Force-d isp lacement relationship obtained f rom push-over analys is . T a b l e 8.6.4 The ver t ica l distr ibut ion factors o f the lateral loads, used for non l inear static (Push-Over ) analys is o f mode l P L - A - S T load distr ibut ion factors F l o o r L e v e l 2nd F l o o r 3rd F l o o r 4th F l o o r 5th F l o o r 6th F l o o r R o o f La te ra l L o a d Fac to r 0.060 0.087 0.121 0.157 0.194 0.381 307 Chapter 9 DISCUSSION OF THE RESULTS OF THE ANALYSES OF THE BURBANK 6-STORY OFFICE BUILDING 9.1 General Remarks The accelerat ion and displacement t ime histories obtained f rom the dynam ic analyses o f the B u r -bank 6-story of f ice bu i ld ing matched c losely w i th those obtained f r om the strong mo t ion data. A s a result, it can be conc luded that the results o f the analyses per formed on the mathemat ica l mode ls o f the bu i l d i ng (presented in Chapter 8), are reasonable representations o f the behav iour o f th is bu i l d ing under se ismic load ing. In general , the results o f the type o f the analyses presented i n the prev ious chapter, can be used for the f o l l ow ing purposes: 1) s tudy ing the behav iour o f the bu i ld ing in actual earthquakes, 2) pred ic t ing the behav iour under higher levels o f shaking, 3) compar ing the results o f var ious analysis techniques w i th the actual response o f the bu i ld ing . Sect ions 9.2 to 9.6 inc lude some conclus ions inferred f rom rev iew ing the results o f the analyses o f the B u r b a n k 6-story of f ice bu i ld ing . The analysis showed that dur ing the Nor th r idge earth-quake, a l though the bu i l d ing experienced a peak ground accelerat ion o f 0.3 g and a peak acce l -erat ion o f 0.45 g at r oo f leve l , the m a x i m u m base shear was on ly 1 4 % o f the we igh t o f the bu i ld ing . T h e m a x i m u m inter-story drift ratios (wh ich was observed i n the f i f th story) was 0 .6% o f the story height, w h i c h is only 30 % o f the m a x i m u m a l lowab le dri f t rat io accord ing to the bu i l d i ng codes. 308 9.2 Possible Structural Damage during the Northridge Earthquake The strong mot ion data indicate a higher natural per iod for the bu i l d ing i n the Nor th r idge earth-quake w h i c h had a h igher peak ground accelerat ion than the Whi t t i e r earthquake. T h e results o f the t ime-history analysis o f M o d e l B (wh ich was scaled to have the same natural f requencies as measured i n the Whi t t i e r earthquake) matched the recorded data. H o w e v e r , ana lyz ing the same mode l w i t h the Nor th r idge earthquake ground accelerations showed good agreement w i t h on ly the f i rst 10 seconds o f the recorded response. T i m e history analys is o f mode l A , w h i c h had sma l l -er natural f requencies, matched the Nor thr idge earthquake data very w e l l . T h i s may indicate that the sti f fness o f the bu i l d ing has dropped due to some damage i n the bu i l d ing (wh i ch may have occur red dur ing the first 10 seconds o f the Whi t t ie r earthquake). S ince the low-st i f fness m o d e l ' s ( M o d e l A ) results matched the smal l d isplacement part at the end o f the Nor th r idge records, it may be conc luded that the drop i n frequency is due to permanent decrease i n the sti f fness o f the system (i.e. some damage i n the bui ld ing) and not because o f nonl inear elast ic behav io r due to h igher d isplacements. T h e nonl inear analysis d id not show any y ie ld i ng i n the m a i n structural elements. Therefore, damage may have occurred i n one o f the f o l l o w i n g areas: 1. B o n d between concrete and steel in composi te act ion o f the beams and interact ion o f concrete slabs and steel co lumns. 2. Inter ior beam to co l umn connect ions w h i c h prov ide part ial f i x i ty i n spite o f be ing considered p i n connect ions. 3. Connec t ions o f r ig id f rame elements. Fur ther invest igat ion is required to con f i rm the existence o f any damage o f above ment ioned types. 309 9.3 Effect of the Higher Modes on the Response The fundamental per iod o f 1.4 seconds is s igni f icant ly h igher than what is usua l ly expected for a s ix story bu i ld ing . Th i s is part ly due to relat ively h igh f loor to f loo r height (17ft h igh 1st story and 13ft h i gh upper stories). The per iod o f 1.4 seconds places the first mode o f the bu i l d i ng i n the l o w ampl i tude part o f the response spectrum (See F igu re 8.4.4). A s a result , the contr ibut ion o f the 2nd and 3rd modes become signif icant. The out o f phase response o f the m idd le f loors (see figures 8.4.7 and 8.4.8), and the smal l decrease i n the leve l o f the forces i n the upper f loors o f the bu i l d ing (Tables 8.3.2, 8.3.4, 8.4.2, & 8.4.4), also con f i rm the s ign i f i cance o f the higher mode effects. In this respect, i t can be conc luded that the bu i l d ing behaved i n a w a y that is usu -a l l y expected f r o m tal ler bu i ld ings. 9.4 Response Spectrum Analysis versus Time-history Analysis The analys is us ing a response spectrum calculated by the program N o n l i n fo r the recorded ground mo t ion over-est imated the base shear and under-est imated the base moment by approx-imate ly 2 0 % (Tab le 8.5.5 and 8.5.6). 9.5 Spectral Analysis with Code Design Response Spectra Spectral A n a l y s i s w i t h code design response spectra showed a more rapid drop i n the forces at the upper stories and a higher base overturning moment to base shear rat io (See Tab le 8.4.6). Th i s i s due to a h igher contr ibut ion o f the first mode in the response w h i c h results f r om the re l -at ive ly h igh ampl i tude o f the code response spectra i n the per iod range o f approx imate ly 0.7 sec-onds and h igher (See F igu re 8.4.4). 310 It may be conc luded that conduct ing a spectral dynamic analys is us ing code design response spectra and sca l ing the results to a designated base shear (wh ich is c o m m o n l y done in pract ice), may result i n unreal is t ic distr ibut ion o f the lateral loads throughout the structure and i n par t icu-lar, i t may under-est imate the forces at the upper levels o f such structures. 9.6 N o n - L i n e a r T i m e - H i s t o r y A n a l y s i s S ince the structural mode l d id not reach the nonl inear range when the recorded ground mot ions were app l ied, it was not possib le to evaluate the accuracy o f this type o f analys is (wh i ch is very sensit ive to the parameters used for def in ing the hysteretic behav ior o f the structural mater ial) . N o n - l i n e a r t ime-history analysis fo r ground mot ions o f two and three t imes those recorded in Nor th r idge earthquake resulted in 3 % and 1 3 % smal ler m a x i m u m r o o f d isp lacements than the l inear elast ic t ime-history analyses results. The close results o f the l inear and nonl inear analyses agree w i t h the equal d isplacement assumption w h i c h is usual ly used for est imat ing the duct i l i ty demand. H o w e v e r , the analys is shows a higher element duct i l i ty demand than the g loba l duc t i l -i ty o f the structure. A s an example, compar ing the results o f the analys is o f mode l B U - A - 3 N to those o f mode l B U - A - N (see Tables 8.6.2 and 8.6.4) showed that an increase i n r o o f m a x i m u m disp lacement by a factor o f 2.35 co inc ided w i th an increase i n the m a x i m u m duct i l i ty o f the c o l -umns by a factor o f 4.7 and m a x i m u m beam duct i l i ty by a factor o f 7.0. 9.7 E f f e c t o f D a m p i n g V a l u e Repea t ing the nonl inear analysis o f model B U - A - 3 N w i th a damping va lue o f 1.5% instead o f 3 . 5 % resulted i n a smal l increase in the roo f m a x i m u m displacement. H o w e v e r , the increase in 311 the ampl i tude o f the response (due to the lower damping value) became more s igni f icant after T=20sec, where the response was main ly i n the l inear elastic range. See F igu res 8.6.1 and 8.6.2. It can be conc luded that the results o f nonl inear analysis are less sensit ive to the damp ing va lue than those o f l inear elast ic analysis. 9.8 N o n - L i n e a r S ta t i c (Push -ove r ) A n a l y s i s N o n - L i n e a r Stat ic (Push-over) Ana l ys i s w i th code def ined lateral d ist r ibut ion o f equivalent static loads under-est imated the element duct i l i ty demands (see Tab le 8.6.4). T h i s is ma in l y due to the fact that the effect o f the h igher modes, (wh ich results i n h igher levels o f inter-story dri f ts fo r the same leve ls o f r o o f m a x i m u m displacement), is not considered i n this type o f analys is . 312 Chapter 10 CONCLUSIONS 10.1 Behaviour of the Buildings T h e object ive o f the f irst part o f this research was to extract as m u c h in fo rmat ion as poss ib le f r om the recorded mot ions o f the selected low-r ise steel f rame bu i ld ings. T h e f o l l o w i n g conc lu -sions can be made f r o m the results o f this part: 1. T h e measured fundamental periods i n most cases were 50 to 1 0 0 % higher than those est imated by empi r i ca l formulae. In the case o f the San Bernard ino 5-story hospi ta l , however , the measured per iod was s ign i f icant ly less than the value suggested by the height dependent per iod fo rmu la for steel f rame bu i ld ings. Since the response o f the low- r ise bu i ld ings is very sensi t ive to their fundamenta l per iod , us ing empir ica l per iod formulae in se ismic design o f these bu i ld ings may result i n unreal is t ic estimates o f the seismic behavior o f these bu i ld ings. 2. S ign i f i cant h igher mode effects were detected i n three o f the bu i ld ings (wh i ch had fundamen-tal per iods greater than 1.0 second). 3. The analys is o f the recorded data indicated that both ground mot ion and structural response have a 3-d imens iona l nature inc lud ing translational and rotational components. 4. De ta i l ed structural analysis o f a computer model o f the Bu rbank 6-story B u i l d i n g (cal ibrated to match the recorded data), d id not show y ie ld ing i n the major lateral load resist ing elements. The bu i l d ing was subjected to a peak ground accelerat ion o f 0.3g. 5. The records f r om two earthquakes (the 1987 Whi t t ie r and the 1994 Nor th r idge earthquakes) were studied fo r the Bu rbank bu i ld ing. A drop in the natural f requency o f this bu i l d ing was ob-served dur ing the Nor thr idge earthquake. Further invest igat ion is required to ver i fy any damage to the secondary elements or connect ions. 313 6. T h e Base- Iso la ted bu i ld ings considered in this study showed a s igni f icant increase i n the nat-ura l per iod o f the structure due to the relat ively soft isolators, resul t ing i n a smal ler se ismic load-ing . The isolators absorbed the major port ion o f the se ismic induced displacements. 7. T h e in format ion extracted f rom the strong mot ion data obtained f rom the selected low- r i se steel f rame bu i ld ings in earthquakes was presented in this thesis as a series o f d iagrams and ta-b les i n order to ga in a better understanding and elucidate s igni f icant features o f the se ismic be-hav io r o f th is type o f bu i ld ings. 10.2 A n a l y s i s T e c h n i q u e s In the second part o f this research the object ive was to investigate the accuracy and e f f i c iency o f var ious analys is methods. The f o l l ow ing conclusions were made by compar ing the results ob-tained f r om the var ious methods used for ana lyz ing the computer mode ls o f the B u r b a n k 6-story bu i l d ing and compar ing the results o f the t ime-history analyses w i th the recorded data: 1. T h e t ime-history analysis results showed that a l inear dynamic t ime-history analys is us ing proper va lues for the mass and stiffness o f the structure can accurately predict the behav iour o f the structures in earthquakes (provided their response is w i th in the elastic range). 2 . S ince the structural mode l d id not enter the non- l inear range, it was not poss ib le to invest igate the accuracy o f this type o f analysis, w h i c h is very sensit ive to the parameters used i n de f in ing the hysteret ic behaviour o f the structural mater ial . 3. T h e response spectrum analysis us ing the response spectrum obtained f r om the recorded ground mot ions, resulted in a reasonable approximat ion o f the response o f the bu i l d ing . The re-sults, however , were not as accurate as those o f t ime-history analysis. 4. The response spectrum analyses w i th code recommended design response spectra, under-es-314 t imated the effect o f the higher modes. In v i e w o f this, it is recommended to conduct spectral dynamic analyses w i th at least two different spectral shapes: one w i th h igh ampl i tude in the h igh per iod reg ion , w h i c h g ives higher f irst mode effects, result ing i n conservat ive results fo r the base over turn ing moment and the displacements in the upper f loors ; the second response spectrum w i t h h igher ampl i tude in the l o w per iod region and lower ampl i tude in the h igh per iod region (s imi la r to code recommended spectra for very st i f f soi l ) . Th is results i n a larger "h igher mode ef fects" and g ives a conservat ive distr ibut ion o f the loads in the upper levels o f the structure. 5. N o n l i n e a r t ime history analysis indicated that the leve l o f duct i l i ty demand fo r the ind iv idua l elements can be s igni f icant ly higher than the g lobal duct i l i ty demand for the structure. 6. The nonl inear static (push-over) analysis performed in this research underest imated the ele-ment duct i l i ty demands. Th is was main ly due to not inc lud ing the effect o f the h igher modes in the se ismic response. In c los ing it is recommended to perform a dynamic analysis i n se ismic des ign o f a l l types o f mul t i -s tory structures to: - Obta in a more real ist ic estimate o f the natural periods o f the bu i ld ings, - Capture the 3 - D behav ior and coup l ing between translational and tors ional modes, - Inc lude the effects o f higher modes in the response. N o n l i n e a r static (push-over) analysis is not recommended for evaluat ing the se ismic behav ior o f the mul t i -s tory bu i ld ings, where the effect o f the higher modes and the coup l i ng between the modes cannot be captured by a static analysis. 315 R E F E R E N C E S B e a u c h a m p , K . G . , 1979, " D i g i t a l Me thods for Signal A n a l y s i s " , George A l l e n & U n w i n L t d . 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Shaka l , A . , H u a n g , M . , Darragah, R., C a o , T., Sherburne, R. , M a l h o t r a , P . , Cramer , C , Sydnor , R. , Graz ie r , R. , M a l d o n a d o , G , and Petersen, C , W a m p o l e , J . , 1994, " C S M I P S t rong -Mo t i on Reco rds f r om the Nor thr idge, Ca l i f o rn ia Earthquake o f January 17, 1994," Ca l i f . Dept . o f C o n -servat ion, D i v i s i o n o f M i n e s and Geo logy , O f f i ce o f Strong M o t i o n Studies, Repor t O S M S 94-07, Sacramento, C A , 308 p. Shaka l , A . F . , H u a n g , M . J . and Darragah, R. , " S o m e Impl icat ions o f St rong M o t i o n records f r om the 1994 Nor th r idge Ear thquake" , Proceedings S M I P 9 4 (Strong M o t i o n Instrumentat ion plan) Seminar on Se ismolog ica l and Eng ineer ing Impl icat ions o f Recen t Strong M o t i o n Da ta , Sacramento Ca l i f o rn i a , M a y 26, 1994. Shaka l , A . F . , H u a n g , M . J . , C a o , T. Q . , Sherburne, R. 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W . , B l a z q u e z , R. , " C S M T P Strong-mot ion Records f rom the Whi t t ier , Ca l i f o rn i a Ear thquake O f 1 October 1987" , Ca l i f o rn i a Depar tment o f Conservat ion, D i v i s i o n o f M i n e s and G e o l o g y , O f f i c e o f Strong M o t i o n Studies, Repor t O S M S 87-05 318 Shen, J . , As taneh , A . , " S e i s m i c Response Eva lua t ion o f an Instrumented S ix -s to ry Steel B u i l d -i n g " , Ear thquake Eng ineer ing Research Center, Un ivers i t y o f Ca l i f o rn ia at Be rke ley , Repor t N o . U C B / E E R C - 9 0 7 2 0 , December 1990 U n i f o r m B u i l d i n g C o d e ( U B C ) , 1997, International Conf . o f B u i l d i n g O f f i c i a l s , Whi t t ie r , C A . 319 APPENDIX A Separated floor accelerations of selected buildings. 320 3x JL5 2D 25_ _3Q 35_ JO 2x _25_ _35_ JO F i g u r e A l A b s o l u t e accelerat ions o f the upper f loors o f the Bu rbank 6-story o f f ice b ldg . i n the E - W ( X ) d i rect ion, obtained f rom the 1987 Whi t t ie r E Q records. 321 0.3 -0.2 -0.3 J F i g u r e A 2 Abso lu te accelerat ions o f the upper f loors o f the B u r b a n k 6-story o f f i ce b ldg . i n the N - S ( Y ) d i rect ion, obtained f rom the 1987 Whi t t ie r E Q records. F i g u r e A 3 Abso lu te accelerat ions o f the upper f loors o f the Red lands 7-story commerc ia l b ldg . i n the E - W ( X ) d i rect ion, obtained f rom the 1992 Landers E Q records. 323 F i g u r e A 4 Abso lu te accelerat ions o f the upper f loors o f the Red lands 7-story commerc ia l b ldg . i n the N - S ( Y ) d i rect ion, obtained f rom the 1992 Landers E Q records. 324 F i g u r e A 5 Abso lu te accelerat ions o f the upper f loors of the San Berna rd ino 3-story office b ldg . i n the E - W ( X ) d i rect ion, obtained from the 1992 Landers E Q records. 325 F i g u r e A 6 Abso lu te accelerat ions o f the upper f loors o f the San Bernard ino 3-story of f ice b ldg . i n the N - S ( Y ) d i rect ion, obtained f rom the 1992 Landers E Q records. 326 APPENDIX B Samples of ME'scope outputs. 327 M r r l <2X/1X> 0.00 10.0 Hertz M#4 <2y/ly> 2.80 Imag -1.64 -6.10 Hertz M#7 <2r/lr> f l i t 1 I 0.00 10.0 Hertz 1.80 F I G 5 - 2 A . B L K M#2 <3x/lx> Imag •1.47 -4.75 4.20 ^ / A J Imag 0.00 10.0 Hertz M#5 <3y/ly> 4.47-Imag 0.00 10.0 Hertz M#8 <3r/lr> -8.28 ait 1 III 11 jk Li Wft il irfj H*7 U /A^r*^1^ ^ 0.00 10.0 Hertz M#3 <7x/lx> 0.00 10.0 Hertz M#6 <7y/ly> Hertz M#9 <7r/lr> Imag -1.47 -115 J La 0.00 10.0 Hertz Figure B l Frequency Response Funct ions o f the instrumented f loors o f the B u r b a n k 6-Story B l d g . , obtained f r om the 1987 Whi t t ie r E Q records. (Plots o f the Imaginary part o f the comp lex values) 328 M#l <2x/lx> F I G 5 - 2 A . B L K M#2 <3x/lx> M#3 <7x/lx> 5.67 0.00 10.0 Hertz M#4 <2y/ly> Real 1.65 -2.36 8.98 Reall 2.09 0.00 10.0 Hertz M#5 <3y/ly> 0.00 10.0 Hertz 5.29 Real 1.46--2.36 0.00 10.0 Hertz M#7 <2r/lr> -4.79 Ii l.iilML_iiiJliiAl 0.00 10.0 Hertz 8.00 Reall 2.39 -3.22 0.00 10.0 Hertz M#8 <3r/lr> Real 3.25--14.2-4 18.2 0.00 10.0 Hertz M#9 <7r/lr> 0.00 10.0 Hertz Reall 4.68 -8.8} 0.00 10.0 Hertz F i g u r e B2 F requency Response Funct ions o f the instrumented f loors o f the B u r b a n k 6-Story B l d g . , obta ined f rom the 1987 Whi t t ie r E Q records. (Plot o f the R e a l part o f the comp lex values) 329 M#l <2x/lx> 6.21 0.00 10.0 Hertz M M <2y/ly> 0.00 10.0 Hertz M#7 <2r/lr> 0.00 10.0 Hertz F I G 5 - 2 A . B L K M#2 <3x/lx> 0.00 10.0 Hertz M#5 <3y/ly> 0.00 10.0 Hertz M#8 <3r/lr> 12.9 M#3 <7x/lx> t 1 8 8-0.00 10.0 Hertz M#6 <7y/ly> 0.00 10.0 Hertz M#9 <7r/lr> 0.00 10.0 Hertz 0.00 10.0 Hertz F i g u r e B3 F requency Response Funct ions o f the instrumented f loors o f the B u r b a n k 6-Story B l d g . , obta ined f rom the 1987 Whi t t ie r E Q records. (Plot o f the M a g n i t u d e o f the comp lex v a l -ues) 330 F I G 5 - 2 A . B L K Hertz Hertz Hertz F i g u r e B4 F requency Response Funct ions o f the instrumented f loors o f the B u r b a n k 6-Story B l d g . , obta ined f r om the 1987 Whi t t ie r E Q records. (Plots o f the Phase angle) 331 B U R B A - N . S T R Top (+Z) BU-W5X.BLK - (781mHertz) [60°] (x,y,z) of BU-W5X.STR 3DView BU-W5X.BLK - (781mHertz) [60°] (x,y,z) of BU-W5X.STR z Y r x z Front (+X) BU-W5X.BLK - (781mHertz) [60°] (x,y,z) of BU-W5X.STR Right (+Y) BU-W5X.BLK - (781mHertz) [60°] (x,y,z) of BU-W5X.STR Z X Y z J X y F i g u r e B 5 1st translat ional mode shape o f the Bu rbank 6-story b ldg . , obta ined f r om the 1987 Whi t t i e r E Q records. 332 Figure B6 2nd translat ional mode shape o f the Bu rbank 6-story b ldg . , obtained f r o m the 1987 Wh i t t i e r E Q records. 333 B U R B A - N . S T R Top (+Z) BU-W5XBLK- (4.1 Hertz) [84°] (x,y,z) of BU-W5X.STR |3DView BU-W5X.BLK- (4.1 Hertz) [84°] (x,y,z) of BU-W5X.STR 1 Y r x z Y<U Front (+X) BU-W5X.BLK - (4.1 Hertz) [84°] (x,y,z) of BU-W5X.STR Right (+Y) BU-W5X.BLK - (4.1 Hertz) [84°] (x,y,z) of BU-W5X.STR Z X y Figure B7 3rd translational mode shape of the Burbank 6-story bldg., obtained from the 1987 Whittier E Q records. 334 BURBA-N.STR Top (+Z) BU-W5R.BLK - (1.0 Hertz) [288°] (x,y,z) of BU-W5R.STR ^DView BU-W5R.BLK - (1.0 Hertz) [288°] (x,y,z) of BU-W5R.STR z Y r x Front (+X) BU-W5R.BLK - (1.0 Hertz) [288") (x,y,z) of BU-W5R.STR Right (+Y) BU-W5R.BLK - (1.0 Hertz) [288°] (x,y,z) of BU-W5R.STR L Z X y Figure B8 1st tors ional mode shape o f the Bu rbank 6-story b ldg . , obtained f r om the 1987 W h i t -t ier E Q records. 335 F i g u r e B9 2nd tors ional mode shape o f the Bu rbank 6-story b ldg . , obtained f r o m the 1987 W h i t -t ier E Q records. 336 APPENDIX C Selected parts of the CANNY-E input file for Model A 337 N o n l i n i e r dynamic a n a l y s i s of Burbank Federal.Savings Bldg. * Ground motion recorded i n Northridge EQ * Including V e r t i c a l & r o t a t i o n a l ground motion * P-D e f f e c t s included * No S o i l Structure I n t e r a c t i o n * 3.50% damping // a n a l y s i s assumptions and output options t i t l e : Burbank,JI, Nonlinear, 3.50% damping force u n i t = N length u n i t = m time u n i t = sec P-Delta f l o o r r o t a t i o n g r a v i t y a c c e l e r a t i o n i s 9.807 output of o v e r a l l response at f l o o r l e v e l s output of nodal displacement, v e l o c i t y and ac c e l e r a t i o n output a l l of beams, column r e s u l t s output of extreme responses // c o n t r o l data of s t a t i c a n a l y s i s loading d i r e c t i o n i n 0 degree (from X-axis) master DOFs f o r a n a l y s i s c o n t r o l : X - t r a n s l a t i o n at 7F displacement l i m i t 5.0 bina r y format output of a n a l y s i s r e s u l t s at every 1-step d e s t i n a t i o n base shear f a c t o r 1.0 by increment 0.01 / • d e s t i n a t i o n displacement 0.3 by increment 0.002 / • d e s t i n a t i o n displacement 0.4 by increment 0.005 // // c o n t r o l data of dynamic response master DOFs f o r a n a l y s i s c o n t r o l : X - t r a n s l a t i o n at 7F i n t e g r a t i o n 1-step f o r one a c c e l e r a t i o n data i n t e g r a t i o n time i n t e r v a l 0.02 s t a r t time 0.0, end time 60.0 check peak displacement 0.02 response l i m i t 5.0 master DOFs f o r a n a l y s i s c o n t r o l : 7F X - t r a n s l a t i o n binary format output of response r e s u l t s at every 1-step Newmark method using Beta-value 0.25 damping constant 0.0350 to f i r s t mode damping constant 0.0350 to second mode /•damping i n time-varying frequency sc a l e f a c t o r 1 to X-EQ f i l e = c:\canny\burbank\burb-n.ew scal e f a c t o r 1 to Y-EQ f i l e = c:\canny\burbank\burb-n.ns sca l e f a c t o r 1 to R-EQ f i l e = c:\canny\burbank\burb-n.rt sc a l e f a c t o r 1 to Z-EQ f i l e = c:\canny\burbank\burb-n.up / / -XI , YI, IF X3 , YI, IF X5 , YI, IF X7 , YI, IF X9 , YI, IF X l l , YI, IF X13, YI, IF XI , Y3, IF X13, Y3, IF X4 , Y4, IF X7 , Y4, IF X10, Y4, IF XI , Y5, IF X13, Y5, IF X4 , Y6, IF X7 , Y6, IF X10, Y6, IF XI , Y7, IF X13, Y7, IF node l o c a t i o n s 338 X4 , Y8, IF X7 , Y8, IF X10, Y6, IF XI , Y9, IF X13, Y9, IF X4 , YIO, IF X7 , YIO, IF XIO, YIO, IF XI , Y l l , IF X13, Y l l , IF XI , Y13, IF X3 , Y13, IF X5 , Y13, IF X7 , Y13, IF X9 , Y13, IF X l l , Y13, IF X13, Y13, IF X1-X13, Y1-Y13, 2F-7F // // node degrees of freedom general DOFs: a l l components node XI , Y l , IF eliminate a l l components node X3 , Y l , IF eliminate a l l components node X5 , Y l , IF eliminate a l l components node X7 , Y l , IF eliminate a l l components node X9 , Y l , IF eliminate a l l components node X l l , Y l , IF eliminate a l l components node X13, Y l , IF eliminate a l l components node XI , Y3, IF eliminate a l l components node X13, Y3, IF eliminate a l l components node X4 , Y4, IF eliminate a l l components node X7 , Y4, IF eliminate a l l components node XIO, Y4, IF eliminate a l l components node XI , Y5, IF eliminate a l l components node X13, Y5, IF eliminate a l l components node X4 , Y6, IF eliminate a l l components node X7 , Y6, IF eliminate a l l components node XIO, Y6, IF eliminate a l l components node XI , Y7, IF eliminate a l l components node X13, Y7, IF eliminate a l l components node X4 , Y8, IF eliminate a l l components node X7 , Y8, IF eliminate a l l components node XIO, Y8, IF eliminate a l l components node XI , Y9, IF eliminate a l l components node X13, Y9, IF eliminate a l l components node X4 , Y10, IF eliminate a l l components node X7 , YIO, IF eliminate a l l components node XIO, Y10, IF eliminate a l l components node XI , Y l l , IF eliminate a l l components node X13, Y l l , IF eliminate a l l components node XI , Y13, IF eliminate a l l components node X3 , Y13, IF eliminate a l l components node X5 , Y13, IF eliminate a l l components node X7 , Y13, IF eliminate a l l components node X9 , Y13, IF eliminate a l l components node X l l , Y13, IF eliminate a l l components node X13, Y13, IF eliminate a l l components // // node weight node XI , Y l 2F w = 0 node X2 , Y l , 2F w = 52150 node X3 , Y l , 2F w = 26100 node X4 , Y l 2F w = 192400 node X5 , Y l r 2F w = 26100 node X6 , Y l r 2F w = 52150 node X7 , Y l i 2F w = 192400 node X8 , Y l t 2F w = 52150 node X9 , Y l i 2F w = 26100 node XIO, Y l r 2F w = 192400 node X l l , Y l f 2F w = 26100 node X12, Y l r 2F w = 52150 339 node X13, YI, 2F w = 0 node XI , Y13, 2F w = 0 node X2 , Y13, 2F w = 52150 node X3 , Y13, 2F w = 26100 node X4 , Y13, 2F w = 192400 node X5 , Y13, 2F w = 26100 node X6 , Y13, 2F w = 52150 node X7 , Y13, 2F w = 192400 node X8 , Y13, 2F w = 52150 node X9 , Y13, 2F w = 26100 node X10, Y13, 2F w = 192400 node X l l , Y13, 2F w = 26100 node X12, Y13, 2F w = 52150 node X13, Y13, 2F w = 0 node XI , Y2 , 2F w = 89600 node XI , Y3 , 2F w = 44800 node XI , Y4 , 2F w = 89600 node XI , Y5 , 2F w = 44800 node XI , Y6 , 2F w = 89600 node XI , Y7 , 2F w = 44800 node XI , Y8 , 2F w = 89600 node XI , Y9 , 2F w = 44800 node XI , Y10, 2F w = 89600 node XI , Y l l , 2F w = 44800 node XI , Y12, 2F w = 89600 node X13, Y2 , 2F w = 89600 node X13, Y3 , 2F w = 44800 node X13, Y4 , 2F w = 89600 node X13, Y5 , 2F w = 44800 node X13, Y6 , 2F w = 89600 node X13, Y7 , 2F w = 44800 node X13, Y8 , 2F w = 89600 node X13, Y9 , 2F w = 44800 node X13, Y10, 2F w = 89600 node X13, Y l l , 2F w = 44800 node X13, Y12, 2F w = 89600 node XI , YI, 3F w = 0 node X2 , YI, 3F w = 31300 node X3 , YI, 3F w = 15600 node X4 , YI, 3F w = 12480( node X5 , YI, 3F w = 15600 node X13, Y10, 7F node X13, Y l l , 7F node X13, Y12, 7F w = 89600 w = 44800 w = 89600 // 7 F ( r i g i d ) 6 F ( r i g i d ) 5 F ( r i g i d ) 4 F ( r i g i d ) 3 F ( r i g i d ) 2 F ( r i g l d ) I F ( f i x e d ) // // frame l o c a t i o n s XI: 0 X2: 3.048 X3: 6.096 X4: 9.144 X5: 12.192 X6: 15.24 X7: 18.288 X8: 21.336 X9: 24.384 X10: 27.432 X l l : 30.48 f l o o r l e v e l Z=24.994 G(18.660,18.300), W=6577000 Rj=1900000000 Z=21.031 G(18.288,18.288), W=4817000 Rj=1150000000 Z=17.069 G(18.288,18.288), W=4817000 Rj=1150000000 Z=13.106 G(18.288,18.288), W=4839000 Rj=1200000000 Z=9.144 G(18.288,18.288), W=4965000 Rj=1250000000 Z=5.182 G(18.288,18.288), W=6085000 Rj=1800000000 Z=0 340 X12 33.528 X13 36.576 YI 0 Y2 3.048 Y3 6.096 Y4 9.144 Y5 12.192 Y6 15.24 Y7 18.288 Y8 21.336 Y9 24.384 Y10 27.432 Y l l 30.48 Y12 33.528 Y13 36.576 // // element data : beam /* 2nd f l o o r perimeter beams frame YI, X1-X2, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame YI, X2-X3, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame YI, X3-X4, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame YI, X4-X5, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame YI, X5-X6, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame YI, X6-X7, 2F LU100 RU100 SU200 r 0 00 0 19 /* W30X116 frame YI, X7-X8, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame YI, X8-X9, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame YI, X9-X10, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame YI, X10-X11, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame YI, X11-X12, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame YI, X12-X13, 2F LU100 SU200 r 0 00 0 00 /* w30xll6 frame Y13, X1-X2, 2F RU100 SU200 r 0 00 0 00 /* w30xll6 frame Y13, X2-X3, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame Y13, X3-X4, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame Y13, X4-X5, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame Y13, X5-X6, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame Y13, X6-X7, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame Y13, X7-X8, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame Y13, X8-X9, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame Y13, X9-X10, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame Y13, X10-X11, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame Y13, X11-X12, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame Y13, X12-X13, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame XI, Y1-Y2, 2F RU100 SU200 r 0 00 0 00 /* w30xll6 frame XI, Y2-Y3, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame XI, Y3-Y4, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame XI, Y4-Y5, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame XI, Y5-Y6, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame XI, Y6-Y7, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame XI, Y7-Y8, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame XI, Y8-Y9, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame XI, Y9-Y10, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame XI, Y10-Y11, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame XI, Y11-Y12, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame XI, Y12-Y13, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame X13, Y1-Y2, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame X13, Y2-Y3, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame X13, Y3-Y4, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame X13, Y4-Y5, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame X13, Y5-Y6, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame X13, Y6-Y7, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame X13, Y7-Y8, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame X13, Y8-Y9, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame X13, Y9-Y10, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame X13, Y10-Y11, 2F LU100 RU100 SU200 r 0 00 0 19 /* w30xll6 frame X13, Y11-Y12, 2F LU100 RU100 SU200 r 0 19 0 00 /* w30xll6 frame X13, Y12-Y13, 2F LU100 SU200 r 0 00 0 00 /* w30xll6 /* 2nd f l o o r i n t e r i o r beams 341 frame Y2, X1-X2, 2F LU101 RU101 SU201 /* wl6x26 frame Y2, X2-X3, 2F LU101 RU101 SU201 /* Wl6x26 frame Y2, X3-X4, 2F LU101 RU101 SU201 1* Wl6x2 6 frame Y2, X4-X5, 2F RU102 SU202 1* wl6x31 frame Y2, X5-X6, 2F LU102 RU102 SU202 1* Wl6x31 frame Y2, X6-X7, 2F LU102 RU102 SU202 I* wl6x31 frame Y2, X7-X8, 2F RU101 SU201 /* Wl6x26 frame X12, Y4-Y5, 7F LU999 RU999 SU201 /* 11 11 frame X12, Y5-Y6, 7F LU999 RU999 SU201 1* 11 11 frame X12, Y6-Y7, 7F LU999 RU999 SU201 /* 11 11 frame X12, Y7-Y8, 7F LU999 RU999 SU201 1* 11 11 frame X12, Y8-Y9, 7F LU999 RU999 SU201 1* 11 11 frame X12, Y9-Y10, 7F LU999 RU999 SU201 1* 11 11 frame X12, Y10-Y11, 7F LU999 RU999 SU201 /* 11 11 frame X12, Y11-Y12, 7F LU999 RU999 SU201 /* 11 11 frame X12, Y12-Y13, 7F LU999 RU999 SU201 I* 11 11 II element data : column /* /* 1st s t o r y columns XI Y l 1 -2F BX301 BY301 TX301 TY301 SX4 X3 Y l 1 -2F BX301 BY301 TX301 TY301 SX4 X5 Y l 1 -2F BX301 BY301 TX301 TY301 SX4 X7 Yl 1 -2F BX301 BY301 TX301 TY301 SX4 X9 Yl 1 -2F BX301 BY301 TX301 TY301 SX4 X l l Y l 1 -2F BX301 BY301 TX301 TY301 SX4 XI3 Yl 1 -2F BX302 BY302 TX302 TY302 SX4 XI Y3 1 -2F BX302 BY302 TX302 TY302 SX4 X13 Y3 1 -2F BX302 BY302 TX302 TY302 SX4 X4 Y4 1 -2F BX304 BY304 TX304 TY304 SX4 X7 Y4 1 -2F BX303 BY303 TX303 TY303 SX4 XIO Y4 1 -2F BX304 BY304 TX304 TY304 SX4 XI Y5 1 -2F BX302 BY302 TX302 TY302 SX4 X13 Y5 1 -2F BX302 BY302 TX302 TY302 SX4 X4 Y6 1 -2F BX303 BY303 TX303 TY303 SX4 X7 Y6 1 -2F BX305 BY305 TX305 TY305 SX4 XIO Y6 1 -2F BX306 BY306 TX306 TY306 SX4 XI Y7 1 -2F BX302 BY302 TX302 TY302 SX4 X13 Y7 1 -2F BX302 BY302 TX302 TY302 SX4 X4 Y8 1 -2F BX303 BY303 TX303 TY303 SX4 X7 Y8 1 -2F BX307 BY307 TX307 TY307 SX4 XIO Y8 1 -2F BX306 BY306 TX306 TY306 SX4 XI Y9 1 -2F BX302 BY302 TX302 TY302 SX4 X13 Y9 1 -2F BX302 BY302 TX302 TY302 SX4 X4 YIO 1 -2F BX304 BY304 TX304 TY304 SX4 X7 YIO 1 -2F BX306 BY306 TX306 TY306 SX4 XIO YIO 1 -2F BX307 BY307 TX307 TY307 SX4 XI Y l l 1 -2F BX302 BY302 TX302 TY302 SX4 X13 Y l l 1 -2F BX302 BY302 TX302 TY302 SX4 XI Y13 1 -2F BX302 BY302 TX302 TY302 SX4 X3 Y13 1 -2F BX301 BY301 TX301 TY301 SX4 X5 Y13 1 -2F BX301 BY301 TX301 TY301 SX4 X7 Y13 1 -2F BX301 BY301 TX301 TY301 SX4 X9 Y13 1 -2F BX301 BY301 TX301 TY301 SX4 X l l Y13 1 -2F BX301 BY301 TX301 TY301 SX4 X13 Y13 1 -2F BX301 BY301 TX301 TY301 SX4 /* 2nd s t o r y columns /* XI Y l 2-3F BX301 BY301 TX301 TY301 SX4 X3 Y l 2-3F BX301 BY301 TX301 TY301 SX4 X5 Y l 2-3F BX301 BY301 TX301 TY301 SX4 X7 Y l 2-3F BX301 BY301 TX301 TY301 SX4 X9 Yl 2-3F BX301 BY301 TX301 TY301 SX4 X l l Y l 2-3F BX301 BY301 TX301 TY301 SX4 01 SY401 AU501 r (0. 00 0. 38 / * wl4xl8 4 H 01 SY401 AU501 r (0. 00 0. 38 / * wl4xl8 4 H 01 SY401 AU501 r (0. 00 0. 38 / * wl4xl8 4 H 01 SY401 AU501 r (0. 00 0. 38 / * W l 4 x l 8 4 H 01 SY401 AU501 r(0. 00 0. 38 / * wl4xl8 4 H 01 SY401 AU501 r (0. 00 0. 38 / * W l 4 x l 8 4 H 02 SY402 AU502 r (0. 00 0. 38 / * wl4xl8 4 I 02 SY402 AU502 r (0. 00 0. 38 / * wl4xl8 4 I 02 SY402 AU502 r (0. 00 0 38 / * wl4xl8 4 I 04 SY404 AU504 /* wl4x87 I 03 SY403 AU503 / * Wl4x87 H 04 SY404 AU504 / * wl4x87 I 02 SY402 AU502 r (0 00 0 38 / * wl4xl8 4 I 02 SY402 AU502 r (0 00 0 38 / * wl4xl8 4 I 03 SY403 AU503 / * Wl4x87 H 05 SY405 AU505 /* w l 4 x l l l I longer 06 SY406 AU506 / * wl4x95 H 02 SY402 AU502 r (0 00 0 38 / * wl4xl8 4 I 02 SY402 AU502 r (0 00 0 38 / * wl4xl8 4 I 03 SY403 AU503 / * Wl4x87 H 07 SY407 AU507 / * wl4x95 I 06 SY406 AU506 / * Wl4x95 H 02 SY402 AU502 r (0 00 0 38 / * Wl4xl8 4 I 02 SY402 AU502 r (0 00 0 38 / * wl4xl8 4 I 04 SY404 AU504 / * Wl4x87 I 06 SY406 AU506 / * wl4x95 H 07 SY407 AU507 / * wl4x95 I 02 SY402 AU502 r (0 00 0 38 /•* wl4xl8 4 I 02 SY402 AU502 r (0 00 0 38 / * Wl4xl8 4 I 02 SY402 AU502 r(0 00 0 38 / * wl4xl8 4 I 01 SY401 AU501 r(0 00 0 38 / * wl4xl8 4 H 01 SY4 01 AU501 r (0 00 0 38 / * wl4xl8 4 H 01 SY401 AU501 r (0 00 0 38 / * wl4xl8 4 H 01 SY401 AU501 r (0 00 0 38 / * wl4xl8 4 H 01 SY401 AU501 r(0 00 0 38 /* W l 4 x l 8 4 H 01 SY401 AU501 r (0 00 0 38 / •• W l 4 x l 8 4 H 01 SY401 AU501 r (0 38 0 34 / * wl4xl6 4 H 01 SY401 AU501 r (0 38 0 34 / * wl4xl6 4 H 01 SY401 AU501 r(0 38 0 34 / * wl4xlS 4 H 01 SY401 AU501 r (0 38 0 34 / * W l 4 x l 8 4 H 01 SY401 AU501 r (0 38 0 34 / * wi4xie 4 H 01 SY401 AU501 r(0 38 0 34 / * wi4xie 4 H 342 X13 Y l 2-3F BX302 BY302 TX302 TY302 SX402 SY402 AU502 r(0.38 0.34 /* wl4xl84 I // s t i f f n e s s and h y s t e r e s i s parameters /* /* Beams /* U100 CA3 2.Oe+ll 2.0e+ll 2.Oe+ll 2.Oe+ll 2. Oe+ll 2.Oe+ll w.30xll6 U101 CA3 wl6x26 U102 CA3 wl6x31 U103 CA3 w24x84 U104 CA3 wl8x55 U105 CA3 Wl6x36 U106 CA3 2.Oe+ll w27xl02 U107 CA3 2.Oe+ll w27x84 U108 CA3 2.Oe+ll w24x68 U109 CA3 2.Oe+ll wl6x 4 5 U110 CA3 2.Oe+ll w24x94 U l l l CA3 2.Oe+ll wl8x64 U112 CA3 Wl6x26 U113 CA3 Wl6x31 U114 CA3 wl6x36 U115 CA3 Wl6x45 U116 CA3 wl6x4 0 U117 CA3 wl8x85 U118 CA3 wl6x4 0 U119 CA3 w24x76 U999 ELI /* Beams /* Bending s e c t i o n properties 2060e-6 C(1614.6e3,1614. 127e-6 C(0189.8e3,0189. 2.Oe+ll 2.Oe+ll 2.Oe+ll 2.Oe+ll 2.Oe+ll 2.Oe+ll 2.Oe+ll 2.Oe+ll 156e-6 C(0230.1e3,0230. 985e-6 C(0954.2e3,0954. 370e-6 C(0475.8e3,0475. 186e-6 C(0273.0e3,0273. 1510e-6 C(1300.0e3,1300. 1190e-6 C(1042.6e3,1042. 764e-6 C(0754.0e3,0754. 246e-6 C(0353.6e3,0353. 1120e-6 C(1079.0e3,1079. 437e-6 C(0562.4e3,0562. 127e-6 C(0189.8e3,0189. 156e-6 C(0230.1e3,0230. 186e-6 C(0273.0e3, 0273. 246e-6 C(0353.6e3,0353. 216e-6 C(0311.0e3,0311. 600e-6 C(0758.Oe3,0758 216e-6 C(0311.0e3,0311 874e-6 C(0856.0e3,0856 6e3) 8e3) le3) 2e3) 8e3) . 0e3) . 0e3) . 6e3) 0e3) . 6e3) . 0e3) 4e3) . 8e3) .le3) . 0e3) . 6e3) 0e3) . 0e3) . 0e3) .Oe3) Y(1615e3,1615e3) A ( l , l ) B(0. 02, 0. 02) P(0. 3 0. 75) /* Y(0190e3,0190e3) A ( l , l ) B(0. 02, 0 02) P(0. 3 0. 75) /* Y(0231e3,0231e3) A ( l , l ) B(0. 02, 0 02) P(0 3 0. 75) /* Y(0955e3,0955e3) A ( l , l ) B(0. 02, 0 02) P(0 3 0 75) /* Y(0476e3,0476e3) A ( l , l ) B(0. 02, 0 02) P ( 0 3 0 75) /* Y(0274e3,0274e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* Y(1301e3,1301e3) A ( l , l ) B(0 02, 0 02 ) P(0 3 0 75) /* Y(104 3e3,1043e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* Y(0755e3,0755e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* Y(0354e3,0354e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* Y(1080e3,1080e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* Y(0563e3,0563e3) A{1,1) B(0 02, 0 02) P(0 3 0 75) /* Y(0190e3,0190e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* Y(0231e3,0231e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* Y(027 4e3, 0274e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* Y(0354e3,0354e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* Y(0312e3,0312e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* Y(0760e3,0760e3) A ( l , l ) B(0 02, 0 02 ) P(0 3 0 75) /* Y(0312e3,0312e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* Y(0857e3,0857e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* 2.0e+l 1000e-6 Shear s e c t i o n p r o p e r t i e s U200 ELI 0 77e+ll 10820e- 6 /* w30xll6 U201 ELI 0 77e+ll 2474e- 6 /* wl6x26 U202 ELI 0 77e+ll 2821e- 6 /* wl6x31 U203 ELI 0 77e+ll 7313e- 6 /* w24x84 U204 ELI 0 77e+ll 4577e- 6 /* wl8x55 U205 ELI 0 77e+ll 3123e- 6 /* wl6x36 U206 ELI 0 77e+ll 8978e- 6 /* w27xl02 U207 ELI 0 77e+ll 8034e- 6 /* w27x84 U208 ELI 0 77e+ll 6181e- 6 /* w24x68 U209 ELI 0 77e+ll 3649e- 6 /* wl6x45 U210 ELI 0 77e+ll 8052e- 6 /* w24x94 U211 ELI 0 77e+ll 4325e- 6 /* wl8x64 U212 ELI 0 77e+ll 2474e- 6 /* wl6x26 U213 ELI 0 77e+ll 2821e- 6 /* wl6x31 U214 ELI 0 77e+ll 3123e- 6 /* wl6x36 U215 ELI 0 77e+ll 3649e- 6 /* wl6x4 5 U216 ELI 0 77e+ll 2337e- 6 /* wl6x40 343 U217 ELI 0 .77e+l l U218 ELI 0 .77e+l l U219 ELI 0 .77e+l l / * / * Column Bending / * X301 CA3 2 .0e+ l l W14xl84 (H) Y301 CA3 2 .0e+ l l X302 CA3 2 .0e+ l l W14xl84 (I) Y302 CA3 2 .0e+ l l X303 CA3 2 .0e+ l l W14x87 (H) Y303 CA3 2 .0e+ l l X304 CA3 2 .0e+ l l W14x87 (I) Y304 CA3 2 .0e+ l l X305 CA3 2 .0e+ l l W14x l l l (I) Y305 CA3 2 .0e+ l l X306 CA3 2 .0e+ l l W14X95 (H) Y306 CA3 2 .0e+ l l X307 CA3 2 .0e+ l l W14X95 (I) Y307 CA3 2 .0e+ l l X308 CA3 2 .0e+ l l W14xl36 (H) Y308 CA3 2 .0e+ l l X309 CA3 2 .0e+ l l W14X136 (I) Y309 CA3 2 .0e+ l l X310 CA3 2 .0e+ l l W14x61 (H) Y310 CA3 2 .0e+ l l X311 CA3 2 .0e+ l l W14x61 (I) Y311 CA3 2 .0e+ l l X312 CA3 2 .0e+ l l W14x84 (I) Y312 CA3 2. Oe+11 X313 CA3 2.Oe+11 W14x74 (H) Y313 CA3 2.Oe+11 X314 CA3 2.Oe+11 W14x74 (I) Y314 CA3 2.Oe+11 X315 CA3 2.Oe+11 W14x43 (H) Y315 CA3 2.Oe+11 X316 CA3 2.Oe+11 W14x43 (I) Y316 CA3 2.Oe+11 X317 CA3 2.Oe+11 W14x68 (I) Y317 CA3 2.Oe+11 X318 CA3 2.Oe+11 W14x53 (H) Y318 CA3 2.Oe+11 X319 CA3 2.Oe+11 W14x53 (I) Y319 CA3 2.Oe+11 X801 CA3 2.Oe+11 W14xl84 (H) Y801 CA3 2.Oe+11 X802 CA3 2.Oe+11 W14xl84 (I) Y802 CA3 2.Oe+11 X803 CA3 2.Oe+11 W14x87 (H) 6217e-6 / * wl8x85 2337e-6 / * wl6x40 6787e-6 / * w24x76 s e c t i o n p r o p e r t i e s 944.8e-6 C(1440.Ie3,1440.Ie3) 367.5e-6 C(0728.6e3, 0728.6e3) 367.5e-6 C(0728.6e3, 0728.6e3) 944.8e-6 C(1440.Ie3,1440.Ie3) 402.5e-6 C(0721.4e3,0721.4e3) 145.6e-6 C(0311.0e3,0311.0e3) 145.6e-6 C(0311.0e3,0311.0e3) 402.5e-6 C(0721.4e3,0721.4e3) 189.4e-6 C(0323.8e3,0323.8e3) 528.6e-6 C(0835.Ie3,0835.Ie3) 441.2e-6 C(0707.4e3,0707.4e3) 159.8e-6 C(0340.4e3,0340.4e3) 159.8e-6 C{0340.4e3,0340.4e3) 441.2e-6 C(0707.4e3,0707.4e3] 661.8e-6 C(1035.3e3,1035.3e3) 236.4e-6 C(0498.5e3,0498.5e3) 236.4e-6 C(0498.5e3,0498.5e3) 661.8e-6 C{1035.3e3,1035.3e3) 266.8e-6 C(0434.6e3,0434.6e3) 44.5e-6 C(0139.3e3,0139.3e3) 44.5e-6 C(0139.3e3,0139.3e3) 266.8e-6 C(0434.6e3,0434.6e3) 93.7e-6 C(0242.9e3,0242.9e3) 386.3e-6 C(0617.8e3,0617.8e3) 407.5e-6 C(0536.8e3,0536. 8e3) 55.4e-6 C(0172.6e3,0172.6e3) 55.4e-6 C(0172.6e3,0172.6e3) 407.5e-6 C(0536.8e3,0536.8e3) 178.6e-6 C(0296.9e3,0296.9e3) 18.8e-6 C(0073.7e3,0073.7e3) 18.8e-6 C{0073.7e3,0073.7e3) 178.6e-6 C(0296.9e3,0296.9e3) 50.4e-6 C(0156.8e3,0156.8e3) 301.4e-6 C(0490.0e3,0490.0e3) 225.6e-6 C(0371.Ie3,0371.Ie3) 023.9e-6 C(0093.3e3,0093.3e3) 023.9e-6 C(0093.3e3,0093.3e3) 225.6e-6 C(0371.Ie3,0371.Ie3) 803.3e-6 C(1440.Ie3,1440.Ie3) 302.0e-6 C(0728.6e3,0728.6e3) 302.0e-6 C(0728.6e3,0728.6e3) 803.3e-6 C(1440.Ie3,1440.Ie3) 334.7e-6 C(0721.4e3,0721.4e3) Y(1441e3,1441e3) A ( l , l ) B(0 .02 ,0 .02) P(0.3 0.75) / Y(0729e3,0729e3) A ( l , l ) Y(0729e3,0729e3) A ( l , l ) Y(1441e3,1441e3) A ( l , l ) Y(0722e3,0722e3) A ( l , l ) Y(0312e3,0312e3) A ( l , l ) Y(0312e3,0312e3) A ( l , l ) Y(0722e3,0722e3) A ( l , l ) Y(0324e3,0324e3) A ( l , l ) Y(0836e3,0836e3) A ( l , l ) Y(0708e3,0708e3) A ( l , l ) Y(0341e3,0341e3) A<1,1) Y(0341e3,0341e3) A ( l , l ) Y(0708e3,0708e3) A ( l , l ) Y(1036e3,1036e3) A ( l , l ) Y(0499e3,0499e3) A ( l , l ) Y(0499e3,0499e3) A ( l , l ) Y(1036e3,1036e3) A ( l , l ) Y(0435e3,0435e3) A ( l , l ) Y(0140e3,0140e3) A ( l , l ) Y(0140e3,0140e3) A ( l , l ) Y(0435e3,0435e3) A ( l , l ) Y(0243e3,0243e3) A ( l , l ) Y(0618e3,0618e3) A ( l , l ) Y(0537e3,0537e3) A ( l , l ) Y(0173e3,0173e3) A ( l , l ) Y(0173e3,0173e3) A ( l , l ) Y(0537e3,0537e3) A ( l , l ) Y(0297e3,0297e3) A ( l , l ) Y(0074e3,0074e3) A ( l , l ) Y(0074e3,0074e3) A ( l , l ) Y(0297e3,0297e3) A ( l , l ) Y(0157e3,0157e3) A ( l , l ) Y(0491e3,0491e3) A ( l , l ) Y(0372e3,0372e3) A ( l , l ) Y(0094e3,0094e3) A ( l , l ) Y(0094e3,0094e3) A ( l , l ) Y(0372e3,0372e3) A ( l , l ) Y(1441e3,1441e3) A ( l , l ) Y(0729e3,0729e3) A ( l , l ) Y(0729e3,0729e3) A ( l , l ) Y(1441e3,1441e3) A ( l , l ) Y(0722e3,0722e3) A ( l , l ) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0. 02, 0. 02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0.02,0.'02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) B(0 .02 ,0 .02) P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P ( 0-. 3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0. 3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 P(0.3 0.75) 0.75) / 0.75) 0.75) / 0.75) 0.75) / 0.75) 0.75) / 0.75) 0.75) / 0.75) 0.75) / 0.75) 0.75) / 0.75) 0.75) / 0.75) 0.75) / 0.75) 0.75) / 0.75) 0.75) / 0.75) 0.75) / 0.75) 0.75) / 0.75) 0.75) / 0.75) 0.75) / 0.75) 0.75) / 0.75) 0.75) / 0.75) 0.75) / 0.75) 0.75) / 0.75) 0.75) / 0.75) 0.75) / 344 Y803 CA3 2. Oe+ll 95 l e - 6 C(0311 0e3, 0311 0e3) Y(0312e3,0312e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) X804 CA3 2. Oe+ll 95 l e - 6 C(0311 0e3, 0311 0e3) Y(0312e3,0312e3) A ( l,l) B(0 02, 0 02) P(0 3 0 75) W14x87 (I) Y804 CA3 2. Oe+ll 334 7e- 6 C(0721 4e3, 0721 4e3) Y(0722e3,0722e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) X805 CA3 2. Oe+ll 141 5e- 6 C(0323 8e3, 0323 8e3) Y(0324e3,0324e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) W14X111 (I) Y805 CA3 2. Oe+ll 457 4e- 6 C(0835 le3, 0835 le3) Y(0836e3,0836e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) X806 CA3 2. Oe+ll 424 3e- 6 C(0707 4e3, 0707 4e3) Y(0708e3,0708e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) W14x95 (H) Y806 CA3 2. Oe+ll 107 6e- 6 C(0340 4e3, 0340 4e3) Y(0341e3,0341e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) X807 CA3 2. Oe+ll 107 6e- 6 C(0340 4e3, 0340 4e3) Y(0341e3,0341e3) A ( l , l ) B{0 02, 0 02) P(0 3 0 75) W14x95 (I) Y807 CA3 2. Oe+ll 424 3e- 6 C(0707 4e3, 0707 4e3) Y(0708e3,0708e3) A ( l , l ) . B(0 02, 0 02) P(0 3 0 75) X808 CA3 2. Oe+ll 551 5e- 6 C(1035 3e3, 1035 3e3) Y(1036e3,1036e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) W14xl36 (H) Y808 CA3 2. Oe+ll 198 l e - 6 C(0498 5e3, 0498 5e3) Y(0499e3,0499e3) A ( l , l ) B(0 02, 0 02) P( 0 3 0 75) X809 CA3 2. Oe+ll 198 l e - 6 C(0498 5e3, 0498 5e3) Y(0499e3,0499e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) W14xl36 (I) Y809 CA3 2. Oe+ll 551 6e- 6 C(1035 3e3, 1035 3e3) Y(1036e3,1036e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) X810 CA3 2. Oe+ll 222 7e- 6 C(0434 6e3, 0434 6e3) Y(0435e3,0435e3) A ( l , l ) B{0 02, 0 02) P(0 3 0 75) W14x61 (H) Y810 CA3 2. Oe+ll 31 7e- 6 C(0139 3e3, 0139 3e3) Y(0140e3,0140e3) A ( l , l ) B{0 02, 0 02) P(0 3 0 75) X811 CA3 2. Oe+ll 31 7e- 6 C(0139 3e3, 0139 3e3) Y(0140e3,0140e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) W14x61 (I) Y811 CA3 2. Oe+ll 222 7e- 6 C(0434 6e3, 0434 6e3) Y(0435e3,0435e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) X812 CA3 2. Oe+ll 72 Oe-6 C(0242 9e3, 0242 9e3) Y(0243e3,0243e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) W14x84 (I) Y812 CA3 2. Oe+ll 343 8e- 6 C(0617 8e3, 0617 8e3) Y(0618e3,0618e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) X813 CA3 2. Oe+ll 316 5e- 6 C(0536 8e3, 0536 8e3) Y(0537e3,0537e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) W14x74 (H) Y813 CA3 2. Oe+ll 39 6e- 6 C(0172 6e3, 0172 6e3) Y(0173e3,0173e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) X814 CA3 2. Oe+ll 39 6e- 6 C(0172 6e3, 0172 6e3) Y(0173e3,0173e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) W14x74 (I) Y814 CA3 2. Oe+ll 316 5e- 6 C(0536 8e3, 0536 8e3) Y(0537e3,0537e3) A ! l , l ) B(0 02, 0 02) P(0 3 0 75) /* Column Shear s e c t i o n p r o p e r t i e s X4 01 ELI 0 77e+ll 8335e- 6 /* W14X184 (H) Y401 ELI 0 77e+ll 27844e- 6 X402 ELI 0 77e+ll 27844e- 6 /* W14xl84 (I) Y402 ELI 0 77e+ll 8335e- 6 X403 ELI 0 77e+ll 3951e- 6 /* W14x87 (H) Y403 ELI 0 77e+ll 12862e- 6 X404 ELI 0 77e+ll 12862e- 6 /* W14x87 (I) Y404 ELI 0 77e+ll 3951e- 6 X405 ELI 0 77e+ll 16513e- 6 /* W14xlll (I) Y405 ELI 0 77e+ll 5217e- 6 X406 ELI 0 77e+ll 3989e- 6 /* W14X95 (H) Y406 ELI 0 77e+ll 14032e- 6 X4 07 ELI 0 77e+ll 14032e- 6 /* W14x95 (I) Y407 ELI 0 77e+ll 3989e- 6 X408 ELI 0 77e+ll 6542e- 6 /* W14X136 (H) Y408 ELI 0 77e+ll 20222e- 6 X409 ELI 0 77e+ll 20222e- 6 /* W14xl36 (I) Y409 ELI 0 77e+ll 6542e- 6 X410 ELI 0 77e+ll 3356e- 6 /* W14x61 (H) Y410 ELI 0 77e+ll 8065e- 6 X411 ELI 0 77e+ll 8065e- 6 /* W14X61 (I) Y411 ELI 0 77e+ll 3356e- 6 X412 ELI 0 77e+ll 11613e- 6 /* W14x84 (I) Y412 ELI 0 77e+ll 3989e- 6 X413 ELI 0 77e+ll 4022e- 6 /* W14x74 (H) Y413 ELI 0 77e+ll 10615e- 6 X414 ELI 0 77e+ll 10615e- 6 /* W14X74 (I) Y414 ELI 0 77e+ll 4022e- 6 X415 ELI 0 77e+ll 2747e- 6 /* W14x43 (H) Y415 ELI 0 77e+ll 5161e- 6 X416 ELI 0 77e+ll 5161e- 6 /* W 1 4 X 4 3 (I) Y416 ELI 0 77e+ll 2747e- 6 X417 ELI 0 77e+ll 8871e- 6 /* W14x68 (I) Y417 ELI 0 77e+ll 3952e- 6 345 X418 ELI 0 77e+ll 3387e-6 /* W14x53 (H) Y418 ELI 0 77e+ll 7097e-6 X419 ELI 0 77e+ll 7097e-6 /* W14x53 (I) Y419 ELI 0 77e+ll 3387e-6 X601 ELI 0 77e+ll 6990e-6 /* Average (H) Y601 ELI 0 77e+ll 22127e-6 X602 ELI 0 77e+ll 22127e-6 /* Average (I) Y602 ELI 0 77e+ll 6990e-6 X603 ELI 0 77e+ll 3505e-6 /* Average (H) Y603 ELI 0 77e+ll 9264e-6 X604 ELI 0 77e+ll 9264e-6 /* Average (I) Y604 ELI 0 77e+ll 3505e-6 X605 ELI 0 77e+ll 12838e- 6 /* Average (I) Y605 ELI 0 77e+ll 4294e-6 X606 ELI 0 77e+ll 4013e- 6 /* Average (H) Y606 ELI 0 77e+ll 11469e- 6 X607 ELI 0 77e+ll 11469e- 6 /* Average (I) Y607 ELI 0 77e+ll 4013e- 6 X608 ELI 0 77e+ll 4626e- 6 /* Average (H) Y608 ELI 0 77e+ll 15580e- 6 X609 ELI 0 77e+ll 15580e- 6 /* Average (I) Y609 ELI 0 77e+ll 4626e- 6 X610 ELI 0 77e+ll 2899e- 6 /* Average (H) Y610 ELI 0 77e+ll 5887e- 6 X611 ELI 0 77e+ll 5887e- 6 /* Average (I) Y611 ELI 0 77e+ll 2899e- 6 X612 ELI 0 77e+ll 9556e- 6 /* Average (I) Y612 ELI 0 77e+ll 3960e- 6 X613 ELI 0 77e+ll 3546e- 6 /* Average (H) Y613 ELI 0 77e+ll 7976e- 6 X614 ELI 0 77e+ll 7976e- 6 /* Average (I) Y614 ELI 0 77e+ll 3546e- 6 /* Column A x i a l s e c t i o n p r o p e r t i e s U501 CA3 2. Oe+11 34903e-6 C(9074. 8e3, 9074 . 8e3) Y(9075e3,9075e3) A ( l , l ) B{0. 02, 0. 02) P(0. 3 0 75) /* W14xl84 (H) U502 CA3 2. Oe+11 34903e-6 C(9074 8e3,9074. 8e3) Y(9075e3,9075e3) A ( l , l ) B{0. 02, 0. 02) P(0 3 0 75) /* W14xl84 (I) U503 CA3 2. Oe+11 16516e-6 C(4293 5e3, 4293 5e3) Y(4294e3,4294e3) A ( l , l ) B(0. 02, 0. 02) P(0 3 0 75) /* W14x87 (H) U504 CA3 2. Oe+11 16516e- 6 C(4293 5e3, 4293 5e3) Y(4294e3, 4294e3) A ( l , l ) B(0. 02, 0 02) P(0 3 0 75) /* W14x87 (I) U505 CA3 2. Oe+11 21097e- 6 C',5484 0e3, 5484 0e3) Y(5485e3,5485e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* W14xlll (I) U506 CA3 2. Oe+11 18000e- 6 C(467 9 0e3, 4 67 9 0e3) Y(4680e3,4680e3) A ( l , l ) B(0 02, 0 02 ) P(0 3 0 75) /* W14x95 (H) U507 CA3 2. Oe+11 18000e- 6 C{4679 0e3, 4 67 9 0e3) Y(4680e3,4680e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* W14x95 (I) U508 CA3 2. Oe+11 25806e- 6 C(6709 6e3, 6709 6e3) Y(6710e3,6710e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* W14X136 (H) U509 CA3 2. Oe+11 25806e- 6 C(6709 6e3, 6709 6e3) Y(6710e3,6710e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* W14X136 (I) U510 CA3 2. Oe+11 11548e- 6 C(3002 5e3, 3002 5e3) Y(3003e3,3003e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* W14x61 (H) U511 CA3 2. Oe+11 11548e- 6 C(3002 5e3, 3002 5e3) Y(3003e3,3003e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* W14X61 (I) U512 CA3 2. Oe+11 15936e- 6 C(4143 3e3, 4143 3e3) Y(4144e3,4144e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* W14x84 (I) U513 CA3 2. Oe+11 14064e- 6 C(3656 5e3, 3656 5e3) Y(3657e3,3657e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* W14x74 (H) U514 CA3 2. Oe+11 14064e- 6 C(3656 5e3, 3656 5e3) Y(3657e3,3657e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* W14X74 (I) U515 CA3 2. Oe+11 8129e- 6 C(2113 5e3, 2113 5e3) Y(2114e3,2114e3) A ( l , l ) 8(0 02, 0 02) P(0 3 0 75) /* W14X43 (H) U516 CA3 2. Oe+11 8129e- 6 C(2113 5e3, 2113 5e3) Y(2114e3,2114e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* W14X43 (I) U517 CA3 2. Oe+11 12903e- 6 C(3354 5e3, 3354 5e3) Y(3355e3,3355e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* W14x68 (I) U518 CA3 2. Oe+11 10064e-•6 C(2616 2e3, 2616 2e3) Y(2617e3,2617e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* W14x53 (H) 346 U519 CA3 2.Oe+ll W14x53 (I) 10064e-6 C(2616.2e3,2616.2e3) Y(2617e3,2617e3) A ( l , l ) B(0.02,0.02) P(0.3 0.75) /* U7 01 CA3 2. Oe+ll 28081e- 6 C(6709. 6e3, 6709. 6e3) Y(6710e3,6710e3) A ( l , l ) BIO. 02, 0. 02) P(0. 3 0 75) /* Average U7 02 CA3 H) 2. Oe+ll 28081e- 6 C(6709. 6e3, 6709. 6e3) Y(6710e3,6710e3) A ( l , l ) B(0. 02, 0. 02) P(0. 3 0 75) /* Average U7 03 CA3 I) 2. Oe+ll 12790e- 6 C(3002 5e3, 3002 5e3) Y(3003e3,3003e3) A ( l , l ) B(0. 02, 0 02) P(0 3 0 75) /* Average U704 CA3 H) 2. Oe+ll 12790e- 6 C(3002 5e3, 3002 5e3) Y(3003e3,3003e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* Average U7 05 CA3 I) 2. Oe+ll 17226e- 6 C(4143 3e3, 4143 3e3) Y(4144e3,4144e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* Average U7 06 CA3 II 2. Oe+ll 15048e- 6 C(3656 5e3, 3656 5e3) Y(3657e3,3657e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* Average U7 07 CA3 H) 2. Oe+ll 15048e- 6 C(3656 5e3, 3656 5e3) Y(3657e3,3657e3) A{1,1) B(0 02, 0 02) P(0 3 0 75) /* Average U7 08 CA3 I) 2. Oe+ll 19952e- 6 C(6709 6e3, 6709 6e3) Y(6710e3,6710e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* Average U7 09 CA3 H) 2. Oe+ll 19952e- 6 C(6709 6e3, 6709 6e3) Y(6710e3,6710e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* Average U710 CA3 I) 2. Oe+ll 8984e- 6 C(2113 5e3, 2113 5e3) Y(2114e3,2114e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* Average U711 CA3 (H) 2. Oe+ll 8984e- 6 C(2113 5e3, 2113 5e3) Y(2114e3,2114e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* Average U712 CA3 (I) 2. Oe+ll 13661e- 6 C(3354 5e3,3354 5e3) Y(3355e3,3355e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 75) /* Average U713 CA3 (I) 2. Oe+ll 11065e- 6 C(2616 2e3, 2616 2e3) Y(2617e3,2617e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 .75) /* Average U714 CA3 (H) 2. Oe+ll 11065e- 6 C(2616 2e3, 2616 2e3) Y(2617e3,2617e3) A ( l , l ) B(0 02, 0 02) P(0 3 0 .75) /* Average (I) II II i n i t i a l load data beam Y l X1-X13 2F (loade 12800) beam Y13 X1-X13 2F 1 loade 12800) beam XI Y1-Y13 2F (loade 22000) beam X13 Y1-Y13 2F (loade 22000) node Y l X4 2F (Pz = 140240) node Y l X7 2F (Pz = 140240) node Yl X10 2F (Pz = 140240) node Y13 X4 2F (Pz = 140240) node Y13 X7 2F (Pz = 140240) node Y13 X10 2F (Pz = 140240) beam Y l X1-X13 3F (loade 7700) beam Y13 XI-XI3 3F (loade 7700) beam XI Y1-Y13 3F (loade 16900) beam X13 Y1-Y13 3F (loade 16900) node Y l X4 3F (Pz = 93500) node Y l X7 3F (Pz = 93500) node Y l X10 3F (Pz = 93500) node Y13 X4 3F (Pz = 93500) node Y13 X7 3F (Pz = 93500) node Y13 X10 3F (Pz = 93500) beam Y l XI-XI3 4F~ 6F (loade 7440) beam Y13 X1-X13 4F~ 6F (loade 7440) beam XI Y1-Y13 4F~ 6F (loade 16640) beam X13 Y1-Y13 4F~ 6F (loade 16640) node Y l X4 4F~ 6F (Pz = 93500) node Y l X7 4F~ 6F (Pz = 93500) node Y l X10 4F~ 6F (Pz = 93500) node Y13 X4 4F~ 6F (Pz = 93500) node Y13 X7 4F~ 6F (Pz = 93500) node Y13 X10 4F~ 6F (Pz = 93500) beam Y l X1-X13 7F (loade 12800) beam Y13 X1-X13 7F (loade 12800) beam XI Y1-Y13 7F (loade 22000) beam X13 Y1-Y13 7F (loade 22000) 347 node YI X4 7F (Pz = 140240) node YI X7 7F (Pz = 140240) node YI X10 7F (Pz = 140240) node Y13 X4 7F (Pz = 140240) node Y13 X7 7F (Pz = 140240) node Y13 X10 7F (Pz = 140240)
Thesis/Dissertation
eng
Civil Engineering
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Graduate
Seismic behavior & computer modeling of low-rise steel frame structures
Text